LMFDB - Embedded newform 840.2.bj.b.517.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			517.34
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.534572 - 1.30929i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.42846 + 1.39982i) q^{4} +(-1.34687 - 1.78492i) q^{5} +(-1.30381 - 0.547806i) q^{6} +(-2.37457 - 1.16680i) q^{7} +(2.59638 + 1.12197i) q^{8} -1.00000i q^{9} +(-1.61698 + 2.71761i) q^{10} +2.73270i q^{11} +(-0.0202571 + 1.99990i) q^{12} +(-0.652103 + 0.652103i) q^{13} +(-0.258300 + 3.73273i) q^{14} +(-2.21451 - 0.309752i) q^{15} +(0.0810241 - 3.99918i) q^{16} +(-4.00888 + 4.00888i) q^{17} +(-1.30929 + 0.534572i) q^{18} -0.695088i q^{19} +(4.42252 + 0.664333i) q^{20} +(-2.50413 + 0.854019i) q^{21} +(3.57788 - 1.46082i) q^{22} +(-4.02681 + 4.02681i) q^{23} +(2.62927 - 1.04257i) q^{24} +(-1.37190 + 4.80811i) q^{25} +(1.20239 + 0.505194i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(5.02530 - 1.65723i) q^{28} +3.86934 q^{29} +(0.778261 + 3.06501i) q^{30} -10.7977i q^{31} +(-5.27939 + 2.03177i) q^{32} +(1.93231 + 1.93231i) q^{33} +(7.39181 + 3.10574i) q^{34} +(1.11558 + 5.80995i) q^{35} +(1.39982 + 1.42846i) q^{36} +(-0.919223 + 0.919223i) q^{37} +(-0.910070 + 0.371575i) q^{38} +0.922213i q^{39} +(-1.49435 - 6.14548i) q^{40} -0.751652i q^{41} +(2.45679 + 2.82209i) q^{42} +(7.48629 + 7.48629i) q^{43} +(-3.82528 - 3.90356i) q^{44} +(-1.78492 + 1.34687i) q^{45} +(7.42488 + 3.11963i) q^{46} +(-5.87362 + 5.87362i) q^{47} +(-2.77055 - 2.88514i) q^{48} +(4.27715 + 5.54130i) q^{49} +(7.02857 - 0.774071i) q^{50} +5.66941i q^{51} +(0.0186813 - 1.84433i) q^{52} +(6.28157 + 6.28157i) q^{53} +(-0.547806 + 1.30381i) q^{54} +(4.87765 - 3.68058i) q^{55} +(-4.85617 - 5.69365i) q^{56} +(-0.491502 - 0.491502i) q^{57} +(-2.06844 - 5.06607i) q^{58} -3.87046i q^{59} +(3.59695 - 2.65744i) q^{60} -2.75222 q^{61} +(-14.1373 + 5.77215i) q^{62} +(-1.16680 + 2.37457i) q^{63} +(5.48238 + 5.82611i) q^{64} +(2.04225 + 0.285658i) q^{65} +(1.49699 - 3.56290i) q^{66} +(-7.35997 + 7.35997i) q^{67} +(0.114846 - 11.3382i) q^{68} +5.69477i q^{69} +(7.01053 - 4.56645i) q^{70} -13.5519 q^{71} +(1.12197 - 2.59638i) q^{72} +(-6.03685 - 6.03685i) q^{73} +(1.69492 + 0.712136i) q^{74} +(2.42977 + 4.36992i) q^{75} +(0.972996 + 0.992909i) q^{76} +(3.18852 - 6.48897i) q^{77} +(1.20744 - 0.492990i) q^{78} -2.86914i q^{79} +(-7.24736 + 5.24174i) q^{80} -1.00000 q^{81} +(-0.984128 + 0.401812i) q^{82} +(-9.60298 + 9.60298i) q^{83} +(2.38159 - 4.72526i) q^{84} +(12.5550 + 1.75611i) q^{85} +(5.79974 - 13.8037i) q^{86} +(2.73604 - 2.73604i) q^{87} +(-3.06600 + 7.09512i) q^{88} -8.00970 q^{89} +(2.71761 + 1.61698i) q^{90} +(2.30934 - 0.787588i) q^{91} +(0.115359 - 11.3890i) q^{92} +(-7.63513 - 7.63513i) q^{93} +(10.8301 + 4.55038i) q^{94} +(-1.24068 + 0.936191i) q^{95} +(-2.29641 + 5.16977i) q^{96} +(-2.08593 + 2.08593i) q^{97} +(4.96871 - 8.56224i) q^{98} +2.73270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.534572	−	1.30929i	−0.378000	−	0.925806i
$2$	−0.534572	−	1.30929i	−0.378000	−	0.925806i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.42846	+	1.39982i	−0.714232	+	0.699909i
$5$	−1.34687	−	1.78492i	−0.602337	−	0.798242i
$5$	−1.34687	−	1.78492i	−0.602337	−	0.798242i
$6$	−1.30381	−	0.547806i	−0.532276	−	0.223641i
$7$	−2.37457	−	1.16680i	−0.897502	−	0.441010i
$7$	−2.37457	−	1.16680i	−0.897502	−	0.441010i
$8$	2.59638	+	1.12197i	0.917959	+	0.396675i
$9$		−	1.00000i		−	0.333333i
$10$	−1.61698	+	2.71761i	−0.511334	+	0.859382i
$11$			2.73270i			0.823939i	0.911198	+	0.411970i	$0.135159\pi$
$11$			2.73270i			0.823939i	−0.911198	+	0.411970i	$0.864841\pi$
$12$	−0.0202571	+	1.99990i	−0.00584771	+	0.577321i
$13$	−0.652103	+	0.652103i	−0.180861	+	0.180861i	−0.791731	−	0.610870i	$-0.790820\pi$
$13$	−0.652103	+	0.652103i	−0.180861	+	0.180861i	0.610870	+	0.791731i	$0.290820\pi$
$14$	−0.258300	+	3.73273i	−0.0690337	+	0.997614i
$15$	−2.21451	−	0.309752i	−0.571784	−	0.0799777i
$16$	0.0810241	−	3.99918i	0.0202560	−	0.999795i
$17$	−4.00888	+	4.00888i	−0.972296	+	0.972296i	−0.999626	−	0.0273302i	$-0.991299\pi$
$17$	−4.00888	+	4.00888i	−0.972296	+	0.972296i	0.0273302	+	0.999626i	$0.491299\pi$
$18$	−1.30929	+	0.534572i	−0.308602	+	0.126000i
$19$		−	0.695088i		−	0.159464i	−0.996816	−	0.0797321i	$-0.974594\pi$
$19$		−	0.695088i		−	0.159464i	0.996816	−	0.0797321i	$-0.0254065\pi$
$20$	4.42252	+	0.664333i	0.988905	+	0.148549i
$21$	−2.50413	+	0.854019i	−0.546445	+	0.186362i
$22$	3.57788	−	1.46082i	0.762808	−	0.311449i
$23$	−4.02681	+	4.02681i	−0.839649	+	0.839649i	−0.988812	−	0.149164i	$-0.952342\pi$
$23$	−4.02681	+	4.02681i	−0.839649	+	0.839649i	0.149164	+	0.988812i	$0.452342\pi$
$24$	2.62927	−	1.04257i	0.536697	−	0.212813i
$25$	−1.37190	+	4.80811i	−0.274380	+	0.961621i
$26$	1.20239	+	0.505194i	0.235807	+	0.0990767i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	5.02530	−	1.65723i	0.949692	−	0.313186i
$29$	3.86934			0.718518			0.359259	−	0.933238i	$-0.383029\pi$
$29$	3.86934			0.718518			0.359259	+	0.933238i	$0.383029\pi$
$30$	0.778261	+	3.06501i	0.142090	+	0.559592i
$31$		−	10.7977i		−	1.93932i	−0.244448	−	0.969662i	$-0.578607\pi$
$31$		−	10.7977i		−	1.93932i	0.244448	−	0.969662i	$-0.421393\pi$
$32$	−5.27939	+	2.03177i	−0.933273	+	0.359169i
$33$	1.93231	+	1.93231i	0.336372	+	0.336372i
$34$	7.39181	+	3.10574i	1.26769	+	0.532630i
$35$	1.11558	+	5.80995i	0.188567	+	0.982060i
$36$	1.39982	+	1.42846i	0.233303	+	0.238077i
$37$	−0.919223	+	0.919223i	−0.151119	+	0.151119i	−0.778618	−	0.627498i	$-0.784079\pi$
$37$	−0.919223	+	0.919223i	−0.151119	+	0.151119i	0.627498	+	0.778618i	$0.284079\pi$
$38$	−0.910070	+	0.371575i	−0.147633	+	0.0602774i
$39$			0.922213i			0.147672i
$40$	−1.49435	−	6.14548i	−0.236278	−	0.971685i
$41$		−	0.751652i		−	0.117388i	−0.998276	−	0.0586942i	$-0.981306\pi$
$41$		−	0.751652i		−	0.117388i	0.998276	−	0.0586942i	$-0.0186937\pi$
$42$	2.45679	+	2.82209i	0.379091	+	0.435457i
$43$	7.48629	+	7.48629i	1.14165	+	1.14165i	0.988149	+	0.153500i	$0.0490546\pi$
$43$	7.48629	+	7.48629i	1.14165	+	1.14165i	0.153500	+	0.988149i	$0.450945\pi$
$44$	−3.82528	−	3.90356i	−0.576682	−	0.588484i
$45$	−1.78492	+	1.34687i	−0.266081	+	0.200779i
$46$	7.42488	+	3.11963i	1.09474	+	0.459965i
$47$	−5.87362	+	5.87362i	−0.856755	+	0.856755i	−0.990954	−	0.134199i	$-0.957154\pi$
$47$	−5.87362	+	5.87362i	−0.856755	+	0.856755i	0.134199	+	0.990954i	$0.457154\pi$
$48$	−2.77055	−	2.88514i	−0.399895	−	0.416434i
$49$	4.27715	+	5.54130i	0.611021	+	0.791614i
$50$	7.02857	−	0.774071i	0.993990	−	0.109470i
$51$			5.66941i			0.793877i
$52$	0.0186813	−	1.84433i	0.00259064	−	0.255763i
$53$	6.28157	+	6.28157i	0.862840	+	0.862840i	0.991667	−	0.128827i	$-0.0411212\pi$
$53$	6.28157	+	6.28157i	0.862840	+	0.862840i	−0.128827	+	0.991667i	$0.541121\pi$
$54$	−0.547806	+	1.30381i	−0.0745470	+	0.177425i
$55$	4.87765	−	3.68058i	0.657703	−	0.496289i
$56$	−4.85617	−	5.69365i	−0.648933	−	0.760846i
$57$	−0.491502	−	0.491502i	−0.0651010	−	0.0651010i
$58$	−2.06844	−	5.06607i	−0.271600	−	0.665208i
$59$		−	3.87046i		−	0.503891i	−0.967741	−	0.251945i	$-0.918930\pi$
$59$		−	3.87046i		−	0.503891i	0.967741	−	0.251945i	$-0.0810703\pi$
$60$	3.59695	−	2.65744i	0.464364	−	0.343074i
$61$	−2.75222			−0.352386			−0.176193	−	0.984356i	$-0.556378\pi$
$61$	−2.75222			−0.352386			−0.176193	+	0.984356i	$0.556378\pi$
$62$	−14.1373	+	5.77215i	−1.79544	+	0.733064i
$63$	−1.16680	+	2.37457i	−0.147003	+	0.299167i
$64$	5.48238	+	5.82611i	0.685297	+	0.728263i
$65$	2.04225	+	0.285658i	0.253310	+	0.0354315i
$66$	1.49699	−	3.56290i	0.184266	−	0.438563i
$67$	−7.35997	+	7.35997i	−0.899164	+	0.899164i	−0.995362	−	0.0961985i	$-0.969332\pi$
$67$	−7.35997	+	7.35997i	−0.899164	+	0.899164i	0.0961985	+	0.995362i	$0.469332\pi$
$68$	0.114846	−	11.3382i	0.0139271	−	1.37496i
$69$			5.69477i			0.685570i
$70$	7.01053	−	4.56645i	0.837919	−	0.545795i
$71$	−13.5519			−1.60832			−0.804158	−	0.594415i	$-0.797384\pi$
$71$	−13.5519			−1.60832			−0.804158	+	0.594415i	$0.797384\pi$
$72$	1.12197	−	2.59638i	0.132225	−	0.305986i
$73$	−6.03685	−	6.03685i	−0.706560	−	0.706560i	0.259250	−	0.965810i	$-0.416525\pi$
$73$	−6.03685	−	6.03685i	−0.706560	−	0.706560i	−0.965810	+	0.259250i	$0.916525\pi$
$74$	1.69492	+	0.712136i	0.197030	+	0.0827841i
$75$	2.42977	+	4.36992i	0.280565	+	0.504595i
$76$	0.972996	+	0.992909i	0.111610	+	0.113894i
$77$	3.18852	−	6.48897i	0.363365	−	0.739487i
$78$	1.20744	−	0.492990i	0.136716	−	0.0558201i
$79$		−	2.86914i		−	0.322804i	−0.986889	−	0.161402i	$-0.948398\pi$
$79$		−	2.86914i		−	0.322804i	0.986889	−	0.161402i	$-0.0516016\pi$
$80$	−7.24736	+	5.24174i	−0.810279	+	0.586044i
$81$	−1.00000			−0.111111
$82$	−0.984128	+	0.401812i	−0.108679	+	0.0443728i
$83$	−9.60298	+	9.60298i	−1.05406	+	1.05406i	−0.0556111	+	0.998453i	$0.517711\pi$
$83$	−9.60298	+	9.60298i	−1.05406	+	1.05406i	−0.998453	+	0.0556111i	$0.982289\pi$
$84$	2.38159	−	4.72526i	0.259852	−	0.515568i
$85$	12.5550	+	1.75611i	1.36178	+	0.190477i
$86$	5.79974	−	13.8037i	0.625402	−	1.48849i
$87$	2.73604	−	2.73604i	0.293334	−	0.293334i
$88$	−3.06600	+	7.09512i	−0.326836	+	0.756342i
$89$	−8.00970			−0.849026			−0.424513	−	0.905422i	$-0.639555\pi$
$89$	−8.00970			−0.849026			−0.424513	+	0.905422i	$0.639555\pi$
$90$	2.71761	+	1.61698i	0.286461	+	0.170445i
$91$	2.30934	−	0.787588i	0.242085	−	0.0825617i
$92$	0.115359	−	11.3890i	0.0120270	−	1.18738i
$93$	−7.63513	−	7.63513i	−0.791726	−	0.791726i
$94$	10.8301	+	4.55038i	1.11704	+	0.469336i
$95$	−1.24068	+	0.936191i	−0.127291	+	0.0960512i
$96$	−2.29641	+	5.16977i	−0.234377	+	0.527637i
$97$	−2.08593	+	2.08593i	−0.211794	+	0.211794i	−0.805029	−	0.593235i	$-0.797850\pi$
$97$	−2.08593	+	2.08593i	−0.211794	+	0.211794i	0.593235	+	0.805029i	$0.297850\pi$
$98$	4.96871	−	8.56224i	0.501916	−	0.864917i
$99$	2.73270			0.274646
$100$	−4.77076	−	8.78862i	−0.477076	−	0.878862i
$101$	7.86838			0.782933			0.391466	−	0.920192i	$-0.371968\pi$
$101$	7.86838			0.782933			0.391466	+	0.920192i	$0.371968\pi$
$102$	7.42289	−	3.03071i	0.734975	−	0.300085i
$103$	−0.103805	−	0.103805i	−0.0102282	−	0.0102282i	0.701974	−	0.712202i	$-0.252302\pi$
$103$	−0.103805	−	0.103805i	−0.0102282	−	0.0102282i	−0.712202	+	0.701974i	$0.752302\pi$
$104$	−2.42475	+	0.961470i	−0.237766	+	0.0942799i
$105$	4.89708	+	3.31942i	0.477906	+	0.323942i
$106$	4.86642	−	11.5823i	0.472669	−	1.12498i
$107$	6.21506	−	6.21506i	0.600832	−	0.600832i	−0.339701	−	0.940533i	$-0.610326\pi$
$107$	6.21506	−	6.21506i	0.600832	−	0.600832i	0.940533	+	0.339701i	$0.110326\pi$
$108$	1.99990	+	0.0202571i	0.192440	+	0.00194924i
$109$	0.997788			0.0955707			0.0477854	−	0.998858i	$-0.484784\pi$
$109$	0.997788			0.0955707			0.0477854	+	0.998858i	$0.484784\pi$
$110$	−7.42639	−	4.41871i	−0.708079	−	0.421308i
$111$			1.29998i			0.123388i
$112$	−4.85865	+	9.40178i	−0.459099	+	0.888385i
$113$	−0.567306	+	0.567306i	−0.0533677	+	0.0533677i	−0.733287	−	0.679919i	$-0.762015\pi$
$113$	−0.567306	+	0.567306i	−0.0533677	+	0.0533677i	0.679919	+	0.733287i	$0.262015\pi$
$114$	−0.380774	+	0.906260i	−0.0356627	+	0.0848790i
$115$	12.6111	+	1.76397i	1.17599	+	0.164491i
$116$	−5.52721	+	5.41637i	−0.513189	+	0.502897i
$117$	0.652103	+	0.652103i	0.0602870	+	0.0602870i
$118$	−5.06754	+	2.06904i	−0.466505	+	0.190471i
$119$	14.1969	−	4.84179i	1.30143	−	0.443846i
$120$	−5.40218	−	3.28884i	−0.493149	−	0.300229i
$121$	3.53237			0.321124
$122$	1.47126	+	3.60344i	0.133202	+	0.326241i
$123$	−0.531498	−	0.531498i	−0.0479236	−	0.0479236i
$124$	15.1148	+	15.4241i	1.35735	+	1.38513i
$125$	10.4299	−	4.02714i	0.932876	−	0.360199i
$126$	3.73273	+	0.258300i	0.332538	+	0.0230112i
$127$	−12.0310	−	12.0310i	−1.06758	−	1.06758i	−0.997545	−	0.0700338i	$-0.977689\pi$
$127$	−12.0310	−	12.0310i	−1.06758	−	1.06758i	−0.0700338	−	0.997545i	$-0.522311\pi$
$128$	4.69732	−	10.2925i	0.415188	−	0.909736i
$129$	10.5872			0.932152
$130$	−0.717723	−	2.82660i	−0.0629484	−	0.247909i
$131$	−15.9812			−1.39629			−0.698143	−	0.715959i	$-0.745990\pi$
$131$	−15.9812			−1.39629			−0.698143	+	0.715959i	$0.745990\pi$
$132$	−5.46511	−	0.0553564i	−0.475677	−	0.00481816i
$133$	−0.811030	+	1.65053i	−0.0703253	+	0.143119i
$134$	13.5708	+	5.70188i	1.17233	+	0.492567i
$135$	−0.309752	+	2.21451i	−0.0266592	+	0.190595i
$136$	−14.9064	+	5.91074i	−1.27821	+	0.506842i
$137$	1.97589	+	1.97589i	0.168812	+	0.168812i	0.786457	−	0.617645i	$-0.211913\pi$
$137$	1.97589	+	1.97589i	0.168812	+	0.168812i	−0.617645	+	0.786457i	$0.711913\pi$
$138$	7.45609	−	3.04427i	0.634705	−	0.259145i
$139$		−	15.2563i		−	1.29402i	−0.762482	−	0.647009i	$-0.776019\pi$
$139$		−	15.2563i		−	1.29402i	0.762482	−	0.647009i	$-0.223981\pi$
$140$	−9.72642	−	6.73771i	−0.822033	−	0.569440i
$141$			8.30655i			0.699538i
$142$	7.24448	+	17.7433i	0.607943	+	1.48899i
$143$	−1.78200	−	1.78200i	−0.149018	−	0.149018i
$144$	−3.99918	−	0.0810241i	−0.333265	−	0.00675201i
$145$	−5.21148	−	6.90647i	−0.432790	−	0.573551i
$146$	−4.67684	+	11.1311i	−0.387058	+	0.921217i
$147$	6.94269	+	0.893893i	0.572623	+	0.0737270i
$148$	0.0263337	−	2.59982i	0.00216462	−	0.213704i
$149$	−16.1624			−1.32408			−0.662038	−	0.749471i	$-0.730308\pi$
$149$	−16.1624			−1.32408			−0.662038	+	0.749471i	$0.730308\pi$
$150$	4.42260	−	5.51730i	0.361104	−	0.450486i
$151$	−12.3945			−1.00865			−0.504325	−	0.863514i	$-0.668259\pi$
$151$	−12.3945			−1.00865			−0.504325	+	0.863514i	$0.668259\pi$
$152$	0.779866	−	1.80471i	0.0632555	−	0.146382i
$153$	4.00888	+	4.00888i	0.324099	+	0.324099i
$154$	−10.2004	−	0.705857i	−0.821973	−	0.0568796i
$155$	−19.2731	+	14.5431i	−1.54805	+	1.16813i
$156$	−1.29093	−	1.31735i	−0.103357	−	0.105472i
$157$	−9.26156	−	9.26156i	−0.739153	−	0.739153i	0.233261	−	0.972414i	$-0.425060\pi$
$157$	−9.26156	−	9.26156i	−0.739153	−	0.739153i	−0.972414	+	0.233261i	$0.925060\pi$
$158$	−3.75653	+	1.53376i	−0.298854	+	0.122020i
$159$	8.88348			0.704506
$160$	10.7372	+	6.68678i	0.848848	+	0.528636i
$161$	14.2604	−	4.86345i	1.12388	−	0.383293i
$162$	0.534572	+	1.30929i	0.0420000	+	0.102867i
$163$	−13.2448	−	13.2448i	−1.03741	−	1.03741i	−0.999272	−	0.0381388i	$-0.987857\pi$
$163$	−13.2448	−	13.2448i	−1.03741	−	1.03741i	−0.0381388	−	0.999272i	$-0.512143\pi$
$164$	1.05218	+	1.07371i	0.0821611	+	0.0838426i
$165$	0.846459	−	6.05158i	0.0658968	−	0.471115i
$166$	17.7065	+	7.43957i	1.37429	+	0.577422i
$167$	−9.33254	+	9.33254i	−0.722173	+	0.722173i	−0.969048	−	0.246874i	$-0.920597\pi$
$167$	−9.33254	+	9.33254i	−0.722173	+	0.722173i	0.246874	+	0.969048i	$0.420597\pi$
$168$	−7.45985	−	0.592189i	−0.575540	−	0.0456883i
$169$			12.1495i			0.934579i
$170$	−4.41228	−	17.3768i	−0.338407	−	1.33274i
$171$	−0.695088			−0.0531547
$172$	−21.1733	−	0.214466i	−1.61445	−	0.0163529i
$173$	4.77151	−	4.77151i	0.362771	−	0.362771i	−0.502061	−	0.864832i	$-0.667425\pi$
$173$	4.77151	−	4.77151i	0.362771	−	0.362771i	0.864832	+	0.502061i	$0.167425\pi$
$174$	−5.04486	−	2.11965i	−0.382450	−	0.160690i
$175$	8.86778	−	9.81644i	0.670341	−	0.742053i
$176$	10.9285	+	0.221414i	0.823770	+	0.0166897i
$177$	−2.73683	−	2.73683i	−0.205712	−	0.205712i
$178$	4.28176	+	10.4870i	0.320932	+	0.786033i
$179$	1.82697			0.136554			0.0682771	−	0.997666i	$-0.478250\pi$
$179$	1.82697			0.136554			0.0682771	+	0.997666i	$0.478250\pi$
$180$	0.664333	−	4.42252i	0.0495164	−	0.329635i
$181$	21.8299			1.62260			0.811302	−	0.584628i	$-0.198759\pi$
$181$	21.8299			1.62260			0.811302	+	0.584628i	$0.198759\pi$
$182$	−2.26569	−	2.60257i	−0.167944	−	0.192915i
$183$	−1.94611	+	1.94611i	−0.143861	+	0.143861i
$184$	−14.9731	+	5.93719i	−1.10383	+	0.437695i
$185$	2.87881	+	0.402671i	0.211655	+	0.0296050i
$186$	−5.91505	+	14.0781i	−0.433712	+	1.03226i
$187$	−10.9551	−	10.9551i	−0.801113	−	0.801113i
$188$	0.168266	−	16.6122i	0.0122721	−	1.21157i
$189$	0.854019	+	2.50413i	0.0621208	+	0.182148i
$190$	1.88898	+	1.12394i	0.137041	+	0.0815394i
$191$	−7.85488			−0.568359			−0.284180	−	0.958771i	$-0.591721\pi$
$191$	−7.85488			−0.568359			−0.284180	+	0.958771i	$0.591721\pi$
$192$	7.99631	+	0.243052i	0.577084	+	0.0175407i
$193$	14.9470	−	14.9470i	1.07591	−	1.07591i	0.0790403	−	0.996871i	$-0.474814\pi$
$193$	14.9470	−	14.9470i	1.07591	−	1.07591i	0.996871	−	0.0790403i	$-0.0251856\pi$
$194$	3.84616	+	1.61600i	0.276139	+	0.116022i
$195$	1.64608	−	1.24210i	0.117878	−	0.0889485i
$196$	−13.8666	−	1.92833i	−0.990469	−	0.137738i
$197$	−8.26668	+	8.26668i	−0.588977	+	0.588977i	−0.937354	−	0.348378i	$-0.886733\pi$
$197$	−8.26668	+	8.26668i	−0.588977	+	0.588977i	0.348378	+	0.937354i	$0.386733\pi$
$198$	−1.46082	−	3.57788i	−0.103816	−	0.254269i
$199$	−19.0640			−1.35141			−0.675705	−	0.737172i	$-0.736161\pi$
$199$	−19.0640			−1.35141			−0.675705	+	0.737172i	$0.736161\pi$
$200$	−8.95651	+	10.9444i	−0.633321	+	0.773889i
$201$			10.4086i			0.734164i
$202$	−4.20622	−	10.3020i	−0.295948	−	0.724844i
$203$	−9.18801	−	4.51475i	−0.644872	−	0.316873i
$204$	−7.93614	−	8.09856i	−0.555641	−	0.567012i
$205$	−1.34164	+	1.01238i	−0.0937043	+	0.0707074i
$206$	−0.0804189	+	0.191401i	−0.00560305	+	0.0133355i
$207$	4.02681	+	4.02681i	0.279883	+	0.279883i
$208$	2.55504	+	2.66071i	0.177160	+	0.184487i
$209$	1.89947			0.131389
$210$	1.72823	−	8.18616i	0.119259	−	0.564899i
$211$			12.9517i			0.891629i	0.895125	+	0.445815i	$0.147086\pi$
$211$			12.9517i			0.891629i	−0.895125	+	0.445815i	$0.852914\pi$
$212$	−17.7661	−	0.179953i	−1.22018	−	0.0123592i
$213$	−9.58265	+	9.58265i	−0.656593	+	0.656593i
$214$	−11.4597	−	4.81490i	−0.783368	−	0.329139i
$215$	3.27942	−	23.4455i	0.223654	−	1.59897i
$216$	−1.04257	−	2.62927i	−0.0709377	−	0.178899i
$217$	−12.5988	+	25.6399i	−0.855261	+	1.74055i
$218$	−0.533390	−	1.30639i	−0.0361257	−	0.0884799i
$219$	−8.53740			−0.576904
$220$	−1.81542	+	12.0854i	−0.122396	+	0.814797i
$221$		−	5.22841i		−	0.351701i
$222$	1.70204	−	0.694932i	0.114234	−	0.0466408i
$223$	0.0345980	+	0.0345980i	0.00231686	+	0.00231686i	0.708264	−	0.705947i	$-0.249479\pi$
$223$	0.0345980	+	0.0345980i	0.00231686	+	0.00231686i	−0.705947	+	0.708264i	$0.749479\pi$
$224$	14.9069	+	1.33543i	0.996011	+	0.0892272i
$225$	4.80811	+	1.37190i	0.320540	+	0.0914600i
$226$	1.04603	+	0.439500i	0.0695811	+	0.0292351i
$227$	−3.52308	−	3.52308i	−0.233835	−	0.233835i	0.580456	−	0.814291i	$-0.302874\pi$
$227$	−3.52308	−	3.52308i	−0.233835	−	0.233835i	−0.814291	+	0.580456i	$0.802874\pi$
$228$	1.39011	+	0.0140804i	0.0920620	+	0.000932500i
$229$		−	3.27763i		−	0.216592i	−0.994119	−	0.108296i	$-0.965461\pi$
$229$		−	3.27763i		−	0.216592i	0.994119	−	0.108296i	$-0.0345394\pi$
$230$	−4.43202	−	17.4546i	−0.292239	−	1.15092i
$231$	−2.33378	−	6.84302i	−0.153551	−	0.450238i
$232$	10.0463	+	4.34127i	0.659570	+	0.285018i
$233$	4.13036	−	4.13036i	0.270589	−	0.270589i	−0.558749	−	0.829337i	$-0.688718\pi$
$233$	4.13036	−	4.13036i	0.270589	−	0.270589i	0.829337	+	0.558749i	$0.188718\pi$
$234$	0.505194	−	1.20239i	0.0330256	−	0.0786025i
$235$	18.3949	+	2.57297i	1.19995	+	0.167842i
$236$	5.41793	+	5.52881i	0.352677	+	0.359895i
$237$	−2.02879	−	2.02879i	−0.131784	−	0.131784i
$238$	−13.9286	−	15.9996i	−0.902855	−	1.03710i
$239$		−	26.1874i		−	1.69392i	−0.531657	−	0.846960i	$-0.678431\pi$
$239$		−	26.1874i		−	1.69392i	0.531657	−	0.846960i	$-0.321569\pi$
$240$	−1.41818	+	8.83112i	−0.0915434	+	0.570047i
$241$			7.43213i			0.478745i	0.970928	+	0.239373i	$0.0769418\pi$
$241$			7.43213i			0.478745i	−0.970928	+	0.239373i	$0.923058\pi$
$242$	−1.88831	−	4.62488i	−0.121385	−	0.297299i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.93145	−	3.85260i	0.251685	−	0.246638i
$245$	4.13005	−	15.0978i	0.263859	−	0.964561i
$246$	−0.411760	+	0.980008i	−0.0262528	+	0.0624830i
$247$	0.453269	+	0.453269i	0.0288408	+	0.0288408i
$248$	12.1147	−	28.0349i	0.769282	−	1.78022i
$249$			13.5807i			0.860639i
$250$	−10.8482	−	11.5029i	−0.686101	−	0.727507i
$251$	−10.3216			−0.651491			−0.325746	−	0.945457i	$-0.605615\pi$
$251$	−10.3216			−0.651491			−0.325746	+	0.945457i	$0.605615\pi$
$252$	−1.65723	−	5.02530i	−0.104395	−	0.316564i
$253$	−11.0041	−	11.0041i	−0.691819	−	0.691819i
$254$	−9.32059	+	22.1835i	−0.584826	+	1.39191i
$255$	10.1195	−	7.63594i	0.633705	−	0.478181i
$256$	−15.9869	−	0.648060i	−0.999179	−	0.0405037i
$257$	−2.42411	+	2.42411i	−0.151212	+	0.151212i	−0.778659	−	0.627447i	$-0.784100\pi$
$257$	−2.42411	+	2.42411i	−0.151212	+	0.151212i	0.627447	+	0.778659i	$0.284100\pi$
$258$	−5.65963	−	13.8617i	−0.352353	−	0.862992i
$259$	3.25531	−	1.11021i	0.202275	−	0.0689849i
$260$	−3.31715	+	2.45073i	−0.205721	+	0.151988i
$261$		−	3.86934i		−	0.239506i
$262$	8.54311	+	20.9240i	0.527795	+	1.29269i
$263$	−7.27231	+	7.27231i	−0.448430	+	0.448430i	−0.894832	−	0.446402i	$-0.852705\pi$
$263$	−7.27231	+	7.27231i	−0.448430	+	0.448430i	0.446402	+	0.894832i	$0.352705\pi$
$264$	2.84902	+	7.18499i	0.175345	+	0.442206i
$265$	2.75168	−	19.6726i	0.169034	−	1.20848i
$266$	2.59458	+	0.179542i	0.159084	+	0.0110084i
$267$	−5.66371	+	5.66371i	−0.346613	+	0.346613i
$268$	0.210847	−	20.8161i	0.0128795	−	1.27154i
$269$			14.1096i			0.860280i	0.902762	+	0.430140i	$0.141536\pi$
$269$			14.1096i			0.860280i	−0.902762	+	0.430140i	$0.858464\pi$
$270$	3.06501	−	0.778261i	0.186531	−	0.0473634i
$271$			25.0835i			1.52372i	0.647744	+	0.761858i	$0.275713\pi$
$271$			25.0835i			1.52372i	−0.647744	+	0.761858i	$0.724287\pi$
$272$	15.7074	+	16.3570i	0.952402	+	0.991792i
$273$	1.07604	−	2.18986i	0.0651249	−	0.132536i
$274$	1.53075	−	3.64326i	0.0924761	−	0.220098i
$275$	−13.1391	−	3.74899i	−0.792317	−	0.226072i
$276$	−7.97164	−	8.13478i	−0.479836	−	0.489656i
$277$	1.90869	−	1.90869i	0.114682	−	0.114682i	−0.647437	−	0.762119i	$-0.724159\pi$
$277$	1.90869	−	1.90869i	0.114682	−	0.114682i	0.762119	+	0.647437i	$0.224159\pi$
$278$	−19.9748	+	8.15557i	−1.19801	+	0.489139i
$279$	−10.7977			−0.646442
$280$	−3.62211	+	16.3365i	−0.216463	+	0.976291i
$281$	4.89611			0.292078			0.146039	−	0.989279i	$-0.453348\pi$
$281$	4.89611			0.292078			0.146039	+	0.989279i	$0.453348\pi$
$282$	10.8757	−	4.44045i	0.647636	−	0.264425i
$283$	20.9419	−	20.9419i	1.24487	−	1.24487i	0.286912	−	0.957957i	$-0.407371\pi$
$283$	20.9419	−	20.9419i	1.24487	−	1.24487i	0.957957	−	0.286912i	$-0.0926288\pi$
$284$	19.3584	−	18.9702i	1.14871	−	1.12567i
$285$	−0.215305	+	1.53928i	−0.0127536	+	0.0911791i
$286$	−1.38054	+	3.28576i	−0.0816332	+	0.194291i
$287$	−0.877029	+	1.78485i	−0.0517694	+	0.105356i
$288$	2.03177	+	5.27939i	0.119723	+	0.311091i
$289$		−	15.1422i		−	0.890720i
$290$	−6.25664	+	10.5153i	−0.367402	+	0.617482i
$291$			2.94995i			0.172929i
$292$	17.0739	+	0.172943i	0.999175	+	0.0101207i
$293$	−17.3735	+	17.3735i	−1.01497	+	1.01497i	−0.0150854	+	0.999886i	$0.504802\pi$
$293$	−17.3735	+	17.3735i	−1.01497	+	1.01497i	−0.999886	+	0.0150854i	$0.995198\pi$
$294$	−2.54101	−	9.56783i	−0.148195	−	0.558007i
$295$	−6.90847	+	5.21299i	−0.402227	+	0.303512i
$296$	−3.41799	+	1.35531i	−0.198667	+	0.0787761i
$297$	1.93231	−	1.93231i	0.112124	−	0.112124i
$298$	8.63997	+	21.1612i	0.500500	+	1.22584i
$299$		−	5.25180i		−	0.303719i
$300$	−9.58793	−	2.84106i	−0.553559	−	0.164028i
$301$	−9.04169	−	26.5117i	−0.521154	−	1.52811i
$302$	6.62576	+	16.2280i	0.381270	+	0.933814i
$303$	5.56378	−	5.56378i	0.319631	−	0.319631i
$304$	−2.77978	−	0.0563189i	−0.159431	−	0.00323011i
$305$	3.70687	+	4.91250i	0.212255	+	0.281289i
$306$	3.10574	−	7.39181i	0.177543	−	0.422562i
$307$	−1.79267	−	1.79267i	−0.102313	−	0.102313i	0.654097	−	0.756410i	$-0.273049\pi$
$307$	−1.79267	−	1.79267i	−0.102313	−	0.102313i	−0.756410	+	0.654097i	$0.773049\pi$
$308$	4.52869	+	13.7326i	0.258046	+	0.782488i
$309$	−0.146802			−0.00835126
$310$	29.3439	+	17.4597i	1.66662	+	0.991642i
$311$			30.9213i			1.75338i	0.481053	+	0.876692i	$0.340255\pi$
$311$			30.9213i			1.75338i	−0.481053	+	0.876692i	$0.659745\pi$
$312$	−1.03469	+	2.39442i	−0.0585780	+	0.135557i
$313$	18.4972	+	18.4972i	1.04553	+	1.04553i	0.998913	+	0.0466126i	$0.0148426\pi$
$313$	18.4972	+	18.4972i	1.04553	+	1.04553i	0.0466126	+	0.998913i	$0.485157\pi$
$314$	−7.17507	+	17.0770i	−0.404912	+	0.963712i
$315$	5.80995	−	1.11558i	0.327353	−	0.0628555i
$316$	4.01628	+	4.09847i	0.225933	+	0.230557i
$317$	12.6408	−	12.6408i	0.709976	−	0.709976i	−0.256554	−	0.966530i	$-0.582587\pi$
$317$	12.6408	−	12.6408i	0.709976	−	0.709976i	0.966530	+	0.256554i	$0.0825870\pi$
$318$	−4.74886	−	11.6310i	−0.266303	−	0.652236i
$319$			10.5737i			0.592015i
$320$	3.01512	−	17.6326i	0.168550	−	0.985693i
$321$		−	8.78942i		−	0.490577i
$322$	−13.9909	−	16.0711i	−0.779681	−	0.895609i
$323$	2.78653	+	2.78653i	0.155046	+	0.155046i
$324$	1.42846	−	1.39982i	0.0793592	−	0.0777676i
$325$	−2.24076	−	4.03000i	−0.124295	−	0.223544i
$326$	−10.2609	+	24.4215i	−0.568300	+	1.35258i
$327$	0.705542	−	0.705542i	0.0390166	−	0.0390166i
$328$	0.843329	−	1.95157i	0.0465651	−	0.107758i
$329$	20.8007	−	7.09396i	1.14678	−	0.391102i
$330$	−8.37575	+	2.12675i	−0.461070	+	0.117074i
$331$		−	9.30926i		−	0.511683i	−0.966719	−	0.255842i	$-0.917647\pi$
$331$		−	9.30926i		−	0.511683i	0.966719	−	0.255842i	$-0.0823526\pi$
$332$	0.275104	−	27.1599i	0.0150983	−	1.49059i
$333$	0.919223	+	0.919223i	0.0503731	+	0.0503731i
$334$	17.2079	+	7.23005i	0.941574	+	0.395611i
$335$	23.0499	+	3.22408i	1.25935	+	0.176150i
$336$	3.21248	+	10.0836i	0.175255	+	0.550108i
$337$	−2.73006	−	2.73006i	−0.148716	−	0.148716i	0.628828	−	0.777544i	$-0.283535\pi$
$337$	−2.73006	−	2.73006i	−0.148716	−	0.148716i	−0.777544	+	0.628828i	$0.783535\pi$
$338$	15.9072	−	6.49480i	0.865238	−	0.353270i
$339$			0.802292i			0.0435745i
$340$	−20.3926	+	15.0661i	−1.10594	+	0.817075i
$341$	29.5069			1.59789
$342$	0.371575	+	0.910070i	0.0200925	+	0.0492109i
$343$	−3.69077	−	18.1488i	−0.199283	−	0.979942i
$344$	11.0379	+	27.8366i	0.595123	+	1.50085i
$345$	10.1647	−	7.67010i	0.547251	−	0.412944i
$346$	−8.79800	−	3.69656i	−0.472983	−	0.198728i
$347$	16.3216	−	16.3216i	0.876190	−	0.876190i	−0.116948	−	0.993138i	$-0.537311\pi$
$347$	16.3216	−	16.3216i	0.876190	−	0.876190i	0.993138	+	0.116948i	$0.0373111\pi$
$348$	−0.0783814	+	7.73828i	−0.00420169	+	0.414815i
$349$			10.1509i			0.543367i	0.962387	+	0.271683i	$0.0875803\pi$
$349$			10.1509i			0.543367i	−0.962387	+	0.271683i	$0.912420\pi$
$350$	−17.5930	−	6.36287i	−0.940386	−	0.340110i
$351$	0.922213			0.0492241
$352$	−5.55220	−	14.4270i	−0.295933	−	0.768960i
$353$	16.7350	+	16.7350i	0.890714	+	0.890714i	0.994590	−	0.103877i	$-0.0331247\pi$
$353$	16.7350	+	16.7350i	0.890714	+	0.890714i	−0.103877	+	0.994590i	$0.533125\pi$
$354$	−2.12026	+	5.04632i	−0.112691	+	0.268209i
$355$	18.2526	+	24.1891i	0.968749	+	1.28383i
$356$	11.4416	−	11.2121i	0.606402	−	0.594241i
$357$	6.61508	−	13.4624i	0.350107	−	0.712506i
$358$	−0.976649	−	2.39203i	−0.0516175	−	0.126423i
$359$			10.7959i			0.569787i	0.958559	+	0.284894i	$0.0919583\pi$
$359$			10.7959i			0.569787i	−0.958559	+	0.284894i	$0.908042\pi$
$360$	−6.14548	+	1.49435i	−0.323895	+	0.0787593i
$361$	18.5169			0.974571
$362$	−11.6697	−	28.5816i	−0.613344	−	1.50222i
$363$	2.49776	−	2.49776i	0.131098	−	0.131098i
$364$	−2.19633	+	4.35770i	−0.115119	+	0.228405i
$365$	−2.64448	+	18.9061i	−0.138418	+	0.989593i
$366$	3.58836	+	1.50768i	0.187566	+	0.0788078i
$367$	3.91321	−	3.91321i	0.204268	−	0.204268i	−0.597558	−	0.801826i	$-0.703862\pi$
$367$	3.91321	−	3.91321i	0.204268	−	0.204268i	0.801826	+	0.597558i	$0.203862\pi$
$368$	15.7777	+	16.4302i	0.822468	+	0.856484i
$369$	−0.751652			−0.0391294
$370$	−1.01172	−	3.98445i	−0.0525969	−	0.207142i
$371$	−7.58667	−	22.2454i	−0.393880	−	1.15492i
$372$	21.5943	+	0.218730i	1.11961	+	0.0113406i
$373$	−17.6115	−	17.6115i	−0.911888	−	0.911888i	0.0845324	−	0.996421i	$-0.473060\pi$
$373$	−17.6115	−	17.6115i	−0.911888	−	0.911888i	−0.996421	+	0.0845324i	$0.973060\pi$
$374$	−8.48704	+	20.1996i	−0.438854	+	1.04450i
$375$	4.52741	−	10.2227i	0.233794	−	0.527895i
$376$	−21.8402	+	8.66014i	−1.12632	+	0.446613i
$377$	−2.52321	+	2.52321i	−0.129952	+	0.129952i
$378$	2.82209	−	2.45679i	0.145152	−	0.126364i
$379$	−2.84540			−0.146158			−0.0730791	−	0.997326i	$-0.523283\pi$
$379$	−2.84540			−0.146158			−0.0730791	+	0.997326i	$0.523283\pi$
$380$	0.461770	−	3.07404i	0.0236883	−	0.157695i
$381$	−17.0144			−0.871674
$382$	4.19900	+	10.2843i	0.214840	+	0.526190i
$383$	2.38999	+	2.38999i	0.122123	+	0.122123i	0.765527	−	0.643404i	$-0.222478\pi$
$383$	2.38999	+	2.38999i	0.122123	+	0.122123i	−0.643404	+	0.765527i	$0.722478\pi$
$384$	−3.95638	−	10.5994i	−0.201898	−	0.540898i
$385$	−15.8768	+	3.04853i	−0.809158	+	0.155367i
$386$	−27.5602	−	11.5797i	−1.40278	−	0.589391i
$387$	7.48629	−	7.48629i	0.380550	−	0.380550i
$388$	0.0597574	−	5.89960i	0.00303372	−	0.299507i
$389$	8.27081			0.419347			0.209673	−	0.977771i	$-0.432760\pi$
$389$	8.27081			0.419347			0.209673	+	0.977771i	$0.432760\pi$
$390$	−2.50621	−	1.49120i	−0.126907	−	0.0755098i
$391$		−	32.2860i		−	1.63277i
$392$	4.88794	+	19.1861i	0.246878	+	0.969047i
$393$	−11.3004	+	11.3004i	−0.570031	+	0.570031i
$394$	15.2426	+	6.40432i	0.767911	+	0.322645i
$395$	−5.12120	+	3.86435i	−0.257676	+	0.194437i
$396$	−3.90356	+	3.82528i	−0.196161	+	0.192227i
$397$	−7.24026	−	7.24026i	−0.363378	−	0.363378i	0.501677	−	0.865055i	$-0.332717\pi$
$397$	−7.24026	−	7.24026i	−0.363378	−	0.363378i	−0.865055	+	0.501677i	$0.832717\pi$
$398$	10.1911	+	24.9602i	0.510833	+	1.25114i
$399$	0.593619	+	1.74059i	0.0297181	+	0.0871384i
$400$	19.1173	+	5.87604i	0.955866	+	0.293802i
$401$	−8.11723			−0.405355			−0.202678	−	0.979246i	$-0.564964\pi$
$401$	−8.11723			−0.405355			−0.202678	+	0.979246i	$0.564964\pi$
$402$	13.6278	−	5.56413i	0.679693	−	0.277514i
$403$	7.04122	+	7.04122i	0.350748	+	0.350748i
$404$	−11.2397	+	11.0143i	−0.559196	+	0.547981i
$405$	1.34687	+	1.78492i	0.0669264	+	0.0886935i
$406$	−0.999452	+	14.4432i	−0.0496020	+	0.716804i
$407$	−2.51196	−	2.51196i	−0.124513	−	0.124513i
$408$	−6.36089	+	14.7200i	−0.314911	+	0.728746i
$409$	−24.9506			−1.23373			−0.616864	−	0.787070i	$-0.711597\pi$
$409$	−24.9506			−1.23373			−0.616864	+	0.787070i	$0.711597\pi$
$410$	2.04269	+	1.21541i	0.100881	+	0.0600246i
$411$	2.79433			0.137834
$412$	0.293588	+	0.00297377i	0.0144641	+	0.000146507i
$413$	−4.51606	+	9.19066i	−0.222221	+	0.452243i
$414$	3.11963	−	7.42488i	0.153322	−	0.364913i
$415$	30.0745	+	4.20664i	1.47630	+	0.206496i
$416$	2.11778	−	4.76763i	0.103833	−	0.233752i
$417$	−10.7878	−	10.7878i	−0.528281	−	0.528281i
$418$	−1.01540	−	2.48695i	−0.0496649	−	0.121640i
$419$		−	2.50608i		−	0.122430i	−0.998125	−	0.0612150i	$-0.980502\pi$
$419$		−	2.50608i		−	0.122430i	0.998125	−	0.0612150i	$-0.0194975\pi$
$420$	−11.6419	+	2.11334i	−0.568066	+	0.103121i
$421$			22.7450i			1.10853i	0.832342	+	0.554263i	$0.187000\pi$
$421$			22.7450i			1.10853i	−0.832342	+	0.554263i	$0.813000\pi$
$422$	16.9574	−	6.92360i	0.825475	−	0.337036i
$423$	5.87362	+	5.87362i	0.285585	+	0.285585i
$424$	9.26163	+	23.3571i	0.449784	+	1.13432i
$425$	−13.7753	−	24.7749i	−0.668202	−	1.20176i
$426$	17.6691	+	7.42382i	0.856069	+	0.359685i
$427$	6.53533	+	3.21130i	0.316267	+	0.155405i
$428$	−0.178048	+	17.5779i	−0.00860626	+	0.849661i
$429$	−2.52013			−0.121673
$430$	−32.4500	+	8.23961i	−1.56488	+	0.397349i
$431$	39.2522			1.89071			0.945357	−	0.326037i	$-0.105713\pi$
$431$	39.2522			1.89071			0.945357	+	0.326037i	$0.105713\pi$
$432$	−2.88514	+	2.77055i	−0.138811	+	0.133298i
$433$	19.8929	+	19.8929i	0.955990	+	0.955990i	0.999072	−	0.0430815i	$-0.0137175\pi$
$433$	19.8929	+	19.8929i	0.955990	+	0.955990i	−0.0430815	+	0.999072i	$0.513718\pi$
$434$	40.3049	+	2.78905i	1.93470	+	0.133879i
$435$	−8.56869	−	1.19854i	−0.410837	−	0.0574654i
$436$	−1.42530	+	1.39672i	−0.0682597	+	0.0668908i
$437$	2.79899	+	2.79899i	0.133894	+	0.133894i
$438$	4.56385	+	11.1779i	0.218069	+	0.534101i
$439$	−10.3186			−0.492478			−0.246239	−	0.969209i	$-0.579195\pi$
$439$	−10.3186			−0.492478			−0.246239	+	0.969209i	$0.579195\pi$
$440$	16.7937	−	4.08361i	0.800610	−	0.194679i
$441$	5.54130	−	4.27715i	0.263871	−	0.203674i
$442$	−6.84549	+	2.79496i	−0.325607	+	0.132943i
$443$	24.3473	+	24.3473i	1.15678	+	1.15678i	0.985165	+	0.171610i	$0.0548969\pi$
$443$	24.3473	+	24.3473i	1.15678	+	1.15678i	0.171610	+	0.985165i	$0.445103\pi$
$444$	−1.81973	−	1.85697i	−0.0863606	−	0.0881280i
$445$	10.7880	+	14.2967i	0.511400	+	0.677728i
$446$	0.0268036	−	0.0637939i	0.00126919	−	0.00302073i
$447$	−11.4285	+	11.4285i	−0.540551	+	0.540551i
$448$	−6.22037	−	20.2313i	−0.293885	−	0.955841i
$449$			15.1405i			0.714523i	0.934004	+	0.357261i	$0.116289\pi$
$449$			15.1405i			0.714523i	−0.934004	+	0.357261i	$0.883711\pi$
$450$	−0.774071	−	7.02857i	−0.0364900	−	0.331330i
$451$	2.05404			0.0967208
$452$	0.0162521	−	1.60450i	0.000764434	−	0.0754694i
$453$	−8.76424	+	8.76424i	−0.411780	+	0.411780i
$454$	−2.72938	+	6.49606i	−0.128096	+	0.304875i
$455$	−4.51616	−	3.06122i	−0.211721	−	0.143512i
$456$	−0.724676	−	1.82757i	−0.0339361	−	0.0855840i
$457$	−21.8374	−	21.8374i	−1.02151	−	1.02151i	−0.999764	−	0.0217457i	$-0.993078\pi$
$457$	−21.8374	−	21.8374i	−1.02151	−	1.02151i	−0.0217457	−	0.999764i	$-0.506922\pi$
$458$	−4.29136	+	1.75213i	−0.200522	+	0.0818717i
$459$	5.66941			0.264626
$460$	−20.4838	+	15.1335i	−0.955062	+	0.705603i
$461$	25.1333			1.17057			0.585287	−	0.810826i	$-0.300982\pi$
$461$	25.1333			1.17057			0.585287	+	0.810826i	$0.300982\pi$
$462$	−7.71190	+	6.71367i	−0.358790	+	0.312348i
$463$	−0.705332	+	0.705332i	−0.0327796	+	0.0327796i	−0.723307	−	0.690527i	$-0.757379\pi$
$463$	−0.705332	+	0.705332i	−0.0327796	+	0.0327796i	0.690527	+	0.723307i	$0.257379\pi$
$464$	0.313510	−	15.4742i	0.0145543	−	0.718371i
$465$	−3.34462	+	23.9116i	−0.155103	+	1.10887i
$466$	−7.61579	−	3.19985i	−0.352795	−	0.148230i
$467$	4.07353	+	4.07353i	0.188501	+	0.188501i	0.795048	−	0.606547i	$-0.207446\pi$
$467$	4.07353	+	4.07353i	0.188501	+	0.188501i	−0.606547	+	0.795048i	$0.707446\pi$
$468$	−1.84433	−	0.0186813i	−0.0852543	−	0.000863545i
$469$	26.0644	−	8.88912i	1.20354	−	0.410462i
$470$	−6.46466	−	25.4597i	−0.298193	−	1.17437i
$471$	−13.0978			−0.603516
$472$	4.34253	−	10.0492i	0.199881	−	0.462551i
$473$	−20.4578	+	20.4578i	−0.940649	+	0.940649i
$474$	−1.57173	+	3.74081i	−0.0721922	+	0.171821i
$475$	3.34206	+	0.953591i	0.153344	+	0.0437538i
$476$	−13.5022	+	26.7894i	−0.618872	+	1.22789i
$477$	6.28157	−	6.28157i	0.287613	−	0.287613i
$478$	−34.2868	+	13.9990i	−1.56824	+	0.640301i
$479$	−3.89552			−0.177991			−0.0889953	−	0.996032i	$-0.528366\pi$
$479$	−3.89552			−0.177991			−0.0889953	+	0.996032i	$0.528366\pi$
$480$	12.3206	−	2.86406i	0.562356	−	0.130726i
$481$		−	1.19886i		−	0.0546632i
$482$	9.73078	−	3.97301i	0.443225	−	0.180966i
$483$	6.64467	−	13.5226i	0.302343	−	0.615301i
$484$	−5.04586	+	4.94467i	−0.229357	+	0.224758i
$485$	6.53270	+	0.913755i	0.296635	+	0.0414915i
$486$	1.30381	+	0.547806i	0.0591418	+	0.0248490i
$487$	0.480177	+	0.480177i	0.0217589	+	0.0217589i	0.717903	−	0.696144i	$-0.245102\pi$
$487$	0.480177	+	0.480177i	0.0217589	+	0.0217589i	−0.696144	+	0.717903i	$0.745102\pi$
$488$	−7.14581	−	3.08790i	−0.323476	−	0.139783i
$489$	−18.7309			−0.847043
$490$	−21.9751	+	2.66343i	−0.992735	+	0.120321i
$491$		−	26.2424i		−	1.18430i	−0.805828	−	0.592150i	$-0.798279\pi$
$491$		−	26.2424i		−	1.18430i	0.805828	−	0.592150i	$-0.201721\pi$
$492$	1.50323	+	0.0152263i	0.0677707	+	0.000686453i
$493$	−15.5117	+	15.5117i	−0.698612	+	0.698612i
$494$	0.351154	−	0.835765i	0.0157992	−	0.0376028i
$495$	−3.68058	−	4.87765i	−0.165430	−	0.219234i
$496$	−43.1820	−	0.874874i	−1.93893	−	0.0392830i
$497$	32.1799	+	15.8124i	1.44347	+	0.709283i
$498$	17.7810	−	7.25984i	0.796785	−	0.325321i
$499$	28.3424			1.26878			0.634389	−	0.773014i	$-0.281252\pi$
$499$	28.3424			1.26878			0.634389	+	0.773014i	$0.281252\pi$
$500$	−9.26143	+	20.3525i	−0.414184	+	0.910193i
$501$			13.1982i			0.589652i
$502$	5.51762	+	13.5139i	0.246264	+	0.603155i
$503$	19.9583	+	19.9583i	0.889897	+	0.889897i	0.994513	−	0.104616i	$-0.0333613\pi$
$503$	19.9583	+	19.9583i	0.889897	+	0.889897i	−0.104616	+	0.994513i	$0.533361\pi$
$504$	−5.69365	+	4.85617i	−0.253615	+	0.216311i
$505$	−10.5977	−	14.0444i	−0.471590	−	0.624970i
$506$	−8.52501	+	20.2899i	−0.378983	+	0.901998i
$507$	8.59101	+	8.59101i	0.381540	+	0.381540i
$508$	34.0271	+	0.344662i	1.50971	+	0.0152919i
$509$		−	35.6134i		−	1.57854i	−0.614048	−	0.789269i	$-0.710460\pi$
$509$		−	35.6134i		−	1.57854i	0.614048	−	0.789269i	$-0.289540\pi$
$510$	−15.4072	−	9.16732i	−0.682243	−	0.405936i
$511$	7.29110	+	21.3787i	0.322539	+	0.945739i
$512$	7.69764	+	21.2778i	0.340191	+	0.940356i
$513$	−0.491502	+	0.491502i	−0.0217003	+	0.0217003i
$514$	4.46972	+	1.87800i	0.197151	+	0.0828349i
$515$	−0.0454722	+	0.325094i	−0.00200374	+	0.0143254i
$516$	−15.1235	+	14.8202i	−0.665773	+	0.652421i
$517$	−16.0508	−	16.0508i	−0.705914	−	0.705914i
$518$	−3.19378	−	3.66865i	−0.140327	−	0.161191i
$519$		−	6.74794i		−	0.296202i
$520$	4.98196	+	3.03301i	0.218473	+	0.133006i
$521$		−	34.0551i		−	1.49198i	−0.665957	−	0.745990i	$-0.731977\pi$
$521$		−	34.0551i		−	1.49198i	0.665957	−	0.745990i	$-0.268023\pi$
$522$	−5.06607	+	2.06844i	−0.221736	+	0.0905332i
$523$	5.30937	−	5.30937i	0.232162	−	0.232162i	−0.581432	−	0.813595i	$-0.697508\pi$
$523$	5.30937	−	5.30937i	0.232162	−	0.232162i	0.813595	+	0.581432i	$0.197508\pi$
$524$	22.8286	−	22.3708i	0.997272	−	0.977272i
$525$	−0.670807	−	13.2117i	−0.0292764	−	0.576608i
$526$	13.4091	+	5.63397i	0.584665	+	0.245653i
$527$	43.2867	+	43.2867i	1.88560	+	1.88560i
$528$	7.88421	−	7.57108i	0.343116	−	0.329489i
$529$		−	9.43044i		−	0.410019i
$530$	−27.2280	+	6.91367i	−1.18271	+	0.300310i
$531$	−3.87046			−0.167964
$532$	−1.15192	−	3.49302i	−0.0499420	−	0.151442i
$533$	0.490155	+	0.490155i	0.0212310	+	0.0212310i
$534$	10.4431	+	4.38776i	0.451917	+	0.189877i
$535$	−19.4642	−	2.72254i	−0.841513	−	0.117706i
$536$	−27.3669	+	10.8516i	−1.18207	+	0.468719i
$537$	1.29186	−	1.29186i	0.0557481	−	0.0557481i
$538$	18.4736	−	7.54262i	0.796452	−	0.325185i
$539$	−15.1427	+	11.6881i	−0.652242	+	0.503444i
$540$	−2.65744	−	3.59695i	−0.114358	−	0.154788i
$541$			37.2988i			1.60360i	0.597592	+	0.801801i	$0.296124\pi$
$541$			37.2988i			1.60360i	−0.597592	+	0.801801i	$0.703876\pi$
$542$	32.8415	−	13.4090i	1.41067	−	0.575964i
$543$	15.4361	−	15.4361i	0.662425	−	0.662425i
$544$	13.0193	−	29.3095i	0.558199	−	1.25664i
$545$	−1.34389	−	1.78097i	−0.0575658	−	0.0762885i
$546$	−3.44237	−	0.238208i	−0.147320	−	0.0101944i
$547$	−24.4386	+	24.4386i	−1.04492	+	1.04492i	−0.0459756	+	0.998943i	$0.514640\pi$
$547$	−24.4386	+	24.4386i	−1.04492	+	1.04492i	−0.998943	+	0.0459756i	$0.985360\pi$
$548$	−5.58838	−	0.0566049i	−0.238724	−	0.00241804i
$549$			2.75222i			0.117462i
$550$	2.11530	+	19.2070i	0.0901967	+	0.818987i
$551$		−	2.68953i		−	0.114578i
$552$	−6.38935	+	14.7858i	−0.271949	+	0.629325i
$553$	−3.34772	+	6.81298i	−0.142360	+	0.289717i
$554$	−3.51935	−	1.47869i	−0.149523	−	0.0628234i
$555$	2.32036	−	1.75090i	0.0984938	−	0.0743214i
$556$	21.3560	+	21.7930i	0.905695	+	0.924230i
$557$	−2.77604	+	2.77604i	−0.117625	+	0.117625i	−0.763469	−	0.645844i	$-0.776505\pi$
$557$	−2.77604	+	2.77604i	−0.117625	+	0.117625i	0.645844	+	0.763469i	$0.276505\pi$
$558$	5.77215	+	14.1373i	0.244355	+	0.598479i
$559$	−9.76367			−0.412959
$560$	23.3254	−	3.99064i	0.985679	−	0.168635i
$561$	−15.4928			−0.654106
$562$	−2.61733	−	6.41042i	−0.110405	−	0.270407i
$563$	−25.4137	+	25.4137i	−1.07106	+	1.07106i	−0.0737860	+	0.997274i	$0.523508\pi$
$563$	−25.4137	+	25.4137i	−1.07106	+	1.07106i	−0.997274	+	0.0737860i	$0.976492\pi$
$564$	−11.6277	−	11.8656i	−0.489612	−	0.499633i
$565$	1.77668	+	0.248512i	0.0747456	+	0.0104550i
$566$	−38.6140	−	16.2240i	−1.62307	−	0.681947i
$567$	2.37457	+	1.16680i	0.0997225	+	0.0490011i
$568$	−35.1859	−	15.2048i	−1.47637	−	0.637979i
$569$		−	26.1170i		−	1.09488i	−0.836844	−	0.547441i	$-0.815602\pi$
$569$		−	26.1170i		−	1.09488i	0.836844	−	0.547441i	$-0.184398\pi$
$570$	2.13046	−	0.540960i	0.0892349	−	0.0226583i
$571$		−	21.3882i		−	0.895068i	−0.894267	−	0.447534i	$-0.852302\pi$
$571$		−	21.3882i		−	0.895068i	0.894267	−	0.447534i	$-0.147698\pi$
$572$	5.04000	+	0.0510504i	0.210733	+	0.00213453i
$573$	−5.55424	+	5.55424i	−0.232032	+	0.232032i
$574$	2.80572	+	0.194152i	0.117108	+	0.00810375i
$575$	−13.8370	−	24.8857i	−0.577041	−	1.03781i
$576$	5.82611	−	5.48238i	0.242754	−	0.228432i
$577$	14.2866	−	14.2866i	0.594758	−	0.594758i	−0.344155	−	0.938913i	$-0.611835\pi$
$577$	14.2866	−	14.2866i	0.594758	−	0.594758i	0.938913	+	0.344155i	$0.111835\pi$
$578$	−19.8255	+	8.09462i	−0.824634	+	0.336692i
$579$		−	21.1383i		−	0.878478i
$580$	17.1122	+	2.57053i	0.710546	+	0.106735i
$581$	34.0077	−	11.5981i	1.41088	−	0.481172i
$582$	3.86233	−	1.57696i	0.160099	−	0.0653672i
$583$	−17.1656	+	17.1656i	−0.710928	+	0.710928i
$584$	−8.90081	−	22.4471i	−0.368318	−	0.928868i
$585$	0.285658	−	2.04225i	0.0118105	−	0.0844367i
$586$	32.0343	+	13.4595i	1.32333	+	0.556008i
$587$	17.7442	+	17.7442i	0.732382	+	0.732382i	0.971091	−	0.238709i	$-0.0767244\pi$
$587$	17.7442	+	17.7442i	0.732382	+	0.732382i	−0.238709	+	0.971091i	$0.576724\pi$
$588$	−11.1687	+	8.44160i	−0.460588	+	0.348126i
$589$	−7.50536			−0.309253
$590$	10.5184	+	6.25845i	0.433035	+	0.257656i
$591$			11.6909i			0.480897i
$592$	3.60166	+	3.75062i	0.148027	+	0.154149i
$593$	−32.2253	−	32.2253i	−1.32334	−	1.32334i	−0.911058	−	0.412278i	$-0.864733\pi$
$593$	−32.2253	−	32.2253i	−1.32334	−	1.32334i	−0.412278	−	0.911058i	$-0.635267\pi$
$594$	−3.56290	−	1.49699i	−0.146188	−	0.0614222i
$595$	−27.7636	−	18.8192i	−1.13820	−	0.771511i
$596$	23.0874	−	22.6244i	0.945698	−	0.926732i
$597$	−13.4803	+	13.4803i	−0.551711	+	0.551711i
$598$	−6.87611	+	2.80747i	−0.281185	+	0.114806i
$599$			8.47680i			0.346353i	0.984891	+	0.173176i	$0.0554031\pi$
$599$			8.47680i			0.346353i	−0.984891	+	0.173176i	$0.944597\pi$
$600$	1.40568	+	14.0721i	0.0573868	+	0.574491i
$601$		−	30.8501i		−	1.25840i	−0.777243	−	0.629201i	$-0.783382\pi$
$601$		−	30.8501i		−	1.25840i	0.777243	−	0.629201i	$-0.216618\pi$
$602$	−29.8780	+	26.0106i	−1.21774	+	1.06011i
$603$	7.35997	+	7.35997i	0.299721	+	0.299721i
$604$	17.7051	−	17.3500i	0.720411	−	0.705963i
$605$	−4.75763	−	6.30501i	−0.193425	−	0.256335i
$606$	−10.2588	−	4.31034i	−0.416737	−	0.175096i
$607$	12.9179	−	12.9179i	0.524319	−	0.524319i	−0.394554	−	0.918873i	$-0.629101\pi$
$607$	12.9179	−	12.9179i	0.524319	−	0.524319i	0.918873	+	0.394554i	$0.129101\pi$
$608$	1.41226	+	3.66964i	0.0572746	+	0.148824i
$609$	−9.68931	+	3.30449i	−0.392631	+	0.133905i
$610$	4.45028	−	7.47945i	0.180187	−	0.302834i
$611$		−	7.66041i		−	0.309907i
$612$	−11.3382	−	0.114846i	−0.458321	−	0.00464236i
$613$	−28.6067	−	28.6067i	−1.15542	−	1.15542i	−0.985450	−	0.169965i	$-0.945635\pi$
$613$	−28.6067	−	28.6067i	−1.15542	−	1.15542i	−0.169965	−	0.985450i	$-0.554365\pi$
$614$	−1.38881	+	3.30543i	−0.0560477	+	0.133396i
$615$	−0.232826	+	1.66454i	−0.00938845	+	0.0671208i
$616$	15.5590	−	13.2704i	0.626891	−	0.534681i
$617$	−24.6084	−	24.6084i	−0.990698	−	0.990698i	0.00925894	−	0.999957i	$-0.497053\pi$
$617$	−24.6084	−	24.6084i	−0.990698	−	0.990698i	−0.999957	+	0.00925894i	$0.997053\pi$
$618$	0.0784762	+	0.192206i	0.00315677	+	0.00773164i
$619$		−	30.0791i		−	1.20898i	−0.796612	−	0.604491i	$-0.793376\pi$
$619$		−	30.0791i		−	1.20898i	0.796612	−	0.604491i	$-0.206624\pi$
$620$	7.17327	−	47.7530i	0.288085	−	1.91781i
$621$	5.69477			0.228523
$622$	40.4848	−	16.5296i	1.62329	−	0.662778i
$623$	19.0196	+	9.34573i	0.762003	+	0.374429i
$624$	3.68810	+	0.0747215i	0.147642	+	0.00299125i
$625$	−21.2358	−	13.1925i	−0.849431	−	0.527699i
$626$	14.3301	−	34.1063i	0.572745	−	1.36316i
$627$	1.34312	−	1.34312i	0.0536392	−	0.0536392i
$628$	26.1943	+	0.265323i	1.04527	+	0.0105876i
$629$		−	7.37011i		−	0.293866i
$630$	−4.56645	−	7.01053i	−0.181932	−	0.279306i
$631$	−11.6754			−0.464790			−0.232395	−	0.972621i	$-0.574656\pi$
$631$	−11.6754			−0.464790			−0.232395	+	0.972621i	$0.574656\pi$
$632$	3.21909	−	7.44939i	0.128048	−	0.296321i
$633$	9.15821	+	9.15821i	0.364006	+	0.364006i
$634$	−23.3078	−	9.79299i	−0.925671	−	0.388929i
$635$	−5.27025	+	37.6786i	−0.209144	+	1.49523i
$636$	−12.6897	+	12.4353i	−0.503181	+	0.493090i
$637$	−6.40264	−	0.824360i	−0.253682	−	0.0326623i
$638$	13.8440	−	5.65242i	0.548091	−	0.223782i
$639$			13.5519i			0.536106i
$640$	−24.6979	+	5.47826i	−0.976272	+	0.216547i
$641$	8.72083			0.344452			0.172226	−	0.985057i	$-0.444904\pi$
$641$	8.72083			0.344452			0.172226	+	0.985057i	$0.444904\pi$
$642$	−11.5079	+	4.69858i	−0.454179	+	0.185438i
$643$	2.51464	−	2.51464i	0.0991677	−	0.0991677i	−0.655782	−	0.754950i	$-0.727661\pi$
$643$	2.51464	−	2.51464i	0.0991677	−	0.0991677i	0.754950	+	0.655782i	$0.227661\pi$
$644$	−13.5626	+	26.9093i	−0.534441	+	1.06037i
$645$	−14.2596	−	18.8974i	−0.561470	−	0.744083i
$646$	2.15876	−	5.13796i	0.0849354	−	0.202150i
$647$	34.3587	−	34.3587i	1.35078	−	1.35078i	0.465987	−	0.884791i	$-0.345699\pi$
$647$	34.3587	−	34.3587i	1.35078	−	1.35078i	0.884791	−	0.465987i	$-0.154301\pi$
$648$	−2.59638	−	1.12197i	−0.101995	−	0.0440750i
$649$	10.5768			0.415175
$650$	−4.07858	+	5.08813i	−0.159975	+	0.199573i
$651$	9.22145	+	27.0388i	0.361417	+	1.05973i
$652$	37.4600	+	0.379434i	1.46705	+	0.0148598i
$653$	19.0429	+	19.0429i	0.745205	+	0.745205i	0.973575	−	0.228369i	$-0.0733394\pi$
$653$	19.0429	+	19.0429i	0.745205	+	0.745205i	−0.228369	+	0.973575i	$0.573339\pi$
$654$	−1.30092	−	0.546594i	−0.0508700	−	0.0213735i
$655$	21.5246	+	28.5252i	0.841034	+	1.11457i
$656$	−3.00599	−	0.0609019i	−0.117364	−	0.00237782i
$657$	−6.03685	+	6.03685i	−0.235520	+	0.235520i
$658$	−20.4075	−	23.4418i	−0.795566	−	0.913856i
$659$	−19.1601			−0.746370			−0.373185	−	0.927757i	$-0.621734\pi$
$659$	−19.1601			−0.746370			−0.373185	+	0.927757i	$0.621734\pi$
$660$	7.26197	+	9.82936i	0.282672	+	0.382607i
$661$	40.5236			1.57618			0.788092	−	0.615557i	$-0.211069\pi$
$661$	40.5236			1.57618			0.788092	+	0.615557i	$0.211069\pi$
$662$	−12.1885	+	4.97647i	−0.473719	+	0.193416i
$663$	−3.69704	−	3.69704i	−0.143581	−	0.143581i
$664$	−35.7072	+	14.1588i	−1.38571	+	0.549466i
$665$	4.03843	−	0.775423i	0.156603	−	0.0300696i
$666$	0.712136	−	1.69492i	0.0275947	−	0.0656767i
$667$	−15.5811	+	15.5811i	−0.603303	+	0.603303i
$668$	0.267357	−	26.3950i	0.0103443	−	1.02125i
$669$	0.0489290			0.00189170
$670$	−8.10058	−	31.9024i	−0.312953	−	1.23250i
$671$		−	7.52098i		−	0.290344i
$672$	11.4851	−	9.59650i	0.443047	−	0.370193i
$673$	−5.40919	+	5.40919i	−0.208509	+	0.208509i	−0.803633	−	0.595125i	$-0.797103\pi$
$673$	−5.40919	+	5.40919i	−0.208509	+	0.208509i	0.595125	+	0.803633i	$0.297103\pi$
$674$	−2.11502	+	5.03385i	−0.0814674	+	0.193897i
$675$	4.36992	−	2.42977i	0.168198	−	0.0935217i
$676$	−17.0071	−	17.3552i	−0.654120	−	0.667506i
$677$	5.06251	+	5.06251i	0.194568	+	0.194568i	0.797667	−	0.603099i	$-0.206067\pi$
$677$	5.06251	+	5.06251i	0.194568	+	0.194568i	−0.603099	+	0.797667i	$0.706067\pi$
$678$	1.05043	−	0.428883i	0.0403415	−	0.0164712i
$679$	7.38706	−	2.51932i	0.283489	−	0.0966825i
$680$	30.6272	+	18.6458i	1.17450	+	0.715034i
$681$	−4.98238			−0.190925
$682$	−15.7735	−	38.6329i	−0.604000	−	1.47933i
$683$	−15.0127	−	15.0127i	−0.574445	−	0.574445i	0.358923	−	0.933367i	$-0.383144\pi$
$683$	−15.0127	−	15.0127i	−0.574445	−	0.574445i	−0.933367	+	0.358923i	$0.883144\pi$
$684$	0.992909	−	0.972996i	0.0379648	−	0.0372034i
$685$	0.865551	−	6.18807i	0.0330710	−	0.236434i
$686$	−21.7890	+	14.5341i	−0.831907	+	0.554915i
$687$	−2.31763	−	2.31763i	−0.0884233	−	0.0884233i
$688$	30.5456	−	29.3325i	1.16454	−	1.11829i
$689$	−8.19247			−0.312108
$690$	−15.4761	−	9.20833i	−0.589167	−	0.350555i
$691$	−23.0407			−0.876509			−0.438255	−	0.898851i	$-0.644403\pi$
$691$	−23.0407			−0.876509			−0.438255	+	0.898851i	$0.644403\pi$
$692$	−0.136693	+	13.4952i	−0.00519630	+	0.513010i
$693$	−6.48897	−	3.18852i	−0.246496	−	0.121122i
$694$	−30.0948	−	12.6446i	−1.14238	−	0.479982i
$695$	−27.2312	+	20.5481i	−1.03294	+	0.779436i
$696$	10.1735	−	4.03405i	0.385627	−	0.152910i
$697$	3.01328	+	3.01328i	0.114136	+	0.114136i
$698$	13.2905	−	5.42640i	0.503052	−	0.205392i
$699$		−	5.84121i		−	0.220935i
$700$	1.07391	+	26.4357i	0.0405901	+	0.999176i
$701$			14.1221i			0.533386i	0.963782	+	0.266693i	$0.0859309\pi$
$701$			14.1221i			0.533386i	−0.963782	+	0.266693i	$0.914069\pi$
$702$	−0.492990	−	1.20744i	−0.0186067	−	0.0455720i
$703$	0.638941	+	0.638941i	0.0240981	+	0.0240981i
$704$	−15.9210	+	14.9817i	−0.600045	+	0.564643i
$705$	14.8266	−	11.1878i	0.558400	−	0.421358i
$706$	12.9648	−	30.8570i	0.487938	−	1.16132i
$707$	−18.6840	−	9.18084i	−0.702684	−	0.345281i
$708$	7.74052	+	0.0784041i	0.290906	+	0.00294661i
$709$	11.5784			0.434834			0.217417	−	0.976079i	$-0.430237\pi$
$709$	11.5784			0.434834			0.217417	+	0.976079i	$0.430237\pi$
$710$	21.9132	−	36.8288i	0.822386	−	1.38216i
$711$	−2.86914			−0.107601
$712$	−20.7962	−	8.98662i	−0.779371	−	0.336788i
$713$	43.4803	+	43.4803i	1.62835	+	1.62835i
$714$	−21.1624	−	1.46441i	−0.791983	−	0.0548042i
$715$	−0.780616	+	5.58085i	−0.0291934	+	0.208712i
$716$	−2.60977	+	2.55743i	−0.0975315	+	0.0955755i
$717$	−18.5173	−	18.5173i	−0.691540	−	0.691540i
$718$	14.1350	−	5.77120i	0.527512	−	0.215379i
$719$	−37.0363			−1.38122			−0.690611	−	0.723227i	$-0.742658\pi$
$719$	−37.0363			−1.38122			−0.690611	+	0.723227i	$0.742658\pi$
$720$	5.24174	+	7.24736i	0.195348	+	0.270093i
$721$	0.125372	+	0.367610i	0.00466908	+	0.0136905i
$722$	−9.89860	−	24.2439i	−0.368388	−	0.902264i
$723$	5.25531	+	5.25531i	0.195447	+	0.195447i
$724$	−31.1832	+	30.5579i	−1.15892	+	1.13567i
$725$	−5.30834	+	18.6042i	−0.197147	+	0.690942i
$726$	−4.60552	−	1.93505i	−0.170927	−	0.0718165i
$727$	−11.7694	+	11.7694i	−0.436503	+	0.436503i	−0.890833	−	0.454330i	$-0.849879\pi$
$727$	−11.7694	+	11.7694i	−0.436503	+	0.436503i	0.454330	+	0.890833i	$0.349879\pi$
$728$	6.87957	+	0.546124i	0.254974	+	0.0202407i
$729$			1.00000i			0.0370370i
$730$	26.1672	−	6.64432i	0.968493	−	0.245917i
$731$	−60.0233			−2.22004
$732$	0.0557519	−	5.50416i	0.00206065	−	0.203439i
$733$	−14.6000	+	14.6000i	−0.539262	+	0.539262i	−0.923312	−	0.384050i	$-0.874529\pi$
$733$	−14.6000	+	14.6000i	−0.539262	+	0.539262i	0.384050	+	0.923312i	$0.374529\pi$
$734$	−7.21541	−	3.03162i	−0.266326	−	0.111899i
$735$	−7.75535	−	13.5961i	−0.286060	−	0.501501i
$736$	13.0776	−	29.4406i	0.482045	−	1.08520i
$737$	−20.1126	−	20.1126i	−0.740856	−	0.740856i
$738$	0.401812	+	0.984128i	0.0147909	+	0.0362263i
$739$	35.9219			1.32141			0.660705	−	0.750646i	$-0.270258\pi$
$739$	35.9219			1.32141			0.660705	+	0.750646i	$0.270258\pi$
$740$	−4.67595	+	3.45461i	−0.171891	+	0.126994i
$741$	0.641020			0.0235484
$742$	−25.0699	+	21.8249i	−0.920347	+	0.801217i
$743$	−5.83345	+	5.83345i	−0.214008	+	0.214008i	−0.805968	−	0.591959i	$-0.798355\pi$
$743$	−5.83345	+	5.83345i	−0.214008	+	0.214008i	0.591959	+	0.805968i	$0.298355\pi$
$744$	−11.2573	−	28.3901i	−0.412714	−	1.04083i
$745$	21.7686	+	28.8486i	0.797540	+	1.05693i
$746$	−13.6439	+	32.4731i	−0.499538	+	1.18892i
$747$	9.60298	+	9.60298i	0.351355	+	0.351355i
$748$	30.9840	+	0.313838i	1.13289	+	0.0114751i
$749$	−22.0098	+	7.50633i	−0.804221	+	0.274275i
$750$	−15.8046	−	0.462930i	−0.577103	−	0.0169038i
$751$	53.2891			1.94455			0.972273	−	0.233850i	$-0.0751324\pi$
$751$	53.2891			1.94455			0.972273	+	0.233850i	$0.0751324\pi$
$752$	23.0137	+	23.9656i	0.839225	+	0.873934i
$753$	−7.29845	+	7.29845i	−0.265970	+	0.265970i
$754$	4.65244	+	1.95477i	0.169432	+	0.0711884i
$755$	16.6937	+	22.1232i	0.607548	+	0.805147i
$756$	−4.72526	−	2.38159i	−0.171856	−	0.0866174i
$757$	−10.7784	+	10.7784i	−0.391748	+	0.391748i	−0.875310	−	0.483562i	$-0.839343\pi$
$757$	−10.7784	+	10.7784i	−0.391748	+	0.391748i	0.483562	+	0.875310i	$0.339343\pi$
$758$	1.52107	+	3.72544i	0.0552477	+	0.135314i
$759$	−15.5621			−0.564868
$760$	−4.27165	+	1.03871i	−0.154949	+	0.0376779i
$761$			17.9007i			0.648898i	0.945903	+	0.324449i	$0.105179\pi$
$761$			17.9007i			0.648898i	−0.945903	+	0.324449i	$0.894821\pi$
$762$	9.09543	+	22.2767i	0.329493	+	0.807001i
$763$	−2.36931	−	1.16422i	−0.0857749	−	0.0421476i
$764$	11.2204	−	10.9954i	0.405941	−	0.397799i
$765$	1.75611	−	12.5550i	0.0634924	−	0.453926i
$766$	1.85156	−	4.40681i	0.0668996	−	0.159224i
$767$	2.52394	+	2.52394i	0.0911341	+	0.0911341i
$768$	−11.7627	+	10.8462i	−0.424449	+	0.391378i
$769$	−15.6268			−0.563516			−0.281758	−	0.959485i	$-0.590918\pi$
$769$	−15.6268			−0.563516			−0.281758	+	0.959485i	$0.590918\pi$
$770$	12.4787	+	19.1577i	0.449701	+	0.690394i
$771$			3.42821i			0.123464i
$772$	−0.428200	+	42.2745i	−0.0154113	+	1.52149i
$773$	10.7314	−	10.7314i	0.385982	−	0.385982i	−0.487270	−	0.873251i	$-0.662007\pi$
$773$	10.7314	−	10.7314i	0.385982	−	0.385982i	0.873251	+	0.487270i	$0.162007\pi$
$774$	−13.8037	−	5.79974i	−0.496163	−	0.208467i
$775$	51.9165	+	14.8134i	1.86490	+	0.532112i
$776$	−7.75622	+	3.07552i	−0.278432	+	0.110405i
$777$	1.51682	−	3.08689i	0.0544155	−	0.110741i
$778$	−4.42135	−	10.8289i	−0.158513	−	0.388234i
$779$	−0.522465			−0.0187192
$780$	−0.612656	+	4.07851i	−0.0219366	+	0.146034i
$781$		−	37.0333i		−	1.32515i
$782$	−42.2717	+	17.2592i	−1.51163	+	0.617188i
$783$	−2.73604	−	2.73604i	−0.0977779	−	0.0977779i
$784$	22.5072	−	16.6561i	0.803829	−	0.594861i
$785$	−4.05708	+	29.0053i	−0.144803	+	1.03524i
$786$	20.8364	+	8.75460i	0.743210	+	0.312266i
$787$	28.5133	+	28.5133i	1.01639	+	1.01639i	0.999863	+	0.0165242i	$0.00526006\pi$
$787$	28.5133	+	28.5133i	1.01639	+	1.01639i	0.0165242	+	0.999863i	$0.494740\pi$
$788$	0.236822	−	23.3805i	0.00843645	−	0.832896i
$789$			10.2846i			0.366141i
$790$	7.79720	+	4.63934i	0.277412	+	0.165060i
$791$	2.00904	−	0.685173i	0.0714333	−	0.0243619i
$792$	7.09512	+	3.06600i	0.252114	+	0.108945i
$793$	1.79473	−	1.79473i	0.0637328	−	0.0637328i
$794$	−5.60914	+	13.3500i	−0.199061	+	0.473774i
$795$	−11.9649	−	15.8563i	−0.424350	−	0.562366i
$796$	27.2322	−	26.6861i	0.965221	−	0.945863i
$797$	−37.8838	−	37.8838i	−1.34191	−	1.34191i	−0.894153	−	0.447761i	$-0.852221\pi$
$797$	−37.8838	−	37.8838i	−1.34191	−	1.34191i	−0.447761	−	0.894153i	$-0.647779\pi$
$798$	1.96160	−	1.70769i	0.0694398	−	0.0604515i
$799$		−	47.0933i		−	1.66604i
$800$	−2.52616	−	28.1712i	−0.0893134	−	0.996004i
$801$			8.00970i			0.283009i
$802$	4.33925	+	10.6278i	0.153224	+	0.375280i
$803$	16.4969	−	16.4969i	0.582162	−	0.582162i
$804$	−14.5701	−	14.8683i	−0.513848	−	0.524364i
$805$	−27.8878	−	18.9034i	−0.982915	−	0.666256i
$806$	5.45494	−	12.9830i	0.192142	−	0.457307i
$807$	9.97702	+	9.97702i	0.351208	+	0.351208i
$808$	20.4293	+	8.82806i	0.718700	+	0.310570i
$809$		−	48.0950i		−	1.69093i	−0.534030	−	0.845466i	$-0.679323\pi$
$809$		−	48.0950i		−	1.69093i	0.534030	−	0.845466i	$-0.320677\pi$
$810$	1.61698	−	2.71761i	0.0568148	−	0.0954869i
$811$	−9.01398			−0.316524			−0.158262	−	0.987397i	$-0.550589\pi$
$811$	−9.01398			−0.316524			−0.158262	+	0.987397i	$0.550589\pi$
$812$	19.4446	−	6.41236i	0.682371	−	0.225030i
$813$	17.7367	+	17.7367i	0.622055	+	0.622055i
$814$	−1.94605	+	4.63170i	−0.0682091	+	0.162341i
$815$	−5.80196	+	41.4799i	−0.203234	+	1.45298i
$816$	22.6730	+	0.459359i	0.793714	+	0.0160808i
$817$	5.20363	−	5.20363i	0.182052	−	0.182052i
$818$	13.3379	+	32.6675i	0.466349	+	1.14219i
$819$	−0.787588	−	2.30934i	−0.0275206	−	0.0806949i
$820$	0.499347	−	3.32419i	0.0174380	−	0.116086i
$821$			45.0380i			1.57184i	0.618329	+	0.785919i	$0.287810\pi$
$821$			45.0380i			1.57184i	−0.618329	+	0.785919i	$0.712190\pi$
$822$	−1.49377	−	3.65858i	−0.0521013	−	0.127608i
$823$	−20.1794	+	20.1794i	−0.703410	+	0.703410i	−0.965141	−	0.261731i	$-0.915707\pi$
$823$	−20.1794	+	20.1794i	−0.703410	+	0.703410i	0.261731	+	0.965141i	$0.415707\pi$
$824$	−0.153051	−	0.385981i	−0.00533178	−	0.0134463i
$825$	−11.9417	+	6.63981i	−0.415756	+	0.231169i
$826$	14.4474	+	0.999741i	0.502689	+	0.0347854i
$827$	−16.2430	+	16.2430i	−0.564824	+	0.564824i	−0.930674	−	0.365850i	$-0.880778\pi$
$827$	−16.2430	+	16.2430i	−0.564824	+	0.564824i	0.365850	+	0.930674i	$0.380778\pi$
$828$	−11.3890	−	0.115359i	−0.395794	−	0.00400902i
$829$			33.9024i			1.17748i	0.808323	+	0.588739i	$0.200375\pi$
$829$			33.9024i			1.17748i	−0.808323	+	0.588739i	$0.799625\pi$
$830$	−10.5693	−	41.6249i	−0.366866	−	1.44482i
$831$		−	2.69929i		−	0.0936374i
$832$	−7.37430	−	0.224145i	−0.255658	−	0.00777084i
$833$	−39.3610	−	5.06785i	−1.36378	−	0.175590i
$834$	−8.35747	+	19.8912i	−0.289395	+	0.688776i
$835$	29.2275	+	4.08817i	1.01146	+	0.141477i
$836$	−2.71332	+	2.65890i	−0.0938421	+	0.0919601i
$837$	−7.63513	+	7.63513i	−0.263909	+	0.263909i
$838$	−3.28118	+	1.33968i	−0.113346	+	0.0462785i
$839$	−4.44797			−0.153561			−0.0767805	−	0.997048i	$-0.524464\pi$
$839$	−4.44797			−0.153561			−0.0767805	+	0.997048i	$0.524464\pi$
$840$	8.99041	+	14.1129i	0.310199	+	0.486940i
$841$	−14.0282			−0.483732
$842$	29.7798	−	12.1589i	1.02628	−	0.419022i
$843$	3.46207	−	3.46207i	0.119240	−	0.119240i
$844$	−18.1300	−	18.5010i	−0.624059	−	0.636831i
$845$	21.6860	−	16.3638i	0.746020	−	0.562931i
$846$	4.55038	−	10.8301i	0.156445	−	0.372347i
$847$	−8.38785	−	4.12157i	−0.288210	−	0.141619i
$848$	25.6301	−	24.6122i	0.880141	−	0.845185i
$849$		−	29.6164i		−	1.01643i
$850$	−25.0735	+	31.2799i	−0.860015	+	1.07289i
$851$		−	7.40308i		−	0.253774i
$852$	0.274522	−	27.1024i	0.00940497	−	0.928514i
$853$	−25.8367	+	25.8367i	−0.884633	+	0.884633i	−0.994001	−	0.109368i	$-0.965117\pi$
$853$	−25.8367	+	25.8367i	−0.884633	+	0.884633i	0.109368	+	0.994001i	$0.465117\pi$
$854$	0.710900	−	10.2733i	0.0243265	−	0.351545i
$855$	0.936191	+	1.24068i	0.0320171	+	0.0424303i
$856$	23.1097	−	9.16356i	0.789875	−	0.313204i
$857$	7.21409	−	7.21409i	0.246429	−	0.246429i	−0.573075	−	0.819503i	$-0.694249\pi$
$857$	7.21409	−	7.21409i	0.246429	−	0.246429i	0.819503	+	0.573075i	$0.194249\pi$
$858$	1.34719	+	3.29957i	0.0459924	+	0.112646i
$859$			12.6174i			0.430500i	0.976559	+	0.215250i	$0.0690567\pi$
$859$			12.6174i			0.430500i	−0.976559	+	0.215250i	$0.930943\pi$
$860$	28.1349	+	38.0816i	0.959391	+	1.29857i
$861$	0.641926	+	1.88223i	0.0218768	+	0.0641463i
$862$	−20.9832	−	51.3925i	−0.714689	−	1.75043i
$863$	1.96768	−	1.96768i	0.0669805	−	0.0669805i	−0.672823	−	0.739803i	$-0.734918\pi$
$863$	1.96768	−	1.96768i	0.0669805	−	0.0669805i	0.739803	+	0.672823i	$0.234918\pi$
$864$	5.16977	+	2.29641i	0.175879	+	0.0781256i
$865$	−14.9434	−	2.09019i	−0.508090	−	0.0710686i
$866$	15.4113	−	36.6796i	0.523697	−	1.24643i
$867$	−10.7072	−	10.7072i	−0.363635	−	0.363635i
$868$	−17.8942	−	54.2617i	−0.607370	−	1.84176i
$869$	7.84050			0.265971
$870$	3.01135	+	11.8596i	0.102094	+	0.402077i
$871$		−	9.59893i		−	0.325247i
$872$	2.59064	+	1.11948i	0.0877300	+	0.0379105i
$873$	2.08593	+	2.08593i	0.0705981	+	0.0705981i
$874$	2.16842	−	5.16094i	0.0733479	−	0.174572i
$875$	−29.4653	−	2.60686i	−0.996109	−	0.0881279i
$876$	12.1954	−	11.9508i	0.412043	−	0.403780i
$877$	−17.9777	+	17.9777i	−0.607065	+	0.607065i	−0.942178	−	0.335113i	$-0.891226\pi$
$877$	−17.9777	+	17.9777i	−0.607065	+	0.607065i	0.335113	+	0.942178i	$0.391226\pi$
$878$	5.51601	+	13.5099i	0.186156	+	0.455939i
$879$			24.5699i			0.828721i
$880$	−14.3241	−	19.8048i	−0.482865	−	0.667620i
$881$		−	22.8009i		−	0.768181i	−0.923295	−	0.384091i	$-0.874515\pi$
$881$		−	22.8009i		−	0.768181i	0.923295	−	0.384091i	$-0.125485\pi$
$882$	−8.56224	−	4.96871i	−0.288306	−	0.167305i
$883$	−15.3917	−	15.3917i	−0.517971	−	0.517971i	0.398986	−	0.916957i	$-0.369362\pi$
$883$	−15.3917	−	15.3917i	−0.517971	−	0.517971i	−0.916957	+	0.398986i	$0.869362\pi$
$884$	7.31882	+	7.46860i	0.246158	+	0.251196i
$885$	−1.19888	+	8.57117i	−0.0403000	+	0.288117i
$886$	18.8622	−	44.8930i	0.633688	−	1.50821i
$887$	−24.7552	+	24.7552i	−0.831200	+	0.831200i	−0.987681	−	0.156481i	$-0.949985\pi$
$887$	−24.7552	+	24.7552i	−0.831200	+	0.831200i	0.156481	+	0.987681i	$0.449985\pi$
$888$	−1.45853	+	3.37524i	−0.0489451	+	0.113266i
$889$	14.5306	+	42.6062i	0.487342	+	1.42897i
$890$	12.9515	−	21.7672i	0.434136	−	0.729638i
$891$		−	2.73270i		−	0.0915488i
$892$	−0.0978530		0.000991158i	−0.00327636		3.31864e-5i
$893$	4.08268	+	4.08268i	0.136622	+	0.136622i
$894$	21.0726	+	8.85386i	0.704774	+	0.296117i
$895$	−2.46069	−	3.26100i	−0.0822517	−	0.109003i
$896$	−23.1634	+	18.9594i	−0.773835	+	0.633388i
$897$	−3.71358	−	3.71358i	−0.123993	−	0.123993i
$898$	19.8232	−	8.09367i	0.661509	−	0.270089i
$899$		−	41.7800i		−	1.39344i
$900$	−8.78862	+	4.77076i	−0.292954	+	0.159025i
$901$	−50.3641			−1.67787
$902$	−1.09803	−	2.68932i	−0.0365604	−	0.0895447i
$903$	−25.1401	−	12.3532i	−0.836609	−	0.411088i
$904$	−2.10944	+	0.836444i	−0.0701590	+	0.0278197i
$905$	−29.4020	−	38.9647i	−0.977354	−	1.29523i
$906$	16.1600	+	6.78978i	0.536881	+	0.225575i
$907$	6.69500	−	6.69500i	0.222304	−	0.222304i	−0.587164	−	0.809468i	$-0.699756\pi$
$907$	6.69500	−	6.69500i	0.222304	−	0.222304i	0.809468	+	0.587164i	$0.199756\pi$
$908$	9.96425	+	0.100928i	0.330675	+	0.00334943i
$909$		−	7.86838i		−	0.260978i
$910$	−1.59380	+	7.54939i	−0.0528339	+	0.250260i
$911$	6.41072			0.212397			0.106198	−	0.994345i	$-0.466132\pi$
$911$	6.41072			0.212397			0.106198	+	0.994345i	$0.466132\pi$
$912$	−2.00543	+	1.92578i	−0.0664063	+	0.0637689i
$913$	−26.2420	−	26.2420i	−0.868484	−	0.868484i
$914$	−16.9177	+	40.2650i	−0.559589	+	1.33185i
$915$	6.09482	+	0.852507i	0.201488	+	0.0281830i
$916$	4.58808	+	4.68198i	0.151595	+	0.154697i
$917$	37.9485	+	18.6469i	1.25317	+	0.615775i
$918$	−3.03071	−	7.42289i	−0.100028	−	0.244992i
$919$			35.0631i			1.15663i	0.815815	+	0.578313i	$0.196289\pi$
$919$			35.0631i			1.15663i	−0.815815	+	0.578313i	$0.803711\pi$
$920$	30.7642	+	18.7292i	1.01426	+	0.617484i
$921$	−2.53522			−0.0835383
$922$	−13.4356	−	32.9067i	−0.442477	−	1.08372i
$923$	8.83725	−	8.83725i	0.290882	−	0.290882i
$924$	12.9127	+	6.50815i	0.424796	+	0.214103i
$925$	−3.15864	−	5.68081i	−0.103855	−	0.186784i
$926$	1.30053	+	0.546431i	0.0427382	+	0.0179568i
$927$	−0.103805	+	0.103805i	−0.00340939	+	0.00340939i
$928$	−20.4277	+	7.86159i	−0.670573	+	0.258069i
$929$	−1.13791			−0.0373336			−0.0186668	−	0.999826i	$-0.505942\pi$
$929$	−1.13791			−0.0373336			−0.0186668	+	0.999826i	$0.505942\pi$
$930$	33.0951	−	8.40343i	1.08523	−	0.275559i
$931$	3.85169	−	2.97299i	0.126234	−	0.0974359i
$932$	−0.118326	+	11.6818i	−0.00387589	+	0.382650i
$933$	21.8646	+	21.8646i	0.715816	+	0.715816i
$934$	3.15582	−	7.51102i	0.103262	−	0.245768i
$935$	−4.79893	+	34.3089i	−0.156942	+	1.12202i
$936$	0.961470	+	2.42475i	0.0314266	+	0.0792553i
$937$	−9.40662	+	9.40662i	−0.307301	+	0.307301i	−0.843862	−	0.536561i	$-0.819723\pi$
$937$	−9.40662	+	9.40662i	−0.307301	+	0.307301i	0.536561	+	0.843862i	$0.319723\pi$
$938$	−25.5717	−	29.3739i	−0.834946	−	0.959091i
$939$	26.1590			0.853668
$940$	−29.8782	+	22.0741i	−0.974520	+	0.719979i
$941$	37.4472			1.22074			0.610372	−	0.792115i	$-0.291020\pi$
$941$	37.4472			1.22074			0.610372	+	0.792115i	$0.291020\pi$
$942$	7.00173	+	17.1488i	0.228129	+	0.558738i
$943$	3.02676	+	3.02676i	0.0985649	+	0.0985649i
$944$	−15.4787	−	0.313600i	−0.503787	−	0.0102068i
$945$	3.31942	−	4.89708i	0.107981	−	0.159302i
$946$	37.7212	+	15.8489i	1.22642	+	0.515293i
$947$	40.7713	−	40.7713i	1.32489	−	1.32489i	0.415125	−	0.909765i	$-0.363738\pi$
$947$	40.7713	−	40.7713i	1.32489	−	1.32489i	0.909765	−	0.415125i	$-0.136262\pi$
$948$	5.73799	+	0.0581204i	0.186361	+	0.00188766i
$949$	7.87330			0.255578
$950$	−0.538047	−	4.88548i	−0.0174566	−	0.158506i
$951$		−	17.8767i		−	0.579693i
$952$	42.2929	+	3.35736i	1.37072	+	0.108813i
$953$	−13.1807	+	13.1807i	−0.426963	+	0.426963i	−0.887593	−	0.460629i	$-0.847624\pi$
$953$	−13.1807	+	13.1807i	−0.426963	+	0.426963i	0.460629	+	0.887593i	$0.347624\pi$
$954$	−11.5823	−	4.86642i	−0.374992	−	0.157556i
$955$	10.5795	+	14.0204i	0.342344	+	0.453688i
$956$	36.6575	+	37.4077i	1.18559	+	1.20985i
$957$	7.47675	+	7.47675i	0.241689	+	0.241689i
$958$	2.08243	+	5.10035i	0.0672804	+	0.164785i
$959$	−2.38641	−	6.99736i	−0.0770613	−	0.225957i
$960$	−10.3361	−	14.6001i	−0.333597	−	0.471218i
$961$	−85.5904			−2.76098
$962$	−1.56965	+	0.640876i	−0.0506075	+	0.0206627i
$963$	−6.21506	−	6.21506i	−0.200277	−	0.200277i
$964$	−10.4036	−	10.6165i	−0.335078	−	0.341935i
$965$	−46.8110	−	6.54764i	−1.50690	−	0.210776i
$966$	−21.2571	−	1.47096i	−0.683935	−	0.0473274i
$967$	−29.9056	−	29.9056i	−0.961698	−	0.961698i	0.0375950	−	0.999293i	$-0.488030\pi$
$967$	−29.9056	−	29.9056i	−0.961698	−	0.961698i	−0.999293	+	0.0375950i	$0.988030\pi$
$968$	9.17137	+	3.96320i	0.294779	+	0.127382i
$969$	3.94074			0.126595
$970$	−2.29583	−	9.04165i	−0.0737147	−	0.290310i
$971$	25.9583			0.833040			0.416520	−	0.909126i	$-0.363250\pi$
$971$	25.9583			0.833040			0.416520	+	0.909126i	$0.363250\pi$
$972$	0.0202571	−	1.99990i	0.000649746	−	0.0641467i
$973$	−17.8010	+	36.2270i	−0.570675	+	1.16138i
$974$	0.372000	−	0.885379i	0.0119197	−	0.0283694i
$975$	−4.43410	−	1.26518i	−0.142005	−	0.0405183i
$976$	−0.222996	+	11.0066i	−0.00713793	+	0.352313i
$977$	−4.90867	−	4.90867i	−0.157042	−	0.157042i	0.624212	−	0.781255i	$-0.285420\pi$
$977$	−4.90867	−	4.90867i	−0.157042	−	0.157042i	−0.781255	+	0.624212i	$0.785420\pi$
$978$	10.0130	+	24.5242i	0.320182	+	0.784197i
$979$		−	21.8881i		−	0.699546i
$980$	15.2345	+	27.3480i	0.486648	+	0.873598i
$981$		−	0.997788i		−	0.0318569i
$982$	−34.3588	+	14.0284i	−1.09643	+	0.447665i
$983$	−21.6602	−	21.6602i	−0.690854	−	0.690854i	0.271566	−	0.962420i	$-0.412459\pi$
$983$	−21.6602	−	21.6602i	−0.690854	−	0.690854i	−0.962420	+	0.271566i	$0.912459\pi$
$984$	−0.783648	−	1.97630i	−0.0249818	−	0.0630020i
$985$	25.8895	+	3.62127i	0.824908	+	0.115383i
$986$	28.6014	+	12.0172i	0.910855	+	0.382704i
$987$	9.69210	−	19.7245i	0.308503	−	0.627837i
$988$	−1.28197	−	0.0129852i	−0.0407850	−	0.000413114i
$989$	−60.2918			−1.91717
$990$	−4.41871	+	7.42639i	−0.140436	+	0.236026i
$991$	24.5393			0.779518			0.389759	−	0.920917i	$-0.372558\pi$
$991$	24.5393			0.779518			0.389759	+	0.920917i	$0.372558\pi$
$992$	21.9384	+	57.0053i	0.696545	+	1.80992i
$993$	−6.58264	−	6.58264i	−0.208894	−	0.208894i
$994$	3.50047	−	50.5857i	0.111028	−	1.60448i
$995$	25.6766	+	34.0277i	0.814004	+	1.07875i
$996$	−19.0104	−	19.3995i	−0.602369	−	0.614697i
$997$	−0.208804	−	0.208804i	−0.00661289	−	0.00661289i	0.703793	−	0.710405i	$-0.251488\pi$
$997$	−0.208804	−	0.208804i	−0.00661289	−	0.00661289i	−0.710405	+	0.703793i	$0.751488\pi$
$998$	−15.1510	−	37.1083i	−0.479598	−	1.17464i
$999$	1.29998			0.0411295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.517.34	yes	184
5.3	odd	4	inner	840.2.bj.b.13.12	yes	184
7.6	odd	2	inner	840.2.bj.b.517.33	yes	184
8.5	even	2	inner	840.2.bj.b.517.11	yes	184
35.13	even	4	inner	840.2.bj.b.13.11	✓	184
40.13	odd	4	inner	840.2.bj.b.13.33	yes	184
56.13	odd	2	inner	840.2.bj.b.517.12	yes	184
280.13	even	4	inner	840.2.bj.b.13.34	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.11	✓	184	35.13	even	4	inner
840.2.bj.b.13.12	yes	184	5.3	odd	4	inner
840.2.bj.b.13.33	yes	184	40.13	odd	4	inner
840.2.bj.b.13.34	yes	184	280.13	even	4	inner
840.2.bj.b.517.11	yes	184	8.5	even	2	inner
840.2.bj.b.517.12	yes	184	56.13	odd	2	inner
840.2.bj.b.517.33	yes	184	7.6	odd	2	inner
840.2.bj.b.517.34	yes	184	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.534572 - 1.30929i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.42846 + 1.39982i) q^{4} +(-1.34687 - 1.78492i) q^{5} +(-1.30381 - 0.547806i) q^{6} +(-2.37457 - 1.16680i) q^{7} +(2.59638 + 1.12197i) q^{8} -1.00000i q^{9} +(-1.61698 + 2.71761i) q^{10} +2.73270i q^{11} +(-0.0202571 + 1.99990i) q^{12} +(-0.652103 + 0.652103i) q^{13} +(-0.258300 + 3.73273i) q^{14} +(-2.21451 - 0.309752i) q^{15} +(0.0810241 - 3.99918i) q^{16} +(-4.00888 + 4.00888i) q^{17} +(-1.30929 + 0.534572i) q^{18} -0.695088i q^{19} +(4.42252 + 0.664333i) q^{20} +(-2.50413 + 0.854019i) q^{21} +(3.57788 - 1.46082i) q^{22} +(-4.02681 + 4.02681i) q^{23} +(2.62927 - 1.04257i) q^{24} +(-1.37190 + 4.80811i) q^{25} +(1.20239 + 0.505194i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(5.02530 - 1.65723i) q^{28} +3.86934 q^{29} +(0.778261 + 3.06501i) q^{30} -10.7977i q^{31} +(-5.27939 + 2.03177i) q^{32} +(1.93231 + 1.93231i) q^{33} +(7.39181 + 3.10574i) q^{34} +(1.11558 + 5.80995i) q^{35} +(1.39982 + 1.42846i) q^{36} +(-0.919223 + 0.919223i) q^{37} +(-0.910070 + 0.371575i) q^{38} +0.922213i q^{39} +(-1.49435 - 6.14548i) q^{40} -0.751652i q^{41} +(2.45679 + 2.82209i) q^{42} +(7.48629 + 7.48629i) q^{43} +(-3.82528 - 3.90356i) q^{44} +(-1.78492 + 1.34687i) q^{45} +(7.42488 + 3.11963i) q^{46} +(-5.87362 + 5.87362i) q^{47} +(-2.77055 - 2.88514i) q^{48} +(4.27715 + 5.54130i) q^{49} +(7.02857 - 0.774071i) q^{50} +5.66941i q^{51} +(0.0186813 - 1.84433i) q^{52} +(6.28157 + 6.28157i) q^{53} +(-0.547806 + 1.30381i) q^{54} +(4.87765 - 3.68058i) q^{55} +(-4.85617 - 5.69365i) q^{56} +(-0.491502 - 0.491502i) q^{57} +(-2.06844 - 5.06607i) q^{58} -3.87046i q^{59} +(3.59695 - 2.65744i) q^{60} -2.75222 q^{61} +(-14.1373 + 5.77215i) q^{62} +(-1.16680 + 2.37457i) q^{63} +(5.48238 + 5.82611i) q^{64} +(2.04225 + 0.285658i) q^{65} +(1.49699 - 3.56290i) q^{66} +(-7.35997 + 7.35997i) q^{67} +(0.114846 - 11.3382i) q^{68} +5.69477i q^{69} +(7.01053 - 4.56645i) q^{70} -13.5519 q^{71} +(1.12197 - 2.59638i) q^{72} +(-6.03685 - 6.03685i) q^{73} +(1.69492 + 0.712136i) q^{74} +(2.42977 + 4.36992i) q^{75} +(0.972996 + 0.992909i) q^{76} +(3.18852 - 6.48897i) q^{77} +(1.20744 - 0.492990i) q^{78} -2.86914i q^{79} +(-7.24736 + 5.24174i) q^{80} -1.00000 q^{81} +(-0.984128 + 0.401812i) q^{82} +(-9.60298 + 9.60298i) q^{83} +(2.38159 - 4.72526i) q^{84} +(12.5550 + 1.75611i) q^{85} +(5.79974 - 13.8037i) q^{86} +(2.73604 - 2.73604i) q^{87} +(-3.06600 + 7.09512i) q^{88} -8.00970 q^{89} +(2.71761 + 1.61698i) q^{90} +(2.30934 - 0.787588i) q^{91} +(0.115359 - 11.3890i) q^{92} +(-7.63513 - 7.63513i) q^{93} +(10.8301 + 4.55038i) q^{94} +(-1.24068 + 0.936191i) q^{95} +(-2.29641 + 5.16977i) q^{96} +(-2.08593 + 2.08593i) q^{97} +(4.96871 - 8.56224i) q^{98} +2.73270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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