-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1047', 'a10': [0.9911314021003612, 0.13288545357025405], 'a2': [0.14231483827328514, -0.9898214418809327], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.009519833939576644, 0.9999546853541729], 'a6': [0.9992750478004736, 0.03807070846938995], 'a7': [-0.0475819158237423, -0.998867339183008], 'a8': [-0.41541501300188644, 0.9096319953545183], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1047', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.3339', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^255', 'a^77', 'a^180', 'a^82', 'a^2', 'a^245', 'a^105', 'a^154', 'a^7', 0, 'a^257', 'a^136', 'a^170', 'a^159', 'a^30', 'a^98', 'a^79', 'a^221', 'a^262', 'a^322', 0, 'a^261', 'a^182', 'a^164', 'a^61', 'a^231', 'a^95', 'a^78', 'a^84', 0, 'a^285', 0, 'a^23', 'a^327', 'a^4', 'a^161', 'a^146', 'a^213', 'a^187', 'a^211', 'a^247', 'a^182', 0, 'a^236', 'a^186', 'a^42', 'a^107', 'a^160', 'a^89', 'a^175', 'a^316', 'a^289', 'a^156', 0, 'a^20', 'a^298', 'a^3', 'a^284', 'a^9', 'a^42', 0, 'a^69', 'a^210', 'a^218', 0, 'a^310', 'a^278', 'a^8', 'a^252', 'a^298', 'a^259', 'a^250', 'a^86', 'a^241', 'a^71', 0, 'a^138', 'a^104', 'a^112', 'a^308', 'a^136', 'a^124', 'a^172', 'a^180', 'a^107', 'a^155', 0, 'a^219', 'a^161', 'a^51', 'a^111', 0, 'a^297', 'a^303', 'a^32', 'a^72', 'a^85', 0, 'a^14'], 'euler_factors': [[1, 'a^255'], [1, 'a^77'], [1, 'a^82'], [1, 'a^245'], [0], [1, 'a^136'], [1, 'a^98'], [1, 'a^221'], [1, 'a^261'], [1, 'a^78'], [0], [1, 'a^161'], [1, 'a^211'], [1, 'a^182'], [1, 'a^42'], [1, 'a^289'], [1, 'a^284'], [1, 'a^42'], [1, 'a^310'], [1, 'a^298'], [1, 'a^250'], [1, 'a^104'], [1, 'a^124'], [1, 'a^219'], [1, 'a^72'], [1, 'a^9']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.1047-r0-0-0', 'leading_term': '0.794718063364560155396862612884-0.451576233885385771561294900643*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/3751/1047', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9140557396833225, 0.165737481427613, -1.4520091941396005, -3.2687592689390814, -3.7493729367538555, -2.262740850920939, -0.03492771337194949, 0.9808268993606327, 0.20989859666772578, -0.9487636310791038, -0.9164452558132138, 0.05916664753152574, 0.3845605910962849, -0.44099956152397385, -0.9077284805949625, 0.2140971241592628, 1.4365550803414706, 0.002271029932656698, -3.9528661630641926, -6.378335243720674, -3.984538059891676, 0.8955815541389363, 2.3207468738630515, -1.9390661635992805, -7.159237273031588, -7.296185997906414, -2.4613259300194192, 1.6025579311424085, 1.1024516900690227, -1.5881458196766918, -2.2381499965989726, -0.5998667586156371, 0.45332121543527815, -0.04928094328426459, -0.31468780225683113, 0.2996027479328943, -0.007788926456709677, -1.7247449563368202, -2.1250281098106645, 0.5246345306413054, 3.2624152660404766, 2.1970919353489613, -1.4392103413734791, -2.8371067585360565, -0.8256209243757496, 0.7454067084764544, -0.3078138783241115, -1.0364630081767545, 0.8378363757731355, 1.8925426015942282, -1.7353711397713885, -6.8888168774593295, -6.917779896686613, -1.73373912886202, 1.7765449411833596, 0.21760709277222653, -1.5881940400144372, 0.9423531002693208, 4.593173974023168, 3.876877255721436, -0.04714207639557253, -1.7415936751628098, -0.2921564348907038, 0.4072572956466983, -0.8670115353992229, -1.1210515685134883, 0.6220149053103622, 1.435890646381261, 0.12864947204075367, -0.6450820464080183, 0.3188564373913921, 0.6358912736464708, -0.34968838691419507, 0.3291073357681015, 2.9586781904070794, 3.0403710084923516, -0.20261973421373614, 0.4623028719047747, 9.526808975052523, 18.977954132469247, 17.65632073335844, 7.100953805361307, -0.9444799950249352, -1.125565907341568, 0.9170297277330397, 0.3611610377395532, -0.3860163217796515, 0.760487582382902, 0.8139062677512483, -1.6529115290224987, -2.809461240797864, -0.6822096210120548, 0.8166789880026266, -0.8765257792591905, -2.2566371702453374, -0.6096188626922531, 0.8701005730126107, -0.47385619197465617, -1.5788657739218286, -0.011001749642814408, 0.8560274052790375, -1.495594500965311, -3.2336793265140917, -1.2496446803974166, 0.7223159878031042, -0.5993841865864562, -1.4235348823972855, 1.3191682135110838, 2.7287943756856956, -1.1182806494422746, -4.116860725513847, 0.021905954901641874, 5.323607323342258, 2.3031905920826885, -5.9436534664890095, -8.491293710115604, -3.797515818865673, 0.010674444310395987, -0.3289563806317519, -0.3748172151688346, 1.4785681247617015, 1.7831136160654761, 0.0839726962484387, -0.4226666032730345, 0.30588505924045506, -0.01041120815630768, -0.1621544675298359, 1.6863063531025118, 2.527407756216975, -0.07268038764927166, -1.570115204030583, 1.915194009611196, 5.13679888988663, 2.479489605977365, -1.2224603671040144, 0.6057585087153624, 3.6175141139446843, 0.7265451046329429, -3.796329784684233, -1.7391993877290401, 3.571069593942042, 3.079023865287881, -1.8962490223592317, -3.1022045767092616, -0.28931012943792217, 0.4737334248478595, -0.9329342476994974, -0.43397500052389615, 0.7196721041297272, -0.4600766237977598, -0.6883142554844044, 3.4365891926186936, 7.067259793199409, 4.796140888151361, 0.31180480883623407, -0.624182139091636, 0.321411514235439, -0.368816440212217, -0.9695271615701024, -0.012343667584816346, -0.20308830578277925, -1.4660901569560976, -0.0036371547711540712, 2.220107754930351, -0.7174166813544638, -5.081104202659069, -0.6268343080519243, 10.148049444818387, 12.829604736420494, 4.4023228523524995, -2.027751932348047, 0.4367967529666864, 3.4972837666263854, 1.23563956628958, -0.9007455078904864, 0.7153237288636264, 1.5889288758303524, -0.20121489507501789, -0.7533920278165105, 0.427917324821429, 0.03575211193187086, -0.9625387192475853, 0.289512856631198, 1.436308948950659, -0.004456674168487698, -0.42572201834183343, 2.181517231161563, 2.8722127278122485, -0.029450627015651185, -0.3793662369914386, 3.075196596635919, 2.7473213860735455, -2.7101290514479484, -4.502736675567708, -0.3819049305436852, 1.1680521182718235, -2.176056902200757, -2.8190547708187568, 0.5579948668009262, 0.9023459534566296, -1.6354893794805443, -0.1038710708568859, 3.550937256536244, 1.2652182871133277, -4.5309282983901396, -4.6289675280838605, 0.003385621189896576, 1.3367613350190035, -0.6199693023053483, -0.5478178297519469, 0.7706031963156783, 0.20499518493524185, -0.32430908122132, 0.4017447888030321, -0.8463195901591175, -3.639477316250325, -3.1025935702144922, -0.02324772824467429, 0.5121712552056605, -0.39267863407687525, 0.4219539420554669, -1.1592020824046736, -6.998724635978122, -7.108419522799604, 3.9005237974807914, 12.767950565768874, 7.588197813267405, -1.940659586039173, -1.8964686416351495, 3.3768851556982673, 3.223620383771779, -0.28121188163287913, -0.650576003903832, 0.23278097947966314, -0.42973046018989913, 0.10228482867972273, 1.8904768950119824, 1.0843039883659595, -0.8461782314326561, 0.10349667919332929, 0.9867612005356092, -1.8047410099090315, -3.4492869859086284, -0.14295559028269403, 2.33621999246453, 0.0903758100747758, -1.4906195368778024, 0.2555090281533693, 0.5469942612716003, -1.0111484131504875, -0.08029168711168791, 0.643996520499636, -3.2675641816864056, -5.252558472493015, 1.1362391442298443, 6.914569604555835, 2.4984932257594705, -4.106751721441629, -2.469028156621029, 1.7196712849915667, 0.3617888784239961, -1.5729753395459274, 0.8800141308731504, 1.8080670758100879, -1.9231682022275427, -3.7518672390048557, -1.264447081488198, -0.022799991569360935, -1.1671230234709111, -0.7973582729432405, 0.33940794770287747, -0.2745725925798727, -0.5387694911850407, 0.37575716589116115, -0.13296304127736838, 0.1965735342635504, 4.852801316071211, 7.140077113045068, 0.07890235075394227, -7.421448945430731, -4.249247220376296, 2.505500743693197, 1.595138020139358, -1.497473064314534, 1.7300355629272757, 4.782987450899354, 0.7845802117408516, -3.072716045909478, -0.8988479392148533, 1.1968286502030134, -0.1527559976793033, 0.19087781914192636, 2.292125885528409, 0.9912404360216829, -1.5370019370992014, -0.4745224810376862, 0.6669411764571471, -1.578295554475481, -2.296379892172559, 0.6123960207672368, 1.3043966044493513, -1.2083049592490709, -1.359301560876831, 0.354784634334572, -0.41491550800483784, -1.114778408368784, 1.042467273109782, 1.2773172834567055, -1.6511555284577395, -1.410911257691019, 1.113547553416521, -1.1744531273532965, -3.438912198404209, 3.886041989636447, 12.355878851596064, 7.3097625480638335, -4.245339063195301, -5.2760054962613046, 1.9750019333241713, 4.123995544918181, 0.9928372789113529, -0.0994333875190647, 0.20220065178287136, -0.5727918400368288, -0.09500848438989125, 1.0771239373785082, -0.0927588016732058, -0.9102585820484131, 1.1980916338443681, 1.700904609543266, -0.9881846063291054, -1.2715643344105496, 0.8020973622967127, -0.6384898608323344, -3.199056210329652, -1.1406331746053069, 0.7635503607602717, -2.0201149058060297, -1.3350139679876962, 6.5501122134559875, 9.677703506695341, 2.6412759975424303, -2.5669086099313008, 0.05980188576799679, 1.6182957744919522, -0.9490269761056407, -1.1432580249971769, 0.014757813664065617, -2.592200981188809, -4.276492289498908, -0.6263041342877632, 1.3414043463653222, -2.211440599269473, -3.7199228937937963, -0.5056179177143028, 0.6700640994513479, -1.0695236818266456, -0.5938968498150667, 0.8013019659282292, -0.2383732972424009, -0.8457990474716572, 0.3017449091799919, -0.0019079064623031719, -0.238449275405698, 2.1304356167436582, 1.6999048109212873, -3.3137644689580648, -3.5713558805534746, 1.4839538868713993, -2.0454523544411014, -14.52739528823787, -17.442655434955782, -6.428451171008183, 1.774980974922825, 0.5365564755707379, -0.4000408331679069, 1.124372571989924, -0.8390156388180917, -3.3219665873382787, -0.994901495531826, 1.610023508421862, 0.602375605506239, 0.03262967832664824, 0.9668362608971774, 0.2691095468681247, -0.4106335363943235, 0.15355488991413316, -2.430835236025539, -6.769214128463624, -5.13330904150887, -0.018554983465168224, -0.6629171602888821, -4.259531768444314, -2.7295610783731266, 0.3133928296398388, -0.3813264245273297, -0.09720870180181677, 2.3655726877538723, 0.8492266740140053, -1.258766340876583, 4.112437067378748, 9.515687543114428, 4.2807254179889584, -3.0475237191689244, -1.1109764044178772, 2.8634400223764933, 0.5881257099003139, -1.165299611016767, 1.7809604356619768, 2.32458589705055, -0.7621805958991128, -1.1741513816208056, 0.09981941442426397, -1.0757760545953854, -1.5684986363898403, 0.5505325845000794, 1.085957956802447, 0.027959912738649357, 0.5309134041670928, -0.034883090411726055, -2.775780323243784, -2.2200811734306107, 0.7993789152840649, -0.09186279833607668, -0.47224201749860617, 5.76173569212683, 7.744155227802487, -3.4166882380437666, -12.591425802287326, -6.052517547583958, 3.7162668334657543, 3.1222464169458863, -0.42659408796293363, 0.7047850258102215, 1.0550764801872103, -1.155645647276159, -0.9426882549615122, 0.28254617653283753, -0.3648360000960268, 0.5168506698468492, 1.9666250943325019, -1.9504936000367041, -7.16029335524122, -5.231449348996768, -0.19822188675614982, 0.45698867251656866, -0.28628558998741604, 0.5619600366224019, -0.5327292060415905, -2.1949012450969856, -0.35595555687367497, 0.6310110521225334, -1.964040668106264, -1.2108962836101924, 3.027961917939172, 1.6854315241076763, -2.5442630261199777, 0.19751342668751506, 4.227335269623471, 0.4631587103043436, -2.0275625539310593, 4.549570665984129, 8.125627121508524, 1.412453293407572, -3.3001362481941823, 0.23806600646974607, 2.4922710755111996, 0.21047385438249672, -0.42065759816090137, 0.4058555076246525, -0.4571812268769536, -0.5465405074737684, 0.4086962571751117, -0.6048689232448575, -1.1488698382391593, 0.7363624853552359, 0.4833660576259587, -1.3947432474349482, 0.8210190024223003, 2.7001079262556473, -2.382003913338834, -6.123766047597202, -1.3199886519224628, 1.693581107183036, -2.981070062276557, -4.240023899718965, 0.9318254758751134, 1.631964904969194, -1.6661263711449221, 0.49610626343859016, 3.769530026352766, 0.2862292571889328, -3.1570285922069994, -0.7453636144232344, 0.7878665668576974, -0.5670700396456397, 0.9443543929953794, 2.9509100175260863, 0.6150201843169907, -0.9872874090607222, 1.086079044784684, 0.8879551946450768, -1.3527240055668108, 0.3966544216382122, 2.99314993791186, 1.0951221693333792, -0.9211254321837318, 0.09634602495098946, 0.26002152717041765, -0.09460865815122715, 0.9925315634869475, -0.40346701265369395, -1.735122922784247, 5.818964812292099, 13.666401895760307, 4.4630290662478185, -12.507749170659057, -13.747177869959877, -2.8175984932308973, 0.7519581274821104, -2.2974920338095752, -1.2654766676447593, 0.8022029642654764, -0.5723410817753114, -0.6680936210887264, 0.7531827391267535, -0.5335389046815145, -1.447896305526874, 0.643493185307719, 1.0763656968394555, -0.41818834969174146, 0.3039390230120227, 0.5280127024877769, -1.8189770193030665, -1.1520335868168794, 1.6799836908245118, -0.8455111445304792, -4.85843157927571, -2.4038413835197763, 0.6406246709535912, -1.3336252454881057, -0.9156810603300238, 2.5272479218116706, -0.9771671701132691, -7.755114413687663, -5.711657365190357, 0.3133818914162948, 0.3122770336002005, -0.4164507258644571, 2.3249869143068755, 1.220386443153995, -2.3913534957979534, 0.6302647096303651, 5.259289182628273, 2.1496914693006075, -2.1610621696593153, -0.17150347305730196, 2.0332722400753322, 0.5766090373011828, 0.07664286597114787, 0.6307863790050322, -0.11541091458107677, 0.277868715272234, 1.0643059109193302, -0.9620161148481958, -1.4994832797999718, 1.8007109067331344, 1.7476005107709507, -1.4097916976524312, 1.0096598249786666, 4.29984058477251, -0.903867588574051, -5.2161576026507035, 0.1071964463954669, 1.417829366568341, -8.730175739918913, -13.579745761272756, -5.46953284235666, 1.0222691763773366, -0.23051001306360183, -0.746645058996717, 0.46774639187500544, -0.48316095773744017, -0.6565123863495143, 0.43502870061831034, -0.9329936309660248, -1.7646412594582666, 0.36551790921414673, -0.24351519917901615, -3.0948894878809603, -0.6502512585086162, 3.567971362380279, 1.5406533660595303, -1.8057178817324084, -0.6863192600960952, -0.009038164591354269, -0.7806390589457042, 1.3323943618013725, 2.0294476045545946, -1.7601930662426184, -1.979176678378704, 1.4128804102347168, -1.5131265044290991, -5.749842301219411, -0.17562718733556254, 5.159481159845307, -1.8494755368846025, -9.042824716652461, -4.970237196495608, 0.14008954401416412, -0.7198639957723182, -0.3821275258465196, 1.7820258485725415, 0.6223406697202041, -0.2839050914157268, 1.6847453934932002, 1.336623023027908, -0.9323586137833235, -0.3530889687743633, 0.5470157855263998, -0.3882707402562343, 0.39073962757916386, 1.480183605892847, 0.014280420287323958, 0.06377418457698941, -0.2856957115739945, -9.071906161649407, -17.554913765267536, -10.707347044876519, 1.1705498035359583, 0.3056586346335408, -4.965018148829742, -1.3460435191062619, 2.9558181892501936, 0.7257507187693741, -0.3158412558145324, 1.055519306629286, -0.785562082111241, -1.4012105637939047, 2.3579937717633443, 2.553306869963466], 'positive_zeros': ['0.35450622858311222324304442815', '1.88079967378865843749369941870', '2.54954844765630795277914299892', '3.41765229634510222508458899433', '3.92473512345674622788298156039', '4.64641762266273178906448008937', '5.312727684618154679309762366834', '6.49928568534312662467251296798', '7.07933416791360316856940555768', '8.27816014638185472625560193387', '8.87628124089558869173155681986', '9.80493476750774243401113208511', '10.29174690954199086495888000918', '10.79522246925986506088638091698', '11.2480402828063740920725290662', '12.14034798908660740276310396272', '13.00092100388359993301889957978', '13.859595086931489053742119673712', '14.31591372154290079439633931625', '14.89143523331757683375020840697', '15.51833959692414692833837394620', '16.668801279330599971139423147652', '17.21108290245865173851025450999', '17.73831817897853572551730576783', '18.745894573956606964255207258226', '19.43123851913919094090559204267', '19.81419806464410518615787514879', '20.52569879839227850333874535844', '21.275971013165732181766525198111', '21.791182377476988131115482119758', '22.385524842696442761269441471589', '22.758971070856560990790775340812', '23.728466489571112952947738915714', '24.03124041923868689991530021148', '25.56302041501583859419365359712', '26.08070643515447654747203795416', '26.646551661009539672735758908267', '27.01661869837578012770124389907', '27.62381391249496711718809718554', '28.52206442081824891829718264382', '28.94551110824356808055484547629', '29.770422307903231209698113946000', '30.23888663718006167214727101691', '30.939163602216256538549757393987', '31.4014627405005316239163236799', '32.33035179886693900986506765420', '32.72225292743453296918997350436', '33.31594394474537297395751526305', '33.993559031767765396735635830118', '34.6864739978657244452242350553', '35.40141238065921304145765052027', '36.56009640566999280996753688288', '36.77801403515980344013047644260', '37.26347185997730250883824893061', '38.14237160889068199841638368120', '38.607736860797927489141619934559', '39.05823682589682402492542547306', '39.42112893751754009667695650243', '40.30547362071489783664220531633', '40.80678938051890331828957361920', '41.73223207573054983928103528656', '42.13829907301123060485807303586', '42.85376263082119626403122494541', '43.531994672765332270492682572714', '44.25323138372425413150016777412', '45.037491721459562937251550498623', '45.419959980449536551324081966996', '46.02136369795761975309222367808', '46.48020844368424903024849719888', '46.95490319982434077723499417046', '48.15869725282680720262601825560', '48.613317398861111732225800387032', '48.96607108628068495601165402918', '49.69185554438132974579917956606', '49.94442673110659909122722649217', '50.62538826677665668186811443049', '51.2070151956965255456555548419', '51.89480677456821096054073347986', '52.9727277221933918614632754299', '53.40823344603574800807363191364', '54.181403098016239827292885495484', '54.588928150756704716446236737437', '55.27977956248341392187962456704', '55.81666576037419931761506077698', '56.258275501753586797570837451178', '56.82897204716015979625333582483', '57.49923832059020419440345542583', '57.88339785824878726548170514908', '58.74669868461215802301081128232', '59.10625807589609855566189528531', '59.85379288146942982635739101706', '60.6534860197657470299049415678', '61.068396287900997929678497568380', '61.820771764307533702950898898166', '62.29342908907567385777715847934', '62.82052014685466752515183529297', '63.5034247930008247633850126269', '64.37473442944177004548407913907', '64.897796284554999136066924795254', '65.42135313789936340382315131547', '65.99452091762357178363980775734', '66.39022403289074222884872999952', '66.75770353471228240615939422097', '67.81559827069795462111100086507', '68.25982482708347653698921432180', '68.6236333215894056751342533799', '68.95818255302743912126906862844', '69.90753299920269310466773064108', '70.85371149565233402829079979837', '71.35703260390555903659005029726', '72.15395369562340976915791779965', '72.67093190796082007333962312539', '72.966103053469322033194343678051', '73.41870752722297022678628053936', '74.20689912013031819960911835010', '74.67101070425587018859722263462', '75.14837928065085660630658494473', '75.947954394010732367499775574307', '76.5715934706898835349654907791', '77.14722414139376578066525410366', '77.60271755813369967493703385006', '78.1374872778622087867906953213', '78.52075276200360704928170854790', '79.3336516270305689936993403404', '80.09576261312684477935869715055', '80.77663286472264729595163730986', '81.2847915574963089201843037405', '81.79008151112033919366976962248', '82.36059138125793735569576408258', '83.35363707789047576573851576155', '83.4217185112218540805967032960', '84.23907895552402827237424713219', '84.604239820476827759556543900778', '85.171890362264460154034954071650', '85.58602610928066017880467643048', '85.91153764992584721803561596289', '86.87747918191883558538841623685', '87.67100547482590099020491761824', '88.2415578056977583817483346015', '88.64007434978303815632660381273', '89.41744051552644130268037787641', '90.08236245590372549992018738559', '90.5933228002366756298750294062', '90.90715362603034149959362757687', '91.66086125301831377135649854438', '92.25491043832577733724106669768', '92.62979558421712253736379492070', '93.37538790063394985688693370047', '93.91736496696356828645874391125', '94.59654548800391281965706228035', '94.92066510793722183277140721555', '95.49510681577226856323027522145', '96.07900201162168209282815790456', '96.70845103367502995095659733850', '97.09782016685972787630559977730', '97.69254587667267508318717681034', '98.62120631115837863853601975482', '99.287622728847847233157779440080', '100.161715854007891858674449174532', '100.37755356119103693489376687640', '100.7303636021421219724160327077', '101.26998260884201505739547069216', '101.859737043335850205210610859', '102.35053163307305831655921699198', '103.01510516216137764198037738663', '103.60888122739803717126566823224', '103.997863278200028393627044387840', '104.79532860941345352270930970765', '105.12283290698573058825525244896', '105.69250695458170462398759640756', '106.66733168313398757844590393445', '107.18266241725734545615958589052', '107.70384544910225128791679632241', '108.36018570940959728290175802499', '108.445191382320235157411672437642', '109.42080258764905539702280516025', '109.8372082719140162273136884534', '110.67676395868404154058654923385', '111.06404285526655451960757014670', '111.66124101503510996535431545939', '112.14148165537770949050579868847', '112.72424678983299633809633161207', '113.124450258801330381088572234250', '113.48503027426292002901814040890', '114.17843997350250069848865370871', '114.89451728421996002350600459548', '115.24057682079552760542922020490', '116.44610675452904182972734120732', '116.940052711355719843482198407274', '117.265305841803933686439518595453', '117.73536862643357814907740086101', '118.52166409992641798830615346417', '119.21754930098295245269772133698', '119.359132938714707161934511663598', '120.0632903735647347476351002052', '120.48974841924939599057209861905', '120.69146725700831159607461849947', '121.87684454330871831811885593988', '122.126425847454632224524087085041', '123.06415689846733545337573888695', '123.35519195176281391091714379678', '123.76319158217117004195015717521', '124.44851754278195898091113759327', '124.8132223316582666593276549671', '125.77420589803229155698113229216', '126.31393092590981439245527260829', '126.92503311226658336632024080346', '127.33801743976027080474444036117', '128.0438272606468566621574031506', '128.68774893803675184630971437951', '128.84284290753078067402591624831', '129.61064541464147404533868566721', '130.341961153835694453056975041877', '130.3899356753059423479975749676', '130.93260420812425200030155184487', '131.76961918628246142091484613319', '132.175662547665094851174353923527', '132.53956420132698633964844928041', '133.36165117618845987632772298836', '134.22664102574072557550001134374', '134.92779864195573861709598365882', '135.20565748190878070179341000087', '135.77317729563913099227892838110', '136.43585065255279449007937493230', '136.73923134620345957368990918862', '137.10527361270665526942899416741', '137.70744115776244055226697422158', '138.77011655969345588027484450864', '139.17872652518384790122798640346', '139.49617086864512329876573400088', '139.92287073842541463296795290478', '140.66812782091143955817097549821', '141.03342837060773638028156063270', '141.649455150195303548131087299964', '142.29074664181722851182458530461', '142.80167223784230989714506874226', '143.46287503309164472213668338879', '143.88196233481098307012058793359', '144.74255857122092453100157505026', '145.2969294653673148816062218097', '145.96768895326682409120544356296', '146.37153781858242887127102122936', '146.75408343571577861807824172301', '147.33299346389512607916920877435', '147.69253234541715525436567300172', '148.32259397815400256315003400349', '148.816064676623064245769098848339', '149.30570795437012849897332621802', '149.8886598304401660095257129391', '150.6935959683387543416438482768', '151.08294188502483423256757865206', '151.81731636517499308479955237914', '152.32486778715965077196252611461', '152.77893320097108661282309039336', '153.45394519415511042064756985210', '154.1368084385915841805916945989', '154.5467805699106246882733830399', '154.89178238243215001721734828157', '155.68562692395505984302917338963', '156.10699589110268705236525953326', '156.66856450901860960592026568748', '157.15181293870645469220659278005', '157.926884989077385573715388610753', '158.414008457240944858581451140959', '158.85180078134479720857349076838', '159.10113793934859975049673353145', '159.643800178436877871174925136132', '160.11906091457727171214747875424', '161.01391264322643316023724999836', '161.99612074569575187834946897191', '162.27350300905646245727673993919', '162.94676049735866221042443139412', '163.340791864536071879163953187139', '163.870179218982796324852073354071', '164.29658510060936034338345369556', '164.91454962182793418920000134776', '165.513388201525490035692389558829', '165.872616296876365284072937917828', '166.332644883673522588579993395745', '166.981695817112133263207201609279', '167.44583853231945332131480701748', '168.30818417180413893278851159536', '168.591992800695903260476738029439', '169.13750172816399306174513588919', '169.64462523292441062122832615874', '170.59923043882107206220965374082', '170.9832799857528052868047375963', '171.31159615498165275709376149909', '171.96240023497538355379261379624', '172.46659326945264856255472651139', '173.241541960575879363990869156', '173.764626275543691322548790665530', '174.530165621321033865101156711893', '174.644325946032641840965189496717', '175.26651042056237837858055727465', '175.55275096700544976127007375907', '176.13452569737320003715575446478', '176.71635138664105820637171679355', '177.33848108694946840255042671023', '177.74724215211621587178547971544', '178.40059097540551584002565911079', '179.05745017632114922243481717521', '179.43780863887148328430808632427', '180.5275758696622999488202652317', '180.90633681894233194632475251476', '181.40475139591417176454986419052', '181.76870926938955736818549330651', '182.3382440428259526607130537593', '182.66832193477102415341878505940', '183.38226511956538781835554710162', '183.72311557234965170895579927822', '184.413821803557313878445321184559', '185.10891550777811917967478340929', '185.76211688503783565475910595735', '185.93416158815269839400752687594', '186.41316117895035881412676073743', '187.05398365339599146856893355049', '187.65957885903805174445060076004', '188.0409374807295216080228708419', '188.75625085572685113778313338609', '189.319554403219042659040099528016', '190.28950485463412896570364165655', '190.49501233468858180812468314424', '190.98606129609060802555805596091', '191.65878353047664959917559842196', '191.93866790066961749665580779064', '192.66249654270600807453589043533', '193.192180288839405283023204819775', '193.622521267560792599383308786663', '193.99046976500257744381447202312', '194.69046301074251544398360858357', '194.985175668455533580647386627095', '195.28776180415683129445754207423', '196.5156262728821637630728176866', '196.889608959972891932460057691378', '197.56564750003934897230865684622', '198.207402828832521281385494851771', '198.50197342811603934597061250151', '198.97317237787046130167245842244', '199.50742536346180160094512205545'], 'prelabel': '1-3751-3751.1047-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.1644788233058801, 'root_number': '0.511857310066418130936196580404-0.859070482633160134538436014707*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.842177027009047830878292512173-0.105993803876366890075098976055*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.354506228583', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.88079967379', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.54954844766', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1047', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1047'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-3751-3751.1047-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3751-3751.1047-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.1644788233058801, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.354506228583', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1047', 'Lhash_array': ['dirichlet_L_3751.1047'], 'factors': ['1-3751-3751.1047-r0-0-0'], 'label': '1-3751-3751.1047-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1047'}
Lfunction data - 1-3751-3751.1047-r0-0-0