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lfunc_lfunctions • Show schema
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{'Lhash': '2037330219696705395628954669277', 'a10': [0, 0], 'a2': [1.224744871391589, -0.7071067811865476], 'a3': [0, 0], 'a4': [1.0, -1.7320508075688772], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.449489742783178, 0], 'a8': [0, -2.8284271247461903], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.373072363830476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.224744871391589, 0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.901', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '1246875175215188634784827404062', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.224744871391589, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.449489742783178, 0], [7.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], 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'4.82843749293151684046092018480995', '5.11235437880107880474462453312909', '6.31099379856755698196844356337260', '6.98476350071855637160169008247889', '7.967175532517274773062957161706751', '8.193699899384178441402860914879369', '9.480093005510564810500590099111756'], 'prelabel': '2-1800-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': 0.5, 'root_number': '0.e-56 + 1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60717016134406587398928268501', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70613910550544931324325307334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78868240524736559286547624578', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.373072363830476, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/2/k/m/901/3'], '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': '2-1800-8.5-c1-0-77', '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': '2-1800-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60717016134406587398928268501', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2037330219696705395628954669277', 'Lhash_array': ['2037330219696705395628954669277'], 'label': '2-1800-8.5-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/2/k/m/901/3'}