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lfunc_lfunctions • Show schema
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{'Lhash': '4435790710662462233947874151820', 'a10': [-4.0119808145003445e-62, 3.1115118379572797], 'a2': [1.2898139781936466, 0.41908596599163617], 'a3': [1.4012585384440734, -1.0180739209102543], 'a4': [-1.7480809260472114, -1.2700551351682934], 'a5': [0.7089785044995666, 2.182011471509447], 'a6': [2.234023342543932, -0.7258781858365965], 'a7': [-5.743464848265122, 7.905201178013826], 'a8': [-4.911032440998303, -6.75945626263748], 'a9': [0.9270509831248422, -2.853169548885461], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8991848723889799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.4012585384440734, 1.0180739209102543]]], [11, [[1.0, 0], [-10.333951241414997, 3.769542643353095]]]], 'bad_primes': [3, 11], 'central_character': '33.13', 'coefficient_field': 'CDF', 'conductor': 33, 'conductor_radical': 33, 'conjugate': '4074740551548767791654790777561', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.49922187538414522079252699550', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.82791462362337011256139196656', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.16200044991718095372141469654', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8991848723889799, 'bad_primes': [3, 11], 'central_character': '11.2', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/3/g/a/13/3'], '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': '2-33-11.2-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33-11.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9482535907598663, 'root_angle': -0.0021691611677930015, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.49922187538414522079252699550', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4435790710662462233947874151820', 'Lhash_array': ['4435790710662462233947874151820'], 'label': '2-33-11.2-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/3/g/a/13/3'}