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lfunc_lfunctions • Show schema
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{'Lhash': '531214365728192111314531304494', 'a10': [-9.242640687119286, -2.0358627531664625e-60], 'a2': [1.2071067811865475, 2.0907702751760278], 'a3': [-1.4142135623730951, 0.0], 'a4': [-1.9142135623730951, 3.3155151465676167], 'a5': [-1.9142135623730951, 3.3155151465676167], 'a6': [-1.7071067811865475, -2.956795678960466], 'a7': [0.0, 0.0], 'a8': [-4.414213562373095, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.5, 0.8660254037844386]]]], 'bad_primes': [7, 13], 'central_character': '637.373', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '3906200059566637161267212005512', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2071067811865475, -2.0907702751760278], [-1.0, 1.7320508075688772]], [[1.0, 0], [1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], 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'9.396326286772014309728901758357324', '10.12019836406894005073649067389666'], 'prelabel': '2-637-91.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.5362640033227589, 'root_number': '-0.11368043814104498 + 0.9935173667249406*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.268132001661', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41905424541474725897567591108', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62759586374102032425066402327', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35898316871274699661793414253', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.9', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/g/f/373/2'], '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': '2-637-91.9-c1-0-5', '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': '2-637-91.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.26813200166137946, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41905424541474725897567591108', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '531214365728192111314531304494', 'Lhash_array': ['531214365728192111314531304494'], 'label': '2-637-91.9-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/g/f/373/2'}