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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6025.4756', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [-0.30901699437494745, 0.9510565162951535], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 27.979982369691584, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [241, [1]]], 'bad_primes': [5, 241], 'central_character': '6025.4756', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 6025, 'conductor_radical': 1205, 'conjugate': 'dirichlet_L_6025.546', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^6', 'a^16', 0, 'a^4', 'a^5', 'a^14', 'a^12', 0, 'a^13', 'a^2', 'a^7', 'a^3', 0, 'a^12', 'a^19', 'a^10', 'a^9', 0, 'a^11', 'a^11', 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'0.874063137290648030129432460849+0.485812342401497425109384144355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28417659468488082337878440927-0.0326513734880773084635148241789*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.715135097331', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.01737554584', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67958666032', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.979982369691584, 'bad_primes': [5, 241], 'central_character': '6025.4756', 'conductor': 6025, 'conductor_radical': 1205, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6025/4756'], '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': '1-6025-6025.4756-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': '1-6025-6025.4756-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.979982369691584, 'root_angle': 0.08073807941407993, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.715135097331', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6025.4756', 'Lhash_array': ['dirichlet_L_6025.4756'], 'label': '1-6025-6025.4756-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6025/4756'}