# Stored data for newform 325.3.t.a, downloaded from the LMFDB on 06 September 2025.
{"Nk2": 2925, "analytic_conductor": 8.855608591709649, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 20, "char_orbit_label": "t", "char_order": 12, "char_parity": -1, "char_values": [325, 12, [27, 301], [12, 7]], "cm_discs": [], "conrey_index": 76, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, -4, 5, -2, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 1305720389957, "hecke_ring_generator_nbound": 2, "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, 13, 6, -1, 12, 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": "325.3.t.a", "level": 325, "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, 13], "level_radical": 65, "minimal_twist": "13.3.f.a", "nf_label": "4.0.144.1", "prim_orbit_index": 6, "qexp_display": "q+(1-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}+\\zeta_{12}^{2}+\\cdots)q^{3}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "2.2.3.c12", "self_twist_discs": [], "self_twist_type": 0, "space_label": "325.3.t", "trace_display": [2, 2, 0, -16], "trace_hash": 1573659072457853661, "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "3.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "48.617", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1011.724", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.083", "prec": 17}, "traces": [0, 4, 2, 2, -6, 0, 10, -16, 6, 10, 0, 4, 0, 26, -40, 0, -2, 12, 2, 10, 0, 40, 4, -18, 42, 0, 52, 32, 44, 2, 0, -20, 20, 32, -18, 0, -54, 68, 0, -26, 0, 100, -44, -180, 88, 0, -30, 68, 50, -72, 0, 0, 0, -128, 16, 0, -84, 20, 40, -164, 0, -124, -6, -52, 0, 0, 80, -118, -72, 72, 0, -86, -72, -58, 68, 0, 14, 0, 104, -40, 0, -2, -24, 188, 4, 0, -180, -38, 204, -110, 0, 52, 156, 20, 26, 0, 40, -178, 14, 208, 0, 336, -114, 0, 234, 0, -64, -14, 96, -104, 0, 106, -292, -236, 36, 0, 0, 260, 64, -264, 0, -384, 250, 86, 122, 0, -52, -78, -162, 0, 0, 92, -88, -68, 222, 0, -222, -226, 84, -148, 0, 16, 0, -364, 172, 0, 146, -114, 182, 460, 0, 124, 54, 240, -184, 0, -78, 100, -20, -226, 0, 48, 224, 212, -238, 0, 360, 380, 0, -338, 0, 106, 180, 252, 80, 0, -452, -64, -110, -516, 0, 0, -260, -500, 198, 0, 36, -528, -94, 16, 0, -58, 270, -796, 0, 0, 88, -46, 52, 438, 0, -392, 126, 220, -42, 0, -690, 0, 26, -160, 0, 134, -132, -172, 278, 0, 408, 124, -66, -350, 0, 0, 484, 566, -172, 0, 146, 686, -32, -296, 0, 144, 162, 0, 130, 0, 688, -272, 240, 580, 0, 490, -322, -82, 120, 0, 0, -52, 180, -188, 0, -210, 260, -48, 102, 0, -50, -738, -540, 0, 0, -124, 46, 196, 168, 0, -124, 80, 184, -64, 0, 268, 0, 572, -376, 0, -48, 720, 292, 82, 0, 406, 16, 144, -106, 0, 104, -896, 374, -104, 0, -356, -88, -778, -200, 0, 840, 464, 0, -234, 0, 360, 274, -42, -188, 0, 174, -64, -344, 948, 0, 0, 78, 1120, 50, 0, -444, 218, -806, 332, 0, -292, -180, -138, 0, 0, -112, 104, -348, -492, 0, -824, -236, 470, 380, 0, -716, 0, 338, -292, 0, -256, 30, 264, -720, 0, 672, 382, 30, 310, 0, 208, -680, 398, 260, 0, 460, -492, 300, 784, 0, -48, -1110, 0, 208, 0, -250, -110, -702, 514, 0, 188, -68, -290, -516, 0, 0, -26, -896, 934, 0, -384, -860, -16, -318, 0, -796, -900, -146, 0, 0, -972, -12, 136, -882, 0, -260, 1574, 288, 56, 0, -1214, 0, -442, -1176, 0, -164, -396, -444, 760, 0, 376, 342, 1632, -102, 0, -338, -584, -80, -94, 0, 226, 754, 794, -1002, 0, -324, 1744, 0, -104, 0, 580, -592, -2346, 8, 0, 530, -132, -350, 624, 0, 0, -624, -1904, -182, 0, 1434, 920, -1024, 274, 0, -628, 888, -424, 0, 0, 120, -364, 154, -984, 0, -428, -224, 1676, 290, 0, -1068, 0, -702, 1832, 0, -202, 1272, 720, -856, 0, 540, 4, 1236, 1222, 0, -494, 424, -48, 508, 0, -344, -448, 618, 112, 0, 1224, -38, 0, 78, 0, -398, 556, 876, -884, 0, 184, 180, -512, 156, 0, 0, -676, -252, 166, 0, 756, -1486, 152, 228, 0, 180, -1368, -1376, 0, 0, -472, -62, 568, 42, 0, 1616, -618, 584, -554, 0, -296, 0, 806, -280, 0, 798, -1416, 496, -460, 0, 886, 268, 1386, -312, 0, 572, 2380, 716, 368, 0, 140, 396, -344, 438, 0, 156, -430, 0, 0, 0, 528, -236, 456, -188, 0, -12, 1364, -450, -1068, 0, 0, 1508, 1720, -448, 0, -762, 722, -568, 10, 0, 656, -744, -1100, 0, 0, -448, -364, -58, -168, 0, 1300, -1114, -322, 464, 0, -106, 0, 156, 1052, 0, 584, 1800, -316, -398, 0, 168, -254, -222, 548, 0, -338, -1176, 1880, -814, 0, -1200, 350, -432, 916, 0, 936, -270, 0, 1300, 0, 560, 136, -654, -1530, 0, -1064, -1320, -620, -198, 0, 0, -936, 440, -782, 0, -1440, 556, -1876, -876, 0, -138, 2586, 894, 0, 0, -16, -904, -104, 48, 0, -254, 500, -200, -1996, 0, -44, 0, 1014, 1344, 0, 8, 522, -208, -1868, 0, -1480, 4, 60, -300, 0, 1014, -1136, -146, 1004, 0, 1372, -8, -946, -280, 0, -288, -604, 0, -832, 0, 1840, 588, -1560, 644, 0, 186, 894, 310, 1116, 0, 0, 1352, -92, 1468, 0, 1254, -1764, -196, -980, 0, 404, 150, 228, 0, 0, -168, -580, -752, 1968, 0, -3276, 670, -424, -6, 0, -842, 0, 0, 652, 0, -360, -246, -2986, -454, 0, -588, 160, 252, -1508, 0, 52, 2576, 320, 12, 0, -286, 140, 2148, 1808, 0, -2628, -310, 0, 494, 0, -512, 244, -774, -96, 0, -1586, -564, 436, 2010, 0, 0, -2548, 428, 94, 0, -1422, 1622, 494, -360, 0, -858, 1572, -822, 0, 0, 1088, -486, 448, 408, 0, 500, -2146, 556, -1420, 0, 2000, 0, -3224, 2348, 0, -738, -660, -248, 474, 0, 1000, -1214, -1524, -52, 0, -78, -992, -1092, 668, 0, 2524, -56, 980, 392, 0, -510, -180, 0, -1352, 0, -2690, -338, 3192, -1644, 0, 200, 1040, 642, -1740, 0, 0, 2418, 132, -292, 0, 672, 416, 1882, 562, 0, 1464, -666, 878, 0, 0, 428, 1264, 1360, 180, 0, 498, 232, -22, 1744, 0, 1098, 0, 520, -6004, 0, -268, -2340, 1700, 88, 0, -2322, 464, -636, -1552, 0, -2210, 588, -958, -132, 0, -176, -2290, -180, 448, 0, 1410, 128, 0, 936, 0, -952, -2240, 1542, 672, 0, 2308, -2132, -308, 2406, 0, 0, 0, 1732, 290, 0, 2046, -896, -2520, 1506, 0, -424, -4116, 934, 0, 0, -880, 188, 1192, -816, 0, 142, -188, -1080, 554, 0, 1564, 0, 260, 608, 0, -484, 678, 370, 376, 0, -260, -876, 276, 1296, 0, -390, -1292, 916, 164, 0, -404, -506, -1914, -860, 0, -360, 2738, 0, -1898, 0, -218, 1272, -744, 422, 0, -352, -440, 1222, -72, 0, 0, 1768, -1364, -1748, 0, -864, 2528, -978, 108, 0, 290, 1098, 2056, 0, 0, 2264, 3044, -380, -2880, 0, 322, -876, 284, 306, 0, -444, 0, 598, 1080, 0, -418, -642, -1648, 1124, 0, 32, 16, -1626, 2632, 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], [1, 0, 0, 0], [1, 0, -1, 1], [0, -1, 1, -1], [-1, -2, -1, 0], [0, 0, 0, 0], [3, -3, -1, 2], [-2, -2, -4, 6], [4, -5, -5, 4], [5, 2, -5, -4], [0, 0, 0, 0], [-4, -6, 10, 10], [-1, 0, 2, 1], [0, 0, 13, 0], [-10, 8, 0, -4], [0, 0, 0, 0], [0, 8, -1, 8], [2, 15, 2, 0], [2, 3, -3, -2], [1, -1, 3, 4], [0, 0, 0, 0], [14, -8, -8, 14], [2, -6, -2, 12], [-6, -15, 3, 15], [8, -13, 5, 5], [0, 0, 0, 0], [13, -13, 0, 13], [8, -24, 0, 12], [10, 12, 2, -2], [0, -6, 1, -6], [0, 0, 0, 0], [-9, -8, 8, 9], [-1, 1, 12, 11], [4, 4, 8, -12], [-11, 13, 13, -11], [0, 0, 0, 0], [-18, -16, 9, 16], [5, -29, 24, 24], [1, 0, -2, 5], [-13, 13, 13, -26], [0, 0, 0, 0], [27, 23, -4, 4], [0, 14, -22, 14], [-30, 0, -30, 0], [34, 24, -24, -34], [0, 0, 0, 0], [-3, -3, -9, 12], [7, 20, 20, 7], [25, -9, -25, 18], [-24, 7, 12, -7], [0, 0, 0, 0], [13, 0, -26, 9], [13, 0, -26, -26], [-32, 54, 0, -27], [20, -12, -32, 32], [0, 0, 0, 0], [-14, 48, -14, 0], [4, -2, 2, -4], [13, -13, -6, 7], [-60, -60, 38, 22], [0, 0, 0, 0], [-62, 21, 62, -42], [-2, -7, 1, 7], [-26, 0, 26, 26], [31, 0, -62, 14], [0, 0, 0, 0], [20, -16, 0, 8], [-48, -11, 37, -37], [0, -19, -36, -19], [12, -6, 12, 0], [0, 0, 0, 0], [-11, 11, -21, -32], [-17, -17, -2, 19], [-34, 39, 39, -34], [34, -29, -34, 58], [0, 0, 0, 0], [10, 3, -13, -13], [44, 0, -88, -20], [13, -26, 26, -13], [-10, 84, 0, -42], [0, 0, 0, 0], [0, -38, -1, -38], [-4, 31, -4, 0], [34, -26, 26, -34], [6, -6, -10, -4], [0, 0, 0, 0], [-60, 30, 30, -60], [-19, 7, 19, -14], [68, 6, -34, -6], [-50, 5, 45, 45], [0, 0, 0, 0], [52, -78, -78, 52], [39, 42, 0, -21], [2, 8, 6, -6], [0, 7, 13, 7], [0, 0, 0, 0], [11, 2, -2, -11], [-35, 35, -19, -54], [-12, -12, 31, -19], [26, 52, 52, 26], [0, 0, 0, 0]]}