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lfunc_lfunctions • Show schema
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{'Lhash': '327471334485332741057251986722', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5229205702367905, -1.6512280512464745], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0, 0], 'a9': [-2.45310815444646, -1.7269222282975816], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5229205702367905, 1.6512280512464745]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.1457', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '1894005711605805969635817784318', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5229205702367905, 1.6512280512464745]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 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{'__RealLiteral__': 0, 'data': '-0.23808407641241677', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25832933335603232619174589690', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30936154727018190317609050370', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90424733256511112653996123317', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '15.2', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/s/b/1457/7'], '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': '2-2100-15.2-c1-0-4', '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': '2-2100-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': -0.23808407641241677, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25832933335603232619174589690', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '327471334485332741057251986722', 'Lhash_array': ['327471334485332741057251986722'], 'label': '2-2100-15.2-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/s/b/1457/7'}