# Stored data for newform 77.4.a.c, downloaded from the LMFDB on 12 September 2024.
{"Nk2": 1232, "analytic_conductor": 4.543147070442028, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, 1], [11, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [77, 1, [45, 57], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 509800, "field_disc_factorization": [[2, 3], [5, 2], [2549, 1]], "field_poly": [15, 5, -10, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [66, -56, -19, 4, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199321849933, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "77.4.a.c", "level": 77, "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": [7, 11], "level_radical": 77, "minimal_twist": "77.4.a.c", "nf_label": "4.4.509800.1", "prim_orbit_index": 1, "qexp_display": "q+(-1+\\beta _{2})q^{2}+(-3+\\beta _{3})q^{3}+(6+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "77.4.a", "trace_display": [-4, -12, -18, -28], "trace_hash": 1445673725602810807, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.733", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "38.129", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "583.641", "prec": 24}], "trace_zratio": 0, "traces": [0, 4, -4, -12, 22, -18, 2, -28, -60, 66, -92, 44, -186, -134, 28, -62, -6, -74, -256, -164, 116, 84, -44, 194, 570, 38, 734, -510, -154, -108, 1252, -412, -4, -132, -346, 126, 1518, 286, 224, -256, -540, -18, -14, -496, 242, 580, -284, 62, -862, 196, 212, -508, -822, -828, 2420, -198, 420, 700, 1388, -1224, -1776, -350, -878, -462, -718, -396, 22, -1498, 1058, -386, 644, 2326, -3000, -1630, -1156, -1362, -3152, -308, -2464, -1020, 3072, 1128, 2118, -1920, 1302, 2008, 1056, 1640, -660, 1550, -5780, 938, 2592, 6046, -1042, 2332, 4082, -2202, -196, 726, 2014, -46, 4568, -1954, 2150, 434, -2892, -1060, -7440, 2488, -1012, -918, 42, 3598, 4760, -2430, -6184, -1150, 2474, 518, 4740, 484, 2450, -2164, -2546, 1770, 1792, -2188, 20, 6304, -2124, 792, -2046, 1148, -1252, -3470, -2130, 450, -4664, -4, -812, 4092, -2996, -1474, 3686, -1676, 5730, -588, -652, 1360, -658, 4156, -640, 4634, 308, -2326, 4792, -4562, -2800, 3744, -1212, -1358, -8728, -9924, 2706, -682, -7520, -1668, -3990, 5704, -2988, -9872, -7168, -2958, -5260, -266, -66, 6090, 4920, 5610, 11400, -5882, -5138, -4884, 580, 4538, -14036, -814, -2234, 3570, 5168, 874, 2434, 2712, 5452, 16904, 1078, -3496, -2816, 3270, -1700, -3238, 14406, 756, -9624, -6688, -2666, 7384, -4734, -1804, -8764, -2148, -904, -5334, 12360, -5200, 16740, 2884, 92, 4444, 1276, 884, 16748, 1568, 28, 8538, 7112, -4404, 8800, -74, -3000, 924, 4700, -6676, 24590, -2340, -7962, 11220, 2422, 496, -17492, 5914, -484, -2562, 7990, -882, -18216, -504, 21930, 10464, 1640, 2668, -10626, 2134, -7632, -9348, 2994, -3544, -21984, -2002, -14388, -21184, 9788, -12, 6270, 12436, -1568, -19690, 4296, -1512, 19480, -2164, 9106, 1792, 5300, 418, -6028, 924, -6616, -17258, 3780, -2256, -7132, -17372, 12768, -5540, 8074, 126, -19696, -9808, 10416, -1678, -11250, 8938, 98, -3098, -14260, -5610, -16360, -3560, -13186, 3472, -9256, 1616, 23416, -4872, -21754, -6332, -1694, 7844, 44436, -19810, -27760, -11074, 20292, -4060, -5600, 94, 21996, -1188, 4776, -1548, 1988, -736, 18954, 9390, -1156, 1260, 7390, -434, 13772, -9170, 3480, -1836, -832, 20670, 6034, -900, -22144, -21706, 16484, -4532, -7408, -1372, 26000, 2914, -17202, -5036, 31900, 58, -1484, 32360, -44, 7486, -25180, -11050, 2440, 3556, -17720, 15264, -40500, 30396, 12272, -1452, 5754, -5888, -17416, -4688, -21156, 12554, -6128, 5796, 65928, 13116, -3806, 16698, 9430, 6012, -16940, 7786, 18456, -19308, 24456, 38164, -29110, 1386, -22672, -31136, -4716, -2522, -30144, -2324, -2940, 13476, 34576, 3540, 16698, -2652, -15210, -4900, -6562, -3088, 38288, -12488, -24718, 38470, -9716, 3146, 23880, 7506, -17212, 46662, -16642, 8568, 5956, 22952, -27746, -12300, 2464, -5830, 12432, -13644, -27112, -15258, 3700, 5342, -1256, 2450, -40360, -2816, 44560, 7232, -27700, -31826, 6146, 22580, 10864, -48708, -36384, 17384, -5940, 3234, 996, 3098, -26744, 3310, 41662, 4400, 5026, 23102, 32, -198, 5864, -18764, -34436, 2772, -28840, 5172, -35976, -17380, -16500, -1286, -154, 18166, 5552, -7434, -1804, 13476, -64310, 10486, 29500, 27522, 35490, -5456, -7480, -28536, -7406, -5232, -24616, 14444, -19308, -30116, -7674, 2702, 2662, 6082, 58262, -13878, 8010, 6344, -4508, 15388, 8, -20412, -81016, 6380, -50662, -16282, 32536, -1612, -18220, -22708, -37138, 16844, 21000, -35724, -3124, 15556, 15496, -30706, 15408, 11410, 40236, 31900, -28776, 29204, 87952, 682, 8092, 5864, 44980, 5542, 49604, -24204, -17364, 9534, 6512, -6388, -9482, -5802, 31584, -28722, 22064, 44836, 38100, 3556, -7620, -49270, -41528, 2156, -77460, 10252, 37564, 47126, -17946, -36144, 17248, -3928, -51540, 35838, 2332, 66984, 25000, 7140, -24904, -43758, 31528, 20328, 78058, 7440, -21504, -5588, 17116, 15928, 38396, -23282, 45132, -7896, -30740, -29484, -106960, 7768, -9042, -23014, -14826, 20292, -9962, 29214, 4448, 38464, -20528, 13440, -9332, -9108, 42250, -74596, -6238, 12406, -9114, -39668, 43828, -928, 57536, -17678, 26620, -14056, 24580, -19060, 76400, 23316, 24310, -8006, -7392, 28352, 58648, -2178, -93456, -26524, 32864, -11480, -35588, -29760, 51402, -30056, 1572, 68196, 4620, -28516, 55636, -28952, -71168, -30590, 22990, -10850, 117544, -42416, -41496, 7700, -74716, -256, 40460, 28542, 33200, 9476, 34696, 73340, 13892, -6566, 15268, 35016, 28900, 59286, 7128, -8076, -18144, 32304, 2536, -57728, -101760, -13464, 29890, -42322, -16652, -38358, -71020, -55868, -59278, -32858, 7294, -10244, -19536, -10002, 58640, 60376, 23760, -16324, -97084, -52716, 14776, 5254, -16920, -3850, -28574, -95872, -8700, -13740, 45982, 32614, -8764, 15414, -41740, 29912, -9658, 16432, -35576, -67034, 1372, 18830, -55776, -22092, 94176, -54432, -374, -5082, -52024, 19572, -96460, -2572, 60522, -64456, -14098, 184, -149920, 82364, -7898, -19528, 34744, 322, 102120, 39066, -41320, -33120, -71800, 38678, -31976, -4356, 65140, 14520, 10056, -9404, 126880, 13678, 59564, -23864, -126856, -37712, 242, 1708, -15050, 4188, 30268, -23824, -25752, 17422, 16678, -3038, -15724, -16478, 96726, -22500, 82764, 90960, 20244, -12120, -124500, 19820, 55664, 1032, 11638, 7420, -84808, 59798, -20818, 52066, -111452, -21500, 52080, 22432, 46004, -4246, 28560, -24898, 179568, -17416, 6412, 56100, -60734, 54896, 64778, -20578, 7084, -11608, 7476, 77032, 140976, -19274, 25900, 6426, 60672, -102960, 180272, 25586, 1824, 89780, -294, -20438, -145936, 21212, -28228, -84156, 84400, -25186, -33000, 81004, 64252, -80396, 27950, 19326, -33320, -17272, -52028, 37400, 55248, -17930, -51324, 17010, -2232, -30120, 45310, -52432, -108980, 45184, 43288, -93704, -12716, 97904, -62608, -2208, -71686, 8050, -82924, 17512, -189052, 32742, -290, -14982, -17318, -1592, 32492, 60398, 86528, 3852, 14538, -3626, 52040, 48980, -34672, 55030, -6190, 13860, -33180, 23772, 80444, 6196, 38376, -39854, 23798, -3388, 47632, -13376, -25222, -62014, -94852, 38174, -17150, 52456, -9000, 6846, -27104, 47404, -104320, 15148, -3792, -54944, 24980, 84076, -18804, 23484, 17822, -11220, -168360, 51520, 16140, 2420, -6992, -12390, 116912, 6588, -128204, -46796, 33792, 26470, -12544, -105864, -69388, 67330, 33512, 21392, 81020, 15316, -147400, 12408, -50886, 936, 63500, 53790, -140, -91048, 17148, -41256, 50234, 42428, 23298, -44128, -72120, 36454, -11416, -33132, 9508, -77110, 14868, 86196, 3880, -21120, -144472, 86596, 12368, -5544, 92720, -28144, -24280, 64712, -120094, -90360, 14322, -47328, -181436, -53890, 57148, 22588, -202776, -8036, 71912, 123516, 24214, 22088, 151910, -80442, 8764, -119306, -26340, 16418, -109452, 76436, -70534, 24290, 11616, 47106, 107680, 113796, -78944, -17258, 14910, -141388, -84948, -66074, -3912, 18040, 4356, -3150, -6476, 185682, -18324, -111624, 23002, -18124, 32648, 4276, -7260, 9320, -10592, -66512, -98346, 28, 188828, -9256, -76890, -39042, 143696, 17050, 5684, 15144, -72168, 11024, -38120, -76756, 33252, -28644, 89368, 6576, -63580, -43996, 117762, 103206, 20972, 41580, 51192, 65938, 44372, -61710, 48040], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [-3, 0, 0, 1], [6, -1, -2, -1], [-5, 1, -2, -1], [-1, 3, -5, -3], [-7, 0, 0, 0], [-14, -2, 2, 3], [18, -3, -6, -5], [-23, 0, -1, 7], [11, 0, 0, 0], [-46, -1, 10, 12], [-32, -3, 10, -4], [7, 0, -7, 0], [-13, -5, 22, 1], [-8, 13, -6, -7], [-18, -1, -10, -6], [-58, -12, 34, 15], [-54, 26, 12, 2], [22, 14, -20, -12], [21, 0, 0, -7], [-11, 0, 11, 0], [59, -21, -10, 1], [142, 1, -40, -24], [16, -13, -2, -9], [196, -25, -34, -4], [-129, 3, 42, 13], [-42, 7, 14, 7], [-42, 30, 40, 12], [325, -24, -37, -35], [-87, -32, -32, 33], [-8, 14, -4, 29], [-33, 0, 0, 11], [-82, -9, 4, 26], [35, -7, 14, 7], [368, 23, -74, -63], [47, 49, 2, -1], [46, 20, -70, 34], [-88, 48, -44, -44], [-134, -2, 74, 28], [22, -53, 18, -14], [7, -21, 35, 21], [-116, -16, 12, 36], [66, -11, -22, -11], [122, 46, -92, -32], [-67, -8, 67, -35], [16, -1, -14, 30], [-204, -23, 150, 18], [49, 0, 0, 0], [72, -38, 36, 3], [-122, -10, 80, 14], [-216, 21, 158, 28], [-214, 14, -68, 4], [605, 0, -197, -75], [-55, 11, -22, -11], [98, 14, -14, -21], [186, -22, 84, -82], [334, 26, -106, -16], [-285, -42, 12, 19], [-418, -52, 256, 86], [-38, -99, -6, -42], [-269, 99, -121, -131], [-126, 21, 42, 35], [-180, 1, -14, 1], [-104, 10, -24, 112], [-11, 33, -55, -33], [-371, -7, -70, -61], [228, 73, -58, -52], [-101, 9, -82, 77], [161, 0, 7, -49], [585, -7, -14, 11], [-752, 4, 296, 189], [-382, -51, 62, 2], [-311, 44, 47, 99], [-364, 47, -14, 38], [-780, -16, -48, -8], [-77, 0, 0, 0], [-596, -40, 44, 272], [-242, -26, -76, 54], [820, -104, -104, -66], [201, 162, -108, -104], [586, -113, 32, -82], [-456, -48, -204, 20], [322, 7, -70, -84], [506, -8, -28, -26], [224, 80, -200, -152], [398, 24, -92, -146], [-154, -22, 22, 33], [317, 141, 166, -99], [-1466, 42, 278, 280], [224, 21, -70, 28], [654, -12, 16, 14], [1577, -131, -230, -89], [-312, 103, -30, -78], [710, -254, 52, 18], [1084, -127, -70, -58], [-521, -59, 30, -57], [-49, 0, 49, 0], [198, -33, -66, -55], [484, 39, 46, -49]]}