Lfunction data - 8-28e4-1.1-c5e4-0-0

Formats: - HTML - YAML - JSON - 2025-12-16T04:49:47.924690

• 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': '143476387526012907831239372637,1436850704379629812432007451119,3076858613393249143506791208193,3299591708747694476835676022174', 'a10': 0, 'a2': 0, 'a3': -28, 'a4': 0, 'a5': -42, 'a6': 0, 'a7': 112, 'a8': 0, 'a9': 573, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 406.70015344818756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -112, 36750, -1882384, 282475249]]], 'bad_primes': [2, 7], 'central_character': '28.1', 'coefficient_field': '1.1.1.1', 'conductor': 614656, 'conductor_radical': 14, 'degree': 8, 'euler_factors': [[1], [1, 28, 211, 2436, 78768, 591948, 12459339, 401769396, 3486784401], [1, 42, -1003, -146286, -7621836, -457143750, -9794921875, 1281738281250, 95367431640625], [1, -112, 36750, -1882384, 282475249], [1, 660, 52667, 40148460, 50546442288, 6465949631460, 1366046341460867, 2756983791814329660, 672749994932560009201], [1, 1288, 1605004, 1244757976, 937878608950, 462169923182968, 221263430851612396, 65927430202148895016, 19004963774880799438801], [1, -210, -2743855, 10869390, 5694083487876, 15432979477230, -5531594943716490895, -601108840817061316530, 4064231406647572522401601], [1, 3724, 5457763, 12878392660, 30265003847344, 31888175187033340, 33461906572374759163, 56534517059253748865476, 37589973457545958193355601], [1, 24, -10516873, -56525688, 69186514920384, -363818716278984, -435677357267022399577, 6399245651145389894568, 1716155831334586342923895201], [1, -11064, 103337804, -629304155496, 3419407892241654, -12907751299697624904, 43474961616158444098604, -95473344303426312654659736, 176994576151109753197786640401], [1, 2800, -30179873, -53867601200, 401429912115328, -1542183688762581200, -24736277608288127618273, 65702733577165120603862800, 671790528819082282036142601601], [1, -13238, 2167093, -455250014606, 12995097229723444, -31568837437087835942, 10420649533376113642957, -4414161695146131035237470334, 23122483666661158726686253786801], [1, -8232, 343680380, -2298585657816, 57460445197611558, -266305401987647717016, 4613104652323715033592380, -12801569329010340082434963432, 180167782956420929503029846064801], [1, -26864, 858661708, -13059395917040, 211272506879911126, -1919841460284607568720, 18556952315536444335837292, -85348818306796280901665943248, 467056167777397914441056671494001], [1, 8064, 128729519, -4212564547968, -63455130075921792, -966130645741672795776, 6771060992535796773516431, 97278841101015449477000525952, 2766668711962335809450748011342401], [1, -53958, 1379702981, -37520871422526, 953847892489790388, -15691059322332871875318, 241292764202847513299699069, -3946334441628206263093931975406, 30585627290848204916791848989276401], [1, 36036, -113258965, -648516000132, 553814151761271216, -463639846784654007468, -57888554472990978913409965, 13167907068498393846605875268364, 261240335504588722483367157995242801], [1, 83986, 3603119341, 147927586544458, 5235321292627805428, 124939092411306598849858, 2570259641777786771475485941, 50600455085959903353702921659386, 508858109619679129936596364708525201], [1, -2660, -2654517485, 102827963140, 5251687000360966576, 138830614736984555980, -4838754824501663353919435765, -6546417168531484755563136114380, 3322737661703085672358476688602579601], [1, -143136, 11355854108, -704396173023648, 34708236326754607014, -1270892250101340138692448, 36966070851276066984967823708, -840667208202601976699154225747936, 10596610576391421032662867140133202401], [1, 31318, -16662743, -98609837824442, -5335963862325578492, -204425253584187631276106, -71610234710512147290971207, 279021019727865207478043875791526, 18469587772135192290560825407466407201], [1, 51136, 637460815, -213578867870912, -13604213472728169344, -657194222073365275565888, 6035654988276317357629928815, 1489817675937851438996275140480064, 89648251976843595444986830377401534401], [1, -12432, 12912997484, -128997167748624, 72773759655186881910, -508125086593718743325232, 200358600812029558577009722316, -759822915139691977961577430853424, 240747534123068430155382383568465195601], [1, 166278, 9871423481, 1098903185221590, 130448064282416194692, 6136340714972816798303910, 307807962294633860334868535081, 28952421437257339242196022655980022, 972299657790850297934682879408841327201], [1, -16520, 23891433628, -338642542836920, 290542898974356522694, -2908038740836330101888440, 1761811958339602826531832975772, -10461309644539760657434918769876360, 5437943429267472574499737549036572950401], [1, -3318, -7625575243, 44406839994930, -52260498746479631436, 466720351278540630459930, -842337913240572230634220168243, -3852094993917655139683960178880318, 12201900399479668244827490915525641902001], [1, -134456, -6444696953, -179852567921768, 257413038842058053824, -2084984191879854730193624, -866113379504585467944241126697, -209478066966472402438717522248835592, 18061112346694138117573133075817258818401], [1, 87060, -17894833189, -224332536244500, 345918024804397233072, -3146379869620439533561500, -3520184539621171061627754012061, 240201285934676969691734165797547580, 38696844624861790832365403138487376998001], [1, -14942, -30215672675, 4983800387578, 686357276126101703284, 76681946627674151922322, -7153148589416062847807253767675, -54425972912650924780702223723038358, 56044107677782919374398655242916531006801], [1, 559416, 190436971868, 41690228513024520, 6709062291510056169606, 768115436454523038914964360, 64645113453864859643700851667932, 3498738917609903949015687471918153912, 115230877647233745723406127208308085892801]], 'euler_factors_factorization': [[1], [[[1, 28, 211, 2436, 78768, 591948, 12459339, 401769396, 3486784401], 1]], [[[1, 42, -1003, -146286, -7621836, -457143750, -9794921875, 1281738281250, 95367431640625], 1]], [[[1, -56, 16807], 2]], [[[1, 660, 52667, 40148460, 50546442288, 6465949631460, 1366046341460867, 2756983791814329660, 672749994932560009201], 1]], [[[1, 644, 595134, 239112692, 137858491849], 2]], [[[1, -210, -2743855, 10869390, 5694083487876, 15432979477230, -5531594943716490895, -601108840817061316530, 4064231406647572522401601], 1]], [[[1, 3724, 5457763, 12878392660, 30265003847344, 31888175187033340, 33461906572374759163, 56534517059253748865476, 37589973457545958193355601], 1]], [[[1, 24, -10516873, -56525688, 69186514920384, -363818716278984, -435677357267022399577, 6399245651145389894568, 1716155831334586342923895201], 1]], [[[1, -5532, 36367390, -113467676268, 420707233300201], 2]], [[[1, 2800, -30179873, -53867601200, 401429912115328, -1542183688762581200, -24736277608288127618273, 65702733577165120603862800, 671790528819082282036142601601], 1]], [[[1, -13238, 2167093, -455250014606, 12995097229723444, -31568837437087835942, 10420649533376113642957, -4414161695146131035237470334, 23122483666661158726686253786801], 1]], [[[1, -4116, 163369462, -476864123316, 13422659310152401], 2]], [[[1, -6716, 147008443], 4]], [[[1, 8064, 128729519, -4212564547968, -63455130075921792, -966130645741672795776, 6771060992535796773516431, 97278841101015449477000525952, 2766668711962335809450748011342401], 1]], [[[1, -53958, 1379702981, -37520871422526, 953847892489790388, -15691059322332871875318, 241292764202847513299699069, -3946334441628206263093931975406, 30585627290848204916791848989276401], 1]], [[[1, 36036, -113258965, -648516000132, 553814151761271216, -463639846784654007468, -57888554472990978913409965, 13167907068498393846605875268364, 261240335504588722483367157995242801], 1]], [[[1, 83986, 3603119341, 147927586544458, 5235321292627805428, 124939092411306598849858, 2570259641777786771475485941, 50600455085959903353702921659386, 508858109619679129936596364708525201], 1]], [[[1, -2660, -2654517485, 102827963140, 5251687000360966576, 138830614736984555980, -4838754824501663353919435765, -6546417168531484755563136114380, 3322737661703085672358476688602579601], 1]], [[[1, -71568, 3116937742, -129125086192368, 3255243551009881201], 2]], [[[1, 31318, -16662743, -98609837824442, -5335963862325578492, -204425253584187631276106, -71610234710512147290971207, 279021019727865207478043875791526, 18469587772135192290560825407466407201], 1]], [[[1, 51136, 637460815, -213578867870912, -13604213472728169344, -657194222073365275565888, 6035654988276317357629928815, 1489817675937851438996275140480064, 89648251976843595444986830377401534401], 1]], [[[1, -6216, 6437179414, -24485076636888, 15516041187205853449], 2]], [[[1, 166278, 9871423481, 1098903185221590, 130448064282416194692, 6136340714972816798303910, 307807962294633860334868535081, 28952421437257339242196022655980022, 972299657790850297934682879408841327201], 1]], [[[1, -8260, 11911603014, -70931430522820, 73742412689492826049], 2]], [[[1, -3318, -7625575243, 44406839994930, -52260498746479631436, 466720351278540630459930, -842337913240572230634220168243, -3852094993917655139683960178880318, 12201900399479668244827490915525641902001], 1]], [[[1, -134456, -6444696953, -179852567921768, 257413038842058053824, -2084984191879854730193624, -866113379504585467944241126697, -209478066966472402438717522248835592, 18061112346694138117573133075817258818401], 1]], [[[1, 87060, -17894833189, -224332536244500, 345918024804397233072, -3146379869620439533561500, -3520184539621171061627754012061, 240201285934676969691734165797547580, 38696844624861790832365403138487376998001], 1]], [[[1, -14942, -30215672675, 4983800387578, 686357276126101703284, 76681946627674151922322, -7153148589416062847807253767675, -54425972912650924780702223723038358, 56044107677782919374398655242916531006801], 1]], [[[1, 279708, 56100203302, 5153438591316444, 339456738992222314849], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '8-28e4-1.1-c5e4-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, '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': [5, 5, 5, 5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/28/6/e/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0439453125', 'prec': 40}, 'plot_values': [0.06336617373277566, 0.05305953265872054, 0.02433918691753434, -0.02244962992898771, -0.08646683628925939, -0.16621447264910094, -0.2594904864077077, -0.36367302457638107, -0.47584758079260736, -0.5928663625737429, -0.711301055504969, -0.8274654918155581, -0.9374784951938447, -1.0373368435580617, -1.1230366168033836, -1.190653485993651, -1.2364198436429232, -1.256801536379353, -1.2485611458780645, -1.2088649072051423, -1.1353743787690314, -1.0263340884818315, -0.8806775844258962, -0.698089833955457, -0.47905942503932675, -0.22493463662753307, 0.06200286924623819, 0.3785461842670069, 0.7205807729405618, 1.0830960284522613, 1.4601818885819822, 1.8451537400351774, 2.2306744693084397, 2.60887038228198, 2.9714511767679825, 3.3099452508562535, 3.6159195227832432, 3.8812007188046698, 4.098128735651995, 4.259831565422747, 4.36047682117112, 4.3955374343871965, 4.362111299178959, 4.259092636296689, 4.087326753179584, 3.849791728549658, 3.551830368726892, 3.201049745081063, 2.807232926253972, 2.3822849197521716, 1.9401905577539933, 1.49654766180619, 1.0681635112734793, 0.672686863135681, 0.3281945331035267, 0.05245108155760807, -0.13770756019488414, -0.2269530111861481, -0.20212390827485321, -0.05291592593298837, 0.22759483158033417, 0.6424771635537952, 1.1904221526586736, 1.8655415361381125, 2.65732463419833, 3.550666689543391, 4.525961728027804, 5.559655879500289, 6.624885954863272, 7.692214774330265, 8.730577368837478, 9.708375411185209, 10.594550892704914, 11.359775190117032, 11.977944724910497, 12.427062120651094, 12.690045205259585, 12.755673140420436, 12.619827629231409, 12.285258473371156, 11.761380764920897, 11.064268623662775, 10.216859649711653, 9.247271497634674, 8.18743417821277, 7.0720431603006855, 5.937677111839201, 4.820403089027873, 3.7540359272842476, 2.7688701434297585, 1.890645706135321, 1.1389312193696592, 0.5263101642214537, 0.05809863715593814, -0.2675894645995524, -0.4596089780562736, -0.5329695753516617, -0.5076436287031488, -0.40705567829551953, -0.2564646072555815, -0.08126459239827656, 0.09475892179336745, 0.25122606550733545, 0.37232842458703636, 0.44768980687492954, 0.4730012499796954, 0.4503914908386819, 0.3876444942858772, 0.2972139930964641, 0.19507673658379865, 0.09929816788341662, 0.027896194547988237, -0.0029699914707443146, 0.019407136060019054, 0.10277036701926513, 0.2487699191284599, 0.4525486440991842, 0.7028242268376159, 0.9824024545964533, 1.2695683926945425, 1.5399048875516044, 1.7683556500672475, 1.931509906236822, 2.0099981320947293, 1.990536243020703, 1.8675589320884654, 1.6443665403526673, 1.3333454319326596, 0.9554233397251809, 0.5387784883850099, 0.11669957221144273, -0.2751420722496605, -0.6016720935756452, -0.8316307116877226, -0.9409634729578465, -0.9151162087633533, -0.7507376243571845, -0.45674762343070485, -0.05442083545854774, 0.42436847513495723, 0.9394835996693323, 1.4456414203884622, 1.8967205159215001, 2.249948538762932, 2.46967345501086, 2.531069422748934, 2.4238408284160706, 2.152928326006351, 1.7382599219025436, 1.2137918854679726, 0.6254469449931053, 0.026091396283603543, -0.5293398497931836, -0.9887308169777616, -1.308146411375059, -1.4566163808617048, -1.4191824076305524, -1.1987242536088638, -0.8166945517739681, -0.310743173753877, 0.2690663069665087, 0.8650237348495612, 1.4176146833977303, 1.87214861131138, 2.1844998256998402, 2.3260036501240524, 2.2874451776109805, 2.0797120513458602, 1.7324847554142062, 1.2913158501295074, 0.812934196697511, 0.35770635623849684, -0.017660025935139514, -0.2670175113087114, -0.3611246639838863, -0.29206215439974287, -0.07483769083011385, 0.25357325024481664, 0.6381446324733844, 1.012705932988909, 1.308299622785218, 1.4626878781260255, 1.4308635699482852, 1.192770622301666, 0.7586242348200608, 0.17184337049468584, -0.4912515574011036, -1.128292653420658, -1.6202599949498102, -1.8431626965922008, -1.6822695601604896, -1.0470335488332965, 0.1162390025236477, 1.8143448856886066, 4.001294924077081, 6.5782175580233995, 9.398136860911833, 12.276461172868201, 15.00952088383914, 17.391428135897648, 19.23173593894933, 20.37545948120799, 20.72622504168446, 20.25165023514673, 18.985700372689816, 17.029389123541804, 14.548374129633805, 11.75041892305213, 8.864368321667301, 6.120271207958221, 3.728964112658874, 1.8579704580721965, 0.6161053435482693, 0.04480386177279989, 0.11597804054616262, 0.7376382465304966, 1.7659774977835403, 3.0226884857379828, 4.318086762691212, 5.471836564899318, 6.330904729925097, 6.785857739881219, 6.785282686806939, 6.334273008437139, 5.4887624221552835, 4.347264664801989, 3.038857606737199, 1.701444093790135, 0.4643711431436896, -0.565623082478712, -1.3165295303664701, -1.757557962628909, -1.8982078633482045, -1.7830238727650307, -1.4832795746735394, -1.082466468199551, -0.6625426334123061, -0.29248405232739966, -0.019582279328944737, 0.1361489220857866, 0.18169650343375435, 0.14628176987197328, 0.07322617153617819, 0.009718716620737882, -0.0035116992572891722, 0.05904049493970525, 0.20210382450477365, 0.4083553416561355, 0.64107599507023, 0.850647246307746, 0.9848430923567691, 0.9985299773155778, 0.8623339091054228, 0.5697530537961824, 0.1411625760945853, -0.3793324216738123, -0.9299262939302199, -1.4398680961451102, -1.841624842671985, -2.082262376441838, -2.131757116499996, -1.9887197001642802, -1.683143966571168, -1.2704078615629735, -0.8221044689512657, -0.41510094420959526, -0.11927038173785318, 0.015199717520108793, -0.033846603553552665, -0.25679926903232675, -0.6139103862475518, -1.042294841550939, -1.4664246927163842, -1.8111749298036683, -2.016564838179139, -2.046954466960207, -1.8962159632086981, -1.589117149506902, -1.1778352306198674, -0.7294529121336291, -0.3130288466462615, 0.0129055561212431, 0.21196962378955356, 0.27715678745054073, 0.2308983408177572, 0.11950902092679914, 0.002570858251232128, -0.06257387950408366, -0.035921886834625126, 0.09300495544617919, 0.29826900437238846, 0.5186249442775543, 0.6669147551706804, 0.6468502709834429, 0.37592450705101904, -0.19215370643047772, -1.0482347499725462, -2.1149211333571905, -3.245814215897564, -4.238431705638408, -4.856816914552964, -4.864552308902656, -4.068621318354701, -2.353699291540457, 0.2903071356046817, 3.749694060800385, 7.785509395662636, 12.057475348164711, 16.15836745455049, 19.662287409994846, 22.19247641440427, 23.46707433972316, 23.334476511858202, 21.803170418527753, 19.06264861911741, 15.44305458669652, 11.36890880766395, 7.309492780074424, 3.7211750076421284, 0.9735245235506822, -0.6981024731644007, -1.219116521031084, -0.6826637293333806, 0.6715860586676856, 2.499602694216806, 4.4082110558464365, 6.021307666365014, 7.0363720807893095, 7.264508075065268, 6.655432170719225, 5.305456569016809, 3.425631196759058, 1.299041768934584, -0.7669652087860444, -2.4921026022459754, -3.6720884806739984, -4.206060862400737, -4.105457648270642, -3.484733864471904, -2.5301897667859263, -1.4600105840677071, -0.48202374134655496, 0.24651768861764972, 0.6444780279235023, 0.7148166485349219, 0.537237641438801, 0.2460457847528927, -0.0059278253314654665, -0.08312250132978423, 0.1019091849527739, 0.5678621709855691, 1.2604953080966037, 2.0634005434760097, 2.821738576654583, 3.3785223990449205, 3.607012054790282, 3.4361252476538944, 2.867593596355669, 1.981307845715954, 0.9159881897494759, -0.15803451872019772, -1.0708755865460027, -1.6881100423097448, -1.936921319286149, -1.818466976958728, -1.4075173274134352, -0.8379556041074987, -0.2713216783754408, 0.1360640800114221, 0.26430667308963884, 0.05555360669685921, -0.47559602972283577, -1.2462255929552366, -2.1217277515104453, -2.9461691769904452, -3.574053293073446, -3.8966472516981563, -3.862857090535837, -3.4929312755432127, -2.86597978068051, -2.0993610705554597, -1.3247390195559319, -0.662032782767866, -0.19224027310710262, 0.05559174731294707, 0.1047825648585881, 0.02024799553689531, -0.11214288021515534, -0.2098935818391484, -0.21644863580879503, -0.11700336041598312, 0.058712259754365115, 0.24451455467135333, 0.3553650821454609, 0.31318840300057005, 0.06986407343128649, -0.37733722297309963, -0.9786612709615043, -1.6361740488116139, -2.226247577909614, -2.6261625359349994, -2.7407316621749445, -2.526257789048213, -2.0039251441125243, -1.2570793020380817, -0.41500755128599204, 0.3749657847132606, 0.9791978031496871, 1.3064652136827974, 1.3285232978111787, 1.0877956001211513, 0.6836397708945574, 0.2473328541016082, -0.09023637152031064, -0.23157694249527758, -0.13812827433334107, 0.15853812894607028, 0.5631851627385919, 0.9460176964225222, 1.1769293444096642, 1.1609928870472463, 0.8728159837140399, 0.3801872044657393, -0.16807103101757298, -0.5681571167638824, -0.5998165532817663, -0.08243813846138934, 1.0751177029368282, 2.845586160410913, 5.07420008529432, 7.492406326678613, 9.764678562595433, 11.547915605643372, 12.558323990783006, 12.640685735912998, 11.788038601657313, 10.139369930427117, 7.960588445048188, 5.603979812214396, 3.414865593097377, 1.6640619987682366, 0.5050909669847329, -0.047578677610095564, -0.11595978643592057, 0.08920427066835862, 0.336523427365555, 0.44527947617847574, 0.34660832716693724, 0.11750917414396111, -0.024094303025067255, 0.23587008569609297, 1.2332682446357224, 3.233633849596278, 6.342475219399784, 10.4536528542005, 15.231426076997884, 20.13039208571874, 24.470550773079637, 27.58839827597023, 28.937621964966144, 28.17788487040109, 25.258717705624438, 20.484104040563093, 14.434415414764743, 7.86751428181038, 1.606131981108923, -3.595055475641439, -7.180648041444081, -8.872417374405206, -8.701510956577483, -6.989825944198001, -4.2563555459825775, -1.1129054548865882, 1.8467864445456479, 4.163114157271365, 5.569646037770339, 6.003639263458081, 5.589830554304741, 4.59966141000967, 3.3499380860890424, 2.1257944825981387, 1.132060078383638, 0.4678600297449386, 0.12155724788817782, 0.004765952017178909, 0.0004996389390589059, 0.008887741074323338, -0.02014059240001555, -0.07556937589665187, -0.09871403674683393, -0.015670797226247004, 0.22373653586660336, 0.6110985643634396, 1.0604072198149503, 1.4191285119079438, 1.4983920466607012, 1.1163601323269738, 0.1512351301385975, -1.4064468323088122, -3.4408804317071806, -5.720490351068163, -7.931146746632296, -9.741183637186344, -10.868189544020794, -11.131904642615266, -10.49464706759306, -9.08446755822267, -7.152756293418175, -5.018217279750283, -3.006615283426367, -1.3890472621029992, -0.3256239687336803, 0.1541568338250218, 0.1416308419159261, -0.18652809188482777, -0.622425426959991, -0.9795890402942274, -1.1355147948998308, -1.0571651657330356, -0.7932600991502943, -0.4471355219772201, -0.13967910513476955, 0.03044461628615492, 0.018436653384035002, -0.15623356743321454, -0.4191313248934035, -0.668686173968198, -0.8105322203150811, -0.7873051323628356, -0.597947910918475, -0.3007921107853603, 0.00798764527222801, 0.22540876351105504, 0.27474571726855107, 0.13338952531840043, -0.15728786221083657, -0.5016043570208303, -0.7756393088436291, -0.8659106340321963, -0.7041028011189416, -0.28908576684736126, 0.30784918963316804, 0.9604537823900248, 1.5240594577926019, 1.8736948734400842, 1.939140050082775, 1.7303163938686856, 1.3265679532099204, 0.8485194371856917, 0.4215159600024701, 0.13582598541924423, 0.012481186446544418, -0.0014996639447034511, -0.011649112477032635, -0.13393628269245691, -0.4425056698677297, -0.9245074863931481, -1.4585921417755583, -1.8321479202260893, -1.790671400108407, -1.1106059381459943, 0.3166521131971079, 2.4148852630054165, 4.907438796200155, 7.344174309890263, 9.180597489562269, 9.922094210399614, 9.248954254577859, 7.113071747641561, 3.8031985701413067, -0.04763615726273901, -3.595710697505794, -5.9528758922765865, -6.367107180585455, -4.405148362566003, -0.08195257627971769, 6.110398577824727, 13.272884440279356, 20.28388885275153, 26.0097108845832, 29.51343880874852, 30.252510393394697, 28.238558101547493, 23.96622414088725, 18.281392223831727, 12.21374531604322, 6.771501396604893, 2.68955438686163, 0.29842282793097374, -0.5051506119670857, -0.19468914341335697, 0.5381733099134509, 0.978947176019325, 0.5795541295386379, -0.897530884974395, -3.3336656553792303, -6.295819110885612, -9.153224298073075, -11.260398803150194, -12.11928708583545, -11.493033188421714, -9.466534079925744, -6.436002225317659, -2.983850894946562, 0.26203780708701757, 2.765661531628098, 4.205884795584071, 4.525803999529544, 3.9097995240223002, 2.7137545120476516, 1.36307260620684, 0.2304907868723529, -0.4468532598096789, -0.6041977837965345, -0.33573424566800514, 0.16211347584502298, 0.6642524015051534, 0.9890698559625818, 1.0535642624849872, 0.8788673235345869, 0.5642528955554214, 0.2431203446662573, 0.0310142628040129, -0.018007825461317874, 0.075931615338943, 0.23344245587500753, 0.3535660438476785, 0.35829537767226033, 0.22637242801687985, 0.006327043453071562, -0.19773238546151226, -0.2660823818488084, -0.11074417733874889, 0.283173136792487, 0.8391202719052634, 1.4041323105727004, 1.7878483074419538, 1.8207859516072007, 1.421828744385604, 0.628779069944617, -0.40054282158144566, -1.4162746666788841, -2.1418821971177424, -2.355116788245781, -1.9475965376183055, -0.961080024561713, 0.4050602766996904, 1.8514604686881941, 3.056440530533322, 3.7546782076911085, 3.804295630320724, 3.2213090347343645, 2.168427894721135, 0.9070217858519755, -0.2798596439813226, -1.1622309462429594, -1.6133288653903142, -1.6317483376769542, -1.3304330648588993, -0.8794477835181002, -0.4457138456127987, -0.14416609459561677, -0.009629045273493482, -0.00014415090883174853, -0.030537592948183187, -0.018573973342217234, 0.07303600853249874, 0.21801706389455455, 0.3386946355829771, 0.34539250927597104, 0.19226683678745066, -0.07624319178480188, -0.3062920134928079, -0.25400383985909836, 0.3500334055271054, 1.7151212803923293, 3.9044136915715653, 6.772721321028343, 9.96917169876614, 12.990970964931227, 15.272839183409355, 16.319819941440443, 15.881254146817241, 13.987386792796022, 10.937246157775409, 7.255054704127617, 3.6014954925093163, 0.5749812605080004, -1.4235547440023901, -2.260556111659337, -2.077827823039431, -1.2319700567288168, -0.17404265344051717, 0.6869399518961381, 1.103210072476199, 1.0345135149377558, 0.6255868710365293, 0.1298176239736219, -0.2043946126803801, -0.24672645254970516, -0.04145239950426754, 0.20165741689163125, 0.1877705396653635, -0.33540435071172614, -1.4515371481811388, -2.9869172414211747, -4.500294785799217, -5.370397517166133, -4.946413878926032, -2.7354421702590193, 1.4094078779171593, 7.2063489510801055, 13.956125585809351, 20.656907296850783, 26.24275523530747, 29.806943489492255, 30.782056512098812, 29.079425307871173, 25.160185362500815, 19.83927363645956, 14.072434117072014, 8.761272585344415, 4.579120896811948, 1.8143705960346332, 0.37668288563192304, -0.09510167116896599, -0.07435287160368777, 0.016461004546887793, -0.06821414691043887, -0.3497991006411486, -0.6714196013631897, -0.8046434363432216, -0.5740894603165396, 0.0376510146917275, 0.852991767955945, 1.5528551664014532, 1.7834265357894088, 1.294946717154543, 0.07831539156631, -1.5941468520512279, -3.2116389006905415, -4.144844258828162, -3.8367492862917953, -1.9833203011506835, 1.3453309201142318, 5.669960151657402, 10.19744128436331, 14.004819496264568, 16.244704102174875, 16.362170722623347, 14.288106215023012, 10.408480180725245, 5.460064866097603, 0.3749200513907032, -3.941746975597902, -6.8419160329984, -8.043139154666061, -7.653398002785624, -6.126897015502333, -4.082323904051899, -2.1220632642154524, -0.6950613763265164, -0.013758575439589178, -0.03468675688066407, -0.5242578068827456, -1.1662962346685037, -1.675613486273352, -1.876009546581696, -1.7304981734047715, -1.3261819184175827, -0.8198332131901477, -0.36512641697504566, -0.06266911357776579, 0.06248498946657873, 0.054601714960456196, -0.007996379525487542, -0.05327251923553794, -0.043844069873407526, 0.0145793977180265, 0.08575079775163037, 0.12820723840459156, 0.11981183143355167, 0.06944435558790867, 0.009119017636464633, -0.02621642881967248, -0.021841202215195313, 0.004088495244781017, 0.011031973106968624, -0.03509720996810372, -0.12270013187557618, -0.16426366858204963, 0.004636622585760071, 0.593993467125933, 1.7945848379464953, 3.681409598406792, 6.147546011541926, 8.879528853867342, 11.386305898045121, 13.102119617717847, 13.524289154450853, 12.347779942481669, 9.578406246566736, 5.588942777674476, 1.0256275407803213, -3.3307340813301947, -6.736785037261659, -8.6846865169011, -9.016018188059473, -7.930383331320753, -5.919392507244562, -3.632507953175457, -1.6645302135233075, -0.40227491949914823, 0.051622324683685154, -0.1293644332652352, -0.5945207843487906, -0.9621168421425068, -0.9610123703320375, -0.5249647922588577, 0.2044022125702096, 0.9498754518116803, 1.41897577778371, 1.4412176631945426, 1.0434263861210118, 0.4463158428032525, -0.008974475212925557, 0.010109966944250797, 0.684596226313781, 1.9568513580429236, 3.525043087921076, 4.9406655019088594, 5.755360162045982, 5.669818962421832, 4.652924828225519, 2.987105733888089, 1.1526809424822222, -0.3377046502560127, -1.114428289161176, -1.0983164942056074, -0.5406279389020887, 0.0717571896249041, 0.20659503453696268, -0.4740537467295885, -1.9169633432646187, -3.6022572966653645, -4.621741707101219, -3.928860782661287, -0.6636895500261125, 5.533356413666409, 14.29733975870695, 24.529022638849945, 34.59710309571272, 42.65831173078697, 47.093858476873265, 47.038230239851096, 42.5123882403852, 34.38056474822677, 24.186311552803286, 13.8459926785782, 5.086382853430198, -0.9350666484957628, -3.821031726786206, -3.9335274214188085, -2.19966598271351, 0.20911941866280964, 2.229125686227076, 3.213704258734334, 3.022627305169065, 1.958947193852317, 0.6063981693538439, -0.4098541194370813, -0.6731564609007734, -0.08878122707331311, 1.1204474563606357, 2.509020818370161, 3.5923069752231873, 4.022135201048791, 3.694549389029397, 2.754774160626284, 1.5250960738506307, 0.38411879734958154, -0.3680695125269347, -0.6158477741538275, -0.43025695954018944, -0.013855194883714082, 0.3865762213815204, 0.581595303675902, 0.5060432419572439, 0.2233799788732765, -0.11868668068557485, -0.36295934003352687, -0.4130666747163545, -0.270361111278266, -0.028009986550915234, 0.17930013524414465, 0.24495018745533478, 0.13921167637573548, -0.07356264577178852, -0.26305362712297875, -0.30017422172963887, -0.12208506357302816, 0.22419901431523753, 0.5757530889900221, 0.7098790468119551, 0.4278531658290273, -0.3633884184935717, -1.600376282951062, -3.064871469396824, -4.437612248511825, -5.393594573019416, -5.7208269961966565, -5.3710468998135426, -4.462481135906702, -3.243133917435421, -2.015024432224265, -1.0200152254148118, -0.37746799169167394, -0.073741107658038, 0.0018836496543944352, -0.012667041515190281, -0.02089274804329304, -0.0041308793832064, -0.008874251183361416, -0.08596061966456721, -0.21537941737008157, -0.25130169373690686, 0.0820805691777593, 1.1228827091284062, 3.1491741073525343, 6.241759659920912, 10.20371420268853, 14.54074974835521, 18.521031050339214, 21.34250534110031, 22.419227756635603, 21.49872974130941, 18.714320153510233, 14.587799048099441, 9.947360371011577, 5.634620612244558, 2.288193896894956, 0.21689314353960445, -0.6402551252379509, -0.6397947312963745, -0.2673591671503611, 0.044064471635610634, 0.05260023425635352, -0.2462471845480982, -0.6723191025423446, -0.981259516560694, -1.0103691241981212, -0.7557787391147017, -0.36639402973805796, -0.06352841941764645, -0.004543218144555097, -0.1536746466541381, -0.23936734605949284, 0.1875247674712865, 1.5876361466031175, 4.224986999013667, 7.998529392228829, 12.37625716978898, 16.49893770257299, 19.39777127835424, 20.26252767789648, 18.72416895033289, 15.07889011847727, 10.157849626420013, 5.088576303330036, 1.0011124693519573, -1.3057306105511954, -1.6460421034220443, -0.4573184434275454, 1.3851649767247727, 2.884340336803114, 3.31869303269739, 2.5340604787785295, 1.0293335968730437, -0.19653854995765285, 0.02915201645757026, 2.6302334779057173, 7.895616499242337, 15.326846168213471, 23.719740144437857, 31.414200550135657, 36.724021344431094, 38.53270996901051, 36.506366079853976, 31.112674852605956, 23.50318457685763, 15.243668680241521, 7.814680871831355, 2.260203424440161, -0.9967511100352033, -2.16141288520795, -1.857249339945648, -0.8637853262565398, 0.13340505931198482, 0.7324102427870824, 0.8493182115235453, 0.6271865638647763, 0.30111281306592586, 0.06311237547974902, -0.02422546345324791, -0.013454490475093167, 0.0034027843460520744, -0.012625004614412365, 0.013617722376113923, 0.26230003861327233, 0.9404088535592265, 2.1709253429327293, 3.8976712886162996, 5.845904298788529, 7.574958068918525, 8.645971388325671, 8.750857710978682, 7.808071991455437, 6.020846085658918, 3.8661145643450903, 1.8987710113280896, 0.5549357848233577, 0.006413660361359675, 0.12870774267795348, 0.6259091772164742], 'positive_zeros': ['0.11318291294161122895451000317118', '1.13347534732436320568214951797367', '2.42721347099846571737991193663270', '2.60291890222245140233199132931463', '4.09354277326655723022911140887586', '4.41451122090685004811587990089536', '4.91130594354686252244896397626459', '4.94184237433482742391751810834301', '5.72545035227542400301365297762161', '6.06975733832410476113673053990937', '6.63770532675173131210176822446985', '7.01128312814749977758585862234548', '7.55618606425390359576298185920939', '7.74554255132664598056058465261757', '8.141526752538879996028832892595120', '8.433881689701672670447128717990593', '9.375985378834124271067946470230978', '9.377911125421513572844738929553741', '10.03804765478070224401771948907756', '10.46309772491494831805346348245495', '10.69025674196006612850213690220681', '10.72835068401309636092867991535511', '11.17462790716574315087503796614588', '11.72317954691420239837339796002292', '11.76425798798792929836030098272352', '12.34651563213238244945505234123339', '12.56954007189261648700886327012909', '12.67234883576040145500978059593280', '12.95140865941871943590600220329904', '13.35518198243849119326151603178364', '14.04038865345788804277564430718835', '14.17515585829513807018397323475809', '14.61691588630095439822576404448478', '15.01217215054131729993599244213230', '15.24763567413731191987067776571108', '15.32063701486055615350295079984637', '15.81358488814936337645525321868582', '16.15417943034381318989137509510773', '16.26587562286421760951033856000921', '16.86093931125846137904368521783522'], 'prelabel': '8-28e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1191382575857243, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e4-0', 'trace_hash': 516718329636877825, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11318291294161122895451000317', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.13347534732436320568214951797', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.42721347099846571737991193663', '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': 406.70015344818756, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 614656, 'conductor_radical': 14, 'degree': 8, 'dirichlet_coefficients': [1, 0, -28, 0, -42, 0, 112, 0, 573, 0, -660, 0, -1288, 0, 1176, 0, 210, 0, -3724, 0, -3136, 0, -24, 0, 2767, 0, -12572, 0, 11064, 0, -2800, 0, 18480, 0, -4704, 0, 13238, 0, 36064, 0, 8232, 0, 26864, 0, -24066, 0, -8064, 0, -24206, 0, -5880, 0, 53958, 0, 27720, 0, 104272, 0, -36036, 0, -83986, 0, 64176, 0, 54096, 0, 2660, 0, 672, 0, 143136, 0, -31318, 0, -77476, 0, -73920, 0, -51136, 0, 220553, 0, 12432, 0, -8820, 0, -309792, 0, -166278, 0, -144256, 0, 78400, 0, 156408, 0, 16520, 0, -378180, 0], 'euler11': [1, 660, 52667, 40148460, 50546442288, 6465949631460, 1366046341460867, 2756983791814329660, 672749994932560009201], 'euler13': [1, 1288, 1605004, 1244757976, 937878608950, 462169923182968, 221263430851612396, 65927430202148895016, 19004963774880799438801], 'euler17': [1, -210, -2743855, 10869390, 5694083487876, 15432979477230, -5531594943716490895, -601108840817061316530, 4064231406647572522401601], 'euler19': [1, 3724, 5457763, 12878392660, 30265003847344, 31888175187033340, 33461906572374759163, 56534517059253748865476, 37589973457545958193355601], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 24, -10516873, -56525688, 69186514920384, -363818716278984, -435677357267022399577, 6399245651145389894568, 1716155831334586342923895201], 'euler29': [1, -11064, 103337804, -629304155496, 3419407892241654, -12907751299697624904, 43474961616158444098604, -95473344303426312654659736, 176994576151109753197786640401], 'euler3': [1, 28, 211, 2436, 78768, 591948, 12459339, 401769396, 3486784401], 'euler31': [1, 2800, -30179873, -53867601200, 401429912115328, -1542183688762581200, -24736277608288127618273, 65702733577165120603862800, 671790528819082282036142601601], 'euler37': [1, -13238, 2167093, -455250014606, 12995097229723444, -31568837437087835942, 10420649533376113642957, -4414161695146131035237470334, 23122483666661158726686253786801], 'euler41': [1, -8232, 343680380, -2298585657816, 57460445197611558, -266305401987647717016, 4613104652323715033592380, -12801569329010340082434963432, 180167782956420929503029846064801], 'euler43': [1, -26864, 858661708, -13059395917040, 211272506879911126, -1919841460284607568720, 18556952315536444335837292, -85348818306796280901665943248, 467056167777397914441056671494001], 'euler47': [1, 8064, 128729519, -4212564547968, -63455130075921792, -966130645741672795776, 6771060992535796773516431, 97278841101015449477000525952, 2766668711962335809450748011342401], 'euler5': [1, 42, -1003, -146286, -7621836, -457143750, -9794921875, 1281738281250, 95367431640625], 'euler53': [1, -53958, 1379702981, -37520871422526, 953847892489790388, -15691059322332871875318, 241292764202847513299699069, -3946334441628206263093931975406, 30585627290848204916791848989276401], 'euler59': [1, 36036, -113258965, -648516000132, 553814151761271216, -463639846784654007468, -57888554472990978913409965, 13167907068498393846605875268364, 261240335504588722483367157995242801], 'euler61': [1, 83986, 3603119341, 147927586544458, 5235321292627805428, 124939092411306598849858, 2570259641777786771475485941, 50600455085959903353702921659386, 508858109619679129936596364708525201], 'euler67': [1, -2660, -2654517485, 102827963140, 5251687000360966576, 138830614736984555980, -4838754824501663353919435765, -6546417168531484755563136114380, 3322737661703085672358476688602579601], 'euler7': [1, -112, 36750, -1882384, 282475249, 0, 0, 0, 0], 'euler71': [1, -143136, 11355854108, -704396173023648, 34708236326754607014, -1270892250101340138692448, 36966070851276066984967823708, -840667208202601976699154225747936, 10596610576391421032662867140133202401], 'euler73': [1, 31318, -16662743, -98609837824442, -5335963862325578492, -204425253584187631276106, -71610234710512147290971207, 279021019727865207478043875791526, 18469587772135192290560825407466407201], 'euler79': [1, 51136, 637460815, -213578867870912, -13604213472728169344, -657194222073365275565888, 6035654988276317357629928815, 1489817675937851438996275140480064, 89648251976843595444986830377401534401], 'euler83': [1, -12432, 12912997484, -128997167748624, 72773759655186881910, -508125086593718743325232, 200358600812029558577009722316, -759822915139691977961577430853424, 240747534123068430155382383568465195601], 'euler89': [1, 166278, 9871423481, 1098903185221590, 130448064282416194692, 6136340714972816798303910, 307807962294633860334868535081, 28952421437257339242196022655980022, 972299657790850297934682879408841327201], 'euler97': [1, -16520, 23891433628, -338642542836920, 290542898974356522694, -2908038740836330101888440, 1761811958339602826531832975772, -10461309644539760657434918769876360, 5437943429267472574499737549036572950401], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 28, 211, 2436, 78768, 591948, 12459339, 401769396, 3486784401], [1, 42, -1003, -146286, -7621836, -457143750, -9794921875, 1281738281250, 95367431640625], [1, -112, 36750, -1882384, 282475249, 0, 0, 0, 0], [1, 660, 52667, 40148460, 50546442288, 6465949631460, 1366046341460867, 2756983791814329660, 672749994932560009201], [1, 1288, 1605004, 1244757976, 937878608950, 462169923182968, 221263430851612396, 65927430202148895016, 19004963774880799438801], [1, -210, -2743855, 10869390, 5694083487876, 15432979477230, -5531594943716490895, -601108840817061316530, 4064231406647572522401601], [1, 3724, 5457763, 12878392660, 30265003847344, 31888175187033340, 33461906572374759163, 56534517059253748865476, 37589973457545958193355601], [1, 24, -10516873, -56525688, 69186514920384, -363818716278984, -435677357267022399577, 6399245651145389894568, 1716155831334586342923895201], [1, -11064, 103337804, -629304155496, 3419407892241654, -12907751299697624904, 43474961616158444098604, -95473344303426312654659736, 176994576151109753197786640401], [1, 2800, -30179873, -53867601200, 401429912115328, -1542183688762581200, -24736277608288127618273, 65702733577165120603862800, 671790528819082282036142601601], [1, -13238, 2167093, -455250014606, 12995097229723444, -31568837437087835942, 10420649533376113642957, -4414161695146131035237470334, 23122483666661158726686253786801], [1, -8232, 343680380, -2298585657816, 57460445197611558, -266305401987647717016, 4613104652323715033592380, -12801569329010340082434963432, 180167782956420929503029846064801], [1, -26864, 858661708, -13059395917040, 211272506879911126, -1919841460284607568720, 18556952315536444335837292, -85348818306796280901665943248, 467056167777397914441056671494001], [1, 8064, 128729519, -4212564547968, -63455130075921792, -966130645741672795776, 6771060992535796773516431, 97278841101015449477000525952, 2766668711962335809450748011342401], [1, -53958, 1379702981, -37520871422526, 953847892489790388, -15691059322332871875318, 241292764202847513299699069, -3946334441628206263093931975406, 30585627290848204916791848989276401], [1, 36036, -113258965, -648516000132, 553814151761271216, -463639846784654007468, -57888554472990978913409965, 13167907068498393846605875268364, 261240335504588722483367157995242801], [1, 83986, 3603119341, 147927586544458, 5235321292627805428, 124939092411306598849858, 2570259641777786771475485941, 50600455085959903353702921659386, 508858109619679129936596364708525201], [1, -2660, -2654517485, 102827963140, 5251687000360966576, 138830614736984555980, -4838754824501663353919435765, -6546417168531484755563136114380, 3322737661703085672358476688602579601], [1, -143136, 11355854108, -704396173023648, 34708236326754607014, -1270892250101340138692448, 36966070851276066984967823708, -840667208202601976699154225747936, 10596610576391421032662867140133202401], [1, 31318, -16662743, -98609837824442, -5335963862325578492, -204425253584187631276106, -71610234710512147290971207, 279021019727865207478043875791526, 18469587772135192290560825407466407201], [1, 51136, 637460815, -213578867870912, -13604213472728169344, -657194222073365275565888, 6035654988276317357629928815, 1489817675937851438996275140480064, 89648251976843595444986830377401534401], [1, -12432, 12912997484, -128997167748624, 72773759655186881910, -508125086593718743325232, 200358600812029558577009722316, -759822915139691977961577430853424, 240747534123068430155382383568465195601], [1, 166278, 9871423481, 1098903185221590, 130448064282416194692, 6136340714972816798303910, 307807962294633860334868535081, 28952421437257339242196022655980022, 972299657790850297934682879408841327201], [1, -16520, 23891433628, -338642542836920, 290542898974356522694, -2908038740836330101888440, 1761811958339602826531832975772, -10461309644539760657434918769876360, 5437943429267472574499737549036572950401]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/28/6/e/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': '8-28e4-1.1-c5e4-0-0', 'motivic_weight': 5, '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': [5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '8-28e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1191382575857243, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e4-0', 'trace_hash': 516718329636877825, 'z1': {'__RealLiteral__': 0, 'data': '0.11318291294161122895451000317', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '143476387526012907831239372637,1436850704379629812432007451119,3076858613393249143506791208193,3299591708747694476835676022174', 'Lhash_array': ['143476387526012907831239372637', '1436850704379629812432007451119', '3076858613393249143506791208193', '3299591708747694476835676022174'], 'factors': ['2-28-7.2-c5-0-0', '2-28-7.4-c5-0-0', '2-28-7.2-c5-0-2', '2-28-7.4-c5-0-1'], 'label': '8-28e4-1.1-c5e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/28/6/e/b'}