Lfunction data - 6-8450e3-1.1-c1e3-0-17

Formats: - HTML - YAML - JSON - 2025-09-11T01:47:48.503072

• 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': '1522958739688201243684876583800,1957881171072948740283902039977,2082974584305406541213705915387', 'a10': 0, 'a2': 3, 'a3': -1, 'a4': 6, 'a5': 0, 'a6': -3, 'a7': 5, 'a8': 10, 'a9': -6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 307186.02054702083, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -3, 3, -1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '8450.1', 'coefficient_field': '1.1.1.1', 'conductor': 603351125000, 'conductor_radical': 130, 'degree': 6, 'euler_factors': [[1, -3, 3, -1], [1, 1, 7, 5, 21, 9, 27], [1], [1, -5, 27, -71, 189, -245, 343], [1, 4, 29, 80, 319, 484, 1331], [1], [1, 10, 75, 348, 1275, 2890, 4913], [1, 8, 69, 296, 1311, 2888, 6859], [1, -3, 23, 1, 529, -1587, 12167], [1, -3, 83, -175, 2407, -2523, 24389], [1, 8, 49, 152, 1519, 7688, 29791], [1, -8, 95, -528, 3515, -10952, 50653], [1, 11, 49, 75, 2009, 18491, 68921], [1, -1, 99, -43, 4257, -1849, 79507], [1, -15, 167, -1339, 7849, -33135, 103823], [1, 4, 43, -144, 2279, 11236, 148877], [1, 24, 341, 3176, 20119, 83544, 205379], [1, 15, 167, 1297, 10187, 55815, 226981], [1, -5, 123, -839, 8241, -22445, 300763], [1, 32, 545, 5656, 38695, 161312, 357911], [1, 26, 379, 3692, 27667, 138554, 389017], [1, -2, 117, 28, 9243, -12482, 493039], [1, -7, 95, -875, 7885, -48223, 571787], [1, -17, 137, -829, 12193, -134657, 704969], [1, 6, 107, 52, 10379, 56454, 912673], [1, 17, 397, 3603, 40097, 173417, 1030301], [1, 19, 343, 3313, 35329, 201571, 1092727], [1, -16, 257, -2912, 27499, -183184, 1225043], [1, 9, 207, 1051, 22563, 106929, 1295029], [1, -4, 279, -1008, 31527, -51076, 1442897]], 'euler_factors_factorization': [[[[1, -1], 3]], [[[1, 1, 7, 5, 21, 9, 27], 1]], [1], [[[1, -5, 27, -71, 189, -245, 343], 1]], [[[1, 4, 29, 80, 319, 484, 1331], 1]], [1], [[[1, 10, 75, 348, 1275, 2890, 4913], 1]], [[[1, 8, 69, 296, 1311, 2888, 6859], 1]], [[[1, -3, 23, 1, 529, -1587, 12167], 1]], [[[1, -3, 83, -175, 2407, -2523, 24389], 1]], [[[1, 8, 49, 152, 1519, 7688, 29791], 1]], [[[1, -8, 95, -528, 3515, -10952, 50653], 1]], [[[1, 11, 49, 75, 2009, 18491, 68921], 1]], [[[1, -1, 99, -43, 4257, -1849, 79507], 1]], [[[1, -15, 167, -1339, 7849, -33135, 103823], 1]], [[[1, 4, 43, -144, 2279, 11236, 148877], 1]], [[[1, 24, 341, 3176, 20119, 83544, 205379], 1]], [[[1, 15, 167, 1297, 10187, 55815, 226981], 1]], [[[1, -5, 123, -839, 8241, -22445, 300763], 1]], [[[1, 32, 545, 5656, 38695, 161312, 357911], 1]], [[[1, 26, 379, 3692, 27667, 138554, 389017], 1]], [[[1, -2, 117, 28, 9243, -12482, 493039], 1]], [[[1, -7, 95, -875, 7885, -48223, 571787], 1]], [[[1, -17, 137, -829, 12193, -134657, 704969], 1]], [[[1, 6, 107, 52, 10379, 56454, 912673], 1]], [[[1, 17, 397, 3603, 40097, 173417, 1030301], 1]], [[[1, 19, 343, 3313, 35329, 201571, 1092727], 1]], [[[1, -16, 257, -2912, 27499, -183184, 1225043], 1]], [[[1, 9, 207, 1051, 22563, 106929, 1295029], 1]], [[[1, -4, 279, -1008, 31527, -51076, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 17, 'label': '6-8450e3-1.1-c1e3-0-17', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/8450/2/a/bz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [-3.1783215379573374e-179, 0.0008310059595011435, 0.006642067045772499, 0.02238336070566608, 0.05294528541642534, 0.10312787422887384, 0.17761047223343823, 0.2809212208729999, 0.41740344986737693, 0.5911854472600891, 0.8061491891636245, 1.0658911489253329, 1.3736944703028082, 1.7324976831490615, 2.144848260854782, 2.612880918925154, 3.138288208967041, 3.7222672047728924, 4.3655083246051705, 5.068170919713874, 5.829826448164907, 6.6494618972077895, 7.5254645271832175, 8.455568339662484, 9.43687473085616, 10.465851138528269, 11.538290891145715, 12.649351178053456, 13.793570209588394, 14.964852933026746, 16.156522939027646, 17.361361682132166, 18.571633400294555, 19.779143525126273, 20.97530144292411, 22.15119676899192, 23.29765267597034, 24.40531070057622, 25.464767109394845, 26.466605914806255, 27.401500651104467, 28.26041410975025, 29.034593361116666, 29.715679738135144, 30.2959683030785, 30.768346613943212, 31.126401019603065, 31.36472479153461, 31.4787842261284, 31.465007486440072, 31.321123574763476, 31.04594395872135, 30.63942023212219, 30.10299125813981, 29.439275787659355, 28.652087574675786, 27.74676615653292, 26.729785375830023, 25.60871933388974, 24.392534066003517, 23.09112747594105, 21.715246251260083, 20.276721218917384, 18.787964528795975, 17.261845524001558, 15.711861210579626, 14.151624909385465, 12.594716819621084, 11.054791513545373, 9.545097052205227, 8.078322137979981, 6.666653043265778, 5.3213620228230525, 4.05267611036486, 2.869804381292946, 1.7806287104762966, 0.7916183741323538, -0.09214682861063073, -0.8671616084649744, -1.5315159797094249, -2.0848512752042043, -2.528414452841212, -2.8650048958465275, -3.0988905740916195, -3.2357424355003275, -3.28250997815024, -3.2472893007858388, -3.139164860841729, -2.968029434434926, -2.744409377798557, -2.4792536243709655, -2.183724732784685, -1.8690004110472764, -1.5460557205131886, -1.2254588230058483, -0.9171786866098384, -0.6304044477131374, -0.37338039056910766, -0.15325506415417964, 0.02402852903157022, 0.1538300024942065, 0.23288779702397328, 0.25934152829228885, 0.23274431848933422, 0.15404057076428246, 0.02550494546443618, -0.14933079966000237, -0.3658066583650361, -0.6182543436096537, -0.9001396701786912, -1.2042875290407482, -1.523020767066495, -1.8483411331170616, -2.1722220504199083, -2.486719141161421, -2.7841506596417047, -3.057416856408038, -3.3000380656007486, -3.5062953592259922, -3.671530624139815, -3.792081584363793, -3.865351973779863, -3.8900515249982592, -3.866018512925042, -3.794204568164121, -3.6768279063887674, -3.517098478469468, -3.3191223054047176, -3.0879614975299376, -2.82929934958088, -2.5492882609406733, -2.2545317419505455, -1.9517414666099013, -1.6475667788275539, -1.3485316427608023, -1.0607389464280232, -0.7897246135192652, -0.5403916797911223, -0.3168077853081566, -0.12212135142949732, 0.04146705520955953, 0.1727882744067707, 0.2717040559899235, 0.33907142343443925, 0.37670785809831125, 0.3873055989172274, 0.37432600340285715, 0.34187306584494276, 0.2945438613586745, 0.23727104687631123, 0.17515061789042888, 0.11326709817053483, 0.056522288410834405, 0.00947030237851612, -0.023836471834358223, -0.03998407791386375, -0.03630873833507019, -0.010988962384309152, 0.036897486862177385, 0.10734124146470199, 0.1993959245290372, 0.31122972204915067, 0.4401713325691436, 0.5827921570758223, 0.7350693208414967, 0.892481523326264, 1.0501547053483204, 1.2031108440536855, 1.3463658395698932, 1.4750954968471406, 1.584921192516481, 1.6719563626153422, 1.732942369033253, 1.7655113584674555, 1.7681386038765199, 1.7402051147946502, 1.6821836201236477, 1.5954787284942586, 1.48239369559272, 1.3462068524219188, 1.1909137919571635, 1.0211042406984778, 0.8419280650874891, 0.6587843379875359, 0.47714276242794995, 0.30243172780953753, 0.13973893246486968, -0.0063682921362460485, -0.13197559201432044, -0.23404231390635366, -0.31052323663159076, -0.36045656729588715, -0.38405565434902883, -0.38272675035318193, -0.3590597960788605, -0.3167727491491739, -0.2606074397986863, -0.19620181666310257, -0.12990691561800954, -0.06857862167785042, -0.019351988553180127, 0.010615683236481306, 0.014406213269642395, -0.014397234202666774, -0.08145068975986337, -0.19140617500700333, -0.3477014291203808, -0.5523650748383959, -0.8058633019569016, -1.107034074429842, -1.4529977427617384, -1.8391443458550583, -2.25928250345269, -2.705654629585918, -3.1690780290410956, -3.639334294504567, -4.105243440842766, -4.554928062389116, -4.976413714468873, -5.357682351267797, -5.686991319753199, -5.953603930615895, -6.147731278311977, -6.260818366508714, -6.286291523725915, -6.219314583299243, -6.056959741437413, -5.798854534411557, -5.446720688656656, -5.00437701788649, -4.478195272226508, -3.876446910044414, -3.209131633709882, -2.4882015961569985, -1.7267968466568808, -0.9389427979596012, -0.13956199791639765, 0.6562835676970049, 1.4337444182220669, 2.178312832761405, 2.876448249560403, 3.5158816858183846, 4.085784895136774, 4.577164553169463, 4.983035068784127, 5.298527518633338, 5.521007620652537, 5.6500703380439505, 5.687519029368184, 5.637228703527567, 5.5049668048148055, 5.2982229134642, 5.025898888556178, 4.698009255144869, 4.325394899594963, 3.9193581077565947, 3.491328111452475, 3.052531692772929, 2.6136935239039887, 2.18475802139165, 1.7746034724435034, 1.3908965469265646, 1.0399394574625689, 0.7264986842631636, 0.4538475399566207, 0.2237654331506089, 0.03651378036551811, -0.1089603567371125, -0.2148942848681672, -0.28460160271911467, -0.3221821877441783, -0.33232124503442634, -0.3201042421490012, -0.2907355203231779, -0.24934252827448553, -0.20078806418280987, -0.1494805113756674, -0.09924932913703215, -0.05322114347054306, -0.01376625522269988, 0.01752039084397635, 0.039843461035228935, 0.053129940620022756, 0.05794994369453237, 0.055447083866672166, 0.04717982265992981, 0.03498719763472873, 0.020867593143586126, 0.00681085426695223, -0.005330450156194225, -0.013953866537575403, -0.017817390920616186, -0.016108730107539732, -0.008497289108003772, 0.004850164936880756, 0.023286220359676264, 0.04571475650716336, 0.07066572206489975, 0.09638735811443704, 0.12094583554909948, 0.14234991104684389, 0.1586764550819454, 0.16818837442120482, 0.16945156034609102, 0.16143770623819223, 0.14359781737908625, 0.11592253629440187, 0.07897590792041881, 0.03387450827842453, -0.01772748018633544, -0.07369055161257486, -0.1315206492094423, -0.1884390333606936, -0.24150045977176218, -0.28780650876016706, -0.3245792633258139, -0.349295626895189, -0.3599218587218565, -0.3549309726011136, -0.33339408554631456, -0.29516404588627354, -0.24079438204518408, -0.1715442373009888, -0.0894569452792627, 0.002823018596940322, 0.10213973851709059, 0.20486588070918074, 0.307147230179939, 0.4050543713592568, 0.4947074002191876, 0.5725103935275182, 0.6353028829434673, 0.6805005125299172, 0.7062439098620934, 0.711482792285338, 0.6960569125835796, 0.6607104203278807, 0.6070646860560469, 0.5375894138616468, 0.45548164827981535, 0.3645268926786944, 0.26895943749292023, 0.17325590299172333, 0.08193094207343854, -0.0006606962930711262, -0.07053393449061567, -0.12426635509302654, -0.1591665604192672, -0.1734060417564442, -0.1661239258341491, -0.13747709106233033, -0.08864873745054128, -0.021820086166581015, 0.05994979999747977, 0.15282655485782673, 0.25235363607863986, 0.3537334613763265, 0.4519728272366159, 0.5420998549289381, 0.6195346065836668, 0.6801791200527328, 0.7206071627691495, 0.7384160077049821, 0.7321739819381957, 0.7014992509693672, 0.6472900045695061, 0.5714934884058178, 0.4770340526757465, 0.36786719707185617, 0.2486064612256585, 0.12432540327869236, 0.0004537099178135335, -0.11763727213015132, -0.2248756142928863, -0.31666511266069, -0.3892123250937174, -0.43970147208048144, -0.4664256673648481, -0.4689212757395682, -0.44798754945212416, -0.40567540666434965, -0.34519316145914497, -0.27074350900041577, -0.1873398023267244, -0.10053616278740804, -0.01613415482331638, 0.06011530066954639, 0.12283274437310035, 0.16731744079443503, 0.18983088778946744, 0.18782217015194075, 0.16011457566129944, 0.10702656541632455, 0.03039736944096204, -0.06644108899374375, -0.1788060992393034, -0.30084967027619186, -0.42580782669731704, -0.5464048705244343, -0.6551542721760404, -0.7447351609303813, -0.8085432792440792, -0.8409372131597034, -0.8375780794712101, -0.7959322476906832, -0.7152887357020897, -0.5968938944362038, -0.444208066499233, -0.26259662180647864, -0.059163303228396205, 0.15735192281140167, 0.37717222050251015, 0.5899223664141854, 0.7850553881423459, 0.9525678498471145, 1.0835495040895606, 1.1707481675964213, 1.209143260137681, 1.1963668176439182, 1.1331308350996188, 1.0234167109547998, 0.8745426962756438, 0.6972003625114674, 0.5051368865045838, 0.3147596396140092, 0.14467083232236794, 0.014903488706797212, -0.05386559506828751, -0.04117399303571432, 0.07225311911512965, 0.30357271614980114, 0.6668983490214595, 1.172445546334306, 1.8258052465737002, 2.6273980465043776, 3.572020848241805, 4.648639156259312, 5.840632456592846, 7.125845577872841, 8.477050202046415, 9.863192337266447, 11.24979880106123, 12.600012536100165, 13.87674777766787, 15.043074423281404, 16.063496665150414, 16.906619007384943, 17.545030250232625, 17.95636753878194, 18.125914083188235, 18.045590652552317, 17.714390028879478, 17.140344740027004, 16.338497320200748, 15.330502270375426, 14.145625584293796, 12.81792138238606, 11.38510939148198, 9.88862175607641, 8.370531607419423, 6.8721067293508, 5.433269728541852, 4.089974448248548, 2.87299135634457, 1.8073538492078713, 0.9107872786758949, 0.1932257469257277, -0.3432107429236142, -0.7044459420942627, -0.9039585304309616, -0.9619922795584607, -0.9045888656981595, -0.7622575128125346, -0.5684912553588218, -0.35813546773928034, -0.16568623623858236, -0.02360943749948859, 0.039233830051839655, -0.0009783447553806046, -0.16184130864029142, -0.45383377218849646, -0.8797072300922378, -1.434398288601074, -2.105102459596688, -2.8717318609242097, -3.708186207436266, -4.583200523169047, -5.4616895982512785, -6.307153831689255, -7.0827111855047225, -7.752777727702925, -8.285958021222719, -8.655513346917342, -8.84067203872629, -8.82916372699613, -8.616538971278157, -8.206536977374425, -7.612559803830649, -6.8556921214893825, -5.963935569339601, -4.972341360095035, -3.920114772533531, -2.849005975402531, -1.8023626687850578, -0.8221209914370226, 0.052977097341317635, 0.7887101626999332, 1.357583405947955, 1.740002330463495, 1.9251337977486866, 1.9116452793530816, 1.7077053149882777, 1.3307629032909067, 0.8066888749187958, 0.16851168998260094, -0.5449833669340711, -1.2912402960924476, -2.0260149769970117, -2.7054588135224513, -3.288344102963588, -3.73814481243729, -4.024890320277219, -4.126693967997245, -4.030972679258357, -3.735118635566789, -3.2467532706257174, -2.583557661887556, -1.7721896019910097, -0.8473113434429509, 0.1499193677238845, 1.1745986585690982, 2.179596264050167, 3.1177683930010103, 3.9456138544146304, 4.624308314032546, 5.121649392431552, 5.415470103224386, 5.493252931480069, 5.3529120741754115, 5.004894209270287, 4.469975982406785, 3.77846937726654, 2.9704810874204144, 2.092267417533254, 1.1941464128286003, 0.32917753557389656, -0.450874300343471, -1.0980190089589434, -1.5699781040930905, -1.833281262092922, -1.8649838224718478, -1.6539665444218563, -1.202034588716701, -0.5239671836638303, 0.35278991574545154, 1.3893398365443372, 2.5371756575425937, 3.7402920855695583, 4.938116352106397, 6.068619657018431, 7.071477326342655, 7.891419845076266, 8.481354894284852, 8.805108600547149, 8.839749565077826, 8.577331151063827, 8.025626519409313, 7.208479287349049, 6.1652593488710785, 4.948596761471499, 3.622791595524144, 2.2610168273370177, 0.9401764628297127, -0.2615381147457115, -1.2686413868494715, -2.015033847076909, -2.4455529132986134, -2.5194440951098276, -2.2164586721754165, -1.53584203412332, -0.4975934779034054, 0.85410700835365, 2.455283239528519, 4.224024602598234, 6.060897297651529, 7.856158555431366, 9.494378551841596, 10.858346710925858, 11.837255177385739, 12.33244744658309, 12.262958108413894, 11.572086549022504, 10.23190406786066, 8.247679294039461, 5.660501953087047, 2.548343641900412, -0.9731922103158798, -4.753353595240949, -8.609748139103903, -12.332528528794706, -15.691420008318866, -18.443272311111905, -20.340429171147555, -21.140140782207617, -20.614028393382412, -18.557885487796984, -14.80049964534725, -9.21196778855697, -1.7109560823079322, 7.72969692669116, 19.07872711170318, 32.24561720326316, 47.07939213099291, 63.370104902843764, 80.8568886487867, 99.2302894878463, 118.13925882120981, 137.20816958472486, 156.03996573369307, 174.22652851597135, 191.3722514597374, 207.0943486447333, 221.03327021215728, 232.87866184574827, 242.3635779401873, 249.2715796930125, 253.46044789641223, 254.8487118808927, 253.41718886559698, 249.2267898557443, 242.39814170595895, 233.10720378526327, 221.59551423572805, 208.14591887239698, 193.07384530934115, 176.73064224416234, 159.47974435270655, 141.6865037228968, 123.71707966274312, 105.91931034768139, 88.61426068800631, 72.093863805177, 56.60938654670767, 42.36702511069855, 29.527050924117603, 18.20056649231896, 8.449937906159539, 0.29087173834643654, -6.304062139271844, -11.401020834114851, -15.100055449676844, -17.527856409431212, -18.831385024644163, -19.171703135333804, -18.71639749313365, -17.63358083322491, -16.086271986975134, -14.227165498887143, -12.194785943845929, -10.109939034804487, -8.074040051153705, -6.168123208996128, -4.451956504755834, -2.9655968985638044, -1.7308183145167406, -0.7524560039638375, -0.02177931037684135, 0.48085526632107767, 0.7835560717193222, 0.9194235496601758, 0.9240171807381293, 0.8330553628460047, 0.6801422134066275, 0.4952969617265555, 0.3036557762581271, 0.12487106860866329, -0.027042192337250588, -0.14380848814972405, -0.22215924658000205, -0.26304599698041464, -0.2709401607366885, -0.2525686188990724, -0.21587750292382551, -0.16919183574809166, -0.12021128161117907, -0.07533970431567068, -0.03925295025128522, -0.014577456031680381, -0.0018489989499620688, 0.00033146656078222354, -0.005010455222124957, -0.013670201542252867, -0.020795227813567886, -0.021443147886590942, -0.011132889022637343, 0.013671535063084633, 0.05517442978493758, 0.11396691412758482, 0.18895332358269845, 0.277346638544557, 0.37480836689831076, 0.47588566322294384, 0.5742954757046013, 0.6633576429218567, 0.7367443852460914, 0.7887509869456931, 0.8147197186387898, 0.8117382823168535, 0.778594038741442, 0.715907285034924, 0.6264669445836679, 0.5147578495175493, 0.38671145752171254, 0.2495929888346936, 0.1112534422939934, -0.020355185127840625, -0.13756419515807802, -0.23368445816062494, -0.30343197070408956, -0.3432583667629374, -0.35168056888382226, -0.3293795763149064, -0.27920089720387536, -0.20599292184739582, -0.11629559476003902, -0.017949681192176648, 0.08042258027843448, 0.16998734397176024, 0.24228487497361847, 0.2897940325164516, 0.30645734053400514, 0.2881136735185274, 0.23279667314507618, 0.14092976330753648, 0.015300164524593176, -0.13903908491134478, -0.3150099815160918, -0.5040823576193054, -0.6966404990579006, -0.8825237333916898, -1.0519586029713937, -1.1958779195726954, -1.3064551803970976, -1.37802549700578, -1.4070323316776825, -1.3922494306233455, -1.3353332144078525, -1.2402534328549037, -1.1130664318458903, -0.9619417780221687, -0.7962159845500747, -0.6258399710894476, -0.46101692324262, -0.3112220685378144, -0.18462711329676085, -0.0876850531405918, -0.024553686868555195, 0.003150930504660995, -0.0035114204444797307, -0.04078215268802253, -0.10249553334648821, -0.18056283909486984, -0.2654576064363086, -0.3466530369914039, -0.4130748278984158, -0.4544936885388558, -0.4627974964854572, -0.43180918136183377], 'positive_zeros': ['1.20140261000468571154143738765652', '1.54449591292778101667943071351027', '1.64317721612752377399884655486506', '2.18323679323464997611626366138733', '2.39440964351478719755700737478931', '2.45745314159954335525828708976042', '2.92114874742559667892189024387531', '3.13361286710680485066308492443804', '3.16629734830210133130574252826812', '3.69022731117469917935044149193960', '4.15978503190235329077529206709717', '4.36572628037845051758791881500987', '4.50831794176930278832691172811860', '4.58876668897420508315600073723789', '4.82293791656479309940895820552586', '5.06204179330375581029066991424990', '5.37486582519885853355668368137674', '5.50442891918078297765751406544815', '5.79693475069551633451222043783324', '6.01876026787627325961492294124257', '6.14585949829227486578238240132007', '6.39496181892641305956165554385947', '6.65862595277436178851223900482966', '6.69505900691942699168668227930691', '7.28630509812147364158799227651662', '7.44130549690675471392561979558105', '7.46859307442175525264193792539809'], 'prelabel': '6-8450e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.214230926141653, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 450404723464063251, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20140261000468571154143738766', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54449591292778101667943071351', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.64317721612752377399884655487', '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': 307186.02054702083, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 603351125000, 'conductor_radical': 130, 'degree': 6, 'dirichlet_coefficients': [1, 3, -1, 6, 0, -3, 5, 10, -6, 0, -4, -6, 0, 15, 0, 15, -10, -18, -8, 0, -5, -12, 3, -10, 0, 0, 8, 30, 3, 0, -8, 21, 4, -30, 0, -36, 8, -24, 0, 0, -11, -15, 1, -24, 0, 9, 15, -15, -2, 0, 10, 0, -4, 24, 0, 50, 8, 9, -24, 0, -15, -24, -30, 28, 0, 12, 5, -60, -3, 0, -32, -60, -26, 24, 0, -48, -20, 0, 2, 0, 18, -33, 7, -30, 0, 3, -3, -40, 17, 0, 0, 18, 8, 45, 0, -21, -6, -6, 24, 0], 'euler11': [1, 4, 29, 80, 319, 484, 1331], 'euler13': [1, 0, 0, 0, 0, 0, 0], 'euler17': [1, 10, 75, 348, 1275, 2890, 4913], 'euler19': [1, 8, 69, 296, 1311, 2888, 6859], 'euler2': [1, -3, 3, -1, 0, 0, 0], 'euler23': [1, -3, 23, 1, 529, -1587, 12167], 'euler29': [1, -3, 83, -175, 2407, -2523, 24389], 'euler3': [1, 1, 7, 5, 21, 9, 27], 'euler31': [1, 8, 49, 152, 1519, 7688, 29791], 'euler37': [1, -8, 95, -528, 3515, -10952, 50653], 'euler41': [1, 11, 49, 75, 2009, 18491, 68921], 'euler43': [1, -1, 99, -43, 4257, -1849, 79507], 'euler47': [1, -15, 167, -1339, 7849, -33135, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 4, 43, -144, 2279, 11236, 148877], 'euler59': [1, 24, 341, 3176, 20119, 83544, 205379], 'euler61': [1, 15, 167, 1297, 10187, 55815, 226981], 'euler67': [1, -5, 123, -839, 8241, -22445, 300763], 'euler7': [1, -5, 27, -71, 189, -245, 343], 'euler71': [1, 32, 545, 5656, 38695, 161312, 357911], 'euler73': [1, 26, 379, 3692, 27667, 138554, 389017], 'euler79': [1, -2, 117, 28, 9243, -12482, 493039], 'euler83': [1, -7, 95, -875, 7885, -48223, 571787], 'euler89': [1, -17, 137, -829, 12193, -134657, 704969], 'euler97': [1, 6, 107, 52, 10379, 56454, 912673], 'euler_factors': [[1, -3, 3, -1, 0, 0, 0], [1, 1, 7, 5, 21, 9, 27], [1, 0, 0, 0, 0, 0, 0], [1, -5, 27, -71, 189, -245, 343], [1, 4, 29, 80, 319, 484, 1331], [1, 0, 0, 0, 0, 0, 0], [1, 10, 75, 348, 1275, 2890, 4913], [1, 8, 69, 296, 1311, 2888, 6859], [1, -3, 23, 1, 529, -1587, 12167], [1, -3, 83, -175, 2407, -2523, 24389], [1, 8, 49, 152, 1519, 7688, 29791], [1, -8, 95, -528, 3515, -10952, 50653], [1, 11, 49, 75, 2009, 18491, 68921], [1, -1, 99, -43, 4257, -1849, 79507], [1, -15, 167, -1339, 7849, -33135, 103823], [1, 4, 43, -144, 2279, 11236, 148877], [1, 24, 341, 3176, 20119, 83544, 205379], [1, 15, 167, 1297, 10187, 55815, 226981], [1, -5, 123, -839, 8241, -22445, 300763], [1, 32, 545, 5656, 38695, 161312, 357911], [1, 26, 379, 3692, 27667, 138554, 389017], [1, -2, 117, 28, 9243, -12482, 493039], [1, -7, 95, -875, 7885, -48223, 571787], [1, -17, 137, -829, 12193, -134657, 704969], [1, 6, 107, 52, 10379, 56454, 912673]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8450/2/a/bz'], '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': '6-8450e3-1.1-c1e3-0-17', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-8450e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.214230926141653, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 450404723464063251, 'z1': {'__RealLiteral__': 0, 'data': '1.20140261000468571154143738766', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1522958739688201243684876583800,1957881171072948740283902039977,2082974584305406541213705915387', 'Lhash_array': ['1522958739688201243684876583800', '1957881171072948740283902039977', '2082974584305406541213705915387'], 'factors': ['2-8450-1.1-c1-0-170', '2-8450-1.1-c1-0-224', '2-8450-1.1-c1-0-231'], 'label': '6-8450e3-1.1-c1e3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8450/2/a/bz'}