# Stored data for newform 320.5.b.c, downloaded from the LMFDB on 23 December 2025.
{"Nk2": 8000, "analytic_conductor": 33.07838818683018, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 4, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": -1, "char_values": [320, 2, [191, 261, 257], [1, 2, 2]], "cm_discs": [], "conrey_index": 191, "dim": 8, "field_disc": 166790560000, "field_disc_factorization": [[2, 8], [5, 4], [1021, 2]], "field_poly": [3481, 0, 2015, 0, 413, 0, 35, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [129413376, 0, 7526016, 0, 117616, 0, 616, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007268058104128, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 26214400, "hecke_ring_index_factorization": [[2, 20], [5, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 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": "320.5.b.c", "level": 320, "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": [2, 5], "level_radical": 10, "minimal_twist": "160.5.b.a", "prim_orbit_index": 2, "qexp_display": "q-\\beta _{1}q^{3}+\\beta _{3}q^{5}+(-2\\beta _{1}-4\\beta _{2}-\\beta _{7})q^{7}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "4.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "320.5.b", "trace_display": [0, 0, 0, 0], "trace_hash": 429041737550185138, "trace_moments": [{"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "6.936", "prec": 17}, {"__RealLiteral__": 0, "data": "2.254", "prec": 17}, {"__RealLiteral__": 0, "data": "260.313", "prec": 24}, {"__RealLiteral__": 0, "data": "281.951", "prec": 24}, {"__RealLiteral__": 0, "data": "14980.678", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, -32, 0, 0, 0, -560, 0, 0, 0, -2384, 0, 0, 0, 1000, 0, 0, 0, 2064, 0, 0, 0, 544, 0, 0, 0, -3616, 0, 0, 0, -5216, 0, 0, 0, 3600, 0, 0, 0, 4088, 0, 0, 0, -5088, 0, 0, 0, 3072, 0, 0, 0, 5504, 0, 0, 0, -7600, 0, 0, 0, 25744, 0, 0, 0, 17936, 0, 0, 0, 15840, 0, 0, 0, 41560, 0, 0, 0, 9600, 0, 0, 0, -50608, 0, 0, 0, -73824, 0, 0, 0, 3440, 0, 0, 0, -50448, 0, 0, 0, -12400, 0, 0, 0, 54400, 0, 0, 0, 14320, 0, 0, 0, -36544, 0, 0, 0, -13112, 0, 0, 0, 0, 0, 0, 0, -143632, 0, 0, 0, 21184, 0, 0, 0, 9264, 0, 0, 0, 23280, 0, 0, 0, -72800, 0, 0, 0, 89472, 0, 0, 0, 309680, 0, 0, 0, -68384, 0, 0, 0, 75344, 0, 0, 0, 128800, 0, 0, 0, -153448, 0, 0, 0, -199584, 0, 0, 0, 85568, 0, 0, 0, -170448, 0, 0, 0, -12400, 0, 0, 0, 302368, 0, 0, 0, 56592, 0, 0, 0, 123328, 0, 0, 0, 96528, 0, 0, 0, 10800, 0, 0, 0, -130944, 0, 0, 0, -194784, 0, 0, 0, -148192, 0, 0, 0, -70976, 0, 0, 0, -73000, 0, 0, 0, 167504, 0, 0, 0, -39376, 0, 0, 0, 60480, 0, 0, 0, 207328, 0, 0, 0, 11600, 0, 0, 0, -228240, 0, 0, 0, -229344, 0, 0, 0, 97584, 0, 0, 0, 55728, 0, 0, 0, -44400, 0, 0, 0, 115328, 0, 0, 0, 23392, 0, 0, 0, -441600, 0, 0, 0, -279776, 0, 0, 0, 62400, 0, 0, 0, 165400, 0, 0, 0, -232544, 0, 0, 0, 361792, 0, 0, 0, -17936, 0, 0, 0, -32400, 0, 0, 0, -1456, 0, 0, 0, -120688, 0, 0, 0, -114048, 0, 0, 0, -211632, 0, 0, 0, -4000, 0, 0, 0, 4272, 0, 0, 0, 667328, 0, 0, 0, -686704, 0, 0, 0, 126272, 0, 0, 0, 206000, 0, 0, 0, -177648, 0, 0, 0, 584080, 0, 0, 0, 985312, 0, 0, 0, 571656, 0, 0, 0, -40000, 0, 0, 0, 513088, 0, 0, 0, 685824, 0, 0, 0, 544512, 0, 0, 0, -74064, 0, 0, 0, 296800, 0, 0, 0, -1291008, 0, 0, 0, -995616, 0, 0, 0, -96544, 0, 0, 0, -781488, 0, 0, 0, -522000, 0, 0, 0, 439040, 0, 0, 0, 1162880, 0, 0, 0, -860864, 0, 0, 0, 438336, 0, 0, 0, -70000, 0, 0, 0, -1403712, 0, 0, 0, -344912, 0, 0, 0, 71616, 0, 0, 0, -137624, 0, 0, 0, -452800, 0, 0, 0, 962944, 0, 0, 0, -823648, 0, 0, 0, 203856, 0, 0, 0, 289456, 0, 0, 0, 191200, 0, 0, 0, 42000, 0, 0, 0, -1668064, 0, 0, 0, -2101376, 0, 0, 0, -325984, 0, 0, 0, 175200, 0, 0, 0, 959088, 0, 0, 0, 561056, 0, 0, 0, 524320, 0, 0, 0, 1635632, 0, 0, 0, 379200, 0, 0, 0, 766032, 0, 0, 0, -1206144, 0, 0, 0, 2444128, 0, 0, 0, -865584, 0, 0, 0, -298000, 0, 0, 0, 961912, 0, 0, 0, 612832, 0, 0, 0, 519744, 0, 0, 0, -194640, 0, 0, 0, 121200, 0, 0, 0, -3319072, 0, 0, 0, -185536, 0, 0, 0, 484992, 0, 0, 0, 34368, 0, 0, 0, -309600, 0, 0, 0, 687104, 0, 0, 0, 2115552, 0, 0, 0, -1542864, 0, 0, 0, -1447440, 0, 0, 0, 969200, 0, 0, 0, 655744, 0, 0, 0, 692368, 0, 0, 0, -722816, 0, 0, 0, 882016, 0, 0, 0, -587200, 0, 0, 0, 2162592, 0, 0, 0, -494656, 0, 0, 0, 190256, 0, 0, 0, 253792, 0, 0, 0, 125000, 0, 0, 0, 608704, 0, 0, 0, -90912, 0, 0, 0, 66752, 0, 0, 0, 111008, 0, 0, 0, 1790800, 0, 0, 0, -2903040, 0, 0, 0, -997312, 0, 0, 0, -1587728, 0, 0, 0, -1311360, 0, 0, 0, -121600, 0, 0, 0, 2460048, 0, 0, 0, 691184, 0, 0, 0, 571648, 0, 0, 0, -2850864, 0, 0, 0, -292000, 0, 0, 0, 1245856, 0, 0, 0, -55840, 0, 0, 0, 2097216, 0, 0, 0, 2346816, 0, 0, 0, -2820400, 0, 0, 0, -2348208, 0, 0, 0, 1299040, 0, 0, 0, -3034560, 0, 0, 0, 1739280, 0, 0, 0, 258000, 0, 0, 0, -5363096, 0, 0, 0, -2238688, 0, 0, 0, -366880, 0, 0, 0, -759168, 0, 0, 0, 1334000, 0, 0, 0, 848336, 0, 0, 0, 1847968, 0, 0, 0, 864640, 0, 0, 0, 885072, 0, 0, 0, -959200, 0, 0, 0, -2074032, 0, 0, 0, -337664, 0, 0, 0, 3892704, 0, 0, 0, -1295040, 0, 0, 0, -1990000, 0, 0, 0, 3192912, 0, 0, 0, 444384, 0, 0, 0, -2715520, 0, 0, 0, 3520944, 0, 0, 0, 1206000, 0, 0, 0, -2855088, 0, 0, 0, -4058784, 0, 0, 0, -3630208, 0, 0, 0, -467392, 0, 0, 0, 68000, 0, 0, 0, 4426112, 0, 0, 0, 524848, 0, 0, 0, 6487488, 0, 0, 0, 2982936, 0, 0, 0, 3200, 0, 0, 0, 763312, 0, 0, 0, -487552, 0, 0, 0, 3170480, 0, 0, 0, 446112, 0, 0, 0, -79600, 0, 0, 0, -443264, 0, 0, 0, 4835280, 0, 0, 0, 1891360, 0, 0, 0, 772512, 0, 0, 0, 2886400, 0, 0, 0, -3453584, 0, 0, 0, 30400, 0, 0, 0, -2261984, 0, 0, 0, -5232832, 0, 0, 0, -176000, 0, 0, 0, 9084944, 0, 0, 0, 1782560, 0, 0, 0, -2232288, 0, 0, 0, -3771120, 0, 0, 0, -452000, 0, 0, 0, 326720, 0, 0, 0, -5913120, 0, 0, 0, -47184, 0, 0, 0, 2129584, 0, 0, 0, -3181600, 0, 0, 0, -1310144, 0, 0, 0, 1548560, 0, 0, 0, -11564352, 0, 0, 0, 2464712, 0, 0, 0, 3630400, 0, 0, 0, -4527360, 0, 0, 0, 1881472, 0, 0, 0, -5031248, 0, 0, 0, -941600, 0, 0, 0, 1190000, 0, 0, 0, 2480720, 0, 0, 0, 5793504, 0, 0, 0, 8341536, 0, 0, 0], "weight": 5, "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, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -4, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-73, 0, 0, 4, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -20, 0, -1, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, -8, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 15, 0, 2, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-70, 0, 0, 10, 0, 1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -30, 0, 5, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-298, 0, 0, -10, 0, 6, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 24, -22, 0, -8, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [125, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 62, 144, 0, 30, 0, 0, 12], [0, 0, 0, 0, 0, 0, 0, 0], [258, 0, 0, -72, 0, 2, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -58, 30, 0, -6, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [68, 0, 0, 138, 0, 23, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -14, 80, 0, 11, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-452, 0, 0, -2, 0, 26, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -18, -252, 0, -22, 0, 0, 24], [0, 0, 0, 0, 0, 0, 0, 0], [-652, 0, 0, -4, 0, -37, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -123, -292, 0, 28, 0, 0, 58], [0, 0, 0, 0, 0, 0, 0, 0], [450, 0, 0, -83, 0, -25, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 474, 0, 64, 0, 0, -25], [0, 0, 0, 0, 0, 0, 0, 0], [511, 0, 0, 8, 0, -9, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 264, 138, 0, 74, 0, 0, 42], [0, 0, 0, 0, 0, 0, 0, 0], [-636, 0, 0, -68, 0, -59, -22, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 104, -105, 0, 4, 0, 0, 14], [0, 0, 0, 0, 0, 0, 0, 0], [384, 0, 0, 66, 0, 9, -21, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 79, 22, 0, -5, 0, 0, 119], [0, 0, 0, 0, 0, 0, 0, 0], [688, 0, 0, -42, 0, -24, -34, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 376, 126, 0, 80, 0, 0, 45], [0, 0, 0, 0, 0, 0, 0, 0], [-950, 0, 0, -2, 0, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 63, -264, 0, 44, 0, 0, 10], [0, 0, 0, 0, 0, 0, 0, 0], [3218, 0, 0, 218, 0, 30, -14, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -188, 134, 0, 104, 0, 0, 122], [0, 0, 0, 0, 0, 0, 0, 0], [2242, 0, 0, -6, 0, 85, -15, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -125, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1980, 0, 0, 334, 0, 93, -14, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, -622, 0, 170, 0, 0, 42], [0, 0, 0, 0, 0, 0, 0, 0], [5195, 0, 0, -620, 0, -245, -65, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -213, -424, 0, 62, 0, 0, -80], [0, 0, 0, 0, 0, 0, 0, 0], [1200, 0, 0, -96, 0, -65, 10, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -54, -1104, 0, -36, 0, 0, 360], [0, 0, 0, 0, 0, 0, 0, 0], [-6326, 0, 0, -428, 0, 62, 10, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 50, -794, 0, -76, 0, 0, 52], [0, 0, 0, 0, 0, 0, 0, 0], [-9228, 0, 0, 212, 0, 52, 78, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 38, -565, 0, 38, 0, 0, 18], [0, 0, 0, 0, 0, 0, 0, 0], [430, 0, 0, 250, 0, 187, 31, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 147, 3726, 0, 253, 0, 0, -291], [0, 0, 0, 0, 0, 0, 0, 0]]}