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lfunc_lfunctions • Show schema
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{'Lhash': '2001631737871287782447525759013', 'a10': [1.5702338143899117, -3.7145527431262524], 'a2': [-0.1744317384564385, -1.403414966650657], 'a3': [1.0921790525671786, 1.3443009027496262], 'a4': [-1.9391471372381293, 0.4896002248173175], 'a5': [2.4695801500447594, 1.4258127644136982], 'a6': [1.6961013157558158, -1.7672691721102902], 'a7': [-1.0203167421013688, 2.4410968325299285], 'a8': [1.0253610894554226, 2.6360262965742183], 'a9': [-0.6142898342669197, 2.9364345726605796], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.1744317384564385, 1.403414966650657]]], [3, [[1.0, 0], [-1.0921790525671786, -1.3443009027496262]]], [7, [[1.0, 0], [1.0203167421013688, -2.4410968325299285]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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[[1.0, 0], [5.612679277260173, -9.721445674803585], [-23.5, -40.703193977868615]], [[1.0, 0], [1.0041664096225407, 1.7392672407202614], [-26.5, 45.89934640057525]], [[1.0, 0], [0.8909962476687426, -0.5144169234384951], [29.5, -51.09549882328188]], [[1.0, 0], [-1.2434746445574156, 2.1537612622970945], [-30.5, -52.827549630850754]], [[1.0, 0], [-5.027772063026167, 2.9027855540122376], [33.5, -58.023702053557386]], [[1.0, 0], [0, 9.752770814403927], [-71.0, 0]], [[1.0, 0], [-0.2910187689225898, 0.16801976457669074], [36.5, -63.21985447626402]], [[1.0, 0], [2.8008190642626904, -4.8511609221105], [-39.5, -68.41600689897065]], [[1.0, 0], [0, 0.1381146039365881], [-83.0, 0]], [[1.0, 0], [0.5809934812884153, -1.0063102284578531], [-44.5, -77.07626093681505]], [[1.0, 0], [0, 11.0953197110982], [-97.0, 0]], [[1.0, 0], [6.162559745333734, -3.557955527865583], [50.5, -87.4685657822283]], [[1.0, 0], [-1.5051879203264946, -0.8690206509814746], [51.5, 89.20061658979718]], [[1.0, 0], [-0.5320281330877119, 0.9214997575639335], [-53.5, -92.66471820493493]], [[1.0, 0], [7.858740909850912, -4.537246179793948], [54.5, -94.39676901250381]], [[1.0, 0], [0, -16.812577504451276], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-168-168.5-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3079910056796022, 1.2872033537562533, 1.2737901610773326, 1.263339663887606, 1.2499370675813992, 1.2266639332117928, 1.1860812176158901, 1.1206592840236334, 1.023170669944077, 0.8870797976446133, 0.7069563040004814, 0.4789203247289469, 0.2011088790929294, -0.12586347230308473, -0.4984883550498794, -0.9100380300973162, -1.3503803606101348, -1.805983023929704, 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'6.55911158969156425161108099610028', '7.58108965671230040690927359612673', '8.482526064608429783630863263506438', '9.658529845256531023518966744483590', '10.19983566971043299989533481369363', '12.42263731563898376072620063718294', '13.17370495002451205857101203118841'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.0022291878638583326, 'root_number': '0.9999754776935879 - 0.007003142971601418*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00111459393193', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57900902465625109773334741940', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.95284831067853628560032509104', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.54480241260678838011553556026', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/11'], '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': '2-168-168.5-c1-0-7', '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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.0011145939319291663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57900902465625109773334741940', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2001631737871287782447525759013', 'Lhash_array': ['2001631737871287782447525759013'], 'label': '2-168-168.5-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/11'}