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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '312195933454901181', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2117.6326616043566, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '265200.1', 'coefficient_field': '1.1.1.1', 'conductor': 265200, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 2, 7], [1, 4, 11], [1, 1], [1, 1], [1, 6, 19], [1, -8, 23], [1, -6, 29], [1, -8, 31], [1, -2, 37], [1, 2, 41], [1, 10, 43], [1, 4, 47], [1, -2, 53], [1, -14, 59], [1, 10, 61], [1, -12, 67], [1, -8, 71], [1, 2, 73], [1, 6, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 76, 'label': '2-265200-1.1-c1-0-76', 'leading_term': '4.41092187112', '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': 1, 'origin': 'EllipticCurve/Q/265200/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8738882261082894, 0.5877930673993919, -0.9353390660565558, -2.117641947626962, -1.003642917815277, 2.133991173080801, 4.246891657480819, 2.889008179128433, -0.2843352984689175, -1.351272752057914, 0.316240497464151, 0.9842183103323835, -1.482332922302149, -3.593224835167549, -1.410794991041005, 2.711147289651876, 3.35811848131863, 0.5879238902593397, -0.6924620694211754, 0.5078322068973732, 0.1099163491335881, -2.585434354344044, -3.07648423580261, -0.3110750116004731, 1.042263139259133, -0.4572300789776988, -0.7039772592322131, 0.6652182887991709, -1.125775478564619, -5.278076260540405, -4.931666422333929, -0.1831897171780888, 1.407630630718131, -0.5327690927578215, 1.227844630020993, 5.98056797001177, 5.462196051623724, 0.1672789115162722, -1.715380186906711, -0.1022314235033949, -0.8360825644089906, -2.280710402683471, -0.3773238956252441, 0.899048384295459, -1.403830710804682, -1.550765927546043, 2.130524229944939, 2.519264099725368, -1.134454441513655, -1.796392357926685, 0.07168555586840444, -0.6227664651760534, -0.9412391307436361, 1.294338119722519, -0.6866925658278644, -6.574955540539602, -5.327184288648022, 2.446588158199261, 4.254370184281363, 0.2440592978294265, 0.0360185058046806, 1.637238604536362, -0.449112239383761, -1.182278793292602, 1.522876239716076, 1.00478185550583, -1.740066820340407, -0.672938894054391, 0.3781633792250857, -1.779682187911989, -0.650148386947979, 3.358579879003878, 2.32315721891753, -0.4437154987259233, 1.398060125025592, 2.059408773818332, -0.769810735314362, 0.09031979434499066, 1.46639693979015, -3.638675405953872, -6.219824627635009, 0.1677171781617638, 3.984412559174607, 0.856150866597577, 0.04369269771646259, 0.7235707807418401, -2.117130562822682, -1.760492300704842, 3.128969718608058, 3.30428250599559, 0.2270348299940869, 0.5631883010354782, 0.5525366111242667, -0.5649670630416466, 1.730708983240408, 1.65692733205394, -3.639471050674009, -3.724813058267817, 0.7707609872226096, -0.8313324213661021, -3.232768628693156, 0.3384757801159146, 0.8474078109202527, -2.340705681458873, 0.1877048772005586, 2.973498483464318, 0.02800789930039418, -0.03097544514669155, 2.21380273801486, -1.323547137739706, -3.28830907461085, 1.323507398636328, 2.489391128268246, -0.2603023469125617, 0.160681311206629, 0.3273578135309971, -0.1209861217547026, 3.008117815690642, 3.215570862713685, -0.356112277760159], 'positive_zeros': ['0.6119253532084352', '1.339082700700702', '2.224519779987872', '2.710184664392117', '3.128660352961745', '3.830915656333933', '4.558235775635974', '4.906026315782800', '5.262903143244612', '6.027793693051681', '6.434618225491900', '6.864803329757206', '7.165348617853432', '8.010887285066569', '8.421727285822796', '8.667681573874535', '9.509089925027143', '10.03064573481622', '10.11010442345842', '10.78537319091946', '11.12094905966910', '11.61302019701396', '12.17149913684048', '12.73272589220000', '12.89149884368283', '13.35777971943164', '13.71588386466054', '14.41827119807306', '15.02109269770069', '15.24575723110076', '15.71032526799231', '16.11475837419056', '16.57900328410333', '17.07491628409634', '17.30973231039980', '17.78893714494078', '18.42223977142957', '18.62058670914689', '19.17422399689824', '19.49223890993319', '19.85254767417185'], 'prelabel': '2-265200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.017742899933246, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 312195933454901181, 'z1': {'__RealLiteral__': 0, 'data': '0.6119253532084352', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.339082700700702', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.224519779987872', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2117.6326616043566, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 265200, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -2, 0, 1, 0, -4, 0, -1, 0, 0, 0, -1, 0, -6, 0, 2, 0, 8, 0, 0, 0, -1, 0, 6, 0, 8, 0, 4, 0, 0, 0, 2, 0, 1, 0, -2, 0, -10, 0, 0, 0, -4, 0, -3, 0, 1, 0, 2, 0, 0, 0, 6, 0, 14, 0, -10, 0, -2, 0, 0, 0, 12, 0, -8, 0, 8, 0, -2, 0, 0, 0, 8, 0, -6, 0, 1, 0, -4, 0, 0, 0, -6, 0, -14, 0, 2, 0, -8, 0, 0, 0, 14, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 10, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -14, 59], 'euler61': [1, 10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 6, 79], 'euler83': [1, 4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 2, 7], [1, 4, 11], [1, 1, 0], [1, 1, 0], [1, 6, 19], [1, -8, 23], [1, -6, 29], [1, -8, 31], [1, -2, 37], [1, 2, 41], [1, 10, 43], [1, 4, 47], [1, -2, 53], [1, -14, 59], [1, 10, 61], [1, -12, 67], [1, -8, 71], [1, 2, 73], [1, 6, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97]], 'index': 76, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/265200/r'], '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': '2-265200-1.1-c1-0-76', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-265200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.017742899933246, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 312195933454901181, 'z1': {'__RealLiteral__': 0, 'data': '0.6119253532084352', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '312195933454901181', 'Lhash_array': ['312195933454901181'], 'label': '2-265200-1.1-c1-0-76', 'type': 'ECQ', 'url': 'EllipticCurve/Q/265200/r'}