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lfunc_lfunctions • Show schema
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{'Lhash': '3575813574560513991062054157778', 'a10': [2.9270509831248424, -5.069801019116659], 'a2': [1.3090169943749475, 2.267283942228512], 'a3': [1.118033988749895, -1.9364916731037085], 'a4': [-2.4270509831248424, 4.203775615332221], 'a5': [-1.118033988749895, -1.9364916731037085], 'a6': [5.854101966249685, -7.778072316129086e-61], 'a7': [-2.0, 1.7320508075688772], 'a8': [-7.47213595499958, 0.0], 'a9': [-1.0, -1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.0, -1.7320508075688772]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.53', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '4250782395969191235641516450959', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3090169943749475, -2.267283942228512], [-1.0, 1.7320508075688772]], [[1.0, 0], [-1.118033988749895, 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'13.89616788215796578725131254381788'], 'prelabel': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.3736792394412256, 'root_number': '0.38651357275915527 - 0.9222837188593069*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.186839619721', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.82081953332938905818375982573', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77734419038093641113834944118', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.64406321105409139521068003200', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '7.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/b/53/2'], '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': '2-91-7.4-c1-0-3', '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': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.1868396197206128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.82081953332938905818375982573', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3575813574560513991062054157778', 'Lhash_array': ['3575813574560513991062054157778'], 'label': '2-91-7.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/b/53/2'}