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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 3, 'A9': -3, 'Lhash': '788062032746937227', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [1.0606601717798212, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 410.63069239443456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [11, [1]], [17, [1, -1]]], 'bad_primes': [5, 11, 17], 'central_character': '51425.1', 'coefficient_field': '1.1.1.1', 'conductor': 51425, 'conductor_radical': 935, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 0, 3], [1], [1, -4, 7], [1], [1, 2, 13], [1, -1], [1, -4, 19], [1, 4, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, -10, 61], [1, 4, 67], [1, 4, 71], [1, 6, 73], [1, 12, 79], [1, 4, 83], [1, -10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 24, 'label': '2-51425-1.1-c1-0-24', 'leading_term': '3.96644245115', '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/51425/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8918176321741821, 1.217204249235503, 0.6582643341529973, -0.4669000734887375, -1.174239515200597, -0.6059194605806209, 0.8768538539054171, 1.624666337627476, 0.2827721379766577, -2.331846903575349, -3.4553216751649, -1.212756397011839, 2.804879977655222, 4.688933620053, 2.49943900104549, -1.281666184254059, -2.614554208951295, -0.8772647946907313, 0.5881575860252726, -0.652042188067724, -2.5898116561106, -1.96128112888079, 0.2300784842166987, -0.5616874016953495, -5.643633277098688, -10.11232483284624, -8.865627544062265, -3.430945142155362, 0.3263193506074268, 0.1176712403429339, -0.9540800911714051, -0.4168318479735102, 0.1055742380541559, -0.9955233128436315, -1.85391327364876, -0.7191114830331433, 0.3568794395164831, -0.840201111524936, -2.153493803847638, -0.6174112808851916, 1.757744649673913, 1.041283832772573, -1.498265755001681, -1.440626178584543, 0.6988953765491208, 0.5115504603090384, -1.425511800277703, 0.05304771709441599, 4.322275185400927, 4.149871025080482, -1.843198101681091, -5.355467418833041, -1.59524401630495, 3.035988397631433, 2.250185202479991, -0.4316751750796733, -0.2153061812390578, 0.06505778819836779, -2.290119740595525, -2.340230009833011, 3.024100504450022, 6.812199354500569, 2.969153829773197, -2.595573795652082, -1.987223599766189, 1.804127243824309, 1.957822339304545, -0.2917535558718446, -0.4634964579569476, 0.2731403909158189, -0.4085926249919491, -0.4355908411260903, 0.9470910205817616, 0.4438303613971851, -1.633732248959589, -0.8126772959787051, 1.861027550041526, 0.9319448853094536, -2.164987612506751, -1.63452271223537, 0.5939729284894442, -0.778197904505541, -2.239598638558411, 1.39623729222348, 4.457978560305227, 0.5648361555958489, -3.961081207399546, -2.142955061162484, 0.2034741556288546, -2.4777762784013, -3.816514688659399, 0.01272917762376563, 1.372551253687205, -2.433620787657158, -2.957590986215307, 1.536489012987825, 2.594004629066087, -0.2521315908341468, 0.7444846675139637, 3.91990131743186, 1.65384836354793, -2.894189100828264, -2.206847305089571, 0.6424220535663959, 0.06742533053122109, -0.7507568902997608, 0.9555218247429186, 1.30189849617205, -0.2470139337894406, 0.1898076248110923, 1.226190480264368, -0.05511984769939869, -0.6310852033087231, 0.2444892012919843, -2.192253215442155, -5.585755604382454, -2.648842391504833, 2.098900602870746, -0.3785803756288552, -4.452759341118203], 'positive_zeros': ['0.8995093476066003', '1.607976447521990', '2.279241292303657', '3.076703723600732', '3.908605924016859', '4.605266775829156', '4.919973397505425', '5.715074210482257', '5.949678720652368', '7.208520869472250', '7.521348616471706', '8.117054859056938', '8.300821220728159', '9.116430766958097', '9.377361559999138', '10.05507257160231', '10.59751145478778', '11.16131101141660', '11.56214108240005', '11.99650984927075', '12.68083711023853', '13.31862439985622', '13.94149304666488', '14.29675986291402', '14.51208444001560', '15.12894445745386', '15.86386977280265', '16.37233488923923', '16.95939331344943', '17.36675255498219', '17.64208630653292', '18.08328860953872', '18.55178641457293', '19.06984789618366', '19.56972232784092'], 'prelabel': '2-51425-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.264024585319536, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 788062032746937227, 'z1': {'__RealLiteral__': 0, 'data': '0.8995093476066003', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.607976447521990', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.279241292303657', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 410.63069239443456, 'bad_primes': [5, 11, 17], 'central_character': '1.1', 'conductor': 51425, 'conductor_radical': 935, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 4, 3, -3, 0, 0, 0, -2, -4, 0, -1, 1, 3, 4, 0, 0, 0, -4, 0, 0, 2, 0, -4, -6, 0, 4, -5, 0, -1, 0, 3, 2, -4, 0, 0, 6, 0, 4, 0, 0, 4, 0, 0, 9, 0, 0, 2, -6, 0, 0, 12, 0, 6, -12, 0, 10, -4, -12, 7, 0, 0, -4, -1, 0, 0, -4, -9, -6, -2, 0, -4, 0, 0, -12, 0, 9, -6, -4, 0, 0, -4, 0, 0, 10, 0, -8, 4, 0, 0, 0, 0, -2, -9, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, -1, 0], 'euler19': [1, -4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 4, 71], 'euler73': [1, 6, 73], 'euler79': [1, 12, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 2], [1, 0, 3], [1, 0, 0], [1, -4, 7], [1, 0, 0], [1, 2, 13], [1, -1, 0], [1, -4, 19], [1, 4, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, -10, 61], [1, 4, 67], [1, 4, 71], [1, 6, 73], [1, 12, 79], [1, 4, 83], [1, -10, 89], [1, 2, 97]], 'index': 24, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/51425/m'], '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': '2-51425-1.1-c1-0-24', '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': '2-51425-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.264024585319536, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 788062032746937227, 'z1': {'__RealLiteral__': 0, 'data': '0.8995093476066003', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '788062032746937227', 'Lhash_array': ['788062032746937227'], 'factors': ['2-51425-1.1-c1-0-24'], 'label': '2-51425-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/51425/m'}