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lfunc_lfunctions • Show schema
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{'Lhash': '1600906977003144435314468091741', 'a10': [0.0, 0.0], 'a2': [5.275147890168183, 1.4134716171253054], 'a3': [-1.9412257547257021, 4.819921427698757], 'a4': [18.9010800204515, 10.912543637782331], 'a5': [0.0, 0.0], 'a6': [-17.0530750792077, 22.68193084336409], 'a7': [-1.1307664455267783, 4.220077826200002], 'a8': [53.38801150479505, 53.38801150479505], 'a9': [-19.463285138379256, -18.71311122240621], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.9412257547257021, -4.819921427698757]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.32', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3341786724234585198147938329896', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.275147890168183, -1.4134716171253054], [6.928203230275509, 4.0]], [[1.0, 0], [1.9412257547257021, 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'3.87521483827730432081301078124221', '5.27781512847904089615676261563648', '6.00545555041887084675210801330687', '6.96807525606258795373391082252556', '8.059749844053269455986107165194983', '10.24400501175143495550802029610935', '10.88260964617621685774943339772429', '12.01166677634534374427811695094861'], 'prelabel': '2-15e2-45.32-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.6356014131983455, 'root_number': '-0.41323562412005976 - 0.9106241370390447*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.317800706599', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26289292705333404837158283356', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61606618871291797345582249111', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87521483827730432081301078124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '45.32', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/p/b/32/16'], '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': '2-15e2-45.32-c3-0-27', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-45.32-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.31780070659917276, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26289292705333404837158283356', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1600906977003144435314468091741', 'Lhash_array': ['1600906977003144435314468091741'], 'label': '2-15e2-45.32-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/p/b/32/16'}