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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_17.15', 'a10': [0.7071067811865476, 0.7071067811865476], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [-0.7071067811865476, -0.7071067811865476], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '17.15', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 17, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_17.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^3', 'a^4', 'a^7', 'a^5', 'a^1', 'a^6', 'a^6', 'a^1', 'a^5', 'a^7', 'a^4', 'a^3', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^3', 'a^4', 'a^7', 'a^5', 'a^1', 'a^6', 'a^6', 'a^1', 'a^5', 'a^7', 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'0.0758860188936232729438840112912+0.997116498778591393361719253238*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.23791074295', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.643250420835616101901074299374+0.415264723150863021988467960630*I']], 'z1': {'__RealLiteral__': 0, 'data': '4.85147420421', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.87734309066', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.45859216052', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.15', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/15'], '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': '1-17-17.15-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': 0.23791074295044418, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.85147420421', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_17.15', 'Lhash_array': ['dirichlet_L_17.15'], 'label': '1-17-17.15-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/17/15'}