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lfunc_lfunctions • Show schema
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{'Lhash': '3177984017354833649205568623551', 'a10': [-19.83057977642077, 0.0], 'a2': [3.966115955284154, 0.0], 'a3': [3.0, 0.0], 'a4': [7.730075770759535, 0.0], 'a5': [-5.0, 0.0], 'a6': [11.898347865852461, 0.0], 'a7': [-32.87165907445772, 0.0], 'a8': [-1.070550792308387, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.66583085249718, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [29, [[1.0, 0], [29.0, 0]]]], 'bad_primes': [3, 5, 29], 'central_character': '435.1', 'coefficient_field': 'CDF', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.966115955284154, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [32.87165907445772, 0], [343.0, 0]], [[1.0, 0], [-12.642611467917243, 0], [1331.0, 0]], [[1.0, 0], [52.29789259874974, 0], [2197.0, 0]], [[1.0, 0], [17.29775975162074, 0], [4913.0, 0]], 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'4.11616575816282889043831038619582', '5.31141969719610588493107176905062', '6.49401552665353551291449814699569', '7.05439974327225007102034326055686', '8.420423375750180586494432961169611', '9.577906284821710044346902103929225', '10.08262203894597119407069920105810'], 'prelabel': '2-435-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.066145561716242, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50698734870844176388196730566', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.37804862897951705431615827181', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11616575816282889043831038620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.66583085249718, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/435/4/a/j/1/7'], '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': '2-435-1.1-c3-0-55', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-435-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.066145561716242, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50698734870844176388196730566', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3177984017354833649205568623551', 'Lhash_array': ['3177984017354833649205568623551'], 'factors': ['2-435-1.1-c3-0-55'], 'label': '2-435-1.1-c3-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/4/a/j/1/7'}