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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '2172387135800766051', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 553.3632860074733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '69300.1', 'coefficient_field': '1.1.1.1', 'conductor': 69300, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 1], [1, -1], [1, -3, 13], [1, -2, 17], [1, 5, 19], [1, -4, 23], [1, 3, 29], [1, 6, 31], [1, -3, 37], [1, 0, 41], [1, -8, 43], [1, 9, 47], [1, 4, 53], [1, -9, 59], [1, 2, 61], [1, -5, 67], [1, 0, 71], [1, -9, 73], [1, 4, 79], [1, 2, 83], [1, 10, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-69300-1.1-c1-0-17', 'leading_term': '2.06103317129', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/69300/bj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.061033171292146, 1.466268131469293, -0.02528051186254946, -1.511113298770124, -1.824635923122248, -0.5338378725464071, 1.291613271325339, 1.769217665049845, 0.1515216021930081, -2.011241363944953, -2.276866435138611, -0.1617022729850278, 2.013656381320951, 1.834923009291707, -0.05455359162701879, -0.7327182259294384, 0.8757329101278692, 2.201693828488175, 0.6148866655438846, -2.39618983192619, -2.896899865553242, -0.182156619188827, 1.977944140103337, 0.8648467325166148, -1.158141857034642, -0.5983092597875695, 1.401556374655443, 1.047468754000845, -1.407992863225402, -1.696272693167981, 1.177412554092016, 2.725240585873662, 0.2614428356773793, -2.456481429893455, -1.53691476093718, 0.4974891636823583, -0.5059742777627535, -2.727378434223842, -1.859435764562946, 0.5661658767790956, -0.3332642299890064, -3.611411044176194, -3.797087235880133, -0.729441238140701, 0.4359176941393343, -0.8060151325325632, 0.4775601696621091, 4.425192623070736, 5.061292230115597, 1.185532693951829, -1.273516647266124, -0.1750270555267777, -0.2107680806398706, -2.488741782297892, -1.990383824422236, 1.676020071385559, 2.358813011119474, -0.879213960662561, -1.832985784084194, 0.5765161767803694, 0.5422143356615875, -2.277604609606726, -1.844886870214352, 1.61984667580699, 1.741086298304335, -1.136392982247218, -1.097439428150632, 0.8100428495346884, -0.5814029933874032, -2.577710701288291, 0.08627768310379286, 3.354936531818773, 1.419192204401914, -1.382216967192319, 0.4176049107564218, 2.448056916840014, 0.5789059351339234, -0.3880430949939791, 1.824897999516961, 1.397696868455075, -2.27222841746875, -2.103695829176485, 1.710828093934716, 1.936705791605392, -0.4354101473353983, 0.6285794901015614, 2.092010430937548, -1.184083164210127, -3.998281744566759, -1.515182627564268, 0.3166139398745061, -2.012591933299688, -2.382747570346293, 0.4532337408951103, 0.3699645566698162, -1.200906997952708, 1.603736032680251, 4.353830542834432, 0.9881764444597368, -2.349630528754645, 4.803297977905284e-05, 1.842760938380792, -0.2922810254647515, -0.7610833091578875, 0.2280332381787499, -2.645281572247588, -5.028545270487225, -1.047916982811935, 2.656428292138323, 0.4170026371402285, -1.198591544764235, 0.6140565104677385, -0.4588192903143848, -3.087097372265919, -0.6680519593804378, 2.443224607206557, 0.3745106754078831, -0.8374792972986841, 2.217257985304335, 2.488672913365145, -0.2211578239682354], 'positive_zeros': ['0.4962495068128487', '1.319559618813250', '2.016230491010734', '2.765111180416812', '3.492351872424062', '3.891744721782130', '4.550111313928942', '5.264241767183408', '5.840673901087807', '6.321106944075893', '6.859535942588454', '7.409869074774715', '8.018265385596244', '8.662420642347431', '8.943418821175752', '9.673815498029960', '9.969631121243047', '10.82372156211901', '11.09590343569493', '11.46135715694759', '12.32691784487189', '12.78411316101788', '12.96503094059549', '13.63770880711046', '14.18565239086903', '14.69027619864150', '15.05244016806126', '15.63032416779549', '16.14637720596412', '16.62205573880721', '16.94688350988141', '17.49507731541974', '18.09424772893769', '18.46727025099004', '19.06172642731076', '19.30979765490295', '19.84690875060940'], 'prelabel': '2-69300-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.523675010666878, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2172387135800766051, 'z1': {'__RealLiteral__': 0, 'data': '0.4962495068128487', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.319559618813250', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.016230491010734', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 553.3632860074733, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 69300, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, 0, -5, 0, 0, 0, 4, 0, 0, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 8, 0, 0, 0, -9, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 0, 9, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 9, 0, 0, 0, -1, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -10, 0, -3, 0, 0, 0, 0, 0, -16, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, -3, 13], 'euler17': [1, -2, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, 6, 31], 'euler37': [1, -3, 37], 'euler41': [1, 0, 41], 'euler43': [1, -8, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, -9, 59], 'euler61': [1, 2, 61], 'euler67': [1, -5, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -9, 73], 'euler79': [1, 4, 79], 'euler83': [1, 2, 83], 'euler89': [1, 10, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -3, 13], [1, -2, 17], [1, 5, 19], [1, -4, 23], [1, 3, 29], [1, 6, 31], [1, -3, 37], [1, 0, 41], [1, -8, 43], [1, 9, 47], [1, 4, 53], [1, -9, 59], [1, 2, 61], [1, -5, 67], [1, 0, 71], [1, -9, 73], [1, 4, 79], [1, 2, 83], [1, 10, 89], [1, 16, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/69300/bj'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-69300-1.1-c1-0-17', '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': '2-69300-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.523675010666878, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2172387135800766051, 'z1': {'__RealLiteral__': 0, 'data': '0.4962495068128487', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2172387135800766051', 'Lhash_array': ['2172387135800766051'], 'label': '2-69300-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/69300/bj'}