-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2865241038952520031804806977877,4890280842231648066956575677202', 'a10': 0, 'a2': 0, 'a3': 10, 'a4': -8, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 73, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0051858213714984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 8]], [3, [1, -10, 27]]], 'bad_primes': [2, 3], 'central_character': '24.1', 'coefficient_field': '1.1.1.1', 'conductor': 576, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 0, 8], [1, -10, 27], [1, 0, 250, 0, 15625], [1, 0, -686, 0, 117649], [1, 0, 2338, 0, 1771561], [1, 0, -4394, 0, 4826809], [1, 0, 1726, 0, 24137569], [1, 212, 24954, 1454108, 47045881], [1, 0, 24334, 0, 148035889], [1, 0, 48778, 0, 594823321], [1, 0, -59582, 0, 887503681], [1, 0, -101306, 0, 2565726409], [1, 0, -134642, 0, 4750104241], [1, -580, 243114, -46114060, 6321363049], [1, 0, 207646, 0, 10779215329], [1, 0, 297754, 0, 22164361129], [1, 0, -304958, 0, 42180533641], [1, 0, -453962, 0, 51520374361], [1, 140, 606426, 42106820, 90458382169], [1, 0, 715822, 0, 128100283921], [1, 860, 962934, 334554620, 151334226289], [1, 0, -986078, 0, 243087455521], [1, 0, -678926, 0, 326940373369], [1, 0, 357262, 0, 496981290961], [1, -3820, 5473446, -3486410860, 832972004929], [1, 0, 2060602, 0, 1061520150601], [1, 0, -2185454, 0, 1194052296529], [1, 0, -474014, 0, 1500730351849], [1, 0, -2590058, 0, 1677100110841], [1, 0, 2812894, 0, 2081951752609]], 'euler_factors_factorization': [[[[1, 0, 8], 1]], [[[1, -10, 27], 1]], [[[1, 0, 125], 2]], [[[1, 0, -343], 2]], [[[1, -18, 1331], 1], [[1, 18, 1331], 1]], [[[1, 0, -2197], 2]], [[[1, -90, 4913], 1], [[1, 90, 4913], 1]], [[[1, 106, 6859], 2]], [[[1, 0, 12167], 2]], [[[1, 0, 24389], 2]], [[[1, 0, -29791], 2]], [[[1, 0, -50653], 2]], [[[1, -522, 68921], 1], [[1, 522, 68921], 1]], [[[1, -290, 79507], 2]], [[[1, 0, 103823], 2]], [[[1, 0, 148877], 2]], [[[1, -846, 205379], 1], [[1, 846, 205379], 1]], [[[1, 0, -226981], 2]], [[[1, 70, 300763], 2]], [[[1, 0, 357911], 2]], [[[1, 430, 389017], 2]], [[[1, 0, -493039], 2]], [[[1, -1350, 571787], 1], [[1, 1350, 571787], 1]], [[[1, -1026, 704969], 1], [[1, 1026, 704969], 1]], [[[1, -1910, 912673], 2]], [[[1, 0, 1030301], 2]], [[[1, 0, -1092727], 2]], [[[1, -1710, 1225043], 1], [[1, 1710, 1225043], 1]], [[[1, 0, -1295029], 2]], [[[1, -270, 1442897], 1], [[1, 270, 1442897], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-24e2-1.1-c3e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/24/4/f/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.087890625', 'prec': 37}, 'plot_values': [1.7610306586150342, 1.7623734982515804, 1.7635384309420516, 1.7661899810975141, 1.7697738018017328, 1.7732379230779876, 1.7758795687374571, 1.7769749809693718, 1.7754741013335407, 1.770185498344052, 1.7598064882258078, 1.7429530511221505, 1.7181325506064864, 1.6838106595228919, 1.6384434613540377, 1.5805280477621741, 1.5086714949057933, 1.4216345506632109, 1.3184491025921152, 1.1984421263384777, 1.0613971006933136, 0.9075455281560446, 0.7377615220645575, 0.5535030158054546, 0.35701705797537975, 0.15121183397330154, -0.06016052986818971, -0.2727169233794387, -0.4813237768668174, -0.6804011823144536, -0.8639077105275644, -1.0257248767184937, -1.1597759220590738, -1.2604560817389416, -1.3228898833203837, -1.3433455915381065, -1.3195976063813495, -1.2512394172365648, -1.1400727256112932, -0.9902212561600994, -0.8084276015624622, -0.6038801952201984, -0.38827815389102327, -0.17532326852911762, 0.019571359368472645, 0.1801019210863925, 0.2897824713021302, 0.33296295477669435, 0.29590524927277095, 0.16778920958077514, -0.058034537744952965, -0.38332454757575984, -0.8038450591757724, -1.3092064121421587, -1.8823172399634394, -2.4999697616449432, -3.133229671877817, -3.748765980098855, -4.310400363435271, -4.78093128698542, -5.124775766971074, -5.309788455647628, -5.310569421300557, -5.1096224043601515, -4.700577639750653, -4.0880604141312595, -3.28991595827108, -2.3354225505199406, -1.2657128307401957, -0.13044370126928265, 1.0139800613324226, 2.1085877489824116, 3.0955701633195343, 3.922133425874504, 4.545248836319424, 4.933815740797371, 5.073037579989983, 4.9638091859934566, 4.625302437272185, 4.0912419987980755, 3.409812721715724, 2.6375222140655454, 1.836509928878078, 1.0676607035464416, 0.3864746354801304, -0.16242077592570764, -0.5489405249083783, -0.7597845044658152, -0.7997382616842253, -0.6899311577200844, -0.4657133211822855, -0.17176955183693787, 0.14301659424318988, 0.43132748716098346, 0.653674855361205, 0.7821832002243546, 0.8053417890391673, 0.727597912440583, 0.5704371297397919, 0.36735807024934947, 0.16080828151954177, -0.0056784154685655865, -0.09293338153025196, -0.07348411582641196, 0.06403813736042897, 0.31151314829198934, 0.6414897092595578, 1.0093855713712683, 1.3598653241903147, 1.6333238535995702, 1.7769482258325908, 1.7514904944025131, 1.5424817214003614, 1.1624022964888794, 0.6564512113651008, 0.09695166831290734, -0.42003871776380075, -0.7873946974509519, -0.8987989273157172, -0.6636297846101529, -0.021715630267814538, 1.0465222167296513, 2.510860385917211, 4.291301171921193, 6.261560564357744, 8.259720272913341, 10.106194511036206, 11.61933480319608, 12.642503780071713, 13.055056272977613, 12.797906271944983, 11.87128161081339, 10.347979720943675, 8.355374837223298, 6.0710807635792206, 3.6951300916211256, 1.4314447788173026, -0.5376460682753501, -2.0735457963759614, -3.092195553677556, -3.577778668081707, -3.573178394220644, -3.178612316507426, -2.52635174871979, -1.7670066877161754, -1.041291466767528, -0.4644093805664051, -0.10877897150266592, 0.0018387429281422722, -0.10835152447197581, -0.3763385744993151, -0.7149655212955429, -1.0323887214169507, -1.2483873044966238, -1.3122824103911845, -1.2083188775175124, -0.9610406392864803, -0.6252975718174507, -0.27669986866636825, 0.007027408298345831, 0.1621577308171641, 0.15306675275073472, -0.01860461294355309, -0.3144960699152405, -0.6661698380719318, -0.989516039076889, -1.2042134175438144, -1.2501548253303754, -1.106078661444613, -0.7934199206103153, -0.37940029635045935, 0.03780217254598065, 0.3456192152808277, 0.44238789188938676, 0.26214618290430686, -0.20739664401367372, -0.9122357929019353, -1.7358518011216315, -2.5134937026143467, -3.056749993305363, -3.1912743558962657, -2.784312418994227, -1.7837483709016526, -0.2256063595801843, 1.7527059144854293, 3.935444975301812, 6.054010410766848, 7.828101850755904, 9.017777083162226, 9.453109639648183, 9.082260937643932, 7.962667674047714, 6.277031718717252, 4.28204946521507, 2.2873242638938174, 0.586028297764181, -0.5804596998175842, -1.0723766003443573, -0.866592964569243, -0.062221160716542157, 1.145374847317437, 2.4969772585708507, 3.7269435353232665, 4.600729323223326, 4.9702655457770675, 4.781427151758427, 4.0949156056483975, 3.0527442711468087, 1.8579215510760474, 0.7214098644758492, -0.17553148221930082, -0.7172176187188376, -0.8734882152918452, -0.6957541346738606, -0.30131472873287907, 0.16105835652616413, 0.5491741993581191, 0.7591219737793707, 0.75343597631935, 0.5609722067162665, 0.2724989355151521, 0.008027616980957558, -0.11270571801693387, -0.00795222610186241, 0.3432360530494586, 0.8890608762181752, 1.5169238306289652, 2.0732050723087143, 2.4080817828087473, 2.4020754725173785, 2.0115407201096187, 1.2687153648051046, 0.2926935877197095, -0.7466751949706064, -1.6588173369667059, -2.278772265123466, -2.5089636398860664, -2.3351595017480693, -1.8407501529607222, -1.1738666475417725, -0.5217218414471, -0.0520736277846072, 0.12424211118933834, -0.009543852741310262, -0.37126435438015704, -0.7933138283810732, -1.068452109371035, -0.9970589141495704, -0.4535974027768205, 0.5824563590776062, 1.995354393773886, 3.55616243581952, 4.958661760784445, 5.8839702096992585, 6.078721855014994, 5.405368881580455, 3.897587686237736, 1.746133195443823, -0.718444943557069, -3.100109893450884, -5.016408159153752, -6.172110268557329, -6.435363715554262, -5.843745792739533, -4.6155660208730325, -3.075265232244497, -1.5971020440838837, -0.5050431605215459, -0.009039735318623024, -0.15573726718246214, -0.8260172344765219, -1.7665041269994475, -2.661598370702188, -3.203292871289503, -3.181793835982239, -2.519209249564181, -1.3043339763523916, 0.24604009105220295, 1.832848357652318, 3.150123162388877, 3.9646077898122694, 4.155153484027451, 3.753954861053299, 2.9106929971289746, 1.8661028578734908, 0.8725096596345214, 0.13837735085208577, -0.2239724530735707, -0.2185723159295694, 0.04954375705802383, 0.4130084173342907, 0.6973363035469993, 0.7787246973734723, 0.6145003823835233, 0.26053865958268224, -0.15667462085732292, -0.47808496327070665, -0.5671193545367728, -0.3570645014410231, 0.12723773236674782, 0.770485379845054, 1.400660252930567, 1.8443734836846981, 1.9732544254874844, 1.7590000972016615, 1.2701785531823966, 0.6712631511753072, 0.15863891184163018, -0.08892827113593917, 0.022557545986947525, 0.47178304951824007, 1.1190365155178617, 1.7491232022715024, 2.132750107914597, 2.117339206533756, 1.6777144594444144, 0.9661164052441293, 0.2774152676781867, -0.0009698622776028829, 0.5010019707266736, 2.0300248631762243, 4.619465751788429, 8.045784899352224, 11.843566850141874, 15.402292172186788, 18.066088964732213, 19.32196172341115, 18.866837182646286, 16.746996344734967, 13.291414216944327, 9.101525728026184, 4.873830121105199, 1.2762694088062525, -1.205138318529921, -2.3657741459320656, -2.2919707100661104, -1.3334210645022813, 0.019818609822339624, 1.261676060953475, 1.9965348318086797, 2.0348968068937716, 1.4059929302040288, 0.33632764582090546, -0.8446676802723526, -1.8080350571756785, -2.314195663069035, -2.2862107988684124, -1.7999590554381693, -1.061722120452547, -0.3200389469239594, 0.2074517245861553, 0.40006218528861753, 0.2635360686771781, -0.08924908572182194, -0.4859553248398352, -0.7590428577790026, -0.8107363547270335, -0.6338364478818448, -0.3195335947745364, -0.005686456770589859, 0.16928478334446245, 0.12925450270946562, -0.11427362834432953, -0.460087732419178, -0.7619774157299246, -0.8779681485540732, -0.7415655886157355, -0.3823665066954864, 0.06228843250263987, 0.4022693000323371, 0.45949918608677615, 0.14424694318180872, -0.48974664458149664, -1.243795551869148, -1.8200722589402083, -1.9092823594995398, -1.3122483210049236, -0.01376786686673959, 1.753473831384831, 3.5574292222842825, 4.854462314034972, 5.135719027584467, 4.096288533173611, 1.7263815895716, -1.6183225348229608, -5.298798411928899, -8.51814641251535, -10.514528527562835, -10.77483246722122, -9.143601537089062, -5.9102693915972795, -1.7138903593084747, 2.5944115218377775, 6.155175318681866, 8.338808253003553, 8.836200597971997, 7.782898327930327, 5.621882600029309, 3.035468337937218, 0.6939511736804008, -0.8747595044792744, -1.432696016747, -1.043688799187132, -0.025415325903729368, 1.1869883165484583, 2.168875338044961, 2.651309424963522, 2.554917142392178, 2.009049542659308, 1.255318098414953, 0.5626417950888742, 0.1213507198026349, -0.011668253607625053, 0.08635581926625871, 0.2526948300501672, 0.31528510430280476, 0.1747232276614107, -0.16208165067738037, -0.5762929902108656, -0.8946129091065013, -0.960966348542018, -0.703789333436673, -0.17788089095578183, 0.45343252735442735, 0.974776314552399, 1.1959982759052585, 1.0405354083857883, 0.5649671834020203, -0.03518223532657055, -0.5138453967719231, -0.6534679555855206, -0.3680499551199469, 0.2595958243459618, 0.9801909404424577, 1.4747157858337914, 1.4435156237526408, 0.7578281391679604, -0.5115610520139127, -2.0574655298041136, -3.4527548182376435, -4.272864607103833, -4.248131535916079, -3.3901782791454678, -1.9921737405214175, -0.5847444744839173, 0.24423378304068147, 0.029779598553923738, -1.4009444698333409, -3.836973039976767, -6.719590656160147, -9.288193490633512, -10.776256591103573, -10.672267616996715, -8.828738034333176, -5.570042211833551, -1.5577774037241272, 2.357699418662788, 5.385800628673037, 7.016830774151969, 7.114229543700727, 5.956699395718226, 4.082541781600563, 2.12770448038688, 0.6142389416724211, -0.2019068912042305, -0.3578539666191787, -0.14944227518320444, 0.03241525726065415, -0.1512890266362326, -0.8467448513668994, -1.9616587164332109, -3.200220337834789, -4.192041491717343, -4.61323320588938, -4.336376264688048, -3.442578549750819, -2.2221366929943054, -1.0403005869597874, -0.22283922618813046, 0.0628779572353337, -0.14372287979767326, -0.628712664537473, -1.0994679992162968, -1.2974381323510378, -1.1118897556241971, -0.6005913499206041, 0.028536701683994387, 0.5220584149164444, 0.6947136129833232, 0.5095229562922219, 0.11527300810000138, -0.21726162487525327, -0.19626354333072712, 0.36735636693108514, 1.463315477214399, 2.8712348635137612, 4.2222774620976145, 5.115607045975623, 5.283527575224901, 4.657768279321447, 3.4395667954947142, 1.9894399944961505, 0.7321802342705024, -0.018542527666995004, -0.15856687543853962, 0.17744354147761837, 0.6831416949014675, 1.0176475590684038, 0.9757410756620433, 0.5688685322328122, 0.061843389304284985, -0.1112794419176335], 'positive_zeros': ['2.26027663966447729927884215960348', '3.85775137198782991165286996682332', '4.37526749996133579850317243105910', '6.07442499956795941981547089926333', '7.44201540410787076520053969814783', '8.045852476982021650881049614038748', '8.873267286634214673132337974017745', '9.108404416454209027254155882529674', '10.12289544376962637171298744556873', '10.54909112750273714796651660758810', '12.01523309172515279372958118806235', '12.99333616926732856934058342173878', '13.01653052415009321306624471507435', '13.97190630998819148280329432401263', '14.23141439033694605645255625898732', '15.02070220758083529490572384490036', '15.34802142870530138950796854847043', '16.09487684216355360453776254408460', '17.17707662552019832708411484595625', '17.49537251847867538030445534777969'], 'prelabel': '4-24e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1899772435377811, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 1412220482867416886, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26027663966447729927884215960', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.85775137198782991165286996682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37526749996133579850317243106', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.0051858213714984, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 576, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 10, -8, 0, 0, 0, 0, 73, 0, 0, -80, 0, 0, 0, 64, 0, 0, -212, 0, 0, 0, 0, 0, -250, 0, 460, 0, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 580, 0, 0, 0, 0, 640, 686, 0, 0, 0, 0, 0, 0, 0, -2120, 0, 0, 0, 0, 0, 0, -512, 0, 0, -140, 0, 0, 0, 0, 0, -860, 0, -2500, 1696, 0, 0, 0, 0, 2629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3820, 0, 0, 2000], 'euler11': [1, 0, 2338, 0, 1771561], 'euler13': [1, 0, -4394, 0, 4826809], 'euler17': [1, 0, 1726, 0, 24137569], 'euler19': [1, 212, 24954, 1454108, 47045881], 'euler2': [1, 0, 8, 0, 0], 'euler23': [1, 0, 24334, 0, 148035889], 'euler29': [1, 0, 48778, 0, 594823321], 'euler3': [1, -10, 27, 0, 0], 'euler31': [1, 0, -59582, 0, 887503681], 'euler37': [1, 0, -101306, 0, 2565726409], 'euler41': [1, 0, -134642, 0, 4750104241], 'euler43': [1, -580, 243114, -46114060, 6321363049], 'euler47': [1, 0, 207646, 0, 10779215329], 'euler5': [1, 0, 250, 0, 15625], 'euler53': [1, 0, 297754, 0, 22164361129], 'euler59': [1, 0, -304958, 0, 42180533641], 'euler61': [1, 0, -453962, 0, 51520374361], 'euler67': [1, 140, 606426, 42106820, 90458382169], 'euler7': [1, 0, -686, 0, 117649], 'euler71': [1, 0, 715822, 0, 128100283921], 'euler73': [1, 860, 962934, 334554620, 151334226289], 'euler79': [1, 0, -986078, 0, 243087455521], 'euler83': [1, 0, -678926, 0, 326940373369], 'euler89': [1, 0, 357262, 0, 496981290961], 'euler97': [1, -3820, 5473446, -3486410860, 832972004929], 'euler_factors': [[1, 0, 8, 0, 0], [1, -10, 27, 0, 0], [1, 0, 250, 0, 15625], [1, 0, -686, 0, 117649], [1, 0, 2338, 0, 1771561], [1, 0, -4394, 0, 4826809], [1, 0, 1726, 0, 24137569], [1, 212, 24954, 1454108, 47045881], [1, 0, 24334, 0, 148035889], [1, 0, 48778, 0, 594823321], [1, 0, -59582, 0, 887503681], [1, 0, -101306, 0, 2565726409], [1, 0, -134642, 0, 4750104241], [1, -580, 243114, -46114060, 6321363049], [1, 0, 207646, 0, 10779215329], [1, 0, 297754, 0, 22164361129], [1, 0, -304958, 0, 42180533641], [1, 0, -453962, 0, 51520374361], [1, 140, 606426, 42106820, 90458382169], [1, 0, 715822, 0, 128100283921], [1, 860, 962934, 334554620, 151334226289], [1, 0, -986078, 0, 243087455521], [1, 0, -678926, 0, 326940373369], [1, 0, 357262, 0, 496981290961], [1, -3820, 5473446, -3486410860, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/24/4/f/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '4-24e2-1.1-c3e2-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-24e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1899772435377811, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1412220482867416886, 'z1': {'__RealLiteral__': 0, 'data': '2.26027663966447729927884215960', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2865241038952520031804806977877,4890280842231648066956575677202', 'Lhash_array': ['2865241038952520031804806977877', '4890280842231648066956575677202'], 'label': '4-24e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/24/4/f/a'}