Lfunction data - 8-4032e4-1.1-c1e4-0-4

Formats: - HTML - YAML - JSON - 2025-09-12T03:32:04.515398

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '180371530402881086619629071174,594767708087684152199230006992,1413104144897424090705408112697,2361824199710700869839164801218', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1074460.6669852738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 0, 2, 0, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.1', 'coefficient_field': '1.1.1.1', 'conductor': 264290829336576, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1], [1, 0, 20, 0, 150, 0, 500, 0, 625], [1, 0, 2, 0, 1], [1, 0, -8, 0, 258, 0, -968, 0, 14641], [1, 0, 20, 0, 438, 0, 3380, 0, 28561], [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], [1, 0, 76, 0, 2166, 0, 27436, 0, 130321], [1, 0, 56, 0, 1842, 0, 29624, 0, 279841], [1, 0, 80, 0, 3282, 0, 67280, 0, 707281], [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], [1, 0, -76, 0, 4182, 0, -104044, 0, 1874161], [1, 0, -20, 0, 3462, 0, -33620, 0, 2825761], [1, 24, 388, 3960, 30966, 170280, 717412, 1908168, 3418801], [1, 0, 44, 0, 4902, 0, 97196, 0, 4879681], [1, 0, -112, 0, 8754, 0, -314608, 0, 7890481], [1, 0, -92, 0, 9078, 0, -320252, 0, 12117361], [1, 0, -172, 0, 14838, 0, -640012, 0, 13845841], [1, -48, 1132, -16560, 163446, -1109520, 5081548, -14436624, 20151121], [1, 0, 248, 0, 25458, 0, 1250168, 0, 25411681], [1, 8, 316, 1784, 35494, 130232, 1683964, 3112136, 28398241], [1, 0, -116, 0, 15846, 0, -723956, 0, 38950081], [1, 0, 244, 0, 28662, 0, 1680916, 0, 47458321], [1, 0, -212, 0, 27078, 0, -1679252, 0, 62742241], [1, 40, 988, 15640, 182854, 1517080, 9296092, 36506920, 88529281], [1, 0, 260, 0, 37302, 0, 2652260, 0, 104060401], [1, 0, -380, 0, 57318, 0, -4031420, 0, 112550881], [1, 0, -104, 0, 25602, 0, -1190696, 0, 131079601], [1, 0, -364, 0, 56886, 0, -4324684, 0, 141158161], [1, 0, -128, 0, 29634, 0, -1634432, 0, 163047361]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 5], 4]], [[[1, 0, 1], 2]], [[[1, 0, -4, 0, 121], 2]], [[[1, -4, 13], 2], [[1, 4, 13], 2]], [[[1, 0, -17], 4]], [[[1, 0, 19], 4]], [[[1, 0, 28, 0, 529], 2]], [[[1, 0, 40, 0, 841], 2]], [[[1, 0, -46, 0, 961], 2]], [[[1, 0, -38, 0, 1369], 2]], [[[1, 0, -10, 0, 1681], 2]], [[[1, 6, 43], 4]], [[[1, 0, 22, 0, 2209], 2]], [[[1, 0, -56, 0, 2809], 2]], [[[1, 0, -46, 0, 3481], 2]], [[[1, 0, -86, 0, 3721], 2]], [[[1, -12, 67], 4]], [[[1, 0, 124, 0, 5041], 2]], [[[1, 2, 73], 4]], [[[1, 0, -58, 0, 6241], 2]], [[[1, 0, 122, 0, 6889], 2]], [[[1, 0, -106, 0, 7921], 2]], [[[1, 10, 97], 4]], [[[1, 0, 130, 0, 10201], 2]], [[[1, 0, -190, 0, 10609], 2]], [[[1, 0, -52, 0, 11449], 2]], [[[1, -20, 109], 2], [[1, 20, 109], 2]], [[[1, 0, -64, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 4, 'label': '8-4032e4-1.1-c1e4-0-4', 'leading_term': '0.56950523507864766373775679313720402885074209595072428848442148129384145739827283135284376', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4032/2/j/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0126953125', 'prec': 40}, 'plot_values': [0.5695052350786475, 0.564371484128081, 0.5492115217846912, 0.5241421113922126, 0.48938792673951836, 0.4453059630907514, 0.39238240884556785, 0.3312018465299967, 0.2624339218790651, 0.18682784930758561, 0.10522739388428022, 0.01856898300137931, -0.07212439133384291, -0.16574965469361294, -0.2611382428575943, -0.35706307916752417, -0.4522458090969816, -0.5453633500580195, -0.6350489969386889, -0.7199073456198561, -0.7985268964466078, -0.8694906368896539, -0.9313871145253798, -0.9828252595301502, -1.0224476559051956, -1.0489429196827256, -1.0610583691549127, -1.0576165670359994, -1.0375295527000725, -0.999813013031745, -0.9436035813224429, -0.8681719983746606, -0.7729350859896316, -0.6574694998215698, -0.5215306645413055, -0.3650596282696314, -0.1881901424147956, 0.008740747897168085, 0.22517542531268558, 0.46033864145886166, 0.7132383187290161, 0.9826616051919055, 1.2671643453373076, 1.5650855869729288, 1.8745583198559368, 2.193515451295569, 2.519691349868513, 2.850647428527442, 3.1837932300054668, 3.516404413857827, 3.84564062885984, 4.16857856990651, 4.482241362615274, 4.783628384653745, 5.069751014018776, 5.337666333559776, 5.584509970930284, 5.807534561798165, 6.004160966471663, 6.17200323613423, 6.308897603071717, 6.412943310867165, 6.482562530163071, 6.516506263802287, 6.513870920190908, 6.474133037557707, 6.397207599352373, 6.283426048747758, 6.133532613656611, 5.9487041150784865, 5.730595001800246, 5.4812829327507995, 5.2032401977107, 4.8993319937275945, 4.572838246259187, 4.22736893186932, 3.8668113538417943, 3.4953050226791134, 3.1172354133514477, 2.7371291008327927, 2.359584306054648, 1.9892269969262313, 1.6306792964302388, 1.2884515949026691, 0.9668699608349673, 0.6700246323830853, 0.40172393640995774, 0.16540449935616575, -0.03592724994084849, -0.19973853722849172, -0.3240137860663144, -0.40730633364298413, -0.4487663249735015, -0.44816001613413614, -0.405892037372196, -0.3230061563122691, -0.20117194489251686, -0.04266851572273737, 0.1496290286404498, 0.37230051119408614, 0.6214355341939503, 0.8926873646589994, 1.1813270055298115, 1.4823320826865443, 1.7904711678012606, 2.1003855440804395, 2.4066754516008766, 2.7040006965990395, 2.987171728810799, 3.2512389246729647, 3.4915904493361887, 3.7040321128414955, 3.8848574327994974, 4.030918605656374, 4.1397086404541525, 4.209391225211739, 4.2388253273520355, 4.227594638625908, 4.176048731260309, 4.08526684493403, 3.9570245879689607, 3.793769859338869, 3.5986095149984623, 3.3752110352234634, 3.127716789845515, 2.8606716492461244, 2.5789602233996654, 2.2876712741622707, 1.9919832906501316, 1.6970668058613687, 1.4079966958445582, 1.129618555730255, 0.8664413481107093, 0.6225492154111624, 0.40152618669265333, 0.20636535506491405, 0.03940468973804301, -0.0977165937078918, -0.20408340043322482, -0.2795253817748124, -0.32461504645473066, -0.34064488282135874, -0.32957987992016113, -0.2940059028677266, -0.2370622993412283, -0.16235390279440867, -0.073833564074162, 0.024294894140087207, 0.12768305228814897, 0.23196390580354823, 0.33290833427609146, 0.42651939972900627, 0.5091328681880704, 0.5775361738265073, 0.629113705398579, 0.6618861043214841, 0.6745579998606107, 0.6665832286606753, 0.6382478944250377, 0.5906196407721096, 0.525512950022881, 0.44547168832324663, 0.35375948333708884, 0.25421822623154655, 0.15115342732272324, 0.04923761636069369, -0.04658601608113657, -0.1312974530699045, -0.19995652541584735, -0.24783978714040428, -0.27057891058457884, -0.2643404471930299, -0.22596273807145142, -0.15307095030308637, -0.044188398527898416, 0.10116725557184104, 0.28242888180783277, 0.49794788216698876, 0.7449760585027182, 1.0196957657951387, 1.3172815839815266, 1.6319841666994035, 1.9572380700347112, 2.285812096066899, 2.609976378123886, 2.9216874363730234, 3.212801264171851, 3.4752850007748894, 3.70143001764616, 3.8840752946037416, 4.016852420834253, 4.0943661935710525, 4.112365737697922, 4.067915768322691, 3.9595723252585677, 3.787443101906832, 3.5532350584383554, 3.2602917566766245, 2.9136121371134016, 2.519744794540039, 2.0866739266697896, 1.6236871836178794, 1.1412049744981834, 0.6505321366321162, 0.16360990022374117, -0.30725274189170626, -0.7496933119915024, -1.1515965160995312, -1.5013870007374912, -1.7883381639993576, -2.0029141496595835, -2.1369991602045433, -2.184116697269186, -2.1396531285833538, -2.0010821503906713, -1.7680187367435591, -1.442267339259805, -1.0278569130989679, -0.5310318490324033, 0.039902999156567205, 0.6747359138581641, 1.3615358989602895, 2.0869296471918712, 2.83640407128201, 3.594604969423561, 4.345691070025458, 5.073809851373242, 5.763407892196969, 6.3995474897366655, 6.968298263936701, 7.4572611278566345, 7.855723144400401, 8.154845723846263, 8.34794381553538, 8.430885065119137, 8.401974150342147, 8.261911710871502, 8.01385514469128, 7.663570658057736, 7.219037500444899, 6.690171708737321, 6.088655749696, 5.427825664926796, 4.722105262096252, 3.986593025224562, 3.236750116450195, 2.4881177375704757, 1.7557714851873678, 1.0539354981945628, 0.3956823253378406, -0.2073549897525848, -0.745317226365328, -1.2103196427308456, -1.5965930851580634, -1.900620602410965, -2.1211528856428106, -2.259144924232529, -2.317667513557103, -2.3018190310028506, -2.2184482158740986, -2.0758661828194764, -1.8835699509762145, -1.651974588580419, -1.3919930352645165, -1.1146648812172397, -0.8308271558900473, -0.550807459812028, -0.2840651795902408, -0.038914208045496446, 0.1776964162508213, 0.3603653759265778, 0.5053737580794209, 0.6107413206715754, 0.6762286002687236, 0.7032973877367247, 0.6949772546840287, 0.6556867703475245, 0.5910230848078039, 0.5075220321231076, 0.4123493460882025, 0.3129925420931002, 0.2169550212018877, 0.13145130435345564, 0.06310093960147536, 0.017661124964119073, -0.00020490712161696744, 0.012882088049213541, 0.05888024795476583, 0.13824356035429103, 0.24989648489206434, 0.39128487690852554, 0.5584705416737895, 0.7462705904183854, 0.9484586172790532, 1.1580559326354776, 1.3675801813189838, 1.5693161050599154, 1.7556364974853989, 1.9193996113425005, 2.0541750713025686, 2.1544739414188463, 2.2160107634128714, 2.236008078492818, 2.213223628156732, 2.1479831597440864, 2.0422323111828278, 1.899594625012706, 1.7251301235890568, 1.5251233739481873, 1.3068915229167202, 1.078579682831857, 0.8487376423702916, 0.6259613627687334, 0.4185692766926063, 0.2342754083625897, 0.07979020522231622, -0.03948665418047896, -0.11971877911195704, -0.15885696978451966, -0.1567996641931465, -0.1154597420647604, -0.038765655761501476, 0.06739904135887738, 0.19537198605475242, 0.33595269509917874, 0.47869926328104817, 0.61229491895614, 0.7249748251033138, 0.8049673623012498, 0.8409580223486075, 0.8225905489171637, 0.740908532466938, 0.5887616050622141, 0.3611852965068587, 0.05574923476694015, -0.3272456453931311, -0.7846353345098637, -1.310335561887657, -1.8953955621116967, -2.5281764820855344, -3.1945977393434646, -3.878488605104484, -4.562104369577186, -5.226593856552002, -5.852518617340281, -6.420480734935548, -6.911914817433206, -7.309571095671642, -7.598034644777264, -7.764330974101737, -7.7986360139106905, -7.6944588199933985, -7.448862878014867, -7.06273685935453, -6.541072242520247, -5.892671183222348, -5.129915945376021, -4.268549686634961, -3.327367511670218, -2.3275355200604637, -1.2919981860475636, -0.24486633792331572, 0.7893437839807643, 1.7864555538335734, 2.7232859134702427, 3.5783422389221347, 4.332673665107684, 4.970278580819992, 5.4784645039814075, 5.848273344398869, 6.0750237807127965, 6.158122167714315, 6.100915595596001, 5.910636996069674, 5.598416587076251, 5.1785340314619965, 4.6678213009313305, 4.085185806591977, 3.451165245716434, 2.786951785735254, 2.1136492690967037, 1.4516684269829003, 0.8201474398478027, 0.23620279959145318, -0.2855711629523969, -0.7334731208676979, -1.099029637453757, -1.3771839678680644, -1.5663005991464176, -1.668083443631299, -1.6874554918149156, -1.632157159446699, -1.5122812501001208, -1.3397928636098346, -1.128035696923352, -0.8910260640548836, -0.6428098663514815, -0.3968803240826687, -0.16563208656780154, 0.040214971141978466, 0.21205070000856163, 0.34369952686908944, 0.43166064799017273, 0.47522537473897847, 0.47645176801623884, 0.44002970598499985, 0.3730512277507971, 0.28463288515418106, 0.18546087035832243, 0.08727992769788465, 0.0023385988128709024, -0.05721783339367006, -0.07994030750193207, -0.055639271679372784, 0.02411236553062136, 0.1655328529913811, 0.37226905855295095, 0.645148375959451, 0.9821089941831834, 1.3781739656795406, 1.8255313886342548, 2.3137830984209815, 2.8304537184100234, 3.3613422125892054, 3.890963735790369, 4.4031729532318336, 4.882060476843324, 5.312358381501511, 5.679918068678256, 5.972353930866461, 6.1799064637739125, 6.2955056890838135, 6.314923297753118, 6.2370714366642845, 6.064437508889327, 5.8026016440519035, 5.4599036376502506, 5.047253777884201, 4.578013918545099, 4.067107696449628, 3.530358882734821, 2.9839876880331517, 2.444157497917063, 1.926091396021458, 1.443464679103237, 1.0079662037651356, 0.6289279586072379, 0.31288514762047964, 0.06338893407877906, -0.1190310759829557, -0.23681866659817272, -0.2952043193812482, -0.3018646360219128, -0.26649463640847715, -0.20031693532437986, -0.11546278262224396, -0.02433502715602634, 0.06102279456803096, 0.12954728378176059, 0.17175354254138955, 0.1802395944186838, 0.15009697301333214, 0.07921843165186031, -0.03154416323042288, -0.17835618750375823, -0.35451209531732625, -0.5507055265633969, -0.7554221950308502, -0.9554287762118154, -1.136371643407561, -1.2835047318093802, -1.3823583236038512, -1.4194237927929556, -1.3828667335100107, -1.2632514230650325, -1.0540098838359064, -0.7518600185249775, -0.3571529243765365, 0.12592799823291573, 0.6894437215332493, 1.3218449320922707, 2.008262716112691, 2.7310752633663804, 3.4704897757981352, 4.2051686333605796, 4.9130286559864835, 5.572355323772489, 6.16246024109511, 6.6643603243930345, 7.061620345292644, 7.3414539222181245, 7.494906082177917, 7.517084922933609, 7.407540105163879, 7.170794705220094, 6.815753064886063, 6.355248967793292, 5.805745270526377, 5.1871023326785926, 4.521388190344101, 3.831947657088037, 3.1426520700257785, 2.4771998867618445, 1.8579010515919139, 1.3047982683917525, 0.8349979108974587, 0.4620943943762307, 0.19554388795444763, 0.04035654241057212, -0.003007897677863039, 0.061400941208811205, 0.22524900114525637, 0.476343051033663, 0.7992001056488289, 1.175765903281287, 1.5862239575062136, 2.009843955147374, 2.4258793259141505, 2.8145486629999548, 3.157804542540661, 3.440023478703511, 3.6486600424021227, 3.7748847922751314, 3.813744683161516, 3.7642300379373426, 3.62927674690733, 3.4156833434242304, 3.1335308216757194, 2.7955946062080907, 2.416733410573021, 2.0132048851365134, 1.601734087157346, 1.1986932727115962, 0.819340529296918, 0.4770717454464298, 0.18277470515322441, -0.05563936269836944, -0.2335818816439737, -0.35002217592824547, -0.4074120399698274, -0.41146927058071175, -0.37084380616072543, -0.2966447538427459, -0.20172115330401869, -0.09992032145683144, -0.005309875707018823, 0.06865854009881124, 0.10997150354190498, 0.10877330854379415, 0.05800630645101641, -0.04604680016589529, -0.20345528780168537, -0.4104889561695985, -0.6596305736917192, -0.9398278785733974, -1.2369395525861817, -1.5342929303213517, -1.813413519940489, -2.055031566987265, -2.2399459848187595, -2.3499015398162166, -2.3685722925684214, -2.28272876177299, -2.0828270466398835, -1.7635408265446126, -1.3243107039491622, -0.7699102979930708, -0.1102042584875047, 0.640133021127577, 1.4619314418269493, 2.3319573845011017, 3.2239822117832238, 4.109791323256589, 4.960205938613352, 5.746241837865715, 6.440395894114331, 7.017764980623465, 7.457108322765789, 7.741944890461239, 7.861236079442922, 7.809867807308463, 7.589015083445067, 7.206398355566946, 6.675892692047817, 6.01701342041795, 5.254284681415179, 4.416425741725139, 3.5351133626638953, 2.6437640638647197, 1.7762724790704232, 0.965630027778295, 0.24263098850506432, -0.3652845839385423, -0.835122784225884, -1.1493689652230132, -1.2965166624926003, -1.271443341207458, -1.0756320510442936, -0.7171325710680441, -0.21004202404710753, 0.4260861389662085, 1.167023310285012, 1.985031620444153, 2.849973475417842, 3.7303965934432948, 4.594806316645525, 5.413326840475185, 6.1585132088951715, 6.806134660310009, 7.336149708324025, 7.733990779194768, 7.990374281339107, 8.101219818481756, 8.067809761892784, 7.89717365759781, 7.600857752055868, 7.194032002556119, 6.694920753148666, 6.124423357116858, 5.504482616200646, 4.856982594329583, 4.203031176821761, 3.5624385586684086, 2.952542674589895, 2.387598865177301, 1.8785281086695187, 1.432849538189765, 1.0544468271319196, 0.743744911401481, 0.49811139217213474, 0.312363174855763, 0.17928768288975552, 0.0903131385120613, 0.0362119884343027, 0.0077759109359203825, -0.0035601568028556176, -0.005171510771727062, -0.0028168192905946303, -0.0003497966895242011, 0.0004206507079408612, -0.00028954200579533237, -0.00041175634621138394, 0.0036657889923871144, 0.01667266051714142, 0.0439420166237413, 0.0908424492975597, 0.1622086514665566, 0.2617869258588834, 0.3917291177804167, 0.5521916879629537, 0.741132389452277, 0.9541632436507015, 1.1845437859012626, 1.4233958145257768, 1.6602495051780413, 1.8834411122442865, 2.080644962616964, 2.239634450110831, 2.349350292507605, 2.4004170313118114, 2.385729737502132, 2.301184393188387, 2.146548677782387, 1.9254365905277933, 1.645321627514886, 1.3175986254133152, 0.9575969727614922, 0.5836929109394826, 0.21652127046246275, -0.12178311526299464, -0.4084611190037692, -0.6215075907741503, -0.7408226089732891, -0.7492541687602375, -0.6336479967059306, -0.3858467058405395, -0.0033632376274908113, 0.5101708095144954, 1.1447609499514926, 1.8841561964483462, 2.706262322973924, 3.5838369190753356, 4.485537505062843, 5.377104474428905, 6.222709278863146, 6.986521263371874, 7.634582883317009, 8.136201630936906, 8.46533354195208, 8.602028660876911, 8.533950282907794, 8.25683986710137, 7.7748890148167185, 7.101020428386759, 6.2569662718014705, 5.272242795574249, 4.183093073150117, 3.0312891602486505, 1.8626095820780084, 0.7248161944358955, -0.33425116428028906, -1.2686351350732834, -2.036406123776458, -2.6014124382650183, -2.934803440503777, -3.016443320310417, -2.836167144160211, -2.3940942814742083, -1.7007437824176421, -0.7768950847099498, 0.3470652170380267, 1.6324573928031678, 3.0336731803028907, 4.499854377398163, 5.977262558932643, 7.411241017678544, 8.748093867947095, 9.937260976471684, 10.93411000420295, 11.70104658922879, 12.20856874756018, 12.436585456773896, 12.376109738621889, 12.028547949185688, 11.40515869768303, 10.526785127914358, 9.423713043163643, 8.133394738392877, 6.698646326387655, 5.166158302884692, 3.5849981098857024, 2.0040781559119414, 0.47027213860961253, -0.9731554646483498, -2.288142507854546, -3.443163253663743, -4.41401801868819, -5.184418351671444, -5.7465780164489635, -6.100734921487043, -6.25448786025122, -6.222142439147242, -6.024100599248796, -5.685144981550485, -5.232960713477063, -4.696891990311636, -4.106837936351786, -3.4915586961975182, -2.8774701381673036, -2.2877860492278015, -1.7418744196762306, -1.2545920006970133, -0.8360680374431909, -0.49177051077125983, -0.22275793677078184, -0.026145378752892825, 0.10423865745343237, 0.17710581886228513, 0.20290923687922946, 0.19295589500369498, 0.15860421914835712, 0.11055936282062177, 0.05826151455215966, 0.00941245135713785, -0.030299040501631538, -0.057314100777597486, -0.07018267906103508, -0.06934279216912682, -0.05678508458493564, -0.035646365856349546, -0.009751829358656927, 0.016897198022123843, 0.040584764026766085, 0.05827419760165281, 0.06791985604413445, 0.06866508283465637, 0.06090271062960403, 0.04620757758975195, 0.027140206527360242, 0.006939308836454395, -0.010860369524797556, -0.022862490674483572, -0.026271397609533505, -0.019296297006130492, -0.0014867476619984162, 0.026025485408124046, 0.06042329269215837, 0.09729373464233995, 0.13086924063881325, 0.15443874710112732, 0.16095604816785664, 0.14375779612989714, 0.09736773686876316, 0.018378853361616404, -0.09363580466981619, -0.23534521800439054, -0.3989694710323527, -0.5717381124172597, -0.7356524141218398, -0.867491812379601, -0.9390533856607508, -0.9177450189973807, -0.7677373955633371, -0.4510955721519858, 0.07085549094169168, 0.8358098264028562, 1.878293500115748, 3.228007411685887, 4.908092625760541, 6.933320342572436, 9.308359758071385, 12.026759601377423, 15.070083730979693, 18.40746388529758, 21.996065463083653, 25.781453254569122, 29.698338955426888, 33.672287887416985, 37.62312774681764, 41.466211323701415, 45.114300370362756, 48.480855952282795, 51.48546549888442, 54.05438017481449, 56.122024310474224, 57.63421326313958, 58.55349056723643, 58.85725458480801, 58.53738821649073, 57.60178092965212, 56.0776390872656, 54.00675881079207, 51.44292510229482, 48.45129334449838, 45.10915230989131, 41.49967115678457, 37.708231455452186, 33.82069679103082, 29.92273586702405, 26.094415692763164, 22.40738937899684, 18.923758061259978, 15.695726160215735, 12.76294584455874, 10.15190854094269, 7.876496788960516, 5.939033662241204, 4.330616363591721, 3.0325732761510498, 2.0184200590487906, 1.2559365098100381, 0.7090498489692314, 0.33993025496565504, 0.11099835185989806, -0.013305604696005686, -0.06505199385120188, -0.07167561640657867, -0.055212007360953656, -0.0319317004331965, -0.012365272120590243, -0.0016948087049216305, -0.0004592748803970421, -0.0055131235215253, -0.01115667153531005, -0.010358808310848577, 0.004007298214001771, 0.03803522557881021, 0.09580165443333591, 0.17856791915106426, 0.28425667448369785, 0.4073639725950444, 0.539022478703895, 0.6673142887552792, 0.7779421651770285, 0.8554029315384648, 0.883870237628697, 0.8481917138573706, 0.7351059350461878, 0.5347249578003025, 0.24116889502207245, -0.14683786247311842, -0.6253677829171786, -1.1847881571230867, -1.810239165967012, -2.4821587233301754, -3.1769294746841132, -3.8678562727933246, -4.526567334653805, -5.124333749197161, -5.633484306894336, -6.029122888752522, -6.2903156525560995, -6.401092155273718, -6.351448329429231, -6.138444411280537, -5.766073511109642, -5.245018381439787, -4.592385062061135, -3.83135428168151, -2.989654875016073, -2.0981704507757337, -1.1896190562995237, -0.29715457482756935, 0.5474753153008286, 1.3154023690217767, 1.9819026216475017, 2.527588578764578, 2.9392037785334186, 3.2100248769754756, 3.340021892509829, 3.335823994909623, 3.20995211871646, 2.979891213244728, 2.6670551561252736, 2.2956128120374673, 1.8909054167449755, 1.478026693870422, 1.0805175418236468, 0.7191333457050961, 0.410789595488282, 0.1678412849185068, -0.002380656224568946, -0.09776898298633939, -0.12118636708289059, -0.07997711495163991, 0.014731630558633033, 0.14899410469883345, 0.3071843756326233, 0.47310665325912565, 0.6311290848346445, 0.7673923787860819, 0.870643004381429, 0.932852468252515, 0.9497034213694545, 0.9209443033187923, 0.850073451903763, 0.7438666446944098, 0.6117913707076577, 0.46526552963327633, 0.31647500748447815, 0.17728368681722756, 0.05821540544567503, -0.03253057451474068, -0.08998580350822491, -0.11300914333502864, -0.10462869704116406, -0.07212975926034569, -0.02676185033519695, 0.016850494437283207, 0.04154689414377922, 0.02873163210434839, -0.04033491923179294, -0.1831937582940408, -0.4148261314107827, -0.7463206524268582, -1.1837765213045832, -1.7274372946660237, -2.3711162867600826, -3.102061795690753, -3.901143045065956, -4.7433706592512515, -5.5988806599475405, -6.43458426020605, -7.215534100126981, -7.9065104618170405, -8.47399841107072, -8.888685473233569, -9.126670705860798, -9.170725988512991, -9.011722853627589, -8.650166696420756, -8.095803506049876, -7.367269595289986, -6.4917352359253755, -5.504295221952303, -4.445773448334371, -3.360769454403822, -2.295721181599757, -1.2966852204726202, -0.4067364816882198, 0.33615825566974245, 0.9010806462989235, 1.2660767034008555, 1.4192259346513432, 1.359221083324091, 1.095629383656797, 0.648757340536886, 0.04834842770145852, -0.6679213817663836, -1.4562108643755138, -2.268797859484071, -3.0566907693582803, -3.7720360868471605, -4.370572310912438, -4.814375296164906, -5.073597573932824, -5.127797832469429, -4.9671258730182615, -4.593425170175277, -4.019567232611556, -3.268561517226286, -2.372541869089588, -1.371485899637262, -0.3105453900213794, 0.7624009753532596, 1.7991168860353315, 2.7535664025586666, 3.584452203188164, 4.257208157420719, 4.7456379082667945, 5.033386351465641, 5.114781571071554, 4.994922299608506, 4.689392079338211, 4.223584774875672, 3.630330171255743, 2.947947364806205, 2.21848030246203, 1.486301603276985, 0.7955375782868532, 0.1867066707369316, -0.3066916469246412, -0.6597698284588343, -0.8526077319088955], 'positive_zeros': ['0.14228804874971602617736121743544', '0.46918899259827702462309735149379', '1.11474261491534579866124691248756', '1.23445644086025279572211032658560', '1.72993651638594484156621580269470', '1.86315077615667525680878371578825', '2.10110872134390969165841895212822', '2.21319651930375439917683443574403', '2.59418935690332892199898002177730', '2.77943286531179220805733196494747', '3.16931585724086181994128067914653', '3.40449678285312499520422442215701', '3.61746058591613972159331306048099', '3.62116990776835524145782518484290', '4.00705067315927215019143456887928', '4.08020597178771150561004771455601', '4.24225296431010947518190985975168', '4.58598802393403868999780784986493', '4.86784729279691208672959611053230', '5.06279258406415346869821531978719', '5.20548079281903520116489852705691', '5.25287280722824407309816137668716', '5.69141735556805144807283262511445', '5.79252410295276734172617003257609', '5.87472715297778390839506675011795', '6.06525497686410357034758676149522', '6.45728967754517725464777800557178', '6.46384623162255478689977856472176', '6.80142377286183488941458998056168', '6.91973077240824308686450639650658', '6.97758220456534074887444198306564', '7.20020020880583669837973944067014', '7.50768685595505047311050377660223', '7.60895450742240635917104821738571', '8.055724235078652438779737146408024', '8.102515148237133141706101506262994', '8.121038423024082749760834662193142', '8.140630737945495921050259538069746', '8.582126208714631061290678870827418', '8.882573728797241316488891784237747'], 'prelabel': '8-4032e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 715319141222246268, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14228804874971602617736121744', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.46918899259827702462309735149', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.11474261491534579866124691249', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 1074460.6669852738, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 264290829336576, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0], 'euler11': [1, 0, -8, 0, 258, 0, -968, 0, 14641], 'euler13': [1, 0, 20, 0, 438, 0, 3380, 0, 28561], 'euler17': [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], 'euler19': [1, 0, 76, 0, 2166, 0, 27436, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 56, 0, 1842, 0, 29624, 0, 279841], 'euler29': [1, 0, 80, 0, 3282, 0, 67280, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], 'euler37': [1, 0, -76, 0, 4182, 0, -104044, 0, 1874161], 'euler41': [1, 0, -20, 0, 3462, 0, -33620, 0, 2825761], 'euler43': [1, 24, 388, 3960, 30966, 170280, 717412, 1908168, 3418801], 'euler47': [1, 0, 44, 0, 4902, 0, 97196, 0, 4879681], 'euler5': [1, 0, 20, 0, 150, 0, 500, 0, 625], 'euler53': [1, 0, -112, 0, 8754, 0, -314608, 0, 7890481], 'euler59': [1, 0, -92, 0, 9078, 0, -320252, 0, 12117361], 'euler61': [1, 0, -172, 0, 14838, 0, -640012, 0, 13845841], 'euler67': [1, -48, 1132, -16560, 163446, -1109520, 5081548, -14436624, 20151121], 'euler7': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler71': [1, 0, 248, 0, 25458, 0, 1250168, 0, 25411681], 'euler73': [1, 8, 316, 1784, 35494, 130232, 1683964, 3112136, 28398241], 'euler79': [1, 0, -116, 0, 15846, 0, -723956, 0, 38950081], 'euler83': [1, 0, 244, 0, 28662, 0, 1680916, 0, 47458321], 'euler89': [1, 0, -212, 0, 27078, 0, -1679252, 0, 62742241], 'euler97': [1, 40, 988, 15640, 182854, 1517080, 9296092, 36506920, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 20, 0, 150, 0, 500, 0, 625], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -8, 0, 258, 0, -968, 0, 14641], [1, 0, 20, 0, 438, 0, 3380, 0, 28561], [1, 0, -68, 0, 1734, 0, -19652, 0, 83521], [1, 0, 76, 0, 2166, 0, 27436, 0, 130321], [1, 0, 56, 0, 1842, 0, 29624, 0, 279841], [1, 0, 80, 0, 3282, 0, 67280, 0, 707281], [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], [1, 0, -76, 0, 4182, 0, -104044, 0, 1874161], [1, 0, -20, 0, 3462, 0, -33620, 0, 2825761], [1, 24, 388, 3960, 30966, 170280, 717412, 1908168, 3418801], [1, 0, 44, 0, 4902, 0, 97196, 0, 4879681], [1, 0, -112, 0, 8754, 0, -314608, 0, 7890481], [1, 0, -92, 0, 9078, 0, -320252, 0, 12117361], [1, 0, -172, 0, 14838, 0, -640012, 0, 13845841], [1, -48, 1132, -16560, 163446, -1109520, 5081548, -14436624, 20151121], [1, 0, 248, 0, 25458, 0, 1250168, 0, 25411681], [1, 8, 316, 1784, 35494, 130232, 1683964, 3112136, 28398241], [1, 0, -116, 0, 15846, 0, -723956, 0, 38950081], [1, 0, 244, 0, 28662, 0, 1680916, 0, 47458321], [1, 0, -212, 0, 27078, 0, -1679252, 0, 62742241], [1, 40, 988, 15640, 182854, 1517080, 9296092, 36506920, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/j/b'], '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': '8-4032e4-1.1-c1e4-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-4032e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 715319141222246268, 'z1': {'__RealLiteral__': 0, 'data': '0.14228804874971602617736121744', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '180371530402881086619629071174,594767708087684152199230006992,1413104144897424090705408112697,2361824199710700869839164801218', 'Lhash_array': ['180371530402881086619629071174', '594767708087684152199230006992', '1413104144897424090705408112697', '2361824199710700869839164801218'], 'factors': ['2-4032-24.11-c1-0-3', '2-4032-24.11-c1-0-12', '2-4032-24.11-c1-0-35', '2-4032-24.11-c1-0-47'], 'label': '8-4032e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/j/b'}