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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '401954531116927126', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 160.97841047490132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '20160.1', 'coefficient_field': '1.1.1.1', 'conductor': 20160, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, 1], [1, 4, 11], [1, 2, 13], [1, -2, 17], [1, 0, 19], [1, -4, 23], [1, -2, 29], [1, -8, 31], [1, 10, 37], [1, 2, 41], [1, 4, 43], [1, 4, 47], [1, -10, 53], [1, -4, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, 6, 73], [1, -8, 79], [1, 4, 83], [1, -6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 74, 'label': '2-20160-1.1-c1-0-74', 'leading_term': '4.1034821129', '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/20160/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9468575027884054, 1.411339505435231, 0.9625791101441052, -0.4738987218894358, -2.297848854260875, -3.381468746612962, -2.82483689354281, -0.8144822761550707, 1.275142063466465, 1.916281691919086, 0.8538717566395002, -0.5065473761793561, -0.4192729197987285, 1.296199788706549, 2.844662979646501, 2.293939772763391, -0.158402303381661, -2.183815485190383, -1.918947438835704, -0.2471101360052269, 0.1878683691477676, -1.656042032558736, -3.644178604105299, -2.992673477064919, 0.05502215899027178, 2.27042176117824, 1.47540986753973, -0.6500410358731153, -0.9115271747728407, 0.9727728979158924, 2.081854432056609, 0.6833432303619406, -1.052068451386308, -0.2451138840357951, 2.107342731159882, 2.211401363646138, -0.9313318879633089, -3.713268798336771, -2.96230022638363, -0.4617198396426228, -0.0008688012522745947, -1.420738216938902, -1.024713382744527, 2.168352626089557, 4.374566443336308, 2.80503417311863, 0.1269498692255904, 0.2484149418010404, 2.127943533782245, 1.782815586873717, -0.8251482873240108, -1.687637036606589, 0.2374029702572158, 0.960733935161847, -1.671213100679049, -3.774432599575581, -1.58757827214206, 2.048380853491771, 2.075440236576039, -0.6999957262631998, -1.473490145264675, 0.2390792687767207, 0.4199684610646352, -1.589280173034209, -1.752640242601737, 0.8862373760509011, 1.807483102469813, -0.9346559724107546, -2.707189933154485, -0.2944307514993148, 2.123460311237106, 0.1480017797386242, -3.076080772640405, -2.48422302533064, 0.153438357680548, 0.1422818740684297, -1.352677247981474, -0.2360277722104823, 1.868451374267895, 0.3474978330991938, -3.175639185059218, -3.149030378244111, -0.1688420872536297, 0.3637606002022477, -1.332688324106367, -0.03400932299842516, 3.750478910881507, 3.838720154754636, -0.2421497988070344, -2.170166241370677, -0.2086699595370452, 0.6155757524501503, -1.001811912593432, -0.5765798602390548, 2.179684502575431, 2.142631038890354, -0.7237260121979473, -0.6639980122848937, 2.433044618126475, 2.298987084111405, -1.471214864020532, -2.282239988100046, 0.8689208796900415, 1.787157911799169, -0.6955178436791365, -1.246012993524997, 0.4537876380750194, -0.6376976164118807, -3.55269068526253, -2.45898528244349, 1.343560850157386, 1.491946936989535, -0.9295976202516901, 0.02788568986068769, 2.860921165524835, 2.046195158984611, -0.2270339008072823, 1.09468111938225, 2.727856211002267, -0.2881532232208968], 'positive_zeros': ['0.9310352554922978', '2.087703396369281', '2.889981345425118', '3.328753162675835', '4.235388360984413', '5.046407976633177', '5.295041582688088', '6.245768861278075', '6.914924179888457', '7.385965758122611', '8.078439411552757', '8.527437784100698', '9.188092288351481', '10.07642635297247', '10.24977571290394', '10.84539179950388', '11.77142089889209', '11.95730891434205', '12.67207867107638', '13.22299607366886', '13.61908667132711', '14.34781121407570', '14.93545961581922', '15.46511113013627', '15.81254717380869', '16.42274787089865', '16.93048763490580', '17.52083850664871', '18.00997431057395', '18.72983248679441', '19.02218687071988', '19.52334922295836'], 'prelabel': '2-20160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.68772676545729, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 401954531116927126, 'z1': {'__RealLiteral__': 0, 'data': '0.9310352554922978', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.087703396369281', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.889981345425118', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 160.97841047490132, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 20160, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -4, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, 0, 8, 0, 0, 0, 1, 0, -10, 0, 0, 0, -2, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, 10, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 4, 0, 8, 0, 0, 0, -4, 0, -2, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 4, 11], [1, 2, 13], [1, -2, 17], [1, 0, 19], [1, -4, 23], [1, -2, 29], [1, -8, 31], [1, 10, 37], [1, 2, 41], [1, 4, 43], [1, 4, 47], [1, -10, 53], [1, -4, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, 6, 73], [1, -8, 79], [1, 4, 83], [1, -6, 89], [1, -10, 97]], 'index': 74, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/20160/g'], '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': '2-20160-1.1-c1-0-74', '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': '2-20160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.68772676545729, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 401954531116927126, 'z1': {'__RealLiteral__': 0, 'data': '0.9310352554922978', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '401954531116927126', 'Lhash_array': ['401954531116927126'], 'label': '2-20160-1.1-c1-0-74', 'type': 'ECQ', 'url': 'EllipticCurve/Q/20160/g'}