-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 2, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 0, 'Lhash': '1364327355159836413036511430084', 'a10': [0.632455532033676, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.526816734072593, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1, -2, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '259200.1', 'coefficient_field': '1.1.1.1', 'conductor': 259200, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1], [1], [1, -2, 5], [1, 0, -6, 0, 49], [1, 0, 10, 0, 121], [1, -2, 26, -26, 169], [1, 0, -18, 0, 289], [1, 0, 34, 0, 361], [1, 0, 2, 0, 529], [1, 0, 18, 0, 841], [1, -4, 62, -124, 961], [1, 6, 58, 222, 1369], [1, 2, 58, 82, 1681], [1, -4, 54, -172, 1849], [1, 0, -34, 0, 2209], [1, -4, 94, -212, 2809], [1, 0, -62, 0, 3481], [1, 0, -10, 0, 3721], [1, -20, 218, -1340, 4489], [1, -8, 58, -568, 5041], [1, 0, 34, 0, 5329], [1, -8, 30, -632, 6241], [1, 0, 150, 0, 6889], [1, 2, 98, 178, 7921], [1, 0, 62, 0, 9409], [1, 0, -46, 0, 10201], [1, 0, 74, 0, 10609], [1, 4, 214, 428, 11449], [1, 0, -34, 0, 11881], [1, 0, -74, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 36, 'label': '4-259200-1.1-c1e2-0-36', 'leading_term': '3.45531477163', 'load_key': 'Costa', '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': 'EllipticCurve/2.2.40.1/162.1/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.052734375', 'prec': 37}, 'plot_values': [3.4553147716290495, 3.4519959522681956, 3.441750527874196, 3.423723422369233, 3.3965288232876496, 3.3583087972383456, 3.306814559123106, 3.2395094222661243, 3.153691938905082, 3.046637073738284, 2.9157524370072583, 2.7587456550303004, 2.57379791100633, 2.359737601930125, 2.116207000977699, 1.843813876362706, 1.5442592963704067, 1.2204324508799897, 0.8764633461142994, 0.5177247766288227, 0.15077612393416384, -0.21675667508780203, -0.5763681903982055, -0.9189277028281716, -1.2349970192968436, -1.5152043087288674, -1.7506620794088388, -1.933413141061671, -2.056884411940356, -2.1163250556952993, -2.1092029901496727, -2.035532616147288, -1.8981069506347332, -1.702609433898082, -1.4575846478649384, -1.1742530489887975, -0.8661624705382973, -0.5486783236522029, -0.23832471228579813, 0.0480004811817047, 0.29390276436745083, 0.48441685648743465, 0.6069294454127975, 0.6520415596234813, 0.6143108770098223, 0.4928157697344466, 0.2914885774007225, 0.019175622617411223, -0.31060436776144695, -0.6802140394109016, -1.0687535610448617, -1.4531874110816232, -1.8096881397798936, -2.1151231701901705, -2.3485937995668915, -2.492923700708336, -2.5359888590283144, -2.471783122994552, -2.301124013292124, -2.0319221534886447, -1.6789640068082468, -1.2631901918899042, -0.8104885081552808, -0.35005936802912757, 0.08755135937893377, 0.47262420559472235, 0.7784894250104192, 0.983633510154496, 1.073518074173738, 1.0419515082842954, 0.8918790815657551, 0.6354954783318436, 0.29363297667655236, -0.10556478136110634, -0.528613498529657, -0.9391752407904838, -1.3008823411387298, -1.5802795567439887, -1.7496430824531761, -1.7894319614083587, -1.6901457916038556, -1.4534022841483958, -1.0921070755315787, -0.6296621650417199, -0.09824263718508477, 0.4637431874909282, 1.0148152192422726, 1.5139434983517936, 1.9241238632509605, 2.2156816765367853, 2.3689887820317312, 2.3763204880093913, 2.242649554074362, 1.985267732318066, 1.6322345128871152, 1.2197673903597235, 0.7887970106977449, 0.3810026223856577, 0.03470798129822933, -0.21895296088046465, -0.35920266201279544, -0.3777740786716227, -0.2797990450407399, -0.08330038061014924, 0.18270045105781624, 0.48130027428834565, 0.771757773227819, 1.014053102779892, 1.1734794270222018, 1.2247581664424567, 1.15520049052327, 0.9665229279568093, 0.6750584998919593, 0.3102743277359325, -0.08830478085427439, -0.47547993793781473, -0.8056174181669341, -1.0381700144048172, -1.142844310101505, -1.1037850762514982, -0.9222288594351452, -0.6172282276963553, -0.2242528865535604, 0.20828653179885107, 0.6242976651728193, 0.9665253981737997, 1.1836263775170768, 1.2369859544196744, 1.106445119691926, 0.7941831188870004, 0.32617384417602274, -0.24911377315598524, -0.8647942969593262, -1.442117721451532, -1.8988770214439286, -2.158795704275521, -2.1608504637367667, -1.867428888368106, -1.2702946209863462, -0.39353131951372067, 0.7070541663840507, 1.9482004799293573, 3.226837507634763, 4.430400219249887, 5.448749594542689, 6.186395544700002, 6.573615807233455, 6.575126761097521, 6.19518791813641, 5.478392485175949, 4.50587413431736, 3.3871921807702137, 2.2486816317963165, 1.2195068089407803, 0.41697899475671685, -0.06715530978489664, -0.17780389829770654, 0.09639770197836837, 0.7209855577702394, 1.6189263868502226, 2.67898634505447, 3.768331821877954, 4.747944449062725, 5.489050568721557, 5.888594788909669, 5.88185644345959, 5.4506158354066105, 4.6257926976512, 3.4841433809787614, 2.139335889808956, 0.7284316042863572, -0.604602045989244, -1.7263220168811684, -2.5300060516366956, -2.948562949970746, -2.9624962982895138, -2.6018747702550318, -1.942022200188315, -1.093450709847891, -0.18731452775895727, 0.6417401565502205, 1.2730953863749739, 1.6157506879047916, 1.6199191615330149, 1.2830861798047335, 0.6497185334176376, -0.19533763096620266, -1.1388766938347028, -2.055135169930342, -2.8232123511753007, -3.3437128038422443, -3.5523080740480286, -3.428330322856105, -2.99719358477651, -2.326297121925106, -1.5149816451616618, -0.679954386582162, 0.061747739674190706, 0.6098220923050391, 0.8953350599179042, 0.8908018599691683, 0.6142257713031604, 0.1264730447787795, -0.4776782422444383, -1.0835531255687252, -1.5736453019572225, -1.8452543368136556, -1.826107217246677, -1.4856469310328808, -0.8402847064426133, 0.048215294386487105, 1.0810450546233241, 2.136191089121785, 3.085808594640763, 3.8145958759931697, 4.2364632625105, 4.307022157798966, 4.03002318219827, 3.456761290764506, 2.6785096675419275, 1.8130872586925941, 0.9875492342257621, 0.3195797988227732, -0.0996298419832424, -0.2184533162918321, -0.031894801778015736, 0.4183971047995975, 1.0511395137474244, 1.7583488914833967, 2.422191884196946, 2.933149222171339, 3.206693541311467, 3.1959218680179773, 2.8982226483501274, 2.354996629521229, 1.6445434954417044, 0.869299481962227, 0.13949475747775777, -0.44414808089261537, -0.8059204593083544, -0.9063945587338446, -0.7477073616289287, -0.3720998352080543, 0.14595046850082644, 0.7126247814549032, 1.2304984664783758, 1.6144835362546355, 1.8053391805422332, 1.7785445661294779, 1.5471292184114296, 1.1580906422188597, 0.6831219991289248, 0.2053390064633611, -0.19563062401658907, -0.45756666739869767, -0.5461474778346674, -0.4601923192915124], 'positive_zeros': ['1.07626451240917742437642025844485', '2.04734299350582736873840896655355', '2.48182597387038766900016225743945', '3.36404350310135243902152774264492', '3.83614887703557357904574380588062', '4.43900568871848024480247765675781', '5.17409208128022102155370988850139', '5.44935345913756341642855777772643', '6.00012058811656471583127714834203', '6.46111627855734693606423617190761', '6.88620236694935056345201968294954', '7.35000497730763797828421881048065', '8.163415009957602753855022303874763', '8.267121893852668072322600252326832', '8.992923436792907318404480712482634'], 'prelabel': '4-259200-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0162635675872824, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 181412337393931855, 'z1': {'__RealLiteral__': 0, 'data': '1.07626451240917742437642025844485', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.04734299350582736873840896655355', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.48182597387038766900016225743945', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 16.526816734072593, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 259200, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, -6, 0, 0, 2, -2, 0, 4, 0, 0, 0, 0, 0, 6, -1, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 1, 4, 0, 20, 0, 0, 0, 8, 0, 0, -6, 0, 0, 0, 0, 8, 2, 0, -2, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -1], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -2, 26, -26, 169], 'euler17': [1, 0, -18, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, 0, 18, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 62, -124, 961], 'euler37': [1, 6, 58, 222, 1369], 'euler41': [1, 2, 58, 82, 1681], 'euler43': [1, -4, 54, -172, 1849], 'euler47': [1, 0, -34, 0, 2209], 'euler5': [1, -2, 5, 0, 0], 'euler53': [1, -4, 94, -212, 2809], 'euler59': [1, 0, -62, 0, 3481], 'euler61': [1, 0, -10, 0, 3721], 'euler67': [1, -20, 218, -1340, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, -8, 58, -568, 5041], 'euler73': [1, 0, 34, 0, 5329], 'euler79': [1, -8, 30, -632, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 2, 98, 178, 7921], 'euler97': [1, 0, 62, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 5, 0, 0], [1, 0, -6, 0, 49], [1, 0, 10, 0, 121], [1, -2, 26, -26, 169], [1, 0, -18, 0, 289], [1, 0, 34, 0, 361], [1, 0, 2, 0, 529], [1, 0, 18, 0, 841], [1, -4, 62, -124, 961], [1, 6, 58, 222, 1369], [1, 2, 58, 82, 1681], [1, -4, 54, -172, 1849], [1, 0, -34, 0, 2209], [1, -4, 94, -212, 2809], [1, 0, -62, 0, 3481], [1, 0, -10, 0, 3721], [1, -20, 218, -1340, 4489], [1, -8, 58, -568, 5041], [1, 0, 34, 0, 5329], [1, -8, 30, -632, 6241], [1, 0, 150, 0, 6889], [1, 2, 98, 178, 7921], [1, 0, 62, 0, 9409]], 'index': 36, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.40.1/162.1/j', 'EllipticCurve/2.2.40.1/162.1/i', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-162.1-i', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-162.1-j'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-259200-1.1-c1e2-0-36', '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': '4-259200-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0162635675872824, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 181412337393931855, 'z1': {'__RealLiteral__': 0, 'data': '1.07626451240917742437642025844485', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9494728
{'Lhash': '1364327355159836413036511430084', 'Lhash_array': ['1364327355159836413036511430084'], 'label': '4-259200-1.1-c1e2-0-36', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-162.1-j'}
-
id: 9494727
{'Lhash': '1364327355159836413036511430084', 'Lhash_array': ['1364327355159836413036511430084'], 'label': '4-259200-1.1-c1e2-0-36', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-162.1-i'}
-
id: 9494258
{'Lhash': '1364327355159836413036511430084', 'Lhash_array': ['1364327355159836413036511430084'], 'label': '4-259200-1.1-c1e2-0-36', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/162.1/i'}
-
id: 9494240
{'Lhash': '1364327355159836413036511430084', 'Lhash_array': ['1364327355159836413036511430084'], 'label': '4-259200-1.1-c1e2-0-36', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/162.1/j'}