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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_304.181', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.984807753012208, 0.17364817766693036], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6427876096865394, 0.766044443118978], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 32.669337137566, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '304.181', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 304, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_304.173', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 'a^13', 0, 'a^42', 0, 'a^38', 0, 'a^21', 0, 'a^53', 0, 'a^14', 0, 'a^16', 0, 0, 0, 'a^43', 0, 'a^50', 0, 'a^26', 0, 'a^39', 0, 'a^29', 0, 'a^6', 0, 'a^22', 0, 'a^55', 0, 'a^27', 0, 'a^18', 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'198.4933935720278593279316393233', '198.8041906488955226528550667130', '199.43326501231579292043630401958'], 'prelabel': '1-304-304.181-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 32.669337137566, 'root_angle': 0.9934855191166961, 'root_number': '-0.999790581898118258005948296054+0.0204644166255011588208038337050*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.496742759558', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.988136905742921618435227386845+0.405981465301028397600151148533*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.10908245786', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.80970095731', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.01657334109', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.669337137566, 'bad_primes': [2, 19], 'central_character': '304.181', 'conductor': 304, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/304/181'], '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': '1-304-304.181-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-304-304.181-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 32.669337137566, 'root_angle': 0.49674275955834807, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10908245786', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_304.181', 'Lhash_array': ['dirichlet_L_304.181'], 'label': '1-304-304.181-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/304/181'}