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lfunc_lfunctions • Show schema
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{'Lhash': '1770296605563459233615678478989', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [2.544949437618122, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [2.544949437618122, 0.0], 'a7': [3.094593219390023, 0.0], 'a8': [1.0, 0.0], 'a9': [3.4767676400327967, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.76924015606564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11, 43], 'central_character': '4730.1', 'coefficient_field': 'CDF', 'conductor': 4730, 'conductor_radical': 4730, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.544949437618122, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.094593219390023, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.1922902477848436, 0], [13.0, 0]], [[1.0, 0], [-1.615783054290136, 0], [17.0, 0]], [[1.0, 0], 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'3.80655434562874271097896222074870', '4.37720908839146925595607876973846', '5.31346982362204426860505952793622', '5.90358880852369708479003355974613', '7.15545596623386154430938094129341', '7.56105815849992683294063136971565', '8.213890433657704664346177263423629'], 'prelabel': '2-4730-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.145668405964126, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39651778277447493487050539592', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18784018172780412778299987893', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78565398088123629936121986157', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.76924015606564, 'bad_primes': [2, 5, 11, 43], 'central_character': '1.1', 'conductor': 4730, 'conductor_radical': 4730, 'degree': 2, 'index': 111, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4730/2/a/bd/1/8'], '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': '2-4730-1.1-c1-0-111', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4730-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.145668405964126, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39651778277447493487050539592', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1770296605563459233615678478989', 'Lhash_array': ['1770296605563459233615678478989'], 'label': '2-4730-1.1-c1-0-111', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4730/2/a/bd/1/8'}