LMFDB - Embedded newform 936.2.bk.c.277.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(277,936)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("936.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$160$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.7
Character	$\chi$	$=$	936.277
Dual form			936.2.bk.c.517.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40082 + 0.194204i) q^{2} +(-1.72956 - 0.0928202i) q^{3} +(1.92457 - 0.544089i) q^{4} +(2.01837 + 3.49592i) q^{5} +(2.44082 - 0.205864i) q^{6} -4.14289i q^{7} +(-2.59030 + 1.13593i) q^{8} +(2.98277 + 0.321077i) q^{9} +(-3.50628 - 4.50516i) q^{10} +(0.455967 + 0.789758i) q^{11} +(-3.37916 + 0.762396i) q^{12} +(2.56331 - 2.53563i) q^{13} +(0.804567 + 5.80343i) q^{14} +(-3.16640 - 6.23375i) q^{15} +(3.40794 - 2.09427i) q^{16} +(-2.50859 - 4.34500i) q^{17} +(-4.24066 + 0.129497i) q^{18} +(-3.12972 - 5.42083i) q^{19} +(5.78658 + 5.62996i) q^{20} +(-0.384544 + 7.16539i) q^{21} +(-0.792100 - 1.01775i) q^{22} -4.15940 q^{23} +(4.58553 - 1.72422i) q^{24} +(-5.64762 + 9.78197i) q^{25} +(-3.09830 + 4.04976i) q^{26} +(-5.12908 - 0.832183i) q^{27} +(-2.25410 - 7.97329i) q^{28} +(3.54970 - 2.04942i) q^{29} +(5.64617 + 8.11741i) q^{30} +(3.50608 - 2.02424i) q^{31} +(-4.36717 + 3.59553i) q^{32} +(-0.715317 - 1.40826i) q^{33} +(4.35789 + 5.59937i) q^{34} +(14.4832 - 8.36188i) q^{35} +(5.91524 - 1.00496i) q^{36} +(-1.88928 + 3.27233i) q^{37} +(5.43690 + 6.98578i) q^{38} +(-4.66877 + 4.14761i) q^{39} +(-9.19929 - 6.76276i) q^{40} -2.56433i q^{41} +(-0.852873 - 10.1121i) q^{42} +4.59652i q^{43} +(1.30724 + 1.27186i) q^{44} +(4.89787 + 11.0756i) q^{45} +(5.82655 - 0.807773i) q^{46} +(-9.45848 - 5.46085i) q^{47} +(-6.08863 + 3.30585i) q^{48} -10.1636 q^{49} +(6.01158 - 14.7995i) q^{50} +(3.93545 + 7.74780i) q^{51} +(3.55366 - 6.27467i) q^{52} -8.85112i q^{53} +(7.34651 + 0.169646i) q^{54} +(-1.84062 + 3.18804i) q^{55} +(4.70603 + 10.7313i) q^{56} +(4.90988 + 9.66616i) q^{57} +(-4.57447 + 3.56023i) q^{58} +(-5.07140 + 8.78392i) q^{59} +(-9.48567 - 10.2745i) q^{60} -5.90863i q^{61} +(-4.51826 + 3.51648i) q^{62} +(1.33019 - 12.3573i) q^{63} +(5.41934 - 5.88479i) q^{64} +(14.0381 + 3.84329i) q^{65} +(1.27552 + 1.83379i) q^{66} +0.155182 q^{67} +(-7.19202 - 6.99736i) q^{68} +(7.19394 + 0.386076i) q^{69} +(-18.6644 + 14.5262i) q^{70} +(7.19828 - 4.15593i) q^{71} +(-8.09099 + 2.55652i) q^{72} -8.57607i q^{73} +(2.01103 - 4.95083i) q^{74} +(10.6759 - 16.3943i) q^{75} +(-8.97277 - 8.72992i) q^{76} +(3.27188 - 1.88902i) q^{77} +(5.73460 - 6.71672i) q^{78} +(2.34194 - 4.05635i) q^{79} +(14.1999 + 7.68684i) q^{80} +(8.79382 + 1.91539i) q^{81} +(0.498003 + 3.59215i) q^{82} +(8.39361 - 14.5382i) q^{83} +(3.15852 + 13.9995i) q^{84} +(10.1265 - 17.5396i) q^{85} +(-0.892664 - 6.43888i) q^{86} +(-6.32966 + 3.21512i) q^{87} +(-2.07820 - 1.52777i) q^{88} +(0.377440 + 0.217915i) q^{89} +(-9.01193 - 14.5636i) q^{90} +(-10.5049 - 10.6195i) q^{91} +(-8.00505 + 2.26308i) q^{92} +(-6.25188 + 3.17561i) q^{93} +(14.3101 + 5.81277i) q^{94} +(12.6338 - 21.8825i) q^{95} +(7.88703 - 5.81332i) q^{96} -5.90985i q^{97} +(14.2373 - 1.97381i) q^{98} +(1.10647 + 2.50207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 3 q^{2} + q^{4} - 3 q^{6} + 10 q^{9} + 8 q^{10} - 7 q^{12} + 2 q^{14} + 24 q^{15} - 15 q^{16} + 8 q^{17} - 6 q^{18} + q^{22} + 20 q^{23} + 12 q^{24} - 144 q^{25} - 20 q^{26} - 6 q^{28} + 7 q^{30}+ \cdots - 99 q^{98}+O(q^{100}) $ 320 * q - 3 * q^2 + q^4 - 3 * q^6 + 10 * q^9 + 8 * q^10 - 7 * q^12 + 2 * q^14 + 24 * q^15 - 15 * q^16 + 8 * q^17 - 6 * q^18 + q^22 + 20 * q^23 + 12 * q^24 - 144 * q^25 - 20 * q^26 - 6 * q^28 + 7 * q^30 + 12 * q^31 - 3 * q^32 + 18 * q^33 - 30 * q^34 + 39 * q^36 - 10 * q^38 + 44 * q^39 - 28 * q^40 + 10 * q^42 - 30 * q^46 - 12 * q^47 - 8 * q^48 - 316 * q^49 - 56 * q^52 + 36 * q^54 + 14 * q^55 + 52 * q^56 + 36 * q^57 - 3 * q^58 + 3 * q^60 - q^62 - 42 * q^63 - 26 * q^64 + 66 * q^65 + 50 * q^66 - 12 * q^68 + 3 * q^70 - 48 * q^71 + 21 * q^72 + 26 * q^74 + 35 * q^78 + 32 * q^79 - 48 * q^80 + 34 * q^81 - 23 * q^82 + 120 * q^84 + 42 * q^86 - 2 * q^87 + 13 * q^88 - 72 * q^89 + 109 * q^90 - 28 * q^92 + 130 * q^94 + 112 * q^95 - 15 * q^96 - 99 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.40082	+	0.194204i	−0.990526	+	0.137323i
$2$	−1.40082	+	0.194204i	−0.990526	+	0.137323i
$3$	−1.72956	−	0.0928202i	−0.998563	−	0.0535898i
$3$	−1.72956	−	0.0928202i	−0.998563	−	0.0535898i
$4$	1.92457	−	0.544089i	0.962285	−	0.272044i
$5$	2.01837	+	3.49592i	0.902642	+	1.56342i	0.824052	+	0.566514i	$0.191708\pi$
$5$	2.01837	+	3.49592i	0.902642	+	1.56342i	0.0785900	+	0.996907i	$0.474958\pi$
$6$	2.44082	−	0.205864i	0.996462	−	0.0840437i
$7$		−	4.14289i		−	1.56587i	−0.622106	−	0.782933i	$-0.713723\pi$
$7$		−	4.14289i		−	1.56587i	0.622106	−	0.782933i	$-0.286277\pi$
$8$	−2.59030	+	1.13593i	−0.915810	+	0.401611i
$9$	2.98277	+	0.321077i	0.994256	+	0.107026i
$10$	−3.50628	−	4.50516i	−1.10878	−	1.42466i
$11$	0.455967	+	0.789758i	0.137479	+	0.238121i	0.926542	−	0.376192i	$-0.122767\pi$
$11$	0.455967	+	0.789758i	0.137479	+	0.238121i	−0.789063	+	0.614313i	$0.789433\pi$
$12$	−3.37916	+	0.762396i	−0.975481	+	0.220085i
$13$	2.56331	−	2.53563i	0.710935	−	0.703258i
$13$	2.56331	−	2.53563i	0.710935	−	0.703258i
$14$	0.804567	+	5.80343i	0.215030	+	1.55103i
$15$	−3.16640	−	6.23375i	−0.817561	−	1.60955i
$16$	3.40794	−	2.09427i	0.851984	−	0.523568i
$17$	−2.50859	−	4.34500i	−0.608422	−	1.05382i	−0.991501	−	0.130102i	$-0.958470\pi$
$17$	−2.50859	−	4.34500i	−0.608422	−	1.05382i	0.383079	−	0.923716i	$-0.374864\pi$
$18$	−4.24066	+	0.129497i	−0.999534	+	0.0305227i
$19$	−3.12972	−	5.42083i	−0.718006	−	1.24362i	−0.961789	−	0.273793i	$-0.911722\pi$
$19$	−3.12972	−	5.42083i	−0.718006	−	1.24362i	0.243783	−	0.969830i	$-0.421612\pi$
$20$	5.78658	+	5.62996i	1.29392	+	1.25890i
$21$	−0.384544	+	7.16539i	−0.0839144	+	1.56362i
$22$	−0.792100	−	1.01775i	−0.168876	−	0.216986i
$23$	−4.15940			−0.867295			−0.433647	−	0.901083i	$-0.642774\pi$
$23$	−4.15940			−0.867295			−0.433647	+	0.901083i	$0.642774\pi$
$24$	4.58553	−	1.72422i	0.936017	−	0.351956i
$25$	−5.64762	+	9.78197i	−1.12952	+	1.95639i
$26$	−3.09830	+	4.04976i	−0.607626	+	0.794223i
$27$	−5.12908	−	0.832183i	−0.987092	−	0.160154i
$28$	−2.25410	−	7.97329i	−0.425985	−	1.50681i
$29$	3.54970	−	2.04942i	0.659163	−	0.380568i	−0.132795	−	0.991144i	$-0.542395\pi$
$29$	3.54970	−	2.04942i	0.659163	−	0.380568i	0.791958	+	0.610576i	$0.209062\pi$
$30$	5.64617	+	8.11741i	1.03084	+	1.48203i
$31$	3.50608	−	2.02424i	0.629711	−	0.363564i	−0.150929	−	0.988545i	$-0.548227\pi$
$31$	3.50608	−	2.02424i	0.629711	−	0.363564i	0.780640	+	0.624981i	$0.214893\pi$
$32$	−4.36717	+	3.59553i	−0.772014	+	0.635605i
$33$	−0.715317	−	1.40826i	−0.124521	−	0.245146i
$34$	4.35789	+	5.59937i	0.747371	+	0.960284i
$35$	14.4832	−	8.36188i	2.44811	−	1.41342i
$36$	5.91524	−	1.00496i	0.985873	−	0.167493i
$37$	−1.88928	+	3.27233i	−0.310596	+	0.537967i	−0.978491	−	0.206287i	$-0.933862\pi$
$37$	−1.88928	+	3.27233i	−0.310596	+	0.537967i	0.667896	+	0.744255i	$0.267195\pi$
$38$	5.43690	+	6.98578i	0.881982	+	1.13324i
$39$	−4.66877	+	4.14761i	−0.747601	+	0.664148i
$40$	−9.19929	−	6.76276i	−1.45454	−	1.06929i
$41$		−	2.56433i		−	0.400481i	−0.979747	−	0.200240i	$-0.935828\pi$
$41$		−	2.56433i		−	0.400481i	0.979747	−	0.200240i	$-0.0641723\pi$
$42$	−0.852873	−	10.1121i	−0.131601	−	1.56033i
$43$			4.59652i			0.700963i	0.936570	+	0.350481i	$0.113982\pi$
$43$			4.59652i			0.700963i	−0.936570	+	0.350481i	$0.886018\pi$
$44$	1.30724	+	1.27186i	0.197074	+	0.191740i
$45$	4.89787	+	11.0756i	0.730131	+	1.65105i
$46$	5.82655	−	0.807773i	0.859078	−	0.119100i
$47$	−9.45848	−	5.46085i	−1.37966	−	0.796547i	−0.387542	−	0.921852i	$-0.626676\pi$
$47$	−9.45848	−	5.46085i	−1.37966	−	0.796547i	−0.992118	+	0.125304i	$0.960009\pi$
$48$	−6.08863	+	3.30585i	−0.878817	+	0.477158i
$49$	−10.1636			−1.45194
$50$	6.01158	−	14.7995i	0.850166	−	2.09297i
$51$	3.93545	+	7.74780i	0.551074	+	1.08491i
$52$	3.55366	−	6.27467i	0.492805	−	0.870140i
$53$		−	8.85112i		−	1.21579i	−0.794016	−	0.607897i	$-0.792013\pi$
$53$		−	8.85112i		−	1.21579i	0.794016	−	0.607897i	$-0.207987\pi$
$54$	7.34651	+	0.169646i	0.999733	+	0.0230859i
$55$	−1.84062	+	3.18804i	−0.248189	+	0.429876i
$56$	4.70603	+	10.7313i	0.628869	+	1.43404i
$57$	4.90988	+	9.66616i	0.650329	+	1.28031i
$58$	−4.57447	+	3.56023i	−0.600657	+	0.467481i
$59$	−5.07140	+	8.78392i	−0.660240	+	1.14357i	0.320313	+	0.947312i	$0.396212\pi$
$59$	−5.07140	+	8.78392i	−0.660240	+	1.14357i	−0.980553	+	0.196257i	$0.937121\pi$
$60$	−9.48567	−	10.2745i	−1.22459	−	1.32643i
$61$		−	5.90863i		−	0.756523i	−0.925699	−	0.378262i	$-0.876522\pi$
$61$		−	5.90863i		−	0.756523i	0.925699	−	0.378262i	$-0.123478\pi$
$62$	−4.51826	+	3.51648i	−0.573820	+	0.446593i
$63$	1.33019	−	12.3573i	0.167588	−	1.55687i
$64$	5.41934	−	5.88479i	0.677417	−	0.735599i
$65$	14.0381	+	3.84329i	1.74121	+	0.476701i
$66$	1.27552	+	1.83379i	0.157005	+	0.225724i
$67$	0.155182			0.0189586			0.00947928	−	0.999955i	$-0.496983\pi$
$67$	0.155182			0.0189586			0.00947928	+	0.999955i	$0.496983\pi$
$68$	−7.19202	−	6.99736i	−0.872160	−	0.848555i
$69$	7.19394	+	0.386076i	0.866049	+	0.0464781i
$70$	−18.6644	+	14.5262i	−2.23082	+	1.73621i
$71$	7.19828	−	4.15593i	0.854279	−	0.493218i	−0.00781323	−	0.999969i	$-0.502487\pi$
$71$	7.19828	−	4.15593i	0.854279	−	0.493218i	0.862092	+	0.506751i	$0.169154\pi$
$72$	−8.09099	+	2.55652i	−0.953533	+	0.301289i
$73$		−	8.57607i		−	1.00375i	−0.864939	−	0.501876i	$-0.832643\pi$
$73$		−	8.57607i		−	1.00375i	0.864939	−	0.501876i	$-0.167357\pi$
$74$	2.01103	−	4.95083i	0.233778	−	0.575523i
$75$	10.6759	−	16.3943i	1.23274	−	1.89305i
$76$	−8.97277	−	8.72992i	−1.02925	−	1.00139i
$77$	3.27188	−	1.88902i	0.372866	−	0.215274i
$78$	5.73460	−	6.71672i	0.649315	−	0.760519i
$79$	2.34194	−	4.05635i	0.263488	−	0.456375i	−0.703678	−	0.710519i	$-0.748460\pi$
$79$	2.34194	−	4.05635i	0.263488	−	0.456375i	0.967167	+	0.254144i	$0.0817936\pi$
$80$	14.1999	+	7.68684i	1.58759	+	0.859415i
$81$	8.79382	+	1.91539i	0.977091	+	0.212822i
$82$	0.498003	+	3.59215i	0.0549953	+	0.396687i
$83$	8.39361	−	14.5382i	0.921318	−	1.59577i	0.123940	−	0.992290i	$-0.460447\pi$
$83$	8.39361	−	14.5382i	0.921318	−	1.59577i	0.797378	−	0.603480i	$-0.206220\pi$
$84$	3.15852	+	13.9995i	0.344623	+	1.52747i
$85$	10.1265	−	17.5396i	1.09837	−	1.90244i
$86$	−0.892664	−	6.43888i	−0.0962584	−	0.694322i
$87$	−6.32966	+	3.21512i	−0.678610	+	0.344697i
$88$	−2.07820	−	1.52777i	−0.221537	−	0.162860i
$89$	0.377440	+	0.217915i	0.0400085	+	0.0230989i	0.519871	−	0.854245i	$-0.325980\pi$
$89$	0.377440	+	0.217915i	0.0400085	+	0.0230989i	−0.479862	+	0.877344i	$0.659313\pi$
$90$	−9.01193	−	14.5636i	−0.949941	−	1.53514i
$91$	−10.5049	−	10.6195i	−1.10121	−	1.11323i
$92$	−8.00505	+	2.26308i	−0.834585	+	0.235943i
$93$	−6.25188	+	3.17561i	−0.648289	+	0.329295i
$94$	14.3101	+	5.81277i	1.47597	+	0.599542i
$95$	12.6338	−	21.8825i	1.29620	−	2.24509i
$96$	7.88703	−	5.81332i	0.804967	−	0.593320i
$97$		−	5.90985i		−	0.600055i	−0.953931	−	0.300027i	$-0.903004\pi$
$97$		−	5.90985i		−	0.600055i	0.953931	−	0.300027i	$-0.0969958\pi$
$98$	14.2373	−	1.97381i	1.43818	−	0.199385i
$99$	1.10647	+	2.50207i	0.111205	+	0.251467i
$100$	−5.54698	+	21.8989i	−0.554698	+	2.18989i
$101$	−4.04985	+	2.33818i	−0.402975	+	0.232658i	−0.687767	−	0.725932i	$-0.741409\pi$
$101$	−4.04985	+	2.33818i	−0.402975	+	0.232658i	0.284792	+	0.958589i	$0.408076\pi$
$102$	−7.01750	−	10.0890i	−0.694836	−	0.998955i
$103$	6.76961	+	11.7253i	0.667030	+	1.15533i	0.978731	+	0.205149i	$0.0657680\pi$
$103$	6.76961	+	11.7253i	0.667030	+	1.15533i	−0.311701	+	0.950180i	$0.600899\pi$
$104$	−3.75946	+	9.47979i	−0.368646	+	0.929570i
$105$	−25.8258	+	13.1181i	−2.52034	+	1.28019i
$106$	1.71892	+	12.3988i	0.166957	+	1.20428i
$107$	8.03245	+	4.63754i	0.776526	+	0.448328i	0.835198	−	0.549950i	$-0.185353\pi$
$107$	8.03245	+	4.63754i	0.776526	+	0.448328i	−0.0586714	+	0.998277i	$0.518686\pi$
$108$	−10.3241	+	1.18908i	−0.993433	+	0.114419i
$109$	−8.27353			−0.792461			−0.396230	−	0.918151i	$-0.629682\pi$
$109$	−8.27353			−0.792461			−0.396230	+	0.918151i	$0.629682\pi$
$110$	1.95924	−	4.82332i	0.186806	−	0.459885i
$111$	3.57136	−	5.48433i	0.338979	−	0.520550i
$112$	−8.67635	−	14.1187i	−0.819838	−	1.33409i
$113$	2.36962	−	4.10431i	0.222915	−	0.386101i	−0.732777	−	0.680469i	$-0.761776\pi$
$113$	2.36962	−	4.10431i	0.222915	−	0.386101i	0.955692	+	0.294369i	$0.0951093\pi$
$114$	−8.75504	−	12.5870i	−0.819984	−	1.17888i
$115$	−8.39520	−	14.5409i	−0.782857	−	1.35595i
$116$	5.71658	−	5.87560i	0.530771	−	0.545536i
$117$	8.45990	−	6.74018i	0.782118	−	0.623130i
$118$	5.39822	−	13.2895i	0.496946	−	1.22340i
$119$	−18.0009	+	10.3928i	−1.65014	+	0.952707i
$120$	15.2830	+	12.5505i	1.39514	+	1.14570i
$121$	5.08419	−	8.80607i	0.462199	−	0.800552i
$122$	1.14748	+	8.27691i	0.103888	+	0.749356i
$123$	−0.238022	+	4.43517i	−0.0214617	+	0.399905i
$124$	5.64633	−	5.80341i	0.507056	−	0.521161i
$125$	−25.4122			−2.27294
$126$	0.536492	+	17.5686i	0.0477945	+	1.56514i
$127$	3.13507	−	5.43010i	0.278193	−	0.481844i	−0.692743	−	0.721184i	$-0.743598\pi$
$127$	3.13507	−	5.43010i	0.278193	−	0.481844i	0.970936	+	0.239341i	$0.0769313\pi$
$128$	−6.44864	+	9.29597i	−0.569985	+	0.821655i
$129$	0.426650	−	7.94997i	0.0375644	−	0.699956i
$130$	−20.4111	−	2.65748i	−1.79017	−	0.233077i
$131$	5.07885	−	2.93227i	0.443741	−	0.256194i	−0.261442	−	0.965219i	$-0.584198\pi$
$131$	5.07885	−	2.93227i	0.443741	−	0.256194i	0.705183	+	0.709025i	$0.250865\pi$
$132$	−2.14290	−	2.32109i	−0.186515	−	0.202025i
$133$	−22.4579	+	12.9661i	−1.94735	+	1.12430i
$134$	−0.217382	+	0.0301371i	−0.0187789	+	0.00260345i
$135$	−7.44313	−	19.6105i	−0.640603	−	1.68780i
$136$	11.4336	+	8.40530i	0.980424	+	0.720748i
$137$		−	13.9255i		−	1.18974i	−0.803823	−	0.594869i	$-0.797204\pi$
$137$		−	13.9255i		−	1.18974i	0.803823	−	0.594869i	$-0.202796\pi$
$138$	−10.1524	+	0.856271i	−0.864226	+	0.0728907i
$139$	14.4958	+	8.36918i	1.22952	+	0.709865i	0.966930	−	0.255042i	$-0.0820893\pi$
$139$	14.4958	+	8.36918i	1.22952	+	0.709865i	0.262592	+	0.964907i	$0.415423\pi$
$140$	23.3243	−	23.9732i	1.97127	−	2.02610i
$141$	15.8521	+	10.3228i	1.33499	+	0.869339i
$142$	−9.27637	+	7.21963i	−0.778456	+	0.605858i
$143$	3.17132	+	0.868232i	0.265199	+	0.0726052i
$144$	10.8375	−	5.15252i	0.903125	−	0.429377i
$145$	14.3292	+	8.27297i	1.18998	+	0.687033i
$146$	1.66551	+	12.0135i	0.137838	+	0.994243i
$147$	17.5785	+	0.943384i	1.44985	+	0.0778090i
$148$	−1.85561	+	7.32576i	−0.152530	+	0.602174i
$149$	−7.62543	+	13.2076i	−0.624699	+	1.08201i	0.363900	+	0.931438i	$0.381445\pi$
$149$	−7.62543	+	13.2076i	−0.624699	+	1.08201i	−0.988599	+	0.150573i	$0.951888\pi$
$150$	−11.7711	+	25.0387i	−0.961106	+	2.04440i
$151$	−1.29778	−	0.749276i	−0.105612	−	0.0609753i	0.446264	−	0.894902i	$-0.352754\pi$
$151$	−1.29778	−	0.749276i	−0.105612	−	0.0609753i	−0.551876	+	0.833926i	$0.686088\pi$
$152$	14.2646	+	10.4865i	1.15701	+	0.850564i
$153$	−6.08746	−	13.7656i	−0.492142	−	1.11288i
$154$	−4.21645	+	3.28158i	−0.339771	+	0.264438i
$155$	14.1531	+	8.17132i	1.13681	+	0.656336i
$156$	−6.72870	+	10.5226i	−0.538727	+	0.842480i
$157$	−1.87817	+	1.08436i	−0.149895	+	0.0865417i	−0.573071	−	0.819505i	$-0.694248\pi$
$157$	−1.87817	+	1.08436i	−0.149895	+	0.0865417i	0.423177	+	0.906047i	$0.360915\pi$
$158$	−2.49286	+	6.13702i	−0.198321	+	0.488235i
$159$	−0.821563	+	15.3086i	−0.0651542	+	1.21405i
$160$	−21.3842	−	8.01018i	−1.69057	−	0.633260i
$161$			17.2320i			1.35807i
$162$	−12.6905	−	0.975319i	−0.997060	−	0.0766283i
$163$	6.90476	+	11.9594i	0.540822	+	0.936732i	0.998857	+	0.0477975i	$0.0152202\pi$
$163$	6.90476	+	11.9594i	0.540822	+	0.936732i	−0.458035	+	0.888934i	$0.651446\pi$
$164$	−1.39522	−	4.93523i	−0.108949	−	0.385377i
$165$	3.47938	−	5.34307i	0.270869	−	0.415958i
$166$	−8.93453	+	21.9953i	−0.693454	+	1.70717i
$167$			7.66997i			0.593520i	0.954952	+	0.296760i	$0.0959062\pi$
$167$			7.66997i			0.593520i	−0.954952	+	0.296760i	$0.904094\pi$
$168$	−7.14328	−	18.9973i	−0.551116	−	1.46568i
$169$	0.141140	−	12.9992i	0.0108569	−	0.999941i
$170$	−10.7791	+	26.5364i	−0.826719	+	2.03525i
$171$	−7.59472	−	17.1740i	−0.580783	−	1.31332i
$172$	2.50091	+	8.84632i	0.190693	+	0.674526i
$173$			18.9390i			1.43991i	0.694022	+	0.719954i	$0.255837\pi$
$173$			18.9390i			1.43991i	−0.694022	+	0.719954i	$0.744163\pi$
$174$	8.24229	−	5.73303i	0.624847	−	0.434620i
$175$	40.5256	+	23.3975i	3.06345	+	1.76868i
$176$	3.20787	+	1.73652i	0.241803	+	0.130895i
$177$	9.58662	−	14.7216i	0.720575	−	1.10654i
$178$	−0.571043	−	0.231958i	−0.0428015	−	0.0173860i
$179$	−2.29155	−	1.32303i	−0.171279	−	0.0988877i	0.411910	−	0.911225i	$-0.364862\pi$
$179$	−2.29155	−	1.32303i	−0.171279	−	0.0988877i	−0.583189	+	0.812337i	$0.698195\pi$
$180$	15.4524	+	18.6508i	1.15175	+	1.39015i
$181$			0.767516i			0.0570490i	0.999593	+	0.0285245i	$0.00908086\pi$
$181$			0.767516i			0.0570490i	−0.999593	+	0.0285245i	$0.990919\pi$
$182$	16.7777	+	12.8359i	1.24365	+	0.951461i
$183$	−0.548441	+	10.2193i	−0.0405419	+	0.755436i
$184$	10.7741	−	4.72478i	0.794278	−	0.348315i
$185$	−15.2530			−1.12143
$186$	8.14101	−	5.66258i	0.596928	−	0.415201i
$187$	2.28767	−	3.96235i	0.167291	−	0.289756i
$188$	−21.1747	−	5.36354i	−1.54432	−	0.391177i
$189$	−3.44765	+	21.2492i	−0.250779	+	1.54565i
$190$	−13.4480	+	33.1068i	−0.975622	+	2.40182i
$191$	4.42502			0.320183			0.160092	−	0.987102i	$-0.448821\pi$
$191$	4.42502			0.320183			0.160092	+	0.987102i	$0.448821\pi$
$192$	−9.91931	+	9.67509i	−0.715864	+	0.698239i
$193$			1.02200i			0.0735655i	0.999323	+	0.0367828i	$0.0117110\pi$
$193$			1.02200i			0.0735655i	−0.999323	+	0.0367828i	$0.988289\pi$
$194$	1.14772	+	8.27862i	0.0824014	+	0.594370i
$195$	−23.9230	−	7.95022i	−1.71316	−	0.569327i
$196$	−19.5605	+	5.52988i	−1.39718	+	0.394991i
$197$	−5.86523	+	10.1589i	−0.417880	+	0.723790i	−0.995726	−	0.0923562i	$-0.970560\pi$
$197$	−5.86523	+	10.1589i	−0.417880	+	0.723790i	0.577846	+	0.816146i	$0.303894\pi$
$198$	−2.03587	−	3.29005i	−0.144683	−	0.233814i
$199$	6.57531	+	11.3888i	0.466111	+	0.807329i	0.999251	−	0.0386986i	$-0.0123212\pi$
$199$	6.57531	+	11.3888i	0.466111	+	0.807329i	−0.533139	+	0.846027i	$0.678988\pi$
$200$	3.51745	−	31.7535i	0.248721	−	2.24532i
$201$	−0.268398	−	0.0144041i	−0.0189313	−	0.00101598i
$202$	5.21901	−	4.06186i	0.367208	−	0.285792i
$203$	−8.49053	−	14.7060i	−0.595918	−	1.03216i
$204$	11.7895	+	12.7699i	0.825433	+	0.894074i
$205$	8.96468	−	5.17576i	0.626121	−	0.361491i
$206$	−11.7601	−	15.1103i	−0.819364	−	1.05279i
$207$	−12.4065	−	1.33549i	−0.862313	−	0.0928227i
$208$	3.42530	−	14.0095i	0.237502	−	0.971387i
$209$	2.85409	−	4.94343i	0.197422	−	0.341945i
$210$	33.6295	−	23.3915i	2.32066	−	1.61416i
$211$		−	5.68202i		−	0.391166i	−0.980687	−	0.195583i	$-0.937340\pi$
$211$		−	5.68202i		−	0.391166i	0.980687	−	0.195583i	$-0.0626600\pi$
$212$	−4.81579	−	17.0346i	−0.330750	−	1.16994i
$213$	−12.8356	+	6.51979i	−0.879483	+	0.446729i
$214$	−12.1526	−	4.93640i	−0.830736	−	0.337445i
$215$	−16.0691	+	9.27747i	−1.09590	+	0.632718i
$216$	14.2312	−	3.67066i	0.968309	−	0.249757i
$217$	−8.38620	−	14.5253i	−0.569292	−	0.986043i
$218$	11.5897	−	1.60675i	0.784953	−	0.108823i
$219$	−0.796032	+	14.8328i	−0.0537909	+	1.00231i
$220$	−1.80782	+	7.13707i	−0.121883	+	0.481181i
$221$	−17.4476	−	4.77674i	−1.17365	−	0.321318i
$222$	−3.93774	+	8.37611i	−0.264284	+	0.562168i
$223$	3.37721	−	1.94983i	0.226154	−	0.130570i	−0.382642	−	0.923897i	$-0.624986\pi$
$223$	3.37721	−	1.94983i	0.226154	−	0.130570i	0.608797	+	0.793326i	$0.291652\pi$
$224$	14.8959	+	18.0927i	0.995273	+	1.20887i
$225$	−19.9863	+	27.3640i	−1.33242	+	1.82427i
$226$	−2.52233	+	6.20957i	−0.167783	+	0.413054i
$227$	−7.35644			−0.488264			−0.244132	−	0.969742i	$-0.578503\pi$
$227$	−7.35644			−0.488264			−0.244132	+	0.969742i	$0.578503\pi$
$228$	14.7086	+	15.9318i	0.974104	+	1.05511i
$229$	2.12979	+	3.68890i	0.140740	+	0.243769i	0.927776	−	0.373139i	$-0.121718\pi$
$229$	2.12979	+	3.68890i	0.140740	+	0.243769i	−0.787035	+	0.616908i	$0.788385\pi$
$230$	14.5840	+	18.7388i	0.961643	+	1.23560i
$231$	−5.83426	+	2.96348i	−0.383866	+	0.194983i
$232$	−6.86681	+	9.34082i	−0.450828	+	0.613255i
$233$	11.6780			0.765053			0.382526	−	0.923945i	$-0.375054\pi$
$233$	11.6780			0.765053			0.382526	+	0.923945i	$0.375054\pi$
$234$	−10.5418	+	11.0847i	−0.689138	+	0.724630i
$235$		−	44.0881i		−	2.87599i
$236$	−4.98103	+	19.6646i	−0.324237	+	1.28005i
$237$	−4.42704	+	6.79834i	−0.287567	+	0.441599i
$238$	23.1976	−	18.0543i	1.50368	−	1.17028i
$239$	−9.95999	+	5.75040i	−0.644258	+	0.371962i	−0.786253	−	0.617905i	$-0.787982\pi$
$239$	−9.95999	+	5.75040i	−0.644258	+	0.371962i	0.141995	+	0.989867i	$0.454648\pi$
$240$	−23.8461	−	14.6129i	−1.53926	−	0.943259i
$241$			18.5420i			1.19439i	0.802095	+	0.597197i	$0.203719\pi$
$241$			18.5420i			1.19439i	−0.802095	+	0.597197i	$0.796281\pi$
$242$	−5.41184	+	13.3231i	−0.347886	+	0.856438i
$243$	−15.0317	−	4.12904i	−0.964282	−	0.264878i
$244$	−3.21482	−	11.3716i	−0.205808	−	0.727991i
$245$	−20.5138	−	35.5310i	−1.31058	−	2.26999i
$246$	−0.527903	−	6.25908i	−0.0336579	−	0.399064i
$247$	−21.7677	−	5.95946i	−1.38504	−	0.379192i
$248$	−6.78243	+	9.22604i	−0.430685	+	0.585854i
$249$	−15.8667	+	24.3655i	−1.00551	+	1.54410i
$250$	35.5979	−	4.93516i	2.25141	−	0.312127i
$251$	−3.69395	+	2.13270i	−0.233160	+	0.134615i	−0.612029	−	0.790835i	$-0.709646\pi$
$251$	−3.69395	+	2.13270i	−0.233160	+	0.134615i	0.378869	+	0.925450i	$0.376313\pi$
$252$	−4.16343	−	24.5062i	−0.262271	−	1.54375i
$253$	−1.89655	−	3.28492i	−0.119235	−	0.206521i
$254$	−3.33711	+	8.21542i	−0.209389	+	0.515481i
$255$	−19.1425	+	29.3959i	−1.19875	+	1.84084i
$256$	7.22805	−	14.2743i	0.451753	−	0.892143i
$257$	17.4166			1.08642			0.543209	−	0.839598i	$-0.317209\pi$
$257$	17.4166			1.08642			0.543209	+	0.839598i	$0.317209\pi$
$258$	0.946259	+	11.2193i	0.0589115	+	0.698483i
$259$	13.5569	+	7.82708i	0.842385	+	0.486351i
$260$	29.1083	−	0.241280i	1.80522	−	0.0149636i
$261$	11.2460	−	4.97322i	0.696107	−	0.307835i
$262$	−6.54507	+	5.09391i	−0.404356	+	0.314703i
$263$	3.34422	+	5.79235i	0.206213	+	0.357172i	0.950519	−	0.310668i	$-0.100553\pi$
$263$	3.34422	+	5.79235i	0.206213	+	0.357172i	−0.744305	+	0.667839i	$0.767219\pi$
$264$	3.45257	+	2.83527i	0.212491	+	0.174499i
$265$	30.9428	−	17.8648i	1.90080	−	1.09743i
$266$	28.9413	−	22.5245i	1.77451	−	1.38107i
$267$	−0.632578	−	0.411931i	−0.0387132	−	0.0252098i
$268$	0.298659	−	0.0844330i	0.0182435	−	0.00515757i
$269$	15.7227	−	9.07751i	0.958630	−	0.553465i	0.0628791	−	0.998021i	$-0.479972\pi$
$269$	15.7227	−	9.07751i	0.958630	−	0.553465i	0.895751	+	0.444556i	$0.146638\pi$
$270$	14.2349	+	26.0252i	0.866308	+	1.58384i
$271$	−13.6971	−	7.90803i	−0.832040	−	0.480379i	0.0225105	−	0.999747i	$-0.492834\pi$
$271$	−13.6971	−	7.90803i	−0.832040	−	0.480379i	−0.854551	+	0.519368i	$0.826167\pi$
$272$	−17.6487	−	9.55382i	−1.07011	−	0.579285i
$273$	17.1831	+	19.3422i	1.03997	+	1.17064i
$274$	2.70440	+	19.5071i	0.163378	+	1.17847i
$275$	−10.3005			−0.621144
$276$	14.0553	−	3.17111i	0.846029	−	0.190878i
$277$		−	2.77892i		−	0.166969i	−0.996509	−	0.0834845i	$-0.973395\pi$
$277$		−	2.77892i		−	0.166969i	0.996509	−	0.0834845i	$-0.0266049\pi$
$278$	−21.9313	−	8.90853i	−1.31535	−	0.534298i
$279$	11.1078	−	4.91211i	0.665005	−	0.294080i
$280$	−28.0174	+	38.1117i	−1.67436	+	2.27761i
$281$	1.55456	+	0.897528i	0.0927375	+	0.0535420i	0.545652	−	0.838012i	$-0.316282\pi$
$281$	1.55456	+	0.897528i	0.0927375	+	0.0535420i	−0.452914	+	0.891554i	$0.649616\pi$
$282$	−24.2107	−	11.3818i	−1.44172	−	0.677778i
$283$		−	1.91188i		−	0.113650i	−0.998384	−	0.0568248i	$-0.981902\pi$
$283$		−	1.91188i		−	0.113650i	0.998384	−	0.0568248i	$-0.0180976\pi$
$284$	11.5924	−	11.9149i	0.687883	−	0.707018i
$285$	−23.8821	+	36.6744i	−1.41466	+	2.17240i
$286$	−4.61105	−	0.600349i	−0.272657	−	0.0354994i
$287$	−10.6237			−0.627100
$288$	−14.1807	+	9.32242i	−0.835606	+	0.549329i
$289$	−4.08602	+	7.07720i	−0.240354	+	0.416306i
$290$	−21.6792	−	8.80612i	−1.27305	−	0.517113i
$291$	−0.548554	+	10.2215i	−0.0321568	+	0.599192i
$292$	−4.66614	−	16.5052i	−0.273065	−	0.965896i
$293$	15.7918	−	27.3523i	0.922569	−	1.59794i	0.127145	−	0.991884i	$-0.459419\pi$
$293$	15.7918	−	27.3523i	0.922569	−	1.59794i	0.795424	−	0.606053i	$-0.207248\pi$
$294$	−24.8075	+	2.09231i	−1.44680	+	0.122026i
$295$	−40.9438			−2.38384
$296$	1.17668	−	10.6224i	0.0683931	−	0.617415i
$297$	−1.68147	−	4.43018i	−0.0975687	−	0.257065i
$298$	8.11684	−	19.9823i	0.470196	−	1.15755i
$299$	−10.6618	+	10.5467i	−0.616590	+	0.609932i
$300$	11.6265	−	37.3606i	0.671257	−	2.15702i
$301$	19.0429			1.09761
$302$	1.96347	+	0.797563i	0.112985	+	0.0458946i
$303$	7.22150	−	3.66812i	0.414864	−	0.210728i
$304$	−22.0186	−	11.9193i	−1.26285	−	0.683622i
$305$	20.6561	−	11.9258i	1.18276	−	0.682869i
$306$	11.2007	+	18.1008i	0.640304	+	1.03476i
$307$	15.8693			0.905709			0.452854	−	0.891584i	$-0.350406\pi$
$307$	15.8693			0.905709			0.452854	+	0.891584i	$0.350406\pi$
$308$	5.26917	−	5.41575i	0.300239	−	0.308591i
$309$	−10.6201	−	20.9080i	−0.604157	−	1.18942i
$310$	−21.4128	−	8.69791i	−1.21617	−	0.494008i
$311$	−7.89542	−	13.6753i	−0.447708	−	0.775453i	0.550528	−	0.834816i	$-0.314426\pi$
$311$	−7.89542	−	13.6753i	−0.447708	−	0.775453i	−0.998236	+	0.0593633i	$0.981093\pi$
$312$	7.38214	−	16.0469i	0.417931	−	0.908479i
$313$	15.9524	−	27.6305i	0.901686	−	1.56177i	0.0763805	−	0.997079i	$-0.475664\pi$
$313$	15.9524	−	27.6305i	0.901686	−	1.56177i	0.825305	−	0.564687i	$-0.191003\pi$
$314$	2.42039	−	1.88374i	0.136590	−	0.106306i
$315$	45.8849	−	20.2913i	2.58532	−	1.14329i
$316$	2.30020	−	9.08096i	0.129397	−	0.510844i
$317$	−13.6493	+	23.6413i	−0.766623	+	1.32783i	0.172761	+	0.984964i	$0.444731\pi$
$317$	−13.6493	+	23.6413i	−0.766623	+	1.32783i	−0.939384	+	0.342867i	$0.888602\pi$
$318$	−1.82213	−	21.6040i	−0.102180	−	1.21149i
$319$	3.23709	+	1.86894i	0.181242	+	0.104640i
$320$	31.5110	+	7.06788i	1.76152	+	0.395106i
$321$	−13.4622	−	8.76648i	−0.751385	−	0.489297i
$322$	−3.34652	−	24.1388i	−0.186494	−	1.34520i
$323$	−15.7023	+	27.1972i	−0.873701	+	1.51329i
$324$	17.9665	−	1.09831i	0.998137	−	0.0610170i
$325$	10.3269	+	39.3945i	0.572831	+	2.18522i
$326$	−11.9949	−	15.4120i	−0.664334	−	0.853590i
$327$	14.3096	+	0.767951i	0.791322	+	0.0424678i
$328$	2.91289	+	6.64239i	0.160838	+	0.366765i
$329$	−22.6237	+	39.1855i	−1.24729	+	2.16036i
$330$	−3.83632	+	8.16037i	−0.211182	+	0.449214i
$331$	17.4054			0.956689			0.478345	−	0.878172i	$-0.341237\pi$
$331$	17.4054			0.956689			0.478345	+	0.878172i	$0.341237\pi$
$332$	8.24404	−	32.5466i	0.452450	−	1.78622i
$333$	−6.68595	+	9.15399i	−0.366388	+	0.501636i
$334$	−1.48954	−	10.7442i	−0.0815040	−	0.587897i
$335$	0.313215	+	0.542505i	0.0171128	+	0.0296402i
$336$	13.6958	+	25.2245i	0.747166	+	1.37611i
$337$	−4.19347	−	7.26330i	−0.228433	−	0.395657i	0.728911	−	0.684608i	$-0.240027\pi$
$337$	−4.19347	−	7.26330i	−0.228433	−	0.395657i	−0.957344	+	0.288951i	$0.906693\pi$
$338$	2.32679	+	18.2369i	0.126561	+	0.991959i
$339$	−4.47937	+	6.87870i	−0.243286	+	0.373600i
$340$	9.94606	−	39.2659i	0.539401	−	2.12949i
$341$	3.19731	+	1.84597i	0.173144	+	0.0999649i
$342$	13.9741	+	22.5826i	0.755630	+	1.22113i
$343$			13.1063i			0.707674i
$344$	−5.22131	−	11.9064i	−0.281514	−	0.641949i
$345$	13.1703	+	25.9287i	0.709067	+	1.39595i
$346$	−3.67804	−	26.5301i	−0.197733	−	1.42627i
$347$	−24.7296	−	14.2777i	−1.32756	−	0.766465i	−0.342635	−	0.939469i	$-0.611319\pi$
$347$	−24.7296	−	14.2777i	−1.32756	−	0.766465i	−0.984921	+	0.173004i	$0.944653\pi$
$348$	−10.4326	+	9.63161i	−0.559244	+	0.516308i
$349$	−11.2939	−	19.5616i	−0.604548	−	1.04711i	−0.992123	−	0.125269i	$-0.960021\pi$
$349$	−11.2939	−	19.5616i	−0.604548	−	1.04711i	0.387575	−	0.921838i	$-0.373313\pi$
$350$	−61.3129	−	24.9053i	−3.27731	−	1.33125i
$351$	−15.2575	+	10.8723i	−0.814388	+	0.580321i
$352$	−4.83088	−	1.80957i	−0.257487	−	0.0964503i
$353$	13.7308	−	7.92749i	0.730817	−	0.421938i	−0.0879038	−	0.996129i	$-0.528017\pi$
$353$	13.7308	−	7.92749i	0.730817	−	0.421938i	0.818721	+	0.574191i	$0.194683\pi$
$354$	−10.5701	+	22.4840i	−0.561794	+	1.19501i
$355$	29.0576	+	16.7764i	1.54222	+	0.890399i
$356$	0.844974	+	0.214032i	0.0447835	+	0.0113437i
$357$	32.0983	−	16.3042i	1.69882	−	0.862908i
$358$	3.46698	+	1.40829i	0.183235	+	0.0744304i
$359$			0.181488i			0.00957855i	0.999989	+	0.00478927i	$0.00152448\pi$
$359$			0.181488i			0.00957855i	−0.999989	+	0.00478927i	$0.998476\pi$
$360$	−25.2680	−	23.1254i	−1.33174	−	1.21882i
$361$	−10.0902	+	17.4768i	−0.531065	+	0.919832i
$362$	−0.149055	−	1.07515i	−0.00783414	−	0.0565085i
$363$	−9.61080	+	14.7587i	−0.504436	+	0.774633i
$364$	−25.9953	−	14.7225i	−1.36252	−	0.771666i
$365$	29.9812	−	17.3097i	1.56929	−	0.906029i
$366$	−1.21638	−	14.4219i	−0.0635810	−	0.753847i
$367$	9.84957	+	17.0600i	0.514143	+	0.890522i	0.999865	+	0.0164091i	$0.00522340\pi$
$367$	9.84957	+	17.0600i	0.514143	+	0.890522i	−0.485722	+	0.874113i	$0.661443\pi$
$368$	−14.1750	+	8.71092i	−0.738921	+	0.454088i
$369$	0.823346	−	7.64880i	0.0428617	−	0.398181i
$370$	21.3667	−	2.96221i	1.11080	−	0.153998i
$371$	−36.6692			−1.90377
$372$	−10.3044	+	9.51326i	−0.534256	+	0.493239i
$373$	0.700306	+	0.404322i	0.0362605	+	0.0209350i	0.518021	−	0.855368i	$-0.326669\pi$
$373$	0.700306	+	0.404322i	0.0362605	+	0.0209350i	−0.481760	+	0.876303i	$0.660002\pi$
$374$	−2.43509	+	5.99480i	−0.125916	+	0.309984i
$375$	43.9521	+	2.35877i	2.26967	+	0.121806i
$376$	30.7035	+	3.40112i	1.58341	+	0.175400i
$377$	3.90241	−	14.2540i	0.200985	−	0.734120i
$378$	0.702827	−	30.4358i	0.0361495	−	1.56545i
$379$	−17.0816	+	29.5862i	−0.877422	+	1.51974i	−0.0232627	+	0.999729i	$0.507405\pi$
$379$	−17.0816	+	29.5862i	−0.877422	+	1.51974i	−0.854160	+	0.520011i	$0.825928\pi$
$380$	12.4087	−	48.9882i	0.636553	−	2.51304i
$381$	−5.92632	+	9.10070i	−0.303615	+	0.466243i
$382$	−6.19864	+	0.859358i	−0.317150	+	0.0439686i
$383$	−22.9277	−	13.2373i	−1.17155	−	0.676395i	−0.217505	−	0.976059i	$-0.569792\pi$
$383$	−22.9277	−	13.2373i	−1.17155	−	0.676395i	−0.954045	+	0.299664i	$0.903125\pi$
$384$	12.0162	−	15.4794i	0.613198	−	0.789929i
$385$	13.2077	+	7.62548i	0.673128	+	0.388631i
$386$	−0.198478	−	1.43164i	−0.0101022	−	0.0728686i
$387$	−1.47584	+	13.7104i	−0.0750209	+	0.696937i
$388$	−3.21548	−	11.3739i	−0.163241	−	0.577423i
$389$	−11.9250	−	6.88492i	−0.604623	−	0.349079i	0.166235	−	0.986086i	$-0.446839\pi$
$389$	−11.9250	−	6.88492i	−0.604623	−	0.349079i	−0.770858	+	0.637007i	$0.780172\pi$
$390$	35.0556	+	6.49085i	1.77511	+	0.328677i
$391$	10.4342	+	18.0726i	0.527681	+	0.913971i
$392$	26.3267	−	11.5451i	1.32970	−	0.583114i
$393$	−9.05636	+	4.60013i	−0.456833	+	0.232046i
$394$	6.24321	−	15.3698i	0.314528	−	0.774317i
$395$	18.9076			0.951343
$396$	3.49083	+	4.21338i	0.175421	+	0.211730i
$397$	−2.08297	−	3.60780i	−0.104541	−	0.181070i	0.809010	−	0.587796i	$-0.200004\pi$
$397$	−2.08297	−	3.60780i	−0.104541	−	0.181070i	−0.913551	+	0.406725i	$0.866671\pi$
$398$	−11.4225	−	14.6766i	−0.572561	−	0.735673i
$399$	40.0459	−	20.3411i	2.00480	−	1.01833i
$400$	1.23938	+	45.1640i	0.0619689	+	2.25820i
$401$			37.2761i			1.86148i	0.365681	+	0.930740i	$0.380836\pi$
$401$			37.2761i			1.86148i	−0.365681	+	0.930740i	$0.619164\pi$
$402$	0.378773	−	0.0319465i	0.0188915	−	0.00159335i
$403$	3.85446	−	14.0789i	0.192004	−	0.701319i
$404$	−6.52204	+	6.70347i	−0.324484	+	0.333510i
$405$	11.0531	+	34.6084i	0.549233	+	1.71971i
$406$	14.7496	+	18.9515i	0.732012	+	0.940549i
$407$	−3.44580			−0.170802
$408$	−18.9949	−	15.5987i	−0.940390	−	0.772253i
$409$	5.32822	+	3.07625i	0.263463	+	0.152111i	0.625913	−	0.779893i	$-0.284726\pi$
$409$	5.32822	+	3.07625i	0.263463	+	0.152111i	−0.362450	+	0.932003i	$0.618060\pi$
$410$	−11.5527	+	8.99127i	−0.570548	+	0.444047i
$411$	−1.29257	+	24.0851i	−0.0637578	+	1.18803i
$412$	19.4082	+	18.8829i	0.956173	+	0.930294i
$413$	36.3908	+	21.0103i	1.79068	+	1.03385i
$414$	17.6386	−	0.538630i	0.866891	−	0.0264722i
$415$	67.7656			3.32648
$416$	−2.07750	+	20.2900i	−0.101858	+	0.994799i
$417$	−24.2946	−	15.8205i	−1.18971	−	0.774735i
$418$	−3.03802	+	7.47912i	−0.148595	+	0.365816i
$419$		−	15.9596i		−	0.779677i	−0.920883	−	0.389839i	$-0.872531\pi$
$419$		−	15.9596i		−	0.779677i	0.920883	−	0.389839i	$-0.127469\pi$
$420$	−42.5661	+	39.2981i	−2.07701	+	1.91755i
$421$	−10.7385	+	18.5997i	−0.523364	+	0.906494i	0.476266	+	0.879301i	$0.341990\pi$
$421$	−10.7385	+	18.5997i	−0.523364	+	0.906494i	−0.999630	+	0.0271922i	$0.991343\pi$
$422$	1.10347	+	7.95946i	0.0537162	+	0.387461i
$423$	−26.4591	−	19.3254i	−1.28649	−	0.939631i
$424$	10.0542	+	22.9271i	0.488276	+	1.11344i
$425$	56.6702			2.74891
$426$	16.7142	−	11.6258i	0.809805	−	0.563270i
$427$	−24.4788			−1.18461
$428$	17.9822	+	4.55490i	0.869204	+	0.220169i
$429$	−5.40441	−	1.79602i	−0.260927	−	0.0867128i
$430$	20.7081	−	16.1167i	0.998631	−	0.777217i
$431$	1.03925	+	0.600013i	0.0500590	+	0.0289016i	0.524821	−	0.851213i	$-0.324132\pi$
$431$	1.03925	+	0.600013i	0.0500590	+	0.0289016i	−0.474762	+	0.880114i	$0.657466\pi$
$432$	−19.2224	+	7.90567i	−0.924838	+	0.380362i
$433$	4.97766	+	8.62156i	0.239211	+	0.414326i	0.960488	−	0.278321i	$-0.0897779\pi$
$433$	4.97766	+	8.62156i	0.239211	+	0.414326i	−0.721277	+	0.692647i	$0.756445\pi$
$434$	14.5684	+	18.7187i	0.699306	+	0.898525i
$435$	−24.0154	−	15.6387i	−1.15145	−	0.749816i
$436$	−15.9230	+	4.50153i	−0.762573	+	0.215584i
$437$	13.0177	+	22.5474i	0.622723	+	1.07859i
$438$	−1.76550	−	20.9327i	−0.0843591	−	1.00020i
$439$	−5.75789	−	9.97295i	−0.274809	−	0.475983i	0.695278	−	0.718741i	$-0.255281\pi$
$439$	−5.75789	−	9.97295i	−0.274809	−	0.475983i	−0.970087	+	0.242758i	$0.921948\pi$
$440$	1.14637	−	10.3488i	0.0546512	−	0.493360i
$441$	−30.3156	−	3.26328i	−1.44360	−	0.155394i
$442$	25.3686	+	3.30293i	1.20666	+	0.157104i
$443$	−1.57113	−	0.907092i	−0.0746466	−	0.0430973i	0.462212	−	0.886769i	$-0.347056\pi$
$443$	−1.57113	−	0.907092i	−0.0746466	−	0.0430973i	−0.536859	+	0.843672i	$0.680389\pi$
$444$	3.88938	−	12.4981i	0.184582	−	0.593134i
$445$			1.75933i			0.0834003i
$446$	−4.35218	+	3.38722i	−0.206082	+	0.160390i
$447$	14.4146	−	22.1356i	0.681786	−	1.04698i
$448$	−24.3801	−	22.4517i	−1.15185	−	1.06074i
$449$	19.9097	−	11.4949i	0.939598	−	0.542477i	0.0497636	−	0.998761i	$-0.484153\pi$
$449$	19.9097	−	11.4949i	0.939598	−	0.542477i	0.889834	+	0.456284i	$0.150820\pi$
$450$	22.6829	−	42.2134i	1.06928	−	1.98996i
$451$	2.02520	−	1.16925i	0.0953629	−	0.0550578i
$452$	2.32740	−	9.18831i	0.109472	−	0.432182i
$453$	2.17505	+	1.41638i	0.102193	+	0.0665474i
$454$	10.3050	−	1.42865i	0.483639	−	0.0670500i
$455$	15.9223	−	58.1582i	0.746450	−	2.72650i
$456$	−23.6981	−	19.4610i	−1.10977	−	0.911345i
$457$	−9.56528	+	5.52252i	−0.447445	+	0.258332i	−0.706751	−	0.707463i	$-0.749840\pi$
$457$	−9.56528	+	5.52252i	−0.447445	+	0.258332i	0.259306	+	0.965795i	$0.416506\pi$
$458$	−3.69984	−	4.75385i	−0.172882	−	0.222133i
$459$	9.25091	+	24.3735i	0.431796	+	1.13766i
$460$	−24.0687	−	23.4173i	−1.12221	−	1.09184i
$461$	−27.0934			−1.26187			−0.630934	−	0.775837i	$-0.717328\pi$
$461$	−27.0934			−1.26187			−0.630934	+	0.775837i	$0.717328\pi$
$462$	7.59720	−	5.28433i	0.353454	−	0.245849i
$463$	−17.7270	+	10.2347i	−0.823843	+	0.475646i	−0.851740	−	0.523965i	$-0.824452\pi$
$463$	−17.7270	+	10.2347i	−0.823843	+	0.475646i	0.0278966	+	0.999611i	$0.491119\pi$
$464$	7.80511	−	14.4183i	0.362343	−	0.669354i
$465$	−23.7203	−	15.4465i	−1.10000	−	0.716314i
$466$	−16.3588	+	2.26792i	−0.757805	+	0.105059i
$467$		−	16.1104i		−	0.745501i	−0.927932	−	0.372751i	$-0.878415\pi$
$467$		−	16.1104i		−	0.745501i	0.927932	−	0.372751i	$-0.121585\pi$
$468$	12.6144	−	17.5749i	0.583101	−	0.812400i
$469$		−	0.642904i		−	0.0296866i
$470$	8.56209	+	61.7593i	0.394940	+	2.84874i
$471$	3.34907	−	1.70114i	0.154317	−	0.0783845i
$472$	3.15856	−	28.5137i	0.145385	−	1.31245i
$473$	−3.63014	+	2.09586i	−0.166914	+	0.0963678i
$474$	4.88120	−	10.3830i	0.224201	−	0.476905i
$475$	70.7018			3.24402
$476$	−28.9893	+	29.7958i	−1.32872	+	1.36569i
$477$	2.84189	−	26.4008i	0.130121	−	1.20881i
$478$	12.8354	−	9.98952i	0.587075	−	0.456910i
$479$	−6.57007	+	3.79323i	−0.300194	+	0.173317i	−0.642530	−	0.766261i	$-0.722115\pi$
$479$	−6.57007	+	3.79323i	−0.300194	+	0.173317i	0.342336	+	0.939578i	$0.388782\pi$
$480$	36.2418	+	15.8390i	1.65421	+	0.722948i
$481$	3.45461	+	13.1785i	0.157517	+	0.600889i
$482$	−3.60093	−	25.9739i	−0.164018	−	1.18308i
$483$	1.59947	−	29.8037i	0.0727786	−	1.35612i
$484$	4.99359	−	19.7141i	0.226981	−	0.896098i
$485$	20.6604	−	11.9283i	0.938138	−	0.541634i
$486$	21.8585	+	2.86481i	0.991521	+	0.129950i
$487$	−32.8937	+	18.9912i	−1.49056	+	0.860573i	−0.999942	−	0.0108046i	$-0.996561\pi$
$487$	−32.8937	+	18.9912i	−1.49056	+	0.860573i	−0.490614	+	0.871377i	$0.663227\pi$
$488$	6.71178	+	15.3052i	0.303828	+	0.692832i
$489$	−10.8321	−	21.3254i	−0.489846	−	0.964368i
$490$	35.6363	+	45.7885i	1.60989	+	2.06851i
$491$			16.0812i			0.725733i	0.931841	+	0.362866i	$0.118202\pi$
$491$			16.0812i			0.725733i	−0.931841	+	0.362866i	$0.881798\pi$
$492$	1.95503	+	8.66529i	0.0881397	+	0.390661i
$493$	−17.8095	−	10.2823i	−0.802098	−	0.463092i
$494$	31.6498	+	4.12074i	1.42399	+	0.185401i
$495$	−6.51374	+	8.91822i	−0.292771	+	0.400844i
$496$	7.70920	−	14.2412i	0.346153	−	0.639447i
$497$	−17.2176	−	29.8217i	−0.772314	−	1.33769i
$498$	17.4944	−	37.2130i	0.783944	−	1.66755i
$499$	−10.6077	−	18.3731i	−0.474867	−	0.822494i	0.524719	−	0.851276i	$-0.324171\pi$
$499$	−10.6077	−	18.3731i	−0.474867	−	0.822494i	−0.999586	+	0.0287818i	$0.990837\pi$
$500$	−48.9076	+	13.8265i	−2.18722	+	0.618340i
$501$	0.711928	−	13.2657i	0.0318066	−	0.592667i
$502$	4.76036	−	3.70491i	0.212465	−	0.165358i
$503$	8.61116	+	14.9150i	0.383953	+	0.665026i	0.991623	−	0.129164i	$-0.0412292\pi$
$503$	8.61116	+	14.9150i	0.383953	+	0.665026i	−0.607671	+	0.794189i	$0.707896\pi$
$504$	10.5914	+	33.5201i	0.471778	+	1.49311i
$505$	−16.3482	−	9.43863i	−0.727485	−	0.420014i
$506$	3.29466	+	4.23325i	0.146466	+	0.188191i
$507$	−1.45070	+	22.4699i	−0.0644279	+	0.997922i
$508$	3.07921	−	12.1564i	0.136618	−	0.539351i
$509$	8.55280			0.379096			0.189548	−	0.981871i	$-0.439298\pi$
$509$	8.55280			0.379096			0.189548	+	0.981871i	$0.439298\pi$
$510$	21.1062	−	44.8958i	0.934600	−	1.98802i
$511$	−35.5297			−1.57174
$512$	−7.35303	+	21.3994i	−0.324961	+	0.945727i
$513$	11.5414	+	30.4084i	0.509567	+	1.34256i
$514$	−24.3974	+	3.38237i	−1.07612	+	0.149190i
$515$	−27.3271	+	47.3320i	−1.20418	+	2.08570i
$516$	−3.50437	−	15.5324i	−0.154271	−	0.683776i
$517$		−	9.95987i		−	0.438035i
$518$	−20.5108	−	8.33149i	−0.901192	−	0.366065i
$519$	1.75793	−	32.7562i	0.0771644	−	1.43784i
$520$	−40.7285	+	5.99095i	−1.78606	+	0.262720i
$521$	41.0352			1.79778			0.898892	−	0.438169i	$-0.144373\pi$
$521$	41.0352			1.79778			0.898892	+	0.438169i	$0.144373\pi$
$522$	−14.7877	+	9.15058i	−0.647240	+	0.400510i
$523$	13.0210	+	7.51768i	0.569369	+	0.328725i	0.756897	−	0.653534i	$-0.226714\pi$
$523$	13.0210	+	7.51768i	0.569369	+	0.328725i	−0.187528	+	0.982259i	$0.560048\pi$
$524$	8.17918	−	8.40671i	0.357309	−	0.367249i
$525$	−67.9199	−	44.2290i	−2.96427	−	1.93031i
$526$	−5.80953	−	7.46456i	−0.253308	−	0.325470i
$527$	−17.5906	−	10.1560i	−0.766260	−	0.442400i
$528$	−5.38703	−	3.30118i	−0.234440	−	0.143666i
$529$	−5.69939			−0.247800
$530$	−39.8757	+	31.0345i	−1.73209	+	1.34805i
$531$	−17.9471	+	24.5721i	−0.778839	+	1.06634i
$532$	−36.1671	+	37.1732i	−1.56804	+	1.61166i
$533$	−6.50220	−	6.57318i	−0.281641	−	0.284716i
$534$	0.966125	+	0.454191i	0.0418083	+	0.0196547i
$535$			37.4410i			1.61872i
$536$	−0.401970	+	0.176276i	−0.0173624	+	0.00761396i
$537$	3.84058	+	2.50096i	0.165733	+	0.107924i
$538$	−20.2617	+	15.7693i	−0.873545	+	0.679864i
$539$	−4.63425	−	8.02675i	−0.199611	−	0.345737i
$540$	−24.9947	−	33.6920i	−1.07560	−	1.44987i
$541$	−21.5345			−0.925841			−0.462921	−	0.886400i	$-0.653199\pi$
$541$	−21.5345			−0.925841			−0.462921	+	0.886400i	$0.653199\pi$
$542$	20.7229	+	8.41766i	0.890125	+	0.361569i
$543$	0.0712410	−	1.32747i	0.00305724	−	0.0569670i
$544$	26.5780	+	9.95568i	1.13952	+	0.426846i
$545$	−16.6990	−	28.9236i	−0.715308	−	1.23895i
$546$	−27.8267	−	23.7578i	−1.19087	−	1.01674i
$547$	−4.34707	−	2.50978i	−0.185867	−	0.107311i	0.404179	−	0.914680i	$-0.367557\pi$
$547$	−4.34707	−	2.50978i	−0.185867	−	0.107311i	−0.590046	+	0.807369i	$0.700891\pi$
$548$	−7.57672	−	26.8006i	−0.323661	−	1.14487i
$549$	1.89712	−	17.6241i	0.0809673	−	0.752178i
$550$	14.4291	−	2.00040i	0.615260	−	0.0852975i
$551$	−22.2191	−	12.8282i	−0.946566	−	0.546500i
$552$	−19.0730	+	7.17174i	−0.811802	+	0.305249i
$553$	−16.8050	−	9.70239i	−0.714623	−	0.412588i
$554$	0.539677	+	3.89275i	0.0229287	+	0.165387i
$555$	26.3811	+	1.41579i	1.11981	+	0.0600970i
$556$	32.4518	+	8.22005i	1.37626	+	0.348608i
$557$	−9.98650	+	17.2971i	−0.423142	+	0.732903i	−0.996245	−	0.0865805i	$-0.972406\pi$
$557$	−9.98650	+	17.2971i	−0.423142	+	0.732903i	0.573103	+	0.819483i	$0.305739\pi$
$558$	−14.6060	+	9.03814i	−0.618321	+	0.382615i
$559$	11.6551	+	11.7823i	0.492958	+	0.498339i
$560$	31.8458	−	58.8285i	1.34573	−	2.48596i
$561$	−4.32445	+	6.64079i	−0.182578	+	0.280374i
$562$	−2.35196	−	0.955368i	−0.0992115	−	0.0402998i
$563$	1.76645	+	1.01986i	0.0744472	+	0.0429821i	0.536762	−	0.843734i	$-0.319647\pi$
$563$	1.76645	+	1.01986i	0.0744472	+	0.0429821i	−0.462314	+	0.886716i	$0.652981\pi$
$564$	36.1251	+	11.2420i	1.52114	+	0.473374i
$565$	19.1311			0.804851
$566$	0.371295	+	2.67819i	0.0156067	+	0.112573i
$567$	7.93528	−	36.4319i	0.333250	−	1.52999i
$568$	−13.9249	+	18.9418i	−0.584276	+	0.794782i
$569$	3.00871	+	5.21124i	0.126132	+	0.218466i	0.922175	−	0.386774i	$-0.126410\pi$
$569$	3.00871	+	5.21124i	0.126132	+	0.218466i	−0.796043	+	0.605240i	$0.793077\pi$
$570$	26.3322	−	56.0121i	1.10293	−	2.34609i
$571$	−6.12091	+	3.53391i	−0.256152	+	0.147890i	−0.622578	−	0.782558i	$-0.713915\pi$
$571$	−6.12091	+	3.53391i	−0.256152	+	0.147890i	0.366426	+	0.930447i	$0.380581\pi$
$572$	6.57582	−	0.0545073i	0.274949	−	0.00227906i
$573$	−7.65335	−	0.410731i	−0.319723	−	0.0171585i
$574$	14.8819	−	2.06318i	0.621159	−	0.0861153i
$575$	23.4907	−	40.6871i	0.979631	−	1.69677i
$576$	18.0541	−	15.8129i	0.752254	−	0.658873i
$577$			19.0242i			0.791989i	0.918253	+	0.395995i	$0.129600\pi$
$577$			19.0242i			0.791989i	−0.918253	+	0.395995i	$0.870400\pi$
$578$	4.34934	−	10.7074i	0.180909	−	0.445368i
$579$	0.0948627	−	1.76762i	0.00394236	−	0.0734598i
$580$	32.0788	+	8.12555i	1.33200	+	0.337395i
$581$	−60.2300	−	34.7738i	−2.49876	−	1.44266i
$582$	−1.21663	−	14.4249i	−0.0504308	−	0.597932i
$583$	6.99024	−	4.03582i	0.289506	−	0.167146i
$584$	9.74179	+	22.2146i	0.403118	+	0.919247i
$585$	40.6383	+	15.9709i	1.68019	+	0.660317i
$586$	−16.8095	+	41.3823i	−0.694396	+	1.70949i
$587$	−2.89778	−	5.01909i	−0.119604	−	0.207160i	0.800007	−	0.599991i	$-0.204829\pi$
$587$	−2.89778	−	5.01909i	−0.119604	−	0.207160i	−0.919611	+	0.392831i	$0.871496\pi$
$588$	34.3443	−	7.74866i	1.41634	−	0.319549i
$589$	−21.9461	−	12.6706i	−0.904273	−	0.522082i
$590$	57.3547	−	7.95146i	2.36126	−	0.327356i
$591$	11.0872	−	17.0260i	0.456067	−	0.700356i
$592$	0.414605	+	15.1085i	0.0170401	+	0.620957i
$593$			8.33420i			0.342245i	0.985250	+	0.171122i	$0.0547393\pi$
$593$			8.33420i			0.342245i	−0.985250	+	0.171122i	$0.945261\pi$
$594$	3.21579	+	5.87932i	0.131945	+	0.241231i
$595$	−72.6648	−	41.9530i	−2.97897	−	1.71991i
$596$	−7.48954	+	29.5679i	−0.306784	+	1.21115i
$597$	−10.3153	−	20.3079i	−0.422177	−	0.831147i
$598$	12.8871	−	16.8446i	0.526991	−	0.688826i
$599$	16.9873	+	29.4228i	0.694081	+	1.20218i	0.970489	+	0.241144i	$0.0775225\pi$
$599$	16.9873	+	29.4228i	0.694081	+	1.20218i	−0.276408	+	0.961040i	$0.589144\pi$
$600$	−9.03101	+	54.5932i	−0.368690	+	2.22876i
$601$	−1.15224	−	1.99573i	−0.0470007	−	0.0814076i	0.841568	−	0.540151i	$-0.181633\pi$
$601$	−1.15224	−	1.99573i	−0.0470007	−	0.0814076i	−0.888569	+	0.458744i	$0.848300\pi$
$602$	−26.6756	+	3.69821i	−1.08722	+	0.150728i
$603$	0.462873	+	0.0498255i	0.0188497	+	0.00202905i
$604$	−2.90535	−	0.735925i	−0.118217	−	0.0299444i
$605$	41.0471			1.66880
$606$	−9.40363	+	6.54081i	−0.381996	+	0.265702i
$607$	18.2124	−	31.5448i	0.739219	−	1.28036i	−0.213629	−	0.976915i	$-0.568528\pi$
$607$	18.2124	−	31.5448i	0.739219	−	1.28036i	0.952848	−	0.303449i	$-0.0981384\pi$
$608$	33.1587	+	12.4207i	1.34476	+	0.503727i
$609$	13.3199	+	26.2231i	0.539749	+	1.06261i
$610$	−26.6193	+	20.7174i	−1.07779	+	0.838821i
$611$	−38.0917	+	9.98534i	−1.54103	+	0.403964i
$612$	−19.2054	−	23.1807i	−0.776334	−	0.937024i
$613$	−15.3716	+	26.6244i	−0.620854	+	1.07535i	0.368473	+	0.929638i	$0.379881\pi$
$613$	−15.3716	+	26.6244i	−0.620854	+	1.07535i	−0.989327	+	0.145712i	$0.953453\pi$
$614$	−22.2300	+	3.08188i	−0.897128	+	0.124375i
$615$	−15.9854	+	8.11970i	−0.644593	+	0.327418i
$616$	−6.32937	+	8.60976i	−0.255018	+	0.346897i
$617$	−25.1190	−	14.5025i	−1.01125	−	0.583847i	−0.0996947	−	0.995018i	$-0.531787\pi$
$617$	−25.1190	−	14.5025i	−1.01125	−	0.583847i	−0.911558	+	0.411171i	$0.865120\pi$
$618$	18.9373	+	27.2258i	0.761768	+	1.09518i
$619$	0.967834	−	1.67634i	0.0389005	−	0.0673777i	−0.845920	−	0.533310i	$-0.820948\pi$
$619$	0.967834	−	1.67634i	0.0389005	−	0.0673777i	0.884820	+	0.465933i	$0.154281\pi$
$620$	31.6846	+	8.02571i	1.27248	+	0.322320i
$621$	21.3339	+	3.46138i	0.856100	+	0.138901i
$622$	13.7158	+	17.6232i	0.549954	+	0.706626i
$623$	0.902798	−	1.56369i	0.0361698	−	0.0626480i
$624$	−7.22463	+	23.9124i	−0.289217	+	0.957264i
$625$	−23.0532	−	39.9292i	−0.922126	−	1.59717i
$626$	−16.9805	+	41.8032i	−0.678677	+	1.67079i
$627$	−5.39518	+	8.28506i	−0.215463	+	0.330873i
$628$	−3.02469	+	3.10883i	−0.120698	+	0.124056i
$629$	18.9577			0.755893
$630$	−60.3356	+	37.3355i	−2.40383	+	1.48748i
$631$	21.4326	−	12.3741i	0.853217	−	0.492605i	−0.00851827	−	0.999964i	$-0.502711\pi$
$631$	21.4326	−	12.3741i	0.853217	−	0.492605i	0.861735	+	0.507359i	$0.169378\pi$
$632$	−1.45860	+	13.1675i	−0.0580201	+	0.523773i
$633$	−0.527406	+	9.82740i	−0.0209625	+	0.390604i
$634$	14.5290	−	35.7679i	0.577019	−	1.42053i
$635$	25.3109			1.00443
$636$	6.74806	+	29.9094i	0.267578	+	1.18598i
$637$	−26.0524	+	25.7711i	−1.03223	+	1.02109i
$638$	−4.89752	−	1.98938i	−0.193895	−	0.0787602i
$639$	22.8052	−	10.0850i	0.902159	−	0.398956i
$640$	−45.5137	−	3.78123i	−1.79909	−	0.149466i
$641$	20.3207			0.802620			0.401310	−	0.915942i	$-0.368555\pi$
$641$	20.3207			0.802620			0.401310	+	0.915942i	$0.368555\pi$
$642$	20.5605	+	9.66582i	0.811458	+	0.381479i
$643$	−0.223117	+	0.386450i	−0.00879887	+	0.0152401i	−0.870391	−	0.492361i	$-0.836134\pi$
$643$	−0.223117	+	0.386450i	−0.00879887	+	0.0152401i	0.861592	+	0.507601i	$0.169467\pi$
$644$	9.37571	+	33.1641i	0.369455	+	1.30685i
$645$	28.6536	−	14.5544i	1.12823	−	0.573080i
$646$	16.7143	−	41.1478i	0.657614	−	1.61894i
$647$	−10.9908	+	19.0367i	−0.432094	+	0.748408i	−0.997053	−	0.0767102i	$-0.975558\pi$
$647$	−10.9908	+	19.0367i	−0.432094	+	0.748408i	0.564960	+	0.825119i	$0.308892\pi$
$648$	−24.9544	+	5.02769i	−0.980302	+	0.197506i
$649$	−9.24956			−0.363077
$650$	−22.1166	−	53.1790i	−0.867485	−	2.08585i
$651$	13.1562	+	25.9009i	0.515632	+	1.01513i
$652$	19.7957	+	19.2599i	0.775258	+	0.754275i
$653$			26.1733i			1.02424i	0.858914	+	0.512121i	$0.171140\pi$
$653$			26.1733i			1.02424i	−0.858914	+	0.512121i	$0.828860\pi$
$654$	−20.1942	+	1.70322i	−0.789657	+	0.0666013i
$655$	20.5020	+	11.8368i	0.801078	+	0.462503i
$656$	−5.37040	−	8.73907i	−0.209679	−	0.341203i
$657$	2.75357	−	25.5804i	0.107427	−	0.997987i
$658$	24.0817	−	59.2852i	0.938803	−	2.31118i
$659$		−	6.41651i		−	0.249952i	−0.992160	−	0.124976i	$-0.960115\pi$
$659$		−	6.41651i		−	0.249952i	0.992160	−	0.124976i	$-0.0398853\pi$
$660$	3.78920	−	12.1762i	0.147494	−	0.473958i
$661$	−9.55934			−0.371815			−0.185908	−	0.982567i	$-0.559523\pi$
$661$	−9.55934			−0.371815			−0.185908	+	0.982567i	$0.559523\pi$
$662$	−24.3818	+	3.38021i	−0.947626	+	0.131376i
$663$	29.7334	+	9.88116i	1.15475	+	0.383752i
$664$	−5.22770	+	47.1927i	−0.202874	+	1.83143i
$665$	−90.6567	−	52.3406i	−3.51551	−	2.02968i
$666$	7.58804	−	14.1215i	0.294031	−	0.547197i
$667$	−14.7646	+	8.52436i	−0.571689	+	0.330065i
$668$	4.17314	+	14.7614i	0.161464	+	0.571135i
$669$	−6.02207	+	3.05888i	−0.232827	+	0.118263i
$670$	−0.544114	−	0.699122i	−0.0210209	−	0.0270094i
$671$	4.66639	−	2.69414i	0.180144	−	0.104006i
$672$	−24.0840	−	32.6751i	−0.929059	−	1.26047i
$673$	21.0715	+	36.4970i	0.812248	+	1.40685i	0.911287	+	0.411771i	$0.135090\pi$
$673$	21.0715	+	36.4970i	0.812248	+	1.40685i	−0.0990396	+	0.995083i	$0.531577\pi$
$674$	7.28484	+	9.36016i	0.280602	+	0.360540i
$675$	37.1075	−	45.4727i	1.42827	−	1.75024i
$676$	−6.80110	−	25.0947i	−0.261581	−	0.965182i
$677$	1.32258	+	0.763592i	0.0508309	+	0.0293472i	0.525200	−	0.850979i	$-0.323990\pi$
$677$	1.32258	+	0.763592i	0.0508309	+	0.0293472i	−0.474369	+	0.880326i	$0.657324\pi$
$678$	4.93890	−	10.5057i	0.189677	−	0.403469i
$679$	−24.4839			−0.939605
$680$	−6.30698	+	56.9359i	−0.241862	+	2.18339i
$681$	12.7234	+	0.682827i	0.487563	+	0.0261660i
$682$	−4.83734	−	1.96493i	−0.185231	−	0.0752412i
$683$	9.69406	+	16.7906i	0.370933	+	0.642475i	0.989709	−	0.143093i	$-0.0457046\pi$
$683$	9.69406	+	16.7906i	0.370933	+	0.642475i	−0.618776	+	0.785567i	$0.712371\pi$
$684$	−23.9607	−	28.9203i	−0.916161	−	1.10579i
$685$	48.6825	−	28.1068i	1.86006	−	1.07391i
$686$	−2.54530	−	18.3595i	−0.0971800	−	0.700969i
$687$	−3.34119	−	6.57786i	−0.127474	−	0.250961i
$688$	9.62637	+	15.6646i	0.367002	+	0.597209i
$689$	−22.4432	−	22.6882i	−0.855017	−	0.864351i
$690$	−23.4847	−	33.7635i	−0.894046	−	1.28536i
$691$	−7.55490	−	13.0855i	−0.287402	−	0.497795i	0.685787	−	0.727802i	$-0.259458\pi$
$691$	−7.55490	−	13.0855i	−0.287402	−	0.497795i	−0.973189	+	0.230008i	$0.926125\pi$
$692$	10.3045	+	36.4495i	0.391719	+	1.38560i
$693$	10.3658	−	4.58399i	0.393764	−	0.174131i
$694$	37.4144	+	15.1978i	1.42023	+	0.576899i
$695$			67.5684i			2.56301i
$696$	12.7436	−	15.5182i	0.483044	−	0.588214i
$697$	−11.1420	+	6.43284i	−0.422034	+	0.243661i
$698$	19.6196	+	25.2088i	0.742612	+	0.954169i
$699$	−20.1979	−	1.08396i	−0.763954	−	0.0409990i
$700$	90.7247	+	22.9806i	3.42907	+	0.868584i
$701$		−	28.5837i		−	1.07959i	−0.841796	−	0.539796i	$-0.818501\pi$
$701$		−	28.5837i		−	1.07959i	0.841796	−	0.539796i	$-0.181499\pi$
$702$	19.2616	−	18.1932i	0.726981	−	0.686658i
$703$	23.6516			0.892038
$704$	7.11860	+	1.59669i	0.268292	+	0.0601777i
$705$	−4.09226	+	76.2530i	−0.154124	+	2.87186i
$706$	−17.6948	+	13.7715i	−0.665952	+	0.518298i
$707$	9.68684	+	16.7781i	0.364311	+	0.631006i
$708$	10.4403	−	33.5487i	0.392369	−	1.26084i
$709$	22.6645			0.851183			0.425591	−	0.904915i	$-0.360066\pi$
$709$	22.6645			0.851183			0.425591	+	0.904915i	$0.360066\pi$
$710$	−43.9624	−	17.8575i	−1.64988	−	0.670182i
$711$	8.28786	−	11.3472i	0.310819	−	0.425554i
$712$	−1.22522	−	0.135722i	−0.0459170	−	0.00508638i
$713$	−14.5832	+	8.41961i	−0.546145	+	0.315317i
$714$	−41.7975	+	29.0727i	−1.56423	+	1.08802i
$715$	3.36563	+	12.8391i	0.125867	+	0.480154i
$716$	−5.13009	−	1.29945i	−0.191721	−	0.0485628i
$717$	17.7602	−	9.02119i	0.663266	−	0.336902i
$718$	−0.0352456	−	0.254231i	−0.00131536	−	0.00948780i
$719$	−17.3326	−	30.0210i	−0.646398	−	1.11959i	−0.983977	−	0.178297i	$-0.942941\pi$
$719$	−17.3326	−	30.0210i	−0.646398	−	1.11959i	0.337579	−	0.941297i	$-0.390392\pi$
$720$	39.8869	+	27.4873i	1.48650	+	1.02439i
$721$	48.5767	−	28.0458i	1.80909	−	1.04448i
$722$	10.7405	−	26.4414i	0.399720	−	0.984046i
$723$	1.72107	−	32.0695i	0.0640073	−	1.19268i
$724$	0.417597	+	1.47714i	0.0155199	+	0.0548974i
$725$			46.2974i			1.71944i
$726$	10.5968	−	22.5407i	0.393282	−	0.836565i
$727$	15.1457	−	26.2331i	0.561723	−	0.972932i	−0.435623	−	0.900129i	$-0.643472\pi$
$727$	15.1457	−	26.2331i	0.561723	−	0.972932i	0.997346	−	0.0728035i	$-0.0231946\pi$
$728$	39.2738	+	15.5750i	1.45558	+	0.577250i
$729$	25.6149	+	8.53667i	0.948702	+	0.316173i
$730$	−38.6365	+	30.0701i	−1.43000	+	1.11295i
$731$	19.9719	−	11.5308i	0.738687	−	0.426481i
$732$	4.50472	+	19.9662i	0.166499	+	0.737974i
$733$	3.34940	+	5.80133i	0.123713	+	0.214277i	0.921229	−	0.389020i	$-0.127186\pi$
$733$	3.34940	+	5.80133i	0.123713	+	0.214277i	−0.797516	+	0.603298i	$0.793853\pi$
$734$	−17.1105	−	21.9850i	−0.631562	−	0.811482i
$735$	32.1819	+	63.3571i	1.18705	+	2.33696i
$736$	18.1648	−	14.9552i	0.669564	−	0.551257i
$737$	0.0707581	+	0.122557i	0.00260641	+	0.00451443i
$738$	0.332073	+	10.8745i	0.0122238	+	0.400294i
$739$	18.5520	−	32.1331i	0.682448	−	1.18203i	−0.291783	−	0.956484i	$-0.594249\pi$
$739$	18.5520	−	32.1331i	0.682448	−	1.18203i	0.974231	−	0.225550i	$-0.0724180\pi$
$740$	−29.3555	+	8.29901i	−1.07913	+	0.305078i
$741$	37.0954	+	12.3277i	1.36273	+	0.452871i
$742$	51.3668	−	7.12132i	1.88574	−	0.261432i
$743$			42.5089i			1.55950i	0.626091	+	0.779750i	$0.284654\pi$
$743$			42.5089i			1.55950i	−0.626091	+	0.779750i	$0.715346\pi$
$744$	12.5870	−	15.3275i	0.461462	−	0.561932i
$745$	−61.5637			−2.25552
$746$	−1.05952	−	0.430378i	−0.0387918	−	0.0157573i
$747$	29.7041	−	40.6690i	1.08681	−	1.48800i
$748$	2.24690	−	8.87052i	0.0821548	−	0.324338i
$749$	19.2128	−	33.2776i	0.702021	−	1.21594i
$750$	−62.0268	+	5.23147i	−2.26490	+	0.191026i
$751$	−3.20261			−0.116865			−0.0584324	−	0.998291i	$-0.518610\pi$
$751$	−3.20261			−0.116865			−0.0584324	+	0.998291i	$0.518610\pi$
$752$	−43.6704	+	1.19839i	−1.59250	+	0.0437008i
$753$	6.58687	−	3.34577i	0.240039	−	0.121927i
$754$	−2.69837	+	20.7252i	−0.0982688	+	0.754765i
$755$		−	6.04926i		−	0.220155i
$756$	4.92623	+	42.7715i	0.179165	+	1.55558i
$757$	33.9440	+	19.5976i	1.23371	+	0.712285i	0.967802	−	0.251712i	$-0.0809936\pi$
$757$	33.9440	+	19.5976i	1.23371	+	0.712285i	0.265912	+	0.963997i	$0.414327\pi$
$758$	18.1824	−	44.7621i	0.660415	−	1.62583i
$759$	2.97529	+	5.85751i	0.107996	+	0.212614i
$760$	−7.86860	+	71.0333i	−0.285424	+	2.57665i
$761$	17.5051	+	10.1065i	0.634558	+	0.366362i	0.782515	−	0.622632i	$-0.213937\pi$
$761$	17.5051	+	10.1065i	0.634558	+	0.366362i	−0.147957	+	0.988994i	$0.547270\pi$
$762$	6.53429	−	13.8993i	0.236712	−	0.503519i
$763$			34.2764i			1.24089i
$764$	8.51626	−	2.40760i	0.308107	−	0.0871040i
$765$	35.8366	−	49.0653i	1.29567	−	1.77396i
$766$	34.6882	+	14.0904i	1.25334	+	0.509106i
$767$	9.27321	+	35.3751i	0.334836	+	1.27732i
$768$	−13.8263	+	24.0174i	−0.498913	+	0.866652i
$769$		−	49.0798i		−	1.76986i	−0.465720	−	0.884932i	$-0.654205\pi$
$769$		−	49.0798i		−	1.76986i	0.465720	−	0.884932i	$-0.345795\pi$
$770$	−19.9825	−	8.11690i	−0.720119	−	0.292513i
$771$	−30.1231	−	1.61661i	−1.08486	−	0.0582209i
$772$	0.556061	+	1.96692i	0.0200131	+	0.0707910i
$773$	7.14933	+	12.3830i	0.257144	+	0.445386i	0.965476	−	0.260494i	$-0.0838853\pi$
$773$	7.14933	+	12.3830i	0.257144	+	0.445386i	−0.708332	+	0.705879i	$0.750552\pi$
$774$	−0.595236	−	19.4923i	−0.0213953	−	0.700636i
$775$			45.7285i			1.64262i
$776$	6.71316	+	15.3083i	0.240989	+	0.549536i
$777$	−22.7210	−	14.7958i	−0.815111	−	0.530796i
$778$	18.0418	+	7.32861i	0.646832	+	0.262743i
$779$	−13.9008	+	8.02562i	−0.498047	+	0.287548i
$780$	−50.3670	−	2.28453i	−1.80343	−	0.0817994i
$781$	6.56436	+	3.78993i	0.234891	+	0.135614i
$782$	−18.1262	−	23.2900i	−0.648191	−	0.832849i
$783$	−19.9122	+	7.55764i	−0.711604	+	0.270088i
$784$	−34.6368	+	21.2853i	−1.23703	+	0.760188i
$785$	−7.58169	−	4.37729i	−0.270602	−	0.156232i
$786$	11.7929	−	8.20272i	0.420640	−	0.292581i
$787$	−3.16626	+	5.48412i	−0.112865	+	0.195488i	−0.916924	−	0.399061i	$-0.869336\pi$
$787$	−3.16626	+	5.48412i	−0.112865	+	0.195488i	0.804059	+	0.594549i	$0.202669\pi$
$788$	−5.76071	+	22.7427i	−0.205217	+	0.810174i
$789$	−5.24638	−	10.3286i	−0.186776	−	0.367710i
$790$	−26.4860	+	3.67193i	−0.942330	+	0.130641i
$791$	−17.0037	−	9.81709i	−0.604582	−	0.349056i
$792$	−5.70826	−	5.22424i	−0.202834	−	0.185635i
$793$	−14.9821	−	15.1457i	−0.532031	−	0.537839i
$794$	3.61850	+	4.64935i	0.128416	+	0.164999i
$795$	−55.1757	+	28.0262i	−1.95688	+	0.993987i
$796$	18.8511	+	18.3409i	0.668161	+	0.650077i
$797$	−15.1639	−	8.75489i	−0.537133	−	0.310114i	0.206783	−	0.978387i	$-0.433701\pi$
$797$	−15.1639	−	8.75489i	−0.537133	−	0.310114i	−0.743916	+	0.668273i	$0.767034\pi$
$798$	−52.1465	+	36.2712i	−1.84597	+	1.28399i
$799$			54.7961i			1.93855i
$800$	−10.5072	−	63.0257i	−0.371485	−	2.22830i
$801$	1.05585	+	0.771177i	0.0373066	+	0.0272482i
$802$	−7.23918	−	52.2170i	−0.255624	−	1.84385i
$803$	6.77301	−	3.91040i	0.239014	−	0.137995i
$804$	−0.524387	+	0.118310i	−0.0184937	+	0.00417249i
$805$	−60.2415	+	34.7804i	−2.12323	+	1.22585i
$806$	−2.66521	+	20.4705i	−0.0938781	+	0.721042i
$807$	−28.0360	+	14.2407i	−0.986913	+	0.501297i
$808$	7.83434	−	10.6569i	0.275611	−	0.374910i
$809$	12.6143	−	21.8485i	0.443494	−	0.768154i	−0.554452	−	0.832216i	$-0.687072\pi$
$809$	12.6143	−	21.8485i	0.443494	−	0.768154i	0.997946	+	0.0640617i	$0.0204055\pi$
$810$	−22.2045	−	46.3335i	−0.780186	−	1.62799i
$811$	27.1229			0.952414			0.476207	−	0.879333i	$-0.342011\pi$
$811$	27.1229			0.952414			0.476207	+	0.879333i	$0.342011\pi$
$812$	−24.3420	−	23.6832i	−0.854237	−	0.831117i
$813$	22.9560	+	14.9488i	0.805101	+	0.524277i
$814$	4.82692	−	0.669188i	0.169184	−	0.0234550i
$815$	−27.8727	+	48.2769i	−0.976338	+	1.69107i
$816$	29.6378	+	18.1621i	1.03753	+	0.635800i
$817$	24.9169	−	14.3858i	0.871734	−	0.503296i
$818$	−8.06127	−	3.27449i	−0.281856	−	0.114490i
$819$	−27.9239	−	35.0485i	−0.975739	−	1.22469i
$820$	14.4371	−	14.8387i	0.504165	−	0.518190i
$821$	−21.1234	−	36.5868i	−0.737211	−	1.27689i	−0.953747	−	0.300612i	$-0.902809\pi$
$821$	−21.1234	−	36.5868i	−0.737211	−	1.27689i	0.216536	−	0.976275i	$-0.430524\pi$
$822$	−2.86677	−	33.9897i	−0.0999900	−	1.18553i
$823$	21.7772	−	37.7193i	0.759107	−	1.31481i	−0.184200	−	0.982889i	$-0.558969\pi$
$823$	21.7772	−	37.7193i	0.759107	−	1.31481i	0.943307	−	0.331923i	$-0.107697\pi$
$824$	−30.8545	−	22.6823i	−1.07487	−	0.790176i
$825$	17.8154	+	0.956096i	0.620252	+	0.0332870i
$826$	−55.0571	−	22.3642i	−1.91568	−	0.778152i
$827$	20.4697			0.711800			0.355900	−	0.934524i	$-0.384174\pi$
$827$	20.4697			0.711800			0.355900	+	0.934524i	$0.384174\pi$
$828$	−24.6039	+	4.18001i	−0.855043	+	0.145266i
$829$	44.0277	+	25.4194i	1.52914	+	0.882851i	0.999398	+	0.0346949i	$0.0110459\pi$
$829$	44.0277	+	25.4194i	1.52914	+	0.882851i	0.529746	+	0.848157i	$0.322287\pi$
$830$	−94.9271	+	13.1604i	−3.29497	+	0.456803i
$831$	−0.257940	+	4.80631i	−0.00894783	+	0.166729i
$832$	−1.03021	−	28.8260i	−0.0357161	−	0.999362i
$833$	25.4962	+	44.1607i	0.883390	+	1.53008i
$834$	37.1047	+	17.4435i	1.28483	+	0.604020i
$835$	−26.8136	+	15.4808i	−0.927922	+	0.535736i
$836$	2.80323	−	11.0669i	0.0969519	−	0.382755i
$837$	−19.6675	+	7.46478i	−0.679809	+	0.258020i
$838$	3.09942	+	22.3564i	0.107068	+	0.772291i
$839$			16.4728i			0.568705i	0.958720	+	0.284352i	$0.0917785\pi$
$839$			16.4728i			0.568705i	−0.958720	+	0.284352i	$0.908221\pi$
$840$	51.9954	−	63.3159i	1.79401	−	2.18461i
$841$	−6.09975	+	10.5651i	−0.210336	+	0.364313i
$842$	11.4306	−	28.1402i	0.393924	−	0.969776i
$843$	−2.60540	−	1.69662i	−0.0897349	−	0.0584348i
$844$	−3.09152	−	10.9354i	−0.106415	−	0.376413i
$845$	45.7291	−	25.7438i	1.57313	−	0.885615i
$846$	40.8174	+	21.9328i	1.40333	+	0.754065i
$847$	−36.4826	−	21.0632i	−1.25356	−	0.723742i
$848$	−18.5367	−	30.1640i	−0.636551	−	1.03584i
$849$	−0.177461	+	3.30672i	−0.00609046	+	0.113486i
$850$	−79.3845	+	11.0056i	−2.72287	+	0.377489i
$851$	7.85827	−	13.6109i	0.269378	−	0.466576i
$852$	−21.1557	+	19.5315i	−0.724783	+	0.669139i
$853$	−19.0265	+	32.9549i	−0.651456	+	1.12835i	0.331314	+	0.943521i	$0.392508\pi$
$853$	−19.0265	+	32.9549i	−0.651456	+	1.12835i	−0.982770	+	0.184834i	$0.940825\pi$
$854$	34.2903	−	4.75389i	1.17339	−	0.162675i
$855$	44.7098	−	61.2139i	1.52904	−	2.09347i
$856$	−26.0744	−	2.88835i	−0.891204	−	0.0987217i
$857$	−14.1397	+	24.4907i	−0.483003	+	0.836586i	−0.999810	−	0.0195162i	$-0.993787\pi$
$857$	−14.1397	+	24.4907i	−0.483003	+	0.836586i	0.516806	+	0.856102i	$0.327121\pi$
$858$	7.91937	+	1.46634i	0.270363	+	0.0500600i
$859$	−31.1068	+	17.9595i	−1.06135	+	0.612770i	−0.925805	−	0.378001i	$-0.876612\pi$
$859$	−31.1068	+	17.9595i	−1.06135	+	0.612770i	−0.135544	+	0.990771i	$0.543278\pi$
$860$	−25.8782	+	26.5981i	−0.882441	+	0.906989i
$861$	18.3744	+	0.986098i	0.626199	+	0.0336061i
$862$	−1.57233	−	0.638680i	−0.0535537	−	0.0217535i
$863$		−	37.5368i		−	1.27777i	−0.769304	−	0.638883i	$-0.779397\pi$
$863$		−	37.5368i		−	1.27777i	0.769304	−	0.638883i	$-0.220603\pi$
$864$	25.3917	−	14.8075i	0.863844	−	0.503760i
$865$	−66.2093	+	38.2260i	−2.25118	+	1.29972i
$866$	−8.64713	−	11.1105i	−0.293841	−	0.377551i
$867$	7.72393	−	11.8612i	0.262319	−	0.402827i
$868$	−24.0429	−	23.3922i	−0.816069	−	0.793982i
$869$	4.27138			0.144897
$870$	36.6782	+	17.2430i	1.24351	+	0.584592i
$871$	0.397781	−	0.393486i	0.0134783	−	0.0133328i
$872$	21.4310	−	9.39813i	0.725744	−	0.318261i
$873$	1.89752	−	17.6277i	0.0642212	−	0.596608i
$874$	−22.6143	−	29.0566i	−0.764939	−	0.982855i
$875$			105.280i			3.55912i
$876$	6.53836	+	28.9799i	0.220911	+	0.979141i
$877$	22.2078	−	38.4650i	0.749903	−	1.29887i	−0.197966	−	0.980209i	$-0.563433\pi$
$877$	22.2078	−	38.4650i	0.749903	−	1.29887i	0.947869	−	0.318661i	$-0.103233\pi$
$878$	10.0025	+	12.8521i	0.337569	+	0.433736i
$879$	−29.8518	+	45.8417i	−1.00688	+	1.54620i
$880$	0.403926	+	14.7194i	0.0136163	+	0.496191i
$881$	8.68946	−	15.0506i	0.292755	−	0.507067i	−0.681705	−	0.731627i	$-0.738761\pi$
$881$	8.68946	−	15.0506i	0.292755	−	0.507067i	0.974460	+	0.224560i	$0.0720945\pi$
$882$	43.1003	−	1.31615i	1.45126	−	0.0443171i
$883$			8.94277i			0.300948i	0.988614	+	0.150474i	$0.0480800\pi$
$883$			8.94277i			0.300948i	−0.988614	+	0.150474i	$0.951920\pi$
$884$	−36.1781	+	0.299882i	−1.21680	+	0.0100861i
$885$	70.8148	+	3.80041i	2.38041	+	0.127749i
$886$	2.37702	+	0.965549i	0.0798577	+	0.0324383i
$887$	−27.7510			−0.931789			−0.465895	−	0.884840i	$-0.654267\pi$
$887$	−27.7510			−0.931789			−0.465895	+	0.884840i	$0.654267\pi$
$888$	−3.02111	+	18.2629i	−0.101382	+	0.612862i
$889$	−22.4963	−	12.9883i	−0.754503	−	0.435612i
$890$	−0.341669	−	2.46450i	−0.0114528	−	0.0826101i
$891$	2.49699	+	7.81834i	0.0836524	+	0.261924i
$892$	5.43879	−	5.59008i	0.182104	−	0.187170i
$893$			68.3637i			2.28770i
$894$	−15.8933	+	33.8073i	−0.531553	+	1.13068i
$895$		−	10.6814i		−	0.357041i
$896$	38.5122	+	26.7160i	1.28660	+	0.892520i
$897$	19.4193	−	17.2516i	0.648390	−	0.576013i
$898$	−25.6575	+	19.9688i	−0.856202	+	0.666366i
$899$	8.29703	−	14.3709i	0.276721	−	0.479296i
$900$	−23.5766	+	63.5383i	−0.785886	+	2.11794i
$901$	−38.4581	+	22.2038i	−1.28123	+	0.739716i
$902$	−2.60986	+	2.03120i	−0.0868987	+	0.0676317i
$903$	−32.9359	−	1.76757i	−1.09604	−	0.0588209i
$904$	−1.47585	+	13.3231i	−0.0490859	+	0.443120i
$905$	−2.68317	+	1.54913i	−0.0891916	+	0.0514948i
$906$	−3.32191	−	1.56168i	−0.110363	−	0.0518835i
$907$	2.53466	−	1.46339i	0.0841619	−	0.0485909i	−0.457328	−	0.889298i	$-0.651194\pi$
$907$	2.53466	−	1.46339i	0.0841619	−	0.0485909i	0.541490	+	0.840707i	$0.317860\pi$
$908$	−14.1580	+	4.00256i	−0.469849	+	0.132830i
$909$	−12.8305	+	5.67395i	−0.425561	+	0.188193i
$910$	−11.0097	+	84.5611i	−0.364967	+	2.80317i
$911$	28.4952	−	49.3551i	0.944088	−	1.63521i	0.186522	−	0.982451i	$-0.440278\pi$
$911$	28.4952	−	49.3551i	0.944088	−	1.63521i	0.757566	−	0.652758i	$-0.226388\pi$
$912$	36.9761	+	22.6590i	1.22440	+	0.750315i
$913$	15.3088			0.506648
$914$	12.3267	−	9.59365i	0.407731	−	0.317330i
$915$	−36.8330	+	18.7091i	−1.21766	+	0.618504i
$916$	6.10601	+	5.94075i	0.201748	+	0.196288i
$917$	−12.1481	−	21.0411i	−0.401166	−	0.694839i
$918$	−17.6923	−	32.3462i	−0.583931	−	1.06758i
$919$	−0.212356	−	0.367812i	−0.00700499	−	0.0121330i	0.862502	−	0.506054i	$-0.168896\pi$
$919$	−0.212356	−	0.367812i	−0.00700499	−	0.0121330i	−0.869507	+	0.493921i	$0.835563\pi$
$920$	38.2635	+	28.1290i	1.26151	+	0.927387i
$921$	−27.4469	−	1.47299i	−0.904407	−	0.0485367i
$922$	37.9529	−	5.26166i	1.24991	−	0.173283i
$923$	7.91354	−	28.9051i	0.260477	−	0.951425i
$924$	−9.61604	+	8.87778i	−0.316345	+	0.292058i
$925$	−21.3399	−	36.9617i	−0.701651	−	1.21529i
$926$	22.8446	−	17.7796i	0.750721	−	0.584273i
$927$	16.4275	+	37.1475i	0.539549	+	1.22008i
$928$	−8.13341	+	21.7132i	−0.266992	+	0.712771i
$929$			36.6831i			1.20353i	0.798671	+	0.601767i	$0.205537\pi$
$929$			36.6831i			1.20353i	−0.798671	+	0.601767i	$0.794463\pi$
$930$	36.2275	+	17.0311i	1.18795	+	0.558472i
$931$	31.8091	+	55.0949i	1.04250	+	1.80566i
$932$	22.4752	−	6.35388i	0.736199	−	0.208128i
$933$	12.3863	+	24.3851i	0.405508	+	0.798331i
$934$	3.12871	+	22.5677i	0.102375	+	0.738438i
$935$	18.4694			0.604014
$936$	−14.2573	+	27.0690i	−0.466016	+	0.884776i
$937$	−7.38008			−0.241097			−0.120548	−	0.992707i	$-0.538465\pi$
$937$	−7.38008			−0.241097			−0.120548	+	0.992707i	$0.538465\pi$
$938$	0.124855	+	0.900591i	0.00407665	+	0.0294053i
$939$	−30.1554	+	46.3079i	−0.984085	+	1.51120i
$940$	−23.9878	−	84.8505i	−0.782396	−	2.76752i
$941$	−10.5733	−	18.3135i	−0.344679	−	0.597001i	0.640616	−	0.767861i	$-0.278679\pi$
$941$	−10.5733	−	18.3135i	−0.344679	−	0.597001i	−0.985295	+	0.170860i	$0.945346\pi$
$942$	−4.36106	+	3.03339i	−0.142091	+	0.0988332i
$943$			10.6661i			0.347335i
$944$	1.11292	+	40.5559i	0.0362226	+	1.31998i
$945$	−81.2442	+	30.8361i	−2.64287	+	1.00310i
$946$	4.67813	−	3.64090i	0.152099	−	0.118376i
$947$	12.2691	+	21.2507i	0.398693	+	0.690556i	0.993565	−	0.113264i	$-0.0361306\pi$
$947$	12.2691	+	21.2507i	0.398693	+	0.690556i	−0.594872	+	0.803820i	$0.702797\pi$
$948$	−4.82124	+	15.4926i	−0.156587	+	0.503175i
$949$	−21.7457	−	21.9831i	−0.705897	−	0.713603i
$950$	−99.0402	+	13.7306i	−3.21329	+	0.445479i
$951$	25.8018	−	39.6222i	0.836680	−	1.28484i
$952$	34.8222	−	47.3682i	1.12860	−	1.53521i
$953$	25.4207	+	44.0300i	0.823459	+	1.42627i	0.903091	+	0.429448i	$0.141292\pi$
$953$	25.4207	+	44.0300i	0.823459	+	1.42627i	−0.0796326	+	0.996824i	$0.525375\pi$
$954$	1.14619	+	37.5346i	0.0371094	+	1.21523i
$955$	8.93132	+	15.4695i	0.289011	+	0.500581i
$956$	−16.0400	+	16.4862i	−0.518769	+	0.533201i
$957$	−5.42528	−	3.53291i	−0.175374	−	0.114203i
$958$	8.46679	−	6.58955i	0.273550	−	0.212899i
$959$	−57.6920			−1.86297
$960$	−53.8441	−	15.1492i	−1.73781	−	0.488938i
$961$	−7.30492	+	12.6525i	−0.235643	+	0.408145i
$962$	−7.39859	−	17.7898i	−0.238540	−	0.573565i
$963$	22.4699	+	16.4117i	0.724084	+	0.528861i
$964$	10.0885	+	35.6853i	0.324928	+	1.14935i
$965$	−3.57284	+	2.06278i	−0.115014	+	0.0664033i
$966$	3.54744	+	42.0602i	0.114137	+	1.35326i
$967$	45.8976	−	26.4990i	1.47597	−	0.852151i	0.476336	−	0.879263i	$-0.341965\pi$
$967$	45.8976	−	26.4990i	1.47597	−	0.852151i	0.999632	+	0.0271123i	$0.00863118\pi$
$968$	−3.16653	+	28.5857i	−0.101776	+	0.918778i
$969$	29.6826	−	45.5818i	0.953543	−	1.46430i
$970$	−26.6248	+	20.7216i	−0.854872	+	0.665331i
$971$	−32.9462	+	19.0215i	−1.05729	+	0.610428i	−0.924682	−	0.380740i	$-0.875669\pi$
$971$	−32.9462	+	19.0215i	−1.05729	+	0.610428i	−0.132610	+	0.991168i	$0.542336\pi$
$972$	−31.1761	+	0.231938i	−0.999972	+	0.00743942i
$973$	34.6726	−	60.0548i	1.11155	−	1.92527i
$974$	42.3898	−	32.9912i	1.35826	−	1.05711i
$975$	−14.2043	−	69.0938i	−0.454902	−	2.21277i
$976$	−12.3743	−	20.1362i	−0.396091	−	0.644546i
$977$		−	33.0653i		−	1.05785i	−0.848668	−	0.528926i	$-0.822595\pi$
$977$		−	33.0653i		−	1.05785i	0.848668	−	0.528926i	$-0.177405\pi$
$978$	19.3153	+	27.7693i	0.617635	+	0.887965i
$979$			0.397448i			0.0127025i
$980$	−58.8123	−	57.2205i	−1.87869	−	1.82784i
$981$	−24.6780	−	2.65644i	−0.787909	−	0.0848135i
$982$	−3.12303	−	22.5267i	−0.0996599	−	0.718857i
$983$	33.5982	+	19.3979i	1.07162	+	0.618698i	0.928622	−	0.371026i	$-0.120994\pi$
$983$	33.5982	+	19.3979i	1.07162	+	0.618698i	0.142993	+	0.989724i	$0.454327\pi$
$984$	−4.42148	−	11.7588i	−0.140952	−	0.374857i
$985$	−47.3528			−1.50878
$986$	26.9447	+	10.9449i	0.858093	+	0.348558i
$987$	42.7664	−	65.6737i	1.36127	−	2.09042i
$988$	−45.1359	+	0.374133i	−1.43596	+	0.0119028i
$989$		−	19.1188i		−	0.607942i
$990$	7.39260	−	13.7578i	0.234952	−	0.437251i
$991$	0.663509	−	1.14923i	0.0210770	−	0.0365065i	−0.855294	−	0.518142i	$-0.826624\pi$
$991$	0.663509	−	1.14923i	0.0210770	−	0.0365065i	0.876372	+	0.481636i	$0.159957\pi$
$992$	−8.03347	+	21.4464i	−0.255063	+	0.680924i
$993$	−30.1038	−	1.61558i	−0.955315	−	0.0512688i
$994$	29.9102	+	38.4310i	0.948693	+	1.21896i
$995$	−26.5428	+	45.9735i	−0.841463	+	1.45746i
$996$	−17.2795	+	55.5261i	−0.547523	+	1.75941i
$997$		−	16.9655i		−	0.537302i	−0.963238	−	0.268651i	$-0.913422\pi$
$997$		−	16.9655i		−	0.537302i	0.963238	−	0.268651i	$-0.0865779\pi$
$998$	18.4276	+	23.6773i	0.583316	+	0.749492i
$999$	12.4134	−	15.2118i	0.392744	−	0.481280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.bk.c.277.7	✓	320
8.5	even	2	inner	936.2.bk.c.277.48	yes	320
9.4	even	3		936.2.ca.c.589.100	yes	320
13.10	even	6		936.2.ca.c.205.61	yes	320
72.13	even	6		936.2.ca.c.589.61	yes	320
104.101	even	6		936.2.ca.c.205.100	yes	320
117.49	even	6	inner	936.2.bk.c.517.48	yes	320
936.517	even	6	inner	936.2.bk.c.517.7	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.bk.c.277.7	✓	320	1.1	even	1	trivial
936.2.bk.c.277.48	yes	320	8.5	even	2	inner
936.2.bk.c.517.7	yes	320	936.517	even	6	inner
936.2.bk.c.517.48	yes	320	117.49	even	6	inner
936.2.ca.c.205.61	yes	320	13.10	even	6
936.2.ca.c.205.100	yes	320	104.101	even	6
936.2.ca.c.589.61	yes	320	72.13	even	6
936.2.ca.c.589.100	yes	320	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40082 + 0.194204i) q^{2} +(-1.72956 - 0.0928202i) q^{3} +(1.92457 - 0.544089i) q^{4} +(2.01837 + 3.49592i) q^{5} +(2.44082 - 0.205864i) q^{6} -4.14289i q^{7} +(-2.59030 + 1.13593i) q^{8} +(2.98277 + 0.321077i) q^{9} +(-3.50628 - 4.50516i) q^{10} +(0.455967 + 0.789758i) q^{11} +(-3.37916 + 0.762396i) q^{12} +(2.56331 - 2.53563i) q^{13} +(0.804567 + 5.80343i) q^{14} +(-3.16640 - 6.23375i) q^{15} +(3.40794 - 2.09427i) q^{16} +(-2.50859 - 4.34500i) q^{17} +(-4.24066 + 0.129497i) q^{18} +(-3.12972 - 5.42083i) q^{19} +(5.78658 + 5.62996i) q^{20} +(-0.384544 + 7.16539i) q^{21} +(-0.792100 - 1.01775i) q^{22} -4.15940 q^{23} +(4.58553 - 1.72422i) q^{24} +(-5.64762 + 9.78197i) q^{25} +(-3.09830 + 4.04976i) q^{26} +(-5.12908 - 0.832183i) q^{27} +(-2.25410 - 7.97329i) q^{28} +(3.54970 - 2.04942i) q^{29} +(5.64617 + 8.11741i) q^{30} +(3.50608 - 2.02424i) q^{31} +(-4.36717 + 3.59553i) q^{32} +(-0.715317 - 1.40826i) q^{33} +(4.35789 + 5.59937i) q^{34} +(14.4832 - 8.36188i) q^{35} +(5.91524 - 1.00496i) q^{36} +(-1.88928 + 3.27233i) q^{37} +(5.43690 + 6.98578i) q^{38} +(-4.66877 + 4.14761i) q^{39} +(-9.19929 - 6.76276i) q^{40} -2.56433i q^{41} +(-0.852873 - 10.1121i) q^{42} +4.59652i q^{43} +(1.30724 + 1.27186i) q^{44} +(4.89787 + 11.0756i) q^{45} +(5.82655 - 0.807773i) q^{46} +(-9.45848 - 5.46085i) q^{47} +(-6.08863 + 3.30585i) q^{48} -10.1636 q^{49} +(6.01158 - 14.7995i) q^{50} +(3.93545 + 7.74780i) q^{51} +(3.55366 - 6.27467i) q^{52} -8.85112i q^{53} +(7.34651 + 0.169646i) q^{54} +(-1.84062 + 3.18804i) q^{55} +(4.70603 + 10.7313i) q^{56} +(4.90988 + 9.66616i) q^{57} +(-4.57447 + 3.56023i) q^{58} +(-5.07140 + 8.78392i) q^{59} +(-9.48567 - 10.2745i) q^{60} -5.90863i q^{61} +(-4.51826 + 3.51648i) q^{62} +(1.33019 - 12.3573i) q^{63} +(5.41934 - 5.88479i) q^{64} +(14.0381 + 3.84329i) q^{65} +(1.27552 + 1.83379i) q^{66} +0.155182 q^{67} +(-7.19202 - 6.99736i) q^{68} +(7.19394 + 0.386076i) q^{69} +(-18.6644 + 14.5262i) q^{70} +(7.19828 - 4.15593i) q^{71} +(-8.09099 + 2.55652i) q^{72} -8.57607i q^{73} +(2.01103 - 4.95083i) q^{74} +(10.6759 - 16.3943i) q^{75} +(-8.97277 - 8.72992i) q^{76} +(3.27188 - 1.88902i) q^{77} +(5.73460 - 6.71672i) q^{78} +(2.34194 - 4.05635i) q^{79} +(14.1999 + 7.68684i) q^{80} +(8.79382 + 1.91539i) q^{81} +(0.498003 + 3.59215i) q^{82} +(8.39361 - 14.5382i) q^{83} +(3.15852 + 13.9995i) q^{84} +(10.1265 - 17.5396i) q^{85} +(-0.892664 - 6.43888i) q^{86} +(-6.32966 + 3.21512i) q^{87} +(-2.07820 - 1.52777i) q^{88} +(0.377440 + 0.217915i) q^{89} +(-9.01193 - 14.5636i) q^{90} +(-10.5049 - 10.6195i) q^{91} +(-8.00505 + 2.26308i) q^{92} +(-6.25188 + 3.17561i) q^{93} +(14.3101 + 5.81277i) q^{94} +(12.6338 - 21.8825i) q^{95} +(7.88703 - 5.81332i) q^{96} -5.90985i q^{97} +(14.2373 - 1.97381i) q^{98} +(1.10647 + 2.50207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 3 q^{2} + q^{4} - 3 q^{6} + 10 q^{9} + 8 q^{10} - 7 q^{12} + 2 q^{14} + 24 q^{15} - 15 q^{16} + 8 q^{17} - 6 q^{18} + q^{22} + 20 q^{23} + 12 q^{24} - 144 q^{25} - 20 q^{26} - 6 q^{28} + 7 q^{30}+ \cdots - 99 q^{98}+O(q^{100}) \) 320 * q - 3 * q^2 + q^4 - 3 * q^6 + 10 * q^9 + 8 * q^10 - 7 * q^12 + 2 * q^14 + 24 * q^15 - 15 * q^16 + 8 * q^17 - 6 * q^18 + q^22 + 20 * q^23 + 12 * q^24 - 144 * q^25 - 20 * q^26 - 6 * q^28 + 7 * q^30 + 12 * q^31 - 3 * q^32 + 18 * q^33 - 30 * q^34 + 39 * q^36 - 10 * q^38 + 44 * q^39 - 28 * q^40 + 10 * q^42 - 30 * q^46 - 12 * q^47 - 8 * q^48 - 316 * q^49 - 56 * q^52 + 36 * q^54 + 14 * q^55 + 52 * q^56 + 36 * q^57 - 3 * q^58 + 3 * q^60 - q^62 - 42 * q^63 - 26 * q^64 + 66 * q^65 + 50 * q^66 - 12 * q^68 + 3 * q^70 - 48 * q^71 + 21 * q^72 + 26 * q^74 + 35 * q^78 + 32 * q^79 - 48 * q^80 + 34 * q^81 - 23 * q^82 + 120 * q^84 + 42 * q^86 - 2 * q^87 + 13 * q^88 - 72 * q^89 + 109 * q^90 - 28 * q^92 + 130 * q^94 + 112 * q^95 - 15 * q^96 - 99 * q^98

Introduction

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