LMFDB - Embedded newform 840.2.bj.b.13.11

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			13.11
Character	$\chi$	$=$	840.13
Dual form			840.2.bj.b.517.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30929 + 0.534572i) 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} +(-1.12197 + 2.59638i) q^{8} +1.00000i q^{9} +(-0.809265 + 3.05697i) q^{10} +2.73270i q^{11} +(-1.99990 - 0.0202571i) q^{12} +(0.652103 + 0.652103i) q^{13} +(2.48525 - 2.79706i) q^{14} +(-2.21451 + 0.309752i) q^{15} +(0.0810241 - 3.99918i) q^{16} +(-4.00888 - 4.00888i) q^{17} +(-0.534572 - 1.30929i) q^{18} -0.695088i q^{19} +(-0.574614 - 4.43507i) q^{20} +(2.50413 + 0.854019i) q^{21} +(-1.46082 - 3.57788i) 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} +(-1.75868 + 4.99070i) q^{28} -3.86934 q^{29} +(2.73384 - 1.58937i) q^{30} +10.7977i q^{31} +(2.03177 + 5.27939i) 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} +(0.371575 + 0.910070i) q^{38} -0.922213i q^{39} +(3.12320 + 5.49960i) q^{40} +0.751652i q^{41} +(-3.73516 + 0.220480i) 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} +(-2.88514 + 2.77055i) q^{48} +(4.27715 - 5.54130i) q^{49} +(4.36649 + 5.56181i) q^{50} +5.66941i q^{51} +(1.84433 + 0.0186813i) q^{52} +(-6.28157 + 6.28157i) q^{53} +(-0.547806 + 1.30381i) q^{54} +(4.87765 + 3.68058i) q^{55} +(-0.365274 - 7.47439i) q^{56} +(-0.491502 + 0.491502i) q^{57} +(5.06607 - 2.06844i) q^{58} -3.87046i q^{59} +(-2.72975 + 3.54238i) q^{60} +2.75222 q^{61} +(-5.77215 - 14.1373i) 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} +(-11.3382 - 0.114846i) q^{68} +5.69477i q^{69} +(-1.64523 - 8.20324i) q^{70} -13.5519 q^{71} +(-2.59638 - 1.12197i) 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} +(0.492990 + 1.20744i) q^{78} +2.86914i q^{79} +(-7.02910 - 5.53098i) q^{80} -1.00000 q^{81} +(-0.401812 - 0.984128i) q^{82} +(9.60298 + 9.60298i) q^{83} +(4.77253 - 2.28538i) q^{84} +(-12.5550 + 1.75611i) q^{85} +(5.79974 - 13.8037i) q^{86} +(2.73604 + 2.73604i) q^{87} +(-7.09512 - 3.06600i) q^{88} -8.00970 q^{89} +(-3.05697 - 0.809265i) q^{90} +(-2.30934 - 0.787588i) q^{91} +(-11.3890 - 0.115359i) 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} +(-2.63779 + 9.54160i) 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.30929	+	0.534572i	−0.925806	+	0.378000i
$2$	−1.30929	+	0.534572i	−0.925806	+	0.378000i
$3$	−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
$8$	−1.12197	+	2.59638i	−0.396675	+	0.917959i
$9$			1.00000i			0.333333i
$10$	−0.809265	+	3.05697i	−0.255912	+	0.966700i
$11$			2.73270i			0.823939i	0.911198	+	0.411970i	$0.135159\pi$
$11$			2.73270i			0.823939i	−0.911198	+	0.411970i	$0.864841\pi$
$12$	−1.99990	−	0.0202571i	−0.577321	−	0.00584771i
$13$	0.652103	+	0.652103i	0.180861	+	0.180861i	0.791731	−	0.610870i	$-0.209180\pi$
$13$	0.652103	+	0.652103i	0.180861	+	0.180861i	−0.610870	+	0.791731i	$0.709180\pi$
$14$	2.48525	−	2.79706i	0.664211	−	0.747545i
$15$	−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	0.0273302	−	0.999626i	$-0.491299\pi$
$17$	−4.00888	−	4.00888i	−0.972296	−	0.972296i	−0.999626	+	0.0273302i	$0.991299\pi$
$18$	−0.534572	−	1.30929i	−0.126000	−	0.308602i
$19$		−	0.695088i		−	0.159464i	−0.996816	−	0.0797321i	$-0.974594\pi$
$19$		−	0.695088i		−	0.159464i	0.996816	−	0.0797321i	$-0.0254065\pi$
$20$	−0.574614	−	4.43507i	−0.128488	−	0.991711i
$21$	2.50413	+	0.854019i	0.546445	+	0.186362i
$22$	−1.46082	−	3.57788i	−0.311449	−	0.762808i
$23$	−4.02681	−	4.02681i	−0.839649	−	0.839649i	0.149164	−	0.988812i	$-0.452342\pi$
$23$	−4.02681	−	4.02681i	−0.839649	−	0.839649i	−0.988812	+	0.149164i	$0.952342\pi$
$24$	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
$28$	−1.75868	+	4.99070i	−0.332359	+	0.943153i
$29$	−3.86934			−0.718518			−0.359259	−	0.933238i	$-0.616971\pi$
$29$	−3.86934			−0.718518			−0.359259	+	0.933238i	$0.616971\pi$
$30$	2.73384	−	1.58937i	0.499129	−	0.290178i
$31$			10.7977i			1.93932i	0.244448	+	0.969662i	$0.421393\pi$
$31$			10.7977i			1.93932i	−0.244448	+	0.969662i	$0.578607\pi$
$32$	2.03177	+	5.27939i	0.359169	+	0.933273i
$33$	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	$-0.215921\pi$
$37$	0.919223	+	0.919223i	0.151119	+	0.151119i	−0.627498	+	0.778618i	$0.715921\pi$
$38$	0.371575	+	0.910070i	0.0602774	+	0.147633i
$39$		−	0.922213i		−	0.147672i
$40$	3.12320	+	5.49960i	0.493821	+	0.869564i
$41$			0.751652i			0.117388i	0.998276	+	0.0586942i	$0.0186937\pi$
$41$			0.751652i			0.117388i	−0.998276	+	0.0586942i	$0.981306\pi$
$42$	−3.73516	+	0.220480i	−0.576347	+	0.0340208i
$43$	−7.48629	+	7.48629i	−1.14165	+	1.14165i	−0.153500	+	0.988149i	$0.549055\pi$
$43$	−7.48629	+	7.48629i	−1.14165	+	1.14165i	−0.988149	+	0.153500i	$0.950945\pi$
$44$	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	0.134199	−	0.990954i	$-0.457154\pi$
$47$	−5.87362	−	5.87362i	−0.856755	−	0.856755i	−0.990954	+	0.134199i	$0.957154\pi$
$48$	−2.88514	+	2.77055i	−0.416434	+	0.399895i
$49$	4.27715	−	5.54130i	0.611021	−	0.791614i
$50$	4.36649	+	5.56181i	0.617515	+	0.786559i
$51$			5.66941i			0.793877i
$52$	1.84433	+	0.0186813i	0.255763	+	0.00259064i
$53$	−6.28157	+	6.28157i	−0.862840	+	0.862840i	−0.991667	−	0.128827i	$-0.958879\pi$
$53$	−6.28157	+	6.28157i	−0.862840	+	0.862840i	0.128827	+	0.991667i	$0.458879\pi$
$54$	−0.547806	+	1.30381i	−0.0745470	+	0.177425i
$55$	4.87765	+	3.68058i	0.657703	+	0.496289i
$56$	−0.365274	−	7.47439i	−0.0488118	−	0.998808i
$57$	−0.491502	+	0.491502i	−0.0651010	+	0.0651010i
$58$	5.06607	−	2.06844i	0.665208	−	0.271600i
$59$		−	3.87046i		−	0.503891i	−0.967741	−	0.251945i	$-0.918930\pi$
$59$		−	3.87046i		−	0.503891i	0.967741	−	0.251945i	$-0.0810703\pi$
$60$	−2.72975	+	3.54238i	−0.352410	+	0.457319i
$61$	2.75222			0.352386			0.176193	−	0.984356i	$-0.443622\pi$
$61$	2.75222			0.352386			0.176193	+	0.984356i	$0.443622\pi$
$62$	−5.77215	−	14.1373i	−0.733064	−	1.79544i
$63$	−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	$-0.0306684\pi$
$67$	7.35997	+	7.35997i	0.899164	+	0.899164i	−0.0961985	+	0.995362i	$0.530668\pi$
$68$	−11.3382	−	0.114846i	−1.37496	−	0.0139271i
$69$			5.69477i			0.685570i
$70$	−1.64523	−	8.20324i	−0.196642	−	0.980475i
$71$	−13.5519			−1.60832			−0.804158	−	0.594415i	$-0.797384\pi$
$71$	−13.5519			−1.60832			−0.804158	+	0.594415i	$0.797384\pi$
$72$	−2.59638	−	1.12197i	−0.305986	−	0.132225i
$73$	−6.03685	+	6.03685i	−0.706560	+	0.706560i	−0.965810	−	0.259250i	$-0.916525\pi$
$73$	−6.03685	+	6.03685i	−0.706560	+	0.706560i	0.259250	+	0.965810i	$0.416525\pi$
$74$	−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
$78$	0.492990	+	1.20744i	0.0558201	+	0.136716i
$79$			2.86914i			0.322804i	0.986889	+	0.161402i	$0.0516016\pi$
$79$			2.86914i			0.322804i	−0.986889	+	0.161402i	$0.948398\pi$
$80$	−7.02910	−	5.53098i	−0.785877	−	0.618383i
$81$	−1.00000			−0.111111
$82$	−0.401812	−	0.984128i	−0.0443728	−	0.108679i
$83$	9.60298	+	9.60298i	1.05406	+	1.05406i	0.998453	+	0.0556111i	$0.0177107\pi$
$83$	9.60298	+	9.60298i	1.05406	+	1.05406i	0.0556111	+	0.998453i	$0.482289\pi$
$84$	4.77253	−	2.28538i	0.520726	−	0.249356i
$85$	−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
$88$	−7.09512	−	3.06600i	−0.756342	−	0.326836i
$89$	−8.00970			−0.849026			−0.424513	−	0.905422i	$-0.639555\pi$
$89$	−8.00970			−0.849026			−0.424513	+	0.905422i	$0.639555\pi$
$90$	−3.05697	−	0.809265i	−0.322233	−	0.0853040i
$91$	−2.30934	−	0.787588i	−0.242085	−	0.0825617i
$92$	−11.3890	−	0.115359i	−1.18738	−	0.0120270i
$93$	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	0.593235	−	0.805029i	$-0.297850\pi$
$97$	−2.08593	−	2.08593i	−0.211794	−	0.211794i	−0.805029	+	0.593235i	$0.797850\pi$
$98$	−2.63779	+	9.54160i	−0.266457	+	0.963847i
$99$	−2.73270			−0.274646
$100$	−8.69018	−	4.94780i	−0.869018	−	0.494780i
$101$	−7.86838			−0.782933			−0.391466	−	0.920192i	$-0.628032\pi$
$101$	−7.86838			−0.782933			−0.391466	+	0.920192i	$0.628032\pi$
$102$	−3.03071	−	7.42289i	−0.300085	−	0.734975i
$103$	−0.103805	+	0.103805i	−0.0102282	+	0.0102282i	−0.712202	−	0.701974i	$-0.752302\pi$
$103$	−0.103805	+	0.103805i	−0.0102282	+	0.0102282i	0.701974	+	0.712202i	$0.252302\pi$
$104$	−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	$-0.389674\pi$
$107$	−6.21506	−	6.21506i	−0.600832	−	0.600832i	−0.940533	+	0.339701i	$0.889674\pi$
$108$	0.0202571	−	1.99990i	0.00194924	−	0.192440i
$109$	−0.997788			−0.0955707			−0.0477854	−	0.998858i	$-0.515216\pi$
$109$	−0.997788			−0.0955707			−0.0477854	+	0.998858i	$0.515216\pi$
$110$	−8.35378	−	2.21148i	−0.796502	−	0.210856i
$111$		−	1.29998i		−	0.123388i
$112$	4.47385	+	9.59086i	0.422739	+	0.906251i
$113$	−0.567306	−	0.567306i	−0.0533677	−	0.0533677i	0.679919	−	0.733287i	$-0.262015\pi$
$113$	−0.567306	−	0.567306i	−0.0533677	−	0.0533677i	−0.733287	+	0.679919i	$0.762015\pi$
$114$	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
$118$	2.06904	+	5.06754i	0.190471	+	0.466505i
$119$	14.1969	+	4.84179i	1.30143	+	0.443846i
$120$	1.68037	−	6.09724i	0.153396	−	0.556599i
$121$	3.53237			0.321124
$122$	−3.60344	+	1.47126i	−0.326241	+	0.133202i
$123$	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
$126$	2.79706	+	2.48525i	0.249182	+	0.221404i
$127$	−12.0310	+	12.0310i	−1.06758	+	1.06758i	−0.0700338	+	0.997545i	$0.522311\pi$
$127$	−12.0310	+	12.0310i	−1.06758	+	1.06758i	−0.997545	+	0.0700338i	$0.977689\pi$
$128$	10.2925	+	4.69732i	0.909736	+	0.415188i
$129$	10.5872			0.932152
$130$	−2.52119	+	1.46574i	−0.221123	+	0.128554i
$131$	15.9812			1.39629			0.698143	−	0.715959i	$-0.254010\pi$
$131$	15.9812			1.39629			0.698143	+	0.715959i	$0.254010\pi$
$132$	0.0553564	−	5.46511i	0.00481816	−	0.475677i
$133$	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	−0.617645	−	0.786457i	$-0.711913\pi$
$137$	1.97589	−	1.97589i	0.168812	−	0.168812i	0.786457	+	0.617645i	$0.211913\pi$
$138$	−3.04427	−	7.45609i	−0.259145	−	0.634705i
$139$		−	15.2563i		−	1.29402i	−0.762482	−	0.647009i	$-0.776019\pi$
$139$		−	15.2563i		−	1.29402i	0.762482	−	0.647009i	$-0.223981\pi$
$140$	6.53930	+	9.86091i	0.552672	+	0.833399i
$141$			8.30655i			0.699538i
$142$	17.7433	−	7.24448i	1.48899	−	0.607943i
$143$	−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
$148$	2.59982	+	0.0263337i	0.213704	+	0.00216462i
$149$	16.1624			1.32408			0.662038	−	0.749471i	$-0.269692\pi$
$149$	16.1624			1.32408			0.662038	+	0.749471i	$0.269692\pi$
$150$	0.845220	−	7.02037i	0.0690119	−	0.573211i
$151$	−12.3945			−1.00865			−0.504325	−	0.863514i	$-0.668259\pi$
$151$	−12.3945			−1.00865			−0.504325	+	0.863514i	$0.668259\pi$
$152$	1.80471	+	0.779866i	0.146382	+	0.0632555i
$153$	4.00888	−	4.00888i	0.324099	−	0.324099i
$154$	7.64351	+	6.79144i	0.615931	+	0.547270i
$155$	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	$-0.574940\pi$
$157$	9.26156	−	9.26156i	0.739153	−	0.739153i	0.972414	+	0.233261i	$0.0749397\pi$
$158$	−1.53376	−	3.75653i	−0.122020	−	0.298854i
$159$	8.88348			0.704506
$160$	12.1598	+	3.48408i	0.961318	+	0.275441i
$161$	14.2604	+	4.86345i	1.12388	+	0.383293i
$162$	1.30929	−	0.534572i	0.102867	−	0.0420000i
$163$	13.2448	−	13.2448i	1.03741	−	1.03741i	0.0381388	−	0.999272i	$-0.487857\pi$
$163$	13.2448	−	13.2448i	1.03741	−	1.03741i	0.999272	−	0.0381388i	$-0.0121429\pi$
$164$	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	0.246874	−	0.969048i	$-0.420597\pi$
$167$	−9.33254	−	9.33254i	−0.722173	−	0.722173i	−0.969048	+	0.246874i	$0.920597\pi$
$168$	−5.02691	+	5.54348i	−0.387834	+	0.427689i
$169$		−	12.1495i		−	0.934579i
$170$	15.4993	−	9.01080i	1.18874	−	0.691097i
$171$	0.695088			0.0531547
$172$	−0.214466	+	21.1733i	−0.0163529	+	1.61445i
$173$	−4.77151	−	4.77151i	−0.362771	−	0.362771i	0.502061	−	0.864832i	$-0.332575\pi$
$173$	−4.77151	−	4.77151i	−0.362771	−	0.362771i	−0.864832	+	0.502061i	$0.832575\pi$
$174$	−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
$178$	10.4870	−	4.28176i	0.786033	−	0.320932i
$179$	−1.82697			−0.136554			−0.0682771	−	0.997666i	$-0.521750\pi$
$179$	−1.82697			−0.136554			−0.0682771	+	0.997666i	$0.521750\pi$
$180$	4.43507	−	0.574614i	0.330570	−	0.0428292i
$181$	−21.8299			−1.62260			−0.811302	−	0.584628i	$-0.801241\pi$
$181$	−21.8299			−1.62260			−0.811302	+	0.584628i	$0.801241\pi$
$182$	3.44461	−	0.203330i	0.255332	−	0.0150718i
$183$	−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
$188$	−16.6122	−	0.168266i	−1.21157	−	0.0122721i
$189$	−0.854019	+	2.50413i	−0.0621208	+	0.182148i
$190$	2.12487	+	0.562511i	0.154154	+	0.0408088i
$191$	−7.85488			−0.568359			−0.284180	−	0.958771i	$-0.591721\pi$
$191$	−7.85488			−0.568359			−0.284180	+	0.958771i	$0.591721\pi$
$192$	−0.243052	+	7.99631i	−0.0175407	+	0.577084i
$193$	14.9470	+	14.9470i	1.07591	+	1.07591i	0.996871	+	0.0790403i	$0.0251856\pi$
$193$	14.9470	+	14.9470i	1.07591	+	1.07591i	0.0790403	+	0.996871i	$0.474814\pi$
$194$	3.84616	+	1.61600i	0.276139	+	0.116022i
$195$	−1.64608	−	1.24210i	−0.117878	−	0.0889485i
$196$	−1.64706	−	13.9028i	−0.117647	−	0.993056i
$197$	8.26668	+	8.26668i	0.588977	+	0.588977i	0.937354	−	0.348378i	$-0.113267\pi$
$197$	8.26668	+	8.26668i	0.588977	+	0.588977i	−0.348378	+	0.937354i	$0.613267\pi$
$198$	3.57788	−	1.46082i	0.254269	−	0.103816i
$199$	−19.0640			−1.35141			−0.675705	−	0.737172i	$-0.736161\pi$
$199$	−19.0640			−1.35141			−0.675705	+	0.737172i	$0.736161\pi$
$200$	14.0229	+	1.83257i	0.991569	+	0.129582i
$201$		−	10.4086i		−	0.734164i
$202$	10.3020	−	4.20622i	0.724844	−	0.295948i
$203$	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
$208$	2.66071	−	2.55504i	0.184487	−	0.177160i
$209$	1.89947			0.131389
$210$	−4.63722	+	6.96392i	−0.319998	+	0.480556i
$211$			12.9517i			0.891629i	0.895125	+	0.445815i	$0.147086\pi$
$211$			12.9517i			0.891629i	−0.895125	+	0.445815i	$0.852914\pi$
$212$	−0.179953	+	17.7661i	−0.0123592	+	1.22018i
$213$	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
$218$	1.30639	−	0.533390i	0.0884799	−	0.0361257i
$219$	8.53740			0.576904
$220$	12.1197	−	1.57024i	0.817110	−	0.105866i
$221$		−	5.22841i		−	0.351701i
$222$	0.694932	+	1.70204i	0.0466408	+	0.114234i
$223$	0.0345980	−	0.0345980i	0.00231686	−	0.00231686i	−0.705947	−	0.708264i	$-0.749479\pi$
$223$	0.0345980	−	0.0345980i	0.00231686	−	0.00231686i	0.708264	+	0.705947i	$0.249479\pi$
$224$	−10.9846	−	10.1656i	−0.733937	−	0.679217i
$225$	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	$-0.697126\pi$
$227$	3.52308	−	3.52308i	0.233835	−	0.233835i	0.814291	+	0.580456i	$0.197126\pi$
$228$	−0.0140804	+	1.39011i	−0.000932500	+	0.0920620i
$229$		−	3.27763i		−	0.216592i	−0.994119	−	0.108296i	$-0.965461\pi$
$229$		−	3.27763i		−	0.216592i	0.994119	−	0.108296i	$-0.0345394\pi$
$230$	15.5686	−	9.05110i	1.02656	−	0.596812i
$231$	−2.33378	+	6.84302i	−0.153551	+	0.450238i
$232$	4.34127	−	10.0463i	0.285018	−	0.659570i
$233$	4.13036	+	4.13036i	0.270589	+	0.270589i	0.829337	−	0.558749i	$-0.188718\pi$
$233$	4.13036	+	4.13036i	0.270589	+	0.270589i	−0.558749	+	0.829337i	$0.688718\pi$
$234$	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
$238$	−21.1761	+	1.24999i	−1.37265	+	0.0810250i
$239$			26.1874i			1.69392i	0.531657	+	0.846960i	$0.321569\pi$
$239$			26.1874i			1.69392i	−0.531657	+	0.846960i	$0.678431\pi$
$240$	1.05933	+	8.88132i	0.0683793	+	0.573287i
$241$		−	7.43213i		−	0.478745i	−0.970928	−	0.239373i	$-0.923058\pi$
$241$		−	7.43213i		−	0.478745i	0.970928	−	0.239373i	$-0.0769418\pi$
$242$	−4.62488	+	1.88831i	−0.297299	+	0.121385i
$243$	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
$248$	−28.0349	−	12.1147i	−1.78022	−	0.769282i
$249$		−	13.5807i		−	0.860639i
$250$	15.8085	−	0.302829i	0.999817	−	0.0191526i
$251$	10.3216			0.651491			0.325746	−	0.945457i	$-0.394385\pi$
$251$	10.3216			0.651491			0.325746	+	0.945457i	$0.394385\pi$
$252$	−4.99070	−	1.75868i	−0.314384	−	0.110786i
$253$	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	0.627447	−	0.778659i	$-0.284100\pi$
$257$	−2.42411	−	2.42411i	−0.151212	−	0.151212i	−0.778659	+	0.627447i	$0.784100\pi$
$258$	−13.8617	+	5.65963i	−0.862992	+	0.352353i
$259$	−3.25531	−	1.11021i	−0.202275	−	0.0689849i
$260$	2.51741	−	3.26683i	0.156123	−	0.202600i
$261$		−	3.86934i		−	0.239506i
$262$	−20.9240	+	8.54311i	−1.29269	+	0.527795i
$263$	−7.27231	−	7.27231i	−0.448430	−	0.448430i	0.446402	−	0.894832i	$-0.352705\pi$
$263$	−7.27231	−	7.27231i	−0.448430	−	0.448430i	−0.894832	+	0.446402i	$0.852705\pi$
$264$	2.84902	+	7.18499i	0.175345	+	0.442206i
$265$	2.75168	+	19.6726i	0.169034	+	1.20848i
$266$	−1.94420	−	1.72747i	−0.119207	−	0.105918i
$267$	5.66371	+	5.66371i	0.346613	+	0.346613i
$268$	20.8161	+	0.210847i	1.27154	+	0.0128795i
$269$			14.1096i			0.860280i	0.902762	+	0.430140i	$0.141536\pi$
$269$			14.1096i			0.860280i	−0.902762	+	0.430140i	$0.858464\pi$
$270$	1.58937	+	2.73384i	0.0967260	+	0.166376i
$271$		−	25.0835i		−	1.52372i	−0.647744	−	0.761858i	$-0.724287\pi$
$271$		−	25.0835i		−	1.52372i	0.647744	−	0.761858i	$-0.275713\pi$
$272$	−16.3570	+	15.7074i	−0.991792	+	0.952402i
$273$	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	$-0.275841\pi$
$277$	−1.90869	−	1.90869i	−0.114682	−	0.114682i	−0.762119	+	0.647437i	$0.775841\pi$
$278$	8.15557	+	19.9748i	0.489139	+	1.19801i
$279$	−10.7977			−0.646442
$280$	−13.8332	−	9.41503i	−0.826691	−	0.562656i
$281$	4.89611			0.292078			0.146039	−	0.989279i	$-0.453348\pi$
$281$	4.89611			0.292078			0.146039	+	0.989279i	$0.453348\pi$
$282$	−4.44045	−	10.8757i	−0.264425	−	0.647636i
$283$	−20.9419	−	20.9419i	−1.24487	−	1.24487i	−0.957957	−	0.286912i	$-0.907371\pi$
$283$	−20.9419	−	20.9419i	−1.24487	−	1.24487i	−0.286912	−	0.957957i	$-0.592629\pi$
$284$	−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
$288$	−5.27939	+	2.03177i	−0.311091	+	0.119723i
$289$			15.1422i			0.890720i
$290$	3.13132	−	11.8285i	0.183877	−	0.694591i
$291$			2.94995i			0.172929i
$292$	−0.172943	+	17.0739i	−0.0101207	+	0.999175i
$293$	17.3735	+	17.3735i	1.01497	+	1.01497i	0.999886	+	0.0150854i	$0.00480202\pi$
$293$	17.3735	+	17.3735i	1.01497	+	1.01497i	0.0150854	+	0.999886i	$0.495198\pi$
$294$	8.61212	−	4.88173i	0.502269	−	0.284708i
$295$	−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
$298$	−21.1612	+	8.63997i	−1.22584	+	0.500500i
$299$		−	5.25180i		−	0.303719i
$300$	2.64626	+	9.64351i	0.152782	+	0.556768i
$301$	9.04169	−	26.5117i	0.521154	−	1.52811i
$302$	16.2280	−	6.62576i	0.933814	−	0.381270i
$303$	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	$-0.726951\pi$
$307$	1.79267	−	1.79267i	0.102313	−	0.102313i	0.756410	+	0.654097i	$0.226951\pi$
$308$	−13.6381	−	4.80593i	−0.777101	−	0.273843i
$309$	0.146802			0.00835126
$310$	−33.0083	−	8.73820i	−1.87475	−	0.496297i
$311$		−	30.9213i		−	1.75338i	−0.481053	−	0.876692i	$-0.659745\pi$
$311$		−	30.9213i		−	1.75338i	0.481053	−	0.876692i	$-0.340255\pi$
$312$	2.39442	+	1.03469i	0.135557	+	0.0585780i
$313$	18.4972	−	18.4972i	1.04553	−	1.04553i	0.0466126	−	0.998913i	$-0.485157\pi$
$313$	18.4972	−	18.4972i	1.04553	−	1.04553i	0.998913	−	0.0466126i	$-0.0148426\pi$
$314$	−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	$-0.417413\pi$
$317$	−12.6408	−	12.6408i	−0.709976	−	0.709976i	−0.966530	+	0.256554i	$0.917413\pi$
$318$	−11.6310	+	4.74886i	−0.652236	+	0.266303i
$319$		−	10.5737i		−	0.592015i
$320$	−17.7832	+	1.93864i	−0.994110	+	0.108373i
$321$			8.78942i			0.490577i
$322$	−21.2709	+	1.25558i	−1.18538	+	0.0699710i
$323$	−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
$328$	−1.95157	−	0.843329i	−0.107758	−	0.0465651i
$329$	20.8007	+	7.09396i	1.14678	+	0.391102i
$330$	4.34327	+	7.47077i	0.239089	+	0.411252i
$331$		−	9.30926i		−	0.511683i	−0.966719	−	0.255842i	$-0.917647\pi$
$331$		−	9.30926i		−	0.511683i	0.966719	−	0.255842i	$-0.0823526\pi$
$332$	27.1599	+	0.275104i	1.49059	+	0.0150983i
$333$	−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
$336$	3.61827	−	9.94526i	0.197393	−	0.542558i
$337$	−2.73006	+	2.73006i	−0.148716	+	0.148716i	−0.777544	−	0.628828i	$-0.783535\pi$
$337$	−2.73006	+	2.73006i	−0.148716	+	0.148716i	0.628828	+	0.777544i	$0.283535\pi$
$338$	6.49480	+	15.9072i	0.353270	+	0.865238i
$339$			0.802292i			0.0435745i
$340$	−15.4761	+	20.0832i	−0.839309	+	1.08916i
$341$	−29.5069			−1.59789
$342$	−0.910070	+	0.371575i	−0.0492109	+	0.0200925i
$343$	−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	$-0.462689\pi$
$347$	−16.3216	−	16.3216i	−0.876190	−	0.876190i	−0.993138	+	0.116948i	$0.962689\pi$
$348$	7.73828	+	0.0783814i	0.414815	+	0.00420169i
$349$			10.1509i			0.543367i	0.962387	+	0.271683i	$0.0875803\pi$
$349$			10.1509i			0.543367i	−0.962387	+	0.271683i	$0.912420\pi$
$350$	−16.8581	−	8.11207i	−0.901101	−	0.433608i
$351$	0.922213			0.0492241
$352$	−14.4270	+	5.55220i	−0.768960	+	0.295933i
$353$	16.7350	−	16.7350i	0.890714	−	0.890714i	−0.103877	−	0.994590i	$-0.533125\pi$
$353$	16.7350	−	16.7350i	0.890714	−	0.890714i	0.994590	+	0.103877i	$0.0331247\pi$
$354$	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
$358$	2.39203	−	0.976649i	0.126423	−	0.0516175i
$359$		−	10.7959i		−	0.569787i	−0.958559	−	0.284894i	$-0.908042\pi$
$359$		−	10.7959i		−	0.569787i	0.958559	−	0.284894i	$-0.0919583\pi$
$360$	−5.49960	+	3.12320i	−0.289855	+	0.164607i
$361$	18.5169			0.974571
$362$	28.5816	−	11.6697i	1.50222	−	0.613344i
$363$	−2.49776	−	2.49776i	−0.131098	−	0.131098i
$364$	−4.40129	+	2.10761i	−0.230690	+	0.110469i
$365$	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	0.801826	−	0.597558i	$-0.203862\pi$
$367$	3.91321	+	3.91321i	0.204268	+	0.204268i	−0.597558	+	0.801826i	$0.703862\pi$
$368$	−16.4302	+	15.7777i	−0.856484	+	0.822468i
$369$	−0.751652			−0.0391294
$370$	−3.55394	+	2.06615i	−0.184760	+	0.107414i
$371$	7.58667	−	22.2454i	0.393880	−	1.15492i
$372$	0.218730	−	21.5943i	0.0113406	−	1.11961i
$373$	17.6115	−	17.6115i	0.911888	−	0.911888i	−0.0845324	−	0.996421i	$-0.526940\pi$
$373$	17.6115	−	17.6115i	0.911888	−	0.911888i	0.996421	+	0.0845324i	$0.0269397\pi$
$374$	−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
$378$	−0.220480	−	3.73516i	−0.0113403	−	0.192116i
$379$	2.84540			0.146158			0.0730791	−	0.997326i	$-0.476717\pi$
$379$	2.84540			0.146158			0.0730791	+	0.997326i	$0.476717\pi$
$380$	−3.08276	+	0.399407i	−0.158142	+	0.0204892i
$381$	17.0144			0.871674
$382$	10.2843	−	4.19900i	0.526190	−	0.214840i
$383$	2.38999	−	2.38999i	0.122123	−	0.122123i	−0.643404	−	0.765527i	$-0.722478\pi$
$383$	2.38999	−	2.38999i	0.122123	−	0.122123i	0.765527	+	0.643404i	$0.222478\pi$
$384$	−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
$388$	−5.89960	−	0.0597574i	−0.299507	−	0.00303372i
$389$	−8.27081			−0.419347			−0.209673	−	0.977771i	$-0.567240\pi$
$389$	−8.27081			−0.419347			−0.209673	+	0.977771i	$0.567240\pi$
$390$	2.81918	+	0.746315i	0.142755	+	0.0377911i
$391$			32.2860i			1.63277i
$392$	9.58851	+	17.3223i	0.484293	+	0.874906i
$393$	−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	$-0.667283\pi$
$397$	7.24026	−	7.24026i	0.363378	−	0.363378i	0.865055	+	0.501677i	$0.167283\pi$
$398$	24.9602	−	10.1911i	1.25114	−	0.510833i
$399$	0.593619	−	1.74059i	0.0297181	−	0.0871384i
$400$	−19.3396	+	5.09690i	−0.966982	+	0.254845i
$401$	−8.11723			−0.405355			−0.202678	−	0.979246i	$-0.564964\pi$
$401$	−8.11723			−0.405355			−0.202678	+	0.979246i	$0.564964\pi$
$402$	5.56413	+	13.6278i	0.277514	+	0.679693i
$403$	−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
$406$	−9.61628	+	10.8228i	−0.477248	+	0.537125i
$407$	−2.51196	+	2.51196i	−0.124513	+	0.124513i
$408$	−14.7200	−	6.36089i	−0.728746	−	0.314911i
$409$	−24.9506			−1.23373			−0.616864	−	0.787070i	$-0.711597\pi$
$409$	−24.9506			−1.23373			−0.616864	+	0.787070i	$0.711597\pi$
$410$	−2.29778	−	0.608286i	−0.113479	−	0.0300411i
$411$	−2.79433			−0.137834
$412$	−0.00297377	+	0.293588i	−0.000146507	+	0.0144641i
$413$	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
$418$	−2.48695	+	1.01540i	−0.121640	+	0.0496649i
$419$		−	2.50608i		−	0.122430i	−0.998125	−	0.0612150i	$-0.980502\pi$
$419$		−	2.50608i		−	0.122430i	0.998125	−	0.0612150i	$-0.0194975\pi$
$420$	2.34873	−	11.5967i	0.114606	−	0.565861i
$421$			22.7450i			1.10853i	0.832342	+	0.554263i	$0.187000\pi$
$421$			22.7450i			1.10853i	−0.832342	+	0.554263i	$0.813000\pi$
$422$	−6.92360	−	16.9574i	−0.337036	−	0.825475i
$423$	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
$428$	−17.5779	−	0.178048i	−0.849661	−	0.00860626i
$429$	2.52013			0.121673
$430$	−16.8270	−	28.9438i	−0.811470	−	1.39579i
$431$	39.2522			1.89071			0.945357	−	0.326037i	$-0.105713\pi$
$431$	39.2522			1.89071			0.945357	+	0.326037i	$0.105713\pi$
$432$	−2.77055	−	2.88514i	−0.133298	−	0.138811i
$433$	19.8929	−	19.8929i	0.955990	−	0.955990i	−0.0430815	−	0.999072i	$-0.513718\pi$
$433$	19.8929	−	19.8929i	0.955990	−	0.955990i	0.999072	+	0.0430815i	$0.0137175\pi$
$434$	30.2018	+	26.8350i	1.44973	+	1.28812i
$435$	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
$438$	−11.1779	+	4.56385i	−0.534101	+	0.218069i
$439$	−10.3186			−0.492478			−0.246239	−	0.969209i	$-0.579195\pi$
$439$	−10.3186			−0.492478			−0.246239	+	0.969209i	$0.579195\pi$
$440$	−15.0287	+	8.53475i	−0.716467	+	0.406878i
$441$	5.54130	+	4.27715i	0.263871	+	0.203674i
$442$	2.79496	+	6.84549i	0.132943	+	0.325607i
$443$	−24.3473	+	24.3473i	−1.15678	+	1.15678i	−0.171610	+	0.985165i	$0.554897\pi$
$443$	−24.3473	+	24.3473i	−1.15678	+	1.15678i	−0.985165	+	0.171610i	$0.945103\pi$
$444$	−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
$448$	19.8162	+	7.43763i	0.936227	+	0.351395i
$449$		−	15.1405i		−	0.714523i	−0.934004	−	0.357261i	$-0.883711\pi$
$449$		−	15.1405i		−	0.714523i	0.934004	−	0.357261i	$-0.116289\pi$
$450$	−5.56181	+	4.36649i	−0.262186	+	0.205838i
$451$	−2.05404			−0.0967208
$452$	−1.60450	−	0.0162521i	−0.0754694	−	0.000764434i
$453$	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	−0.0217457	+	0.999764i	$0.506922\pi$
$457$	−21.8374	+	21.8374i	−1.02151	+	1.02151i	−0.999764	+	0.0217457i	$0.993078\pi$
$458$	1.75213	+	4.29136i	0.0818717	+	0.200522i
$459$	−5.66941			−0.264626
$460$	−15.5453	+	20.1730i	−0.724804	+	0.940573i
$461$	−25.1333			−1.17057			−0.585287	−	0.810826i	$-0.699018\pi$
$461$	−25.1333			−1.17057			−0.585287	+	0.810826i	$0.699018\pi$
$462$	−0.602505	−	10.2070i	−0.0280311	−	0.474875i
$463$	−0.705332	−	0.705332i	−0.0327796	−	0.0327796i	0.690527	−	0.723307i	$-0.257379\pi$
$463$	−0.705332	−	0.705332i	−0.0327796	−	0.0327796i	−0.723307	+	0.690527i	$0.757379\pi$
$464$	−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	$-0.792554\pi$
$467$	−4.07353	+	4.07353i	−0.188501	+	0.188501i	0.606547	+	0.795048i	$0.292554\pi$
$468$	−0.0186813	+	1.84433i	−0.000863545	+	0.0852543i
$469$	−26.0644	−	8.88912i	−1.20354	−	0.410462i
$470$	22.7088	−	13.2022i	1.04748	−	0.608971i
$471$	−13.0978			−0.603516
$472$	10.0492	+	4.34253i	0.462551	+	0.199881i
$473$	−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
$476$	27.0574	−	12.9568i	1.24018	−	0.593873i
$477$	−6.28157	−	6.28157i	−0.287613	−	0.287613i
$478$	−13.9990	−	34.2868i	−0.640301	−	1.56824i
$479$	−3.89552			−0.177991			−0.0889953	−	0.996032i	$-0.528366\pi$
$479$	−3.89552			−0.177991			−0.0889953	+	0.996032i	$0.528366\pi$
$480$	−6.13467	−	11.0619i	−0.280008	−	0.504905i
$481$			1.19886i			0.0546632i
$482$	3.97301	+	9.73078i	0.180966	+	0.443225i
$483$	−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	−0.696144	−	0.717903i	$-0.745102\pi$
$487$	0.480177	−	0.480177i	0.0217589	−	0.0217589i	0.717903	+	0.696144i	$0.245102\pi$
$488$	−3.08790	+	7.14581i	−0.139783	+	0.323476i
$489$	−18.7309			−0.847043
$490$	13.4783	+	17.5595i	0.608886	+	0.793258i
$491$		−	26.2424i		−	1.18430i	−0.805828	−	0.592150i	$-0.798279\pi$
$491$		−	26.2424i		−	1.18430i	0.805828	−	0.592150i	$-0.201721\pi$
$492$	0.0152263	−	1.50323i	0.000686453	−	0.0677707i
$493$	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
$498$	7.25984	+	17.7810i	0.325321	+	0.796785i
$499$	−28.3424			−1.26878			−0.634389	−	0.773014i	$-0.718748\pi$
$499$	−28.3424			−1.26878			−0.634389	+	0.773014i	$0.718748\pi$
$500$	−20.5360	+	8.84727i	−0.918396	+	0.395662i
$501$			13.1982i			0.589652i
$502$	−13.5139	+	5.51762i	−0.603155	+	0.246264i
$503$	19.9583	−	19.9583i	0.889897	−	0.889897i	−0.104616	−	0.994513i	$-0.533361\pi$
$503$	19.9583	−	19.9583i	0.889897	−	0.889897i	0.994513	+	0.104616i	$0.0333613\pi$
$504$	7.47439	−	0.365274i	0.332936	−	0.0162706i
$505$	−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
$508$	−0.344662	+	34.0271i	−0.0152919	+	1.50971i
$509$		−	35.6134i		−	1.57854i	−0.614048	−	0.789269i	$-0.710460\pi$
$509$		−	35.6134i		−	1.57854i	0.614048	−	0.789269i	$-0.289540\pi$
$510$	−17.3312	−	4.58806i	−0.767441	−	0.203163i
$511$	7.29110	−	21.3787i	0.322539	−	0.945739i
$512$	21.2778	−	7.69764i	0.940356	−	0.340191i
$513$	−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
$518$	4.85562	−	0.286619i	0.213344	−	0.0125933i
$519$			6.74794i			0.296202i
$520$	−1.54966	+	5.62296i	−0.0679572	+	0.246583i
$521$			34.0551i			1.49198i	0.665957	+	0.745990i	$0.268023\pi$
$521$			34.0551i			1.49198i	−0.665957	+	0.745990i	$0.731977\pi$
$522$	2.06844	+	5.06607i	0.0905332	+	0.221736i
$523$	−5.30937	−	5.30937i	−0.232162	−	0.232162i	0.581432	−	0.813595i	$-0.302492\pi$
$523$	−5.30937	−	5.30937i	−0.232162	−	0.232162i	−0.813595	+	0.581432i	$0.802492\pi$
$524$	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
$528$	−7.57108	−	7.88421i	−0.329489	−	0.343116i
$529$			9.43044i			0.410019i
$530$	−14.1191	−	24.2861i	−0.613296	−	1.05492i
$531$	3.87046			0.167964
$532$	3.46897	+	1.22244i	0.150399	+	0.0529993i
$533$	−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
$538$	−7.54262	−	18.4736i	−0.325185	−	0.796452i
$539$	15.1427	+	11.6881i	0.652242	+	0.503444i
$540$	−3.54238	−	2.72975i	−0.152440	−	0.117470i
$541$			37.2988i			1.60360i	0.597592	+	0.801801i	$0.296124\pi$
$541$			37.2988i			1.60360i	−0.597592	+	0.801801i	$0.703876\pi$
$542$	13.4090	+	32.8415i	0.575964	+	1.41067i
$543$	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
$546$	−2.57948	−	2.29193i	−0.110392	−	0.0980856i
$547$	24.4386	+	24.4386i	1.04492	+	1.04492i	0.998943	+	0.0459756i	$0.0146396\pi$
$547$	24.4386	+	24.4386i	1.04492	+	1.04492i	0.0459756	+	0.998943i	$0.485360\pi$
$548$	0.0566049	−	5.58838i	0.00241804	−	0.238724i
$549$			2.75222i			0.117462i
$550$	−15.1987	+	11.9323i	−0.648077	+	0.508795i
$551$			2.68953i			0.114578i
$552$	−14.7858	−	6.38935i	−0.629325	−	0.271949i
$553$	−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	$-0.223495\pi$
$557$	2.77604	+	2.77604i	0.117625	+	0.117625i	−0.645844	+	0.763469i	$0.723495\pi$
$558$	14.1373	−	5.77215i	0.598479	−	0.244355i
$559$	−9.76367			−0.412959
$560$	23.1446	+	4.93213i	0.978039	+	0.208421i
$561$	−15.4928			−0.654106
$562$	−6.41042	+	2.61733i	−0.270407	+	0.110405i
$563$	25.4137	+	25.4137i	1.07106	+	1.07106i	0.997274	+	0.0737860i	$0.0235082\pi$
$563$	25.4137	+	25.4137i	1.07106	+	1.07106i	0.0737860	+	0.997274i	$0.476492\pi$
$564$	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
$568$	15.2048	−	35.1859i	0.637979	−	1.47637i
$569$			26.1170i			1.09488i	0.836844	+	0.547441i	$0.184398\pi$
$569$			26.1170i			1.09488i	−0.836844	+	0.547441i	$0.815602\pi$
$570$	−1.10475	−	1.90026i	−0.0462730	−	0.0795932i
$571$		−	21.3882i		−	0.895068i	−0.894267	−	0.447534i	$-0.852302\pi$
$571$		−	21.3882i		−	0.895068i	0.894267	−	0.447534i	$-0.147698\pi$
$572$	−0.0510504	+	5.04000i	−0.00213453	+	0.210733i
$573$	5.55424	+	5.55424i	0.232032	+	0.232032i
$574$	2.10241	+	1.86804i	0.0877531	+	0.0779707i
$575$	−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	0.938913	−	0.344155i	$-0.111835\pi$
$577$	14.2866	+	14.2866i	0.594758	+	0.594758i	−0.344155	+	0.938913i	$0.611835\pi$
$578$	−8.09462	−	19.8255i	−0.336692	−	0.824634i
$579$		−	21.1383i		−	0.878478i
$580$	2.22337	+	17.1608i	0.0923206	+	0.712562i
$581$	−34.0077	−	11.5981i	−1.41088	−	0.481172i
$582$	−1.57696	−	3.86233i	−0.0653672	−	0.160099i
$583$	−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	$-0.923276\pi$
$587$	−17.7442	+	17.7442i	−0.732382	+	0.732382i	0.238709	+	0.971091i	$0.423276\pi$
$588$	−8.66610	+	10.9954i	−0.357384	+	0.453442i
$589$	7.50536			0.309253
$590$	11.8319	+	3.13223i	0.487111	+	0.128952i
$591$		−	11.6909i		−	0.480897i
$592$	3.75062	−	3.60166i	0.154149	−	0.148027i
$593$	−32.2253	+	32.2253i	−1.32334	+	1.32334i	−0.412278	+	0.911058i	$0.635267\pi$
$593$	−32.2253	+	32.2253i	−1.32334	+	1.32334i	−0.911058	+	0.412278i	$0.864733\pi$
$594$	−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
$598$	2.80747	+	6.87611i	0.114806	+	0.281185i
$599$		−	8.47680i		−	0.346353i	−0.984891	−	0.173176i	$-0.944597\pi$
$599$		−	8.47680i		−	0.346353i	0.984891	−	0.173176i	$-0.0554031\pi$
$600$	−8.61987	−	11.2115i	−0.351905	−	0.457708i
$601$			30.8501i			1.25840i	0.777243	+	0.629201i	$0.216618\pi$
$601$			30.8501i			1.25840i	−0.777243	+	0.629201i	$0.783382\pi$
$602$	2.33427	+	39.5449i	0.0951378	+	1.61173i
$603$	−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	0.918873	−	0.394554i	$-0.129101\pi$
$607$	12.9179	+	12.9179i	0.524319	+	0.524319i	−0.394554	+	0.918873i	$0.629101\pi$
$608$	3.66964	−	1.41226i	0.148824	−	0.0572746i
$609$	−9.68931	−	3.30449i	−0.392631	−	0.133905i
$610$	−2.22727	+	8.41346i	−0.0901797	+	0.340651i
$611$		−	7.66041i		−	0.309907i
$612$	0.114846	−	11.3382i	0.00464236	−	0.458321i
$613$	28.6067	−	28.6067i	1.15542	−	1.15542i	0.169965	−	0.985450i	$-0.445635\pi$
$613$	28.6067	−	28.6067i	1.15542	−	1.15542i	0.985450	−	0.169965i	$-0.0543655\pi$
$614$	−1.38881	+	3.30543i	−0.0560477	+	0.133396i
$615$	−0.232826	−	1.66454i	−0.00938845	−	0.0671208i
$616$	20.4253	−	0.998184i	0.822957	−	0.0402180i
$617$	−24.6084	+	24.6084i	−0.990698	+	0.990698i	−0.999957	−	0.00925894i	$-0.997053\pi$
$617$	−24.6084	+	24.6084i	−0.990698	+	0.990698i	0.00925894	+	0.999957i	$0.497053\pi$
$618$	−0.192206	+	0.0784762i	−0.00773164	+	0.00315677i
$619$		−	30.0791i		−	1.20898i	−0.796612	−	0.604491i	$-0.793376\pi$
$619$		−	30.0791i		−	1.20898i	0.796612	−	0.604491i	$-0.206624\pi$
$620$	47.8885	−	6.20451i	1.92325	−	0.249179i
$621$	−5.69477			−0.228523
$622$	16.5296	+	40.4848i	0.662778	+	1.62329i
$623$	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
$628$	0.265323	−	26.1943i	0.0105876	−	1.04527i
$629$		−	7.37011i		−	0.293866i
$630$	8.20324	−	1.64523i	0.326825	−	0.0655475i
$631$	−11.6754			−0.464790			−0.232395	−	0.972621i	$-0.574656\pi$
$631$	−11.6754			−0.464790			−0.232395	+	0.972621i	$0.574656\pi$
$632$	−7.44939	−	3.21909i	−0.296321	−	0.128048i
$633$	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
$638$	5.65242	+	13.8440i	0.223782	+	0.548091i
$639$		−	13.5519i		−	0.536106i
$640$	22.2470	−	12.0446i	0.879388	−	0.476106i
$641$	8.72083			0.344452			0.172226	−	0.985057i	$-0.444904\pi$
$641$	8.72083			0.344452			0.172226	+	0.985057i	$0.444904\pi$
$642$	−4.69858	−	11.5079i	−0.185438	−	0.454179i
$643$	−2.51464	−	2.51464i	−0.0991677	−	0.0991677i	0.655782	−	0.754950i	$-0.272339\pi$
$643$	−2.51464	−	2.51464i	−0.0991677	−	0.0991677i	−0.754950	+	0.655782i	$0.772339\pi$
$644$	27.1785	−	13.0147i	1.07098	−	0.512852i
$645$	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	0.884791	+	0.465987i	$0.154301\pi$
$647$	34.3587	+	34.3587i	1.35078	+	1.35078i	0.465987	+	0.884791i	$0.345699\pi$
$648$	1.12197	−	2.59638i	0.0440750	−	0.101995i
$649$	10.5768			0.415175
$650$	−0.779473	+	6.47428i	−0.0305735	+	0.253942i
$651$	−9.22145	+	27.0388i	−0.361417	+	1.05973i
$652$	0.379434	−	37.4600i	0.0148598	−	1.46705i
$653$	−19.0429	+	19.0429i	−0.745205	+	0.745205i	−0.973575	−	0.228369i	$-0.926661\pi$
$653$	−19.0429	+	19.0429i	−0.745205	+	0.745205i	0.228369	+	0.973575i	$0.426661\pi$
$654$	−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
$658$	−31.0263	+	1.83143i	−1.20953	+	0.0713965i
$659$	19.1601			0.746370			0.373185	−	0.927757i	$-0.378266\pi$
$659$	19.1601			0.746370			0.373185	+	0.927757i	$0.378266\pi$
$660$	−9.68025	−	7.45959i	−0.376803	−	0.290364i
$661$	−40.5236			−1.57618			−0.788092	−	0.615557i	$-0.788931\pi$
$661$	−40.5236			−1.57618			−0.788092	+	0.615557i	$0.788931\pi$
$662$	4.97647	+	12.1885i	0.193416	+	0.473719i
$663$	−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
$668$	−26.3950	−	0.267357i	−1.02125	−	0.0103443i
$669$	−0.0489290			−0.00189170
$670$	−28.4554	+	16.5431i	−1.09933	+	0.639115i
$671$			7.52098i			0.290344i
$672$	0.579102	+	14.9554i	0.0223393	+	0.576918i
$673$	−5.40919	−	5.40919i	−0.208509	−	0.208509i	0.595125	−	0.803633i	$-0.297103\pi$
$673$	−5.40919	−	5.40919i	−0.208509	−	0.208509i	−0.803633	+	0.595125i	$0.797103\pi$
$674$	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	$-0.793933\pi$
$677$	−5.06251	+	5.06251i	−0.194568	+	0.194568i	0.603099	+	0.797667i	$0.293933\pi$
$678$	−0.428883	−	1.05043i	−0.0164712	−	0.0403415i
$679$	7.38706	+	2.51932i	0.283489	+	0.0966825i
$680$	9.52672	−	34.5678i	0.365333	−	1.32561i
$681$	−4.98238			−0.190925
$682$	38.6329	−	15.7735i	1.47933	−	0.604000i
$683$	15.0127	−	15.0127i	0.574445	−	0.574445i	−0.358923	−	0.933367i	$-0.616856\pi$
$683$	15.0127	−	15.0127i	0.574445	−	0.574445i	0.933367	+	0.358923i	$0.116856\pi$
$684$	0.992909	−	0.972996i	0.0379648	−	0.0372034i
$685$	−0.865551	−	6.18807i	−0.0330710	−	0.236434i
$686$	−4.86955	−	25.7349i	−0.185920	−	0.982565i
$687$	−2.31763	+	2.31763i	−0.0884233	+	0.0884233i
$688$	29.3325	+	30.5456i	1.11829	+	1.16454i
$689$	−8.19247			−0.312108
$690$	−17.4088	−	4.60858i	−0.662741	−	0.175446i
$691$	23.0407			0.876509			0.438255	−	0.898851i	$-0.355597\pi$
$691$	23.0407			0.876509			0.438255	+	0.898851i	$0.355597\pi$
$692$	−13.4952	−	0.136693i	−0.513010	−	0.00519630i
$693$	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
$698$	−5.42640	−	13.2905i	−0.205392	−	0.503052i
$699$		−	5.84121i		−	0.220935i
$700$	26.4085	+	1.60918i	0.998149	+	0.0608211i
$701$			14.1221i			0.533386i	0.963782	+	0.266693i	$0.0859309\pi$
$701$			14.1221i			0.533386i	−0.963782	+	0.266693i	$0.914069\pi$
$702$	−1.20744	+	0.492990i	−0.0455720	+	0.0186067i
$703$	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
$708$	−0.0784041	+	7.74052i	−0.00294661	+	0.290906i
$709$	−11.5784			−0.434834			−0.217417	−	0.976079i	$-0.569763\pi$
$709$	−11.5784			−0.434834			−0.217417	+	0.976079i	$0.569763\pi$
$710$	10.9671	−	41.4279i	0.411588	−	1.55476i
$711$	−2.86914			−0.107601
$712$	8.98662	−	20.7962i	0.336788	−	0.779371i
$713$	43.4803	−	43.4803i	1.62835	−	1.62835i
$714$	15.8577	+	14.0899i	0.593458	+	0.527302i
$715$	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
$718$	5.77120	+	14.1350i	0.215379	+	0.527512i
$719$	−37.0363			−1.38122			−0.690611	−	0.723227i	$-0.742658\pi$
$719$	−37.0363			−1.38122			−0.690611	+	0.723227i	$0.742658\pi$
$720$	5.53098	−	7.02910i	0.206128	−	0.261959i
$721$	0.125372	−	0.367610i	0.00466908	−	0.0136905i
$722$	−24.2439	+	9.89860i	−0.902264	+	0.368388i
$723$	−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	0.454330	−	0.890833i	$-0.349879\pi$
$727$	−11.7694	−	11.7694i	−0.436503	−	0.436503i	−0.890833	+	0.454330i	$0.849879\pi$
$728$	4.63588	−	5.11227i	0.171817	−	0.189474i
$729$		−	1.00000i		−	0.0370370i
$730$	−13.5691	−	23.3399i	−0.502214	−	0.863849i
$731$	60.0233			2.22004
$732$	−5.50416	−	0.0557519i	−0.203439	−	0.00206065i
$733$	14.6000	+	14.6000i	0.539262	+	0.539262i	0.923312	−	0.384050i	$-0.125471\pi$
$733$	14.6000	+	14.6000i	0.539262	+	0.539262i	−0.384050	+	0.923312i	$0.625471\pi$
$734$	−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
$738$	0.984128	−	0.401812i	0.0362263	−	0.0147909i
$739$	−35.9219			−1.32141			−0.660705	−	0.750646i	$-0.729742\pi$
$739$	−35.9219			−1.32141			−0.660705	+	0.750646i	$0.729742\pi$
$740$	3.54862	−	4.60501i	0.130450	−	0.169284i
$741$	−0.641020			−0.0235484
$742$	1.95863	+	33.1812i	0.0719036	+	1.21812i
$743$	−5.83345	−	5.83345i	−0.214008	−	0.214008i	0.591959	−	0.805968i	$-0.298355\pi$
$743$	−5.83345	−	5.83345i	−0.214008	−	0.214008i	−0.805968	+	0.591959i	$0.798355\pi$
$744$	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
$748$	0.313838	−	30.9840i	0.0114751	−	1.13289i
$749$	22.0098	+	7.50633i	0.804221	+	0.274275i
$750$	−11.3924	−	10.9642i	−0.415992	−	0.400354i
$751$	53.2891			1.94455			0.972273	−	0.233850i	$-0.0751324\pi$
$751$	53.2891			1.94455			0.972273	+	0.233850i	$0.0751324\pi$
$752$	−23.9656	+	23.0137i	−0.873934	+	0.839225i
$753$	−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
$756$	2.28538	+	4.77253i	0.0831186	+	0.173575i
$757$	10.7784	+	10.7784i	0.391748	+	0.391748i	0.875310	−	0.483562i	$-0.160657\pi$
$757$	10.7784	+	10.7784i	0.391748	+	0.391748i	−0.483562	+	0.875310i	$0.660657\pi$
$758$	−3.72544	+	1.52107i	−0.135314	+	0.0552477i
$759$	−15.5621			−0.564868
$760$	3.82271	−	2.17090i	0.138664	−	0.0787468i
$761$		−	17.9007i		−	0.648898i	−0.945903	−	0.324449i	$-0.894821\pi$
$761$		−	17.9007i		−	0.648898i	0.945903	−	0.324449i	$-0.105179\pi$
$762$	−22.2767	+	9.09543i	−0.807001	+	0.329493i
$763$	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
$768$	10.8462	+	11.7627i	0.391378	+	0.424449i
$769$	−15.6268			−0.563516			−0.281758	−	0.959485i	$-0.590918\pi$
$769$	−15.6268			−0.563516			−0.281758	+	0.959485i	$0.590918\pi$
$770$	22.4170	−	4.49591i	0.807852	−	0.162021i
$771$			3.42821i			0.123464i
$772$	42.2745	+	0.428200i	1.52149	+	0.0154113i
$773$	−10.7314	−	10.7314i	−0.385982	−	0.385982i	0.487270	−	0.873251i	$-0.337993\pi$
$773$	−10.7314	−	10.7314i	−0.385982	−	0.385982i	−0.873251	+	0.487270i	$0.837993\pi$
$774$	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
$778$	10.8289	−	4.42135i	0.388234	−	0.158513i
$779$	0.522465			0.0187192
$780$	−4.09008	+	0.529916i	−0.146448	+	0.0189741i
$781$		−	37.0333i		−	1.32515i
$782$	−17.2592	−	42.2717i	−0.617188	−	1.51163i
$783$	−2.73604	+	2.73604i	−0.0977779	+	0.0977779i
$784$	−21.8141	−	17.5541i	−0.779075	−	0.626930i
$785$	−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	−0.0165242	+	0.999863i	$0.505260\pi$
$787$	−28.5133	+	28.5133i	−1.01639	+	1.01639i	−0.999863	+	0.0165242i	$0.994740\pi$
$788$	23.3805	+	0.236822i	0.832896	+	0.00843645i
$789$			10.2846i			0.366141i
$790$	−8.77090	−	2.32190i	−0.312055	−	0.0826094i
$791$	2.00904	+	0.685173i	0.0714333	+	0.0243619i
$792$	3.06600	−	7.09512i	0.108945	−	0.252114i
$793$	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	0.447761	−	0.894153i	$-0.352221\pi$
$797$	37.8838	−	37.8838i	1.34191	−	1.34191i	0.894153	−	0.447761i	$-0.147779\pi$
$798$	0.153253	+	2.59626i	0.00542510	+	0.0919067i
$799$			47.0933i			1.66604i
$800$	22.5965	−	17.0117i	0.798906	−	0.601456i
$801$		−	8.00970i		−	0.283009i
$802$	10.6278	−	4.33925i	0.375280	−	0.153224i
$803$	−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
$808$	8.82806	−	20.4293i	0.310570	−	0.718700i
$809$			48.0950i			1.69093i	0.534030	+	0.845466i	$0.320677\pi$
$809$			48.0950i			1.69093i	−0.534030	+	0.845466i	$0.679323\pi$
$810$	0.809265	−	3.05697i	0.0284347	−	0.107411i
$811$	9.01398			0.316524			0.158262	−	0.987397i	$-0.449411\pi$
$811$	9.01398			0.316524			0.158262	+	0.987397i	$0.449411\pi$
$812$	6.80492	−	19.3107i	0.238806	−	0.677672i
$813$	−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
$818$	32.6675	−	13.3379i	1.14219	−	0.466349i
$819$	0.787588	−	2.30934i	0.0275206	−	0.0806949i
$820$	3.33363	−	0.431910i	0.116415	−	0.0150829i
$821$			45.0380i			1.57184i	0.618329	+	0.785919i	$0.287810\pi$
$821$			45.0380i			1.57184i	−0.618329	+	0.785919i	$0.712190\pi$
$822$	3.65858	−	1.49377i	0.127608	−	0.0521013i
$823$	−20.1794	−	20.1794i	−0.703410	−	0.703410i	0.261731	−	0.965141i	$-0.415707\pi$
$823$	−20.1794	−	20.1794i	−0.703410	−	0.703410i	−0.965141	+	0.261731i	$0.915707\pi$
$824$	−0.153051	−	0.385981i	−0.00533178	−	0.0134463i
$825$	−11.9417	−	6.63981i	−0.415756	−	0.231169i
$826$	−10.8259	−	9.61906i	−0.376681	−	0.334690i
$827$	16.2430	+	16.2430i	0.564824	+	0.564824i	0.930674	−	0.365850i	$-0.119222\pi$
$827$	16.2430	+	16.2430i	0.564824	+	0.564824i	−0.365850	+	0.930674i	$0.619222\pi$
$828$	0.115359	−	11.3890i	0.00400902	−	0.395794i
$829$			33.9024i			1.17748i	0.808323	+	0.588739i	$0.200375\pi$
$829$			33.9024i			1.17748i	−0.808323	+	0.588739i	$0.799625\pi$
$830$	−37.1274	+	21.5847i	−1.28871	+	0.749216i
$831$			2.69929i			0.0936374i
$832$	0.224145	−	7.37430i	0.00777084	−	0.255658i
$833$	−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
$838$	1.33968	+	3.28118i	0.0462785	+	0.113346i
$839$	−4.44797			−0.153561			−0.0767805	−	0.997048i	$-0.524464\pi$
$839$	−4.44797			−0.153561			−0.0767805	+	0.997048i	$0.524464\pi$
$840$	3.12412	+	16.4390i	0.107792	+	0.567199i
$841$	−14.0282			−0.483732
$842$	−12.1589	−	29.7798i	−0.419022	−	1.02628i
$843$	−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
$848$	24.6122	+	25.6301i	0.845185	+	0.880141i
$849$			29.6164i			1.01643i
$850$	4.79190	−	39.8014i	0.164361	−	1.36518i
$851$		−	7.40308i		−	0.253774i
$852$	27.1024	+	0.274522i	0.928514	+	0.00940497i
$853$	25.8367	+	25.8367i	0.884633	+	0.884633i	0.994001	−	0.109368i	$-0.0348828\pi$
$853$	25.8367	+	25.8367i	0.884633	+	0.884633i	−0.109368	+	0.994001i	$0.534883\pi$
$854$	6.83996	−	7.69811i	0.234058	−	0.263424i
$855$	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	0.819503	−	0.573075i	$-0.194249\pi$
$857$	7.21409	+	7.21409i	0.246429	+	0.246429i	−0.573075	+	0.819503i	$0.694249\pi$
$858$	−3.29957	+	1.34719i	−0.112646	+	0.0459924i
$859$			12.6174i			0.430500i	0.976559	+	0.215250i	$0.0690567\pi$
$859$			12.6174i			0.430500i	−0.976559	+	0.215250i	$0.930943\pi$
$860$	37.5039	+	28.9005i	1.27887	+	0.985498i
$861$	−0.641926	+	1.88223i	−0.0218768	+	0.0641463i
$862$	−51.3925	+	20.9832i	−1.75043	+	0.714689i
$863$	1.96768	+	1.96768i	0.0669805	+	0.0669805i	0.739803	−	0.672823i	$-0.234918\pi$
$863$	1.96768	+	1.96768i	0.0669805	+	0.0669805i	−0.672823	+	0.739803i	$0.734918\pi$
$864$	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
$868$	−53.8881	−	18.9897i	−1.82908	−	0.644552i
$869$	−7.84050			−0.265971
$870$	−10.5782	+	6.14981i	−0.358633	+	0.208498i
$871$			9.59893i			0.325247i
$872$	1.11948	−	2.59064i	0.0379105	−	0.0877300i
$873$	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	$-0.108774\pi$
$877$	17.9777	+	17.9777i	0.607065	+	0.607065i	−0.335113	+	0.942178i	$0.608774\pi$
$878$	13.5099	−	5.51601i	0.455939	−	0.186156i
$879$		−	24.5699i		−	0.828721i
$880$	15.1145	−	19.2084i	0.509510	−	0.647515i
$881$			22.8009i			0.768181i	0.923295	+	0.384091i	$0.125485\pi$
$881$			22.8009i			0.768181i	−0.923295	+	0.384091i	$0.874515\pi$
$882$	−9.54160	−	2.63779i	−0.321282	−	0.0888189i
$883$	15.3917	−	15.3917i	0.517971	−	0.517971i	−0.398986	−	0.916957i	$-0.630638\pi$
$883$	15.3917	−	15.3917i	0.517971	−	0.517971i	0.916957	+	0.398986i	$0.130638\pi$
$884$	−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	0.156481	−	0.987681i	$-0.449985\pi$
$887$	−24.7552	−	24.7552i	−0.831200	−	0.831200i	−0.987681	+	0.156481i	$0.949985\pi$
$888$	3.37524	+	1.45853i	0.113266	+	0.0489451i
$889$	14.5306	−	42.6062i	0.487342	−	1.42897i
$890$	6.48197	−	24.4854i	0.217276	−	0.820754i
$891$		−	2.73270i		−	0.0915488i
$892$	0.000991158	−	0.0978530i	3.31864e−5	−	0.00327636i
$893$	−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
$896$	−29.9210	+	0.855192i	−0.999592	+	0.0285699i
$897$	−3.71358	+	3.71358i	−0.123993	+	0.123993i
$898$	8.09367	+	19.8232i	0.270089	+	0.661509i
$899$		−	41.7800i		−	1.39344i
$900$	4.94780	−	8.69018i	0.164927	−	0.289673i
$901$	50.3641			1.67787
$902$	2.68932	−	1.09803i	0.0895447	−	0.0365604i
$903$	−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	$-0.300244\pi$
$907$	−6.69500	−	6.69500i	−0.222304	−	0.222304i	−0.809468	+	0.587164i	$0.800244\pi$
$908$	0.100928	−	9.96425i	0.00334943	−	0.330675i
$909$		−	7.86838i		−	0.260978i
$910$	4.27650	−	6.42222i	0.141765	−	0.212895i
$911$	6.41072			0.212397			0.106198	−	0.994345i	$-0.466132\pi$
$911$	6.41072			0.212397			0.106198	+	0.994345i	$0.466132\pi$
$912$	1.92578	+	2.00543i	0.0637689	+	0.0664063i
$913$	−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
$918$	7.42289	−	3.03071i	0.244992	−	0.100028i
$919$		−	35.0631i		−	1.15663i	−0.815815	−	0.578313i	$-0.803711\pi$
$919$		−	35.0631i		−	1.15663i	0.815815	−	0.578313i	$-0.196289\pi$
$920$	9.56934	−	34.7224i	0.315492	−	1.14476i
$921$	−2.53522			−0.0835383
$922$	32.9067	−	13.4356i	1.08372	−	0.442477i
$923$	−8.83725	−	8.83725i	−0.290882	−	0.290882i
$924$	6.24526	+	13.0419i	0.205454	+	0.429046i
$925$	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
$928$	−7.86159	−	20.4277i	−0.258069	−	0.670573i
$929$	−1.13791			−0.0373336			−0.0186668	−	0.999826i	$-0.505942\pi$
$929$	−1.13791			−0.0373336			−0.0186668	+	0.999826i	$0.505942\pi$
$930$	17.1616	+	29.5192i	0.562749	+	0.967974i
$931$	−3.85169	−	2.97299i	−0.126234	−	0.0974359i
$932$	11.6818	+	0.118326i	0.382650	+	0.00387589i
$933$	−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	0.536561	−	0.843862i	$-0.319723\pi$
$937$	−9.40662	−	9.40662i	−0.307301	−	0.307301i	−0.843862	+	0.536561i	$0.819723\pi$
$938$	38.8776	−	2.29488i	1.26940	−	0.0749306i
$939$	−26.1590			−0.853668
$940$	−22.6748	+	29.4249i	−0.739571	+	0.959736i
$941$	−37.4472			−1.22074			−0.610372	−	0.792115i	$-0.708980\pi$
$941$	−37.4472			−1.22074			−0.610372	+	0.792115i	$0.708980\pi$
$942$	17.1488	−	7.00173i	0.558738	−	0.228129i
$943$	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	−0.909765	−	0.415125i	$-0.863738\pi$
$947$	−40.7713	−	40.7713i	−1.32489	−	1.32489i	−0.415125	−	0.909765i	$-0.636262\pi$
$948$	0.0581204	−	5.73799i	0.00188766	−	0.186361i
$949$	−7.87330			−0.255578
$950$	3.86595	−	3.03510i	0.125428	−	0.0984715i
$951$			17.8767i			0.579693i
$952$	−28.4996	+	31.4283i	−0.923678	+	1.01860i
$953$	−13.1807	−	13.1807i	−0.426963	−	0.426963i	0.460629	−	0.887593i	$-0.347624\pi$
$953$	−13.1807	−	13.1807i	−0.426963	−	0.426963i	−0.887593	+	0.460629i	$0.847624\pi$
$954$	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
$958$	5.10035	−	2.08243i	0.164785	−	0.0672804i
$959$	−2.38641	+	6.99736i	−0.0770613	+	0.225957i
$960$	13.9454	+	11.2038i	0.450087	+	0.361601i
$961$	−85.5904			−2.76098
$962$	−0.640876	−	1.56965i	−0.0206627	−	0.0506075i
$963$	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
$966$	15.9286	+	14.1529i	0.512494	+	0.455363i
$967$	−29.9056	+	29.9056i	−0.961698	+	0.961698i	−0.999293	−	0.0375950i	$-0.988030\pi$
$967$	−29.9056	+	29.9056i	−0.961698	+	0.961698i	0.0375950	+	0.999293i	$0.488030\pi$
$968$	−3.96320	+	9.17137i	−0.127382	+	0.294779i
$969$	3.94074			0.126595
$970$	8.06471	−	4.68857i	0.258942	−	0.150541i
$971$	−25.9583			−0.833040			−0.416520	−	0.909126i	$-0.636750\pi$
$971$	−25.9583			−0.833040			−0.416520	+	0.909126i	$0.636750\pi$
$972$	1.99990	+	0.0202571i	0.0641467	+	0.000649746i
$973$	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	−0.781255	−	0.624212i	$-0.785420\pi$
$977$	−4.90867	+	4.90867i	−0.157042	+	0.157042i	0.624212	+	0.781255i	$0.285420\pi$
$978$	24.5242	−	10.0130i	0.784197	−	0.320182i
$979$		−	21.8881i		−	0.699546i
$980$	−27.0337	−	15.7853i	−0.863561	−	0.504244i
$981$		−	0.997788i		−	0.0318569i
$982$	14.0284	+	34.3588i	0.447665	+	1.09643i
$983$	−21.6602	+	21.6602i	−0.690854	+	0.690854i	−0.962420	−	0.271566i	$-0.912459\pi$
$983$	−21.6602	+	21.6602i	−0.690854	+	0.690854i	0.271566	+	0.962420i	$0.412459\pi$
$984$	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
$988$	0.0129852	−	1.28197i	0.000413114	−	0.0407850i
$989$	60.2918			1.91717
$990$	2.21148	−	8.35378i	0.0702853	−	0.265501i
$991$	24.5393			0.779518			0.389759	−	0.920917i	$-0.372558\pi$
$991$	24.5393			0.779518			0.389759	+	0.920917i	$0.372558\pi$
$992$	−57.0053	+	21.9384i	−1.80992	+	0.696545i
$993$	−6.58264	+	6.58264i	−0.208894	+	0.208894i
$994$	−33.6799	+	37.9055i	−1.06826	+	1.20229i
$995$	−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	$-0.748512\pi$
$997$	0.208804	−	0.208804i	0.00661289	−	0.00661289i	0.710405	+	0.703793i	$0.248512\pi$
$998$	37.1083	−	15.1510i	1.17464	−	0.479598i
$999$	1.29998			0.0411295

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.11	✓	184	1.1	even	1	trivial
840.2.bj.b.13.12	yes	184	7.6	odd	2	inner
840.2.bj.b.13.33	yes	184	56.13	odd	2	inner
840.2.bj.b.13.34	yes	184	8.5	even	2	inner
840.2.bj.b.517.11	yes	184	280.237	even	4	inner
840.2.bj.b.517.12	yes	184	40.37	odd	4	inner
840.2.bj.b.517.33	yes	184	5.2	odd	4	inner
840.2.bj.b.517.34	yes	184	35.27	even	4	inner

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+(-1.30929 + 0.534572i) 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} +(-1.12197 + 2.59638i) q^{8} +1.00000i q^{9} +(-0.809265 + 3.05697i) q^{10} +2.73270i q^{11} +(-1.99990 - 0.0202571i) q^{12} +(0.652103 + 0.652103i) q^{13} +(2.48525 - 2.79706i) q^{14} +(-2.21451 + 0.309752i) q^{15} +(0.0810241 - 3.99918i) q^{16} +(-4.00888 - 4.00888i) q^{17} +(-0.534572 - 1.30929i) q^{18} -0.695088i q^{19} +(-0.574614 - 4.43507i) q^{20} +(2.50413 + 0.854019i) q^{21} +(-1.46082 - 3.57788i) 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} +(-1.75868 + 4.99070i) q^{28} -3.86934 q^{29} +(2.73384 - 1.58937i) q^{30} +10.7977i q^{31} +(2.03177 + 5.27939i) 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} +(0.371575 + 0.910070i) q^{38} -0.922213i q^{39} +(3.12320 + 5.49960i) q^{40} +0.751652i q^{41} +(-3.73516 + 0.220480i) 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} +(-2.88514 + 2.77055i) q^{48} +(4.27715 - 5.54130i) q^{49} +(4.36649 + 5.56181i) q^{50} +5.66941i q^{51} +(1.84433 + 0.0186813i) q^{52} +(-6.28157 + 6.28157i) q^{53} +(-0.547806 + 1.30381i) q^{54} +(4.87765 + 3.68058i) q^{55} +(-0.365274 - 7.47439i) q^{56} +(-0.491502 + 0.491502i) q^{57} +(5.06607 - 2.06844i) q^{58} -3.87046i q^{59} +(-2.72975 + 3.54238i) q^{60} +2.75222 q^{61} +(-5.77215 - 14.1373i) 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} +(-11.3382 - 0.114846i) q^{68} +5.69477i q^{69} +(-1.64523 - 8.20324i) q^{70} -13.5519 q^{71} +(-2.59638 - 1.12197i) 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} +(0.492990 + 1.20744i) q^{78} +2.86914i q^{79} +(-7.02910 - 5.53098i) q^{80} -1.00000 q^{81} +(-0.401812 - 0.984128i) q^{82} +(9.60298 + 9.60298i) q^{83} +(4.77253 - 2.28538i) q^{84} +(-12.5550 + 1.75611i) q^{85} +(5.79974 - 13.8037i) q^{86} +(2.73604 + 2.73604i) q^{87} +(-7.09512 - 3.06600i) q^{88} -8.00970 q^{89} +(-3.05697 - 0.809265i) q^{90} +(-2.30934 - 0.787588i) q^{91} +(-11.3890 - 0.115359i) 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} +(-2.63779 + 9.54160i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more