-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '743186119772082029476029059574,919040499620392472084136257935', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 16, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9136.127898623889, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -5, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, -5, 25], [1, -16, -87, -5488, 117649], [1, 60, 2269, 79860, 1771561], [1, 86, 5199, 188942, 4826809], [1, 36, 10150, 176868, 24137569], [1, -88, 15654, -603592, 47045881], [1, -48, -9863, -584016, 148035889], [1, 186, 10207, 4536354, 594823321], [1, 176, 1185, 5243216, 887503681], [1, -508, 165822, -25731724, 2565726409], [1, -186, -34325, -12819306, 4750104241], [1, -100, -69507, -7950700, 6321363049], [1, -168, -75599, -17442264, 10779215329], [1, -996, 545758, -148281492, 22164361129], [1, 252, -141875, 51755508, 42180533641], [1, -58, -223617, -13164898, 51520374361], [1, -1036, 772533, -311590468, 90458382169], [1, 336, 744046, 120258096, 128100283921], [1, -1012, 1034070, -393685204, 151334226289], [1, 272, -419055, 134106608, 243087455521], [1, -948, 326917, -542054076, 326940373369], [1, -2028, 2438134, -1429677132, 496981290961], [1, -766, -325917, -699107518, 832972004929], [1, 1314, 696295, 1353815514, 1061520150601], [1, -448, -892023, -489541696, 1194052296529], [1, 3096, 4846390, 3792733128, 1500730351849], [1, -556, 2667342, -720036124, 1677100110841], [1, 558, -1131533, 805136526, 2081951752609]], 'euler_factors_factorization': [[1], [1], [[[1, -5, 25], 1]], [[[1, -16, -87, -5488, 117649], 1]], [[[1, 60, 2269, 79860, 1771561], 1]], [[[1, 86, 5199, 188942, 4826809], 1]], [[[1, 18, 4913], 2]], [[[1, -44, 6859], 2]], [[[1, -48, -9863, -584016, 148035889], 1]], [[[1, 186, 10207, 4536354, 594823321], 1]], [[[1, 176, 1185, 5243216, 887503681], 1]], [[[1, -254, 50653], 2]], [[[1, -186, -34325, -12819306, 4750104241], 1]], [[[1, -100, -69507, -7950700, 6321363049], 1]], [[[1, -168, -75599, -17442264, 10779215329], 1]], [[[1, -498, 148877], 2]], [[[1, 252, -141875, 51755508, 42180533641], 1]], [[[1, -58, -223617, -13164898, 51520374361], 1]], [[[1, -1036, 772533, -311590468, 90458382169], 1]], [[[1, 168, 357911], 2]], [[[1, -506, 389017], 2]], [[[1, 272, -419055, 134106608, 243087455521], 1]], [[[1, -948, 326917, -542054076, 326940373369], 1]], [[[1, -1014, 704969], 2]], [[[1, -766, -325917, -699107518, 832972004929], 1]], [[[1, 1314, 696295, 1353815514, 1061520150601], 1]], [[[1, -448, -892023, -489541696, 1194052296529], 1]], [[[1, 1548, 1225043], 2]], [[[1, -278, 1295029], 2]], [[[1, 558, -1131533, 805136526, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 7, 'label': '4-1620e2-1.1-c3e2-0-7', 'leading_term': '3.65751244784205407436134815267336393854327817085639259994337492222608564560165992095923750', '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/1620/4/i/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [3.657512447842054, 3.63350590324725, 3.586999702666598, 3.501688391088301, 3.3804749465095996, 3.2300229011796118, 3.0526769987169735, 2.8504608049148987, 2.6271778720008525, 2.387196305629766, 2.1349384076723035, 1.8750226610552976, 1.6123760206788125, 1.3520250319338278, 1.0990352024589567, 0.8583950697916806, 0.6349774005664781, 0.4334123979749818, 0.25803122890691, 0.11276071750201445, 0.0010647372440373915, -0.07414078885654084, -0.11054376573356427, -0.10649507685136884, -0.06105383332450236, 0.025981660012728693, 0.1540470873407553, 0.32181009848305314, 0.5271695088913018, 0.7672805983675407, 1.0385870132488133, 1.336869231885363, 1.657314239343538, 1.9945804222611152, 2.342907801845028, 2.6961902398996216, 3.0481261487271074, 3.3922869758212486, 3.722305053112349, 4.0319261431564835, 4.315227710977545, 4.56664309525159, 4.781200315459927, 4.9545063510065885, 5.082993999324313, 5.163856885636227, 5.195290224626362, 5.176370507277418, 5.107275600654156, 4.989107395368578, 4.8240777195803695, 4.6152772731381395, 4.36681640885177, 4.08354899444777, 3.7711611313871782, 3.435863645923766, 3.0844269918015983, 2.723860301380536, 2.3613965919175848, 2.00417914391209, 1.6592070903819698, 1.333050850816361, 1.031773523665597, 0.7606958607695317, 0.5243128820476777, 0.32612531115610877, 0.16857283774812873, 0.052943193551289944, -0.020656980932819393, -0.05331173863966511, -0.04726956889728073, -0.005876565676663661, 0.06651722552108855, 0.16468744457159074, 0.28270052855908756, 0.4140846395967913, 0.5520609804334574, 0.6897285105013741, 0.8203465892095231, 0.9375028083438868, 1.0354234090478875, 1.1090938762559428, 1.1545671171101077, 1.169010560053801, 1.150978979294909, 1.1003695497105335, 1.018627274063052, 0.908600102518215, 0.7746505177151523, 0.6224153067781755, 0.45880675790457554, 0.29169447806373017, 0.12979300953743303, -0.017705482903342205, -0.14134497592026182, -0.23178484666526117, -0.2800872561742232, -0.27806733256365174, -0.21861278380901836, -0.09596564543420062, 0.09397689503399018, 0.3534810730642916, 0.6827494168173704, 1.0798587275648552, 1.5406585762196112, 2.05883092151437, 2.6259560547222485, 3.2316771904616455, 3.8639591303865393, 4.5093227178414494, 5.1533001783880685, 5.780689033554719, 6.376184513484967, 6.924592890533352, 7.411598613763541, 7.823874995848896, 8.149925017104803, 8.380033910461517, 8.507110851469259, 8.52644310641406, 8.436463231925531, 8.238286691898882, 7.936336752974437, 7.537674271307174, 7.052429801004462, 6.492962129553978, 5.874072361104292, 5.212052796254882, 4.524687747175324, 3.830272651235919, 3.147437021814751, 2.4942220682008855, 1.8877880045177697, 1.3436349533211458, 0.8752756251687163, 0.4936685711846178, 0.20694476026817443, 0.02009579567136256, -0.0651625606229819, -0.05043856167065872, 0.059400770880003555, 0.2564168381774189, 0.5299023445672347, 0.8667411662558502, 1.2519493337358072, 1.6691182447236532, 2.1011574731816594, 2.53071763497517, 2.9410664853920885, 3.3163885225772223, 3.6427034191656964, 3.907955997706354, 4.102877510520658, 4.220810114637965, 4.25841882308847, 4.215234881685402, 4.094148780572382, 3.9007010219122895, 3.6433212214485446, 3.3324357447272894, 2.9804592506320815, 2.6008197994441664, 2.207750380083142, 1.8153478740637368, 1.4372460274805243, 1.0858218893000071, 0.771852103472702, 0.5039588828570094, 0.28835422878521344, 0.12858007651379136, 0.02542884699668869, -0.02301512507689627, -0.021223360275959464, 0.024076737139514602, 0.10429647054283152, 0.20945798444047348, 0.32879329031536597, 0.4512725766661052, 0.5663260446606849, 0.6643025455347866, 0.7372023000285745, 0.7789523249085936, 0.7860277533816882, 0.7574635474762637, 0.6952549911078204, 0.6040736556609896, 0.4913728632621388, 0.3668314050882087, 0.24214229923806946, 0.13026026209329353, 0.04491326516874343, -0.00023081144957064166, 0.007768654673041192, 0.08034453516295624, 0.22672010951340596, 0.45330759879739424, 0.7631383967852602, 1.1555336435402754, 1.6258272548454729, 2.1653477014841642, 2.761558920288219, 3.3983271622377824, 4.056544149480559, 4.7145880912501585, 5.3494171432347715, 5.937082105013205, 6.454199303620977, 6.878344988627506, 7.1897494183856985, 7.3714065358677825, 7.410788159832383, 7.299538612736479, 7.034998543010672, 6.619418093996958, 6.061107279794497, 5.373182708181678, 4.574222183229434, 3.6866446088322897, 2.7368307891993267, 1.753308145315184, 0.7663928783522921, -0.1936037948797087, -1.097071792674246, -1.9166495692490404, -2.6280572095946786, -3.2112049246422614, -3.650936870478176, -3.9375769141070225, -4.067373897073657, -4.042454799413655, -3.8708186411034764, -3.5657698164561507, -3.145393859373153, -2.6316361078690873, -2.0492921211638673, -1.424961179005379, -0.7856780876484714, -0.15799422979727565, 0.4335527294141452, 0.9670010726151029, 1.424429559722622, 1.7920008067397446, 2.061146162501269, 2.228026760505874, 2.29428207735379, 2.265956998099476, 2.153746900352925, 1.9715424414632947, 1.7362079176691159, 1.4659698618672958, 1.1798623664228614, 0.8962156826128704, 0.6319716606675979, 0.40150760350017817, 0.216051641637512, 0.08300854219298369, 0.005681975490699423, -0.016833939590409776, 0.010512722723255723, 0.07913610991566644, 0.17746220089964043, 0.2916868253223141, 0.4068324439030849, 0.5076267639039218, 0.5797925027169467, 0.6107885665417084, 0.5910951136490711, 0.5145890740271077, 0.3795746221922216, 0.18864400412141372, -0.05075220577598764, -0.32699568210776897, -0.6243021138393972, -0.9238783356709147, -1.2044826188678932, -1.443859331522046, -1.6197132816895332, -1.7111697511274784, -1.6999100679923977, -1.5713981679235862, -1.31586360089531, -0.9290889540815066, -0.4129285594446432, 0.22444560031018093, 0.9687333660202904, 1.7997723411847089, 2.692557104551124, 3.6178551852451326, 4.544024289284991, 5.437714238791119, 6.266297368408075, 6.998344612966135, 7.606363511800578, 8.066757021546556, 8.362501634607794, 8.482385097433609, 8.42326856459248, 8.18853831797876, 7.789679787754336, 7.2440406001952535, 6.575584121255692, 5.812212321176682, 4.9857330896662555, 4.129098077193132, 3.2757757481220193, 2.4572965531103166, 1.702338108660764, 1.03492708644054, 0.4735885458978604, 0.030437318413755687, -0.2892902379254785, -0.4871899333816909, -0.5715634126928335, -0.5565348765231406, -0.461272923692663, -0.30854845725421615, -0.12341603654561484, 0.06840684118404099, 0.2421442795053746, 0.37536015606119455, 0.4495099711027198, 0.4507806393803657, 0.3712473617343477, 0.2089568458251961, -0.031573718713560885, -0.34004878704136493, -0.7006704100115603, -1.0934438137177398, -1.4951654749668675, -1.8810397347926928, -2.2261438723381124, -2.506985722802684, -2.70308665358816, -2.7981317922890114, -2.781266822128164, -2.647599023407163, -2.3988506969341707, -2.043136412925417, -1.5947462446184417, -1.0733132121553666, -0.5026850477827387, 0.09023927729764603, 0.6773919211597564, 1.2306509017144527, 1.724153830142885, 2.1349736101222456, 2.4454480342833187, 2.6431106644143636, 2.722623919060149, 2.684821174862208, 2.5379307942158764, 2.295787701840379, 1.9782100105540699, 1.6086332189827175, 1.2137090273312496, 0.820755616683171, 0.45684023152821673, 0.14648938720968485, -0.08935403595414154, -0.2349708875726865, -0.28060962392375727, -0.22323506949063485, -0.06662032206933924, 0.17882878695943535, 0.4968254988048233, 0.8661148496823861, 1.2620483233083954, 1.6578682731975578, 2.0268724775929865, 2.343612398540016, 2.5862563127727394, 2.7372614180799903, 2.7854807878282912, 2.7259952182322875, 2.5615595225367342, 2.3014849743990546, 1.9621752827824985, 1.5651853369780384, 1.136820989972491, 0.7057067481713145, 0.30166224881267356, -0.04676171162064942, -0.31372285940844125, -0.4781106755189233, -0.5247955633618275, -0.4458456044582093, -0.2411018756049642, 0.08157464362931134, 0.5067404661881374, 1.0120065538867336, 1.5695937706730367, 2.147533282363949, 2.712178217620602, 3.2294874767560526, 3.6680963299147926, 4.000161528481959, 4.204449347822605, 4.266309599011326, 4.180224889117274, 3.948683914950128, 3.583757397049045, 3.104909027647417, 2.539394592142667, 1.919316355154386, 1.2809271963833757, 0.6614335045390106, 0.0975556954356142, -0.3773363835591174, -0.7348690477652169, -0.9536774953703596, -1.0206653512700032, -0.9318418605491113, -0.6926959343123436, -0.31781495368229906, 0.16990708573828747, 0.7406148478350708, 1.3594378628907202, 1.9883064769562213, 2.5887488479271887, 3.1235645704216943, 3.5599508833658917, 3.8704532357356274, 4.035811426547734, 4.044784895013864, 3.896175915032845, 3.5974091785251443, 3.1653942220817006, 2.624053799653134, 2.0039800517520603, 1.3393744421091667, 0.666757185018025, 0.021934054371554573, -0.5617425667814806, -1.0557682732680755, -1.4380654797347405, -1.694288039128052, -1.8186797721487868, -1.8141150473239203, -1.6918719448661161, -1.4705582508485626, -1.1747258370783393, -0.8331176920357168, -0.476361652653092, -0.1351481317560268, 0.16251008147468018, 0.3925440456735275, 0.5373977699773397, 0.5862607346254358, 0.536906311565916, 0.39468595004530027, 0.17327663797277143, -0.10744123092153361, -0.4217858818581182, -0.7410970756244751, -1.0350219010334107, -1.2744414129042012, -1.4331152626677004, -1.4900951717536424, -1.4310809810333296, -1.2498526998959614, -0.9487409783857046, -0.5388878109487377, -0.03944797577295512, 0.5231779837894888, 1.1174722169823113, 1.708152631337347, 2.2593450727588893, 2.7359007325030236, 3.107047224333475, 3.3470383527642014, 3.438585070141251, 3.3723713439668606, 3.1496145928514307, 2.7802812399974526, 2.2843471747727433, 1.6889010935689577, 1.0280115037562136, 0.33921906183942285, -0.3377216866003558, -0.9642747359446519, -1.5049480173914134, -1.9299607345725882, -2.216938618041107, -2.35230873189705, -2.332217592884083, -2.162468239044409, -1.8582409878282808, -1.4427641713048747, -0.9457588182208155, -0.4013636961945348, 0.15441269188753715, 0.6858006314176079, 1.1602444495996533, 1.5498326728279341, 1.8340132852480706, 1.9998262145347152, 2.043742472738687, 1.9705177883232803, 1.7937951889759725, 1.5337699320273566, 1.216530272923843, 0.8711016164757539, 0.5279224226977105, 0.21584615444295915, -0.039717820308885626, -0.21877874326062374, -0.30822156619588287, -0.3031935112563696, -0.2065468025730999, -0.028322661421535774, 0.20946316563563414, 0.47902262865295925], 'positive_zeros': ['0.58627047519109592959446195251625', '0.72499512046531376205107894598712', '1.98209275957300328714694989695185', '2.08298483898253741426287811653500', '2.72086869462026572569919216896339', '2.91650645943529010021570550827036', '4.01826878880991430906009923768794', '4.08872410076742705348402316440813', '4.99201408668383777456252213252170', '5.05589447741276233784417044507590', '5.59538125781267118791102383593142', '5.61750741845705150279946543301983', '6.46858962337563083240182925232015', '6.95096419176899790254904630779137', '7.50361661724204225904122205033358', '7.55170625375127014940184902966842', '7.904356345376900398919844958316615', '8.281281775387026206272623789039747', '9.055100537876502153046050223847083', '9.276534331209755032247706263206894'], 'prelabel': '4-1620e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.77666068805192, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 2251728238888802442, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58627047519109592959446195252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.72499512046531376205107894599', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.98209275957300328714694989695', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9136.127898623889, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, 16, 0, 0, 0, -60, 0, -86, 0, 0, 0, -36, 0, 88, 0, 0, 0, 48, 0, 0, 0, 0, 0, -186, 0, -176, 0, 0, 0, 80, 0, 508, 0, 0, 0, 186, 0, 100, 0, 0, 0, 168, 0, 343, 0, 0, 0, 996, 0, -300, 0, 0, 0, -252, 0, 58, 0, 0, 0, -430, 0, 1036, 0, 0, 0, -336, 0, 1012, 0, 0, 0, -960, 0, -272, 0, 0, 0, 948, 0, -180, 0, 0, 0, 2028, 0, -1376, 0, 0, 0, 440, 0, 766, 0, 0, 0], 'euler11': [1, 60, 2269, 79860, 1771561], 'euler13': [1, 86, 5199, 188942, 4826809], 'euler17': [1, 36, 10150, 176868, 24137569], 'euler19': [1, -88, 15654, -603592, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -48, -9863, -584016, 148035889], 'euler29': [1, 186, 10207, 4536354, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 176, 1185, 5243216, 887503681], 'euler37': [1, -508, 165822, -25731724, 2565726409], 'euler41': [1, -186, -34325, -12819306, 4750104241], 'euler43': [1, -100, -69507, -7950700, 6321363049], 'euler47': [1, -168, -75599, -17442264, 10779215329], 'euler5': [1, -5, 25, 0, 0], 'euler53': [1, -996, 545758, -148281492, 22164361129], 'euler59': [1, 252, -141875, 51755508, 42180533641], 'euler61': [1, -58, -223617, -13164898, 51520374361], 'euler67': [1, -1036, 772533, -311590468, 90458382169], 'euler7': [1, -16, -87, -5488, 117649], 'euler71': [1, 336, 744046, 120258096, 128100283921], 'euler73': [1, -1012, 1034070, -393685204, 151334226289], 'euler79': [1, 272, -419055, 134106608, 243087455521], 'euler83': [1, -948, 326917, -542054076, 326940373369], 'euler89': [1, -2028, 2438134, -1429677132, 496981290961], 'euler97': [1, -766, -325917, -699107518, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -5, 25, 0, 0], [1, -16, -87, -5488, 117649], [1, 60, 2269, 79860, 1771561], [1, 86, 5199, 188942, 4826809], [1, 36, 10150, 176868, 24137569], [1, -88, 15654, -603592, 47045881], [1, -48, -9863, -584016, 148035889], [1, 186, 10207, 4536354, 594823321], [1, 176, 1185, 5243216, 887503681], [1, -508, 165822, -25731724, 2565726409], [1, -186, -34325, -12819306, 4750104241], [1, -100, -69507, -7950700, 6321363049], [1, -168, -75599, -17442264, 10779215329], [1, -996, 545758, -148281492, 22164361129], [1, 252, -141875, 51755508, 42180533641], [1, -58, -223617, -13164898, 51520374361], [1, -1036, 772533, -311590468, 90458382169], [1, 336, 744046, 120258096, 128100283921], [1, -1012, 1034070, -393685204, 151334226289], [1, 272, -419055, 134106608, 243087455521], [1, -948, 326917, -542054076, 326940373369], [1, -2028, 2438134, -1429677132, 496981290961], [1, -766, -325917, -699107518, 832972004929]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/4/i/j'], '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': '4-1620e2-1.1-c3e2-0-7', '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': '4-1620e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.77666068805192, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2251728238888802442, 'z1': {'__RealLiteral__': 0, 'data': '0.58627047519109592959446195252', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '743186119772082029476029059574,919040499620392472084136257935', 'Lhash_array': ['743186119772082029476029059574', '919040499620392472084136257935'], 'label': '4-1620e2-1.1-c3e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/4/i/j'}