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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': -1, 'A6': -1, 'A7': 0, 'A8': 1, 'A9': 1, 'Lhash': '468305694228224288', 'a10': [-0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1241.8813624761658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1]], [23, [1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '155526.1', 'coefficient_field': '1.1.1.1', 'conductor': 155526, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 1, 5], [1], [1, 4, 11], [1, 1, 13], [1, -3, 17], [1, 4, 19], [1], [1, 6, 29], [1, 6, 31], [1, 2, 37], [1, -10, 41], [1, 4, 43], [1, 1, 47], [1, -1, 53], [1, -4, 59], [1, 4, 61], [1, -7, 67], [1, -5, 71], [1, 9, 73], [1, -4, 79], [1, -2, 83], [1, 6, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 35, 'label': '2-155526-1.1-c1-0-35', 'leading_term': '6.5360418035', '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/155526/bw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.372441010140645, 1.319156446097543, -0.7249558102713354, -3.600835943127956, -4.893166330704439, -3.240394127300568, -0.234947249785961, 0.9243356156846365, -0.7989510475564436, -2.754110541586146, -1.933808702905153, 0.874647810039284, 2.101876405146458, 0.5300933807108458, -1.002534608523585, -0.1202917531185379, 1.393964986250334, 0.7776134246612731, -0.9492905744438802, -0.8553382405341349, 0.6628146636587808, 0.8069070351834925, -0.1092855425109935, 0.8317488397658104, 2.968525980080802, 2.298968279978426, -0.9918143200777669, -1.890682834782282, 0.5947650412460759, 1.539653042108821, -0.1185407555870942, 1.041431797342303, 5.439880727256701, 4.924381395454924, -2.749375205742311, -7.131089837514858, -1.501480525711345, 5.31268399135805, 3.821133446762819, -0.933300409008037, -0.4701955636635573, 2.288777222281712, 1.258872801896524, -0.8002480920451063, 0.1247281182041209, 0.5997279765888281, -1.827283302145043, -2.802679643082357, -0.7113834073372878, 0.05012970137309857, -0.9513185559450315, 0.02807980376332289, 1.138290323080087, -1.230058203125214, -2.721939113691243, 0.9257718158260124, 3.941438135113101, 1.616469518642178, -0.4053165028708506, 1.294504862531513, 1.306275970845021, -1.378557096155124, -1.252143796795401, 0.3813440282406401, -1.345997321852331, -2.600579460157446, 0.1150251682198102, 0.3087218027977499, -3.567138715290162, -2.363391490056425, 3.603166932314388, 3.384707033546479, -1.277342718969939, 0.1366506732726822, 3.714599314722155, 0.86097316061308, -1.741012665723115, 1.961739823652849, 2.820470585638676, -2.542572421528468, -3.626688056422658, 0.7628252832785741, 1.133109712092636, -1.451261193157607, -0.5811622408057298, 0.1185480082921216, -2.021990204208007, -1.393078286337579, 1.456596094790322, 0.6027756069629088, -1.279349436205739, -0.1178433045311988, 0.4159239569097632, -0.5064833807413053, 0.2230707506759206, -0.130131072017736, -2.166028562936226, -0.03683312234758766, 2.92857432480075, -0.9447060424442641, -4.217796011789287, 0.4355310153629107, 2.722169398594032, -1.306095902905147, -0.2760434033250635, 3.453957509979587, -1.923978291494718, -8.041462562013361, -3.603222771463666, 1.224256425142306, -0.2129497970825282, 1.341362863392496, 4.805766481999867, 1.934177804446167, -0.8270269415618466, 1.888593794873049, 2.208783567522562, -0.2817164112570214, 0.4441548243786752, -0.1900816652395495], 'positive_zeros': ['0.6816781694852415', '1.773884624032203', '2.165432317070131', '2.922160555648755', '3.561819480417853', '4.016626840594643', '4.604337677721589', '5.138010364618216', '5.701377300593837', '5.866463085213187', '6.673782251972989', '7.196009161117676', '7.727808421174062', '7.906400825374529', '8.669789925970515', '9.293613104662486', '9.934413598406095', '10.28739461336224', '10.87001291414852', '11.23138844231829', '11.58204790491843', '12.35858210669861', '12.51573856428122', '12.99640029995197', '13.40302229855070', '13.95237572782058', '14.63642322032116', '14.84550925892588', '15.37067720544897', '15.90257628745005', '16.11390137557244', '16.74014251322128', '17.02447329346259', '17.59710747519019', '18.16565097709712', '18.49241422178838', '19.04554579458695', '19.39397226421134', '19.88981903542849'], 'prelabel': '2-155526-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.24033715043268, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 468305694228224288, 'z1': {'__RealLiteral__': 0, 'data': '0.6816781694852415', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.773884624032203', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.165432317070131', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1241.8813624761658, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 155526, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -1, -1, 0, 1, 1, -1, -4, -1, -1, 0, 1, 1, 3, 1, -4, -1, 0, -4, 0, -1, -4, -1, -1, 0, -6, 1, -6, 1, 4, 3, 0, 1, -2, -4, 1, -1, 10, 0, -4, -4, -1, 0, -1, -1, 0, -4, -3, -1, 1, -1, 4, 0, 4, -6, 4, 1, -4, -6, 0, 1, 1, 4, 7, 3, 0, 0, 5, 1, -9, -2, 4, -4, 0, 1, 4, -1, 1, 10, 2, 0, -3, -4, 6, -4, -6, -1, 0, 0, 6, -1, 4, -1, 12, 0, -4, -4], 'euler11': [1, 4, 11], 'euler13': [1, 1, 13], 'euler17': [1, -3, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 0], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 1, 47], 'euler5': [1, 1, 5], 'euler53': [1, -1, 53], 'euler59': [1, -4, 59], 'euler61': [1, 4, 61], 'euler67': [1, -7, 67], 'euler7': [1, 0, 0], 'euler71': [1, -5, 71], 'euler73': [1, 9, 73], 'euler79': [1, -4, 79], 'euler83': [1, -2, 83], 'euler89': [1, 6, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 1, 5], [1, 0, 0], [1, 4, 11], [1, 1, 13], [1, -3, 17], [1, 4, 19], [1, 0, 0], [1, 6, 29], [1, 6, 31], [1, 2, 37], [1, -10, 41], [1, 4, 43], [1, 1, 47], [1, -1, 53], [1, -4, 59], [1, 4, 61], [1, -7, 67], [1, -5, 71], [1, 9, 73], [1, -4, 79], [1, -2, 83], [1, 6, 89], [1, -12, 97]], 'index': 35, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/155526/bw'], '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': '2-155526-1.1-c1-0-35', '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': '2-155526-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.24033715043268, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 468305694228224288, 'z1': {'__RealLiteral__': 0, 'data': '0.6816781694852415', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '468305694228224288', 'Lhash_array': ['468305694228224288'], 'label': '2-155526-1.1-c1-0-35', 'type': 'ECQ', 'url': 'EllipticCurve/Q/155526/bw'}