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lfunc_lfunctions • Show schema
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{'Lhash': '2096682930320400131471572845292', 'a10': [0, 0], 'a2': [0, 1.5376734361988202], 'a3': [0, -1.0], 'a4': [-0.364439596391487, 0], 'a5': [0, 0], 'a6': [1.5376734361988202, 0], 'a7': [0, -1.6860070307592052], 'a8': [0, 2.5149577859274315], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1249', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'conjugate': '293367428906047069578191908001', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.5376734361988202], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.6860070307592052], [-7.0, 0]], [[1.0, 0], [2.9775713571932747, 0], [11.0, 0]], [[1.0, 0], [0, -0.23289195996704043], [-13.0, 0]], [[1.0, 0], [0, 7.459014748146172], [-17.0, 0]], [[1.0, 0], 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'3.47769162408851830981928585914082', '4.16847927458703746206682019237882', '5.34311503320807342420373426916204', '6.01568273408854165207441549095679', '7.07403183758328225674382181896489', '8.133808506787857937562900590670504', '8.813141793429107860070660940932189', '9.692935328283473696433025384770190'], 'prelabel': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.5, 'root_number': '0.e-54 + 1.000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65399119437399446748084905264', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51205577883179882120818359832', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47769162408851830981928585914', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 66, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/b/h/1249/14'], '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': '2-1875-5.4-c1-0-66', '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': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65399119437399446748084905264', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2096682930320400131471572845292', 'Lhash_array': ['2096682930320400131471572845292'], 'label': '2-1875-5.4-c1-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/b/h/1249/14'}