LMFDB - Embedded newform 961.2.g.v.844.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			844.5
Character	$\chi$	$=$	961.844
Dual form			961.2.g.v.846.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.384764 - 1.18418i) q^{2} +(-2.62010 + 0.556919i) q^{3} +(0.363788 - 0.264307i) q^{4} +(-1.30938 + 2.26791i) q^{5} +(1.66762 + 2.88840i) q^{6} +(1.10040 + 0.489932i) q^{7} +(-2.46761 - 1.79283i) q^{8} +(3.81413 - 1.69816i) q^{9} +(3.18942 + 0.677933i) q^{10} +(0.459609 + 4.37289i) q^{11} +(-0.805963 + 0.895113i) q^{12} +(-0.815200 - 0.905371i) q^{13} +(0.156772 - 1.49159i) q^{14} +(2.16766 - 6.67137i) q^{15} +(-0.895675 + 2.75661i) q^{16} +(-0.382443 + 3.63870i) q^{17} +(-3.47847 - 3.86324i) q^{18} +(4.30235 - 4.77825i) q^{19} +(0.123089 + 1.17112i) q^{20} +(-3.15602 - 0.670833i) q^{21} +(5.00146 - 2.22679i) q^{22} +(-3.19080 - 2.31825i) q^{23} +(7.46386 + 3.32312i) q^{24} +(-0.928943 - 1.60898i) q^{25} +(-0.758465 + 1.31370i) q^{26} +(-2.54648 + 1.85013i) q^{27} +(0.529807 - 0.112614i) q^{28} +(-0.414206 - 1.27479i) q^{29} -8.73416 q^{30} -2.49133 q^{32} +(-3.63957 - 11.2014i) q^{33} +(4.45604 - 0.947161i) q^{34} +(-2.55197 + 1.85411i) q^{35} +(0.938698 - 1.62587i) q^{36} +(-3.21787 - 5.57351i) q^{37} +(-7.31371 - 3.25627i) q^{38} +(2.64012 + 1.91816i) q^{39} +(7.29701 - 3.24884i) q^{40} +(-2.04245 - 0.434135i) q^{41} +(0.419936 + 3.99542i) q^{42} +(-6.29858 + 6.99528i) q^{43} +(1.32299 + 1.46933i) q^{44} +(-1.14287 + 10.8736i) q^{45} +(-1.51753 + 4.67048i) q^{46} +(0.233002 - 0.717105i) q^{47} +(0.811552 - 7.72140i) q^{48} +(-3.71306 - 4.12377i) q^{49} +(-1.54790 + 1.71912i) q^{50} +(-1.02443 - 9.74676i) q^{51} +(-0.535856 - 0.113900i) q^{52} +(-4.30646 + 1.91736i) q^{53} +(3.17068 + 2.30364i) q^{54} +(-10.5191 - 4.68342i) q^{55} +(-1.83701 - 3.18180i) q^{56} +(-8.61150 + 14.9156i) q^{57} +(-1.35022 + 0.980990i) q^{58} +(-3.90409 + 0.829840i) q^{59} +(-0.974724 - 2.99989i) q^{60} -2.21839 q^{61} +5.02907 q^{63} +(2.74992 + 8.46340i) q^{64} +(3.12070 - 0.663326i) q^{65} +(-11.8642 + 8.61984i) q^{66} +(-6.00489 + 10.4008i) q^{67} +(0.822608 + 1.42480i) q^{68} +(9.65130 + 4.29704i) q^{69} +(3.17751 + 2.30860i) q^{70} +(-6.87245 + 3.05981i) q^{71} +(-12.4563 - 2.64767i) q^{72} +(-1.03736 - 9.86983i) q^{73} +(-5.36194 + 5.95503i) q^{74} +(3.32999 + 3.69833i) q^{75} +(0.302218 - 2.87541i) q^{76} +(-1.63666 + 5.03713i) q^{77} +(1.25563 - 3.86443i) q^{78} +(0.988929 - 9.40903i) q^{79} +(-5.07895 - 5.64075i) q^{80} +(-2.73937 + 3.04238i) q^{81} +(0.271765 + 2.58567i) q^{82} +(-5.48687 - 1.16627i) q^{83} +(-1.32543 + 0.590119i) q^{84} +(-7.75149 - 5.63178i) q^{85} +(10.7072 + 4.76713i) q^{86} +(1.79522 + 3.10941i) q^{87} +(6.70570 - 11.6146i) q^{88} +(11.2812 - 8.19625i) q^{89} +(13.3161 - 2.83043i) q^{90} +(-0.453480 - 1.39567i) q^{91} -1.77351 q^{92} -0.938835 q^{94} +(5.20323 + 16.0139i) q^{95} +(6.52753 - 1.38747i) q^{96} +(3.64843 - 2.65074i) q^{97} +(-3.45464 + 5.98362i) q^{98} +(9.17888 + 15.8983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) $ 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.384764	−	1.18418i	−0.272070	−	0.837344i	−0.989980	−	0.141208i	$-0.954901\pi$
$2$	−0.384764	−	1.18418i	−0.272070	−	0.837344i	0.717910	−	0.696136i	$-0.245099\pi$
$3$	−2.62010	+	0.556919i	−1.51272	+	0.321538i	−0.888194	−	0.459470i	$-0.848040\pi$
$3$	−2.62010	+	0.556919i	−1.51272	+	0.321538i	−0.624522	+	0.781007i	$0.714706\pi$
$4$	0.363788	−	0.264307i	0.181894	−	0.132154i
$5$	−1.30938	+	2.26791i	−0.585572	+	1.01424i	0.409232	+	0.912430i	$0.365797\pi$
$5$	−1.30938	+	2.26791i	−0.585572	+	1.01424i	−0.994804	+	0.101810i	$0.967537\pi$
$6$	1.66762	+	2.88840i	0.680801	+	1.17918i
$7$	1.10040	+	0.489932i	0.415914	+	0.185177i	0.604015	−	0.796973i	$-0.293567\pi$
$7$	1.10040	+	0.489932i	0.415914	+	0.185177i	−0.188101	+	0.982150i	$0.560233\pi$
$8$	−2.46761	−	1.79283i	−0.872433	−	0.633860i
$9$	3.81413	−	1.69816i	1.27138	−	0.566053i
$10$	3.18942	+	0.677933i	1.00858	+	0.214381i
$11$	0.459609	+	4.37289i	0.138577	+	1.31848i	0.813922	+	0.580974i	$0.197328\pi$
$11$	0.459609	+	4.37289i	0.138577	+	1.31848i	−0.675345	+	0.737502i	$0.736005\pi$
$12$	−0.805963	+	0.895113i	−0.232662	+	0.258397i
$13$	−0.815200	−	0.905371i	−0.226096	−	0.251105i	0.619414	−	0.785064i	$-0.287370\pi$
$13$	−0.815200	−	0.905371i	−0.226096	−	0.251105i	−0.845510	+	0.533960i	$0.820703\pi$
$14$	0.156772	−	1.49159i	0.0418992	−	0.398644i
$15$	2.16766	−	6.67137i	0.559687	−	1.72254i
$16$	−0.895675	+	2.75661i	−0.223919	+	0.689151i
$17$	−0.382443	+	3.63870i	−0.0927561	+	0.882515i	0.844894	+	0.534934i	$0.179664\pi$
$17$	−0.382443	+	3.63870i	−0.0927561	+	0.882515i	−0.937650	+	0.347581i	$0.887003\pi$
$18$	−3.47847	−	3.86324i	−0.819884	−	0.910574i
$19$	4.30235	−	4.77825i	0.987027	−	1.09621i	−0.00833069	−	0.999965i	$-0.502652\pi$
$19$	4.30235	−	4.77825i	0.987027	−	1.09621i	0.995358	−	0.0962398i	$-0.0306816\pi$
$20$	0.123089	+	1.17112i	0.0275236	+	0.261870i
$21$	−3.15602	−	0.670833i	−0.688701	−	0.146388i
$22$	5.00146	−	2.22679i	1.06632	−	0.474754i
$23$	−3.19080	−	2.31825i	−0.665328	−	0.483389i	0.203130	−	0.979152i	$-0.434889\pi$
$23$	−3.19080	−	2.31825i	−0.665328	−	0.483389i	−0.868458	+	0.495763i	$0.834889\pi$
$24$	7.46386	+	3.32312i	1.52355	+	0.678330i
$25$	−0.928943	−	1.60898i	−0.185789	−	0.321795i
$26$	−0.758465	+	1.31370i	−0.148747	+	0.257638i
$27$	−2.54648	+	1.85013i	−0.490070	+	0.356057i
$28$	0.529807	−	0.112614i	0.100124	−	0.0212820i
$29$	−0.414206	−	1.27479i	−0.0769160	−	0.236723i	0.905205	−	0.424976i	$-0.139718\pi$
$29$	−0.414206	−	1.27479i	−0.0769160	−	0.236723i	−0.982121	+	0.188253i	$0.939718\pi$
$30$	−8.73416			−1.59463
$31$		0			0
$31$		0			0
$32$	−2.49133			−0.440409
$33$	−3.63957	−	11.2014i	−0.633568	−	1.94992i
$34$	4.45604	−	0.947161i	0.764205	−	0.162437i
$35$	−2.55197	+	1.85411i	−0.431361	+	0.313402i
$36$	0.938698	−	1.62587i	0.156450	−	0.270979i
$37$	−3.21787	−	5.57351i	−0.529014	−	0.916280i	−0.999427	−	0.0338334i	$-0.989228\pi$
$37$	−3.21787	−	5.57351i	−0.529014	−	0.916280i	0.470413	−	0.882446i	$-0.344105\pi$
$38$	−7.31371	−	3.25627i	−1.18644	−	0.528237i
$39$	2.64012	+	1.91816i	0.422758	+	0.307152i
$40$	7.29701	−	3.24884i	1.15376	−	0.513686i
$41$	−2.04245	−	0.434135i	−0.318976	−	0.0678005i	0.0456412	−	0.998958i	$-0.485467\pi$
$41$	−2.04245	−	0.434135i	−0.318976	−	0.0678005i	−0.364618	+	0.931157i	$0.618800\pi$
$42$	0.419936	+	3.99542i	0.0647975	+	0.616507i
$43$	−6.29858	+	6.99528i	−0.960524	+	1.06677i	0.0371980	+	0.999308i	$0.488157\pi$
$43$	−6.29858	+	6.99528i	−0.960524	+	1.06677i	−0.997722	+	0.0674619i	$0.978510\pi$
$44$	1.32299	+	1.46933i	0.199448	+	0.221509i
$45$	−1.14287	+	10.8736i	−0.170368	+	1.62095i
$46$	−1.51753	+	4.67048i	−0.223748	+	0.688624i
$47$	0.233002	−	0.717105i	0.0339868	−	0.104601i	−0.932624	−	0.360850i	$-0.882487\pi$
$47$	0.233002	−	0.717105i	0.0339868	−	0.104601i	0.966611	+	0.256249i	$0.0824867\pi$
$48$	0.811552	−	7.72140i	0.117137	−	1.11449i
$49$	−3.71306	−	4.12377i	−0.530437	−	0.589110i
$50$	−1.54790	+	1.71912i	−0.218906	+	0.243120i
$51$	−1.02443	−	9.74676i	−0.143448	−	1.36482i
$52$	−0.535856	−	0.113900i	−0.0743099	−	0.0157951i
$53$	−4.30646	+	1.91736i	−0.591537	+	0.263369i	−0.680598	−	0.732657i	$-0.738280\pi$
$53$	−4.30646	+	1.91736i	−0.591537	+	0.263369i	0.0890610	+	0.996026i	$0.471613\pi$
$54$	3.17068	+	2.30364i	0.431475	+	0.313485i
$55$	−10.5191	−	4.68342i	−1.41840	−	0.631512i
$56$	−1.83701	−	3.18180i	−0.245481	−	0.425185i
$57$	−8.61150	+	14.9156i	−1.14062	+	1.97561i
$58$	−1.35022	+	0.980990i	−0.177292	+	0.128810i
$59$	−3.90409	+	0.829840i	−0.508269	+	0.108036i	−0.454906	−	0.890539i	$-0.650327\pi$
$59$	−3.90409	+	0.829840i	−0.508269	+	0.108036i	−0.0533628	+	0.998575i	$0.516994\pi$
$60$	−0.974724	−	2.99989i	−0.125836	−	0.387284i
$61$	−2.21839			−0.284036			−0.142018	−	0.989864i	$-0.545359\pi$
$61$	−2.21839			−0.284036			−0.142018	+	0.989864i	$0.545359\pi$
$62$		0			0
$63$	5.02907			0.633603
$64$	2.74992	+	8.46340i	0.343741	+	1.05792i
$65$	3.12070	−	0.663326i	0.387076	−	0.0822755i
$66$	−11.8642	+	8.61984i	−1.46038	+	1.06103i
$67$	−6.00489	+	10.4008i	−0.733614	+	1.27066i	0.221715	+	0.975112i	$0.428835\pi$
$67$	−6.00489	+	10.4008i	−0.733614	+	1.27066i	−0.955329	+	0.295545i	$0.904499\pi$
$68$	0.822608	+	1.42480i	0.0997559	+	0.172782i
$69$	9.65130	+	4.29704i	1.16188	+	0.517302i
$70$	3.17751	+	2.30860i	0.379786	+	0.275930i
$71$	−6.87245	+	3.05981i	−0.815609	+	0.363133i	−0.771767	−	0.635906i	$-0.780627\pi$
$71$	−6.87245	+	3.05981i	−0.815609	+	0.363133i	−0.0438425	+	0.999038i	$0.513960\pi$
$72$	−12.4563	−	2.64767i	−1.46799	−	0.312031i
$73$	−1.03736	−	9.86983i	−0.121414	−	1.15518i	−0.870315	−	0.492495i	$-0.836085\pi$
$73$	−1.03736	−	9.86983i	−0.121414	−	1.15518i	0.748901	−	0.662681i	$-0.230582\pi$
$74$	−5.36194	+	5.95503i	−0.623313	+	0.692259i
$75$	3.32999	+	3.69833i	0.384515	+	0.427047i
$76$	0.302218	−	2.87541i	0.0346668	−	0.329833i
$77$	−1.63666	+	5.03713i	−0.186515	+	0.574034i
$78$	1.25563	−	3.86443i	0.142172	−	0.437560i
$79$	0.988929	−	9.40903i	0.111263	−	1.05860i	−0.786340	−	0.617794i	$-0.788027\pi$
$79$	0.988929	−	9.40903i	0.111263	−	1.05860i	0.897603	−	0.440804i	$-0.145307\pi$
$80$	−5.07895	−	5.64075i	−0.567844	−	0.630655i
$81$	−2.73937	+	3.04238i	−0.304374	+	0.338042i
$82$	0.271765	+	2.58567i	0.0300114	+	0.285539i
$83$	−5.48687	−	1.16627i	−0.602262	−	0.128015i	−0.103317	−	0.994648i	$-0.532946\pi$
$83$	−5.48687	−	1.16627i	−0.602262	−	0.128015i	−0.498945	+	0.866634i	$0.666279\pi$
$84$	−1.32543	+	0.590119i	−0.144616	+	0.0643873i
$85$	−7.75149	−	5.63178i	−0.840767	−	0.610853i
$86$	10.7072	+	4.76713i	1.15458	+	0.514053i
$87$	1.79522	+	3.10941i	0.192468	+	0.333364i
$88$	6.70570	−	11.6146i	0.714830	−	1.23812i
$89$	11.2812	−	8.19625i	1.19580	−	0.868800i	0.201936	−	0.979399i	$-0.435277\pi$
$89$	11.2812	−	8.19625i	1.19580	−	0.868800i	0.993865	+	0.110598i	$0.0352767\pi$
$90$	13.3161	−	2.83043i	1.40364	−	0.298353i
$91$	−0.453480	−	1.39567i	−0.0475376	−	0.146306i
$92$	−1.77351			−0.184901
$93$		0			0
$94$	−0.938835			−0.0968334
$95$	5.20323	+	16.0139i	0.533840	+	1.64299i
$96$	6.52753	−	1.38747i	0.666213	−	0.141608i
$97$	3.64843	−	2.65074i	0.370441	−	0.269141i	−0.386953	−	0.922100i	$-0.626472\pi$
$97$	3.64843	−	2.65074i	0.370441	−	0.269141i	0.757394	+	0.652958i	$0.226472\pi$
$98$	−3.45464	+	5.98362i	−0.348972	+	0.604437i
$99$	9.17888	+	15.8983i	0.922512	+	1.59784i
$100$	−0.763203	−	0.339800i	−0.0763203	−	0.0339800i
$101$	−1.52813	−	1.11025i	−0.152055	−	0.110474i	0.509157	−	0.860674i	$-0.329957\pi$
$101$	−1.52813	−	1.11025i	−0.152055	−	0.110474i	−0.661211	+	0.750200i	$0.729957\pi$
$102$	−11.1478	+	4.96331i	−1.10379	+	0.491441i
$103$	−11.0442	−	2.34752i	−1.08822	−	0.231308i	−0.371334	−	0.928499i	$-0.621099\pi$
$103$	−11.0442	−	2.34752i	−1.08822	−	0.231308i	−0.716885	+	0.697191i	$0.754433\pi$
$104$	0.388425	+	3.69562i	0.0380882	+	0.362385i
$105$	5.65382	−	6.27920i	0.551756	−	0.612787i
$106$	3.92747	+	4.36190i	0.381470	+	0.423665i
$107$	−0.506156	+	4.81576i	−0.0489320	+	0.465557i	0.942430	+	0.334403i	$0.108535\pi$
$107$	−0.506156	+	4.81576i	−0.0489320	+	0.465557i	−0.991362	+	0.131153i	$0.958132\pi$
$108$	−0.437377	+	1.34611i	−0.0420866	+	0.129529i
$109$	−3.93566	+	12.1127i	−0.376968	+	1.16019i	0.565174	+	0.824972i	$0.308809\pi$
$109$	−3.93566	+	12.1127i	−0.376968	+	1.16019i	−0.942141	+	0.335216i	$0.891191\pi$
$110$	−1.49864	+	14.2586i	−0.142889	+	1.35950i
$111$	11.5351	+	12.8111i	1.09487	+	1.21597i
$112$	−2.33615	+	2.59456i	−0.220746	+	0.245163i
$113$	−0.934694	−	8.89302i	−0.0879286	−	0.836585i	−0.946242	−	0.323459i	$-0.895154\pi$
$113$	−0.934694	−	8.89302i	−0.0879286	−	0.836585i	0.858313	−	0.513126i	$-0.171513\pi$
$114$	20.9761	+	4.45862i	1.96460	+	0.417588i
$115$	9.43556	−	4.20098i	0.879870	−	0.391743i
$116$	−0.487620	−	0.354277i	−0.0452744	−	0.0328938i
$117$	−4.64674	−	2.06886i	−0.429591	−	0.191266i
$118$	2.48484	+	4.30386i	0.228748	+	0.396203i
$119$	−2.20356	+	3.81667i	−0.202000	+	0.349874i
$120$	−17.3096	+	12.5761i	−1.58014	+	1.14804i
$121$	−8.15131	+	1.73261i	−0.741028	+	0.157510i
$122$	0.853558	+	2.62698i	0.0772775	+	0.237836i
$123$	5.59319			0.504321
$124$		0			0
$125$	−8.22843			−0.735973
$126$	−1.93501	−	5.95534i	−0.172384	−	0.530544i
$127$	−4.98687	+	1.05999i	−0.442513	+	0.0940590i	−0.423779	−	0.905766i	$-0.639297\pi$
$127$	−4.98687	+	1.05999i	−0.442513	+	0.0940590i	−0.0187336	+	0.999825i	$0.505963\pi$
$128$	4.93309	−	3.58410i	0.436027	−	0.316793i
$129$	12.6071	−	21.8361i	1.10999	−	1.92256i
$130$	−1.98624	−	3.44026i	−0.174204	−	0.301731i
$131$	2.53461	+	1.12848i	0.221450	+	0.0985959i	0.514463	−	0.857513i	$-0.327991\pi$
$131$	2.53461	+	1.12848i	0.221450	+	0.0985959i	−0.293013	+	0.956108i	$0.594658\pi$
$132$	−4.28466	−	3.11299i	−0.372932	−	0.270951i
$133$	7.07534	−	3.15015i	0.613510	−	0.273152i
$134$	14.6269	+	3.10904i	1.26357	+	0.268580i
$135$	−0.861613	−	8.19770i	−0.0741558	−	0.705546i
$136$	7.46728	−	8.29326i	0.640314	−	0.711141i
$137$	−6.91986	−	7.68529i	−0.591204	−	0.656598i	0.371094	−	0.928595i	$-0.378983\pi$
$137$	−6.91986	−	7.68529i	−0.591204	−	0.656598i	−0.962298	+	0.271997i	$0.912316\pi$
$138$	1.37500	−	13.0823i	0.117048	−	1.11364i
$139$	−0.0991287	+	0.305087i	−0.00840799	+	0.0258771i	−0.955172	−	0.296050i	$-0.904331\pi$
$139$	−0.0991287	+	0.305087i	−0.00840799	+	0.0258771i	0.946765	+	0.321927i	$0.104331\pi$
$140$	−0.438319	+	1.34901i	−0.0370447	+	0.114012i
$141$	−0.211118	+	2.00865i	−0.0177793	+	0.169159i
$142$	6.26765	+	6.96093i	0.525969	+	0.584148i
$143$	3.58441	−	3.98090i	0.299744	−	0.332899i
$144$	1.26493	+	12.0350i	0.105411	+	1.00292i
$145$	3.43347	+	0.729806i	0.285134	+	0.0606071i
$146$	−11.2885	+	5.02599i	−0.934247	+	0.415954i
$147$	12.0252	+	8.73681i	0.991821	+	0.720600i
$148$	−2.64374	−	1.17707i	−0.217314	−	0.0967546i
$149$	−10.9051	−	18.8882i	−0.893382	−	1.54738i	−0.835795	−	0.549042i	$-0.814993\pi$
$149$	−10.9051	−	18.8882i	−0.893382	−	1.54738i	−0.0575872	−	0.998340i	$-0.518341\pi$
$150$	3.09824	−	5.36631i	0.252970	−	0.438157i
$151$	2.89262	−	2.10161i	0.235398	−	0.171027i	−0.463832	−	0.885923i	$-0.653526\pi$
$151$	2.89262	−	2.10161i	0.235398	−	0.171027i	0.699231	+	0.714896i	$0.253526\pi$
$152$	−19.1831	+	4.07750i	−1.55596	+	0.330729i
$153$	4.72041	+	14.5279i	0.381623	+	1.17451i
$154$	6.59461			0.531409
$155$		0			0
$156$	1.46743			0.117488
$157$	−5.60402	−	17.2474i	−0.447249	−	1.37649i	−0.879998	−	0.474977i	$-0.842456\pi$
$157$	−5.60402	−	17.2474i	−0.447249	−	1.37649i	0.432749	−	0.901515i	$-0.357544\pi$
$158$	−11.5225	+	2.44919i	−0.916682	+	0.194847i
$159$	10.2155	−	7.42202i	0.810145	−	0.588604i
$160$	3.26209	−	5.65010i	0.257891	−	0.446680i
$161$	−2.37539	−	4.11429i	−0.187207	−	0.324252i
$162$	4.65674	+	2.07332i	0.365868	+	0.162895i
$163$	6.36032	+	4.62104i	0.498179	+	0.361948i	0.808321	−	0.588742i	$-0.200377\pi$
$163$	6.36032	+	4.62104i	0.498179	+	0.361948i	−0.310142	+	0.950690i	$0.600377\pi$
$164$	−0.857762	+	0.381900i	−0.0669800	+	0.0298214i
$165$	30.1694	+	6.41271i	2.34869	+	0.499229i
$166$	0.730075	+	6.94620i	0.0566648	+	0.539130i
$167$	13.2311	−	14.6946i	1.02385	−	1.13710i	0.0333715	−	0.999443i	$-0.489376\pi$
$167$	13.2311	−	14.6946i	1.02385	−	1.13710i	0.990480	−	0.137659i	$-0.0439578\pi$
$168$	6.58516	+	7.31356i	0.508056	+	0.564253i
$169$	1.20372	−	11.4527i	0.0925942	−	0.880975i
$170$	−3.68657	+	11.3461i	−0.282747	+	0.870205i
$171$	8.29550	−	25.5309i	0.634373	−	1.95240i
$172$	−0.442442	+	4.20956i	−0.0337359	+	0.320976i
$173$	10.8040	+	11.9991i	0.821413	+	0.912271i	0.997396	−	0.0721219i	$-0.0229771\pi$
$173$	10.8040	+	11.9991i	0.821413	+	0.912271i	−0.175983	+	0.984393i	$0.556310\pi$
$174$	2.99137	−	3.32226i	0.226775	−	0.251860i
$175$	−0.233925	−	2.22564i	−0.0176830	−	0.168243i
$176$	−12.4660	−	2.64973i	−0.939660	−	0.199731i
$177$	9.76695	−	4.34853i	0.734129	−	0.326855i
$178$	−14.0464	−	10.2053i	−1.05283	−	0.764923i
$179$	−3.61759	−	1.61065i	−0.270391	−	0.120386i	0.267062	−	0.963679i	$-0.413947\pi$
$179$	−3.61759	−	1.61065i	−0.270391	−	0.120386i	−0.537454	+	0.843293i	$0.680614\pi$
$180$	2.45822	+	4.25777i	0.183225	+	0.317355i
$181$	10.2011	−	17.6688i	0.758239	−	1.31331i	−0.185508	−	0.982643i	$-0.559393\pi$
$181$	10.2011	−	17.6688i	0.758239	−	1.31331i	0.943748	−	0.330667i	$-0.107274\pi$
$182$	−1.47824	+	1.07401i	−0.109575	+	0.0796106i
$183$	5.81240	−	1.23546i	0.429665	−	0.0913282i
$184$	3.71744	+	11.4411i	0.274053	+	0.843450i
$185$	16.8536			1.23910
$186$		0			0
$187$	−16.0874			−1.17643
$188$	−0.104773	−	0.322458i	−0.00764136	−	0.0235177i
$189$	−3.70859	+	0.788286i	−0.269761	+	0.0573394i
$190$	16.9614	−	12.3231i	1.23051	−	0.894015i
$191$	−9.50926	+	16.4705i	−0.688066	+	1.19176i	0.284397	+	0.958707i	$0.408207\pi$
$191$	−9.50926	+	16.4705i	−0.688066	+	1.19176i	−0.972463	+	0.233058i	$0.925127\pi$
$192$	−11.9185	−	20.6435i	−0.860144	−	1.48981i
$193$	−19.3100	−	8.59738i	−1.38997	−	0.618853i	−0.430995	−	0.902354i	$-0.641837\pi$
$193$	−19.3100	−	8.59738i	−1.38997	−	0.618853i	−0.958972	+	0.283501i	$0.908504\pi$
$194$	−4.54274	−	3.30049i	−0.326150	−	0.236962i
$195$	−7.80714	+	3.47596i	−0.559081	+	0.248919i
$196$	−2.44071	−	0.518789i	−0.174336	−	0.0370563i
$197$	−0.667062	−	6.34667i	−0.0475262	−	0.452182i	−0.992245	−	0.124299i	$-0.960332\pi$
$197$	−0.667062	−	6.34667i	−0.0475262	−	0.452182i	0.944719	−	0.327882i	$-0.106335\pi$
$198$	15.2948	−	16.9866i	1.08695	−	1.20718i
$199$	−10.3453	−	11.4896i	−0.733360	−	0.814478i	0.254947	−	0.966955i	$-0.417942\pi$
$199$	−10.3453	−	11.4896i	−0.733360	−	0.814478i	−0.988307	+	0.152477i	$0.951275\pi$
$200$	−0.592343	+	5.63576i	−0.0418850	+	0.398509i
$201$	9.94102	−	30.5953i	0.701185	−	2.15803i
$202$	−0.726771	+	2.23677i	−0.0511354	+	0.157379i
$203$	0.168768	−	1.60572i	0.0118452	−	0.112700i
$204$	−2.94881	−	3.27499i	−0.206458	−	0.229295i
$205$	3.65891	−	4.06363i	0.255550	−	0.283817i
$206$	1.46953	+	13.9816i	0.102387	+	0.974145i
$207$	−16.1069	−	3.42363i	−1.11951	−	0.237959i
$208$	3.22590	−	1.43627i	0.223676	−	0.0995871i
$209$	22.8722	+	16.6176i	1.58210	+	1.14946i
$210$	−9.61111	−	4.27914i	−0.663230	−	0.295289i
$211$	13.3454	+	23.1150i	0.918738	+	1.59130i	0.801335	+	0.598216i	$0.204123\pi$
$211$	13.3454	+	23.1150i	0.918738	+	1.59130i	0.117402	+	0.993084i	$0.462543\pi$
$212$	−1.05987	+	1.83574i	−0.0727918	+	0.126079i
$213$	16.3024	−	11.8444i	1.11702	−	0.811565i
$214$	5.89749	−	1.25355i	0.403144	−	0.0856909i
$215$	−7.61744	−	23.4441i	−0.519505	−	1.59887i
$216$	9.60068			0.653244
$217$		0			0
$218$	15.8580			1.07404
$219$	8.21469	+	25.2822i	0.555097	+	1.70841i
$220$	−5.06459	+	1.07651i	−0.341455	+	0.0725785i
$221$	3.60614	−	2.62002i	0.242575	−	0.176241i
$222$	10.7323	−	18.5890i	0.720307	−	1.24761i
$223$	6.33493	+	10.9724i	0.424218	+	0.734768i	0.996347	−	0.0853960i	$-0.0272155\pi$
$223$	6.33493	+	10.9724i	0.424218	+	0.734768i	−0.572129	+	0.820164i	$0.693882\pi$
$224$	−2.74147	−	1.22058i	−0.183172	−	0.0815534i
$225$	−6.27541	−	4.55935i	−0.418360	−	0.303957i
$226$	−10.1713	+	4.52857i	−0.676587	+	0.301236i
$227$	11.3241	+	2.40700i	0.751604	+	0.159758i	0.567757	−	0.823196i	$-0.307811\pi$
$227$	11.3241	+	2.40700i	0.751604	+	0.159758i	0.183847	+	0.982955i	$0.441145\pi$
$228$	0.809532	+	7.70218i	0.0536126	+	0.510089i
$229$	−19.2250	+	21.3515i	−1.27042	+	1.41095i	−0.401608	+	0.915812i	$0.631549\pi$
$229$	−19.2250	+	21.3515i	−1.27042	+	1.41095i	−0.868815	+	0.495136i	$0.835118\pi$
$230$	−8.60520	−	9.55704i	−0.567410	−	0.630172i
$231$	1.48294	−	14.1093i	0.0975705	−	0.928322i
$232$	−1.26338	+	3.88830i	−0.0829452	+	0.255279i
$233$	3.53689	−	10.8854i	0.231709	−	0.713127i	−0.765832	−	0.643041i	$-0.777672\pi$
$233$	3.53689	−	10.8854i	0.231709	−	0.713127i	0.997541	−	0.0700864i	$-0.0223275\pi$
$234$	−0.662011	+	6.29862i	−0.0432770	+	0.411753i
$235$	1.32124	+	1.46739i	0.0861884	+	0.0957219i
$236$	−1.20093	+	1.33377i	−0.0781738	+	0.0868208i
$237$	2.64898	+	25.2033i	0.172070	+	1.63713i
$238$	5.36749	+	1.14090i	0.347923	+	0.0739533i
$239$	−23.0350	+	10.2559i	−1.49001	+	0.663397i	−0.980402	−	0.197008i	$-0.936878\pi$
$239$	−23.0350	+	10.2559i	−1.49001	+	0.663397i	−0.509611	+	0.860405i	$0.670211\pi$
$240$	16.4488	+	11.9508i	1.06177	+	0.771418i
$241$	9.48052	+	4.22100i	0.610694	+	0.271899i	0.688691	−	0.725055i	$-0.258186\pi$
$241$	9.48052	+	4.22100i	0.610694	+	0.271899i	−0.0779968	+	0.996954i	$0.524852\pi$
$242$	5.18807	+	8.98600i	0.333502	+	0.577642i
$243$	10.2045	−	17.6747i	0.654619	−	1.13383i
$244$	−0.807024	+	0.586337i	−0.0516644	+	0.0375364i
$245$	14.2141	−	3.02131i	0.908107	−	0.193024i
$246$	−2.15206	−	6.62336i	−0.137210	−	0.422290i
$247$	−7.83336			−0.498425
$248$		0			0
$249$	15.0257			0.952213
$250$	3.16601	+	9.74397i	0.200236	+	0.616263i
$251$	−1.44478	+	0.307098i	−0.0911939	+	0.0193839i	−0.253283	−	0.967392i	$-0.581510\pi$
$251$	−1.44478	+	0.307098i	−0.0911939	+	0.0193839i	0.162089	+	0.986776i	$0.448177\pi$
$252$	1.82951	−	1.32922i	0.115249	−	0.0837330i
$253$	8.67095	−	15.0185i	0.545138	−	0.944206i
$254$	3.17399	+	5.49752i	0.199154	+	0.344945i
$255$	23.4461	+	10.4389i	1.46825	+	0.653708i
$256$	8.25649	+	5.99869i	0.516030	+	0.374918i
$257$	15.4064	−	6.85935i	0.961022	−	0.427875i	0.134584	−	0.990902i	$-0.457030\pi$
$257$	15.4064	−	6.85935i	0.961022	−	0.427875i	0.826438	+	0.563028i	$0.190364\pi$
$258$	−30.7087	−	6.52734i	−1.91184	−	0.406375i
$259$	−0.810317	−	7.70965i	−0.0503507	−	0.479055i
$260$	0.959953	−	1.06614i	0.0595337	−	0.0661189i
$261$	−3.74464	−	4.15884i	−0.231787	−	0.257426i
$262$	0.361101	−	3.43564i	0.0223089	−	0.212255i
$263$	−7.25651	+	22.3332i	−0.447455	+	1.37713i	0.432313	+	0.901724i	$0.357698\pi$
$263$	−7.25651	+	22.3332i	−0.447455	+	1.37713i	−0.879768	+	0.475403i	$0.842302\pi$
$264$	−11.1012	+	34.1660i	−0.683231	+	2.10277i
$265$	1.29039	−	12.2772i	0.0792678	−	0.754182i
$266$	−6.45269	−	7.16644i	−0.395640	−	0.439403i
$267$	−24.9931	+	27.7577i	−1.52955	+	1.69874i
$268$	0.564495	+	5.37081i	0.0344820	+	0.328075i
$269$	12.8362	+	2.72842i	0.782637	+	0.166355i	0.581867	−	0.813284i	$-0.302322\pi$
$269$	12.8362	+	2.72842i	0.782637	+	0.166355i	0.200770	+	0.979638i	$0.435656\pi$
$270$	−9.37606	+	4.17449i	−0.570609	+	0.254051i
$271$	−9.11186	−	6.62016i	−0.553506	−	0.402146i	0.275570	−	0.961281i	$-0.411133\pi$
$271$	−9.11186	−	6.62016i	−0.553506	−	0.402146i	−0.829077	+	0.559135i	$0.811133\pi$
$272$	−9.68792	−	4.31334i	−0.587417	−	0.261535i
$273$	1.96544	+	3.40423i	0.118954	+	0.206034i
$274$	−6.43827	+	11.1514i	−0.388950	+	0.673681i
$275$	6.60893	−	4.80167i	0.398533	−	0.289551i
$276$	4.64677	−	0.987701i	0.279703	−	0.0594526i
$277$	−0.689671	−	2.12259i	−0.0414383	−	0.127534i	0.928197	−	0.372089i	$-0.121358\pi$
$277$	−0.689671	−	2.12259i	−0.0414383	−	0.127534i	−0.969636	+	0.244555i	$0.921358\pi$
$278$	0.399420			0.0239556
$279$		0			0
$280$	9.62137			0.574987
$281$	−1.64907	−	5.07532i	−0.0983754	−	0.302768i	0.889743	−	0.456461i	$-0.150883\pi$
$281$	−1.64907	−	5.07532i	−0.0983754	−	0.302768i	−0.988119	+	0.153693i	$0.950883\pi$
$282$	2.45984	−	0.522855i	0.146481	−	0.0311356i
$283$	−9.57350	+	6.95556i	−0.569086	+	0.413465i	−0.834773	−	0.550594i	$-0.814401\pi$
$283$	−9.57350	+	6.95556i	−0.569086	+	0.413465i	0.265687	+	0.964059i	$0.414401\pi$
$284$	−1.69138	+	2.92956i	−0.100365	+	0.173837i
$285$	−22.5514	−	39.0602i	−1.33583	−	2.31373i
$286$	−6.09326	−	2.71290i	−0.360302	−	0.160417i
$287$	−2.03482	−	1.47838i	−0.120112	−	0.0872662i
$288$	−9.50224	+	4.23067i	−0.559925	+	0.249295i
$289$	3.53461	+	0.751305i	0.207918	+	0.0441944i
$290$	−0.456852	−	4.34666i	−0.0268273	−	0.255245i
$291$	−8.08299	+	8.97707i	−0.473833	+	0.526245i
$292$	−2.98605	−	3.31634i	−0.174745	−	0.194074i
$293$	−2.79467	+	26.5895i	−0.163266	+	1.55338i	0.539519	+	0.841974i	$0.318606\pi$
$293$	−2.79467	+	26.5895i	−0.163266	+	1.55338i	−0.702785	+	0.711402i	$0.748060\pi$
$294$	5.71912	−	17.6016i	0.333546	−	1.02655i
$295$	3.22993	−	9.94070i	0.188054	−	0.578770i
$296$	−2.05188	+	19.5224i	−0.119263	+	1.13471i
$297$	−9.26079	−	10.2851i	−0.537365	−	0.596805i
$298$	−18.1712	+	20.1812i	−1.05263	+	1.16906i
$299$	0.502261	+	4.77870i	0.0290465	+	0.276359i
$300$	2.18891	+	0.465267i	0.126377	+	0.0268622i
$301$	−10.3582	+	4.61176i	−0.597036	+	0.265818i
$302$	−3.60168	−	2.61677i	−0.207253	−	0.150578i
$303$	4.62217	+	2.05792i	0.265537	+	0.118225i
$304$	9.31823	+	16.1396i	0.534437	+	0.925672i
$305$	2.90471	−	5.03111i	0.166323	−	0.288080i
$306$	15.3875	−	11.1797i	0.879644	−	0.639099i
$307$	13.9402	−	2.96309i	0.795610	−	0.169112i	0.207864	−	0.978158i	$-0.433349\pi$
$307$	13.9402	−	2.96309i	0.795610	−	0.169112i	0.587746	+	0.809045i	$0.300015\pi$
$308$	0.735952	+	2.26503i	0.0419348	+	0.129062i
$309$	30.2443			1.72054
$310$		0			0
$311$	20.2466			1.14808			0.574040	−	0.818827i	$-0.305375\pi$
$311$	20.2466			1.14808			0.574040	+	0.818827i	$0.305375\pi$
$312$	−3.07587	−	9.46656i	−0.174137	−	0.535939i
$313$	−8.84833	+	1.88077i	−0.500137	+	0.106307i	−0.451071	−	0.892488i	$-0.648958\pi$
$313$	−8.84833	+	1.88077i	−0.500137	+	0.106307i	−0.0490661	+	0.998796i	$0.515624\pi$
$314$	−18.2678	+	13.2724i	−1.03091	+	0.749003i
$315$	−6.58495	+	11.4055i	−0.371020	+	0.642626i
$316$	−2.12712	−	3.68427i	−0.119660	−	0.207257i
$317$	−27.4518	−	12.2223i	−1.54184	−	0.686473i	−0.552695	−	0.833384i	$-0.686400\pi$
$317$	−27.4518	−	12.2223i	−1.54184	−	0.686473i	−0.989150	+	0.146910i	$0.953067\pi$
$318$	−12.7196	−	9.24133i	−0.713280	−	0.518228i
$319$	5.38416	−	2.39718i	0.301455	−	0.134216i
$320$	−22.7949	−	4.84521i	−1.27427	−	0.270855i
$321$	−1.35581	−	12.8997i	−0.0756738	−	0.719988i
$322$	−3.95811	+	4.39593i	−0.220577	+	0.244975i
$323$	15.7412	+	17.4824i	0.875865	+	0.972746i
$324$	−0.192427	+	1.83082i	−0.0106904	+	0.101712i
$325$	−0.699446	+	2.15267i	−0.0387983	+	0.119409i
$326$	3.02494	−	9.30980i	0.167536	−	0.515622i
$327$	3.56602	−	33.9284i	0.197201	−	1.87624i
$328$	4.26164	+	4.73303i	0.235310	+	0.261338i
$329$	0.607729	−	0.674951i	0.0335052	−	0.0372113i
$330$	−4.01430	−	38.1935i	−0.220980	−	2.10248i
$331$	14.9330	+	3.17412i	0.820794	+	0.174465i	0.599124	−	0.800656i	$-0.295516\pi$
$331$	14.9330	+	3.17412i	0.820794	+	0.174465i	0.221670	+	0.975122i	$0.428849\pi$
$332$	−2.30431	+	1.02595i	−0.126466	+	0.0563061i
$333$	−21.7381	−	15.7936i	−1.19124	−	0.865486i
$334$	−22.4919	−	10.0141i	−1.23070	−	0.547945i
$335$	−15.7253	−	27.2371i	−0.859167	−	1.48812i
$336$	4.67600	−	8.09906i	0.255096	−	0.441840i
$337$	−6.65928	+	4.83825i	−0.362754	+	0.263556i	−0.754200	−	0.656645i	$-0.771975\pi$
$337$	−6.65928	+	4.83825i	−0.362754	+	0.263556i	0.391446	+	0.920201i	$0.371975\pi$
$338$	−14.0252	+	2.98115i	−0.762871	+	0.162153i
$339$	7.40169	+	22.7801i	0.402005	+	1.23724i
$340$	−4.30842			−0.233657
$341$		0			0
$342$	−33.4251			−1.80742
$343$	−4.67107	−	14.3761i	−0.252214	−	0.776235i
$344$	28.0838	−	5.96939i	1.51418	−	0.321848i
$345$	−22.3825	+	16.2618i	−1.20503	+	0.875508i
$346$	10.0521	−	17.4107i	0.540403	−	0.936006i
$347$	1.74062	+	3.01484i	0.0934413	+	0.161845i	0.908957	−	0.416890i	$-0.136880\pi$
$347$	1.74062	+	3.01484i	0.0934413	+	0.161845i	−0.815516	+	0.578735i	$0.803547\pi$
$348$	1.47492	+	0.656676i	0.0790639	+	0.0352015i
$349$	14.3592	+	10.4326i	0.768632	+	0.558444i	0.901546	−	0.432684i	$-0.142433\pi$
$349$	14.3592	+	10.4326i	0.768632	+	0.558444i	−0.132914	+	0.991128i	$0.542433\pi$
$350$	−2.54556	+	1.13336i	−0.136066	+	0.0605805i
$351$	3.75094	+	0.797287i	0.200210	+	0.0425560i
$352$	−1.14504	−	10.8943i	−0.0610307	−	0.580668i
$353$	3.41121	−	3.78854i	0.181561	−	0.201643i	−0.645494	−	0.763766i	$-0.723348\pi$
$353$	3.41121	−	3.78854i	0.181561	−	0.201643i	0.827054	+	0.562122i	$0.190015\pi$
$354$	−8.90743	−	9.89270i	−0.473424	−	0.525791i
$355$	2.05926	−	19.5925i	0.109294	−	1.03986i
$356$	1.93762	−	5.96339i	0.102694	−	0.316059i
$357$	3.64796	−	11.2273i	0.193071	−	0.594210i
$358$	−0.515390	+	4.90361i	−0.0272392	+	0.259164i
$359$	−5.19039	−	5.76451i	−0.273938	−	0.304239i	0.590440	−	0.807082i	$-0.298954\pi$
$359$	−5.19039	−	5.76451i	−0.273938	−	0.304239i	−0.864378	+	0.502842i	$0.832288\pi$
$360$	22.3147	−	24.7830i	1.17609	−	1.30618i
$361$	−2.33536	−	22.2195i	−0.122914	−	1.16945i
$362$	−24.8481	−	5.28162i	−1.30599	−	0.277596i
$363$	20.3923	−	9.07925i	1.07032	−	0.476537i
$364$	−0.533855	−	0.387869i	−0.0279816	−	0.0203298i
$365$	23.7422	+	10.5707i	1.24272	+	0.553296i
$366$	−3.69942	−	6.40759i	−0.193372	−	0.334930i
$367$	−15.1302	+	26.2063i	−0.789791	+	1.36796i	0.136303	+	0.990667i	$0.456478\pi$
$367$	−15.1302	+	26.2063i	−0.789791	+	1.36796i	−0.926095	+	0.377291i	$0.876856\pi$
$368$	9.24843	−	6.71938i	0.482108	−	0.350272i
$369$	−8.52738	+	1.81255i	−0.443918	+	0.0943576i
$370$	−6.48468	−	19.9578i	−0.337122	−	1.03756i
$371$	−5.67822			−0.294798
$372$		0			0
$373$	−11.6354			−0.602458			−0.301229	−	0.953552i	$-0.597397\pi$
$373$	−11.6354			−0.602458			−0.301229	+	0.953552i	$0.597397\pi$
$374$	6.18987	+	19.0505i	0.320071	+	0.985076i
$375$	21.5593	−	4.58257i	1.11332	−	0.236643i
$376$	−1.86060	+	1.35181i	−0.0959533	+	0.0697141i
$377$	−0.816501	+	1.41422i	−0.0420519	+	0.0728361i
$378$	2.36041	+	4.08835i	0.121406	+	0.210282i
$379$	31.2003	+	13.8913i	1.60265	+	0.713547i	0.996640	−	0.0819068i	$-0.0261010\pi$
$379$	31.2003	+	13.8913i	1.60265	+	0.713547i	0.606014	+	0.795454i	$0.292768\pi$
$380$	6.12546	+	4.45041i	0.314229	+	0.228301i
$381$	12.4758	−	5.55457i	0.639153	−	0.284569i
$382$	23.1629	+	4.92343i	1.18512	+	0.251905i
$383$	−0.0612924	−	0.583158i	−0.00313190	−	0.0297980i	0.992844	−	0.119416i	$-0.0381021\pi$
$383$	−0.0612924	−	0.583158i	−0.00313190	−	0.0297980i	−0.995976	+	0.0896177i	$0.971435\pi$
$384$	−10.9291	+	12.1380i	−0.557725	+	0.619416i
$385$	−9.28074	−	10.3073i	−0.472990	−	0.525309i
$386$	−2.75106	+	26.1746i	−0.140025	+	1.33225i
$387$	−12.1445	+	37.3769i	−0.617339	+	1.89997i
$388$	0.626644	−	1.92861i	0.0318130	−	0.0979104i
$389$	−1.94571	+	18.5122i	−0.0986516	+	0.938607i	0.827503	+	0.561462i	$0.189761\pi$
$389$	−1.94571	+	18.5122i	−0.0986516	+	0.938607i	−0.926154	+	0.377145i	$0.876906\pi$
$390$	7.12008	+	7.90765i	0.360539	+	0.400420i
$391$	9.65574	−	10.7238i	0.488312	−	0.542325i
$392$	1.76919	+	16.8327i	0.0893577	+	0.850181i
$393$	−7.26941	−	1.54516i	−0.366693	−	0.0779430i
$394$	−7.25896	+	3.23190i	−0.365701	+	0.162821i
$395$	20.0439	+	14.5628i	1.00852	+	0.732733i
$396$	7.54120	+	3.35756i	0.378960	+	0.168724i
$397$	−6.98331	−	12.0954i	−0.350482	−	0.607053i	0.635852	−	0.771811i	$-0.280649\pi$
$397$	−6.98331	−	12.0954i	−0.350482	−	0.607053i	−0.986334	+	0.164758i	$0.947316\pi$
$398$	−9.62532	+	16.6715i	−0.482474	+	0.835669i
$399$	−16.7837	+	12.1941i	−0.840238	+	0.610468i
$400$	5.26734	−	1.11961i	0.263367	−	0.0559804i
$401$	−1.09621	−	3.37379i	−0.0547421	−	0.168479i	0.919947	−	0.392042i	$-0.128231\pi$
$401$	−1.09621	−	3.37379i	−0.0547421	−	0.168479i	−0.974690	+	0.223563i	$0.928231\pi$
$402$	−40.0554			−1.99778
$403$		0			0
$404$	−0.849363			−0.0422574
$405$	−3.31297	−	10.1963i	−0.164623	−	0.506656i
$406$	−1.96640	+	0.417972i	−0.0975910	+	0.0207436i
$407$	22.8934	−	16.6330i	1.13478	−	0.824469i
$408$	−14.9464	+	25.8878i	−0.739955	+	1.28164i
$409$	8.56426	+	14.8337i	0.423476	+	0.733481i	0.996277	−	0.0862131i	$-0.0274766\pi$
$409$	8.56426	+	14.8337i	0.423476	+	0.733481i	−0.572801	+	0.819694i	$0.694143\pi$
$410$	−6.21991	−	2.76928i	−0.307179	−	0.136765i
$411$	22.4108	+	16.2824i	1.10544	+	0.803152i
$412$	−4.63822	+	2.06507i	−0.228509	+	0.101739i
$413$	−4.70264	−	0.999578i	−0.231402	−	0.0491860i
$414$	2.14316	+	20.3908i	0.105331	+	1.00215i
$415$	9.82938	−	10.9166i	0.482505	−	0.535877i
$416$	2.03093	+	2.25557i	0.0995745	+	0.110589i
$417$	0.0898184	−	0.854565i	0.00439842	−	0.0418482i
$418$	10.8779	−	33.4787i	0.532055	−	1.63750i
$419$	−5.62933	+	17.3253i	−0.275011	+	0.846396i	0.714206	+	0.699936i	$0.246788\pi$
$419$	−5.62933	+	17.3253i	−0.275011	+	0.846396i	−0.989217	+	0.146461i	$0.953212\pi$
$420$	0.397152	−	3.77864i	0.0193790	−	0.184379i
$421$	−2.33391	−	2.59207i	−0.113748	−	0.126330i	0.683582	−	0.729874i	$-0.260421\pi$
$421$	−2.33391	−	2.59207i	−0.113748	−	0.126330i	−0.797329	+	0.603544i	$0.793755\pi$
$422$	22.2375	−	24.6973i	1.08250	−	1.20224i
$423$	−0.329061	−	3.13081i	−0.0159995	−	0.152225i
$424$	14.0642	+	2.98943i	0.683016	+	0.145180i
$425$	6.20985	−	2.76481i	0.301222	−	0.134113i
$426$	−20.2985	−	14.7478i	−0.983467	−	0.714531i
$427$	−2.44113	−	1.08686i	−0.118134	−	0.0525968i
$428$	1.08871	+	1.88570i	0.0526246	+	0.0911485i
$429$	−7.17449	+	12.4266i	−0.346387	+	0.599961i
$430$	−24.8311	+	18.0409i	−1.19746	+	0.870009i
$431$	−13.9100	+	2.95666i	−0.670021	+	0.142417i	−0.530348	−	0.847780i	$-0.677939\pi$
$431$	−13.9100	+	2.95666i	−0.670021	+	0.142417i	−0.139674	+	0.990198i	$0.544605\pi$
$432$	−2.81925	−	8.67675i	−0.135641	−	0.417460i
$433$	−32.1386			−1.54448			−0.772242	−	0.635328i	$-0.780865\pi$
$433$	−32.1386			−1.54448			−0.772242	+	0.635328i	$0.780865\pi$
$434$		0			0
$435$	−9.40247			−0.450814
$436$	1.76974	+	5.44668i	0.0847549	+	0.260849i
$437$	−24.8051	+	5.27250i	−1.18659	+	0.252218i
$438$	26.7781	−	19.4554i	1.27951	−	0.929615i
$439$	−5.93040	+	10.2718i	−0.283043	+	0.490244i	−0.972133	−	0.234431i	$-0.924677\pi$
$439$	−5.93040	+	10.2718i	−0.283043	+	0.490244i	0.689090	+	0.724676i	$0.258011\pi$
$440$	17.5606	+	30.4158i	0.837168	+	1.45002i
$441$	−21.1649	−	9.42322i	−1.00785	−	0.448725i
$442$	−4.49009	−	3.26224i	−0.213572	−	0.155169i
$443$	−31.0985	+	13.8459i	−1.47753	+	0.657841i	−0.978029	−	0.208470i	$-0.933152\pi$
$443$	−31.0985	+	13.8459i	−1.47753	+	0.657841i	−0.499506	+	0.866311i	$0.666485\pi$
$444$	7.58240	+	1.61169i	0.359845	+	0.0764874i
$445$	3.81703	+	36.3166i	0.180945	+	1.72157i
$446$	10.5559	−	11.7235i	0.499836	−	0.555125i
$447$	39.0917	+	43.4157i	1.84897	+	2.05349i
$448$	−1.12046	+	10.6604i	−0.0529366	+	0.503658i
$449$	−3.35187	+	10.3160i	−0.158185	+	0.486842i	−0.998470	−	0.0553026i	$-0.982388\pi$
$449$	−3.35187	+	10.3160i	−0.158185	+	0.486842i	0.840285	+	0.542145i	$0.182388\pi$
$450$	−2.98455	+	9.18551i	−0.140693	+	0.433009i
$451$	0.959699	−	9.13092i	0.0451904	−	0.429958i
$452$	−2.69052	−	2.98813i	−0.126552	−	0.140550i
$453$	−6.40854	+	7.11740i	−0.301099	+	0.334405i
$454$	−1.50676	−	14.3359i	−0.0707159	−	0.672817i
$455$	3.75902	+	0.799005i	0.176226	+	0.0374579i
$456$	47.9908	−	21.3669i	2.24738	−	1.00060i
$457$	9.47069	+	6.88086i	0.443020	+	0.321873i	0.786834	−	0.617165i	$-0.211719\pi$
$457$	9.47069	+	6.88086i	0.443020	+	0.321873i	−0.343814	+	0.939038i	$0.611719\pi$
$458$	32.6812	+	14.5506i	1.52709	+	0.679905i
$459$	−5.75818	−	9.97345i	−0.268769	−	0.465521i
$460$	2.32219	−	4.02215i	0.108273	−	0.187534i
$461$	−29.4551	+	21.4004i	−1.37186	+	0.996716i	−0.374273	+	0.927319i	$0.622108\pi$
$461$	−29.4551	+	21.4004i	−1.37186	+	0.996716i	−0.997589	+	0.0693975i	$0.977892\pi$
$462$	−17.2785	+	3.67267i	−0.803870	+	0.170868i
$463$	5.61400	+	17.2781i	0.260905	+	0.802983i	0.992609	+	0.121360i	$0.0387255\pi$
$463$	5.61400	+	17.2781i	0.260905	+	0.802983i	−0.731704	+	0.681623i	$0.761274\pi$
$464$	3.88510			0.180361
$465$		0			0
$466$	−14.2512			−0.660174
$467$	−1.54490	−	4.75471i	−0.0714894	−	0.220022i	0.908928	−	0.416954i	$-0.136902\pi$
$467$	−1.54490	−	4.75471i	−0.0714894	−	0.220022i	−0.980417	+	0.196932i	$0.936902\pi$
$468$	−2.23724	+	0.475541i	−0.103417	+	0.0219819i
$469$	−11.7035	+	8.50307i	−0.540416	+	0.392635i
$470$	1.22929	−	2.12919i	0.0567029	−	0.0982123i
$471$	24.2885	+	42.0689i	1.11915	+	1.93843i
$472$	11.1215	+	4.95163i	0.511911	+	0.227917i
$473$	−33.4845	−	24.3279i	−1.53962	−	1.11860i
$474$	28.8261	−	12.8342i	1.32403	−	0.589496i
$475$	−11.6847	−	2.48366i	−0.536132	−	0.113958i
$476$	0.207148	+	1.97088i	0.00949459	+	0.0903350i
$477$	−13.1694	+	14.6261i	−0.602986	+	0.669683i
$478$	21.0079	+	23.3316i	0.960878	+	1.06716i
$479$	0.276355	−	2.62934i	0.0126270	−	0.120138i	−0.986393	−	0.164407i	$-0.947429\pi$
$479$	0.276355	−	2.62934i	0.0126270	−	0.120138i	0.999020	+	0.0442687i	$0.0140958\pi$
$480$	−5.40035	+	16.6206i	−0.246491	+	0.758621i
$481$	−2.42289	+	7.45689i	−0.110474	+	0.340005i
$482$	1.35067	−	12.8508i	0.0615213	−	0.585336i
$483$	8.51508	+	9.45696i	0.387450	+	0.430307i
$484$	−2.50741	+	2.78476i	−0.113973	+	0.126580i
$485$	1.23446	+	11.7451i	0.0560540	+	0.533318i
$486$	−24.8564	−	5.28339i	−1.12751	−	0.239660i
$487$	21.3499	−	9.50560i	0.967458	−	0.430740i	0.138692	−	0.990336i	$-0.455710\pi$
$487$	21.3499	−	9.50560i	0.967458	−	0.430740i	0.828766	+	0.559596i	$0.189044\pi$
$488$	5.47413	+	3.97719i	0.247802	+	0.180039i
$489$	−19.2382	−	8.56541i	−0.869983	−	0.387341i
$490$	−9.04687	−	15.6696i	−0.408696	−	0.707882i
$491$	2.49844	−	4.32742i	0.112753	−	0.195294i	−0.804126	−	0.594458i	$-0.797366\pi$
$491$	2.49844	−	4.32742i	0.112753	−	0.195294i	0.916879	+	0.399165i	$0.130700\pi$
$492$	2.03474	−	1.47832i	0.0917330	−	0.0666479i
$493$	4.79701	−	1.01963i	0.216046	−	0.0459220i
$494$	3.01400	+	9.27613i	0.135606	+	0.417353i
$495$	−48.0745			−2.16079
$496$		0			0
$497$	−9.06157			−0.406467
$498$	−5.78134	−	17.7931i	−0.259068	−	0.797330i
$499$	−16.9952	+	3.61245i	−0.760811	+	0.161715i	−0.571950	−	0.820288i	$-0.693813\pi$
$499$	−16.9952	+	3.61245i	−0.760811	+	0.161715i	−0.188861	+	0.982004i	$0.560480\pi$
$500$	−2.99341	+	2.17484i	−0.133869	+	0.0972616i
$501$	−26.4830	+	45.8700i	−1.18317	+	2.04932i
$502$	0.919561	+	1.59273i	0.0410420	+	0.0710869i
$503$	3.55491	+	1.58275i	0.158506	+	0.0705712i	0.484456	−	0.874816i	$-0.339018\pi$
$503$	3.55491	+	1.58275i	0.158506	+	0.0705712i	−0.325950	+	0.945387i	$0.605684\pi$
$504$	−12.4098	−	9.01625i	−0.552776	−	0.401616i
$505$	4.51885	−	2.01192i	0.201086	−	0.0895293i
$506$	−21.1210	−	4.48940i	−0.938941	−	0.199578i
$507$	3.22434	+	30.6775i	0.143198	+	1.36244i
$508$	−1.53400	+	1.70368i	−0.0680602	+	0.0755885i
$509$	−10.5766	−	11.7466i	−0.468801	−	0.520657i	0.461655	−	0.887060i	$-0.347256\pi$
$509$	−10.5766	−	11.7466i	−0.468801	−	0.520657i	−0.930456	+	0.366403i	$0.880589\pi$
$510$	3.34032	−	31.7810i	0.147912	−	1.40729i
$511$	3.69403	−	11.3690i	0.163414	−	0.502937i
$512$	7.69529	−	23.6837i	0.340087	−	1.04668i
$513$	−2.11550	+	20.1276i	−0.0934015	+	0.888656i
$514$	−14.0505	−	15.6047i	−0.619743	−	0.688294i
$515$	19.7850	−	21.9735i	0.871832	−	0.968268i
$516$	−1.18514	−	11.2759i	−0.0521730	−	0.496393i
$517$	3.24291	+	0.689302i	0.142623	+	0.0303155i
$518$	−8.81786	+	3.92596i	−0.387435	+	0.172497i
$519$	−34.9901	−	25.4218i	−1.53589	−	1.11589i
$520$	−8.88992	−	3.95805i	−0.389849	−	0.173572i
$521$	15.4138	+	26.6975i	0.675291	+	1.16964i	0.976384	+	0.216043i	$0.0693151\pi$
$521$	15.4138	+	26.6975i	0.675291	+	1.16964i	−0.301093	+	0.953595i	$0.597352\pi$
$522$	−3.48403	+	6.03451i	−0.152492	+	0.264123i
$523$	−1.04675	+	0.760508i	−0.0457712	+	0.0332547i	−0.610436	−	0.792066i	$-0.709006\pi$
$523$	−1.04675	+	0.760508i	−0.0457712	+	0.0332547i	0.564664	+	0.825321i	$0.309006\pi$
$524$	1.22033	−	0.259389i	0.0533102	−	0.0113314i
$525$	1.85241	+	5.70113i	0.0808458	+	0.248818i
$526$	29.2387			1.27487
$527$		0			0
$528$	34.1378			1.48566
$529$	−2.30047	−	7.08012i	−0.100020	−	0.307831i
$530$	−15.0349	+	3.19578i	−0.653076	+	0.138816i
$531$	−13.4815	+	9.79489i	−0.585047	+	0.425062i
$532$	1.74132	−	3.01605i	0.0754957	−	0.130762i
$533$	1.27195	+	2.20308i	0.0550941	+	0.0954259i
$534$	42.4867	+	18.9163i	1.83858	+	0.818587i
$535$	−10.2589	−	7.45356i	−0.443533	−	0.322246i
$536$	33.4645	−	14.8994i	1.44545	−	0.643555i
$537$	10.3754	+	2.20537i	0.447734	+	0.0951687i
$538$	−1.70797	−	16.2502i	−0.0736356	−	0.700596i
$539$	16.3262	−	18.1321i	0.703221	−	0.781005i
$540$	−2.48016	−	2.75449i	−0.106729	−	0.118535i
$541$	1.37220	−	13.0556i	0.0589954	−	0.561303i	−0.924603	−	0.380932i	$-0.875603\pi$
$541$	1.37220	−	13.0556i	0.0589954	−	0.561303i	0.983599	−	0.180372i	$-0.0577300\pi$
$542$	−4.33356	+	13.3373i	−0.186142	+	0.572887i
$543$	−16.8877	+	51.9751i	−0.724722	+	2.23047i
$544$	0.952791	−	9.06520i	0.0408506	−	0.388667i
$545$	−22.3173	−	24.7858i	−0.955967	−	1.06171i
$546$	3.27501	−	3.63726i	0.140157	−	0.155661i
$547$	−3.14174	−	29.8917i	−0.134331	−	1.27808i	−0.829205	−	0.558944i	$-0.811207\pi$
$547$	−3.14174	−	29.8917i	−0.134331	−	1.27808i	0.694874	−	0.719131i	$-0.255460\pi$
$548$	−4.54864	−	0.966844i	−0.194308	−	0.0413015i
$549$	−8.46123	+	3.76718i	−0.361116	+	0.160779i
$550$	−8.22893	−	5.97867i	−0.350883	−	0.254931i
$551$	−7.87334	−	3.50544i	−0.335415	−	0.149337i
$552$	−16.1118	−	27.9065i	−0.685766	−	1.18778i
$553$	5.69800	−	9.86923i	0.242304	−	0.419682i
$554$	−2.24817	+	1.63339i	−0.0955157	+	0.0693962i
$555$	−44.1582	+	9.38611i	−1.87441	+	0.398418i
$556$	0.0445749	+	0.137187i	0.00189040	+	0.00581804i
$557$	12.8904			0.546184			0.273092	−	0.961988i	$-0.411954\pi$
$557$	12.8904			0.546184			0.273092	+	0.961988i	$0.411954\pi$
$558$		0			0
$559$	11.4679			0.485041
$560$	−2.82532	−	8.69545i	−0.119392	−	0.367450i
$561$	42.1507	−	8.95940i	1.77960	−	0.378266i
$562$	−5.37561	+	3.90561i	−0.226756	+	0.164748i
$563$	−6.37499	+	11.0418i	−0.268674	+	0.465357i	−0.968520	−	0.248937i	$-0.919919\pi$
$563$	−6.37499	+	11.0418i	−0.268674	+	0.465357i	0.699846	+	0.714294i	$0.253252\pi$
$564$	0.454099	+	0.786523i	0.0191210	+	0.0331186i
$565$	21.3924	+	9.52453i	0.899987	+	0.400700i
$566$	11.9202	+	8.66053i	0.501043	+	0.364029i
$567$	−4.50497	+	2.00574i	−0.189191	+	0.0842333i
$568$	22.4442	+	4.77067i	0.941740	+	0.200173i
$569$	−0.351166	−	3.34112i	−0.0147216	−	0.140067i	0.984692	−	0.174302i	$-0.0557670\pi$
$569$	−0.351166	−	3.34112i	−0.0147216	−	0.140067i	−0.999414	+	0.0342355i	$0.989100\pi$
$570$	−37.5774	+	41.7340i	−1.57395	+	1.74804i
$571$	−5.40433	−	6.00211i	−0.226164	−	0.251181i	0.619374	−	0.785096i	$-0.287387\pi$
$571$	−5.40433	−	6.00211i	−0.226164	−	0.251181i	−0.845538	+	0.533916i	$0.820720\pi$
$572$	0.251787	−	2.39559i	0.0105277	−	0.100165i
$573$	15.7425	−	48.4503i	0.657650	−	2.02404i
$574$	−0.967750	+	2.97843i	−0.0403931	+	0.124317i
$575$	−0.765942	+	7.28745i	−0.0319420	+	0.303908i
$576$	24.8608	+	27.6107i	1.03587	+	1.15045i
$577$	12.0898	−	13.4271i	0.503305	−	0.558977i	−0.436933	−	0.899494i	$-0.643935\pi$
$577$	12.0898	−	13.4271i	0.503305	−	0.558977i	0.940238	+	0.340517i	$0.110602\pi$
$578$	−0.470310	−	4.47470i	−0.0195623	−	0.186123i
$579$	55.3823	+	11.7719i	2.30161	+	0.489222i
$580$	1.44195	−	0.641997i	0.0598736	−	0.0266575i
$581$	−5.46638	−	3.97156i	−0.226784	−	0.164768i
$582$	13.7405	+	6.11769i	0.569564	+	0.253586i
$583$	−10.3637	−	17.9504i	−0.429220	−	0.743431i
$584$	−15.1351	+	26.2147i	−0.626294	+	1.08477i
$585$	10.7763	−	7.82947i	0.445547	−	0.323709i
$586$	32.5621	−	6.92130i	1.34513	−	0.285916i
$587$	5.14978	+	15.8494i	0.212554	+	0.654174i	0.999318	+	0.0369204i	$0.0117548\pi$
$587$	5.14978	+	15.8494i	0.212554	+	0.654174i	−0.786764	+	0.617254i	$0.788245\pi$
$588$	6.68382			0.275636
$589$		0			0
$590$	−13.0144			−0.535793
$591$	5.28235	+	16.2574i	0.217287	+	0.668741i
$592$	18.2461	−	3.87834i	0.749912	−	0.159399i
$593$	−26.4201	+	19.1953i	−1.08494	+	0.788258i	−0.978538	−	0.206064i	$-0.933934\pi$
$593$	−26.4201	+	19.1953i	−1.08494	+	0.788258i	−0.106406	+	0.994323i	$0.533934\pi$
$594$	−8.61627	+	14.9238i	−0.353530	+	0.612332i
$595$	−5.77058	−	9.99494i	−0.236571	−	0.409753i
$596$	−8.95945	−	3.98900i	−0.366993	−	0.163396i
$597$	33.5045	+	24.3425i	1.37125	+	0.996271i
$598$	5.46560	−	2.43344i	0.223505	−	0.0995109i
$599$	−20.5733	−	4.37299i	−0.840602	−	0.178675i	−0.232561	−	0.972582i	$-0.574711\pi$
$599$	−20.5733	−	4.37299i	−0.840602	−	0.178675i	−0.608040	+	0.793906i	$0.708044\pi$
$600$	−1.58667	−	15.0962i	−0.0647755	−	0.616298i
$601$	11.1968	−	12.4353i	0.456726	−	0.507245i	−0.470164	−	0.882579i	$-0.655805\pi$
$601$	11.1968	−	12.4353i	0.456726	−	0.507245i	0.926890	+	0.375334i	$0.122472\pi$
$602$	9.44664	+	10.4916i	0.385016	+	0.427604i
$603$	−5.24125	+	49.8671i	−0.213440	+	2.03075i
$604$	0.496830	−	1.52908i	0.0202157	−	0.0622176i
$605$	6.74374	−	20.7551i	0.274172	−	0.843814i
$606$	0.658511	−	6.26531i	0.0267502	−	0.254511i
$607$	−1.05440	−	1.17103i	−0.0427967	−	0.0475306i	0.721366	−	0.692554i	$-0.243514\pi$
$607$	−1.05440	−	1.17103i	−0.0427967	−	0.0475306i	−0.764163	+	0.645023i	$0.776848\pi$
$608$	−10.7186	+	11.9042i	−0.434695	+	0.482778i
$609$	0.452068	+	4.30114i	0.0183187	+	0.174291i
$610$	−7.07538	−	1.50392i	−0.286474	−	0.0608919i
$611$	−0.839189	+	0.373631i	−0.0339500	+	0.0151155i
$612$	5.55707	+	4.03745i	0.224631	+	0.163204i
$613$	41.1334	+	18.3138i	1.66136	+	0.739686i	0.999947	−	0.0103336i	$-0.00328935\pi$
$613$	41.1334	+	18.3138i	1.66136	+	0.739686i	0.661416	+	0.750020i	$0.269956\pi$
$614$	−8.87254	−	15.3677i	−0.358066	−	0.620189i
$615$	−7.32360	+	12.6848i	−0.295316	+	0.511502i
$616$	13.0693	−	9.49543i	0.526579	−	0.382582i
$617$	32.7047	−	6.95160i	1.31664	−	0.279861i	0.504546	−	0.863385i	$-0.331660\pi$
$617$	32.7047	−	6.95160i	1.31664	−	0.279861i	0.812096	+	0.583524i	$0.198326\pi$
$618$	−11.6369	−	35.8148i	−0.468107	−	1.44068i
$619$	10.7700			0.432881			0.216440	−	0.976296i	$-0.430555\pi$
$619$	10.7700			0.432881			0.216440	+	0.976296i	$0.430555\pi$
$620$		0			0
$621$	12.4144			0.498172
$622$	−7.79017	−	23.9757i	−0.312357	−	0.961338i
$623$	16.4294	−	3.49219i	0.658232	−	0.139912i
$624$	−7.65231	+	5.55973i	−0.306337	+	0.222567i
$625$	15.4188	−	26.7062i	0.616754	−	1.06825i
$626$	5.63170	+	9.75438i	0.225088	+	0.389864i
$627$	−69.1820	−	30.8018i	−2.76286	−	1.23011i
$628$	−6.59729	−	4.79321i	−0.263260	−	0.191270i
$629$	21.5110	−	9.57732i	0.857700	−	0.381873i
$630$	16.0398	+	3.40937i	0.639042	+	0.135833i
$631$	−1.92789	−	18.3426i	−0.0767480	−	0.730208i	−0.963454	−	0.267874i	$-0.913679\pi$
$631$	−1.92789	−	18.3426i	−0.0767480	−	0.730208i	0.886706	−	0.462334i	$-0.152988\pi$
$632$	−19.3090	+	21.4449i	−0.768073	+	0.853031i
$633$	−47.8396	−	53.1312i	−1.90145	−	2.11178i
$634$	−3.91099	+	37.2106i	−0.155325	+	1.47782i
$635$	4.12573	−	12.6977i	0.163725	−	0.503892i
$636$	1.75459	−	5.40008i	0.0695742	−	0.214127i
$637$	−0.706656	+	6.72339i	−0.0279987	+	0.266390i
$638$	−4.91034	−	5.45348i	−0.194402	−	0.215905i
$639$	−21.0163	+	23.3410i	−0.831394	+	0.923357i
$640$	1.66913	+	15.8807i	0.0659783	+	0.627741i
$641$	−37.1339	−	7.89306i	−1.46670	−	0.311757i	−0.595768	−	0.803157i	$-0.703152\pi$
$641$	−37.1339	−	7.89306i	−1.46670	−	0.311757i	−0.870934	+	0.491400i	$0.836485\pi$
$642$	−14.7539	+	6.56885i	−0.582289	+	0.259252i
$643$	13.0408	+	9.47467i	0.514278	+	0.373645i	0.814444	−	0.580242i	$-0.197042\pi$
$643$	13.0408	+	9.47467i	0.514278	+	0.373645i	−0.300166	+	0.953887i	$0.597042\pi$
$644$	−1.95158	−	0.868898i	−0.0769029	−	0.0342394i
$645$	33.0149	+	57.1835i	1.29996	+	2.25160i
$646$	14.6457	−	25.3671i	0.576227	−	0.998055i
$647$	5.58116	−	4.05495i	0.219418	−	0.159416i	−0.472647	−	0.881252i	$-0.656701\pi$
$647$	5.58116	−	4.05495i	0.219418	−	0.159416i	0.692065	+	0.721836i	$0.256701\pi$
$648$	12.2142	−	2.59620i	0.479817	−	0.101988i
$649$	−5.42316	−	16.6908i	−0.212877	−	0.655170i
$650$	2.81828			0.110542
$651$		0			0
$652$	3.53518			0.138448
$653$	2.49784	+	7.68757i	0.0977481	+	0.300838i	0.987960	−	0.154709i	$-0.0494439\pi$
$653$	2.49784	+	7.68757i	0.0977481	+	0.300838i	−0.890212	+	0.455546i	$0.849444\pi$
$654$	−41.5495	+	8.83161i	−1.62471	+	0.345343i
$655$	−5.87806	+	4.27066i	−0.229675	+	0.166868i
$656$	3.02611	−	5.24137i	0.118150	−	0.204641i
$657$	−20.7172	−	35.8832i	−0.808254	−	1.39994i
$658$	−1.03310	−	0.459965i	−0.0402744	−	0.0179313i
$659$	−20.0393	−	14.5594i	−0.780621	−	0.567154i	0.124544	−	0.992214i	$-0.460253\pi$
$659$	−20.0393	−	14.5594i	−0.780621	−	0.567154i	−0.905165	+	0.425060i	$0.860253\pi$
$660$	12.6702	−	5.64114i	0.493187	−	0.219581i
$661$	−38.8980	−	8.26803i	−1.51296	−	0.321589i	−0.624674	−	0.780886i	$-0.714768\pi$
$661$	−38.8980	−	8.26803i	−1.51296	−	0.321589i	−0.888283	+	0.459297i	$0.848101\pi$
$662$	−1.98697	−	18.9047i	−0.0772257	−	0.734754i
$663$	−7.98932	+	8.87304i	−0.310279	+	0.344600i
$664$	11.4486	+	12.7149i	0.444290	+	0.493434i
$665$	−2.12005	+	20.1710i	−0.0822122	+	0.782197i
$666$	−10.3385	+	31.8187i	−0.400610	+	1.23295i
$667$	−1.63365	+	5.02785i	−0.0632551	+	0.194679i
$668$	0.929415	−	8.84279i	0.0359601	−	0.342138i
$669$	−22.7089	−	25.2208i	−0.877977	−	0.975093i
$670$	−26.2031	+	29.1015i	−1.01232	+	1.12429i
$671$	−1.01959	−	9.70078i	−0.0393609	−	0.374494i
$672$	7.86269	+	1.67127i	0.303310	+	0.0644705i
$673$	13.3015	−	5.92220i	0.512734	−	0.228284i	−0.134026	−	0.990978i	$-0.542790\pi$
$673$	13.3015	−	5.92220i	0.512734	−	0.228284i	0.646759	+	0.762694i	$0.276124\pi$
$674$	8.29162	+	6.02422i	0.319381	+	0.232044i
$675$	5.34234	+	2.37856i	0.205627	+	0.0915510i
$676$	−2.58913	−	4.48450i	−0.0995818	−	0.172481i
$677$	0.110509	−	0.191408i	0.00424722	−	0.00735641i	−0.863894	−	0.503674i	$-0.831981\pi$
$677$	0.110509	−	0.191408i	0.00424722	−	0.00735641i	0.868141	+	0.496317i	$0.165315\pi$
$678$	24.1279	−	17.5299i	0.926625	−	0.673232i
$679$	5.31342	−	1.12940i	0.203910	−	0.0433425i
$680$	9.03086	+	27.7941i	0.346318	+	1.06586i
$681$	−31.0107			−1.18833
$682$		0			0
$683$	−16.3674			−0.626280			−0.313140	−	0.949707i	$-0.601381\pi$
$683$	−16.3674			−0.626280			−0.313140	+	0.949707i	$0.601381\pi$
$684$	−3.73021	−	11.4804i	−0.142628	−	0.438965i
$685$	26.4903	−	5.63068i	1.01214	−	0.215137i
$686$	−15.2266	+	11.0628i	−0.581356	+	0.422380i
$687$	38.4803	−	66.6499i	1.46812	−	2.54285i
$688$	−13.6417	−	23.6282i	−0.520086	−	0.900816i
$689$	5.24654	+	2.33591i	0.199877	+	0.0889911i
$690$	27.8690	+	20.2480i	1.06095	+	0.770828i
$691$	−43.2172	+	19.2415i	−1.64406	+	0.731983i	−0.999470	−	0.0325457i	$-0.989639\pi$
$691$	−43.2172	+	19.2415i	−1.64406	+	0.731983i	−0.644590	+	0.764528i	$0.722972\pi$
$692$	7.10181	+	1.50954i	0.269970	+	0.0573839i
$693$	2.31141	+	21.9916i	0.0878031	+	0.835391i
$694$	2.90039	−	3.22121i	0.110097	−	0.122276i
$695$	−0.562112	−	0.624289i	−0.0213221	−	0.0236806i
$696$	1.14472	−	10.8913i	0.0433907	−	0.412835i
$697$	2.36081	−	7.26582i	0.0894220	−	0.275213i
$698$	6.82917	−	21.0180i	0.258488	−	0.795544i
$699$	−3.20470	+	30.4906i	−0.121213	+	1.15326i
$700$	−0.673353	−	0.747834i	−0.0254504	−	0.0282655i
$701$	16.2745	−	18.0747i	0.614680	−	0.682671i	−0.352777	−	0.935708i	$-0.614762\pi$
$701$	16.2745	−	18.0747i	0.614680	−	0.682671i	0.967457	+	0.253036i	$0.0814292\pi$
$702$	−0.499094	−	4.74857i	−0.0188371	−	0.179223i
$703$	−40.4760	−	8.60344i	−1.52658	−	0.324485i
$704$	−35.7456	+	15.9150i	−1.34721	+	0.599818i
$705$	−4.27901	−	3.10888i	−0.161157	−	0.117087i
$706$	−5.79883	−	2.58181i	−0.218242	−	0.0971676i
$707$	−1.13761	−	1.97040i	−0.0427844	−	0.0741047i
$708$	2.40375	−	4.16342i	0.0903385	−	0.156471i
$709$	14.5737	−	10.5884i	0.547329	−	0.397657i	−0.279471	−	0.960154i	$-0.590159\pi$
$709$	14.5737	−	10.5884i	0.547329	−	0.397657i	0.826800	+	0.562497i	$0.190159\pi$
$710$	−23.9935	+	5.09997i	−0.900459	+	0.191398i
$711$	−12.2061	−	37.5666i	−0.457766	−	1.40886i
$712$	−42.5320			−1.59395
$713$		0			0
$714$	−14.6988			−0.550087
$715$	4.33496	+	13.3416i	0.162118	+	0.498949i
$716$	−1.74174	+	0.370219i	−0.0650920	+	0.0138357i
$717$	54.6424	−	39.7001i	2.04066	−	1.48263i
$718$	−4.82916	+	8.36435i	−0.180223	+	0.312155i
$719$	−15.6914	−	27.1784i	−0.585192	−	1.01358i	−0.994852	−	0.101343i	$-0.967686\pi$
$719$	−15.6914	−	27.1784i	−0.585192	−	1.01358i	0.409660	−	0.912238i	$-0.365647\pi$
$720$	−28.9507	−	12.8897i	−1.07893	−	0.480370i
$721$	−11.0030	−	7.99413i	−0.409772	−	0.297717i
$722$	−25.4134	+	11.3148i	−0.945788	+	0.421092i
$723$	−27.1907	−	5.77956i	−1.01123	−	0.214944i
$724$	−0.958961	−	9.12391i	−0.0356395	−	0.339087i
$725$	−1.66634	+	1.85066i	−0.0618863	+	0.0687317i
$726$	−18.5977	−	20.6549i	−0.690227	−	0.766574i
$727$	0.486726	−	4.63089i	0.0180517	−	0.171750i	−0.981782	−	0.190013i	$-0.939147\pi$
$727$	0.486726	−	4.63089i	0.0180517	−	0.171750i	0.999833	+	0.0182630i	$0.00581362\pi$
$728$	−1.38318	+	4.25698i	−0.0512639	+	0.157774i
$729$	−13.0981	+	40.3119i	−0.485116	+	1.49303i
$730$	3.38250	−	32.1823i	0.125192	−	1.19112i
$731$	−23.0449	−	25.5939i	−0.852346	−	0.946626i
$732$	1.78794	−	1.98571i	0.0660842	−	0.0733939i
$733$	5.20395	+	49.5123i	0.192212	+	1.82878i	0.487217	+	0.873281i	$0.338012\pi$
$733$	5.20395	+	49.5123i	0.192212	+	1.82878i	−0.295004	+	0.955496i	$0.595321\pi$
$734$	36.8546	+	7.83370i	1.36033	+	0.289147i
$735$	−35.5598	+	15.8322i	−1.31164	+	0.583981i
$736$	7.94933	+	5.77553i	0.293016	+	0.212889i
$737$	−48.2413	−	21.4784i	−1.77699	−	0.791168i
$738$	5.42742	+	9.40058i	0.199786	+	0.346040i
$739$	−16.3597	+	28.3359i	−0.601802	+	1.04235i	0.390746	+	0.920498i	$0.372217\pi$
$739$	−16.3597	+	28.3359i	−0.601802	+	1.04235i	−0.992548	+	0.121853i	$0.961116\pi$
$740$	6.13115	−	4.45454i	0.225385	−	0.163752i
$741$	20.5242	−	4.36255i	0.753975	−	0.160262i
$742$	2.18478	+	6.72405i	0.0802057	+	0.246848i
$743$	34.5763			1.26848			0.634241	−	0.773136i	$-0.281313\pi$
$743$	34.5763			1.26848			0.634241	+	0.773136i	$0.281313\pi$
$744$		0			0
$745$	57.1157			2.09256
$746$	4.47689	+	13.7784i	0.163910	+	0.504464i
$747$	−22.9081	+	4.86928i	−0.838165	+	0.178158i
$748$	−5.85241	+	4.25203i	−0.213985	+	0.155470i
$749$	−2.91637	+	5.05130i	−0.106562	+	0.184570i
$750$	−13.7219	−	23.7670i	−0.501052	−	0.867847i
$751$	14.8584	+	6.61539i	0.542191	+	0.241399i	0.659511	−	0.751695i	$-0.270764\pi$
$751$	14.8584	+	6.61539i	0.542191	+	0.241399i	−0.117320	+	0.993094i	$0.537430\pi$
$752$	1.76808	+	1.28459i	0.0644753	+	0.0468441i
$753$	3.61445	−	1.60925i	0.131718	−	0.0586445i
$754$	1.98886	+	0.422745i	0.0724299	+	0.0153954i
$755$	0.978733	+	9.31202i	0.0356197	+	0.338899i
$756$	−1.14079	+	1.26698i	−0.0414902	+	0.0460795i
$757$	27.4111	+	30.4431i	0.996273	+	1.10647i	0.994315	+	0.106475i	$0.0339565\pi$
$757$	27.4111	+	30.4431i	0.996273	+	1.10647i	0.00195782	+	0.999998i	$0.499377\pi$
$758$	4.44505	−	42.2918i	0.161451	−	1.53611i
$759$	−14.3546	+	44.1791i	−0.521041	+	1.60360i
$760$	15.8706	−	48.8446i	0.575686	−	1.77178i
$761$	−0.00659250	+	0.0627235i	−0.000238978	+	0.00227372i	−0.994641	−	0.103392i	$-0.967031\pi$
$761$	−0.00659250	+	0.0627235i	−0.000238978	+	0.00227372i	0.994402	+	0.105665i	$0.0336972\pi$
$762$	−11.3779	−	12.6364i	−0.412176	−	0.457768i
$763$	−10.2652	+	11.4007i	−0.371626	+	0.412732i
$764$	0.893927	+	8.50514i	0.0323411	+	0.307705i
$765$	−39.1288	−	8.31709i	−1.41471	−	0.300705i
$766$	−0.666983	+	0.296960i	−0.0240991	+	0.0107296i
$767$	3.93393	+	2.85816i	0.142046	+	0.103202i
$768$	−24.9736	−	11.1190i	−0.901158	−	0.401221i
$769$	20.2449	+	35.0652i	0.730050	+	1.26448i	0.956861	+	0.290545i	$0.0938368\pi$
$769$	20.2449	+	35.0652i	0.730050	+	1.26448i	−0.226811	+	0.973939i	$0.572830\pi$
$770$	−8.63484	+	14.9560i	−0.311178	+	0.538976i
$771$	−36.5461	+	26.5523i	−1.31618	+	0.956257i
$772$	−9.29711	+	1.97616i	−0.334610	+	0.0711236i
$773$	−11.3468	−	34.9218i	−0.408115	−	1.25605i	−0.918266	−	0.395965i	$-0.870410\pi$
$773$	−11.3468	−	34.9218i	−0.408115	−	1.25605i	0.510150	−	0.860085i	$-0.329590\pi$
$774$	48.9338			1.75889
$775$		0			0
$776$	−13.7552			−0.493783
$777$	6.41677	+	19.7488i	0.230200	+	0.708484i
$778$	22.6705	−	4.81877i	0.812777	−	0.172761i
$779$	−10.8617	+	7.89151i	−0.389162	+	0.282743i
$780$	−1.92142	+	3.32800i	−0.0687979	+	0.119161i
$781$	−16.5389	−	28.6461i	−0.591807	−	1.02504i
$782$	−16.4141	−	7.30803i	−0.586967	−	0.261335i
$783$	3.41329	+	2.47990i	0.121981	+	0.0886245i
$784$	14.6933	−	6.54188i	0.524760	−	0.233638i
$785$	46.4533	+	9.87395i	1.65799	+	0.352417i
$786$	0.967257	+	9.20283i	0.0345009	+	0.328254i
$787$	−4.52346	+	5.02381i	−0.161244	+	0.179080i	−0.818353	−	0.574716i	$-0.805112\pi$
$787$	−4.52346	+	5.02381i	−0.161244	+	0.179080i	0.657109	+	0.753796i	$0.271779\pi$
$788$	−1.92014	−	2.13253i	−0.0684022	−	0.0759684i
$789$	6.57496	−	62.5566i	0.234075	−	2.22707i
$790$	9.53280	−	29.3389i	0.339162	−	1.04383i
$791$	3.32843	−	10.2439i	0.118345	−	0.364230i
$792$	5.85293	−	55.6870i	0.207975	−	1.97875i
$793$	1.80843	+	2.00847i	0.0642193	+	0.0713227i
$794$	−11.6363	+	12.9234i	−0.412957	+	0.458635i
$795$	3.45647	+	32.8861i	0.122588	+	1.16635i
$796$	−6.80030	−	1.44545i	−0.241030	−	0.0512325i
$797$	−20.1708	+	8.98060i	−0.714485	+	0.318109i	−0.731590	−	0.681745i	$-0.761222\pi$
$797$	−20.1708	+	8.98060i	−0.714485	+	0.318109i	0.0171054	+	0.999854i	$0.494555\pi$
$798$	20.8978	+	15.1832i	0.739775	+	0.537478i
$799$	2.52022	+	1.12208i	0.0891591	+	0.0396962i
$800$	2.31430	+	4.00849i	0.0818229	+	0.141721i
$801$	29.1093	−	50.4188i	1.02853	−	1.78146i
$802$	−3.57340	+	2.59623i	−0.126181	+	0.0916760i
$803$	42.6829	−	9.07253i	1.50625	−	0.320163i
$804$	−4.47014	−	13.7577i	−0.157650	−	0.485196i
$805$	12.4411			0.438492
$806$		0			0
$807$	−35.1516			−1.23740
$808$	1.78035	+	5.47934i	0.0626324	+	0.192763i
$809$	−24.4696	+	5.20117i	−0.860305	+	0.182863i	−0.616881	−	0.787057i	$-0.711604\pi$
$809$	−24.4696	+	5.20117i	−0.860305	+	0.182863i	−0.243424	+	0.969920i	$0.578271\pi$
$810$	−10.7995	+	7.84632i	−0.379457	+	0.275692i
$811$	−1.30069	+	2.25286i	−0.0456734	+	0.0791087i	−0.887958	−	0.459924i	$-0.847877\pi$
$811$	−1.30069	+	2.25286i	−0.0456734	+	0.0791087i	0.842285	+	0.539033i	$0.181210\pi$
$812$	−0.363008	−	0.628749i	−0.0127391	−	0.0220648i
$813$	27.5609	+	12.2709i	0.966602	+	0.430359i
$814$	−28.5051	−	20.7102i	−0.999104	−	0.725891i
$815$	−18.8082	+	8.37394i	−0.658821	+	0.293326i
$816$	27.7855	+	5.90599i	0.972688	+	0.206751i
$817$	6.32647	+	60.1923i	0.221335	+	2.10586i
$818$	14.2706	−	15.8492i	0.498961	−	0.554153i
$819$	−4.09969	−	4.55317i	−0.143255	−	0.159101i
$820$	0.257020	−	2.44538i	0.00897552	−	0.0853963i
$821$	8.01153	−	24.6569i	0.279604	−	0.860533i	−0.708360	−	0.705851i	$-0.750565\pi$
$821$	8.01153	−	24.6569i	0.279604	−	0.860533i	0.987964	−	0.154682i	$-0.0494353\pi$
$822$	10.6585	−	32.8034i	0.371757	−	1.14415i
$823$	−3.35430	+	31.9140i	−0.116924	+	1.11245i	0.765969	+	0.642878i	$0.222260\pi$
$823$	−3.35430	+	31.9140i	−0.116924	+	1.11245i	−0.882892	+	0.469575i	$0.844407\pi$
$824$	23.0442	+	25.5931i	0.802781	+	0.891579i
$825$	−14.6419	+	16.2615i	−0.509766	+	0.566152i
$826$	0.625727	+	5.95339i	0.0217718	+	0.207145i
$827$	21.2682	+	4.52069i	0.739567	+	0.157200i	0.562266	−	0.826957i	$-0.309930\pi$
$827$	21.2682	+	4.52069i	0.739567	+	0.157200i	0.177302	+	0.984157i	$0.443263\pi$
$828$	−6.76439	+	3.01170i	−0.235079	+	0.104664i
$829$	16.6954	+	12.1299i	0.579855	+	0.421289i	0.838672	−	0.544637i	$-0.183333\pi$
$829$	16.6954	+	12.1299i	0.579855	+	0.421289i	−0.258817	+	0.965926i	$0.583333\pi$
$830$	−16.7093	−	7.43946i	−0.579988	−	0.258227i
$831$	2.98912	+	5.17730i	0.103691	+	0.179599i
$832$	5.42078	−	9.38906i	0.187932	−	0.325507i
$833$	16.4252	−	11.9336i	0.569099	−	0.413475i
$834$	−1.04652	+	0.222445i	−0.0362380	+	0.00770263i
$835$	16.0015	+	49.2477i	0.553756	+	1.70429i
$836$	12.7128			0.439680
$837$		0			0
$838$	22.6823			0.783547
$839$	−2.37625	−	7.31334i	−0.0820372	−	0.252485i	0.901622	−	0.432525i	$-0.142377\pi$
$839$	−2.37625	−	7.31334i	−0.0820372	−	0.252485i	−0.983659	+	0.180040i	$0.942377\pi$
$840$	−25.2090	+	5.35833i	−0.869792	+	0.184880i
$841$	22.0080	−	15.9897i	0.758895	−	0.551370i
$842$	−2.17148	+	3.76111i	−0.0748341	+	0.129616i
$843$	7.14728	+	12.3795i	0.246165	+	0.426371i
$844$	10.9644	+	4.88165i	0.377409	+	0.168033i
$845$	24.3975	+	17.7258i	0.839299	+	0.609786i
$846$	−3.58084	+	1.59429i	−0.123112	+	0.0548129i
$847$	−9.81861	−	2.08701i	−0.337371	−	0.0717105i
$848$	−1.42821	−	13.5885i	−0.0490450	−	0.466632i
$849$	21.2099	−	23.5559i	0.727920	−	0.808437i
$850$	−5.66337	−	6.28981i	−0.194252	−	0.215739i
$851$	−2.65323	+	25.2438i	−0.0909516	+	0.865347i
$852$	2.80006	−	8.61771i	0.0959286	−	0.295238i
$853$	−0.274664	+	0.845328i	−0.00940430	+	0.0289435i	−0.955649	−	0.294509i	$-0.904844\pi$
$853$	−0.274664	+	0.845328i	−0.00940430	+	0.0289435i	0.946244	+	0.323453i	$0.104844\pi$
$854$	−0.347782	+	3.30893i	−0.0119009	+	0.113229i
$855$	47.0399	+	52.2431i	1.60873	+	1.78668i
$856$	9.88281	−	10.9760i	0.337788	−	0.375151i
$857$	−1.55288	−	14.7747i	−0.0530454	−	0.504693i	−0.988497	−	0.151239i	$-0.951674\pi$
$857$	−1.55288	−	14.7747i	−0.0530454	−	0.504693i	0.935452	−	0.353454i	$-0.114993\pi$
$858$	17.4758	+	3.71460i	0.596615	+	0.126814i
$859$	37.8785	−	16.8646i	1.29240	−	0.575412i	0.358692	−	0.933456i	$-0.383223\pi$
$859$	37.8785	−	16.8646i	1.29240	−	0.575412i	0.933705	+	0.358044i	$0.116556\pi$
$860$	−8.96757	−	6.51532i	−0.305792	−	0.222171i
$861$	6.15477	+	2.74028i	0.209754	+	0.0933885i
$862$	8.85330	+	15.3344i	0.301545	+	0.522291i
$863$	11.1992	−	19.3977i	0.381227	−	0.660304i	−0.610011	−	0.792393i	$-0.708835\pi$
$863$	11.1992	−	19.3977i	0.381227	−	0.660304i	0.991238	+	0.132089i	$0.0421685\pi$
$864$	6.34411	−	4.60927i	0.215831	−	0.156811i
$865$	−41.3593	+	8.79119i	−1.40626	+	0.298909i
$866$	12.3658	+	38.0580i	0.420207	+	1.29327i
$867$	−9.67946			−0.328732
$868$		0			0
$869$	41.5992			1.41116
$870$	3.61774	+	11.1343i	0.122653	+	0.377486i
$871$	14.3117	−	3.04205i	0.484935	−	0.103076i
$872$	31.4277	−	22.8335i	1.06428	−	0.773241i
$873$	9.41419	−	16.3059i	0.318622	−	0.551870i
$874$	15.7877	+	27.3452i	0.534028	+	0.924964i
$875$	−9.05461	−	4.03137i	−0.306102	−	0.136285i
$876$	9.67069	+	7.02617i	0.326742	+	0.237392i
$877$	−28.1277	+	12.5233i	−0.949806	+	0.422881i	−0.822362	−	0.568965i	$-0.807344\pi$
$877$	−28.1277	+	12.5233i	−0.949806	+	0.422881i	−0.127444	+	0.991846i	$0.540677\pi$
$878$	14.4455	+	3.07048i	0.487511	+	0.103624i
$879$	−7.48590	−	71.2236i	−0.252493	−	2.40231i
$880$	22.3321	−	24.8023i	0.752813	−	0.836084i
$881$	−1.91335	−	2.12500i	−0.0644626	−	0.0715929i	0.710051	−	0.704150i	$-0.248672\pi$
$881$	−1.91335	−	2.12500i	−0.0644626	−	0.0715929i	−0.774513	+	0.632557i	$0.782005\pi$
$882$	−3.01532	+	28.6888i	−0.101531	+	0.966003i
$883$	−7.39527	+	22.7603i	−0.248871	+	0.765945i	0.746105	+	0.665828i	$0.231922\pi$
$883$	−7.39527	+	22.7603i	−0.248871	+	0.765945i	−0.994976	+	0.100117i	$0.968078\pi$
$884$	0.619382	−	1.90626i	0.0208321	−	0.0641145i
$885$	−2.92657	+	27.8444i	−0.0983755	+	0.935980i
$886$	28.3617	+	31.4989i	0.952831	+	1.05823i
$887$	17.6552	−	19.6080i	0.592802	−	0.658373i	−0.369857	−	0.929089i	$-0.620593\pi$
$887$	17.6552	−	19.6080i	0.592802	−	0.658373i	0.962660	+	0.270715i	$0.0872601\pi$
$888$	−5.49624	−	52.2933i	−0.184442	−	1.75485i
$889$	−6.00689	−	1.27680i	−0.201465	−	0.0428227i
$890$	41.5369	−	18.4934i	1.39232	−	0.619901i
$891$	−14.5630	−	10.5807i	−0.487880	−	0.354465i
$892$	5.20467	+	2.31727i	0.174265	+	0.0775878i
$893$	−2.42405	−	4.19858i	−0.0811178	−	0.140500i
$894$	36.3711	−	62.9966i	1.21643	−	2.10692i
$895$	8.38961	−	6.09541i	0.280434	−	0.203747i
$896$	7.18436	−	1.52708i	0.240013	−	0.0510162i
$897$	−3.97733	−	12.2409i	−0.132799	−	0.408713i
$898$	13.5057			0.450692
$899$		0			0
$900$	−3.48799			−0.116266
$901$	−5.32972	−	16.4032i	−0.177559	−	0.546470i
$902$	−11.1819	+	2.37680i	−0.372318	+	0.0791386i
$903$	24.5711	−	17.8520i	0.817676	−	0.594076i
$904$	−13.6372	+	23.6203i	−0.453566	+	0.785599i
$905$	26.7141	+	46.2702i	0.888007	+	1.53807i
$906$	10.8941	+	4.85036i	0.361932	+	0.161142i
$907$	−8.26629	−	6.00581i	−0.274478	−	0.199420i	0.442028	−	0.897001i	$-0.354259\pi$
$907$	−8.26629	−	6.00581i	−0.274478	−	0.199420i	−0.716505	+	0.697582i	$0.754259\pi$
$908$	4.75575	−	2.11739i	0.157825	−	0.0702682i
$909$	−7.71387	−	1.63963i	−0.255853	−	0.0543832i
$910$	−0.500170	−	4.75880i	−0.0165805	−	0.157753i
$911$	4.27764	−	4.75080i	0.141725	−	0.157401i	−0.668103	−	0.744068i	$-0.732894\pi$
$911$	4.27764	−	4.75080i	0.141725	−	0.157401i	0.809828	+	0.586667i	$0.199560\pi$
$912$	−33.4032	−	37.0980i	−1.10609	−	1.22844i
$913$	2.57816	−	24.5295i	0.0853245	−	0.811808i
$914$	4.50421	−	13.8625i	0.148986	−	0.458532i
$915$	−4.80871	+	14.7997i	−0.158971	+	0.489263i
$916$	−1.35046	+	12.8487i	−0.0446203	+	0.424534i
$917$	2.23622	+	2.48357i	0.0738464	+	0.0820148i
$918$	−9.59485	+	10.6562i	−0.316677	+	0.351706i
$919$	2.85246	+	27.1394i	0.0940940	+	0.895245i	0.935139	+	0.354280i	$0.115274\pi$
$919$	2.85246	+	27.1394i	0.0940940	+	0.895245i	−0.841045	+	0.540965i	$0.818059\pi$
$920$	−30.8149	−	6.54992i	−1.01594	−	0.215944i
$921$	−34.8746	+	15.5272i	−1.14916	+	0.511637i
$922$	36.6753	+	26.6462i	1.20784	+	0.877544i
$923$	8.37268	+	3.72776i	0.275590	+	0.122701i
$924$	−3.18971	−	5.52474i	−0.104934	−	0.181750i
$925$	−5.97843	+	10.3549i	−0.196570	+	0.340469i
$926$	18.3004	−	13.2960i	0.601388	−	0.436934i
$927$	−46.1105	+	9.80110i	−1.51447	+	0.321910i
$928$	1.03192	+	3.17593i	0.0338745	+	0.104255i
$929$	−6.67079			−0.218861			−0.109431	−	0.993994i	$-0.534903\pi$
$929$	−6.67079			−0.218861			−0.109431	+	0.993994i	$0.534903\pi$
$930$		0			0
$931$	−35.6793			−1.16934
$932$	−1.59042	−	4.89481i	−0.0520959	−	0.160335i
$933$	−53.0481	+	11.2757i	−1.73672	+	0.369151i
$934$	−5.03602	+	3.65889i	−0.164784	+	0.119722i
$935$	21.0645	−	36.4848i	0.688884	−	1.19318i
$936$	7.75725	+	13.4360i	0.253554	+	0.439168i
$937$	0.424525	+	0.189011i	0.0138686	+	0.00617472i	0.413659	−	0.910432i	$-0.364250\pi$
$937$	0.424525	+	0.189011i	0.0138686	+	0.00617472i	−0.399791	+	0.916606i	$0.630917\pi$
$938$	14.5723	+	10.5874i	0.475802	+	0.345690i
$939$	22.1361	−	9.85561i	0.722383	−	0.321626i
$940$	0.868494	+	0.184604i	0.0283272	+	0.00602112i
$941$	−4.47695	−	42.5953i	−0.145944	−	1.38857i	−0.785042	−	0.619442i	$-0.787359\pi$
$941$	−4.47695	−	42.5953i	−0.145944	−	1.38857i	0.639098	−	0.769125i	$-0.279308\pi$
$942$	40.4719	−	44.9486i	1.31865	−	1.46451i
$943$	5.51060	+	6.12015i	0.179450	+	0.199299i
$944$	1.20926	−	11.5053i	0.0393579	−	0.374466i
$945$	3.06819	−	9.44292i	0.0998083	−	0.307178i
$946$	−15.9250	+	49.0123i	−0.517768	+	1.59353i
$947$	−2.43739	+	23.1902i	−0.0792045	+	0.753581i	0.880780	+	0.473526i	$0.157019\pi$
$947$	−2.43739	+	23.1902i	−0.0792045	+	0.753581i	−0.959984	+	0.280054i	$0.909648\pi$
$948$	7.62510	+	8.46853i	0.247652	+	0.275045i
$949$	−8.09020	+	8.98508i	−0.262619	+	0.291668i
$950$	1.55475	+	14.7925i	0.0504428	+	0.479931i
$951$	78.7332	+	16.7353i	2.55310	+	0.542678i
$952$	12.2802	−	5.46748i	0.398002	−	0.177202i
$953$	−20.1582	−	14.6458i	−0.652988	−	0.474424i	0.211300	−	0.977421i	$-0.432230\pi$
$953$	−20.1582	−	14.6458i	−0.652988	−	0.474424i	−0.864288	+	0.502998i	$0.832230\pi$
$954$	22.3871	+	9.96738i	0.724809	+	0.322706i
$955$	−24.9024	−	43.1323i	−0.805824	−	1.39573i
$956$	−5.66917	+	9.81930i	−0.183354	+	0.317579i
$957$	−12.7720	+	9.27940i	−0.412860	+	0.299961i
$958$	−3.21996	+	0.684423i	−0.104032	+	0.0221127i
$959$	−3.84938	−	11.8472i	−0.124303	−	0.382566i
$960$	62.4234			2.01470
$961$		0			0
$962$	9.76256			0.314758
$963$	6.24738	+	19.2275i	0.201319	+	0.619596i
$964$	4.56454	−	0.970223i	0.147014	−	0.0312488i
$965$	44.7822	−	32.5362i	1.44159	−	1.04738i
$966$	7.92247	−	13.7221i	0.254901	−	0.441502i
$967$	−11.2887	−	19.5526i	−0.363021	−	0.628771i	0.625436	−	0.780276i	$-0.284921\pi$
$967$	−11.2887	−	19.5526i	−0.363021	−	0.628771i	−0.988456	+	0.151505i	$0.951588\pi$
$968$	23.2206	+	10.3385i	0.746337	+	0.332291i
$969$	−50.9799	−	37.0390i	−1.63771	−	1.18987i
$970$	13.4334	−	5.98093i	0.431320	−	0.192036i
$971$	5.96299	+	1.26747i	0.191361	+	0.0406751i	0.302595	−	0.953119i	$-0.402147\pi$
$971$	5.96299	+	1.26747i	0.191361	+	0.0406751i	−0.111234	+	0.993794i	$0.535480\pi$
$972$	−0.959283	−	9.12697i	−0.0307690	−	0.292748i
$973$	−0.258553	+	0.287153i	−0.00828884	+	0.00920569i
$974$	−19.4711	−	21.6248i	−0.623893	−	0.692903i
$975$	0.633753	−	6.02976i	0.0202963	−	0.193107i
$976$	1.98696	−	6.11523i	0.0636010	−	0.195744i
$977$	−4.16327	+	12.8132i	−0.133195	+	0.409932i	−0.995305	−	0.0967896i	$-0.969143\pi$
$977$	−4.16327	+	12.8132i	−0.133195	+	0.409932i	0.862110	+	0.506721i	$0.169143\pi$
$978$	−2.74083	+	26.0772i	−0.0876420	+	0.833858i
$979$	41.0262	+	45.5642i	1.31120	+	1.45624i
$980$	4.37238	−	4.85602i	0.139670	−	0.155120i
$981$	5.55821	+	52.8828i	0.177460	+	1.68842i
$982$	−6.08577	−	1.29357i	−0.194205	−	0.0412795i
$983$	17.1380	−	7.63031i	0.546616	−	0.243369i	−0.114800	−	0.993389i	$-0.536623\pi$
$983$	17.1380	−	7.63031i	0.546616	−	0.243369i	0.661416	+	0.750019i	$0.269956\pi$
$984$	−13.8018	−	10.0276i	−0.439986	−	0.319669i
$985$	15.2671	+	6.79736i	0.486451	+	0.216582i
$986$	−3.05315	−	5.28821i	−0.0972322	−	0.168411i
$987$	−1.21642	+	2.10690i	−0.0387190	+	0.0670632i
$988$	−2.84968	+	2.07042i	−0.0906605	+	0.0658687i
$989$	36.3143	−	7.71885i	1.15473	−	0.245445i
$990$	18.4974	+	56.9290i	0.587884	+	1.80932i
$991$	57.0730			1.81298			0.906491	−	0.422225i	$-0.138751\pi$
$991$	57.0730			1.81298			0.906491	+	0.422225i	$0.138751\pi$
$992$		0			0
$993$	−40.8938			−1.29773
$994$	3.48657	+	10.7306i	0.110587	+	0.340353i
$995$	39.6034	−	8.41796i	1.25551	−	0.266867i
$996$	5.46616	−	3.97140i	0.173202	−	0.125838i
$997$	12.4444	−	21.5544i	0.394119	−	0.682635i	−0.598869	−	0.800847i	$-0.704383\pi$
$997$	12.4444	−	21.5544i	0.394119	−	0.682635i	0.992988	+	0.118212i	$0.0377163\pi$
$998$	10.8170	+	18.7355i	0.342405	+	0.593063i
$999$	18.5059	+	8.23937i	0.585502	+	0.260682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.v.844.5		96
31.2	even	5	inner	961.2.g.v.338.7		96
31.3	odd	30		961.2.a.k.1.5	✓	12
31.4	even	5	inner	961.2.g.v.732.8		96
31.5	even	3	inner	961.2.g.v.547.6		96
31.6	odd	6		961.2.d.r.531.5		48
31.7	even	15		961.2.d.r.374.7		48
31.8	even	5	inner	961.2.g.v.448.6		96
31.9	even	15	inner	961.2.g.v.846.5		96
31.10	even	15	inner	961.2.g.v.235.8		96
31.11	odd	30	inner	961.2.g.v.816.8		96
31.12	odd	30		961.2.d.r.388.8		48
31.13	odd	30		961.2.c.k.439.6		24
31.14	even	15		961.2.d.r.628.6		48
31.15	odd	10		961.2.c.k.521.6		24
31.16	even	5		961.2.c.k.521.5		24
31.17	odd	30		961.2.d.r.628.5		48
31.18	even	15		961.2.c.k.439.5		24
31.19	even	15		961.2.d.r.388.7		48
31.20	even	15	inner	961.2.g.v.816.7		96
31.21	odd	30	inner	961.2.g.v.235.7		96
31.22	odd	30	inner	961.2.g.v.846.6		96
31.23	odd	10	inner	961.2.g.v.448.5		96
31.24	odd	30		961.2.d.r.374.8		48
31.25	even	3		961.2.d.r.531.6		48
31.26	odd	6	inner	961.2.g.v.547.5		96
31.27	odd	10	inner	961.2.g.v.732.7		96
31.28	even	15		961.2.a.k.1.6	yes	12
31.29	odd	10	inner	961.2.g.v.338.8		96
31.30	odd	2	inner	961.2.g.v.844.6		96
93.59	odd	30		8649.2.a.bp.1.8		12
93.65	even	30		8649.2.a.bp.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.5	✓	12	31.3	odd	30
961.2.a.k.1.6	yes	12	31.28	even	15
961.2.c.k.439.5		24	31.18	even	15
961.2.c.k.439.6		24	31.13	odd	30
961.2.c.k.521.5		24	31.16	even	5
961.2.c.k.521.6		24	31.15	odd	10
961.2.d.r.374.7		48	31.7	even	15
961.2.d.r.374.8		48	31.24	odd	30
961.2.d.r.388.7		48	31.19	even	15
961.2.d.r.388.8		48	31.12	odd	30
961.2.d.r.531.5		48	31.6	odd	6
961.2.d.r.531.6		48	31.25	even	3
961.2.d.r.628.5		48	31.17	odd	30
961.2.d.r.628.6		48	31.14	even	15
961.2.g.v.235.7		96	31.21	odd	30	inner
961.2.g.v.235.8		96	31.10	even	15	inner
961.2.g.v.338.7		96	31.2	even	5	inner
961.2.g.v.338.8		96	31.29	odd	10	inner
961.2.g.v.448.5		96	31.23	odd	10	inner
961.2.g.v.448.6		96	31.8	even	5	inner
961.2.g.v.547.5		96	31.26	odd	6	inner
961.2.g.v.547.6		96	31.5	even	3	inner
961.2.g.v.732.7		96	31.27	odd	10	inner
961.2.g.v.732.8		96	31.4	even	5	inner
961.2.g.v.816.7		96	31.20	even	15	inner
961.2.g.v.816.8		96	31.11	odd	30	inner
961.2.g.v.844.5		96	1.1	even	1	trivial
961.2.g.v.844.6		96	31.30	odd	2	inner
961.2.g.v.846.5		96	31.9	even	15	inner
961.2.g.v.846.6		96	31.22	odd	30	inner
8649.2.a.bp.1.7		12	93.65	even	30
8649.2.a.bp.1.8		12	93.59	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.384764 - 1.18418i) q^{2} +(-2.62010 + 0.556919i) q^{3} +(0.363788 - 0.264307i) q^{4} +(-1.30938 + 2.26791i) q^{5} +(1.66762 + 2.88840i) q^{6} +(1.10040 + 0.489932i) q^{7} +(-2.46761 - 1.79283i) q^{8} +(3.81413 - 1.69816i) q^{9} +(3.18942 + 0.677933i) q^{10} +(0.459609 + 4.37289i) q^{11} +(-0.805963 + 0.895113i) q^{12} +(-0.815200 - 0.905371i) q^{13} +(0.156772 - 1.49159i) q^{14} +(2.16766 - 6.67137i) q^{15} +(-0.895675 + 2.75661i) q^{16} +(-0.382443 + 3.63870i) q^{17} +(-3.47847 - 3.86324i) q^{18} +(4.30235 - 4.77825i) q^{19} +(0.123089 + 1.17112i) q^{20} +(-3.15602 - 0.670833i) q^{21} +(5.00146 - 2.22679i) q^{22} +(-3.19080 - 2.31825i) q^{23} +(7.46386 + 3.32312i) q^{24} +(-0.928943 - 1.60898i) q^{25} +(-0.758465 + 1.31370i) q^{26} +(-2.54648 + 1.85013i) q^{27} +(0.529807 - 0.112614i) q^{28} +(-0.414206 - 1.27479i) q^{29} -8.73416 q^{30} -2.49133 q^{32} +(-3.63957 - 11.2014i) q^{33} +(4.45604 - 0.947161i) q^{34} +(-2.55197 + 1.85411i) q^{35} +(0.938698 - 1.62587i) q^{36} +(-3.21787 - 5.57351i) q^{37} +(-7.31371 - 3.25627i) q^{38} +(2.64012 + 1.91816i) q^{39} +(7.29701 - 3.24884i) q^{40} +(-2.04245 - 0.434135i) q^{41} +(0.419936 + 3.99542i) q^{42} +(-6.29858 + 6.99528i) q^{43} +(1.32299 + 1.46933i) q^{44} +(-1.14287 + 10.8736i) q^{45} +(-1.51753 + 4.67048i) q^{46} +(0.233002 - 0.717105i) q^{47} +(0.811552 - 7.72140i) q^{48} +(-3.71306 - 4.12377i) q^{49} +(-1.54790 + 1.71912i) q^{50} +(-1.02443 - 9.74676i) q^{51} +(-0.535856 - 0.113900i) q^{52} +(-4.30646 + 1.91736i) q^{53} +(3.17068 + 2.30364i) q^{54} +(-10.5191 - 4.68342i) q^{55} +(-1.83701 - 3.18180i) q^{56} +(-8.61150 + 14.9156i) q^{57} +(-1.35022 + 0.980990i) q^{58} +(-3.90409 + 0.829840i) q^{59} +(-0.974724 - 2.99989i) q^{60} -2.21839 q^{61} +5.02907 q^{63} +(2.74992 + 8.46340i) q^{64} +(3.12070 - 0.663326i) q^{65} +(-11.8642 + 8.61984i) q^{66} +(-6.00489 + 10.4008i) q^{67} +(0.822608 + 1.42480i) q^{68} +(9.65130 + 4.29704i) q^{69} +(3.17751 + 2.30860i) q^{70} +(-6.87245 + 3.05981i) q^{71} +(-12.4563 - 2.64767i) q^{72} +(-1.03736 - 9.86983i) q^{73} +(-5.36194 + 5.95503i) q^{74} +(3.32999 + 3.69833i) q^{75} +(0.302218 - 2.87541i) q^{76} +(-1.63666 + 5.03713i) q^{77} +(1.25563 - 3.86443i) q^{78} +(0.988929 - 9.40903i) q^{79} +(-5.07895 - 5.64075i) q^{80} +(-2.73937 + 3.04238i) q^{81} +(0.271765 + 2.58567i) q^{82} +(-5.48687 - 1.16627i) q^{83} +(-1.32543 + 0.590119i) q^{84} +(-7.75149 - 5.63178i) q^{85} +(10.7072 + 4.76713i) q^{86} +(1.79522 + 3.10941i) q^{87} +(6.70570 - 11.6146i) q^{88} +(11.2812 - 8.19625i) q^{89} +(13.3161 - 2.83043i) q^{90} +(-0.453480 - 1.39567i) q^{91} -1.77351 q^{92} -0.938835 q^{94} +(5.20323 + 16.0139i) q^{95} +(6.52753 - 1.38747i) q^{96} +(3.64843 - 2.65074i) q^{97} +(-3.45464 + 5.98362i) q^{98} +(9.17888 + 15.8983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) \) 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

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