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{'Lhash': 'dirichlet_L_308.135', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.6691306063588582, -0.7431448254773942], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 33.099196836744504, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [11, [1]]], 'bad_primes': [2, 7, 11], 'central_character': '308.135', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 308, 'conductor_radical': 154, 'conjugate': 'dirichlet_L_308.235', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 'a^26', 0, 0, 0, 'a^14', 0, 0, 0, 'a^24', 0, 'a^33', 0, 'a^16', 0, 'a^17', 0, 0, 0, 'a^35', 0, 'a^22', 0, 'a^21', 0, 'a^18', 0, 'a^19', 0, 0, 0, 0, 0, 'a^8', 0, 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'199.146726491736613588282282913373', '199.41597269510803047008170337398'], 'prelabel': '1-308-308.135-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 33.099196836744504, 'root_angle': -0.6207278544837307, 'root_number': '-0.370249636082401233832813264645-0.928932294077910422135695505600*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.310363927242', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.959171084931436842837107673457+0.0236987257537771612528365542951*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.219570059655', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.97370884592', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.2989605862', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.099196836744504, 'bad_primes': [2, 7, 11], 'central_character': '308.135', 'conductor': 308, 'conductor_radical': 154, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/308/135'], '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': '1-308-308.135-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': '1-308-308.135-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 33.099196836744504, 'root_angle': -0.31036392724186534, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.219570059655', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_308.135', 'Lhash_array': ['dirichlet_L_308.135'], 'label': '1-308-308.135-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/308/135'}