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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.35', 'a10': [-0.6358918939778535, -0.7717781411605659], 'a2': [-0.7434217230486163, 0.6688229524316779], 'a3': [0.7678152414234967, 0.6406713315248135], 'a4': [0.10535171660114712, -0.9944350234224414], 'a5': [-0.04344708749957805, 0.9990557294704856], 'a6': [-0.9993062212508053, 0.03724347150087643], 'a7': [0.6262596677501294, 0.7796145384415926], 'a8': [0.5867802136851077, 0.8097462447135271], 'a9': [0.17908048992444497, 0.9838344261756755], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.35', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.393', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^97', 'a^28', 'a^194', 'a^65', 'a^125', 'a^36', 'a^38', 'a^56', 'a^162', 'a^90', 'a^222', 'a^206', 'a^133', 'a^93', 'a^135', 'a^114', 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[1, 'a^111'], [1, 'a^193'], [1, 'a^219'], [1, 'a^1']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23e2-529.35-r0-0-0', 'leading_term': '0.0621211797058290779770668291951+1.14378827231326705950216388906*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/529/35', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1454739861076777, 1.899623490930544, 2.9056037349294632, 3.554512231853128, 3.285293517428732, 2.0232970117479843, 0.34190429214810597, -0.7791225925467482, -0.5515725764173184, 1.0105747034804127, 2.934811822876755, 3.8239718795762108, 2.8170999425609278, 0.30459234284562603, -2.2138572641178875, -3.147641880219044, -2.0073491586530188, 0.1758462454060168, 1.6163498551135975, 1.1772336244784032, -0.7298239070665878, -2.5299404697597785, -2.8507573475057324, 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'198.848258640457876320036967016431', '199.27136103833850838565516844929', '199.56887376301511685610276989941'], 'prelabel': '1-23e2-529.35-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.965457982471215, 'root_number': '-0.994117811695738433765330864759+0.108304092578610993638351798805*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.482728991236', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(253)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.633626868780265686458935073045+0.719076700311540242525106231846*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.9463641098', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.63557388693', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.09632399804', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.35', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/35'], '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': '1-23e2-529.35-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': '1-23e2-529.35-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.4827289912356075, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.9463641098', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.35', 'Lhash_array': ['dirichlet_L_529.35'], 'label': '1-23e2-529.35-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/35'}