# Stored data for newform 490.3.f.b, downloaded from the LMFDB on 25 April 2024.
{"label": "490.3.f.b", "space_label": "490.3.f", "level": 490, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503943275086314, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1540428060361885336, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [8, -4, 1]], [11, [8, 1]]], "qexp_display": "q+(-1-i)q^{2}+(2-2i)q^{3}+2iq^{4}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": false, "Nk2": 4410, "analytic_conductor": 13.351532953654548, "hecke_ring_index": 1, "level_radical": 70, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.248", "prec": 17}, "analytic_rank_proved": true, "char_values": [490, 4, [197, 101], [1, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 7], "conrey_indexes": [197, 393], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "1.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.151", "prec": 17}, {"__RealLiteral__": 0, "data": "11.408", "prec": 20}, {"__RealLiteral__": 0, "data": "0.284", "prec": 17}, {"__RealLiteral__": 0, "data": "92.037", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c4", "trace_display": [-2, 4, 0, 0], "traces": [0, 2, -2, 4, 0, 0, -8, 0, 4, 0, 10, -16, 8, -6, 0, 20, -8, -14, 2, 0, -20, 0, 16, -4, 0, -50, 12, 40, 0, 0, 0, -104, 8, -32, 0, 0, -4, -6, 40, 0, 20, 16, 0, -84, 0, -10, 8, 36, -16, 0, 50, -56, -12, 106, 0, 0, 0, 80, 80, 0, -40, 96, 104, 0, 0, -30, 64, 124, 28, 0, 0, -56, 4, 94, 0, -100, -80, 0, 24, 0, 0, 142, -16, -36, 0, 70, 168, 160, -32, 0, 10, 0, -8, -208, 0, -200, 32, 126, 0, 0, 0, -124, 56, -236, 0, 0, -212, 284, -80, 0, -80, -24, 0, 46, 0, -20, -160, -6, 40, 0, 80, -114, -96, 32, 0, 0, 0, -236, -16, 0, 0, 256, -64, 0, 0, -200, -56, -126, 16, 0, 0, 144, 56, 48, 0, -400, -188, 0, 12, 0, 200, 104, 80, 14, 0, 0, -48, -54, 0, 0, -40, 0, -142, -164, 0, -160, 72, -124, 0, 0, -140, -40, -168, 214, 0, 0, 64, 80, -160, 0, 0, -4, 0, 192, 0, 30, 416, 112, -72, 0, 200, 424, -32, -114, 0, -120, 0, -6, -16, 0, -100, 496, 124, 0, 0, 0, 472, -4, 24, 0, 0, -656, 212, -112, 0, -420, 160, 0, -20, 0, 160, 84, 24, -276, 0, 0, -92, -4, -160, 0, 0, 0, 160, 366, 0, -180, -80, 0, 0, 0, -80, -464, 114, -76, 0, 0, -64, -120, -208, 0, -250, 96, 0, 32, 0, 0, 32, 626, 336, 0, 60, -80, -256, -524, 0, 530, 0, -320, -248, 0, 400, -504, 56, 0, 0, 400, -32, 534, -280, 0, 0, 624, -144, 524, 0, -400, -96, 0, -8, 0, 400, 504, 188, -486, 0, -200, -24, -320, -300, 0, -200, 0, -104, -248, 0, 0, -28, 36, 0, 0, -520, 776, 48, -366, 0, 0, 0, -426, -424, 0, 80, 1136, 0, 280, 0, 150, 328, -40, 32, 0, 0, 464, -72, 6, 0, -620, 0, 834, 302, 0, 140, 832, 40, 0, 0, -80, -428, 404, -320, 0, 0, -240, -64, 894, 0, 0, 320, 0, -440, 0, -20, -78, 4, -228, 0, 470, -384, 236, 16, 0, -60, 0, -416, -214, 0, -500, 144, -240, 0, 0, 0, -944, -424, 684, 0, 0, 228, -84, -252, 0, 120, 56, 0, 512, 0, 0, 32, 646, 240, 0, 200, 1284, -496, 312, 0, 0, 0, 48, -112, 0, 80, -504, -472, 0, 0, -180, -48, -560, -320, 0, 0, -416, 656, -36, 0, 350, 224, 0, -568, 0, 0, -1576, -160, 734, 0, -800, 40, -80, -376, 0, -160, 0, -84, 756, 0, 800, 552, -600, 0, 0, -50, -128, 92, 208, 0, 0, 320, -786, -240, 0, 40, -1244, 0, 556, 0, -1040, -732, 76, 12, 0, 360, -216, 80, 672, 0, 0, 0, 106, 240, 0, 0, 36, 464, 0, 0, -630, 152, 1044, 192, 0, 0, -656, 64, 560, 0, 80, 416, 0, 144, 0, 500, -496, -96, 84, 0, 0, -64, 604, 472, 0, -280, 0, -32, -800, 0, -1180, -672, -288, 0, 0, -120, 516, 80, -516, 0, 0, 1048, 728, 128, 0, 0, -40, 0, -48, 0, -1420, 496, -880, -20, 0, -400, -676, 504, -8, 0, 100, 0, -1116, 252, 0, -400, -1600, 32, 0, 0, 0, 560, -6, -104, 0, 0, 448, -624, 84, 0, 230, -1048, 0, -112, 0, 800, 784, 96, 848, 0, 100, 16, 946, -382, 0, 0, 0, -504, -848, 0, 30, 972, 396, 0, 0, 200, -24, 24, 94, 0, 0, 600, 480, -24, 0, 0, 656, 0, -124, 0, 0, 496, -924, -160, 0, 480, -216, 28, 1446, 0, 160, 0, 654, 944, 0, 1040, -160, -776, 0, 0, 1250, 732, -640, 108, 0, 0, -1096, 0, -1312, 0, 1180, 848, 0, -640, 0, -80, -1136, -1136, 684, 0, -1680, -560, 236, 284, 0, -300, 0, -328, 906, 0, 0, -64, 94, 0, 0, 320, -1024, -464, 168, 0, 0, -12, -160, 248, 0, 1240, -768, 0, 386, 0, -1000, -604, -314, -184, 0, 0, -16, -832, 876, 0, 630, 0, -480, 336, 0, 80, -2064, 428, 0, 0, 1400, 640, -112, 880, 0, 0, -256, 240, 120, 0, 0, -1788, 0, -160, 0, -280, 0, -320, 208, 0, 240, 880, 480, -800, 0, 40, 0, 78, -928, 0, 0, 456, 1116, 0, 0, 0, 1176, 384, 1654, 0, 0, -32, -992, 16, 0, 60, -480, 0, -764, 0, 1500, 428, -36, -224, 0, 0, -1176, -144, 192, 0, 0, 0, 1974, 680, 0, -400, 316, 944, 0, 0, 70, -1368, -120, 64, 0, 0, 2504, -228, -486, 0, 2600, 504, 0, 780, 0, 0, 448, -56, -1600, 0, 270, -1024, -524, 12, 0, 0, 0, -32, -288, 0, 2120, -480, -534, 0, 0, -200, 160, -1284, -752, 0, 0, -624, -40, -248, 0, 710, 416, 0, -1008, 0, -820, 224, -1680, 300, 0, -160, -3136, 504, -1124, 0, 800, 0, 1524, 8, 0, 0, 2136, 48, 0, 0, 620, 640, -2080, -600, 0, 0, -1518, 416, 1248, 0, -1510, 72, 0, -424, 0, 0, 24, -224, -2246, 0, 0, 1136, -834, -192, 0, 840, 0, 1576, -484, 0, 1070, -1468, -764, 0, 0, 1600, -744, -40, -126, 0, 0, 752, -906, -1120, 0, 0, -1424, 0, 236, 0, -400, -1512, 2316, -48, 0, -800, -1136, -552, -720, 0, 2200, 0, -48, -820, 0, 100, -1484, 128, 0, 0, 0, -416, 284, 8, 0, 0, 2344, -320, 288, 0, 960, 480, 0, -560, 0, -80, 144, 1244, 168, 0, 150, -1112, -236, -320, 0, 0, 0, 732, 1552, 0, -560, -24, 466, 0, 0, -360, 156, 216, -32, 0, 0, -1344, 124, 0, 0, -1000, -1704, 0, -2034, 0, 0, -480, -1280, 880, 0, 160, 3486, -36, -284, 0, -570, 0, 1004, -228, 0, 1260, -1984, -152, 0, 0, 0, -384, -1566, 656, 0, 0, 20, 656, -2116, 0, 30, -1120, 0, 240, 0, -80, -136, -416, 928, 0, -1200, -288, 1546, 760, 0, -500], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "10.3.c.a", "char_is_minimal": true, "conrey_index": 197, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, -1], [2, -2], [0, 2], [0, 5], [-4, 0], [0, 0], [2, -2], [0, 1], [5, -5], [-8, 0], [4, 4], [-3, 3], [0, 0], [10, 10], [-4, 0], [-7, -7], [1, -1], [0, 20], [-10, 0], [0, 0], [8, 8], [-2, 2], [0, -8], [-25, 0], [6, 0], [20, 20], [0, 0], [0, 40], [0, -20], [-52, 0], [4, 4], [-16, 16], [0, 14], [0, 0], [-2, 0], [-3, -3], [20, -20], [0, 12], [10, 10], [8, 0], [0, 0], [-42, 42], [0, -16], [-5, 0], [4, 0], [18, 18], [-8, 8], [0, 0], [25, 25], [-28, 0], [-6, -6], [53, -53], [0, -40], [0, -40], [0, 0], [40, 40], [40, -40], [0, 20], [-20, 20], [48, 0], [52, 52], [0, 0], [0, -8], [-15, -15], [32, 0], [62, 62], [14, -14], [0, 8], [0, 0], [-28, 0], [2, 2], [47, -47], [0, 6], [-50, 50], [-40, 0], [0, 0], [12, -12], [0, 0], [0, -20], [71, 0], [-8, -8], [-18, 18], [0, 0], [35, -35], [84, 0], [80, 80], [-16, 16], [0, -80], [5, 5], [0, 0], [-4, -4], [-104, 104], [0, -36], [-100, 0], [16, 0], [63, 63], [0, 0], [0, -8], [0, -50]]}