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lfunc_lfunctions • Show schema
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{'Lhash': '990662271742580691305901360677', 'a10': [-0.8541019662496846, 0.0], 'a2': [-0.38196601125010515, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.8541019662496845, 0.0], 'a5': [2.23606797749979, 0.0], 'a6': [0.38196601125010515, 0.0], 'a7': [0.0, 0.0], 'a8': [1.4721359549995794, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.911810006841044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.1', 'coefficient_field': 'CDF', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.38196601125010515, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.23606797749979, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.47213595499958, 0], [13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [-0.2360679774997897, 0], [19.0, 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-1617-1.1-c1-0-10', 'leading_term': '1.0488431817557821493554389759539', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1617/2/a/k/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.0488431817557822, 1.0435749055367973, 1.0276862261985944, 1.0009343150283982, 0.9629428634810532, 0.9132424444758029, 0.8513228661359383, 0.7766940701187823, 0.6889519379818871, 0.5878454975401535, 0.4733423537151945, 0.34568958900942803, 0.20546779700548637, 0.05363627549787778, -0.10843230248857072, -0.27892919124765414, -0.4556001058309866, -0.6357500556876057, -0.8162633380801437, -0.993639297711977, -1.1640441485140174, -1.3233787796440233, -1.4673620316066036, -1.5916284374565792, 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'5.81786533971778180846308007372143', '7.22462958634975854523566779290447', '7.62819729944523810633617193585719', '8.903886452063052013559117840168182', '9.443169202973369641617311594020700'], 'prelabel': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78149473645515618841021118899', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11404604697061054501098014160', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43532907550187378214860793328', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.911810006841044, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1617/2/a/k/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1617-1.1-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78149473645515618841021118899', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '990662271742580691305901360677', 'Lhash_array': ['990662271742580691305901360677'], 'label': '2-1617-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1617/2/a/k/1/2'}