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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_709.473', 'a10': [-0.9810010943735475, -0.19400219802337837], 'a2': [0.04435821777865651, -0.9990156898244898], 'a3': [0.22004820646562467, 0.9754889988263639], 'a4': [-0.9960646970310025, -0.08862911106705897], 'a5': [0.15029577950047043, -0.9886410767636281], 'a6': [0.9842897613429259, -0.17656065732627432], 'a7': [-0.6717644168907928, 0.7407648535124849], 'a8': [-0.13272552728372197, 0.9911528310040072], 'a9': [-0.9031575736625236, 0.4293092092373785], 'algebraic': True, 'analytic_conductor': 3.292582157694827, 'analytic_normalization': 0, 'bad_lfactors': [[709, [1]]], 'bad_primes': [709], 'central_character': '709.473', 'coeff_info': ['x^177 - 1', '0.999370004274994 + 0.0354907671852732*I', '\\\\zeta_{177}'], 'conductor': 709, 'conductor_radical': 709, 'conjugate': 'dirichlet_L_709.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^134', 'a^38', 'a^91', 'a^137', 'a^172', 'a^65', 'a^48', 'a^76', 'a^94', 'a^41', 'a^129', 'a^171', 'a^22', 'a^175', 'a^5', 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[1, 'a^58'], [1, 'a^165'], [1, 'a^167'], [1, 'a^67'], [1, 'a^69']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-709-709.473-r0-0-0', 'leading_term': '0.117918208283170152270249097907+0.243975847235523686377397725276*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/709/473', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.27097770734694154, 1.0294696862233728, 1.8692927982382808, 2.2908056733213753, 1.8505278697209189, 0.6601595658707775, -0.5920869734585706, -1.0886935438712944, -0.5117536284969799, 0.6438638248437589, 1.406812079407033, 1.129001709776916, 0.08889745359859093, -0.7077870190505942, -0.4710009017617926, 0.5041941539092747, 0.9589703008068733, -0.11934204453357868, -2.2123080891500657, -3.2445602448296578, -1.170255783377795, 4.0299955373077845, 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'192.30703703925438107637975540611', '192.90211899200261269483405351500', '193.22424411660407712980128843601', '194.06204371474871470397943700572', '194.491974381424532026992643703562', '195.4171344779889310849183682400', '196.00881152238881119593782027872', '196.68606131268283226355038085501', '197.26061009453557103843247536169', '198.05013086055902441168285456957', '199.0914525270600668970748994443', '199.2159487671066188911612385248', '199.77828762481741161546198183003'], 'prelabel': '1-709-709.473-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.292582157694827, 'root_angle': 0.7133847835028979, 'root_number': '-0.621274444827714712328802738687+0.783593047572536128311062593851*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.356692391751', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(177)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.739509947500936268023216760638-0.102012995435170970366706292674*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.71538284753', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.6427674552', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.77539211961', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.292582157694827, 'bad_primes': [709], 'central_character': '709.473', 'conductor': 709, 'conductor_radical': 709, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/709/473'], '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': '1-709-709.473-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': '1-709-709.473-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.292582157694827, 'root_angle': 0.35669239175144896, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71538284753', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_709.473', 'Lhash_array': ['dirichlet_L_709.473'], 'label': '1-709-709.473-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/709/473'}