LMFDB - Embedded newform 1.76.a.a.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,76,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 76, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			1.4
Root			$1.46671e9$ 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)

$f(q)$	$=$	\(q+9.60898e10 q^{2} -6.47242e17 q^{3} -2.85457e22 q^{4} -1.49650e26 q^{5} -6.21934e28 q^{6} -3.16100e31 q^{7} -6.37312e33 q^{8} -1.89344e35 q^{9} -1.43799e37 q^{10} -9.04175e38 q^{11} +1.84760e40 q^{12} -1.02333e42 q^{13} -3.03740e42 q^{14} +9.68599e43 q^{15} +4.66033e44 q^{16} +2.82749e45 q^{17} -1.81941e46 q^{18} +5.13524e47 q^{19} +4.27187e48 q^{20} +2.04593e49 q^{21} -8.68820e49 q^{22} -1.06901e51 q^{23} +4.12495e51 q^{24} -4.07461e51 q^{25} -9.83316e52 q^{26} +5.16248e53 q^{27} +9.02328e53 q^{28} -5.54224e54 q^{29} +9.30725e54 q^{30} -6.85555e55 q^{31} +2.85551e56 q^{32} +5.85220e56 q^{33} +2.71693e56 q^{34} +4.73044e57 q^{35} +5.40496e57 q^{36} +1.00154e59 q^{37} +4.93445e58 q^{38} +6.62342e59 q^{39} +9.53739e59 q^{40} +4.31368e60 q^{41} +1.96593e60 q^{42} -1.74752e61 q^{43} +2.58103e61 q^{44} +2.83354e61 q^{45} -1.02721e62 q^{46} -9.73598e62 q^{47} -3.01636e62 q^{48} -1.41267e63 q^{49} -3.91528e62 q^{50} -1.83007e63 q^{51} +2.92116e64 q^{52} -2.55811e63 q^{53} +4.96061e64 q^{54} +1.35310e65 q^{55} +2.01454e65 q^{56} -3.32375e65 q^{57} -5.32553e65 q^{58} +5.98212e65 q^{59} -2.76493e66 q^{60} -1.23057e67 q^{61} -6.58749e66 q^{62} +5.98517e66 q^{63} +9.83229e66 q^{64} +1.53141e68 q^{65} +5.62337e67 q^{66} -9.36690e67 q^{67} -8.07127e67 q^{68} +6.91907e68 q^{69} +4.54547e68 q^{70} -3.34843e69 q^{71} +1.20671e69 q^{72} -1.44439e70 q^{73} +9.62381e69 q^{74} +2.63726e69 q^{75} -1.46589e70 q^{76} +2.85810e70 q^{77} +6.36444e70 q^{78} +1.89027e71 q^{79} -6.97419e70 q^{80} -2.18965e71 q^{81} +4.14501e71 q^{82} -1.25156e72 q^{83} -5.84025e71 q^{84} -4.23135e71 q^{85} -1.67919e72 q^{86} +3.58717e72 q^{87} +5.76242e72 q^{88} -1.25211e73 q^{89} +2.72275e72 q^{90} +3.23474e73 q^{91} +3.05156e73 q^{92} +4.43720e73 q^{93} -9.35529e73 q^{94} -7.68490e73 q^{95} -1.84820e74 q^{96} -8.39965e73 q^{97} -1.35744e74 q^{98} +1.71200e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3} + 17\!\cdots\!28 q^{4} - 38\!\cdots\!40 q^{5} + 31\!\cdots\!92 q^{6} + 19\!\cdots\!00 q^{7} + 44\!\cdots\!20 q^{8} + 21\!\cdots\!82 q^{9} + 13\!\cdots\!60 q^{10}+ \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

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 $

$2$	9.60898e10	0.494371	0.247185	−	0.968968i	$-0.420494\pi$
$2$	9.60898e10	0.494371	0.247185	+	0.968968i	$0.420494\pi$
$3$	−6.47242e17	−0.829888	−0.414944	−	0.909847i	$-0.636199\pi$
$3$	−6.47242e17	−0.829888	−0.414944	+	0.909847i	$0.636199\pi$
$4$	−2.85457e22	−0.755598
$5$	−1.49650e26	−0.919818	−0.459909	−	0.887966i	$-0.652118\pi$
$5$	−1.49650e26	−0.919818	−0.459909	+	0.887966i	$0.652118\pi$
$6$	−6.21934e28	−0.410272
$7$	−3.16100e31	−0.643647	−0.321824	−	0.946800i	$-0.604296\pi$
$7$	−3.16100e31	−0.643647	−0.321824	+	0.946800i	$0.604296\pi$
$8$	−6.37312e33	−0.867916
$9$	−1.89344e35	−0.311285
$10$	−1.43799e37	−0.454731
$11$	−9.04175e38	−0.801727	−0.400864	−	0.916138i	$-0.631290\pi$
$11$	−9.04175e38	−0.801727	−0.400864	+	0.916138i	$0.631290\pi$
$12$	1.84760e40	0.627062
$13$	−1.02333e42	−1.72639	−0.863197	−	0.504867i	$-0.831541\pi$
$13$	−1.02333e42	−1.72639	−0.863197	+	0.504867i	$0.831541\pi$
$14$	−3.03740e42	−0.318200
$15$	9.68599e43	0.763347
$16$	4.66033e44	0.326526
$17$	2.82749e45	0.203970	0.101985	−	0.994786i	$-0.467481\pi$
$17$	2.82749e45	0.203970	0.101985	+	0.994786i	$0.467481\pi$
$18$	−1.81941e46	−0.153890
$19$	5.13524e47	0.571875	0.285937	−	0.958248i	$-0.407695\pi$
$19$	5.13524e47	0.571875	0.285937	+	0.958248i	$0.407695\pi$
$20$	4.27187e48	0.695013
$21$	2.04593e49	0.534155
$22$	−8.68820e49	−0.396350
$23$	−1.06901e51	−0.920846	−0.460423	−	0.887700i	$-0.652302\pi$
$23$	−1.06901e51	−0.920846	−0.460423	+	0.887700i	$0.652302\pi$
$24$	4.12495e51	0.720273
$25$	−4.07461e51	−0.153934
$26$	−9.83316e52	−0.853478
$27$	5.16248e53	1.08822
$28$	9.02328e53	0.486338
$29$	−5.54224e54	−0.801236	−0.400618	−	0.916245i	$-0.631204\pi$
$29$	−5.54224e54	−0.801236	−0.400618	+	0.916245i	$0.631204\pi$
$30$	9.30725e54	0.377376
$31$	−6.85555e55	−0.812791	−0.406396	−	0.913697i	$-0.633215\pi$
$31$	−6.85555e55	−0.812791	−0.406396	+	0.913697i	$0.633215\pi$
$32$	2.85551e56	1.02934
$33$	5.85220e56	0.665344
$34$	2.71693e56	0.100837
$35$	4.73044e57	0.592038
$36$	5.40496e57	0.235206
$37$	1.00154e59	1.55993	0.779965	−	0.625823i	$-0.215237\pi$
$37$	1.00154e59	1.55993	0.779965	+	0.625823i	$0.215237\pi$
$38$	4.93445e58	0.282718
$39$	6.62342e59	1.43271
$40$	9.53739e59	0.798325
$41$	4.31368e60	1.43039	0.715193	−	0.698927i	$-0.246339\pi$
$41$	4.31368e60	1.43039	0.715193	+	0.698927i	$0.246339\pi$
$42$	1.96593e60	0.264071
$43$	−1.74752e61	−0.971303	−0.485651	−	0.874153i	$-0.661418\pi$
$43$	−1.74752e61	−0.971303	−0.485651	+	0.874153i	$0.661418\pi$
$44$	2.58103e61	0.605783
$45$	2.83354e61	0.286326
$46$	−1.02721e62	−0.455239
$47$	−9.73598e62	−1.92624	−0.963119	−	0.269076i	$-0.913282\pi$
$47$	−9.73598e62	−1.92624	−0.963119	+	0.269076i	$0.913282\pi$
$48$	−3.01636e62	−0.270980
$49$	−1.41267e63	−0.585718
$50$	−3.91528e62	−0.0761006
$51$	−1.83007e63	−0.169273
$52$	2.92116e64	1.30446
$53$	−2.55811e63	−0.0559209	−0.0279604	−	0.999609i	$-0.508901\pi$
$53$	−2.55811e63	−0.0559209	−0.0279604	+	0.999609i	$0.508901\pi$
$54$	4.96061e64	0.537984
$55$	1.35310e65	0.737444
$56$	2.01454e65	0.558631
$57$	−3.32375e65	−0.474592
$58$	−5.32553e65	−0.396107
$59$	5.98212e65	0.234372	0.117186	−	0.993110i	$-0.462613\pi$
$59$	5.98212e65	0.234372	0.117186	+	0.993110i	$0.462613\pi$
$60$	−2.76493e66	−0.576783
$61$	−1.23057e67	−1.38114	−0.690571	−	0.723265i	$-0.742641\pi$
$61$	−1.23057e67	−1.38114	−0.690571	+	0.723265i	$0.742641\pi$
$62$	−6.58749e66	−0.401820
$63$	5.98517e66	0.200358
$64$	9.83229e66	0.182350
$65$	1.53141e68	1.58797
$66$	5.62337e67	0.328927
$67$	−9.36690e67	−0.311739	−0.155869	−	0.987778i	$-0.549818\pi$
$67$	−9.36690e67	−0.311739	−0.155869	+	0.987778i	$0.549818\pi$
$68$	−8.07127e67	−0.154120
$69$	6.91907e68	0.764200
$70$	4.54547e68	0.292686
$71$	−3.34843e69	−1.26664	−0.633320	−	0.773890i	$-0.718308\pi$
$71$	−3.34843e69	−1.26664	−0.633320	+	0.773890i	$0.718308\pi$
$72$	1.20671e69	0.270169
$73$	−1.44439e70	−1.92787	−0.963934	−	0.266141i	$-0.914251\pi$
$73$	−1.44439e70	−1.92787	−0.963934	+	0.266141i	$0.914251\pi$
$74$	9.62381e69	0.771183
$75$	2.63726e69	0.127748
$76$	−1.46589e70	−0.432107
$77$	2.85810e70	0.516029
$78$	6.36444e70	0.708292
$79$	1.89027e71	1.30469	0.652347	−	0.757920i	$-0.273784\pi$
$79$	1.89027e71	1.30469	0.652347	+	0.757920i	$0.273784\pi$
$80$	−6.97419e70	−0.300344
$81$	−2.18965e71	−0.591816
$82$	4.14501e71	0.707140
$83$	−1.25156e72	−1.35526	−0.677630	−	0.735403i	$-0.736993\pi$
$83$	−1.25156e72	−1.35526	−0.677630	+	0.735403i	$0.736993\pi$
$84$	−5.84025e71	−0.403607
$85$	−4.23135e71	−0.187616
$86$	−1.67919e72	−0.480184
$87$	3.58717e72	0.664936
$88$	5.76242e72	0.695832
$89$	−1.25211e73	−0.989728	−0.494864	−	0.868971i	$-0.664782\pi$
$89$	−1.25211e73	−0.989728	−0.494864	+	0.868971i	$0.664782\pi$
$90$	2.72275e72	0.141551
$91$	3.23474e73	1.11119
$92$	3.05156e73	0.695789
$93$	4.43720e73	0.674526
$94$	−9.35529e73	−0.952275
$95$	−7.68490e73	−0.526021
$96$	−1.84820e74	−0.854238
$97$	−8.39965e73	−0.263221	−0.131611	−	0.991301i	$-0.542015\pi$
$97$	−8.39965e73	−0.263221	−0.131611	+	0.991301i	$0.542015\pi$
$98$	−1.35744e74	−0.289562
$99$	1.71200e74	0.249566
$100$	1.16312e74	0.116312
$101$	8.71215e74	0.599893	0.299947	−	0.953956i	$-0.403031\pi$
$101$	8.71215e74	0.599893	0.299947	+	0.953956i	$0.403031\pi$
$102$	−1.75851e74	−0.0836834
$103$	5.77353e74	0.190566	0.0952831	−	0.995450i	$-0.469624\pi$
$103$	5.77353e74	0.190566	0.0952831	+	0.995450i	$0.469624\pi$
$104$	6.52180e75	1.49836
$105$	−3.06174e75	−0.491326
$106$	−2.45808e74	−0.0276456
$107$	−1.00257e76	−0.792909	−0.396455	−	0.918054i	$-0.629760\pi$
$107$	−1.00257e76	−0.792909	−0.396455	+	0.918054i	$0.629760\pi$
$108$	−1.47366e76	−0.822257
$109$	1.41952e76	0.560593	0.280296	−	0.959914i	$-0.409567\pi$
$109$	1.41952e76	0.560593	0.280296	+	0.959914i	$0.409567\pi$
$110$	1.30019e76	0.364570
$111$	−6.48241e76	−1.29457
$112$	−1.47313e76	−0.210167
$113$	5.89790e76	0.602914	0.301457	−	0.953480i	$-0.402527\pi$
$113$	5.89790e76	0.602914	0.301457	+	0.953480i	$0.402527\pi$
$114$	−3.19378e76	−0.234625
$115$	1.59977e77	0.847011
$116$	1.58207e77	0.605412
$117$	1.93762e77	0.537401
$118$	5.74821e76	0.115866
$119$	−8.93770e76	−0.131285
$120$	−6.17300e77	−0.662521
$121$	−4.54363e77	−0.357233
$122$	−1.18245e78	−0.682796
$123$	−2.79199e78	−1.18706
$124$	1.95696e78	0.614143
$125$	4.57097e78	1.06141
$126$	5.75114e77	0.0990510
$127$	8.79169e77	0.112573	0.0562863	−	0.998415i	$-0.482074\pi$
$127$	8.79169e77	0.112573	0.0562863	+	0.998415i	$0.482074\pi$
$128$	−9.84302e78	−0.939192
$129$	1.13107e79	0.806073
$130$	1.47153e79	0.785045
$131$	1.67353e79	0.669823	0.334911	−	0.942250i	$-0.391294\pi$
$131$	1.67353e79	0.669823	0.334911	+	0.942250i	$0.391294\pi$
$132$	−1.67055e79	−0.502733
$133$	−1.62325e79	−0.368086
$134$	−9.00064e78	−0.154114
$135$	−7.72565e79	−1.00097
$136$	−1.80200e79	−0.177029
$137$	6.01048e78	0.0448629	0.0224315	−	0.999748i	$-0.492859\pi$
$137$	6.01048e78	0.0448629	0.0224315	+	0.999748i	$0.492859\pi$
$138$	6.64852e79	0.377798
$139$	−1.32009e80	−0.572201	−0.286101	−	0.958200i	$-0.592359\pi$
$139$	−1.32009e80	−0.572201	−0.286101	+	0.958200i	$0.592359\pi$
$140$	−1.35034e80	−0.447343
$141$	6.30154e80	1.59856
$142$	−3.21750e80	−0.626190
$143$	9.25269e80	1.38410
$144$	−8.82408e79	−0.101643
$145$	8.29397e80	0.736991
$146$	−1.38791e81	−0.953081
$147$	9.14342e80	0.486081
$148$	−2.85897e81	−1.17868
$149$	−4.92682e81	−1.57791	−0.788955	−	0.614451i	$-0.789377\pi$
$149$	−4.92682e81	−1.57791	−0.788955	+	0.614451i	$0.789377\pi$
$150$	2.53414e80	0.0631550
$151$	7.65678e81	1.48734	0.743670	−	0.668546i	$-0.233083\pi$
$151$	7.65678e81	1.48734	0.743670	+	0.668546i	$0.233083\pi$
$152$	−3.27275e81	−0.496339
$153$	−5.35370e80	−0.0634929
$154$	2.74634e81	0.255110
$155$	1.02593e82	0.747620
$156$	−1.89070e82	−1.08256
$157$	2.43970e82	1.09926	0.549629	−	0.835409i	$-0.314769\pi$
$157$	2.43970e82	1.09926	0.549629	+	0.835409i	$0.314769\pi$
$158$	1.81636e82	0.645003
$159$	1.65572e81	0.0464081
$160$	−4.27327e82	−0.946806
$161$	3.37913e82	0.592700
$162$	−2.10403e82	−0.292577
$163$	1.18316e82	0.130620	0.0653099	−	0.997865i	$-0.479196\pi$
$163$	1.18316e82	0.130620	0.0653099	+	0.997865i	$0.479196\pi$
$164$	−1.23137e83	−1.08080
$165$	−8.75783e82	−0.611996
$166$	−1.20262e83	−0.670001
$167$	1.90144e83	0.845698	0.422849	−	0.906200i	$-0.361030\pi$
$167$	1.90144e83	0.845698	0.422849	+	0.906200i	$0.361030\pi$
$168$	−1.30390e83	−0.463602
$169$	6.95845e83	1.98044
$170$	−4.06590e82	−0.0927517
$171$	−9.72330e82	−0.178016
$172$	4.98841e83	0.733914
$173$	−5.07453e83	−0.600713	−0.300356	−	0.953827i	$-0.597106\pi$
$173$	−5.07453e83	−0.600713	−0.300356	+	0.953827i	$0.597106\pi$
$174$	3.44691e83	0.328725
$175$	1.28798e83	0.0990794
$176$	−4.21375e83	−0.261785
$177$	−3.87188e83	−0.194502
$178$	−1.20315e84	−0.489292
$179$	−3.95061e84	−1.30219	−0.651097	−	0.758994i	$-0.725691\pi$
$179$	−3.95061e84	−1.30219	−0.651097	+	0.758994i	$0.725691\pi$
$180$	−8.08854e83	−0.216347
$181$	9.70552e83	0.210898	0.105449	−	0.994425i	$-0.466372\pi$
$181$	9.70552e83	0.210898	0.105449	+	0.994425i	$0.466372\pi$
$182$	3.10826e84	0.549339
$183$	7.96478e84	1.14619
$184$	6.81292e84	0.799217
$185$	−1.49881e85	−1.43485
$186$	4.26370e84	0.333466
$187$	−2.55655e84	−0.163529
$188$	2.77920e85	1.45546
$189$	−1.63186e85	−0.700430
$190$	−7.38441e84	−0.260049
$191$	1.65608e85	0.478995	0.239498	−	0.970897i	$-0.423017\pi$
$191$	1.65608e85	0.478995	0.239498	+	0.970897i	$0.423017\pi$
$192$	−6.36387e84	−0.151330
$193$	−3.10563e85	−0.607787	−0.303893	−	0.952706i	$-0.598287\pi$
$193$	−3.10563e85	−0.607787	−0.303893	+	0.952706i	$0.598287\pi$
$194$	−8.07121e84	−0.130129
$195$	−9.91196e85	−1.31784
$196$	4.03257e85	0.442568
$197$	−8.70072e85	−0.788990	−0.394495	−	0.918898i	$-0.629081\pi$
$197$	−8.70072e85	−0.788990	−0.394495	+	0.918898i	$0.629081\pi$
$198$	1.64506e85	0.123378
$199$	2.78509e86	1.72921	0.864606	−	0.502450i	$-0.167568\pi$
$199$	2.78509e86	1.72921	0.864606	+	0.502450i	$0.167568\pi$
$200$	2.59680e85	0.133602
$201$	6.06265e85	0.258708
$202$	8.37149e85	0.296570
$203$	1.75190e86	0.515713
$204$	5.22407e85	0.127902
$205$	−6.45542e86	−1.31569
$206$	5.54778e85	0.0942103
$207$	2.02411e86	0.286646
$208$	−4.76906e86	−0.563712
$209$	−4.64316e86	−0.458488
$210$	−2.94202e86	−0.242897
$211$	−7.50575e86	−0.518564	−0.259282	−	0.965802i	$-0.583486\pi$
$211$	−7.50575e86	−0.518564	−0.259282	+	0.965802i	$0.583486\pi$
$212$	7.30230e85	0.0422537
$213$	2.16725e87	1.05117
$214$	−9.63369e86	−0.391991
$215$	2.61516e87	0.893422
$216$	−3.29011e87	−0.944484
$217$	2.16704e87	0.523151
$218$	1.36401e87	0.277140
$219$	9.34870e87	1.59992
$220$	−3.86251e87	−0.557211
$221$	−2.89346e87	−0.352133
$222$	−6.22894e87	−0.639996
$223$	−7.58008e86	−0.0658023	−0.0329012	−	0.999459i	$-0.510475\pi$
$223$	−7.58008e86	−0.0658023	−0.0329012	+	0.999459i	$0.510475\pi$
$224$	−9.02625e87	−0.662532
$225$	7.71504e86	0.0479175
$226$	5.66728e87	0.298063
$227$	−3.93121e87	−0.175209	−0.0876046	−	0.996155i	$-0.527921\pi$
$227$	−3.93121e87	−0.175209	−0.0876046	+	0.996155i	$0.527921\pi$
$228$	9.48786e87	0.358601
$229$	−4.79839e88	−1.53909	−0.769546	−	0.638591i	$-0.779518\pi$
$229$	−4.79839e88	−1.53909	−0.769546	+	0.638591i	$0.779518\pi$
$230$	1.53722e88	0.418737
$231$	−1.84988e88	−0.428247
$232$	3.53213e88	0.695405
$233$	6.03818e88	1.01172	0.505859	−	0.862616i	$-0.331176\pi$
$233$	6.03818e88	1.01172	0.505859	+	0.862616i	$0.331176\pi$
$234$	1.86185e88	0.265675
$235$	1.45699e89	1.77179
$236$	−1.70764e88	−0.177091
$237$	−1.22347e89	−1.08275
$238$	−8.58822e87	−0.0649034
$239$	−1.88840e89	−1.21947	−0.609737	−	0.792604i	$-0.708725\pi$
$239$	−1.88840e89	−1.21947	−0.609737	+	0.792604i	$0.708725\pi$
$240$	4.51399e88	0.249252
$241$	−1.29168e89	−0.610261	−0.305131	−	0.952311i	$-0.598700\pi$
$241$	−1.29168e89	−0.610261	−0.305131	+	0.952311i	$0.598700\pi$
$242$	−4.36597e88	−0.176606
$243$	−1.72293e89	−0.597079
$244$	3.51275e89	1.04359
$245$	2.11407e89	0.538755
$246$	−2.68282e89	−0.586848
$247$	−5.25505e89	−0.987282
$248$	4.36913e89	0.705434
$249$	8.10061e89	1.12471
$250$	4.39224e89	0.524730
$251$	−6.21006e89	−0.638751	−0.319375	−	0.947628i	$-0.603473\pi$
$251$	−6.21006e89	−0.638751	−0.319375	+	0.947628i	$0.603473\pi$
$252$	−1.70851e89	−0.151390
$253$	9.66570e89	0.738268
$254$	8.44792e88	0.0556526
$255$	2.73871e89	0.155700
$256$	−1.31727e90	−0.646659
$257$	−4.17118e89	−0.176916	−0.0884580	−	0.996080i	$-0.528194\pi$
$257$	−4.17118e89	−0.176916	−0.0884580	+	0.996080i	$0.528194\pi$
$258$	1.08684e90	0.398499
$259$	−3.16588e90	−1.00404
$260$	−4.37153e90	−1.19987
$261$	1.04939e90	0.249413
$262$	1.60809e90	0.331141
$263$	4.77873e90	0.853045	0.426523	−	0.904477i	$-0.359738\pi$
$263$	4.77873e90	0.853045	0.426523	+	0.904477i	$0.359738\pi$
$264$	−3.72968e90	−0.577463
$265$	3.82821e89	0.0514370
$266$	−1.55978e90	−0.181971
$267$	8.10416e90	0.821364
$268$	2.67385e90	0.235549
$269$	1.60979e91	1.23327	0.616636	−	0.787249i	$-0.288495\pi$
$269$	1.60979e91	1.23327	0.616636	+	0.787249i	$0.288495\pi$
$270$	−7.42357e90	−0.494848
$271$	4.15988e90	0.241397	0.120699	−	0.992689i	$-0.461486\pi$
$271$	4.15988e90	0.241397	0.120699	+	0.992689i	$0.461486\pi$
$272$	1.31771e90	0.0666016
$273$	−2.09366e91	−0.922163
$274$	5.77546e89	0.0221789
$275$	3.68416e90	0.123413
$276$	−1.97510e91	−0.577428
$277$	−4.01519e91	−1.02498	−0.512489	−	0.858694i	$-0.671277\pi$
$277$	−4.01519e91	−1.02498	−0.512489	+	0.858694i	$0.671277\pi$
$278$	−1.26847e91	−0.282879
$279$	1.29806e91	0.253010
$280$	−3.01477e91	−0.513839
$281$	4.24980e91	0.633697	0.316848	−	0.948476i	$-0.397375\pi$
$281$	4.24980e91	0.633697	0.316848	+	0.948476i	$0.397375\pi$
$282$	6.05513e91	0.790282
$283$	−1.80371e91	−0.206146	−0.103073	−	0.994674i	$-0.532868\pi$
$283$	−1.80371e91	−0.206146	−0.103073	+	0.994674i	$0.532868\pi$
$284$	9.55833e91	0.957071
$285$	4.97399e91	0.436539
$286$	8.89090e91	0.684257
$287$	−1.36355e92	−0.920663
$288$	−5.40674e91	−0.320418
$289$	−1.84168e92	−0.958396
$290$	7.96966e91	0.364347
$291$	5.43660e91	0.218444
$292$	4.12311e92	1.45669
$293$	−3.12319e92	−0.970650	−0.485325	−	0.874334i	$-0.661299\pi$
$293$	−3.12319e92	−0.970650	−0.485325	+	0.874334i	$0.661299\pi$
$294$	8.78590e91	0.240304
$295$	−8.95226e91	−0.215579
$296$	−6.38296e92	−1.35389
$297$	−4.66778e92	−0.872456
$298$	−4.73418e92	−0.780072
$299$	1.09395e93	1.58974
$300$	−7.52823e91	−0.0965263
$301$	5.52390e92	0.625176
$302$	7.35738e92	0.735298
$303$	−5.63887e92	−0.497844
$304$	2.39319e92	0.186732
$305$	1.84155e93	1.27040
$306$	−5.14436e91	−0.0313890
$307$	−6.03921e92	−0.326055	−0.163028	−	0.986622i	$-0.552126\pi$
$307$	−6.03921e92	−0.326055	−0.163028	+	0.986622i	$0.552126\pi$
$308$	−8.15863e92	−0.389911
$309$	−3.73688e92	−0.158149
$310$	9.85819e92	0.369601
$311$	8.09285e92	0.268897	0.134449	−	0.990921i	$-0.457074\pi$
$311$	8.09285e92	0.268897	0.134449	+	0.990921i	$0.457074\pi$
$312$	−4.22119e93	−1.24348
$313$	−3.76956e93	−0.984869	−0.492434	−	0.870350i	$-0.663893\pi$
$313$	−3.76956e93	−0.984869	−0.492434	+	0.870350i	$0.663893\pi$
$314$	2.34431e93	0.543441
$315$	−8.95682e92	−0.184293
$316$	−5.39592e93	−0.985824
$317$	4.64348e93	0.753565	0.376783	−	0.926302i	$-0.377030\pi$
$317$	4.64348e93	0.753565	0.376783	+	0.926302i	$0.377030\pi$
$318$	1.59097e92	0.0229428
$319$	5.01115e93	0.642373
$320$	−1.47140e93	−0.167729
$321$	6.48906e93	0.658026
$322$	3.24700e93	0.293013
$323$	1.45199e93	0.116646
$324$	6.25051e93	0.447175
$325$	4.16967e93	0.265751
$326$	1.13690e93	0.0645746
$327$	−9.18772e93	−0.465229
$328$	−2.74916e94	−1.24145
$329$	3.07754e94	1.23982
$330$	−8.41538e93	−0.302553
$331$	−6.01033e94	−1.92907	−0.964536	−	0.263952i	$-0.914974\pi$
$331$	−6.01033e94	−1.92907	−0.964536	+	0.263952i	$0.914974\pi$
$332$	3.57266e94	1.02403
$333$	−1.89637e94	−0.485583
$334$	1.82709e94	0.418088
$335$	1.40176e94	0.286743
$336$	9.53472e93	0.174415
$337$	−9.17041e94	−1.50061	−0.750304	−	0.661093i	$-0.770093\pi$
$337$	−9.17041e94	−1.50061	−0.750304	+	0.661093i	$0.770093\pi$
$338$	6.68636e94	0.979070
$339$	−3.81737e94	−0.500352
$340$	1.20787e94	0.141762
$341$	6.19862e94	0.651637
$342$	−9.34310e93	−0.0880060
$343$	1.20894e95	1.02064
$344$	1.11371e95	0.843009
$345$	−1.03544e95	−0.702925
$346$	−4.87611e94	−0.296975
$347$	1.82468e95	0.997311	0.498655	−	0.866800i	$-0.333827\pi$
$347$	1.82468e95	0.997311	0.498655	+	0.866800i	$0.333827\pi$
$348$	−1.02398e95	−0.502424
$349$	2.90622e94	0.128049	0.0640244	−	0.997948i	$-0.479606\pi$
$349$	2.90622e94	0.128049	0.0640244	+	0.997948i	$0.479606\pi$
$350$	1.23762e94	0.0489819
$351$	−5.28292e95	−1.87870
$352$	−2.58188e95	−0.825251
$353$	−2.60592e95	−0.748876	−0.374438	−	0.927252i	$-0.622164\pi$
$353$	−2.60592e95	−0.748876	−0.374438	+	0.927252i	$0.622164\pi$
$354$	−3.72049e94	−0.0961562
$355$	5.01094e95	1.16508
$356$	3.57422e95	0.747836
$357$	5.78486e94	0.108952
$358$	−3.79614e95	−0.643767
$359$	1.18369e96	1.80798	0.903992	−	0.427549i	$-0.140623\pi$
$359$	1.18369e96	1.80798	0.903992	+	0.427549i	$0.140623\pi$
$360$	−1.80585e95	−0.248507
$361$	−5.42636e95	−0.672959
$362$	9.32602e94	0.104262
$363$	2.94083e95	0.296464
$364$	−9.23380e95	−0.839612
$365$	2.16153e96	1.77329
$366$	7.65334e95	0.566644
$367$	−1.04271e96	−0.696923	−0.348462	−	0.937323i	$-0.613296\pi$
$367$	−1.04271e96	−0.696923	−0.348462	+	0.937323i	$0.613296\pi$
$368$	−4.98193e95	−0.300680
$369$	−8.16771e95	−0.445258
$370$	−1.44020e96	−0.709349
$371$	8.08618e94	0.0359933
$372$	−1.26663e96	−0.509670
$373$	−1.28066e96	−0.465966	−0.232983	−	0.972481i	$-0.574849\pi$
$373$	−1.28066e96	−0.465966	−0.232983	+	0.972481i	$0.574849\pi$
$374$	−2.45658e95	−0.0808437
$375$	−2.95853e96	−0.880852
$376$	6.20486e96	1.67181
$377$	5.67154e96	1.38325
$378$	−1.56805e96	−0.346272
$379$	−7.43491e96	−1.48698	−0.743490	−	0.668747i	$-0.766831\pi$
$379$	−7.43491e96	−1.48698	−0.743490	+	0.668747i	$0.766831\pi$
$380$	2.19371e96	0.397460
$381$	−5.69035e95	−0.0934227
$382$	1.59133e96	0.236801
$383$	7.91229e96	1.06745	0.533726	−	0.845658i	$-0.320791\pi$
$383$	7.91229e96	1.06745	0.533726	+	0.845658i	$0.320791\pi$
$384$	6.37082e96	0.779425
$385$	−4.27714e96	−0.474653
$386$	−2.98420e96	−0.300472
$387$	3.30883e96	0.302352
$388$	2.39774e96	0.198889
$389$	−5.40930e96	−0.407409	−0.203705	−	0.979032i	$-0.565298\pi$
$389$	−5.40930e96	−0.407409	−0.203705	+	0.979032i	$0.565298\pi$
$390$	−9.52439e96	−0.651500
$391$	−3.02261e96	−0.187825
$392$	9.00314e96	0.508354
$393$	−1.08318e97	−0.555878
$394$	−8.36051e96	−0.390054
$395$	−2.82880e97	−1.20008
$396$	−4.88703e96	−0.188571
$397$	1.66947e96	0.0586051	0.0293025	−	0.999571i	$-0.490671\pi$
$397$	1.66947e96	0.0586051	0.0293025	+	0.999571i	$0.490671\pi$
$398$	2.67619e97	0.854872
$399$	1.05064e97	0.305470
$400$	−1.89890e96	−0.0502635
$401$	3.18207e97	0.767001	0.383501	−	0.923541i	$-0.374718\pi$
$401$	3.18207e97	0.767001	0.383501	+	0.923541i	$0.374718\pi$
$402$	5.82559e96	0.127898
$403$	7.01549e97	1.40320
$404$	−2.48694e97	−0.453278
$405$	3.27682e97	0.544364
$406$	1.68340e97	0.254953
$407$	−9.05570e97	−1.25064
$408$	1.16633e97	0.146914
$409$	−4.59307e97	−0.527812	−0.263906	−	0.964548i	$-0.585011\pi$
$409$	−4.59307e97	−0.527812	−0.263906	+	0.964548i	$0.585011\pi$
$410$	−6.20301e97	−0.650441
$411$	−3.89023e96	−0.0372312
$412$	−1.64809e97	−0.143991
$413$	−1.89095e97	−0.150853
$414$	1.94496e97	0.141709
$415$	1.87296e98	1.24659
$416$	−2.92213e98	−1.77705
$417$	8.54418e97	0.474863
$418$	−4.46160e97	−0.226663
$419$	−4.37040e97	−0.203000	−0.101500	−	0.994836i	$-0.532364\pi$
$419$	−4.37040e97	−0.203000	−0.101500	+	0.994836i	$0.532364\pi$
$420$	8.73994e97	0.371245
$421$	9.39287e97	0.364939	0.182469	−	0.983212i	$-0.441591\pi$
$421$	9.39287e97	0.364939	0.182469	+	0.983212i	$0.441591\pi$
$422$	−7.21226e97	−0.256363
$423$	1.84345e98	0.599609
$424$	1.63031e97	0.0485346
$425$	−1.15209e97	−0.0313980
$426$	2.08250e98	0.519668
$427$	3.88984e98	0.888968
$428$	2.86191e98	0.599120
$429$	−5.98873e98	−1.14865
$430$	2.51291e98	0.441682
$431$	−7.00214e98	−1.12806	−0.564032	−	0.825753i	$-0.690750\pi$
$431$	−7.00214e98	−1.12806	−0.564032	+	0.825753i	$0.690750\pi$
$432$	2.40588e98	0.355332
$433$	−6.63616e98	−0.898712	−0.449356	−	0.893353i	$-0.648346\pi$
$433$	−6.63616e98	−0.898712	−0.449356	+	0.893353i	$0.648346\pi$
$434$	2.08230e98	0.258630
$435$	−5.36821e98	−0.611620
$436$	−4.05211e98	−0.423582
$437$	−5.48962e98	−0.526609
$438$	8.98315e98	0.790951
$439$	1.20506e99	0.974067	0.487033	−	0.873383i	$-0.338079\pi$
$439$	1.20506e99	0.974067	0.487033	+	0.873383i	$0.338079\pi$
$440$	−8.62346e98	−0.640039
$441$	2.67482e98	0.182325
$442$	−2.78032e98	−0.174084
$443$	−2.73293e99	−1.57213	−0.786067	−	0.618141i	$-0.787886\pi$
$443$	−2.73293e99	−1.57213	−0.786067	+	0.618141i	$0.787886\pi$
$444$	1.85045e99	0.978172
$445$	1.87378e99	0.910370
$446$	−7.28368e97	−0.0325307
$447$	3.18885e99	1.30949
$448$	−3.10799e98	−0.117369
$449$	4.89234e99	1.69933	0.849667	−	0.527319i	$-0.176803\pi$
$449$	4.89234e99	1.69933	0.849667	+	0.527319i	$0.176803\pi$
$450$	7.41337e97	0.0236890
$451$	−3.90032e99	−1.14678
$452$	−1.68359e99	−0.455561
$453$	−4.95579e99	−1.23433
$454$	−3.77750e98	−0.0866183
$455$	−4.84080e99	−1.02209
$456$	2.11826e99	0.411906
$457$	3.25924e99	0.583792	0.291896	−	0.956450i	$-0.405714\pi$
$457$	3.25924e99	0.583792	0.291896	+	0.956450i	$0.405714\pi$
$458$	−4.61076e99	−0.760882
$459$	1.45969e99	0.221965
$460$	−4.56666e99	−0.640000
$461$	3.65189e99	0.471773	0.235887	−	0.971781i	$-0.424201\pi$
$461$	3.65189e99	0.471773	0.235887	+	0.971781i	$0.424201\pi$
$462$	−1.77755e99	−0.211713
$463$	1.23373e100	1.35498	0.677492	−	0.735530i	$-0.263067\pi$
$463$	1.23373e100	1.35498	0.677492	+	0.735530i	$0.263067\pi$
$464$	−2.58287e99	−0.261624
$465$	−6.64028e99	−0.620441
$466$	5.80208e99	0.500163
$467$	1.09207e100	0.868698	0.434349	−	0.900745i	$-0.356978\pi$
$467$	1.09207e100	0.868698	0.434349	+	0.900745i	$0.356978\pi$
$468$	−5.53106e99	−0.406059
$469$	2.96088e99	0.200650
$470$	1.40002e100	0.875920
$471$	−1.57908e100	−0.912262
$472$	−3.81248e99	−0.203415
$473$	1.58006e100	0.778720
$474$	−1.17563e100	−0.535280
$475$	−2.09241e99	−0.0880312
$476$	2.55133e99	0.0991986
$477$	4.84364e98	0.0174073
$478$	−1.81456e100	−0.602872
$479$	2.78687e100	0.856119	0.428060	−	0.903751i	$-0.359197\pi$
$479$	2.78687e100	0.856119	0.428060	+	0.903751i	$0.359197\pi$
$480$	2.76584e100	0.785744
$481$	−1.02491e101	−2.69305
$482$	−1.24117e100	−0.301695
$483$	−2.18712e100	−0.491875
$484$	1.29701e100	0.269925
$485$	1.25701e100	0.242116
$486$	−1.65556e100	−0.295178
$487$	4.50886e100	0.744271	0.372135	−	0.928178i	$-0.378626\pi$
$487$	4.50886e100	0.744271	0.372135	+	0.928178i	$0.378626\pi$
$488$	7.84258e100	1.19871
$489$	−7.65793e99	−0.108400
$490$	2.03141e100	0.266344
$491$	2.15050e100	0.261206	0.130603	−	0.991435i	$-0.458309\pi$
$491$	2.15050e100	0.261206	0.130603	+	0.991435i	$0.458309\pi$
$492$	7.96993e100	0.896940
$493$	−1.56706e100	−0.163428
$494$	−5.04957e100	−0.488083
$495$	−2.56202e100	−0.229555
$496$	−3.19491e100	−0.265397
$497$	1.05844e101	0.815270
$498$	7.78386e100	0.556026
$499$	−1.72948e101	−1.14590	−0.572948	−	0.819592i	$-0.694200\pi$
$499$	−1.72948e101	−1.14590	−0.572948	+	0.819592i	$0.694200\pi$
$500$	−1.30482e101	−0.801999
$501$	−1.23069e101	−0.701835
$502$	−5.96724e100	−0.315780
$503$	2.47749e101	1.21678	0.608391	−	0.793637i	$-0.291815\pi$
$503$	2.47749e101	1.21678	0.608391	+	0.793637i	$0.291815\pi$
$504$	−3.81442e100	−0.173894
$505$	−1.30377e101	−0.551793
$506$	9.28776e100	0.364978
$507$	−4.50380e101	−1.64354
$508$	−2.50965e100	−0.0850596
$509$	2.05274e101	0.646276	0.323138	−	0.946352i	$-0.395262\pi$
$509$	2.05274e101	0.646276	0.323138	+	0.946352i	$0.395262\pi$
$510$	2.63162e100	0.0769735
$511$	4.56572e101	1.24087
$512$	2.45283e101	0.619503
$513$	2.65106e101	0.622326
$514$	−4.00808e100	−0.0874620
$515$	−8.64010e100	−0.175286
$516$	−3.22871e101	−0.609067
$517$	8.80303e101	1.54432
$518$	−3.04209e101	−0.496370
$519$	3.28445e101	0.498525
$520$	−9.75989e101	−1.37822
$521$	−6.95456e101	−0.913808	−0.456904	−	0.889516i	$-0.651042\pi$
$521$	−6.95456e101	−0.913808	−0.456904	+	0.889516i	$0.651042\pi$
$522$	1.00836e101	0.123302
$523$	3.62848e101	0.412963	0.206481	−	0.978451i	$-0.433799\pi$
$523$	3.62848e101	0.412963	0.206481	+	0.978451i	$0.433799\pi$
$524$	−4.77721e101	−0.506117
$525$	−8.33637e100	−0.0822248
$526$	4.59187e101	0.421720
$527$	−1.93840e101	−0.165785
$528$	2.72732e101	0.217252
$529$	−2.04904e101	−0.152042
$530$	3.67853e100	0.0254290
$531$	−1.13268e101	−0.0729564
$532$	4.63368e101	0.278125
$533$	−4.41431e102	−2.46941
$534$	7.78727e101	0.406058
$535$	1.50035e102	0.729332
$536$	5.96964e101	0.270563
$537$	2.55700e102	1.08068
$538$	1.54684e102	0.609693
$539$	1.27730e102	0.469587
$540$	2.20534e102	0.756327
$541$	−1.59160e102	−0.509257	−0.254628	−	0.967039i	$-0.581953\pi$
$541$	−1.59160e102	−0.509257	−0.254628	+	0.967039i	$0.581953\pi$
$542$	3.99723e101	0.119340
$543$	−6.28182e101	−0.175022
$544$	8.07393e101	0.209955
$545$	−2.12431e102	−0.515643
$546$	−2.01180e102	−0.455890
$547$	−4.34376e102	−0.919053	−0.459527	−	0.888164i	$-0.651981\pi$
$547$	−4.34376e102	−0.919053	−0.459527	+	0.888164i	$0.651981\pi$
$548$	−1.71573e101	−0.0338983
$549$	2.33002e102	0.429929
$550$	3.54010e101	0.0610119
$551$	−2.84607e102	−0.458207
$552$	−4.40961e102	−0.663261
$553$	−5.97515e102	−0.839763
$554$	−3.85819e102	−0.506719
$555$	9.70094e102	1.19077
$556$	3.76829e102	0.432354
$557$	−4.83045e102	−0.518105	−0.259053	−	0.965863i	$-0.583410\pi$
$557$	−4.83045e102	−0.518105	−0.259053	+	0.965863i	$0.583410\pi$
$558$	1.24730e102	0.125081
$559$	1.78829e103	1.67685
$560$	2.20454e102	0.193316
$561$	1.65471e102	0.135711
$562$	4.08362e102	0.313281
$563$	8.05465e102	0.578072	0.289036	−	0.957318i	$-0.406665\pi$
$563$	8.05465e102	0.578072	0.289036	+	0.957318i	$0.406665\pi$
$564$	−1.79882e103	−1.20787
$565$	−8.82621e102	−0.554571
$566$	−1.73318e102	−0.101912
$567$	6.92149e102	0.380921
$568$	2.13400e103	1.09934
$569$	−5.36992e102	−0.258975	−0.129488	−	0.991581i	$-0.541333\pi$
$569$	−5.36992e102	−0.258975	−0.129488	+	0.991581i	$0.541333\pi$
$570$	4.77950e102	0.215812
$571$	−3.90521e102	−0.165116	−0.0825582	−	0.996586i	$-0.526309\pi$
$571$	−3.90521e102	−0.165116	−0.0825582	+	0.996586i	$0.526309\pi$
$572$	−2.64124e103	−1.04582
$573$	−1.07189e103	−0.397513
$574$	−1.31024e103	−0.455149
$575$	4.35579e102	0.141750
$576$	−1.86169e102	−0.0567628
$577$	−1.53569e103	−0.438743	−0.219372	−	0.975641i	$-0.570401\pi$
$577$	−1.53569e103	−0.438743	−0.219372	+	0.975641i	$0.570401\pi$
$578$	−1.76967e103	−0.473803
$579$	2.01010e103	0.504395
$580$	−2.36757e103	−0.556869
$581$	3.95617e103	0.872309
$582$	5.22402e102	0.107992
$583$	2.31298e102	0.0448333
$584$	9.20527e103	1.67323
$585$	−2.89965e103	−0.494311
$586$	−3.00107e103	−0.479861
$587$	4.98256e103	0.747349	0.373674	−	0.927560i	$-0.378098\pi$
$587$	4.98256e103	0.747349	0.373674	+	0.927560i	$0.378098\pi$
$588$	−2.61005e103	−0.367282
$589$	−3.52049e103	−0.464815
$590$	−8.60221e102	−0.106576
$591$	5.63147e103	0.654774
$592$	4.66752e103	0.509357
$593$	−8.67897e101	−0.00889031	−0.00444516	−	0.999990i	$-0.501415\pi$
$593$	−8.67897e101	−0.00889031	−0.00444516	+	0.999990i	$0.501415\pi$
$594$	−4.48526e103	−0.431317
$595$	1.33753e103	0.120758
$596$	1.40640e104	1.19226
$597$	−1.80263e104	−1.43505
$598$	1.05117e104	0.785922
$599$	−2.53386e104	−1.77942	−0.889708	−	0.456531i	$-0.849092\pi$
$599$	−2.53386e104	−1.77942	−0.889708	+	0.456531i	$0.849092\pi$
$600$	−1.68076e103	−0.110875
$601$	−9.89909e103	−0.613483	−0.306742	−	0.951793i	$-0.599239\pi$
$601$	−9.89909e103	−0.613483	−0.306742	+	0.951793i	$0.599239\pi$
$602$	5.30791e103	0.309069
$603$	1.77357e103	0.0970397
$604$	−2.18568e104	−1.12383
$605$	6.79955e103	0.328590
$606$	−5.41838e103	−0.246120
$607$	3.73213e103	0.159361	0.0796803	−	0.996820i	$-0.474610\pi$
$607$	3.73213e103	0.159361	0.0796803	+	0.996820i	$0.474610\pi$
$608$	1.46637e104	0.588654
$609$	−1.13390e104	−0.427984
$610$	1.76955e104	0.628048
$611$	9.96312e104	3.32545
$612$	1.52825e103	0.0479751
$613$	−4.35614e104	−1.28627	−0.643137	−	0.765751i	$-0.722368\pi$
$613$	−4.35614e104	−1.28627	−0.643137	+	0.765751i	$0.722368\pi$
$614$	−5.80306e103	−0.161192
$615$	4.17822e104	1.09188
$616$	−1.82150e104	−0.447870
$617$	−5.43863e104	−1.25833	−0.629167	−	0.777270i	$-0.716604\pi$
$617$	−5.43863e104	−1.25833	−0.629167	+	0.777270i	$0.716604\pi$
$618$	−3.59076e103	−0.0781841
$619$	2.50377e104	0.513093	0.256546	−	0.966532i	$-0.417415\pi$
$619$	2.50377e104	0.513093	0.256546	+	0.966532i	$0.417415\pi$
$620$	−2.92860e104	−0.564900
$621$	−5.51873e104	−1.00208
$622$	7.77640e103	0.132935
$623$	3.95790e104	0.637035
$624$	3.08673e104	0.467818
$625$	−5.76193e104	−0.822370
$626$	−3.62217e104	−0.486890
$627$	3.00525e104	0.380494
$628$	−6.96430e104	−0.830597
$629$	2.83186e104	0.318179
$630$	−8.60660e103	−0.0911089
$631$	8.30271e104	0.828169	0.414085	−	0.910238i	$-0.364102\pi$
$631$	8.30271e104	0.828169	0.414085	+	0.910238i	$0.364102\pi$
$632$	−1.20469e105	−1.13237
$633$	4.85804e104	0.430350
$634$	4.46191e104	0.372540
$635$	−1.31568e104	−0.103546
$636$	−4.72635e103	−0.0350658
$637$	1.44563e105	1.01118
$638$	4.81521e104	0.317570
$639$	6.34007e104	0.394287
$640$	1.47301e105	0.863886
$641$	−2.75789e105	−1.52546	−0.762729	−	0.646718i	$-0.776141\pi$
$641$	−2.75789e105	−1.52546	−0.762729	+	0.646718i	$0.776141\pi$
$642$	6.23533e104	0.325309
$643$	1.32726e105	0.653198	0.326599	−	0.945163i	$-0.394097\pi$
$643$	1.32726e105	0.653198	0.326599	+	0.945163i	$0.394097\pi$
$644$	−9.64596e104	−0.447843
$645$	−1.69264e105	−0.741441
$646$	1.39521e104	0.0576661
$647$	2.44039e103	0.00951806	0.00475903	−	0.999989i	$-0.498485\pi$
$647$	2.44039e103	0.00951806	0.00475903	+	0.999989i	$0.498485\pi$
$648$	1.39549e105	0.513647
$649$	−5.40889e104	−0.187902
$650$	4.00663e104	0.131380
$651$	−1.40260e105	−0.434157
$652$	−3.37742e104	−0.0986961
$653$	−6.41133e105	−1.76890	−0.884451	−	0.466632i	$-0.845467\pi$
$653$	−6.41133e105	−1.76890	−0.884451	+	0.466632i	$0.845467\pi$
$654$	−8.82847e104	−0.229996
$655$	−2.50444e105	−0.616115
$656$	2.01032e105	0.467058
$657$	2.73487e105	0.600117
$658$	2.95720e105	0.612929
$659$	4.80095e105	0.939992	0.469996	−	0.882669i	$-0.344255\pi$
$659$	4.80095e105	0.939992	0.469996	+	0.882669i	$0.344255\pi$
$660$	2.49998e105	0.462423
$661$	−4.07366e105	−0.711919	−0.355959	−	0.934501i	$-0.615846\pi$
$661$	−4.07366e105	−0.711919	−0.355959	+	0.934501i	$0.615846\pi$
$662$	−5.77531e105	−0.953676
$663$	1.87277e105	0.292231
$664$	7.97633e105	1.17625
$665$	2.42920e105	0.338572
$666$	−1.82221e105	−0.240058
$667$	5.92470e105	0.737815
$668$	−5.42779e105	−0.639008
$669$	4.90614e104	0.0546086
$670$	1.34695e105	0.141757
$671$	1.11265e106	1.10730
$672$	5.84217e105	0.549828
$673$	−7.62407e105	−0.678613	−0.339306	−	0.940676i	$-0.610192\pi$
$673$	−7.62407e105	−0.678613	−0.339306	+	0.940676i	$0.610192\pi$
$674$	−8.81183e105	−0.741856
$675$	−2.10351e105	−0.167514
$676$	−1.98634e106	−1.49641
$677$	−1.87091e106	−1.33345	−0.666727	−	0.745302i	$-0.732305\pi$
$677$	−1.87091e106	−1.33345	−0.666727	+	0.745302i	$0.732305\pi$
$678$	−3.66810e105	−0.247359
$679$	2.65513e105	0.169422
$680$	2.69669e105	0.162835
$681$	2.54445e105	0.145404
$682$	5.95624e105	0.322150
$683$	1.12098e106	0.573881	0.286941	−	0.957948i	$-0.407362\pi$
$683$	1.12098e106	0.573881	0.286941	+	0.957948i	$0.407362\pi$
$684$	2.77558e105	0.134509
$685$	−8.99469e104	−0.0412657
$686$	1.16166e106	0.504576
$687$	3.10572e106	1.27728
$688$	−8.14401e105	−0.317155
$689$	2.61779e105	0.0965415
$690$	−9.94953e105	−0.347505
$691$	−2.18789e106	−0.723768	−0.361884	−	0.932223i	$-0.617866\pi$
$691$	−2.18789e106	−0.723768	−0.361884	+	0.932223i	$0.617866\pi$
$692$	1.44856e106	0.453897
$693$	−5.41164e105	−0.160632
$694$	1.75333e106	0.493041
$695$	1.97552e106	0.526321
$696$	−2.28615e106	−0.577109
$697$	1.21969e106	0.291756
$698$	2.79258e105	0.0633035
$699$	−3.90817e106	−0.839613
$700$	−3.67663e105	−0.0748641
$701$	6.49232e106	1.25307	0.626533	−	0.779395i	$-0.284473\pi$
$701$	6.49232e106	1.25307	0.626533	+	0.779395i	$0.284473\pi$
$702$	−5.07634e106	−0.928773
$703$	5.14317e106	0.892085
$704$	−8.89011e105	−0.146195
$705$	−9.43026e106	−1.47039
$706$	−2.50402e106	−0.370222
$707$	−2.75391e106	−0.386119
$708$	1.10526e106	0.146965
$709$	−8.42609e106	−1.06266	−0.531328	−	0.847166i	$-0.678307\pi$
$709$	−8.42609e106	−1.06266	−0.531328	+	0.847166i	$0.678307\pi$
$710$	4.81500e106	0.575981
$711$	−3.57913e106	−0.406132
$712$	7.97982e106	0.859000
$713$	7.32864e106	0.748456
$714$	5.55866e105	0.0538626
$715$	−1.38467e107	−1.27312
$716$	1.12773e107	0.983936
$717$	1.22225e107	1.01203
$718$	1.13740e107	0.893814
$719$	−2.53914e106	−0.189388	−0.0946942	−	0.995506i	$-0.530187\pi$
$719$	−2.53914e106	−0.189388	−0.0946942	+	0.995506i	$0.530187\pi$
$720$	1.32052e106	0.0934927
$721$	−1.82501e106	−0.122657
$722$	−5.21418e106	−0.332691
$723$	8.36030e106	0.506449
$724$	−2.77051e106	−0.159354
$725$	2.25824e106	0.123338
$726$	2.82584e106	0.146563
$727$	−2.75247e107	−1.35576	−0.677880	−	0.735172i	$-0.737101\pi$
$727$	−2.75247e107	−1.35576	−0.677880	+	0.735172i	$0.737101\pi$
$728$	−2.06154e107	−0.964418
$729$	2.44704e107	1.08733
$730$	2.07701e107	0.876662
$731$	−4.94110e106	−0.198117
$732$	−2.27360e107	−0.866061
$733$	−1.63836e107	−0.592938	−0.296469	−	0.955042i	$-0.595809\pi$
$733$	−1.63836e107	−0.592938	−0.296469	+	0.955042i	$0.595809\pi$
$734$	−1.00194e107	−0.344538
$735$	−1.36831e107	−0.447106
$736$	−3.05256e107	−0.947864
$737$	8.46932e106	0.249930
$738$	−7.84834e106	−0.220122
$739$	2.59618e107	0.692100	0.346050	−	0.938216i	$-0.387523\pi$
$739$	2.59618e107	0.692100	0.346050	+	0.938216i	$0.387523\pi$
$740$	4.27846e107	1.08417
$741$	3.40129e107	0.819334
$742$	7.77000e105	0.0177940
$743$	−1.39254e107	−0.303199	−0.151600	−	0.988442i	$-0.548442\pi$
$743$	−1.39254e107	−0.303199	−0.151600	+	0.988442i	$0.548442\pi$
$744$	−2.82788e107	−0.585432
$745$	7.37300e107	1.45139
$746$	−1.23059e107	−0.230360
$747$	2.36976e107	0.421872
$748$	7.29784e106	0.123562
$749$	3.16912e107	0.510354
$750$	−2.84284e107	−0.435467
$751$	−1.89224e107	−0.275726	−0.137863	−	0.990451i	$-0.544023\pi$
$751$	−1.89224e107	−0.275726	−0.137863	+	0.990451i	$0.544023\pi$
$752$	−4.53729e107	−0.628966
$753$	4.01941e107	0.530092
$754$	5.44977e107	0.683837
$755$	−1.14584e108	−1.36808
$756$	4.65825e107	0.529243
$757$	−6.82237e107	−0.737632	−0.368816	−	0.929502i	$-0.620237\pi$
$757$	−6.82237e107	−0.737632	−0.368816	+	0.929502i	$0.620237\pi$
$758$	−7.14419e107	−0.735120
$759$	−6.25605e107	−0.612680
$760$	4.89768e107	0.456542
$761$	5.62396e107	0.499020	0.249510	−	0.968372i	$-0.419731\pi$
$761$	5.62396e107	0.499020	0.249510	+	0.968372i	$0.419731\pi$
$762$	−5.46785e106	−0.0461855
$763$	−4.48710e107	−0.360824
$764$	−4.72741e107	−0.361928
$765$	8.01182e106	0.0584020
$766$	7.60291e107	0.527717
$767$	−6.12169e107	−0.404618
$768$	8.52591e107	0.536655
$769$	1.14718e108	0.687694	0.343847	−	0.939026i	$-0.388270\pi$
$769$	1.14718e108	0.687694	0.343847	+	0.939026i	$0.388270\pi$
$770$	−4.10990e107	−0.234655
$771$	2.69976e107	0.146821
$772$	8.86524e107	0.459242
$773$	−3.23382e108	−1.59582	−0.797912	−	0.602774i	$-0.794062\pi$
$773$	−3.23382e108	−1.59582	−0.797912	+	0.602774i	$0.794062\pi$
$774$	3.17945e107	0.149474
$775$	2.79337e107	0.125116
$776$	5.35320e107	0.228454
$777$	2.04909e108	0.833245
$778$	−5.19779e107	−0.201411
$779$	2.21518e108	0.818001
$780$	2.82944e108	0.995755
$781$	3.02757e108	1.01550
$782$	−2.90442e107	−0.0928553
$783$	−2.86117e108	−0.871921
$784$	−6.58353e107	−0.191252
$785$	−3.65102e108	−1.01112
$786$	−1.04083e108	−0.274810
$787$	−7.72858e108	−1.94557	−0.972786	−	0.231704i	$-0.925570\pi$
$787$	−7.72858e108	−1.94557	−0.972786	+	0.231704i	$0.925570\pi$
$788$	2.48368e108	0.596159
$789$	−3.09300e108	−0.707932
$790$	−2.71819e108	−0.593285
$791$	−1.86432e108	−0.388064
$792$	−1.09108e108	−0.216602
$793$	1.25928e109	2.38439
$794$	1.60419e107	0.0289726
$795$	−2.47778e107	−0.0426870
$796$	−7.95022e108	−1.30659
$797$	9.15620e108	1.43558	0.717791	−	0.696259i	$-0.245153\pi$
$797$	9.15620e108	1.43558	0.717791	+	0.696259i	$0.245153\pi$
$798$	1.00955e108	0.151015
$799$	−2.75284e108	−0.392895
$800$	−1.16351e108	−0.158451
$801$	2.37079e108	0.308088
$802$	3.05765e108	0.379183
$803$	1.30598e109	1.54562
$804$	−1.73063e108	−0.195480
$805$	−5.05688e108	−0.545176
$806$	6.74118e108	0.693700
$807$	−1.04192e109	−1.02348
$808$	−5.55236e108	−0.520657
$809$	1.40487e109	1.25767	0.628837	−	0.777538i	$-0.283531\pi$
$809$	1.40487e109	1.25767	0.628837	+	0.777538i	$0.283531\pi$
$810$	3.14869e108	0.269117
$811$	−3.14760e108	−0.256860	−0.128430	−	0.991719i	$-0.540994\pi$
$811$	−3.14760e108	−0.256860	−0.128430	+	0.991719i	$0.540994\pi$
$812$	−5.00092e108	−0.389672
$813$	−2.69245e108	−0.200333
$814$	−8.70161e108	−0.618279
$815$	−1.77060e108	−0.120147
$816$	−8.52874e107	−0.0552719
$817$	−8.97393e108	−0.555464
$818$	−4.41348e108	−0.260935
$819$	−6.12481e108	−0.345896
$820$	1.84274e109	0.994136
$821$	−2.88576e109	−1.48727	−0.743637	−	0.668583i	$-0.766901\pi$
$821$	−2.88576e109	−1.48727	−0.743637	+	0.668583i	$0.766901\pi$
$822$	−3.73812e107	−0.0184060
$823$	1.73999e109	0.818567	0.409283	−	0.912407i	$-0.365779\pi$
$823$	1.73999e109	0.818567	0.409283	+	0.912407i	$0.365779\pi$
$824$	−3.67954e108	−0.165395
$825$	−2.38454e108	−0.102419
$826$	−1.81701e108	−0.0745771
$827$	3.34216e109	1.31090	0.655451	−	0.755238i	$-0.272479\pi$
$827$	3.34216e109	1.31090	0.655451	+	0.755238i	$0.272479\pi$
$828$	−5.77795e108	−0.216589
$829$	−2.05561e107	−0.00736455	−0.00368228	−	0.999993i	$-0.501172\pi$
$829$	−2.05561e107	−0.00736455	−0.00368228	+	0.999993i	$0.501172\pi$
$830$	1.79972e109	0.616279
$831$	2.59880e109	0.850618
$832$	−1.00617e109	−0.314808
$833$	−3.99433e108	−0.119469
$834$	8.21009e108	0.234758
$835$	−2.84551e109	−0.777889
$836$	1.32542e109	0.346432
$837$	−3.53916e109	−0.884496
$838$	−4.19951e108	−0.100357
$839$	6.16118e109	1.40796	0.703981	−	0.710219i	$-0.251404\pi$
$839$	6.16118e109	1.40796	0.703981	+	0.710219i	$0.251404\pi$
$840$	1.95128e109	0.426429
$841$	−1.71301e109	−0.358022
$842$	9.02559e108	0.180415
$843$	−2.75065e109	−0.525897
$844$	2.14257e109	0.391826
$845$	−1.04133e110	−1.82164
$846$	1.77137e109	0.296429
$847$	1.43624e109	0.229932
$848$	−1.19216e108	−0.0182596
$849$	1.16744e109	0.171078
$850$	−1.10704e108	−0.0155223
$851$	−1.07066e110	−1.43646
$852$	−6.18655e109	−0.794262
$853$	3.10108e107	0.00380999	0.00190499	−	0.999998i	$-0.499394\pi$
$853$	3.10108e107	0.00380999	0.00190499	+	0.999998i	$0.499394\pi$
$854$	3.73774e109	0.439480
$855$	1.45509e109	0.163743
$856$	6.38950e109	0.688178
$857$	2.75939e109	0.284467	0.142234	−	0.989833i	$-0.454572\pi$
$857$	2.75939e109	0.284467	0.142234	+	0.989833i	$0.454572\pi$
$858$	−5.75456e109	−0.567857
$859$	1.64858e110	1.55728	0.778638	−	0.627474i	$-0.215911\pi$
$859$	1.64858e110	1.55728	0.778638	+	0.627474i	$0.215911\pi$
$860$	−7.46516e109	−0.675068
$861$	8.82549e109	0.764048
$862$	−6.72835e109	−0.557681
$863$	6.66654e109	0.529049	0.264525	−	0.964379i	$-0.414785\pi$
$863$	6.66654e109	0.529049	0.264525	+	0.964379i	$0.414785\pi$
$864$	1.47415e110	1.12015
$865$	7.59404e109	0.552547
$866$	−6.37667e109	−0.444297
$867$	1.19201e110	0.795362
$868$	−6.18596e109	−0.395292
$869$	−1.70914e110	−1.04601
$870$	−5.15830e109	−0.302367
$871$	9.58543e109	0.538184
$872$	−9.04676e109	−0.486547
$873$	1.59043e109	0.0819369
$874$	−5.27497e109	−0.260340
$875$	−1.44488e110	−0.683173
$876$	−2.66865e110	−1.20889
$877$	−4.10529e110	−1.78180	−0.890901	−	0.454197i	$-0.849926\pi$
$877$	−4.10529e110	−1.78180	−0.890901	+	0.454197i	$0.849926\pi$
$878$	1.15794e110	0.481550
$879$	2.02146e110	0.805531
$880$	6.30589e109	0.240794
$881$	2.60424e110	0.952980	0.476490	−	0.879180i	$-0.341909\pi$
$881$	2.60424e110	0.952980	0.476490	+	0.879180i	$0.341909\pi$
$882$	2.57023e109	0.0901363
$883$	2.39725e110	0.805725	0.402863	−	0.915260i	$-0.368015\pi$
$883$	2.39725e110	0.805725	0.402863	+	0.915260i	$0.368015\pi$
$884$	8.25957e109	0.266071
$885$	5.79428e109	0.178907
$886$	−2.62607e110	−0.777217
$887$	−5.65377e110	−1.60399	−0.801996	−	0.597330i	$-0.796228\pi$
$887$	−5.65377e110	−1.60399	−0.801996	+	0.597330i	$0.796228\pi$
$888$	4.13132e110	1.12358
$889$	−2.77905e109	−0.0724571
$890$	1.80051e110	0.450060
$891$	1.97983e110	0.474475
$892$	2.16378e109	0.0497201
$893$	−4.99966e110	−1.10157
$894$	3.06416e110	0.647373
$895$	5.91210e110	1.19778
$896$	3.11138e110	0.604508
$897$	−7.08049e110	−1.31931
$898$	4.70104e110	0.840101
$899$	3.79951e110	0.651237
$900$	−2.20231e109	−0.0362063
$901$	−7.23304e108	−0.0114062
$902$	−3.74781e110	−0.566934
$903$	−3.57530e110	−0.518827
$904$	−3.75880e110	−0.523279
$905$	−1.45243e110	−0.193988
$906$	−4.76201e110	−0.610215
$907$	−6.45915e110	−0.794150	−0.397075	−	0.917786i	$-0.629975\pi$
$907$	−6.45915e110	−0.794150	−0.397075	+	0.917786i	$0.629975\pi$
$908$	1.12219e110	0.132388
$909$	−1.64960e110	−0.186738
$910$	−4.65152e110	−0.505292
$911$	8.29756e110	0.864991	0.432495	−	0.901636i	$-0.357633\pi$
$911$	8.29756e110	0.864991	0.432495	+	0.901636i	$0.357633\pi$
$912$	−1.54898e110	−0.154967
$913$	1.13163e111	1.08655
$914$	3.13180e110	0.288610
$915$	−1.19193e111	−1.05429
$916$	1.36973e111	1.16294
$917$	−5.29003e110	−0.431130
$918$	1.40261e110	0.109733
$919$	−1.37516e111	−1.03282	−0.516408	−	0.856343i	$-0.672731\pi$
$919$	−1.37516e111	−1.03282	−0.516408	+	0.856343i	$0.672731\pi$
$920$	−1.01955e111	−0.735135
$921$	3.90883e110	0.270589
$922$	3.50910e110	0.233231
$923$	3.42655e111	2.18672
$924$	5.28061e110	0.323582
$925$	−4.08089e110	−0.240127
$926$	1.18549e111	0.669864
$927$	−1.09319e110	−0.0593204
$928$	−1.58259e111	−0.824744
$929$	2.86857e111	1.43574	0.717870	−	0.696177i	$-0.245117\pi$
$929$	2.86857e111	1.43574	0.717870	+	0.696177i	$0.245117\pi$
$930$	−6.38064e110	−0.306728
$931$	−7.25443e110	−0.334958
$932$	−1.72364e111	−0.764451
$933$	−5.23803e110	−0.223155
$934$	1.04937e111	0.429459
$935$	3.82588e110	0.150417
$936$	−1.23487e111	−0.466419
$937$	−4.28248e111	−1.55403	−0.777017	−	0.629480i	$-0.783268\pi$
$937$	−4.28248e111	−1.55403	−0.777017	+	0.629480i	$0.783268\pi$
$938$	2.84510e110	0.0991953
$939$	2.43982e111	0.817331
$940$	−4.15908e111	−1.33876
$941$	1.54957e111	0.479294	0.239647	−	0.970860i	$-0.422968\pi$
$941$	1.54957e111	0.479294	0.239647	+	0.970860i	$0.422968\pi$
$942$	−1.51733e111	−0.450996
$943$	−4.61136e111	−1.31716
$944$	2.78787e110	0.0765284
$945$	2.44208e111	0.644268
$946$	1.51828e111	0.384976
$947$	−4.69614e111	−1.14450	−0.572251	−	0.820079i	$-0.693930\pi$
$947$	−4.69614e111	−1.14450	−0.572251	+	0.820079i	$0.693930\pi$
$948$	3.49246e111	0.818124
$949$	1.47809e112	3.32826
$950$	−2.01059e110	−0.0435200
$951$	−3.00545e111	−0.625375
$952$	5.69611e110	0.113944
$953$	−5.56877e110	−0.107097	−0.0535483	−	0.998565i	$-0.517053\pi$
$953$	−5.56877e110	−0.107097	−0.0535483	+	0.998565i	$0.517053\pi$
$954$	4.65424e109	0.00860568
$955$	−2.47833e111	−0.440589
$956$	5.39056e111	0.921432
$957$	−3.24343e111	−0.533098
$958$	2.67789e111	0.423240
$959$	−1.89991e110	−0.0288759
$960$	9.52355e110	0.139196
$961$	−2.41435e111	−0.339370
$962$	−9.84833e111	−1.33137
$963$	1.89831e111	0.246821
$964$	3.68719e111	0.461112
$965$	4.64759e111	0.559053
$966$	−2.10160e111	−0.243168
$967$	−8.93151e111	−0.994104	−0.497052	−	0.867721i	$-0.665584\pi$
$967$	−8.93151e111	−0.994104	−0.497052	+	0.867721i	$0.665584\pi$
$968$	2.89571e111	0.310048
$969$	−9.39787e110	−0.0968028
$970$	1.20786e111	0.119695
$971$	−1.46304e112	−1.39487	−0.697436	−	0.716647i	$-0.745676\pi$
$971$	−1.46304e112	−1.39487	−0.697436	+	0.716647i	$0.745676\pi$
$972$	4.91821e111	0.451151
$973$	4.17280e111	0.368296
$974$	4.33256e111	0.367946
$975$	−2.69878e111	−0.220544
$976$	−5.73487e111	−0.450978
$977$	−5.34284e111	−0.404321	−0.202161	−	0.979352i	$-0.564796\pi$
$977$	−5.34284e111	−0.404321	−0.202161	+	0.979352i	$0.564796\pi$
$978$	−7.35849e110	−0.0535897
$979$	1.13212e112	0.793492
$980$	−6.03475e111	−0.407082
$981$	−2.68778e111	−0.174504
$982$	2.06641e111	0.129133
$983$	−2.30266e111	−0.138508	−0.0692538	−	0.997599i	$-0.522062\pi$
$983$	−2.30266e111	−0.138508	−0.0692538	+	0.997599i	$0.522062\pi$
$984$	1.77937e112	1.03027
$985$	1.30206e112	0.725728
$986$	−1.50579e111	−0.0807941
$987$	−1.99191e112	−1.02891
$988$	1.50009e112	0.745988
$989$	1.86811e112	0.894421
$990$	−2.46184e111	−0.113485
$991$	2.38412e112	1.05820	0.529098	−	0.848560i	$-0.322530\pi$
$991$	2.38412e112	1.05820	0.529098	+	0.848560i	$0.322530\pi$
$992$	−1.95761e112	−0.836639
$993$	3.89014e112	1.60091
$994$	1.01705e112	0.403045
$995$	−4.16789e112	−1.59056
$996$	−2.31237e112	−0.849832
$997$	−3.57199e112	−1.26427	−0.632137	−	0.774856i	$-0.717822\pi$
$997$	−3.57199e112	−1.26427	−0.632137	+	0.774856i	$0.717822\pi$
$998$	−1.66185e112	−0.566497
$999$	5.17044e112	1.69755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.76.a.a.1.4	✓	6
3.2	odd	2		9.76.a.c.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.4	✓	6	1.1	even	1	trivial
9.76.a.c.1.3		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+9.60898e10 q^{2} -6.47242e17 q^{3} -2.85457e22 q^{4} -1.49650e26 q^{5} -6.21934e28 q^{6} -3.16100e31 q^{7} -6.37312e33 q^{8} -1.89344e35 q^{9} -1.43799e37 q^{10} -9.04175e38 q^{11} +1.84760e40 q^{12} -1.02333e42 q^{13} -3.03740e42 q^{14} +9.68599e43 q^{15} +4.66033e44 q^{16} +2.82749e45 q^{17} -1.81941e46 q^{18} +5.13524e47 q^{19} +4.27187e48 q^{20} +2.04593e49 q^{21} -8.68820e49 q^{22} -1.06901e51 q^{23} +4.12495e51 q^{24} -4.07461e51 q^{25} -9.83316e52 q^{26} +5.16248e53 q^{27} +9.02328e53 q^{28} -5.54224e54 q^{29} +9.30725e54 q^{30} -6.85555e55 q^{31} +2.85551e56 q^{32} +5.85220e56 q^{33} +2.71693e56 q^{34} +4.73044e57 q^{35} +5.40496e57 q^{36} +1.00154e59 q^{37} +4.93445e58 q^{38} +6.62342e59 q^{39} +9.53739e59 q^{40} +4.31368e60 q^{41} +1.96593e60 q^{42} -1.74752e61 q^{43} +2.58103e61 q^{44} +2.83354e61 q^{45} -1.02721e62 q^{46} -9.73598e62 q^{47} -3.01636e62 q^{48} -1.41267e63 q^{49} -3.91528e62 q^{50} -1.83007e63 q^{51} +2.92116e64 q^{52} -2.55811e63 q^{53} +4.96061e64 q^{54} +1.35310e65 q^{55} +2.01454e65 q^{56} -3.32375e65 q^{57} -5.32553e65 q^{58} +5.98212e65 q^{59} -2.76493e66 q^{60} -1.23057e67 q^{61} -6.58749e66 q^{62} +5.98517e66 q^{63} +9.83229e66 q^{64} +1.53141e68 q^{65} +5.62337e67 q^{66} -9.36690e67 q^{67} -8.07127e67 q^{68} +6.91907e68 q^{69} +4.54547e68 q^{70} -3.34843e69 q^{71} +1.20671e69 q^{72} -1.44439e70 q^{73} +9.62381e69 q^{74} +2.63726e69 q^{75} -1.46589e70 q^{76} +2.85810e70 q^{77} +6.36444e70 q^{78} +1.89027e71 q^{79} -6.97419e70 q^{80} -2.18965e71 q^{81} +4.14501e71 q^{82} -1.25156e72 q^{83} -5.84025e71 q^{84} -4.23135e71 q^{85} -1.67919e72 q^{86} +3.58717e72 q^{87} +5.76242e72 q^{88} -1.25211e73 q^{89} +2.72275e72 q^{90} +3.23474e73 q^{91} +3.05156e73 q^{92} +4.43720e73 q^{93} -9.35529e73 q^{94} -7.68490e73 q^{95} -1.84820e74 q^{96} -8.39965e73 q^{97} -1.35744e74 q^{98} +1.71200e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3} + 17\!\cdots\!28 q^{4} - 38\!\cdots\!40 q^{5} + 31\!\cdots\!92 q^{6} + 19\!\cdots\!00 q^{7} + 44\!\cdots\!20 q^{8} + 21\!\cdots\!82 q^{9} + 13\!\cdots\!60 q^{10}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) \) 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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