Lfunction data - 8-1872e4-1.1-c1e4-0-21

Formats: - HTML - YAML - JSON - 2025-09-10T11:46:34.810918

• 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': '576742519990662101346081996611,800972511516719079036358545111,1663175379515060526446439389444,2612224340092550963251839603731', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49926.578622459405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, 6, 18, 78, 169]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': '1.1.1.1', 'conductor': 12280707219456, 'conductor_radical': 78, 'degree': 8, 'euler_factors': [[1], [1], [1, 0, -11, 0, 76, 0, -275, 0, 625], [1, 0, -7, 0, 4, 0, -343, 0, 2401], [1, 0, -8, 0, 190, 0, -968, 0, 14641], [1, 6, 18, 78, 169], [1, -6, 73, -294, 1908, -4998, 21097, -29478, 83521], [1, 0, -68, 0, 1878, 0, -24548, 0, 130321], [1, -4, 64, -212, 2142, -4876, 33856, -48668, 279841], [1, -4, 88, -284, 3678, -8236, 74008, -97556, 707281], [1, 0, -88, 0, 3790, 0, -84568, 0, 923521], [1, 0, -27, 0, 1964, 0, -36963, 0, 1874161], [1, 0, -36, 0, 3686, 0, -60516, 0, 2825761], [1, 30, 501, 5430, 42092, 233490, 926349, 2385210, 3418801], [1, 0, -119, 0, 7444, 0, -262871, 0, 4879681], [1, 16, 172, 1712, 15318, 90736, 483148, 2382032, 7890481], [1, 0, -36, 0, 7286, 0, -125316, 0, 12117361], [1, -28, 504, -6020, 55070, -367220, 1875384, -6355468, 13845841], [1, 0, -184, 0, 15742, 0, -825976, 0, 20151121], [1, 0, -207, 0, 20756, 0, -1043487, 0, 25411681], [1, 0, 32, 0, 5406, 0, 170528, 0, 28398241], [1, -28, 576, -7532, 79550, -595028, 3594816, -13805092, 38950081], [1, 0, -196, 0, 23382, 0, -1350244, 0, 47458321], [1, 0, -320, 0, 41374, 0, -2534720, 0, 62742241], [1, 0, -244, 0, 32614, 0, -2295796, 0, 88529281], [1, 4, 104, 604, 23710, 61004, 1060904, 4121204, 104060401], [1, -4, 384, -1172, 58142, -120716, 4073856, -4370908, 112550881], [1, 16, 524, 5392, 89494, 576944, 5999276, 19600688, 131079601], [1, 0, -179, 0, 17964, 0, -2126699, 0, 141158161], [1, 40, 1052, 17560, 222214, 1984280, 13432988, 57715880, 163047361]], 'euler_factors_factorization': [[1], [1], [[[1, 0, -11, 0, 76, 0, -275, 0, 625], 1]], [[[1, 0, -7, 0, 4, 0, -343, 0, 2401], 1]], [[[1, 0, -8, 0, 190, 0, -968, 0, 14641], 1]], [[[1, 6, 18, 78, 169], 1]], [[[1, -3, 32, -51, 289], 2]], [[[1, 0, -34, 0, 361], 2]], [[[1, -2, 30, -46, 529], 2]], [[[1, -2, 42, -58, 841], 2]], [[[1, 0, -88, 0, 3790, 0, -84568, 0, 923521], 1]], [[[1, 0, -27, 0, 1964, 0, -36963, 0, 1874161], 1]], [[[1, -10, 41], 2], [[1, 10, 41], 2]], [[[1, 15, 138, 645, 1849], 2]], [[[1, 0, -119, 0, 7444, 0, -262871, 0, 4879681], 1]], [[[1, 8, 54, 424, 2809], 2]], [[[1, 0, -18, 0, 3481], 2]], [[[1, -14, 154, -854, 3721], 2]], [[[1, 0, -184, 0, 15742, 0, -825976, 0, 20151121], 1]], [[[1, 0, -207, 0, 20756, 0, -1043487, 0, 25411681], 1]], [[[1, 0, 32, 0, 5406, 0, 170528, 0, 28398241], 1]], [[[1, -14, 190, -1106, 6241], 2]], [[[1, 0, -98, 0, 6889], 2]], [[[1, 0, -320, 0, 41374, 0, -2534720, 0, 62742241], 1]], [[[1, 0, -244, 0, 32614, 0, -2295796, 0, 88529281], 1]], [[[1, 2, 50, 202, 10201], 2]], [[[1, -2, 190, -206, 10609], 2]], [[[1, 4, 107], 4]], [[[1, 0, -179, 0, 17964, 0, -2126699, 0, 141158161], 1]], [[[1, 10, 113], 4]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 21, 'label': '8-1872e4-1.1-c1e4-0-21', 'leading_term': '3.6559237145878535419055351841708317681405947073228255962314883406296097749159194211629491', '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/1872/2/c/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [3.655923714587853, 3.6489743399669012, 3.6306703818582946, 3.6006420928569423, 3.558593344256251, 3.5044925237842457, 3.4386729974606065, 3.361572602663239, 3.273669115844699, 3.175434598008503, 3.0673422200383054, 2.9499203405377012, 2.8237771955370796, 2.689595349695833, 2.548120485967532, 2.400160960553723, 2.2465893593885693, 2.0883331196860504, 1.9263664085169474, 1.7617237628003348, 1.5954936436304332, 1.4288058172214122, 1.2628290586829725, 1.0987746644942533, 0.9378791958874486, 0.7813957156386313, 0.6305939689520815, 0.4867465928764385, 0.35111330363548493, 0.224935083227248, 0.10942519304904774, 0.0057483311076693576, -0.08499134336780388, -0.16175828242237045, -0.22360471770221818, -0.2696864188200662, -0.29927402576611245, -0.311767862723163, -0.30671319355591103, -0.2838113833150551, -0.24293373126554338, -0.1841321273808468, -0.10764557232642764, -0.01391012974264926, 0.09643276586198656, 0.22253877137101236, 0.3633604514102, 0.5176410579860357, 0.6839253565724386, 0.8605716956070185, 1.045757394950312, 1.2374908361138628, 1.433636709159654, 1.6319354049882357, 1.8300219384384586, 2.0254581829004716, 2.215762900757367, 2.3984392766322933, 2.571015669958573, 2.7310805405674956, 2.876315198447595, 3.0045322088594664, 3.1137238079911738, 3.202089701997107, 3.268072190357787, 3.310392146472475, 3.328089166062578, 3.320540614027476, 3.2874880001822233, 3.22904897761723, 3.145745606440988, 3.0385117173944183, 2.9086814506606484, 2.7579782565065627, 2.5885293832636385, 2.402839890683965, 2.2037394780368964, 1.9943550674952895, 1.7781043819166187, 1.5586177370764764, 1.3396694405181937, 1.1251370003109094, 0.9189538733677299, 0.7250093574443456, 0.5470799880121086, 0.38877518964022245, 0.2534594024323969, 0.1441698084170332, 0.06355596658756608, 0.013817775374447918, -0.0033558601586288505, 0.013163062199068576, 0.06389911711611224, 0.14874136735668242, 0.2669248288845027, 0.41701863734388933, 0.5969271029161974, 0.8039146857008834, 1.034634373703817, 1.2851629236192061, 1.5510674558901834, 1.8274790448294091, 2.109166769457588, 2.390630291818341, 2.6662081212459614, 2.9301831592326, 3.1768991807928653, 3.4008795861738874, 3.5969400588430736, 3.760307919141297, 3.886748920052211, 3.9726570672041888, 4.01514572961488, 4.01214930814976, 3.9624950067541977, 3.8659348448947335, 3.723195982003106, 3.535999534624906, 3.3070485877333904, 3.0399961111361566, 2.7394176489012976, 2.4107167568584043, 2.06003834644462, 1.6941788645287374, 1.320445962102939, 0.9464977553355468, 0.5802066646160062, 0.22950803186027882, -0.09780039393620116, -0.3942291288712635, -0.6527446002639392, -0.8669493620223679, -1.0312492947719691, -1.140984641970192, -1.1925455711784008, -1.183491736020287, -1.1126345374028248, -0.9800845912078634, -0.7872621154106082, -0.5369065016837394, -0.23305388357262408, 0.11903166394281474, 0.5130032697934416, 0.9415165164251419, 1.3963505726067478, 1.868593091736694, 2.348919965266394, 2.827727826816749, 3.295309109476076, 3.7420935877177914, 4.158999561855098, 4.537542781367894, 4.869973067036023, 5.1494945362551094, 5.3706089766674205, 5.529099566529932, 5.6220548166189035, 5.64800328592975, 5.607154399062754, 5.501189970723086, 5.333158230210093, 5.107488704412523, 4.830042037716659, 4.507757489979762, 4.1484407656423965, 3.760646645827527, 3.3535628038073897, 2.936614002487809, 2.519206158684215, 2.1105219929209635, 1.7193608319979659, 1.353802991184871, 1.020989396256829, 0.7269613321147956, 0.47655971687484555, 0.27324077507572336, 0.1189880364060316, 0.014297756380319814, -0.04179763728246219, -0.05171244995309487, -0.019211301397116663, 0.0507334922639536, 0.1521077390840406, 0.278050328682986, 0.421082808963918, 0.5733566831320115, 0.7269101533585242, 0.8739244373392027, 1.0069774818580328, 1.1192970598792824, 1.2049833466527553, 1.2591892511484069, 1.278284089345083, 1.2599846175023313, 1.2034281808454745, 1.1091854175765024, 0.9792497339966286, 0.8169670724277548, 0.6269244513150879, 0.41477993061689766, 0.18706706277553606, -0.04903224562734464, -0.2859424745025586, -0.515975085646194, -0.7315973425919144, -0.9257004724651762, -1.0918886806437471, -1.2247121078001502, -1.319853356710006, -1.3743069102656247, -1.3865515295979594, -1.3565817703094225, -1.2859124270900097, -1.1775692944267926, -1.0360236103901936, -0.866999138187274, -0.6772754963925455, -0.4744678190455871, -0.26675390058016657, -0.06254552358894197, 0.12982933296148372, 0.3024437766322606, 0.44810018198347523, 0.5606389974730139, 0.6352056757035174, 0.6684677077227791, 0.6588280109656406, 0.6065390080429442, 0.5137332364379139, 0.38441234945861946, 0.22441037114976858, 0.04120391262380735, -0.15632912679228167, -0.3581709056670126, -0.5534809111340957, -0.7310073411817158, -0.8794846915259944, -0.9880500998624802, -1.046691525937461, -1.046646694641801, -0.9807689474950635, -0.8438820101790008, -0.633087249172294, -0.3479398901749693, 0.009432804601239072, 0.4342893139024097, 0.9192694090635106, 1.4545734142841675, 2.0282449671511094, 2.6264790550316026, 3.233936595731509, 3.8342882536345892, 4.410787328731734, 4.946748264952043, 5.426081293411645, 5.833994370306939, 6.157474947197887, 6.385735412628501, 6.510753148721825, 6.527657166344797, 6.434878700180019, 6.234349096468978, 5.931702550438737, 5.536058400819683, 5.059788862055567, 4.518324370669706, 3.929759734866741, 3.314213102598113, 2.69325410482376, 2.089308165838624, 1.524905240175576, 1.0219145065307826, 0.6008455548921783, 0.2801535470517853, 0.07558374873730607, -0.00040558680622567275, 0.06089051426551975, 0.264065654487635, 0.6093629226916539, 1.0926019191902343, 1.7052303966111357, 2.4344799261109906, 3.263748401935002, 4.173125588279817, 5.139857412394856, 6.138984425383601, 7.144351358491372, 8.129284439236333, 9.06721955406463, 9.932668466322442, 10.70231868981261, 11.355353352875156, 11.874011960876944, 12.244521310098612, 12.457462313243992, 12.507678621511722, 12.394590728566834, 12.122351721085971, 11.699467580028063, 11.138358458162509, 10.455212763079155, 9.669159043193776, 8.801633991532682, 7.875764236895537, 6.915577589428065, 5.944998673351185, 4.987262553516959, 4.064279614767011, 3.1957594590061733, 2.3986587565914674, 1.6868670829160999, 1.0708109972273316, 0.5571975713590105, 0.14901217645236434, -0.1544019656115665, -0.3571451061192738, -0.4663972615499868, -0.49199739344008364, -0.44594666539796657, -0.34177218564733924, -0.19391283149028932, -0.017128214257157638, 0.174143202242115, 0.366369780484324, 0.5474082020077993, 0.7069290036842806, 0.8367639254157748, 0.9311058636315664, 0.986602775636519, 1.0023385741099455, 0.9797178874744389, 0.9222299989264355, 0.835117764951318, 0.7249845143567265, 0.5993680283199821, 0.46627064271363733, 0.3336779218270385, 0.2091153239794392, 0.09923457090224039, 0.009468743591732864, -0.05622855482445031, -0.09556503503417242, -0.10800784823936395, -0.09474236211748065, -0.058552378867274546, -0.003623131479052567, 0.06474674256520328, 0.14050286561462808, 0.21721794519599869, 0.2885009824070042, 0.34841865429487545, 0.39186441574324127, 0.4148907860936173, 0.4149652894387266, 0.39117738793348644, 0.3443055849840426, 0.27678277098445087, 0.19256521470671148, 0.09693951336775516, -0.003824643683616138, -0.10288937827150695, -0.19328564379995614, -0.26839706862562684, -0.3224823799360427, -0.3511349156712681, -0.3517044963141738, -0.32368569099281974, -0.26894562180195375, -0.19184196135351061, -0.09925199182737122, -0.00043193855042001977, 0.09330779966325625, 0.16901846512941804, 0.2126509072580205, 0.20976008552260697, 0.14625168001606173, 0.00916388748042405, -0.2125115188155232, -0.5269938623030203, -0.9389981809065303, -1.4491196014479581, -2.053328485446748, -2.742598435316103, -3.502807358038662, -4.314819330489469, -5.154735723876126, -5.994453911867849, -6.802453409666504, -7.544602981253225, -8.185223709963703, -8.688579840584442, -9.020029053259671, -9.147179999504756, -9.041368941618419, -8.679230681784027, -8.0434346248144, -7.123586339433723, -5.9172802273911955, -4.4306037275905625, -2.678060489523831, -0.6825779049216673, 1.5247501982705471, 3.905463321738206, 6.414761428680244, 9.002717645220386, 11.61557631605262, 14.197510915745895, 16.692404577504966, 19.045488021923752, 21.204684594355392, 23.122813303581708, 24.759282475003513, 26.080539337135015, 27.060952100364673, 27.684847063317406, 27.946367139862296, 27.848539820357814, 27.40347743527804, 26.633236992486463, 25.56743137817336, 24.241727518924954, 22.697491408889757, 20.98060493301837, 19.13871201277229, 17.219830604938494, 15.271440016658582, 13.33855976335671, 11.46208557137011, 9.678094917230935, 8.0168179194911, 6.501850189830041, 5.149906439327438, 3.970909290455161, 2.967957987764268, 2.1378830598503105, 1.4720920948889913, 0.9573713563987628, 0.5768754266836772, 0.3112866155226043, 0.13998842599113198, 0.04213914688177171, -0.0022900891236014233, -0.011607922052704184, -0.0016524041649202176, 0.014755461213312959, 0.028145263396976972, 0.03251948764528333, 0.025262921151235653, 0.006851903283096362, -0.019603137027979736, -0.04895687944877802, -0.07471962908271833, -0.08979177198558778, -0.08720849946630807, -0.06085827028563087, -0.006087978507356638, 0.07980985313875205, 0.19723076019846744, 0.344086188912377, 0.5158272894142651, 0.7056114880213582, 0.904608267283762, 1.1025760846357733, 1.288477569561276, 1.4510664146649608, 1.579592925886493, 1.6647254072515822, 1.69909721638116, 1.6777318155940772, 1.5985354072723839, 1.4628038130063097, 1.2750666597552935, 1.0429083298383646, 0.7767702406230859, 0.48956809585136607, 0.19586288722883785, -0.08891548357463691, -0.3492889268955994, -0.5706214614899238, -0.7400718403653345, -0.8474340760444481, -0.8858514815847088, -0.8524197393051294, -0.7485602216455675, -0.5801716320916016, -0.35752628823002597, -0.09504351648989916, 0.18931845196672173, 0.4748806321350173, 0.739158786440667, 0.9588879742344657, 1.1112876977916029, 1.1752379602528467, 1.1324057854025265, 0.968374163521772, 0.6735480543619239, 0.24381990740692586, -0.3189233709574671, -1.0065806477352683, -1.805004461725984, -2.6943627622119695, -3.6498022493269953, -4.642492830021407, -5.640702311894133, -6.611068161741014, -7.5200832233999435, -8.33570599731879, -9.028576017239935, -9.573371059546679, -9.949899910008462, -10.144324534573824, -10.149603136111867, -9.96571866301801, -9.599640174791107, -9.065475747687888, -8.383573196626784, -7.579324995361724, -6.6821669293895205, -5.724649448459181, -4.740569461237775, -3.763376410951593, -2.8248839577969416, -1.9540073030216099, -1.1753385171564907, -0.5082246150015645, 0.03392451491450311, 0.44404324848083826, 0.7214654210179194, 0.8716765138285527, 0.9058236869766844, 0.8398547287532215, 0.6934401941085245, 0.48880041890283915, 0.2493664882131133, -0.0015346282506105125, -0.2419796942456622, -0.4526436277521933, -0.6177829028924852, -0.7259910205918303, -0.7707220589265228, -0.7504661565509954, -0.6686187115579418, -0.5331548853347965, -0.3559467909353119, -0.15182760539632711, 0.062429627511540076, 0.2692374816497679, 0.4514414827464441, 0.5934616719071879, 0.6823393645996935, 0.7086612901441626, 0.6671868802524833, 0.5572343435283287, 0.38283353427162137, 0.15253309541644486, -0.1211099032617053, -0.4222515313897027, -0.7327171970036261, -1.0331433411553153, -1.304185116640186, -1.5277936110124066, -1.6883827714755475, -1.7739520237323525, -1.776969056712263, -1.6949958078070644, -1.530993609336813, -1.2934611089047603, -0.996096762156426, -0.6571135769857701, -0.29838437326483225, 0.05567593818763499, 0.3795248522447762, 0.6478874381234287, 0.8372014566306981, 0.9271746259385221, 0.9019825474944982, 0.7512734949606018, 0.47103716245825855, 0.06415931658394604, -0.4596030132589899, -1.0838981475312515, -1.7864572973265347, -2.5399734798624616, -3.31339197756194, -4.07359146097375, -4.7870544158761295, -5.421356083840047, -5.946958615307173, -6.339093136638761, -6.5787343540454915, -6.653623453732118, -6.5593660293380305, -6.299543483482498, -5.885283246972314, -5.335058260210965, -4.673923186213248, -3.931739905253446, -3.1416737093418394, -2.3388092084151406, -1.557969389363063, -0.8317079794824206, -0.18870519569704342, 0.34779868279511905, 0.7614493098832403, 1.0436429971352932, 1.1940427942479792, 1.220672768667817, 1.1394758676881014, 0.9735048715253835, 0.7517077832577217, 0.5072657732950699, 0.27578961960591275, 0.09337418332370058, -0.005507146989476715, 0.01000668704174924, 0.16540611514225156, 0.47922867315269996, 0.9618382211335719, 1.6147529204561626, 2.430339194631709, 3.3918796458004508, 4.474169069744003, 5.645019733916413, 6.866590387140322, 8.096801722132701, 9.291408336880439, 10.407042313136671, 11.402532940109698, 12.240427511750845, 12.889352944318759, 13.326239810002786, 13.536180950207346, 13.512948789166188, 13.259944221735102, 12.790005516443399, 12.123758204894163, 11.288831457408758, 10.31841653535725, 9.249723443840233, 8.121750447821816, 6.973554304340352, 5.842107382847386, 4.7610547784038575, 3.7592031865908315, 2.8591808757042547, 2.076752375741626, 1.4208374262310774, 0.8934609244686061, 0.49012751809116223, 0.2007927011733359, 0.011080903996174677, -0.09646835291981826, -0.1409267233692333, -0.14147549011351523, -0.1160024001164876, -0.07986476921738915, -0.04489056245408121, -0.01868033764507445, -0.00423541352839157, 4.28942462959287e-05, 1.0588141898700761e-05, 0.005119302892083906, 0.027481283950420498, 0.08073654215985705, 0.1787862989836821, 0.3344794189406188, 0.5584056345957957, 0.8577924249911053, 1.235577417759005, 1.689755583450054, 2.2132625666908083, 2.794022182959492, 3.415180258248098, 4.055788337004846, 4.692319858811427, 5.299698258331067, 5.85230188284864, 6.325515364640527, 6.697972002608846, 6.952137249562738, 7.075044540476429, 7.059545636795643, 6.905360419589003, 6.618340451109106, 6.210135289590219, 5.698024527240183, 5.104088501329588, 4.453485366582014, 3.7731954787800674, 3.0905405830046964, 2.431750511447209, 1.8203640183640404, 1.2760050904062457, 0.8132934496984413, 0.4412497072857362, 0.1629437877329838, -0.02449851903920059, -0.12945636790770107, -0.16503491077611004, -0.14798071947565025, -0.09737336167207494, -0.03319918660191835, 0.025112935094953756, 0.06014106828120854, 0.05772681927998092, 0.007991713748104243, -0.09394358962852593, -0.2476296179746297, -0.44732657673548004, -0.6824357059196271, -0.9383847253942424, -1.1977218323619903, -1.4414327123990156, -1.650496871341805, -1.8076455498806017, -1.89871898637234, -1.9139590815469485, -1.8491300884068012, -1.7065203893875946, -1.4950144830783385, -1.229871168652531, -0.9322159898557577, -0.6282534565784705, -0.34756719503903283, -0.12134790510511996, 0.01942650720723898, 0.04596904408290108, -0.0661651681766123, -0.3352812485047308, -0.7720250995818548, -1.378201977140296, -2.1460810635080017, -3.0582268731284357, -4.088040945218176, -5.2007472901854435, -6.354744505927571, -7.503588011891132, -8.598661748853814, -9.591427230849204, -10.435795649341662, -11.091082872728018, -11.524236235448997, -11.711597438163128, -11.640366728015286, -11.309839201395029, -10.731038115600201, -9.926664165878194, -8.930224566090416, -7.783935370245953, -6.5363504865875495, -5.240403040340468, -3.9504093772546818, -2.7187462002696066, -1.5932357077122852, -0.6148345584276601, 0.1848288299691835, 0.7850886134734106, 1.1771977350673908, 1.3647471586133428, 1.3632461529955588, 1.1990465515437503, 0.9077362602696063, 0.5319461220898557, 0.11868620797008081, -0.28348859781617247, -0.627409495325007, -0.8700921281596287, -0.9752980794470403, -0.915772820491167, -0.6747874621065592, -0.24714554069365816, 0.3605105581729304, 1.13012027286003, 2.0332197331560793, 3.0326362291981392, 4.084864290065616, 5.142369605129974, 6.15611625307779, 7.0789862231621665, 7.868383682251836, 8.48793749517018, 8.909646096811219, 9.116444059140935, 9.10197513010255, 8.870385065972615, 8.436711551678492, 7.826058679771257, 7.070951929057434, 6.209535695790624, 5.283911315331577, 4.337136602534359, 3.4105159844788617, 2.5417663811932263, 1.7628719566072057, 1.0983092183908054, 0.5641171725747198, 0.16750505900956802, -0.0932776515069309, -0.22823974329740776, -0.2544343917950628, -0.19447228942747913, -0.07467144258730479, 0.07703206430438952, 0.23310441659398065, 0.36833336145608586, 0.4615573596386456, 0.4970935201607183, 0.4655913275956753, 0.36446566372669337, 0.19788099008436585, -0.02382244465774698, -0.285158147732327, -0.5667785434426852, -0.8470877733499428, -1.1041631570830166, -1.317373279506665, -1.4689371181925992, -1.545421435129056, -1.5390093373548455, -1.4479126237660453, -1.2765468491927714, -1.0353626173508903, -0.7402737137932929, -0.41131666648405446, -0.07123648321523268, 0.2560195754104131, 0.5470813173110027, 0.7809972065476725, 0.9406124470477136, 1.0137948162459298, 0.9946328098307383, 0.8837941088149869, 0.6883767348107642, 0.42157286077716, 0.10197762013288374, -0.2479226992464912, -0.6032943655635798, -0.9386387351665109, -1.2296430077074012, -1.4549170547927759, -1.5974921146633723, -1.6461634707153667, -1.596375147725434, -1.4504906187045419, -1.2177494170658807, -0.9136727261541926, -0.5591142414483281, -0.17876999485202, 0.2005526938052007, 0.5518215524069341, 0.8495659454944761, 1.0717897719100309, 1.201584526500431, 1.2282844062933322, 1.1483345023618543, 0.9656913603465203, 0.6914865661503119, 0.34332587197472014, -0.055713959540328505, -0.47876762703115194, -0.8970748479890521, -1.281864714003228, -1.6063844218619001, -1.8478547035348774, -1.989012301270405, -2.019263622521912, -1.9356736385132873, -1.7431101876005828, -1.4538062191879677, -1.0865326690051988, -0.6655242543029628, -0.2185898131753698, 0.22510911242491913, 0.6369234426379308, 0.9907435649907693, 1.2650269406160872, 1.4443473060940215, 1.5205153595099532, 1.4936984698807474, 1.3728552741109816, 1.174213196633493, 0.9199517717490495, 0.6366428664676343, 0.35413389371612614, 0.10408766553693063, -0.08297986973175704, -0.18192007513228728, -0.1751038291374273], 'positive_zeros': ['0.45496962639928120241791814650768', '0.63185590049222631617486496413424', '1.31201403542555050136527497524001', '1.32508606747883888322352882164341', '1.87049109018256597770189845081617', '2.06068165756576995417378386789993', '2.59554790396441503191610691221012', '2.64155128804851092594943799162467', '2.94131362120832157522131717645272', '3.21264334872218690900545378011295', '3.38690996426272490826926904327479', '3.57386563942310045777182783852294', '4.02777993189891491782365708954567', '4.03065762355027308747164910572148', '4.59153717962696794662305695724849', '4.70349036536317583575687078665171', '4.96762695112950495745669876255010', '5.05455336271707573896929649595148', '5.25823550191147760265720406523873', '5.41998665353216203785081250322510', '5.50855859480688106425942763243021', '5.86404619159394590824807599482026', '6.45864926357889635205969156102348', '6.49083422531267311649780103706010', '6.56663973272642162165162911589470', '6.66628762164618603458557892779363', '6.96798403314110494765788067091747', '7.12411334617835385499496656906858', '7.27239303928679959118285867577030', '7.68939687695533267508233156449602', '7.82217568955950543863983115296483', '7.979131306639523358339765810238061', '8.123632524500633029882532290499372', '8.347248950135516497998885035635478', '8.468775024347580624916427818400009', '8.808517141440456417613599164226741', '8.977952376815993165073939234583646', '8.992106411615982787367974780623270', '9.522625503901194689255639443602073', '9.667736478744522173391170664709840'], 'prelabel': '8-1872e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.866263733681873, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 2284556086766016313, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45496962639928120241791814651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.63185590049222631617486496413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.31201403542555050136527497524', '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': 49926.578622459405, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 12280707219456, 'conductor_radical': 78, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, 11, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 7, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -8, 0, 190, 0, -968, 0, 14641], 'euler13': [1, 6, 18, 78, 169, 0, 0, 0, 0], 'euler17': [1, -6, 73, -294, 1908, -4998, 21097, -29478, 83521], 'euler19': [1, 0, -68, 0, 1878, 0, -24548, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -4, 64, -212, 2142, -4876, 33856, -48668, 279841], 'euler29': [1, -4, 88, -284, 3678, -8236, 74008, -97556, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -88, 0, 3790, 0, -84568, 0, 923521], 'euler37': [1, 0, -27, 0, 1964, 0, -36963, 0, 1874161], 'euler41': [1, 0, -36, 0, 3686, 0, -60516, 0, 2825761], 'euler43': [1, 30, 501, 5430, 42092, 233490, 926349, 2385210, 3418801], 'euler47': [1, 0, -119, 0, 7444, 0, -262871, 0, 4879681], 'euler5': [1, 0, -11, 0, 76, 0, -275, 0, 625], 'euler53': [1, 16, 172, 1712, 15318, 90736, 483148, 2382032, 7890481], 'euler59': [1, 0, -36, 0, 7286, 0, -125316, 0, 12117361], 'euler61': [1, -28, 504, -6020, 55070, -367220, 1875384, -6355468, 13845841], 'euler67': [1, 0, -184, 0, 15742, 0, -825976, 0, 20151121], 'euler7': [1, 0, -7, 0, 4, 0, -343, 0, 2401], 'euler71': [1, 0, -207, 0, 20756, 0, -1043487, 0, 25411681], 'euler73': [1, 0, 32, 0, 5406, 0, 170528, 0, 28398241], 'euler79': [1, -28, 576, -7532, 79550, -595028, 3594816, -13805092, 38950081], 'euler83': [1, 0, -196, 0, 23382, 0, -1350244, 0, 47458321], 'euler89': [1, 0, -320, 0, 41374, 0, -2534720, 0, 62742241], 'euler97': [1, 0, -244, 0, 32614, 0, -2295796, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -11, 0, 76, 0, -275, 0, 625], [1, 0, -7, 0, 4, 0, -343, 0, 2401], [1, 0, -8, 0, 190, 0, -968, 0, 14641], [1, 6, 18, 78, 169, 0, 0, 0, 0], [1, -6, 73, -294, 1908, -4998, 21097, -29478, 83521], [1, 0, -68, 0, 1878, 0, -24548, 0, 130321], [1, -4, 64, -212, 2142, -4876, 33856, -48668, 279841], [1, -4, 88, -284, 3678, -8236, 74008, -97556, 707281], [1, 0, -88, 0, 3790, 0, -84568, 0, 923521], [1, 0, -27, 0, 1964, 0, -36963, 0, 1874161], [1, 0, -36, 0, 3686, 0, -60516, 0, 2825761], [1, 30, 501, 5430, 42092, 233490, 926349, 2385210, 3418801], [1, 0, -119, 0, 7444, 0, -262871, 0, 4879681], [1, 16, 172, 1712, 15318, 90736, 483148, 2382032, 7890481], [1, 0, -36, 0, 7286, 0, -125316, 0, 12117361], [1, -28, 504, -6020, 55070, -367220, 1875384, -6355468, 13845841], [1, 0, -184, 0, 15742, 0, -825976, 0, 20151121], [1, 0, -207, 0, 20756, 0, -1043487, 0, 25411681], [1, 0, 32, 0, 5406, 0, 170528, 0, 28398241], [1, -28, 576, -7532, 79550, -595028, 3594816, -13805092, 38950081], [1, 0, -196, 0, 23382, 0, -1350244, 0, 47458321], [1, 0, -320, 0, 41374, 0, -2534720, 0, 62742241], [1, 0, -244, 0, 32614, 0, -2295796, 0, 88529281]], 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/2/c/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': '8-1872e4-1.1-c1e4-0-21', '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': '8-1872e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.866263733681873, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2284556086766016313, 'z1': {'__RealLiteral__': 0, 'data': '0.45496962639928120241791814651', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '576742519990662101346081996611,800972511516719079036358545111,1663175379515060526446439389444,2612224340092550963251839603731', 'Lhash_array': ['576742519990662101346081996611', '800972511516719079036358545111', '1663175379515060526446439389444', '2612224340092550963251839603731'], 'factors': ['2-1872-13.12-c1-0-4', '2-1872-13.12-c1-0-8', '2-1872-13.12-c1-0-23', '2-1872-13.12-c1-0-32'], 'label': '8-1872e4-1.1-c1e4-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/2/c/j'}