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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_101.11', 'a10': [-7.040766286173228e-31, 1.0], 'a2': [0.6845471059286887, 0.7289686274214116], 'a3': [0.9822872507286887, -0.18738131458572463], 'a4': [-0.06279051952931337, 0.9980267284282716], 'a5': [0.7289686274214116, 0.6845471059286887], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [0.48175367410171527, 0.8763066800438636], 'a8': [-0.7705132427757893, 0.6374239897486897], 'a9': [0.9297764858882515, -0.368124552684678], 'algebraic': True, 'analytic_conductor': 10.853957404257127, 'analytic_normalization': 0, 'bad_lfactors': [[101, [1]]], 'bad_primes': [101], 'central_character': '101.11', 'coeff_info': ['x^100 - 1', '0.998026728428272 + 0.0627905195293134*I', '\\\\zeta_{100}'], 'conductor': 101, 'conductor_radical': 101, 'conjugate': 'dirichlet_L_101.46', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^97', 'a^26', 'a^12', 'a^10', 'a^17', 'a^39', 'a^94', 'a^25', 'a^69', 'a^23', 'a^58', 'a^30', 'a^9', 'a^52', 'a^90', 'a^7', 'a^48', 'a^38', 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[[1], []], 'index': 0, 'label': '1-101-101.11-r1-0-0', 'leading_term': '2.59584782681122624604183721463+2.65653944728043449328383704314*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/101/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.7142465958680777, 4.233698177000828, 4.512047903406142, 4.439966889695124, 3.9281264180498265, 2.985298701373567, 1.76478449515021, 0.5496029359903054, -0.32745502836384865, -0.6059383345818474, -0.21563547943943656, 0.6650455982191787, 1.6502607111287266, 2.2882150426605006, 2.2541645451872454, 1.510174893765939, 0.3473506677759629, -0.728393632271259, -1.2305489514407155, -0.9398246616046834, -0.03522340188055655, 0.9772208809840485, 1.5228600796556517, 1.2802322327353715, 0.3884021589832902, -0.5960508078037109, -0.9991432584747794, 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'199.07869008018713095187878394885'], 'prelabel': '1-101-101.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.853957404257127, 'root_angle': 0.4926441512948566, 'root_number': '0.0231070234858068506892009731549+0.999732997087535553061005630335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.253677924353', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(100)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.93075200289133306862061079705+1.17288123336603985057229723974*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.36136883452', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.21435993854', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.09121025314', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.853957404257127, 'bad_primes': [101], 'central_character': '101.11', 'conductor': 101, 'conductor_radical': 101, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/101/11'], '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': '1-101-101.11-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': '1-101-101.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.853957404257127, 'root_angle': 0.2463220756474283, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.36136883452', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_101.11', 'Lhash_array': ['dirichlet_L_101.11'], 'label': '1-101-101.11-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/101/11'}