LMFDB - Embedded newform 1.82.a.a.1.6

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			1.6
Root			$-1.73117e10$ 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)

$f(q)$	$=$	$q+2.41607e12 q^{2} -1.10180e19 q^{3} +3.41956e24 q^{4} -1.95525e27 q^{5} -2.66202e31 q^{6} +1.09563e34 q^{7} +2.42020e36 q^{8} -3.22031e38 q^{9} +O(q^{10})$	\(q+2.41607e12 q^{2} -1.10180e19 q^{3} +3.41956e24 q^{4} -1.95525e27 q^{5} -2.66202e31 q^{6} +1.09563e34 q^{7} +2.42020e36 q^{8} -3.22031e38 q^{9} -4.72402e39 q^{10} -2.45659e42 q^{11} -3.76765e43 q^{12} +1.04827e45 q^{13} +2.64712e46 q^{14} +2.15428e46 q^{15} -2.42061e48 q^{16} +7.60247e49 q^{17} -7.78051e50 q^{18} -5.17134e51 q^{19} -6.68608e51 q^{20} -1.20716e53 q^{21} -5.93531e54 q^{22} -1.96011e55 q^{23} -2.66656e55 q^{24} -4.09767e56 q^{25} +2.53270e57 q^{26} +8.43378e57 q^{27} +3.74656e58 q^{28} -7.07167e58 q^{29} +5.20490e58 q^{30} -3.03406e60 q^{31} -1.17001e61 q^{32} +2.70666e61 q^{33} +1.83681e62 q^{34} -2.14222e61 q^{35} -1.10120e63 q^{36} +3.76143e62 q^{37} -1.24943e64 q^{38} -1.15498e64 q^{39} -4.73208e63 q^{40} +1.34796e65 q^{41} -2.91658e65 q^{42} -2.04430e66 q^{43} -8.40046e66 q^{44} +6.29650e65 q^{45} -4.73576e67 q^{46} +2.88861e67 q^{47} +2.66702e67 q^{48} -1.63713e68 q^{49} -9.90028e68 q^{50} -8.37636e68 q^{51} +3.58462e69 q^{52} +8.48669e69 q^{53} +2.03766e70 q^{54} +4.80324e69 q^{55} +2.65164e70 q^{56} +5.69776e70 q^{57} -1.70857e71 q^{58} -4.61708e71 q^{59} +7.36669e70 q^{60} +2.95815e72 q^{61} -7.33052e72 q^{62} -3.52826e72 q^{63} -2.24155e73 q^{64} -2.04962e72 q^{65} +6.53949e73 q^{66} +1.59714e73 q^{67} +2.59971e74 q^{68} +2.15964e74 q^{69} -5.17577e73 q^{70} -7.76456e74 q^{71} -7.79379e74 q^{72} +1.29321e74 q^{73} +9.08789e74 q^{74} +4.51480e75 q^{75} -1.76837e76 q^{76} -2.69151e76 q^{77} -2.79051e76 q^{78} +8.99349e76 q^{79} +4.73289e75 q^{80} +4.98742e76 q^{81} +3.25677e77 q^{82} +8.55650e77 q^{83} -4.12795e77 q^{84} -1.48647e77 q^{85} -4.93918e78 q^{86} +7.79153e77 q^{87} -5.94544e78 q^{88} +1.10189e79 q^{89} +1.52128e78 q^{90} +1.14851e79 q^{91} -6.70270e79 q^{92} +3.34292e79 q^{93} +6.97910e79 q^{94} +1.01112e79 q^{95} +1.28911e80 q^{96} +3.05910e80 q^{97} -3.95544e80 q^{98} +7.91099e80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.41607e12	1.55380	0.776900	−	0.629624i	$-0.216791\pi$
$2$	2.41607e12	1.55380	0.776900	+	0.629624i	$0.216791\pi$
$3$	−1.10180e19	−0.523227	−0.261613	−	0.965173i	$-0.584255\pi$
$3$	−1.10180e19	−0.523227	−0.261613	+	0.965173i	$0.584255\pi$
$4$	3.41956e24	1.41430
$5$	−1.95525e27	−0.0961427	−0.0480713	−	0.998844i	$-0.515307\pi$
$5$	−1.95525e27	−0.0961427	−0.0480713	+	0.998844i	$0.515307\pi$
$6$	−2.66202e31	−0.812990
$7$	1.09563e34	0.650418	0.325209	−	0.945642i	$-0.394565\pi$
$7$	1.09563e34	0.650418	0.325209	+	0.945642i	$0.394565\pi$
$8$	2.42020e36	0.643734
$9$	−3.22031e38	−0.726234
$10$	−4.72402e39	−0.149387
$11$	−2.45659e42	−1.63655	−0.818275	−	0.574827i	$-0.805069\pi$
$11$	−2.45659e42	−1.63655	−0.818275	+	0.574827i	$0.805069\pi$
$12$	−3.76765e43	−0.739998
$13$	1.04827e45	0.804947	0.402473	−	0.915432i	$-0.368151\pi$
$13$	1.04827e45	0.804947	0.402473	+	0.915432i	$0.368151\pi$
$14$	2.64712e46	1.01062
$15$	2.15428e46	0.0503044
$16$	−2.42061e48	−0.414062
$17$	7.60247e49	1.11628	0.558140	−	0.829747i	$-0.311515\pi$
$17$	7.60247e49	1.11628	0.558140	+	0.829747i	$0.311515\pi$
$18$	−7.78051e50	−1.12842
$19$	−5.17134e51	−0.839620	−0.419810	−	0.907612i	$-0.637903\pi$
$19$	−5.17134e51	−0.839620	−0.419810	+	0.907612i	$0.637903\pi$
$20$	−6.68608e51	−0.135974
$21$	−1.20716e53	−0.340316
$22$	−5.93531e54	−2.54287
$23$	−1.96011e55	−1.38772	−0.693861	−	0.720109i	$-0.744092\pi$
$23$	−1.96011e55	−1.38772	−0.693861	+	0.720109i	$0.744092\pi$
$24$	−2.66656e55	−0.336819
$25$	−4.09767e56	−0.990757
$26$	2.53270e57	1.25073
$27$	8.43378e57	0.903212
$28$	3.74656e58	0.919884
$29$	−7.07167e58	−0.419183	−0.209591	−	0.977789i	$-0.567213\pi$
$29$	−7.07167e58	−0.419183	−0.209591	+	0.977789i	$0.567213\pi$
$30$	5.20490e58	0.0781631
$31$	−3.03406e60	−1.20747	−0.603735	−	0.797185i	$-0.706321\pi$
$31$	−3.03406e60	−1.20747	−0.603735	+	0.797185i	$0.706321\pi$
$32$	−1.17001e61	−1.28710
$33$	2.70666e61	0.856287
$34$	1.83681e62	1.73448
$35$	−2.14222e61	−0.0625329
$36$	−1.10120e63	−1.02711
$37$	3.76143e62	0.115660	0.0578300	−	0.998326i	$-0.481582\pi$
$37$	3.76143e62	0.115660	0.0578300	+	0.998326i	$0.481582\pi$
$38$	−1.24943e64	−1.30460
$39$	−1.15498e64	−0.421170
$40$	−4.73208e63	−0.0618903
$41$	1.34796e65	0.648531	0.324266	−	0.945966i	$-0.394883\pi$
$41$	1.34796e65	0.648531	0.324266	+	0.945966i	$0.394883\pi$
$42$	−2.91658e65	−0.528784
$43$	−2.04430e66	−1.42913	−0.714566	−	0.699568i	$-0.753376\pi$
$43$	−2.04430e66	−1.42913	−0.714566	+	0.699568i	$0.753376\pi$
$44$	−8.40046e66	−2.31457
$45$	6.29650e65	0.0698220
$46$	−4.73576e67	−2.15624
$47$	2.88861e67	0.550460	0.275230	−	0.961378i	$-0.411246\pi$
$47$	2.88861e67	0.550460	0.275230	+	0.961378i	$0.411246\pi$
$48$	2.66702e67	0.216649
$49$	−1.63713e68	−0.576956
$50$	−9.90028e68	−1.53944
$51$	−8.37636e68	−0.584068
$52$	3.58462e69	1.13843
$53$	8.48669e69	1.24614	0.623068	−	0.782168i	$-0.285886\pi$
$53$	8.48669e69	1.24614	0.623068	+	0.782168i	$0.285886\pi$
$54$	2.03766e70	1.40341
$55$	4.80324e69	0.157342
$56$	2.65164e70	0.418696
$57$	5.69776e70	0.439312
$58$	−1.70857e71	−0.651326
$59$	−4.61708e71	−0.880767	−0.440383	−	0.897810i	$-0.645157\pi$
$59$	−4.61708e71	−0.880767	−0.440383	+	0.897810i	$0.645157\pi$
$60$	7.36669e70	0.0711454
$61$	2.95815e72	1.46272	0.731361	−	0.681991i	$-0.238886\pi$
$61$	2.95815e72	1.46272	0.731361	+	0.681991i	$0.238886\pi$
$62$	−7.33052e72	−1.87617
$63$	−3.52826e72	−0.472355
$64$	−2.24155e73	−1.58584
$65$	−2.04962e72	−0.0773897
$66$	6.53949e73	1.33050
$67$	1.59714e73	0.176731	0.0883654	−	0.996088i	$-0.471836\pi$
$67$	1.59714e73	0.176731	0.0883654	+	0.996088i	$0.471836\pi$
$68$	2.59971e74	1.57875
$69$	2.15964e74	0.726094
$70$	−5.17577e73	−0.0971637
$71$	−7.76456e74	−0.820641	−0.410321	−	0.911941i	$-0.634583\pi$
$71$	−7.76456e74	−0.820641	−0.410321	+	0.911941i	$0.634583\pi$
$72$	−7.79379e74	−0.467501
$73$	1.29321e74	0.0443705	0.0221853	−	0.999754i	$-0.492938\pi$
$73$	1.29321e74	0.0443705	0.0221853	+	0.999754i	$0.492938\pi$
$74$	9.08789e74	0.179713
$75$	4.51480e75	0.518391
$76$	−1.76837e76	−1.18747
$77$	−2.69151e76	−1.06444
$78$	−2.79051e76	−0.654414
$79$	8.99349e76	1.25902	0.629508	−	0.776994i	$-0.283257\pi$
$79$	8.99349e76	1.25902	0.629508	+	0.776994i	$0.283257\pi$
$80$	4.73289e75	0.0398091
$81$	4.98742e76	0.253649
$82$	3.25677e77	1.00769
$83$	8.55650e77	1.62044	0.810221	−	0.586125i	$-0.199347\pi$
$83$	8.55650e77	1.62044	0.810221	+	0.586125i	$0.199347\pi$
$84$	−4.12795e77	−0.481308
$85$	−1.48647e77	−0.107322
$86$	−4.93918e78	−2.22059
$87$	7.79153e77	0.219328
$88$	−5.94544e78	−1.05350
$89$	1.10189e79	1.23550	0.617750	−	0.786375i	$-0.288045\pi$
$89$	1.10189e79	1.23550	0.617750	+	0.786375i	$0.288045\pi$
$90$	1.52128e78	0.108490
$91$	1.14851e79	0.523552
$92$	−6.70270e79	−1.96265
$93$	3.34292e79	0.631780
$94$	6.97910e79	0.855306
$95$	1.01112e79	0.0807233
$96$	1.28911e80	0.673448
$97$	3.05910e80	1.05036	0.525181	−	0.850991i	$-0.323998\pi$
$97$	3.05910e80	1.05036	0.525181	+	0.850991i	$0.323998\pi$
$98$	−3.95544e80	−0.896475
$99$	7.91099e80	1.18852
$100$	−1.40122e81	−1.40122
$101$	−2.73530e81	−1.82806	−0.914028	−	0.405651i	$-0.867045\pi$
$101$	−2.73530e81	−1.82806	−0.914028	+	0.405651i	$0.867045\pi$
$102$	−2.02379e81	−0.907525
$103$	2.59921e81	0.785116	0.392558	−	0.919727i	$-0.371590\pi$
$103$	2.59921e81	0.785116	0.392558	+	0.919727i	$0.371590\pi$
$104$	2.53702e81	0.518171
$105$	2.36029e80	0.0327189
$106$	2.05045e82	1.93625
$107$	−2.21960e82	−1.43296	−0.716478	−	0.697610i	$-0.754247\pi$
$107$	−2.21960e82	−1.43296	−0.716478	+	0.697610i	$0.754247\pi$
$108$	2.88398e82	1.27741
$109$	−1.81444e82	−0.553311	−0.276656	−	0.960969i	$-0.589226\pi$
$109$	−1.81444e82	−0.553311	−0.276656	+	0.960969i	$0.589226\pi$
$110$	1.16050e82	0.244478
$111$	−4.14432e81	−0.0605164
$112$	−2.65209e82	−0.269314
$113$	−1.03987e83	−0.736718	−0.368359	−	0.929684i	$-0.620080\pi$
$113$	−1.03987e83	−0.736718	−0.368359	+	0.929684i	$0.620080\pi$
$114$	1.37662e83	0.682603
$115$	3.83249e82	0.133419
$116$	−2.41820e83	−0.592848
$117$	−3.37575e83	−0.584579
$118$	−1.11552e84	−1.36854
$119$	8.32948e83	0.726049
$120$	5.21378e82	0.0323827
$121$	3.78160e84	1.67830
$122$	7.14711e84	2.27278
$123$	−1.48518e84	−0.339329
$124$	−1.03752e85	−1.70772
$125$	1.60987e84	0.191397
$126$	−8.52455e84	−0.733946
$127$	−4.55702e84	−0.284859	−0.142430	−	0.989805i	$-0.545491\pi$
$127$	−4.55702e84	−0.284859	−0.142430	+	0.989805i	$0.545491\pi$
$128$	−2.58685e85	−1.17698
$129$	2.25240e85	0.747760
$130$	−4.95204e84	−0.120248
$131$	−2.83953e83	−0.00505544	−0.00252772	−	0.999997i	$-0.500805\pi$
$131$	−2.83953e83	−0.00505544	−0.00252772	+	0.999997i	$0.500805\pi$
$132$	9.25559e85	1.21104
$133$	−5.66587e85	−0.546104
$134$	3.85880e85	0.274605
$135$	−1.64901e85	−0.0868372
$136$	1.83995e86	0.718587
$137$	−4.69797e86	−1.36373	−0.681863	−	0.731480i	$-0.738830\pi$
$137$	−4.69797e86	−1.36373	−0.681863	+	0.731480i	$0.738830\pi$
$138$	5.21784e86	1.12820
$139$	5.71964e86	0.923144	0.461572	−	0.887103i	$-0.347286\pi$
$139$	5.71964e86	0.923144	0.461572	+	0.887103i	$0.347286\pi$
$140$	−7.32545e85	−0.0884401
$141$	−3.18266e86	−0.288016
$142$	−1.87597e87	−1.27511
$143$	−2.57517e87	−1.31734
$144$	7.79512e86	0.300706
$145$	1.38269e86	0.0403013
$146$	3.12450e86	0.0689430
$147$	1.80379e87	0.301879
$148$	1.28624e87	0.163577
$149$	1.40161e88	1.35701	0.678506	−	0.734595i	$-0.262628\pi$
$149$	1.40161e88	1.35701	0.678506	+	0.734595i	$0.262628\pi$
$150$	1.09081e88	0.805476
$151$	1.21103e88	0.683263	0.341632	−	0.939834i	$-0.389020\pi$
$151$	1.21103e88	0.683263	0.341632	+	0.939834i	$0.389020\pi$
$152$	−1.25157e88	−0.540491
$153$	−2.44823e88	−0.810680
$154$	−6.50289e88	−1.65393
$155$	5.93234e87	0.116089
$156$	−3.94952e88	−0.595659
$157$	2.02144e87	0.0235355	0.0117678	−	0.999931i	$-0.496254\pi$
$157$	2.02144e87	0.0235355	0.0117678	+	0.999931i	$0.496254\pi$
$158$	2.17289e89	1.95626
$159$	−9.35059e88	−0.652012
$160$	2.28765e88	0.123746
$161$	−2.14755e89	−0.902600
$162$	1.20500e89	0.394119
$163$	−2.86179e89	−0.729525	−0.364762	−	0.931101i	$-0.618850\pi$
$163$	−2.86179e89	−0.729525	−0.364762	+	0.931101i	$0.618850\pi$
$164$	4.60943e89	0.917216
$165$	−5.29219e88	−0.0823257
$166$	2.06731e90	2.51784
$167$	−1.21974e90	−1.16480	−0.582398	−	0.812904i	$-0.697885\pi$
$167$	−1.21974e90	−1.16480	−0.582398	+	0.812904i	$0.697885\pi$
$168$	−2.92156e89	−0.219073
$169$	−5.97075e89	−0.352061
$170$	−3.59142e89	−0.166757
$171$	1.66533e90	0.609760
$172$	−6.99060e90	−2.02122
$173$	−2.41069e90	−0.551155	−0.275577	−	0.961279i	$-0.588869\pi$
$173$	−2.41069e90	−0.551155	−0.275577	+	0.961279i	$0.588869\pi$
$174$	1.88249e90	0.340791
$175$	−4.48953e90	−0.644406
$176$	5.94645e90	0.677634
$177$	5.08708e90	0.460841
$178$	2.66224e91	1.91972
$179$	1.25746e91	0.722681	0.361341	−	0.932434i	$-0.382319\pi$
$179$	1.25746e91	0.722681	0.361341	+	0.932434i	$0.382319\pi$
$180$	2.15313e90	0.0987490
$181$	−4.59827e91	−1.68505	−0.842523	−	0.538660i	$-0.818931\pi$
$181$	−4.59827e91	−1.68505	−0.842523	+	0.538660i	$0.818931\pi$
$182$	2.77489e91	0.813495
$183$	−3.25928e91	−0.765336
$184$	−4.74385e91	−0.893324
$185$	−7.35452e89	−0.0111199
$186$	8.07673e91	0.981661
$187$	−1.86762e92	−1.82685
$188$	9.87778e91	0.778514
$189$	9.24028e91	0.587465
$190$	2.44295e91	0.125428
$191$	−1.78047e92	−0.739065	−0.369532	−	0.929218i	$-0.620482\pi$
$191$	−1.78047e92	−0.739065	−0.369532	+	0.929218i	$0.620482\pi$
$192$	2.46973e92	0.829755
$193$	−5.37925e92	−1.46437	−0.732185	−	0.681106i	$-0.761499\pi$
$193$	−5.37925e92	−1.46437	−0.732185	+	0.681106i	$0.761499\pi$
$194$	7.39102e92	1.63205
$195$	2.25827e91	0.0404924
$196$	−5.59828e92	−0.815987
$197$	5.95922e91	0.0706817	0.0353409	−	0.999375i	$-0.488748\pi$
$197$	5.95922e91	0.0706817	0.0353409	+	0.999375i	$0.488748\pi$
$198$	1.91135e93	1.84672
$199$	1.19376e93	0.940522	0.470261	−	0.882527i	$-0.344160\pi$
$199$	1.19376e93	0.940522	0.470261	+	0.882527i	$0.344160\pi$
$200$	−9.91718e92	−0.637783
$201$	−1.75972e92	−0.0924704
$202$	−6.60869e93	−2.84043
$203$	−7.74792e92	−0.272644
$204$	−2.86435e93	−0.826045
$205$	−2.63559e92	−0.0623515
$206$	6.27989e93	1.21991
$207$	6.31216e93	1.00781
$208$	−2.53745e93	−0.333298
$209$	1.27039e94	1.37408
$210$	5.70263e92	0.0508387
$211$	−1.50516e94	−1.10699	−0.553496	−	0.832852i	$-0.686706\pi$
$211$	−1.50516e94	−1.10699	−0.553496	+	0.832852i	$0.686706\pi$
$212$	2.90207e94	1.76241
$213$	8.55495e93	0.429382
$214$	−5.36273e94	−2.22653
$215$	3.99711e93	0.137401
$216$	2.04114e94	0.581428
$217$	−3.32420e94	−0.785360
$218$	−4.38382e94	−0.859736
$219$	−1.42486e93	−0.0232159
$220$	1.64250e94	0.222529
$221$	7.96943e94	0.898546
$222$	−1.00130e94	−0.0940304
$223$	4.43990e94	0.347557	0.173779	−	0.984785i	$-0.444402\pi$
$223$	4.43990e94	0.347557	0.173779	+	0.984785i	$0.444402\pi$
$224$	−1.28189e95	−0.837156
$225$	1.31958e95	0.719521
$226$	−2.51240e95	−1.14471
$227$	−1.64130e93	−0.00625376	−0.00312688	−	0.999995i	$-0.500995\pi$
$227$	−1.64130e93	−0.00625376	−0.00312688	+	0.999995i	$0.500995\pi$
$228$	1.94838e95	0.621317
$229$	5.28950e95	1.41279	0.706395	−	0.707818i	$-0.250320\pi$
$229$	5.28950e95	1.41279	0.706395	+	0.707818i	$0.250320\pi$
$230$	9.25958e94	0.207307
$231$	2.96549e95	0.556944
$232$	−1.71148e95	−0.269842
$233$	−4.06009e95	−0.537800	−0.268900	−	0.963168i	$-0.586660\pi$
$233$	−4.06009e95	−0.537800	−0.268900	+	0.963168i	$0.586660\pi$
$234$	−8.15607e95	−0.908320
$235$	−5.64795e94	−0.0529227
$236$	−1.57884e96	−1.24567
$237$	−9.90898e95	−0.658751
$238$	2.01246e96	1.12813
$239$	−2.21661e96	−1.04851	−0.524256	−	0.851561i	$-0.675657\pi$
$239$	−2.21661e96	−1.04851	−0.524256	+	0.851561i	$0.675657\pi$
$240$	−5.21468e94	−0.0208292
$241$	7.77775e95	0.262521	0.131260	−	0.991348i	$-0.458098\pi$
$241$	7.77775e95	0.262521	0.131260	+	0.991348i	$0.458098\pi$
$242$	9.13663e96	2.60774
$243$	−4.28927e96	−1.03593
$244$	1.01156e97	2.06872
$245$	3.20100e95	0.0554701
$246$	−3.58830e96	−0.527250
$247$	−5.42096e96	−0.675849
$248$	−7.34303e96	−0.777289
$249$	−9.42751e96	−0.847859
$250$	3.88956e96	0.297392
$251$	−9.22205e96	−0.599849	−0.299924	−	0.953963i	$-0.596961\pi$
$251$	−9.22205e96	−0.599849	−0.299924	+	0.953963i	$0.596961\pi$
$252$	−1.20651e97	−0.668050
$253$	4.81518e97	2.27108
$254$	−1.10101e97	−0.442614
$255$	1.63778e96	0.0561538
$256$	−8.30285e96	−0.242945
$257$	−6.53948e97	−1.63400	−0.816999	−	0.576639i	$-0.804364\pi$
$257$	−6.53948e97	−1.63400	−0.816999	+	0.576639i	$0.804364\pi$
$258$	5.44196e97	1.16187
$259$	4.12113e96	0.0752273
$260$	−7.00881e96	−0.109452
$261$	2.27730e97	0.304424
$262$	−6.86051e95	−0.00785515
$263$	1.21377e98	1.19105	0.595524	−	0.803337i	$-0.296944\pi$
$263$	1.21377e98	1.19105	0.595524	+	0.803337i	$0.296944\pi$
$264$	6.55065e97	0.551221
$265$	−1.65936e97	−0.119807
$266$	−1.36892e98	−0.848536
$267$	−1.21406e98	−0.646446
$268$	5.46150e97	0.249950
$269$	2.83784e98	1.11692	0.558458	−	0.829533i	$-0.311393\pi$
$269$	2.83784e98	1.11692	0.558458	+	0.829533i	$0.311393\pi$
$270$	−3.98413e97	−0.134928
$271$	−6.20737e98	−1.80989	−0.904944	−	0.425531i	$-0.860087\pi$
$271$	−6.20737e98	−1.80989	−0.904944	+	0.425531i	$0.860087\pi$
$272$	−1.84026e98	−0.462210
$273$	−1.26543e98	−0.273936
$274$	−1.13506e99	−2.11896
$275$	1.00663e99	1.62142
$276$	7.38501e98	1.02691
$277$	4.30712e98	0.517317	0.258658	−	0.965969i	$-0.416720\pi$
$277$	4.30712e98	0.517317	0.258658	+	0.965969i	$0.416720\pi$
$278$	1.38191e99	1.43438
$279$	9.77063e98	0.876905
$280$	−5.18460e97	−0.0402545
$281$	−8.03373e98	−0.539897	−0.269949	−	0.962875i	$-0.587007\pi$
$281$	−8.03373e98	−0.539897	−0.269949	+	0.962875i	$0.587007\pi$
$282$	−7.68954e98	−0.447519
$283$	1.04623e99	0.527566	0.263783	−	0.964582i	$-0.415030\pi$
$283$	1.04623e99	0.527566	0.263783	+	0.964582i	$0.415030\pi$
$284$	−2.65513e99	−1.16063
$285$	−1.11405e98	−0.0422366
$286$	−6.22180e99	−2.04688
$287$	1.47686e99	0.421817
$288$	3.76778e99	0.934738
$289$	1.14141e99	0.246082
$290$	3.34067e98	0.0626202
$291$	−3.37051e99	−0.549578
$292$	4.42222e98	0.0627531
$293$	1.88779e99	0.233247	0.116623	−	0.993176i	$-0.462793\pi$
$293$	1.88779e99	0.233247	0.116623	+	0.993176i	$0.462793\pi$
$294$	4.35808e99	0.469060
$295$	9.02753e98	0.0846793
$296$	9.10340e98	0.0744542
$297$	−2.07183e100	−1.47815
$298$	3.38640e100	2.10853
$299$	−2.05472e100	−1.11704
$300$	1.54386e100	0.733158
$301$	−2.23979e100	−0.929533
$302$	2.92594e100	1.06166
$303$	3.01374e100	0.956488
$304$	1.25178e100	0.347655
$305$	−5.78391e99	−0.140630
$306$	−5.91511e100	−1.25964
$307$	−3.44926e100	−0.643609	−0.321804	−	0.946806i	$-0.604289\pi$
$307$	−3.44926e100	−0.643609	−0.321804	+	0.946806i	$0.604289\pi$
$308$	−9.20378e100	−1.50544
$309$	−2.86380e100	−0.410794
$310$	1.43330e100	0.180380
$311$	9.09772e99	0.100493	0.0502466	−	0.998737i	$-0.483999\pi$
$311$	9.09772e99	0.100493	0.0502466	+	0.998737i	$0.483999\pi$
$312$	−2.79528e100	−0.271121
$313$	2.21518e101	1.88740	0.943699	−	0.330804i	$-0.107320\pi$
$313$	2.21518e101	1.88740	0.943699	+	0.330804i	$0.107320\pi$
$314$	4.88394e99	0.0365695
$315$	6.89862e99	0.0454135
$316$	3.07538e101	1.78062
$317$	−5.44905e100	−0.277601	−0.138800	−	0.990320i	$-0.544325\pi$
$317$	−5.44905e100	−0.277601	−0.138800	+	0.990320i	$0.544325\pi$
$318$	−2.25917e101	−1.01310
$319$	1.73722e101	0.686013
$320$	4.38278e100	0.152467
$321$	2.44555e101	0.749761
$322$	−5.18864e101	−1.40246
$323$	−3.93150e101	−0.937251
$324$	1.70548e101	0.358734
$325$	−4.29547e101	−0.797506
$326$	−6.91430e101	−1.13354
$327$	1.99914e101	0.289507
$328$	3.26233e101	0.417482
$329$	3.16485e101	0.358029
$330$	−1.27863e101	−0.127918
$331$	4.31900e101	0.382252	0.191126	−	0.981566i	$-0.438786\pi$
$331$	4.31900e101	0.382252	0.191126	+	0.981566i	$0.438786\pi$
$332$	2.92594e102	2.29178
$333$	−1.21130e101	−0.0839961
$334$	−2.94698e102	−1.80986
$335$	−3.12279e100	−0.0169914
$336$	2.92206e101	0.140912
$337$	−1.76336e101	−0.0753930	−0.0376965	−	0.999289i	$-0.512002\pi$
$337$	−1.76336e101	−0.0753930	−0.0376965	+	0.999289i	$0.512002\pi$
$338$	−1.44258e102	−0.547032
$339$	1.14572e102	0.385471
$340$	−5.08307e101	−0.151785
$341$	7.45345e102	1.97608
$342$	4.02357e102	0.947445
$343$	−4.90257e102	−1.02568
$344$	−4.94761e102	−0.919980
$345$	−4.22262e101	−0.0698086
$346$	−5.82439e102	−0.856384
$347$	−6.69404e102	−0.875678	−0.437839	−	0.899053i	$-0.644256\pi$
$347$	−6.69404e102	−0.875678	−0.437839	+	0.899053i	$0.644256\pi$
$348$	2.66436e102	0.310194
$349$	−5.08612e102	−0.527177	−0.263589	−	0.964635i	$-0.584906\pi$
$349$	−5.08612e102	−0.527177	−0.263589	+	0.964635i	$0.584906\pi$
$350$	−1.08470e103	−1.00128
$351$	8.84087e102	0.727038
$352$	2.87423e103	2.10641
$353$	−2.29436e103	−1.49895	−0.749473	−	0.662035i	$-0.769693\pi$
$353$	−2.29436e103	−1.49895	−0.749473	+	0.662035i	$0.769693\pi$
$354$	1.22908e103	0.716055
$355$	1.51816e102	0.0788987
$356$	3.76797e103	1.74736
$357$	−9.17738e102	−0.379888
$358$	3.03812e103	1.12290
$359$	4.04753e102	0.133618	0.0668090	−	0.997766i	$-0.478718\pi$
$359$	4.04753e102	0.133618	0.0668090	+	0.997766i	$0.478718\pi$
$360$	1.52388e102	0.0449468
$361$	−1.11923e103	−0.295039
$362$	−1.11097e104	−2.61823
$363$	−4.16655e103	−0.878129
$364$	3.92741e103	0.740457
$365$	−2.52855e101	−0.00426590
$366$	−7.87465e103	−1.18918
$367$	5.19277e103	0.702139	0.351070	−	0.936349i	$-0.385818\pi$
$367$	5.19277e103	0.702139	0.351070	+	0.936349i	$0.385818\pi$
$368$	4.74466e103	0.574604
$369$	−4.34085e103	−0.470985
$370$	−1.77691e102	−0.0172780
$371$	9.29825e103	0.810509
$372$	1.14313e104	0.893525
$373$	2.75979e104	1.93494	0.967471	−	0.252983i	$-0.0814116\pi$
$373$	2.75979e104	1.93494	0.967471	+	0.252983i	$0.0814116\pi$
$374$	−4.51230e104	−2.83856
$375$	−1.77374e103	−0.100144
$376$	6.99101e103	0.354350
$377$	−7.41302e103	−0.337420
$378$	2.23252e104	0.912804
$379$	1.08706e104	0.399360	0.199680	−	0.979861i	$-0.436010\pi$
$379$	1.08706e104	0.399360	0.199680	+	0.979861i	$0.436010\pi$
$380$	3.45760e103	0.114167
$381$	5.02090e103	0.149046
$382$	−4.30174e104	−1.14836
$383$	−1.96036e103	−0.0470744	−0.0235372	−	0.999723i	$-0.507493\pi$
$383$	−1.96036e103	−0.0470744	−0.0235372	+	0.999723i	$0.507493\pi$
$384$	2.85018e104	0.615826
$385$	5.26256e103	0.102338
$386$	−1.29967e105	−2.27534
$387$	6.58328e104	1.03788
$388$	1.04608e105	1.48552
$389$	−6.50767e104	−0.832658	−0.416329	−	0.909214i	$-0.636684\pi$
$389$	−6.50767e104	−0.832658	−0.416329	+	0.909214i	$0.636684\pi$
$390$	5.45614e103	0.0629171
$391$	−1.49017e105	−1.54909
$392$	−3.96219e104	−0.371406
$393$	3.12858e102	0.00264514
$394$	1.43979e104	0.109825
$395$	−1.75845e104	−0.121045
$396$	2.70521e105	1.68092
$397$	3.42316e104	0.192049	0.0960244	−	0.995379i	$-0.469387\pi$
$397$	3.42316e104	0.192049	0.0960244	+	0.995379i	$0.469387\pi$
$398$	2.88422e105	1.46138
$399$	6.24263e104	0.285736
$400$	9.91888e104	0.410235
$401$	1.64711e105	0.615709	0.307855	−	0.951433i	$-0.400389\pi$
$401$	1.64711e105	0.615709	0.307855	+	0.951433i	$0.400389\pi$
$402$	−4.25161e104	−0.143681
$403$	−3.18052e105	−0.971948
$404$	−9.35352e105	−2.58541
$405$	−9.75163e103	−0.0243865
$406$	−1.87195e105	−0.423634
$407$	−9.24029e104	−0.189283
$408$	−2.02724e105	−0.375984
$409$	8.09693e104	0.135996	0.0679980	−	0.997685i	$-0.478339\pi$
$409$	8.09693e104	0.135996	0.0679980	+	0.997685i	$0.478339\pi$
$410$	−6.36779e104	−0.0968819
$411$	5.17620e105	0.713539
$412$	8.88816e105	1.11039
$413$	−5.05860e105	−0.572867
$414$	1.52506e106	1.56594
$415$	−1.67301e105	−0.155794
$416$	−1.22648e106	−1.03605
$417$	−6.30188e105	−0.483014
$418$	3.06935e106	2.13505
$419$	−1.32493e106	−0.836611	−0.418306	−	0.908306i	$-0.637376\pi$
$419$	−1.32493e106	−0.836611	−0.418306	+	0.908306i	$0.637376\pi$
$420$	8.07115e104	0.0462742
$421$	2.12938e106	1.10874	0.554369	−	0.832271i	$-0.312960\pi$
$421$	2.12938e106	1.10874	0.554369	+	0.832271i	$0.312960\pi$
$422$	−3.63658e106	−1.72004
$423$	−9.30223e105	−0.399763
$424$	2.05395e106	0.802180
$425$	−3.11524e106	−1.10596
$426$	2.06694e106	0.667174
$427$	3.24103e106	0.951381
$428$	−7.59007e106	−2.02662
$429$	2.83731e106	0.689265
$430$	9.65731e105	0.213493
$431$	5.23722e106	1.05383	0.526916	−	0.849918i	$-0.323348\pi$
$431$	5.23722e106	1.05383	0.526916	+	0.849918i	$0.323348\pi$
$432$	−2.04149e106	−0.373986
$433$	−5.09355e106	−0.849690	−0.424845	−	0.905266i	$-0.639671\pi$
$433$	−5.09355e106	−0.849690	−0.424845	+	0.905266i	$0.639671\pi$
$434$	−8.03152e106	−1.22029
$435$	−1.52344e105	−0.0210867
$436$	−6.20459e106	−0.782546
$437$	1.01364e107	1.16516
$438$	−3.44256e105	−0.0360728
$439$	1.41527e107	1.35216	0.676078	−	0.736830i	$-0.263678\pi$
$439$	1.41527e107	1.35216	0.676078	+	0.736830i	$0.263678\pi$
$440$	1.16248e106	0.101287
$441$	5.27208e106	0.419005
$442$	1.92547e107	1.39616
$443$	−8.09669e106	−0.535743	−0.267871	−	0.963455i	$-0.586320\pi$
$443$	−8.09669e106	−0.535743	−0.267871	+	0.963455i	$0.586320\pi$
$444$	−1.41718e106	−0.0855881
$445$	−2.15446e106	−0.118784
$446$	1.07271e107	0.540034
$447$	−1.54429e107	−0.710026
$448$	−2.45591e107	−1.03146
$449$	−1.78149e107	−0.683606	−0.341803	−	0.939772i	$-0.611038\pi$
$449$	−1.78149e107	−0.683606	−0.341803	+	0.939772i	$0.611038\pi$
$450$	3.18820e107	1.11799
$451$	−3.31139e107	−1.06135
$452$	−3.55589e107	−1.04194
$453$	−1.33431e107	−0.357502
$454$	−3.96550e105	−0.00971709
$455$	−2.24563e106	−0.0503357
$456$	1.37897e107	0.282800
$457$	−3.94961e107	−0.741221	−0.370611	−	0.928788i	$-0.620852\pi$
$457$	−3.94961e107	−0.741221	−0.370611	+	0.928788i	$0.620852\pi$
$458$	1.27798e108	2.19519
$459$	6.41175e107	1.00824
$460$	1.31054e107	0.188694
$461$	−2.95679e106	−0.0389882	−0.0194941	−	0.999810i	$-0.506206\pi$
$461$	−2.95679e106	−0.0389882	−0.0194941	+	0.999810i	$0.506206\pi$
$462$	7.16485e107	0.865381
$463$	−1.31699e107	−0.145731	−0.0728655	−	0.997342i	$-0.523214\pi$
$463$	−1.31699e107	−0.145731	−0.0728655	+	0.997342i	$0.523214\pi$
$464$	1.71178e107	0.173568
$465$	−6.53622e106	−0.0607410
$466$	−9.80948e107	−0.835635
$467$	−1.31297e108	−1.02546	−0.512732	−	0.858549i	$-0.671367\pi$
$467$	−1.31297e108	−1.02546	−0.512732	+	0.858549i	$0.671367\pi$
$468$	−1.15436e108	−0.826768
$469$	1.74987e107	0.114949
$470$	−1.36459e107	−0.0822314
$471$	−2.22721e106	−0.0123144
$472$	−1.11742e108	−0.566979
$473$	5.02201e108	2.33885
$474$	−2.39408e108	−1.02357
$475$	2.11905e108	0.831859
$476$	2.84831e108	1.02685
$477$	−2.73298e108	−0.904986
$478$	−5.35548e108	−1.62918
$479$	−3.75891e108	−1.05069	−0.525344	−	0.850890i	$-0.676063\pi$
$479$	−3.75891e108	−1.05069	−0.525344	+	0.850890i	$0.676063\pi$
$480$	−2.52052e107	−0.0647470
$481$	3.94299e107	0.0931001
$482$	1.87916e108	0.407905
$483$	2.36616e108	0.472264
$484$	1.29314e109	2.37361
$485$	−5.98130e107	−0.100985
$486$	−1.03632e109	−1.60963
$487$	1.64053e108	0.234456	0.117228	−	0.993105i	$-0.462599\pi$
$487$	1.64053e108	0.234456	0.117228	+	0.993105i	$0.462599\pi$
$488$	7.15930e108	0.941603
$489$	3.15311e108	0.381707
$490$	7.73385e107	0.0861895
$491$	6.82374e108	0.700200	0.350100	−	0.936712i	$-0.386148\pi$
$491$	6.82374e108	0.700200	0.350100	+	0.936712i	$0.386148\pi$
$492$	−5.07865e108	−0.479912
$493$	−5.37621e108	−0.467925
$494$	−1.30974e109	−1.05013
$495$	−1.54679e108	−0.114267
$496$	7.34429e108	0.499968
$497$	−8.50707e108	−0.533760
$498$	−2.27776e109	−1.31740
$499$	−1.45297e109	−0.774791	−0.387396	−	0.921914i	$-0.626625\pi$
$499$	−1.45297e109	−0.774791	−0.387396	+	0.921914i	$0.626625\pi$
$500$	5.50503e108	0.270692
$501$	1.34390e109	0.609453
$502$	−2.22811e109	−0.932045
$503$	1.78726e109	0.689739	0.344869	−	0.938651i	$-0.387923\pi$
$503$	1.78726e109	0.689739	0.344869	+	0.938651i	$0.387923\pi$
$504$	−8.53909e108	−0.304071
$505$	5.34818e108	0.175754
$506$	1.16338e110	3.52880
$507$	6.57855e108	0.184208
$508$	−1.55830e109	−0.402875
$509$	−6.63065e108	−0.158302	−0.0791510	−	0.996863i	$-0.525221\pi$
$509$	−6.63065e108	−0.158302	−0.0791510	+	0.996863i	$0.525221\pi$
$510$	3.95701e108	0.0872519
$511$	1.41688e108	0.0288594
$512$	4.24859e109	0.799487
$513$	−4.36140e109	−0.758354
$514$	−1.57999e110	−2.53891
$515$	−5.08210e108	−0.0754832
$516$	7.70222e109	1.05755
$517$	−7.09614e109	−0.900856
$518$	9.95695e108	0.116888
$519$	2.65608e109	0.288379
$520$	−4.96049e108	−0.0498184
$521$	−2.32219e109	−0.215760	−0.107880	−	0.994164i	$-0.534406\pi$
$521$	−2.32219e109	−0.215760	−0.107880	+	0.994164i	$0.534406\pi$
$522$	5.50212e109	0.473015
$523$	−1.15930e110	−0.922311	−0.461155	−	0.887319i	$-0.652565\pi$
$523$	−1.15930e110	−0.922311	−0.461155	+	0.887319i	$0.652565\pi$
$524$	−9.70994e107	−0.00714989
$525$	4.94654e109	0.337171
$526$	2.93256e110	1.85065
$527$	−2.30664e110	−1.34787
$528$	−6.55178e109	−0.354556
$529$	1.84697e110	0.925773
$530$	−4.00912e109	−0.186156
$531$	1.48684e110	0.639642
$532$	−1.93748e110	−0.772352
$533$	1.41303e110	0.522033
$534$	−2.93325e110	−1.00445
$535$	4.33987e109	0.137768
$536$	3.86538e109	0.113768
$537$	−1.38546e110	−0.378126
$538$	6.85643e110	1.73547
$539$	4.02177e110	0.944218
$540$	−5.63889e109	−0.122814
$541$	6.02154e110	1.21680	0.608399	−	0.793631i	$-0.291812\pi$
$541$	6.02154e110	1.21680	0.608399	+	0.793631i	$0.291812\pi$
$542$	−1.49975e111	−2.81220
$543$	5.06635e110	0.881661
$544$	−8.89493e110	−1.43677
$545$	3.54768e109	0.0531968
$546$	−3.05736e110	−0.425643
$547$	−5.44322e110	−0.703670	−0.351835	−	0.936062i	$-0.614442\pi$
$547$	−5.44322e110	−0.703670	−0.351835	+	0.936062i	$0.614442\pi$
$548$	−1.60650e111	−1.92871
$549$	−9.52616e110	−1.06228
$550$	2.43209e111	2.51937
$551$	3.65700e110	0.351954
$552$	5.22675e110	0.467411
$553$	9.85352e110	0.818886
$554$	1.04063e111	0.803807
$555$	8.10317e108	0.00581821
$556$	1.95587e111	1.30560
$557$	−1.37636e111	−0.854275	−0.427137	−	0.904187i	$-0.640478\pi$
$557$	−1.37636e111	−0.854275	−0.427137	+	0.904187i	$0.640478\pi$
$558$	2.36066e111	1.36253
$559$	−2.14298e111	−1.15037
$560$	5.18549e109	0.0258925
$561$	2.05773e111	0.955856
$562$	−1.94101e111	−0.838893
$563$	−4.54012e111	−1.82590	−0.912950	−	0.408070i	$-0.866202\pi$
$563$	−4.54012e111	−1.82590	−0.912950	+	0.408070i	$0.866202\pi$
$564$	−1.08833e111	−0.407340
$565$	2.03320e110	0.0708300
$566$	2.52777e111	0.819733
$567$	5.46436e110	0.164978
$568$	−1.87918e111	−0.528275
$569$	−4.78435e111	−1.25250	−0.626248	−	0.779624i	$-0.715410\pi$
$569$	−4.78435e111	−1.25250	−0.626248	+	0.779624i	$0.715410\pi$
$570$	−2.69163e110	−0.0656272
$571$	5.09517e111	1.15717	0.578584	−	0.815623i	$-0.303605\pi$
$571$	5.09517e111	1.15717	0.578584	+	0.815623i	$0.303605\pi$
$572$	−8.80594e111	−1.86310
$573$	1.96171e111	0.386699
$574$	3.56821e111	0.655419
$575$	8.03188e111	1.37489
$576$	7.21849e111	1.15169
$577$	−1.02672e112	−1.52698	−0.763488	−	0.645822i	$-0.776515\pi$
$577$	−1.02672e112	−1.52698	−0.763488	+	0.645822i	$0.776515\pi$
$578$	2.75773e111	0.382362
$579$	5.92683e111	0.766198
$580$	4.72817e110	0.0569980
$581$	9.37474e111	1.05396
$582$	−8.14339e111	−0.853934
$583$	−2.08483e112	−2.03936
$584$	3.12983e110	0.0285628
$585$	6.60043e110	0.0562030
$586$	4.56104e111	0.362419
$587$	5.68440e111	0.421543	0.210771	−	0.977535i	$-0.432402\pi$
$587$	5.68440e111	0.421543	0.210771	+	0.977535i	$0.432402\pi$
$588$	6.16815e111	0.426947
$589$	1.56902e112	1.01381
$590$	2.18112e111	0.131575
$591$	−6.56584e110	−0.0369826
$592$	−9.10496e110	−0.0478904
$593$	−1.19671e112	−0.587858	−0.293929	−	0.955827i	$-0.594963\pi$
$593$	−1.19671e112	−0.587858	−0.293929	+	0.955827i	$0.594963\pi$
$594$	−5.00570e112	−2.29675
$595$	−1.62862e111	−0.0698043
$596$	4.79289e112	1.91922
$597$	−1.31528e112	−0.492106
$598$	−4.96436e112	−1.73566
$599$	−1.71608e112	−0.560725	−0.280363	−	0.959894i	$-0.590455\pi$
$599$	−1.71608e112	−0.560725	−0.280363	+	0.959894i	$0.590455\pi$
$600$	1.09267e112	0.333705
$601$	6.36761e112	1.81786	0.908930	−	0.416948i	$-0.136900\pi$
$601$	6.36761e112	1.81786	0.908930	+	0.416948i	$0.136900\pi$
$602$	−5.41150e112	−1.44431
$603$	−5.14328e111	−0.128348
$604$	4.14118e112	0.966337
$605$	−7.39396e111	−0.161356
$606$	7.28142e112	1.48619
$607$	1.92645e112	0.367804	0.183902	−	0.982945i	$-0.441127\pi$
$607$	1.92645e112	0.367804	0.183902	+	0.982945i	$0.441127\pi$
$608$	6.05050e112	1.08068
$609$	8.53662e111	0.142655
$610$	−1.39743e112	−0.218511
$611$	3.02804e112	0.443091
$612$	−8.37187e112	−1.14654
$613$	6.29200e112	0.806565	0.403282	−	0.915076i	$-0.367869\pi$
$613$	6.29200e112	0.806565	0.403282	+	0.915076i	$0.367869\pi$
$614$	−8.33367e112	−1.00004
$615$	2.90389e111	0.0326240
$616$	−6.51399e112	−0.685217
$617$	−2.13054e112	−0.209865	−0.104933	−	0.994479i	$-0.533463\pi$
$617$	−2.13054e112	−0.209865	−0.104933	+	0.994479i	$0.533463\pi$
$618$	−6.91915e112	−0.638292
$619$	−1.80351e113	−1.55829	−0.779143	−	0.626846i	$-0.784345\pi$
$619$	−1.80351e113	−1.55829	−0.779143	+	0.626846i	$0.784345\pi$
$620$	2.02860e112	0.164185
$621$	−1.65311e113	−1.25341
$622$	2.19808e112	0.156146
$623$	1.20726e113	0.803591
$624$	2.79575e112	0.174391
$625$	1.66328e113	0.972355
$626$	5.35204e113	2.93264
$627$	−1.39971e113	−0.718955
$628$	6.91242e111	0.0332862
$629$	2.85961e112	0.129109
$630$	1.66676e112	0.0705635
$631$	−4.77991e113	−1.89771	−0.948856	−	0.315709i	$-0.897758\pi$
$631$	−4.77991e113	−1.89771	−0.948856	+	0.315709i	$0.897758\pi$
$632$	2.17660e113	0.810470
$633$	1.65838e113	0.579208
$634$	−1.31653e113	−0.431336
$635$	8.91009e111	0.0273871
$636$	−3.19749e113	−0.922138
$637$	−1.71616e113	−0.464419
$638$	4.19725e113	1.06593
$639$	2.50043e113	0.595977
$640$	5.05793e112	0.113158
$641$	−2.57522e113	−0.540833	−0.270417	−	0.962743i	$-0.587161\pi$
$641$	−2.57522e113	−0.540833	−0.270417	+	0.962743i	$0.587161\pi$
$642$	5.90863e113	1.16498
$643$	−1.67597e113	−0.310258	−0.155129	−	0.987894i	$-0.549579\pi$
$643$	−1.67597e113	−0.310258	−0.155129	+	0.987894i	$0.549579\pi$
$644$	−7.34367e113	−1.27654
$645$	−4.40400e112	−0.0718917
$646$	−9.49878e113	−1.45630
$647$	3.03414e113	0.436931	0.218465	−	0.975845i	$-0.429895\pi$
$647$	3.03414e113	0.436931	0.218465	+	0.975845i	$0.429895\pi$
$648$	1.20705e113	0.163282
$649$	1.13423e114	1.44142
$650$	−1.03782e114	−1.23917
$651$	3.66259e113	0.410921
$652$	−9.78607e113	−1.03176
$653$	4.88486e113	0.484026	0.242013	−	0.970273i	$-0.422192\pi$
$653$	4.88486e113	0.484026	0.242013	+	0.970273i	$0.422192\pi$
$654$	4.83008e113	0.449837
$655$	5.55198e110	0.000486044 0
$656$	−3.26289e113	−0.268533
$657$	−4.16455e112	−0.0322234
$658$	7.64650e113	0.556306
$659$	−1.18985e113	−0.0814013	−0.0407007	−	0.999171i	$-0.512959\pi$
$659$	−1.18985e113	−0.0814013	−0.0407007	+	0.999171i	$0.512959\pi$
$660$	−1.80969e113	−0.116433
$661$	2.33519e114	1.41307	0.706535	−	0.707678i	$-0.250257\pi$
$661$	2.33519e114	1.41307	0.706535	+	0.707678i	$0.250257\pi$
$662$	1.04350e114	0.593943
$663$	−8.78069e113	−0.470144
$664$	2.07084e114	1.04313
$665$	1.10782e113	0.0525039
$666$	−2.92658e113	−0.130513
$667$	1.38612e114	0.581709
$668$	−4.17097e114	−1.64737
$669$	−4.89186e113	−0.181851
$670$	−7.54490e112	−0.0264012
$671$	−7.26696e114	−2.39382
$672$	1.41238e114	0.438022
$673$	−3.17725e114	−0.927771	−0.463885	−	0.885895i	$-0.653545\pi$
$673$	−3.17725e114	−0.927771	−0.463885	+	0.885895i	$0.653545\pi$
$674$	−4.26042e113	−0.117146
$675$	−3.45589e114	−0.894863
$676$	−2.04173e114	−0.497918
$677$	7.91759e114	1.81866	0.909331	−	0.416074i	$-0.136594\pi$
$677$	7.91759e114	1.81866	0.909331	+	0.416074i	$0.136594\pi$
$678$	2.76815e114	0.598944
$679$	3.35164e114	0.683174
$680$	−3.59755e113	−0.0690869
$681$	1.80838e112	0.00327213
$682$	1.80081e115	3.07044
$683$	−7.97601e114	−1.28159	−0.640793	−	0.767714i	$-0.721394\pi$
$683$	−7.97601e114	−1.28159	−0.640793	+	0.767714i	$0.721394\pi$
$684$	5.69471e114	0.862381
$685$	9.18569e113	0.131112
$686$	−1.18450e115	−1.59370
$687$	−5.82794e114	−0.739209
$688$	4.94846e114	0.591750
$689$	8.89633e114	1.00307
$690$	−1.02022e114	−0.108469
$691$	−6.85346e114	−0.687146	−0.343573	−	0.939126i	$-0.611637\pi$
$691$	−6.85346e114	−0.687146	−0.343573	+	0.939126i	$0.611637\pi$
$692$	−8.24348e114	−0.779496
$693$	8.66750e114	0.773033
$694$	−1.61733e115	−1.36063
$695$	−1.11833e114	−0.0887535
$696$	1.88570e114	0.141189
$697$	1.02478e115	0.723943
$698$	−1.22884e115	−0.819128
$699$	4.47339e114	0.281392
$700$	−1.53522e115	−0.911381
$701$	−4.43843e114	−0.248685	−0.124342	−	0.992239i	$-0.539682\pi$
$701$	−4.43843e114	−0.248685	−0.124342	+	0.992239i	$0.539682\pi$
$702$	2.13602e115	1.12967
$703$	−1.94516e114	−0.0971104
$704$	5.50657e115	2.59531
$705$	6.22288e113	0.0276906
$706$	−5.54334e115	−2.32906
$707$	−2.99687e115	−1.18900
$708$	1.73956e115	0.651766
$709$	−9.80069e114	−0.346804	−0.173402	−	0.984851i	$-0.555476\pi$
$709$	−9.80069e114	−0.346804	−0.173402	+	0.984851i	$0.555476\pi$
$710$	3.66799e114	0.122593
$711$	−2.89618e115	−0.914339
$712$	2.66679e115	0.795332
$713$	5.94709e115	1.67563
$714$	−2.21732e115	−0.590271
$715$	5.03509e114	0.126652
$716$	4.29996e115	1.02209
$717$	2.44225e115	0.548610
$718$	9.77913e114	0.207616
$719$	2.77664e114	0.0557186	0.0278593	−	0.999612i	$-0.491131\pi$
$719$	2.77664e114	0.0557186	0.0278593	+	0.999612i	$0.491131\pi$
$720$	−1.52414e114	−0.0289107
$721$	2.84777e115	0.510654
$722$	−2.70415e115	−0.458432
$723$	−8.56949e114	−0.137358
$724$	−1.57240e116	−2.38315
$725$	2.89774e115	0.415308
$726$	−1.00667e116	−1.36444
$727$	−2.96271e114	−0.0379792	−0.0189896	−	0.999820i	$-0.506045\pi$
$727$	−2.96271e114	−0.0379792	−0.0189896	+	0.999820i	$0.506045\pi$
$728$	2.77963e115	0.337028
$729$	2.51435e115	0.288377
$730$	−6.10917e113	−0.00662836
$731$	−1.55417e116	−1.59531
$732$	−1.11453e116	−1.08241
$733$	1.99971e116	1.83762	0.918812	−	0.394695i	$-0.129150\pi$
$733$	1.99971e116	1.83762	0.918812	+	0.394695i	$0.129150\pi$
$734$	1.25461e116	1.09098
$735$	−3.52685e114	−0.0290235
$736$	2.29334e116	1.78614
$737$	−3.92351e115	−0.289229
$738$	−1.04878e116	−0.731817
$739$	2.00957e115	0.132740	0.0663701	−	0.997795i	$-0.478858\pi$
$739$	2.00957e115	0.132740	0.0663701	+	0.997795i	$0.478858\pi$
$740$	−2.51492e114	−0.0157268
$741$	5.97279e115	0.353622
$742$	2.24653e116	1.25937
$743$	−1.11989e116	−0.594466	−0.297233	−	0.954805i	$-0.596064\pi$
$743$	−1.11989e116	−0.594466	−0.297233	+	0.954805i	$0.596064\pi$
$744$	8.09052e115	0.406698
$745$	−2.74050e115	−0.130467
$746$	6.66785e116	3.00651
$747$	−2.75546e116	−1.17682
$748$	−6.38642e116	−2.58370
$749$	−2.43186e116	−0.932020
$750$	−4.28549e115	−0.155604
$751$	−4.00717e116	−1.37854	−0.689271	−	0.724504i	$-0.742069\pi$
$751$	−4.00717e116	−1.37854	−0.689271	+	0.724504i	$0.742069\pi$
$752$	−6.99221e115	−0.227925
$753$	1.01608e116	0.313857
$754$	−1.79104e116	−0.524283
$755$	−2.36786e115	−0.0656908
$756$	3.15977e116	0.830850
$757$	4.95196e116	1.23422	0.617112	−	0.786876i	$-0.288303\pi$
$757$	4.95196e116	1.23422	0.617112	+	0.786876i	$0.288303\pi$
$758$	2.62641e116	0.620525
$759$	−5.30535e116	−1.18829
$760$	2.44712e115	0.0519643
$761$	9.13010e116	1.83822	0.919109	−	0.394004i	$-0.128910\pi$
$761$	9.13010e116	1.83822	0.919109	+	0.394004i	$0.128910\pi$
$762$	1.21309e116	0.231588
$763$	−1.98795e116	−0.359884
$764$	−6.08841e116	−1.04526
$765$	4.78689e115	0.0779409
$766$	−4.73637e115	−0.0731442
$767$	−4.83994e116	−0.708970
$768$	9.14804e115	0.127116
$769$	3.66597e116	0.483251	0.241625	−	0.970370i	$-0.422319\pi$
$769$	3.66597e116	0.483251	0.241625	+	0.970370i	$0.422319\pi$
$770$	1.27147e116	0.159013
$771$	7.20517e116	0.854952
$772$	−1.83947e117	−2.07105
$773$	1.65148e116	0.176442	0.0882212	−	0.996101i	$-0.471882\pi$
$773$	1.65148e116	0.176442	0.0882212	+	0.996101i	$0.471882\pi$
$774$	1.59057e117	1.61266
$775$	1.24326e117	1.19631
$776$	7.40363e116	0.676153
$777$	−4.54064e115	−0.0393610
$778$	−1.57230e117	−1.29378
$779$	−6.97077e116	−0.544520
$780$	7.72227e115	0.0572682
$781$	1.90743e117	1.34302
$782$	−3.60035e117	−2.40697
$783$	−5.96409e116	−0.378611
$784$	3.96287e116	0.238896
$785$	−3.95241e114	−0.00226277
$786$	7.55888e114	0.00411003
$787$	−1.71855e117	−0.887535	−0.443767	−	0.896142i	$-0.646358\pi$
$787$	−1.71855e117	−0.887535	−0.443767	+	0.896142i	$0.646358\pi$
$788$	2.03779e116	0.0999649
$789$	−1.33733e117	−0.623189
$790$	−4.24854e116	−0.188080
$791$	−1.13931e117	−0.479175
$792$	1.91462e117	0.765089
$793$	3.10094e117	1.17741
$794$	8.27060e116	0.298406
$795$	1.82827e116	0.0626862
$796$	4.08215e117	1.33018
$797$	−2.22332e117	−0.688556	−0.344278	−	0.938868i	$-0.611876\pi$
$797$	−2.22332e117	−0.688556	−0.344278	+	0.938868i	$0.611876\pi$
$798$	1.50826e117	0.443977
$799$	2.19606e117	0.614468
$800$	4.79430e117	1.27521
$801$	−3.54843e117	−0.897261
$802$	3.97954e117	0.956689
$803$	−3.17690e116	−0.0726146
$804$	−6.01746e116	−0.130780
$805$	4.19899e116	0.0867783
$806$	−7.68436e117	−1.51021
$807$	−3.12672e117	−0.584401
$808$	−6.61997e117	−1.17678
$809$	−9.77019e117	−1.65192	−0.825958	−	0.563732i	$-0.809365\pi$
$809$	−9.77019e117	−1.65192	−0.825958	+	0.563732i	$0.809365\pi$
$810$	−2.35607e116	−0.0378917
$811$	4.27401e117	0.653870	0.326935	−	0.945047i	$-0.393984\pi$
$811$	4.27401e117	0.653870	0.326935	+	0.945047i	$0.393984\pi$
$812$	−2.64945e117	−0.385599
$813$	6.83925e117	0.946982
$814$	−2.23252e117	−0.294108
$815$	5.59551e116	0.0701385
$816$	2.02759e117	0.241841
$817$	1.05718e118	1.19993
$818$	1.95628e117	0.211311
$819$	−3.69857e117	−0.380221
$820$	−9.01257e116	−0.0881835
$821$	−2.83374e117	−0.263914	−0.131957	−	0.991255i	$-0.542126\pi$
$821$	−2.83374e117	−0.263914	−0.131957	+	0.991255i	$0.542126\pi$
$822$	1.25061e118	1.10870
$823$	−2.15540e117	−0.181901	−0.0909504	−	0.995855i	$-0.528990\pi$
$823$	−2.15540e117	−0.181901	−0.0909504	+	0.995855i	$0.528990\pi$
$824$	6.29060e117	0.505406
$825$	−1.10910e118	−0.848372
$826$	−1.22220e118	−0.890121
$827$	9.73580e116	0.0675147	0.0337574	−	0.999430i	$-0.489253\pi$
$827$	9.73580e116	0.0675147	0.0337574	+	0.999430i	$0.489253\pi$
$828$	2.15848e118	1.42534
$829$	2.64408e118	1.66271	0.831355	−	0.555741i	$-0.187565\pi$
$829$	2.64408e118	1.66271	0.831355	+	0.555741i	$0.187565\pi$
$830$	−4.04210e117	−0.242072
$831$	−4.74557e117	−0.270674
$832$	−2.34975e118	−1.27652
$833$	−1.24463e118	−0.644045
$834$	−1.52258e118	−0.750507
$835$	2.38489e117	0.111987
$836$	4.34417e118	1.94335
$837$	−2.55886e118	−1.09060
$838$	−3.20112e118	−1.29993
$839$	3.19388e118	1.23583	0.617915	−	0.786245i	$-0.287978\pi$
$839$	3.19388e118	1.23583	0.617915	+	0.786245i	$0.287978\pi$
$840$	5.71237e116	0.0210623
$841$	−2.34593e118	−0.824286
$842$	5.14475e118	1.72276
$843$	8.85152e117	0.282489
$844$	−5.14699e118	−1.56561
$845$	1.16743e117	0.0338480
$846$	−2.24749e118	−0.621152
$847$	4.14323e118	1.09159
$848$	−2.05430e118	−0.515978
$849$	−1.15273e118	−0.276037
$850$	−7.52665e118	−1.71844
$851$	−7.37280e117	−0.160504
$852$	2.92542e118	0.607273
$853$	−8.55794e117	−0.169408	−0.0847039	−	0.996406i	$-0.526994\pi$
$853$	−8.55794e117	−0.169408	−0.0847039	+	0.996406i	$0.526994\pi$
$854$	7.83057e118	1.47826
$855$	−3.25614e117	−0.0586239
$856$	−5.37188e118	−0.922442
$857$	7.27197e118	1.19105	0.595523	−	0.803338i	$-0.296945\pi$
$857$	7.27197e118	1.19105	0.595523	+	0.803338i	$0.296945\pi$
$858$	6.85515e118	1.07098
$859$	9.35991e118	1.39492	0.697459	−	0.716625i	$-0.254314\pi$
$859$	9.35991e118	1.39492	0.697459	+	0.716625i	$0.254314\pi$
$860$	1.36683e118	0.194325
$861$	−1.62720e118	−0.220706
$862$	1.26535e119	1.63744
$863$	−9.13910e117	−0.112841	−0.0564204	−	0.998407i	$-0.517969\pi$
$863$	−9.13910e117	−0.112841	−0.0564204	+	0.998407i	$0.517969\pi$
$864$	−9.86756e118	−1.16253
$865$	4.71348e117	0.0529895
$866$	−1.23064e119	−1.32025
$867$	−1.25760e118	−0.128756
$868$	−1.13673e119	−1.11073
$869$	−2.20933e119	−2.06044
$870$	−3.68073e117	−0.0327646
$871$	1.67423e118	0.142259
$872$	−4.39130e118	−0.356185
$873$	−9.85127e118	−0.762808
$874$	2.44903e119	1.81042
$875$	1.76381e118	0.124488
$876$	−4.87238e117	−0.0328341
$877$	−1.18082e119	−0.759802	−0.379901	−	0.925027i	$-0.624042\pi$
$877$	−1.18082e119	−0.759802	−0.379901	+	0.925027i	$0.624042\pi$
$878$	3.41940e119	2.10098
$879$	−2.07996e118	−0.122041
$880$	−1.16268e118	−0.0651495
$881$	−3.61720e119	−1.93575	−0.967873	−	0.251440i	$-0.919096\pi$
$881$	−3.61720e119	−1.93575	−0.967873	+	0.251440i	$0.919096\pi$
$882$	1.27377e119	0.651050
$883$	3.73604e119	1.82391	0.911954	−	0.410291i	$-0.134573\pi$
$883$	3.73604e119	1.82391	0.911954	+	0.410291i	$0.134573\pi$
$884$	2.72519e119	1.27081
$885$	−9.94649e117	−0.0443065
$886$	−1.95622e119	−0.832438
$887$	1.97664e119	0.803566	0.401783	−	0.915735i	$-0.368391\pi$
$887$	1.97664e119	0.803566	0.401783	+	0.915735i	$0.368391\pi$
$888$	−1.00301e118	−0.0389565
$889$	−4.99280e118	−0.185278
$890$	−5.20534e118	−0.184567
$891$	−1.22521e119	−0.415109
$892$	1.51825e119	0.491549
$893$	−1.49380e119	−0.462177
$894$	−3.73112e119	−1.10324
$895$	−2.45864e118	−0.0694805
$896$	−2.83423e119	−0.765526
$897$	2.26388e119	0.584467
$898$	−4.30420e119	−1.06219
$899$	2.14559e119	0.506150
$900$	4.51238e119	1.01762
$901$	6.45198e119	1.39104
$902$	−8.00056e119	−1.64913
$903$	2.46779e119	0.486357
$904$	−2.51668e119	−0.474250
$905$	8.99074e118	0.162005
$906$	−3.22378e119	−0.555487
$907$	−3.42004e119	−0.563555	−0.281777	−	0.959480i	$-0.590924\pi$
$907$	−3.42004e119	−0.563555	−0.281777	+	0.959480i	$0.590924\pi$
$908$	−5.61252e117	−0.00884466
$909$	8.80852e119	1.32760
$910$	−5.42560e118	−0.0782116
$911$	6.98876e119	0.963620	0.481810	−	0.876276i	$-0.339979\pi$
$911$	6.98876e119	0.963620	0.481810	+	0.876276i	$0.339979\pi$
$912$	−1.37921e119	−0.181902
$913$	−2.10198e120	−2.65193
$914$	−9.54254e119	−1.15171
$915$	6.37268e118	0.0735814
$916$	1.80877e120	1.99810
$917$	−3.11107e117	−0.00328815
$918$	1.54913e120	1.56660
$919$	7.46775e119	0.722623	0.361311	−	0.932445i	$-0.382329\pi$
$919$	7.46775e119	0.722623	0.361311	+	0.932445i	$0.382329\pi$
$920$	9.27538e118	0.0858865
$921$	3.80038e119	0.336754
$922$	−7.14383e118	−0.0605799
$923$	−8.13935e119	−0.660573
$924$	1.01407e120	0.787684
$925$	−1.54131e119	−0.114591
$926$	−3.18194e119	−0.226437
$927$	−8.37027e119	−0.570178
$928$	8.27389e119	0.539532
$929$	−1.75314e120	−1.09441	−0.547205	−	0.836999i	$-0.684308\pi$
$929$	−1.75314e120	−1.09441	−0.547205	+	0.836999i	$0.684308\pi$
$930$	−1.57920e119	−0.0943795
$931$	8.46618e119	0.484424
$932$	−1.38837e120	−0.760609
$933$	−1.00238e119	−0.0525808
$934$	−3.17223e120	−1.59337
$935$	3.65165e119	0.175638
$936$	−8.16999e119	−0.376313
$937$	7.97609e119	0.351833	0.175917	−	0.984405i	$-0.443711\pi$
$937$	7.97609e119	0.351833	0.175917	+	0.984405i	$0.443711\pi$
$938$	4.22781e119	0.178608
$939$	−2.44068e120	−0.987538
$940$	−1.93135e119	−0.0748484
$941$	2.31142e120	0.858024	0.429012	−	0.903299i	$-0.358862\pi$
$941$	2.31142e120	0.858024	0.429012	+	0.903299i	$0.358862\pi$
$942$	−5.38110e118	−0.0191342
$943$	−2.64215e120	−0.899982
$944$	1.11762e120	0.364692
$945$	−1.80670e119	−0.0564805
$946$	1.21335e121	3.63410
$947$	2.94297e120	0.844522	0.422261	−	0.906474i	$-0.361237\pi$
$947$	2.94297e120	0.844522	0.422261	+	0.906474i	$0.361237\pi$
$948$	−3.38843e120	−0.931668
$949$	1.35564e119	0.0357159
$950$	5.11977e120	1.29254
$951$	6.00374e119	0.145248
$952$	2.01590e120	0.467382
$953$	−1.72509e118	−0.00383309	−0.00191654	−	0.999998i	$-0.500610\pi$
$953$	−1.72509e118	−0.00383309	−0.00191654	+	0.999998i	$0.500610\pi$
$954$	−6.60307e120	−1.40617
$955$	3.48125e119	0.0710557
$956$	−7.57981e120	−1.48291
$957$	−1.91406e120	−0.358941
$958$	−9.08181e120	−1.63256
$959$	−5.14723e120	−0.886992
$960$	−4.82893e119	−0.0797748
$961$	2.89165e120	0.457982
$962$	9.52656e119	0.144659
$963$	7.14782e120	1.04066
$964$	2.65965e120	0.371282
$965$	1.05178e120	0.140788
$966$	5.71681e120	0.733805
$967$	−1.30973e121	−1.61217	−0.806083	−	0.591802i	$-0.798417\pi$
$967$	−1.30973e121	−1.61217	−0.806083	+	0.591802i	$0.798417\pi$
$968$	9.15222e120	1.08038
$969$	4.33170e120	0.490395
$970$	−1.44513e120	−0.156910
$971$	1.50046e119	0.0156260	0.00781298	−	0.999969i	$-0.497513\pi$
$971$	1.50046e119	0.0156260	0.00781298	+	0.999969i	$0.497513\pi$
$972$	−1.46674e121	−1.46511
$973$	6.26660e120	0.600430
$974$	3.96365e120	0.364298
$975$	4.73272e120	0.417277
$976$	−7.16053e120	−0.605658
$977$	2.74062e120	0.222392	0.111196	−	0.993799i	$-0.464532\pi$
$977$	2.74062e120	0.222392	0.111196	+	0.993799i	$0.464532\pi$
$978$	7.61814e120	0.593097
$979$	−2.70689e121	−2.02196
$980$	1.09460e120	0.0784512
$981$	5.84307e120	0.401833
$982$	1.64867e121	1.08797
$983$	2.98161e121	1.88814	0.944068	−	0.329751i	$-0.106965\pi$
$983$	2.98161e121	1.88814	0.944068	+	0.329751i	$0.106965\pi$
$984$	−3.59442e120	−0.218438
$985$	−1.16517e119	−0.00679553
$986$	−1.29893e121	−0.727062
$987$	−3.48701e120	−0.187331
$988$	−1.85373e121	−0.955851
$989$	4.00705e121	1.98324
$990$	−3.73717e120	−0.177548
$991$	−3.44828e121	−1.57261	−0.786303	−	0.617841i	$-0.788008\pi$
$991$	−3.44828e121	−1.57261	−0.786303	+	0.617841i	$0.788008\pi$
$992$	3.54987e121	1.55414
$993$	−4.75866e120	−0.200004
$994$	−2.05537e121	−0.829357
$995$	−2.33410e120	−0.0904243
$996$	−3.22379e121	−1.19912
$997$	2.95661e121	1.05594	0.527972	−	0.849262i	$-0.322953\pi$
$997$	2.95661e121	1.05594	0.527972	+	0.849262i	$0.322953\pi$
$998$	−3.51048e121	−1.20387
$999$	3.17231e120	0.104465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.82.a.a.1.6	✓	6
3.2	odd	2		9.82.a.b.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.82.a.a.1.6	✓	6	1.1	even	1	trivial
9.82.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:	\( k \)	\(=\)	\( 82 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41607e12 q^{2} -1.10180e19 q^{3} +3.41956e24 q^{4} -1.95525e27 q^{5} -2.66202e31 q^{6} +1.09563e34 q^{7} +2.42020e36 q^{8} -3.22031e38 q^{9} +O(q^{10})\)	\(q+2.41607e12 q^{2} -1.10180e19 q^{3} +3.41956e24 q^{4} -1.95525e27 q^{5} -2.66202e31 q^{6} +1.09563e34 q^{7} +2.42020e36 q^{8} -3.22031e38 q^{9} -4.72402e39 q^{10} -2.45659e42 q^{11} -3.76765e43 q^{12} +1.04827e45 q^{13} +2.64712e46 q^{14} +2.15428e46 q^{15} -2.42061e48 q^{16} +7.60247e49 q^{17} -7.78051e50 q^{18} -5.17134e51 q^{19} -6.68608e51 q^{20} -1.20716e53 q^{21} -5.93531e54 q^{22} -1.96011e55 q^{23} -2.66656e55 q^{24} -4.09767e56 q^{25} +2.53270e57 q^{26} +8.43378e57 q^{27} +3.74656e58 q^{28} -7.07167e58 q^{29} +5.20490e58 q^{30} -3.03406e60 q^{31} -1.17001e61 q^{32} +2.70666e61 q^{33} +1.83681e62 q^{34} -2.14222e61 q^{35} -1.10120e63 q^{36} +3.76143e62 q^{37} -1.24943e64 q^{38} -1.15498e64 q^{39} -4.73208e63 q^{40} +1.34796e65 q^{41} -2.91658e65 q^{42} -2.04430e66 q^{43} -8.40046e66 q^{44} +6.29650e65 q^{45} -4.73576e67 q^{46} +2.88861e67 q^{47} +2.66702e67 q^{48} -1.63713e68 q^{49} -9.90028e68 q^{50} -8.37636e68 q^{51} +3.58462e69 q^{52} +8.48669e69 q^{53} +2.03766e70 q^{54} +4.80324e69 q^{55} +2.65164e70 q^{56} +5.69776e70 q^{57} -1.70857e71 q^{58} -4.61708e71 q^{59} +7.36669e70 q^{60} +2.95815e72 q^{61} -7.33052e72 q^{62} -3.52826e72 q^{63} -2.24155e73 q^{64} -2.04962e72 q^{65} +6.53949e73 q^{66} +1.59714e73 q^{67} +2.59971e74 q^{68} +2.15964e74 q^{69} -5.17577e73 q^{70} -7.76456e74 q^{71} -7.79379e74 q^{72} +1.29321e74 q^{73} +9.08789e74 q^{74} +4.51480e75 q^{75} -1.76837e76 q^{76} -2.69151e76 q^{77} -2.79051e76 q^{78} +8.99349e76 q^{79} +4.73289e75 q^{80} +4.98742e76 q^{81} +3.25677e77 q^{82} +8.55650e77 q^{83} -4.12795e77 q^{84} -1.48647e77 q^{85} -4.93918e78 q^{86} +7.79153e77 q^{87} -5.94544e78 q^{88} +1.10189e79 q^{89} +1.52128e78 q^{90} +1.14851e79 q^{91} -6.70270e79 q^{92} +3.34292e79 q^{93} +6.97910e79 q^{94} +1.01112e79 q^{95} +1.28911e80 q^{96} +3.05910e80 q^{97} -3.95544e80 q^{98} +7.91099e80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3}+ \cdots + 11\!\cdots\!98 q^{9}+O(q^{10}) \) 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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