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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': 2, 'A4': 1, 'A5': 1, 'A6': -2, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '1465096193611722074', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [-0.8164965809277261, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 537.1536543971534, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1, -1]], [7, [1, 1]], [31, [1]]], 'bad_primes': [2, 5, 7, 31], 'central_character': '67270.1', 'coefficient_field': '1.1.1.1', 'conductor': 67270, 'conductor_radical': 2170, 'degree': 2, 'euler_factors': [[1, 1], [1, -2, 3], [1, -1], [1, 1], [1, 0, 11], [1, 0, 13], [1, 6, 17], [1, -4, 19], [1, 6, 23], [1, -2, 29], [1], [1, -10, 37], [1, -10, 41], [1, 0, 43], [1, 4, 47], [1, 2, 53], [1, 4, 59], [1, -8, 61], [1, -4, 67], [1, 8, 71], [1, -6, 73], [1, -2, 79], [1, 14, 83], [1, 2, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 32, 'label': '2-67270-1.1-c1-0-32', 'leading_term': '6.76873372437', '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/67270/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.548223858376463, 2.26434074816251, 1.607169500347938, -0.1392981475097071, -1.737273500889471, -1.900880573586706, -0.6120541191570423, 0.7007726636979962, 0.71938144153126, -0.0956918167579569, -0.02853706737285198, 1.403775096397602, 2.284629812190856, 0.7063705810861317, -1.968395812926009, -2.025390742128635, 1.509077224684758, 4.319423568566017, 1.584143041504296, -5.195828102522452, -9.02907495210746, -6.055227013724626, -0.5576168434257528, 0.9715663511965094, -1.475580383930808, -2.417250435822338, 0.395353302539988, 3.011656005111532, 2.076949517442511, -0.06101256860630521, 0.1528965977483261, 1.681131378915002, 1.494795859367995, 0.1410451609750041, 0.194377786643629, 1.159112217409841, 0.7345078985240874, -0.3936022892043629, -0.1775835675648962, -0.1532808214021324, -2.856040887021666, -5.61592332826129, -3.953034858454414, -0.2620071500241293, -0.7757721600223413, -4.0638058280028, -2.419362278959797, 4.158472672475146, 6.478196455521663, 1.512350739867577, -2.408081441061218, -0.1376942173956506, 2.395929130320319, 0.4256997960346837, -1.411573215556011, 0.4749359003425954, 1.580202013830975, -0.6120960755680324, -1.006574789851664, 2.356417761359109, 3.665302906235593, 0.931695550612386, -0.1037886338120107, 1.925448541913223, 1.282810911669936, -2.115565746739137, -1.452679175763736, 3.070347947929694, 3.797460138155096, 0.1735936965895262, -1.087740738509718, 0.3778785500179397, -0.4600174070212126, -2.205801127526041, -0.3348475350877481, 2.405193379757533, 1.515365165926676, -0.3016927396640963, 0.1096879194833836, 0.1791576350147736, -0.7718855971681094, 0.3001308560782766, 1.281503725799477, -1.714796013886534, -3.830427513659273, -0.147097369237602, 2.37685614529177, -1.390810663590537, -2.410582040471963, 3.595650622233044, 4.066499709482359, -5.822229490047163, -10.33726993339273, -1.609320730540714, 5.770295517856883, 2.316219291505934, -2.027258194428765, -0.4953301007462308, 0.7130335663574519, -0.5988074802079935, 0.1076794906656809, 1.655231998254915, 0.690293853708623, -0.1003240752690652, 0.7032640792309678, 0.2486581772065073, -0.1065597848296089, 1.728825383967011, 0.920406470215953, -3.742543207689534, -4.089319835693433, 0.9975033419263244, 2.423348112901009, -0.1579763639694357, 0.5915100384470503, 2.010273093690627, -1.096837984948708, -2.385517499452887, 1.62248593198937, 2.306068606635065], 'positive_zeros': ['0.9819846335113499', '1.848278861814404', '2.466265116623955', '2.757804641857639', '3.562813259246847', '4.159719780615718', '4.813887627846912', '5.785809671137604', '6.119054381789373', '6.722804510383854', '7.488393719977544', '7.721600153376872', '8.546521083677824', '8.685226755844498', '9.393147939130652', '9.817744695169343', '9.961020170302105', '11.03372907337193', '11.16805015635774', '11.84775958436961', '12.56429837711289', '13.00887260931343', '13.53467263411777', '13.95466638648963', '14.43988652268202', '14.84106830038056', '15.60028832126084', '15.76971826907231', '16.34273684721939', '16.83418646974384', '17.51305770185621', '17.92584445840637', '18.19357924872452', '18.77447090075253', '19.43036713111765', '19.71913875442348'], 'prelabel': '2-67270-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.176575553717022, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1465096193611722074, 'z1': {'__RealLiteral__': 0, 'data': '0.9819846335113499', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.848278861814404', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.466265116623955', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 537.1536543971534, 'bad_primes': [2, 5, 7, 31], 'central_character': '1.1', 'conductor': 67270, 'conductor_radical': 2170, 'degree': 2, 'dirichlet_coefficients': [1, -1, 2, 1, 1, -2, -1, -1, 1, -1, 0, 2, 0, 1, 2, 1, -6, -1, 4, 1, -2, 0, -6, -2, 1, 0, -4, -1, 2, -2, 0, -1, 0, 6, -1, 1, 10, -4, 0, -1, 10, 2, 0, 0, 1, 6, -4, 2, 1, -1, -12, 0, -2, 4, 0, 1, 8, -2, -4, 2, 8, 0, -1, 1, 0, 0, 4, -6, -12, 1, -8, -1, 6, -10, 2, 4, 0, 0, 2, 1, -11, -10, -14, -2, -6, 0, 4, 0, -2, -1, 0, -6, 0, 4, 4, -2, -6, -1, 0, 1], 'euler11': [1, 0, 11], 'euler13': [1, 0, 13], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 6, 23], 'euler29': [1, -2, 29], 'euler3': [1, -2, 3], 'euler31': [1, 0, 0], 'euler37': [1, -10, 37], 'euler41': [1, -10, 41], 'euler43': [1, 0, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 4, 59], 'euler61': [1, -8, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -6, 73], 'euler79': [1, -2, 79], 'euler83': [1, 14, 83], 'euler89': [1, 2, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 1, 0], [1, -2, 3], [1, -1, 0], [1, 1, 0], [1, 0, 11], [1, 0, 13], [1, 6, 17], [1, -4, 19], [1, 6, 23], [1, -2, 29], [1, 0, 0], [1, -10, 37], [1, -10, 41], [1, 0, 43], [1, 4, 47], [1, 2, 53], [1, 4, 59], [1, -8, 61], [1, -4, 67], [1, 8, 71], [1, -6, 73], [1, -2, 79], [1, 14, 83], [1, 2, 89], [1, 6, 97]], 'index': 32, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/67270/s'], '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': '2-67270-1.1-c1-0-32', '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': '2-67270-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.176575553717022, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1465096193611722074, 'z1': {'__RealLiteral__': 0, 'data': '0.9819846335113499', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1465096193611722074', 'Lhash_array': ['1465096193611722074'], 'label': '2-67270-1.1-c1-0-32', 'type': 'ECQ', 'url': 'EllipticCurve/Q/67270/s'}