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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6027.1004', 'a10': [-0.01495940701526362, 0.9998881018102734], 'a2': [-0.9995524322835033, -0.029915466169398455], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9982101297677352, 0.05980415394503417], 'a5': [-0.01495940701526362, -0.9998881018102734], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9959742939952391, -0.0896393089034335], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.989270330644178, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [41, [1]]], 'bad_primes': [3, 7, 41], 'central_character': '6027.1004', 'coeff_info': ['x^420 - 1', '0.999888101810273 + 0.0149594070152636*I', '\\\\zeta_{420}'], 'conductor': 6027, 'conductor_radical': 861, 'conjugate': 'dirichlet_L_6027.4016', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^212', 0, 'a^4', 'a^314', 0, 0, 'a^216', 0, 'a^106', 'a^121', 0, 'a^177', 0, 0, 'a^8', 'a^241', 0, 'a^203', 'a^318', 0, 'a^333', 'a^242', 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'0.585354155874603582616743284660-0.810777720587048625217062930895*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(420)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.522971462901782994663841632565-0.0524128102013000541742871702572*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.289790105117', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.52893491753', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.04795962188', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.989270330644178, 'bad_primes': [3, 7, 41], 'central_character': '6027.1004', 'conductor': 6027, 'conductor_radical': 861, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6027/1004'], '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': '1-6027-6027.1004-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': '1-6027-6027.1004-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.989270330644178, 'root_angle': -0.15047774044196718, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.289790105117', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6027.1004', 'Lhash_array': ['dirichlet_L_6027.1004'], 'label': '1-6027-6027.1004-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6027/1004'}