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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_173.140', 'a10': [-0.6940741952206338, -0.7199034737579958], 'a2': [0.25293338239168073, -0.9674836970574252], 'a3': [-0.5818589155579529, 0.8132897407355654], 'a4': [-0.8720494081438076, -0.4894178478110855], 'a5': [0.5209403404879303, -0.8535930890373464], 'a6': [0.6396730215588913, 0.768647139778532], 'a7': [0.7447721827437819, 0.6673188112222395], 'a8': [-0.6940741952206338, 0.7199034737579958], 'a9': [-0.3228804047714462, -0.9464397731576093], 'algebraic': True, 'analytic_conductor': 0.803408622399443, 'analytic_normalization': 0, 'bad_lfactors': [[173, [1]]], 'bad_primes': [173], 'central_character': '173.140', 'coeff_info': ['x^43 - 1', '0.989343368075110 + 0.145601167735005*I', '\\\\zeta_{43}'], 'conductor': 173, 'conductor_radical': 173, 'conjugate': 'dirichlet_L_173.152', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^15', 'a^25', 'a^36', 'a^6', 'a^5', 'a^16', 'a^30', 'a^27', 'a^8', 'a^40', 'a^34', 'a^39', 'a^8', 'a^7', 'a^31', 'a^21', 'a^4', 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[[0], []], 'index': 0, 'label': '1-173-173.140-r0-0-0', 'leading_term': '0.946609775915609253911150519402-0.626219628876731320366182724714*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/173/140', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1349982781702845, 1.0851574076287616, 0.9521554619968389, 0.48388877449378787, -0.27765622328037526, -1.072366637377194, -1.5499280031842047, -1.434346867460021, -0.6796089421412524, 0.46255526643723, 1.522150052974568, 2.027234566552178, 1.7603419240130465, 0.908670519683892, -0.006959980786288526, -0.42509697725950346, -0.11595465437876669, 0.593372947516705, 0.9201957154142038, 0.056314790349176004, -2.287685869342914, -5.55677173477174, -8.496265325409997, -9.755305006132888, -8.63699120819225, -5.54470987145028, 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'0.391174347022588576557421357204-0.920316592391689658615353613404*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.186034470958', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(43)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.986423589686184252169709025803-0.417072247878060040546853932324*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.14426992083', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.69109895009', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.37208803609', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.803408622399443, 'bad_primes': [173], 'central_character': '173.140', 'conductor': 173, 'conductor_radical': 173, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/173/140'], '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': '1-173-173.140-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': '1-173-173.140-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': -0.18603447095761536, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14426992083', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_173.140', 'Lhash_array': ['dirichlet_L_173.140'], 'label': '1-173-173.140-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/173/140'}