LMFDB - Embedded newform 1.76.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,76,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, 76, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 76);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 76 $
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:	$35.6228392822$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 $ x^6 - 3x^5 - 38457853073924058692x^4 - 10276556354621685339901678086x^3 + 371187556674475060057870954681799784505x^2 + 52686123927652036687598761277591247931691204025*x - 675344021115865838575279495800656435684060652010336995750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.19848e9$ 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)

$f(q)$	$=$	$q+2.20777e11 q^{2} +1.08881e18 q^{3} +1.09637e22 q^{4} -2.30711e25 q^{5} +2.40385e29 q^{6} +1.96027e31 q^{7} -5.92020e33 q^{8} +5.77242e35 q^{9} +O(q^{10})$	\(q+2.20777e11 q^{2} +1.08881e18 q^{3} +1.09637e22 q^{4} -2.30711e25 q^{5} +2.40385e29 q^{6} +1.96027e31 q^{7} -5.92020e33 q^{8} +5.77242e35 q^{9} -5.09358e36 q^{10} +9.40509e38 q^{11} +1.19374e40 q^{12} +1.14147e42 q^{13} +4.32784e42 q^{14} -2.51201e43 q^{15} -1.72124e45 q^{16} +1.79040e46 q^{17} +1.27442e47 q^{18} +1.43901e48 q^{19} -2.52945e47 q^{20} +2.13436e49 q^{21} +2.07643e50 q^{22} -1.23136e51 q^{23} -6.44597e51 q^{24} -2.59375e52 q^{25} +2.52010e53 q^{26} -3.37806e52 q^{27} +2.14918e53 q^{28} -2.48097e54 q^{29} -5.54594e54 q^{30} +1.95055e55 q^{31} -1.56352e56 q^{32} +1.02404e57 q^{33} +3.95280e57 q^{34} -4.52257e56 q^{35} +6.32870e57 q^{36} -2.65296e58 q^{37} +3.17702e59 q^{38} +1.24284e60 q^{39} +1.36586e59 q^{40} +3.61594e59 q^{41} +4.71219e60 q^{42} +8.98859e59 q^{43} +1.03115e61 q^{44} -1.33176e61 q^{45} -2.71857e62 q^{46} +2.48355e62 q^{47} -1.87411e63 q^{48} -2.02760e63 q^{49} -5.72641e63 q^{50} +1.94941e64 q^{51} +1.25147e64 q^{52} +3.59994e64 q^{53} -7.45799e63 q^{54} -2.16986e64 q^{55} -1.16052e65 q^{56} +1.56681e66 q^{57} -5.47742e65 q^{58} -4.00811e66 q^{59} -2.75409e65 q^{60} -1.59203e67 q^{61} +4.30637e66 q^{62} +1.13155e67 q^{63} +3.05076e67 q^{64} -2.63349e67 q^{65} +2.26084e68 q^{66} +1.61324e68 q^{67} +1.96294e68 q^{68} -1.34072e69 q^{69} -9.98480e67 q^{70} +2.63303e69 q^{71} -3.41738e69 q^{72} -2.52652e69 q^{73} -5.85713e69 q^{74} -2.82410e70 q^{75} +1.57769e70 q^{76} +1.84365e70 q^{77} +2.74391e71 q^{78} -9.29901e70 q^{79} +3.97110e70 q^{80} -3.87898e71 q^{81} +7.98318e70 q^{82} -7.84087e71 q^{83} +2.34005e71 q^{84} -4.13066e71 q^{85} +1.98448e71 q^{86} -2.70130e72 q^{87} -5.56800e72 q^{88} +2.05618e73 q^{89} -2.94023e72 q^{90} +2.23759e73 q^{91} -1.35003e73 q^{92} +2.12378e73 q^{93} +5.48312e73 q^{94} -3.31997e73 q^{95} -1.70238e74 q^{96} -4.10454e74 q^{97} -4.47648e74 q^{98} +5.42901e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3}+ \cdots + 21\!\cdots\!82 q^{9}+O(q^{10}) $ 6 * q - 57080822040 * q^2 - 785092363818710040 * q^3 + 172600466200162028593728 * q^4 - 38982947396479621874420940 * q^5 + 31673308599187435504995050592 * q^6 + 1924474634802918779239478643600 * q^7 + 4434903997968330342413437320645120 * q^8 + 2119498765962992970568250560046009982 * q^9	$ 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) $ 6 * q - 57080822040 * q^2 - 785092363818710040 * q^3 + 172600466200162028593728 * q^4 - 38982947396479621874420940 * q^5 + 31673308599187435504995050592 * q^6 + 1924474634802918779239478643600 * q^7 + 4434903997968330342413437320645120 * q^8 + 2119498765962992970568250560046009982 * q^9 + 133267935677460241037537052811576902960 * q^10 - 945659951949983071650740113735111214088 * q^11 - 115150003643542480663442829411536163866880 * q^12 + 533185179266852519941169625089098069764420 * q^13 + 8213946953162263647781694565284746353072576 * q^14 - 309603328848013864510094045586663272616092880 * q^15 + 2681978005634517266622433394712415602648354816 * q^16 + 18261354095776132566172834671579513215483393580 * q^17 - 439276854274063146050579040790064492160853960440 * q^18 + 1061534856238354155312794852768417904375328867080 * q^19 + 9296557595621768320156983882258818695571369489280 * q^20 - 100259704699697889376866621361897766152209395224128 * q^21 + 153315952874260268106194796405555863940172791589920 * q^22 + 1514929449877410771078348320690686508954384916853680 * q^23 - 7662424782495949976733296347258884300404709513308160 * q^24 + 19310380328261093150952553553121815533899364092239850 * q^25 + 117730941166816926498584842564210483616872200198362352 * q^26 - 1074213478466937258572560754951503958791056763891563120 * q^27 + 1465885017268620651444113586751990931877154821040657920 * q^28 + 14718767377678125816030788545177391174717388984245534820 * q^29 - 25550285934396345286029563779360588150614380222554150080 * q^30 - 41742874787360498453628839393549579933009794702042980288 * q^31 + 1174660148719991756036751189163540495635749096221862952960 * q^32 + 592070005239220743874129160617285870488467768711527333920 * q^33 + 3034358950124956876257603978888653679838045546922892395856 * q^34 + 27299672493656883988453292135086250689495956464846953371360 * q^35 + 179176299070088941546343921251311713064325363113137876471616 * q^36 + 98517772547646219221591850851651469983797181732879949140340 * q^37 + 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 2481484269951087933260675611242651218102907933795356739592944 * q^39 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 + 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 43775096530001421204709465357678460315555651574798436125415680 * q^42 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 - 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 237966843556414434005003864386125719471571617536701728123349180 * q^45 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 - 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 8212215903718675701941242530692185525776363042145818555572305920 * q^48 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 + 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 283284046705467654069692648207344729396412677737329641196945232 * q^51 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 + 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 780320815712097175721587535401535151075152637184894982834238943680 * q^54 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 + 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 671954656600624358379440578322093895610678807911638904039760657440 * q^57 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 - 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 31792921597254948192279089096854272160617709162962021109081069309440 * q^60 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 - 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 42929132343455570369238205341690645702689225620502517839786884793040 * q^63 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 + 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 930528105441795930909966787493137282089786427774739900252891166297984 * q^66 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 + 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 1408360468152512186955736181867470428051018587723566870538767575903936 * q^69 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 - 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 21189962510693790174049281425747631548583047301946833368066212728860160 * q^72 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 - 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 19463431192157531038934013606638975862465120463567077259244690008282200 * q^75 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 + 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 135490258190773913577197940793442636786883342442786889886654637067611200 * q^78 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 + 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 + 294279639721966061337542444477716876114885567907972876173645426056517686 * q^81 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 - 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 9175580553861138859894612698264948459030459925276038063627639364295153664 * q^84 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 + 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 14159312341342352586604709816323870081891838395129433788110753788803266960 * q^87 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 + 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 85648802068325073636273691125068892379540509730396664184966156591547899120 * q^90 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 + 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 166703912520796821824619485532876155501181179490548097775502842243408462080 * q^93 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 + 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 892786287645978875167763571227022376777771426534553548077964657447900151808 * q^96 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 - 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98 - 187241780708811231174609640862544518464431146740439798697006075456653933736 * 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 $

$2$	2.20777e11	1.13587	0.567936	−	0.823072i	$-0.307742\pi$
$2$	2.20777e11	1.13587	0.567936	+	0.823072i	$0.307742\pi$
$3$	1.08881e18	1.39606	0.698032	−	0.716067i	$-0.254059\pi$
$3$	1.08881e18	1.39606	0.698032	+	0.716067i	$0.254059\pi$
$4$	1.09637e22	0.290207
$5$	−2.30711e25	−0.141806	−0.0709028	−	0.997483i	$-0.522588\pi$
$5$	−2.30711e25	−0.141806	−0.0709028	+	0.997483i	$0.522588\pi$
$6$	2.40385e29	1.58575
$7$	1.96027e31	0.399153	0.199577	−	0.979882i	$-0.436043\pi$
$7$	1.96027e31	0.399153	0.199577	+	0.979882i	$0.436043\pi$
$8$	−5.92020e33	−0.806235
$9$	5.77242e35	0.948994
$10$	−5.09358e36	−0.161073
$11$	9.40509e38	0.833945	0.416972	−	0.908919i	$-0.363091\pi$
$11$	9.40509e38	0.833945	0.416972	+	0.908919i	$0.363091\pi$
$12$	1.19374e40	0.405147
$13$	1.14147e42	1.92570	0.962848	−	0.270042i	$-0.0870377\pi$
$13$	1.14147e42	1.92570	0.962848	+	0.270042i	$0.0870377\pi$
$14$	4.32784e42	0.453387
$15$	−2.51201e43	−0.197970
$16$	−1.72124e45	−1.20599
$17$	1.79040e46	1.29156	0.645782	−	0.763522i	$-0.276531\pi$
$17$	1.79040e46	1.29156	0.645782	+	0.763522i	$0.276531\pi$
$18$	1.27442e47	1.07794
$19$	1.43901e48	1.60253	0.801263	−	0.598312i	$-0.204162\pi$
$19$	1.43901e48	1.60253	0.801263	+	0.598312i	$0.204162\pi$
$20$	−2.52945e47	−0.0411529
$21$	2.13436e49	0.557244
$22$	2.07643e50	0.947255
$23$	−1.23136e51	−1.06070	−0.530349	−	0.847779i	$-0.677939\pi$
$23$	−1.23136e51	−1.06070	−0.530349	+	0.847779i	$0.677939\pi$
$24$	−6.44597e51	−1.12556
$25$	−2.59375e52	−0.979891
$26$	2.52010e53	2.18735
$27$	−3.37806e52	−0.0712075
$28$	2.14918e53	0.115837
$29$	−2.48097e54	−0.358671	−0.179336	−	0.983788i	$-0.557395\pi$
$29$	−2.48097e54	−0.358671	−0.179336	+	0.983788i	$0.557395\pi$
$30$	−5.54594e54	−0.224868
$31$	1.95055e55	0.231256	0.115628	−	0.993293i	$-0.463112\pi$
$31$	1.95055e55	0.231256	0.115628	+	0.993293i	$0.463112\pi$
$32$	−1.56352e56	−0.563613
$33$	1.02404e57	1.16424
$34$	3.95280e57	1.46705
$35$	−4.52257e56	−0.0566022
$36$	6.32870e57	0.275404
$37$	−2.65296e58	−0.413205	−0.206603	−	0.978425i	$-0.566241\pi$
$37$	−2.65296e58	−0.413205	−0.206603	+	0.978425i	$0.566241\pi$
$38$	3.17702e59	1.82027
$39$	1.24284e60	2.68840
$40$	1.36586e59	0.114329
$41$	3.61594e59	0.119902	0.0599511	−	0.998201i	$-0.480906\pi$
$41$	3.61594e59	0.119902	0.0599511	+	0.998201i	$0.480906\pi$
$42$	4.71219e60	0.632958
$43$	8.98859e59	0.0499603	0.0249801	−	0.999688i	$-0.492048\pi$
$43$	8.98859e59	0.0499603	0.0249801	+	0.999688i	$0.492048\pi$
$44$	1.03115e61	0.242016
$45$	−1.33176e61	−0.134573
$46$	−2.71857e62	−1.20482
$47$	2.48355e62	0.491364	0.245682	−	0.969350i	$-0.420988\pi$
$47$	2.48355e62	0.491364	0.245682	+	0.969350i	$0.420988\pi$
$48$	−1.87411e63	−1.68363
$49$	−2.02760e63	−0.840677
$50$	−5.72641e63	−1.11303
$51$	1.94941e64	1.80311
$52$	1.25147e64	0.558850
$53$	3.59994e64	0.786955	0.393477	−	0.919334i	$-0.371272\pi$
$53$	3.59994e64	0.786955	0.393477	+	0.919334i	$0.371272\pi$
$54$	−7.45799e63	−0.0808827
$55$	−2.16986e64	−0.118258
$56$	−1.16052e65	−0.321811
$57$	1.56681e66	2.23723
$58$	−5.47742e65	−0.407405
$59$	−4.00811e66	−1.57032	−0.785162	−	0.619291i	$-0.787420\pi$
$59$	−4.00811e66	−1.57032	−0.785162	+	0.619291i	$0.787420\pi$
$60$	−2.75409e65	−0.0574521
$61$	−1.59203e67	−1.78683	−0.893413	−	0.449237i	$-0.851696\pi$
$61$	−1.59203e67	−1.78683	−0.893413	+	0.449237i	$0.851696\pi$
$62$	4.30637e66	0.262678
$63$	1.13155e67	0.378794
$64$	3.05076e67	0.565795
$65$	−2.63349e67	−0.273075
$66$	2.26084e68	1.32243
$67$	1.61324e68	0.536900	0.268450	−	0.963294i	$-0.413489\pi$
$67$	1.61324e68	0.536900	0.268450	+	0.963294i	$0.413489\pi$
$68$	1.96294e68	0.374821
$69$	−1.34072e69	−1.48080
$70$	−9.98480e67	−0.0642929
$71$	2.63303e69	0.996020	0.498010	−	0.867171i	$-0.334064\pi$
$71$	2.63303e69	0.996020	0.498010	+	0.867171i	$0.334064\pi$
$72$	−3.41738e69	−0.765112
$73$	−2.52652e69	−0.337221	−0.168611	−	0.985683i	$-0.553928\pi$
$73$	−2.52652e69	−0.337221	−0.168611	+	0.985683i	$0.553928\pi$
$74$	−5.85713e69	−0.469348
$75$	−2.82410e70	−1.36799
$76$	1.57769e70	0.465064
$77$	1.84365e70	0.332872
$78$	2.74391e71	3.05368
$79$	−9.29901e70	−0.641831	−0.320916	−	0.947108i	$-0.603991\pi$
$79$	−9.29901e70	−0.641831	−0.320916	+	0.947108i	$0.603991\pi$
$80$	3.97110e70	0.171016
$81$	−3.87898e71	−1.04840
$82$	7.98318e70	0.136194
$83$	−7.84087e71	−0.849055	−0.424528	−	0.905415i	$-0.639560\pi$
$83$	−7.84087e71	−0.849055	−0.424528	+	0.905415i	$0.639560\pi$
$84$	2.34005e71	0.161716
$85$	−4.13066e71	−0.183151
$86$	1.98448e71	0.0567485
$87$	−2.70130e72	−0.500728
$88$	−5.56800e72	−0.672355
$89$	2.05618e73	1.62531	0.812656	−	0.582744i	$-0.198021\pi$
$89$	2.05618e73	1.62531	0.812656	+	0.582744i	$0.198021\pi$
$90$	−2.94023e72	−0.152857
$91$	2.23759e73	0.768648
$92$	−1.35003e73	−0.307822
$93$	2.12378e73	0.322848
$94$	5.48312e73	0.558127
$95$	−3.31997e73	−0.227247
$96$	−1.70238e74	−0.786839
$97$	−4.10454e74	−1.28625	−0.643123	−	0.765763i	$-0.722362\pi$
$97$	−4.10454e74	−1.28625	−0.643123	+	0.765763i	$0.722362\pi$
$98$	−4.47648e74	−0.954902
$99$	5.42901e74	0.791409
$100$	−2.84371e74	−0.284371
$101$	1.81290e75	1.24831	0.624154	−	0.781302i	$-0.285444\pi$
$101$	1.81290e75	1.24831	0.624154	+	0.781302i	$0.285444\pi$
$102$	4.30385e75	2.04810
$103$	−1.54416e75	−0.509677	−0.254839	−	0.966984i	$-0.582022\pi$
$103$	−1.54416e75	−0.509677	−0.254839	+	0.966984i	$0.582022\pi$
$104$	−6.75771e75	−1.55256
$105$	−4.92422e74	−0.0790203
$106$	7.94784e75	0.893880
$107$	−4.90777e73	−0.00388144	−0.00194072	−	0.999998i	$-0.500618\pi$
$107$	−4.90777e73	−0.00388144	−0.00194072	+	0.999998i	$0.500618\pi$
$108$	−3.70360e74	−0.0206649
$109$	−1.45643e76	−0.575171	−0.287586	−	0.957755i	$-0.592853\pi$
$109$	−1.45643e76	−0.575171	−0.287586	+	0.957755i	$0.592853\pi$
$110$	−4.79056e75	−0.134326
$111$	−2.88857e76	−0.576861
$112$	−3.37410e76	−0.481374
$113$	−1.13049e77	−1.15564	−0.577822	−	0.816163i	$-0.696097\pi$
$113$	−1.13049e77	−1.15564	−0.577822	+	0.816163i	$0.696097\pi$
$114$	3.45917e77	2.54121
$115$	2.84089e76	0.150413
$116$	−2.72006e76	−0.104089
$117$	6.58903e77	1.82747
$118$	−8.84899e77	−1.78369
$119$	3.50968e77	0.515532
$120$	1.48716e77	0.159610
$121$	−3.87338e77	−0.304536
$122$	−3.51484e78	−2.02961
$123$	3.93708e77	0.167391
$124$	2.13852e77	0.0671121
$125$	1.20909e78	0.280760
$126$	2.49821e78	0.430262
$127$	1.39623e78	0.178779	0.0893894	−	0.995997i	$-0.471508\pi$
$127$	1.39623e78	0.178779	0.0893894	+	0.995997i	$0.471508\pi$
$128$	1.26422e79	1.20628
$129$	9.78688e77	0.0697477
$130$	−5.81416e78	−0.310178
$131$	−3.06227e79	−1.22566	−0.612830	−	0.790215i	$-0.709969\pi$
$131$	−3.06227e79	−1.22566	−0.612830	+	0.790215i	$0.709969\pi$
$132$	1.12272e79	0.337870
$133$	2.82086e79	0.639654
$134$	3.56167e79	0.609850
$135$	7.79356e77	0.0100976
$136$	−1.05995e80	−1.04130
$137$	−1.01580e80	−0.758207	−0.379103	−	0.925354i	$-0.623768\pi$
$137$	−1.01580e80	−0.758207	−0.379103	+	0.925354i	$0.623768\pi$
$138$	−2.96001e80	−1.68200
$139$	2.74853e80	1.19137	0.595684	−	0.803219i	$-0.296881\pi$
$139$	2.74853e80	1.19137	0.595684	+	0.803219i	$0.296881\pi$
$140$	−4.95840e78	−0.0164263
$141$	2.70412e80	0.685976
$142$	5.81314e80	1.13135
$143$	1.07356e81	1.60592
$144$	−9.93572e80	−1.14447
$145$	5.72387e79	0.0508616
$146$	−5.57798e80	−0.383041
$147$	−2.20767e81	−1.17364
$148$	−2.90862e80	−0.119915
$149$	3.12728e81	1.00157	0.500786	−	0.865571i	$-0.333045\pi$
$149$	3.12728e81	1.00157	0.500786	+	0.865571i	$0.333045\pi$
$150$	−6.23498e81	−1.55386
$151$	3.88189e81	0.754062	0.377031	−	0.926201i	$-0.376945\pi$
$151$	3.88189e81	0.754062	0.377031	+	0.926201i	$0.376945\pi$
$152$	−8.51925e81	−1.29201
$153$	1.03349e82	1.22569
$154$	4.07037e81	0.378100
$155$	−4.50014e80	−0.0327934
$156$	1.36261e82	0.780190
$157$	−3.39510e81	−0.152973	−0.0764867	−	0.997071i	$-0.524370\pi$
$157$	−3.39510e81	−0.152973	−0.0764867	+	0.997071i	$0.524370\pi$
$158$	−2.05301e82	−0.729039
$159$	3.91965e82	1.09864
$160$	3.60723e81	0.0799234
$161$	−2.41380e82	−0.423381
$162$	−8.56390e82	−1.19085
$163$	8.90306e82	0.982888	0.491444	−	0.870909i	$-0.336469\pi$
$163$	8.90306e82	0.982888	0.491444	+	0.870909i	$0.336469\pi$
$164$	3.96441e81	0.0347964
$165$	−2.36257e82	−0.165096
$166$	−1.73109e83	−0.964419
$167$	−3.38631e83	−1.50612	−0.753059	−	0.657952i	$-0.771423\pi$
$167$	−3.38631e83	−1.50612	−0.753059	+	0.657952i	$0.771423\pi$
$168$	−1.26359e83	−0.449269
$169$	9.51589e83	2.70831
$170$	−9.11956e82	−0.208036
$171$	8.30659e83	1.52079
$172$	9.85482e81	0.0144988
$173$	4.90633e83	0.580801	0.290401	−	0.956905i	$-0.406211\pi$
$173$	4.90633e83	0.580801	0.290401	+	0.956905i	$0.406211\pi$
$174$	−5.96387e83	−0.568763
$175$	−5.08446e83	−0.391127
$176$	−1.61884e84	−1.00573
$177$	−4.36407e84	−2.19227
$178$	4.53959e84	1.84615
$179$	−1.46434e84	−0.482674	−0.241337	−	0.970441i	$-0.577586\pi$
$179$	−1.46434e84	−0.482674	−0.241337	+	0.970441i	$0.577586\pi$
$180$	−1.46010e83	−0.0390539
$181$	5.14219e84	1.11738	0.558691	−	0.829376i	$-0.311304\pi$
$181$	5.14219e84	1.11738	0.558691	+	0.829376i	$0.311304\pi$
$182$	4.94009e84	0.873087
$183$	−1.73342e85	−2.49452
$184$	7.28990e84	0.855172
$185$	6.12067e83	0.0585948
$186$	4.68882e84	0.366715
$187$	1.68389e85	1.07709
$188$	2.72289e84	0.142597
$189$	−6.62191e83	−0.0284227
$190$	−7.32973e84	−0.258124
$191$	−3.57215e85	−1.03318	−0.516592	−	0.856231i	$-0.672800\pi$
$191$	−3.57215e85	−1.03318	−0.516592	+	0.856231i	$0.672800\pi$
$192$	3.32170e85	0.789886
$193$	9.29438e84	0.181895	0.0909476	−	0.995856i	$-0.471010\pi$
$193$	9.29438e84	0.181895	0.0909476	+	0.995856i	$0.471010\pi$
$194$	−9.06189e85	−1.46101
$195$	−2.86738e85	−0.381230
$196$	−2.22300e85	−0.243970
$197$	5.56745e85	0.504862	0.252431	−	0.967615i	$-0.418770\pi$
$197$	5.56745e85	0.504862	0.252431	+	0.967615i	$0.418770\pi$
$198$	1.19860e86	0.898939
$199$	−2.63184e86	−1.63407	−0.817033	−	0.576591i	$-0.804382\pi$
$199$	−2.63184e86	−1.63407	−0.817033	+	0.576591i	$0.804382\pi$
$200$	1.53555e86	0.790022
$201$	1.75651e86	0.749547
$202$	4.00247e86	1.41792
$203$	−4.86337e85	−0.143165
$204$	2.13727e86	0.523273
$205$	−8.34238e84	−0.0170028
$206$	−3.40915e86	−0.578928
$207$	−7.10793e86	−1.00660
$208$	−1.96474e87	−2.32237
$209$	1.35341e87	1.33642
$210$	−1.08716e86	−0.0897570
$211$	−5.62170e86	−0.388397	−0.194199	−	0.980962i	$-0.562211\pi$
$211$	−5.62170e86	−0.388397	−0.194199	+	0.980962i	$0.562211\pi$
$212$	3.94686e86	0.228379
$213$	2.86687e87	1.39051
$214$	−1.08353e85	−0.00440882
$215$	−2.07377e85	−0.00708465
$216$	1.99988e86	0.0574100
$217$	3.82361e86	0.0923067
$218$	−3.21548e87	−0.653321
$219$	−2.75090e87	−0.470783
$220$	−2.37897e86	−0.0343193
$221$	2.04369e88	2.48716
$222$	−6.37730e87	−0.655240
$223$	2.95997e87	0.256954	0.128477	−	0.991712i	$-0.458991\pi$
$223$	2.95997e87	0.256954	0.128477	+	0.991712i	$0.458991\pi$
$224$	−3.06493e87	−0.224968
$225$	−1.49722e88	−0.929911
$226$	−2.49586e88	−1.31266
$227$	−1.99529e88	−0.889275	−0.444638	−	0.895711i	$-0.646668\pi$
$227$	−1.99529e88	−0.889275	−0.444638	+	0.895711i	$0.646668\pi$
$228$	1.71781e88	0.649259
$229$	6.29641e87	0.201959	0.100979	−	0.994889i	$-0.467802\pi$
$229$	6.29641e87	0.201959	0.100979	+	0.994889i	$0.467802\pi$
$230$	6.27204e87	0.170850
$231$	2.00739e88	0.464710
$232$	1.46878e88	0.289173
$233$	−9.92233e87	−0.166252	−0.0831260	−	0.996539i	$-0.526490\pi$
$233$	−9.92233e87	−0.166252	−0.0831260	+	0.996539i	$0.526490\pi$
$234$	1.45471e89	2.07578
$235$	−5.72983e87	−0.0696783
$236$	−4.39437e88	−0.455718
$237$	−1.01249e89	−0.896038
$238$	7.74857e88	0.585579
$239$	−1.09445e89	−0.706764	−0.353382	−	0.935479i	$-0.614968\pi$
$239$	−1.09445e89	−0.706764	−0.353382	+	0.935479i	$0.614968\pi$
$240$	4.32377e88	0.238749
$241$	−3.43159e88	−0.162127	−0.0810636	−	0.996709i	$-0.525832\pi$
$241$	−3.43159e88	−0.162127	−0.0810636	+	0.996709i	$0.525832\pi$
$242$	−8.55155e88	−0.345914
$243$	−4.01799e89	−1.39243
$244$	−1.74545e89	−0.518549
$245$	4.67790e88	0.119213
$246$	8.69217e88	0.190135
$247$	1.64259e90	3.08598
$248$	−1.15476e89	−0.186447
$249$	−8.53723e89	−1.18534
$250$	2.66941e89	0.318907
$251$	3.39159e89	0.348851	0.174425	−	0.984670i	$-0.444193\pi$
$251$	3.39159e89	0.348851	0.174425	+	0.984670i	$0.444193\pi$
$252$	1.24060e89	0.109929
$253$	−1.15811e90	−0.884564
$254$	3.08255e89	0.203070
$255$	−4.49750e89	−0.255691
$256$	1.63857e90	0.804389
$257$	−4.75773e89	−0.201794	−0.100897	−	0.994897i	$-0.532171\pi$
$257$	−4.75773e89	−0.201794	−0.100897	+	0.994897i	$0.532171\pi$
$258$	2.16072e89	0.0792245
$259$	−5.20052e89	−0.164932
$260$	−2.88728e89	−0.0792481
$261$	−1.43212e90	−0.340377
$262$	−6.76080e90	−1.39219
$263$	2.04074e90	0.364289	0.182145	−	0.983272i	$-0.441696\pi$
$263$	2.04074e90	0.364289	0.182145	+	0.983272i	$0.441696\pi$
$264$	−6.06249e90	−0.938651
$265$	−8.30546e89	−0.111595
$266$	6.22782e90	0.726565
$267$	2.23879e91	2.26904
$268$	1.76871e90	0.155812
$269$	1.37778e91	1.05553	0.527764	−	0.849391i	$-0.323031\pi$
$269$	1.37778e91	1.05553	0.527764	+	0.849391i	$0.323031\pi$
$270$	1.72064e89	0.0114696
$271$	−7.60957e90	−0.441582	−0.220791	−	0.975321i	$-0.570864\pi$
$271$	−7.60957e90	−0.441582	−0.220791	+	0.975321i	$0.570864\pi$
$272$	−3.08172e91	−1.55761
$273$	2.43631e91	1.07308
$274$	−2.24266e91	−0.861226
$275$	−2.43945e91	−0.817175
$276$	−1.46992e91	−0.429739
$277$	−4.78450e91	−1.22136	−0.610682	−	0.791876i	$-0.709105\pi$
$277$	−4.78450e91	−1.22136	−0.610682	+	0.791876i	$0.709105\pi$
$278$	6.06814e91	1.35324
$279$	1.12594e91	0.219461
$280$	2.67745e90	0.0456347
$281$	1.67133e91	0.249215	0.124608	−	0.992206i	$-0.460233\pi$
$281$	1.67133e91	0.249215	0.124608	+	0.992206i	$0.460233\pi$
$282$	5.97008e91	0.779182
$283$	−1.00325e92	−1.14662	−0.573310	−	0.819339i	$-0.694341\pi$
$283$	−1.00325e92	−1.14662	−0.573310	+	0.819339i	$0.694341\pi$
$284$	2.88678e91	0.289052
$285$	−3.61482e91	−0.317252
$286$	2.37018e92	1.82413
$287$	7.08823e90	0.0478593
$288$	−9.02532e91	−0.534865
$289$	1.28391e92	0.668138
$290$	1.26370e91	0.0577723
$291$	−4.46906e92	−1.79568
$292$	−2.77000e91	−0.0978639
$293$	3.51636e92	1.09284	0.546421	−	0.837511i	$-0.315990\pi$
$293$	3.51636e92	1.09284	0.546421	+	0.837511i	$0.315990\pi$
$294$	−4.87404e92	−1.33310
$295$	9.24715e91	0.222681
$296$	1.57060e92	0.333140
$297$	−3.17709e91	−0.0593832
$298$	6.90433e92	1.13766
$299$	−1.40556e93	−2.04258
$300$	−3.09626e92	−0.397000
$301$	1.76201e91	0.0199418
$302$	8.57032e92	0.856519
$303$	1.97390e93	1.74272
$304$	−2.47689e93	−1.93263
$305$	3.67299e92	0.253382
$306$	2.28172e93	1.39222
$307$	2.83130e93	1.52861	0.764305	−	0.644855i	$-0.223082\pi$
$307$	2.83130e93	1.52861	0.764305	+	0.644855i	$0.223082\pi$
$308$	2.02133e92	0.0966016
$309$	−1.68129e93	−0.711542
$310$	−9.93528e91	−0.0372492
$311$	−1.00581e93	−0.334196	−0.167098	−	0.985940i	$-0.553440\pi$
$311$	−1.00581e93	−0.334196	−0.167098	+	0.985940i	$0.553440\pi$
$312$	−7.35787e93	−2.16748
$313$	−3.95730e93	−1.03392	−0.516959	−	0.856010i	$-0.672936\pi$
$313$	−3.95730e93	−1.03392	−0.516959	+	0.856010i	$0.672936\pi$
$314$	−7.49562e92	−0.173758
$315$	−2.61061e92	−0.0537151
$316$	−1.01952e93	−0.186264
$317$	1.02388e94	1.66161	0.830804	−	0.556565i	$-0.187881\pi$
$317$	1.02388e94	1.66161	0.830804	+	0.556565i	$0.187881\pi$
$318$	8.65369e93	1.24791
$319$	−2.33337e93	−0.299112
$320$	−7.03844e92	−0.0802329
$321$	−5.34364e91	−0.00541874
$322$	−5.32913e93	−0.480907
$323$	2.57641e94	2.06977
$324$	−4.25279e93	−0.304254
$325$	−2.96068e94	−1.88697
$326$	1.96559e94	1.11644
$327$	−1.58578e94	−0.802976
$328$	−2.14071e93	−0.0966693
$329$	4.86844e93	0.196130
$330$	−5.21601e93	−0.187528
$331$	4.19453e94	1.34627	0.673137	−	0.739518i	$-0.264947\pi$
$331$	4.19453e94	1.34627	0.673137	+	0.739518i	$0.264947\pi$
$332$	−8.59650e93	−0.246402
$333$	−1.53140e94	−0.392129
$334$	−7.47621e94	−1.71076
$335$	−3.72192e93	−0.0761355
$336$	−3.67376e94	−0.672028
$337$	−1.23784e94	−0.202554	−0.101277	−	0.994858i	$-0.532293\pi$
$337$	−1.23784e94	−0.202554	−0.101277	+	0.994858i	$0.532293\pi$
$338$	2.10089e95	3.07629
$339$	−1.23089e95	−1.61335
$340$	−4.52873e93	−0.0531517
$341$	1.83451e94	0.192855
$342$	1.83391e95	1.72742
$343$	−8.70256e94	−0.734712
$344$	−5.32142e93	−0.0402797
$345$	3.09319e94	0.209986
$346$	1.08321e95	0.659716
$347$	−7.20855e93	−0.0393996	−0.0196998	−	0.999806i	$-0.506271\pi$
$347$	−7.20855e93	−0.0393996	−0.0196998	+	0.999806i	$0.506271\pi$
$348$	−2.96163e94	−0.145315
$349$	−1.02804e95	−0.452958	−0.226479	−	0.974016i	$-0.572721\pi$
$349$	−1.02804e95	−0.452958	−0.226479	+	0.974016i	$0.572721\pi$
$350$	−1.12253e95	−0.444270
$351$	−3.85595e94	−0.137124
$352$	−1.47051e95	−0.470022
$353$	2.67413e95	0.768477	0.384239	−	0.923234i	$-0.374464\pi$
$353$	2.67413e95	0.768477	0.384239	+	0.923234i	$0.374464\pi$
$354$	−9.63488e95	−2.49014
$355$	−6.07470e94	−0.141241
$356$	2.25434e95	0.471676
$357$	3.82137e95	0.719716
$358$	−3.23294e95	−0.548257
$359$	7.10202e95	1.08478	0.542388	−	0.840128i	$-0.317520\pi$
$359$	7.10202e95	1.08478	0.542388	+	0.840128i	$0.317520\pi$
$360$	7.88428e94	0.108497
$361$	1.26442e96	1.56809
$362$	1.13528e96	1.26920
$363$	−4.21738e95	−0.425152
$364$	2.45322e95	0.223067
$365$	5.82896e94	0.0478199
$366$	−3.82699e96	−2.83346
$367$	−1.75912e96	−1.17576	−0.587878	−	0.808950i	$-0.700036\pi$
$367$	−1.75912e96	−1.17576	−0.587878	+	0.808950i	$0.700036\pi$
$368$	2.11947e96	1.27919
$369$	2.08727e95	0.113786
$370$	1.35130e95	0.0665562
$371$	7.05685e95	0.314116
$372$	2.32845e95	0.0936928
$373$	−3.67079e96	−1.33561	−0.667803	−	0.744338i	$-0.732765\pi$
$373$	−3.67079e96	−1.33561	−0.667803	+	0.744338i	$0.732765\pi$
$374$	3.71765e96	1.22344
$375$	1.31647e96	0.391958
$376$	−1.47031e96	−0.396155
$377$	−2.83195e96	−0.690692
$378$	−1.46197e95	−0.0322846
$379$	−4.49109e95	−0.0898217	−0.0449108	−	0.998991i	$-0.514300\pi$
$379$	−4.49109e95	−0.0898217	−0.0449108	+	0.998991i	$0.514300\pi$
$380$	−3.63991e95	−0.0659487
$381$	1.52022e96	0.249587
$382$	−7.88649e96	−1.17357
$383$	1.26028e97	1.70025	0.850123	−	0.526583i	$-0.176527\pi$
$383$	1.26028e97	1.70025	0.850123	+	0.526583i	$0.176527\pi$
$384$	1.37650e97	1.68405
$385$	−4.25351e95	−0.0472031
$386$	2.05199e96	0.206610
$387$	5.18859e95	0.0474120
$388$	−4.50009e96	−0.373277
$389$	−5.15319e96	−0.388120	−0.194060	−	0.980990i	$-0.562166\pi$
$389$	−5.15319e96	−0.388120	−0.194060	+	0.980990i	$0.562166\pi$
$390$	−6.33052e96	−0.433028
$391$	−2.20463e97	−1.36996
$392$	1.20038e97	0.677783
$393$	−3.33423e97	−1.71110
$394$	1.22917e97	0.573459
$395$	2.14539e96	0.0910153
$396$	5.95220e96	0.229672
$397$	1.73194e97	0.607979	0.303989	−	0.952675i	$-0.401681\pi$
$397$	1.73194e97	0.607979	0.303989	+	0.952675i	$0.401681\pi$
$398$	−5.81051e97	−1.85609
$399$	3.07138e97	0.892997
$400$	4.46447e97	1.18174
$401$	−8.61687e96	−0.207700	−0.103850	−	0.994593i	$-0.533116\pi$
$401$	−8.61687e96	−0.207700	−0.103850	+	0.994593i	$0.533116\pi$
$402$	3.87798e97	0.851390
$403$	2.22649e97	0.445329
$404$	1.98761e97	0.362267
$405$	8.94923e96	0.148670
$406$	−1.07372e97	−0.162617
$407$	−2.49513e97	−0.344590
$408$	−1.15409e98	−1.45373
$409$	1.42017e98	1.63198	0.815990	−	0.578065i	$-0.196192\pi$
$409$	1.42017e98	1.63198	0.815990	+	0.578065i	$0.196192\pi$
$410$	−1.84181e96	−0.0193130
$411$	−1.10602e98	−1.05850
$412$	−1.69297e97	−0.147912
$413$	−7.85698e97	−0.626800
$414$	−1.56927e98	−1.14337
$415$	1.80898e97	0.120401
$416$	−1.78471e98	−1.08535
$417$	2.99263e98	1.66323
$418$	2.98801e98	1.51800
$419$	5.15399e97	0.239396	0.119698	−	0.992810i	$-0.461807\pi$
$419$	5.15399e97	0.239396	0.119698	+	0.992810i	$0.461807\pi$
$420$	−5.39876e96	−0.0229322
$421$	−2.32868e97	−0.0904757	−0.0452378	−	0.998976i	$-0.514405\pi$
$421$	−2.32868e97	−0.0904757	−0.0452378	+	0.998976i	$0.514405\pi$
$422$	−1.24114e98	−0.441170
$423$	1.43361e98	0.466302
$424$	−2.13123e98	−0.634470
$425$	−4.64386e98	−1.26559
$426$	6.32941e98	1.57944
$427$	−3.12081e98	−0.713217
$428$	−5.38074e95	−0.00112642
$429$	1.16890e99	2.24197
$430$	−4.57841e96	−0.00804726
$431$	−6.03815e98	−0.972762	−0.486381	−	0.873747i	$-0.661683\pi$
$431$	−6.03815e98	−0.972762	−0.486381	+	0.873747i	$0.661683\pi$
$432$	5.81446e97	0.0858754
$433$	−1.62785e98	−0.220455	−0.110227	−	0.993906i	$-0.535158\pi$
$433$	−1.62785e98	−0.220455	−0.110227	+	0.993906i	$0.535158\pi$
$434$	8.44166e97	0.104849
$435$	6.23221e97	0.0710060
$436$	−1.59679e98	−0.166919
$437$	−1.77195e99	−1.69980
$438$	−6.07336e98	−0.534749
$439$	−1.67222e99	−1.35168	−0.675840	−	0.737048i	$-0.736219\pi$
$439$	−1.67222e99	−1.35168	−0.675840	+	0.737048i	$0.736219\pi$
$440$	1.28460e98	0.0953438
$441$	−1.17041e99	−0.797797
$442$	4.51200e99	2.82510
$443$	2.94738e99	1.69549	0.847747	−	0.530401i	$-0.177959\pi$
$443$	2.94738e99	1.69549	0.847747	+	0.530401i	$0.177959\pi$
$444$	−3.16694e98	−0.167409
$445$	−4.74385e98	−0.230478
$446$	6.53495e98	0.291867
$447$	3.40502e99	1.39826
$448$	5.98032e98	0.225839
$449$	−2.98962e99	−1.03843	−0.519216	−	0.854643i	$-0.673776\pi$
$449$	−2.98962e99	−1.03843	−0.519216	+	0.854643i	$0.673776\pi$
$450$	−3.30552e99	−1.05626
$451$	3.40083e98	0.0999917
$452$	−1.23943e99	−0.335376
$453$	4.22664e99	1.05272
$454$	−4.40515e99	−1.01010
$455$	−5.16236e98	−0.108999
$456$	−9.27585e99	−1.80373
$457$	5.57415e99	0.998438	0.499219	−	0.866476i	$-0.333620\pi$
$457$	5.57415e99	0.998438	0.499219	+	0.866476i	$0.333620\pi$
$458$	1.39010e99	0.229399
$459$	−6.04808e98	−0.0919691
$460$	3.11467e98	0.0436508
$461$	−7.38632e99	−0.954209	−0.477104	−	0.878847i	$-0.658314\pi$
$461$	−7.38632e99	−0.954209	−0.477104	+	0.878847i	$0.658314\pi$
$462$	4.43186e99	0.527852
$463$	5.44068e99	0.597539	0.298769	−	0.954325i	$-0.403424\pi$
$463$	5.44068e99	0.597539	0.298769	+	0.954325i	$0.403424\pi$
$464$	4.27035e99	0.432553
$465$	−4.89979e98	−0.0457817
$466$	−2.19063e99	−0.188841
$467$	2.61476e99	0.207993	0.103996	−	0.994578i	$-0.466837\pi$
$467$	2.61476e99	0.207993	0.103996	+	0.994578i	$0.466837\pi$
$468$	7.22401e99	0.530345
$469$	3.16239e99	0.214306
$470$	−1.26502e99	−0.0791456
$471$	−3.69663e99	−0.213561
$472$	2.37288e100	1.26605
$473$	8.45385e98	0.0416641
$474$	−2.23534e100	−1.01778
$475$	−3.73244e100	−1.57030
$476$	3.84790e99	0.149611
$477$	2.07803e100	0.746815
$478$	−2.41630e100	−0.802794
$479$	4.90702e100	1.50743	0.753713	−	0.657204i	$-0.228261\pi$
$479$	4.90702e100	1.50743	0.753713	+	0.657204i	$0.228261\pi$
$480$	3.92759e99	0.111578
$481$	−3.02827e100	−0.795708
$482$	−7.57616e99	−0.184156
$483$	−2.62818e100	−0.591067
$484$	−4.24666e99	−0.0883784
$485$	9.46963e99	0.182397
$486$	−8.87082e100	−1.58163
$487$	−2.18940e100	−0.361402	−0.180701	−	0.983538i	$-0.557837\pi$
$487$	−2.18940e100	−0.361402	−0.180701	+	0.983538i	$0.557837\pi$
$488$	9.42512e100	1.44060
$489$	9.69374e100	1.37217
$490$	1.03277e100	0.135410
$491$	−5.47812e100	−0.665389	−0.332694	−	0.943035i	$-0.607958\pi$
$491$	−5.47812e100	−0.665389	−0.332694	+	0.943035i	$0.607958\pi$
$492$	4.31649e99	0.0485780
$493$	−4.44193e100	−0.463247
$494$	3.62646e101	3.50528
$495$	−1.25253e100	−0.112226
$496$	−3.35737e100	−0.278892
$497$	5.16146e100	0.397565
$498$	−1.88483e101	−1.34639
$499$	−1.49760e101	−0.992257	−0.496128	−	0.868249i	$-0.665246\pi$
$499$	−1.49760e101	−0.992257	−0.496128	+	0.868249i	$0.665246\pi$
$500$	1.32561e100	0.0814783
$501$	−3.68705e101	−2.10264
$502$	7.48787e100	0.396250
$503$	−1.80374e101	−0.885879	−0.442939	−	0.896552i	$-0.646064\pi$
$503$	−1.80374e101	−0.885879	−0.442939	+	0.896552i	$0.646064\pi$
$504$	−6.69900e100	−0.305397
$505$	−4.18256e100	−0.177017
$506$	−2.55684e101	−1.00475
$507$	1.03610e102	3.78097
$508$	1.53078e100	0.0518828
$509$	2.40040e101	0.755729	0.377865	−	0.925861i	$-0.376658\pi$
$509$	2.40040e101	0.755729	0.377865	+	0.925861i	$0.376658\pi$
$510$	−9.92947e100	−0.290432
$511$	−4.95266e100	−0.134603
$512$	−1.15850e101	−0.292599
$513$	−4.86108e100	−0.114112
$514$	−1.05040e101	−0.229212
$515$	3.56254e100	0.0722751
$516$	1.07300e100	0.0202412
$517$	2.33580e101	0.409771
$518$	−1.14816e101	−0.187342
$519$	5.34206e101	0.810836
$520$	1.55908e101	0.220162
$521$	−1.00783e102	−1.32425	−0.662126	−	0.749392i	$-0.730346\pi$
$521$	−1.00783e102	−1.32425	−0.662126	+	0.749392i	$0.730346\pi$
$522$	−3.16179e101	−0.386625
$523$	9.80597e101	1.11603	0.558017	−	0.829830i	$-0.311562\pi$
$523$	9.80597e101	1.11603	0.558017	+	0.829830i	$0.311562\pi$
$524$	−3.35738e101	−0.355695
$525$	−5.53601e101	−0.546038
$526$	4.50548e101	0.413786
$527$	3.49227e101	0.298682
$528$	−1.76261e102	−1.40406
$529$	1.68569e101	0.125081
$530$	−1.83366e101	−0.126757
$531$	−2.31365e102	−1.49023
$532$	3.09271e101	0.185632
$533$	4.12748e101	0.230895
$534$	4.94275e102	2.57734
$535$	1.13228e99	0.000550410 0
$536$	−9.55069e101	−0.432868
$537$	−1.59439e102	−0.673844
$538$	3.04183e102	1.19894
$539$	−1.90697e102	−0.701078
$540$	8.54462e99	0.00293040
$541$	1.90764e102	0.610378	0.305189	−	0.952292i	$-0.401280\pi$
$541$	1.90764e102	0.610378	0.305189	+	0.952292i	$0.401280\pi$
$542$	−1.68002e102	−0.501581
$543$	5.59887e102	1.55994
$544$	−2.79934e102	−0.727942
$545$	3.36016e101	0.0815625
$546$	5.37882e102	1.21888
$547$	−3.72021e102	−0.787123	−0.393562	−	0.919298i	$-0.628757\pi$
$547$	−3.72021e102	−0.787123	−0.393562	+	0.919298i	$0.628757\pi$
$548$	−1.11369e102	−0.220037
$549$	−9.18985e102	−1.69569
$550$	−5.38574e102	−0.928207
$551$	−3.57015e102	−0.574780
$552$	7.93732e102	1.19387
$553$	−1.82286e102	−0.256189
$554$	−1.05631e103	−1.38731
$555$	6.66425e101	0.0818021
$556$	3.01341e102	0.345743
$557$	9.39626e102	1.00782	0.503912	−	0.863755i	$-0.331893\pi$
$557$	9.39626e102	1.00782	0.503912	+	0.863755i	$0.331893\pi$
$558$	2.48582e102	0.249279
$559$	1.02602e102	0.0962083
$560$	7.78443e101	0.0682615
$561$	1.83344e103	1.50369
$562$	3.68991e102	0.283077
$563$	1.45593e103	1.04490	0.522450	−	0.852670i	$-0.325018\pi$
$563$	1.45593e103	1.04490	0.522450	+	0.852670i	$0.325018\pi$
$564$	2.96471e102	0.199075
$565$	2.60816e102	0.163877
$566$	−2.21496e103	−1.30241
$567$	−7.60385e102	−0.418474
$568$	−1.55881e103	−0.803026
$569$	−3.42122e103	−1.64995	−0.824976	−	0.565168i	$-0.808811\pi$
$569$	−3.42122e103	−1.64995	−0.824976	+	0.565168i	$0.808811\pi$
$570$	−7.98069e102	−0.360357
$571$	4.10130e103	1.73407	0.867036	−	0.498245i	$-0.166022\pi$
$571$	4.10130e103	1.73407	0.867036	+	0.498245i	$0.166022\pi$
$572$	1.17702e103	0.466050
$573$	−3.88939e103	−1.44239
$574$	1.56492e102	0.0543621
$575$	3.19385e103	1.03937
$576$	1.76102e103	0.536936
$577$	−4.20900e103	−1.20250	−0.601251	−	0.799060i	$-0.705331\pi$
$577$	−4.20900e103	−1.20250	−0.601251	+	0.799060i	$0.705331\pi$
$578$	2.83459e103	0.758920
$579$	1.01198e103	0.253937
$580$	6.27548e101	0.0147604
$581$	−1.53702e103	−0.338903
$582$	−9.86668e103	−2.03967
$583$	3.38577e103	0.656277
$584$	1.49575e103	0.271880
$585$	−1.52016e103	−0.259146
$586$	7.76332e103	1.24133
$587$	1.81185e103	0.271764	0.135882	−	0.990725i	$-0.456613\pi$
$587$	1.81185e103	0.271764	0.135882	+	0.990725i	$0.456613\pi$
$588$	−2.42042e103	−0.340598
$589$	2.80687e103	0.370594
$590$	2.04156e103	0.252937
$591$	6.06189e103	0.704819
$592$	4.56638e103	0.498320
$593$	5.45632e103	0.558919	0.279459	−	0.960158i	$-0.409845\pi$
$593$	5.45632e103	0.558919	0.279459	+	0.960158i	$0.409845\pi$
$594$	−7.01431e102	−0.0674517
$595$	−8.09721e102	−0.0731054
$596$	3.42866e103	0.290663
$597$	−2.86558e104	−2.28126
$598$	−3.10316e104	−2.32011
$599$	1.50324e104	1.05565	0.527826	−	0.849352i	$-0.323007\pi$
$599$	1.50324e104	1.05565	0.527826	+	0.849352i	$0.323007\pi$
$600$	1.67192e104	1.10292
$601$	−3.00993e104	−1.86536	−0.932682	−	0.360699i	$-0.882538\pi$
$601$	−3.00993e104	−1.86536	−0.932682	+	0.360699i	$0.882538\pi$
$602$	3.89012e102	0.0226514
$603$	9.31228e103	0.509515
$604$	4.25598e103	0.218834
$605$	8.93632e102	0.0431849
$606$	4.35793e104	1.97950
$607$	−2.70698e104	−1.15587	−0.577936	−	0.816082i	$-0.696142\pi$
$607$	−2.70698e104	−1.15587	−0.577936	+	0.816082i	$0.696142\pi$
$608$	−2.24993e104	−0.903204
$609$	−5.29529e103	−0.199867
$610$	8.10912e103	0.287810
$611$	2.83490e104	0.946219
$612$	1.13309e104	0.355702
$613$	1.37369e104	0.405621	0.202810	−	0.979218i	$-0.434993\pi$
$613$	1.37369e104	0.405621	0.202810	+	0.979218i	$0.434993\pi$
$614$	6.25086e104	1.73631
$615$	−9.08327e102	−0.0237370
$616$	−1.09148e104	−0.268373
$617$	−1.04793e104	−0.242459	−0.121229	−	0.992625i	$-0.538684\pi$
$617$	−1.04793e104	−0.242459	−0.121229	+	0.992625i	$0.538684\pi$
$618$	−3.71191e104	−0.808221
$619$	−1.99374e104	−0.408573	−0.204286	−	0.978911i	$-0.565487\pi$
$619$	−1.99374e104	−0.408573	−0.204286	+	0.978911i	$0.565487\pi$
$620$	−4.93381e102	−0.00951687
$621$	4.15961e103	0.0755297
$622$	−2.22060e104	−0.379604
$623$	4.03068e104	0.648749
$624$	−2.13923e105	−3.24217
$625$	6.58665e104	0.940078
$626$	−8.73682e104	−1.17440
$627$	1.47360e105	1.86573
$628$	−3.72229e103	−0.0443939
$629$	−4.74986e104	−0.533681
$630$	−5.76364e103	−0.0610136
$631$	7.56039e104	0.754125	0.377062	−	0.926188i	$-0.376934\pi$
$631$	7.56039e104	0.754125	0.377062	+	0.926188i	$0.376934\pi$
$632$	5.50520e104	0.517467
$633$	−6.12097e104	−0.542227
$634$	2.26050e105	1.88738
$635$	−3.22125e103	−0.0253518
$636$	4.29738e104	0.318832
$637$	−2.31444e105	−1.61889
$638$	−5.15156e104	−0.339753
$639$	1.51990e105	0.945217
$640$	−2.91670e104	−0.171058
$641$	−2.20699e105	−1.22074	−0.610371	−	0.792116i	$-0.708980\pi$
$641$	−2.20699e105	−1.22074	−0.610371	+	0.792116i	$0.708980\pi$
$642$	−1.17975e103	−0.00615500
$643$	1.66481e105	0.819317	0.409659	−	0.912239i	$-0.365648\pi$
$643$	1.66481e105	0.819317	0.409659	+	0.912239i	$0.365648\pi$
$644$	−2.64642e104	−0.122868
$645$	−2.25794e103	−0.00989062
$646$	5.68814e105	2.35099
$647$	−2.95788e104	−0.115364	−0.0576819	−	0.998335i	$-0.518371\pi$
$647$	−2.95788e104	−0.115364	−0.0576819	+	0.998335i	$0.518371\pi$
$648$	2.29643e105	0.845260
$649$	−3.76966e105	−1.30956
$650$	−6.53652e105	−2.14336
$651$	4.16318e104	0.128866
$652$	9.76104e104	0.285241
$653$	−1.46213e105	−0.403406	−0.201703	−	0.979447i	$-0.564648\pi$
$653$	−1.46213e105	−0.403406	−0.201703	+	0.979447i	$0.564648\pi$
$654$	−3.50104e105	−0.912078
$655$	7.06500e104	0.173805
$656$	−6.22391e104	−0.144600
$657$	−1.45841e105	−0.320021
$658$	1.07484e105	0.222778
$659$	−1.49655e105	−0.293013	−0.146507	−	0.989210i	$-0.546803\pi$
$659$	−1.49655e105	−0.293013	−0.146507	+	0.989210i	$0.546803\pi$
$660$	−2.59025e104	−0.0479119
$661$	−8.31783e105	−1.45363	−0.726817	−	0.686831i	$-0.759001\pi$
$661$	−8.31783e105	−1.45363	−0.726817	+	0.686831i	$0.759001\pi$
$662$	9.26056e105	1.52919
$663$	2.22519e106	3.47224
$664$	4.64195e105	0.684538
$665$	−6.50804e104	−0.0907065
$666$	−3.38098e105	−0.445409
$667$	3.05497e105	0.380442
$668$	−3.71265e105	−0.437086
$669$	3.22285e105	0.358724
$670$	−8.21716e104	−0.0864802
$671$	−1.49732e106	−1.49011
$672$	−3.33713e105	−0.314069
$673$	−1.42322e106	−1.26680	−0.633400	−	0.773824i	$-0.718341\pi$
$673$	−1.42322e106	−1.26680	−0.633400	+	0.773824i	$0.718341\pi$
$674$	−2.73286e105	−0.230076
$675$	8.76184e104	0.0697756
$676$	1.04329e106	0.785969
$677$	2.39084e106	1.70402	0.852012	−	0.523523i	$-0.175382\pi$
$677$	2.39084e106	1.70402	0.852012	+	0.523523i	$0.175382\pi$
$678$	−2.71752e106	−1.83256
$679$	−8.04601e105	−0.513410
$680$	2.44543e105	0.147663
$681$	−2.17249e106	−1.24149
$682$	4.05018e105	0.219059
$683$	2.42848e106	1.24325	0.621624	−	0.783316i	$-0.286473\pi$
$683$	2.42848e106	1.24325	0.621624	+	0.783316i	$0.286473\pi$
$684$	9.10709e105	0.441343
$685$	2.34357e105	0.107518
$686$	−1.92133e106	−0.834540
$687$	6.85560e105	0.281947
$688$	−1.54715e105	−0.0602514
$689$	4.10921e106	1.51544
$690$	6.82906e105	0.238517
$691$	−1.62806e106	−0.538573	−0.269287	−	0.963060i	$-0.586788\pi$
$691$	−1.62806e106	−0.538573	−0.269287	+	0.963060i	$0.586788\pi$
$692$	5.37915e105	0.168552
$693$	1.06423e106	0.315893
$694$	−1.59148e105	−0.0447530
$695$	−6.34118e105	−0.168943
$696$	1.59923e106	0.403704
$697$	6.47399e105	0.154861
$698$	−2.26968e106	−0.514502
$699$	−1.08035e106	−0.232098
$700$	−5.57444e105	−0.113508
$701$	−4.65996e106	−0.899408	−0.449704	−	0.893178i	$-0.648470\pi$
$701$	−4.65996e106	−0.899408	−0.449704	+	0.893178i	$0.648470\pi$
$702$	−8.51305e105	−0.155756
$703$	−3.81764e106	−0.662172
$704$	2.86927e106	0.471842
$705$	−6.23870e105	−0.0972753
$706$	5.90387e106	0.872892
$707$	3.55377e106	0.498266
$708$	−4.78464e106	−0.636212
$709$	5.38281e106	0.678853	0.339426	−	0.940633i	$-0.389767\pi$
$709$	5.38281e106	0.678853	0.339426	+	0.940633i	$0.389767\pi$
$710$	−1.34116e106	−0.160432
$711$	−5.36778e106	−0.609094
$712$	−1.21730e107	−1.31038
$713$	−2.40183e106	−0.245293
$714$	8.43672e106	0.817506
$715$	−2.47682e106	−0.227729
$716$	−1.60546e106	−0.140075
$717$	−1.19165e107	−0.986688
$718$	1.56796e107	1.23217
$719$	2.39201e107	1.78414	0.892071	−	0.451895i	$-0.149252\pi$
$719$	2.39201e107	1.78414	0.892071	+	0.451895i	$0.149252\pi$
$720$	2.29228e106	0.162293
$721$	−3.02697e106	−0.203439
$722$	2.79155e107	1.78115
$723$	−3.73635e106	−0.226340
$724$	5.63774e106	0.324272
$725$	6.43501e106	0.351459
$726$	−9.31101e106	−0.482918
$727$	−2.28277e107	−1.12440	−0.562202	−	0.827000i	$-0.690046\pi$
$727$	−2.28277e107	−1.12440	−0.562202	+	0.827000i	$0.690046\pi$
$728$	−1.32470e107	−0.619711
$729$	−2.01538e107	−0.895519
$730$	1.28690e106	0.0543173
$731$	1.60932e106	0.0645269
$732$	−1.90047e107	−0.723927
$733$	−1.58880e107	−0.575004	−0.287502	−	0.957780i	$-0.592825\pi$
$733$	−1.58880e107	−0.575004	−0.287502	+	0.957780i	$0.592825\pi$
$734$	−3.88373e107	−1.33551
$735$	5.09334e106	0.166428
$736$	1.92527e107	0.597823
$737$	1.51727e107	0.447745
$738$	4.60822e106	0.129247
$739$	−5.34509e107	−1.42491	−0.712457	−	0.701715i	$-0.752418\pi$
$739$	−5.34509e107	−1.42491	−0.712457	+	0.701715i	$0.752418\pi$
$740$	6.71052e105	0.0170046
$741$	1.78847e108	4.30822
$742$	1.55799e107	0.356795
$743$	2.60517e107	0.567226	0.283613	−	0.958939i	$-0.408467\pi$
$743$	2.60517e107	0.567226	0.283613	+	0.958939i	$0.408467\pi$
$744$	−1.25732e107	−0.260292
$745$	−7.21499e106	−0.142028
$746$	−8.10428e107	−1.51708
$747$	−4.52608e107	−0.805748
$748$	1.84617e107	0.312580
$749$	−9.62057e104	−0.00154929
$750$	2.90648e107	0.445215
$751$	3.70994e107	0.540592	0.270296	−	0.962777i	$-0.412879\pi$
$751$	3.70994e107	0.540592	0.270296	+	0.962777i	$0.412879\pi$
$752$	−4.27480e107	−0.592579
$753$	3.69280e107	0.487018
$754$	−6.25229e107	−0.784538
$755$	−8.95595e106	−0.106930
$756$	−7.26007e105	−0.00824847
$757$	8.77971e107	0.949259	0.474629	−	0.880186i	$-0.342582\pi$
$757$	8.77971e107	0.949259	0.474629	+	0.880186i	$0.342582\pi$
$758$	−9.91530e106	−0.102026
$759$	−1.26096e108	−1.23491
$760$	1.96549e107	0.183215
$761$	−5.45469e107	−0.484000	−0.242000	−	0.970276i	$-0.577803\pi$
$761$	−5.45469e107	−0.484000	−0.242000	+	0.970276i	$0.577803\pi$
$762$	3.35631e107	0.283499
$763$	−2.85501e107	−0.229582
$764$	−3.91639e107	−0.299837
$765$	−2.38439e107	−0.173809
$766$	2.78241e108	1.93126
$767$	−4.57513e108	−3.02397
$768$	1.78409e108	1.12298
$769$	5.31194e107	0.318431	0.159215	−	0.987244i	$-0.449104\pi$
$769$	5.31194e107	0.318431	0.159215	+	0.987244i	$0.449104\pi$
$770$	−9.39080e106	−0.0536167
$771$	−5.18027e107	−0.281717
$772$	1.01901e107	0.0527872
$773$	3.36099e108	1.65858	0.829290	−	0.558818i	$-0.188745\pi$
$773$	3.36099e108	1.65858	0.829290	+	0.558818i	$0.188745\pi$
$774$	1.14552e107	0.0538540
$775$	−5.05924e107	−0.226606
$776$	2.42997e108	1.03702
$777$	−5.66238e107	−0.230256
$778$	−1.13771e108	−0.440855
$779$	5.20339e107	0.192146
$780$	−3.14370e107	−0.110635
$781$	2.47639e108	0.830626
$782$	−4.86733e108	−1.55610
$783$	8.38086e106	0.0255401
$784$	3.48999e108	1.01384
$785$	7.83289e106	0.0216925
$786$	−7.36123e108	−1.94359
$787$	3.71560e108	0.935356	0.467678	−	0.883899i	$-0.345091\pi$
$787$	3.71560e108	0.935356	0.467678	+	0.883899i	$0.345091\pi$
$788$	6.10398e107	0.146514
$789$	2.22198e108	0.508571
$790$	4.73653e107	0.103382
$791$	−2.21606e108	−0.461279
$792$	−3.21408e108	−0.638061
$793$	−1.81725e109	−3.44088
$794$	3.82373e108	0.690586
$795$	−9.04307e107	−0.155793
$796$	−2.88547e108	−0.474217
$797$	8.59521e108	1.34763	0.673813	−	0.738901i	$-0.264655\pi$
$797$	8.59521e108	1.34763	0.673813	+	0.738901i	$0.264655\pi$
$798$	6.78091e108	1.01433
$799$	4.44656e108	0.634629
$800$	4.05539e108	0.552279
$801$	1.18691e109	1.54241
$802$	−1.90241e108	−0.235920
$803$	−2.37621e108	−0.281224
$804$	1.92579e108	0.217524
$805$	5.56892e107	0.0600379
$806$	4.91558e108	0.505837
$807$	1.50014e109	1.47358
$808$	−1.07327e109	−1.00643
$809$	−7.94957e108	−0.711663	−0.355831	−	0.934550i	$-0.615802\pi$
$809$	−7.94957e108	−0.711663	−0.355831	+	0.934550i	$0.615802\pi$
$810$	1.97579e108	0.168870
$811$	−1.89106e109	−1.54320	−0.771602	−	0.636106i	$-0.780544\pi$
$811$	−1.89106e109	−1.54320	−0.771602	+	0.636106i	$0.780544\pi$
$812$	−5.33206e107	−0.0415474
$813$	−8.28538e108	−0.616477
$814$	−5.50868e108	−0.391411
$815$	−2.05404e108	−0.139379
$816$	−3.35540e109	−2.17452
$817$	1.29347e108	0.0800626
$818$	3.13540e109	1.85372
$819$	1.29163e109	0.729443
$820$	−9.14633e106	−0.00493432
$821$	2.82901e109	1.45803	0.729015	−	0.684497i	$-0.239978\pi$
$821$	2.82901e109	1.45803	0.729015	+	0.684497i	$0.239978\pi$
$822$	−2.44183e109	−1.20233
$823$	2.24716e109	1.05716	0.528579	−	0.848884i	$-0.322725\pi$
$823$	2.24716e109	1.05716	0.528579	+	0.848884i	$0.322725\pi$
$824$	9.14170e108	0.410919
$825$	−2.65609e109	−1.14083
$826$	−1.73464e109	−0.711965
$827$	−1.40884e109	−0.552591	−0.276296	−	0.961073i	$-0.589107\pi$
$827$	−1.40884e109	−0.552591	−0.276296	+	0.961073i	$0.589107\pi$
$828$	−7.79292e108	−0.292121
$829$	4.51132e109	1.61625	0.808125	−	0.589011i	$-0.200483\pi$
$829$	4.51132e109	1.61625	0.808125	+	0.589011i	$0.200483\pi$
$830$	3.99381e108	0.136760
$831$	−5.20941e109	−1.70510
$832$	3.48234e109	1.08955
$833$	−3.63022e109	−1.08579
$834$	6.60706e109	1.88921
$835$	7.81260e108	0.213576
$836$	1.48383e109	0.387837
$837$	−6.58907e107	−0.0164672
$838$	1.13788e109	0.271924
$839$	1.09964e109	0.251290	0.125645	−	0.992075i	$-0.459900\pi$
$839$	1.09964e109	0.251290	0.125645	+	0.992075i	$0.459900\pi$
$840$	2.91523e108	0.0637089
$841$	−4.16913e109	−0.871355
$842$	−5.14120e108	−0.102769
$843$	1.81976e109	0.347920
$844$	−6.16347e108	−0.112715
$845$	−2.19542e109	−0.384053
$846$	3.16509e109	0.529660
$847$	−7.59288e108	−0.121557
$848$	−6.19636e109	−0.949057
$849$	−1.09235e110	−1.60075
$850$	−1.02526e110	−1.43755
$851$	3.26675e109	0.438286
$852$	3.14315e109	0.403535
$853$	1.44601e110	1.77657	0.888287	−	0.459289i	$-0.151896\pi$
$853$	1.44601e110	1.77657	0.888287	+	0.459289i	$0.151896\pi$
$854$	−6.89004e109	−0.810124
$855$	−1.91642e109	−0.215656
$856$	2.90550e107	0.00312935
$857$	−9.49435e109	−0.978778	−0.489389	−	0.872066i	$-0.662780\pi$
$857$	−9.49435e109	−0.978778	−0.489389	+	0.872066i	$0.662780\pi$
$858$	2.58068e110	2.54660
$859$	9.18306e109	0.867449	0.433724	−	0.901046i	$-0.357199\pi$
$859$	9.18306e109	0.867449	0.433724	+	0.901046i	$0.357199\pi$
$860$	−2.27362e107	−0.00205601
$861$	7.71774e108	0.0668147
$862$	−1.33309e110	−1.10493
$863$	1.19495e110	0.948299	0.474150	−	0.880444i	$-0.342756\pi$
$863$	1.19495e110	0.948299	0.474150	+	0.880444i	$0.342756\pi$
$864$	5.28168e108	0.0401335
$865$	−1.13194e109	−0.0823609
$866$	−3.59393e109	−0.250408
$867$	1.39794e110	0.932764
$868$	4.19209e108	0.0267880
$869$	−8.74581e109	−0.535252
$870$	1.37593e109	0.0806538
$871$	1.84146e110	1.03391
$872$	8.62238e109	0.463723
$873$	−2.36931e110	−1.22064
$874$	−3.91206e110	−1.93075
$875$	2.37015e109	0.112066
$876$	−3.01600e109	−0.136624
$877$	−1.79278e110	−0.778112	−0.389056	−	0.921214i	$-0.627199\pi$
$877$	−1.79278e110	−0.778112	−0.389056	+	0.921214i	$0.627199\pi$
$878$	−3.69188e110	−1.53534
$879$	3.82864e110	1.52568
$880$	3.73485e109	0.142618
$881$	−1.61512e110	−0.591030	−0.295515	−	0.955338i	$-0.595491\pi$
$881$	−1.61512e110	−0.591030	−0.295515	+	0.955338i	$0.595491\pi$
$882$	−2.58401e110	−0.906196
$883$	2.02977e110	0.682214	0.341107	−	0.940024i	$-0.389198\pi$
$883$	2.02977e110	0.682214	0.341107	+	0.940024i	$0.389198\pi$
$884$	2.24064e110	0.721791
$885$	1.00684e110	0.310876
$886$	6.50714e110	1.92586
$887$	−1.52176e110	−0.431729	−0.215865	−	0.976423i	$-0.569257\pi$
$887$	−1.52176e110	−0.431729	−0.215865	+	0.976423i	$0.569257\pi$
$888$	1.71009e110	0.465085
$889$	2.73698e109	0.0713601
$890$	−1.04733e110	−0.261794
$891$	−3.64821e110	−0.874311
$892$	3.24523e109	0.0745698
$893$	3.57387e110	0.787424
$894$	7.51750e110	1.58824
$895$	3.37840e109	0.0684459
$896$	2.47822e110	0.481492
$897$	−1.53039e111	−2.85158
$898$	−6.60040e110	−1.17953
$899$	−4.83925e109	−0.0829449
$900$	−1.64151e110	−0.269866
$901$	6.44533e110	1.01640
$902$	7.50825e109	0.113578
$903$	1.91849e109	0.0278400
$904$	6.69271e110	0.931720
$905$	−1.18636e110	−0.158451
$906$	9.33146e110	1.19575
$907$	−4.71321e110	−0.579486	−0.289743	−	0.957104i	$-0.593570\pi$
$907$	−4.71321e110	−0.579486	−0.289743	+	0.957104i	$0.593570\pi$
$908$	−2.18757e110	−0.258074
$909$	1.04648e111	1.18464
$910$	−1.13973e110	−0.123809
$911$	−1.43595e111	−1.49693	−0.748465	−	0.663174i	$-0.769209\pi$
$911$	−1.43595e111	−1.49693	−0.748465	+	0.663174i	$0.769209\pi$
$912$	−2.69687e111	−2.69807
$913$	−7.37441e110	−0.708065
$914$	1.23065e111	1.13410
$915$	3.99919e110	0.353737
$916$	6.90319e109	0.0586097
$917$	−6.00288e110	−0.489226
$918$	−1.33528e110	−0.104465
$919$	4.57653e110	0.343720	0.171860	−	0.985121i	$-0.445022\pi$
$919$	4.57653e110	0.343720	0.171860	+	0.985121i	$0.445022\pi$
$920$	−1.68186e110	−0.121268
$921$	3.08275e111	2.13404
$922$	−1.63073e111	−1.08386
$923$	3.00552e111	1.91803
$924$	2.20084e110	0.134862
$925$	6.88111e110	0.404896
$926$	1.20118e111	0.678728
$927$	−8.91351e110	−0.483681
$928$	3.87906e110	0.202152
$929$	1.05558e111	0.528325	0.264163	−	0.964478i	$-0.414904\pi$
$929$	1.05558e111	0.528325	0.264163	+	0.964478i	$0.414904\pi$
$930$	−1.08176e110	−0.0520022
$931$	−2.91774e111	−1.34721
$932$	−1.08785e110	−0.0482474
$933$	−1.09514e111	−0.466559
$934$	5.77279e110	0.236253
$935$	−3.88492e110	−0.152738
$936$	−3.90083e111	−1.47337
$937$	−8.13002e110	−0.295024	−0.147512	−	0.989060i	$-0.547126\pi$
$937$	−8.13002e110	−0.295024	−0.147512	+	0.989060i	$0.547126\pi$
$938$	6.98183e110	0.243424
$939$	−4.30875e111	−1.44342
$940$	−6.28202e109	−0.0202211
$941$	1.60666e111	0.496950	0.248475	−	0.968638i	$-0.420071\pi$
$941$	1.60666e111	0.496950	0.248475	+	0.968638i	$0.420071\pi$
$942$	−8.16131e110	−0.242578
$943$	−4.45253e110	−0.127180
$944$	6.89892e111	1.89379
$945$	1.52775e109	0.00403050
$946$	1.86642e110	0.0473251
$947$	1.93183e111	0.470809	0.235404	−	0.971898i	$-0.424359\pi$
$947$	1.93183e111	0.470809	0.235404	+	0.971898i	$0.424359\pi$
$948$	−1.11006e111	−0.260036
$949$	−2.88394e111	−0.649386
$950$	−8.24039e111	−1.78366
$951$	1.11482e112	2.31971
$952$	−2.07780e111	−0.415640
$953$	4.48955e111	0.863414	0.431707	−	0.902014i	$-0.357912\pi$
$953$	4.48955e111	0.863414	0.431707	+	0.902014i	$0.357912\pi$
$954$	4.58783e111	0.848287
$955$	8.24134e110	0.146511
$956$	−1.19992e111	−0.205108
$957$	−2.54060e111	−0.417579
$958$	1.08336e112	1.71224
$959$	−1.99125e111	−0.302641
$960$	−7.66353e110	−0.112010
$961$	−6.73375e111	−0.946521
$962$	−6.68572e111	−0.903823
$963$	−2.83297e109	−0.00368346
$964$	−3.76229e110	−0.0470504
$965$	−2.14432e110	−0.0257938
$966$	−5.80242e111	−0.671377
$967$	−1.19520e112	−1.33030	−0.665148	−	0.746712i	$-0.731631\pi$
$967$	−1.19520e112	−1.33030	−0.665148	+	0.746712i	$0.731631\pi$
$968$	2.29312e111	0.245528
$969$	2.80523e112	2.88952
$970$	2.09068e111	0.207180
$971$	−2.02515e112	−1.93079	−0.965395	−	0.260790i	$-0.916017\pi$
$971$	−2.02515e112	−1.93079	−0.965395	+	0.260790i	$0.916017\pi$
$972$	−4.40521e111	−0.404093
$973$	5.38788e111	0.475539
$974$	−4.83371e111	−0.410506
$975$	−3.22362e112	−2.63434
$976$	2.74027e112	2.15489
$977$	−4.99871e111	−0.378279	−0.189140	−	0.981950i	$-0.560570\pi$
$977$	−4.99871e111	−0.378279	−0.189140	+	0.981950i	$0.560570\pi$
$978$	2.14016e112	1.55862
$979$	1.93386e112	1.35542
$980$	5.12870e110	0.0345963
$981$	−8.40714e111	−0.545834
$982$	−1.20944e112	−0.755797
$983$	−5.82663e111	−0.350478	−0.175239	−	0.984526i	$-0.556070\pi$
$983$	−5.82663e111	−0.350478	−0.175239	+	0.984526i	$0.556070\pi$
$984$	−2.33083e111	−0.134956
$985$	−1.28447e111	−0.0715922
$986$	−9.80678e111	−0.526189
$987$	5.30081e111	0.273810
$988$	1.80088e112	0.895572
$989$	−1.10682e111	−0.0529928
$990$	−2.76531e111	−0.127475
$991$	5.49657e111	0.243966	0.121983	−	0.992532i	$-0.461075\pi$
$991$	5.49657e111	0.243966	0.121983	+	0.992532i	$0.461075\pi$
$992$	−3.04973e111	−0.130339
$993$	4.56704e112	1.87948
$994$	1.13953e112	0.451583
$995$	6.07195e111	0.231720
$996$	−9.35996e111	−0.343992
$997$	1.26397e112	0.447372	0.223686	−	0.974661i	$-0.428191\pi$
$997$	1.26397e112	0.447372	0.223686	+	0.974661i	$0.428191\pi$
$998$	−3.30635e112	−1.12708
$999$	8.96185e110	0.0294233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.76.a.a.1.5	✓	6
3.2	odd	2		9.76.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.5	✓	6	1.1	even	1	trivial
9.76.a.c.1.2		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.20777e11 q^{2} +1.08881e18 q^{3} +1.09637e22 q^{4} -2.30711e25 q^{5} +2.40385e29 q^{6} +1.96027e31 q^{7} -5.92020e33 q^{8} +5.77242e35 q^{9} +O(q^{10})\)	\(q+2.20777e11 q^{2} +1.08881e18 q^{3} +1.09637e22 q^{4} -2.30711e25 q^{5} +2.40385e29 q^{6} +1.96027e31 q^{7} -5.92020e33 q^{8} +5.77242e35 q^{9} -5.09358e36 q^{10} +9.40509e38 q^{11} +1.19374e40 q^{12} +1.14147e42 q^{13} +4.32784e42 q^{14} -2.51201e43 q^{15} -1.72124e45 q^{16} +1.79040e46 q^{17} +1.27442e47 q^{18} +1.43901e48 q^{19} -2.52945e47 q^{20} +2.13436e49 q^{21} +2.07643e50 q^{22} -1.23136e51 q^{23} -6.44597e51 q^{24} -2.59375e52 q^{25} +2.52010e53 q^{26} -3.37806e52 q^{27} +2.14918e53 q^{28} -2.48097e54 q^{29} -5.54594e54 q^{30} +1.95055e55 q^{31} -1.56352e56 q^{32} +1.02404e57 q^{33} +3.95280e57 q^{34} -4.52257e56 q^{35} +6.32870e57 q^{36} -2.65296e58 q^{37} +3.17702e59 q^{38} +1.24284e60 q^{39} +1.36586e59 q^{40} +3.61594e59 q^{41} +4.71219e60 q^{42} +8.98859e59 q^{43} +1.03115e61 q^{44} -1.33176e61 q^{45} -2.71857e62 q^{46} +2.48355e62 q^{47} -1.87411e63 q^{48} -2.02760e63 q^{49} -5.72641e63 q^{50} +1.94941e64 q^{51} +1.25147e64 q^{52} +3.59994e64 q^{53} -7.45799e63 q^{54} -2.16986e64 q^{55} -1.16052e65 q^{56} +1.56681e66 q^{57} -5.47742e65 q^{58} -4.00811e66 q^{59} -2.75409e65 q^{60} -1.59203e67 q^{61} +4.30637e66 q^{62} +1.13155e67 q^{63} +3.05076e67 q^{64} -2.63349e67 q^{65} +2.26084e68 q^{66} +1.61324e68 q^{67} +1.96294e68 q^{68} -1.34072e69 q^{69} -9.98480e67 q^{70} +2.63303e69 q^{71} -3.41738e69 q^{72} -2.52652e69 q^{73} -5.85713e69 q^{74} -2.82410e70 q^{75} +1.57769e70 q^{76} +1.84365e70 q^{77} +2.74391e71 q^{78} -9.29901e70 q^{79} +3.97110e70 q^{80} -3.87898e71 q^{81} +7.98318e70 q^{82} -7.84087e71 q^{83} +2.34005e71 q^{84} -4.13066e71 q^{85} +1.98448e71 q^{86} -2.70130e72 q^{87} -5.56800e72 q^{88} +2.05618e73 q^{89} -2.94023e72 q^{90} +2.23759e73 q^{91} -1.35003e73 q^{92} +2.12378e73 q^{93} +5.48312e73 q^{94} -3.31997e73 q^{95} -1.70238e74 q^{96} -4.10454e74 q^{97} -4.47648e74 q^{98} +5.42901e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3}+ \cdots + 21\!\cdots\!82 q^{9}+O(q^{10}) \) 6 * q - 57080822040 * q^2 - 785092363818710040 * q^3 + 172600466200162028593728 * q^4 - 38982947396479621874420940 * q^5 + 31673308599187435504995050592 * q^6 + 1924474634802918779239478643600 * q^7 + 4434903997968330342413437320645120 * q^8 + 2119498765962992970568250560046009982 * q^9	\( 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) \) 6 * q - 57080822040 * q^2 - 785092363818710040 * q^3 + 172600466200162028593728 * q^4 - 38982947396479621874420940 * q^5 + 31673308599187435504995050592 * q^6 + 1924474634802918779239478643600 * q^7 + 4434903997968330342413437320645120 * q^8 + 2119498765962992970568250560046009982 * q^9 + 133267935677460241037537052811576902960 * q^10 - 945659951949983071650740113735111214088 * q^11 - 115150003643542480663442829411536163866880 * q^12 + 533185179266852519941169625089098069764420 * q^13 + 8213946953162263647781694565284746353072576 * q^14 - 309603328848013864510094045586663272616092880 * q^15 + 2681978005634517266622433394712415602648354816 * q^16 + 18261354095776132566172834671579513215483393580 * q^17 - 439276854274063146050579040790064492160853960440 * q^18 + 1061534856238354155312794852768417904375328867080 * q^19 + 9296557595621768320156983882258818695571369489280 * q^20 - 100259704699697889376866621361897766152209395224128 * q^21 + 153315952874260268106194796405555863940172791589920 * q^22 + 1514929449877410771078348320690686508954384916853680 * q^23 - 7662424782495949976733296347258884300404709513308160 * q^24 + 19310380328261093150952553553121815533899364092239850 * q^25 + 117730941166816926498584842564210483616872200198362352 * q^26 - 1074213478466937258572560754951503958791056763891563120 * q^27 + 1465885017268620651444113586751990931877154821040657920 * q^28 + 14718767377678125816030788545177391174717388984245534820 * q^29 - 25550285934396345286029563779360588150614380222554150080 * q^30 - 41742874787360498453628839393549579933009794702042980288 * q^31 + 1174660148719991756036751189163540495635749096221862952960 * q^32 + 592070005239220743874129160617285870488467768711527333920 * q^33 + 3034358950124956876257603978888653679838045546922892395856 * q^34 + 27299672493656883988453292135086250689495956464846953371360 * q^35 + 179176299070088941546343921251311713064325363113137876471616 * q^36 + 98517772547646219221591850851651469983797181732879949140340 * q^37 + 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 2481484269951087933260675611242651218102907933795356739592944 * q^39 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 + 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 43775096530001421204709465357678460315555651574798436125415680 * q^42 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 - 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 237966843556414434005003864386125719471571617536701728123349180 * q^45 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 - 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 8212215903718675701941242530692185525776363042145818555572305920 * q^48 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 + 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 283284046705467654069692648207344729396412677737329641196945232 * q^51 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 + 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 780320815712097175721587535401535151075152637184894982834238943680 * q^54 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 + 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 671954656600624358379440578322093895610678807911638904039760657440 * q^57 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 - 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 31792921597254948192279089096854272160617709162962021109081069309440 * q^60 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 - 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 42929132343455570369238205341690645702689225620502517839786884793040 * q^63 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 + 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 930528105441795930909966787493137282089786427774739900252891166297984 * q^66 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 + 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 1408360468152512186955736181867470428051018587723566870538767575903936 * q^69 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 - 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 21189962510693790174049281425747631548583047301946833368066212728860160 * q^72 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 - 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 19463431192157531038934013606638975862465120463567077259244690008282200 * q^75 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 + 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 135490258190773913577197940793442636786883342442786889886654637067611200 * q^78 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 + 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 + 294279639721966061337542444477716876114885567907972876173645426056517686 * q^81 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 - 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 9175580553861138859894612698264948459030459925276038063627639364295153664 * q^84 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 + 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 14159312341342352586604709816323870081891838395129433788110753788803266960 * q^87 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 + 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 85648802068325073636273691125068892379540509730396664184966156591547899120 * q^90 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 + 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 166703912520796821824619485532876155501181179490548097775502842243408462080 * q^93 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 + 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 892786287645978875167763571227022376777771426534553548077964657447900151808 * q^96 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 - 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98 - 187241780708811231174609640862544518464431146740439798697006075456653933736 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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