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lfunc_lfunctions • Show schema
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{'Lhash': '1587176913894204442713091309597', 'a10': [-0.5491331463393184, 3.333303489519565], 'a2': [-0.49861966615298003, -1.3233965499900213], 'a3': [0.0, 0.0], 'a4': [-1.5027568570509815, 1.31974309188806], 'a5': [-2.0687368759993223, -1.1943857922407142], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, -0.5], 'a8': [2.495847577049684, 1.3306933802101901], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.49861966615298003, 1.3233965499900213]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.8660254037844386, 0.5]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.71', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '907601065575564109008258624440', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.49861966615298003, 1.3233965499900213]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0687368759993223, 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'9.324776714051510642454166495542771', '10.84637877738333285092114374243906'], 'prelabel': '2-756-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.6268959456331833, 'root_number': '-0.38817950492427017 + 0.9215837845561023*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.313447972817', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25206181704047402618124364237', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46317494470370882069613049472', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16495363306963121633690424312', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '36.23', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/14'], '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': '2-756-36.23-c1-0-16', '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': '2-756-36.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.31344797281659165, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25206181704047402618124364237', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1587176913894204442713091309597', 'Lhash_array': ['1587176913894204442713091309597'], 'label': '2-756-36.23-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/ba/a/71/14'}