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lfunc_lfunctions • Show schema
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{'A10': 12, 'A2': -2, 'A3': 2, 'A4': 3, 'A5': -6, 'A6': -4, 'A7': -2, 'A8': -4, 'A9': -3, 'Lhash': '1833436193401394957', 'a10': [0.12371134020618557, 0.0], 'a2': [-0.020618556701030927, 0.0], 'a3': [0.020618556701030927, 0.0], 'a4': [0.030927835051546393, 0.0], 'a5': [-0.061855670103092786, 0.0], 'a6': [-0.041237113402061855, 0.0], 'a7': [-0.020618556701030927, 0.0], 'a8': [-0.041237113402061855, 0.0], 'a9': [-0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 0.04310234611201031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 2, 1]], [13, [1, -2, 1]]], 'bad_primes': [2, 13], 'central_character': '676.1', 'coefficient_field': '1.1.1.1', 'conductor': 676, 'conductor_radical': 26, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -2, 7, -6, 9], [1, 6, 19, 30, 25], [1, 2, 15, 14, 49], [1, -12, 58, -132, 121], [1, -2, 1], [1, 6, 43, 102, 289], [1, -4, 42, -76, 361], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 14, 123, 518, 1369], [1, 0, 82, 0, 1681], [1, 2, 87, 86, 1849], [1, -6, 103, -282, 2209], [1, 0, 106, 0, 2809], [1, 12, 154, 708, 3481], [1, -16, 186, -976, 3721], [1, -28, 330, -1876, 4489], [1, 6, 151, 426, 5041], [1, -4, 150, -292, 5329], [1, -16, 222, -1264, 6241], [1, -24, 310, -1992, 6889], [1, 12, 214, 1068, 7921], [1, 20, 294, 1940, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 3, 'label': '4-26e2-1.1-c1e2-0-3', 'leading_term': '0.265819283342', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'Genus2Curve/Q/676/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.2658192833423089, 0.2771498032627012, 0.3118282927349164, 0.3717873224949016, 0.459801577921884, 0.5787606434532505, 0.7305652670060486, 0.9146319499618518, 1.126085289941597, 1.353875575721451, 1.57926992725179, 1.775390184101593, 1.908635768733991, 1.942827247378487, 1.846613294272409, 1.604001684638399, 1.226789291128903, 0.7663129347359312, 0.3206562659586048, 0.03275080216100128, 0.0753146208562211, 0.6207768998014495, 1.798338016847849, 3.645535658810493, 6.066743751977135, 8.813897511100034, 11.50329756897498, 13.67527613284702, 14.89124808938444, 14.84804002285279, 13.47737500947808, 10.99479354440914, 7.871401568374557, 4.723858469014434, 2.147459249854066, 0.5434356868993795, 0.002392801291513794, 0.2925420472119258, 0.9646638160169472, 1.537633563104536, 1.689536666493036, 1.370588402970123, 0.785002858843616, 0.2503436635776644, 0.007011384233594601, 0.08258280260762493, 0.2924002890476142, 0.3837042575876836, 0.2417285998689409, 0.02483100549369891, 0.1212352255115113, 0.9205562450887111, 2.517903147633026, 4.5391183065772, 6.233885036959259, 6.833641011601382, 5.992829388447458, 4.041332446898883, 1.853530893651327, 0.3654003791696578, 0.01670072090652038, 0.4910945788887805, 0.9756605986659573, 0.8237565421776095, 0.1900386901340576, 0.1476658095269976, 2.087652077645102, 6.692663548422961, 13.14870779020868, 19.21398273255919, 22.26449485947847, 20.76986351273978, 15.27776585702667, 8.212980551157537, 2.536920844798127, 0.08716492098005484, 0.6679510980654081, 2.470488041358855, 3.481885520642331, 2.853500754007991, 1.265540867051449, 0.1112128300397576, 0.2323549288852456, 1.253530030622157, 2.025437332496616, 1.737060986365563, 0.686110705189526, 0.005329478477261667, 0.5796009280060164, 2.141293614885366, 3.411699406646868, 3.230269995637155, 1.686226461681421, 0.194491447547763, 0.3594570103600763, 2.57050636221878, 5.567032984082307, 7.3885127156477, 6.902611889386641, 4.598129138608911, 2.016077490843522, 0.4298840932396546, 0.002294770053959455, 0.07218259186399988, 0.06815669131132052, 0.0001023110284613503, 0.09631456773300143, 0.2332742013481744, 0.09783768919176852, 0.09535911451794284, 1.849891208660337, 7.181555078566205, 15.9805507771873, 24.98255564024049, 29.21681127267465, 25.59986989187727, 15.78695566595659, 5.472394818853181, 0.2440504548217196, 1.350122986809713, 5.123353879407224, 6.634583423813935, 4.232806247896867, 0.7626864831024893, 0.4187909716914665, 4.399674764527712, 9.627512336718475, 11.69191220901444, 8.987814493189282, 3.968534426709348, 0.501773610500505, 0.2361941992623239, 1.615397487076109, 2.147736766552764, 1.155864527697214, 0.07934972548548697, 0.3852089263719927, 1.750841891351379, 2.566774936032784, 1.926522576198588, 0.6127893311203771, 0.0003670088171672523, 0.3901187701602461, 0.8545999999803757, 0.6269987534759456, 0.09432650029982802, 0.09440498992529422, 0.5872044628957958, 0.6855115432287552, 0.1507650105168513, 0.2194541157054112, 2.204567476721859, 5.32819907405314, 6.80825413992182, 4.832027073186287, 1.214671823526647, 0.1841004158904875, 3.970114077117476, 9.97203472135931, 13.01602147878525, 10.53512742936867], 'positive_zeros': [3.640287616260134, 3.640287616260134, 6.764231323278578, 6.764231323278578, 8.289125051595985, 8.289125051595985, 9.25208611998247, 9.25208611998247, 11.21486999262722, 11.21486999262722, 12.10810868275674, 12.10810868275674, 14.10812305484995, 14.10812305484995, 15.26212233610873, 15.26212233610873, 16.32893427071431, 16.32893427071431, 17.51877200404443, 17.51877200404443, 19.14446932223225, 19.14446932223225, 19.69339975173152, 19.69339975173152], 'prelabel': '4-26e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.45564355065701206, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'E_1', 'trace_hash': 1833436193401394957, 'z1': {'__RealLiteral__': 0, 'data': '3.64028761626', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.64028761626', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.76423132328', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04310234611201031, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 676, 'conductor_radical': 26, 'degree': 4, 'dirichlet_coefficients': [1, -2, 2, 3, -6, -4, -2, -4, -3, 12, 12, 6, 2, 4, -12, 5, -6, 6, 4, -18, -4, -24, 0, -8, 17, -4, -14, -6, 12, 24, -8, -6, 24, 12, 12, -9, -14, -8, 4, 24, 0, 8, -2, 36, 18, 0, 6, 10, -11, -34, -12, 6, 0, 28, -72, 8, 8, -24, -12, -36, 16, 16, 6, 7, -12, -48, 28, -18, 0, -24, -6, 12, 4, 28, 34, 12, -24, -8, 16, -30, -4, 0, 24, -12, 36, 4, 24, -48, -12, -36, -4, 0, -16, -12, -24, -12, -20, 22, -36, 51], 'euler11': [1, -12, 58, -132, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, -2, 7, -6, 9], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, -6, 103, -282, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, -28, 330, -1876, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 6, 151, 426, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -2, 7, -6, 9], [1, 6, 19, 30, 25], [1, 2, 15, 14, 49], [1, -12, 58, -132, 121], [1, -2, 1, 0, 0], [1, 6, 43, 102, 289], [1, -4, 42, -76, 361], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 14, 123, 518, 1369], [1, 0, 82, 0, 1681], [1, 2, 87, 86, 1849], [1, -6, 103, -282, 2209], [1, 0, 106, 0, 2809], [1, 12, 154, 708, 3481], [1, -16, 186, -976, 3721], [1, -28, 330, -1876, 4489], [1, 6, 151, 426, 5041], [1, -4, 150, -292, 5329], [1, -16, 222, -1264, 6241], [1, -24, 310, -1992, 6889], [1, 12, 214, 1068, 7921], [1, 20, 294, 1940, 9409]], 'index': 3, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/676/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-26e2-1.1-c1e2-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-26e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.45564355065701206, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1833436193401394957, 'z1': {'__RealLiteral__': 0, 'data': '3.64028761626', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9953326
{'Lhash': '1833436193401394957', 'Lhash_array': ['1833436193401394957'], 'label': '4-26e2-1.1-c1e2-0-3', 'type': 'ECQP', 'url': 'EllipticCurve/Q/26/a|EllipticCurve/Q/26/a'}
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id: 1222943
{'Lhash': '1833436193401394957', 'Lhash_array': ['1833436193401394957'], 'label': '4-26e2-1.1-c1e2-0-3', 'type': 'G2Q', 'url': 'Genus2Curve/Q/676/b'}