Table lfunc_lfunctions
L-functions
{'Lhash': '1154233882887970581464901765893,1424600482724643411961248802458', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 10, 'a8': 0, 'a9': 10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 279.9025443165034, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[2, [1, 0, 2]], [307, [1, -614, 94249]]], 'bad_primes': [2, 307], 'central_character': '614.1', 'coefficient_field': '1.1.1.1', 'conductor': 376996, 'conductor_radical': 614, 'degree': 4, 'euler_factors': [[1, 0, 2], [1, 0, -10, 0, 81], [1, 0, -32, 0, 625], [1, -10, 123, -490, 2401], [1, 26, 411, 3146, 14641], [1, 0, -320, 0, 28561], [1, -22, 699, -6358, 83521], [1, -58, 1563, -20938, 130321], [1, 0, -608, 0, 279841], [1, 0, -1394, 0, 707281], [1, 0, -1904, 0, 923521], [1, -94, 4947, -128686, 1874161], [1, -70, 4587, -117670, 2825761], [1, 0, -1520, 0, 3418801], [1, 0, 2080, 0, 4879681], [1, -22, 5739, -61798, 7890481], [1, 0, -6512, 0, 12117361], [1, 0, -7154, 0, 13845841], [1, 0, -6800, 0, 20151121], [1, 86, 11931, 433526, 25411681], [1, 0, 5542, 0, 28398241], [1, 44, 12966, 274604, 38950081], [1, -280, 33378, -1928920, 47458321], [1, 248, 31218, 1964408, 62742241], [1, 80, 20418, 752720, 88529281], [1, -226, 33171, -2305426, 104060401], [1, 182, 29499, 1930838, 112550881], [1, None, None, None, 131079601], [1, -202, 33963, -2399962, 141158161], [1, 38, 25899, 485222, 163047361]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 0, -10, 0, 81], 1]], [[[1, 0, -32, 0, 625], 1]], [[[1, -5, 49], 2]], [[[1, 13, 121], 2]], [[[1, 0, -320, 0, 28561], 1]], [[[1, -11, 289], 2]], [[[1, -29, 361], 2]], [[[1, 0, -608, 0, 279841], 1]], [[[1, 0, -1394, 0, 707281], 1]], [[[1, 0, -1904, 0, 923521], 1]], [[[1, -47, 1369], 2]], [[[1, -35, 1681], 2]], [[[1, 0, -1520, 0, 3418801], 1]], [[[1, 0, 2080, 0, 4879681], 1]], [[[1, -11, 2809], 2]], [[[1, 0, -6512, 0, 12117361], 1]], [[[1, 0, -7154, 0, 13845841], 1]], [[[1, 0, -6800, 0, 20151121], 1]], [[[1, 43, 5041], 2]], [[[1, 0, 5542, 0, 28398241], 1]], [[[1, 22, 6241], 2]], [[[1, -140, 6889], 2]], [[[1, 124, 7921], 2]], [[[1, 40, 9409], 2]], [[[1, -113, 10201], 2]], [[[1, 91, 10609], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 23252544, 'index': 0, 'label': '4-614e2-1.1-c2e2-0-0', 'leading_term': '3.51016081993259643391225227329961191409019236299740505532941887456040725640126527431129969', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/614/3/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 14}, 'plot_values': [3.510160819932596, 3.5007499191430966, 3.4815010275430813, 3.4464225521398, 3.396165431840161, 3.3326442506404095, 3.256103289179218, 3.1665690251538106, 3.0646193792160745, 2.95100422130671, 2.8264453744332303, 2.691739669602824, 2.547815327734501, 2.3957018447680123, 2.2365229155406725, 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'10.43599040141691277377986410599184'], 'prelabel': '4-614e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.090267501242704, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 229853714356258474, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.910529985691767800832238684377', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.12381162638045259243943202655', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.19901762204570409839326621571', 'prec': 100}}