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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6027.5396', 'a10': [0.5508969814521025, 0.8345732537213026], 'a2': [0.3930250316539236, -0.9195277725514507], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6910626489868646, -0.7227948638273916], 'a5': [-0.5508969814521025, 0.8345732537213026], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9362348706397372, 0.3513748240813427], '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': '6027.5396', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 6027, 'conductor_radical': 861, 'conjugate': 'dirichlet_L_6027.4451', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^57', 0, 'a^44', 'a^24', 0, 0, 'a^31', 0, 'a^11', 'a^36', 0, 'a^22', 0, 0, 'a^18', 'a^61', 0, 'a^28', 'a^68', 0, 'a^23', 'a^37', 0, 'a^48', 'a^9', 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(70)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.764721020128938317640807445204-0.288758229199931926623370034081*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.386019662596', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.78292220015', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.34729553925', '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': '6027.5396', 'conductor': 6027, 'conductor_radical': 861, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6027/5396'], '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': '1-6027-6027.5396-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': '1-6027-6027.5396-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.989270330644178, 'root_angle': -0.16394917536719528, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.386019662596', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6027.5396', 'Lhash_array': ['dirichlet_L_6027.5396'], 'label': '1-6027-6027.5396-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6027/5396'}