Κατάλογος τῶν Συγκερασµῶν ὅλων τῶν Βυζαντινῶν ιατονικῶν Κλιµάκων µέχρι καὶ σὲ 1200 µουσικὰ διαστήµατα (κόµµατα)

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1 Κατάλογος τῶν Συγκερασµῶν ὅλων τῶν Βυζαντινῶν ιατονικῶν Κλιµάκων µέχρι καὶ σὲ 1200 µουσικὰ διαστήµατα (κόµµατα) τοῦ Παναγιώτη. Παπαδηµητρίου ρ. Ἠλεκτρ. Μηχανικοῦ, Φυσικοῦ Περιεχόµενα 1. Εἰσαγωγή Συγκερασµοὶ ιατονικῆς ιδύµου - Μέχρι 100 κόµµατα Συγκερασµοὶ ιατονικῆς ιδύµου - Μέχρι 1200 κόµµατα Συγκερασµοὶ ιατονικῆς Ἐπιτροπῆς Μέχρι 100 κόµµατα Συγκερασµοὶ ιατονικῆς Ἐπιτροπῆς Μέχρι 1200 κόµµατα Συγκερασµοὶ ιατονικῆς Χρυσάνθου - Μέχρι 100 κόµµατα Συγκερασµοὶ ιατονικῆς Χρυσάνθου - Μέχρι 1200 κόµµατα * * * 1. Εἰσαγωγή Σὲ αὐτὸ τὸ κείµενο, ἐφαρµόζουµε τὴν µέθοδο συγκερασµοῦ µας 1, στὶς διάφορες διατονικὲς κλίµακες Βυζαντινῆς µουσικῆς ποὺ ἀπαντῶνται στὰ διάφορα θεωρητικὰ βιβλία. Ἡ µέθοδος µοντελοποίησης (modelling of data) στὴν µέθοδο συγκερασµοῦ µας, ποὺ ἀκολουθοῦµε σὲ αὐτὸν τὸν κατάλογο, εἶναι αὐτὴ τῶν ἐλαχίστων τετραγώνων. Ὁ κατάλογος ἔχει ὡς ἐξῆς: Οἱ συγκερασµοὶ εἶναι ταξινοµηµένοι κατὰ φθίνουσα ἀκρίβεια συγκερασµοῦ, ποὺ δίνεται ἀπὸ τὸν ἀριθµὸ Φ τῆς µεθόδου µας (µικρότερο Φ, µεγαλύτερη ἀκρίβεια συγκερασµοῦ). Ἡ µεταβλητὴ Ν εἶναι τὸ ἄθροισµα τῶν κοµµάτων τῆς συγκερασµένης κλίµακας. Στὸ ἀντίστοιχο Ν, ὑπάρχει ἕνα διάνυσµα t = [t 1, t 2,...] µὲ τὰ κόµµατα (µουσικὰ διαστήµατα). Ἡ ἀντιστοίχιση τῶν κοµµάτων στὴν κλίµακα, δίνεται πρὶν ἀπὸ κάθε πίνακα συγκερασµῶν. 1 Παναγιώτης. Παπαδηµητρίου, Μέθοδος συγκερασµοῦ κλιµάκων - οἱ διατονικὲς κλίµακες τοῦ ιδύµου, τῆς Ἐπιτροπῆς, τοῦ Χρυσάνθου, καὶ οἱ συγκράσεις τους, ἔκδ. 29/6/05 [ ] 1

2 2. Συγκερασµοὶ ιατονικῆς ιδύµου - Μέχρι 100 κόµµατα Ἡ διατονικὴ κλίµακα τοῦ ιδύµου εἶναι ἡ ἐξῆς: Νη - 9/8 - Πα - 10/9 - Βου - 16/15 - Γα - 9/8 - ι - 9/8 - Κε - 10/9 - Ζω' - 16/15 - Νη', Ἡ συγκερασµένη κλίµακα, δίνεται ὡς ἐξῆς: Νη - t 1 - Πα - t 2 - Βου - t 3 - Γα - t 1 - ι - t 1 - Κε - t 2 - Ζω' - t 3 - Νη', ὅπου οἱ τιµὲς t 1, t 2, t 3 δίνονται στὰ ἀντίστοιχα διανύσµατα t = [ t 1 t 2 t 3 ] στὸν παρακάτω πίνακα. 1. N = 53, t = [ ], Φ = e N = 65, t = [ ], Φ = e N = 99, t = [ ], Φ = e N = 94, t = [ ], Φ = e N = 87, t = [ ], Φ = e N = 77, t = [ ], Φ = e N = 84, t = [ ], Φ = e N = 72, t = [ ], Φ = e N = 96, t = [ ], Φ = e N = 89, t = [ ], Φ = e N = 75, t = [ ], Φ = e N = 41, t = [ ], Φ = e N = 82, t = [ ], Φ = e N = 46, t = [ ], Φ = e N = 92, t = [ ], Φ = e N = 58, t = [ ], Φ = e N = 60, t = [ ], Φ = e N = 80, t = [ ], Φ = e N = 91, t = [ ], Φ = e N = 70, t = [ ], Φ = e N = 97, t = [ ], Φ = e N = 79, t = [ ], Φ = e N = 34, t = [ ], Φ = e N = 68, t = [ ], Φ = e N = 63, t = [ ], Φ = e N = 98, t = [ ], Φ = e N = 48, t = [ ], Φ = e N = 90, t = [ ], Φ = e N = 85, t = [ ], Φ = e N = 67, t = [ ], Φ = e N = 43, t = [ ], Φ = e N = 86, t = [ ], Φ = e N = 74, t = [ ], Φ = e N = 55, t = [ ], Φ = e N = 56, t = [ ], Φ = e N = 31, t = [ ], Φ = e N = 62, t = [ ], Φ = e N = 93, t = [ ], Φ = e N = 73, t = [ ], Φ = e N = 95, t = [ ], Φ = e N = 81, t = [ ], Φ = e N = 50, t = [ ], Φ = e-004 2

3 43. N = 100, t = [ ], Φ = e N = 78, t = [ ], Φ = e N = 51, t = [ ], Φ = e N = 69, t = [ ], Φ = e N = 61, t = [ ], Φ = e N = 29, t = [ ], Φ = e N = 83, t = [ ], Φ = e N = 88, t = [ ], Φ = e N = 12, t = [ ], Φ = e N = 24, t = [ ], Φ = e N = 36, t = [ ], Φ = e N = 39, t = [ ], Φ = e N = 19, t = [ ], Φ = e N = 38, t = [ ], Φ = e N = 57, t = [ ], Φ = e N = 76, t = [ ], Φ = e N = 71, t = [ ], Φ = e N = 22, t = [ ], Φ = e N = 44, t = [ ], Φ = e N = 66, t = [ ], Φ = e N = 49, t = [ ], Φ = e N = 64, t = [ ], Φ = e N = 45, t = [ ], Φ = e N = 27, t = [ ], Φ = e N = 54, t = [ ], Φ = e N = 59, t = [ ], Φ = e N = 26, t = [ ], Φ = e N = 52, t = [ ], Φ = e N = 37, t = [ ], Φ = e N = 42, t = [ ], Φ = e N = 32, t = [ ], Φ = e N = 33, t = [ ], Φ = e N = 47, t = [ ], Φ = e N = 40, t = [ ], Φ = e N = 17, t = [ ], Φ = e N = 15, t = [ ], Φ = e N = 30, t = [ ], Φ = e N = 25, t = [ ], Φ = e N = 35, t = [ ], Φ = e N = 20, t = [ ], Φ = e N = 7, t = [ ], Φ = e N = 14, t = [ ], Φ = e N = 21, t = [ ], Φ = e N = 28, t = [ ], Φ = e N = 10, t = [ ], Φ = e N = 23, t = [ ], Φ = e N = 18, t = [ ], Φ = e N = 13, t = [ ], Φ = e N = 16, t = [ ], Φ = e-002 3

4 3. Συγκερασµοὶ ιατονικῆς ιδύµου - Μέχρι 1200 κόµµατα Ἡ διατονικὴ κλίµακα τοῦ ιδύµου εἶναι ἡ ἐξῆς: Νη - 9/8 - Πα - 10/9 - Βου - 16/15 - Γα - 9/8 - ι - 9/8 - Κε - 10/9 - Ζω' - 16/15 - Νη', Ἡ συγκερασµένη κλίµακα, δίνεται ὡς ἐξῆς: Νη - t 1 - Πα - t 2 - Βου - t 3 - Γα - t 1 - ι - t 1 - Κε - t 2 - Ζω' - t 3 - Νη', ὅπου οἱ τιµὲς t 1, t 2, t 3 δίνονται στὰ ἀντίστοιχα διανύσµατα t = [ t 1 t 2 t 3 ] στὸν παρακάτω πίνακα. 1. N = 1171, t = [ ], Φ = e N = 612, t = [ ], Φ = e N = 730, t = [ ], Φ = e N = 559, t = [ ], Φ = e N = 1118, t = [ ], Φ = e N = 1053, t = [ ], Φ = e N = 1106, t = [ ], Φ = e N = 1000, t = [ ], Φ = e N = 783, t = [ ], Φ = e N = 677, t = [ ], Φ = e N = 665, t = [ ], Φ = e N = 1159, t = [ ], Φ = e N = 1065, t = [ ], Φ = e N = 901, t = [ ], Φ = e N = 848, t = [ ], Φ = e N = 1183, t = [ ], Φ = e N = 947, t = [ ], Φ = e N = 935, t = [ ], Φ = e N = 836, t = [ ], Φ = e N = 954, t = [ ], Φ = e N = 494, t = [ ], Φ = e N = 988, t = [ ], Φ = e N = 441, t = [ ], Φ = e N = 882, t = [ ], Φ = e N = 1019, t = [ ], Φ = e N = 795, t = [ ], Φ = e N = 1072, t = [ ], Φ = e N = 966, t = [ ], Φ = e N = 1041, t = [ ], Φ = e N = 718, t = [ ], Φ = e N = 1007, t = [ ], Φ = e N = 1130, t = [ ], Φ = e N = 506, t = [ ], Φ = e N = 1012, t = [ ], Φ = e N = 1125, t = [ ], Φ = e N = 1190, t = [ ], Φ = e N = 1137, t = [ ], Φ = e N = 624, t = [ ], Φ = e N = 829, t = [ ], Φ = e N = 889, t = [ ], Φ = e N = 913, t = [ ], Φ = e N = 894, t = [ ], Φ = e N = 547, t = [ ], Φ = e-007 4

5 44. N = 1094, t = [ ], Φ = e N = 1084, t = [ ], Φ = e N = 1178, t = [ ], Φ = e N = 1060, t = [ ], Φ = e N = 742, t = [ ], Φ = e N = 817, t = [ ], Φ = e N = 1152, t = [ ], Φ = e N = 1031, t = [ ], Φ = e N = 1147, t = [ ], Φ = e N = 870, t = [ ], Φ = e N = 771, t = [ ], Φ = e N = 942, t = [ ], Φ = e N = 1077, t = [ ], Φ = e N = 1195, t = [ ], Φ = e N = 764, t = [ ], Φ = e N = 959, t = [ ], Φ = e N = 1113, t = [ ], Φ = e N = 860, t = [ ], Φ = e N = 388, t = [ ], Φ = e N = 776, t = [ ], Φ = e N = 1164, t = [ ], Φ = e N = 923, t = [ ], Φ = e N = 1149, t = [ ], Φ = e N = 1099, t = [ ], Φ = e N = 600, t = [ ], Φ = e N = 1200, t = [ ], Φ = e N = 1193, t = [ ], Φ = e N = 1140, t = [ ], Φ = e N = 841, t = [ ], Φ = e N = 978, t = [ ], Φ = e N = 976, t = [ ], Φ = e N = 995, t = [ ], Φ = e N = 711, t = [ ], Φ = e N = 1166, t = [ ], Φ = e N = 1087, t = [ ], Φ = e N = 824, t = [ ], Φ = e N = 1096, t = [ ], Φ = e N = 571, t = [ ], Φ = e N = 1142, t = [ ], Φ = e N = 1111, t = [ ], Φ = e N = 689, t = [ ], Φ = e N = 1034, t = [ ], Φ = e N = 1024, t = [ ], Φ = e N = 1029, t = [ ], Φ = e N = 1046, t = [ ], Φ = e N = 807, t = [ ], Φ = e N = 1176, t = [ ], Φ = e N = 1048, t = [ ], Φ = e N = 453, t = [ ], Φ = e N = 906, t = [ ], Φ = e N = 653, t = [ ], Φ = e N = 723, t = [ ], Φ = e N = 925, t = [ ], Φ = e N = 1082, t = [ ], Φ = e N = 877, t = [ ], Φ = e N = 981, t = [ ], Φ = e N = 658, t = [ ], Φ = e N = 1043, t = [ ], Φ = e N = 1075, t = [ ], Φ = e N = 376, t = [ ], Φ = e N = 752, t = [ ], Φ = e N = 1128, t = [ ], Φ = e N = 1101, t = [ ], Φ = e-007 5

6 107. N = 699, t = [ ], Φ = e N = 1161, t = [ ], Φ = e N = 1181, t = [ ], Φ = e N = 1022, t = [ ], Φ = e N = 788, t = [ ], Φ = e N = 1135, t = [ ], Φ = e N = 993, t = [ ], Φ = e N = 1058, t = [ ], Φ = e N = 1089, t = [ ], Φ = e N = 805, t = [ ], Φ = e N = 706, t = [ ], Φ = e N = 323, t = [ ], Φ = e N = 646, t = [ ], Φ = e N = 969, t = [ ], Φ = e N = 930, t = [ ], Φ = e N = 971, t = [ ], Φ = e N = 1123, t = [ ], Φ = e N = 429, t = [ ], Φ = e N = 858, t = [ ], Φ = e N = 1154, t = [ ], Φ = e N = 928, t = [ ], Φ = e N = 631, t = [ ], Φ = e N = 1091, t = [ ], Φ = e N = 802, t = [ ], Φ = e N = 1188, t = [ ], Φ = e N = 460, t = [ ], Φ = e N = 920, t = [ ], Φ = e N = 973, t = [ ], Φ = e N = 1144, t = [ ], Φ = e N = 749, t = [ ], Φ = e N = 1038, t = [ ], Φ = e N = 171, t = [ ], Φ = e N = 342, t = [ ], Φ = e N = 513, t = [ ], Φ = e N = 684, t = [ ], Φ = e N = 855, t = [ ], Φ = e N = 1026, t = [ ], Φ = e N = 1197, t = [ ], Φ = e N = 289, t = [ ], Φ = e N = 578, t = [ ], Φ = e N = 867, t = [ ], Φ = e N = 1156, t = [ ], Φ = e N = 754, t = [ ], Φ = e N = 872, t = [ ], Φ = e N = 911, t = [ ], Φ = e N = 916, t = [ ], Φ = e N = 985, t = [ ], Φ = e N = 990, t = [ ], Φ = e N = 1079, t = [ ], Φ = e N = 696, t = [ ], Φ = e N = 636, t = [ ], Φ = e N = 1108, t = [ ], Φ = e N = 853, t = [ ], Φ = e N = 908, t = [ ], Φ = e N = 1103, t = [ ], Φ = e N = 1198, t = [ ], Φ = e N = 983, t = [ ], Φ = e N = 737, t = [ ], Φ = e N = 407, t = [ ], Φ = e N = 814, t = [ ], Φ = e N = 566, t = [ ], Φ = e N = 1132, t = [ ], Φ = e N = 759, t = [ ], Φ = e-007 6

7 170. N = 593, t = [ ], Φ = e N = 1186, t = [ ], Φ = e N = 932, t = [ ], Φ = e N = 482, t = [ ], Φ = e N = 964, t = [ ], Φ = e N = 961, t = [ ], Φ = e N = 940, t = [ ], Φ = e N = 335, t = [ ], Φ = e N = 670, t = [ ], Φ = e N = 1005, t = [ ], Φ = e N = 525, t = [ ], Φ = e N = 1050, t = [ ], Φ = e N = 605, t = [ ], Φ = e N = 518, t = [ ], Φ = e N = 1036, t = [ ], Φ = e N = 395, t = [ ], Φ = e N = 790, t = [ ], Φ = e N = 1185, t = [ ], Φ = e N = 1168, t = [ ], Φ = e N = 863, t = [ ], Φ = e N = 643, t = [ ], Φ = e N = 1014, t = [ ], Φ = e N = 875, t = [ ], Φ = e N = 1017, t = [ ], Φ = e N = 1070, t = [ ], Φ = e N = 761, t = [ ], Φ = e N = 619, t = [ ], Φ = e N = 1133, t = [ ], Φ = e N = 1010, t = [ ], Φ = e N = 1063, t = [ ], Φ = e N = 1145, t = [ ], Φ = e N = 879, t = [ ], Φ = e N = 1116, t = [ ], Φ = e N = 957, t = [ ], Φ = e N = 843, t = [ ], Φ = e N = 812, t = [ ], Φ = e N = 735, t = [ ], Φ = e N = 918, t = [ ], Φ = e N = 997, t = [ ], Φ = e N = 1174, t = [ ], Φ = e N = 1173, t = [ ], Φ = e N = 1067, t = [ ], Φ = e N = 1115, t = [ ], Φ = e N = 1055, t = [ ], Φ = e N = 1169, t = [ ], Φ = e N = 535, t = [ ], Φ = e N = 937, t = [ ], Φ = e N = 904, t = [ ], Φ = e N = 819, t = [ ], Φ = e N = 224, t = [ ], Φ = e N = 448, t = [ ], Φ = e N = 672, t = [ ], Φ = e N = 896, t = [ ], Φ = e N = 1120, t = [ ], Φ = e N = 1121, t = [ ], Φ = e N = 1157, t = [ ], Φ = e N = 865, t = [ ], Φ = e N = 851, t = [ ], Φ = e N = 270, t = [ ], Φ = e N = 540, t = [ ], Φ = e N = 810, t = [ ], Φ = e N = 1080, t = [ ], Φ = e N = 701, t = [ ], Φ = e-007 7

8 233. N = 118, t = [ ], Φ = e N = 236, t = [ ], Φ = e N = 354, t = [ ], Φ = e N = 472, t = [ ], Φ = e N = 590, t = [ ], Φ = e N = 708, t = [ ], Φ = e N = 826, t = [ ], Φ = e N = 944, t = [ ], Φ = e N = 1062, t = [ ], Φ = e N = 1180, t = [ ], Φ = e N = 887, t = [ ], Φ = e N = 400, t = [ ], Φ = e N = 800, t = [ ], Φ = e N = 952, t = [ ], Φ = e N = 949, t = [ ], Φ = e N = 1092, t = [ ], Φ = e N = 687, t = [ ], Φ = e N = 588, t = [ ], Φ = e N = 634, t = [ ], Φ = e N = 725, t = [ ], Φ = e N = 1068, t = [ ], Φ = e N = 740, t = [ ], Φ = e N = 822, t = [ ], Φ = e N = 793, t = [ ], Φ = e N = 501, t = [ ], Φ = e N = 1002, t = [ ], Φ = e N = 798, t = [ ], Φ = e N = 581, t = [ ], Φ = e N = 1162, t = [ ], Φ = e N = 583, t = [ ], Φ = e N = 846, t = [ ], Φ = e N = 1127, t = [ ], Φ = e N = 778, t = [ ], Φ = e N = 1027, t = [ ], Φ = e N = 1109, t = [ ], Φ = e N = 1009, t = [ ], Φ = e N = 617, t = [ ], Φ = e N = 641, t = [ ], Φ = e N = 552, t = [ ], Φ = e N = 1104, t = [ ], Φ = e N = 884, t = [ ], Φ = e N = 891, t = [ ], Φ = e N = 1015, t = [ ], Φ = e N = 899, t = [ ], Φ = e N = 773, t = [ ], Φ = e N = 757, t = [ ], Φ = e N = 528, t = [ ], Φ = e N = 1056, t = [ ], Φ = e N = 1039, t = [ ], Φ = e N = 998, t = [ ], Φ = e N = 277, t = [ ], Φ = e N = 554, t = [ ], Φ = e N = 831, t = [ ], Φ = e N = 1051, t = [ ], Φ = e N = 945, t = [ ], Φ = e N = 655, t = [ ], Φ = e N = 682, t = [ ], Φ = e N = 766, t = [ ], Φ = e N = 745, t = [ ], Φ = e N = 892, t = [ ], Φ = e N = 1192, t = [ ], Φ = e N = 694, t = [ ], Φ = e N = 834, t = [ ], Φ = e-007 8

9 296. N = 537, t = [ ], Φ = e N = 1074, t = [ ], Φ = e N = 1163, t = [ ], Φ = e N = 839, t = [ ], Φ = e N = 1003, t = [ ], Φ = e N = 1175, t = [ ], Φ = e N = 465, t = [ ], Φ = e N = 962, t = [ ], Φ = e N = 1110, t = [ ], Φ = e N = 956, t = [ ], Φ = e N = 487, t = [ ], Φ = e N = 974, t = [ ], Φ = e N = 607, t = [ ], Φ = e N = 769, t = [ ], Φ = e N = 747, t = [ ], Φ = e N = 1151, t = [ ], Φ = e N = 1098, t = [ ], Φ = e N = 1150, t = [ ], Φ = e N = 648, t = [ ], Φ = e N = 1057, t = [ ], Φ = e N = 786, t = [ ], Φ = e N = 1122, t = [ ], Φ = e N = 419, t = [ ], Φ = e N = 838, t = [ ], Φ = e N = 1045, t = [ ], Φ = e N = 1179, t = [ ], Φ = e N = 1187, t = [ ], Φ = e N = 992, t = [ ], Φ = e N = 1097, t = [ ], Φ = e N = 1139, t = [ ], Φ = e N = 1191, t = [ ], Φ = e N = 475, t = [ ], Φ = e N = 950, t = [ ], Φ = e N = 330, t = [ ], Φ = e N = 660, t = [ ], Φ = e N = 1004, t = [ ], Φ = e N = 1167, t = [ ], Φ = e N = 986, t = [ ], Φ = e N = 720, t = [ ], Φ = e N = 939, t = [ ], Φ = e N = 1069, t = [ ], Φ = e N = 692, t = [ ], Φ = e N = 1044, t = [ ], Φ = e N = 1021, t = [ ], Φ = e N = 1033, t = [ ], Φ = e N = 980, t = [ ], Φ = e N = 704, t = [ ], Φ = e N = 1086, t = [ ], Φ = e N = 733, t = [ ], Φ = e N = 927, t = [ ], Φ = e N = 1134, t = [ ], Φ = e N = 909, t = [ ], Φ = e N = 874, t = [ ], Φ = e N = 886, t = [ ], Φ = e N = 713, t = [ ], Φ = e N = 951, t = [ ], Φ = e N = 301, t = [ ], Φ = e N = 602, t = [ ], Φ = e N = 903, t = [ ], Φ = e N = 991, t = [ ], Φ = e N = 1199, t = [ ], Φ = e N = 1155, t = [ ], Φ = e N = 921, t = [ ], Φ = e-006 9

10 359. N = 1126, t = [ ], Φ = e N = 1016, t = [ ], Φ = e N = 821, t = [ ], Φ = e N = 1114, t = [ ], Φ = e N = 897, t = [ ], Φ = e N = 530, t = [ ], Φ = e N = 383, t = [ ], Φ = e N = 1138, t = [ ], Φ = e N = 282, t = [ ], Φ = e N = 564, t = [ ], Φ = e N = 1081, t = [ ], Φ = e N = 781, t = [ ], Φ = e N = 833, t = [ ], Φ = e N = 785, t = [ ], Φ = e N = 499, t = [ ], Φ = e N = 675, t = [ ], Φ = e N = 915, t = [ ], Φ = e N = 862, t = [ ], Φ = e N = 364, t = [ ], Φ = e N = 728, t = [ ], Φ = e N = 938, t = [ ], Φ = e N = 768, t = [ ], Φ = e N = 898, t = [ ], Φ = e N = 968, t = [ ], Φ = e N = 680, t = [ ], Φ = e N = 809, t = [ ], Φ = e N = 311, t = [ ], Φ = e N = 622, t = [ ], Φ = e N = 933, t = [ ], Φ = e N = 1196, t = [ ], Φ = e N = 629, t = [ ], Φ = e N = 1146, t = [ ], Φ = e N = 716, t = [ ], Φ = e N = 880, t = [ ], Φ = e N = 417, t = [ ], Φ = e N = 756, t = [ ], Φ = e N = 1102, t = [ ], Φ = e N = 484, t = [ ], Φ = e N = 963, t = [ ], Φ = e N = 569, t = [ ], Φ = e N = 827, t = [ ], Φ = e N = 703, t = [ ], Φ = e N = 1085, t = [ ], Φ = e N = 470, t = [ ], Φ = e N = 436, t = [ ], Φ = e N = 1143, t = [ ], Φ = e N = 639, t = [ ], Φ = e N = 856, t = [ ], Φ = e N = 1061, t = [ ], Φ = e N = 1073, t = [ ], Φ = e N = 715, t = [ ], Φ = e N = 1028, t = [ ], Φ = e N = 780, t = [ ], Φ = e N = 667, t = [ ], Φ = e N = 885, t = [ ], Φ = e N = 347, t = [ ], Φ = e N = 422, t = [ ], Φ = e N = 844, t = [ ], Φ = e N = 258, t = [ ], Φ = e N = 516, t = [ ], Φ = e N = 774, t = [ ], Φ = e N = 1032, t = [ ], Φ = e N = 523, t = [ ], Φ = e

11 422. N = 845, t = [ ], Φ = e N = 850, t = [ ], Φ = e N = 650, t = [ ], Φ = e N = 1093, t = [ ], Φ = e N = 595, t = [ ], Φ = e N = 217, t = [ ], Φ = e N = 434, t = [ ], Φ = e N = 651, t = [ ], Φ = e N = 868, t = [ ], Φ = e N = 1049, t = [ ], Φ = e N = 489, t = [ ], Φ = e N = 1090, t = [ ], Φ = e N = 576, t = [ ], Φ = e N = 979, t = [ ], Φ = e N = 910, t = [ ], Φ = e N = 797, t = [ ], Φ = e N = 627, t = [ ], Φ = e N = 744, t = [ ], Φ = e N = 721, t = [ ], Φ = e N = 691, t = [ ], Φ = e N = 1158, t = [ ], Φ = e N = 1184, t = [ ], Φ = e N = 662, t = [ ], Φ = e N = 638, t = [ ], Φ = e N = 542, t = [ ], Φ = e N = 975, t = [ ], Φ = e N = 727, t = [ ], Φ = e N = 1182, t = [ ], Φ = e N = 832, t = [ ], Φ = e N = 463, t = [ ], Φ = e N = 926, t = [ ], Φ = e N = 183, t = [ ], Φ = e N = 366, t = [ ], Φ = e N = 549, t = [ ], Φ = e N = 732, t = [ ], Φ = e N = 597, t = [ ], Φ = e N = 1194, t = [ ], Φ = e N = 1008, t = [ ], Φ = e N = 1020, t = [ ], Φ = e N = 1037, t = [ ], Φ = e N = 585, t = [ ], Φ = e N = 1170, t = [ ], Φ = e N = 1131, t = [ ], Φ = e N = 792, t = [ ], Φ = e N = 412, t = [ ], Φ = e N = 1129, t = [ ], Φ = e N = 1040, t = [ ], Φ = e N = 996, t = [ ], Φ = e N = 668, t = [ ], Φ = e N = 791, t = [ ], Φ = e N = 803, t = [ ], Φ = e N = 1117, t = [ ], Φ = e N = 1141, t = [ ], Φ = e N = 857, t = [ ], Φ = e N = 873, t = [ ], Φ = e N = 1105, t = [ ], Φ = e N = 1076, t = [ ], Φ = e N = 1078, t = [ ], Φ = e N = 663, t = [ ], Φ = e N = 532, t = [ ], Φ = e N = 1064, t = [ ], Φ = e N = 586, t = [ ], Φ = e N = 1172, t = [ ], Φ = e

12 485. N = 1160, t = [ ], Φ = e N = 1153, t = [ ], Φ = e N = 609, t = [ ], Φ = e N = 922, t = [ ], Φ = e N = 984, t = [ ], Φ = e N = 1189, t = [ ], Φ = e N = 544, t = [ ], Φ = e N = 1088, t = [ ], Φ = e N = 779, t = [ ], Φ = e N = 815, t = [ ], Φ = e N = 614, t = [ ], Φ = e N = 1011, t = [ ], Φ = e N = 1052, t = [ ], Φ = e N = 674, t = [ ], Φ = e N = 574, t = [ ], Φ = e N = 1148, t = [ ], Φ = e N = 1023, t = [ ], Φ = e N = 511, t = [ ], Φ = e N = 955, t = [ ], Φ = e N = 205, t = [ ], Φ = e N = 410, t = [ ], Φ = e N = 615, t = [ ], Φ = e N = 820, t = [ ], Φ = e N = 1025, t = [ ], Φ = e N = 477, t = [ ], Φ = e N = 679, t = [ ], Φ = e N = 987, t = [ ], Φ = e N = 999, t = [ ], Φ = e N = 943, t = [ ], Φ = e N = 626, t = [ ], Φ = e N = 967, t = [ ], Φ = e N = 739, t = [ ], Φ = e N = 431, t = [ ], Φ = e N = 573, t = [ ], Φ = e N = 479, t = [ ], Φ = e N = 958, t = [ ], Φ = e N = 1100, t = [ ], Φ = e N = 446, t = [ ], Φ = e N = 598, t = [ ], Φ = e N = 1165, t = [ ], Φ = e N = 1035, t = [ ], Φ = e N = 1119, t = [ ], Φ = e N = 946, t = [ ], Φ = e N = 762, t = [ ], Φ = e N = 1136, t = [ ], Φ = e N = 970, t = [ ], Φ = e N = 804, t = [ ], Φ = e N = 520, t = [ ], Φ = e N = 914, t = [ ], Φ = e N = 369, t = [ ], Φ = e N = 738, t = [ ], Φ = e N = 1107, t = [ ], Φ = e N = 1177, t = [ ], Φ = e N = 931, t = [ ], Φ = e N = 972, t = [ ], Φ = e N = 1095, t = [ ], Φ = e N = 750, t = [ ], Φ = e N = 905, t = [ ], Φ = e N = 893, t = [ ], Φ = e N = 610, t = [ ], Φ = e N = 1066, t = [ ], Φ = e N = 869, t = [ ], Φ = e N = 709, t = [ ], Φ = e

13 548. N = 767, t = [ ], Φ = e N = 467, t = [ ], Φ = e N = 934, t = [ ], Φ = e N = 726, t = [ ], Φ = e N = 1047, t = [ ], Φ = e N = 491, t = [ ], Φ = e N = 982, t = [ ], Φ = e N = 556, t = [ ], Φ = e N = 1112, t = [ ], Φ = e N = 861, t = [ ], Φ = e N = 557, t = [ ], Φ = e N = 917, t = [ ], Φ = e N = 881, t = [ ], Φ = e N = 902, t = [ ], Φ = e N = 562, t = [ ], Φ = e N = 1124, t = [ ], Φ = e N = 1083, t = [ ], Φ = e N = 890, t = [ ], Φ = e N = 248, t = [ ], Φ = e N = 496, t = [ ], Φ = e N = 621, t = [ ], Φ = e N = 840, t = [ ], Φ = e N = 1013, t = [ ], Φ = e N = 426, t = [ ], Φ = e N = 852, t = [ ], Φ = e N = 381, t = [ ], Φ = e N = 919, t = [ ], Φ = e N = 656, t = [ ], Φ = e N = 686, t = [ ], Φ = e N = 414, t = [ ], Φ = e N = 828, t = [ ], Φ = e N = 1054, t = [ ], Φ = e N = 878, t = [ ], Φ = e N = 504, t = [ ], Φ = e N = 808, t = [ ], Φ = e N = 521, t = [ ], Φ = e N = 1042, t = [ ], Φ = e N = 533, t = [ ], Φ = e N = 994, t = [ ], Φ = e N = 751, t = [ ], Φ = e N = 929, t = [ ], Φ = e N = 1059, t = [ ], Φ = e N = 787, t = [ ], Φ = e N = 357, t = [ ], Φ = e N = 714, t = [ ], Φ = e N = 1071, t = [ ], Φ = e N = 960, t = [ ], Φ = e N = 864, t = [ ], Φ = e N = 561, t = [ ], Φ = e N = 775, t = [ ], Φ = e N = 1030, t = [ ], Φ = e N = 816, t = [ ], Φ = e N = 685, t = [ ], Φ = e N = 799, t = [ ], Φ = e N = 603, t = [ ], Φ = e N = 673, t = [ ], Φ = e N = 866, t = [ ], Φ = e N = 451, t = [ ], Φ = e N = 755, t = [ ], Φ = e N = 837, t = [ ], Φ = e N = 697, t = [ ], Φ = e N = 53, t = [ ], Φ = e N = 106, t = [ ], Φ = e

14 611. N = 159, t = [ ], Φ = e N = 212, t = [ ], Φ = e N = 265, t = [ ], Φ = e N = 318, t = [ ], Φ = e N = 371, t = [ ], Φ = e N = 424, t = [ ], Φ = e N = 508, t = [ ], Φ = e N = 849, t = [ ], Φ = e N = 313, t = [ ], Φ = e N = 361, t = [ ], Φ = e N = 722, t = [ ], Φ = e N = 763, t = [ ], Φ = e N = 907, t = [ ], Φ = e N = 734, t = [ ], Φ = e N = 545, t = [ ], Φ = e N = 458, t = [ ], Φ = e N = 509, t = [ ], Φ = e N = 1018, t = [ ], Φ = e N = 941, t = [ ], Φ = e N = 1001, t = [ ], Φ = e N = 503, t = [ ], Φ = e N = 1006, t = [ ], Φ = e N = 438, t = [ ], Φ = e N = 876, t = [ ], Φ = e N = 989, t = [ ], Φ = e N = 825, t = [ ], Φ = e N = 294, t = [ ], Φ = e N = 455, t = [ ], Φ = e N = 811, t = [ ], Φ = e N = 568, t = [ ], Φ = e N = 405, t = [ ], Φ = e N = 977, t = [ ], Φ = e N = 359, t = [ ], Φ = e N = 229, t = [ ], Φ = e N = 710, t = [ ], Φ = e N = 633, t = [ ], Φ = e N = 373, t = [ ], Φ = e N = 746, t = [ ], Φ = e N = 661, t = [ ], Φ = e N = 550, t = [ ], Φ = e N = 698, t = [ ], Φ = e N = 402, t = [ ], Φ = e N = 948, t = [ ], Φ = e N = 669, t = [ ], Φ = e N = 702, t = [ ], Φ = e N = 352, t = [ ], Φ = e N = 813, t = [ ], Φ = e N = 854, t = [ ], Φ = e N = 378, t = [ ], Φ = e N = 398, t = [ ], Φ = e N = 796, t = [ ], Φ = e N = 681, t = [ ], Φ = e N = 965, t = [ ], Φ = e N = 657, t = [ ], Φ = e N = 953, t = [ ], Φ = e N = 888, t = [ ], Φ = e N = 393, t = [ ], Φ = e N = 823, t = [ ], Φ = e N = 784, t = [ ], Φ = e N = 468, t = [ ], Φ = e N = 936, t = [ ], Φ = e N = 758, t = [ ], Φ = e N = 316, t = [ ], Φ = e

15 674. N = 632, t = [ ], Φ = e N = 620, t = [ ], Φ = e N = 895, t = [ ], Φ = e N = 644, t = [ ], Φ = e N = 349, t = [ ], Φ = e N = 772, t = [ ], Φ = e N = 443, t = [ ], Φ = e N = 924, t = [ ], Φ = e N = 299, t = [ ], Φ = e N = 693, t = [ ], Φ = e N = 480, t = [ ], Φ = e N = 743, t = [ ], Φ = e N = 308, t = [ ], Φ = e N = 616, t = [ ], Φ = e N = 912, t = [ ], Φ = e N = 604, t = [ ], Φ = e N = 801, t = [ ], Φ = e N = 649, t = [ ], Φ = e N = 645, t = [ ], Φ = e N = 900, t = [ ], Φ = e N = 497, t = [ ], Φ = e N = 152, t = [ ], Φ = e N = 304, t = [ ], Φ = e N = 456, t = [ ], Φ = e N = 608, t = [ ], Φ = e N = 760, t = [ ], Φ = e N = 628, t = [ ], Φ = e N = 842, t = [ ], Φ = e N = 591, t = [ ], Φ = e N = 450, t = [ ], Φ = e N = 515, t = [ ], Φ = e N = 835, t = [ ], Φ = e N = 859, t = [ ], Φ = e N = 580, t = [ ], Φ = e N = 871, t = [ ], Φ = e N = 385, t = [ ], Φ = e N = 770, t = [ ], Φ = e N = 345, t = [ ], Φ = e N = 690, t = [ ], Φ = e N = 847, t = [ ], Φ = e N = 296, t = [ ], Φ = e N = 592, t = [ ], Φ = e N = 883, t = [ ], Φ = e N = 705, t = [ ], Φ = e N = 551, t = [ ], Φ = e N = 246, t = [ ], Φ = e N = 492, t = [ ], Φ = e N = 164, t = [ ], Φ = e N = 328, t = [ ], Φ = e N = 563, t = [ ], Φ = e N = 731, t = [ ], Φ = e N = 320, t = [ ], Φ = e N = 640, t = [ ], Φ = e N = 748, t = [ ], Φ = e N = 719, t = [ ], Φ = e N = 806, t = [ ], Φ = e N = 789, t = [ ], Φ = e N = 794, t = [ ], Φ = e N = 596, t = [ ], Φ = e N = 538, t = [ ], Φ = e N = 818, t = [ ], Φ = e N = 567, t = [ ], Φ = e N = 539, t = [ ], Φ = e

16 737. N = 707, t = [ ], Φ = e N = 575, t = [ ], Φ = e N = 579, t = [ ], Φ = e N = 637, t = [ ], Φ = e N = 782, t = [ ], Φ = e N = 830, t = [ ], Φ = e N = 390, t = [ ], Φ = e N = 439, t = [ ], Φ = e N = 444, t = [ ], Φ = e N = 555, t = [ ], Φ = e N = 717, t = [ ], Φ = e N = 498, t = [ ], Φ = e N = 753, t = [ ], Φ = e N = 741, t = [ ], Φ = e N = 415, t = [ ], Φ = e N = 652, t = [ ], Φ = e N = 736, t = [ ], Φ = e N = 255, t = [ ], Φ = e N = 510, t = [ ], Φ = e N = 765, t = [ ], Φ = e N = 695, t = [ ], Φ = e N = 243, t = [ ], Φ = e N = 486, t = [ ], Φ = e N = 729, t = [ ], Φ = e N = 403, t = [ ], Φ = e N = 337, t = [ ], Φ = e N = 587, t = [ ], Φ = e N = 485, t = [ ], Φ = e N = 678, t = [ ], Φ = e N = 527, t = [ ], Φ = e N = 427, t = [ ], Φ = e N = 777, t = [ ], Φ = e N = 666, t = [ ], Φ = e N = 462, t = [ ], Φ = e N = 65, t = [ ], Φ = e N = 130, t = [ ], Φ = e N = 195, t = [ ], Φ = e N = 260, t = [ ], Φ = e N = 325, t = [ ], Φ = e N = 543, t = [ ], Φ = e N = 292, t = [ ], Φ = e N = 584, t = [ ], Φ = e N = 688, t = [ ], Φ = e N = 193, t = [ ], Φ = e N = 386, t = [ ], Φ = e N = 397, t = [ ], Φ = e N = 700, t = [ ], Φ = e N = 654, t = [ ], Φ = e N = 522, t = [ ], Φ = e N = 306, t = [ ], Φ = e N = 676, t = [ ], Φ = e N = 340, t = [ ], Φ = e N = 712, t = [ ], Φ = e N = 683, t = [ ], Φ = e N = 332, t = [ ], Φ = e N = 664, t = [ ], Φ = e N = 445, t = [ ], Φ = e N = 474, t = [ ], Φ = e N = 514, t = [ ], Φ = e N = 625, t = [ ], Φ = e N = 284, t = [ ], Φ = e N = 724, t = [ ], Φ = e N = 433, t = [ ], Φ = e

17 800. N = 642, t = [ ], Φ = e N = 599, t = [ ], Φ = e N = 263, t = [ ], Φ = e N = 526, t = [ ], Φ = e N = 251, t = [ ], Φ = e N = 502, t = [ ], Φ = e N = 391, t = [ ], Φ = e N = 457, t = [ ], Φ = e N = 635, t = [ ], Φ = e N = 241, t = [ ], Φ = e N = 432, t = [ ], Φ = e N = 623, t = [ ], Φ = e N = 647, t = [ ], Φ = e N = 267, t = [ ], Φ = e N = 534, t = [ ], Φ = e N = 531, t = [ ], Φ = e N = 613, t = [ ], Φ = e N = 333, t = [ ], Φ = e N = 421, t = [ ], Φ = e N = 659, t = [ ], Φ = e N = 611, t = [ ], Φ = e N = 490, t = [ ], Φ = e N = 671, t = [ ], Φ = e N = 630, t = [ ], Φ = e N = 572, t = [ ], Φ = e N = 601, t = [ ], Φ = e N = 253, t = [ ], Φ = e N = 469, t = [ ], Φ = e N = 231, t = [ ], Φ = e N = 582, t = [ ], Φ = e N = 362, t = [ ], Φ = e N = 473, t = [ ], Φ = e N = 190, t = [ ], Φ = e N = 380, t = [ ], Φ = e N = 570, t = [ ], Φ = e N = 392, t = [ ], Φ = e N = 589, t = [ ], Φ = e N = 350, t = [ ], Φ = e N = 409, t = [ ], Φ = e N = 275, t = [ ], Φ = e N = 594, t = [ ], Φ = e N = 287, t = [ ], Φ = e N = 546, t = [ ], Φ = e N = 558, t = [ ], Φ = e N = 374, t = [ ], Φ = e N = 176, t = [ ], Φ = e N = 461, t = [ ], Φ = e N = 618, t = [ ], Φ = e N = 368, t = [ ], Φ = e N = 202, t = [ ], Φ = e N = 404, t = [ ], Φ = e N = 606, t = [ ], Φ = e N = 379, t = [ ], Φ = e N = 344, t = [ ], Φ = e N = 239, t = [ ], Φ = e N = 478, t = [ ], Φ = e N = 519, t = [ ], Φ = e N = 449, t = [ ], Φ = e N = 577, t = [ ], Φ = e N = 481, t = [ ], Φ = e N = 200, t = [ ], Φ = e N = 338, t = [ ], Φ = e N = 560, t = [ ], Φ = e

18 863. N = 517, t = [ ], Φ = e N = 529, t = [ ], Φ = e N = 548, t = [ ], Φ = e N = 140, t = [ ], Φ = e N = 280, t = [ ], Φ = e N = 420, t = [ ], Φ = e N = 505, t = [ ], Φ = e N = 437, t = [ ], Φ = e N = 541, t = [ ], Φ = e N = 279, t = [ ], Φ = e N = 536, t = [ ], Φ = e N = 416, t = [ ], Φ = e N = 327, t = [ ], Φ = e N = 272, t = [ ], Φ = e N = 234, t = [ ], Φ = e N = 565, t = [ ], Φ = e N = 339, t = [ ], Φ = e N = 178, t = [ ], Φ = e N = 356, t = [ ], Φ = e N = 493, t = [ ], Φ = e N = 553, t = [ ], Φ = e N = 466, t = [ ], Φ = e N = 315, t = [ ], Φ = e N = 524, t = [ ], Φ = e N = 464, t = [ ], Φ = e N = 507, t = [ ], Φ = e N = 425, t = [ ], Φ = e N = 476, t = [ ], Φ = e N = 452, t = [ ], Φ = e N = 326, t = [ ], Φ = e N = 321, t = [ ], Φ = e N = 351, t = [ ], Φ = e N = 207, t = [ ], Φ = e N = 214, t = [ ], Φ = e N = 428, t = [ ], Φ = e N = 367, t = [ ], Φ = e N = 408, t = [ ], Φ = e N = 488, t = [ ], Φ = e N = 99, t = [ ], Φ = e N = 198, t = [ ], Φ = e N = 297, t = [ ], Φ = e N = 396, t = [ ], Φ = e N = 495, t = [ ], Φ = e N = 309, t = [ ], Φ = e N = 147, t = [ ], Φ = e N = 440, t = [ ], Φ = e N = 210, t = [ ], Φ = e N = 512, t = [ ], Φ = e N = 483, t = [ ], Φ = e N = 303, t = [ ], Φ = e N = 384, t = [ ], Φ = e N = 219, t = [ ], Φ = e N = 500, t = [ ], Φ = e N = 291, t = [ ], Φ = e N = 285, t = [ ], Φ = e N = 227, t = [ ], Φ = e N = 454, t = [ ], Φ = e N = 413, t = [ ], Φ = e N = 363, t = [ ], Φ = e N = 137, t = [ ], Φ = e N = 274, t = [ ], Φ = e N = 411, t = [ ], Φ = e N = 471, t = [ ], Φ = e