LMFDB - Embedded newform 1.80.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,80,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 80, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 80);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 80 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$39.5237048722$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 76\!\cdots\!88 $ x^6 - 3x^5 - 4493465009931118088598x^4 - 13617827867154853888266546820774x^3 + 5183423914918797826459016270129188352477541x^2 + 36020237378286283561256608380952541686850032723239033*x - 768426424275848216319978876834525014212769442584294247793970688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{54}\cdot 3^{24}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 13^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$4.48729e10$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.07427e12 q^{2} -9.45275e18 q^{3} +5.49591e23 q^{4} -5.27758e26 q^{5} -1.01548e31 q^{6} -3.45278e33 q^{7} -5.89470e34 q^{8} +4.00848e37 q^{9} +O(q^{10})$	\(q+1.07427e12 q^{2} -9.45275e18 q^{3} +5.49591e23 q^{4} -5.27758e26 q^{5} -1.01548e31 q^{6} -3.45278e33 q^{7} -5.89470e34 q^{8} +4.00848e37 q^{9} -5.66955e38 q^{10} +2.33372e41 q^{11} -5.19515e42 q^{12} -5.41960e43 q^{13} -3.70921e45 q^{14} +4.98877e45 q^{15} -3.95532e47 q^{16} +5.59497e48 q^{17} +4.30619e49 q^{18} -2.84556e48 q^{19} -2.90051e50 q^{20} +3.26382e52 q^{21} +2.50704e53 q^{22} -7.81076e52 q^{23} +5.57211e53 q^{24} -1.62651e55 q^{25} -5.82211e55 q^{26} +8.68218e55 q^{27} -1.89761e57 q^{28} +9.18474e57 q^{29} +5.35928e57 q^{30} +1.25842e59 q^{31} -3.89277e59 q^{32} -2.20601e60 q^{33} +6.01051e60 q^{34} +1.82223e60 q^{35} +2.20302e61 q^{36} +3.95553e61 q^{37} -3.05689e60 q^{38} +5.12301e62 q^{39} +3.11098e61 q^{40} +5.78663e62 q^{41} +3.50622e64 q^{42} +2.81552e64 q^{43} +1.28259e65 q^{44} -2.11551e64 q^{45} -8.39086e64 q^{46} -2.26774e65 q^{47} +3.73887e66 q^{48} +6.13077e66 q^{49} -1.74731e67 q^{50} -5.28878e67 q^{51} -2.97857e67 q^{52} -1.18330e68 q^{53} +9.32699e67 q^{54} -1.23164e68 q^{55} +2.03531e68 q^{56} +2.68983e67 q^{57} +9.86689e69 q^{58} -1.26078e70 q^{59} +2.74178e69 q^{60} +2.75036e70 q^{61} +1.35188e71 q^{62} -1.38404e71 q^{63} -1.79104e71 q^{64} +2.86024e70 q^{65} -2.36984e72 q^{66} +6.88030e71 q^{67} +3.07495e72 q^{68} +7.38332e71 q^{69} +1.95757e72 q^{70} +2.19266e72 q^{71} -2.36288e72 q^{72} +1.79419e72 q^{73} +4.24931e73 q^{74} +1.53750e74 q^{75} -1.56389e72 q^{76} -8.05781e74 q^{77} +5.50349e74 q^{78} -1.14491e75 q^{79} +2.08746e74 q^{80} -2.79567e75 q^{81} +6.21640e74 q^{82} +6.74200e75 q^{83} +1.79377e76 q^{84} -2.95279e75 q^{85} +3.02463e76 q^{86} -8.68211e76 q^{87} -1.37566e76 q^{88} +3.78339e76 q^{89} -2.27263e76 q^{90} +1.87127e77 q^{91} -4.29273e76 q^{92} -1.18955e78 q^{93} -2.43616e77 q^{94} +1.50177e75 q^{95} +3.67974e78 q^{96} -2.34072e78 q^{97} +6.58610e78 q^{98} +9.35467e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 98\!\cdots\!22 q^{9}+O(q^{10}) $ 6 * q - 16086577320 * q^2 + 1942174928281180680 * q^3 + 1549737362258405903681088 * q^4 + 6092984858773763455723827540 * q^5 - 2227106590325939088404927087328 * q^6 - 204133057837186288371299604423600 * q^7 + 542570064661378776298915601390568960 * q^8 + 98496326492153316059886441015309696222 * q^9	$ 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 12\!\cdots\!24 q^{99}+O(q^{100}) $ 6 * q - 16086577320 * q^2 + 1942174928281180680 * q^3 + 1549737362258405903681088 * q^4 + 6092984858773763455723827540 * q^5 - 2227106590325939088404927087328 * q^6 - 204133057837186288371299604423600 * q^7 + 542570064661378776298915601390568960 * q^8 + 98496326492153316059886441015309696222 * q^9 + 2720626696366658228219065452729623532240 * q^10 + 326182707503353434196853598345012484552152 * q^11 + 3662741799314627362069151990938777789858560 * q^12 - 249286867791526696387831019648013646893106140 * q^13 + 1866634067474695788912841823339193553138295616 * q^14 + 53939724989186019570794541522119517534771796080 * q^15 - 681627631644510368706137880459644753465449181184 * q^16 + 829554518710324966978506506427078451803483469740 * q^17 + 20783419681388619276512545895581772264264550807480 * q^18 - 50727940848110344442361931427855575819428647228760 * q^19 - 1467030065046629207751264576643706806587735144958080 * q^20 + 11440846038310308150487768012211089482880511198926272 * q^21 + 36817507512313772519930542191150104222671820963556960 * q^22 - 1046924887201563380993656359631631933258453525094738960 * q^23 + 4647998047182641817986339484942489649049309172966328320 * q^24 + 10836995626543537474051791335153252813979338793331307850 * q^25 - 165657588130323625805363235243378873928973276983585168368 * q^26 + 452244485424938477892504860024752019079362449583874943440 * q^27 + 1004680642640065837930850364413184139977872155405489282560 * q^28 - 7120822866262655112931363073018274881104708247497947521340 * q^29 - 1093089132342530488188112356341250721972394415479943059520 * q^30 + 134345039550847531062964315804153164343444264343589333172032 * q^31 - 367680407387361126658464447414461787802285956837455133573120 * q^32 + 694937277679484430969386562214930563011269531321798125315360 * q^33 + 3154306959722239121253159757854043021326472297974364404980016 * q^34 + 9191056770903655504272784196241783249847740561191433159558240 * q^35 + 19880287065959074647932230862843896929437344679866234828597056 * q^36 + 200218543091040103155222783880989961642213560574664429550198420 * q^37 + 866365883974611161836395390925862263352921297032838009795060640 * q^38 + 1846928010477803855453412626793191219191424716227436821180804144 * q^39 + 9116669264447274408945009430906339427674431802850195585057510400 * q^40 + 19216804901837266991242147464997667315402616992351385711235458972 * q^41 + 112315174478490788723912174839938916243710780267342081630678531840 * q^42 + 108832931910908864051094641347526853298463718485111641638401400600 * q^43 + 495514650695382135238363336424200091081783038631873261666636656896 * q^44 + 1089311173064980984859644147008913582964905804089164802662670706980 * q^45 + 2339423217798161589056888023635021837153755261863446723443331974592 * q^46 + 766732507168785220421816169748850175208159379232549271592508353760 * q^47 - 1227537570851109157458973684400646232156423736031048093315900456960 * q^48 + 3801016219812200810689187746878210669081675204402752707309154018358 * q^49 - 50723521315108078882353551947661611720805543300108849711322864485400 * q^50 - 139865466375558864334882784640098531626186142446280524443365433199728 * q^51 - 279692249004488191323071540832092417841619330373410063262542264310400 * q^52 - 312193237964710957330604375297544855480450344577449082153802391971020 * q^53 - 996221038973994559873624494431619704350011373216284617130312268666560 * q^54 - 861958222068919393142591787960630586871784969446963670182827020790320 * q^55 + 1123629643438673418216699268533992018915072902064015953839024305295360 * q^56 + 7795598779799587371741461301046795526293245245773998812837273820000480 * q^57 + 16584702356914156466182151363602691995360915944935914137385742159510160 * q^58 + 24289171784532714189639095038219795042285164994033400426178461238907320 * q^59 + 73025956047571458013400417312791668535879728806786116560639243534051840 * q^60 + 80560570425826852880081093564684385117241348668836108242495308815618052 * q^61 + 59777568713863815377707698536571620658579394379949737090862924510332160 * q^62 - 276708678056196744256455115102015383166989187390931876478468368856762480 * q^63 - 719203226636338274682481908236724651863342420498670194455988567598170112 * q^64 - 1007462919483461647300380829039677154191109543250817689988654733030592520 * q^65 - 3347562853423538991999694027669961627986534585541581689746575315495214976 * q^66 - 1851521876973893932513297183455714100127257334040085257904842903903517560 * q^67 - 5899582938115809421316043854246769288699297144820927766700932855979726720 * q^68 - 1427672735602453311144050658084524391331260046448660152415370050225171136 * q^69 + 31159148342952686307596185437939815723517531766889921556924090292621741440 * q^70 + 38507401093845789827495210229167852070939724868887506542264571604541264592 * q^71 + 87904411000641647434917578390462554629488250565124366592415232306933521920 * q^72 + 61123654206386061400310438862981106227383729069503080628162601940159787740 * q^73 + 136513352063977853606694381822259496818965955504365628093794971441921163216 * q^74 + 113188706706427317048365034543759604727098826077328333023878456326260918200 * q^75 - 249903768766885839664688587580825575582546834454828556400015599314274074880 * q^76 - 1195099252106099653800449972868194220235362175583181442486256041652274244800 * q^77 - 3022231856978250782599441544561070134871217051487771942772538597436408443200 * q^78 - 188234723479363903277484397100590307076741783512190126828886315155446684640 * q^79 - 2750248132852209015421484068233717972689944891189322073844459755369097666560 * q^80 - 4202996734890713231427597758184507891641102417282671988811370042535012566794 * q^81 + 3834792966214046709977047126406184257851543195738078433637414913324683717360 * q^82 + 14506845760765784842493952470927474286413727909244314121162679395439622145320 * q^83 + 48942789227023150657016145376829988370028655394086238910889917134273615865856 * q^84 + 38946066828627954832778050727572362568084538101228336437758435671222134267240 * q^85 + 66363633323077708072616297459993363454350669286030390599179655949306835458912 * q^86 - 12188467007600920252987005731487987332580129454574096199578444638747687628880 * q^87 - 68086553439664359269830684533538140843829745277114000504065479672707840583680 * q^88 + 88790169947368466670673875396871954428202115924137373286785364937730407494780 * q^89 - 678121360108159288271315537216087664710338266311311066150921870820864233179120 * q^90 - 1105665330428280782729905276805137770501582996765091919549546053816493845198368 * q^91 - 581852119074779563003978084378550280950528927013853021971971412987670782543360 * q^92 - 724063571132401087495277238269757837179269218308363767014177350097338957840640 * q^93 - 342394004508386413823498343959337212855421843329465021317054652742559913721984 * q^94 + 4133010515441143062055572903340407460351722715065934937506390604234109634359600 * q^95 + 4500277093535091993817003185543220432802869972147132801867826645045331188908032 * q^96 + 2053881285944963905800936410853289740689894385863240159901124624782493905690060 * q^97 + 21591608457226642856925919189308208713047358263642522360137695155926522503830040 * q^98 + 12210721611676619111412804269965201185505307365258823385190308559518832844781624 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.07427e12	1.38175	0.690873	−	0.722976i	$-0.257226\pi$
$2$	1.07427e12	1.38175	0.690873	+	0.722976i	$0.257226\pi$
$3$	−9.45275e18	−1.34669	−0.673346	−	0.739327i	$-0.735144\pi$
$3$	−9.45275e18	−1.34669	−0.673346	+	0.739327i	$0.735144\pi$
$4$	5.49591e23	0.909222
$5$	−5.27758e26	−0.129754	−0.0648769	−	0.997893i	$-0.520665\pi$
$5$	−5.27758e26	−0.129754	−0.0648769	+	0.997893i	$0.520665\pi$
$6$	−1.01548e31	−1.86079
$7$	−3.45278e33	−1.43481	−0.717407	−	0.696654i	$-0.754671\pi$
$7$	−3.45278e33	−1.43481	−0.717407	+	0.696654i	$0.754671\pi$
$8$	−5.89470e34	−0.125432
$9$	4.00848e37	0.813580
$10$	−5.66955e38	−0.179287
$11$	2.33372e41	1.71016	0.855082	−	0.518493i	$-0.173507\pi$
$11$	2.33372e41	1.71016	0.855082	+	0.518493i	$0.173507\pi$
$12$	−5.19515e42	−1.22444
$13$	−5.41960e43	−0.541010	−0.270505	−	0.962719i	$-0.587191\pi$
$13$	−5.41960e43	−0.541010	−0.270505	+	0.962719i	$0.587191\pi$
$14$	−3.70921e45	−1.98255
$15$	4.98877e45	0.174738
$16$	−3.95532e47	−1.08254
$17$	5.59497e48	1.39658	0.698290	−	0.715815i	$-0.253945\pi$
$17$	5.59497e48	1.39658	0.698290	+	0.715815i	$0.253945\pi$
$18$	4.30619e49	1.12416
$19$	−2.84556e48	−0.00877809	−0.00438905	−	0.999990i	$-0.501397\pi$
$19$	−2.84556e48	−0.00877809	−0.00438905	+	0.999990i	$0.501397\pi$
$20$	−2.90051e50	−0.117975
$21$	3.26382e52	1.93225
$22$	2.50704e53	2.36301
$23$	−7.81076e52	−0.127187	−0.0635937	−	0.997976i	$-0.520256\pi$
$23$	−7.81076e52	−0.127187	−0.0635937	+	0.997976i	$0.520256\pi$
$24$	5.57211e53	0.168918
$25$	−1.62651e55	−0.983164
$26$	−5.82211e55	−0.747538
$27$	8.68218e55	0.251050
$28$	−1.89761e57	−1.30457
$29$	9.18474e57	1.57887	0.789435	−	0.613835i	$-0.210374\pi$
$29$	9.18474e57	1.57887	0.789435	+	0.613835i	$0.210374\pi$
$30$	5.35928e57	0.241444
$31$	1.25842e59	1.55252	0.776261	−	0.630412i	$-0.217114\pi$
$31$	1.25842e59	1.55252	0.776261	+	0.630412i	$0.217114\pi$
$32$	−3.89277e59	−1.37036
$33$	−2.20601e60	−2.30307
$34$	6.01051e60	1.92972
$35$	1.82223e60	0.186173
$36$	2.20302e61	0.739725
$37$	3.95553e61	0.450025	0.225013	−	0.974356i	$-0.427758\pi$
$37$	3.95553e61	0.450025	0.225013	+	0.974356i	$0.427758\pi$
$38$	−3.05689e60	−0.0121291
$39$	5.12301e62	0.728574
$40$	3.11098e61	0.0162752
$41$	5.78663e62	0.114147	0.0570734	−	0.998370i	$-0.481823\pi$
$41$	5.78663e62	0.114147	0.0570734	+	0.998370i	$0.481823\pi$
$42$	3.50622e64	2.66988
$43$	2.81552e64	0.846360	0.423180	−	0.906046i	$-0.360914\pi$
$43$	2.81552e64	0.846360	0.423180	+	0.906046i	$0.360914\pi$
$44$	1.28259e65	1.55492
$45$	−2.11551e64	−0.105565
$46$	−8.39086e64	−0.175741
$47$	−2.26774e65	−0.203108	−0.101554	−	0.994830i	$-0.532382\pi$
$47$	−2.26774e65	−0.203108	−0.101554	+	0.994830i	$0.532382\pi$
$48$	3.73887e66	1.45784
$49$	6.13077e66	1.05869
$50$	−1.74731e67	−1.35848
$51$	−5.28878e67	−1.88076
$52$	−2.97857e67	−0.491898
$53$	−1.18330e68	−0.920867	−0.460433	−	0.887694i	$-0.652306\pi$
$53$	−1.18330e68	−0.920867	−0.460433	+	0.887694i	$0.652306\pi$
$54$	9.32699e67	0.346887
$55$	−1.23164e68	−0.221900
$56$	2.03531e68	0.179971
$57$	2.68983e67	0.0118214
$58$	9.86689e69	2.18160
$59$	−1.26078e70	−1.41901	−0.709506	−	0.704700i	$-0.751082\pi$
$59$	−1.26078e70	−1.41901	−0.709506	+	0.704700i	$0.751082\pi$
$60$	2.74178e69	0.158876
$61$	2.75036e70	0.829587	0.414793	−	0.909916i	$-0.363854\pi$
$61$	2.75036e70	0.829587	0.414793	+	0.909916i	$0.363854\pi$
$62$	1.35188e71	2.14519
$63$	−1.38404e71	−1.16734
$64$	−1.79104e71	−0.810952
$65$	2.86024e70	0.0701981
$66$	−2.36984e72	−3.18225
$67$	6.88030e71	0.510097	0.255048	−	0.966928i	$-0.417909\pi$
$67$	6.88030e71	0.510097	0.255048	+	0.966928i	$0.417909\pi$
$68$	3.07495e72	1.26980
$69$	7.38332e71	0.171282
$70$	1.95757e72	0.257243
$71$	2.19266e72	0.164538	0.0822689	−	0.996610i	$-0.473783\pi$
$71$	2.19266e72	0.164538	0.0822689	+	0.996610i	$0.473783\pi$
$72$	−2.36288e72	−0.102049
$73$	1.79419e72	0.0449382	0.0224691	−	0.999748i	$-0.492847\pi$
$73$	1.79419e72	0.0449382	0.0224691	+	0.999748i	$0.492847\pi$
$74$	4.24931e73	0.621820
$75$	1.53750e74	1.32402
$76$	−1.56389e72	−0.00798124
$77$	−8.05781e74	−2.45377
$78$	5.50349e74	1.00670
$79$	−1.14491e75	−1.26620	−0.633100	−	0.774070i	$-0.718218\pi$
$79$	−1.14491e75	−1.26620	−0.633100	+	0.774070i	$0.718218\pi$
$80$	2.08746e74	0.140463
$81$	−2.79567e75	−1.15167
$82$	6.21640e74	0.157722
$83$	6.74200e75	1.05975	0.529876	−	0.848075i	$-0.322239\pi$
$83$	6.74200e75	1.05975	0.529876	+	0.848075i	$0.322239\pi$
$84$	1.79377e76	1.75685
$85$	−2.95279e75	−0.181211
$86$	3.02463e76	1.16945
$87$	−8.68211e76	−2.12625
$88$	−1.37566e76	−0.214509
$89$	3.78339e76	0.377551	0.188776	−	0.982020i	$-0.439548\pi$
$89$	3.78339e76	0.377551	0.188776	+	0.982020i	$0.439548\pi$
$90$	−2.27263e76	−0.145864
$91$	1.87127e77	0.776249
$92$	−4.29273e76	−0.115642
$93$	−1.18955e78	−2.09077
$94$	−2.43616e77	−0.280644
$95$	1.50177e75	0.00113899
$96$	3.67974e78	1.84545
$97$	−2.34072e78	−0.779588	−0.389794	−	0.920902i	$-0.627454\pi$
$97$	−2.34072e78	−0.779588	−0.389794	+	0.920902i	$0.627454\pi$
$98$	6.58610e78	1.46284
$99$	9.35467e78	1.39136
$100$	−8.93915e78	−0.893915
$101$	2.64076e78	0.178252	0.0891259	−	0.996020i	$-0.471593\pi$
$101$	2.64076e78	0.178252	0.0891259	+	0.996020i	$0.471593\pi$
$102$	−5.68158e79	−2.59874
$103$	2.61273e79	0.812877	0.406439	−	0.913678i	$-0.366770\pi$
$103$	2.61273e79	0.812877	0.406439	+	0.913678i	$0.366770\pi$
$104$	3.19469e78	0.0678598
$105$	−1.72251e79	−0.250717
$106$	−1.27118e80	−1.27240
$107$	1.65210e80	1.14124	0.570620	−	0.821215i	$-0.306703\pi$
$107$	1.65210e80	1.14124	0.570620	+	0.821215i	$0.306703\pi$
$108$	4.77165e79	0.228260
$109$	2.81435e80	0.935473	0.467736	−	0.883868i	$-0.345070\pi$
$109$	2.81435e80	0.935473	0.467736	+	0.883868i	$0.345070\pi$
$110$	−1.32311e80	−0.306610
$111$	−3.73906e80	−0.606045
$112$	1.36568e81	1.55324
$113$	−1.19335e81	−0.955369	−0.477684	−	0.878532i	$-0.658524\pi$
$113$	−1.19335e81	−0.955369	−0.477684	+	0.878532i	$0.658524\pi$
$114$	2.88960e79	0.0163342
$115$	4.12220e79	0.0165030
$116$	5.04785e81	1.43554
$117$	−2.17244e81	−0.440155
$118$	−1.35442e82	−1.96071
$119$	−1.93182e82	−2.00383
$120$	−2.94073e80	−0.0219177
$121$	3.58407e82	1.92466
$122$	2.95463e82	1.14628
$123$	−5.46996e81	−0.153721
$124$	6.91615e82	1.41159
$125$	1.73151e82	0.257323
$126$	−1.48683e83	−1.61296
$127$	−2.81311e81	−0.0223326	−0.0111663	−	0.999938i	$-0.503554\pi$
$127$	−2.81311e81	−0.0223326	−0.0111663	+	0.999938i	$0.503554\pi$
$128$	4.28981e82	0.249830
$129$	−2.66144e83	−1.13979
$130$	3.07267e82	0.0969959
$131$	6.71513e83	1.56617	0.783084	−	0.621916i	$-0.213645\pi$
$131$	6.71513e83	1.56617	0.783084	+	0.621916i	$0.213645\pi$
$132$	−1.21240e84	−2.09400
$133$	9.82507e81	0.0125949
$134$	7.39129e83	0.704824
$135$	−4.58209e82	−0.0325747
$136$	−3.29807e83	−0.175175
$137$	9.25833e83	0.368188	0.184094	−	0.982909i	$-0.441065\pi$
$137$	9.25833e83	0.368188	0.184094	+	0.982909i	$0.441065\pi$
$138$	7.93167e83	0.236669
$139$	3.22747e84	0.724064	0.362032	−	0.932166i	$-0.382083\pi$
$139$	3.22747e84	0.724064	0.362032	+	0.932166i	$0.382083\pi$
$140$	1.00148e84	0.169272
$141$	2.14364e84	0.273524
$142$	2.35550e84	0.227349
$143$	−1.26478e85	−0.925215
$144$	−1.58548e85	−0.880731
$145$	−4.84733e84	−0.204864
$146$	1.92744e84	0.0620932
$147$	−5.79526e85	−1.42573
$148$	2.17393e85	0.409173
$149$	−2.07212e85	−0.298921	−0.149461	−	0.988768i	$-0.547754\pi$
$149$	−2.07212e85	−0.298921	−0.149461	+	0.988768i	$0.547754\pi$
$150$	1.65169e86	1.82946
$151$	1.95573e86	1.66617	0.833083	−	0.553148i	$-0.186573\pi$
$151$	1.95573e86	1.66617	0.833083	+	0.553148i	$0.186573\pi$
$152$	1.67737e83	0.00110105
$153$	2.24273e86	1.13623
$154$	−8.65626e86	−3.39048
$155$	−6.64140e85	−0.201446
$156$	2.81556e86	0.662435
$157$	4.73993e86	0.866434	0.433217	−	0.901290i	$-0.357378\pi$
$157$	4.73993e86	0.866434	0.433217	+	0.901290i	$0.357378\pi$
$158$	−1.22994e87	−1.74957
$159$	1.11854e87	1.24012
$160$	2.05444e86	0.177809
$161$	2.69688e86	0.182490
$162$	−3.00330e87	−1.59131
$163$	−1.40881e87	−0.585384	−0.292692	−	0.956207i	$-0.594551\pi$
$163$	−1.40881e87	−0.585384	−0.292692	+	0.956207i	$0.594551\pi$
$164$	3.18028e86	0.103785
$165$	1.16424e87	0.298831
$166$	7.24272e87	1.46431
$167$	9.17896e87	1.46384	0.731919	−	0.681392i	$-0.238625\pi$
$167$	9.17896e87	1.46384	0.731919	+	0.681392i	$0.238625\pi$
$168$	−1.92393e87	−0.242366
$169$	−7.09796e87	−0.707308
$170$	−3.17209e87	−0.250388
$171$	−1.14064e86	−0.00714168
$172$	1.54739e88	0.769529
$173$	−1.24224e88	−0.491343	−0.245671	−	0.969353i	$-0.579008\pi$
$173$	−1.24224e88	−0.491343	−0.245671	+	0.969353i	$0.579008\pi$
$174$	−9.32692e88	−2.93794
$175$	5.61597e88	1.41066
$176$	−9.23062e88	−1.85132
$177$	1.19179e89	1.91097
$178$	4.06438e88	0.521680
$179$	−2.32290e88	−0.238966	−0.119483	−	0.992836i	$-0.538124\pi$
$179$	−2.32290e88	−0.238966	−0.119483	+	0.992836i	$0.538124\pi$
$180$	−1.16266e88	−0.0959822
$181$	2.15390e89	1.42864	0.714319	−	0.699820i	$-0.246736\pi$
$181$	2.15390e89	1.42864	0.714319	+	0.699820i	$0.246736\pi$
$182$	2.01024e89	1.07258
$183$	−2.59985e89	−1.11720
$184$	4.60421e87	0.0159533
$185$	−2.08756e88	−0.0583925
$186$	−1.27790e90	−2.88891
$187$	1.30571e90	2.38838
$188$	−1.24633e89	−0.184671
$189$	−2.99776e89	−0.360210
$190$	1.61330e87	0.00157380
$191$	−6.43448e89	−0.510147	−0.255073	−	0.966922i	$-0.582100\pi$
$191$	−6.43448e89	−0.510147	−0.255073	+	0.966922i	$0.582100\pi$
$192$	1.69302e90	1.09210
$193$	−1.16176e90	−0.610384	−0.305192	−	0.952291i	$-0.598721\pi$
$193$	−1.16176e90	−0.610384	−0.305192	+	0.952291i	$0.598721\pi$
$194$	−2.51456e90	−1.07719
$195$	−2.70371e89	−0.0945352
$196$	3.36942e90	0.962587
$197$	−4.05869e90	−0.948352	−0.474176	−	0.880430i	$-0.657254\pi$
$197$	−4.05869e90	−0.948352	−0.474176	+	0.880430i	$0.657254\pi$
$198$	1.00494e91	1.92250
$199$	1.10053e91	1.72546	0.862732	−	0.505661i	$-0.168751\pi$
$199$	1.10053e91	1.72546	0.862732	+	0.505661i	$0.168751\pi$
$200$	9.58778e89	0.123320
$201$	−6.50377e90	−0.686943
$202$	2.83688e90	0.246299
$203$	−3.17129e91	−2.26538
$204$	−2.90667e91	−1.71003
$205$	−3.05394e89	−0.0148110
$206$	2.80678e91	1.12319
$207$	−3.13093e90	−0.103477
$208$	2.14363e91	0.585663
$209$	−6.64073e89	−0.0150120
$210$	−1.85044e91	−0.346428
$211$	1.10259e92	1.71103	0.855515	−	0.517778i	$-0.173241\pi$
$211$	1.10259e92	1.71103	0.855515	+	0.517778i	$0.173241\pi$
$212$	−6.50329e91	−0.837273
$213$	−2.07266e91	−0.221582
$214$	1.77480e92	1.57690
$215$	−1.48592e91	−0.109818
$216$	−5.11788e90	−0.0314896
$217$	−4.34503e92	−2.22758
$218$	3.02337e92	1.29259
$219$	−1.69600e91	−0.0605179
$220$	−6.76899e91	−0.201757
$221$	−3.03225e92	−0.755563
$222$	−4.01676e92	−0.837401
$223$	3.25670e92	0.568506	0.284253	−	0.958749i	$-0.408254\pi$
$223$	3.25670e92	0.568506	0.284253	+	0.958749i	$0.408254\pi$
$224$	1.34409e93	1.96621
$225$	−6.51982e92	−0.799883
$226$	−1.28198e93	−1.32008
$227$	2.79664e92	0.241889	0.120944	−	0.992659i	$-0.461408\pi$
$227$	2.79664e92	0.241889	0.120944	+	0.992659i	$0.461408\pi$
$228$	1.47831e91	0.0107483
$229$	−3.76585e92	−0.230336	−0.115168	−	0.993346i	$-0.536741\pi$
$229$	−3.76585e92	−0.230336	−0.115168	+	0.993346i	$0.536741\pi$
$230$	4.42835e91	0.0228030
$231$	7.61685e93	3.30447
$232$	−5.41413e92	−0.198040
$233$	−1.66591e93	−0.514152	−0.257076	−	0.966391i	$-0.582759\pi$
$233$	−1.66591e93	−0.514152	−0.257076	+	0.966391i	$0.582759\pi$
$234$	−2.33378e93	−0.608182
$235$	1.19682e92	0.0263541
$236$	−6.92915e93	−1.29020
$237$	1.08226e94	1.70518
$238$	−2.07529e94	−2.76879
$239$	−5.22899e93	−0.591154	−0.295577	−	0.955319i	$-0.595512\pi$
$239$	−5.22899e93	−0.591154	−0.295577	+	0.955319i	$0.595512\pi$
$240$	−1.97322e93	−0.189161
$241$	−1.47011e94	−1.19585	−0.597924	−	0.801553i	$-0.704007\pi$
$241$	−1.47011e94	−1.19585	−0.597924	+	0.801553i	$0.704007\pi$
$242$	3.85026e94	2.65939
$243$	2.21490e94	1.29989
$244$	1.51158e94	0.754279
$245$	−3.23557e93	−0.137369
$246$	−5.87621e93	−0.212403
$247$	1.54218e92	0.00474903
$248$	−7.41799e93	−0.194735
$249$	−6.37304e94	−1.42716
$250$	1.86010e94	0.355555
$251$	7.60703e94	1.24195	0.620974	−	0.783831i	$-0.286737\pi$
$251$	7.60703e94	1.24195	0.620974	+	0.783831i	$0.286737\pi$
$252$	−7.60655e94	−1.06137
$253$	−1.82281e94	−0.217511
$254$	−3.02203e93	−0.0308580
$255$	2.79120e94	0.244036
$256$	1.54346e95	1.15615
$257$	−1.43756e95	−0.923138	−0.461569	−	0.887104i	$-0.652713\pi$
$257$	−1.43756e95	−0.923138	−0.461569	+	0.887104i	$0.652713\pi$
$258$	−2.85910e95	−1.57490
$259$	−1.36576e95	−0.645703
$260$	1.57196e94	0.0638256
$261$	3.68169e95	1.28454
$262$	7.21386e95	2.16405
$263$	−4.82305e95	−1.24471	−0.622357	−	0.782733i	$-0.713825\pi$
$263$	−4.82305e95	−1.24471	−0.622357	+	0.782733i	$0.713825\pi$
$264$	1.30038e95	0.288877
$265$	6.24495e94	0.119486
$266$	1.05548e94	0.0174030
$267$	−3.57634e95	−0.508446
$268$	3.78135e95	0.463791
$269$	8.60187e95	0.910705	0.455352	−	0.890311i	$-0.349513\pi$
$269$	8.60187e95	0.910705	0.455352	+	0.890311i	$0.349513\pi$
$270$	−4.92240e94	−0.0450099
$271$	−2.49307e95	−0.196991	−0.0984956	−	0.995137i	$-0.531403\pi$
$271$	−2.49307e95	−0.196991	−0.0984956	+	0.995137i	$0.531403\pi$
$272$	−2.21299e96	−1.51185
$273$	−1.76886e96	−1.04537
$274$	9.94593e95	0.508743
$275$	−3.79582e96	−1.68137
$276$	4.05781e95	0.155734
$277$	1.60114e96	0.532696	0.266348	−	0.963877i	$-0.414183\pi$
$277$	1.60114e96	0.532696	0.266348	+	0.963877i	$0.414183\pi$
$278$	3.46717e96	1.00047
$279$	5.04434e96	1.26310
$280$	−1.07415e95	−0.0233519
$281$	6.93177e96	1.30901	0.654507	−	0.756056i	$-0.272876\pi$
$281$	6.93177e96	1.30901	0.654507	+	0.756056i	$0.272876\pi$
$282$	2.30284e96	0.377941
$283$	−8.40692e96	−1.19970	−0.599850	−	0.800112i	$-0.704773\pi$
$283$	−8.40692e96	−1.19970	−0.599850	+	0.800112i	$0.704773\pi$
$284$	1.20506e96	0.149601
$285$	−1.41958e94	−0.00153387
$286$	−1.35872e97	−1.27841
$287$	−1.99799e96	−0.163779
$288$	−1.56041e97	−1.11490
$289$	1.52541e97	0.950433
$290$	−5.20733e96	−0.283070
$291$	2.21262e97	1.04987
$292$	9.86071e95	0.0408588
$293$	1.87676e97	0.679420	0.339710	−	0.940530i	$-0.389671\pi$
$293$	1.87676e97	0.679420	0.339710	+	0.940530i	$0.389671\pi$
$294$	−6.22567e97	−1.97000
$295$	6.65389e96	0.184122
$296$	−2.33167e96	−0.0564474
$297$	2.02618e97	0.429336
$298$	−2.22601e97	−0.413033
$299$	4.23312e96	0.0688096
$300$	8.44995e97	1.20383
$301$	−9.72137e97	−1.21437
$302$	2.10098e98	2.30222
$303$	−2.49624e97	−0.240050
$304$	1.12551e96	0.00950261
$305$	−1.45153e97	−0.107642
$306$	2.40930e98	1.56998
$307$	−2.23594e98	−1.28084	−0.640419	−	0.768026i	$-0.721239\pi$
$307$	−2.23594e98	−1.28084	−0.640419	+	0.768026i	$0.721239\pi$
$308$	−4.42850e98	−2.23102
$309$	−2.46975e98	−1.09470
$310$	−7.13465e97	−0.278347
$311$	2.16035e98	0.742145	0.371072	−	0.928604i	$-0.378990\pi$
$311$	2.16035e98	0.742145	0.371072	+	0.928604i	$0.378990\pi$
$312$	−3.01986e97	−0.0913863
$313$	1.95768e98	0.522085	0.261042	−	0.965327i	$-0.415934\pi$
$313$	1.95768e98	0.522085	0.261042	+	0.965327i	$0.415934\pi$
$314$	5.09196e98	1.19719
$315$	7.30438e97	0.151466
$316$	−6.29234e98	−1.15126
$317$	−7.87109e98	−1.27114	−0.635571	−	0.772042i	$-0.719235\pi$
$317$	−7.87109e98	−1.27114	−0.635571	+	0.772042i	$0.719235\pi$
$318$	1.20161e99	1.71354
$319$	2.14346e99	2.70013
$320$	9.45234e97	0.105224
$321$	−1.56169e99	−1.53690
$322$	2.89718e98	0.252155
$323$	−1.59208e97	−0.0122593
$324$	−1.53647e99	−1.04712
$325$	8.81503e98	0.531901
$326$	−1.51344e99	−0.808852
$327$	−2.66033e99	−1.25979
$328$	−3.41105e97	−0.0143176
$329$	7.82999e98	0.291423
$330$	1.25071e99	0.412909
$331$	−2.57751e99	−0.755083	−0.377542	−	0.925993i	$-0.623231\pi$
$331$	−2.57751e99	−0.755083	−0.377542	+	0.925993i	$0.623231\pi$
$332$	3.70534e99	0.963549
$333$	1.58557e99	0.366132
$334$	9.86067e99	2.02265
$335$	−3.63113e98	−0.0661869
$336$	−1.29095e100	−2.09174
$337$	−5.57083e99	−0.802673	−0.401337	−	0.915931i	$-0.631454\pi$
$337$	−5.57083e99	−0.802673	−0.401337	+	0.915931i	$0.631454\pi$
$338$	−7.62512e99	−0.977321
$339$	1.12805e100	1.28659
$340$	−1.62283e99	−0.164761
$341$	2.93679e100	2.65507
$342$	−1.22535e98	−0.00986799
$343$	−1.17354e99	−0.0842129
$344$	−1.65967e99	−0.106160
$345$	−3.89661e98	−0.0222245
$346$	−1.33450e100	−0.678911
$347$	−3.84347e99	−0.174465	−0.0872327	−	0.996188i	$-0.527802\pi$
$347$	−3.84347e99	−0.174465	−0.0872327	+	0.996188i	$0.527802\pi$
$348$	−4.77161e100	−1.93324
$349$	−2.69142e100	−0.973592	−0.486796	−	0.873516i	$-0.661834\pi$
$349$	−2.69142e100	−0.973592	−0.486796	+	0.873516i	$0.661834\pi$
$350$	6.03306e100	1.94917
$351$	−4.70539e99	−0.135820
$352$	−9.08464e100	−2.34354
$353$	−1.75149e100	−0.403930	−0.201965	−	0.979393i	$-0.564733\pi$
$353$	−1.75149e100	−0.403930	−0.201965	+	0.979393i	$0.564733\pi$
$354$	1.28030e101	2.64048
$355$	−1.15719e99	−0.0213494
$356$	2.07932e100	0.343278
$357$	1.82610e101	2.69855
$358$	−2.49542e100	−0.330190
$359$	−7.68429e100	−0.910695	−0.455348	−	0.890314i	$-0.650485\pi$
$359$	−7.68429e100	−0.910695	−0.455348	+	0.890314i	$0.650485\pi$
$360$	1.24703e99	0.0132412
$361$	−1.05075e101	−0.999923
$362$	2.31387e101	1.97402
$363$	−3.38793e101	−2.59193
$364$	1.02843e101	0.705783
$365$	−9.46899e98	−0.00583090
$366$	−2.79294e101	−1.54368
$367$	6.39679e100	0.317434	0.158717	−	0.987324i	$-0.449264\pi$
$367$	6.39679e100	0.317434	0.158717	+	0.987324i	$0.449264\pi$
$368$	3.08941e100	0.137685
$369$	2.31956e100	0.0928676
$370$	−2.24261e100	−0.0806835
$371$	4.08566e101	1.32127
$372$	−6.53766e101	−1.90097
$373$	−4.25955e101	−1.11395	−0.556974	−	0.830530i	$-0.688038\pi$
$373$	−4.25955e101	−1.11395	−0.556974	+	0.830530i	$0.688038\pi$
$374$	1.40268e102	3.30013
$375$	−1.63675e101	−0.346535
$376$	1.33676e100	0.0254762
$377$	−4.97777e101	−0.854184
$378$	−3.22040e101	−0.497719
$379$	1.34244e102	1.86916	0.934579	−	0.355757i	$-0.115777\pi$
$379$	1.34244e102	1.86916	0.934579	+	0.355757i	$0.115777\pi$
$380$	8.25358e98	0.00103560
$381$	2.65916e100	0.0300751
$382$	−6.91236e101	−0.704893
$383$	1.72528e101	0.158675	0.0793375	−	0.996848i	$-0.474720\pi$
$383$	1.72528e101	0.158675	0.0793375	+	0.996848i	$0.474720\pi$
$384$	−4.05505e101	−0.336444
$385$	4.25258e101	0.318386
$386$	−1.24804e102	−0.843396
$387$	1.12860e102	0.688582
$388$	−1.28644e102	−0.708819
$389$	1.98658e102	0.988776	0.494388	−	0.869241i	$-0.335392\pi$
$389$	1.98658e102	0.988776	0.494388	+	0.869241i	$0.335392\pi$
$390$	−2.90452e101	−0.130624
$391$	−4.37010e101	−0.177627
$392$	−3.61391e101	−0.132794
$393$	−6.34765e102	−2.10915
$394$	−4.36012e102	−1.31038
$395$	6.04237e101	0.164294
$396$	5.14124e102	1.26505
$397$	2.24529e102	0.500089	0.250045	−	0.968234i	$-0.419555\pi$
$397$	2.24529e102	0.500089	0.250045	+	0.968234i	$0.419555\pi$
$398$	1.18227e103	2.38415
$399$	−9.28739e100	−0.0169615
$400$	6.43337e102	1.06431
$401$	6.69315e102	1.00329	0.501647	−	0.865072i	$-0.332728\pi$
$401$	6.69315e102	1.00329	0.501647	+	0.865072i	$0.332728\pi$
$402$	−6.98680e102	−0.949181
$403$	−6.82012e102	−0.839929
$404$	1.45134e102	0.162071
$405$	1.47544e102	0.149433
$406$	−3.40681e103	−3.13019
$407$	9.23111e102	0.769617
$408$	3.11758e102	0.235907
$409$	−1.88536e103	−1.29516	−0.647579	−	0.761998i	$-0.724218\pi$
$409$	−1.88536e103	−1.29516	−0.647579	+	0.761998i	$0.724218\pi$
$410$	−3.28076e101	−0.0204650
$411$	−8.75166e102	−0.495837
$412$	1.43594e103	0.739086
$413$	4.35320e103	2.03602
$414$	−3.36346e102	−0.142979
$415$	−3.55815e102	−0.137507
$416$	2.10973e103	0.741378
$417$	−3.05084e103	−0.975092
$418$	−7.13394e101	−0.0207427
$419$	−2.58746e103	−0.684574	−0.342287	−	0.939596i	$-0.611201\pi$
$419$	−2.58746e103	−0.684574	−0.342287	+	0.939596i	$0.611201\pi$
$420$	−9.46676e102	−0.227958
$421$	1.62093e103	0.355321	0.177661	−	0.984092i	$-0.443147\pi$
$421$	1.62093e103	0.355321	0.177661	+	0.984092i	$0.443147\pi$
$422$	1.18448e104	2.36421
$423$	−9.09018e102	−0.165245
$424$	6.97518e102	0.115506
$425$	−9.10027e103	−1.37307
$426$	−2.22660e103	−0.306170
$427$	−9.49639e103	−1.19030
$428$	9.07979e103	1.03764
$429$	1.19557e104	1.24598
$430$	−1.59627e103	−0.151741
$431$	−8.45501e103	−0.733267	−0.366633	−	0.930366i	$-0.619490\pi$
$431$	−8.45501e103	−0.733267	−0.366633	+	0.930366i	$0.619490\pi$
$432$	−3.43408e103	−0.271771
$433$	1.02517e104	0.740498	0.370249	−	0.928932i	$-0.379272\pi$
$433$	1.02517e104	0.740498	0.370249	+	0.928932i	$0.379272\pi$
$434$	−4.66773e104	−3.07795
$435$	4.58205e103	0.275889
$436$	1.54674e104	0.850552
$437$	2.22260e101	0.00111646
$438$	−1.82196e103	−0.0836204
$439$	2.73039e104	1.14519	0.572594	−	0.819839i	$-0.305937\pi$
$439$	2.73039e104	1.14519	0.572594	+	0.819839i	$0.305937\pi$
$440$	7.26016e102	0.0278333
$441$	2.45751e104	0.861332
$442$	−3.25746e104	−1.04400
$443$	4.57824e104	1.34200	0.670999	−	0.741459i	$-0.265866\pi$
$443$	4.57824e104	1.34200	0.670999	+	0.741459i	$0.265866\pi$
$444$	−2.05496e104	−0.551030
$445$	−1.99672e103	−0.0489887
$446$	3.49857e104	0.785531
$447$	1.95872e104	0.402555
$448$	6.18404e104	1.16357
$449$	−6.26982e104	−1.08025	−0.540125	−	0.841585i	$-0.681623\pi$
$449$	−6.26982e104	−1.08025	−0.540125	+	0.841585i	$0.681623\pi$
$450$	−7.00405e104	−1.10524
$451$	1.35044e104	0.195210
$452$	−6.55857e104	−0.868643
$453$	−1.84870e105	−2.24381
$454$	3.00435e104	0.334229
$455$	−9.87577e103	−0.100721
$456$	−1.58558e102	−0.00148278
$457$	1.20539e105	1.03381	0.516903	−	0.856044i	$-0.327085\pi$
$457$	1.20539e105	1.03381	0.516903	+	0.856044i	$0.327085\pi$
$458$	−4.04554e104	−0.318266
$459$	4.85765e104	0.350611
$460$	2.26552e103	0.0150049
$461$	−5.78357e104	−0.351568	−0.175784	−	0.984429i	$-0.556246\pi$
$461$	−5.78357e104	−0.351568	−0.175784	+	0.984429i	$0.556246\pi$
$462$	8.18254e105	4.56594
$463$	−6.25930e104	−0.320683	−0.160342	−	0.987062i	$-0.551260\pi$
$463$	−6.25930e104	−0.320683	−0.160342	+	0.987062i	$0.551260\pi$
$464$	−3.63286e105	−1.70918
$465$	6.27795e104	0.271285
$466$	−1.78963e105	−0.710428
$467$	−3.28434e104	−0.119793	−0.0598965	−	0.998205i	$-0.519077\pi$
$467$	−3.28434e104	−0.119793	−0.0598965	+	0.998205i	$0.519077\pi$
$468$	−1.19395e105	−0.400199
$469$	−2.37561e105	−0.731894
$470$	1.28570e104	0.0364146
$471$	−4.48054e105	−1.16682
$472$	7.43194e104	0.177989
$473$	6.57064e105	1.44741
$474$	1.16263e106	2.35613
$475$	4.62832e103	0.00863030
$476$	−1.06171e106	−1.82193
$477$	−4.74322e105	−0.749199
$478$	−5.61734e105	−0.816824
$479$	4.93334e105	0.660524	0.330262	−	0.943889i	$-0.392863\pi$
$479$	4.93334e105	0.660524	0.330262	+	0.943889i	$0.392863\pi$
$480$	−1.94201e105	−0.239454
$481$	−2.14374e105	−0.243468
$482$	−1.57929e106	−1.65236
$483$	−2.54929e105	−0.245758
$484$	1.96977e106	1.74995
$485$	1.23533e105	0.101155
$486$	2.37940e106	1.79612
$487$	3.06992e105	0.213665	0.106832	−	0.994277i	$-0.465929\pi$
$487$	3.06992e105	0.213665	0.106832	+	0.994277i	$0.465929\pi$
$488$	−1.62126e105	−0.104056
$489$	1.33171e106	0.788332
$490$	−3.47587e105	−0.189810
$491$	−3.10863e106	−1.56621	−0.783106	−	0.621888i	$-0.786366\pi$
$491$	−3.10863e106	−1.56621	−0.783106	+	0.621888i	$0.786366\pi$
$492$	−3.00624e105	−0.139766
$493$	5.13884e106	2.20502
$494$	1.65672e104	0.00656196
$495$	−4.93701e105	−0.180534
$496$	−4.97745e106	−1.68066
$497$	−7.57075e105	−0.236081
$498$	−6.84636e106	−1.97197
$499$	4.21073e106	1.12043	0.560217	−	0.828346i	$-0.310718\pi$
$499$	4.21073e106	1.12043	0.560217	+	0.828346i	$0.310718\pi$
$500$	9.51621e105	0.233964
$501$	−8.67664e106	−1.97134
$502$	8.17200e106	1.71606
$503$	−1.73268e106	−0.336344	−0.168172	−	0.985758i	$-0.553786\pi$
$503$	−1.73268e106	−0.336344	−0.168172	+	0.985758i	$0.553786\pi$
$504$	8.15849e105	0.146421
$505$	−1.39368e105	−0.0231288
$506$	−1.95819e106	−0.300545
$507$	6.70952e106	0.952527
$508$	−1.54606e105	−0.0203053
$509$	1.10439e107	1.34205	0.671027	−	0.741433i	$-0.265853\pi$
$509$	1.10439e107	1.34205	0.671027	+	0.741433i	$0.265853\pi$
$510$	2.99850e106	0.337196
$511$	−6.19494e105	−0.0644780
$512$	1.39878e107	1.34768
$513$	−2.47056e104	−0.00220374
$514$	−1.54432e107	−1.27554
$515$	−1.37889e106	−0.105474
$516$	−1.46270e107	−1.03632
$517$	−5.29227e106	−0.347348
$518$	−1.46719e107	−0.892197
$519$	1.17426e107	0.661688
$520$	−1.68603e105	−0.00880506
$521$	−1.38091e107	−0.668462	−0.334231	−	0.942491i	$-0.608477\pi$
$521$	−1.38091e107	−0.668462	−0.334231	+	0.942491i	$0.608477\pi$
$522$	3.95512e107	1.77490
$523$	−3.33514e107	−1.38771	−0.693854	−	0.720116i	$-0.744089\pi$
$523$	−3.33514e107	−1.38771	−0.693854	+	0.720116i	$0.744089\pi$
$524$	3.69058e107	1.42400
$525$	−5.30863e107	−1.89972
$526$	−5.18125e107	−1.71988
$527$	7.04081e107	2.16822
$528$	8.72547e107	2.49315
$529$	−3.71036e107	−0.983823
$530$	6.70875e106	0.165099
$531$	−5.05382e107	−1.15448
$532$	5.39977e105	0.0114516
$533$	−3.13613e106	−0.0617545
$534$	−3.84196e107	−0.702543
$535$	−8.71909e106	−0.148080
$536$	−4.05573e106	−0.0639823
$537$	2.19578e107	0.321813
$538$	9.24072e107	1.25836
$539$	1.43075e108	1.81054
$540$	−2.51828e106	−0.0296176
$541$	1.58373e108	1.73137	0.865683	−	0.500593i	$-0.166885\pi$
$541$	1.58373e108	1.73137	0.865683	+	0.500593i	$0.166885\pi$
$542$	−2.67822e107	−0.272192
$543$	−2.03603e108	−1.92394
$544$	−2.17799e108	−1.91382
$545$	−1.48530e107	−0.121381
$546$	−1.90023e108	−1.44443
$547$	5.10706e107	0.361137	0.180568	−	0.983562i	$-0.442206\pi$
$547$	5.10706e107	0.361137	0.180568	+	0.983562i	$0.442206\pi$
$548$	5.08829e107	0.334765
$549$	1.10248e108	0.674936
$550$	−4.07773e108	−2.32323
$551$	−2.61357e106	−0.0138595
$552$	−4.35225e106	−0.0214842
$553$	3.95313e108	1.81676
$554$	1.72006e108	0.736050
$555$	1.97332e107	0.0786367
$556$	1.77379e108	0.658336
$557$	1.85707e108	0.642020	0.321010	−	0.947076i	$-0.395978\pi$
$557$	1.85707e108	0.642020	0.321010	+	0.947076i	$0.395978\pi$
$558$	5.41898e108	1.74529
$559$	−1.52590e108	−0.457889
$560$	−7.20752e107	−0.201539
$561$	−1.23425e109	−3.21641
$562$	7.44658e108	1.80873
$563$	−1.49916e108	−0.339442	−0.169721	−	0.985492i	$-0.554287\pi$
$563$	−1.49916e108	−0.339442	−0.169721	+	0.985492i	$0.554287\pi$
$564$	1.17812e108	0.248694
$565$	6.29803e107	0.123963
$566$	−9.03129e108	−1.65768
$567$	9.65281e108	1.65243
$568$	−1.29251e107	−0.0206383
$569$	−4.95282e108	−0.737765	−0.368882	−	0.929476i	$-0.620259\pi$
$569$	−4.95282e108	−0.737765	−0.368882	+	0.929476i	$0.620259\pi$
$570$	−1.52501e106	−0.00211942
$571$	−8.59128e108	−1.11412	−0.557059	−	0.830473i	$-0.688070\pi$
$571$	−8.59128e108	−1.11412	−0.557059	+	0.830473i	$0.688070\pi$
$572$	−6.95114e108	−0.841227
$573$	6.08235e108	0.687011
$574$	−2.14638e108	−0.226302
$575$	1.27043e108	0.125046
$576$	−7.17933e108	−0.659775
$577$	1.49177e109	1.28014	0.640068	−	0.768318i	$-0.278906\pi$
$577$	1.49177e109	1.28014	0.640068	+	0.768318i	$0.278906\pi$
$578$	1.63870e109	1.31326
$579$	1.09818e109	0.821999
$580$	−2.66405e108	−0.186267
$581$	−2.32786e109	−1.52055
$582$	2.37695e109	1.45065
$583$	−2.76148e109	−1.57483
$584$	−1.05762e107	−0.00563668
$585$	1.14652e108	0.0571118
$586$	2.01615e109	0.938786
$587$	1.47270e109	0.641078	0.320539	−	0.947235i	$-0.396136\pi$
$587$	1.47270e109	0.641078	0.320539	+	0.947235i	$0.396136\pi$
$588$	−3.18502e109	−1.29631
$589$	−3.58090e107	−0.0136282
$590$	7.14807e108	0.254410
$591$	3.83657e109	1.27714
$592$	−1.56454e109	−0.487169
$593$	−2.01675e109	−0.587479	−0.293739	−	0.955886i	$-0.594900\pi$
$593$	−2.01675e109	−0.587479	−0.293739	+	0.955886i	$0.594900\pi$
$594$	2.17666e109	0.593234
$595$	1.01953e109	0.260005
$596$	−1.13882e109	−0.271786
$597$	−1.04030e110	−2.32367
$598$	4.54751e108	0.0950774
$599$	4.23335e109	0.828562	0.414281	−	0.910149i	$-0.364033\pi$
$599$	4.23335e109	0.828562	0.414281	+	0.910149i	$0.364033\pi$
$600$	−9.06309e108	−0.166074
$601$	−3.70845e109	−0.636284	−0.318142	−	0.948043i	$-0.603059\pi$
$601$	−3.70845e109	−0.636284	−0.318142	+	0.948043i	$0.603059\pi$
$602$	−1.04434e110	−1.67795
$603$	2.75795e109	0.415005
$604$	1.07485e110	1.51492
$605$	−1.89152e109	−0.249732
$606$	−2.68163e109	−0.331689
$607$	8.28290e109	0.959907	0.479954	−	0.877294i	$-0.340654\pi$
$607$	8.28290e109	0.959907	0.479954	+	0.877294i	$0.340654\pi$
$608$	1.10771e108	0.0120291
$609$	2.99774e110	3.05078
$610$	−1.55933e109	−0.148734
$611$	1.22902e109	0.109884
$612$	1.23259e110	1.03309
$613$	−9.01285e109	−0.708228	−0.354114	−	0.935202i	$-0.615218\pi$
$613$	−9.01285e109	−0.708228	−0.354114	+	0.935202i	$0.615218\pi$
$614$	−2.40200e110	−1.76979
$615$	2.88682e108	0.0199458
$616$	4.74984e109	0.307780
$617$	−1.09544e110	−0.665772	−0.332886	−	0.942967i	$-0.608022\pi$
$617$	−1.09544e110	−0.665772	−0.332886	+	0.942967i	$0.608022\pi$
$618$	−2.65318e110	−1.51259
$619$	−1.54129e110	−0.824333	−0.412166	−	0.911109i	$-0.635228\pi$
$619$	−1.54129e110	−0.824333	−0.412166	+	0.911109i	$0.635228\pi$
$620$	−3.65005e109	−0.183159
$621$	−6.78144e108	−0.0319304
$622$	2.32080e110	1.02546
$623$	−1.30632e110	−0.541716
$624$	−2.02632e110	−0.788708
$625$	2.59945e110	0.949775
$626$	2.10308e110	0.721389
$627$	6.27732e108	0.0202165
$628$	2.60502e110	0.787781
$629$	2.21311e110	0.628496
$630$	7.84686e109	0.209288
$631$	3.18856e110	0.798795	0.399398	−	0.916778i	$-0.369219\pi$
$631$	3.18856e110	0.798795	0.399398	+	0.916778i	$0.369219\pi$
$632$	6.74892e109	0.158822
$633$	−1.04225e111	−2.30423
$634$	−8.45567e110	−1.75640
$635$	1.48464e108	0.00289774
$636$	6.14740e110	1.12755
$637$	−3.32263e110	−0.572763
$638$	2.30266e111	3.73089
$639$	8.78921e109	0.133865
$640$	−2.26398e109	−0.0324164
$641$	−1.69586e110	−0.228296	−0.114148	−	0.993464i	$-0.536414\pi$
$641$	−1.69586e110	−0.228296	−0.114148	+	0.993464i	$0.536414\pi$
$642$	−1.67767e111	−2.12360
$643$	−9.91154e109	−0.117980	−0.0589899	−	0.998259i	$-0.518788\pi$
$643$	−9.91154e109	−0.117980	−0.0589899	+	0.998259i	$0.518788\pi$
$644$	1.48218e110	0.165924
$645$	1.40460e110	0.147892
$646$	−1.71032e109	−0.0169392
$647$	−6.66427e110	−0.620917	−0.310459	−	0.950587i	$-0.600483\pi$
$647$	−6.66427e110	−0.620917	−0.310459	+	0.950587i	$0.600483\pi$
$648$	1.64796e110	0.144456
$649$	−2.94231e111	−2.42674
$650$	9.46971e110	0.734953
$651$	4.10725e111	2.99987
$652$	−7.74268e110	−0.532244
$653$	−2.31996e110	−0.150110	−0.0750550	−	0.997179i	$-0.523913\pi$
$653$	−2.31996e110	−0.150110	−0.0750550	+	0.997179i	$0.523913\pi$
$654$	−2.85791e111	−1.74072
$655$	−3.54397e110	−0.203216
$656$	−2.28880e110	−0.123568
$657$	7.19198e109	0.0365608
$658$	8.41152e110	0.402672
$659$	3.59915e111	1.62265	0.811327	−	0.584593i	$-0.198746\pi$
$659$	3.59915e111	1.62265	0.811327	+	0.584593i	$0.198746\pi$
$660$	6.39855e110	0.271704
$661$	1.09300e111	0.437182	0.218591	−	0.975817i	$-0.429854\pi$
$661$	1.09300e111	0.437182	0.218591	+	0.975817i	$0.429854\pi$
$662$	−2.76894e111	−1.04333
$663$	2.86631e111	1.01751
$664$	−3.97421e110	−0.132926
$665$	−5.18526e108	−0.00163424
$666$	1.70333e111	0.505901
$667$	−7.17399e110	−0.200812
$668$	5.04468e111	1.33095
$669$	−3.07847e111	−0.765603
$670$	−3.90081e110	−0.0914536
$671$	6.41858e111	1.41873
$672$	−1.27053e112	−2.64788
$673$	−8.56268e111	−1.68273	−0.841365	−	0.540467i	$-0.818248\pi$
$673$	−8.56268e111	−1.68273	−0.841365	+	0.540467i	$0.818248\pi$
$674$	−5.98457e111	−1.10909
$675$	−1.41216e111	−0.246823
$676$	−3.90098e111	−0.643101
$677$	−5.58926e111	−0.869165	−0.434582	−	0.900632i	$-0.643104\pi$
$677$	−5.58926e111	−0.869165	−0.434582	+	0.900632i	$0.643104\pi$
$678$	1.21183e112	1.77774
$679$	8.08197e111	1.11856
$680$	1.74058e110	0.0227297
$681$	−2.64360e111	−0.325750
$682$	3.15491e112	3.66863
$683$	−9.72923e111	−1.06773	−0.533864	−	0.845570i	$-0.679261\pi$
$683$	−9.72923e111	−1.06773	−0.533864	+	0.845570i	$0.679261\pi$
$684$	−6.26883e109	−0.00649338
$685$	−4.88616e110	−0.0477738
$686$	−1.26069e111	−0.116361
$687$	3.55976e111	0.310192
$688$	−1.11363e112	−0.916216
$689$	6.41300e111	0.498198
$690$	−4.18600e110	−0.0307086
$691$	1.90980e112	1.32314	0.661568	−	0.749885i	$-0.269891\pi$
$691$	1.90980e112	1.32314	0.661568	+	0.749885i	$0.269891\pi$
$692$	−6.82724e111	−0.446740
$693$	−3.22996e112	−1.99634
$694$	−4.12892e111	−0.241067
$695$	−1.70332e111	−0.0939501
$696$	5.11784e111	0.266699
$697$	3.23761e111	0.159415
$698$	−2.89131e112	−1.34526
$699$	1.57474e112	0.692405
$700$	3.08649e112	1.28260
$701$	1.97147e112	0.774334	0.387167	−	0.922010i	$-0.373454\pi$
$701$	1.97147e112	0.774334	0.387167	+	0.922010i	$0.373454\pi$
$702$	−5.05486e111	−0.187669
$703$	−1.12557e110	−0.00395036
$704$	−4.17978e112	−1.38686
$705$	−1.13132e111	−0.0354908
$706$	−1.88157e112	−0.558129
$707$	−9.11794e111	−0.255758
$708$	6.54995e112	1.73750
$709$	−6.84549e112	−1.71743	−0.858714	−	0.512455i	$-0.828736\pi$
$709$	−6.84549e112	−1.71743	−0.858714	+	0.512455i	$0.828736\pi$
$710$	−1.24314e111	−0.0294994
$711$	−4.58936e112	−1.03016
$712$	−2.23020e111	−0.0473569
$713$	−9.82920e111	−0.197461
$714$	1.96172e113	3.72870
$715$	6.67500e111	0.120050
$716$	−1.27665e112	−0.217273
$717$	4.94283e112	0.796102
$718$	−8.25500e112	−1.25835
$719$	1.23925e113	1.78800	0.894001	−	0.448064i	$-0.147886\pi$
$719$	1.23925e113	1.78800	0.894001	+	0.448064i	$0.147886\pi$
$720$	8.36752e111	0.114278
$721$	−9.02119e112	−1.16633
$722$	−1.12879e113	−1.38164
$723$	1.38965e113	1.61044
$724$	1.18377e113	1.29895
$725$	−1.49391e113	−1.55229
$726$	−3.63955e113	−3.58138
$727$	1.56727e113	1.46061	0.730304	−	0.683122i	$-0.239378\pi$
$727$	1.56727e113	1.46061	0.730304	+	0.683122i	$0.239378\pi$
$728$	−1.10306e112	−0.0973662
$729$	−7.16279e112	−0.598887
$730$	−1.01722e111	−0.00805682
$731$	1.57528e113	1.18201
$732$	−1.42885e113	−1.01578
$733$	−8.85535e112	−0.596484	−0.298242	−	0.954490i	$-0.596400\pi$
$733$	−8.85535e112	−0.596484	−0.298242	+	0.954490i	$0.596400\pi$
$734$	6.87188e112	0.438613
$735$	3.05850e112	0.184994
$736$	3.04055e112	0.174292
$737$	1.60567e113	0.872349
$738$	2.49183e112	0.128319
$739$	−1.21483e113	−0.593006	−0.296503	−	0.955032i	$-0.595820\pi$
$739$	−1.21483e113	−0.593006	−0.296503	+	0.955032i	$0.595820\pi$
$740$	−1.14731e112	−0.0530917
$741$	−1.45778e111	−0.00639549
$742$	4.38910e113	1.82566
$743$	1.99359e113	0.786280	0.393140	−	0.919479i	$-0.371389\pi$
$743$	1.99359e113	0.786280	0.393140	+	0.919479i	$0.371389\pi$
$744$	7.01204e112	0.262249
$745$	1.09358e112	0.0387862
$746$	−4.57590e113	−1.53919
$747$	2.70252e113	0.862193
$748$	7.17607e113	2.17157
$749$	−5.70432e113	−1.63747
$750$	−1.75831e113	−0.478823
$751$	−5.55602e113	−1.43544	−0.717722	−	0.696330i	$-0.754815\pi$
$751$	−5.55602e113	−1.43544	−0.717722	+	0.696330i	$0.754815\pi$
$752$	8.96964e112	0.219872
$753$	−7.19074e113	−1.67252
$754$	−5.34746e113	−1.18026
$755$	−1.03215e113	−0.216191
$756$	−1.64754e113	−0.327511
$757$	2.27184e113	0.428638	0.214319	−	0.976764i	$-0.431247\pi$
$757$	2.27184e113	0.428638	0.214319	+	0.976764i	$0.431247\pi$
$758$	1.44214e114	2.58270
$759$	1.72306e113	0.292921
$760$	−8.85247e109	−0.000142866 0
$761$	7.74048e113	1.18597	0.592986	−	0.805213i	$-0.297949\pi$
$761$	7.74048e113	1.18597	0.592986	+	0.805213i	$0.297949\pi$
$762$	2.85665e112	0.0415562
$763$	−9.71731e113	−1.34223
$764$	−3.53633e113	−0.463837
$765$	−1.18362e113	−0.147430
$766$	1.85342e113	0.219248
$767$	6.83294e113	0.767699
$768$	−1.45899e114	−1.55698
$769$	−1.04163e113	−0.105590	−0.0527952	−	0.998605i	$-0.516813\pi$
$769$	−1.04163e113	−0.105590	−0.0527952	+	0.998605i	$0.516813\pi$
$770$	4.56841e113	0.439928
$771$	1.35889e114	1.24318
$772$	−6.38494e113	−0.554975
$773$	2.18648e113	0.180574	0.0902870	−	0.995916i	$-0.471222\pi$
$773$	2.18648e113	0.180574	0.0902870	+	0.995916i	$0.471222\pi$
$774$	1.21242e114	0.951445
$775$	−2.04683e114	−1.52638
$776$	1.37978e113	0.0977851
$777$	1.29101e114	0.869563
$778$	2.13413e114	1.36624
$779$	−1.64662e111	−0.00100199
$780$	−1.48594e113	−0.0859535
$781$	5.11704e113	0.281387
$782$	−4.69466e113	−0.245436
$783$	7.97436e113	0.396375
$784$	−2.42492e114	−1.14607
$785$	−2.50154e113	−0.112423
$786$	−6.81908e114	−2.91431
$787$	−3.25635e114	−1.32352	−0.661759	−	0.749717i	$-0.730190\pi$
$787$	−3.25635e114	−1.32352	−0.661759	+	0.749717i	$0.730190\pi$
$788$	−2.23062e114	−0.862263
$789$	4.55911e114	1.67625
$790$	6.49113e113	0.227013
$791$	4.12039e114	1.37078
$792$	−5.51430e113	−0.174520
$793$	−1.49059e114	−0.448814
$794$	2.41205e114	0.690997
$795$	−5.90319e113	−0.160911
$796$	6.04842e114	1.56883
$797$	−1.79961e114	−0.444197	−0.222099	−	0.975024i	$-0.571291\pi$
$797$	−1.79961e114	−0.444197	−0.222099	+	0.975024i	$0.571291\pi$
$798$	−9.97715e112	−0.0234365
$799$	−1.26879e114	−0.283657
$800$	6.33162e114	1.34729
$801$	1.51657e114	0.307168
$802$	7.19025e114	1.38630
$803$	4.18714e113	0.0768517
$804$	−3.57441e114	−0.624584
$805$	−1.42330e113	−0.0236788
$806$	−7.32664e114	−1.16057
$807$	−8.13113e114	−1.22644
$808$	−1.55665e113	−0.0223584
$809$	−1.12931e114	−0.154471	−0.0772354	−	0.997013i	$-0.524609\pi$
$809$	−1.12931e114	−0.154471	−0.0772354	+	0.997013i	$0.524609\pi$
$810$	1.58502e114	0.206479
$811$	−3.63218e114	−0.450654	−0.225327	−	0.974283i	$-0.572345\pi$
$811$	−3.63218e114	−0.450654	−0.225327	+	0.974283i	$0.572345\pi$
$812$	−1.74291e115	−2.05974
$813$	2.35663e114	0.265287
$814$	9.91669e114	1.06342
$815$	7.43509e113	0.0759558
$816$	2.09189e115	2.03600
$817$	−8.01173e112	−0.00742942
$818$	−2.02538e115	−1.78958
$819$	7.50094e114	0.631541
$820$	−1.67842e113	−0.0134665
$821$	−1.71630e115	−1.31232	−0.656159	−	0.754623i	$-0.727820\pi$
$821$	−1.71630e115	−1.31232	−0.656159	+	0.754623i	$0.727820\pi$
$822$	−9.40164e114	−0.685120
$823$	1.66755e114	0.115821	0.0579104	−	0.998322i	$-0.481556\pi$
$823$	1.66755e114	0.115821	0.0579104	+	0.998322i	$0.481556\pi$
$824$	−1.54013e114	−0.101961
$825$	3.58809e115	2.26429
$826$	4.67651e115	2.81326
$827$	−8.34556e114	−0.478617	−0.239308	−	0.970944i	$-0.576921\pi$
$827$	−8.34556e114	−0.478617	−0.239308	+	0.970944i	$0.576921\pi$
$828$	−1.72073e114	−0.0940837
$829$	−2.94439e115	−1.53494	−0.767470	−	0.641085i	$-0.778484\pi$
$829$	−2.94439e115	−1.53494	−0.767470	+	0.641085i	$0.778484\pi$
$830$	−3.82241e114	−0.189999
$831$	−1.51352e115	−0.717377
$832$	9.70670e114	0.438733
$833$	3.43015e115	1.47855
$834$	−3.27743e115	−1.34733
$835$	−4.84427e114	−0.189938
$836$	−3.64969e113	−0.0136492
$837$	1.09258e115	0.389760
$838$	−2.77963e115	−0.945907
$839$	−1.29380e115	−0.420019	−0.210009	−	0.977699i	$-0.567349\pi$
$839$	−1.29380e115	−0.420019	−0.210009	+	0.977699i	$0.567349\pi$
$840$	1.01537e114	0.0314479
$841$	5.05186e115	1.49283
$842$	1.74131e115	0.490963
$843$	−6.55242e115	−1.76284
$844$	6.05974e115	1.55571
$845$	3.74601e114	0.0917759
$846$	−9.76530e114	−0.228326
$847$	−1.23750e116	−2.76153
$848$	4.68032e115	0.996872
$849$	7.94685e115	1.61563
$850$	−9.77614e115	−1.89723
$851$	−3.08957e114	−0.0572375
$852$	−1.13912e115	−0.201467
$853$	4.24945e114	0.0717540	0.0358770	−	0.999356i	$-0.488578\pi$
$853$	4.24945e114	0.0717540	0.0358770	+	0.999356i	$0.488578\pi$
$854$	−1.02017e116	−1.64470
$855$	6.01980e112	0.000926660 0
$856$	−9.73863e114	−0.143148
$857$	1.29728e116	1.82092	0.910458	−	0.413601i	$-0.135729\pi$
$857$	1.29728e116	1.82092	0.910458	+	0.413601i	$0.135729\pi$
$858$	1.28436e116	1.72163
$859$	1.48414e116	1.89996	0.949981	−	0.312309i	$-0.101102\pi$
$859$	1.48414e116	1.89996	0.949981	+	0.312309i	$0.101102\pi$
$860$	−8.16646e114	−0.0998493
$861$	1.88865e115	0.220561
$862$	−9.08296e115	−1.01319
$863$	1.68412e116	1.79451	0.897255	−	0.441512i	$-0.145558\pi$
$863$	1.68412e116	1.79451	0.897255	+	0.441512i	$0.145558\pi$
$864$	−3.37977e115	−0.344029
$865$	6.55603e114	0.0637536
$866$	1.10131e116	1.02318
$867$	−1.44193e116	−1.27994
$868$	−2.38799e116	−2.02537
$869$	−2.67191e116	−2.16541
$870$	4.92236e115	0.381209
$871$	−3.72885e115	−0.275967
$872$	−1.65897e115	−0.117338
$873$	−9.38271e115	−0.634258
$874$	2.38767e113	0.00154267
$875$	−5.97850e115	−0.369211
$876$	−9.32108e114	−0.0550243
$877$	2.35500e116	1.32894	0.664471	−	0.747314i	$-0.268657\pi$
$877$	2.35500e116	1.32894	0.664471	+	0.747314i	$0.268657\pi$
$878$	2.93318e116	1.58236
$879$	−1.77406e116	−0.914970
$880$	4.87154e115	0.240215
$881$	−7.51430e115	−0.354275	−0.177137	−	0.984186i	$-0.556684\pi$
$881$	−7.51430e115	−0.354275	−0.177137	+	0.984186i	$0.556684\pi$
$882$	2.64002e116	1.19014
$883$	−1.08680e116	−0.468491	−0.234245	−	0.972177i	$-0.575262\pi$
$883$	−1.08680e116	−0.468491	−0.234245	+	0.972177i	$0.575262\pi$
$884$	−1.66650e116	−0.686975
$885$	−6.28975e115	−0.247956
$886$	4.91826e116	1.85430
$887$	1.84793e116	0.666351	0.333176	−	0.942865i	$-0.391880\pi$
$887$	1.84793e116	0.666351	0.333176	+	0.942865i	$0.391880\pi$
$888$	2.20407e115	0.0760173
$889$	9.71303e114	0.0320431
$890$	−2.14501e115	−0.0676900
$891$	−6.52430e116	−1.96954
$892$	1.78985e116	0.516899
$893$	6.45298e113	0.00178290
$894$	2.10419e116	0.556229
$895$	1.22593e115	0.0310067
$896$	−1.48118e116	−0.358459
$897$	−4.00146e115	−0.0926654
$898$	−6.73547e116	−1.49263
$899$	1.15582e117	2.45123
$900$	−3.58324e116	−0.727271
$901$	−6.62051e116	−1.28606
$902$	1.45073e116	0.269730
$903$	9.18936e116	1.63538
$904$	7.03447e115	0.119834
$905$	−1.13674e116	−0.185371
$906$	−1.98600e117	−3.10038
$907$	4.65134e116	0.695168	0.347584	−	0.937649i	$-0.387002\pi$
$907$	4.65134e116	0.695168	0.347584	+	0.937649i	$0.387002\pi$
$908$	1.53701e116	0.219931
$909$	1.05854e116	0.145022
$910$	−1.06092e116	−0.139171
$911$	−9.14000e116	−1.14808	−0.574038	−	0.818829i	$-0.694624\pi$
$911$	−9.14000e116	−1.14808	−0.574038	+	0.818829i	$0.694624\pi$
$912$	−1.06392e115	−0.0127971
$913$	1.57339e117	1.81235
$914$	1.29492e117	1.42846
$915$	1.37209e116	0.144961
$916$	−2.06968e116	−0.209427
$917$	−2.31858e117	−2.24716
$918$	5.21843e116	0.484455
$919$	−3.70609e116	−0.329574	−0.164787	−	0.986329i	$-0.552694\pi$
$919$	−3.70609e116	−0.329574	−0.164787	+	0.986329i	$0.552694\pi$
$920$	−2.42991e114	−0.00207000
$921$	2.11358e117	1.72490
$922$	−6.21311e116	−0.485778
$923$	−1.18833e116	−0.0890165
$924$	4.18615e117	3.00450
$925$	−6.43370e116	−0.442448
$926$	−6.72417e116	−0.443103
$927$	1.04731e117	0.661341
$928$	−3.57541e117	−2.16362
$929$	1.35076e116	0.0783354	0.0391677	−	0.999233i	$-0.487529\pi$
$929$	1.35076e116	0.0783354	0.0391677	+	0.999233i	$0.487529\pi$
$930$	6.74420e116	0.374847
$931$	−1.74455e115	−0.00929330
$932$	−9.15567e116	−0.467479
$933$	−2.04212e117	−0.999441
$934$	−3.52827e116	−0.165524
$935$	−6.89099e116	−0.309901
$936$	1.28059e116	0.0552094
$937$	3.39256e117	1.40221	0.701107	−	0.713056i	$-0.252690\pi$
$937$	3.39256e117	1.40221	0.701107	+	0.713056i	$0.252690\pi$
$938$	−2.55205e117	−1.01129
$939$	−1.85055e117	−0.703088
$940$	6.57761e115	0.0239617
$941$	−4.48885e117	−1.56800	−0.783998	−	0.620764i	$-0.786823\pi$
$941$	−4.48885e117	−1.56800	−0.783998	+	0.620764i	$0.786823\pi$
$942$	−4.81330e117	−1.61225
$943$	−4.51980e115	−0.0145180
$944$	4.98681e117	1.53613
$945$	1.58209e116	0.0467386
$946$	7.05864e117	1.99996
$947$	4.74425e117	1.28927	0.644635	−	0.764491i	$-0.277009\pi$
$947$	4.74425e117	1.28927	0.644635	+	0.764491i	$0.277009\pi$
$948$	5.94799e117	1.55039
$949$	−9.72380e115	−0.0243120
$950$	4.97206e115	0.0119249
$951$	7.44035e117	1.71184
$952$	1.13875e117	0.251344
$953$	−3.95583e117	−0.837661	−0.418831	−	0.908064i	$-0.637560\pi$
$953$	−3.95583e117	−0.837661	−0.418831	+	0.908064i	$0.637560\pi$
$954$	−5.09549e117	−1.03520
$955$	3.39585e116	0.0661935
$956$	−2.87380e117	−0.537490
$957$	−2.02616e118	−3.63624
$958$	5.29974e117	0.912677
$959$	−3.19669e117	−0.528282
$960$	−8.93506e116	−0.141704
$961$	9.26600e117	1.41032
$962$	−2.30295e117	−0.336411
$963$	6.62240e117	0.928490
$964$	−8.07958e117	−1.08729
$965$	6.13129e116	0.0791996
$966$	−2.73863e117	−0.339576
$967$	7.48651e117	0.891115	0.445558	−	0.895253i	$-0.353005\pi$
$967$	7.48651e117	0.891115	0.445558	+	0.895253i	$0.353005\pi$
$968$	−2.11270e117	−0.241414
$969$	1.50495e116	0.0165095
$970$	1.32708e117	0.139770
$971$	2.39236e117	0.241918	0.120959	−	0.992658i	$-0.461403\pi$
$971$	2.39236e117	0.241918	0.120959	+	0.992658i	$0.461403\pi$
$972$	1.21729e118	1.18189
$973$	−1.11437e118	−1.03890
$974$	3.29792e117	0.295231
$975$	−8.33262e117	−0.716307
$976$	−1.08786e118	−0.898058
$977$	−1.36422e118	−1.08155	−0.540777	−	0.841166i	$-0.681870\pi$
$977$	−1.36422e118	−1.08155	−0.540777	+	0.841166i	$0.681870\pi$
$978$	1.43061e118	1.08928
$979$	8.82938e117	0.645675
$980$	−1.77824e117	−0.124899
$981$	1.12813e118	0.761082
$982$	−3.33951e118	−2.16411
$983$	2.53693e118	1.57923	0.789614	−	0.613604i	$-0.210281\pi$
$983$	2.53693e118	1.57923	0.789614	+	0.613604i	$0.210281\pi$
$984$	3.22438e116	0.0192814
$985$	2.14201e117	0.123052
$986$	5.52050e118	3.04677
$987$	−7.40149e117	−0.392457
$988$	8.47568e115	0.00431793
$989$	−2.19914e117	−0.107646
$990$	−5.30367e117	−0.249452
$991$	6.91741e116	0.0312633	0.0156316	−	0.999878i	$-0.495024\pi$
$991$	6.91741e116	0.0312633	0.0156316	+	0.999878i	$0.495024\pi$
$992$	−4.89873e118	−2.12751
$993$	2.43646e118	1.01687
$994$	−8.13302e117	−0.326204
$995$	−5.80815e117	−0.223886
$996$	−3.50257e118	−1.29760
$997$	−1.42780e118	−0.508404	−0.254202	−	0.967151i	$-0.581813\pi$
$997$	−1.42780e118	−0.508404	−0.254202	+	0.967151i	$0.581813\pi$
$998$	4.52346e118	1.54816
$999$	3.43426e117	0.112979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.80.a.a.1.5	✓	6
3.2	odd	2		9.80.a.b.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.80.a.a.1.5	✓	6	1.1	even	1	trivial
9.80.a.b.1.2		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 80 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.07427e12 q^{2} -9.45275e18 q^{3} +5.49591e23 q^{4} -5.27758e26 q^{5} -1.01548e31 q^{6} -3.45278e33 q^{7} -5.89470e34 q^{8} +4.00848e37 q^{9} +O(q^{10})\)	\(q+1.07427e12 q^{2} -9.45275e18 q^{3} +5.49591e23 q^{4} -5.27758e26 q^{5} -1.01548e31 q^{6} -3.45278e33 q^{7} -5.89470e34 q^{8} +4.00848e37 q^{9} -5.66955e38 q^{10} +2.33372e41 q^{11} -5.19515e42 q^{12} -5.41960e43 q^{13} -3.70921e45 q^{14} +4.98877e45 q^{15} -3.95532e47 q^{16} +5.59497e48 q^{17} +4.30619e49 q^{18} -2.84556e48 q^{19} -2.90051e50 q^{20} +3.26382e52 q^{21} +2.50704e53 q^{22} -7.81076e52 q^{23} +5.57211e53 q^{24} -1.62651e55 q^{25} -5.82211e55 q^{26} +8.68218e55 q^{27} -1.89761e57 q^{28} +9.18474e57 q^{29} +5.35928e57 q^{30} +1.25842e59 q^{31} -3.89277e59 q^{32} -2.20601e60 q^{33} +6.01051e60 q^{34} +1.82223e60 q^{35} +2.20302e61 q^{36} +3.95553e61 q^{37} -3.05689e60 q^{38} +5.12301e62 q^{39} +3.11098e61 q^{40} +5.78663e62 q^{41} +3.50622e64 q^{42} +2.81552e64 q^{43} +1.28259e65 q^{44} -2.11551e64 q^{45} -8.39086e64 q^{46} -2.26774e65 q^{47} +3.73887e66 q^{48} +6.13077e66 q^{49} -1.74731e67 q^{50} -5.28878e67 q^{51} -2.97857e67 q^{52} -1.18330e68 q^{53} +9.32699e67 q^{54} -1.23164e68 q^{55} +2.03531e68 q^{56} +2.68983e67 q^{57} +9.86689e69 q^{58} -1.26078e70 q^{59} +2.74178e69 q^{60} +2.75036e70 q^{61} +1.35188e71 q^{62} -1.38404e71 q^{63} -1.79104e71 q^{64} +2.86024e70 q^{65} -2.36984e72 q^{66} +6.88030e71 q^{67} +3.07495e72 q^{68} +7.38332e71 q^{69} +1.95757e72 q^{70} +2.19266e72 q^{71} -2.36288e72 q^{72} +1.79419e72 q^{73} +4.24931e73 q^{74} +1.53750e74 q^{75} -1.56389e72 q^{76} -8.05781e74 q^{77} +5.50349e74 q^{78} -1.14491e75 q^{79} +2.08746e74 q^{80} -2.79567e75 q^{81} +6.21640e74 q^{82} +6.74200e75 q^{83} +1.79377e76 q^{84} -2.95279e75 q^{85} +3.02463e76 q^{86} -8.68211e76 q^{87} -1.37566e76 q^{88} +3.78339e76 q^{89} -2.27263e76 q^{90} +1.87127e77 q^{91} -4.29273e76 q^{92} -1.18955e78 q^{93} -2.43616e77 q^{94} +1.50177e75 q^{95} +3.67974e78 q^{96} -2.34072e78 q^{97} +6.58610e78 q^{98} +9.35467e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 98\!\cdots\!22 q^{9}+O(q^{10}) \) 6 * q - 16086577320 * q^2 + 1942174928281180680 * q^3 + 1549737362258405903681088 * q^4 + 6092984858773763455723827540 * q^5 - 2227106590325939088404927087328 * q^6 - 204133057837186288371299604423600 * q^7 + 542570064661378776298915601390568960 * q^8 + 98496326492153316059886441015309696222 * q^9	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 12\!\cdots\!24 q^{99}+O(q^{100}) \) 6 * q - 16086577320 * q^2 + 1942174928281180680 * q^3 + 1549737362258405903681088 * q^4 + 6092984858773763455723827540 * q^5 - 2227106590325939088404927087328 * q^6 - 204133057837186288371299604423600 * q^7 + 542570064661378776298915601390568960 * q^8 + 98496326492153316059886441015309696222 * q^9 + 2720626696366658228219065452729623532240 * q^10 + 326182707503353434196853598345012484552152 * q^11 + 3662741799314627362069151990938777789858560 * q^12 - 249286867791526696387831019648013646893106140 * q^13 + 1866634067474695788912841823339193553138295616 * q^14 + 53939724989186019570794541522119517534771796080 * q^15 - 681627631644510368706137880459644753465449181184 * q^16 + 829554518710324966978506506427078451803483469740 * q^17 + 20783419681388619276512545895581772264264550807480 * q^18 - 50727940848110344442361931427855575819428647228760 * q^19 - 1467030065046629207751264576643706806587735144958080 * q^20 + 11440846038310308150487768012211089482880511198926272 * q^21 + 36817507512313772519930542191150104222671820963556960 * q^22 - 1046924887201563380993656359631631933258453525094738960 * q^23 + 4647998047182641817986339484942489649049309172966328320 * q^24 + 10836995626543537474051791335153252813979338793331307850 * q^25 - 165657588130323625805363235243378873928973276983585168368 * q^26 + 452244485424938477892504860024752019079362449583874943440 * q^27 + 1004680642640065837930850364413184139977872155405489282560 * q^28 - 7120822866262655112931363073018274881104708247497947521340 * q^29 - 1093089132342530488188112356341250721972394415479943059520 * q^30 + 134345039550847531062964315804153164343444264343589333172032 * q^31 - 367680407387361126658464447414461787802285956837455133573120 * q^32 + 694937277679484430969386562214930563011269531321798125315360 * q^33 + 3154306959722239121253159757854043021326472297974364404980016 * q^34 + 9191056770903655504272784196241783249847740561191433159558240 * q^35 + 19880287065959074647932230862843896929437344679866234828597056 * q^36 + 200218543091040103155222783880989961642213560574664429550198420 * q^37 + 866365883974611161836395390925862263352921297032838009795060640 * q^38 + 1846928010477803855453412626793191219191424716227436821180804144 * q^39 + 9116669264447274408945009430906339427674431802850195585057510400 * q^40 + 19216804901837266991242147464997667315402616992351385711235458972 * q^41 + 112315174478490788723912174839938916243710780267342081630678531840 * q^42 + 108832931910908864051094641347526853298463718485111641638401400600 * q^43 + 495514650695382135238363336424200091081783038631873261666636656896 * q^44 + 1089311173064980984859644147008913582964905804089164802662670706980 * q^45 + 2339423217798161589056888023635021837153755261863446723443331974592 * q^46 + 766732507168785220421816169748850175208159379232549271592508353760 * q^47 - 1227537570851109157458973684400646232156423736031048093315900456960 * q^48 + 3801016219812200810689187746878210669081675204402752707309154018358 * q^49 - 50723521315108078882353551947661611720805543300108849711322864485400 * q^50 - 139865466375558864334882784640098531626186142446280524443365433199728 * q^51 - 279692249004488191323071540832092417841619330373410063262542264310400 * q^52 - 312193237964710957330604375297544855480450344577449082153802391971020 * q^53 - 996221038973994559873624494431619704350011373216284617130312268666560 * q^54 - 861958222068919393142591787960630586871784969446963670182827020790320 * q^55 + 1123629643438673418216699268533992018915072902064015953839024305295360 * q^56 + 7795598779799587371741461301046795526293245245773998812837273820000480 * q^57 + 16584702356914156466182151363602691995360915944935914137385742159510160 * q^58 + 24289171784532714189639095038219795042285164994033400426178461238907320 * q^59 + 73025956047571458013400417312791668535879728806786116560639243534051840 * q^60 + 80560570425826852880081093564684385117241348668836108242495308815618052 * q^61 + 59777568713863815377707698536571620658579394379949737090862924510332160 * q^62 - 276708678056196744256455115102015383166989187390931876478468368856762480 * q^63 - 719203226636338274682481908236724651863342420498670194455988567598170112 * q^64 - 1007462919483461647300380829039677154191109543250817689988654733030592520 * q^65 - 3347562853423538991999694027669961627986534585541581689746575315495214976 * q^66 - 1851521876973893932513297183455714100127257334040085257904842903903517560 * q^67 - 5899582938115809421316043854246769288699297144820927766700932855979726720 * q^68 - 1427672735602453311144050658084524391331260046448660152415370050225171136 * q^69 + 31159148342952686307596185437939815723517531766889921556924090292621741440 * q^70 + 38507401093845789827495210229167852070939724868887506542264571604541264592 * q^71 + 87904411000641647434917578390462554629488250565124366592415232306933521920 * q^72 + 61123654206386061400310438862981106227383729069503080628162601940159787740 * q^73 + 136513352063977853606694381822259496818965955504365628093794971441921163216 * q^74 + 113188706706427317048365034543759604727098826077328333023878456326260918200 * q^75 - 249903768766885839664688587580825575582546834454828556400015599314274074880 * q^76 - 1195099252106099653800449972868194220235362175583181442486256041652274244800 * q^77 - 3022231856978250782599441544561070134871217051487771942772538597436408443200 * q^78 - 188234723479363903277484397100590307076741783512190126828886315155446684640 * q^79 - 2750248132852209015421484068233717972689944891189322073844459755369097666560 * q^80 - 4202996734890713231427597758184507891641102417282671988811370042535012566794 * q^81 + 3834792966214046709977047126406184257851543195738078433637414913324683717360 * q^82 + 14506845760765784842493952470927474286413727909244314121162679395439622145320 * q^83 + 48942789227023150657016145376829988370028655394086238910889917134273615865856 * q^84 + 38946066828627954832778050727572362568084538101228336437758435671222134267240 * q^85 + 66363633323077708072616297459993363454350669286030390599179655949306835458912 * q^86 - 12188467007600920252987005731487987332580129454574096199578444638747687628880 * q^87 - 68086553439664359269830684533538140843829745277114000504065479672707840583680 * q^88 + 88790169947368466670673875396871954428202115924137373286785364937730407494780 * q^89 - 678121360108159288271315537216087664710338266311311066150921870820864233179120 * q^90 - 1105665330428280782729905276805137770501582996765091919549546053816493845198368 * q^91 - 581852119074779563003978084378550280950528927013853021971971412987670782543360 * q^92 - 724063571132401087495277238269757837179269218308363767014177350097338957840640 * q^93 - 342394004508386413823498343959337212855421843329465021317054652742559913721984 * q^94 + 4133010515441143062055572903340407460351722715065934937506390604234109634359600 * q^95 + 4500277093535091993817003185543220432802869972147132801867826645045331188908032 * q^96 + 2053881285944963905800936410853289740689894385863240159901124624782493905690060 * q^97 + 21591608457226642856925919189308208713047358263642522360137695155926522503830040 * q^98 + 12210721611676619111412804269965201185505307365258823385190308559518832844781624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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