Lfunction data - 8-637e4-1.1-c1e4-0-26

Formats: - HTML - YAML - JSON - 2024-04-19T00:01:20.593589

• 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
  instance_types	text[]
  instance_urls	text[]
  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': '1279437110370628098444849551602,2049975564391855016977535200462,2541985636152703784318922740139,3290192248697484695265610379944', 'a10': 9, 'a2': -3, 'a3': -6, 'a4': 5, 'a5': -3, 'a6': 18, 'a7': 0, 'a8': -6, 'a9': 13, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 669.3698663148037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, 10, 51, 130, 169]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'euler_factors': [[1, 3, 4, 3, 3, 6, 16, 24, 16], [1, 6, 23, 60, 121, 180, 207, 162, 81], [1, 3, -2, 3, 51, 15, -50, 375, 625], [1], [1, 6, 35, 144, 609, 1584, 4235, 7986, 14641], [1, 10, 51, 130, 169], [1, 6, 13, -66, -372, -1122, 3757, 29478, 83521], [1, -6, 67, -288, 1905, -5472, 24187, -41154, 130321], [1, 0, -26, 0, 147, 0, -13754, 0, 279841], [1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], [1, 4, -5, -164, -1016, -5084, -4805, 119164, 923521], [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], [1, 6, -50, 24, 4239, 984, -84050, 413526, 2825761], [1, 5, 34, -475, -2843, -20425, 62866, 397535, 3418801], [1, 0, -89, 0, 5712, 0, -196601, 0, 4879681], [1, 12, 7, 372, 8328, 19716, 19663, 1786524, 7890481], [1, 0, -113, 0, 9288, 0, -393353, 0, 12117361], [1, 24, 460, 5256, 49974, 320616, 1711660, 5447544, 13845841], [1, 24, 394, 4608, 43899, 308736, 1768666, 7218312, 20151121], [1, -6, 10, 696, -6921, 49416, 50410, -2147466, 25411681], [1, -4, -134, -16, 16003, -1168, -714086, -1556068, 28398241], [1, 8, -110, 128, 18979, 10112, -686510, 3944312, 38950081], [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], [1, 21, 184, 1659, 18879, 147651, 1457464, 14804349, 62742241], [1, 31, 538, 7099, 76303, 688603, 5062042, 28292863, 88529281], [1, 6, 215, 1224, 32829, 123624, 2193215, 6181806, 104060401], [1, -4, -149, 164, 14968, 16892, -1580741, -4370908, 112550881], [1, -9, -152, -171, 34173, -18297, -1740248, -11025387, 131079601], [1, 8, -125, -232, 16864, -25288, -1485125, 10360232, 141158161], [1, -6, -179, 66, 29388, 7458, -2285651, -8657382, 163047361]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 4], 1], [[1, 3, 5, 6, 4], 1]], [[[1, 3, 7, 9, 9], 2]], [[[1, 3, -2, 3, 51, 15, -50, 375, 625], 1]], [1], [[[1, 3, 13, 33, 121], 2]], [[[1, 5, 13], 2]], [[[1, 6, 13, -66, -372, -1122, 3757, 29478, 83521], 1]], [[[1, -3, 29, -57, 361], 2]], [[[1, 0, -26, 0, 147, 0, -13754, 0, 279841], 1]], [[[1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], 1]], [[[1, 4, -5, -164, -1016, -5084, -4805, 119164, 923521], 1]], [[[1, 4, -21, 148, 1369], 2]], [[[1, 6, -50, 24, 4239, 984, -84050, 413526, 2825761], 1]], [[[1, 5, 34, -475, -2843, -20425, 62866, 397535, 3418801], 1]], [[[1, 0, -89, 0, 5712, 0, -196601, 0, 4879681], 1]], [[[1, 12, 7, 372, 8328, 19716, 19663, 1786524, 7890481], 1]], [[[1, 0, -113, 0, 9288, 0, -393353, 0, 12117361], 1]], [[[1, 6, 61], 4]], [[[1, 12, 125, 804, 4489], 2]], [[[1, -6, 10, 696, -6921, 49416, 50410, -2147466, 25411681], 1]], [[[1, -2, -69, -146, 5329], 2]], [[[1, -13, 79], 2], [[1, 17, 79], 2]], [[[1, 0, 121, 0, 6889], 2]], [[[1, 21, 184, 1659, 18879, 147651, 1457464, 14804349, 62742241], 1]], [[[1, 31, 538, 7099, 76303, 688603, 5062042, 28292863, 88529281], 1]], [[[1, 3, 103, 303, 10201], 2]], [[[1, -4, -149, 164, 14968, 16892, -1580741, -4370908, 112550881], 1]], [[[1, -9, -152, -171, 34173, -18297, -1740248, -11025387, 131079601], 1]], [[[1, 8, -125, -232, 16864, -25288, -1485125, 10360232, 141158161], 1]], [[[1, -6, -179, 66, 29388, 7458, -2285651, -8657382, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 26, 'label': '8-637e4-1.1-c1e4-0-26', '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': 4, 'origin': 'ModularForm/GL2/Q/holomorphic/637/2/g/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [3.9248351252011154e-244, 2.4525378699628967e-06, 3.923601678767528e-05, 0.0001985858377900443, 0.0006273719551066198, 0.0015305380074239004, 0.0031692615140462435, 0.005858049566271695, 0.009960885864459307, 0.01588477991156523, 0.02406459144158949, 0.03494878730452986, 0.04898313464097132, 0.06658581652033856, 0.08809973545082667, 0.11376168938233666, 0.14366915896347382, 0.17773088225294872, 0.21557796021045103, 0.2565311691533115, 0.299568645074398, 0.3432753301827876, 0.38575159651708657, 0.4246307123031578, 0.4571052812207574, 0.4799470659695219, 0.48950897896542084, 0.48186875214971137, 0.45299199439459836, 0.3989087699278591, 0.31590468706981883, 0.20081253849247255, 0.05132052523082455, -0.133706145800858, -0.3539042965581097, -0.6071229404806162, -0.8891486396924274, -1.1934771129558974, -1.5112116276351386, -1.8311146665523996, -2.139724699961175, -2.42164110701307, -2.66015806822049, -2.837925942321289, -2.937694777519201, -2.94333242875189, -2.841344339808086, -2.6218440473336457, -2.2795425730699432, -1.8149782373455479, -1.2360912186337578, -0.5583995983226203, 0.19489708974841888, 0.9927794067023291, 1.7964375117979163, 2.5610826854830813, 3.237764175809284, 3.775331987303872, 4.123048706495793, 4.234081491771629, 4.068618219988434, 3.596967905598404, 2.803133935194238, 1.6872770472623921, 0.26728356972942585, -1.4202329260749365, -3.319434488216698, -5.357118472142897, -7.445575313809811, -9.486439080449069, -11.375924392414559, -13.010744815624271, -14.29433998941628, -15.143703910905282, -15.497064369752955, -15.318007484181349, -14.598987619172293, -13.36430986811991, -11.671959274604907, -9.609291820725764, -7.28826913439964, -4.839516505064775, -2.4037996635889254, -0.1210023682999805, 1.8796720039833283, 3.489769811542667, 4.632905152126423, 5.270107556874879, 5.402633453480752, 5.0735435882825834, 4.367466510431671, 3.3996515932268796, 2.3043652176522147, 1.2226049619691004, 0.28755626891591446, -0.3948372076590684, -0.7611370405592364, -0.8028654597417002, -0.5766434041384658, -0.2085016232096775, 0.10876323184938515, 0.12387787972780101, -0.4573169616568529, -1.9495473564611165, -4.662835235080947, -8.874397421559857, -14.795996773674606, -22.547443348080733, -32.13529901009728, -43.436835707867985, -56.191071143335385, -70.00335019016083, -84.35868354083763, -98.64674203010954, -112.20451054624662, -124.35035778547486, -134.42266806585624, -141.8299219697066, -146.1180103570315, -146.98292342821117, -144.2858072508379, -138.07748689868907, -128.6322062230632, -116.39596814929003, -101.94830406904828, -85.97800934744345, -69.26500240514864, -52.591474569746524, -36.68482797414905, -22.183117191067634, -9.611512159574223, 0.6694286534269465, 8.478933891832094, 13.809153315532216, 16.806020541578665, 17.75255120855841, 17.033545350907247, 15.09264340936555, 12.38719612325482, 9.351330634784599, 6.363036494551099, 3.718167660033123, 1.6130025897515647, 0.14409403365876922, -0.6836120544351307, -0.9421378941143402, -0.7596241976519243, -0.29273814436690415, 0.2979371531102874, 0.8690405364471744, 1.3118984345149203, 1.5619021603486622, 1.5999569374099087, 1.4480795405382225, 1.1601662494715588, 0.8073082423164366, 0.46304124830411997, 0.19014369794422156, 0.030277631739619178, -0.0017686991660827976, 0.08132500524833253, 0.24351363634733136, 0.4339891673061703, 0.5975876488109029, 0.6851324715934329, 0.6629616832017691, 0.5202582707867086, 0.27007198075899097, -0.053162334511330636, -0.39929186487132967, -0.7118025358873703, -0.9389779690376832, -1.0432638332022002, -1.0087711362511003, -0.8463822180595747, -0.5922358078294108, -0.30205934092041603, -0.04256423378289325, 0.11961696635576281, 0.1307672393439402, -0.03937360496787315, -0.39046322880308204, -0.8892686997001551, -1.4724508003300145, -2.0542218657925537, -2.538539944663467, -2.835383700111567, -2.874178531236917, -2.6155902210824786, -2.0605208560694517, -1.2533794800554432, -0.2763796403755123, 0.7596412660614532, 1.7293204353072922, 2.5136191383494717, 3.014991308140117, 3.1696733215953463, 2.958882328642698, 2.4174232168544822, 1.6236058395514974, 0.6875191073803288, -0.26191852624419654, -1.094032367759654, -1.6987233171514267, -2.0005965780035866, -1.967990928414423, -1.6192072948631369, -1.0172889397133091, -0.25784230019033705, 0.5456582358974815, 1.277460565479215, 1.8394050716200694, 2.165426484199021, 2.2295925525900038, 2.047630278965927, 1.672686358490804, 1.184747739502579, 0.675858173142353, 0.23344177342585556, -0.07361066378652635, -0.20534616232184683, -0.1564357418273863, 0.04502321819705365, 0.34545583054656326, 0.6764024370173888, 0.9676524349510414, 1.1626517953399855, 1.2272421079213964, 1.1537380353930797, 0.9616187110134271, 0.6941334295759263, 0.4055939469276924, 0.1492437243345057, -0.03312355060000909, -0.11961042875845347, -0.11310564994356892, -0.0390382481744461, 0.06195991909038175, 0.14513382603705505, 0.17472935710051868, 0.13576056524100247, 0.04196180889665978, -0.06185243060205839, -0.10478396677369267, -0.001335512003208107, 0.3322851712240425, 0.9602162655609994, 1.9101790182311391, 3.1604349492242036, 4.63487222155308, 6.212760464744784, 7.739827123581799, 9.044971575339833, 9.966648517121728, 10.390590366099943, 10.25865113092845, 9.57484537412336, 8.411743638391334, 6.912915074253081, 5.256589577725455, 3.626273002657444, 2.1876157102340446, 1.0666724181310043, 0.3228661851462993, -0.05643773279745431, -0.14746901928552272, -0.07255365560869297, 0.026066539864814373, 0.01798008207401583, -0.1863075210716238, -0.6135005148742657, -1.217473749623775, -1.8836702647340309, -2.447631048019193, -2.725116595787128, -2.5467880839459553, -1.793396735594273, -0.4254938969830097, 1.5022800937259353, 3.8426390198194222, 6.368624339556845, 8.80318064776814, 10.871357007511047, 12.335436939227604, 13.024786571052344, 12.866044930311443, 11.911227565264051, 10.311714275774511, 8.288451460310805, 6.102861426327377, 4.023875822367367, 2.272495171790105, 0.9903523562400534, 0.22690376460373257, -0.060402927563520434, 0.007084543794734536, 0.26067941901787217, 0.5223613122735825, 0.6418392263118391, 0.5273760857188816, 0.16396734124806372, -0.3847124004316383, -0.9913006044180943, -1.4914500269483728, -1.7181456318389634, -1.5384258779519728, -0.88332629902124, 0.2366531633154946, 1.727107332517212, 3.420970861145906, 5.112726080759807, 6.589165058731664, 7.658870200664382, 8.184876084464396, 8.119668262582406, 7.498232218715226, 6.42460118293078, 5.05677478628654, 3.586796495722156, 2.197308128389284, 1.0332073521897496, 0.18581606587731037, -0.31447501648325205, -0.4976719273070829, -0.43924741317047716, -0.23880881767187725, 0.002535183827671433, 0.20228390915758013, 0.31023146794678097, 0.3137487354899337, 0.23424713224011506, 0.11609563008351824, 0.012167570198815687, -0.03124951076658996, 0.013588337642543876, 0.15010384036835192, 0.3571391609394582, 0.5945955780740105, 0.815901265452417, 0.9784160414624957, 1.0516227891236036, 1.0238370885852583, 0.90646052659772, 0.7268878993926241, 0.5203415154501041, 0.32231598248668925, 0.1615153917217764, 0.052873080887758564, -0.003488147935560452, -0.01922358663621642, -0.012383871543058277, -0.0009327367348681969, 0.0030858889117921953, -0.003153467476600944, -0.013394687036726798, -0.015579978978671255, 0.002843953562089084, 0.04905384134183129, 0.12074163534140417, 0.2051018527331901, 0.28073978924323795, 0.3229999084068124, 0.31279273754812803, 0.24246966073663942, 0.11946155547911601, -0.03243623326812114, -0.17607283221896144, -0.27084536144405463, -0.2824608099675887, -0.19169690085901708, -0.0017879693873801212, 0.26025726738381383, 0.5486588924517249, 0.808451233137626, 0.9885900897515215, 1.0537722529025098, 0.9927604469271661, 0.8220787742415475, 0.583460365721174, 0.33087372149151945, 0.11655336111920861, -0.022237402313077664, -0.07398740618018525, -0.056747631069763056, -0.012580980101549682, 0.0045640660932399395, -0.05435947593721952, -0.21680145042722962, -0.477797457993748, -0.7976018008700464, -1.1102426441706228, -1.3411010298076327, -1.4277077156747873, -1.339989304625358, -1.0952920191820936, -0.7541715705538217, -0.40391773263470604, -0.1333924076199368, -0.002515049016330445, -0.014976342725263148, -0.11102164920466813, -0.18407986652181896, -0.12399523386147102, 0.11706777771168113, 0.4507148594809972, 0.5874504852717162, 0.005496449689637834, -2.029055725088579, -6.3855259023954805, -13.930334662622464, -25.3304727949954, -40.86246970487682, -60.23971797728288, -82.49620494153224, -106.00493790511247, -128.59434124691015, -147.75315411720143, -160.9661734483548, -166.22607374408787, -162.3063119731213, -148.9726985974265, -127.16088684994332, -99.06737374448502, -67.73016305663705, -36.581227340268775, -8.98647140274057, 12.264988842882085, 25.491065247922545, 30.37425318508209, 27.997771265513492, 20.674301565737508, 11.478083247098086, 3.6467932403387433, -0.04572524855291417, 2.1412416093460886, 10.529503200150472, 23.905213303258932, 39.694611762407526, 54.48081560137774, 64.6456059252268, 67.05405130208612, 59.74546100288041, 42.52153775645673, 16.986993395193668, -13.648445516590312, -45.00079635071125, -72.27185484297665, -91.1666818137411, -98.62547313794548, -93.4082044096179, -76.52325694717358, -51.021117033100566, -21.472579679579376, 6.735474342372915, 28.240581242112363, 38.69417503624638, 35.50024877451984, 18.23767560136433, -11.330838685919456, -49.54380047324629, -91.39735839742121, -131.36973439967352, -164.51115386990907, -187.01584376556806, -196.62732426566026, -192.9479045864612, -177.5908522821593, -153.48805383592526, -124.26147191772431, -93.68497699871516, -65.18115115946411, -41.21208189242812, -23.06588289000085, -10.899211559062737, -3.944903544912465, -0.8360310056859193, -0.0013954884861400426, -0.024737712792501906, 0.09706239286642772, 0.8416309112568121, 2.1856483911212967, 3.7380863336786603, 4.9597283847216955, 5.368566976318065, 4.691410724632349, 2.9497372953146916, 0.467315746068786, -2.234452691464212, -4.576476702404261, -6.067552745066902, -6.426526895910285, -5.638598554079472, -3.949699007552754, -1.802454212930707, 0.28571045157213387, 1.84653965922861, 2.556389896022112, 2.30332884485887, 1.2106927781013375, -0.42297299861423227, -2.2044687153915414, -3.7347321951298746, -4.705175308585039, -4.958257474360341, -4.500955026843198, -3.4867068464337407, -2.173164340651223, -0.8455350191502863, 0.25016134213346414, 0.954266614508536, 1.2165628517501565, 1.0889892697460553, 0.696808340093694, 0.19799021303127426, -0.2612229435431231, -0.5793147409814303, -0.713442231278967, -0.677881618200517, -0.5284294945463589, -0.33580136164501345, -0.16239688144250597, -0.04624027460600053, 0.005577117169022565, 0.010902795055395573, -0.0004392994977629924, -0.001305238406390956, 0.02048783831376381, 0.057078965230496895, 0.08373586201396097, 0.06807329762468205, -0.016799314746497686, -0.18100404037777726, -0.4120660120593685, -0.6760861832220454, -0.9262296792020853, -1.1140403005318482, -1.2015621876991418, -1.172011013671994, -1.0351600732504782, -0.8211978758191943, -0.5726141270016897, -0.33423596528350363, -0.1414651477494612, -0.012695702127264483, 0.05130769153353945, 0.06425055814939128, 0.04828293592208201, 0.024608490215292295, 0.007174246085831854, 0.0003426634596162812, 0.00013619247404239118, -0.0014151116759727827, -0.010620281916966968, -0.027877838667421037, -0.04648917952995403, -0.05508385061981269, -0.04285777917415365, -0.0058225849606100225, 0.0488121064514989, 0.10214809917349513, 0.12688168138326344, 0.09475181156933576, -0.012572255330960394, -0.19664788619386836, -0.43898926970897606, -0.7018879034903195, -0.9360371217019348, -1.0937865128331763, -1.1405027687052884, -1.0636708739390046, -0.879386529064039, -0.6270427664701805, -0.3582822770610406, -0.12432994049029153, 0.036185602317993254, 0.10779728985469776, 0.1003839926912628, 0.043698106970117556, -0.023633454534460228, -0.06689169817970685, -0.0660075184108711, -0.021154895489478062, 0.049460941674125646, 0.11817784119189716, 0.15868375027450146, 0.15662327536846088, 0.1164860086542097, 0.05817687672335932, 0.008065344497977965, -0.012545120202932818, 0.0014508112116552595, 0.03436982974848404, 0.05628318150663107, 0.03912537551314213, -0.02032851675752326, -0.07856918362700492, -0.03373790898569975, 0.2695423363645167, 1.015022211877781, 2.3710454464521513, 4.435911157052769, 7.187302859357759, 10.46230583193857, 13.952110013763383, 17.223929254808073, 19.790830882636442, 21.246229556957367, 21.316312024708584, 19.905479807926177, 17.147488144515393, 13.440789268607995, 9.320749608345341, 5.351837984428911, 2.0408809448551906, -0.24912830056676485, -1.3910876962063217, -1.4964879852290962, -0.8649382238517314, 0.09587206898284831, 0.9751296368983372, 1.458432945626147, 1.3944728190836424, 0.8145269474420008, -0.10018242035333129, -1.0836603074336075, -1.8691788864643475, -2.2753224320169227, -2.245613892603115, -1.8484765713623152, -1.246811821143688, -0.6408722434509175, -0.18902011533592214, 0.03914213688309949, 0.07272956905906919, 0.012708450227613157, -0.02697907824776165, 0.009506532713710839, 0.0650049513014828, -0.046155921932817076, -0.6006724413417188, -1.8826251431064644, -4.072201066794216, -7.142105712980342, -10.796977861906122, -14.474755881659432, -17.42856654601985, -18.904746187351222, -18.314677084294544, -15.39519120501913, -10.325317664744864, -3.7392214236250103, 3.388049761513901, 9.913603456958898, 14.773572731612305, 17.296197281646677, 17.285158699643134, 15.026488924458857, 11.245637598165919, 6.974955012783565, 3.1859339064137933, 0.5489200524154152, -0.690326059794627, -0.7391417979274615, -0.16508780838310308, 0.35910585368662146, 0.35262696047228775, -0.21758517911507086, -0.7946473235145992, -0.2683560594467296, 2.7933416198592362, 9.765401023675818, 21.52959575183899, 38.06030908856671, 58.16557247327185, 79.59617160673761, 99.2849661442757, 113.75139832948015, 119.75954019165948, 115.25878382098945, 99.64967031785459, 73.89852150134348, 40.56793863813483, 3.6352548118147716, -32.42389637061776, -63.39214308892288, -85.91928526710606, -98.05576336283882, -99.53154164836201, -91.63496087275037, -76.84477451365414, -58.29090208269783, -39.124539790640824, -21.996435036673397, -8.675680502624932, 0.15234483441442123, 4.716704671683702, 5.896583834228101, 4.917479629680305, 3.0217014536787183, 1.1591848425911324, -0.12342402733303146, -0.6737880952895539, -0.6451402889772401, -0.33050294960335524, -0.009145920313596442, 0.15107397808578923, 0.1276208012203155, 0.01364183745680729, -0.05565614145691988, 0.01881091186673105, 0.245324838428634, 0.532719828379575, 0.7257736718235, 0.6684848947374571, 0.2713232203281825, -0.4460161094823584, -1.3480520227672639, -2.2175116853396033, -2.8303293063155635, -3.0228279697447755, -2.738159839919925, -2.047840295016577, -1.1397955253964696, -0.24662306140057266, 0.4266426344143222, 0.7588575263929815, 0.7426991929164867, 0.47974155824991566, 0.13671898608075334, -0.11784653149892757, -0.17622958122688198, -0.024270660978046914, 0.25935557239846224, 0.5365636333924936, 0.6702512727108868, 0.5820823198769256, 0.2858209657439349, -0.11133533022739268, -0.4475054415318255, -0.5758764006781119, -0.43248855385413215, -0.08474882392555132, 0.25900238293338107, 0.2961374092249572, -0.2880293741126986, -1.7201908316545036, -4.04728984375507, -7.0948288923098115, -10.476471695999951, -13.662407442964588, -16.11842290072092, -17.42004792021885, -17.33853161057885, -15.901418449232162, -13.413681881327143, -10.342181990705773, -7.1951436412926935, -4.416856032703131, -2.302783839756128, -0.944512868680323, -0.251251928616693, -0.016989353547681985, -0.007558445236626565, -0.04064933959883175, -0.030102185292518704, 0.013823698570017896, 0.024610193540000436, -0.05880246236851056, -0.23703375064029603, -0.4237213139470487, -0.4663947766547646, -0.2017032163082802, 0.4747748221743445, 1.543676629162123, 2.834036305008743, 4.059486736824201, 4.892826857700552, 5.0690745689979, 4.503284322788359, 3.332630467083155, 1.8925234490695568, 0.6344341486830126, -0.007640664945414139, 0.22516619975364138, 1.3096875834879822, 2.916313383659734, 4.502492835279777, 5.476815165094988, 5.392590439250867, 4.147061763116851, 2.120195868790034, 0.09198052561320173, -0.9320011162217251, 0.02781428376620664, 3.5815802845945766, 9.704684441125018, 17.65926168216217, 26.07205878821026, 33.17760335405466, 37.27965043415925, 37.208507009162325, 32.678810820656906, 24.482759473224732, 14.402304292891838, 4.866420497828727, -1.5769443064726427, -2.86254324479418, 2.0924675234172065, 13.066842691914399, 28.493702643085317, 45.85904014035207, 62.192513910092764, 74.59651323399694, 80.87176850056596, 80.20605189442311, 73.0675642939117, 60.95056992911182, 46.087026375381974, 31.065790595907668, 18.065171808164546, 8.448404298947528, 2.6437906335547536, 0.20913775849580268, 0.05088229763775267, 0.8242527639430337, 1.3354916115547995, 0.83534992394116, -0.8469949551353687, -3.3405841480400773, -5.922411736549343, -7.8090349346712795, -8.399313374205477, -7.443802001878782, -5.118224753168913, -1.9554922193655582, 1.344311336690231, 4.097383714220283, 5.804888893467438, 6.2941550286290795, 5.70293297791764, 4.387424360352274, 2.8054973566415136, 1.3916334856721324, 0.42913452731926294, 0.004686535694164508, 0.029559911970350003, 0.3053763460551253, 0.6109664262358383, 0.7788740730884796, 0.7403570009501775, 0.5289772271548493, 0.2434759782564575, -0.0036287893177028505, -0.13439742663779902, -0.13498875669050128, -0.05285578102715006, 0.02985333083017208, 0.03488039275461325, -0.07503614841079047, -0.2797455949502105, -0.5083581149462452, -0.6650523918691148, -0.6693147933733188, -0.4881511355965115, -0.14985549382495603, 0.26155936772130206, 0.6317357418027006, 0.8556862434950353, 0.871635626146629, 0.6800049474185555, 0.341918610364618, -0.042729821412773386, -0.3679934379874357, -0.5562613772913337, -0.5814015602388951, -0.46882545996232944, -0.2827078037633227, -0.1011233683697276, 0.017801144995440266, 0.05170616735519191, 0.014920729620618387, -0.05019982910252051, -0.09236519934397917, -0.07989853889953855, -0.01461057179855474, 0.0684986745388243, 0.11359976260760586, 0.06733762367305646, -0.09694455939089223, -0.3644652246926638, -0.6793707589419358, -0.9583388372628001, -1.1149884751745358, -1.0891561068975602, -0.8692064450051478, -0.4930800394295781, -0.03986268976448776, 0.3899645843000674, 0.7085380208438915, 0.8629522059373925, 0.8428032518334367, 0.6798761194271467, 0.4402012445840213, 0.19548423507516066, 0.0015715178414323705, -0.11259063261929227, -0.1470716038800205, -0.12466954874582399, -0.07737126198344133, -0.03295659126419365, -0.006345902150919436, 0.0019515238002094243, 0.0007781221997368561, 0.0004858566992112897, 0.0062091470298978445, 0.015509638956113037, 0.020940037572129915, 0.015796761650061598, -0.00018237788421545558, -0.01914072013853859, -0.028048125466828947, -0.015458177072465445, 0.020002966693760848, 0.06577569075043932, 0.09773389983331411, 0.08822895035220536, 0.018207539555786755, -0.11204316869301345, -0.2789190157572464, -0.44064372301866267, -0.552126104154713, -0.5808081929942833, -0.5188657271241848, -0.3879329574310545, -0.23220721792749183, -0.0984516860988256, -0.0176286823845684, 0.006794578137856819, -0.0019605928862147137, -0.01075485180541602, 0.0018268979778337513, 0.02979069730724721, 0.042090460724511974, 0.014977980388738361, -0.01389674532482092, 0.11452827465805279, 0.7213826843971477, 2.2783061381027436, 5.3285055857232955, 10.344622690182078, 17.55375637416435, 26.765014222760318, 37.24848516035358, 47.75061668118566, 56.76775425643821, 62.7692917870603, 64.47114654103464, 61.20756537076014, 53.36183576154801, 42.15438675163052, 29.360613983868014, 17.008682887517477, 6.995764815415985, 0.49022241094513774, -2.3101726137984526, -2.135574845380092, -0.37584142420235817, 1.4018916316151067, 1.9869922227095325, 0.9384061789744528, -1.2589415375802968, -3.39628956785151, -4.024361295005769, -2.1011678400735203, 2.335824427803545, 7.856926976294286, 11.746440542282807, 10.516027687277171, 0.7720777843132743, -19.68007120816689, -50.90879810756467, -90.3680304690179, -133.2458491741883, -173.16869011040174, -203.28700524949178, -217.77763334987563, -213.6904299481688, -191.26692104585447, -153.79100293140084, -107.10494064770089, -58.618180651731016, -15.379483885480932, 17.282261772382878, 36.60708786421318, 42.78913204939338, 38.4516126752448, 27.66591020503191, 14.839169284602686, 3.6289314342623635, -3.8074008417185383, -6.9418849187639005, -6.5954307106261325, -4.370009194034325, -1.8539278931884493, -0.10073859823854037, 0.5637902529108944, 0.4406062906384277, 0.10680476808173699, -0.005388525059810335, 0.11252486392338333, 0.0114806422414936, -0.9762345242960508, -3.3229297986442763, -6.910519288979254, -10.892103362773392, -13.838269870864368, -14.134437784618433, -10.553146374341647, -2.869443079595385, 7.692571313931379, 18.468361985290723, 25.96700538558433, 27.269798252568762, 21.187764746043385], 'positive_zeros': ['1.00929791706032927283141065070906', '1.61714557940711332385785988549815', '2.00527308999423146027154061935639', '2.59550403565865417696718474522130', '2.94912396629309653339228610912955', '3.11221270724253022948343790275516', '3.16748509140987734906855591611650', '4.09147235014513230646258640690339', '4.47283315213456736615072293224331', '4.60954723869384635520296905504140', '4.95170586053693634784177388736228', '4.97042761414765212222222217189683', '5.24514147000313573403109994682387', '5.53756554414450238262609527406519', '5.62005578126017163805885598092944', '5.97710591948254184475290006370349', '6.27242090166650313935153716974852', '6.50999378888106660827924594467217', '6.83450220255063357740806204950200', '6.93190067328791730404683455112844', '7.27421483754488196004475840243682', '7.38729008597001431775717312410155', '7.54322386340171729115201190046900', '7.62520217637335834017986954306155', '8.242991401730279972782828780389676', '8.333604882163238787259929773250718', '8.380001488722985264309081015691984', '8.663908478121610016983128225278350', '9.175503516444045614660392955669224', '9.217576369505501305152041262604203', '9.385204885034420512337350535831437', '9.588013591285614976467569094391593', '10.04060797145740518792909287204845', '10.18714678372792025162868558901289', '10.38007379119849548121637713620936', '10.43243036520273762396641914601142'], 'prelabel': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1802964082974503751, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00929791706032927283141065071', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61714557940711332385785988550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.00527308999423146027154061936', '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': 669.3698663148037, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'dirichlet_coefficients': [1, -3, -6, 5, -3, 18, 0, -6, 13, 9, -6, -30, -10, 0, 18, 4, -6, -39, 6, -15, 0, 18, 0, 36, 11, 30, 0, 0, -3, -54, -4, 0, 36, 18, 0, 65, -8, -18, 60, 18, -6, 0, -5, -30, -39, 0, 0, -24, 0, -33, 36, -50, -12, 0, 18, 0, -36, 9, 0, 90, -24, 12, 0, -11, 30, -108, -24, -30, 0, 0, 6, -78, 4, 24, -66, 30, 0, -180, -8, -12, -60, 18, 0, 0, 18, 15, 18, 36, -21, 117, 0, 0, 24, 0, -18, 0, -31, 0, -78, 55], 'euler11': [1, 6, 35, 144, 609, 1584, 4235, 7986, 14641], 'euler13': [1, 10, 51, 130, 169, 0, 0, 0, 0], 'euler17': [1, 6, 13, -66, -372, -1122, 3757, 29478, 83521], 'euler19': [1, -6, 67, -288, 1905, -5472, 24187, -41154, 130321], 'euler2': [1, 3, 4, 3, 3, 6, 16, 24, 16], 'euler23': [1, 0, -26, 0, 147, 0, -13754, 0, 279841], 'euler29': [1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], 'euler3': [1, 6, 23, 60, 121, 180, 207, 162, 81], 'euler31': [1, 4, -5, -164, -1016, -5084, -4805, 119164, 923521], 'euler37': [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], 'euler41': [1, 6, -50, 24, 4239, 984, -84050, 413526, 2825761], 'euler43': [1, 5, 34, -475, -2843, -20425, 62866, 397535, 3418801], 'euler47': [1, 0, -89, 0, 5712, 0, -196601, 0, 4879681], 'euler5': [1, 3, -2, 3, 51, 15, -50, 375, 625], 'euler53': [1, 12, 7, 372, 8328, 19716, 19663, 1786524, 7890481], 'euler59': [1, 0, -113, 0, 9288, 0, -393353, 0, 12117361], 'euler61': [1, 24, 460, 5256, 49974, 320616, 1711660, 5447544, 13845841], 'euler67': [1, 24, 394, 4608, 43899, 308736, 1768666, 7218312, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -6, 10, 696, -6921, 49416, 50410, -2147466, 25411681], 'euler73': [1, -4, -134, -16, 16003, -1168, -714086, -1556068, 28398241], 'euler79': [1, 8, -110, 128, 18979, 10112, -686510, 3944312, 38950081], 'euler83': [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], 'euler89': [1, 21, 184, 1659, 18879, 147651, 1457464, 14804349, 62742241], 'euler97': [1, 31, 538, 7099, 76303, 688603, 5062042, 28292863, 88529281], 'euler_factors': [[1, 3, 4, 3, 3, 6, 16, 24, 16], [1, 6, 23, 60, 121, 180, 207, 162, 81], [1, 3, -2, 3, 51, 15, -50, 375, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, 35, 144, 609, 1584, 4235, 7986, 14641], [1, 10, 51, 130, 169, 0, 0, 0, 0], [1, 6, 13, -66, -372, -1122, 3757, 29478, 83521], [1, -6, 67, -288, 1905, -5472, 24187, -41154, 130321], [1, 0, -26, 0, 147, 0, -13754, 0, 279841], [1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], [1, 4, -5, -164, -1016, -5084, -4805, 119164, 923521], [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], [1, 6, -50, 24, 4239, 984, -84050, 413526, 2825761], [1, 5, 34, -475, -2843, -20425, 62866, 397535, 3418801], [1, 0, -89, 0, 5712, 0, -196601, 0, 4879681], [1, 12, 7, 372, 8328, 19716, 19663, 1786524, 7890481], [1, 0, -113, 0, 9288, 0, -393353, 0, 12117361], [1, 24, 460, 5256, 49974, 320616, 1711660, 5447544, 13845841], [1, 24, 394, 4608, 43899, 308736, 1768666, 7218312, 20151121], [1, -6, 10, 696, -6921, 49416, 50410, -2147466, 25411681], [1, -4, -134, -16, 16003, -1168, -714086, -1556068, 28398241], [1, 8, -110, 128, 18979, 10112, -686510, 3944312, 38950081], [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], [1, 21, 184, 1659, 18879, 147651, 1457464, 14804349, 62742241], [1, 31, 538, 7099, 76303, 688603, 5062042, 28292863, 88529281]], 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/g/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': '8-637e4-1.1-c1e4-0-26', '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': 4, 'prelabel': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1802964082974503751, 'z1': {'__RealLiteral__': 0, 'data': '1.00929791706032927283141065071', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1279437110370628098444849551602,2049975564391855016977535200462,2541985636152703784318922740139,3290192248697484695265610379944', 'Lhash_array': ['1279437110370628098444849551602', '2049975564391855016977535200462', '2541985636152703784318922740139', '3290192248697484695265610379944'], 'label': '8-637e4-1.1-c1e4-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/g/b'}