Lfunction data - 4-7e4-1.1-c11e2-0-3

Formats: - HTML - YAML - JSON - 2024-05-19T05:10:17.856966

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '1535638817458466642330244785832,2747263295484131128898868470207', 'a10': -729000, 'a2': -54, 'a3': -120, 'a4': 1460, 'a5': 13500, 'a6': 6480, 'a7': 0, 'a8': -110808, 'a9': -222210, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1417.433334712933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.1', 'coefficient_field': '1.1.1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'euler_factors': [[1, 54, 1456, 110592, 4194304], [1, 120, 236610, 21257640, 31381059609], [1, -13500, 142881850, -659179687500, 2384185791015625], [1], [1, 750816, 653251941286, 214216567281468576, 81402749386839761113321], [1, -9548, 580074739914, -17111547442265276, 3211838877954855105157369], [1, 4160052, 72837924685942, 142572870778361276916, 1174562876521148458974062689], [1, -17998712, 293399338219938, -2096674620714481093928, 13569980418174090907801371961], [1, 66161016, 2994683043115918, 63038861638299450869832, 907846434775996175406740561329], [1, -61515612, 12823193731307518, -750521824949370682902348, 148852438543083302439338564577241], [1, -15281552, 44544265736191854, -388280960933209037977712, 645590698195138073036733040138561], [1, 527218340, 315935809764623790, 93801433211314965037574420, 31654680139659126296833481434130569], [1, -178276140, 1103495454485680198, -98110535504310347342497740, 302862043149743582494593171234930481], [1, -1826745232, 2408495597390567334, -1697582907706506281222383024, 863586854220408743801513785592407849], [1, 568240704, 125222806434661774, 1404781492779426570201381312, 6111571184724799803076702357055363809], [1, 4185816372, 8708326678160294206, 38798482345822355268243426084, 85915027059992607611268303810877410409], [1, 3111345000, 25961868574953911218, 93825372733092863067866355000, 909377607891473342964601076981440190281], [1, 15042595060, 132687608070481407978, 654562242103031746148915614660, 1893461025894826042494075073080422272921], [1, -9856523968, 129702594922488028518, -1203778582192842726652022945344, 14915769363385151583217201855136979828889], [1, 24312011328, 597505389277438985902, 5619047784216133609503883389888, 53417513915589153425653513253411473303441], [1, -30890001932, 732337997571614090646, -9691017923326587909836486584364, 98424433237708439716398638596388483974129], [1, -1992804256, 859518062328101582238, -1490605249080901312199144509024, 559494740587480879172162808385362976196641], [1, 5277014568, 2204575834826769599746, 6795905156753584220815421737656, 1658509762573818415340429240403156732495289], [1, -101541312828, 7614486854691881979478, -281794717235216286543647783492892, 7701585589361325209940623087797432152759121], [1, -192228621116, 23404654196344203605814, -1375014023979618020239011676316348, 51165609725977649453468030598885114890323009], [1, 89366698548, -510485298069389106566, 997035968159849056275181356501348, 124471585975092095765485234829277073042312201], [1, 23530148512, 22607840916003365344734, 325712285534868134816652864852064, 191610340886078111289333368801345298804416209], [1, -61425120528, 25693030776713418516118, -1292907848636134652238248598099504, 443040174110042643239751500532541979250113449], [1, 134390659028, 32597265440783399096958, 3467852051822467878479600307050852, 665860043319738865087230422941091304891802681], [1, 120232669140, 73888951802072951146630, 4611958245885257895445814044764180, 1471383076677527699142172838322885948765175969]], 'euler_factors_factorization': [[[[1, 54, 1456, 110592, 4194304], 1]], [[[1, 120, 236610, 21257640, 31381059609], 1]], [[[1, -13500, 142881850, -659179687500, 2384185791015625], 1]], [1], [[[1, 750816, 653251941286, 214216567281468576, 81402749386839761113321], 1]], [[[1, -9548, 580074739914, -17111547442265276, 3211838877954855105157369], 1]], [[[1, 4160052, 72837924685942, 142572870778361276916, 1174562876521148458974062689], 1]], [[[1, -17998712, 293399338219938, -2096674620714481093928, 13569980418174090907801371961], 1]], [[[1, 66161016, 2994683043115918, 63038861638299450869832, 907846434775996175406740561329], 1]], [[[1, -61515612, 12823193731307518, -750521824949370682902348, 148852438543083302439338564577241], 1]], [[[1, -15281552, 44544265736191854, -388280960933209037977712, 645590698195138073036733040138561], 1]], [[[1, 527218340, 315935809764623790, 93801433211314965037574420, 31654680139659126296833481434130569], 1]], [[[1, -178276140, 1103495454485680198, -98110535504310347342497740, 302862043149743582494593171234930481], 1]], [[[1, -1826745232, 2408495597390567334, -1697582907706506281222383024, 863586854220408743801513785592407849], 1]], [[[1, 568240704, 125222806434661774, 1404781492779426570201381312, 6111571184724799803076702357055363809], 1]], [[[1, 4185816372, 8708326678160294206, 38798482345822355268243426084, 85915027059992607611268303810877410409], 1]], [[[1, 3111345000, 25961868574953911218, 93825372733092863067866355000, 909377607891473342964601076981440190281], 1]], [[[1, 15042595060, 132687608070481407978, 654562242103031746148915614660, 1893461025894826042494075073080422272921], 1]], [[[1, -9856523968, 129702594922488028518, -1203778582192842726652022945344, 14915769363385151583217201855136979828889], 1]], [[[1, 24312011328, 597505389277438985902, 5619047784216133609503883389888, 53417513915589153425653513253411473303441], 1]], [[[1, -30890001932, 732337997571614090646, -9691017923326587909836486584364, 98424433237708439716398638596388483974129], 1]], [[[1, -1992804256, 859518062328101582238, -1490605249080901312199144509024, 559494740587480879172162808385362976196641], 1]], [[[1, 5277014568, 2204575834826769599746, 6795905156753584220815421737656, 1658509762573818415340429240403156732495289], 1]], [[[1, -101541312828, 7614486854691881979478, -281794717235216286543647783492892, 7701585589361325209940623087797432152759121], 1]], [[[1, -192228621116, 23404654196344203605814, -1375014023979618020239011676316348, 51165609725977649453468030598885114890323009], 1]], [[[1, 89366698548, -510485298069389106566, 997035968159849056275181356501348, 124471585975092095765485234829277073042312201], 1]], [[[1, 23530148512, 22607840916003365344734, 325712285534868134816652864852064, 191610340886078111289333368801345298804416209], 1]], [[[1, -61425120528, 25693030776713418516118, -1292907848636134652238248598099504, 443040174110042643239751500532541979250113449], 1]], [[[1, 134390659028, 32597265440783399096958, 3467852051822467878479600307050852, 665860043319738865087230422941091304891802681], 1]], [[[1, 120232669140, 73888951802072951146630, 4611958245885257895445814044764180, 1471383076677527699142172838322885948765175969], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-7e4-1.1-c11e2-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11, 11], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/49/12/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.037109375', 'prec': 37}, 'plot_values': [2.8233325882988857e-120, 0.010161674147762548, 0.04041770222030125, 0.09008505625826804, 0.15804165125333158, 0.24274573079381845, 0.3422718707522482, 0.4543411292489155, 0.5763786238922611, 0.7055489374717077, 0.8388342297666848, 0.9730689314175385, 1.1050358392993382, 1.2314940914972474, 1.3492893620520936, 1.45536949843424, 1.5469038715024988, 1.6212818535272056, 1.6762356695227836, 1.709818051357561, 1.7205226316143274, 1.707238555218244, 1.6693625842996653, 1.6067300896824408, 1.5197135932552235, 1.409131288749776, 1.2763277052284376, 1.123062602215217, 0.951570733527122, 0.7644355070357969, 0.5646263757802485, 0.3553629349715891, 0.1401301596742455, -0.07746046708671912, -0.2936759357860438, -0.5047964739426404, -0.7071372034970373, -0.8971717224519916, -1.0715655188298616, -1.2272818046738623, -1.3616207396518896, -1.4723019458291993, -1.5575030106281924, -1.6159145381218416, -1.6467713295835467, -1.6498776010441245, -1.6256247129383692, -1.5749861887503436, -1.499516876674238, -1.4013195024455463, -1.2830216471886355, -1.1477176074993842, -0.9989214754219236, -0.8404899057252111, -0.67655175958783, -0.5114188459899507, -0.349494882997009, -0.19518225993428429, -0.05277530103480687, 0.07362850939987349, 0.18024399381428863, 0.2636743969179509, 0.32102706408437515, 0.34996959878964834, 0.3488362756303122, 0.316658449532723, 0.25325199123473385, 0.1592181856950387, 0.03600304827630232, -0.11413264358292319, -0.28808989365313564, -0.48199107233874805, -0.6911978651658737, -0.9103966299549553, -1.1336604137584738, -1.3545538733251574, -1.5662386217832827, -1.7615895928912593, -1.933339281739991, -2.0741961720536106, -2.1770197100555087, -2.2349309604778065, -2.24150669114642, -2.19087287867758, -2.077903378100005, -1.8982882949414797, -1.6487206435997712, -1.3269338916854316, -0.9318590025197705, -0.46362851203108807, 0.07631343280482612, 0.6852394899732341, 1.3590919585080072, 2.092538810631339, 2.879002476558447, 3.7107347463335065, 4.578930630553173, 5.473809894174617, 6.384820253139146, 7.300710532713883, 8.209821994054192, 9.100136371939874, 9.959648452793697, 10.776371788627745, 11.53878020349236, 12.235754959695319, 12.857078095859022, 13.39330728397844, 13.836300212561802, 14.179007239499544, 14.416003774138865, 14.543195892953072, 14.558337088663087, 14.460647943765863, 14.251294816398367, 13.932931029394037, 13.510118016119616, 12.988801776662077, 12.37666152208795, 11.682540839064494, 10.916714610534678, 10.090298893292463, 9.215433394592353, 8.304697043163706, 7.371210012903672, 6.428083003654942, 5.488449129873215, 4.564973818280738, 3.6698322368961125, 2.8143034347697795, 2.0087128576616866, 1.2621290649836596, 0.5822928659820433, -0.024571994794365302, -0.5538216734908206, -1.00246425532542, -1.3691954291317985, -1.6543584606317392, -1.859937813911324, -1.9894205921022121, -2.047739040335908, -2.041054266221991, -1.9766454073443673, -1.8626420464120492, -1.707865005796114, -1.5215372299316108, -1.313087923091905, -1.0918724171815464, -0.8669569504980754, -0.6468760417431728, -0.4394189600051303, -0.25144851713212124, -0.08871170996919696, 0.04426298263477965, 0.14430946142764914, 0.2096395316268811, 0.23992368774419573, 0.236219972926167, 0.20098015088558854, 0.1379014498488694, 0.051854377772400664, -0.05132514883393702, -0.16498132671664012, -0.28188244684758357, -0.3944259257647889, -0.49489151201034653, -0.5756841304265526, -0.6295690993524912, -0.6499250935771681, -0.6309369815541342, -0.5678278610403837, -0.456990866106246, -0.29616904420375323, -0.08451556830468906, 0.177306602244832, 0.48713709595468396, 0.8413203854989834, 1.234781739577157, 1.6611441023099396, 2.112849339779733, 2.581391686745639, 3.0574585748526775, 3.531271178546118, 3.9927144785363198, 4.431764620128139, 4.8385766968030275, 5.2039696439730285, 5.5194428147379675, 5.777683050768592, 5.972487326724701, 6.099254258993917, 6.1547993430767605, 6.137794874919118, 6.048475634151452, 5.888996933599689, 5.663040754761338, 5.376070864053677, 5.034860972530848, 4.647637584726474, 4.223561325507562, 3.7727611068238205, 3.3058061109766927, 2.83364747070546, 2.3671206261222455, 1.9168214994703066, 1.4926766205322102, 1.1037883973617324, 0.7581036375266993, 0.462265975681044, 0.22140286092488035, 0.03902199286539202, -0.08307635179540526, -0.14482783965297005, -0.14787385627963398, -0.09549372606461493, 0.007522257401514924, 0.15504559988296487, 0.3398007722207474, 0.553637858532355, 0.7877477679611661, 1.0330163978946867, 1.2802209896737644, 1.5204364750070072, 1.7451726408403985, 1.9467961438420636, 2.1185758382959605, 2.2550815770702677, 2.352116998538553, 2.4070590965534575, 2.4186725067909283, 2.3873616373184627, 2.314876175499311, 2.204459351734394, 2.060468956859792, 1.8884195114295423, 1.6945545776494397, 1.4857952850540177, 1.2693065322374326, 1.0523774065087854, 0.8420249784840118, 0.6448417350248099, 0.4666758044435, 0.3124851221708032, 0.1861226336568643, 0.0902357220094381, 0.026170540420715118, -0.0060517436208418355, -0.007713895924274456, 0.018670097854735338, 0.06947397345772444, 0.1401328170122668, 0.22532714080913555, 0.3192455496756786, 0.4157918461315138, 0.5089098669205915, 0.592768210089616, 0.6621090889074416, 0.7123686568887522, 0.7400060673667025, 0.7425271094422984, 0.7187507930203146, 0.6687188031344424, 0.5938650385655833, 0.4968111336190308, 0.38141858789382704, 0.2524886475444604, 0.11569510820201863, -0.022777614694202485, -0.1564028789576311, -0.27869124244989824, -0.38342330621561055, -0.46499877858792327, -0.5186828457518096, -0.5408813007608281, -0.5293422866945273, -0.48332575032027675, -0.4037037055384777, -0.29301015166241307, -0.15539321227575784, 0.0034469570159242893, 0.17648267216922647, 0.3555036661715405, 0.5315229819342782, 0.6949572389768109, 0.8361925440821636, 0.945740649705355, 1.0149189167308819, 1.0359199237702754, 1.0025403287276489, 0.9101085284873587, 0.7561867736052612, 0.540318224674163, 0.2646270213125723, -0.06662937008028409, -0.4466256554623817, -0.8665961012716057, -1.3156070741545711, -1.7813198039441358, -2.2499819464376527, -2.707256231014943, -3.138410272673465, -3.5291249705353533, -3.8658307161431, -4.13640444900466, -4.330575988706166, -4.4404309755106475, -4.4607975316972395, -4.389493561230305, -4.227604094927987, -3.979443206328651, -3.652646992897376, -3.2578585113352334, -2.808588921932642, -2.3206729343117627, -1.8118875649574004, -1.3012597166814468, -0.8084729226237959, -0.3531323828715832, 0.04597133182612103, 0.3715253651709292, 0.6084750153091074, 0.7445081551208079, 0.7707650436845072, 0.682061295952195, 0.47741393488083916, 0.1599575439225143, -0.26280651779221054, -0.7794005181215876, -1.3744545692354002, -2.0293562553567144, -2.722676687763699, -3.4309908595731247, -4.129600915230669, -4.793410235869999, -5.397849485140344, -5.919676685858763, -6.337973018336784, -6.634750659938935, -6.79586465351403, -6.8113394190111585, -6.676044513376297, -6.389695674477737, -5.957166919317555, -5.38817619892804, -4.697151382348754, -3.9026657292963676, -3.0268348640767653, -2.0946144082156706, -1.1327704610178042, -0.16918285200746133, 0.7685070183525441, 1.6534345409104587, 2.461035315728317, 3.1692873763879734, 3.760228728376966, 4.219803662476809, 4.539198117536634, 4.7142460831203845, 4.746434710202764, 4.641892044793465, 4.4119658387375935, 4.071878313765657, 3.640850945994357, 3.140565058809114, 2.594879068242832, 2.0282662812323484, 1.4652394913342535, 0.928943250534572, 0.44045214969811186, 0.017672026463329275, -0.325295994397435, -0.578839734940621, -0.7382188841053561, -0.8037968308510782, -0.7810185917964074, -0.6802285832391741, -0.5161524686768372, -0.30741143380282426, -0.07549396394589766, 0.15586674188001953, 0.3621639222070516, 0.5186801236018642, 0.6022621162805158, 0.5916296676013427, 0.46926405963644263, 0.2213035808278497, -0.16066582624846254, -0.6802239510110091, -1.334622750125307, -2.115921738055612, -3.0099465587761918, -3.9978711458549383, -5.055714469371188, -6.15621437495794, -7.2688660083773815, -8.361874323783631, -9.402655393877007, -10.359628767041666, -11.2030346911835, -11.906338902607112, -12.447176317158796, -12.80818849192298, -12.977894830068553, -12.950859858605527, -12.728318054576167, -12.317662214695282, -11.732703216236118, -10.992567037135462, -10.121546357394875, -9.147576583341511, -8.101718733044823, -7.016440589780942, -5.924845008467626, -4.859001983648602, -3.8490898451653086, -2.922004551205515, -2.10060340079824, -1.4027628729698522, -0.8409011815614971, -0.4215751645467363, -0.1454113176178394, -0.007239692019732982, 0.003508890377332027, -0.09777780632917167, -0.2917301580278132, -0.5558650857823177, -0.8657539997660906, -1.1959823604592652, -1.5214765060273059, -1.8183571834692749, -2.065218215653968, -2.2437124973825693, -2.339576572070425, -2.342852178139257, -2.248487737099002, -2.0561794708095404, -1.7704470110638877, -1.4001599385443428, -0.9580683094242416, -0.4601477330724478, 0.0753484917737167, 0.6285525208570514, 1.1792687444018846, 1.707466273976663, 2.194718395519157, 2.6243750890812305, 2.9829560975778686, 3.259912928483732, 3.448799118099351, 3.546607525022302, 3.554594252960741, 3.477256091078267, 3.322756820841228, 3.101676041669842, 2.827063845301906, 2.513133203962457, 2.1750361878798388, 1.8276798712621292, 1.485361633535947, 1.1608620199393604, 0.8650902678612745, 0.6065524032382588, 0.3911394179945487, 0.22199640496985146, 0.09953988482501634, 0.02167866838618065, -0.015915636208102844, -0.019348009323038578, 0.003982691382781067, 0.04593431391788464, 0.09822218758003597, 0.15290412467845352, 0.20297551512072323, 0.2426599406777786, 0.2678753202841917, 0.27625423309305325, 0.26738829245209905, 0.24256947619645605, 0.20477351648102668, 0.15818016071855304, 0.10792102530694472, 0.0594880238043049, 0.018331992908783307, -0.010706888551536516, -0.02382070315685994, -0.01865527490513828, 0.0053908342868382265, 0.04698061768265667, 0.10278555942388981, 0.16756272505993372, 0.23442101021300524, 0.29511890917311734, 0.34065299620591494, 0.36167267717803403, 0.3493180829748279, 0.2956086567014368, 0.19439292139282605, 0.04156182339543345, -0.1640622552639602, -0.42081098593665417, -0.7235235997975583, -1.0639794391614095, -1.4305994012356702, -1.8092602885574562, -2.183525442942831, -2.5355248226806744, -2.8462174378347855, -3.0970547791651892, -3.271957604701324, -3.3560778046024775, -3.3324569245365883, -3.1913060035987466], 'positive_zeros': ['1.21140542763281010288777580288139', '2.16720861015607171635815597964183', '2.53294342489107854684642164936050', '3.33487864033064992997976933758548', '4.93394815933968296097972652090225', '5.66436002545152060946769471323532', '5.95677381188123483946378908192496', '6.43269232891223512667039671578473', '7.80301022621852801861021199698594', '7.976282909673634197872119276196318', '9.118239769779742969999386994404894', '9.181392927418900040200293843282768', '9.902057681664807588427017111537749', '10.35274861449342546499229175346017', '10.86603076261353902873417974893122', '11.79616546142252160558415392976009', '12.07565486470200023105733234462568', '12.95776021716272696957431266281747'], 'prelabel': '4-7e4-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.135863089038074, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c11e2-0', 'trace_hash': 1136300459244489319, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21140542763281010288777580288', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16720861015607171635815597964', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.53294342489107854684642164936', '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': 1417.433334712933, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'dirichlet_coefficients': [1, -54, -120, 1460, 13500, 6480, 0, -110808, -222210, -729000, -750816, -175200, 9548, 0, -1620000, 5635536, -4160052, 11999340, 17998712, 19710000, 0, 40544064, -66161016, 13296960, 39368150, -515592, 33800760, 0, 61515612, 87480000, 15281552, -77954400, 90097920, 224642808, 0, -324426600, -527218340, -971930448, -1145760, -1495908000, 178276140, 0, 1826745232, -1096191360, -2999835000, 3572694864, -568240704, -676264320, 0, -2125880100, 499206240, 13940080, -4185816372, -1825241040, -10136016000, 0, -2159845440, -3321843048, -3111345000, -2365200000, -15042595060, -825203808, 0, 2134991680, 128898000, -4865287680, 9856523968, -6073675920, 7939321920, 0, -24312011328, 24622645680, 30890001932, 28469790360, -4724178000, 26278119520, 0, 61871040, 1992804256, 76079736000, 19690874091, -9626911560, -5277014568, 0, -56160702000, -98644242528, -7381873440, 83196419328, 101541312828, 161991090000, 0, -96595083360, -1833786240, 30684998016, 242982612000, 9354528000, 192228621116, 0, 166838823360, 57477499000], 'euler11': [1, 750816, 653251941286, 214216567281468576, 81402749386839761113321], 'euler13': [1, -9548, 580074739914, -17111547442265276, 3211838877954855105157369], 'euler17': [1, 4160052, 72837924685942, 142572870778361276916, 1174562876521148458974062689], 'euler19': [1, -17998712, 293399338219938, -2096674620714481093928, 13569980418174090907801371961], 'euler2': [1, 54, 1456, 110592, 4194304], 'euler23': [1, 66161016, 2994683043115918, 63038861638299450869832, 907846434775996175406740561329], 'euler29': [1, -61515612, 12823193731307518, -750521824949370682902348, 148852438543083302439338564577241], 'euler3': [1, 120, 236610, 21257640, 31381059609], 'euler31': [1, -15281552, 44544265736191854, -388280960933209037977712, 645590698195138073036733040138561], 'euler37': [1, 527218340, 315935809764623790, 93801433211314965037574420, 31654680139659126296833481434130569], 'euler41': [1, -178276140, 1103495454485680198, -98110535504310347342497740, 302862043149743582494593171234930481], 'euler43': [1, -1826745232, 2408495597390567334, -1697582907706506281222383024, 863586854220408743801513785592407849], 'euler47': [1, 568240704, 125222806434661774, 1404781492779426570201381312, 6111571184724799803076702357055363809], 'euler5': [1, -13500, 142881850, -659179687500, 2384185791015625], 'euler53': [1, 4185816372, 8708326678160294206, 38798482345822355268243426084, 85915027059992607611268303810877410409], 'euler59': [1, 3111345000, 25961868574953911218, 93825372733092863067866355000, 909377607891473342964601076981440190281], 'euler61': [1, 15042595060, 132687608070481407978, 654562242103031746148915614660, 1893461025894826042494075073080422272921], 'euler67': [1, -9856523968, 129702594922488028518, -1203778582192842726652022945344, 14915769363385151583217201855136979828889], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 24312011328, 597505389277438985902, 5619047784216133609503883389888, 53417513915589153425653513253411473303441], 'euler73': [1, -30890001932, 732337997571614090646, -9691017923326587909836486584364, 98424433237708439716398638596388483974129], 'euler79': [1, -1992804256, 859518062328101582238, -1490605249080901312199144509024, 559494740587480879172162808385362976196641], 'euler83': [1, 5277014568, 2204575834826769599746, 6795905156753584220815421737656, 1658509762573818415340429240403156732495289], 'euler89': [1, -101541312828, 7614486854691881979478, -281794717235216286543647783492892, 7701585589361325209940623087797432152759121], 'euler97': [1, -192228621116, 23404654196344203605814, -1375014023979618020239011676316348, 51165609725977649453468030598885114890323009], 'euler_factors': [[1, 54, 1456, 110592, 4194304], [1, 120, 236610, 21257640, 31381059609], [1, -13500, 142881850, -659179687500, 2384185791015625], [1, 0, 0, 0, 0], [1, 750816, 653251941286, 214216567281468576, 81402749386839761113321], [1, -9548, 580074739914, -17111547442265276, 3211838877954855105157369], [1, 4160052, 72837924685942, 142572870778361276916, 1174562876521148458974062689], [1, -17998712, 293399338219938, -2096674620714481093928, 13569980418174090907801371961], [1, 66161016, 2994683043115918, 63038861638299450869832, 907846434775996175406740561329], [1, -61515612, 12823193731307518, -750521824949370682902348, 148852438543083302439338564577241], [1, -15281552, 44544265736191854, -388280960933209037977712, 645590698195138073036733040138561], [1, 527218340, 315935809764623790, 93801433211314965037574420, 31654680139659126296833481434130569], [1, -178276140, 1103495454485680198, -98110535504310347342497740, 302862043149743582494593171234930481], [1, -1826745232, 2408495597390567334, -1697582907706506281222383024, 863586854220408743801513785592407849], [1, 568240704, 125222806434661774, 1404781492779426570201381312, 6111571184724799803076702357055363809], [1, 4185816372, 8708326678160294206, 38798482345822355268243426084, 85915027059992607611268303810877410409], [1, 3111345000, 25961868574953911218, 93825372733092863067866355000, 909377607891473342964601076981440190281], [1, 15042595060, 132687608070481407978, 654562242103031746148915614660, 1893461025894826042494075073080422272921], [1, -9856523968, 129702594922488028518, -1203778582192842726652022945344, 14915769363385151583217201855136979828889], [1, 24312011328, 597505389277438985902, 5619047784216133609503883389888, 53417513915589153425653513253411473303441], [1, -30890001932, 732337997571614090646, -9691017923326587909836486584364, 98424433237708439716398638596388483974129], [1, -1992804256, 859518062328101582238, -1490605249080901312199144509024, 559494740587480879172162808385362976196641], [1, 5277014568, 2204575834826769599746, 6795905156753584220815421737656, 1658509762573818415340429240403156732495289], [1, -101541312828, 7614486854691881979478, -281794717235216286543647783492892, 7701585589361325209940623087797432152759121], [1, -192228621116, 23404654196344203605814, -1375014023979618020239011676316348, 51165609725977649453468030598885114890323009]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/12/a/c'], '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': '4-7e4-1.1-c11e2-0-3', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11, 11], 'order_of_vanishing': 2, 'prelabel': '4-7e4-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.135863089038074, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e2-0', 'trace_hash': 1136300459244489319, 'z1': {'__RealLiteral__': 0, 'data': '1.21140542763281010288777580288', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1535638817458466642330244785832,2747263295484131128898868470207', 'Lhash_array': ['1535638817458466642330244785832', '2747263295484131128898868470207'], 'label': '4-7e4-1.1-c11e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/12/a/c'}