LMFDB - Embedded newform 1.80.a.a.1.6

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			1.6
Root			$5.13724e10$ 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)

$f(q)$	$=$	$q+1.23026e12 q^{2} +8.35089e18 q^{3} +9.09069e23 q^{4} +3.84167e27 q^{5} +1.02737e31 q^{6} +3.79445e33 q^{7} +3.74744e35 q^{8} +2.04677e37 q^{9} +O(q^{10})$	\(q+1.23026e12 q^{2} +8.35089e18 q^{3} +9.09069e23 q^{4} +3.84167e27 q^{5} +1.02737e31 q^{6} +3.79445e33 q^{7} +3.74744e35 q^{8} +2.04677e37 q^{9} +4.72625e39 q^{10} +5.69076e40 q^{11} +7.59153e42 q^{12} -1.86943e44 q^{13} +4.66815e45 q^{14} +3.20814e46 q^{15} -8.84676e46 q^{16} -4.20866e48 q^{17} +2.51806e49 q^{18} +2.63459e50 q^{19} +3.49235e51 q^{20} +3.16871e52 q^{21} +7.00109e52 q^{22} +4.17236e53 q^{23} +3.12944e54 q^{24} -1.78515e54 q^{25} -2.29987e56 q^{26} -2.40521e56 q^{27} +3.44942e57 q^{28} -6.41555e57 q^{29} +3.94684e58 q^{30} -3.24599e57 q^{31} -3.35356e59 q^{32} +4.75229e59 q^{33} -5.17773e60 q^{34} +1.45771e61 q^{35} +1.86066e61 q^{36} +8.16250e61 q^{37} +3.24122e62 q^{38} -1.56114e63 q^{39} +1.43964e63 q^{40} +6.43833e63 q^{41} +3.89832e64 q^{42} +3.95195e63 q^{43} +5.17329e64 q^{44} +7.86304e64 q^{45} +5.13307e65 q^{46} -4.35572e65 q^{47} -7.38783e65 q^{48} +8.60698e66 q^{49} -2.19619e66 q^{50} -3.51460e67 q^{51} -1.69944e68 q^{52} +9.71309e67 q^{53} -2.95903e68 q^{54} +2.18620e68 q^{55} +1.42195e69 q^{56} +2.20011e69 q^{57} -7.89278e69 q^{58} +6.57600e68 q^{59} +2.91642e70 q^{60} +3.50542e70 q^{61} -3.99340e69 q^{62} +7.76639e70 q^{63} -3.59099e71 q^{64} -7.18172e71 q^{65} +5.84654e71 q^{66} -4.53890e71 q^{67} -3.82596e72 q^{68} +3.48429e72 q^{69} +1.79335e73 q^{70} -8.10072e72 q^{71} +7.67016e72 q^{72} -5.59922e73 q^{73} +1.00420e74 q^{74} -1.49076e73 q^{75} +2.39502e74 q^{76} +2.15933e74 q^{77} -1.92060e75 q^{78} +1.00900e74 q^{79} -3.39864e74 q^{80} -3.01700e75 q^{81} +7.92080e75 q^{82} -3.41719e75 q^{83} +2.88057e76 q^{84} -1.61683e76 q^{85} +4.86191e75 q^{86} -5.35756e76 q^{87} +2.13258e76 q^{88} +8.47827e76 q^{89} +9.67356e76 q^{90} -7.09345e77 q^{91} +3.79296e77 q^{92} -2.71069e76 q^{93} -5.35865e77 q^{94} +1.01212e78 q^{95} -2.80052e78 q^{96} +2.15272e78 q^{97} +1.05888e79 q^{98} +1.16477e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.23026e12	1.58238	0.791190	−	0.611570i	$-0.209462\pi$
$2$	1.23026e12	1.58238	0.791190	+	0.611570i	$0.209462\pi$
$3$	8.35089e18	1.18972	0.594858	−	0.803831i	$-0.297208\pi$
$3$	8.35089e18	1.18972	0.594858	+	0.803831i	$0.297208\pi$
$4$	9.09069e23	1.50393
$5$	3.84167e27	0.944507	0.472254	−	0.881463i	$-0.343441\pi$
$5$	3.84167e27	0.944507	0.472254	+	0.881463i	$0.343441\pi$
$6$	1.02737e31	1.88258
$7$	3.79445e33	1.57680	0.788400	−	0.615163i	$-0.210910\pi$
$7$	3.79445e33	1.57680	0.788400	+	0.615163i	$0.210910\pi$
$8$	3.74744e35	0.797406
$9$	2.04677e37	0.415423
$10$	4.72625e39	1.49457
$11$	5.69076e40	0.417022	0.208511	−	0.978020i	$-0.433138\pi$
$11$	5.69076e40	0.417022	0.208511	+	0.978020i	$0.433138\pi$
$12$	7.59153e42	1.78925
$13$	−1.86943e44	−1.86615	−0.933073	−	0.359687i	$-0.882884\pi$
$13$	−1.86943e44	−1.86615	−0.933073	+	0.359687i	$0.882884\pi$
$14$	4.66815e45	2.49510
$15$	3.20814e46	1.12370
$16$	−8.84676e46	−0.242128
$17$	−4.20866e48	−1.05054	−0.525268	−	0.850937i	$-0.676035\pi$
$17$	−4.20866e48	−1.05054	−0.525268	+	0.850937i	$0.676035\pi$
$18$	2.51806e49	0.657358
$19$	2.63459e50	0.812728	0.406364	−	0.913711i	$-0.366797\pi$
$19$	2.63459e50	0.812728	0.406364	+	0.913711i	$0.366797\pi$
$20$	3.49235e51	1.42047
$21$	3.16871e52	1.87594
$22$	7.00109e52	0.659888
$23$	4.17236e53	0.679410	0.339705	−	0.940532i	$-0.389673\pi$
$23$	4.17236e53	0.679410	0.339705	+	0.940532i	$0.389673\pi$
$24$	3.12944e54	0.948687
$25$	−1.78515e54	−0.107906
$26$	−2.29987e56	−2.95295
$27$	−2.40521e56	−0.695480
$28$	3.44942e57	2.37139
$29$	−6.41555e57	−1.10284	−0.551421	−	0.834227i	$-0.685914\pi$
$29$	−6.41555e57	−1.10284	−0.551421	+	0.834227i	$0.685914\pi$
$30$	3.94684e58	1.77811
$31$	−3.24599e57	−0.0400461	−0.0200231	−	0.999800i	$-0.506374\pi$
$31$	−3.24599e57	−0.0400461	−0.0200231	+	0.999800i	$0.506374\pi$
$32$	−3.35356e59	−1.18054
$33$	4.75229e59	0.496138
$34$	−5.17773e60	−1.66235
$35$	1.45771e61	1.48930
$36$	1.86066e61	0.624767
$37$	8.16250e61	0.928657	0.464328	−	0.885663i	$-0.346296\pi$
$37$	8.16250e61	0.928657	0.464328	+	0.885663i	$0.346296\pi$
$38$	3.24122e62	1.28604
$39$	−1.56114e63	−2.22018
$40$	1.43964e63	0.753156
$41$	6.43833e63	1.27002	0.635011	−	0.772503i	$-0.280996\pi$
$41$	6.43833e63	1.27002	0.635011	+	0.772503i	$0.280996\pi$
$42$	3.89832e64	2.96846
$43$	3.95195e63	0.118797	0.0593987	−	0.998234i	$-0.481082\pi$
$43$	3.95195e63	0.118797	0.0593987	+	0.998234i	$0.481082\pi$
$44$	5.17329e64	0.627171
$45$	7.86304e64	0.392370
$46$	5.13307e65	1.07509
$47$	−4.35572e65	−0.390116	−0.195058	−	0.980792i	$-0.562490\pi$
$47$	−4.35572e65	−0.390116	−0.195058	+	0.980792i	$0.562490\pi$
$48$	−7.38783e65	−0.288063
$49$	8.60698e66	1.48630
$50$	−2.19619e66	−0.170748
$51$	−3.51460e67	−1.24984
$52$	−1.69944e68	−2.80655
$53$	9.71309e67	0.755893	0.377947	−	0.925827i	$-0.376630\pi$
$53$	9.71309e67	0.755893	0.377947	+	0.925827i	$0.376630\pi$
$54$	−2.95903e68	−1.10051
$55$	2.18620e68	0.393881
$56$	1.42195e69	1.25735
$57$	2.20011e69	0.966915
$58$	−7.89278e69	−1.74512
$59$	6.57600e68	0.0740129	0.0370065	−	0.999315i	$-0.488218\pi$
$59$	6.57600e68	0.0740129	0.0370065	+	0.999315i	$0.488218\pi$
$60$	2.91642e70	1.68996
$61$	3.50542e70	1.05733	0.528666	−	0.848830i	$-0.322692\pi$
$61$	3.50542e70	1.05733	0.528666	+	0.848830i	$0.322692\pi$
$62$	−3.99340e69	−0.0633682
$63$	7.76639e70	0.655039
$64$	−3.59099e71	−1.62594
$65$	−7.18172e71	−1.76259
$66$	5.84654e71	0.785079
$67$	−4.53890e71	−0.336508	−0.168254	−	0.985744i	$-0.553813\pi$
$67$	−4.53890e71	−0.336508	−0.168254	+	0.985744i	$0.553813\pi$
$68$	−3.82596e72	−1.57993
$69$	3.48429e72	0.808305
$70$	1.79335e73	2.35664
$71$	−8.10072e72	−0.607882	−0.303941	−	0.952691i	$-0.598303\pi$
$71$	−8.10072e72	−0.607882	−0.303941	+	0.952691i	$0.598303\pi$
$72$	7.67016e72	0.331261
$73$	−5.59922e73	−1.40241	−0.701204	−	0.712960i	$-0.747354\pi$
$73$	−5.59922e73	−1.40241	−0.701204	+	0.712960i	$0.747354\pi$
$74$	1.00420e74	1.46949
$75$	−1.49076e73	−0.128377
$76$	2.39502e74	1.22228
$77$	2.15933e74	0.657560
$78$	−1.92060e75	−3.51317
$79$	1.00900e74	0.111589	0.0557947	−	0.998442i	$-0.482231\pi$
$79$	1.00900e74	0.111589	0.0557947	+	0.998442i	$0.482231\pi$
$80$	−3.39864e74	−0.228692
$81$	−3.01700e75	−1.24285
$82$	7.92080e75	2.00966
$83$	−3.41719e75	−0.537137	−0.268568	−	0.963261i	$-0.586551\pi$
$83$	−3.41719e75	−0.537137	−0.268568	+	0.963261i	$0.586551\pi$
$84$	2.88057e76	2.82128
$85$	−1.61683e76	−0.992239
$86$	4.86191e75	0.187983
$87$	−5.35756e76	−1.31207
$88$	2.13258e76	0.332536
$89$	8.47827e76	0.846061	0.423031	−	0.906115i	$-0.360966\pi$
$89$	8.47827e76	0.846061	0.423031	+	0.906115i	$0.360966\pi$
$90$	9.67356e76	0.620879
$91$	−7.09345e77	−2.94254
$92$	3.79296e77	1.02178
$93$	−2.71069e76	−0.0476435
$94$	−5.35865e77	−0.617313
$95$	1.01212e78	0.767628
$96$	−2.80052e78	−1.40451
$97$	2.15272e78	0.716974	0.358487	−	0.933535i	$-0.383293\pi$
$97$	2.15272e78	0.716974	0.358487	+	0.933535i	$0.383293\pi$
$98$	1.05888e79	2.35189
$99$	1.16477e78	0.173241
$100$	−1.62282e78	−0.162282
$101$	1.46164e79	0.986611	0.493305	−	0.869856i	$-0.335788\pi$
$101$	1.46164e79	0.986611	0.493305	+	0.869856i	$0.335788\pi$
$102$	−4.32386e79	−1.97772
$103$	−5.01395e79	−1.55995	−0.779973	−	0.625813i	$-0.784767\pi$
$103$	−5.01395e79	−1.55995	−0.779973	+	0.625813i	$0.784767\pi$
$104$	−7.00555e79	−1.48808
$105$	1.21731e80	1.77184
$106$	1.19496e80	1.19611
$107$	3.61467e79	0.249695	0.124848	−	0.992176i	$-0.460156\pi$
$107$	3.61467e79	0.249695	0.124848	+	0.992176i	$0.460156\pi$
$108$	−2.18650e80	−1.04595
$109$	−1.29760e80	−0.431315	−0.215657	−	0.976469i	$-0.569189\pi$
$109$	−1.29760e80	−0.431315	−0.215657	+	0.976469i	$0.569189\pi$
$110$	2.68959e80	0.623269
$111$	6.81642e80	1.10484
$112$	−3.35686e80	−0.381787
$113$	−7.95719e80	−0.637032	−0.318516	−	0.947917i	$-0.603184\pi$
$113$	−7.95719e80	−0.637032	−0.318516	+	0.947917i	$0.603184\pi$
$114$	2.70671e81	1.53003
$115$	1.60288e81	0.641708
$116$	−5.83218e81	−1.65859
$117$	−3.82629e81	−0.775241
$118$	8.09017e80	0.117117
$119$	−1.59695e82	−1.65649
$120$	1.20223e82	0.896042
$121$	−1.53833e82	−0.826093
$122$	4.31256e82	1.67310
$123$	5.37658e82	1.51096
$124$	−2.95083e81	−0.0602265
$125$	−7.04131e82	−1.04643
$126$	9.55465e82	1.03652
$127$	6.56289e82	0.521013	0.260506	−	0.965472i	$-0.416110\pi$
$127$	6.56289e82	0.521013	0.260506	+	0.965472i	$0.416110\pi$
$128$	−2.39074e83	−1.39232
$129$	3.30023e82	0.141335
$130$	−8.83536e83	−2.78909
$131$	5.14636e83	1.20028	0.600142	−	0.799893i	$-0.295111\pi$
$131$	5.14636e83	1.20028	0.600142	+	0.799893i	$0.295111\pi$
$132$	4.32016e83	0.746156
$133$	9.99681e83	1.28151
$134$	−5.58401e83	−0.532484
$135$	−9.24004e83	−0.656886
$136$	−1.57717e84	−0.837704
$137$	−9.77136e83	−0.388591	−0.194295	−	0.980943i	$-0.562242\pi$
$137$	−9.77136e83	−0.388591	−0.194295	+	0.980943i	$0.562242\pi$
$138$	4.28657e84	1.27905
$139$	2.11215e84	0.473850	0.236925	−	0.971528i	$-0.423860\pi$
$139$	2.11215e84	0.473850	0.236925	+	0.971528i	$0.423860\pi$
$140$	1.32515e85	2.23980
$141$	−3.63741e84	−0.464128
$142$	−9.96597e84	−0.961900
$143$	−1.06384e85	−0.778224
$144$	−1.81073e84	−0.100586
$145$	−2.46465e85	−1.04164
$146$	−6.88848e85	−2.21914
$147$	7.18760e85	1.76827
$148$	7.42028e85	1.39663
$149$	−1.90384e85	−0.274646	−0.137323	−	0.990526i	$-0.543850\pi$
$149$	−1.90384e85	−0.274646	−0.137323	+	0.990526i	$0.543850\pi$
$150$	−1.83402e85	−0.203141
$151$	9.88359e85	0.842026	0.421013	−	0.907055i	$-0.361675\pi$
$151$	9.88359e85	0.842026	0.421013	+	0.907055i	$0.361675\pi$
$152$	9.87294e85	0.648074
$153$	−8.61417e85	−0.436417
$154$	2.65653e86	1.04051
$155$	−1.24700e85	−0.0378239
$156$	−1.41918e87	−3.33900
$157$	6.84340e86	1.25094	0.625469	−	0.780249i	$-0.284908\pi$
$157$	6.84340e86	1.25094	0.625469	+	0.780249i	$0.284908\pi$
$158$	1.24133e86	0.176577
$159$	8.11129e86	0.899298
$160$	−1.28833e87	−1.11503
$161$	1.58318e87	1.07129
$162$	−3.71169e87	−1.96666
$163$	−1.08141e87	−0.449345	−0.224673	−	0.974434i	$-0.572131\pi$
$163$	−1.08141e87	−0.449345	−0.224673	+	0.974434i	$0.572131\pi$
$164$	5.85289e87	1.91002
$165$	1.82568e87	0.468606
$166$	−4.20403e87	−0.849955
$167$	−6.21984e87	−0.991925	−0.495962	−	0.868344i	$-0.665185\pi$
$167$	−6.21984e87	−0.991925	−0.495962	+	0.868344i	$0.665185\pi$
$168$	1.18745e88	1.49589
$169$	2.49123e88	2.48250
$170$	−1.98911e88	−1.57010
$171$	5.39240e87	0.337626
$172$	3.59259e87	0.178663
$173$	−3.59770e88	−1.42299	−0.711497	−	0.702689i	$-0.751983\pi$
$173$	−3.59770e88	−1.42299	−0.711497	+	0.702689i	$0.751983\pi$
$174$	−6.59117e88	−2.07619
$175$	−6.77366e87	−0.170146
$176$	−5.03448e87	−0.100973
$177$	5.49155e87	0.0880543
$178$	1.04304e89	1.33879
$179$	1.85431e89	1.90760	0.953800	−	0.300441i	$-0.0971339\pi$
$179$	1.85431e89	1.90760	0.953800	+	0.300441i	$0.0971339\pi$
$180$	7.14805e88	0.590097
$181$	1.78968e89	1.18706	0.593529	−	0.804813i	$-0.297734\pi$
$181$	1.78968e89	1.18706	0.593529	+	0.804813i	$0.297734\pi$
$182$	−8.72676e89	−4.65622
$183$	2.92734e89	1.25792
$184$	1.56356e89	0.541766
$185$	3.13577e89	0.877123
$186$	−3.33485e88	−0.0753902
$187$	−2.39504e89	−0.438097
$188$	−3.95965e89	−0.586707
$189$	−9.12646e89	−1.09663
$190$	1.24517e90	1.21468
$191$	5.33195e89	0.422735	0.211367	−	0.977407i	$-0.432208\pi$
$191$	5.33195e89	0.422735	0.211367	+	0.977407i	$0.432208\pi$
$192$	−2.99880e90	−1.93441
$193$	1.13485e90	0.596245	0.298123	−	0.954528i	$-0.403640\pi$
$193$	1.13485e90	0.596245	0.298123	+	0.954528i	$0.403640\pi$
$194$	2.64839e90	1.13453
$195$	−5.99738e90	−2.09698
$196$	7.82434e90	2.23529
$197$	−2.09628e90	−0.489817	−0.244908	−	0.969546i	$-0.578758\pi$
$197$	−2.09628e90	−0.489817	−0.244908	+	0.969546i	$0.578758\pi$
$198$	1.43297e90	0.274133
$199$	7.85083e90	1.23089	0.615445	−	0.788180i	$-0.288977\pi$
$199$	7.85083e90	1.23089	0.615445	+	0.788180i	$0.288977\pi$
$200$	−6.68973e89	−0.0860446
$201$	−3.79038e90	−0.400349
$202$	1.79819e91	1.56119
$203$	−2.43435e91	−1.73896
$204$	−3.19502e91	−1.87967
$205$	2.47340e91	1.19954
$206$	−6.16844e91	−2.46843
$207$	8.53988e90	0.282243
$208$	1.65384e91	0.451846
$209$	1.49928e91	0.338926
$210$	1.49761e92	2.80373
$211$	−8.24340e91	−1.27923	−0.639616	−	0.768694i	$-0.720907\pi$
$211$	−8.24340e91	−1.27923	−0.639616	+	0.768694i	$0.720907\pi$
$212$	8.82987e91	1.13681
$213$	−6.76483e91	−0.723206
$214$	4.44698e91	0.395113
$215$	1.51821e91	0.112205
$216$	−9.01338e91	−0.554580
$217$	−1.23168e91	−0.0631447
$218$	−1.59638e92	−0.682504
$219$	−4.67585e92	−1.66847
$220$	1.98741e92	0.592368
$221$	7.86777e92	1.96045
$222$	8.38594e92	1.74827
$223$	−9.70997e92	−1.69502	−0.847512	−	0.530777i	$-0.821900\pi$
$223$	−9.70997e92	−1.69502	−0.847512	+	0.530777i	$0.821900\pi$
$224$	−1.27249e93	−1.86148
$225$	−3.65380e91	−0.0448265
$226$	−9.78939e92	−1.00803
$227$	2.07950e92	0.179861	0.0899307	−	0.995948i	$-0.471335\pi$
$227$	2.07950e92	0.179861	0.0899307	+	0.995948i	$0.471335\pi$
$228$	2.00006e93	1.45417
$229$	1.29764e93	0.793694	0.396847	−	0.917885i	$-0.370104\pi$
$229$	1.29764e93	0.793694	0.396847	+	0.917885i	$0.370104\pi$
$230$	1.97196e93	1.01543
$231$	1.80323e93	0.782310
$232$	−2.40419e93	−0.879413
$233$	2.00899e93	0.620039	0.310020	−	0.950730i	$-0.399664\pi$
$233$	2.00899e93	0.620039	0.310020	+	0.950730i	$0.399664\pi$
$234$	−4.70732e93	−1.22673
$235$	−1.67332e93	−0.368468
$236$	5.97804e92	0.111310
$237$	8.42608e92	0.132760
$238$	−1.96466e94	−2.62119
$239$	1.15264e94	1.30309	0.651547	−	0.758608i	$-0.274120\pi$
$239$	1.15264e94	1.30309	0.651547	+	0.758608i	$0.274120\pi$
$240$	−2.83816e93	−0.272078
$241$	1.23070e94	1.00110	0.500550	−	0.865708i	$-0.333131\pi$
$241$	1.23070e94	1.00110	0.500550	+	0.865708i	$0.333131\pi$
$242$	−1.89255e94	−1.30719
$243$	−1.33443e94	−0.783154
$244$	3.18667e94	1.59015
$245$	3.30652e94	1.40382
$246$	6.61457e94	2.39092
$247$	−4.92516e94	−1.51667
$248$	−1.21641e93	−0.0319330
$249$	−2.85366e94	−0.639040
$250$	−8.66262e94	−1.65584
$251$	−3.48266e94	−0.568590	−0.284295	−	0.958737i	$-0.591760\pi$
$251$	−3.48266e94	−0.568590	−0.284295	+	0.958737i	$0.591760\pi$
$252$	7.06018e94	0.985132
$253$	2.37439e94	0.283329
$254$	8.07405e94	0.824441
$255$	−1.35020e95	−1.18048
$256$	−7.70599e94	−0.577231
$257$	9.02550e94	0.579579	0.289790	−	0.957090i	$-0.406415\pi$
$257$	9.02550e94	0.579579	0.289790	+	0.957090i	$0.406415\pi$
$258$	4.06013e94	0.223646
$259$	3.09722e95	1.46431
$260$	−6.52868e95	−2.65081
$261$	−1.31312e95	−0.458146
$262$	6.33135e95	1.89931
$263$	−5.23889e95	−1.35203	−0.676016	−	0.736887i	$-0.736295\pi$
$263$	−5.23889e95	−1.35203	−0.676016	+	0.736887i	$0.736295\pi$
$264$	1.78089e95	0.395623
$265$	3.73145e95	0.713947
$266$	1.22986e96	2.02784
$267$	7.08011e95	1.00657
$268$	−4.12617e95	−0.506084
$269$	−1.82801e96	−1.93537	−0.967683	−	0.252170i	$-0.918856\pi$
$269$	−1.82801e96	−1.93537	−0.967683	+	0.252170i	$0.918856\pi$
$270$	−1.13676e96	−1.03944
$271$	2.17940e96	1.72206	0.861032	−	0.508551i	$-0.169819\pi$
$271$	2.17940e96	1.72206	0.861032	+	0.508551i	$0.169819\pi$
$272$	3.72330e95	0.254364
$273$	−5.92366e96	−3.50078
$274$	−1.20213e96	−0.614898
$275$	−1.01589e95	−0.0449990
$276$	3.16746e96	1.21563
$277$	2.45788e96	0.817731	0.408866	−	0.912595i	$-0.365924\pi$
$277$	2.45788e96	0.817731	0.408866	+	0.912595i	$0.365924\pi$
$278$	2.59849e96	0.749811
$279$	−6.64381e94	−0.0166361
$280$	5.46266e96	1.18758
$281$	5.55224e96	1.04850	0.524250	−	0.851564i	$-0.324346\pi$
$281$	5.55224e96	1.04850	0.524250	+	0.851564i	$0.324346\pi$
$282$	−4.47495e96	−0.734427
$283$	−7.47419e96	−1.06660	−0.533298	−	0.845927i	$-0.679048\pi$
$283$	−7.47419e96	−1.06660	−0.533298	+	0.845927i	$0.679048\pi$
$284$	−7.36412e96	−0.914211
$285$	8.45212e96	0.913259
$286$	−1.30880e97	−1.23145
$287$	2.44299e97	2.00257
$288$	−6.86399e96	−0.490426
$289$	1.66317e96	0.103626
$290$	−3.03215e97	−1.64827
$291$	1.79771e97	0.852995
$292$	−5.09008e97	−2.10912
$293$	−1.60895e97	−0.582466	−0.291233	−	0.956652i	$-0.594065\pi$
$293$	−1.60895e97	−0.582466	−0.291233	+	0.956652i	$0.594065\pi$
$294$	8.84259e97	2.79808
$295$	2.52629e96	0.0699058
$296$	3.05885e97	0.740517
$297$	−1.36875e97	−0.290031
$298$	−2.34222e97	−0.434595
$299$	−7.79991e97	−1.26788
$300$	−1.35520e97	−0.193070
$301$	1.49955e97	0.187320
$302$	1.21594e98	1.33240
$303$	1.22060e98	1.17379
$304$	−2.33075e97	−0.196784
$305$	1.34667e98	0.998658
$306$	−1.05976e98	−0.690578
$307$	−1.88678e98	−1.08083	−0.540413	−	0.841400i	$-0.681732\pi$
$307$	−1.88678e98	−1.08083	−0.540413	+	0.841400i	$0.681732\pi$
$308$	1.96298e98	0.988924
$309$	−4.18709e98	−1.85589
$310$	−1.53414e97	−0.0598517
$311$	−4.37919e98	−1.50438	−0.752191	−	0.658945i	$-0.771003\pi$
$311$	−4.37919e98	−1.50438	−0.752191	+	0.658945i	$0.771003\pi$
$312$	−5.85026e98	−1.77039
$313$	3.17743e98	0.847372	0.423686	−	0.905809i	$-0.360736\pi$
$313$	3.17743e98	0.847372	0.423686	+	0.905809i	$0.360736\pi$
$314$	8.41914e98	1.97946
$315$	2.98359e98	0.618690
$316$	9.17254e97	0.167822
$317$	5.66441e98	0.914774	0.457387	−	0.889268i	$-0.348785\pi$
$317$	5.66441e98	0.914774	0.457387	+	0.889268i	$0.348785\pi$
$318$	9.97898e98	1.42303
$319$	−3.65094e98	−0.459909
$320$	−1.37954e99	−1.53572
$321$	3.01857e98	0.297066
$322$	1.94772e99	1.69519
$323$	−1.10881e99	−0.853800
$324$	−2.74266e99	−1.86915
$325$	3.33720e98	0.201368
$326$	−1.33041e99	−0.711036
$327$	−1.08361e99	−0.513142
$328$	2.41272e99	1.01272
$329$	−1.65276e99	−0.615136
$330$	2.24605e99	0.741513
$331$	4.89344e99	1.43354	0.716768	−	0.697312i	$-0.245621\pi$
$331$	4.89344e99	1.43354	0.716768	+	0.697312i	$0.245621\pi$
$332$	−3.10647e99	−0.807816
$333$	1.67068e99	0.385786
$334$	−7.65200e99	−1.56960
$335$	−1.74370e99	−0.317834
$336$	−2.80328e99	−0.454218
$337$	8.77991e97	0.0126505	0.00632527	−	0.999980i	$-0.497987\pi$
$337$	8.77991e97	0.0126505	0.00632527	+	0.999980i	$0.497987\pi$
$338$	3.06486e100	3.92826
$339$	−6.64496e99	−0.757887
$340$	−1.46981e100	−1.49226
$341$	−1.84722e98	−0.0167001
$342$	6.63404e99	0.534253
$343$	1.06855e100	0.766794
$344$	1.48097e99	0.0947299
$345$	1.33855e100	0.763450
$346$	−4.42609e100	−2.25172
$347$	1.97081e100	0.894602	0.447301	−	0.894383i	$-0.352385\pi$
$347$	1.97081e100	0.894602	0.447301	+	0.894383i	$0.352385\pi$
$348$	−4.87039e100	−1.97326
$349$	−8.21827e99	−0.297287	−0.148643	−	0.988891i	$-0.547491\pi$
$349$	−8.21827e99	−0.297287	−0.148643	+	0.988891i	$0.547491\pi$
$350$	−8.33334e99	−0.269235
$351$	4.49636e100	1.29787
$352$	−1.90843e100	−0.492313
$353$	7.13245e98	0.0164489	0.00822447	−	0.999966i	$-0.497382\pi$
$353$	7.13245e98	0.0164489	0.00822447	+	0.999966i	$0.497382\pi$
$354$	6.75601e99	0.139335
$355$	−3.11203e100	−0.574149
$356$	7.70733e100	1.27242
$357$	−1.33360e101	−1.97075
$358$	2.28128e101	3.01855
$359$	9.85585e100	1.16806	0.584028	−	0.811734i	$-0.301476\pi$
$359$	9.85585e100	1.16806	0.584028	+	0.811734i	$0.301476\pi$
$360$	2.94662e100	0.312879
$361$	−3.56730e100	−0.339473
$362$	2.20177e101	1.87838
$363$	−1.28465e101	−0.982815
$364$	−6.44843e101	−4.42537
$365$	−2.15104e101	−1.32459
$366$	3.60137e101	1.99051
$367$	−2.50336e101	−1.24226	−0.621132	−	0.783706i	$-0.713327\pi$
$367$	−2.50336e101	−1.24226	−0.621132	+	0.783706i	$0.713327\pi$
$368$	−3.69118e100	−0.164504
$369$	1.31778e101	0.527597
$370$	3.85780e101	1.38794
$371$	3.68559e101	1.19189
$372$	−2.46421e100	−0.0716524
$373$	6.33795e100	0.165749	0.0828743	−	0.996560i	$-0.473590\pi$
$373$	6.33795e100	0.165749	0.0828743	+	0.996560i	$0.473590\pi$
$374$	−2.94652e101	−0.693236
$375$	−5.88012e101	−1.24495
$376$	−1.63228e101	−0.311081
$377$	1.19934e102	2.05806
$378$	−1.12279e102	−1.73529
$379$	1.15116e101	0.160282	0.0801411	−	0.996784i	$-0.474463\pi$
$379$	1.15116e101	0.160282	0.0801411	+	0.996784i	$0.474463\pi$
$380$	9.20089e101	1.15446
$381$	5.48060e101	0.619857
$382$	6.55967e101	0.668927
$383$	−6.06995e101	−0.558256	−0.279128	−	0.960254i	$-0.590045\pi$
$383$	−6.06995e101	−0.558256	−0.279128	+	0.960254i	$0.590045\pi$
$384$	−1.99648e102	−1.65646
$385$	8.29545e101	0.621071
$386$	1.39616e102	0.943487
$387$	8.08875e100	0.0493512
$388$	1.95697e102	1.07828
$389$	−2.39539e102	−1.19225	−0.596126	−	0.802891i	$-0.703294\pi$
$389$	−2.39539e102	−1.19225	−0.596126	+	0.802891i	$0.703294\pi$
$390$	−7.37831e102	−3.31822
$391$	−1.75600e102	−0.713745
$392$	3.22541e102	1.18518
$393$	4.29767e102	1.42800
$394$	−2.57897e102	−0.775077
$395$	3.87627e101	0.105397
$396$	1.05886e102	0.260542
$397$	−3.59524e102	−0.800761	−0.400380	−	0.916349i	$-0.631122\pi$
$397$	−3.59524e102	−0.800761	−0.400380	+	0.916349i	$0.631122\pi$
$398$	9.65853e102	1.94774
$399$	8.34823e102	1.52463
$400$	1.57928e101	0.0261270
$401$	−3.64404e101	−0.0546237	−0.0273118	−	0.999627i	$-0.508695\pi$
$401$	−3.64404e101	−0.0546237	−0.0273118	+	0.999627i	$0.508695\pi$
$402$	−4.66314e102	−0.633504
$403$	6.06814e101	0.0747319
$404$	1.32873e103	1.48379
$405$	−1.15903e103	−1.17388
$406$	−2.99488e103	−2.75170
$407$	4.64508e102	0.387270
$408$	−1.31707e103	−0.996630
$409$	9.77226e102	0.671312	0.335656	−	0.941985i	$-0.391042\pi$
$409$	9.77226e102	0.671312	0.335656	+	0.941985i	$0.391042\pi$
$410$	3.04291e103	1.89814
$411$	−8.15995e102	−0.462312
$412$	−4.55802e103	−2.34605
$413$	2.49523e102	0.116704
$414$	1.05062e103	0.446616
$415$	−1.31277e103	−0.507330
$416$	6.26924e103	2.20307
$417$	1.76384e103	0.563747
$418$	1.84450e103	0.536309
$419$	−3.51118e103	−0.928964	−0.464482	−	0.885582i	$-0.653760\pi$
$419$	−3.51118e103	−0.928964	−0.464482	+	0.885582i	$0.653760\pi$
$420$	1.10662e104	2.66472
$421$	−6.96208e103	−1.52615	−0.763073	−	0.646312i	$-0.776311\pi$
$421$	−6.96208e103	−1.52615	−0.763073	+	0.646312i	$0.776311\pi$
$422$	−1.01415e104	−2.02423
$423$	−8.91517e102	−0.162063
$424$	3.63992e103	0.602754
$425$	7.51308e102	0.113359
$426$	−8.32247e103	−1.14439
$427$	1.33011e104	1.66720
$428$	3.28599e103	0.375524
$429$	−8.88405e103	−0.925866
$430$	1.86779e103	0.177551
$431$	7.46194e103	0.647142	0.323571	−	0.946204i	$-0.395116\pi$
$431$	7.46194e103	0.647142	0.323571	+	0.946204i	$0.395116\pi$
$432$	2.12783e103	0.168395
$433$	−8.67869e103	−0.626877	−0.313438	−	0.949609i	$-0.601481\pi$
$433$	−8.67869e103	−0.626877	−0.313438	+	0.949609i	$0.601481\pi$
$434$	−1.51528e103	−0.0999190
$435$	−2.05820e104	−1.23926
$436$	−1.17961e104	−0.648666
$437$	1.09924e104	0.552176
$438$	−5.75249e104	−2.64015
$439$	3.30817e104	1.38752	0.693761	−	0.720205i	$-0.255952\pi$
$439$	3.30817e104	1.38752	0.693761	+	0.720205i	$0.255952\pi$
$440$	8.19266e103	0.314083
$441$	1.76166e104	0.617443
$442$	9.67937e104	3.10218
$443$	7.86947e103	0.230674	0.115337	−	0.993326i	$-0.463205\pi$
$443$	7.86947e103	0.230674	0.115337	+	0.993326i	$0.463205\pi$
$444$	6.19659e104	1.66160
$445$	3.25707e104	0.799111
$446$	−1.19458e105	−2.68217
$447$	−1.58988e104	−0.326751
$448$	−1.36258e105	−2.56379
$449$	4.60758e104	0.793857	0.396928	−	0.917850i	$-0.370076\pi$
$449$	4.60758e104	0.793857	0.396928	+	0.917850i	$0.370076\pi$
$450$	−4.49511e103	−0.0709326
$451$	3.66390e104	0.529627
$452$	−7.23364e104	−0.958051
$453$	8.25368e104	1.00177
$454$	2.55832e104	0.284609
$455$	−2.72507e105	−2.77925
$456$	8.24479e104	0.771024
$457$	−1.38428e105	−1.18723	−0.593615	−	0.804749i	$-0.702300\pi$
$457$	−1.38428e105	−1.18723	−0.593615	+	0.804749i	$0.702300\pi$
$458$	1.59643e105	1.25593
$459$	1.01227e105	0.730627
$460$	1.45713e105	0.965083
$461$	4.66640e104	0.283658	0.141829	−	0.989891i	$-0.454702\pi$
$461$	4.66640e104	0.283658	0.141829	+	0.989891i	$0.454702\pi$
$462$	2.21844e105	1.23791
$463$	−2.20666e105	−1.13054	−0.565270	−	0.824906i	$-0.691228\pi$
$463$	−2.20666e105	−1.13054	−0.565270	+	0.824906i	$0.691228\pi$
$464$	5.67568e104	0.267029
$465$	−1.04136e104	−0.0449996
$466$	2.47157e105	0.981138
$467$	−1.53708e105	−0.560633	−0.280317	−	0.959908i	$-0.590439\pi$
$467$	−1.53708e105	−0.560633	−0.280317	+	0.959908i	$0.590439\pi$
$468$	−3.47836e105	−1.16591
$469$	−1.72226e105	−0.530606
$470$	−2.05862e105	−0.583056
$471$	5.71485e105	1.48826
$472$	2.46432e104	0.0590184
$473$	2.24896e104	0.0495412
$474$	1.03662e105	0.210076
$475$	−4.70313e104	−0.0876979
$476$	−1.45174e106	−2.49124
$477$	1.98805e105	0.314016
$478$	1.41804e106	2.06199
$479$	1.56833e105	0.209983	0.104992	−	0.994473i	$-0.466518\pi$
$479$	1.56833e105	0.209983	0.104992	+	0.994473i	$0.466518\pi$
$480$	−1.07587e106	−1.32657
$481$	−1.52592e106	−1.73301
$482$	1.51407e106	1.58412
$483$	1.32210e106	1.27453
$484$	−1.39845e106	−1.24238
$485$	8.27004e105	0.677187
$486$	−1.64169e106	−1.23925
$487$	6.28762e105	0.437615	0.218807	−	0.975768i	$-0.429783\pi$
$487$	6.28762e105	0.437615	0.218807	+	0.975768i	$0.429783\pi$
$488$	1.31363e106	0.843123
$489$	−9.03074e105	−0.534593
$490$	4.06787e106	2.22138
$491$	−3.14103e106	−1.58253	−0.791267	−	0.611471i	$-0.790578\pi$
$491$	−3.14103e106	−1.58253	−0.791267	+	0.611471i	$0.790578\pi$
$492$	4.88768e106	2.27238
$493$	2.70009e106	1.15858
$494$	−6.05921e106	−2.39995
$495$	4.47467e105	0.163627
$496$	2.87165e104	0.00969628
$497$	−3.07378e106	−0.958508
$498$	−3.51074e106	−1.01120
$499$	2.70493e106	0.719755	0.359878	−	0.932999i	$-0.382818\pi$
$499$	2.70493e106	0.719755	0.359878	+	0.932999i	$0.382818\pi$
$500$	−6.40104e106	−1.57375
$501$	−5.19412e106	−1.18011
$502$	−4.28457e106	−0.899726
$503$	2.43286e106	0.472260	0.236130	−	0.971721i	$-0.424121\pi$
$503$	2.43286e106	0.472260	0.236130	+	0.971721i	$0.424121\pi$
$504$	2.91040e106	0.522333
$505$	5.61514e106	0.931861
$506$	2.92111e106	0.448334
$507$	2.08040e107	2.95347
$508$	5.96612e106	0.783566
$509$	1.32069e107	1.60491	0.802453	−	0.596715i	$-0.203528\pi$
$509$	1.32069e107	1.60491	0.802453	+	0.596715i	$0.203528\pi$
$510$	−1.66109e107	−1.86797
$511$	−2.12460e107	−2.21132
$512$	4.97077e106	0.478917
$513$	−6.33674e106	−0.565236
$514$	1.11037e107	0.917115
$515$	−1.92620e107	−1.47338
$516$	3.00013e106	0.212558
$517$	−2.47873e106	−0.162687
$518$	3.81038e107	2.31709
$519$	−3.00440e107	−1.69296
$520$	−2.69130e107	−1.40550
$521$	2.67706e107	1.29589	0.647946	−	0.761686i	$-0.275628\pi$
$521$	2.67706e107	1.29589	0.647946	+	0.761686i	$0.275628\pi$
$522$	−1.61547e107	−0.724962
$523$	2.07136e106	0.0861865	0.0430932	−	0.999071i	$-0.486279\pi$
$523$	2.07136e106	0.0861865	0.0430932	+	0.999071i	$0.486279\pi$
$524$	4.67840e107	1.80514
$525$	−5.65661e106	−0.202425
$526$	−6.44518e107	−2.13943
$527$	1.36613e106	0.0420699
$528$	−4.20424e106	−0.120129
$529$	−2.03051e107	−0.538402
$530$	4.59065e107	1.12974
$531$	1.34596e106	0.0307467
$532$	9.08779e107	1.92730
$533$	−1.20360e108	−2.37005
$534$	8.71035e107	1.59278
$535$	1.38864e107	0.235839
$536$	−1.70092e107	−0.268334
$537$	1.54851e108	2.26950
$538$	−2.24892e108	−3.06249
$539$	4.89803e107	0.619819
$540$	−8.39983e107	−0.987910
$541$	−6.38679e107	−0.698217	−0.349109	−	0.937082i	$-0.613516\pi$
$541$	−6.38679e107	−0.698217	−0.349109	+	0.937082i	$0.613516\pi$
$542$	2.68122e108	2.72496
$543$	1.49454e108	1.41226
$544$	1.41140e108	1.24021
$545$	−4.98496e107	−0.407380
$546$	−7.28762e108	−5.53957
$547$	3.37408e107	0.238592	0.119296	−	0.992859i	$-0.461936\pi$
$547$	3.37408e107	0.238592	0.119296	+	0.992859i	$0.461936\pi$
$548$	−8.88284e107	−0.584413
$549$	7.17480e107	0.439240
$550$	−1.24980e107	−0.0712056
$551$	−1.69023e108	−0.896310
$552$	1.30572e108	0.644548
$553$	3.82862e107	0.175954
$554$	3.02383e108	1.29396
$555$	2.61865e108	1.04353
$556$	1.92009e108	0.712636
$557$	4.00405e107	0.138427	0.0692133	−	0.997602i	$-0.477951\pi$
$557$	4.00405e107	0.138427	0.0692133	+	0.997602i	$0.477951\pi$
$558$	−8.17360e106	−0.0263246
$559$	−7.38787e107	−0.221693
$560$	−1.28960e108	−0.360601
$561$	−2.00008e108	−0.521211
$562$	6.83068e108	1.65913
$563$	7.82011e108	1.77064	0.885322	−	0.464978i	$-0.153938\pi$
$563$	7.82011e108	1.77064	0.885322	+	0.464978i	$0.153938\pi$
$564$	−3.30666e108	−0.698015
$565$	−3.05689e108	−0.601682
$566$	−9.19518e108	−1.68776
$567$	−1.14479e109	−1.95972
$568$	−3.03569e108	−0.484729
$569$	−3.30571e108	−0.492414	−0.246207	−	0.969217i	$-0.579184\pi$
$569$	−3.30571e108	−0.492414	−0.246207	+	0.969217i	$0.579184\pi$
$570$	1.03983e109	1.44512
$571$	−3.46359e108	−0.449159	−0.224580	−	0.974456i	$-0.572101\pi$
$571$	−3.46359e108	−0.449159	−0.224580	+	0.974456i	$0.572101\pi$
$572$	−9.67108e108	−1.17039
$573$	4.45265e108	0.502934
$574$	3.00551e109	3.16883
$575$	−7.44828e107	−0.0733122
$576$	−7.34995e108	−0.675455
$577$	1.02423e108	0.0878931	0.0439465	−	0.999034i	$-0.486007\pi$
$577$	1.02423e108	0.0878931	0.0439465	+	0.999034i	$0.486007\pi$
$578$	2.04612e108	0.163977
$579$	9.47701e108	0.709362
$580$	−2.24053e109	−1.56656
$581$	−1.29664e109	−0.846957
$582$	2.21165e109	1.34976
$583$	5.52749e108	0.315224
$584$	−2.09827e109	−1.11829
$585$	−1.46994e109	−0.732221
$586$	−1.97942e109	−0.921682
$587$	4.07944e109	1.77581	0.887903	−	0.460030i	$-0.152162\pi$
$587$	4.07944e109	1.77581	0.887903	+	0.460030i	$0.152162\pi$
$588$	6.53402e109	2.65935
$589$	−8.55185e107	−0.0325466
$590$	3.10798e108	0.110618
$591$	−1.75058e109	−0.582743
$592$	−7.22117e108	−0.224854
$593$	7.92403e107	0.0230827	0.0115413	−	0.999933i	$-0.496326\pi$
$593$	7.92403e107	0.0230827	0.0115413	+	0.999933i	$0.496326\pi$
$594$	−1.68391e109	−0.458939
$595$	−6.13498e109	−1.56456
$596$	−1.73072e109	−0.413048
$597$	6.55614e109	1.46441
$598$	−9.59589e109	−2.00627
$599$	−5.68595e109	−1.11287	−0.556434	−	0.830892i	$-0.687831\pi$
$599$	−5.68595e109	−1.11287	−0.556434	+	0.830892i	$0.687831\pi$
$600$	−5.58652e108	−0.102369
$601$	5.91730e109	1.01527	0.507635	−	0.861572i	$-0.330520\pi$
$601$	5.91730e109	1.01527	0.507635	+	0.861572i	$0.330520\pi$
$602$	1.84483e109	0.296411
$603$	−9.29010e108	−0.139793
$604$	8.98486e109	1.26635
$605$	−5.90978e109	−0.780251
$606$	1.50165e110	1.85738
$607$	1.01558e110	1.17696	0.588478	−	0.808513i	$-0.299727\pi$
$607$	1.01558e110	1.17696	0.588478	+	0.808513i	$0.299727\pi$
$608$	−8.83525e109	−0.959462
$609$	−2.03290e110	−2.06887
$610$	1.65675e110	1.58026
$611$	8.14269e109	0.728014
$612$	−7.83087e109	−0.656340
$613$	2.46344e110	1.93576	0.967882	−	0.251405i	$-0.0808925\pi$
$613$	2.46344e110	1.93576	0.967882	+	0.251405i	$0.0808925\pi$
$614$	−2.32123e110	−1.71028
$615$	2.06551e110	1.42712
$616$	8.09196e109	0.524343
$617$	−1.07700e110	−0.654562	−0.327281	−	0.944927i	$-0.606132\pi$
$617$	−1.07700e110	−0.654562	−0.327281	+	0.944927i	$0.606132\pi$
$618$	−5.15120e110	−2.93673
$619$	3.99627e109	0.213734	0.106867	−	0.994273i	$-0.465918\pi$
$619$	3.99627e109	0.213734	0.106867	+	0.994273i	$0.465918\pi$
$620$	−1.13361e109	−0.0568844
$621$	−1.00354e110	−0.472516
$622$	−5.38752e110	−2.38050
$623$	3.21704e110	1.33407
$624$	1.38110e110	0.537568
$625$	−2.40972e110	−0.880451
$626$	3.90905e110	1.34087
$627$	1.25203e110	0.403225
$628$	6.22112e110	1.88132
$629$	−3.43532e110	−0.975588
$630$	3.67059e110	0.979002
$631$	−6.37150e109	−0.159618	−0.0798090	−	0.996810i	$-0.525431\pi$
$631$	−6.37150e109	−0.159618	−0.0798090	+	0.996810i	$0.525431\pi$
$632$	3.78118e109	0.0889821
$633$	−6.88397e110	−1.52192
$634$	6.96868e110	1.44752
$635$	2.52125e110	0.492101
$636$	7.37373e110	1.35248
$637$	−1.60901e111	−2.77365
$638$	−4.49159e110	−0.727752
$639$	−1.65804e110	−0.252528
$640$	−9.18443e110	−1.31505
$641$	1.31257e111	1.76697	0.883487	−	0.468456i	$-0.155189\pi$
$641$	1.31257e111	1.76697	0.883487	+	0.468456i	$0.155189\pi$
$642$	3.71362e110	0.470072
$643$	7.09938e110	0.845059	0.422529	−	0.906349i	$-0.361142\pi$
$643$	7.09938e110	0.845059	0.422529	+	0.906349i	$0.361142\pi$
$644$	1.43922e111	1.61115
$645$	1.26784e110	0.133492
$646$	−1.36412e111	−1.35104
$647$	−1.32425e111	−1.23382	−0.616908	−	0.787035i	$-0.711615\pi$
$647$	−1.32425e111	−1.23382	−0.616908	+	0.787035i	$0.711615\pi$
$648$	−1.13060e111	−0.991054
$649$	3.74224e109	0.0308650
$650$	4.10562e110	0.318640
$651$	−1.02856e110	−0.0751243
$652$	−9.83077e110	−0.675783
$653$	1.41575e111	0.916041	0.458020	−	0.888942i	$-0.348559\pi$
$653$	1.41575e111	0.916041	0.458020	+	0.888942i	$0.348559\pi$
$654$	−1.33312e111	−0.811986
$655$	1.97707e111	1.13368
$656$	−5.69584e110	−0.307508
$657$	−1.14603e111	−0.582593
$658$	−2.03331e111	−0.973379
$659$	−1.90804e109	−0.00860230	−0.00430115	−	0.999991i	$-0.501369\pi$
$659$	−1.90804e109	−0.00860230	−0.00430115	+	0.999991i	$0.501369\pi$
$660$	1.65966e111	0.704750
$661$	−7.70837e110	−0.308322	−0.154161	−	0.988046i	$-0.549267\pi$
$661$	−7.70837e110	−0.308322	−0.154161	+	0.988046i	$0.549267\pi$
$662$	6.02019e111	2.26840
$663$	6.57029e111	2.33238
$664$	−1.28057e111	−0.428316
$665$	3.84045e111	1.21040
$666$	2.05537e111	0.610460
$667$	−2.67680e111	−0.749282
$668$	−5.65427e111	−1.49178
$669$	−8.10869e111	−2.01660
$670$	−2.14519e111	−0.502935
$671$	1.99485e111	0.440931
$672$	−1.06265e112	−2.21464
$673$	−5.16676e111	−1.01537	−0.507684	−	0.861543i	$-0.669498\pi$
$673$	−5.16676e111	−1.01537	−0.507684	+	0.861543i	$0.669498\pi$
$674$	1.08015e110	0.0200180
$675$	4.29366e110	0.0750462
$676$	2.26470e112	3.73350
$677$	−3.67481e111	−0.571456	−0.285728	−	0.958311i	$-0.592235\pi$
$677$	−3.67481e111	−0.571456	−0.285728	+	0.958311i	$0.592235\pi$
$678$	−8.17501e111	−1.19927
$679$	8.16838e111	1.13052
$680$	−6.05896e111	−0.791218
$681$	1.73657e111	0.213984
$682$	−2.27255e110	−0.0264259
$683$	8.30250e110	0.0911153	0.0455576	−	0.998962i	$-0.485494\pi$
$683$	8.30250e110	0.0911153	0.0455576	+	0.998962i	$0.485494\pi$
$684$	4.90207e111	0.507766
$685$	−3.75384e111	−0.367027
$686$	1.31460e112	1.21336
$687$	1.08365e112	0.944270
$688$	−3.49619e110	−0.0287642
$689$	−1.81579e112	−1.41061
$690$	1.64676e112	1.20807
$691$	2.65692e111	0.184075	0.0920375	−	0.995756i	$-0.470662\pi$
$691$	2.65692e111	0.184075	0.0920375	+	0.995756i	$0.470662\pi$
$692$	−3.27055e112	−2.14008
$693$	4.41966e111	0.273166
$694$	2.42460e112	1.41560
$695$	8.11420e111	0.447555
$696$	−2.00771e112	−1.04625
$697$	−2.70967e112	−1.33420
$698$	−1.01106e112	−0.470421
$699$	1.67769e112	0.737670
$700$	−6.15773e111	−0.255887
$701$	−4.59646e112	−1.80535	−0.902676	−	0.430320i	$-0.858401\pi$
$701$	−4.59646e112	−1.80535	−0.902676	+	0.430320i	$0.858401\pi$
$702$	5.53168e112	2.05372
$703$	2.15048e112	0.754745
$704$	−2.04355e112	−0.678054
$705$	−1.39738e112	−0.438372
$706$	8.77474e110	0.0260285
$707$	5.54612e112	1.55569
$708$	4.99220e111	0.132427
$709$	−2.87153e112	−0.720422	−0.360211	−	0.932871i	$-0.617295\pi$
$709$	−2.87153e112	−0.720422	−0.360211	+	0.932871i	$0.617295\pi$
$710$	−3.82860e112	−0.908522
$711$	2.06520e111	0.0463568
$712$	3.17718e112	0.674655
$713$	−1.35434e111	−0.0272077
$714$	−1.64067e113	−3.11847
$715$	−4.08695e112	−0.735039
$716$	1.68569e113	2.86889
$717$	9.62556e112	1.55031
$718$	1.21252e113	1.84831
$719$	6.16765e112	0.889875	0.444937	−	0.895562i	$-0.353226\pi$
$719$	6.16765e112	0.889875	0.444937	+	0.895562i	$0.353226\pi$
$720$	−6.95624e111	−0.0950038
$721$	−1.90252e113	−2.45972
$722$	−4.38870e112	−0.537176
$723$	1.02774e113	1.19102
$724$	1.62694e113	1.78525
$725$	1.14527e112	0.119003
$726$	−1.58044e113	−1.55519
$727$	−1.56694e113	−1.46030	−0.730150	−	0.683286i	$-0.760550\pi$
$727$	−1.56694e113	−1.46030	−0.730150	+	0.683286i	$0.760550\pi$
$728$	−2.65822e113	−2.34640
$729$	3.72100e112	0.311116
$730$	−2.64633e113	−2.09600
$731$	−1.66324e112	−0.124801
$732$	2.66115e113	1.89183
$733$	2.53103e113	1.70487	0.852433	−	0.522837i	$-0.175126\pi$
$733$	2.53103e113	1.70487	0.852433	+	0.522837i	$0.175126\pi$
$734$	−3.07978e113	−1.96573
$735$	2.76124e113	1.67015
$736$	−1.39923e113	−0.802074
$737$	−2.58298e112	−0.140331
$738$	1.62121e113	0.834858
$739$	2.83847e113	1.38557	0.692786	−	0.721143i	$-0.256383\pi$
$739$	2.83847e113	1.38557	0.692786	+	0.721143i	$0.256383\pi$
$740$	2.85063e113	1.31913
$741$	−4.11295e113	−1.80441
$742$	4.53422e113	1.88603
$743$	−1.02192e112	−0.0403051	−0.0201525	−	0.999797i	$-0.506415\pi$
$743$	−1.02192e112	−0.0403051	−0.0201525	+	0.999797i	$0.506415\pi$
$744$	−1.01581e112	−0.0379912
$745$	−7.31394e112	−0.259405
$746$	7.79731e112	0.262277
$747$	−6.99423e112	−0.223139
$748$	−2.17726e113	−0.658866
$749$	1.37157e113	0.393719
$750$	−7.23406e113	−1.96998
$751$	−5.65154e113	−1.46012	−0.730061	−	0.683382i	$-0.760508\pi$
$751$	−5.65154e113	−1.46012	−0.730061	+	0.683382i	$0.760508\pi$
$752$	3.85340e112	0.0944581
$753$	−2.90833e113	−0.676461
$754$	1.47550e114	3.25664
$755$	3.79695e113	0.795299
$756$	−8.29658e113	−1.64926
$757$	−7.61642e113	−1.43702	−0.718512	−	0.695515i	$-0.755176\pi$
$757$	−7.61642e113	−1.43702	−0.718512	+	0.695515i	$0.755176\pi$
$758$	1.41622e113	0.253627
$759$	1.98283e113	0.337081
$760$	3.79286e113	0.612111
$761$	9.86160e112	0.151096	0.0755481	−	0.997142i	$-0.475929\pi$
$761$	9.86160e112	0.151096	0.0755481	+	0.997142i	$0.475929\pi$
$762$	6.74255e113	0.980850
$763$	−4.92368e113	−0.680097
$764$	4.84711e113	0.635763
$765$	−3.30928e113	−0.412199
$766$	−7.46760e113	−0.883374
$767$	−1.22933e113	−0.138119
$768$	−6.43519e113	−0.686741
$769$	−6.73261e113	−0.682485	−0.341242	−	0.939975i	$-0.610848\pi$
$769$	−6.73261e113	−0.682485	−0.341242	+	0.939975i	$0.610848\pi$
$770$	1.02055e114	0.982770
$771$	7.53710e113	0.689535
$772$	1.03166e114	0.896710
$773$	7.74278e113	0.639451	0.319725	−	0.947510i	$-0.396409\pi$
$773$	7.74278e113	0.639451	0.319725	+	0.947510i	$0.396409\pi$
$774$	9.95124e112	0.0780925
$775$	5.79458e111	0.00432120
$776$	8.06717e113	0.571720
$777$	2.58646e114	1.74211
$778$	−2.94695e114	−1.88660
$779$	1.69623e114	1.03218
$780$	−5.45203e114	−3.15371
$781$	−4.60993e113	−0.253500
$782$	−2.16033e114	−1.12942
$783$	1.54308e114	0.767004
$784$	−7.61439e113	−0.359874
$785$	2.62901e114	1.18152
$786$	5.28724e114	2.25964
$787$	−9.19447e113	−0.373702	−0.186851	−	0.982388i	$-0.559828\pi$
$787$	−9.19447e113	−0.373702	−0.186851	+	0.982388i	$0.559828\pi$
$788$	−1.90567e114	−0.736650
$789$	−4.37494e114	−1.60853
$790$	4.76880e113	0.166778
$791$	−3.01932e114	−1.00447
$792$	4.36490e113	0.138143
$793$	−6.55312e114	−1.97314
$794$	−4.42307e114	−1.26711
$795$	3.11610e114	0.849394
$796$	7.13694e114	1.85117
$797$	5.98420e114	1.47707	0.738537	−	0.674213i	$-0.235517\pi$
$797$	5.98420e114	1.47707	0.738537	+	0.674213i	$0.235517\pi$
$798$	1.02705e115	2.41255
$799$	1.83317e114	0.409832
$800$	5.98661e113	0.127387
$801$	1.73531e114	0.351474
$802$	−4.48311e113	−0.0864354
$803$	−3.18638e114	−0.584835
$804$	−3.44572e114	−0.602096
$805$	6.08207e114	1.01184
$806$	7.46537e113	0.118254
$807$	−1.52655e115	−2.30254
$808$	5.47740e114	0.786730
$809$	2.98990e114	0.408969	0.204484	−	0.978870i	$-0.434448\pi$
$809$	2.98990e114	0.408969	0.204484	+	0.978870i	$0.434448\pi$
$810$	−1.42591e115	−1.85752
$811$	−1.01598e115	−1.26056	−0.630279	−	0.776369i	$-0.717059\pi$
$811$	−1.01598e115	−1.26056	−0.630279	+	0.776369i	$0.717059\pi$
$812$	−2.21299e115	−2.61527
$813$	1.81999e115	2.04877
$814$	5.71465e114	0.612809
$815$	−4.15443e114	−0.424410
$816$	3.10928e114	0.302621
$817$	1.04117e114	0.0965500
$818$	1.20224e115	1.06227
$819$	−1.45187e115	−1.22240
$820$	2.24849e115	1.80403
$821$	2.10333e115	1.60825	0.804123	−	0.594463i	$-0.202635\pi$
$821$	2.10333e115	1.60825	0.804123	+	0.594463i	$0.202635\pi$
$822$	−1.00388e115	−0.731554
$823$	1.42789e115	0.991751	0.495875	−	0.868394i	$-0.334847\pi$
$823$	1.42789e115	0.991751	0.495875	+	0.868394i	$0.334847\pi$
$824$	−1.87895e115	−1.24391
$825$	−8.48354e113	−0.0535361
$826$	3.06978e114	0.184669
$827$	−3.17337e115	−1.81993	−0.909963	−	0.414690i	$-0.863890\pi$
$827$	−3.17337e115	−1.81993	−0.909963	+	0.414690i	$0.863890\pi$
$828$	7.76334e114	0.424473
$829$	−8.50411e114	−0.443328	−0.221664	−	0.975123i	$-0.571149\pi$
$829$	−8.50411e114	−0.443328	−0.221664	+	0.975123i	$0.571149\pi$
$830$	−1.61505e115	−0.802789
$831$	2.05255e115	0.972868
$832$	6.71309e115	3.03425
$833$	−3.62238e115	−1.56141
$834$	2.16997e115	0.892062
$835$	−2.38946e115	−0.936881
$836$	1.36295e115	0.509720
$837$	7.80730e113	0.0278513
$838$	−4.31965e115	−1.46998
$839$	1.18148e115	0.383558	0.191779	−	0.981438i	$-0.438574\pi$
$839$	1.18148e115	0.383558	0.191779	+	0.981438i	$0.438574\pi$
$840$	4.56180e115	1.41288
$841$	7.31841e114	0.216259
$842$	−8.56515e115	−2.41495
$843$	4.63661e115	1.24742
$844$	−7.49382e115	−1.92387
$845$	9.57051e115	2.34474
$846$	−1.09680e115	−0.256446
$847$	−5.83714e115	−1.30258
$848$	−8.59294e114	−0.183023
$849$	−6.24162e115	−1.26895
$850$	9.24302e114	0.179377
$851$	3.40569e115	0.630939
$852$	−6.14969e115	−1.08765
$853$	−7.36429e115	−1.24350	−0.621748	−	0.783217i	$-0.713577\pi$
$853$	−7.36429e115	−1.24350	−0.621748	+	0.783217i	$0.713577\pi$
$854$	1.63638e116	2.63815
$855$	2.07159e115	0.318890
$856$	1.35458e115	0.199108
$857$	1.40516e116	1.97235	0.986177	−	0.165698i	$-0.0529877\pi$
$857$	1.40516e116	1.97235	0.986177	+	0.165698i	$0.0529877\pi$
$858$	−1.09297e116	−1.46507
$859$	−5.37749e114	−0.0688414	−0.0344207	−	0.999407i	$-0.510959\pi$
$859$	−5.37749e114	−0.0688414	−0.0344207	+	0.999407i	$0.510959\pi$
$860$	1.38016e115	0.168748
$861$	2.04012e116	2.38249
$862$	9.18011e115	1.02403
$863$	−1.26435e116	−1.34722	−0.673612	−	0.739085i	$-0.735258\pi$
$863$	−1.26435e116	−1.34722	−0.673612	+	0.739085i	$0.735258\pi$
$864$	8.06603e115	0.821045
$865$	−1.38212e116	−1.34403
$866$	−1.06770e116	−0.991958
$867$	1.38889e115	0.123286
$868$	−1.11968e115	−0.0949651
$869$	5.74200e114	0.0465352
$870$	−2.53211e116	−1.96098
$871$	8.48513e115	0.627973
$872$	−4.86267e115	−0.343933
$873$	4.40613e115	0.297848
$874$	1.35235e116	0.873752
$875$	−2.67179e116	−1.65000
$876$	−4.25067e116	−2.50926
$877$	2.83519e116	1.59992	0.799961	−	0.600053i	$-0.204854\pi$
$877$	2.83519e116	1.59992	0.799961	+	0.600053i	$0.204854\pi$
$878$	4.06990e116	2.19559
$879$	−1.34361e116	−0.692968
$880$	−1.93408e115	−0.0953695
$881$	−2.80876e116	−1.32424	−0.662120	−	0.749398i	$-0.730343\pi$
$881$	−2.80876e116	−1.32424	−0.662120	+	0.749398i	$0.730343\pi$
$882$	2.16729e116	0.977029
$883$	−3.09875e116	−1.33579	−0.667897	−	0.744254i	$-0.732805\pi$
$883$	−3.09875e116	−1.33579	−0.667897	+	0.744254i	$0.732805\pi$
$884$	7.15234e116	2.94838
$885$	2.10967e115	0.0831680
$886$	9.68146e115	0.365014
$887$	−1.92140e115	−0.0692844	−0.0346422	−	0.999400i	$-0.511029\pi$
$887$	−1.92140e115	−0.0692844	−0.0346422	+	0.999400i	$0.511029\pi$
$888$	2.55441e116	0.881005
$889$	2.49026e116	0.821533
$890$	4.00704e116	1.26450
$891$	−1.71690e116	−0.518295
$892$	−8.82703e116	−2.54919
$893$	−1.14755e116	−0.317059
$894$	−1.95596e116	−0.517044
$895$	7.12365e116	1.80174
$896$	−9.07154e116	−2.19540
$897$	−6.51362e116	−1.50842
$898$	5.66850e116	1.25618
$899$	2.08248e115	0.0441645
$900$	−3.32155e115	−0.0674159
$901$	−4.08791e116	−0.794094
$902$	4.50754e116	0.838072
$903$	1.25226e116	0.222857
$904$	−2.98191e116	−0.507973
$905$	6.87537e116	1.12118
$906$	1.01541e117	1.58518
$907$	9.12542e116	1.36385	0.681923	−	0.731424i	$-0.261144\pi$
$907$	9.12542e116	1.36385	0.681923	+	0.731424i	$0.261144\pi$
$908$	1.89041e116	0.270499
$909$	2.99165e116	0.409861
$910$	−3.35254e117	−4.39783
$911$	−1.36442e117	−1.71384	−0.856921	−	0.515448i	$-0.827626\pi$
$911$	−1.36442e117	−1.71384	−0.856921	+	0.515448i	$0.827626\pi$
$912$	−1.94639e116	−0.234117
$913$	−1.94464e116	−0.223998
$914$	−1.70302e117	−1.87865
$915$	1.12459e117	1.18812
$916$	1.17964e117	1.19366
$917$	1.95276e117	1.89261
$918$	1.24535e117	1.15613
$919$	5.31017e116	0.472222	0.236111	−	0.971726i	$-0.424127\pi$
$919$	5.31017e116	0.472222	0.236111	+	0.971726i	$0.424127\pi$
$920$	6.00671e116	0.511702
$921$	−1.57563e117	−1.28588
$922$	5.74087e116	0.448855
$923$	1.51437e117	1.13440
$924$	1.63926e117	1.17654
$925$	−1.45713e116	−0.100207
$926$	−2.71476e117	−1.78895
$927$	−1.02624e117	−0.648038
$928$	2.15150e117	1.30195
$929$	−2.64474e117	−1.53377	−0.766887	−	0.641782i	$-0.778196\pi$
$929$	−2.64474e117	−1.53377	−0.766887	+	0.641782i	$0.778196\pi$
$930$	−1.28114e116	−0.0712066
$931$	2.26758e117	1.20796
$932$	1.82631e117	0.932494
$933$	−3.65701e117	−1.78979
$934$	−1.89100e117	−0.887135
$935$	−9.20098e116	−0.413786
$936$	−1.43388e117	−0.618182
$937$	−4.74231e117	−1.96009	−0.980044	−	0.198778i	$-0.936303\pi$
$937$	−4.74231e117	−1.96009	−0.980044	+	0.198778i	$0.936303\pi$
$938$	−2.11883e117	−0.839620
$939$	2.65343e117	1.00813
$940$	−1.52117e117	−0.554149
$941$	3.62656e117	1.26679	0.633396	−	0.773828i	$-0.281661\pi$
$941$	3.62656e117	1.26679	0.633396	+	0.773828i	$0.281661\pi$
$942$	7.03073e117	2.35499
$943$	2.68630e117	0.862865
$944$	−5.81763e115	−0.0179206
$945$	−3.50609e117	−1.03578
$946$	2.76680e116	0.0783930
$947$	−3.68385e117	−1.00110	−0.500550	−	0.865707i	$-0.666869\pi$
$947$	−3.68385e117	−1.00110	−0.500550	+	0.865707i	$0.666869\pi$
$948$	7.65989e116	0.199661
$949$	1.04673e118	2.61710
$950$	−5.78606e116	−0.138771
$951$	4.73029e117	1.08832
$952$	−5.98449e117	−1.32089
$953$	−6.07912e117	−1.28728	−0.643638	−	0.765330i	$-0.722576\pi$
$953$	−6.07912e117	−1.28728	−0.643638	+	0.765330i	$0.722576\pi$
$954$	2.44581e117	0.496892
$955$	2.04836e117	0.399276
$956$	1.04783e118	1.95976
$957$	−3.04886e117	−0.547161
$958$	1.92945e117	0.332274
$959$	−3.70769e117	−0.612730
$960$	−1.15204e118	−1.82707
$961$	−6.55959e117	−0.998396
$962$	−1.87727e118	−2.74228
$963$	7.39842e116	0.103729
$964$	1.11879e118	1.50558
$965$	4.35973e117	0.563158
$966$	1.62652e118	2.01680
$967$	2.78325e117	0.331288	0.165644	−	0.986186i	$-0.447030\pi$
$967$	2.78325e117	0.331288	0.165644	+	0.986186i	$0.447030\pi$
$968$	−5.76481e117	−0.658731
$969$	−9.25952e117	−1.01578
$970$	1.01743e118	1.07157
$971$	−9.77903e117	−0.988863	−0.494431	−	0.869217i	$-0.664624\pi$
$971$	−9.77903e117	−0.988863	−0.494431	+	0.869217i	$0.664624\pi$
$972$	−1.21309e118	−1.17781
$973$	8.01446e117	0.747166
$974$	7.73538e117	0.692473
$975$	2.78686e117	0.239570
$976$	−3.10116e117	−0.256009
$977$	1.82577e117	0.144747	0.0723737	−	0.997378i	$-0.476943\pi$
$977$	1.82577e117	0.144747	0.0723737	+	0.997378i	$0.476943\pi$
$978$	−1.11101e118	−0.845930
$979$	4.82478e117	0.352826
$980$	3.00586e118	2.11124
$981$	−2.65590e117	−0.179178
$982$	−3.86427e118	−2.50417
$983$	1.22137e118	0.760296	0.380148	−	0.924926i	$-0.375873\pi$
$983$	1.22137e118	0.760296	0.380148	+	0.924926i	$0.375873\pi$
$984$	2.01484e118	1.20485
$985$	−8.05323e117	−0.462636
$986$	3.32180e118	1.83331
$987$	−1.38020e118	−0.731836
$988$	−4.47731e118	−2.28096
$989$	1.64889e117	0.0807122
$990$	5.50499e117	0.258920
$991$	2.94733e118	1.33204	0.666022	−	0.745932i	$-0.267996\pi$
$991$	2.94733e118	1.33204	0.666022	+	0.745932i	$0.267996\pi$
$992$	1.08856e117	0.0472762
$993$	4.08646e118	1.70550
$994$	−3.78154e118	−1.51672
$995$	3.01603e118	1.16258
$996$	−2.59417e118	−0.961071
$997$	−5.65634e117	−0.201408	−0.100704	−	0.994916i	$-0.532110\pi$
$997$	−5.65634e117	−0.201408	−0.100704	+	0.994916i	$0.532110\pi$
$998$	3.32776e118	1.13893
$999$	−1.96325e118	−0.645862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.80.a.a.1.6	✓	6
3.2	odd	2		9.80.a.b.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.80.a.a.1.6	✓	6	1.1	even	1	trivial
9.80.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q+1.23026e12 q^{2} +8.35089e18 q^{3} +9.09069e23 q^{4} +3.84167e27 q^{5} +1.02737e31 q^{6} +3.79445e33 q^{7} +3.74744e35 q^{8} +2.04677e37 q^{9} +O(q^{10})\)	\(q+1.23026e12 q^{2} +8.35089e18 q^{3} +9.09069e23 q^{4} +3.84167e27 q^{5} +1.02737e31 q^{6} +3.79445e33 q^{7} +3.74744e35 q^{8} +2.04677e37 q^{9} +4.72625e39 q^{10} +5.69076e40 q^{11} +7.59153e42 q^{12} -1.86943e44 q^{13} +4.66815e45 q^{14} +3.20814e46 q^{15} -8.84676e46 q^{16} -4.20866e48 q^{17} +2.51806e49 q^{18} +2.63459e50 q^{19} +3.49235e51 q^{20} +3.16871e52 q^{21} +7.00109e52 q^{22} +4.17236e53 q^{23} +3.12944e54 q^{24} -1.78515e54 q^{25} -2.29987e56 q^{26} -2.40521e56 q^{27} +3.44942e57 q^{28} -6.41555e57 q^{29} +3.94684e58 q^{30} -3.24599e57 q^{31} -3.35356e59 q^{32} +4.75229e59 q^{33} -5.17773e60 q^{34} +1.45771e61 q^{35} +1.86066e61 q^{36} +8.16250e61 q^{37} +3.24122e62 q^{38} -1.56114e63 q^{39} +1.43964e63 q^{40} +6.43833e63 q^{41} +3.89832e64 q^{42} +3.95195e63 q^{43} +5.17329e64 q^{44} +7.86304e64 q^{45} +5.13307e65 q^{46} -4.35572e65 q^{47} -7.38783e65 q^{48} +8.60698e66 q^{49} -2.19619e66 q^{50} -3.51460e67 q^{51} -1.69944e68 q^{52} +9.71309e67 q^{53} -2.95903e68 q^{54} +2.18620e68 q^{55} +1.42195e69 q^{56} +2.20011e69 q^{57} -7.89278e69 q^{58} +6.57600e68 q^{59} +2.91642e70 q^{60} +3.50542e70 q^{61} -3.99340e69 q^{62} +7.76639e70 q^{63} -3.59099e71 q^{64} -7.18172e71 q^{65} +5.84654e71 q^{66} -4.53890e71 q^{67} -3.82596e72 q^{68} +3.48429e72 q^{69} +1.79335e73 q^{70} -8.10072e72 q^{71} +7.67016e72 q^{72} -5.59922e73 q^{73} +1.00420e74 q^{74} -1.49076e73 q^{75} +2.39502e74 q^{76} +2.15933e74 q^{77} -1.92060e75 q^{78} +1.00900e74 q^{79} -3.39864e74 q^{80} -3.01700e75 q^{81} +7.92080e75 q^{82} -3.41719e75 q^{83} +2.88057e76 q^{84} -1.61683e76 q^{85} +4.86191e75 q^{86} -5.35756e76 q^{87} +2.13258e76 q^{88} +8.47827e76 q^{89} +9.67356e76 q^{90} -7.09345e77 q^{91} +3.79296e77 q^{92} -2.71069e76 q^{93} -5.35865e77 q^{94} +1.01212e78 q^{95} -2.80052e78 q^{96} +2.15272e78 q^{97} +1.05888e79 q^{98} +1.16477e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16086577320 q^{2} + 19\!\cdots\!80 q^{3}+ \cdots + 98\!\cdots\!22 q^{9}+O(q^{10}) \) 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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