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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_13.8', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [1.0, 0.0], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [-7.040766286173228e-31, 1.0], 'a6': [-7.040766286173228e-31, 1.0], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 1.3970440223301253, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]]], 'bad_primes': [13], 'central_character': '13.8', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 13, 'conductor_radical': 13, 'conjugate': 'dirichlet_L_13.5', 'degree': 1, 'dirichlet_coefficients': [1, 'I', 1, -1, 'I', 'I', '-I', '-I', 1, -1, '-I', -1, 0, 1, 'I', 1, -1, 'I', 'I', '-I', '-I', 1, -1, '-I', -1, 0, 1, 'I', 1, -1, 'I', 'I', '-I', '-I', 1, -1, '-I', -1, 0, 1, 'I', 1, -1, 'I', 'I', '-I', '-I', 1, -1, '-I', -1, 0, 1, 'I', 1, -1, 'I', 'I', '-I', '-I', 1, -1, '-I', -1, 0, 1, 'I', 1, 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'198.19371485903139535836624095635', '199.11511286598685180360841483669'], 'prelabel': '1-13-13.8-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3970440223301253, 'root_angle': 0.4064164790945006, 'root_number': '0.289784148688430089716825558519+0.957092026489052849592220722565*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.203208239547', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08642943411465667904756436037+0.581439387881469050796952624011*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.74382156415', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.72941969669', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '8.20662320146', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3970440223301253, 'bad_primes': [13], 'central_character': '13.8', 'conductor': 13, 'conductor_radical': 13, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/13/8'], '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': '1-13-13.8-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': '1-13-13.8-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3970440223301253, 'root_angle': 0.2032082395472503, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.74382156415', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_13.8', 'Lhash_array': ['dirichlet_L_13.8'], 'label': '1-13-13.8-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/13/8'}