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lfunc_lfunctions • Show schema
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{'Lhash': '3147945274342587038124243413342', 'a10': [0.0, 0.0], 'a2': [0.0, -2.414213562373095], 'a3': [0.0, -1.0], 'a4': [-3.8284271247461903, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.414213562373095, 0.0], 'a7': [0.0, -2.8284271247461903], 'a8': [0.0, 4.414213562373095], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.785414197074841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.274', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '373296746239682942453199628403', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.414213562373095], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 3.65685424949238], [-17.0, 0]], [[1.0, 0], 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'7.38328318365397481590527685070650', '8.184213187641571372812647508006641', '8.802602219291349782385387471679340', '9.444791562545566582866647218747931', '10.49370504414654693588041742015090'], 'prelabel': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': -0.35241638234956674, 'root_number': '0.44721359549995804 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.176208191175', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48329095870409955935573450255', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98509939943295872239769294276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91034121126452710860501708403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.785414197074841, 'bad_primes': [3, 5, 13], 'central_character': '5.4', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/c/h/274/1'], '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': '2-975-5.4-c1-0-35', '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': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48329095870409955935573450255', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3147945274342587038124243413342', 'Lhash_array': ['3147945274342587038124243413342'], 'label': '2-975-5.4-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/c/h/274/1'}