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lfunc_lfunctions • Show schema
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{'Lhash': '2155540368884636208719677326584', 'a10': [0.0, 0.0], 'a2': [1.1020925135274777, -0.924765421624148], 'a3': [-0.8238682636063046, -0.29986352490927604], 'a4': [0.18576864567469503, -1.053546342869902], 'a5': [0.0, 0.0], 'a6': [-1.1852824644958206, 0.43140753627416556], 'a7': [0.9902680687415704, -1.7151946081735094], 'a8': [-0.05020919397979293, -0.08696487498008275], 'a9': [-0.17720366091232664, -0.14869152651479706], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]]], [19, [[1.0, 0], [0.5591929034707468, -0.8290375725550417]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.2001', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '1385076919856991825466777497558', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [-1.9225233918766378, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-2717-2717.2001-c0-0-6', 'leading_term': '1.91566898831529970222818676392', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/2001/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.9156689883152997, 2.0008763092441146, 2.1026865764398748, 2.221571254666319, 2.357015213211773, 2.5076163681101726, 2.671235930145809, 2.8451586601007746, 3.0262362298808982, 3.2110025610278567, 3.395761541277821, 3.5766533960551805, 3.7497075683301597, 3.9108891738261926, 4.056144413128364, 4.181448549584535, 4.282858538169335, 4.356571192329511, 4.398986869945976, 4.406777982494457, 4.3769611239113, 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'4.97851245899415795457430813038969', '5.42900970329363063950860733612586', '6.03112996828884271150662243976716', '6.46334539248456435624051355766486', '7.67289667776896416876260414592408', '8.477931670551389289195040333848001', '8.932404028084394284721310903402893'], 'prelabel': '2-2717-2717.2001-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.6937122133900252, 'root_number': '-0.57169056623181291133375595141412 + 0.82046931477146001488247414822688*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.34685610669501254', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70042152663876782877143037590', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04035904165380091798070171343', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06056544538674418730759128078', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.2001', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/2001/3'], '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': '2-2717-2717.2001-c0-0-6', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2717-2717.2001-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.3468561066950126, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70042152663876782877143037590', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2155540368884636208719677326584', 'Lhash_array': ['2155540368884636208719677326584'], 'label': '2-2717-2717.2001-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/2001/3'}