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lfunc_lfunctions • Show schema
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{'Lhash': '1229112729091346772090825484378', 'a10': [0, 0], 'a2': [-0.7580299930219739, -1.8507810593582121], 'a3': [0, 0], 'a4': [-2.850781059358212, 2.8058951070210143], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-4.0957302279980805, 0], 'a8': [7.354075065152858, 3.149218940641788], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.523223792426723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7580299930219739, 1.8507810593582121]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.199', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '657569892765614519897844642448', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7580299930219739, 1.8507810593582121]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.0957302279980805, 0], [49.0, 0]], [[1.0, 0], [0, -0.9842548580888555], [-121.0, 0]], [[1.0, 0], [0, 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0.3538931183661113], 'positive_zeros': ['0.969598980089668065611412714303800', '2.67787396352231454237284867120182', '4.16070521290905087866267979210654', '4.98216718127223026621559727741739', '6.04396219553318926745611677661665', '6.90436520916632570368887317521937', '7.35740836393375759495643420736582', '8.670798213810436710449381653671436', '9.153827736660361509895900575995520', '9.851457490363748496212088236457101'], 'prelabel': '2-30e2-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9520928699315325, 'root_angle': 0.6049421310574048, 'root_number': '-0.323745413917730765057461275072623687892713517046686075 + 0.946144231587994822165419298272885324902068984720047276*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3024710655287024', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.969598980089668065611412714304', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.523223792426723, 'bad_primes': [2, 3, 5], 'central_character': '20.19', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/3/f/d/199/3'], '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': '2-30e2-20.19-c2-0-49', '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': '2-30e2-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9520928699315325, 'root_angle': 0.3024710655287024, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.969598980089668065611412714304', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1229112729091346772090825484378', 'Lhash_array': ['1229112729091346772090825484378'], 'label': '2-30e2-20.19-c2-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/3/f/d/199/3'}