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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_97.20', 'a10': [0.5555702330196022, 0.8314696123025452], 'a2': [-0.9238795325112867, 0.3826834323650898], 'a3': [-0.3826834323650898, 0.9238795325112867], 'a4': [0.7071067811865476, -0.7071067811865476], 'a5': [-0.19509032201612828, -0.9807852804032304], 'a6': [2.9010907910729803e-30, -1.0], 'a7': [-0.19509032201612828, 0.9807852804032304], 'a8': [-0.3826834323650898, 0.9238795325112867], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 10.424097705078626, 'analytic_normalization': 0, 'bad_lfactors': [[97, [1]]], 'bad_primes': [97], 'central_character': '97.20', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 97, 'conductor_radical': 97, 'conjugate': 'dirichlet_L_97.34', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^10', 'a^28', 'a^23', 'a^24', 'a^9', 'a^10', 'a^20', 'a^5', 'a^26', 'a^6', 'a^31', 'a^23', 'a^1', 'a^24', 'a^31', 'a^2', 'a^7', 'a^19', 'a^19', 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'root_analytic_conductor': 10.424097705078626, 'root_angle': 0.48186294289148907, 'root_number': '0.0569484185780499450455341674669+0.998377121944137507926627662351*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.240931471446', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.609432754769024624367840500157+0.255486361600511864372068944648*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.1029978543', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.45748268228', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.40772432392', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.424097705078626, 'bad_primes': [97], 'central_character': '97.20', 'conductor': 97, 'conductor_radical': 97, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/97/20'], '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': '1-97-97.20-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': '1-97-97.20-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.424097705078626, 'root_angle': 0.24093147144574453, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1029978543', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_97.20', 'Lhash_array': ['dirichlet_L_97.20'], 'label': '1-97-97.20-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/97/20'}