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{'Lhash': 'dirichlet_L_49.15', 'a10': [-0.2225209339563144, 0.9749279121818236], 'a2': [-0.9009688679024191, -0.4338837391175581], 'a3': [-0.2225209339563144, -0.9749279121818236], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [-0.2225209339563144, -0.9749279121818236], 'a6': [-0.2225209339563144, 0.9749279121818236], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.2225209339563144, -0.9749279121818236], 'a9': [-0.9009688679024191, 0.4338837391175581], 'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.15', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 49, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_49.36', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^5', 'a^1', 'a^5', 'a^2', 0, 'a^5', 'a^3', 'a^2', 'a^4', 'a^6', 'a^4', 0, 'a^3', 'a^2', 'a^6', 'a^0', 'a^0', 'a^6', 0, 'a^1', 'a^1', 'a^3', 'a^3', 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'197.3550710399752743020780248145', '198.57736981751910710605416268184', '199.43451407666601714892350204529'], 'prelabel': '1-7e2-49.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': -0.7755102040816327, 'root_number': '-0.761445958369134435405982779436-0.648228395307788401626567681892*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.387755102041', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.436684505744865138972824839571-0.382544101343815454711664931319*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.871228361334', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.76062525074', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.37401624872', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'bad_primes': [7], 'central_character': '49.15', 'conductor': 49, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/49/15'], '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': '1-7e2-49.15-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': '1-7e2-49.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': -0.38775510204081637, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.871228361334', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_49.15', 'Lhash_array': ['dirichlet_L_49.15'], 'label': '1-7e2-49.15-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/49/15'}