Lfunction data - 12-3800e6-1.1-c1e6-0-6

Formats: - HTML - YAML - JSON - 2025-09-05T13:33:13.056347

• 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': '436082832229611298142410520587,471231924244663090452368597788,496208218504572591453452252941,1509842123967915986689438841913,1982259441850717304180760960337,2086392677493521122635575306991', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 780484390.6529279, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, 6, 15, 20, 15, 6, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': '1.1.1.1', 'conductor': 3010936384000000000000, 'conductor_radical': 190, 'degree': 12, 'euler_factors': [[1], [1, 0, -5, 0, 23, 0, -86, 0, 207, 0, -405, 0, 729], [1], [1, 0, -17, 0, 211, 0, -1718, 0, 10339, 0, -40817, 0, 117649], [1, 0, 66, 0, 1815, 0, 26620, 0, 219615, 0, 966306, 0, 1771561], [1, 0, -57, 0, 1487, 0, -23774, 0, 251303, 0, -1627977, 0, 4826809], [1, 0, -69, 0, 2147, 0, -42926, 0, 620483, 0, -5762949, 0, 24137569], [1, 6, 15, 20, 15, 6, 1], [1, 0, -73, 0, 3107, 0, -85926, 0, 1643603, 0, -20428393, 0, 148035889], [1, 34, 631, 8034, 76899, 576820, 3462954, 16727780, 64672059, 195941226, 446294311, 697379066, 594823321], [1, -4, 94, -172, 4799, -9064, 192836, -280984, 4611839, -5124052, 86810974, -114516604, 887503681], [1, 0, -158, 0, 11191, 0, -496772, 0, 15320479, 0, -296117438, 0, 2565726409], [1, -12, 178, -1724, 16095, -117016, 862332, -4797656, 27055695, -118819804, 502985458, -1390274412, 4750104241], [1, 0, -174, 0, 13991, 0, -717764, 0, 25869359, 0, -594871374, 0, 6321363049], [1, 0, -106, 0, 5423, 0, -232716, 0, 11979407, 0, -517246186, 0, 10779215329], [1, 0, -209, 0, 20271, 0, -1269614, 0, 56941239, 0, -1649110529, 0, 22164361129], [1, 30, 523, 6442, 69363, 661988, 5569122, 39057292, 241452603, 1323051518, 6337379803, 21447728970, 42180533641], [1, -16, 422, -4688, 68471, -560736, 5670996, -34204896, 254780591, -1064086928, 5842944902, -13513540816, 51520374361], [1, 0, -37, 0, 7511, 0, -169110, 0, 33716879, 0, -745591477, 0, 90458382169], [1, 8, 58, -744, -225, 33104, 1147692, 2350384, -1134225, -266285784, 1473877498, 14433834808, 128100283921], [1, 0, -229, 0, 27155, 0, -2216718, 0, 144708995, 0, -6503197189, 0, 151334226289], [1, 4, 430, 1420, 80159, 213256, 8284964, 16847224, 500272319, 700115380, 16748534830, 12308225596, 243087455521], [1, 0, -366, 0, 60407, 0, -6127364, 0, 416143823, 0, -17369745486, 0, 326940373369], [1, 12, 466, 4348, 95103, 704792, 10989756, 62726488, 753310863, 3065205212, 29237884306, 67008713388, 496981290961], [1, 0, -358, 0, 62671, 0, -7159060, 0, 589671439, 0, -31693482598, 0, 832972004929], [1, 24, 358, 5080, 63207, 772976, 8888724, 78070576, 644774607, 5233929080, 37253623558, 252242412024, 1061520150601], [1, 0, -94, 0, 18655, 0, -822628, 0, 197910895, 0, -10579782814, 0, 1194052296529], [1, 0, -389, 0, 73287, 0, -9126326, 0, 839062863, 0, -50989964789, 0, 1500730351849], [1, 38, 1015, 18878, 300803, 3915716, 44885738, 426813044, 3573840443, 24447557462, 143275533415, 584677102862, 1677100110841], [1, 0, -634, 0, 171855, 0, -25533676, 0, 2194416495, 0, -103372026874, 0, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, 0, -5, 0, 23, 0, -86, 0, 207, 0, -405, 0, 729], 1]], [1], [[[1, 0, -17, 0, 211, 0, -1718, 0, 10339, 0, -40817, 0, 117649], 1]], [[[1, 0, 11], 6]], [[[1, 0, -57, 0, 1487, 0, -23774, 0, 251303, 0, -1627977, 0, 4826809], 1]], [[[1, 0, -69, 0, 2147, 0, -42926, 0, 620483, 0, -5762949, 0, 24137569], 1]], [[[1, 1], 6]], [[[1, 0, -73, 0, 3107, 0, -85926, 0, 1643603, 0, -20428393, 0, 148035889], 1]], [[[1, 17, 171, 1110, 4959, 14297, 24389], 2]], [[[1, -2, 45, 4, 1395, -1922, 29791], 2]], [[[1, 0, -158, 0, 11191, 0, -496772, 0, 15320479, 0, -296117438, 0, 2565726409], 1]], [[[1, -6, 71, -436, 2911, -10086, 68921], 2]], [[[1, 0, -174, 0, 13991, 0, -717764, 0, 25869359, 0, -594871374, 0, 6321363049], 1]], [[[1, 0, -106, 0, 5423, 0, -232716, 0, 11979407, 0, -517246186, 0, 10779215329], 1]], [[[1, 0, -209, 0, 20271, 0, -1269614, 0, 56941239, 0, -1649110529, 0, 22164361129], 1]], [[[1, 15, 149, 986, 8791, 52215, 205379], 2]], [[[1, -8, 179, -912, 10919, -29768, 226981], 2]], [[[1, 0, -37, 0, 7511, 0, -169110, 0, 33716879, 0, -745591477, 0, 90458382169], 1]], [[[1, 4, 21, -456, 1491, 20164, 357911], 2]], [[[1, 0, -229, 0, 27155, 0, -2216718, 0, 144708995, 0, -6503197189, 0, 151334226289], 1]], [[[1, 2, 213, 284, 16827, 12482, 493039], 2]], [[[1, 0, -366, 0, 60407, 0, -6127364, 0, 416143823, 0, -17369745486, 0, 326940373369], 1]], [[[1, 6, 215, 884, 19135, 47526, 704969], 2]], [[[1, 0, -358, 0, 62671, 0, -7159060, 0, 589671439, 0, -31693482598, 0, 832972004929], 1]], [[[1, 12, 107, 1256, 10807, 122412, 1030301], 2]], [[[1, 0, -94, 0, 18655, 0, -822628, 0, 197910895, 0, -10579782814, 0, 1194052296529], 1]], [[[1, 0, -389, 0, 73287, 0, -9126326, 0, 839062863, 0, -50989964789, 0, 1500730351849], 1]], [[[1, 19, 327, 3226, 35643, 225739, 1295029], 2]], [[[1, 0, -634, 0, 171855, 0, -25533676, 0, 2194416495, 0, -103372026874, 0, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 6, 'label': '12-3800e6-1.1-c1e6-0-6', 'leading_term': '3.6617800614583114040878277407445403022693871947953616136445158023249226215864857864381198', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3800/2/d/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.009765625', 'prec': 37}, 'plot_values': [3.6617800614583107, 3.6525150539170363, 3.6271445402907796, 3.585756226415183, 3.5285923123817673, 3.456051773859882, 3.368675082184992, 3.2672050098713545, 3.152645315392218, 3.0261471680712777, 2.888974203920908, 2.742498183904558, 2.5881649085269656, 2.4274659393914493, 2.261930109961181, 2.093123765361369, 1.9226356171627785, 1.7520618651326687, 1.5829892366725515, 1.416970850782468, 1.255506206209715, 1.1000214364449823, 0.951845270956569, 0.812186863767132, 0.682117625111094, 0.5625524759096056, 0.45423218208479094, 0.35770524168260137, 0.27331197184641126, 0.20116968593758314, 0.14116041315191058, 0.09292041319703773, 0.05583081941502132, 0.02901217279337523, 0.011321440644791313, 0.0013521507421942374, -0.002562612131256111, -0.002343809373161389, -0.00015637290863992743, 0.0016043528006773268, 0.0003298814044834545, -0.00678035975225542, -0.022694418893841915, -0.05051973181017708, -0.09347136052800732, -0.1548363677646906, -0.23793566032301616, -0.34608374492764693, -0.48254564073829315, -0.65049044456542, -0.8529429760604301, -1.0927370082262595, -1.3724680749327043, -1.6944455100118498, -2.060641516024186, -2.4726439539900698, -2.9316157118364266, -3.438254927617076, -3.9927580103967073, -4.5947818925823585, -5.243415968365565, -5.937163783671186, -6.673929414301882, -7.451008147125335, -8.265083539928298, -9.112233876149986, -9.987947356827346, -10.887145964624096, -11.804222674131802, -12.73308824258847, -13.667215689095528, -14.599690347482426, -15.523272176953292, -16.430474102792033, -17.313673176583006, -18.165178561977324, -18.977300109398776, -19.74243540819522, -20.4531775713034, -21.10244263811212, -21.683569473840766, -22.190373322520088, -22.617220979021273, -22.95914694225792, -23.211946302351368, -23.372239469505736, -23.437534021175665, -23.406238552094127, -23.277745642168554, -23.052445056790567, -22.731726840631573, -22.31797764384669, -21.81457672565516, -21.225899139078724, -20.55721599454931, -19.81463264373049, -19.005023236502264, -18.135939241987533, -17.215598698542813, -16.252682428294502, -15.256212053461665, -14.235452054776566, -13.199775755852663, -12.158573106549094, -11.121090589423906, -10.096279060603626, -9.092690569543626, -8.118366124353694, -7.180724107402169, -6.286435539793648, -5.4413693042828974, -4.650519294800188, -3.9179524754685953, -3.2467518007811065, -2.6389844520695602, -2.0957157653172684, -1.6170505462890945, -1.202154787458891, -0.8492859420739391, -0.555862100149798, -0.31855206746300835, -0.13337817737650237, 0.004176052200978219, 0.09906576255636278, 0.15656268336048887, 0.18212841185868286, 0.1812914898414639, 0.15952946296052303, 0.12214986410880284, 0.07418400943001169, 0.020290125609493944, -0.03532865665462076, -0.08899437646033402, -0.13761127610808832, -0.17870102174069216, -0.21042028496336637, -0.23156069378534594, -0.24153435036476723, -0.24033980816736578, -0.2285106043011005, -0.2070506151077423, -0.17736061186844168, -0.141154188499827, -0.10036441083091202, -0.05704715131223339, -0.013285702615400744, 0.028900282475044486, 0.06764421958666782, 0.10131317196792342, 0.12857568629200417, 0.1484546300520673, 0.16036447750973026, 0.16413430885101432, 0.16001149774478693, 0.14864473761597083, 0.1310487117765425, 0.10855207075516317, 0.08272982800615442, 0.05532093958536249, 0.028133207610343748, 0.0029401925307623645, -0.018626571218031577, -0.035186856370385815, -0.04571888734021889, -0.04965941223683446, -0.04699281057440802, -0.03832578833439047, -0.024944086895950447, -0.008848280363133773, 0.007234713003761812, 0.019865872187195287, 0.02493484377874614, 0.017727861673731696, -0.006977734592570256, -0.054793975923562756, -0.1315796125227791, -0.24327742763689353, -0.3957347999525602, -0.5945145378550584, -0.8447046057895741, -1.1507208024820863, -1.5161129021437245, -1.9433823621936201, -2.4338214751797183, -2.987402940995205, -3.602661030101252, -4.2766003114003395, -5.004647955010113, -5.78065950530008, -6.597035838360201, -7.444783756470415, -8.31360099258526, -9.192029950036844, -10.067669566981015, -10.927554939798247, -11.758387319475458, -12.546726531329195, -13.279274062012988, -13.943200318499963, -14.526607735911043, -15.018833676821604, -15.410558631767858, -15.694026435137992, -15.863305172801992, -15.914573648961758, -15.846298237254263, -15.659119013371273, -15.355817957099312, -14.941347593723687, -14.42277292706861, -13.809219326458194, -13.111481325669018, -12.341743534457121, -11.513356241332977, -10.640487598751829, -9.737892312926169, -8.820431531659576, -7.902666456127472, -6.998579274683693, -6.121191896664037, -5.282348063628154, -4.492405626173798, -3.759973298626393, -3.0917818481435684, -2.4925625052540186, -1.9650468502392313, -1.5099851361699754, -1.126198454763513, -0.810730775908454, -0.5590449634948377, -0.36528488461497266, -0.2225596612379052, -0.12324047374645469, -0.059289952276389835, -0.022598495096393435, -0.005313322310561524, -0.00014387591560370252, -0.0006357299957379809, -0.0014066966715599776, 0.0016678012023745455, 0.01132794266243312, 0.02886359507232492, 0.05411329776958224, 0.08553065655587168, 0.12031418129840225, 0.15459475237544823, 0.18367168841936668, 0.20229521157184296, 0.20498091349974978, 0.18633941829921877, 0.14140948733174863, 0.0659837714413787, -0.04308679472648944, -0.18763183685542614, -0.36795157646664567, -0.5826684128846384, -0.8286427177222768, -1.1009706677571005, -1.3930690538120316, -1.6968377713374476, -2.0029005249905305, -2.3009147748253884, -2.579955987168264, -2.828947907522237, -3.0371272384511405, -3.194529324198533, -3.2924784397119744, -3.324069331364999, -3.2845957014598732, -3.1719215425579295, -2.98678673848724, -2.7330217506133105, -2.4176559244566227, -2.0509115683979298, -1.646072228109522, -1.2192393127860022, -0.7889617672679332, -0.3757486244075736, -0.0014825610746449867, 0.3112437087119177, 0.5398635996515719, 0.6626230022259387, 0.6593878516636617, 0.5124384086877719, 0.20719332984855304, -0.2670949430255294, -0.9167329132429808, -1.743092430497604, -2.7422712973966257, -3.9049213149488478, -5.216313179106803, -6.656439547626346, -8.20030913813404, -9.818516756475045, -11.477919348056599, -13.14250181307198, -14.774390094256637, -16.334769122418077, -17.78509559529876, -19.0883196375036, -20.20995107906545, -21.11909257430301, -21.7895795583423, -22.200928601339193, -22.339271404646517, -22.197686095052006, -21.77644140559956, -21.083206910046723, -20.1332910518163, -18.94953618906209, -17.56134913043701, -16.003850715684415, -14.316985561036564, -12.544611844453554, -10.733621896900038, -8.932111459548517, -7.187895732366778, -5.547177917539242, -4.053304053956612, -2.745617741995703, -1.6580679269158343, -0.8181318612208883, -0.24606180714777695, 0.045654151579692305, 0.052650891619659246, -0.22115139008184445, -0.7637137617988962, -1.5553297105434496, -2.569262596801419, -3.772578631176659, -5.127200159611881, -6.59114933274884, -8.119904690075963, -9.667745051336004, -11.189145793536644, -12.640161659177252, -13.979752227389103, -15.170974229602948, -16.1820711322086, -16.987291226851152, -17.56752221483822, -17.91068898535798, -18.011909269760153, -17.87344257211813, -17.504427065901037, -16.920328284243976, -16.142182258933566, -15.195708495128285, -14.110296025132277, -12.917883913947831, -11.651860815068545, -10.345873778505672, -9.032703243783782, -7.743210231911741, -6.5053940844595495, -5.343614717288894, -4.2779826503658445, -3.323934714367678, -2.4919850227566855, -1.7876810818101525, -1.2117507479096532, -0.7604265947564829, -0.4259408766030995, -0.19714731504583896, -0.06023440649288402, 0.000496980944379618, 0.0018193820378903356, -0.03924035363901465, -0.10617870748689123, -0.18371742787955042, -0.2584083091998875, -0.3191280185061397, -0.3574297155514244, -0.3677517771350076, -0.347485147613929, -0.2968825488972274, -0.21883715275410803, -0.11854021215351314, -0.0030469496187963798, 0.1192302725116659, 0.23908456252658916, 0.3471069123754186, 0.4342462617630213, 0.492329547039134, 0.5145300838556695, 0.49576454695092337, 0.43299205018949927, 0.3253545411996313, 0.17423494142963, -0.01678877921213511, -0.2420970560169624, -0.49430667623752256, -0.7646875907470793, -1.0435504390615973, -1.3206751083608832, -1.5857851030041197, -1.8290351716853714, -2.0415386208677555, -2.215733037425681, -2.3456388024612953, -2.427112367535055, -2.4579947161403277, -2.4382372871050064, -2.3698316586024872, -2.2566109389989997, -2.1040262011056865, -1.918826657812123, -1.7087627019571612, -1.4822061349626166, -1.247679839510104, -1.0134885571070118, -0.7873261986187494, -0.5759821463088842, -0.38509933917494577, -0.21893959731543433, -0.08027938036331006, 0.02961314243984784, 0.11091449593795688, 0.165111704551992, 0.19482448800730431, 0.2035585186988309, 0.19541937960133987, 0.17481694332536984, 0.14617702066035193, 0.11366850151356561, 0.08096124471843845, 0.051037527677086775, 0.026067967229822412, 0.0073561913814715555, -0.004655583725854725, -0.01031546396772098, -0.010627721063884491, -0.007071936896799303, -0.0013910269116059037, 0.004634484075437757, 0.009410048745629384, 0.011728342030142074, 0.010929382644141408, 0.007004484956197302, 0.0006322665241363077, -0.0068625571384817756, -0.013630086190629838, -0.01749329734629588, -0.01621498809547559, -0.007820674281679431, 0.009042068535363688, 0.034733853808742936, 0.06826318083345063, 0.10696537302678044, 0.1462501908606574, 0.17944442051991502, 0.19775579401090854, 0.19037864121684026, 0.14473267977013848, 0.046858182835201836, -0.11803438689979016, -0.3648690127172463, -0.7078872200916788, -1.159777868172416, -1.7307530005344227, -2.427596262587122, -3.252717249855092, -4.203290923441361, -5.270585216381938, -6.439630773661271, -7.688930953783788, -8.990321351609653, -10.309205062362707, -11.605069700261843, -12.832381740195839, -13.942340998373961, -14.883914708349172, -15.605341051763855, -16.055818407177792, -16.187251253777575, -15.95655227913927, -15.328323538864437, -14.276030122310546, -12.783141209973621, -10.844304700265987, -8.466387690146542, -5.669308883849143, -2.487236412529563, 1.032836157037885, 4.8322453295093535, 8.841918556810038, 12.984213655670045, 17.174736644391572, 21.323519057652252, 25.338601594661515, 29.129203618471905, 32.609000396841786, 35.69873607901273, 38.328052239285846, 40.43685537290568, 41.97826023330406, 42.92127933770792, 43.25130895031985, 42.96993529855611, 42.09454847549448, 40.657475839299956, 38.70637887198043, 36.30197046987806, 33.51528129782939, 30.425180632177554, 27.115833345737652, 23.674488586005626, 20.18815798398121, 16.740475626803555, 13.409149239504286, 10.263875476333858, 7.364627682704426, 4.759741617140762, 2.484793767686061, 0.5621744687369805, -0.9987400283817464, -2.201090014998118, -3.0597398703541754, -3.599869389521287, -3.85519912730411, -3.8659615459269654, -3.6768265137159, -3.334778736723809, -2.886939521765409, -2.378542021335294, -1.851125412075771, -1.3410487456563764, -0.8783347366665407, -0.485876731383114, -0.17904190873565876, 0.03433336294839561, 0.15357114403109223, 0.18444651546012686, 0.13820535568278458, 0.030378028562362453, -0.12055158362732644, -0.2945466555228594, -0.47141051814238827, -0.6320769716149841, -0.7597417419348268, -0.8408050522997085, -0.8655688994710545, -0.8286603254563347, -0.7291289203835714, -0.570311946988352, -0.35945165242549926, -0.10709621208205226, 0.17369543804424564, 0.468359843776862, 0.7617439107874223, 1.039025616743627, 1.28659443235235, 1.4928510902397694, 1.6489861476945065, 1.7493566259148807, 1.7916135660599468, 1.7766973690559127, 1.7086500964978477, 1.5943390290546784, 1.4428497927209598, 1.2647114690393708, 1.0711464734781104, 0.8733223353165278, 0.6816724391004383, 0.5052204085803302, 0.35099792831321214, 0.22370312599577052, 0.12553409844829258, 0.056217429426225346, 0.013212383582857019, -0.007896742668685766, -0.012842463923887076, -0.00801028212176124, 0.0002861606818984896, 0.006545245633225595, 0.0067865262535013295, -0.0008430376819611074, -0.015608211229642956, -0.033906426868718205, -0.04919670828890707, -0.05216580517538037, -0.03112749559035132, 0.027365034036469355, 0.1377186854533417, 0.3143388062223108, 0.5705750545592968, 0.9176413580257413, 1.3635735439960144, 1.9122920554533152, 2.562816473668908, 3.308700882120127, 4.13776278975897, 5.032133546857221, 5.968612352999828, 6.919347966959669, 7.852890219652642, 8.735405013658063, 9.532168000599192, 10.209140645817635, 10.734645815517533, 11.081195928829253, 11.226936468493074, 11.156974392579063, 10.86434349365732, 10.350698546000269, 9.626846599835618, 8.712499541851523, 7.635588010069117, 6.431226476721323, 5.140277638033785, 3.8077612493448973, 2.480793686050783, 1.206294537963784, 0.02877222056984206, -1.0118442074334209, -1.882186673996359, -2.557181582219202, -3.021445878233419, -3.270204847179103, -3.3097201347403566, -3.157202551889713, -2.840089232452866, -2.394843961538836, -1.865343905419647, -1.3008497710496416, -0.7536433809232063, -0.2764218382466895, 0.08025930774553687, 0.27049816481449535, 0.2554148015116379, 0.005236674367924931, -0.4991089389677444, -1.2649161361400565, -2.2870900069918982, -3.548076414503807, -5.018532745764698, -6.658700210186123, -8.419963768252176, -10.246854163062359, -12.079364536127256, -13.855894410653933, -15.516114963112502, -17.003409168419502, -18.267041771678993, -19.26443432779029, -19.963371496146287, -20.343075620634576, -20.39491536643247, -20.12211851750489, -19.539504923292586, -18.67314355531736, -17.5584045282211, -16.238333182006123, -14.761161828899521, -13.178149575717395, -11.541470404351248, -9.901699272005066, -8.305856361652486, -6.795368084323317, -5.404649356226605, -4.160084254534401, -3.079369379647982, -2.1715673414842676, -1.4373634405147373, -0.8698015089826197, -0.455396689445659, -0.17553658301872957, -0.008080556307476526, 0.07101618790696945, 0.0861111380160182, 0.06037271352917121, 0.014485650850738704, -0.03435722825632692, -0.07313648567836961, -0.09334265056728004, -0.090959573944689, -0.0661098307741586, -0.02241115202347879, 0.033894072359851916, 0.09496675399215891, 0.1524736126408685, 0.19866738045544713, 0.22736335533732693, 0.23474279742070786, 0.21990742356310158, 0.1851385682924338, 0.13584186837242673, 0.08017131149730923, 0.028355449759612728, -0.00824186427008651, -0.018257345429379145, 0.00841767468809156, 0.07934958335225117, 0.19833883518914375, 0.364355588647438, 0.5707129237012951, 0.8045531508281495, 1.046711201781621, 1.2720108905337901, 1.4499789871995785, 1.545926694211987, 1.5224197737473828, 1.3410549172472486, 0.9644418106267464, 0.3583470979442629, -0.5062349689943355, -1.6510570314106436, -3.088909600358076, -4.822259612228179, -6.842209476391666, -9.128005162444927, -11.646955268654724, -14.3553201513602, -17.199412793343154, -20.11722044269413, -23.04048372002468, -25.897024852102252, -28.61401080966683, -31.120217461416413, -33.34880939951849, -35.240131437295595, -36.74368367718882, -37.82108373387463, -38.446386976999996, -38.60703323481996, -38.304771769764606, -37.554984592875286, -36.38634150569107, -34.83865938648487, -32.96106516818748, -30.8106043353533, -28.44962008538184, -25.94309356213999, -23.35558385326058, -20.74922446252391, -18.18207833770866, -15.70621782920886, -13.365845736076482, -11.196127438082021, -9.222887075722932, -7.462926941337801, -5.924291100040128, -4.606623539684619, -3.5022283039196593, -2.5974423927416384, -1.8741591756012983, -1.3112782371054843, -0.8859764936434407, -0.575055860884732, -0.35612131172367933, -0.20852353039494728, -0.11402767971025109, -0.057212217460818456, -0.025645544551027532, -0.009834650997483036, -0.002982038392233708, -0.0006007951383597521, -4.309622043698584e-05, 3.2580251194379437e-06, 5.990021656496306e-07, -1.500901164045544e-05, -0.00010648081873643109, -0.00022629433504953693, -0.00013289823446348004, 0.0005727338096736305, 0.0023088509858624597, 0.00530219099053406, 0.009341279772189053, 0.013534476493650516, 0.016114431542100963, 0.014326147922423153, 0.0044287326626571005, -0.01816889105726418, -0.05862943816105146, -0.1222757468579123, -0.21407690406058857, -0.3380433461277481, -0.4965888413789873, -0.6898947878565773, -0.9153922834138734, -1.1673875857079816, -1.4367885520375743, -1.7111165740732965, -1.974706857825771, -2.2093530647704047, -2.395085768174861, -2.511031118371819, -2.5366118143436056, -2.4528485924683805, -2.2439876210512297, -1.8986286140060795, -1.4107106745545404, -0.7804791794557272, -0.015230983671659738, 0.8700421405970925, 1.853179042619489, 2.9055013300986117, 3.9927798580984253, 5.076440839148124, 6.115059330770205, 7.066751725800681, 7.891226679478263, 8.551888599597815, 9.01786004921507, 9.265710621978325, 9.281078998779664, 9.059707997486031, 8.60788255646344, 7.9425751381226615, 7.090695328329738, 6.087771876972125, 4.976216594691611, 3.803251069106902, 2.618622884540348, 1.471780253950276, 0.4090972541339366, -0.5286047840723527, -1.3082004780810532, -1.905997287522609, -2.3091255828952835, -2.5161224203115915, -2.5367914418714728, -2.39137356933807, -2.109144307089041, -1.7264604632174543, -1.284180560018301, -0.8248360173556686, -0.38968491734810223, -0.015821885133622874, 0.26649602816885404, 0.43614833489713195, 0.48286254801845213, 0.40823242014148015, 0.2259615160572172, -0.038704173329770726, -0.35034250645028253, -0.6654481103069845, -0.9351546332425008, -1.1084245154416024, -1.13550347694377, -0.9714417048846267, -0.5794914605723367, 0.06585854466141067, 0.9764740673119897, 2.148990163907777, 3.5640126440759725, 5.1861582739421515, 6.9652189647542135, 8.838227581788601, 10.732564325479277, 12.569655090944233, 14.26887680810412, 15.752015487275157, 16.947459774862395, 17.794721245872143, 18.24831335169063, 18.280445635310535, 17.882898229327537, 17.067638828251617, 15.866858455468922, 14.332183714612741, 12.532033741105982, 10.54765496847754, 8.468687340327431, 6.388507144454736, 4.3994236930042225, 2.5876121152423406, 1.0276509257499802, -0.2217801871453062, -1.121261205697225, -1.6529542872658578, -1.82184489980255, -1.65594067671465, -1.2049071427714677, -0.5375065581022715, 0.26215734135404883, 1.0993338404935964, 1.873740687704544, 2.4851328818951153, 2.8389003020163313, 2.851645021971658, 2.4564580687443476, 1.606553257550905, 0.27811606161116803, -1.5279637829478232, -3.7855011089944854, -6.443524779289631, -9.428990476863827, -12.650265333797545, -16.0013935227745, -19.36716934581907, -22.628710084085466, -25.66938169713586, -28.380279045597113, -30.66519366096026, -32.44499446768157, -33.66162814340911, -34.28042011449968, -34.2907761557199, -33.70604139825444, -32.562182434830085, -30.91574692835251, -28.84077070767345, -26.424075842894574, -23.7607295997153, -20.949259592197553, -18.08706911767725, -15.266189135426913, -12.569063575032855, -10.065384677907561, -7.809756016545567, -5.8403431079969765, -4.178496848471992, -2.8292069946194336, -1.7824659659076107, -1.0153591141029539, -0.49468429025053157, -0.17991293117408844, -0.02636312718099993, 0.011702723498544735, -0.021776635868040177, -0.08713027239796, -0.15093357619316733, -0.18738943376750758, -0.17904962618137202, -0.11691442858710274, 6.792785734049138e-05, 0.16597713118650093, 0.36931943724588473, 0.5946753341130145, 0.8244543346331996, 1.0406662610267632, 1.226640214599211, 1.3684027048592537, 1.4556493587288326, 1.4824056259235843, 1.4473109924031256, 1.3535444921698887, 1.208379143410695, 1.0223016601075894, 0.8080336758129729, 0.5794739853810719, 0.3505688253606251, 0.13421858749971202, -0.058570540385822545, -0.21936009724550484, -0.3426804834101478, -0.42624242493008, -0.47085116419460876, -0.47996277501388157, -0.459123564042546, -0.4152908381783307, -0.35614658461154686, -0.2893464835839105, -0.22181972598024424, -0.1592350423972712, -0.10566591557855774, -0.06344579309533893, -0.033185508892910755, -0.013989824326388229, -0.0038266403227238187, 1.2110705022168043e-06, 0.0003494882360089407, -0.0002521998396774062, -1.2059823950760787e-05, 0.0018402922909805982, 0.004934833981676214, 0.007822970541621163, 0.008219068292695657, 0.003398300162899832, -0.009291785190639515, -0.0318654158275469, -0.06514682144429489, -0.1083097490533963, -0.1585855204280786, -0.21120282996311251, -0.25960393154823863, -0.29596761876982464, -0.31204156085018736, -0.3002578987240195, -0.2550674574155008, -0.17440330098528642, -0.06117500842486319, 0.07533205691377234, 0.2182885559583847, 0.3425322603575167, 0.414272604304864, 0.391327690211535, 0.22401938601984733, -0.14324190955842503, -0.7697387899205961, -1.7156358488116301, -3.038742934204834, -4.790895240106943, -7.014139554479574, -9.737374962440555, -12.97301726827425, -16.713989184968092, -20.93187808424106, -25.575470738754095, -30.571670105172505, -35.826684468289734, -41.22711103418702, -46.64306337318515, -51.93327079205925, -56.95168524091025, -61.55354577858424, -65.59890539777759, -68.95804511339587, -71.51760166001465, -73.18949740819359, -73.91546699440744, -73.6660704495456, -72.44173762982665, -70.27359214419499, -67.22449590847542, -63.389815004945746, -58.888702780143966, -53.85785103682303, -48.44653057798985, -42.81108337747682, -37.11050430545757, -31.498410648294016, -26.11512379520668, -21.08295072042681, -16.502300136435416, -12.449707616215498, -8.975492157790283, -6.102744275987999, -3.828406899100552, -2.125665310554797, -0.9475661573684735, -0.2309576505911806, 0.09908383908337845, 0.12420681638687778, -0.07220325050299581, -0.40961765582366255, -0.8142827665509196, -1.2225401041389306, -1.5832415931461636, -1.8591465179159647, -2.0272673339646112, -2.0782543421211486, -2.0150693904127923, -1.8509290052456957, -1.6067278051105915, -1.3082062731707849, -0.9831127694024706, -0.6585308613216169, -0.35853981779082544, -0.10237134712765295, 0.09684503460888157, 0.23269917923414302, 0.3053827697669141, 0.32102092958771594, 0.2905280082116367, 0.22809710805349068, 0.14947447052888532, 0.07016738536127279, 0.0037562178552361567, -0.03950046739137405, -0.05368651426194934, -0.03779314992978073, 0.004225409722865378, 0.06389206661977528, 0.12910574699296476, 0.18540429672380643, 0.2174903182096548, 0.21086474392170865, 0.15342194864508488, 0.036900382405307824, -0.14199036657185676, -0.3808842421125979, -0.6715472798742167, -1.000098911048833, -1.3477299995062304, -1.6919942729814577, -2.008514257255109, -2.272745521812554, -2.461763857438672, -2.5560158689095767, -2.5410514309954184, -2.4092441093724397, -2.1603678587657478, -1.8017763375101112, -1.3481019039036304, -0.8205354322311502, -0.24563289957992548, 0.34622643382373364, 0.9230995799352418, 1.4536901872061734, 1.9094895744609692, 2.266790852417389, 2.508177038328683, 2.623590639470684, 2.6110986444215927, 2.477113734443757, 2.235800884383261, 1.907818775908469, 1.5187580190759309, 1.0971898793173653, 0.6726876119937485, 0.27353665270237704, -0.07537008470739884, -0.35426739552406294, -0.5498375075893396, -0.6560110527064997, -0.6742266834231656, -0.6130183512178945, -0.48703256591226884, -0.3155677735901617, -0.12074210129209564, 0.07462829130055858, 0.24919183492398747, 0.38509197475168355, 0.4696982334358329, 0.49692015935500145, 0.46799402299398196, 0.3916171760364808, 0.28341500414226833, 0.16478242669214238, 0.06119981224496332, 0.00011388820339427074, 0.008536662804192869, 0.1105521988338568, 0.3249742306081802, 0.6633227555958512, 1.128233491686853, 1.7124625009763725, 2.398617392726423, 3.159882311473456, 3.961334408693709, 4.761753819218587, 5.5160640882512215, 6.178228335954832, 6.7046475223678454, 7.057352834025687, 7.206404373701394, 7.132131891173437, 6.82691009212936, 6.296233256748107, 5.558757145907845, 4.645226845591764, 3.5966799479528144, 2.462124448207212, 1.2955488879460146, 0.15239854153016497, -0.913916954474979, -1.8553249299402805, -2.6321219314075313, -3.215425479615514, -3.589154182771783, -3.7506395795078333, -3.710352798745095, -3.491049007085383, -3.125782133722756, -2.655522640609867, -2.1259031639010515, -1.583650933914216, -1.0732631095891403, -0.6338756601552882, -0.29653764391126125, -0.08207196281660675, 0.00023330873749344462, -0.047102478911229075, -0.21039817166254457, -0.4662614417175243, -0.7837946129678544, -1.127474127392441, -1.460377870026752, -1.7474581680328878, -1.958640626599303, -2.071558197454187, -2.0736910411624176, -1.9635892732746627, -1.7511534606850003, -1.4569970756586341, -1.1109512587627763, -0.7496755439649999, -0.41352595484724086, -0.1431005534577067, 0.024323789249253835, 0.058217113413768895, -0.06215194862542183, -0.3453562975699207, -0.7863837806534054, -1.3662321179723176, -2.0525850561411754, -2.8015714331033843, -3.5605123272011414, -4.2715096056288475, -4.875519948258787, -5.316714290954608, -5.54683166964169, -5.528987699793535, -5.240905433507227, -4.677263475132824, -3.85065264676021, -2.7914594540817, -1.546328135945134, -0.17552626978580826, 1.250753093715971, 2.6571372845562937, 3.968088589109386, 5.113021829666266, 6.031147111667911, 6.675915473887511, 7.0186363875024504, 7.050635093008801, 6.783838186931771, 6.249954941242335, 5.498421239050166, 4.5929952088516774, 3.607213948170011, 2.6190840902507393, 1.705048510005339, 0.934107826311308, 0.36207842973682425, 0.026895618986470658, -0.05463637050819087, 0.11136074209137016, 0.49526443994369673, 1.0446667013296032, 1.6868176854340438, 2.3332438746540403, 2.886313746946426, 3.248743451172864, 3.3294922128231783, 3.0476191128280052], 'positive_zeros': ['0.34400869778399379051097310846098', '0.37173644232868418529930824676708', '0.39143926442762275536399869670640', '1.19105542465414532992862668458505', '1.27309282765583189636570105611192', '1.41903135605133277498661569867863', '1.56372697768125446551306778271329', '1.64587361621402961688956936470881', '1.68738148471675665015981328022354', '2.30617675650838253723635086167304', '2.30883090086229616369517314445384', '2.33068654746527686165677783328639', '2.45743926949288468244277081775928', '2.71488540180933286473424904123020', '2.77814777577673496579588190348992', '3.15188261646090351558425730707057', '3.16697465462797393106678710151421', '3.56428376748819566317412804000246', '3.57495112561867474205829030121697', '3.69165310339962767369560678963634', '3.79803893725793442786446647294479', '4.05960019480092712013542013189611', '4.18499771242696888959210147480785', '4.23071940256840709222236083897312', '4.28796108798481282090230690788040', '4.34110647764074058205566265298685', '4.43685415299385165283372326624863', '4.71402143406213401837962130828532', '5.02279608309189650407825623625427', '5.17386682172516514936360606493638', '5.21700491204007778372766033472456', '5.33584631366324475094662907076825', '5.56164227805018773157424575509612', '5.59536003204884577479617124481972', '5.62427070833614467710536656699803', '5.67991062778095768005943445612669', '5.98658062194261384487469943740822', '6.12045306858802990808457147828252', '6.15247918805716268122484083626149', '6.51435156681031873418921353191176', '6.55555989541343719961267021207742', '6.61540710152001833228520760372802', '6.72572131064042491774303449444134', '6.74615932107751762551100395850268', '6.87942598608891239478802721835397', '7.39728571894688107367864330328330', '7.40843104755245891182732277940874', '7.40892776960227057789642078788987', '7.41607900878032059559042503365563', '7.45420776331670077984164848906350', '7.53182315848715269852763828934625', '7.74432118609443604928201055271160', '7.963064896663921291227471183230562', '8.086405394290603406167985462811915', '8.143234769137201269677742368950301', '8.221816399255326661475320467941304', '8.541826102884353559587103949549799', '8.968708136977542248444540908585339', '8.979844754746252746078036013070700', '9.042962221810729308856415128899945'], 'prelabel': '12-3800e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.508461923993535, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 1753245735743196595, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34400869778399379051097310846', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.37173644232868418529930824677', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.39143926442762275536399869671', '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': 780484390.6529279, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3010936384000000000000, 'conductor_radical': 190, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 66, 0, 1815, 0, 26620, 0, 219615, 0, 966306, 0, 1771561], 'euler13': [1, 0, -57, 0, 1487, 0, -23774, 0, 251303, 0, -1627977, 0, 4826809], 'euler17': [1, 0, -69, 0, 2147, 0, -42926, 0, 620483, 0, -5762949, 0, 24137569], 'euler19': [1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -73, 0, 3107, 0, -85926, 0, 1643603, 0, -20428393, 0, 148035889], 'euler29': [1, 34, 631, 8034, 76899, 576820, 3462954, 16727780, 64672059, 195941226, 446294311, 697379066, 594823321], 'euler3': [1, 0, -5, 0, 23, 0, -86, 0, 207, 0, -405, 0, 729], 'euler31': [1, -4, 94, -172, 4799, -9064, 192836, -280984, 4611839, -5124052, 86810974, -114516604, 887503681], 'euler37': [1, 0, -158, 0, 11191, 0, -496772, 0, 15320479, 0, -296117438, 0, 2565726409], 'euler41': [1, -12, 178, -1724, 16095, -117016, 862332, -4797656, 27055695, -118819804, 502985458, -1390274412, 4750104241], 'euler43': [1, 0, -174, 0, 13991, 0, -717764, 0, 25869359, 0, -594871374, 0, 6321363049], 'euler47': [1, 0, -106, 0, 5423, 0, -232716, 0, 11979407, 0, -517246186, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -209, 0, 20271, 0, -1269614, 0, 56941239, 0, -1649110529, 0, 22164361129], 'euler59': [1, 30, 523, 6442, 69363, 661988, 5569122, 39057292, 241452603, 1323051518, 6337379803, 21447728970, 42180533641], 'euler61': [1, -16, 422, -4688, 68471, -560736, 5670996, -34204896, 254780591, -1064086928, 5842944902, -13513540816, 51520374361], 'euler67': [1, 0, -37, 0, 7511, 0, -169110, 0, 33716879, 0, -745591477, 0, 90458382169], 'euler7': [1, 0, -17, 0, 211, 0, -1718, 0, 10339, 0, -40817, 0, 117649], 'euler71': [1, 8, 58, -744, -225, 33104, 1147692, 2350384, -1134225, -266285784, 1473877498, 14433834808, 128100283921], 'euler73': [1, 0, -229, 0, 27155, 0, -2216718, 0, 144708995, 0, -6503197189, 0, 151334226289], 'euler79': [1, 4, 430, 1420, 80159, 213256, 8284964, 16847224, 500272319, 700115380, 16748534830, 12308225596, 243087455521], 'euler83': [1, 0, -366, 0, 60407, 0, -6127364, 0, 416143823, 0, -17369745486, 0, 326940373369], 'euler89': [1, 12, 466, 4348, 95103, 704792, 10989756, 62726488, 753310863, 3065205212, 29237884306, 67008713388, 496981290961], 'euler97': [1, 0, -358, 0, 62671, 0, -7159060, 0, 589671439, 0, -31693482598, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -5, 0, 23, 0, -86, 0, 207, 0, -405, 0, 729], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -17, 0, 211, 0, -1718, 0, 10339, 0, -40817, 0, 117649], [1, 0, 66, 0, 1815, 0, 26620, 0, 219615, 0, 966306, 0, 1771561], [1, 0, -57, 0, 1487, 0, -23774, 0, 251303, 0, -1627977, 0, 4826809], [1, 0, -69, 0, 2147, 0, -42926, 0, 620483, 0, -5762949, 0, 24137569], [1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0], [1, 0, -73, 0, 3107, 0, -85926, 0, 1643603, 0, -20428393, 0, 148035889], [1, 34, 631, 8034, 76899, 576820, 3462954, 16727780, 64672059, 195941226, 446294311, 697379066, 594823321], [1, -4, 94, -172, 4799, -9064, 192836, -280984, 4611839, -5124052, 86810974, -114516604, 887503681], [1, 0, -158, 0, 11191, 0, -496772, 0, 15320479, 0, -296117438, 0, 2565726409], [1, -12, 178, -1724, 16095, -117016, 862332, -4797656, 27055695, -118819804, 502985458, -1390274412, 4750104241], [1, 0, -174, 0, 13991, 0, -717764, 0, 25869359, 0, -594871374, 0, 6321363049], [1, 0, -106, 0, 5423, 0, -232716, 0, 11979407, 0, -517246186, 0, 10779215329], [1, 0, -209, 0, 20271, 0, -1269614, 0, 56941239, 0, -1649110529, 0, 22164361129], [1, 30, 523, 6442, 69363, 661988, 5569122, 39057292, 241452603, 1323051518, 6337379803, 21447728970, 42180533641], [1, -16, 422, -4688, 68471, -560736, 5670996, -34204896, 254780591, -1064086928, 5842944902, -13513540816, 51520374361], [1, 0, -37, 0, 7511, 0, -169110, 0, 33716879, 0, -745591477, 0, 90458382169], [1, 8, 58, -744, -225, 33104, 1147692, 2350384, -1134225, -266285784, 1473877498, 14433834808, 128100283921], [1, 0, -229, 0, 27155, 0, -2216718, 0, 144708995, 0, -6503197189, 0, 151334226289], [1, 4, 430, 1420, 80159, 213256, 8284964, 16847224, 500272319, 700115380, 16748534830, 12308225596, 243087455521], [1, 0, -366, 0, 60407, 0, -6127364, 0, 416143823, 0, -17369745486, 0, 326940373369], [1, 12, 466, 4348, 95103, 704792, 10989756, 62726488, 753310863, 3065205212, 29237884306, 67008713388, 496981290961], [1, 0, -358, 0, 62671, 0, -7159060, 0, 589671439, 0, -31693482598, 0, 832972004929]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/d/l'], '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': '12-3800e6-1.1-c1e6-0-6', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-3800e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.508461923993535, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1753245735743196595, 'z1': {'__RealLiteral__': 0, 'data': '0.34400869778399379051097310846', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '436082832229611298142410520587,471231924244663090452368597788,496208218504572591453452252941,1509842123967915986689438841913,1982259441850717304180760960337,2086392677493521122635575306991', 'Lhash_array': ['436082832229611298142410520587', '471231924244663090452368597788', '496208218504572591453452252941', '1509842123967915986689438841913', '1982259441850717304180760960337', '2086392677493521122635575306991'], 'factors': ['2-3800-5.4-c1-0-10', '2-3800-5.4-c1-0-12', '2-3800-5.4-c1-0-13', '2-3800-5.4-c1-0-58', '2-3800-5.4-c1-0-73', '2-3800-5.4-c1-0-76'], 'label': '12-3800e6-1.1-c1e6-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/d/l'}