LMFDB - Embedded newform 1.82.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,82,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, 82, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 82);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 82 $
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:	$41.5501285538$
Analytic rank:	$1$
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 - 27\!\cdots\!00 $ x^6 - 3x^5 - 457312410974129060102x^4 - 374381904318715551718938507366x^3 + 44188779498690494552956207183337235151045x^2 + 43570916530513802078515169165814719895908350666425*x - 274514886475906972833021199940770859283985201013623777350000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.10202e9$ 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)

$f(q)$	$=$	$q-3.79502e11 q^{2} -3.74133e19 q^{3} -2.27383e24 q^{4} -3.57322e28 q^{5} +1.41984e31 q^{6} -3.75122e33 q^{7} +1.78050e36 q^{8} +9.56330e38 q^{9} +O(q^{10})$	\(q-3.79502e11 q^{2} -3.74133e19 q^{3} -2.27383e24 q^{4} -3.57322e28 q^{5} +1.41984e31 q^{6} -3.75122e33 q^{7} +1.78050e36 q^{8} +9.56330e38 q^{9} +1.35605e40 q^{10} -3.06461e41 q^{11} +8.50715e43 q^{12} +2.01230e44 q^{13} +1.42360e45 q^{14} +1.33686e48 q^{15} +4.82208e48 q^{16} -5.61961e49 q^{17} -3.62930e50 q^{18} -7.00483e51 q^{19} +8.12490e52 q^{20} +1.40346e53 q^{21} +1.16303e53 q^{22} -4.09838e54 q^{23} -6.66146e55 q^{24} +8.63203e56 q^{25} -7.63673e55 q^{26} -1.91894e58 q^{27} +8.52964e57 q^{28} +2.44103e59 q^{29} -5.07342e59 q^{30} +8.85416e59 q^{31} -6.13499e60 q^{32} +1.14657e61 q^{33} +2.13266e61 q^{34} +1.34040e62 q^{35} -2.17453e63 q^{36} +3.25478e63 q^{37} +2.65835e63 q^{38} -7.52869e63 q^{39} -6.36214e64 q^{40} -3.25964e65 q^{41} -5.32615e64 q^{42} -4.15451e65 q^{43} +6.96840e65 q^{44} -3.41718e67 q^{45} +1.55535e66 q^{46} +2.63440e67 q^{47} -1.80410e68 q^{48} -2.69682e68 q^{49} -3.27588e68 q^{50} +2.10248e69 q^{51} -4.57563e68 q^{52} +6.39417e69 q^{53} +7.28244e69 q^{54} +1.09505e70 q^{55} -6.67907e69 q^{56} +2.62074e71 q^{57} -9.26376e70 q^{58} +1.38928e71 q^{59} -3.03980e72 q^{60} +1.44130e72 q^{61} -3.36017e71 q^{62} -3.58741e72 q^{63} -9.33082e72 q^{64} -7.19040e72 q^{65} -4.35127e72 q^{66} +1.23051e74 q^{67} +1.27780e74 q^{68} +1.53334e74 q^{69} -5.08683e73 q^{70} -7.39626e74 q^{71} +1.70275e75 q^{72} +1.73876e75 q^{73} -1.23520e75 q^{74} -3.22953e76 q^{75} +1.59278e76 q^{76} +1.14960e75 q^{77} +2.85715e75 q^{78} +8.72563e76 q^{79} -1.72304e77 q^{80} +2.93878e77 q^{81} +1.23704e77 q^{82} +4.46190e76 q^{83} -3.19122e77 q^{84} +2.00801e78 q^{85} +1.57665e77 q^{86} -9.13269e78 q^{87} -5.45655e77 q^{88} -5.92956e78 q^{89} +1.29683e79 q^{90} -7.54858e77 q^{91} +9.31902e78 q^{92} -3.31263e79 q^{93} -9.99763e78 q^{94} +2.50298e80 q^{95} +2.29530e80 q^{96} -3.76964e80 q^{97} +1.02345e80 q^{98} -2.93078e80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) $ 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9	$ 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots - 63\!\cdots\!24 q^{99}+O(q^{100}) $ 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9 - 66472312087527710620452553569669697173600 * q^10 - 2302475295973581620809306061775551681990328 * q^11 - 53870867926220164150329513348046663235681280 * q^12 + 1313253814255449492724146018729804193778100180 * q^13 + 41225372723246048337281629784765672712004401024 * q^14 - 156056001993392003275961063842210281482861266800 * q^15 + 2799490233261278434402974316306719898117729222656 * q^16 + 2377848571505238562780180385684069414829577769580 * q^17 + 506306622204276540508620731115428014111485052430640 * q^18 - 17422016964741760630179674590582970665727618619375240 * q^19 + 148672889698640611477740875719636714144962866333222400 * q^20 - 114072752249915469711576730788399479267919883382138688 * q^21 - 1258034178625689345497738618244246726621220713529586880 * q^22 + 10526595063181453314046018770874462030150898790798283920 * q^23 - 12327611736558023893782629055720670133074337356786974720 * q^24 + 411037910011361515508644334216291479522821661187695496250 * q^25 - 3180570114716540139250277986112641638356676984048903123168 * q^26 + 14621431460046183096199709161966291993457773283863231280880 * q^27 - 82116517748637002885903417761702653442063276903193852344320 * q^28 + 155464359052154485146727469597467543970919715236853926245940 * q^29 + 164012983787559943750248070451087782537372525868704541558400 * q^30 + 1259277021063335018777245090979655984137503836933555134668992 * q^31 - 13036312845125683749178794475020758767431562303480221102243840 * q^32 + 21091354949357251433966784004957297352147245536782330440814880 * q^33 + 11899550405754031112224464347628728246396477955985557631122144 * q^34 - 232034356615504837711196063040035766391492406317925929510437600 * q^35 - 2071479648832132808682929357240066191852277967275841354377712384 * q^36 + 414692688584236378963319357622814947056491742931883680122973540 * q^37 - 2455417714037465297201999851134772037590829998762172946918415680 * q^38 - 92285563929532296901251298670288831485071753513924535804838199984 * q^39 - 258059824285668605758122263287555971608050642150708772544789504000 * q^40 - 250252788823194090638944408016236187978548863949167831014660870148 * q^41 - 3774470339882908627686770098374833879180889302300694800640098910720 * q^42 - 5362516930786214192203446564720631507618558180640993338648106782200 * q^43 - 17252465656682175267213991915222412585785021276568609411813835518976 * q^44 - 62055994195911488597384173133359170181530078929941731114719230089900 * q^45 - 123763409427226200113215389587151615608344054530127843046255996688768 * q^46 - 230717394511751791462615349254196337530205542984846694602934639341280 * q^47 - 691982889190309031684460851104240936972943285356349640319551063982080 * q^48 - 148965540042877735285285650175007198234557699456949204802064464556458 * q^49 - 1416105420952806525015169807922957339416756851287952031511031347670000 * q^50 + 723978686772453055369497103847414979467127084371963703072714225585072 * q^51 + 12562371185881747636341658298037576485393840750032566447999727917043200 * q^52 + 25898990256961205776642859216859182171010424056472082121008236344959940 * q^53 + 60731909939285801872082597253734783721512219559188195805336458971800960 * q^54 + 70427859302095658379065386305135120838252257009889309990749877277396400 * q^55 + 350275852246953465289512615368698332984392220622408793911163576939151360 * q^56 + 303622382725256536236947985463289143154200643659779472092208351796091360 * q^57 - 312514134877257928766126367534026770462807935435519457753987287493386720 * q^58 - 38532453307459913471042984274454520116124717672121643571528434328282520 * q^59 - 5854438714408546634435977504160054633094179506942282108438463374797465600 * q^60 - 4585192544270629640163935422584783189092178505653567017169797728495170828 * q^61 - 11745445982868867354760701788812677993661414140303262885466836339630318080 * q^62 - 35632339418998518169074915366562958999484559616578607415025802007025188240 * q^63 - 24049189879736877632355406073912155582619770074517134096672197458230509568 * q^64 + 40108571425620140080303901416556158312567794172295521521551039993118238200 * q^65 + 46637466443959380664183766096173047575934541297502070623350605582042365184 * q^66 + 278606964486964374833906544600580027758780739521508130980859112605565987480 * q^67 + 591059149620766869951154898169335214276013402788475417448362648514550551040 * q^68 + 783789679110178241786835392836945981604400905715238386162022702382323722816 * q^69 + 2635837114104224632390936486964777102611174135296488988531978806621369068800 * q^70 - 554281436103188717611008447226924711986842423491780222553301787426789861968 * q^71 - 3169897304032072056282604590226317130165389286798806197352424269626436341760 * q^72 - 1159677538409433721867557656635958525415325708297922475676033828300683142980 * q^73 - 14870996314347354169518203977127998385153668929299472477677600807989626002016 * q^74 - 40272209656064989140640078595938035284494253817756477276130430269166782335000 * q^75 - 56365824164857229782022127848008365902008884166434980738114640515976798612480 * q^76 - 22951272837324694774527636903423616359482790364245898655274441101674154673600 * q^77 + 29994870322699852265351947769035786178441787146653937638111333726813935158400 * q^78 + 76488528596848273963909721387433081359345259080220208993600380062891411190240 * q^79 + 326185463863660018876021371340485226979224823762794013840530768719064527667200 * q^80 + 713659220427214109967671419496287178348529210497808359051350032218775138774486 * q^81 + 836977463852743303549437738986542975894462808796250502348000478828556860551520 * q^82 + 440718478462773776637617020819789880594300172591745821478345102532528865997560 * q^83 + 2327207348086698397722806131221331490656683214148360655124465557042000906952704 * q^84 + 1165607138975709364402518400492567424057357396402879557680723771041190675179400 * q^85 - 10339197506820945136003281093027314178240703830345630490304599234644673765234368 * q^86 - 13777097629225807302706950021773234863450868385225572161845501405567814463584560 * q^87 - 9603847126452588175246186358824265187739652448840879006569656469218022549667840 * q^88 - 18886228493337874501351816155449414708824427288664596668607356717228138798590180 * q^89 - 27536035459180423419106541648329015873635894588277179325118018321007646877848800 * q^90 - 14576226325987997036142564032100430704897317032265698214767987870608618538920288 * q^91 + 66364414655655668275929797141498084164407535259475789695165805684452941775738880 * q^92 + 130065128543178746783515152749840115744191801626425494555088565985583783043572480 * q^93 + 331286952814608158700187065887753978184064043063622410298763861434514546852072704 * q^94 + 267699559747800180626411366716842325842865933645649558098598518850783266973922000 * q^95 + 495554087106091786297185708372687557293322071836937974888325742175573190348111872 * q^96 + 113832498161281214584608062040287314379413598012089688107897449655058469975263820 * q^97 - 858118355318723523117883130491863373979750018711838274840266757637744872892872080 * q^98 - 630632406390824053363198011181718527371969259570962092705191903378628178893256024 * 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 $

$2$	−3.79502e11	−0.244062	−0.122031	−	0.992526i	$-0.538941\pi$
$2$	−3.79502e11	−0.244062	−0.122031	+	0.992526i	$0.538941\pi$
$3$	−3.74133e19	−1.77671	−0.888353	−	0.459161i	$-0.848150\pi$
$3$	−3.74133e19	−1.77671	−0.888353	+	0.459161i	$0.848150\pi$
$4$	−2.27383e24	−0.940434
$5$	−3.57322e28	−1.75701	−0.878507	−	0.477730i	$-0.841460\pi$
$5$	−3.57322e28	−1.75701	−0.878507	+	0.477730i	$0.841460\pi$
$6$	1.41984e31	0.433626
$7$	−3.75122e33	−0.222691	−0.111345	−	0.993782i	$-0.535516\pi$
$7$	−3.75122e33	−0.222691	−0.111345	+	0.993782i	$0.535516\pi$
$8$	1.78050e36	0.473586
$9$	9.56330e38	2.15668
$10$	1.35605e40	0.428820
$11$	−3.06461e41	−0.204160	−0.102080	−	0.994776i	$-0.532550\pi$
$11$	−3.06461e41	−0.204160	−0.102080	+	0.994776i	$0.532550\pi$
$12$	8.50715e43	1.67087
$13$	2.01230e44	0.154521	0.0772604	−	0.997011i	$-0.475383\pi$
$13$	2.01230e44	0.154521	0.0772604	+	0.997011i	$0.475383\pi$
$14$	1.42360e45	0.0543503
$15$	1.33686e48	3.12170
$16$	4.82208e48	0.824850
$17$	−5.61961e49	−0.825135	−0.412567	−	0.910927i	$-0.635368\pi$
$17$	−5.61961e49	−0.825135	−0.412567	+	0.910927i	$0.635368\pi$
$18$	−3.62930e50	−0.526364
$19$	−7.00483e51	−1.13730	−0.568652	−	0.822578i	$-0.692535\pi$
$19$	−7.00483e51	−1.13730	−0.568652	+	0.822578i	$0.692535\pi$
$20$	8.12490e52	1.65235
$21$	1.40346e53	0.395656
$22$	1.16303e53	0.0498278
$23$	−4.09838e54	−0.290158	−0.145079	−	0.989420i	$-0.546344\pi$
$23$	−4.09838e54	−0.290158	−0.145079	+	0.989420i	$0.546344\pi$
$24$	−6.66146e55	−0.841422
$25$	8.63203e56	2.08710
$26$	−7.63673e55	−0.0377126
$27$	−1.91894e58	−2.05509
$28$	8.52964e57	0.209426
$29$	2.44103e59	1.44695	0.723475	−	0.690350i	$-0.242544\pi$
$29$	2.44103e59	1.44695	0.723475	+	0.690350i	$0.242544\pi$
$30$	−5.07342e59	−0.761887
$31$	8.85416e59	0.352370	0.176185	−	0.984357i	$-0.443624\pi$
$31$	8.85416e59	0.352370	0.176185	+	0.984357i	$0.443624\pi$
$32$	−6.13499e60	−0.674900
$33$	1.14657e61	0.362733
$34$	2.13266e61	0.201384
$35$	1.34040e62	0.391270
$36$	−2.17453e63	−2.02822
$37$	3.25478e63	1.00081	0.500405	−	0.865792i	$-0.333185\pi$
$37$	3.25478e63	1.00081	0.500405	+	0.865792i	$0.333185\pi$
$38$	2.65835e63	0.277573
$39$	−7.52869e63	−0.274538
$40$	−6.36214e64	−0.832097
$41$	−3.25964e65	−1.56828	−0.784140	−	0.620584i	$-0.786895\pi$
$41$	−3.25964e65	−1.56828	−0.784140	+	0.620584i	$0.786895\pi$
$42$	−5.32615e64	−0.0965644
$43$	−4.15451e65	−0.290434	−0.145217	−	0.989400i	$-0.546388\pi$
$43$	−4.15451e65	−0.290434	−0.145217	+	0.989400i	$0.546388\pi$
$44$	6.96840e65	0.191999
$45$	−3.41718e67	−3.78932
$46$	1.55535e66	0.0708166
$47$	2.63440e67	0.502018	0.251009	−	0.967985i	$-0.419238\pi$
$47$	2.63440e67	0.502018	0.251009	+	0.967985i	$0.419238\pi$
$48$	−1.80410e68	−1.46552
$49$	−2.69682e68	−0.950409
$50$	−3.27588e68	−0.509380
$51$	2.10248e69	1.46602
$52$	−4.57563e68	−0.145317
$53$	6.39417e69	0.938884	0.469442	−	0.882963i	$-0.344455\pi$
$53$	6.39417e69	0.938884	0.469442	+	0.882963i	$0.344455\pi$
$54$	7.28244e69	0.501568
$55$	1.09505e70	0.358713
$56$	−6.67907e69	−0.105463
$57$	2.62074e71	2.02066
$58$	−9.26376e70	−0.353145
$59$	1.38928e71	0.265024	0.132512	−	0.991181i	$-0.457696\pi$
$59$	1.38928e71	0.265024	0.132512	+	0.991181i	$0.457696\pi$
$60$	−3.03980e72	−2.93575
$61$	1.44130e72	0.712681	0.356340	−	0.934356i	$-0.384024\pi$
$61$	1.44130e72	0.712681	0.356340	+	0.934356i	$0.384024\pi$
$62$	−3.36017e71	−0.0860000
$63$	−3.58741e72	−0.480273
$64$	−9.33082e72	−0.660132
$65$	−7.19040e72	−0.271495
$66$	−4.35127e72	−0.0885292
$67$	1.23051e74	1.36162	0.680810	−	0.732460i	$-0.261628\pi$
$67$	1.23051e74	1.36162	0.680810	+	0.732460i	$0.261628\pi$
$68$	1.27780e74	0.775985
$69$	1.53334e74	0.515526
$70$	−5.08683e73	−0.0954942
$71$	−7.39626e74	−0.781716	−0.390858	−	0.920451i	$-0.627822\pi$
$71$	−7.39626e74	−0.781716	−0.390858	+	0.920451i	$0.627822\pi$
$72$	1.70275e75	1.02137
$73$	1.73876e75	0.596573	0.298286	−	0.954476i	$-0.403585\pi$
$73$	1.73876e75	0.596573	0.298286	+	0.954476i	$0.403585\pi$
$74$	−1.23520e75	−0.244259
$75$	−3.22953e76	−3.70816
$76$	1.59278e76	1.06956
$77$	1.14960e75	0.0454646
$78$	2.85715e75	0.0670043
$79$	8.72563e76	1.22152	0.610759	−	0.791817i	$-0.290864\pi$
$79$	8.72563e76	1.22152	0.610759	+	0.791817i	$0.290864\pi$
$80$	−1.72304e77	−1.44927
$81$	2.93878e77	1.49460
$82$	1.23704e77	0.382757
$83$	4.46190e76	0.0845001	0.0422500	−	0.999107i	$-0.486547\pi$
$83$	4.46190e76	0.0845001	0.0422500	+	0.999107i	$0.486547\pi$
$84$	−3.19122e77	−0.372088
$85$	2.00801e78	1.44977
$86$	1.57665e77	0.0708839
$87$	−9.13269e78	−2.57081
$88$	−5.45655e77	−0.0966875
$89$	−5.92956e78	−0.664856	−0.332428	−	0.943129i	$-0.607868\pi$
$89$	−5.92956e78	−0.664856	−0.332428	+	0.943129i	$0.607868\pi$
$90$	1.29683e79	0.924828
$91$	−7.54858e77	−0.0344104
$92$	9.31902e78	0.272875
$93$	−3.31263e79	−0.626057
$94$	−9.99763e78	−0.122523
$95$	2.50298e80	1.99826
$96$	2.29530e80	1.19910
$97$	−3.76964e80	−1.29433	−0.647165	−	0.762350i	$-0.724045\pi$
$97$	−3.76964e80	−1.29433	−0.647165	+	0.762350i	$0.724045\pi$
$98$	1.02345e80	0.231958
$99$	−2.93078e80	−0.440309
$100$	−1.96278e81	−1.96278
$101$	1.83104e81	1.22372	0.611861	−	0.790965i	$-0.290421\pi$
$101$	1.83104e81	1.22372	0.611861	+	0.790965i	$0.290421\pi$
$102$	−7.97898e80	−0.357800
$103$	1.21255e79	0.00366262	0.00183131	−	0.999998i	$-0.499417\pi$
$103$	1.21255e79	0.00366262	0.00183131	+	0.999998i	$0.499417\pi$
$104$	3.58291e80	0.0731789
$105$	−5.01486e81	−0.695172
$106$	−2.42660e81	−0.229146
$107$	5.43169e81	0.350665	0.175332	−	0.984509i	$-0.443900\pi$
$107$	5.43169e81	0.350665	0.175332	+	0.984509i	$0.443900\pi$
$108$	4.36335e82	1.93267
$109$	3.42601e82	1.04476	0.522378	−	0.852714i	$-0.325045\pi$
$109$	3.42601e82	1.04476	0.522378	+	0.852714i	$0.325045\pi$
$110$	−4.15576e81	−0.0875480
$111$	−1.21772e83	−1.77814
$112$	−1.80887e82	−0.183686
$113$	1.72952e82	0.122532	0.0612658	−	0.998121i	$-0.480486\pi$
$113$	1.72952e82	0.122532	0.0612658	+	0.998121i	$0.480486\pi$
$114$	−9.94577e82	−0.493165
$115$	1.46444e83	0.509812
$116$	−5.55048e83	−1.36076
$117$	1.92442e83	0.333253
$118$	−5.27237e82	−0.0646821
$119$	2.10804e83	0.183750
$120$	2.38029e84	1.47839
$121$	−2.15932e84	−0.958319
$122$	−5.46976e83	−0.173938
$123$	1.21954e85	2.78637
$124$	−2.01328e84	−0.331380
$125$	−1.60657e85	−1.91004
$126$	1.36143e84	0.117216
$127$	−2.28074e85	−1.42569	−0.712844	−	0.701322i	$-0.752593\pi$
$127$	−2.28074e85	−1.42569	−0.712844	+	0.701322i	$0.752593\pi$
$128$	1.83746e85	0.836013
$129$	1.55434e85	0.516016
$130$	2.72878e84	0.0662616
$131$	−7.46595e85	−1.32922	−0.664611	−	0.747189i	$-0.731403\pi$
$131$	−7.46595e85	−1.32922	−0.664611	+	0.747189i	$0.731403\pi$
$132$	−2.60711e85	−0.341126
$133$	2.62767e85	0.253267
$134$	−4.66982e85	−0.332319
$135$	6.85682e86	3.61081
$136$	−1.00057e86	−0.390772
$137$	−1.74721e86	−0.507181	−0.253591	−	0.967312i	$-0.581612\pi$
$137$	−1.74721e86	−0.507181	−0.253591	+	0.967312i	$0.581612\pi$
$138$	−5.81907e85	−0.125820
$139$	−3.88619e86	−0.627226	−0.313613	−	0.949551i	$-0.601540\pi$
$139$	−3.88619e86	−0.627226	−0.313613	+	0.949551i	$0.601540\pi$
$140$	−3.04783e86	−0.367964
$141$	−9.85618e86	−0.891938
$142$	2.80690e86	0.190787
$143$	−6.16692e85	−0.0315470
$144$	4.61150e87	1.77894
$145$	−8.72234e87	−2.54231
$146$	−6.59863e86	−0.145601
$147$	1.00897e88	1.68860
$148$	−7.40081e87	−0.941195
$149$	5.64987e87	0.547009	0.273505	−	0.961871i	$-0.411817\pi$
$149$	5.64987e87	0.547009	0.273505	+	0.961871i	$0.411817\pi$
$150$	1.22561e88	0.905019
$151$	3.14859e88	1.77644	0.888218	−	0.459423i	$-0.151944\pi$
$151$	3.14859e88	1.77644	0.888218	+	0.459423i	$0.151944\pi$
$152$	−1.24721e88	−0.538611
$153$	−5.37420e88	−1.77955
$154$	−4.36277e86	−0.0110962
$155$	−3.16379e88	−0.619118
$156$	1.71189e88	0.258185
$157$	3.73484e88	0.434847	0.217423	−	0.976077i	$-0.430235\pi$
$157$	3.73484e88	0.434847	0.217423	+	0.976077i	$0.430235\pi$
$158$	−3.31140e88	−0.298126
$159$	−2.39227e89	−1.66812
$160$	2.19217e89	1.18581
$161$	1.53739e88	0.0646155
$162$	−1.11528e89	−0.364774
$163$	3.01549e89	0.768705	0.384353	−	0.923186i	$-0.374425\pi$
$163$	3.01549e89	0.768705	0.384353	+	0.923186i	$0.374425\pi$
$164$	7.41187e89	1.47486
$165$	−4.09696e89	−0.637327
$166$	−1.69330e88	−0.0206232
$167$	7.74441e89	0.739557	0.369778	−	0.929120i	$-0.379434\pi$
$167$	7.74441e89	0.739557	0.369778	+	0.929120i	$0.379434\pi$
$168$	2.49886e89	0.187377
$169$	−1.65545e90	−0.976123
$170$	−7.62046e89	−0.353834
$171$	−6.69893e90	−2.45281
$172$	9.44665e89	0.273134
$173$	7.70338e90	1.76122	0.880611	−	0.473839i	$-0.157132\pi$
$173$	7.70338e90	1.76122	0.880611	+	0.473839i	$0.157132\pi$
$174$	3.46588e90	0.627435
$175$	−3.23806e90	−0.464777
$176$	−1.47778e90	−0.168402
$177$	−5.19777e90	−0.470869
$178$	2.25028e90	0.162266
$179$	−3.04682e91	−1.75105	−0.875526	−	0.483171i	$-0.839485\pi$
$179$	−3.04682e91	−1.75105	−0.875526	+	0.483171i	$0.839485\pi$
$180$	7.77009e91	3.56361
$181$	2.48233e91	0.909656	0.454828	−	0.890579i	$-0.349701\pi$
$181$	2.48233e91	0.909656	0.454828	+	0.890579i	$0.349701\pi$
$182$	2.86471e89	0.00839825
$183$	−5.39237e91	−1.26622
$184$	−7.29719e90	−0.137415
$185$	−1.16300e92	−1.75844
$186$	1.25715e91	0.152797
$187$	1.72219e91	0.168460
$188$	−5.99019e91	−0.472115
$189$	7.19838e91	0.457648
$190$	−9.49888e91	−0.487699
$191$	1.55237e92	0.644381	0.322191	−	0.946675i	$-0.395581\pi$
$191$	1.55237e92	0.644381	0.322191	+	0.946675i	$0.395581\pi$
$192$	3.49097e92	1.17286
$193$	−4.94244e92	−1.34546	−0.672730	−	0.739888i	$-0.734878\pi$
$193$	−4.94244e92	−1.34546	−0.672730	+	0.739888i	$0.734878\pi$
$194$	1.43059e92	0.315896
$195$	2.69017e92	0.482367
$196$	6.13211e92	0.893797
$197$	1.58345e91	0.0187811	0.00939057	−	0.999956i	$-0.497011\pi$
$197$	1.58345e91	0.0187811	0.00939057	+	0.999956i	$0.497011\pi$
$198$	1.11224e92	0.107463
$199$	−4.27789e92	−0.337039	−0.168519	−	0.985698i	$-0.553899\pi$
$199$	−4.27789e92	−0.337039	−0.168519	+	0.985698i	$0.553899\pi$
$200$	1.53694e93	0.988419
$201$	−4.60375e93	−2.41920
$202$	−6.94886e92	−0.298664
$203$	−9.15683e92	−0.322222
$204$	−4.78069e93	−1.37870
$205$	1.16474e94	2.75549
$206$	−4.60166e90	−0.000893906 0
$207$	−3.91941e93	−0.625779
$208$	9.70347e92	0.127456
$209$	2.14671e93	0.232193
$210$	1.90315e93	0.169665
$211$	7.01697e93	0.516072	0.258036	−	0.966135i	$-0.416925\pi$
$211$	7.01697e93	0.516072	0.258036	+	0.966135i	$0.416925\pi$
$212$	−1.45393e94	−0.882958
$213$	2.76719e94	1.38888
$214$	−2.06134e93	−0.0855839
$215$	1.48450e94	0.510297
$216$	−3.41669e94	−0.973259
$217$	−3.32139e93	−0.0784694
$218$	−1.30018e94	−0.254985
$219$	−6.50527e94	−1.05993
$220$	−2.48997e94	−0.337345
$221$	−1.13083e94	−0.127501
$222$	4.62128e94	0.433977
$223$	−1.90011e95	−1.48741	−0.743707	−	0.668505i	$-0.766934\pi$
$223$	−1.90011e95	−1.48741	−0.743707	+	0.668505i	$0.766934\pi$
$224$	2.30137e94	0.150294
$225$	8.25507e95	4.50121
$226$	−6.56357e93	−0.0299053
$227$	−2.11287e95	−0.805053	−0.402527	−	0.915408i	$-0.631868\pi$
$227$	−2.11287e95	−0.805053	−0.402527	+	0.915408i	$0.631868\pi$
$228$	−5.95912e95	−1.90029
$229$	2.27028e95	0.606377	0.303188	−	0.952931i	$-0.401949\pi$
$229$	2.27028e95	0.606377	0.303188	+	0.952931i	$0.401949\pi$
$230$	−5.55760e94	−0.124426
$231$	−4.30105e94	−0.0807772
$232$	4.34626e95	0.685255
$233$	4.56036e95	0.604065	0.302033	−	0.953298i	$-0.402335\pi$
$233$	4.56036e95	0.604065	0.302033	+	0.953298i	$0.402335\pi$
$234$	−7.30324e94	−0.0813342
$235$	−9.41332e95	−0.882052
$236$	−3.15899e95	−0.249237
$237$	−3.26455e96	−2.17028
$238$	−8.00006e94	−0.0448463
$239$	−9.42203e95	−0.445686	−0.222843	−	0.974854i	$-0.571534\pi$
$239$	−9.42203e95	−0.445686	−0.222843	+	0.974854i	$0.571534\pi$
$240$	6.44645e96	2.57493
$241$	2.23123e96	0.753103	0.376551	−	0.926396i	$-0.377110\pi$
$241$	2.23123e96	0.753103	0.376551	+	0.926396i	$0.377110\pi$
$242$	8.19468e95	0.233889
$243$	−2.48586e96	−0.600376
$244$	−3.27726e96	−0.670229
$245$	9.63634e96	1.66988
$246$	−4.62818e96	−0.680047
$247$	−1.40958e96	−0.175737
$248$	1.57649e96	0.166877
$249$	−1.66935e96	−0.150132
$250$	6.09696e96	0.466168
$251$	−2.14581e97	−1.39574	−0.697871	−	0.716224i	$-0.745869\pi$
$251$	−2.14581e97	−1.39574	−0.697871	+	0.716224i	$0.745869\pi$
$252$	8.15715e96	0.451665
$253$	1.25599e96	0.0592388
$254$	8.65546e96	0.347956
$255$	−7.51264e97	−2.57582
$256$	1.55874e97	0.456094
$257$	3.39404e97	0.848057	0.424028	−	0.905649i	$-0.360616\pi$
$257$	3.39404e97	0.848057	0.424028	+	0.905649i	$0.360616\pi$
$258$	−5.89876e96	−0.125940
$259$	−1.22094e97	−0.222871
$260$	1.63497e97	0.255323
$261$	2.33443e98	3.12061
$262$	2.83335e97	0.324413
$263$	−1.27513e98	−1.25126	−0.625628	−	0.780122i	$-0.715157\pi$
$263$	−1.27513e98	−1.25126	−0.625628	+	0.780122i	$0.715157\pi$
$264$	2.04148e97	0.171785
$265$	−2.28478e98	−1.64963
$266$	−9.97206e96	−0.0618128
$267$	2.21845e98	1.18125
$268$	−2.79797e98	−1.28051
$269$	7.89467e97	0.310718	0.155359	−	0.987858i	$-0.450347\pi$
$269$	7.89467e97	0.310718	0.155359	+	0.987858i	$0.450347\pi$
$270$	−2.60218e98	−0.881261
$271$	3.56501e98	1.03945	0.519725	−	0.854333i	$-0.326034\pi$
$271$	3.56501e98	1.03945	0.519725	+	0.854333i	$0.326034\pi$
$272$	−2.70982e98	−0.680612
$273$	2.82418e97	0.0611371
$274$	6.63072e97	0.123784
$275$	−2.64538e98	−0.426102
$276$	−3.48656e98	−0.484818
$277$	7.12121e98	0.855310	0.427655	−	0.903942i	$-0.359340\pi$
$277$	7.12121e98	0.855310	0.427655	+	0.903942i	$0.359340\pi$
$278$	1.47482e98	0.153082
$279$	8.46750e98	0.759950
$280$	2.38658e98	0.185300
$281$	2.80730e97	0.0188661	0.00943307	−	0.999956i	$-0.496997\pi$
$281$	2.80730e97	0.0188661	0.00943307	+	0.999956i	$0.496997\pi$
$282$	3.74045e98	0.217688
$283$	2.84247e99	1.43333	0.716664	−	0.697419i	$-0.245668\pi$
$283$	2.84247e99	1.43333	0.716664	+	0.697419i	$0.245668\pi$
$284$	1.68178e99	0.735152
$285$	−9.36449e99	−3.55032
$286$	2.34036e97	0.00769943
$287$	1.22276e99	0.349241
$288$	−5.86707e99	−1.45555
$289$	−1.48034e99	−0.319153
$290$	3.31015e99	0.620481
$291$	1.41035e100	2.29964
$292$	−3.95364e99	−0.561037
$293$	−5.89339e99	−0.728160	−0.364080	−	0.931368i	$-0.618617\pi$
$293$	−5.89339e99	−0.728160	−0.364080	+	0.931368i	$0.618617\pi$
$294$	−3.82906e99	−0.412122
$295$	−4.96422e99	−0.465650
$296$	5.79514e99	0.473969
$297$	5.88082e99	0.419567
$298$	−2.14414e99	−0.133504
$299$	−8.24718e98	−0.0448355
$300$	7.34340e100	3.48728
$301$	1.55845e99	0.0646770
$302$	−1.19490e100	−0.433560
$303$	−6.85054e100	−2.17420
$304$	−3.37778e100	−0.938106
$305$	−5.15008e100	−1.25219
$306$	2.03952e100	0.434321
$307$	3.81688e100	0.712203	0.356102	−	0.934447i	$-0.384106\pi$
$307$	3.81688e100	0.712203	0.356102	+	0.934447i	$0.384106\pi$
$308$	−2.61400e99	−0.0427565
$309$	−4.53655e98	−0.00650740
$310$	1.20067e100	0.151103
$311$	−2.82206e100	−0.311725	−0.155862	−	0.987779i	$-0.549816\pi$
$311$	−2.82206e100	−0.311725	−0.155862	+	0.987779i	$0.549816\pi$
$312$	−1.34049e100	−0.130017
$313$	1.11893e101	0.953364	0.476682	−	0.879076i	$-0.341839\pi$
$313$	1.11893e101	0.953364	0.476682	+	0.879076i	$0.341839\pi$
$314$	−1.41738e100	−0.106130
$315$	1.28186e101	0.843846
$316$	−1.98406e101	−1.14876
$317$	9.19069e100	0.468218	0.234109	−	0.972210i	$-0.424783\pi$
$317$	9.19069e100	0.468218	0.234109	+	0.972210i	$0.424783\pi$
$318$	9.07873e100	0.407124
$319$	−7.48080e100	−0.295410
$320$	3.33411e101	1.15986
$321$	−2.03218e101	−0.623028
$322$	−5.83444e99	−0.0157702
$323$	3.93644e101	0.938430
$324$	−6.68229e101	−1.40557
$325$	1.73702e101	0.322500
$326$	−1.14439e101	−0.187612
$327$	−1.28178e102	−1.85622
$328$	−5.80380e101	−0.742715
$329$	−9.88223e100	−0.111795
$330$	1.55481e101	0.155547
$331$	1.97273e102	1.74596	0.872981	−	0.487755i	$-0.162184\pi$
$331$	1.97273e102	1.74596	0.872981	+	0.487755i	$0.162184\pi$
$332$	−1.01456e101	−0.0794667
$333$	3.11264e102	2.15843
$334$	−2.93902e101	−0.180498
$335$	−4.39689e102	−2.39239
$336$	6.76757e101	0.326356
$337$	4.42557e102	1.89216	0.946080	−	0.323932i	$-0.105005\pi$
$337$	4.42557e102	1.89216	0.946080	+	0.323932i	$0.105005\pi$
$338$	6.28248e101	0.238234
$339$	−6.47070e101	−0.217703
$340$	−4.56588e102	−1.36342
$341$	−2.71345e101	−0.0719399
$342$	2.54226e102	0.598636
$343$	2.07606e102	0.434338
$344$	−7.39713e101	−0.137545
$345$	−5.47897e102	−0.905786
$346$	−2.92345e102	−0.429847
$347$	−1.07845e103	−1.41077	−0.705387	−	0.708822i	$-0.749227\pi$
$347$	−1.07845e103	−1.41077	−0.705387	+	0.708822i	$0.749227\pi$
$348$	2.07662e103	2.41767
$349$	−1.89399e103	−1.96313	−0.981564	−	0.191133i	$-0.938784\pi$
$349$	−1.89399e103	−1.96313	−0.981564	+	0.191133i	$0.938784\pi$
$350$	1.22885e102	0.113434
$351$	−3.86149e102	−0.317554
$352$	1.88013e102	0.137788
$353$	2.19494e103	1.43399	0.716997	−	0.697076i	$-0.245516\pi$
$353$	2.19494e103	1.43399	0.716997	+	0.697076i	$0.245516\pi$
$354$	1.97257e102	0.114921
$355$	2.64285e103	1.37349
$356$	1.34828e103	0.625253
$357$	−7.88688e102	−0.326469
$358$	1.15628e103	0.427365
$359$	−3.89952e103	−1.28732	−0.643659	−	0.765312i	$-0.722585\pi$
$359$	−3.89952e103	−1.28732	−0.643659	+	0.765312i	$0.722585\pi$
$360$	−6.08431e103	−1.79457
$361$	1.11325e103	0.293462
$362$	−9.42050e102	−0.222012
$363$	8.07874e103	1.70265
$364$	1.71642e102	0.0323607
$365$	−6.21297e103	−1.04819
$366$	2.04642e103	0.309037
$367$	8.50514e103	1.15002	0.575011	−	0.818146i	$-0.304998\pi$
$367$	8.50514e103	1.15002	0.575011	+	0.818146i	$0.304998\pi$
$368$	−1.97627e103	−0.239337
$369$	−3.11729e104	−3.38228
$370$	4.41363e103	0.429167
$371$	−2.39860e103	−0.209081
$372$	7.53236e103	0.588765
$373$	1.67136e103	0.117182	0.0585911	−	0.998282i	$-0.481339\pi$
$373$	1.67136e103	0.117182	0.0585911	+	0.998282i	$0.481339\pi$
$374$	−6.53576e102	−0.0411146
$375$	6.01070e104	3.39358
$376$	4.69057e103	0.237748
$377$	4.91208e103	0.223584
$378$	−2.73180e103	−0.111694
$379$	−4.29958e104	−1.57957	−0.789783	−	0.613387i	$-0.789807\pi$
$379$	−4.29958e104	−1.57957	−0.789783	+	0.613387i	$0.789807\pi$
$380$	−5.69136e104	−1.87923
$381$	8.53300e104	2.53303
$382$	−5.89127e103	−0.157269
$383$	−1.67933e104	−0.403260	−0.201630	−	0.979462i	$-0.564624\pi$
$383$	−1.67933e104	−0.403260	−0.201630	+	0.979462i	$0.564624\pi$
$384$	−6.87453e104	−1.48535
$385$	−4.10779e103	−0.0798819
$386$	1.87567e104	0.328375
$387$	−3.97309e104	−0.626374
$388$	8.57152e104	1.21723
$389$	−8.92675e104	−1.14218	−0.571090	−	0.820887i	$-0.693479\pi$
$389$	−8.92675e104	−1.14218	−0.571090	+	0.820887i	$0.693479\pi$
$390$	−1.02093e104	−0.117727
$391$	2.30313e104	0.239420
$392$	−4.80170e104	−0.450100
$393$	2.79326e105	2.36164
$394$	−6.00923e102	−0.00458376
$395$	−3.11786e105	−2.14622
$396$	6.66409e104	0.414082
$397$	1.90746e105	1.07014	0.535070	−	0.844808i	$-0.320285\pi$
$397$	1.90746e105	1.07014	0.535070	+	0.844808i	$0.320285\pi$
$398$	1.62347e104	0.0822583
$399$	−9.83098e104	−0.449981
$400$	4.16243e105	1.72154
$401$	−9.88841e103	−0.0369641	−0.0184820	−	0.999829i	$-0.505883\pi$
$401$	−9.88841e103	−0.0369641	−0.0184820	+	0.999829i	$0.505883\pi$
$402$	1.74713e105	0.590434
$403$	1.78172e104	0.0544485
$404$	−4.16348e105	−1.15083
$405$	−1.05009e106	−2.62603
$406$	3.47504e104	0.0786422
$407$	−9.97462e104	−0.204326
$408$	3.74348e105	0.694287
$409$	2.13820e105	0.359133	0.179566	−	0.983746i	$-0.442531\pi$
$409$	2.13820e105	0.359133	0.179566	+	0.983746i	$0.442531\pi$
$410$	−4.42023e105	−0.672509
$411$	6.53691e105	0.901112
$412$	−2.75713e103	−0.00344445
$413$	−5.21151e104	−0.0590183
$414$	1.48742e105	0.152729
$415$	−1.59434e105	−0.148468
$416$	−1.23454e105	−0.104286
$417$	1.45395e106	1.11440
$418$	−8.14681e104	−0.0566693
$419$	−1.91653e106	−1.21017	−0.605087	−	0.796159i	$-0.706862\pi$
$419$	−1.91653e106	−1.21017	−0.605087	+	0.796159i	$0.706862\pi$
$420$	1.14029e106	0.653764
$421$	1.88232e106	0.980096	0.490048	−	0.871696i	$-0.336979\pi$
$421$	1.88232e106	0.980096	0.490048	+	0.871696i	$0.336979\pi$
$422$	−2.66296e105	−0.125953
$423$	2.51936e106	1.08269
$424$	1.13849e106	0.444642
$425$	−4.85086e106	−1.72214
$426$	−1.05015e106	−0.338972
$427$	−5.40662e105	−0.158707
$428$	−1.23507e106	−0.329777
$429$	2.30725e105	0.0560498
$430$	−5.63372e105	−0.124544
$431$	−7.37739e106	−1.48448	−0.742238	−	0.670136i	$-0.766236\pi$
$431$	−7.37739e106	−1.48448	−0.742238	+	0.670136i	$0.766236\pi$
$432$	−9.25329e106	−1.69514
$433$	2.79633e106	0.466475	0.233238	−	0.972420i	$-0.425068\pi$
$433$	2.79633e106	0.466475	0.233238	+	0.972420i	$0.425068\pi$
$434$	1.26048e105	0.0191514
$435$	3.26332e107	4.51694
$436$	−7.79015e106	−0.982524
$437$	2.87085e106	0.329998
$438$	2.46877e106	0.258689
$439$	4.57514e106	0.437110	0.218555	−	0.975825i	$-0.429866\pi$
$439$	4.57514e106	0.437110	0.218555	+	0.975825i	$0.429866\pi$
$440$	1.94975e106	0.169881
$441$	−2.57905e107	−2.04973
$442$	4.29155e105	0.0311180
$443$	−2.18748e107	−1.44742	−0.723708	−	0.690106i	$-0.757564\pi$
$443$	−2.18748e107	−1.44742	−0.723708	+	0.690106i	$0.757564\pi$
$444$	2.76889e107	1.67223
$445$	2.11877e107	1.16816
$446$	7.21097e106	0.363021
$447$	−2.11380e107	−0.971874
$448$	3.50020e106	0.147005
$449$	1.61856e107	0.621087	0.310544	−	0.950559i	$-0.399489\pi$
$449$	1.61856e107	0.621087	0.310544	+	0.950559i	$0.399489\pi$
$450$	−3.13282e107	−1.09857
$451$	9.98953e106	0.320181
$452$	−3.93263e106	−0.115233
$453$	−1.17799e108	−3.15620
$454$	8.01838e106	0.196483
$455$	2.69728e106	0.0604595
$456$	4.66624e107	0.956954
$457$	5.34765e107	1.00359	0.501796	−	0.864986i	$-0.332673\pi$
$457$	5.34765e107	1.00359	0.501796	+	0.864986i	$0.332673\pi$
$458$	−8.61577e106	−0.147993
$459$	1.07837e108	1.69572
$460$	−3.32989e107	−0.479445
$461$	−4.21923e106	−0.0556347	−0.0278173	−	0.999613i	$-0.508856\pi$
$461$	−4.21923e106	−0.0556347	−0.0278173	+	0.999613i	$0.508856\pi$
$462$	1.63226e106	0.0197146
$463$	−8.90462e107	−0.985338	−0.492669	−	0.870217i	$-0.663979\pi$
$463$	−8.90462e107	−0.985338	−0.492669	+	0.870217i	$0.663979\pi$
$464$	1.17708e108	1.19352
$465$	1.18368e108	1.09999
$466$	−1.73067e107	−0.147429
$467$	−1.04474e108	−0.815967	−0.407983	−	0.912989i	$-0.633768\pi$
$467$	−1.04474e108	−0.815967	−0.407983	+	0.912989i	$0.633768\pi$
$468$	−4.37581e107	−0.313402
$469$	−4.61592e107	−0.303220
$470$	3.57238e107	0.215275
$471$	−1.39733e108	−0.772595
$472$	2.47363e107	0.125511
$473$	1.27320e107	0.0592952
$474$	1.23890e108	0.529682
$475$	−6.04659e108	−2.37366
$476$	−4.79332e107	−0.172805
$477$	6.11494e108	2.02487
$478$	3.57568e107	0.108775
$479$	2.03463e108	0.568719	0.284360	−	0.958718i	$-0.408219\pi$
$479$	2.03463e108	0.568719	0.284360	+	0.958718i	$0.408219\pi$
$480$	−8.20163e108	−2.10683
$481$	6.54959e107	0.154646
$482$	−8.46757e107	−0.183804
$483$	−5.75190e107	−0.114803
$484$	4.90993e108	0.901235
$485$	1.34698e109	2.27415
$486$	9.43392e107	0.146529
$487$	5.87130e108	0.839096	0.419548	−	0.907733i	$-0.362189\pi$
$487$	5.87130e108	0.839096	0.419548	+	0.907733i	$0.362189\pi$
$488$	2.56624e108	0.337516
$489$	−1.12819e109	−1.36576
$490$	−3.65701e108	−0.407554
$491$	1.11746e109	1.14665	0.573327	−	0.819326i	$-0.305652\pi$
$491$	1.11746e109	1.14665	0.573327	+	0.819326i	$0.305652\pi$
$492$	−2.77303e109	−2.62040
$493$	−1.37176e109	−1.19393
$494$	5.34940e107	0.0428908
$495$	1.04723e109	0.773629
$496$	4.26954e108	0.290652
$497$	2.77450e108	0.174081
$498$	6.33521e107	0.0366414
$499$	−1.78819e109	−0.953543	−0.476772	−	0.879027i	$-0.658193\pi$
$499$	−1.78819e109	−0.953543	−0.476772	+	0.879027i	$0.658193\pi$
$500$	3.65306e109	1.79627
$501$	−2.89744e109	−1.31397
$502$	8.14339e108	0.340647
$503$	2.16067e109	0.833845	0.416923	−	0.908942i	$-0.363109\pi$
$503$	2.16067e109	0.833845	0.416923	+	0.908942i	$0.363109\pi$
$504$	−6.38739e108	−0.227450
$505$	−6.54273e109	−2.15010
$506$	−4.76653e107	−0.0144579
$507$	6.19359e109	1.73428
$508$	5.18601e109	1.34077
$509$	−3.46848e109	−0.828073	−0.414036	−	0.910260i	$-0.635881\pi$
$509$	−3.46848e109	−0.828073	−0.414036	+	0.910260i	$0.635881\pi$
$510$	2.85107e109	0.628659
$511$	−6.52247e108	−0.132851
$512$	−5.03424e109	−0.947328
$513$	1.34419e110	2.33726
$514$	−1.28805e109	−0.206978
$515$	−4.33271e107	−0.00643527
$516$	−3.53431e109	−0.485279
$517$	−8.07342e108	−0.102492
$518$	4.63349e108	0.0543942
$519$	−2.88209e110	−3.12917
$520$	−1.28025e109	−0.128576
$521$	−6.12405e109	−0.568999	−0.284499	−	0.958676i	$-0.591827\pi$
$521$	−6.12405e109	−0.568999	−0.284499	+	0.958676i	$0.591827\pi$
$522$	−8.85921e109	−0.761622
$523$	1.61031e110	1.28112	0.640562	−	0.767906i	$-0.278701\pi$
$523$	1.61031e110	1.28112	0.640562	+	0.767906i	$0.278701\pi$
$524$	1.69763e110	1.25005
$525$	1.21147e110	0.825772
$526$	4.83914e109	0.305384
$527$	−4.97569e109	−0.290752
$528$	5.52886e109	0.299200
$529$	−1.82709e110	−0.915808
$530$	8.67080e109	0.402612
$531$	1.32861e110	0.571572
$532$	−5.97487e109	−0.238181
$533$	−6.55938e109	−0.242332
$534$	−8.41906e109	−0.288299
$535$	−1.94087e110	−0.616123
$536$	2.19093e110	0.644844
$537$	1.13992e111	3.11110
$538$	−2.99605e109	−0.0758344
$539$	8.26470e109	0.194036
$540$	−1.55912e111	−3.39573
$541$	5.55223e110	1.12196	0.560981	−	0.827828i	$-0.310424\pi$
$541$	5.55223e110	1.12196	0.560981	+	0.827828i	$0.310424\pi$
$542$	−1.35293e110	−0.253690
$543$	−9.28722e110	−1.61619
$544$	3.44762e110	0.556883
$545$	−1.22419e111	−1.83565
$546$	−1.07178e109	−0.0149212
$547$	6.36918e110	0.823374	0.411687	−	0.911325i	$-0.364940\pi$
$547$	6.36918e110	0.823374	0.411687	+	0.911325i	$0.364940\pi$
$548$	3.97287e110	0.476970
$549$	1.37836e111	1.53703
$550$	1.00393e110	0.103995
$551$	−1.70990e111	−1.64562
$552$	2.73012e110	0.244146
$553$	−3.27318e110	−0.272021
$554$	−2.70252e110	−0.208748
$555$	4.35119e111	3.12422
$556$	8.83653e110	0.589865
$557$	−2.47083e111	−1.53358	−0.766792	−	0.641896i	$-0.778148\pi$
$557$	−2.47083e111	−1.53358	−0.766792	+	0.641896i	$0.778148\pi$
$558$	−3.21344e110	−0.185475
$559$	−8.36013e109	−0.0448781
$560$	6.46349e110	0.322739
$561$	−6.44329e110	−0.299304
$562$	−1.06538e109	−0.00460450
$563$	−1.88593e111	−0.758465	−0.379233	−	0.925301i	$-0.623812\pi$
$563$	−1.88593e111	−0.758465	−0.379233	+	0.925301i	$0.623812\pi$
$564$	2.24113e111	0.838809
$565$	−6.17996e110	−0.215290
$566$	−1.07873e111	−0.349821
$567$	−1.10240e111	−0.332833
$568$	−1.31691e111	−0.370210
$569$	2.22287e111	0.581926	0.290963	−	0.956734i	$-0.406024\pi$
$569$	2.22287e111	0.581926	0.290963	+	0.956734i	$0.406024\pi$
$570$	3.55385e111	0.866497
$571$	−4.44296e111	−1.00904	−0.504522	−	0.863399i	$-0.668331\pi$
$571$	−4.44296e111	−1.00904	−0.504522	+	0.863399i	$0.668331\pi$
$572$	1.40225e110	0.0296679
$573$	−5.80792e111	−1.14488
$574$	−4.64041e110	−0.0852364
$575$	−3.53773e111	−0.605588
$576$	−8.92335e111	−1.42370
$577$	6.70422e111	0.997074	0.498537	−	0.866868i	$-0.333871\pi$
$577$	6.70422e111	0.997074	0.498537	+	0.866868i	$0.333871\pi$
$578$	5.61792e110	0.0778929
$579$	1.84913e112	2.39049
$580$	1.98331e112	2.39088
$581$	−1.67376e110	−0.0188174
$582$	−5.35231e111	−0.561255
$583$	−1.95957e111	−0.191683
$584$	3.09587e111	0.282528
$585$	−6.87640e111	−0.585529
$586$	2.23656e111	0.177716
$587$	−7.57753e111	−0.561933	−0.280966	−	0.959718i	$-0.590655\pi$
$587$	−7.57753e111	−0.561933	−0.280966	+	0.959718i	$0.590655\pi$
$588$	−2.29422e112	−1.58801
$589$	−6.20219e111	−0.400752
$590$	1.88393e111	0.113647
$591$	−5.92421e110	−0.0333686
$592$	1.56948e112	0.825517
$593$	1.17979e111	0.0579549	0.0289775	−	0.999580i	$-0.490775\pi$
$593$	1.17979e111	0.0579549	0.0289775	+	0.999580i	$0.490775\pi$
$594$	−2.23178e111	−0.102400
$595$	−7.53250e111	−0.322851
$596$	−1.28468e112	−0.514426
$597$	1.60050e112	0.598819
$598$	3.12982e110	0.0109426
$599$	2.09862e112	0.685721	0.342861	−	0.939386i	$-0.388604\pi$
$599$	2.09862e112	0.685721	0.342861	+	0.939386i	$0.388604\pi$
$600$	−5.75019e112	−1.75613
$601$	−2.84629e112	−0.812573	−0.406287	−	0.913746i	$-0.633177\pi$
$601$	−2.84629e112	−0.812573	−0.406287	+	0.913746i	$0.633177\pi$
$602$	−5.91435e110	−0.0157852
$603$	1.17677e113	2.93658
$604$	−7.15935e112	−1.67062
$605$	7.71574e112	1.68378
$606$	2.59980e112	0.530638
$607$	−9.19586e112	−1.75570	−0.877850	−	0.478936i	$-0.841023\pi$
$607$	−9.19586e112	−1.75570	−0.877850	+	0.478936i	$0.841023\pi$
$608$	4.29745e112	0.767567
$609$	3.42587e112	0.572494
$610$	1.95447e112	0.305612
$611$	5.30121e111	0.0775722
$612$	1.22200e113	1.67355
$613$	3.81327e112	0.488820	0.244410	−	0.969672i	$-0.421406\pi$
$613$	3.81327e112	0.488820	0.244410	+	0.969672i	$0.421406\pi$
$614$	−1.44851e112	−0.173822
$615$	−4.35769e113	−4.89569
$616$	2.04687e111	0.0215314
$617$	4.87605e112	0.480307	0.240153	−	0.970735i	$-0.422802\pi$
$617$	4.87605e112	0.480307	0.240153	+	0.970735i	$0.422802\pi$
$618$	1.72163e110	0.00158821
$619$	−7.64577e112	−0.660617	−0.330309	−	0.943873i	$-0.607153\pi$
$619$	−7.64577e112	−0.660617	−0.330309	+	0.943873i	$0.607153\pi$
$620$	7.19392e112	0.582240
$621$	7.86456e112	0.596300
$622$	1.07098e112	0.0760800
$623$	2.22431e112	0.148057
$624$	−3.63039e112	−0.226453
$625$	2.17050e113	1.26887
$626$	−4.24638e112	−0.232680
$627$	−8.03155e112	−0.412538
$628$	−8.49240e112	−0.408945
$629$	−1.82906e113	−0.825802
$630$	−4.86469e112	−0.205951
$631$	2.50673e113	0.995218	0.497609	−	0.867401i	$-0.334211\pi$
$631$	2.50673e113	0.995218	0.497609	+	0.867401i	$0.334211\pi$
$632$	1.55360e113	0.578493
$633$	−2.62528e113	−0.916908
$634$	−3.48789e112	−0.114274
$635$	8.14959e113	2.50495
$636$	5.43962e113	1.56876
$637$	−5.42681e112	−0.146858
$638$	2.83898e112	0.0720983
$639$	−7.07327e113	−1.68591
$640$	−6.56564e113	−1.46889
$641$	−1.17812e112	−0.0247423	−0.0123711	−	0.999923i	$-0.503938\pi$
$641$	−1.17812e112	−0.0247423	−0.0123711	+	0.999923i	$0.503938\pi$
$642$	7.71216e112	0.152057
$643$	−1.33001e112	−0.0246212	−0.0123106	−	0.999924i	$-0.503919\pi$
$643$	−1.33001e112	−0.0246212	−0.0123106	+	0.999924i	$0.503919\pi$
$644$	−3.49577e112	−0.0607666
$645$	−5.55401e113	−0.906647
$646$	−1.49389e113	−0.229035
$647$	−4.63584e113	−0.667582	−0.333791	−	0.942647i	$-0.608328\pi$
$647$	−4.63584e113	−0.667582	−0.333791	+	0.942647i	$0.608328\pi$
$648$	5.23252e113	0.707820
$649$	−4.25761e112	−0.0541073
$650$	−6.59205e112	−0.0787099
$651$	1.24264e113	0.139417
$652$	−6.85671e113	−0.722916
$653$	6.08168e113	0.602614	0.301307	−	0.953527i	$-0.402577\pi$
$653$	6.08168e113	0.602614	0.301307	+	0.953527i	$0.402577\pi$
$654$	4.86440e113	0.453033
$655$	2.66775e114	2.33546
$656$	−1.57182e114	−1.29359
$657$	1.66283e114	1.28662
$658$	3.75033e112	0.0272848
$659$	−1.25041e114	−0.855450	−0.427725	−	0.903909i	$-0.640685\pi$
$659$	−1.25041e114	−0.855450	−0.427725	+	0.903909i	$0.640685\pi$
$660$	9.31579e113	0.599364
$661$	−7.85997e113	−0.475622	−0.237811	−	0.971311i	$-0.576430\pi$
$661$	−7.85997e113	−0.475622	−0.237811	+	0.971311i	$0.576430\pi$
$662$	−7.48657e113	−0.426122
$663$	4.23083e113	0.226531
$664$	7.94443e112	0.0400180
$665$	−9.38924e113	−0.444994
$666$	−1.18125e114	−0.526790
$667$	−1.00043e114	−0.419845
$668$	−1.76095e114	−0.695504
$669$	7.10895e114	2.64270
$670$	1.66863e114	0.583890
$671$	−4.41701e113	−0.145501
$672$	−8.61018e113	−0.267028
$673$	−2.02421e114	−0.591078	−0.295539	−	0.955331i	$-0.595499\pi$
$673$	−2.02421e114	−0.591078	−0.295539	+	0.955331i	$0.595499\pi$
$674$	−1.67951e114	−0.461804
$675$	−1.65644e115	−4.28916
$676$	3.76421e114	0.917979
$677$	3.43210e114	0.788349	0.394174	−	0.919036i	$-0.371031\pi$
$677$	3.43210e114	0.788349	0.394174	+	0.919036i	$0.371031\pi$
$678$	2.45565e113	0.0531329
$679$	1.41408e114	0.288235
$680$	3.57528e114	0.686592
$681$	7.90493e114	1.43034
$682$	1.02976e113	0.0175578
$683$	−6.46313e114	−1.03849	−0.519247	−	0.854624i	$-0.673788\pi$
$683$	−6.46313e114	−1.03849	−0.519247	+	0.854624i	$0.673788\pi$
$684$	1.52322e115	2.30670
$685$	6.24319e114	0.891124
$686$	−7.87869e113	−0.106005
$687$	−8.49387e114	−1.07735
$688$	−2.00334e114	−0.239564
$689$	1.28670e114	0.145077
$690$	2.07928e114	0.221068
$691$	−5.11403e114	−0.512746	−0.256373	−	0.966578i	$-0.582528\pi$
$691$	−5.11403e114	−0.512746	−0.256373	+	0.966578i	$0.582528\pi$
$692$	−1.75162e115	−1.65631
$693$	1.09940e114	0.0980528
$694$	4.09276e114	0.344316
$695$	1.38862e115	1.10205
$696$	−1.62608e115	−1.21750
$697$	1.83179e115	1.29404
$698$	7.18775e114	0.479125
$699$	−1.70618e115	−1.07325
$700$	7.36281e114	0.437092
$701$	−3.28917e115	−1.84292	−0.921461	−	0.388470i	$-0.873004\pi$
$701$	−3.28917e115	−1.84292	−0.921461	+	0.388470i	$0.873004\pi$
$702$	1.46545e114	0.0775027
$703$	−2.27992e115	−1.13823
$704$	2.85953e114	0.134773
$705$	3.52183e115	1.56715
$706$	−8.32986e114	−0.349983
$707$	−6.86865e114	−0.272512
$708$	1.18188e115	0.442821
$709$	−1.24906e115	−0.441990	−0.220995	−	0.975275i	$-0.570930\pi$
$709$	−1.24906e115	−0.441990	−0.220995	+	0.975275i	$0.570930\pi$
$710$	−1.00297e115	−0.335215
$711$	8.34459e115	2.63443
$712$	−1.05576e115	−0.314866
$713$	−3.62877e114	−0.102243
$714$	2.99309e114	0.0796787
$715$	2.20358e114	0.0554286
$716$	6.92795e115	1.64675
$717$	3.52509e115	0.791854
$718$	1.47988e115	0.314185
$719$	−5.00160e115	−1.00367	−0.501833	−	0.864965i	$-0.667341\pi$
$719$	−5.00160e115	−1.00367	−0.501833	+	0.864965i	$0.667341\pi$
$720$	−1.64779e116	−3.12562
$721$	−4.54854e112	−0.000815631 0
$722$	−4.22482e114	−0.0716229
$723$	−8.34777e115	−1.33804
$724$	−5.64439e115	−0.855471
$725$	2.10710e116	3.01993
$726$	−3.06590e115	−0.415552
$727$	−3.14283e115	−0.402881	−0.201441	−	0.979501i	$-0.564562\pi$
$727$	−3.14283e115	−0.402881	−0.201441	+	0.979501i	$0.564562\pi$
$728$	−1.34403e114	−0.0162963
$729$	−3.73090e115	−0.427907
$730$	2.35784e115	0.255822
$731$	2.33467e115	0.239647
$732$	1.22613e116	1.19080
$733$	7.31776e115	0.672461	0.336230	−	0.941780i	$-0.390848\pi$
$733$	7.31776e115	0.672461	0.336230	+	0.941780i	$0.390848\pi$
$734$	−3.22772e115	−0.280676
$735$	−3.60527e116	−2.96689
$736$	2.51435e115	0.195828
$737$	−3.77104e115	−0.277989
$738$	1.18302e116	0.825486
$739$	1.31619e115	0.0869397	0.0434699	−	0.999055i	$-0.486159\pi$
$739$	1.31619e115	0.0869397	0.0434699	+	0.999055i	$0.486159\pi$
$740$	2.64447e116	1.65369
$741$	5.27372e115	0.312234
$742$	9.10273e114	0.0510286
$743$	2.84896e116	1.51231	0.756153	−	0.654395i	$-0.227077\pi$
$743$	2.84896e116	1.51231	0.756153	+	0.654395i	$0.227077\pi$
$744$	−5.89816e115	−0.296492
$745$	−2.01883e116	−0.961102
$746$	−6.34284e114	−0.0285997
$747$	4.26705e115	0.182240
$748$	−3.91597e115	−0.158425
$749$	−2.03755e115	−0.0780898
$750$	−2.28107e116	−0.828244
$751$	−3.66713e116	−1.26156	−0.630781	−	0.775961i	$-0.717265\pi$
$751$	−3.66713e116	−1.26156	−0.630781	+	0.775961i	$0.717265\pi$
$752$	1.27033e116	0.414089
$753$	8.02818e116	2.47982
$754$	−1.86415e115	−0.0545683
$755$	−1.12506e117	−3.12122
$756$	−1.63679e116	−0.430388
$757$	−4.31137e116	−1.07456	−0.537282	−	0.843403i	$-0.680549\pi$
$757$	−4.31137e116	−1.07456	−0.537282	+	0.843403i	$0.680549\pi$
$758$	1.63170e116	0.385512
$759$	−4.69909e115	−0.105250
$760$	4.45657e116	0.946347
$761$	7.20067e116	1.44975	0.724877	−	0.688878i	$-0.241896\pi$
$761$	7.20067e116	1.44975	0.724877	+	0.688878i	$0.241896\pi$
$762$	−3.23829e116	−0.618216
$763$	−1.28517e116	−0.232657
$764$	−3.52982e116	−0.605998
$765$	1.92032e117	3.12670
$766$	6.37309e115	0.0984204
$767$	2.79566e115	0.0409517
$768$	−5.83175e116	−0.810344
$769$	2.35888e116	0.310949	0.155474	−	0.987840i	$-0.450309\pi$
$769$	2.35888e116	0.310949	0.155474	+	0.987840i	$0.450309\pi$
$770$	1.55892e115	0.0194961
$771$	−1.26982e117	−1.50675
$772$	1.12383e117	1.26532
$773$	−1.23077e117	−1.31494	−0.657472	−	0.753479i	$-0.728374\pi$
$773$	−1.23077e117	−1.31494	−0.657472	+	0.753479i	$0.728374\pi$
$774$	1.50780e116	0.152874
$775$	7.64293e116	0.735429
$776$	−6.71186e116	−0.612976
$777$	4.56794e116	0.395976
$778$	3.38772e116	0.278763
$779$	2.28332e117	1.78361
$780$	−6.11698e116	−0.453634
$781$	2.26667e116	0.159596
$782$	−8.74044e115	−0.0584332
$783$	−4.68419e117	−2.97361
$784$	−1.30043e117	−0.783944
$785$	−1.33454e117	−0.764032
$786$	−1.06005e117	−0.576386
$787$	−1.29600e116	−0.0669312	−0.0334656	−	0.999440i	$-0.510654\pi$
$787$	−1.29600e116	−0.0669312	−0.0334656	+	0.999440i	$0.510654\pi$
$788$	−3.60049e115	−0.0176624
$789$	4.77068e117	2.22311
$790$	1.18324e117	0.523811
$791$	−6.48781e115	−0.0272867
$792$	−5.21827e116	−0.208524
$793$	2.90032e116	0.110124
$794$	−7.23887e116	−0.261180
$795$	8.54813e117	2.93091
$796$	9.72719e116	0.316963
$797$	−1.06786e117	−0.330712	−0.165356	−	0.986234i	$-0.552877\pi$
$797$	−1.06786e117	−0.330712	−0.165356	+	0.986234i	$0.552877\pi$
$798$	3.73088e116	0.109823
$799$	−1.48043e117	−0.414232
$800$	−5.29574e117	−1.40858
$801$	−5.67062e117	−1.43388
$802$	3.75268e115	0.00902151
$803$	−5.32862e116	−0.121797
$804$	1.04681e118	2.27510
$805$	−5.49345e116	−0.113530
$806$	−6.76168e115	−0.0132888
$807$	−2.95366e117	−0.552054
$808$	3.26018e117	0.579538
$809$	−8.58529e117	−1.45158	−0.725788	−	0.687918i	$-0.758525\pi$
$809$	−8.58529e117	−1.45158	−0.725788	+	0.687918i	$0.758525\pi$
$810$	3.98513e117	0.640913
$811$	3.67251e117	0.561848	0.280924	−	0.959730i	$-0.409359\pi$
$811$	3.67251e117	0.561848	0.280924	+	0.959730i	$0.409359\pi$
$812$	2.08211e117	0.303029
$813$	−1.33379e118	−1.84680
$814$	3.78539e116	0.0498681
$815$	−1.07750e118	−1.35063
$816$	1.01383e118	1.20925
$817$	2.91017e117	0.330312
$818$	−8.11453e116	−0.0876506
$819$	−7.21894e116	−0.0742122
$820$	−2.64843e118	−2.59135
$821$	1.61388e118	1.50305	0.751526	−	0.659703i	$-0.229318\pi$
$821$	1.61388e118	1.50305	0.751526	+	0.659703i	$0.229318\pi$
$822$	−2.48077e117	−0.219927
$823$	1.54075e118	1.30029	0.650145	−	0.759810i	$-0.274708\pi$
$823$	1.54075e118	1.30029	0.650145	+	0.759810i	$0.274708\pi$
$824$	2.15895e115	0.00173456
$825$	9.89725e117	0.757059
$826$	1.97778e116	0.0144041
$827$	2.66618e118	1.84891	0.924455	−	0.381292i	$-0.124521\pi$
$827$	2.66618e118	1.84891	0.924455	+	0.381292i	$0.124521\pi$
$828$	8.91206e117	0.588504
$829$	2.17162e117	0.136561	0.0682803	−	0.997666i	$-0.478249\pi$
$829$	2.17162e117	0.136561	0.0682803	+	0.997666i	$0.478249\pi$
$830$	6.05055e116	0.0362353
$831$	−2.66428e118	−1.51963
$832$	−1.87764e117	−0.102004
$833$	1.51551e118	0.784215
$834$	−5.51778e117	−0.271982
$835$	−2.76725e118	−1.29941
$836$	−4.88125e117	−0.218362
$837$	−1.69906e118	−0.724150
$838$	7.27328e117	0.295357
$839$	−2.71229e118	−1.04949	−0.524743	−	0.851261i	$-0.675838\pi$
$839$	−2.71229e118	−1.04949	−0.524743	+	0.851261i	$0.675838\pi$
$840$	−8.92899e117	−0.329224
$841$	3.11259e118	1.09367
$842$	−7.14345e117	−0.239204
$843$	−1.05030e117	−0.0335196
$844$	−1.59554e118	−0.485332
$845$	5.91530e118	1.71506
$846$	−9.56104e117	−0.264244
$847$	8.10009e117	0.213409
$848$	3.08332e118	0.774438
$849$	−1.06346e119	−2.54660
$850$	1.84091e118	0.420308
$851$	−1.33393e118	−0.290393
$852$	−6.29211e118	−1.30615
$853$	3.29251e118	0.651766	0.325883	−	0.945410i	$-0.394339\pi$
$853$	3.29251e118	0.651766	0.325883	+	0.945410i	$0.394339\pi$
$854$	2.05183e117	0.0387344
$855$	2.39368e119	4.30961
$856$	9.67115e117	0.166070
$857$	−3.31095e118	−0.542287	−0.271144	−	0.962539i	$-0.587402\pi$
$857$	−3.31095e118	−0.542287	−0.271144	+	0.962539i	$0.587402\pi$
$858$	−8.75607e116	−0.0136796
$859$	−7.50069e118	−1.11784	−0.558918	−	0.829223i	$-0.688783\pi$
$859$	−7.50069e118	−1.11784	−0.558918	+	0.829223i	$0.688783\pi$
$860$	−3.37550e118	−0.479900
$861$	−4.57476e118	−0.620499
$862$	2.79974e118	0.362304
$863$	1.54440e119	1.90687	0.953436	−	0.301596i	$-0.0975192\pi$
$863$	1.54440e119	1.90687	0.953436	+	0.301596i	$0.0975192\pi$
$864$	1.17727e119	1.38698
$865$	−2.75259e119	−3.09449
$866$	−1.06121e118	−0.113849
$867$	5.53844e118	0.567040
$868$	7.55227e117	0.0737953
$869$	−2.67407e118	−0.249386
$870$	−1.23844e119	−1.10241
$871$	2.47616e118	0.210399
$872$	6.10002e118	0.494782
$873$	−3.60502e119	−2.79146
$874$	−1.08949e118	−0.0805400
$875$	6.02658e118	0.425349
$876$	1.47919e119	0.996798
$877$	−5.18725e118	−0.333775	−0.166887	−	0.985976i	$-0.553372\pi$
$877$	−5.18725e118	−0.333775	−0.166887	+	0.985976i	$0.553372\pi$
$878$	−1.73628e118	−0.106682
$879$	2.20491e119	1.29373
$880$	5.28043e118	0.295884
$881$	1.59805e119	0.855199	0.427599	−	0.903968i	$-0.359359\pi$
$881$	1.59805e119	0.855199	0.427599	+	0.903968i	$0.359359\pi$
$882$	9.78756e118	0.500261
$883$	−1.70129e119	−0.830560	−0.415280	−	0.909694i	$-0.636316\pi$
$883$	−1.70129e119	−0.830560	−0.415280	+	0.909694i	$0.636316\pi$
$884$	2.57133e118	0.119906
$885$	1.85728e119	0.827323
$886$	8.30154e118	0.353259
$887$	−3.77254e119	−1.53365	−0.766827	−	0.641854i	$-0.778166\pi$
$887$	−3.77254e119	−1.53365	−0.766827	+	0.641854i	$0.778166\pi$
$888$	−2.16816e119	−0.842103
$889$	8.55555e118	0.317488
$890$	−8.04077e118	−0.285103
$891$	−9.00623e118	−0.305138
$892$	4.32053e119	1.39882
$893$	−1.84536e119	−0.570947
$894$	8.02194e118	0.237197
$895$	1.08870e120	3.07662
$896$	−6.89270e118	−0.186172
$897$	3.08554e118	0.0796595
$898$	−6.14249e118	−0.151584
$899$	2.16132e119	0.509861
$900$	−1.87706e120	−4.23309
$901$	−3.59328e119	−0.774705
$902$	−3.79105e118	−0.0781438
$903$	−5.83068e118	−0.114912
$904$	3.07942e118	0.0580292
$905$	−8.86992e119	−1.59828
$906$	4.47051e119	0.770308
$907$	−5.28558e119	−0.870958	−0.435479	−	0.900199i	$-0.643421\pi$
$907$	−5.28558e119	−0.870958	−0.435479	+	0.900199i	$0.643421\pi$
$908$	4.80430e119	0.757099
$909$	1.75108e120	2.63918
$910$	−1.02362e118	−0.0147558
$911$	−9.22512e119	−1.27197	−0.635986	−	0.771700i	$-0.719407\pi$
$911$	−9.22512e119	−1.27197	−0.635986	+	0.771700i	$0.719407\pi$
$912$	1.26374e120	1.66674
$913$	−1.36740e118	−0.0172516
$914$	−2.02945e119	−0.244938
$915$	1.92681e120	2.22477
$916$	−5.16223e119	−0.570257
$917$	2.80064e119	0.296006
$918$	−4.09245e119	−0.413861
$919$	−1.02318e120	−0.990085	−0.495043	−	0.868869i	$-0.664848\pi$
$919$	−1.02318e120	−0.990085	−0.495043	+	0.868869i	$0.664848\pi$
$920$	2.60745e119	0.241440
$921$	−1.42802e120	−1.26538
$922$	1.60121e118	0.0135783
$923$	−1.48835e119	−0.120791
$924$	9.77985e118	0.0759656
$925$	2.80953e120	2.08878
$926$	3.37932e119	0.240483
$927$	1.15960e118	0.00789911
$928$	−1.49757e120	−0.976547
$929$	−2.80455e120	−1.75076	−0.875381	−	0.483433i	$-0.839390\pi$
$929$	−2.80455e120	−1.75076	−0.875381	+	0.483433i	$0.839390\pi$
$930$	−4.49209e119	−0.268466
$931$	1.88908e120	1.08090
$932$	−1.03695e120	−0.568083
$933$	1.05583e120	0.553843
$934$	3.96480e119	0.199146
$935$	−6.15378e119	−0.295986
$936$	3.42645e119	0.157824
$937$	−2.22682e120	−0.982271	−0.491136	−	0.871083i	$-0.663418\pi$
$937$	−2.22682e120	−0.982271	−0.491136	+	0.871083i	$0.663418\pi$
$938$	1.75175e119	0.0740044
$939$	−4.18630e120	−1.69385
$940$	2.14043e120	0.829512
$941$	6.04115e119	0.224254	0.112127	−	0.993694i	$-0.464234\pi$
$941$	6.04115e119	0.224254	0.112127	+	0.993694i	$0.464234\pi$
$942$	5.30290e119	0.188561
$943$	1.33592e120	0.455049
$944$	6.69923e119	0.218605
$945$	−2.57214e120	−0.804094
$946$	−4.83181e118	−0.0144717
$947$	4.31944e120	1.23952	0.619759	−	0.784792i	$-0.287230\pi$
$947$	4.31944e120	1.23952	0.619759	+	0.784792i	$0.287230\pi$
$948$	7.42303e120	2.04100
$949$	3.49891e119	0.0921830
$950$	2.29470e120	0.579321
$951$	−3.43854e120	−0.831885
$952$	3.75337e119	0.0870213
$953$	8.34558e119	0.185436	0.0927180	−	0.995692i	$-0.470444\pi$
$953$	8.34558e119	0.185436	0.0927180	+	0.995692i	$0.470444\pi$
$954$	−2.32064e120	−0.494194
$955$	−5.54696e120	−1.13219
$956$	2.14241e120	0.419139
$957$	2.79881e120	0.524857
$958$	−7.72148e119	−0.138803
$959$	6.55419e119	0.112945
$960$	−1.24740e121	−2.06073
$961$	−5.52993e120	−0.875836
$962$	−2.48558e119	−0.0377431
$963$	5.19449e120	0.756273
$964$	−5.07344e120	−0.708243
$965$	1.76605e121	2.36399
$966$	2.18286e119	0.0280190
$967$	2.21295e120	0.272395	0.136198	−	0.990682i	$-0.456512\pi$
$967$	2.21295e120	0.272395	0.136198	+	0.990682i	$0.456512\pi$
$968$	−3.84468e120	−0.453846
$969$	−1.47275e121	−1.66731
$970$	−5.11181e120	−0.555034
$971$	−1.40797e120	−0.146628	−0.0733138	−	0.997309i	$-0.523357\pi$
$971$	−1.40797e120	−0.146628	−0.0733138	+	0.997309i	$0.523357\pi$
$972$	5.65243e120	0.564614
$973$	1.45779e120	0.139677
$974$	−2.22817e120	−0.204791
$975$	−6.49878e120	−0.572987
$976$	6.95004e120	0.587855
$977$	2.09763e121	1.70216	0.851078	−	0.525040i	$-0.175950\pi$
$977$	2.09763e121	1.70216	0.851078	+	0.525040i	$0.175950\pi$
$978$	4.28153e120	0.333330
$979$	1.81718e120	0.135737
$980$	−2.19114e121	−1.57041
$981$	3.27639e121	2.25321
$982$	−4.24080e120	−0.279855
$983$	−1.84469e121	−1.16817	−0.584086	−	0.811692i	$-0.698547\pi$
$983$	−1.84469e121	−1.16817	−0.584086	+	0.811692i	$0.698547\pi$
$984$	2.17140e121	1.31959
$985$	−5.65802e119	−0.0329987
$986$	5.20587e120	0.291392
$987$	3.69727e120	0.198626
$988$	3.20515e120	0.165269
$989$	1.70268e120	0.0842719
$990$	−3.97428e120	−0.188813
$991$	−7.96609e120	−0.363298	−0.181649	−	0.983363i	$-0.558143\pi$
$991$	−7.96609e120	−0.363298	−0.181649	+	0.983363i	$0.558143\pi$
$992$	−5.43201e120	−0.237814
$993$	−7.38065e121	−3.10206
$994$	−1.05293e120	−0.0424865
$995$	1.52859e121	0.592182
$996$	3.79581e120	0.141189
$997$	2.41216e121	0.861496	0.430748	−	0.902472i	$-0.358250\pi$
$997$	2.41216e121	0.861496	0.430748	+	0.902472i	$0.358250\pi$
$998$	6.78621e120	0.232723
$999$	−6.24573e121	−2.05675

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.82.a.a.1.3	✓	6
3.2	odd	2		9.82.a.b.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.82.a.a.1.3	✓	6	1.1	even	1	trivial
9.82.a.b.1.4		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:	\( k \)	\(=\)	\( 82 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-3.79502e11 q^{2} -3.74133e19 q^{3} -2.27383e24 q^{4} -3.57322e28 q^{5} +1.41984e31 q^{6} -3.75122e33 q^{7} +1.78050e36 q^{8} +9.56330e38 q^{9} +O(q^{10})\)	\(q-3.79502e11 q^{2} -3.74133e19 q^{3} -2.27383e24 q^{4} -3.57322e28 q^{5} +1.41984e31 q^{6} -3.75122e33 q^{7} +1.78050e36 q^{8} +9.56330e38 q^{9} +1.35605e40 q^{10} -3.06461e41 q^{11} +8.50715e43 q^{12} +2.01230e44 q^{13} +1.42360e45 q^{14} +1.33686e48 q^{15} +4.82208e48 q^{16} -5.61961e49 q^{17} -3.62930e50 q^{18} -7.00483e51 q^{19} +8.12490e52 q^{20} +1.40346e53 q^{21} +1.16303e53 q^{22} -4.09838e54 q^{23} -6.66146e55 q^{24} +8.63203e56 q^{25} -7.63673e55 q^{26} -1.91894e58 q^{27} +8.52964e57 q^{28} +2.44103e59 q^{29} -5.07342e59 q^{30} +8.85416e59 q^{31} -6.13499e60 q^{32} +1.14657e61 q^{33} +2.13266e61 q^{34} +1.34040e62 q^{35} -2.17453e63 q^{36} +3.25478e63 q^{37} +2.65835e63 q^{38} -7.52869e63 q^{39} -6.36214e64 q^{40} -3.25964e65 q^{41} -5.32615e64 q^{42} -4.15451e65 q^{43} +6.96840e65 q^{44} -3.41718e67 q^{45} +1.55535e66 q^{46} +2.63440e67 q^{47} -1.80410e68 q^{48} -2.69682e68 q^{49} -3.27588e68 q^{50} +2.10248e69 q^{51} -4.57563e68 q^{52} +6.39417e69 q^{53} +7.28244e69 q^{54} +1.09505e70 q^{55} -6.67907e69 q^{56} +2.62074e71 q^{57} -9.26376e70 q^{58} +1.38928e71 q^{59} -3.03980e72 q^{60} +1.44130e72 q^{61} -3.36017e71 q^{62} -3.58741e72 q^{63} -9.33082e72 q^{64} -7.19040e72 q^{65} -4.35127e72 q^{66} +1.23051e74 q^{67} +1.27780e74 q^{68} +1.53334e74 q^{69} -5.08683e73 q^{70} -7.39626e74 q^{71} +1.70275e75 q^{72} +1.73876e75 q^{73} -1.23520e75 q^{74} -3.22953e76 q^{75} +1.59278e76 q^{76} +1.14960e75 q^{77} +2.85715e75 q^{78} +8.72563e76 q^{79} -1.72304e77 q^{80} +2.93878e77 q^{81} +1.23704e77 q^{82} +4.46190e76 q^{83} -3.19122e77 q^{84} +2.00801e78 q^{85} +1.57665e77 q^{86} -9.13269e78 q^{87} -5.45655e77 q^{88} -5.92956e78 q^{89} +1.29683e79 q^{90} -7.54858e77 q^{91} +9.31902e78 q^{92} -3.31263e79 q^{93} -9.99763e78 q^{94} +2.50298e80 q^{95} +2.29530e80 q^{96} -3.76964e80 q^{97} +1.02345e80 q^{98} -2.93078e80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) \) 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots - 63\!\cdots\!24 q^{99}+O(q^{100}) \) 6 * q - 460872026640 * q^2 - 15648291925893129960 * q^3 + 4493950976700073762513152 * q^4 - 18364304155649862126617790300 * q^5 + 79543552376002656592687080272832 * q^6 - 31430760593927655842892725138869200 * q^7 - 5498145101596630185016447889074360320 * q^8 + 1187896030123132129876714384590115355598 * q^9 - 66472312087527710620452553569669697173600 * q^10 - 2302475295973581620809306061775551681990328 * q^11 - 53870867926220164150329513348046663235681280 * q^12 + 1313253814255449492724146018729804193778100180 * q^13 + 41225372723246048337281629784765672712004401024 * q^14 - 156056001993392003275961063842210281482861266800 * q^15 + 2799490233261278434402974316306719898117729222656 * q^16 + 2377848571505238562780180385684069414829577769580 * q^17 + 506306622204276540508620731115428014111485052430640 * q^18 - 17422016964741760630179674590582970665727618619375240 * q^19 + 148672889698640611477740875719636714144962866333222400 * q^20 - 114072752249915469711576730788399479267919883382138688 * q^21 - 1258034178625689345497738618244246726621220713529586880 * q^22 + 10526595063181453314046018770874462030150898790798283920 * q^23 - 12327611736558023893782629055720670133074337356786974720 * q^24 + 411037910011361515508644334216291479522821661187695496250 * q^25 - 3180570114716540139250277986112641638356676984048903123168 * q^26 + 14621431460046183096199709161966291993457773283863231280880 * q^27 - 82116517748637002885903417761702653442063276903193852344320 * q^28 + 155464359052154485146727469597467543970919715236853926245940 * q^29 + 164012983787559943750248070451087782537372525868704541558400 * q^30 + 1259277021063335018777245090979655984137503836933555134668992 * q^31 - 13036312845125683749178794475020758767431562303480221102243840 * q^32 + 21091354949357251433966784004957297352147245536782330440814880 * q^33 + 11899550405754031112224464347628728246396477955985557631122144 * q^34 - 232034356615504837711196063040035766391492406317925929510437600 * q^35 - 2071479648832132808682929357240066191852277967275841354377712384 * q^36 + 414692688584236378963319357622814947056491742931883680122973540 * q^37 - 2455417714037465297201999851134772037590829998762172946918415680 * q^38 - 92285563929532296901251298670288831485071753513924535804838199984 * q^39 - 258059824285668605758122263287555971608050642150708772544789504000 * q^40 - 250252788823194090638944408016236187978548863949167831014660870148 * q^41 - 3774470339882908627686770098374833879180889302300694800640098910720 * q^42 - 5362516930786214192203446564720631507618558180640993338648106782200 * q^43 - 17252465656682175267213991915222412585785021276568609411813835518976 * q^44 - 62055994195911488597384173133359170181530078929941731114719230089900 * q^45 - 123763409427226200113215389587151615608344054530127843046255996688768 * q^46 - 230717394511751791462615349254196337530205542984846694602934639341280 * q^47 - 691982889190309031684460851104240936972943285356349640319551063982080 * q^48 - 148965540042877735285285650175007198234557699456949204802064464556458 * q^49 - 1416105420952806525015169807922957339416756851287952031511031347670000 * q^50 + 723978686772453055369497103847414979467127084371963703072714225585072 * q^51 + 12562371185881747636341658298037576485393840750032566447999727917043200 * q^52 + 25898990256961205776642859216859182171010424056472082121008236344959940 * q^53 + 60731909939285801872082597253734783721512219559188195805336458971800960 * q^54 + 70427859302095658379065386305135120838252257009889309990749877277396400 * q^55 + 350275852246953465289512615368698332984392220622408793911163576939151360 * q^56 + 303622382725256536236947985463289143154200643659779472092208351796091360 * q^57 - 312514134877257928766126367534026770462807935435519457753987287493386720 * q^58 - 38532453307459913471042984274454520116124717672121643571528434328282520 * q^59 - 5854438714408546634435977504160054633094179506942282108438463374797465600 * q^60 - 4585192544270629640163935422584783189092178505653567017169797728495170828 * q^61 - 11745445982868867354760701788812677993661414140303262885466836339630318080 * q^62 - 35632339418998518169074915366562958999484559616578607415025802007025188240 * q^63 - 24049189879736877632355406073912155582619770074517134096672197458230509568 * q^64 + 40108571425620140080303901416556158312567794172295521521551039993118238200 * q^65 + 46637466443959380664183766096173047575934541297502070623350605582042365184 * q^66 + 278606964486964374833906544600580027758780739521508130980859112605565987480 * q^67 + 591059149620766869951154898169335214276013402788475417448362648514550551040 * q^68 + 783789679110178241786835392836945981604400905715238386162022702382323722816 * q^69 + 2635837114104224632390936486964777102611174135296488988531978806621369068800 * q^70 - 554281436103188717611008447226924711986842423491780222553301787426789861968 * q^71 - 3169897304032072056282604590226317130165389286798806197352424269626436341760 * q^72 - 1159677538409433721867557656635958525415325708297922475676033828300683142980 * q^73 - 14870996314347354169518203977127998385153668929299472477677600807989626002016 * q^74 - 40272209656064989140640078595938035284494253817756477276130430269166782335000 * q^75 - 56365824164857229782022127848008365902008884166434980738114640515976798612480 * q^76 - 22951272837324694774527636903423616359482790364245898655274441101674154673600 * q^77 + 29994870322699852265351947769035786178441787146653937638111333726813935158400 * q^78 + 76488528596848273963909721387433081359345259080220208993600380062891411190240 * q^79 + 326185463863660018876021371340485226979224823762794013840530768719064527667200 * q^80 + 713659220427214109967671419496287178348529210497808359051350032218775138774486 * q^81 + 836977463852743303549437738986542975894462808796250502348000478828556860551520 * q^82 + 440718478462773776637617020819789880594300172591745821478345102532528865997560 * q^83 + 2327207348086698397722806131221331490656683214148360655124465557042000906952704 * q^84 + 1165607138975709364402518400492567424057357396402879557680723771041190675179400 * q^85 - 10339197506820945136003281093027314178240703830345630490304599234644673765234368 * q^86 - 13777097629225807302706950021773234863450868385225572161845501405567814463584560 * q^87 - 9603847126452588175246186358824265187739652448840879006569656469218022549667840 * q^88 - 18886228493337874501351816155449414708824427288664596668607356717228138798590180 * q^89 - 27536035459180423419106541648329015873635894588277179325118018321007646877848800 * q^90 - 14576226325987997036142564032100430704897317032265698214767987870608618538920288 * q^91 + 66364414655655668275929797141498084164407535259475789695165805684452941775738880 * q^92 + 130065128543178746783515152749840115744191801626425494555088565985583783043572480 * q^93 + 331286952814608158700187065887753978184064043063622410298763861434514546852072704 * q^94 + 267699559747800180626411366716842325842865933645649558098598518850783266973922000 * q^95 + 495554087106091786297185708372687557293322071836937974888325742175573190348111872 * q^96 + 113832498161281214584608062040287314379413598012089688107897449655058469975263820 * q^97 - 858118355318723523117883130491863373979750018711838274840266757637744872892872080 * q^98 - 630632406390824053363198011181718527371969259570962092705191903378628178893256024 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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