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{'Lhash': 'dirichlet_L_4004.647', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.10452846326765347, -0.9945218953682733], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 18.59449782709462, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [2, 7, 11, 13], 'central_character': '4004.647', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 4004, 'conductor_radical': 2002, 'conjugate': 'dirichlet_L_4004.1083', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^24', 0, 'a^22', 0, 0, 0, 'a^18', 0, 0, 0, 0, 0, 'a^16', 0, 'a^7', 0, 'a^39', 0, 0, 0, 'a^35', 0, 'a^14', 0, 'a^42', 0, 'a^16', 0, 'a^23', 0, 0, 0, 0, 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'197.888459666751627462800864398568', '198.336792096567918092468092343097', '199.28888900967598986663422130673', '199.71004391172211701235741494457'], 'prelabel': '1-4004-4004.647-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.59449782709462, 'root_angle': -0.08250359014978806, 'root_number': '0.966597211321868934256857978022-0.256300275194519154413939137147*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.994203721889561319349013935255-0.356015915666230373258364044691*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.888442559158', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.6016843794', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.26812611994', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.59449782709462, 'bad_primes': [2, 7, 11, 13], 'central_character': '4004.647', 'conductor': 4004, 'conductor_radical': 2002, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4004/647'], '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': '1-4004-4004.647-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': '1-4004-4004.647-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.59449782709462, 'root_angle': -0.04125179507489403, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.888442559158', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4004.647', 'Lhash_array': ['dirichlet_L_4004.647'], 'label': '1-4004-4004.647-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4004/647'}