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lfunc_lfunctions • Show schema
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{'Lhash': '1255816177236714642682473704750', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.3529776354319595, -0.8521633946742225], 'a6': [0, 0], 'a7': [3.4339317323434555, 3.4339317323434555], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.1007', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1582853773684986695300085138958', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3529776354319595, 0.8521633946742225], [-3.5355339059327378, 3.5355339059327378]], [[1.0, 0], [-3.4339317323434555, -3.4339317323434555], [0, 7.0]], [[1.0, 0], [1.4465005843888257, 3.4921613288121107], [-7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [0.258636298350075, 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'7.950355132181693571774246249024166', '8.827384864018473517967959943246387', '9.998794874547604982961687402860949'], 'prelabel': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.1254504340367763, 'root_number': '0.92333707990859679787754781107277666191709653059743522014 - 0.38399041246607386029629591964605153294917622131566121545*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.06272521701838815', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.990664286366145312849589442730', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.32432543964116659718234860413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62773031725392868894850156194', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '96.83', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/a/1007/4'], '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': '2-1152-96.83-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': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.06272521701838815, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.990664286366145312849589442730', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1255816177236714642682473704750', 'Lhash_array': ['1255816177236714642682473704750'], 'label': '2-1152-96.83-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/a/1007/4'}