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lfunc_lfunctions • Show schema
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{'Lhash': '377256738833463155900854109775', 'a10': [0, 0], 'a2': [-5.4247399283314275, 5.4247399283314275], 'a3': [34.443263216557156, 34.443263216557156], 'a4': [0, 5.144393419933484], 'a5': [0, 0], 'a6': [-373.69149046577354, 0], 'a7': [-361.77086103038835, 361.77086103038835], 'a8': [-375.09035180536995, -375.09035180536995], 'a9': [0, 1643.6767620100788], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.756760452481377, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]]], 'bad_primes': [5], 'central_character': '125.68', 'coefficient_field': 'CDF', 'conductor': 125, 'conductor_radical': 5, 'conjugate': '3523897106281596974288874054408', 'degree': 2, 'euler_factors': [[[1.0, 0], [5.4247399283314275, -5.4247399283314275], [0, -64.0]], [[1.0, 0], [-34.443263216557156, -34.443263216557156], [0, 729.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [361.77086103038835, -361.77086103038835], [0, -117649.0]], [[1.0, 0], 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5.362533025770692, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29760309249689258240142852562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48797257805861142281469563548', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.53696024497938528803817390488', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.756760452481377, 'bad_primes': [5], 'central_character': '5.3', 'conductor': 125, 'conductor_radical': 5, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/125/7/c/b/68/7'], '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': '2-5e3-5.3-c6-0-8', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-5e3-5.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.362533025770692, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29760309249689258240142852562', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '377256738833463155900854109775', 'Lhash_array': ['377256738833463155900854109775'], 'label': '2-5e3-5.3-c6-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/125/7/c/b/68/7'}