# Stored data for newform 275.3.q.c, downloaded from the LMFDB on 03 September 2025. {"Nk2": 2475, "analytic_conductor": 7.493207269908165, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 55, "char_degree": 4, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 17, "char_orbit_label": "q", "char_order": 10, "char_parity": -1, "char_values": [275, 10, [177, 101], [5, 1]], "cm_discs": [], "conrey_index": 24, "dim": 8, "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 20, "has_non_self_twist": 1, "hecke_cutters": [[2, [25, 0, 75, 0, 85, 0, -5, 0, 1]], [3, [65536, 0, -4096, 0, 256, 0, -16, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008298816700691, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 11, 4, -1, 10, 0], [1, 1, 55, 8, -1, 10, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "275.3.q.c", "level": 275, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 11], "level_radical": 55, "minimal_twist": "55.3.i.a", "nf_label": "8.0.4000000.1", "prim_orbit_index": 8, "qexp_display": "q+(-2\\zeta_{20}-2\\zeta_{20}^{5}+\\zeta_{20}^{7})q^{2}+4\\zeta_{20}q^{3}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c10", "self_twist_discs": [], "self_twist_type": 0, "space_label": "275.3.q", "trace_display": [0, 0, 0, 0], "trace_hash": 2202792106494061803, "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "7.890", "prec": 17}, {"__RealLiteral__": 0, "data": "0.493", "prec": 17}, {"__RealLiteral__": 0, "data": "344.966", "prec": 24}, {"__RealLiteral__": 0, "data": "53.399", "prec": 20}, {"__RealLiteral__": 0, "data": "23172.143", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.558", "prec": 17}, "traces": [0, 8, 0, 0, 18, 0, -40, 0, 0, 14, 0, -2, 0, 0, 30, 0, 38, 0, 0, -100, 0, 0, 0, 0, -40, 0, -80, 0, 0, -180, 0, 76, 0, 0, 240, 0, -126, 0, 0, -40, 0, 170, 0, 0, 38, 0, 260, 0, 0, -112, 0, -560, 0, 0, 0, 0, 140, 0, 0, 256, 0, 280, 0, 0, 298, 0, 280, 0, 0, 232, 0, 16, 0, 0, -260, 0, 0, 0, 0, 420, 0, 190, 0, 0, -680, 0, -340, 0, 0, 156, 0, -150, 0, 0, -750, 0, -920, 0, 0, -266, 0, 400, 0, 0, 130, 0, -710, 0, 0, 0, 0, 112, 0, 0, 400, 0, -700, 0, 0, -640, 0, 838, 0, 0, 316, 0, 560, 0, 0, 240, 0, 0, 0, 0, 240, 0, -220, 0, 0, -550, 0, 872, 0, 0, -56, 0, 40, 0, 0, 80, 0, 540, 0, 0, -180, 0, -1320, 0, 0, 912, 0, -760, 0, 0, 0, 0, 2160, 0, 0, 168, 0, 630, 0, 0, 1520, 0, 18, 0, 0, -294, 0, -464, 0, 0, 790, 0, 0, 0, 0, 160, 0, -144, 0, 0, 1140, 0, -72, 0, 0, -1104, 0, 432, 0, 0, -2320, 0, 440, 0, 0, -680, 0, -1040, 0, 0, -880, 0, -240, 0, 0, 0, 0, -2280, 0, 0, -450, 0, 160, 0, 0, 316, 0, -200, 0, 0, 560, 0, 1486, 0, 0, 880, 0, 0, 0, 0, 200, 0, -680, 0, 0, -1040, 0, 176, 0, 0, -780, 0, 38, 0, 0, 370, 0, -1260, 0, 0, -1320, 0, -470, 0, 0, -844, 0, 2020, 0, 0, 0, 0, -688, 0, 0, 868, 0, -1080, 0, 0, -224, 0, 510, 0, 0, -22, 0, -1408, 0, 0, 1080, 0, 0, 0, 0, 350, 0, 340, 0, 0, 420, 0, 1820, 0, 0, 1712, 0, -1164, 0, 0, 1840, 0, 360, 0, 0, 1220, 0, 2240, 0, 0, 2090, 0, 3120, 0, 0, 0, 0, 476, 0, 0, -180, 0, 560, 0, 0, -1568, 0, -444, 0, 0, 820, 0, -980, 0, 0, 80, 0, 0, 0, 0, -2840, 0, -134, 0, 0, 1020, 0, -1522, 0, 0, -2520, 0, 80, 0, 0, 1400, 0, 1700, 0, 0, -3860, 0, -70, 0, 0, -744, 0, -1040, 0, 0, 0, 0, -2680, 0, 0, -1204, 0, 680, 0, 0, 220, 0, -336, 0, 0, 440, 0, -1834, 0, 0, 2560, 0, 0, 0, 0, -1310, 0, -208, 0, 0, 1750, 0, -1530, 0, 0, 1036, 0, 456, 0, 0, -1440, 0, 80, 0, 0, -3320, 0, 2360, 0, 0, 840, 0, 1620, 0, 0, 0, 0, 924, 0, 0, -48, 0, 1620, 0, 0, -294, 0, -3080, 0, 0, 1680, 0, 280, 0, 0, 1120, 0, 0, 0, 0, -1340, 0, -400, 0, 0, -520, 0, -1168, 0, 0, 160, 0, 1260, 0, 0, 1140, 0, 730, 0, 0, 3218, 0, -3080, 0, 0, -3728, 0, -4220, 0, 0, 0, 0, 1696, 0, 0, 1786, 0, 1400, 0, 0, 840, 0, -690, 0, 0, 2016, 0, 1300, 0, 0, -2600, 0, 0, 0, 0, 3360, 0, 1606, 0, 0, 800, 0, -2890, 0, 0, -1396, 0, -1792, 0, 0, -2720, 0, 820, 0, 0, -812, 0, 920, 0, 0, 2620, 0, 5320, 0, 0, 0, 0, 3240, 0, 0, 1790, 0, -3060, 0, 0, 2180, 0, 2800, 0, 0, -4448, 0, 2540, 0, 0, -3930, 0, 0, 0, 0, 3270, 0, 434, 0, 0, 1680, 0, -3760, 0, 0, 1240, 0, -1770, 0, 0, -3980, 0, -3240, 0, 0, -80, 0, 2240, 0, 0, 1976, 0, 1400, 0, 0, 0, 0, -5760, 0, 0, -1520, 0, 780, 0, 0, -1500, 0, -1650, 0, 0, 456, 0, 384, 0, 0, 640, 0, 0, 0, 0, -2180, 0, 1976, 0, 0, -3340, 0, 3152, 0, 0, -952, 0, 3276, 0, 0, -2530, 0, -1400, 0, 0, 5466, 0, -640, 0, 0, -320, 0, 2110, 0, 0, 0, 0, -1824, 0, 0, 3020, 0, -770, 0, 0, -128, 0, 640, 0, 0, -840, 0, -322, 0, 0, -2800, 0, 0, 0, 0, 3430, 0, -950, 0, 0, 1810, 0, 1536, 0, 0, -1920, 0, 400, 0, 0, 3760, 0, -2760, 0, 0, -3862, 0, 2980, 0, 0, -3984, 0, -3080, 0, 0, 0, 0, 2196, 0, 0, 1356, 0, -230, 0, 0, -704, 0, -5560, 0, 0, -754, 0, -3800, 0, 0, -2300, 0, 0, 0, 0, 5700, 0, 3640, 0, 0, -1040, 0, 2730, 0, 0, 3200, 0, 3776, 0, 0, 4260, 0, 1360, 0, 0, 3472, 0, -1440, 0, 0, 1496, 0, -5690, 0, 0, 0, 0, 8032, 0, 0, -420, 0, 1960, 0, 0, -2170, 0, 936, 0, 0, 1418, 0, -4000, 0, 0, 4400, 0, 0, 0, 0, 4240, 0, -3064, 0, 0, -10160, 0, 3668, 0, 0, 672, 0, -360, 0, 0, 450, 0, -3210, 0, 0, 2360, 0, -4880, 0, 0, -2590, 0, -3280, 0, 0, 0, 0, -5960, 0, 0, -3284, 0, -3680, 0, 0, 960, 0, -1160, 0, 0, -4984, 0, 2278, 0, 0, -3440, 0, 0, 0, 0, -9040, 0, 1822, 0, 0, 3440, 0, -2000, 0, 0, 2076, 0, -2160, 0, 0, -80, 0, 6820, 0, 0, 6480, 0, 1140, 0, 0, -2850, 0, 7520, 0, 0, 0, 0, -644, 0, 0, -4880, 0, 560, 0, 0, 650, 0, 5890, 0, 0, -2160, 0, 3480, 0, 0, -40, 0, 0, 0, 0, -3440, 0, -2160, 0, 0, 2240, 0, 3456, 0, 0, -1760, 0, -2144, 0, 0, 2660, 0, -400, 0, 0, 6880, 0, -3790, 0, 0, 1796, 0, -2810, 0, 0, 0, 0, 3500, 0, 0, -6128, 0, -2200, 0, 0, -2774, 0, 4460, 0, 0, 4540, 0, 3912, 0, 0, -4970, 0, 0, 0, 0, -2340, 0, -1766, 0, 0, 4990, 0, 8120, 0, 0, 12640, 0, -1274, 0, 0, 1020, 0, 2300, 0, 0, -9254, 0, 4200, 0, 0, 3760, 0, -9800, 0, 0, 0, 0, -2184, 0, 0, 160, 0, -880, 0, 0, -656, 0], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -2, 0, 1], [0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, -1, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -4, 0, -4, 0, -4, 0], [0, 2, 0, 3, 0, 3, 0, 2], [0, -1, 0, 2, 0, -4, 0, -2], [0, 0, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -2, 0, -7, 0, 10, 0], [0, 0, 0, 16, 0, -4, 0, 16], [0, 7, 0, 9, 0, -2, 0, 1], [11, 0, -11, 0, 0, 0, -18, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 5, 0, -5, 0, -3, 0], [0, -12, 0, 14, 0, -16, 0, 28], [0, -7, 0, -7, 0, -7, 0, -7], [-1, 0, -19, 0, 18, 0, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 16, 0, 4, 0, 20, 0], [0, 23, 0, 6, 0, 10, 0, -8], [0, 0, 0, -1, 0, 27, 0, -1], [8, 0, -12, 0, 16, 0, -24, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -23, 0, -6, 0, -23, 0], [0, 0, 0, -8, 0, 0, 0, 0], [0, -27, 0, 17, 0, -7, 0, 34], [-36, 0, 16, 0, -18, 0, 20, 0], [0, 0, 0, 0, 0, 0, 0, 0], [20, 0, -22, 0, 20, 0, 0, 0], [0, -46, 0, 24, 0, -23, 0, 22], [0, -16, 0, -8, 0, -28, 0, 40], [50, 0, 0, 0, 40, 0, -40, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-28, 0, 28, 0, 0, 0, 21, 0], [0, 11, 0, 4, 0, -4, 0, -11], [0, 21, 0, -8, 0, 21, 0, 0], [-4, 0, 32, 0, 32, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [37, 0, -3, 0, 40, 0, -20, 0], [0, 44, 0, -44, 0, 0, 0, -72], [0, 12, 0, 16, 0, 6, 0, -28], [-1, 0, -17, 0, -43, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [51, 0, -25, 0, -1, 0, -50, 0], [0, 75, 0, 0, 0, 17, 0, -17], [0, 12, 0, 20, 0, -20, 0, -12], [2, 0, -31, 0, 31, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-112, 0, 64, 0, -56, 0, 48, 0], [0, -33, 0, 66, 0, -13, 0, 53], [0, 43, 0, -43, 0, 0, 0, -28], [-8, 0, 16, 0, 0, 0, 16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [26, 0, 0, 0, 17, 0, -17, 0], [0, -4, 0, -76, 0, 72, 0, -36], [0, 78, 0, 0, 0, 56, 0, -56], [0, 0, 19, 0, -90, 0, 19, 0], [0, 0, 0, 0, 0, 0, 0, 0], [28, 0, 2, 0, 2, 0, 28, 0], [0, 2, 0, -18, 0, -18, 0, 2], [0, -14, 0, 28, 0, 7, 0, 35], [36, 0, 41, 0, 36, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [32, 0, 60, 0, 56, 0, 8, 0], [0, 0, 0, -10, 0, 34, 0, -10], [0, -92, 0, 24, 0, -116, 0, 58], [4, 0, -4, 0, 0, 0, 104, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 22, 0, -22, 0, 12, 0], [0, 14, 0, -21, 0, 28, 0, -42], [0, -50, 0, 4, 0, 4, 0, -50], [-37, 0, -15, 0, -22, 0, 11, 0], [0, 0, 0, 0, 0, 0, 0, 0], [49, 0, -98, 0, 55, 0, -43, 0], [0, -29, 0, -31, 0, -37, 0, -10], [0, 0, 0, -92, 0, -24, 0, -92], [-2, 0, 44, 0, -86, 0, 88, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -95, 0, 0, 0], [0, -71, 0, -57, 0, -71, 0, 0], [0, -108, 0, 26, 0, 56, 0, 52], [-136, 0, 28, 0, -68, 0, 108, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-40, 0, -50, 0, -40, 0, 0, 0], [0, -144, 0, 64, 0, -72, 0, 80], [0, -22, 0, 66, 0, -33, 0, 44], [68, 0, 0, 0, 97, 0, -97, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-52, 0, 52, 0, 0, 0, 81, 0], [0, -74, 0, -31, 0, 31, 0, 74], [0, 80, 0, -88, 0, 80, 0, 0], [-75, 0, -92, 0, -92, 0, -75, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-88, 0, -96, 0, 8, 0, -4, 0], [0, -62, 0, 62, 0, 0, 0, 52], [0, 54, 0, -29, 0, 27, 0, -25], [-70, 0, 42, 0, -84, 0, 21, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}