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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '175945582661496720', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 118.05083434826098, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '14784.1', 'coefficient_field': '1.1.1.1', 'conductor': 14784, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, 1], [1, -1], [1, -6, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, 2, 29], [1, -8, 31], [1, 6, 37], [1, 2, 41], [1, -8, 43], [1, -4, 47], [1, 2, 53], [1, 12, 59], [1, 10, 61], [1, 12, 67], [1, -12, 71], [1, -10, 73], [1, -8, 79], [1, -12, 83], [1, -10, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 35, 'label': '2-14784-1.1-c1-0-35', 'leading_term': '3.36007277445', '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/14784/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7798273822029163, 1.189124836020845, 0.8853480117872456, -0.2057989315433844, -1.608318150451933, -2.35831326906398, -1.590805538587258, 0.6644523516759283, 3.180502531015568, 4.230735832302367, 2.954931944645889, 0.2454939470895521, -1.849336492948383, -1.911113158233985, -0.4896219228107273, 0.4847089883047645, -0.1891685006953, -1.557452257940171, -1.512689027092247, 0.6846505711372424, 3.255038192030373, 3.712104191103077, 1.723910940229592, -0.4525887653105375, -0.7110516109875157, 0.2940726899543178, 0.1074662975139705, -2.049085091929475, -3.89360813245093, -2.960116154652116, -0.1116567343022041, 1.253282856703875, -0.3658383979374452, -2.468504992125413, -1.999229063262846, 0.1743383244525586, 0.200227660268725, -3.293538262201149, -6.805882209883342, -6.334824881922227, -2.616971407850017, 0.1258726253260517, 0.02695601407128762, -0.5036217806635118, 0.7591243468654745, 2.238262736976431, 1.433174259172411, -0.5776514396312864, -0.635172040471492, 1.195013243976728, 1.404849570704808, -1.168578639767913, -2.957435372744079, -1.290864951739254, 0.6570011768862422, -1.749191907286689, -7.01704372201205, -8.89283372195275, -5.237529634993353, -0.8517012247940888, -0.04909368759249022, -0.9374248303466738, 0.002164999512914908, 1.601881030987895, 0.6995088642857958, -1.532202978182742, -1.296660426295602, 0.9560496379828329, 1.052071462062191, -1.374535617724554, -1.739929782764095, 1.594130564892601, 4.051202117325419, 2.307837300230493, -0.3550196478848486, -0.16795350094086, 0.6318801432898877, -1.304328586185459, -3.315983539480177, -1.090563421277556, 2.885023334812943, 2.647967956721699, -1.165573113068065, -2.453348071625623, -0.3407748582252053, -0.3885704246764986, -4.180093225987105, -6.148776796528401, -3.250594867407, 0.1170217737868618, 0.2216682961132847, -0.4103745265066435, 0.6195392387252961, 0.8753361506933551, -0.800291558339657, -0.6720259959663536, 2.393405341472656, 3.069366481253146, -1.170132323598975, -4.312449113416321, -1.743255844239649, 1.548442798058193, 0.05929468106146435, -2.359611078224969, -0.1951142153200903, 3.11665882875397, 1.641688637285819, -2.093957308044107, -2.203390200603875, 0.0070733055193633, 0.01655859905149071, -0.7756539553385327, 0.8186819242810883, 2.056489524590383, -0.1576774826996489, -1.846566494463185, 0.8494851821120099, 3.493092339310149, 1.359657917955449, -1.513954990059569], 'positive_zeros': ['0.9618170965035186', '1.936451465172219', '3.022528499874497', '3.837141043925026', '4.213204824490428', '4.937945076651696', '5.931942291099760', '6.423527265282056', '6.769005646706982', '7.760591591714704', '8.212765872368441', '8.976228884313233', '9.273385437864477', '10.47688704600195', '10.75738902494129', '11.14005958841486', '11.91809664617286', '12.34485926986902', '12.90295052954974', '13.62361771807136', '13.88416657606029', '15.11921488883406', '15.23297130880236', '15.74971236864546', '16.32319535807932', '16.89166686333723', '17.36655075342033', '17.89835070273295', '18.69946109148374', '19.03156580306108', '19.37434912802491'], 'prelabel': '2-14784-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.865120079790236, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 175945582661496720, 'z1': {'__RealLiteral__': 0, 'data': '0.9618170965035186', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.936451465172219', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.022528499874497', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 118.05083434826098, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 14784, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, -1, 0, 1, 0, 1, 0, 6, 0, 2, 0, -2, 0, -8, 0, 1, 0, 4, 0, -1, 0, -1, 0, -2, 0, 8, 0, -1, 0, 2, 0, -6, 0, -6, 0, -2, 0, 8, 0, -2, 0, 4, 0, 1, 0, 2, 0, -2, 0, -2, 0, 8, 0, -12, 0, -10, 0, -1, 0, -12, 0, -12, 0, -4, 0, 12, 0, 10, 0, 1, 0, -1, 0, 8, 0, 1, 0, 12, 0, 4, 0, 2, 0, 10, 0, -6, 0, -8, 0, 16, 0, -14, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, -4, 47], 'euler5': [1, 2, 5], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 12, 67], 'euler7': [1, 1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -10, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, 1, 0], [1, -1, 0], [1, -6, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, 2, 29], [1, -8, 31], [1, 6, 37], [1, 2, 41], [1, -8, 43], [1, -4, 47], [1, 2, 53], [1, 12, 59], [1, 10, 61], [1, 12, 67], [1, -12, 71], [1, -10, 73], [1, -8, 79], [1, -12, 83], [1, -10, 89], [1, 14, 97]], 'index': 35, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/14784/f'], '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': '2-14784-1.1-c1-0-35', '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': '2-14784-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.865120079790236, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 175945582661496720, 'z1': {'__RealLiteral__': 0, 'data': '0.9618170965035186', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '175945582661496720', 'Lhash_array': ['175945582661496720'], 'label': '2-14784-1.1-c1-0-35', 'type': 'ECQ', 'url': 'EllipticCurve/Q/14784/f'}