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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '1301228459584044992', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 329.6224595438456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [43, [1, -1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '41280.1', 'coefficient_field': '1.1.1.1', 'conductor': 41280, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -2, 7], [1, 2, 11], [1, 2, 13], [1, -8, 17], [1, 2, 19], [1, -6, 23], [1, -6, 29], [1, 0, 31], [1, 10, 37], [1, -2, 41], [1, -1], [1, -6, 47], [1, 2, 53], [1, -10, 59], [1, 4, 61], [1, -4, 67], [1, 0, 71], [1, 8, 73], [1, 8, 79], [1, -4, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-41280-1.1-c1-0-19', 'leading_term': '2.49245072073', '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/41280/bk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.492450720726159, 2.025570101363002, 0.8069067587691017, -0.5496187370023127, -1.132489728310673, -0.4036165998433645, 1.075879779519004, 1.81499231509808, 0.7255086091548003, -1.514852516680639, -2.752160238138721, -1.523975082603707, 1.018325313624408, 1.927253618900788, -0.3277830991661127, -3.801240662517847, -4.981132300768384, -2.801957823533581, 0.1386367662219406, 0.8874667914094457, -0.2581954326439348, -0.7092645048538162, 0.3074203087673565, 0.5907179530877523, -1.333046811158597, -3.290516128992318, -2.30433179175079, 0.6837821090536687, 1.757325075416707, -0.1446825903638713, -1.462648030901601, 0.3913650300173902, 2.643553742436118, 1.420385507301644, -1.67249778416983, -1.561200559639408, 2.220926123636839, 4.352919700595044, 1.823223812444068, -1.578622170798229, -1.597423298394049, 0.01079768293710314, -0.5047530666098436, -1.963251246841008, -0.7925823748635307, 1.833442987669425, 1.638599966145377, -1.013864669865777, -1.615931421770909, 0.300733983911069, 0.4811135701151001, -1.626244736710916, -1.278097997854853, 2.53264089351581, 4.200233931543547, 1.135582638015934, -1.428642845787761, 0.2197213147572324, 1.871110834190957, -0.05246919053205675, -1.310016451953945, 1.913926221146748, 4.979233180006409, 2.885661872429725, -0.44477890938229, 0.6064190115202445, 3.315070138279908, 2.476426684712767, -0.002108305172421161, -0.08768898502059204, 0.2035248955497014, -1.8202981226834, -2.809689295959738, -0.3107344722864863, 1.176470642056596, -1.059256459459925, -2.046091455612272, 0.3315655626125599, -0.5200579245972529, -7.054351308781473, -10.59598548141113, -5.79830524504458, 0.07125282217989592, 0.4466100065389595, -0.717607724052928, 0.307716263528473, 0.03483256362705341, -2.203357976886311, -1.135741419642092, 2.868318933257208, 3.1308990675145, -0.1977138262055383, -0.677843375438149, 1.279662101708067, 0.4959296401100135, -1.057039109363907, 0.9556752550965979, 2.608415663035153, -0.2515911090298169, -2.393562951568016, -0.06012311822535455, 0.7899513761236894, -2.345065174944915, -2.393198333285291, 1.856124612423363, 1.946616446701451, -2.872304975968496, -3.680505421701389, 0.2610560946046697, 1.331661454482846, -0.2450717124328024, 0.9241442243132819, 2.135485588522833, -0.7003329793495663, -2.678305629078253, -0.3505610884430508, 0.759713838422628, -1.219135117053064, -0.8255874935130106, 1.394315749402913, 0.2418582343132361], 'positive_zeros': ['0.6412987206949875', '1.321756191459917', '2.085028673183570', '2.897660217614926', '3.475738165779368', '4.484299274882506', '4.949587953514400', '5.435566607133047', '5.855875034149000', '6.690336467406376', '7.234899869575452', '7.715418596189541', '8.358393158428959', '8.866287384181611', '9.615387282443483', '10.24698411357922', '10.40460342536298', '11.07074992087718', '11.65447157077066', '12.21024108944224', '12.56521615049352', '13.09581199956597', '13.82497121531958', '14.23000051082432', '14.74520935138928', '15.13529890907427', '15.94567210388022', '16.19428401706984', '16.99965496859865', '17.27445470893472', '17.54318112304983', '18.27611380339080', '18.65609636480228', '19.21456991337769', '19.46688275465733'], 'prelabel': '2-41280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.15550769171288, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1301228459584044992, 'z1': {'__RealLiteral__': 0, 'data': '0.6412987206949875', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.321756191459917', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.085028673183570', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 329.6224595438456, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 41280, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 2, 0, 1, 0, -2, 0, -2, 0, -1, 0, 8, 0, -2, 0, -2, 0, 6, 0, 1, 0, -1, 0, 6, 0, 0, 0, 2, 0, 2, 0, -10, 0, 2, 0, 2, 0, 1, 0, 1, 0, 6, 0, -3, 0, -8, 0, -2, 0, -2, 0, 2, 0, 10, 0, -4, 0, 2, 0, -2, 0, 4, 0, -6, 0, 0, 0, -8, 0, -1, 0, -4, 0, -8, 0, 1, 0, 4, 0, 8, 0, -6, 0, 6, 0, -4, 0, 0, 0, -2, 0, -2, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, -8, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, -1, 0], 'euler47': [1, -6, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -10, 59], 'euler61': [1, 4, 61], 'euler67': [1, -4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 8, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -2, 7], [1, 2, 11], [1, 2, 13], [1, -8, 17], [1, 2, 19], [1, -6, 23], [1, -6, 29], [1, 0, 31], [1, 10, 37], [1, -2, 41], [1, -1, 0], [1, -6, 47], [1, 2, 53], [1, -10, 59], [1, 4, 61], [1, -4, 67], [1, 0, 71], [1, 8, 73], [1, 8, 79], [1, -4, 83], [1, -6, 89], [1, 2, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/41280/bk'], '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': '2-41280-1.1-c1-0-19', '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': '2-41280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.15550769171288, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1301228459584044992, 'z1': {'__RealLiteral__': 0, 'data': '0.6412987206949875', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1301228459584044992', 'Lhash_array': ['1301228459584044992'], 'factors': ['2-41280-1.1-c1-0-19'], 'label': '2-41280-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/41280/bk'}