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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6027.2729', 'a10': [0.9959742939952391, -0.0896393089034335], 'a2': [-0.9839295885986297, 0.17855689479863665], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9362348706397372, -0.3513748240813427], 'a5': [-0.9959742939952391, -0.0896393089034335], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8584487936018661, 0.5128992774059061], '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': '6027.2729', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 6027, 'conductor_radical': 861, 'conjugate': 'dirichlet_L_6027.1091', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^33', 0, 'a^66', 'a^36', 0, 0, 'a^29', 0, 'a^69', 'a^54', 0, 'a^68', 0, 0, 'a^62', 'a^39', 0, 'a^42', 'a^32', 0, 'a^17', 'a^3', 0, 'a^2', 'a^31', 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0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(70)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.519800978298694524214899258369-0.114074453897896997392512363951*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.160143957621', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.771224361751', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.83823753823', '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': '6027.2729', 'conductor': 6027, 'conductor_radical': 861, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6027/2729'], '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': '1-6027-6027.2729-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': '1-6027-6027.2729-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.989270330644178, 'root_angle': 0.4700716243467871, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.160143957621', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6027.2729', 'Lhash_array': ['dirichlet_L_6027.2729'], 'label': '1-6027-6027.2729-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6027/2729'}