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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1375.294', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8763066800438636, 0.48175367410171527], 'a3': [0.6374239897486897, -0.7705132427757893], 'a4': [0.5358267949789967, 0.8443279255020151], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9297764858882515, -0.368124552684678], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [0.06279051952931337, 0.9980267284282716], 'a9': [-0.18738131458572463, -0.9822872507286887], 'algebraic': True, 'analytic_conductor': 147.76427159260942, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '1375.294', 'coeff_info': ['x^50 - 1', '0.992114701314478 + 0.125333233564304*I', '\\\\zeta_{50}'], 'conductor': 1375, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_1375.304', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^43', 'a^8', 0, 'a^47', 'a^20', 'a^12', 'a^36', 0, 0, 'a^1', 'a^36', 'a^24', 0, 'a^16', 'a^32', 'a^40', 'a^47', 0, 'a^13', 0, 'a^9', 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'199.578712936054690050685511614836'], 'prelabel': '1-1375-1375.294-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.76427159260942, 'root_angle': 0.6661332140651299, 'root_number': '-0.498547934542803759652094279113+0.866862132615737378549062768332*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.333066607033', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(50)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.70941174737247015895705985977+0.403654979637176659190295427167*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.19305342214', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.61632145779', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93798011253', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.76427159260942, 'bad_primes': [5, 11], 'central_character': '1375.294', 'conductor': 1375, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1375/294'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1375-1375.294-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1375-1375.294-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.76427159260942, 'root_angle': 0.33306660703256497, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19305342214', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1375.294', 'Lhash_array': ['dirichlet_L_1375.294'], 'label': '1-1375-1375.294-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1375/294'}