LMFDB - Embedded newform 1.76.a.a.1.6

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			1.6
Root			$5.23553e9$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.67444e11 q^{2} -8.83049e17 q^{3} +9.72365e22 q^{4} +2.43619e26 q^{5} -3.24471e29 q^{6} +1.21530e31 q^{7} +2.18473e34 q^{8} +1.71508e35 q^{9} +8.95165e37 q^{10} -5.65037e38 q^{11} -8.58645e40 q^{12} +5.30382e40 q^{13} +4.46553e42 q^{14} -2.15128e44 q^{15} +4.35419e45 q^{16} +1.14821e45 q^{17} +6.30198e46 q^{18} +1.24645e48 q^{19} +2.36887e49 q^{20} -1.07316e49 q^{21} -2.07620e50 q^{22} +8.02205e50 q^{23} -1.92923e52 q^{24} +3.28805e52 q^{25} +1.94886e52 q^{26} +3.85679e53 q^{27} +1.18171e54 q^{28} +8.53673e54 q^{29} -7.90474e55 q^{30} -6.18737e55 q^{31} +7.74555e56 q^{32} +4.98956e56 q^{33} +4.21904e56 q^{34} +2.96069e57 q^{35} +1.66769e58 q^{36} -5.98766e58 q^{37} +4.58002e59 q^{38} -4.68354e58 q^{39} +5.32243e60 q^{40} -5.32628e60 q^{41} -3.94328e60 q^{42} +2.59254e61 q^{43} -5.49422e61 q^{44} +4.17827e61 q^{45} +2.94766e62 q^{46} -5.76440e62 q^{47} -3.84496e63 q^{48} -2.26417e63 q^{49} +1.20818e64 q^{50} -1.01393e63 q^{51} +5.15725e63 q^{52} +5.92558e63 q^{53} +1.41716e65 q^{54} -1.37654e65 q^{55} +2.65510e65 q^{56} -1.10068e66 q^{57} +3.13677e66 q^{58} +2.82712e66 q^{59} -2.09183e67 q^{60} +5.43239e66 q^{61} -2.27352e67 q^{62} +2.08433e66 q^{63} +1.20109e68 q^{64} +1.29211e67 q^{65} +1.83338e68 q^{66} -2.61376e68 q^{67} +1.11648e68 q^{68} -7.08386e68 q^{69} +1.08789e69 q^{70} +1.78760e67 q^{71} +3.74700e69 q^{72} -1.09051e70 q^{73} -2.20013e70 q^{74} -2.90351e70 q^{75} +1.21201e71 q^{76} -6.86687e69 q^{77} -1.72094e70 q^{78} -1.49375e71 q^{79} +1.06076e72 q^{80} -4.44896e71 q^{81} -1.95711e72 q^{82} +3.39100e71 q^{83} -1.04351e72 q^{84} +2.79727e71 q^{85} +9.52613e72 q^{86} -7.53835e72 q^{87} -1.23446e73 q^{88} +2.45405e72 q^{89} +1.53528e73 q^{90} +6.44571e71 q^{91} +7.80036e73 q^{92} +5.46375e73 q^{93} -2.11810e74 q^{94} +3.03660e74 q^{95} -6.83970e74 q^{96} +1.36838e74 q^{97} -8.31957e74 q^{98} -9.69086e73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.67444e11	1.89046	0.945229	−	0.326409i	$-0.105839\pi$
$2$	3.67444e11	1.89046	0.945229	+	0.326409i	$0.105839\pi$
$3$	−8.83049e17	−1.13224	−0.566119	−	0.824324i	$-0.691556\pi$
$3$	−8.83049e17	−1.13224	−0.566119	+	0.824324i	$0.691556\pi$
$4$	9.72365e22	2.57383
$5$	2.43619e26	1.49739	0.748697	−	0.662912i	$-0.230680\pi$
$5$	2.43619e26	1.49739	0.748697	+	0.662912i	$0.230680\pi$
$6$	−3.24471e29	−2.14045
$7$	1.21530e31	0.247460	0.123730	−	0.992316i	$-0.460514\pi$
$7$	1.21530e31	0.247460	0.123730	+	0.992316i	$0.460514\pi$
$8$	2.18473e34	2.97525
$9$	1.71508e35	0.281962
$10$	8.95165e37	2.83076
$11$	−5.65037e38	−0.501016	−0.250508	−	0.968115i	$-0.580598\pi$
$11$	−5.65037e38	−0.501016	−0.250508	+	0.968115i	$0.580598\pi$
$12$	−8.58645e40	−2.91419
$13$	5.30382e40	0.0894774	0.0447387	−	0.998999i	$-0.485754\pi$
$13$	5.30382e40	0.0894774	0.0447387	+	0.998999i	$0.485754\pi$
$14$	4.46553e42	0.467813
$15$	−2.15128e44	−1.69541
$16$	4.35419e45	3.05076
$17$	1.14821e45	0.0828300	0.0414150	−	0.999142i	$-0.486813\pi$
$17$	1.14821e45	0.0828300	0.0414150	+	0.999142i	$0.486813\pi$
$18$	6.30198e46	0.533038
$19$	1.24645e48	1.38808	0.694042	−	0.719935i	$-0.255828\pi$
$19$	1.24645e48	1.38808	0.694042	+	0.719935i	$0.255828\pi$
$20$	2.36887e49	3.85404
$21$	−1.07316e49	−0.280184
$22$	−2.07620e50	−0.947149
$23$	8.02205e50	0.691022	0.345511	−	0.938415i	$-0.387706\pi$
$23$	8.02205e50	0.691022	0.345511	+	0.938415i	$0.387706\pi$
$24$	−1.92923e52	−3.36869
$25$	3.28805e52	1.24219
$26$	1.94886e52	0.169153
$27$	3.85679e53	0.812989
$28$	1.18171e54	0.636920
$29$	8.53673e54	1.23415	0.617073	−	0.786906i	$-0.288318\pi$
$29$	8.53673e54	1.23415	0.617073	+	0.786906i	$0.288318\pi$
$30$	−7.90474e55	−3.20509
$31$	−6.18737e55	−0.733572	−0.366786	−	0.930305i	$-0.619542\pi$
$31$	−6.18737e55	−0.733572	−0.366786	+	0.930305i	$0.619542\pi$
$32$	7.74555e56	2.79208
$33$	4.98956e56	0.567269
$34$	4.21904e56	0.156587
$35$	2.96069e57	0.370546
$36$	1.66769e58	0.725723
$37$	−5.98766e58	−0.932594	−0.466297	−	0.884628i	$-0.654412\pi$
$37$	−5.98766e58	−0.932594	−0.466297	+	0.884628i	$0.654412\pi$
$38$	4.58002e59	2.62411
$39$	−4.68354e58	−0.101310
$40$	5.32243e60	4.45513
$41$	−5.32628e60	−1.76616	−0.883079	−	0.469224i	$-0.844534\pi$
$41$	−5.32628e60	−1.76616	−0.883079	+	0.469224i	$0.844534\pi$
$42$	−3.94328e60	−0.529675
$43$	2.59254e61	1.44098	0.720489	−	0.693466i	$-0.243917\pi$
$43$	2.59254e61	1.44098	0.720489	+	0.693466i	$0.243917\pi$
$44$	−5.49422e61	−1.28953
$45$	4.17827e61	0.422209
$46$	2.94766e62	1.30635
$47$	−5.76440e62	−1.14047	−0.570236	−	0.821481i	$-0.693148\pi$
$47$	−5.76440e62	−1.14047	−0.570236	+	0.821481i	$0.693148\pi$
$48$	−3.84496e63	−3.45419
$49$	−2.26417e63	−0.938763
$50$	1.20818e64	2.34831
$51$	−1.01393e63	−0.0937833
$52$	5.15725e63	0.230299
$53$	5.92558e63	0.129535	0.0647673	−	0.997900i	$-0.479370\pi$
$53$	5.92558e63	0.129535	0.0647673	+	0.997900i	$0.479370\pi$
$54$	1.41716e65	1.53692
$55$	−1.37654e65	−0.750219
$56$	2.65510e65	0.736257
$57$	−1.10068e66	−1.57164
$58$	3.13677e66	2.33310
$59$	2.82712e66	1.10763	0.553814	−	0.832640i	$-0.313172\pi$
$59$	2.82712e66	1.10763	0.553814	+	0.832640i	$0.313172\pi$
$60$	−2.09183e67	−4.36369
$61$	5.43239e66	0.609708	0.304854	−	0.952399i	$-0.401392\pi$
$61$	5.43239e66	0.609708	0.304854	+	0.952399i	$0.401392\pi$
$62$	−2.27352e67	−1.38679
$63$	2.08433e66	0.0697745
$64$	1.20109e68	2.22755
$65$	1.29211e67	0.133983
$66$	1.83338e68	1.07240
$67$	−2.61376e68	−0.869883	−0.434941	−	0.900459i	$-0.643231\pi$
$67$	−2.61376e68	−0.869883	−0.434941	+	0.900459i	$0.643231\pi$
$68$	1.11648e68	0.213190
$69$	−7.08386e68	−0.782401
$70$	1.08789e69	0.700501
$71$	1.78760e67	0.00676213	0.00338106	−	0.999994i	$-0.498924\pi$
$71$	1.78760e67	0.00676213	0.00338106	+	0.999994i	$0.498924\pi$
$72$	3.74700e69	0.838910
$73$	−1.09051e70	−1.45554	−0.727770	−	0.685821i	$-0.759443\pi$
$73$	−1.09051e70	−1.45554	−0.727770	+	0.685821i	$0.759443\pi$
$74$	−2.20013e70	−1.76303
$75$	−2.90351e70	−1.40646
$76$	1.21201e71	3.57269
$77$	−6.86687e69	−0.123981
$78$	−1.72094e70	−0.191522
$79$	−1.49375e71	−1.03101	−0.515504	−	0.856887i	$-0.672395\pi$
$79$	−1.49375e71	−1.03101	−0.515504	+	0.856887i	$0.672395\pi$
$80$	1.06076e72	4.56820
$81$	−4.44896e71	−1.20246
$82$	−1.95711e72	−3.33885
$83$	3.39100e71	0.367197	0.183599	−	0.983001i	$-0.441225\pi$
$83$	3.39100e71	0.367197	0.183599	+	0.983001i	$0.441225\pi$
$84$	−1.04351e72	−0.721145
$85$	2.79727e71	0.124029
$86$	9.52613e72	2.72411
$87$	−7.53835e72	−1.39735
$88$	−1.23446e73	−1.49065
$89$	2.45405e72	0.193981	0.0969905	−	0.995285i	$-0.469078\pi$
$89$	2.45405e72	0.193981	0.0969905	+	0.995285i	$0.469078\pi$
$90$	1.53528e73	0.798168
$91$	6.44571e71	0.0221421
$92$	7.80036e73	1.77857
$93$	5.46375e73	0.830578
$94$	−2.11810e74	−2.15601
$95$	3.03660e74	2.07851
$96$	−6.83970e74	−3.16130
$97$	1.36838e74	0.428811	0.214405	−	0.976745i	$-0.431219\pi$
$97$	1.36838e74	0.428811	0.214405	+	0.976745i	$0.431219\pi$
$98$	−8.31957e74	−1.77469
$99$	−9.69086e73	−0.141268
$100$	3.19719e75	3.19719
$101$	−2.90130e74	−0.199775	−0.0998875	−	0.994999i	$-0.531848\pi$
$101$	−2.90130e74	−0.199775	−0.0998875	+	0.994999i	$0.531848\pi$
$102$	−3.72562e74	−0.177293
$103$	4.39725e74	0.145139	0.0725696	−	0.997363i	$-0.476880\pi$
$103$	4.39725e74	0.145139	0.0725696	+	0.997363i	$0.476880\pi$
$104$	1.15874e75	0.266218
$105$	−2.61444e75	−0.419546
$106$	2.17732e75	0.244879
$107$	−1.61246e76	−1.27526	−0.637629	−	0.770344i	$-0.720085\pi$
$107$	−1.61246e76	−1.27526	−0.637629	+	0.770344i	$0.720085\pi$
$108$	3.75021e76	2.09249
$109$	−3.51780e76	−1.38924	−0.694620	−	0.719376i	$-0.744428\pi$
$109$	−3.51780e76	−1.38924	−0.694620	+	0.719376i	$0.744428\pi$
$110$	−5.05802e76	−1.41826
$111$	5.28740e76	1.05592
$112$	5.29163e76	0.754942
$113$	−3.77510e76	−0.385911	−0.192955	−	0.981208i	$-0.561807\pi$
$113$	−3.77510e76	−0.385911	−0.192955	+	0.981208i	$0.561807\pi$
$114$	−4.04438e77	−2.97112
$115$	1.95433e77	1.03473
$116$	8.30081e77	3.17648
$117$	9.09650e75	0.0252293
$118$	1.03881e78	2.09392
$119$	1.39542e76	0.0204971
$120$	−4.69997e78	−5.04427
$121$	−9.52628e77	−0.748983
$122$	1.99610e78	1.15263
$123$	4.70337e78	1.99971
$124$	−6.01638e78	−1.88809
$125$	1.56178e78	0.362656
$126$	7.65876e77	0.131906
$127$	5.76725e78	0.738464	0.369232	−	0.929337i	$-0.379621\pi$
$127$	5.76725e78	0.738464	0.369232	+	0.929337i	$0.379621\pi$
$128$	1.48716e79	1.41900
$129$	−2.28934e79	−1.63153
$130$	4.74780e78	0.253289
$131$	−1.75382e79	−0.701960	−0.350980	−	0.936383i	$-0.614151\pi$
$131$	−1.75382e79	−0.701960	−0.350980	+	0.936383i	$0.614151\pi$
$132$	4.85167e79	1.46005
$133$	1.51481e79	0.343495
$134$	−9.60412e79	−1.64448
$135$	9.39588e79	1.21737
$136$	2.50854e79	0.246440
$137$	−2.46770e80	−1.84192	−0.920961	−	0.389654i	$-0.872595\pi$
$137$	−2.46770e80	−1.84192	−0.920961	+	0.389654i	$0.872595\pi$
$138$	−2.60293e80	−1.47910
$139$	7.49076e79	0.324691	0.162346	−	0.986734i	$-0.448094\pi$
$139$	7.49076e79	0.324691	0.162346	+	0.986734i	$0.448094\pi$
$140$	2.87887e80	0.953721
$141$	5.09025e80	1.29129
$142$	6.56845e78	0.0127835
$143$	−2.99686e79	−0.0448296
$144$	7.46780e80	0.860200
$145$	2.07971e81	1.84800
$146$	−4.00704e81	−2.75164
$147$	1.99937e81	1.06290
$148$	−5.82219e81	−2.40034
$149$	3.07560e81	0.985020	0.492510	−	0.870307i	$-0.336080\pi$
$149$	3.07560e81	0.985020	0.492510	+	0.870307i	$0.336080\pi$
$150$	−1.06688e82	−2.65884
$151$	−1.13847e81	−0.221151	−0.110575	−	0.993868i	$-0.535269\pi$
$151$	−1.13847e81	−0.221151	−0.110575	+	0.993868i	$0.535269\pi$
$152$	2.72317e82	4.12990
$153$	1.96928e80	0.0233550
$154$	−2.52319e81	−0.234382
$155$	−1.50736e82	−1.09845
$156$	−4.55410e81	−0.260754
$157$	2.14834e82	0.967979	0.483989	−	0.875074i	$-0.339187\pi$
$157$	2.14834e82	0.967979	0.483989	+	0.875074i	$0.339187\pi$
$158$	−5.48870e82	−1.94908
$159$	−5.23257e81	−0.146664
$160$	1.88696e83	4.18085
$161$	9.74916e81	0.171000
$162$	−1.63475e83	−2.27320
$163$	1.14457e83	1.26359	0.631795	−	0.775135i	$-0.282318\pi$
$163$	1.14457e83	1.26359	0.631795	+	0.775135i	$0.282318\pi$
$164$	−5.17909e83	−4.54579
$165$	1.21555e83	0.849426
$166$	1.24600e83	0.694171
$167$	3.68869e83	1.64061	0.820304	−	0.571928i	$-0.193804\pi$
$167$	3.68869e83	1.64061	0.820304	+	0.571928i	$0.193804\pi$
$168$	−2.34458e83	−0.833618
$169$	−3.48546e83	−0.991994
$170$	1.02784e83	0.234472
$171$	2.13777e83	0.391387
$172$	2.52089e84	3.70883
$173$	4.14388e83	0.490544	0.245272	−	0.969454i	$-0.421123\pi$
$173$	4.14388e83	0.490544	0.245272	+	0.969454i	$0.421123\pi$
$174$	−2.76992e84	−2.64162
$175$	3.99596e83	0.307393
$176$	−2.46028e84	−1.52848
$177$	−2.49649e84	−1.25410
$178$	9.01729e83	0.366713
$179$	1.08783e84	0.358570	0.179285	−	0.983797i	$-0.442622\pi$
$179$	1.08783e84	0.358570	0.179285	+	0.983797i	$0.442622\pi$
$180$	4.06280e84	1.08669
$181$	−2.20049e84	−0.478161	−0.239080	−	0.971000i	$-0.576846\pi$
$181$	−2.20049e84	−0.478161	−0.239080	+	0.971000i	$0.576846\pi$
$182$	2.36844e83	0.0418587
$183$	−4.79706e84	−0.690335
$184$	1.75260e85	2.05596
$185$	−1.45871e85	−1.39646
$186$	2.00763e85	1.57017
$187$	−6.48783e83	−0.0414992
$188$	−5.60510e85	−2.93538
$189$	4.68714e84	0.201182
$190$	1.11578e86	3.92933
$191$	−8.56878e84	−0.247838	−0.123919	−	0.992292i	$-0.539546\pi$
$191$	−8.56878e84	−0.247838	−0.123919	+	0.992292i	$0.539546\pi$
$192$	−1.06062e86	−2.52211
$193$	2.83853e85	0.555513	0.277756	−	0.960652i	$-0.410409\pi$
$193$	2.83853e85	0.555513	0.277756	+	0.960652i	$0.410409\pi$
$194$	5.02802e85	0.810648
$195$	−1.14100e85	−0.151701
$196$	−2.20160e86	−2.41622
$197$	−1.39395e86	−1.26405	−0.632024	−	0.774949i	$-0.717776\pi$
$197$	−1.39395e86	−1.26405	−0.632024	+	0.774949i	$0.717776\pi$
$198$	−3.56085e85	−0.267060
$199$	1.12515e86	0.698587	0.349294	−	0.937013i	$-0.386422\pi$
$199$	1.12515e86	0.698587	0.349294	+	0.937013i	$0.386422\pi$
$200$	7.18352e86	3.69583
$201$	2.30808e86	0.984914
$202$	−1.06607e86	−0.377666
$203$	1.03746e86	0.305402
$204$	−9.85908e85	−0.241382
$205$	−1.29758e87	−2.64464
$206$	1.61574e86	0.274379
$207$	1.37585e86	0.194842
$208$	2.30939e86	0.272974
$209$	−7.04292e86	−0.695452
$210$	−9.60660e86	−0.793133
$211$	1.53042e87	1.05735	0.528675	−	0.848824i	$-0.322689\pi$
$211$	1.53042e87	1.05735	0.528675	+	0.848824i	$0.322689\pi$
$212$	5.76182e86	0.333400
$213$	−1.57854e85	−0.00765634
$214$	−5.92490e87	−2.41082
$215$	6.31591e87	2.15771
$216$	8.42606e87	2.41885
$217$	−7.51948e86	−0.181530
$218$	−1.29260e88	−2.62630
$219$	9.62978e87	1.64802
$220$	−1.33850e88	−1.93093
$221$	6.08992e85	0.00741142
$222$	1.94283e88	1.99617
$223$	−5.54993e87	−0.481787	−0.240893	−	0.970552i	$-0.577440\pi$
$223$	−5.54993e87	−0.481787	−0.240893	+	0.970552i	$0.577440\pi$
$224$	9.41313e87	0.690929
$225$	5.63929e87	0.350251
$226$	−1.38714e88	−0.729548
$227$	−5.62742e87	−0.250807	−0.125403	−	0.992106i	$-0.540023\pi$
$227$	−5.62742e87	−0.250807	−0.125403	+	0.992106i	$0.540023\pi$
$228$	−1.07026e89	−4.04513
$229$	−5.39160e86	−0.0172937	−0.00864684	−	0.999963i	$-0.502752\pi$
$229$	−5.39160e86	−0.0172937	−0.00864684	+	0.999963i	$0.502752\pi$
$230$	7.18106e88	1.95612
$231$	6.06378e87	0.140377
$232$	1.86505e89	3.67190
$233$	−1.05527e89	−1.76814	−0.884072	−	0.467351i	$-0.845209\pi$
$233$	−1.05527e89	−1.76814	−0.884072	+	0.467351i	$0.845209\pi$
$234$	3.34246e87	0.0476948
$235$	−1.40432e89	−1.70774
$236$	2.74899e89	2.85085
$237$	1.31905e89	1.16735
$238$	5.12738e87	0.0387490
$239$	−1.07654e89	−0.695201	−0.347600	−	0.937643i	$-0.613003\pi$
$239$	−1.07654e89	−0.695201	−0.347600	+	0.937643i	$0.613003\pi$
$240$	−9.36707e89	−5.17228
$241$	3.81853e89	1.80409	0.902043	−	0.431647i	$-0.142067\pi$
$241$	3.81853e89	1.80409	0.902043	+	0.431647i	$0.142067\pi$
$242$	−3.50038e89	−1.41592
$243$	1.58269e89	0.548481
$244$	5.28226e89	1.56928
$245$	−5.51595e89	−1.40570
$246$	1.72823e90	3.78037
$247$	6.61097e88	0.124202
$248$	−1.35178e90	−2.18256
$249$	−2.99442e89	−0.415755
$250$	5.73868e89	0.685586
$251$	−4.93768e89	−0.507877	−0.253939	−	0.967220i	$-0.581726\pi$
$251$	−4.93768e89	−0.507877	−0.253939	+	0.967220i	$0.581726\pi$
$252$	2.02673e89	0.179587
$253$	−4.53276e89	−0.346213
$254$	2.11915e90	1.39603
$255$	−2.47012e89	−0.140431
$256$	9.26877e89	0.455012
$257$	3.14677e90	1.33467	0.667334	−	0.744759i	$-0.267435\pi$
$257$	3.14677e90	1.33467	0.667334	+	0.744759i	$0.267435\pi$
$258$	−8.41203e90	−3.08434
$259$	−7.27678e89	−0.230780
$260$	1.25641e90	0.344849
$261$	1.46412e90	0.347983
$262$	−6.44433e90	−1.32702
$263$	−4.16943e90	−0.744279	−0.372140	−	0.928177i	$-0.621376\pi$
$263$	−4.16943e90	−0.744279	−0.372140	+	0.928177i	$0.621376\pi$
$264$	1.09009e91	1.68777
$265$	1.44358e90	0.193964
$266$	5.56608e90	0.649363
$267$	−2.16705e90	−0.219633
$268$	−2.54153e91	−2.23893
$269$	1.97317e91	1.51166	0.755829	−	0.654769i	$-0.227234\pi$
$269$	1.97317e91	1.51166	0.755829	+	0.654769i	$0.227234\pi$
$270$	3.45246e91	2.30138
$271$	2.23482e91	1.29686	0.648432	−	0.761273i	$-0.275425\pi$
$271$	2.23482e91	1.29686	0.648432	+	0.761273i	$0.275425\pi$
$272$	4.99954e90	0.252695
$273$	−5.69188e89	−0.0250701
$274$	−9.06743e91	−3.48208
$275$	−1.85787e91	−0.622358
$276$	−6.88810e91	−2.01376
$277$	3.38744e91	0.864729	0.432365	−	0.901699i	$-0.357679\pi$
$277$	3.38744e91	0.864729	0.432365	+	0.901699i	$0.357679\pi$
$278$	2.75244e91	0.613815
$279$	−1.06119e91	−0.206840
$280$	6.46833e91	1.10247
$281$	−7.17828e91	−1.07037	−0.535184	−	0.844735i	$-0.679758\pi$
$281$	−7.17828e91	−1.07037	−0.535184	+	0.844735i	$0.679758\pi$
$282$	1.87038e92	2.44112
$283$	1.11121e92	1.27000	0.635000	−	0.772512i	$-0.281000\pi$
$283$	1.11121e92	1.27000	0.635000	+	0.772512i	$0.281000\pi$
$284$	1.73820e90	0.0174046
$285$	−2.68146e92	−2.35337
$286$	−1.10118e91	−0.0847484
$287$	−6.47300e91	−0.437054
$288$	1.32843e92	0.787262
$289$	−1.90844e92	−0.993139
$290$	7.64178e92	3.49357
$291$	−1.20834e92	−0.485515
$292$	−1.06038e93	−3.74631
$293$	4.84927e91	0.150709	0.0753547	−	0.997157i	$-0.475991\pi$
$293$	4.84927e91	0.150709	0.0753547	+	0.997157i	$0.475991\pi$
$294$	7.34659e92	2.00937
$295$	6.88741e92	1.65856
$296$	−1.30815e93	−2.77470
$297$	−2.17923e92	−0.407321
$298$	1.13011e93	1.86214
$299$	4.25476e91	0.0618308
$300$	−2.82327e93	−3.61998
$301$	3.15070e92	0.356585
$302$	−4.18326e92	−0.418076
$303$	2.56199e92	0.226193
$304$	5.42729e93	4.23471
$305$	1.32343e93	0.912974
$306$	7.23601e91	0.0441515
$307$	−5.53608e92	−0.298891	−0.149446	−	0.988770i	$-0.547749\pi$
$307$	−5.53608e92	−0.298891	−0.149446	+	0.988770i	$0.547749\pi$
$308$	−6.67710e92	−0.319107
$309$	−3.88298e92	−0.164332
$310$	−5.53872e93	−2.07657
$311$	−3.84755e93	−1.27841	−0.639204	−	0.769037i	$-0.720736\pi$
$311$	−3.84755e93	−1.27841	−0.639204	+	0.769037i	$0.720736\pi$
$312$	−1.02323e93	−0.301422
$313$	2.85920e93	0.747019	0.373509	−	0.927626i	$-0.378154\pi$
$313$	2.85920e93	0.747019	0.373509	+	0.927626i	$0.378154\pi$
$314$	7.89395e93	1.82992
$315$	5.07784e92	0.104480
$316$	−1.45247e94	−2.65364
$317$	−7.23036e92	−0.117338	−0.0586688	−	0.998278i	$-0.518686\pi$
$317$	−7.23036e92	−0.117338	−0.0586688	+	0.998278i	$0.518686\pi$
$318$	−1.92268e93	−0.277262
$319$	−4.82357e93	−0.618327
$320$	2.92609e94	3.33552
$321$	1.42388e94	1.44389
$322$	3.58228e93	0.323269
$323$	1.43119e93	0.114975
$324$	−4.32601e94	−3.09492
$325$	1.74393e93	0.111148
$326$	4.20565e94	2.38876
$327$	3.10639e94	1.57295
$328$	−1.16365e95	−5.25477
$329$	−7.00545e93	−0.282221
$330$	4.46648e94	1.60580
$331$	−1.94545e94	−0.624409	−0.312205	−	0.950015i	$-0.601067\pi$
$331$	−1.94545e94	−0.624409	−0.312205	+	0.950015i	$0.601067\pi$
$332$	3.29729e94	0.945102
$333$	−1.02693e94	−0.262957
$334$	1.35539e95	3.10150
$335$	−6.36762e94	−1.30256
$336$	−4.67277e94	−0.854774
$337$	−6.36785e94	−1.04201	−0.521005	−	0.853554i	$-0.674443\pi$
$337$	−6.36785e94	−1.04201	−0.521005	+	0.853554i	$0.674443\pi$
$338$	−1.28071e95	−1.87532
$339$	3.33360e94	0.436943
$340$	2.71996e94	0.319230
$341$	3.49610e94	0.367531
$342$	7.85512e94	0.739901
$343$	−5.68276e94	−0.479767
$344$	5.66400e95	4.28728
$345$	−1.72577e95	−1.17156
$346$	1.52264e95	0.927353
$347$	2.45590e94	0.134232	0.0671160	−	0.997745i	$-0.478620\pi$
$347$	2.45590e94	0.134232	0.0671160	+	0.997745i	$0.478620\pi$
$348$	−7.33002e95	−3.59653
$349$	2.80433e94	0.123559	0.0617796	−	0.998090i	$-0.480322\pi$
$349$	2.80433e94	0.123559	0.0617796	+	0.998090i	$0.480322\pi$
$350$	1.46829e95	0.581113
$351$	2.04557e94	0.0727442
$352$	−4.37652e95	−1.39888
$353$	3.99820e95	1.14898	0.574491	−	0.818511i	$-0.305200\pi$
$353$	3.99820e95	1.14898	0.574491	+	0.818511i	$0.305200\pi$
$354$	−9.17320e95	−2.37082
$355$	4.35495e93	0.0101256
$356$	2.38624e95	0.499274
$357$	−1.23222e94	−0.0232076
$358$	3.99718e95	0.677860
$359$	7.73805e95	1.18192	0.590962	−	0.806699i	$-0.298748\pi$
$359$	7.73805e95	1.18192	0.590962	+	0.806699i	$0.298748\pi$
$360$	9.12841e95	1.25618
$361$	7.47301e95	0.926777
$362$	−8.08560e95	−0.903942
$363$	8.41217e95	0.848027
$364$	6.26758e94	0.0569899
$365$	−2.65670e96	−2.17952
$366$	−1.76265e96	−1.30505
$367$	5.77357e95	0.385893	0.192946	−	0.981209i	$-0.438196\pi$
$367$	5.77357e95	0.385893	0.192946	+	0.981209i	$0.438196\pi$
$368$	3.49296e96	2.10814
$369$	−9.13502e95	−0.497990
$370$	−5.35995e96	−2.63995
$371$	7.20132e94	0.0320546
$372$	5.31276e96	2.13776
$373$	3.37386e96	1.22757	0.613784	−	0.789474i	$-0.289646\pi$
$373$	3.37386e96	1.22757	0.613784	+	0.789474i	$0.289646\pi$
$374$	−2.38392e95	−0.0784524
$375$	−1.37913e96	−0.410613
$376$	−1.25937e97	−3.39319
$377$	4.52773e95	0.110428
$378$	1.72226e96	0.380327
$379$	−3.66618e96	−0.733235	−0.366618	−	0.930372i	$-0.619484\pi$
$379$	−3.66618e96	−0.733235	−0.366618	+	0.930372i	$0.619484\pi$
$380$	2.95268e97	5.34973
$381$	−5.09277e96	−0.836117
$382$	−3.14855e96	−0.468527
$383$	−7.65115e96	−1.03222	−0.516111	−	0.856522i	$-0.672621\pi$
$383$	−7.65115e96	−1.03222	−0.516111	+	0.856522i	$0.672621\pi$
$384$	−1.31323e97	−1.60665
$385$	−1.67290e96	−0.185649
$386$	1.04300e97	1.05017
$387$	4.44641e96	0.406302
$388$	1.33056e97	1.10368
$389$	2.43483e97	1.83383	0.916913	−	0.399087i	$-0.130673\pi$
$389$	2.43483e97	1.83383	0.916913	+	0.399087i	$0.130673\pi$
$390$	−4.19254e96	−0.286784
$391$	9.21102e95	0.0572373
$392$	−4.94661e97	−2.79306
$393$	1.54871e97	0.794785
$394$	−5.12199e97	−2.38963
$395$	−3.63906e97	−1.54383
$396$	−9.42305e96	−0.363599
$397$	5.68145e96	0.199441	0.0997207	−	0.995015i	$-0.468205\pi$
$397$	5.68145e96	0.199441	0.0997207	+	0.995015i	$0.468205\pi$
$398$	4.13431e97	1.32065
$399$	−1.33765e97	−0.388919
$400$	1.43168e98	3.78963
$401$	−2.25071e97	−0.542507	−0.271254	−	0.962508i	$-0.587438\pi$
$401$	−2.25071e97	−0.542507	−0.271254	+	0.962508i	$0.587438\pi$
$402$	8.48090e97	1.86194
$403$	−3.28167e96	−0.0656381
$404$	−2.82112e97	−0.514187
$405$	−1.08385e98	−1.80056
$406$	3.81211e97	0.577349
$407$	3.38325e97	0.467245
$408$	−2.21516e97	−0.279029
$409$	4.79631e97	0.551168	0.275584	−	0.961277i	$-0.411129\pi$
$409$	4.79631e97	0.551168	0.275584	+	0.961277i	$0.411129\pi$
$410$	−4.76790e98	−4.99957
$411$	2.17910e98	2.08549
$412$	4.27573e97	0.373563
$413$	3.43579e97	0.274094
$414$	5.05548e97	0.368341
$415$	8.26113e97	0.549839
$416$	4.10810e97	0.249828
$417$	−6.61470e97	−0.367628
$418$	−2.58788e98	−1.31472
$419$	2.11564e98	0.982688	0.491344	−	0.870966i	$-0.336506\pi$
$419$	2.11564e98	0.982688	0.491344	+	0.870966i	$0.336506\pi$
$420$	−2.54219e98	−1.07984
$421$	−2.18038e97	−0.0847137	−0.0423569	−	0.999103i	$-0.513487\pi$
$421$	−2.18038e97	−0.0847137	−0.0423569	+	0.999103i	$0.513487\pi$
$422$	5.62345e98	1.99887
$423$	−9.88643e97	−0.321570
$424$	1.29458e98	0.385398
$425$	3.77539e97	0.102891
$426$	−5.80027e96	−0.0144740
$427$	6.60196e97	0.150878
$428$	−1.56790e99	−3.28229
$429$	2.64637e97	0.0507578
$430$	2.32075e99	4.07907
$431$	−3.92051e98	−0.631605	−0.315802	−	0.948825i	$-0.602274\pi$
$431$	−3.92051e98	−0.631605	−0.315802	+	0.948825i	$0.602274\pi$
$432$	1.67932e99	2.48024
$433$	−9.09183e98	−1.23128	−0.615638	−	0.788029i	$-0.711102\pi$
$433$	−9.09183e98	−1.23128	−0.615638	+	0.788029i	$0.711102\pi$
$434$	−2.76299e98	−0.343174
$435$	−1.83649e99	−2.09238
$436$	−3.42058e99	−3.57567
$437$	9.99911e98	0.959196
$438$	3.53841e99	3.11551
$439$	−9.19604e98	−0.743330	−0.371665	−	0.928367i	$-0.621213\pi$
$439$	−9.19604e98	−0.743330	−0.371665	+	0.928367i	$0.621213\pi$
$440$	−3.00737e99	−2.23209
$441$	−3.88324e98	−0.264696
$442$	2.23771e97	0.0140110
$443$	3.04060e99	1.74912	0.874561	−	0.484915i	$-0.161150\pi$
$443$	3.04060e99	1.74912	0.874561	+	0.484915i	$0.161150\pi$
$444$	5.14128e99	2.71775
$445$	5.97855e98	0.290466
$446$	−2.03929e99	−0.910798
$447$	−2.71591e99	−1.11528
$448$	1.45968e99	0.551229
$449$	1.16326e99	0.404055	0.202027	−	0.979380i	$-0.435247\pi$
$449$	1.16326e99	0.404055	0.202027	+	0.979380i	$0.435247\pi$
$450$	2.07212e99	0.662135
$451$	3.00955e99	0.884873
$452$	−3.67077e99	−0.993268
$453$	1.00533e99	0.250395
$454$	−2.06776e99	−0.474140
$455$	1.57030e98	0.0331555
$456$	−2.40469e100	−4.67603
$457$	2.88576e99	0.516895	0.258447	−	0.966025i	$-0.416789\pi$
$457$	2.88576e99	0.516895	0.258447	+	0.966025i	$0.416789\pi$
$458$	−1.98111e98	−0.0326929
$459$	4.42842e98	0.0673399
$460$	1.90032e100	2.66322
$461$	−8.99071e99	−1.16147	−0.580737	−	0.814092i	$-0.697235\pi$
$461$	−8.99071e99	−1.16147	−0.580737	+	0.814092i	$0.697235\pi$
$462$	2.22810e99	0.265376
$463$	4.13924e98	0.0454604	0.0227302	−	0.999742i	$-0.492764\pi$
$463$	4.13924e98	0.0454604	0.0227302	+	0.999742i	$0.492764\pi$
$464$	3.71706e100	3.76509
$465$	1.33107e100	1.24370
$466$	−3.87754e100	−3.34260
$467$	1.66999e99	0.132840	0.0664202	−	0.997792i	$-0.478842\pi$
$467$	1.66999e99	0.132840	0.0664202	+	0.997792i	$0.478842\pi$
$468$	8.84512e98	0.0649358
$469$	−3.17649e99	−0.215261
$470$	−5.16009e100	−3.22840
$471$	−1.89709e100	−1.09598
$472$	6.17651e100	3.29548
$473$	−1.46488e100	−0.721953
$474$	4.84679e100	2.20682
$475$	4.09840e100	1.72427
$476$	1.35685e99	0.0527561
$477$	1.01629e99	0.0365239
$478$	−3.95570e100	−1.31425
$479$	−3.76475e99	−0.115652	−0.0578262	−	0.998327i	$-0.518417\pi$
$479$	−3.76475e99	−0.115652	−0.0578262	+	0.998327i	$0.518417\pi$
$480$	−1.66628e101	−4.73371
$481$	−3.17575e99	−0.0834461
$482$	1.40310e101	3.41055
$483$	−8.60899e99	−0.193613
$484$	−9.26302e100	−1.92775
$485$	3.33363e100	0.642099
$486$	5.81552e100	1.03688
$487$	−4.27929e100	−0.706376	−0.353188	−	0.935552i	$-0.614902\pi$
$487$	−4.27929e100	−0.706376	−0.353188	+	0.935552i	$0.614902\pi$
$488$	1.18683e101	1.81404
$489$	−1.01071e101	−1.43068
$490$	−2.02681e101	−2.65741
$491$	7.91421e100	0.961284	0.480642	−	0.876917i	$-0.340404\pi$
$491$	7.91421e100	0.961284	0.480642	+	0.876917i	$0.340404\pi$
$492$	4.57339e101	5.14691
$493$	9.80198e99	0.102224
$494$	2.42916e100	0.234799
$495$	−2.36088e100	−0.211533
$496$	−2.69410e101	−2.23795
$497$	2.17247e98	0.00167336
$498$	−1.10028e101	−0.785966
$499$	1.93019e101	1.27888	0.639441	−	0.768840i	$-0.279166\pi$
$499$	1.93019e101	1.27888	0.639441	+	0.768840i	$0.279166\pi$
$500$	1.51862e101	0.933415
$501$	−3.25729e101	−1.85756
$502$	−1.81432e101	−0.960120
$503$	−3.34549e101	−1.64308	−0.821542	−	0.570147i	$-0.806886\pi$
$503$	−3.34549e101	−1.64308	−0.821542	+	0.570147i	$0.806886\pi$
$504$	4.55371e100	0.207597
$505$	−7.06813e100	−0.299142
$506$	−1.66554e101	−0.654500
$507$	3.07783e101	1.12317
$508$	5.60787e101	1.90068
$509$	2.90608e101	0.914935	0.457467	−	0.889226i	$-0.348757\pi$
$509$	2.90608e101	0.914935	0.457467	+	0.889226i	$0.348757\pi$
$510$	−9.07633e100	−0.265478
$511$	−1.32530e101	−0.360188
$512$	−2.21256e101	−0.558819
$513$	4.80731e101	1.12850
$514$	1.15626e102	2.52313
$515$	1.07125e101	0.217331
$516$	−2.22607e102	−4.19928
$517$	3.25710e101	0.571394
$518$	−2.67381e101	−0.436280
$519$	−3.65925e101	−0.555413
$520$	2.82292e101	0.398634
$521$	9.37841e101	1.23230	0.616148	−	0.787631i	$-0.288692\pi$
$521$	9.37841e101	1.23230	0.616148	+	0.787631i	$0.288692\pi$
$522$	5.37983e101	0.657846
$523$	7.17575e101	0.816684	0.408342	−	0.912829i	$-0.366107\pi$
$523$	7.17575e101	0.816684	0.408342	+	0.912829i	$0.366107\pi$
$524$	−1.70536e102	−1.80672
$525$	−3.52862e101	−0.348042
$526$	−1.53203e102	−1.40703
$527$	−7.10442e100	−0.0607618
$528$	2.17255e102	1.73060
$529$	−7.04150e101	−0.522489
$530$	5.30437e101	0.366681
$531$	4.84875e101	0.312310
$532$	1.47295e102	0.884098
$533$	−2.82497e101	−0.158031
$534$	−7.96271e101	−0.415206
$535$	−3.92827e102	−1.90956
$536$	−5.71037e102	−2.58812
$537$	−9.60609e101	−0.405986
$538$	7.25030e102	2.85773
$539$	1.27934e102	0.470335
$540$	9.13622e102	3.13329
$541$	−4.17380e102	−1.33547	−0.667734	−	0.744400i	$-0.732736\pi$
$541$	−4.17380e102	−1.33547	−0.667734	+	0.744400i	$0.732736\pi$
$542$	8.21173e102	2.45167
$543$	1.94314e102	0.541392
$544$	8.89354e101	0.231268
$545$	−8.57004e102	−2.08024
$546$	−2.09145e101	−0.0473940
$547$	5.04913e102	1.06830	0.534148	−	0.845391i	$-0.320633\pi$
$547$	5.04913e102	1.06830	0.534148	+	0.845391i	$0.320633\pi$
$548$	−2.39951e103	−4.74079
$549$	9.31700e101	0.171915
$550$	−6.82665e102	−1.17654
$551$	1.06406e103	1.71310
$552$	−1.54764e103	−2.32784
$553$	−1.81535e102	−0.255133
$554$	1.24470e103	1.63473
$555$	1.28811e103	1.58113
$556$	7.28375e102	0.835700
$557$	2.22240e102	0.238371	0.119185	−	0.992872i	$-0.461972\pi$
$557$	2.22240e102	0.238371	0.119185	+	0.992872i	$0.461972\pi$
$558$	−3.89927e102	−0.391022
$559$	1.37504e102	0.128935
$560$	1.28914e103	1.13045
$561$	5.72907e101	0.0469869
$562$	−2.63762e103	−2.02349
$563$	−2.54936e103	−1.82964	−0.914822	−	0.403858i	$-0.867669\pi$
$563$	−2.54936e103	−1.82964	−0.914822	+	0.403858i	$0.867669\pi$
$564$	4.94958e103	3.32355
$565$	−9.19687e102	−0.577861
$566$	4.08307e103	2.40088
$567$	−5.40680e102	−0.297561
$568$	3.90544e101	0.0201191
$569$	−6.38673e102	−0.308013	−0.154006	−	0.988070i	$-0.549218\pi$
$569$	−6.38673e102	−0.308013	−0.154006	+	0.988070i	$0.549218\pi$
$570$	−9.85289e103	−4.44894
$571$	2.66278e103	1.12585	0.562925	−	0.826508i	$-0.309676\pi$
$571$	2.66278e103	1.12585	0.562925	+	0.826508i	$0.309676\pi$
$572$	−2.91404e102	−0.115384
$573$	7.56665e102	0.280611
$574$	−2.37847e103	−0.826231
$575$	2.63769e103	0.858381
$576$	2.05997e103	0.628084
$577$	1.56700e103	0.447689	0.223844	−	0.974625i	$-0.428139\pi$
$577$	1.56700e103	0.447689	0.223844	+	0.974625i	$0.428139\pi$
$578$	−7.01247e103	−1.87749
$579$	−2.50656e103	−0.628972
$580$	2.02224e104	4.75644
$581$	4.12107e102	0.0908667
$582$	−4.43999e103	−0.917846
$583$	−3.34817e102	−0.0648988
$584$	−2.38248e104	−4.33060
$585$	2.21608e102	0.0377782
$586$	1.78184e103	0.284910
$587$	8.05760e102	0.120858	0.0604292	−	0.998172i	$-0.480753\pi$
$587$	8.05760e102	0.120858	0.0604292	+	0.998172i	$0.480753\pi$
$588$	1.94412e104	2.73573
$589$	−7.71227e103	−1.01826
$590$	2.53074e104	3.13543
$591$	1.23093e104	1.43120
$592$	−2.60714e104	−2.84512
$593$	−6.05490e103	−0.620234	−0.310117	−	0.950698i	$-0.600368\pi$
$593$	−6.05490e103	−0.620234	−0.310117	+	0.950698i	$0.600368\pi$
$594$	−8.00746e103	−0.770022
$595$	3.39951e102	0.0306923
$596$	2.99061e104	2.53527
$597$	−9.93563e103	−0.790967
$598$	1.56339e103	0.116889
$599$	2.34648e104	1.64782	0.823912	−	0.566718i	$-0.191787\pi$
$599$	2.34648e104	1.64782	0.823912	+	0.566718i	$0.191787\pi$
$600$	−6.34340e104	−4.18456
$601$	−1.86432e104	−1.15539	−0.577693	−	0.816254i	$-0.696047\pi$
$601$	−1.86432e104	−1.15539	−0.577693	+	0.816254i	$0.696047\pi$
$602$	1.15771e104	0.674108
$603$	−4.48282e103	−0.245274
$604$	−1.10701e104	−0.569203
$605$	−2.32078e104	−1.12152
$606$	9.41389e103	0.427608
$607$	−1.83308e104	−0.782718	−0.391359	−	0.920238i	$-0.627995\pi$
$607$	−1.83308e104	−0.782718	−0.391359	+	0.920238i	$0.627995\pi$
$608$	9.65446e104	3.87564
$609$	−9.16132e103	−0.345788
$610$	4.86288e104	1.72594
$611$	−3.05734e103	−0.102046
$612$	1.91486e103	0.0601116
$613$	−3.12669e104	−0.923244	−0.461622	−	0.887077i	$-0.652732\pi$
$613$	−3.12669e104	−0.923244	−0.461622	+	0.887077i	$0.652732\pi$
$614$	−2.03420e104	−0.565041
$615$	1.14583e105	2.99436
$616$	−1.50023e104	−0.368876
$617$	−2.66517e103	−0.0616640	−0.0308320	−	0.999525i	$-0.509816\pi$
$617$	−2.66517e103	−0.0616640	−0.0308320	+	0.999525i	$0.509816\pi$
$618$	−1.42678e104	−0.310663
$619$	1.58700e103	0.0325220	0.0162610	−	0.999868i	$-0.494824\pi$
$619$	1.58700e103	0.0325220	0.0162610	+	0.999868i	$0.494824\pi$
$620$	−1.46571e105	−2.82721
$621$	3.09394e104	0.561793
$622$	−1.41376e105	−2.41677
$623$	2.98240e103	0.0480026
$624$	−2.03930e104	−0.309072
$625$	−4.89860e104	−0.699152
$626$	1.05060e105	1.41221
$627$	6.21924e104	0.787417
$628$	2.08897e105	2.49141
$629$	−6.87511e103	−0.0772468
$630$	1.86582e104	0.197515
$631$	1.59377e105	1.58974	0.794868	−	0.606782i	$-0.207540\pi$
$631$	1.59377e105	1.58974	0.794868	+	0.606782i	$0.207540\pi$
$632$	−3.26345e105	−3.06751
$633$	−1.35144e105	−1.19717
$634$	−2.65675e104	−0.221822
$635$	1.40501e105	1.10577
$636$	−5.08797e104	−0.377488
$637$	−1.20088e104	−0.0839981
$638$	−1.77239e105	−1.16892
$639$	3.06589e102	0.00190667
$640$	3.62300e105	2.12480
$641$	1.17862e105	0.651925	0.325962	−	0.945383i	$-0.394312\pi$
$641$	1.17862e105	0.651925	0.325962	+	0.945383i	$0.394312\pi$
$642$	5.23198e105	2.72962
$643$	−2.50923e105	−1.23489	−0.617447	−	0.786612i	$-0.711833\pi$
$643$	−2.50923e105	−1.23489	−0.617447	+	0.786612i	$0.711833\pi$
$644$	9.47974e104	0.440125
$645$	−5.57726e105	−2.44305
$646$	5.25884e104	0.217355
$647$	4.06698e105	1.58621	0.793107	−	0.609082i	$-0.208462\pi$
$647$	4.06698e105	1.58621	0.793107	+	0.609082i	$0.208462\pi$
$648$	−9.71980e105	−3.57762
$649$	−1.59743e105	−0.554940
$650$	6.40796e104	0.210121
$651$	6.64007e104	0.205535
$652$	1.11294e106	3.25226
$653$	−3.54682e105	−0.978576	−0.489288	−	0.872122i	$-0.662743\pi$
$653$	−3.54682e105	−0.978576	−0.489288	+	0.872122i	$0.662743\pi$
$654$	1.14143e106	2.97360
$655$	−4.27265e105	−1.05111
$656$	−2.31917e106	−5.38813
$657$	−1.87032e105	−0.410408
$658$	−2.57411e105	−0.533527
$659$	1.86786e105	0.365714	0.182857	−	0.983140i	$-0.441465\pi$
$659$	1.86786e105	0.365714	0.182857	+	0.983140i	$0.441465\pi$
$660$	1.18196e106	2.18628
$661$	6.71414e105	1.17337	0.586686	−	0.809815i	$-0.300432\pi$
$661$	6.71414e105	1.17337	0.586686	+	0.809815i	$0.300432\pi$
$662$	−7.14843e105	−1.18042
$663$	−5.37770e103	−0.00839149
$664$	7.40843e105	1.09251
$665$	3.69036e105	0.514348
$666$	−3.77341e105	−0.497108
$667$	6.84821e105	0.852822
$668$	3.58675e106	4.22264
$669$	4.90086e105	0.545497
$670$	−2.33975e106	−2.46243
$671$	−3.06950e105	−0.305473
$672$	−8.31225e105	−0.782296
$673$	−2.00080e106	−1.78090	−0.890448	−	0.455086i	$-0.849609\pi$
$673$	−2.00080e106	−1.78090	−0.890448	+	0.455086i	$0.849609\pi$
$674$	−2.33983e106	−1.96987
$675$	1.26813e106	1.00989
$676$	−3.38914e106	−2.55322
$677$	7.19375e105	0.512720	0.256360	−	0.966581i	$-0.417477\pi$
$677$	7.19375e105	0.512720	0.256360	+	0.966581i	$0.417477\pi$
$678$	1.22491e106	0.826021
$679$	1.66298e105	0.106114
$680$	6.11128e105	0.369019
$681$	4.96928e105	0.283973
$682$	1.28462e106	0.694802
$683$	2.35846e106	1.20740	0.603700	−	0.797211i	$-0.293692\pi$
$683$	2.35846e106	1.20740	0.603700	+	0.797211i	$0.293692\pi$
$684$	2.07869e106	1.00736
$685$	−6.01180e106	−2.75809
$686$	−2.08810e106	−0.906978
$687$	4.76105e104	0.0195805
$688$	1.12884e107	4.39608
$689$	3.14282e104	0.0115904
$690$	−6.34123e106	−2.21479
$691$	−3.49985e105	−0.115777	−0.0578885	−	0.998323i	$-0.518437\pi$
$691$	−3.49985e105	−0.115777	−0.0578885	+	0.998323i	$0.518437\pi$
$692$	4.02936e106	1.26258
$693$	−1.17773e105	−0.0349581
$694$	9.02408e105	0.253760
$695$	1.82489e106	0.486191
$696$	−1.64693e107	−4.15746
$697$	−6.11571e105	−0.146291
$698$	1.03043e106	0.233583
$699$	9.31857e106	2.00196
$700$	3.88553e106	0.791176
$701$	1.66052e106	0.320493	0.160247	−	0.987077i	$-0.448771\pi$
$701$	1.66052e106	0.320493	0.160247	+	0.987077i	$0.448771\pi$
$702$	7.51635e105	0.137520
$703$	−7.46334e106	−1.29452
$704$	−6.78661e106	−1.11604
$705$	1.24008e107	1.93356
$706$	1.46912e107	2.17210
$707$	−3.52594e105	−0.0494364
$708$	−2.42750e107	−3.22783
$709$	−1.35084e107	−1.70361	−0.851805	−	0.523858i	$-0.824492\pi$
$709$	−1.35084e107	−1.70361	−0.851805	+	0.523858i	$0.824492\pi$
$710$	1.60020e105	0.0191420
$711$	−2.56191e106	−0.290705
$712$	5.36146e106	0.577143
$713$	−4.96354e106	−0.506914
$714$	−4.52773e105	−0.0438730
$715$	−7.30092e105	−0.0671276
$716$	1.05777e107	0.922896
$717$	9.50640e106	0.787133
$718$	2.84330e107	2.23438
$719$	−1.69563e107	−1.26473	−0.632364	−	0.774671i	$-0.717915\pi$
$719$	−1.69563e107	−1.26473	−0.632364	+	0.774671i	$0.717915\pi$
$720$	1.81930e107	1.28806
$721$	5.34395e105	0.0359162
$722$	2.74591e107	1.75203
$723$	−3.37195e107	−2.04265
$724$	−2.13968e107	−1.23070
$725$	2.80692e107	1.53305
$726$	3.09101e107	1.60316
$727$	−3.53639e107	−1.74189	−0.870944	−	0.491382i	$-0.836492\pi$
$727$	−3.53639e107	−1.74189	−0.870944	+	0.491382i	$0.836492\pi$
$728$	1.40822e106	0.0658784
$729$	1.30856e107	0.581449
$730$	−9.76191e107	−4.12029
$731$	2.97678e106	0.119356
$732$	−4.66450e107	−1.77680
$733$	1.06459e107	0.385286	0.192643	−	0.981269i	$-0.438294\pi$
$733$	1.06459e107	0.385286	0.192643	+	0.981269i	$0.438294\pi$
$734$	2.12147e107	0.729514
$735$	4.87086e107	1.59159
$736$	6.21352e107	1.92939
$737$	1.47687e107	0.435825
$738$	−3.35661e107	−0.941429
$739$	−1.41863e107	−0.378184	−0.189092	−	0.981959i	$-0.560554\pi$
$739$	−1.41863e107	−0.378184	−0.189092	+	0.981959i	$0.560554\pi$
$740$	−1.41840e108	−3.59425
$741$	−5.83780e106	−0.140626
$742$	2.64609e106	0.0605979
$743$	5.02005e107	1.09302	0.546510	−	0.837453i	$-0.315956\pi$
$743$	5.02005e107	1.09302	0.546510	+	0.837453i	$0.315956\pi$
$744$	1.19368e108	2.47118
$745$	7.49276e107	1.47496
$746$	1.23971e108	2.32067
$747$	5.81585e106	0.103536
$748$	−6.30854e106	−0.106812
$749$	−1.95962e107	−0.315575
$750$	−5.06754e107	−0.776246
$751$	−7.03488e107	−1.02508	−0.512541	−	0.858663i	$-0.671296\pi$
$751$	−7.03488e107	−1.02508	−0.512541	+	0.858663i	$0.671296\pi$
$752$	−2.50993e108	−3.47931
$753$	4.36022e107	0.575038
$754$	1.66369e107	0.208760
$755$	−2.77354e107	−0.331150
$756$	4.55761e107	0.517809
$757$	−1.78445e108	−1.92934	−0.964670	−	0.263461i	$-0.915136\pi$
$757$	−1.78445e108	−1.92934	−0.964670	+	0.263461i	$0.915136\pi$
$758$	−1.34712e108	−1.38615
$759$	4.00265e107	0.391995
$760$	6.63416e108	6.18409
$761$	1.13160e108	1.00408	0.502041	−	0.864844i	$-0.332583\pi$
$761$	1.13160e108	1.00408	0.502041	+	0.864844i	$0.332583\pi$
$762$	−1.87131e108	−1.58064
$763$	−4.27517e107	−0.343782
$764$	−8.33197e107	−0.637892
$765$	4.79755e106	0.0349716
$766$	−2.81137e108	−1.95137
$767$	1.49946e107	0.0991077
$768$	−8.18477e107	−0.515182
$769$	4.36032e107	0.261385	0.130692	−	0.991423i	$-0.458280\pi$
$769$	4.36032e107	0.261385	0.130692	+	0.991423i	$0.458280\pi$
$770$	−6.14698e107	−0.350962
$771$	−2.77875e108	−1.51116
$772$	2.76008e108	1.42979
$773$	1.42158e108	0.701518	0.350759	−	0.936466i	$-0.385924\pi$
$773$	1.42158e108	0.701518	0.350759	+	0.936466i	$0.385924\pi$
$774$	1.63381e108	0.768096
$775$	−2.03444e108	−0.911237
$776$	2.98954e108	1.27582
$777$	6.42575e107	0.261298
$778$	8.94664e108	3.46677
$779$	−6.63896e108	−2.45158
$780$	−1.10947e108	−0.390451
$781$	−1.01006e106	−0.00338793
$782$	3.38454e107	0.108205
$783$	3.29244e108	1.00335
$784$	−9.85864e108	−2.86394
$785$	5.23377e108	1.44945
$786$	5.69065e108	1.50251
$787$	2.52484e108	0.635597	0.317799	−	0.948158i	$-0.397056\pi$
$787$	2.52484e108	0.635597	0.317799	+	0.948158i	$0.397056\pi$
$788$	−1.35543e109	−3.25344
$789$	3.68181e108	0.842701
$790$	−1.33715e109	−2.91854
$791$	−4.58786e107	−0.0954975
$792$	−2.11720e108	−0.420307
$793$	2.88124e107	0.0545551
$794$	2.08762e108	0.377035
$795$	−1.27476e108	−0.219614
$796$	1.09406e109	1.79804
$797$	−3.24886e108	−0.509383	−0.254691	−	0.967022i	$-0.581974\pi$
$797$	−3.24886e108	−0.509383	−0.254691	+	0.967022i	$0.581974\pi$
$798$	−4.91512e108	−0.735234
$799$	−6.61876e107	−0.0944653
$800$	2.54678e109	3.46830
$801$	4.20891e107	0.0546953
$802$	−8.27011e108	−1.02559
$803$	6.16182e108	0.729249
$804$	2.24429e109	2.53500
$805$	2.37508e108	0.256055
$806$	−1.20583e108	−0.124086
$807$	−1.74240e109	−1.71156
$808$	−6.33857e108	−0.594382
$809$	7.50813e108	0.672144	0.336072	−	0.941836i	$-0.390901\pi$
$809$	7.50813e108	0.672144	0.336072	+	0.941836i	$0.390901\pi$
$810$	−3.98256e109	−3.40388
$811$	−7.73314e108	−0.631065	−0.315533	−	0.948915i	$-0.602183\pi$
$811$	−7.73314e108	−0.631065	−0.315533	+	0.948915i	$0.602183\pi$
$812$	1.00879e109	0.786052
$813$	−1.97346e109	−1.46836
$814$	1.24316e109	0.883306
$815$	2.78839e109	1.89209
$816$	−4.41484e108	−0.286111
$817$	3.23147e109	2.00020
$818$	1.76238e109	1.04196
$819$	1.10549e107	0.00624324
$820$	−1.26173e110	−6.80684
$821$	−3.36586e109	−1.73471	−0.867356	−	0.497689i	$-0.834182\pi$
$821$	−3.36586e109	−1.73471	−0.867356	+	0.497689i	$0.834182\pi$
$822$	8.00699e109	3.94254
$823$	1.81695e109	0.854768	0.427384	−	0.904070i	$-0.359435\pi$
$823$	1.81695e109	0.854768	0.427384	+	0.904070i	$0.359435\pi$
$824$	9.60681e108	0.431826
$825$	1.64059e109	0.704657
$826$	1.26246e109	0.518163
$827$	−2.22688e109	−0.873454	−0.436727	−	0.899594i	$-0.643862\pi$
$827$	−2.22688e109	−0.873454	−0.436727	+	0.899594i	$0.643862\pi$
$828$	1.33783e109	0.501490
$829$	−1.37867e109	−0.493931	−0.246965	−	0.969024i	$-0.579433\pi$
$829$	−1.37867e109	−0.493931	−0.246965	+	0.969024i	$0.579433\pi$
$830$	3.03551e109	1.03945
$831$	−2.99127e109	−0.979079
$832$	6.37037e108	0.199315
$833$	−2.59975e108	−0.0777578
$834$	−2.43054e109	−0.694985
$835$	8.98636e109	2.45664
$836$	−6.84829e109	−1.78997
$837$	−2.38634e109	−0.596386
$838$	7.77379e109	1.85773
$839$	−4.92096e109	−1.12454	−0.562272	−	0.826953i	$-0.690072\pi$
$839$	−4.92096e109	−1.12454	−0.562272	+	0.826953i	$0.690072\pi$
$840$	−5.71185e109	−1.24826
$841$	2.50293e109	0.523116
$842$	−8.01169e108	−0.160148
$843$	6.33877e109	1.21191
$844$	1.48813e110	2.72144
$845$	−8.49126e109	−1.48541
$846$	−3.63271e109	−0.607915
$847$	−1.15772e109	−0.185343
$848$	2.58011e109	0.395179
$849$	−9.81251e109	−1.43794
$850$	1.38724e109	0.194511
$851$	−4.80334e109	−0.644443
$852$	−1.53492e108	−0.0197061
$853$	−1.45733e110	−1.79048	−0.895239	−	0.445587i	$-0.852995\pi$
$853$	−1.45733e110	−1.79048	−0.895239	+	0.445587i	$0.852995\pi$
$854$	2.42585e109	0.285229
$855$	5.20802e109	0.586062
$856$	−3.52280e110	−3.79422
$857$	1.15609e109	0.119182	0.0595910	−	0.998223i	$-0.481020\pi$
$857$	1.15609e109	0.119182	0.0595910	+	0.998223i	$0.481020\pi$
$858$	9.72395e108	0.0959554
$859$	1.68941e110	1.59585	0.797924	−	0.602758i	$-0.205932\pi$
$859$	1.68941e110	1.59585	0.797924	+	0.602758i	$0.205932\pi$
$860$	6.14137e110	5.55359
$861$	5.71598e109	0.494849
$862$	−1.44057e110	−1.19402
$863$	6.04075e109	0.479386	0.239693	−	0.970849i	$-0.422953\pi$
$863$	6.04075e109	0.479386	0.239693	+	0.970849i	$0.422953\pi$
$864$	2.98730e110	2.26993
$865$	1.00953e110	0.734538
$866$	−3.34074e110	−2.32767
$867$	1.68525e110	1.12447
$868$	−7.31168e109	−0.467227
$869$	8.44025e109	0.516551
$870$	−6.74807e110	−3.95555
$871$	−1.38629e109	−0.0778348
$872$	−7.68546e110	−4.13334
$873$	2.34688e109	0.120908
$874$	3.67412e110	1.81332
$875$	1.89803e109	0.0897430
$876$	9.36366e110	4.24171
$877$	−6.52884e107	−0.00283368	−0.00141684	−	0.999999i	$-0.500451\pi$
$877$	−6.52884e107	−0.00283368	−0.00141684	+	0.999999i	$0.500451\pi$
$878$	−3.37904e110	−1.40523
$879$	−4.28214e109	−0.170639
$880$	−5.99372e110	−2.28874
$881$	3.50306e110	1.28189	0.640946	−	0.767586i	$-0.278542\pi$
$881$	3.50306e110	1.28189	0.640946	+	0.767586i	$0.278542\pi$
$882$	−1.42688e110	−0.500396
$883$	−2.71634e110	−0.912973	−0.456487	−	0.889730i	$-0.650892\pi$
$883$	−2.71634e110	−0.912973	−0.456487	+	0.889730i	$0.650892\pi$
$884$	5.92162e108	0.0190757
$885$	−6.08192e110	−1.87788
$886$	1.11725e111	3.30664
$887$	−1.19560e110	−0.339194	−0.169597	−	0.985513i	$-0.554247\pi$
$887$	−1.19560e110	−0.339194	−0.169597	+	0.985513i	$0.554247\pi$
$888$	1.15516e111	3.14163
$889$	7.00892e109	0.182740
$890$	2.19678e110	0.549114
$891$	2.51383e110	0.602451
$892$	−5.39655e110	−1.24004
$893$	−7.18505e110	−1.58307
$894$	−9.97944e110	−2.10838
$895$	2.65017e110	0.536920
$896$	1.80733e110	0.351146
$897$	−3.75716e109	−0.0700072
$898$	4.27434e110	0.763848
$899$	−5.28199e110	−0.905335
$900$	5.48344e110	0.901486
$901$	6.80382e108	0.0107293
$902$	1.10584e111	1.67281
$903$	−2.78222e110	−0.403739
$904$	−8.24759e110	−1.14818
$905$	−5.36083e110	−0.715995
$906$	3.69402e110	0.473361
$907$	1.20263e111	1.47863	0.739315	−	0.673359i	$-0.235149\pi$
$907$	1.20263e111	1.47863	0.739315	+	0.673359i	$0.235149\pi$
$908$	−5.47190e110	−0.645534
$909$	−4.97597e109	−0.0563291
$910$	5.76998e109	0.0626790
$911$	1.56417e111	1.63059	0.815297	−	0.579042i	$-0.196573\pi$
$911$	1.56417e111	1.63059	0.815297	+	0.579042i	$0.196573\pi$
$912$	−4.79257e111	−4.79470
$913$	−1.91604e110	−0.183972
$914$	1.06036e111	0.977168
$915$	−1.16866e111	−1.03370
$916$	−5.24260e109	−0.0445109
$917$	−2.13141e110	−0.173707
$918$	1.62720e110	0.127303
$919$	1.97001e111	1.47957	0.739787	−	0.672841i	$-0.234926\pi$
$919$	1.97001e111	1.47957	0.739787	+	0.672841i	$0.234926\pi$
$920$	4.26968e111	3.07859
$921$	4.88863e110	0.338416
$922$	−3.30359e111	−2.19571
$923$	9.48114e107	0.000605058 0
$924$	5.89621e110	0.361305
$925$	−1.96878e111	−1.15846
$926$	1.52094e110	0.0859409
$927$	7.54164e109	0.0409238
$928$	6.61216e111	3.44583
$929$	−5.85098e110	−0.292846	−0.146423	−	0.989222i	$-0.546776\pi$
$929$	−5.85098e110	−0.292846	−0.146423	+	0.989222i	$0.546776\pi$
$930$	4.89096e111	2.35117
$931$	−2.82218e111	−1.30308
$932$	−1.02611e112	−4.55090
$933$	3.39757e111	1.44746
$934$	6.13628e110	0.251129
$935$	−1.58056e110	−0.0621406
$936$	1.98734e110	0.0750635
$937$	4.05778e111	1.47249	0.736247	−	0.676713i	$-0.236596\pi$
$937$	4.05778e111	1.47249	0.736247	+	0.676713i	$0.236596\pi$
$938$	−1.16718e111	−0.406942
$939$	−2.52481e111	−0.845803
$940$	−1.36551e112	−4.39542
$941$	3.76642e111	1.16498	0.582489	−	0.812839i	$-0.302079\pi$
$941$	3.76642e111	1.16498	0.582489	+	0.812839i	$0.302079\pi$
$942$	−6.97074e111	−2.07191
$943$	−4.27277e111	−1.22045
$944$	1.23098e112	3.37911
$945$	1.14188e111	0.301250
$946$	−5.38262e111	−1.36482
$947$	−1.55286e111	−0.378450	−0.189225	−	0.981934i	$-0.560597\pi$
$947$	−1.55286e111	−0.378450	−0.189225	+	0.981934i	$0.560597\pi$
$948$	1.28260e112	3.00455
$949$	−5.78390e110	−0.130238
$950$	1.50594e112	3.25965
$951$	6.38476e110	0.132854
$952$	3.04862e110	0.0609842
$953$	3.52427e111	0.677775	0.338887	−	0.940827i	$-0.389949\pi$
$953$	3.52427e111	0.677775	0.338887	+	0.940827i	$0.389949\pi$
$954$	3.73429e110	0.0690468
$955$	−2.08752e111	−0.371111
$956$	−1.04679e112	−1.78933
$957$	4.25945e111	0.700093
$958$	−1.38334e111	−0.218636
$959$	−2.99899e111	−0.455803
$960$	−2.58388e112	−3.77660
$961$	−3.28586e111	−0.461872
$962$	−1.16691e111	−0.157751
$963$	−2.76551e111	−0.359575
$964$	3.71300e112	4.64341
$965$	6.91520e111	0.831822
$966$	−3.16332e111	−0.366017
$967$	−5.78672e111	−0.644080	−0.322040	−	0.946726i	$-0.604369\pi$
$967$	−5.78672e111	−0.644080	−0.322040	+	0.946726i	$0.604369\pi$
$968$	−2.08124e112	−2.22841
$969$	−1.26381e111	−0.130179
$970$	1.22492e112	1.21386
$971$	−1.04108e111	−0.0992577	−0.0496288	−	0.998768i	$-0.515804\pi$
$971$	−1.04108e111	−0.0992577	−0.0496288	+	0.998768i	$0.515804\pi$
$972$	1.53896e112	1.41170
$973$	9.10348e110	0.0803482
$974$	−1.57240e112	−1.33537
$975$	−1.53997e111	−0.125846
$976$	2.36537e112	1.86007
$977$	1.54003e111	0.116542	0.0582711	−	0.998301i	$-0.481441\pi$
$977$	1.54003e111	0.116542	0.0582711	+	0.998301i	$0.481441\pi$
$978$	−3.71379e112	−2.70465
$979$	−1.38663e111	−0.0971875
$980$	−5.36352e112	−3.61803
$981$	−6.03332e111	−0.391714
$982$	2.90803e112	1.81727
$983$	−9.94251e110	−0.0598052	−0.0299026	−	0.999553i	$-0.509520\pi$
$983$	−9.94251e110	−0.0598052	−0.0299026	+	0.999553i	$0.509520\pi$
$984$	1.02756e113	5.94965
$985$	−3.39593e112	−1.89278
$986$	3.60168e111	0.193251
$987$	6.18615e111	0.319542
$988$	6.42827e111	0.319675
$989$	2.07975e112	0.995748
$990$	−8.67492e111	−0.399895
$991$	−2.08266e112	−0.924392	−0.462196	−	0.886778i	$-0.652938\pi$
$991$	−2.08266e112	−0.924392	−0.462196	+	0.886778i	$0.652938\pi$
$992$	−4.79246e112	−2.04819
$993$	1.71792e112	0.706980
$994$	7.98261e109	0.00316341
$995$	2.74108e112	1.04606
$996$	−2.91167e112	−1.07008
$997$	1.02320e112	0.362152	0.181076	−	0.983469i	$-0.442042\pi$
$997$	1.02320e112	0.362152	0.181076	+	0.983469i	$0.442042\pi$
$998$	7.09239e112	2.41767
$999$	−2.30932e112	−0.758189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.76.a.a.1.6	✓	6
3.2	odd	2		9.76.a.c.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.6	✓	6	1.1	even	1	trivial
9.76.a.c.1.1		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.67444e11 q^{2} -8.83049e17 q^{3} +9.72365e22 q^{4} +2.43619e26 q^{5} -3.24471e29 q^{6} +1.21530e31 q^{7} +2.18473e34 q^{8} +1.71508e35 q^{9} +8.95165e37 q^{10} -5.65037e38 q^{11} -8.58645e40 q^{12} +5.30382e40 q^{13} +4.46553e42 q^{14} -2.15128e44 q^{15} +4.35419e45 q^{16} +1.14821e45 q^{17} +6.30198e46 q^{18} +1.24645e48 q^{19} +2.36887e49 q^{20} -1.07316e49 q^{21} -2.07620e50 q^{22} +8.02205e50 q^{23} -1.92923e52 q^{24} +3.28805e52 q^{25} +1.94886e52 q^{26} +3.85679e53 q^{27} +1.18171e54 q^{28} +8.53673e54 q^{29} -7.90474e55 q^{30} -6.18737e55 q^{31} +7.74555e56 q^{32} +4.98956e56 q^{33} +4.21904e56 q^{34} +2.96069e57 q^{35} +1.66769e58 q^{36} -5.98766e58 q^{37} +4.58002e59 q^{38} -4.68354e58 q^{39} +5.32243e60 q^{40} -5.32628e60 q^{41} -3.94328e60 q^{42} +2.59254e61 q^{43} -5.49422e61 q^{44} +4.17827e61 q^{45} +2.94766e62 q^{46} -5.76440e62 q^{47} -3.84496e63 q^{48} -2.26417e63 q^{49} +1.20818e64 q^{50} -1.01393e63 q^{51} +5.15725e63 q^{52} +5.92558e63 q^{53} +1.41716e65 q^{54} -1.37654e65 q^{55} +2.65510e65 q^{56} -1.10068e66 q^{57} +3.13677e66 q^{58} +2.82712e66 q^{59} -2.09183e67 q^{60} +5.43239e66 q^{61} -2.27352e67 q^{62} +2.08433e66 q^{63} +1.20109e68 q^{64} +1.29211e67 q^{65} +1.83338e68 q^{66} -2.61376e68 q^{67} +1.11648e68 q^{68} -7.08386e68 q^{69} +1.08789e69 q^{70} +1.78760e67 q^{71} +3.74700e69 q^{72} -1.09051e70 q^{73} -2.20013e70 q^{74} -2.90351e70 q^{75} +1.21201e71 q^{76} -6.86687e69 q^{77} -1.72094e70 q^{78} -1.49375e71 q^{79} +1.06076e72 q^{80} -4.44896e71 q^{81} -1.95711e72 q^{82} +3.39100e71 q^{83} -1.04351e72 q^{84} +2.79727e71 q^{85} +9.52613e72 q^{86} -7.53835e72 q^{87} -1.23446e73 q^{88} +2.45405e72 q^{89} +1.53528e73 q^{90} +6.44571e71 q^{91} +7.80036e73 q^{92} +5.46375e73 q^{93} -2.11810e74 q^{94} +3.03660e74 q^{95} -6.83970e74 q^{96} +1.36838e74 q^{97} -8.31957e74 q^{98} -9.69086e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 57080822040 q^{2} - 78\!\cdots\!40 q^{3} + 17\!\cdots\!28 q^{4} - 38\!\cdots\!40 q^{5} + 31\!\cdots\!92 q^{6} + 19\!\cdots\!00 q^{7} + 44\!\cdots\!20 q^{8} + 21\!\cdots\!82 q^{9} + 13\!\cdots\!60 q^{10}+ \cdots - 18\!\cdots\!36 q^{99}+O(q^{100}) \) 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

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Database

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