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{'Lhash': 'dirichlet_L_324.295', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.05814482891047583, 0.9983081582712682], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9730448705798238, 0.23061587074244017], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 34.818635633458506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '324.295', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 324, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_324.67', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^14', 0, 'a^79', 0, 0, 0, 'a^49', 0, 'a^26', 0, 0, 0, 'a^6', 0, 'a^75', 0, 0, 0, 'a^29', 0, 'a^28', 0, 0, 0, 'a^46', 0, 'a^65', 0, 0, 0, 'a^39', 0, 'a^42', 0, 0, 0, 'a^44', 0, 'a^31', 0, 0, 0, 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'198.89325993960567805917068434786', '199.98878553029000480798948988155'], 'prelabel': '1-18e2-324.295-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 34.818635633458506, 'root_angle': -0.30864197530864196, 'root_number': '-0.360177724804710417248584671617-0.932883704732000499008205033097*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.308641975309', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.783929551596673716206696869378+0.104580942472352689816351204642*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.116536763132', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.05144844754', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.20810937883', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.818635633458506, 'bad_primes': [2, 3], 'central_character': '324.295', 'conductor': 324, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/324/295'], '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': '1-18e2-324.295-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': '1-18e2-324.295-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 34.818635633458506, 'root_angle': -0.30864197530864196, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.116536763132', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_324.295', 'Lhash_array': ['dirichlet_L_324.295'], 'factors': ['1-18e2-324.295-r1-0-0'], 'label': '1-18e2-324.295-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/324/295'}