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lfunc_lfunctions • Show schema
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{'Lhash': '2752598668669024474039467892214', 'a10': [0.2553467535071702, 0.4422735506221852], 'a2': [-0.2695451162601043, -0.4668658362945605], 'a3': [-1.4090724747022432, 1.0072312351374417], 'a4': [0.8546908606006537, -1.480367995325101], 'a5': [-0.9473247263762961, 0.0], 'a6': [0.8500504569469738, 0.38635353892557855], 'a7': [1.1842964221122574, -2.0512615743204674], 'a8': [-1.9996914545886242, 0.0], 'a9': [0.9709704779270072, -2.838523618185024], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4090724747022432, -1.0072312351374417]]], [19, [[1.0, 0], [-2.4668833508586534, 3.5936731255438885]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '1227283017714935739417424762114', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2695451162601043, 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'7.70894092315960960116898958160928', '8.561767781060179800358772967790386', '10.03457604699364588548634358111089', '11.54781768200174527921297078986097', '11.89428233876477100662521717523200', '12.55557318073402515130093161984945'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.4508686007653001, 'root_number': '0.15373869210420282 + 0.9881115395288576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.225434300383', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.17141747747639859339438519442', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20856716448416238275068385277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.73704032729122835262940721343', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-171-171.106-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.22543430038265005, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.17141747747639859339438519442', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2752598668669024474039467892214', 'Lhash_array': ['2752598668669024474039467892214'], 'label': '2-171-171.106-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/7'}