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lfunc_lfunctions • Show schema
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{'Lhash': '1389033471762215949199442208360', 'a10': [-309556614217260000000, 0], 'a2': [0, 719233.1512647187], 'a3': [5625399572.72777, 8818949414.678972], 'a4': [3880750185225.8223, 0], 'a5': [0, 430398145125718.1], 'a6': [-6342880778363704.0, 4045973861816196.5], 'a7': [612563096460018200, 0], 'a8': [0, 5954385036581241000], 'a9': [-46128748425820810000, 99220228538485820000], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.518312151630795, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '21.0', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [-5625399572.72777, -8818949414.678972]]]], 'bad_primes': [3], 'central_character': '3.2', 'coefficient_field': 'CDF', 'conductor': 3, 'conductor_radical': 3, 'conjugate': '2422240108031921234121706351133', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -719233.1512647187], [-4398046511104.0, 0]], [[1.0, 0], [-5625399572.72777, -8818949414.678972]], [[1.0, 0], [0, -430398145125718.1], [-227373675443232070000000000000, 0]], 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'-0.5377829470533003540878627681897013441236063616009119796 - 0.8430833303171562222096968339716258934994793220603000694*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.34036900445167295', 'prec': 67}, 'spectral_label': 'c42-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09575420191662641386239464217', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73378305462453579469954437658', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49725392401181606356192516968', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.518312151630795, 'bad_primes': [3], 'central_character': '3.2', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3/43/b/b/2/7'], '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': '2-3-3.2-c42-0-7', 'motivic_weight': 42, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [42], 'order_of_vanishing': 0, 'prelabel': '2-3-3.2-c42-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.7895001642310016, 'root_angle': -0.34036900445167295, 'self_dual': False, 'spectral_label': 'c42-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09575420191662641386239464217', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1389033471762215949199442208360', 'Lhash_array': ['1389033471762215949199442208360'], 'label': '2-3-3.2-c42-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/43/b/b/2/7'}