# Stored data for newform 435.3.h.b, downloaded from the LMFDB on 15 January 2025.
{"Nk2": 3915, "analytic_conductor": 11.852891499672916, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 87, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 8, "char_orbit_label": "h", "char_order": 2, "char_parity": -1, "char_values": [435, 2, [146, 262, 31], [1, 2, 1]], "cm_discs": [], "conrey_index": 86, "dim": 2, "field_disc": -20, "field_disc_factorization": [[-1, 1], [2, 2], [5, 1]], "field_poly": [5, 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": [[2, [-2, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504080714039731, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 87, 4, -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": true, "label": "435.3.h.b", "level": 435, "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": true, "level_primes": [3, 5, 29], "level_radical": 435, "minimal_twist": "435.3.h.a", "nf_label": "2.0.20.1", "prim_orbit_index": 4, "qexp_display": "q+2q^{2}+(2-\\beta )q^{3}+\\beta q^{5}+(4-2\\beta )q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "435.3.h", "trace_display": [4, 4, 0, 16], "trace_hash": 2072160202113307164, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.907", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.352", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "154.958", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.516", "prec": 17}, "traces": [0, 2, 4, 4, 0, 0, 8, 16, -16, -2, 0, 22, 0, 4, 32, 10, -32, 64, -4, 0, 0, 32, 44, 0, -32, -10, 8, -44, 0, -58, 20, 0, 0, 44, 128, 0, 0, 0, 0, 8, 0, -74, 64, 0, 0, 40, 0, 4, -64, 30, -20, 128, 0, 0, -88, 0, -128, -60, -116, 0, 0, 0, 0, -16, 128, 0, 88, 76, 0, -150, 0, 0, 16, 0, 0, -20, 0, 176, 16, 0, 0, -158, -148, 0, 0, 0, 0, -116, -176, -332, 80, 32, 0, 120, 8, 60, 0, 0, 60, -22, 0, 22, 256, 52, -32, 80, 0, 0, 0, 202, 0, 150, -256, -284, -120, 150, 0, -4, 0, 512, -80, 0, 0, -148, 0, 0, -32, 0, 256, 210, 0, 172, 0, 0, 152, 70, -512, -188, -300, -38, 0, 8, 0, 44, 32, 0, 0, 60, 0, 0, -40, -386, 0, -64, 352, -120, 0, 0, 0, 90, 0, 0, -316, 0, 0, 110, 0, 0, -256, -330, 0, -240, 0, 0, -232, -80, -352, 300, -664, 0, 0, -122, 64, -60, 0, -150, 240, 704, 0, -352, 120, 46, 256, 0, 0, 20, 0, 0, -44, 202, 80, 152, 44, -464, 0, 0, 104, -600, -64, 0, 160, 0, 0, -420, 0, -210, 352, 0, 404, 330, 0, 128, 300, 4, 0, 10, -568, 0, 0, 0, 300, 352, 464, 0, -8, 0, 0, -60, 1024, 0, -160, 118, 0, -236, 0, 0, -296, 0, 0, 210, 0, 52, 0, 0, 0, 320, 0, 0, 420, 0, 0, 58, 344, 568, -352, -90, 0, -664, 0, 148, 140, 0, -1024, 64, -376, -110, 0, 496, -76, 480, 0, 0, 16, -848, 0, 120, 88, -592, 0, 1470, 0, 630, 0, 556, 120, -300, 0, -484, 0, 0, 0, 0, -772, 44, 0, 60, -128, 0, 0, 104, -240, 862, -64, -536, 0, 320, 0, -416, 180, -638, 0, -780, 0, 0, 0, -20, 0, 404, 592, 32, 220, 0, 0, 600, 0, 0, -512, 0, -660, -568, 0, 0, -480, -544, 0, 300, 0, 0, 0, 1306, -160, -88, 0, 0, 600, 420, 0, 1024, 0, 634, -320, 362, -244, 0, 0, -330, -120, 0, 0, 74, -300, 0, 0, 1312, 1408, -50, -32, -116, -704, 0, 0, 630, 92, 0, 512, 0, 0, 840, 0, -62, 40, 0, -240, 344, 0, 60, 0, -1292, 404, -480, 160, 0, 304, 0, 0, -80, -928, 0, -1024, 0, 0, -376, 0, 0, -1200, -210, 0, -76, 0, 0, 0, 0, 0, -4, 0, -320, -840, 0, 0, 88, -420, 0, 704, 0, 0, -290, 0, -900, 660, 52, 0, -30, 256, 676, 0, 0, 8, 900, 1024, 1018, 20, -814, 0, -772, 0, 0, 480, 136, 0, -1408, 0, 766, 704, -416, 928, -240, 0, -248, 0, 608, 0, 540, 0, 0, -120, 0, 0, 360, 0, -1196, 0, 0, 236, -1200, 0, -630, -472, -932, 0, -1110, 0, 556, 0, -1856, 0, 440, 0, 0, 420, -1628, 0, 1260, 104, 1396, 128, 0, 0, -660, 0, 0, 640, 0, -1024, -420, 0, 0, 0, 44, 0, -990, 0, 0, 116, 304, 0, -160, 1136, 0, -704, -1192, -180, 1200, 0, -148, -1328, 780, -608, -960, 296, 330, 0, 0, 0, -244, 0, 0, 128, 256, 0, -240, -220, 0, 1200, 0, 992, -300, 0, 0, 960, 0, 0, 1408, 0, -1784, 0, 0, -1696, -1264, 0, -332, 240, -1226, 0, 92, -1184, 0, -128, 0, 2940, 540, 0, 0, 1260, 0, 0, 80, 1112, 0, 0, 720, -600, -1050, 0, 0, -968, 0, 0, 404, 0, 1828, 160, 0, 0, -76, 0, 0, 88, 0, 0, -928, 120, 8, 0, 664, 0, -370, -1408, -1208, 208, 0, 0, -1050, 1724, -2656, -128, 50, -1072, -660, 0, 0, 640, -2012, 0, 1260, -832, -630, 0, 60, -1276, -1680, 0, -818, -1560, -416, 0, -420, 0, 0, 1264, 0, -40, 960, 0, -1844, 808, 0, 1184, 1320, 64, -2342, 0, 2638, 0, 256, 0, 480, 1200, 0, 0, 8, 0, 0, 0, 424, 0, 220, 0, 2524, -1136, 0, 0, -330, 0, 0, 0, 0, -1088, -900, 0, 0, 600, 1228, 0, -176, 0, 0, 928, -2368, 2612, -1830, 0, 0, -176, 900, 1408, 20, 0, 176, 0, -494, 840, -240, 2656, 1800, 2048, 0, 0, 840, 1268, 0, -640, 416, 724, 236, 0, 290, 0, 0, -256, 478, -660, 0, 0, 0, 0, 150, 0, 836, 148, 0, 0, -120, 0, 556, -960, -900, 2624, 840, 0, 0, -100, 0, -64, 104, -232, 0, 0, 0, 0, -1650, -480, 0, 1260, 1616, 0, 1280, 0, 0, 0, 0, 0, -570, 0, 148, 1680, 0, 0, 1200, -124, 0, 0, 0, 0, 1276, -480, -540, 688, -92, 0, 1136, 120, -2272, 176, 0, -2584, -180, 0, 52, -960, 128, 0, 332, 0, 0, 0, 1200, 0, 296, -176, 2458, -160, 1558, 0, -60, 0, 1110, -2048, 1260, 0, -32, 0, 0, -752, 0, -416, -220, 0, -2048, 0, 0, -420, 992, 256, 960, -152, -1260, 0, 840, 0, 388, -640, 1682, 0, -420, 0, 0, -8, 0, 0, -1696, -640, 2250, 0, 0, 0, -60, 0, 0, 176, 0, 0, -1184, 0, 0, 0, 990, 0, 2940, 0, 0, -580, 152, -1616, 2520, -1800, 0, 0, -1712, 104, 1112, 0, -2258, -60, -248, 0, -600, 1352, 1264, -1200, 0, 0, -1738, 0, 0, 1800, 960, 2048, -300, 2036, 0, 0, 0, -1628, 1680, 2272, 0, -1544, 0, 0, -22, 0, 1942, 960, 0, 272, 120, 0, 1376, -2816, -1628, -1200, -1050, 1532, 0, 0, 0, -832, -52, 0, 0, -480, 0, 0, 1724, -496, 0, 32, -2684, 1216, -1072, 0, 0, 1080, 0, 0, 560, 0, -3356, 0, 0, 0, -832, -4096, 0, 720, 0, 0, -1276, -2392, -1504, 640, 482, 0, -3120, 0, -540, -2400, 0, 0, -1920, -1260, 886, 0, -304, -1864, -40, 0, 0, -2220, -3652, 0, -202, 1112, -692, 1184, 1050, -3712, 64, 0, 3150, 880, 2638, 0, -480, 0, 0, 0, 0, -3256, 1050, 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], [1, 0], [2, 0], [2, -1], [0, 0], [0, 1], [4, -2], [8, 0], [-8, 0], [-1, -4], [0, 2], [11, 0], [0, 0], [2, 0], [16, 0], [5, 2], [-16, 0], [32, 0], [-2, -8], [0, -6], [0, 0], [16, -8], [22, 0], [0, -15], [-16, 8], [-5, 0], [4, 0], [-22, -7], [0, 0], [-29, 0], [10, 4], [0, 12], [0, 0], [22, -11], [64, 0], [0, 8], [0, 0], [0, 15], [0, -12], [4, -2], [0, -8], [-37, 0], [32, -16], [0, 21], [0, 0], [20, -1], [0, -30], [2, 0], [-32, 16], [15, 0], [-10, 0], [64, -32], [0, 0], [0, 9], [-44, -14], [0, 11], [-64, 0], [-30, -12], [-58, 0], [0, 30], [0, 0], [0, -6], [0, 24], [-8, -32], [64, 0], [0, 2], [44, -22], [38, 0], [0, 0], [-75, -30], [0, 16], [0, -42], [8, 32], [0, 33], [0, 30], [-10, 5], [0, 0], [88, 0], [8, -4], [0, -6], [0, -16], [-79, 8], [-74, 0], [0, 21], [0, 0], [0, 32], [0, 42], [-58, 29], [-88, 0], [-166, 0], [40, -2], [16, 0], [0, 0], [60, 24], [4, 0], [30, 0], [0, 0], [0, 63], [30, 0], [-11, -44], [0, 0]]}