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lfunc_lfunctions • Show schema
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{'Lhash': '2608555594078768943147392252782', 'a10': [2.5615528128088303, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.5615528128088303, 0.0], 'a4': [-1.0, 0.0], 'a5': [-2.5615528128088303, 0.0], 'a6': [-2.5615528128088303, 0.0], 'a7': [0.0, 0.0], 'a8': [3.0, 0.0], 'a9': [3.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.837064387755599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [17, 43], 'central_character': '731.1', 'coefficient_field': 'CDF', 'conductor': 731, 'conductor_radical': 731, 'conjugate': '2608555594078768943147392252782', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0], [2.0, 0]], [[1.0, 0], [-2.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [2.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [4.56155281280883, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-731-1.1-c1-0-45', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/731/2/a/b/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-3.2960126017596346e-120, 0.23898974447615454, 0.4814674187690507, 0.7290541722788405, 0.9800511680542096, 1.228645527836864, 1.4648185262732312, 1.6748800259915873, 1.842527885596444, 1.950344007807899, 1.98164025805519, 1.9225407743363903, 1.7641389236721503, 1.5045131241923737, 1.1503426038198656, 0.7178464136212334, 0.23278783538117992, -0.2706514833322457, -0.7522166132199734, -1.1690870150739925, -1.4803188636372329, -1.651817333992789, -1.6612778221515434, -1.5024277142486915, -1.1878691589287047, -0.7498894024403407, -0.23877866068817016, 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'9.073808570621472557868833840016131', '9.601340392971392986442761877741085'], 'prelabel': '2-731-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.05778752726431189114135828943', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30663455735130281510159129433', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18682650965189249457311233395', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.837064387755599, 'bad_primes': [17, 43], 'central_character': '1.1', 'conductor': 731, 'conductor_radical': 731, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/731/2/a/b/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': '2-731-1.1-c1-0-45', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-731-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05778752726431189114135828943', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2608555594078768943147392252782', 'Lhash_array': ['2608555594078768943147392252782'], 'label': '2-731-1.1-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/731/2/a/b/1/2'}