LMFDB - Embedded newform 968.2.o.d.565.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			565.5
Character	$\chi$	$=$	968.565
Dual form			968.2.o.d.245.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.546541 + 1.30434i) q^{2} +(-0.513977 - 0.167001i) q^{3} +(-1.40259 - 1.42575i) q^{4} +(-1.70510 - 2.34687i) q^{5} +(0.498735 - 0.579126i) q^{6} +(-0.804837 - 2.47703i) q^{7} +(2.62622 - 1.05022i) q^{8} +(-2.19077 - 1.59169i) q^{9} +(3.99302 - 0.941367i) q^{10} +(0.482796 + 0.967034i) q^{12} +(-1.53843 + 2.11746i) q^{13} +(3.67076 + 0.304021i) q^{14} +(0.484453 + 1.49099i) q^{15} +(-0.0655010 + 3.99946i) q^{16} +(5.57496 - 4.05044i) q^{17} +(3.27344 - 1.98758i) q^{18} +(-1.52231 - 0.494630i) q^{19} +(-0.954489 + 5.72274i) q^{20} +1.40755i q^{21} -4.01642 q^{23} +(-1.52520 + 0.101205i) q^{24} +(-1.05535 + 3.24804i) q^{25} +(-1.92107 - 3.16390i) q^{26} +(1.81316 + 2.49560i) q^{27} +(-2.40277 + 4.62175i) q^{28} +(-1.89980 + 0.617281i) q^{29} +(-2.20953 - 0.182999i) q^{30} +(4.19113 + 3.04503i) q^{31} +(-5.18085 - 2.27130i) q^{32} +(2.23620 + 9.48535i) q^{34} +(-4.44095 + 6.11245i) q^{35} +(0.803403 + 5.35596i) q^{36} +(-8.16901 + 2.65427i) q^{37} +(1.47717 - 1.71527i) q^{38} +(1.14433 - 0.831407i) q^{39} +(-6.94271 - 4.37268i) q^{40} +(-1.15845 + 3.56533i) q^{41} +(-1.83591 - 0.769281i) q^{42} -2.47162i q^{43} +7.85545i q^{45} +(2.19513 - 5.23876i) q^{46} +(-3.66085 + 11.2669i) q^{47} +(0.701581 - 2.04469i) q^{48} +(0.175189 - 0.127282i) q^{49} +(-3.65975 - 3.15172i) q^{50} +(-3.54183 + 1.15081i) q^{51} +(5.17674 - 0.776520i) q^{52} +(-0.760478 + 1.04671i) q^{53} +(-4.24606 + 1.00102i) q^{54} +(-4.71510 - 5.65999i) q^{56} +(0.699830 + 0.508456i) q^{57} +(0.233173 - 2.81534i) q^{58} +(0.334314 - 0.108625i) q^{59} +(1.44629 - 2.78195i) q^{60} +(-1.81119 - 2.49289i) q^{61} +(-6.26237 + 3.80241i) q^{62} +(-2.17945 + 6.70765i) q^{63} +(5.79409 - 5.51621i) q^{64} +7.59259 q^{65} -10.3946i q^{67} +(-13.5943 - 2.26737i) q^{68} +(2.06434 + 0.670746i) q^{69} +(-5.54553 - 9.13320i) q^{70} +(-2.80750 + 2.03977i) q^{71} +(-7.42506 - 1.87934i) q^{72} +(-0.412353 - 1.26909i) q^{73} +(1.00263 - 12.1058i) q^{74} +(1.08485 - 1.49317i) q^{75} +(1.42996 + 2.86419i) q^{76} +(0.459010 + 1.94699i) q^{78} +(3.49723 + 2.54089i) q^{79} +(9.49792 - 6.66578i) q^{80} +(1.99524 + 6.14073i) q^{81} +(-4.01725 - 3.45960i) q^{82} +(9.39420 + 12.9300i) q^{83} +(2.00680 - 1.97421i) q^{84} +(-19.0118 - 6.17729i) q^{85} +(3.22383 + 1.35084i) q^{86} +1.07954 q^{87} -13.1240 q^{89} +(-10.2461 - 4.29332i) q^{90} +(6.48321 + 2.10652i) q^{91} +(5.63337 + 5.72639i) q^{92} +(-1.64562 - 2.26500i) q^{93} +(-12.6951 - 10.9328i) q^{94} +(1.43487 + 4.41607i) q^{95} +(2.28352 + 2.03261i) q^{96} +(-6.96770 - 5.06233i) q^{97} +(0.0702709 + 0.298070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.546541	+	1.30434i	−0.386463	+	0.922305i
$2$	−0.546541	+	1.30434i	−0.386463	+	0.922305i
$3$	−0.513977	−	0.167001i	−0.296745	−	0.0964182i	0.156861	−	0.987621i	$-0.449863\pi$
$3$	−0.513977	−	0.167001i	−0.296745	−	0.0964182i	−0.453606	+	0.891203i	$0.649863\pi$
$4$	−1.40259	−	1.42575i	−0.701293	−	0.712873i
$5$	−1.70510	−	2.34687i	−0.762546	−	1.04955i	−0.996998	−	0.0774264i	$-0.975330\pi$
$5$	−1.70510	−	2.34687i	−0.762546	−	1.04955i	0.234452	−	0.972128i	$-0.424670\pi$
$6$	0.498735	−	0.579126i	0.203608	−	0.236427i
$7$	−0.804837	−	2.47703i	−0.304200	−	0.936230i	−0.979975	−	0.199122i	$-0.936191\pi$
$7$	−0.804837	−	2.47703i	−0.304200	−	0.936230i	0.675775	−	0.737108i	$-0.263809\pi$
$8$	2.62622	−	1.05022i	0.928510	−	0.371308i
$9$	−2.19077	−	1.59169i	−0.730256	−	0.530562i
$10$	3.99302	−	0.941367i	1.26270	−	0.297686i
$11$		0			0
$11$		0			0
$12$	0.482796	+	0.967034i	0.139371	+	0.279159i
$13$	−1.53843	+	2.11746i	−0.426683	+	0.587278i	−0.967188	−	0.254062i	$-0.918233\pi$
$13$	−1.53843	+	2.11746i	−0.426683	+	0.587278i	0.540505	+	0.841341i	$0.318233\pi$
$14$	3.67076	+	0.304021i	0.981052	+	0.0812531i
$15$	0.484453	+	1.49099i	0.125085	+	0.384973i
$16$	−0.0655010	+	3.99946i	−0.0163752	+	0.999866i
$17$	5.57496	−	4.05044i	1.35213	−	0.982377i	0.353223	−	0.935539i	$-0.385086\pi$
$17$	5.57496	−	4.05044i	1.35213	−	0.982377i	0.998903	−	0.0468375i	$-0.0149143\pi$
$18$	3.27344	−	1.98758i	0.771557	−	0.468477i
$19$	−1.52231	−	0.494630i	−0.349243	−	0.113476i	0.129142	−	0.991626i	$-0.458778\pi$
$19$	−1.52231	−	0.494630i	−0.349243	−	0.113476i	−0.478385	+	0.878150i	$0.658778\pi$
$20$	−0.954489	+	5.72274i	−0.213430	+	1.27964i
$21$			1.40755i			0.307152i
$22$		0			0
$23$	−4.01642			−0.837480			−0.418740	−	0.908106i	$-0.637528\pi$
$23$	−4.01642			−0.837480			−0.418740	+	0.908106i	$0.637528\pi$
$24$	−1.52520	+	0.101205i	−0.311331	+	0.0206584i
$25$	−1.05535	+	3.24804i	−0.211071	+	0.649609i
$26$	−1.92107	−	3.16390i	−0.376753	−	0.620493i
$27$	1.81316	+	2.49560i	0.348942	+	0.480277i
$28$	−2.40277	+	4.62175i	−0.454080	+	0.873428i
$29$	−1.89980	+	0.617281i	−0.352783	+	0.114626i	−0.480047	−	0.877243i	$-0.659380\pi$
$29$	−1.89980	+	0.617281i	−0.352783	+	0.114626i	0.127264	+	0.991869i	$0.459380\pi$
$30$	−2.20953	−	0.182999i	−0.403403	−	0.0334108i
$31$	4.19113	+	3.04503i	0.752749	+	0.546904i	0.896678	−	0.442684i	$-0.145974\pi$
$31$	4.19113	+	3.04503i	0.752749	+	0.546904i	−0.143929	+	0.989588i	$0.545974\pi$
$32$	−5.18085	−	2.27130i	−0.915853	−	0.401514i
$33$		0			0
$34$	2.23620	+	9.48535i	0.383505	+	1.62672i
$35$	−4.44095	+	6.11245i	−0.750658	+	1.03319i
$36$	0.803403	+	5.35596i	0.133900	+	0.892659i
$37$	−8.16901	+	2.65427i	−1.34298	+	0.436360i	−0.890324	−	0.455327i	$-0.849522\pi$
$37$	−8.16901	+	2.65427i	−1.34298	+	0.436360i	−0.452653	+	0.891687i	$0.649522\pi$
$38$	1.47717	−	1.71527i	0.239629	−	0.278254i
$39$	1.14433	−	0.831407i	0.183240	−	0.133132i
$40$	−6.94271	−	4.37268i	−1.09774	−	0.691382i
$41$	−1.15845	+	3.56533i	−0.180919	+	0.556811i	−0.999854	−	0.0170750i	$-0.994565\pi$
$41$	−1.15845	+	3.56533i	−0.180919	+	0.556811i	0.818935	+	0.573886i	$0.194565\pi$
$42$	−1.83591	−	0.769281i	−0.283288	−	0.118703i
$43$		−	2.47162i		−	0.376919i	−0.982081	−	0.188460i	$-0.939651\pi$
$43$		−	2.47162i		−	0.376919i	0.982081	−	0.188460i	$-0.0603494\pi$
$44$		0			0
$45$			7.85545i			1.17102i
$46$	2.19513	−	5.23876i	0.323655	−	0.772413i
$47$	−3.66085	+	11.2669i	−0.533990	+	1.64345i	0.211831	+	0.977306i	$0.432057\pi$
$47$	−3.66085	+	11.2669i	−0.533990	+	1.64345i	−0.745821	+	0.666146i	$0.767943\pi$
$48$	0.701581	−	2.04469i	0.101265	−	0.295126i
$49$	0.175189	−	0.127282i	0.0250270	−	0.0181832i
$50$	−3.65975	−	3.15172i	−0.517567	−	0.445721i
$51$	−3.54183	+	1.15081i	−0.495955	+	0.161146i
$52$	5.17674	−	0.776520i	0.717884	−	0.107684i
$53$	−0.760478	+	1.04671i	−0.104460	+	0.143776i	−0.858047	−	0.513572i	$-0.828322\pi$
$53$	−0.760478	+	1.04671i	−0.104460	+	0.143776i	0.753587	+	0.657348i	$0.228322\pi$
$54$	−4.24606	+	1.00102i	−0.577815	+	0.136222i
$55$		0			0
$56$	−4.71510	−	5.65999i	−0.630082	−	0.756347i
$57$	0.699830	+	0.508456i	0.0926948	+	0.0673467i
$58$	0.233173	−	2.81534i	0.0306172	−	0.369672i
$59$	0.334314	−	0.108625i	0.0435240	−	0.0141418i	−0.287174	−	0.957878i	$-0.592716\pi$
$59$	0.334314	−	0.108625i	0.0435240	−	0.0141418i	0.330698	+	0.943737i	$0.392716\pi$
$60$	1.44629	−	2.78195i	0.186715	−	0.359149i
$61$	−1.81119	−	2.49289i	−0.231899	−	0.319181i	0.677171	−	0.735826i	$-0.263206\pi$
$61$	−1.81119	−	2.49289i	−0.231899	−	0.319181i	−0.909069	+	0.416645i	$0.863206\pi$
$62$	−6.26237	+	3.80241i	−0.795322	+	0.482906i
$63$	−2.17945	+	6.70765i	−0.274585	+	0.845085i
$64$	5.79409	−	5.51621i	0.724261	−	0.689526i
$65$	7.59259			0.941745
$66$		0			0
$67$		−	10.3946i		−	1.26990i	−0.772553	−	0.634950i	$-0.781021\pi$
$67$		−	10.3946i		−	1.26990i	0.772553	−	0.634950i	$-0.218979\pi$
$68$	−13.5943	−	2.26737i	−1.64855	−	0.274959i
$69$	2.06434	+	0.670746i	0.248518	+	0.0807483i
$70$	−5.54553	−	9.13320i	−0.662817	−	1.09163i
$71$	−2.80750	+	2.03977i	−0.333189	+	0.242076i	−0.741783	−	0.670640i	$-0.766019\pi$
$71$	−2.80750	+	2.03977i	−0.333189	+	0.242076i	0.408593	+	0.912717i	$0.366019\pi$
$72$	−7.42506	−	1.87934i	−0.875052	−	0.221482i
$73$	−0.412353	−	1.26909i	−0.0482623	−	0.148536i	0.924021	−	0.382341i	$-0.124882\pi$
$73$	−0.412353	−	1.26909i	−0.0482623	−	0.148536i	−0.972283	+	0.233805i	$0.924882\pi$
$74$	1.00263	−	12.1058i	0.116554	−	1.40727i
$75$	1.08485	−	1.49317i	0.125268	−	0.172417i
$76$	1.42996	+	2.86419i	0.164028	+	0.328545i
$77$		0			0
$78$	0.459010	+	1.94699i	0.0519726	+	0.220454i
$79$	3.49723	+	2.54089i	0.393469	+	0.285872i	0.766876	−	0.641796i	$-0.221810\pi$
$79$	3.49723	+	2.54089i	0.393469	+	0.285872i	−0.373406	+	0.927668i	$0.621810\pi$
$80$	9.49792	−	6.66578i	1.06190	−	0.745257i
$81$	1.99524	+	6.14073i	0.221694	+	0.682303i
$82$	−4.01725	−	3.45960i	−0.443631	−	0.382049i
$83$	9.39420	+	12.9300i	1.03115	+	1.41925i	0.904082	+	0.427358i	$0.140556\pi$
$83$	9.39420	+	12.9300i	1.03115	+	1.41925i	0.127065	+	0.991894i	$0.459444\pi$
$84$	2.00680	−	1.97421i	0.218960	−	0.215403i
$85$	−19.0118	−	6.17729i	−2.06211	−	0.670022i
$86$	3.22383	+	1.35084i	0.347634	+	0.145665i
$87$	1.07954			0.115739
$88$		0			0
$89$	−13.1240			−1.39114			−0.695571	−	0.718457i	$-0.744849\pi$
$89$	−13.1240			−1.39114			−0.695571	+	0.718457i	$0.744849\pi$
$90$	−10.2461	−	4.29332i	−1.08004	−	0.452556i
$91$	6.48321	+	2.10652i	0.679625	+	0.220823i
$92$	5.63337	+	5.72639i	0.587320	+	0.597017i
$93$	−1.64562	−	2.26500i	−0.170643	−	0.234870i
$94$	−12.6951	−	10.9328i	−1.30940	−	1.12763i
$95$	1.43487	+	4.41607i	0.147214	+	0.453079i
$96$	2.28352	+	2.03261i	0.233061	+	0.207452i
$97$	−6.96770	−	5.06233i	−0.707463	−	0.514002i	0.174891	−	0.984588i	$-0.444043\pi$
$97$	−6.96770	−	5.06233i	−0.707463	−	0.514002i	−0.882354	+	0.470586i	$0.844043\pi$
$98$	0.0702709	+	0.298070i	0.00709843	+	0.0301096i
$99$		0			0
$100$	6.11111	−	3.05100i	0.611111	−	0.305100i
$101$	5.11721	−	7.04323i	0.509181	−	0.700828i	−0.474600	−	0.880202i	$-0.657407\pi$
$101$	5.11721	−	7.04323i	0.509181	−	0.700828i	0.983781	+	0.179374i	$0.0574071\pi$
$102$	0.434710	−	5.24870i	0.0430427	−	0.519699i
$103$	0.385523	+	1.18652i	0.0379867	+	0.116911i	0.968252	−	0.249977i	$-0.0804231\pi$
$103$	0.385523	+	1.18652i	0.0379867	+	0.116911i	−0.930265	+	0.366888i	$0.880423\pi$
$104$	−1.81645	+	7.17661i	−0.178118	+	0.703724i
$105$	3.30333	−	2.40001i	0.322372	−	0.234217i
$106$	−0.949627	−	1.56399i	−0.0922360	−	0.151908i
$107$	17.8586	+	5.80262i	1.72646	+	0.560960i	0.992930	−	0.118699i	$-0.0378723\pi$
$107$	17.8586	+	5.80262i	1.72646	+	0.560960i	0.733528	+	0.679659i	$0.237872\pi$
$108$	1.01498	−	6.08539i	0.0976660	−	0.585567i
$109$		−	12.1780i		−	1.16644i	−0.812313	−	0.583221i	$-0.801792\pi$
$109$		−	12.1780i		−	1.16644i	0.812313	−	0.583221i	$-0.198208\pi$
$110$		0			0
$111$	4.64195			0.440594
$112$	9.95952	−	3.05667i	0.941086	−	0.288828i
$113$	−1.64044	+	5.04877i	−0.154320	+	0.474948i	−0.998091	−	0.0617546i	$-0.980330\pi$
$113$	−1.64044	+	5.04877i	−0.154320	+	0.474948i	0.843771	+	0.536703i	$0.180330\pi$
$114$	−1.04568	+	0.634922i	−0.0979372	+	0.0594659i
$115$	6.84840	+	9.42602i	0.638617	+	0.878981i
$116$	3.54471	+	1.84284i	0.329118	+	0.171103i
$117$	6.74067	−	2.19018i	0.623175	−	0.202482i
$118$	−0.0410324	+	0.495426i	−0.00377733	+	0.0456076i
$119$	−14.5200	−	10.5494i	−1.33105	−	0.967062i
$120$	2.83815	+	3.40690i	0.259086	+	0.311006i
$121$		0			0
$122$	4.24145	−	0.999934i	0.384003	−	0.0905298i
$123$	1.19083	−	1.63903i	0.107373	−	0.147787i
$124$	−1.53698	−	10.2464i	−0.138025	−	0.920155i
$125$	−4.37234	+	1.42066i	−0.391074	+	0.127068i
$126$	−7.55788	−	6.50874i	−0.673309	−	0.579845i
$127$	8.01911	−	5.82622i	0.711581	−	0.516994i	−0.172102	−	0.985079i	$-0.555056\pi$
$127$	8.01911	−	5.82622i	0.711581	−	0.516994i	0.883683	+	0.468085i	$0.155056\pi$
$128$	4.02828	+	10.5723i	0.356053	+	0.934466i
$129$	−0.412764	+	1.27036i	−0.0363419	+	0.111849i
$130$	−4.14966	+	9.90330i	−0.363949	+	0.868576i
$131$			11.4291i			0.998568i	0.866438	+	0.499284i	$0.166404\pi$
$131$			11.4291i			0.998568i	−0.866438	+	0.499284i	$0.833596\pi$
$132$		0			0
$133$			4.16892i			0.361491i
$134$	13.5580	+	5.68106i	1.17124	+	0.490769i
$135$	2.76523	−	8.51050i	0.237993	−	0.732467i
$136$	10.3872	−	16.4923i	0.890698	−	1.41420i
$137$	−0.949326	+	0.689726i	−0.0811064	+	0.0589272i	−0.627600	−	0.778536i	$-0.715962\pi$
$137$	−0.949326	+	0.689726i	−0.0811064	+	0.0589272i	0.546493	+	0.837464i	$0.315962\pi$
$138$	−2.00313	+	2.32601i	−0.170517	+	0.198003i
$139$	−6.88705	+	2.23774i	−0.584152	+	0.189803i	−0.586160	−	0.810195i	$-0.699361\pi$
$139$	−6.88705	+	2.23774i	−0.584152	+	0.189803i	0.00200768	+	0.999998i	$0.499361\pi$
$140$	14.9436	−	2.24157i	1.26297	−	0.189447i
$141$	3.76318	−	5.17958i	0.316917	−	0.436199i
$142$	−1.12613	−	4.77675i	−0.0945029	−	0.400856i
$143$		0			0
$144$	6.50939	−	8.65764i	0.542449	−	0.721470i
$145$	4.68803	+	3.40605i	0.389320	+	0.282857i
$146$	1.88069	+	0.155764i	0.155647	+	0.0128911i
$147$	−0.111299	+	0.0361633i	−0.00917981	+	0.00298270i
$148$	15.2421	+	7.92409i	1.25289	+	0.651356i
$149$	−7.22411	−	9.94314i	−0.591822	−	0.814574i	0.403107	−	0.915153i	$-0.367930\pi$
$149$	−7.22411	−	9.94314i	−0.591822	−	0.814574i	−0.994929	+	0.100579i	$0.967930\pi$
$150$	1.35468	+	2.23110i	0.110610	+	0.182168i
$151$	−4.46722	+	13.7487i	−0.363537	+	1.11885i	0.587355	+	0.809330i	$0.300169\pi$
$151$	−4.46722	+	13.7487i	−0.363537	+	1.11885i	−0.950892	+	0.309523i	$0.899831\pi$
$152$	−4.51740	+	0.299752i	−0.366410	+	0.0243131i
$153$	−18.6605			−1.50861
$154$		0			0
$155$		−	15.0281i		−	1.20709i
$156$	−2.79040	−	0.465408i	−0.223411	−	0.0372625i
$157$	−16.8777	−	5.48388i	−1.34698	−	0.437662i	−0.455307	−	0.890334i	$-0.650471\pi$
$157$	−16.8777	−	5.48388i	−1.34698	−	0.437662i	−0.891677	+	0.452673i	$0.850471\pi$
$158$	−5.22555	+	3.17287i	−0.415722	+	0.252420i
$159$	0.565670	−	0.410983i	0.0448605	−	0.0325931i
$160$	3.50342	+	16.0316i	0.276969	+	1.26741i
$161$	3.23256	+	9.94879i	0.254761	+	0.784075i
$162$	−9.10006	−	0.753689i	−0.714968	−	0.0592154i
$163$	3.38769	−	4.66275i	0.265344	−	0.365215i	−0.655467	−	0.755224i	$-0.727528\pi$
$163$	3.38769	−	4.66275i	0.265344	−	0.365215i	0.920811	+	0.390009i	$0.127528\pi$
$164$	6.70807	−	3.34903i	0.523812	−	0.261516i
$165$		0			0
$166$	−21.9994	+	5.18642i	−1.70748	+	0.402545i
$167$	−1.91319	−	1.39002i	−0.148047	−	0.107563i	0.511296	−	0.859405i	$-0.329166\pi$
$167$	−1.91319	−	1.39002i	−0.148047	−	0.107563i	−0.659343	+	0.751842i	$0.729166\pi$
$168$	1.47823	+	3.69653i	0.114048	+	0.285193i
$169$	1.90033	+	5.84862i	0.146179	+	0.449894i
$170$	18.4480	−	21.4216i	1.41489	−	1.64296i
$171$	2.54774	+	3.50666i	0.194831	+	0.268161i
$172$	−3.52391	+	3.46667i	−0.268695	+	0.264331i
$173$	−2.35595	−	0.765495i	−0.179120	−	0.0581995i	0.218084	−	0.975930i	$-0.430019\pi$
$173$	−2.35595	−	0.765495i	−0.179120	−	0.0581995i	−0.397204	+	0.917730i	$0.630019\pi$
$174$	−0.590011	+	1.40808i	−0.0447286	+	0.106746i
$175$	8.89490			0.672391
$176$		0			0
$177$	−0.189970			−0.0142790
$178$	7.17281	−	17.1181i	0.537625	−	1.28306i
$179$	−19.4656	−	6.32476i	−1.45493	−	0.472735i	−0.528411	−	0.848989i	$-0.677212\pi$
$179$	−19.4656	−	6.32476i	−1.45493	−	0.472735i	−0.926516	+	0.376254i	$0.877212\pi$
$180$	11.1999	−	11.0179i	0.834789	−	0.821229i
$181$	−10.1360	−	13.9509i	−0.753400	−	1.03697i	−0.997734	−	0.0672748i	$-0.978570\pi$
$181$	−10.1360	−	13.9509i	−0.753400	−	1.03697i	0.244335	−	0.969691i	$-0.421430\pi$
$182$	−6.29095	+	7.30498i	−0.466316	+	0.541481i
$183$	0.514594	+	1.58376i	0.0380398	+	0.117075i
$184$	−10.5480	+	4.21811i	−0.777609	+	0.310963i
$185$	20.1583	+	14.6458i	1.48206	+	1.07678i
$186$	3.85372	−	0.908526i	0.282568	−	0.0666164i
$187$		0			0
$188$	21.1985	−	10.5834i	1.54606	−	0.771875i
$189$	4.72238	−	6.49979i	0.343502	−	0.472790i
$190$	−6.54426	−	0.542011i	−0.474770	−	0.0393216i
$191$	6.26612	+	19.2851i	0.453400	+	1.39542i	0.873003	+	0.487715i	$0.162170\pi$
$191$	6.26612	+	19.2851i	0.453400	+	1.39542i	−0.419602	+	0.907708i	$0.637830\pi$
$192$	−3.89924	+	1.86758i	−0.281403	+	0.134781i
$193$	2.08839	−	1.51731i	0.150326	−	0.109218i	−0.510080	−	0.860127i	$-0.670384\pi$
$193$	2.08839	−	1.51731i	0.150326	−	0.109218i	0.660406	+	0.750909i	$0.270384\pi$
$194$	10.4111	−	6.32146i	0.747475	−	0.453854i
$195$	−3.90242	−	1.26797i	−0.279458	−	0.0908014i
$196$	−0.427189	−	0.0712504i	−0.0305135	−	0.00508932i
$197$			21.0439i			1.49931i	0.661826	+	0.749657i	$0.269782\pi$
$197$			21.0439i			1.49931i	−0.661826	+	0.749657i	$0.730218\pi$
$198$		0			0
$199$	7.98438			0.565998			0.282999	−	0.959120i	$-0.408671\pi$
$199$	7.98438			0.565998			0.282999	+	0.959120i	$0.408671\pi$
$200$	0.639558	+	9.63844i	0.0452236	+	0.681541i
$201$	−1.73591	+	5.34257i	−0.122441	+	0.376836i
$202$	6.38998	+	10.5240i	0.449598	+	0.740464i
$203$	3.05805	+	4.20905i	0.214633	+	0.295417i
$204$	6.60848	+	3.43563i	0.462686	+	0.240543i
$205$	10.3426	−	3.36053i	0.722362	−	0.234710i
$206$	−1.75832	−	0.145629i	−0.122508	−	0.0101464i
$207$	8.79904	+	6.39287i	0.611575	+	0.444335i
$208$	−8.36794	−	6.29158i	−0.580213	−	0.436242i
$209$		0			0
$210$	1.32502	+	5.62036i	0.0914349	+	0.387842i
$211$	−5.54041	+	7.62572i	−0.381418	+	0.524976i	−0.955959	−	0.293499i	$-0.905180\pi$
$211$	−5.54041	+	7.62572i	−0.381418	+	0.524976i	0.574542	+	0.818475i	$0.305180\pi$
$212$	2.55898	−	0.383851i	0.175751	−	0.0263630i
$213$	1.78364	−	0.579539i	0.122213	−	0.0397093i
$214$	−17.3290	+	20.1223i	−1.18459	+	1.37553i
$215$	−5.80059	+	4.21437i	−0.395597	+	0.287418i
$216$	7.38267	+	4.64978i	0.502327	+	0.316377i
$217$	4.16947	−	12.8323i	0.283042	−	0.871115i
$218$	15.8842	+	6.65578i	1.07582	+	0.450786i
$219$			0.721148i			0.0487307i
$220$		0			0
$221$			18.0361i			1.21324i
$222$	−2.53701	+	6.05466i	−0.170273	+	0.406362i
$223$	4.48299	−	13.7972i	0.300203	−	0.923931i	−0.681220	−	0.732078i	$-0.738550\pi$
$223$	4.48299	−	13.7972i	0.300203	−	0.923931i	0.981424	−	0.191853i	$-0.0614495\pi$
$224$	−1.45636	+	14.6612i	−0.0973072	+	0.979590i
$225$	7.48190	−	5.43592i	0.498794	−	0.362395i
$226$	−5.68872	−	4.89905i	−0.378408	−	0.325880i
$227$	2.59106	−	0.841887i	0.171975	−	0.0558780i	−0.221764	−	0.975100i	$-0.571181\pi$
$227$	2.59106	−	0.841887i	0.171975	−	0.0558780i	0.393739	+	0.919222i	$0.371181\pi$
$228$	−0.256643	−	1.71093i	−0.0169966	−	0.113309i
$229$	−8.20634	+	11.2951i	−0.542290	+	0.746399i	−0.988941	−	0.148310i	$-0.952617\pi$
$229$	−8.20634	+	11.2951i	−0.542290	+	0.746399i	0.446651	+	0.894708i	$0.352617\pi$
$230$	−16.0376	+	3.78092i	−1.05749	+	0.249307i
$231$		0			0
$232$	−4.34101	+	3.61632i	−0.285001	+	0.237423i
$233$	10.0579	+	7.30748i	0.658914	+	0.478729i	0.866296	−	0.499531i	$-0.166494\pi$
$233$	10.0579	+	7.30748i	0.658914	+	0.478729i	−0.207382	+	0.978260i	$0.566494\pi$
$234$	−0.827323	+	9.98912i	−0.0540838	+	0.653009i
$235$	32.6842	−	10.6197i	2.13208	−	0.692756i
$236$	−0.623776	−	0.324290i	−0.0406044	−	0.0211095i
$237$	−1.37316	−	1.89000i	−0.0891966	−	0.122769i
$238$	21.6957	−	13.1733i	1.40633	−	0.853898i
$239$	5.51721	−	16.9802i	0.356878	−	1.09836i	−0.598034	−	0.801471i	$-0.704051\pi$
$239$	5.51721	−	16.9802i	0.356878	−	1.09836i	0.954912	−	0.296888i	$-0.0959488\pi$
$240$	−5.99491	+	1.83989i	−0.386969	+	0.118764i
$241$	−0.714420			−0.0460198			−0.0230099	−	0.999735i	$-0.507325\pi$
$241$	−0.714420			−0.0460198			−0.0230099	+	0.999735i	$0.507325\pi$
$242$		0			0
$243$		−	12.7436i		−	0.817501i
$244$	−1.01387	+	6.07878i	−0.0649066	+	0.389154i
$245$	−0.597430	−	0.194117i	−0.0381684	−	0.0124017i
$246$	1.48702	+	2.44904i	0.0948087	+	0.156145i
$247$	3.38933	−	2.46249i	0.215658	−	0.156684i
$248$	14.2048	+	3.59534i	0.902005	+	0.228304i
$249$	−2.66907	−	8.21457i	−0.169146	−	0.520577i
$250$	0.536644	−	6.47945i	0.0339403	−	0.409796i
$251$	−0.888676	+	1.22316i	−0.0560928	+	0.0772051i	−0.836142	−	0.548513i	$-0.815194\pi$
$251$	−0.888676	+	1.22316i	−0.0560928	+	0.0772051i	0.780049	+	0.625718i	$0.215194\pi$
$252$	12.6203	−	6.30073i	0.795002	−	0.396908i
$253$		0			0
$254$	3.21659	+	13.6439i	0.201827	+	0.856094i
$255$	8.73999	+	6.34997i	0.547319	+	0.397651i
$256$	−15.9914	−	0.523938i	−0.999464	−	0.0327461i
$257$	−5.69479	−	17.5268i	−0.355231	−	1.09329i	−0.955875	−	0.293773i	$-0.905089\pi$
$257$	−5.69479	−	17.5268i	−0.355231	−	1.09329i	0.600644	−	0.799517i	$-0.294911\pi$
$258$	−1.43138	−	1.23269i	−0.0891139	−	0.0767436i
$259$	13.1494	+	18.0987i	0.817067	+	1.12460i
$260$	−10.6493	−	10.8251i	−0.660440	−	0.671345i
$261$	5.14453	+	1.67156i	0.318438	+	0.103467i
$262$	−14.9074	−	6.24649i	−0.920984	−	0.385909i
$263$	−11.2903			−0.696191			−0.348096	−	0.937459i	$-0.613172\pi$
$263$	−11.2903			−0.696191			−0.348096	+	0.937459i	$0.613172\pi$
$264$		0			0
$265$	3.75319			0.230556
$266$	−5.43767	−	2.27848i	−0.333405	−	0.139703i
$267$	6.74544	+	2.19173i	0.412814	+	0.134131i
$268$	−14.8200	+	14.5793i	−0.905277	+	0.890573i
$269$	−10.3346	−	14.2243i	−0.630109	−	0.867271i	0.367930	−	0.929853i	$-0.380066\pi$
$269$	−10.3346	−	14.2243i	−0.630109	−	0.867271i	−0.998040	+	0.0625822i	$0.980066\pi$
$270$	9.58924	+	8.25812i	0.583583	+	0.502573i
$271$	−2.01687	−	6.20729i	−0.122516	−	0.377066i	0.870924	−	0.491418i	$-0.163521\pi$
$271$	−2.01687	−	6.20729i	−0.122516	−	0.377066i	−0.993440	+	0.114351i	$0.963521\pi$
$272$	15.8344	+	22.5621i	0.960104	+	1.36803i
$273$	−2.98043	−	2.16541i	−0.180384	−	0.131056i
$274$	−0.380789	−	1.61520i	−0.0230043	−	0.0975780i
$275$		0			0
$276$	−1.93911	−	3.88401i	−0.116721	−	0.233790i
$277$	−0.150651	+	0.207353i	−0.00905172	+	0.0124586i	−0.813519	−	0.581539i	$-0.802451\pi$
$277$	−0.150651	+	0.207353i	−0.00905172	+	0.0124586i	0.804467	+	0.593997i	$0.202451\pi$
$278$	0.845289	−	10.2060i	0.0506971	−	0.612118i
$279$	−4.33505	−	13.3419i	−0.259533	−	0.798760i
$280$	−5.24354	+	20.7166i	−0.313361	+	1.23805i
$281$	−21.0008	+	15.2580i	−1.25280	+	0.910215i	−0.998381	−	0.0568787i	$-0.981885\pi$
$281$	−21.0008	+	15.2580i	−1.25280	+	0.910215i	−0.254422	+	0.967093i	$0.581885\pi$
$282$	4.69918	+	7.73931i	0.279832	+	0.460869i
$283$	8.95062	+	2.90823i	0.532059	+	0.172877i	0.562711	−	0.826654i	$-0.309758\pi$
$283$	8.95062	+	2.90823i	0.532059	+	0.172877i	−0.0306519	+	0.999530i	$0.509758\pi$
$284$	6.84596	+	1.14183i	0.406233	+	0.0677552i
$285$		−	2.50938i		−	0.148643i
$286$		0			0
$287$	9.76379			0.576339
$288$	7.73483	+	13.2222i	0.455779	+	0.779125i
$289$	9.42076	−	28.9941i	0.554162	−	1.70554i
$290$	−7.00484	+	4.25322i	−0.411338	+	0.249758i
$291$	2.73582	+	3.76554i	0.160377	+	0.220740i
$292$	−1.23104	+	2.36792i	−0.0720413	+	0.138572i
$293$	1.82548	−	0.593134i	0.106646	−	0.0346513i	−0.255208	−	0.966886i	$-0.582144\pi$
$293$	1.82548	−	0.593134i	0.106646	−	0.0346513i	0.361854	+	0.932235i	$0.382144\pi$
$294$	0.0136604	−	0.164936i	0.000796692	−	0.00961928i
$295$	−0.824969	−	0.599375i	−0.0480316	−	0.0348970i
$296$	−18.6661	+	15.5499i	−1.08494	+	0.903822i
$297$		0			0
$298$	16.9175	−	3.98834i	0.980002	−	0.231039i
$299$	6.17896	−	8.50461i	0.357338	−	0.491834i
$300$	−3.65049	+	0.547580i	−0.210761	+	0.0316145i
$301$	−6.12229	+	1.98925i	−0.352883	+	0.114659i
$302$	−15.4914	−	13.3410i	−0.891430	−	0.767687i
$303$	−3.80636	+	2.76548i	−0.218669	+	0.158873i
$304$	2.07797	−	6.05604i	0.119180	−	0.347338i
$305$	−2.76223	+	8.50126i	−0.158165	+	0.486781i
$306$	10.1987	−	24.3395i	0.583021	−	1.39140i
$307$		−	10.2272i		−	0.583696i	−0.956465	−	0.291848i	$-0.905730\pi$
$307$		−	10.2272i		−	0.583696i	0.956465	−	0.291848i	$-0.0942702\pi$
$308$		0			0
$309$		−	0.674226i		−	0.0383554i
$310$	19.6018	+	8.21349i	1.11331	+	0.466495i
$311$	−4.62268	+	14.2272i	−0.262128	+	0.806748i	0.730213	+	0.683220i	$0.239421\pi$
$311$	−4.62268	+	14.2272i	−0.262128	+	0.806748i	−0.992341	+	0.123528i	$0.960579\pi$
$312$	2.13212	−	3.38526i	0.120707	−	0.191653i
$313$	3.93324	−	2.85767i	0.222320	−	0.161525i	−0.471050	−	0.882106i	$-0.656125\pi$
$313$	3.93324	−	2.85767i	0.222320	−	0.161525i	0.693370	+	0.720581i	$0.256125\pi$
$314$	16.3772	−	19.0170i	0.924216	−	1.07319i
$315$	19.4582	−	6.32235i	1.09635	−	0.356224i
$316$	−1.28251	−	8.54998i	−0.0721469	−	0.480974i
$317$	−6.28307	+	8.64790i	−0.352892	+	0.485715i	−0.948151	−	0.317819i	$-0.897049\pi$
$317$	−6.28307	+	8.64790i	−0.352892	+	0.485715i	0.595259	+	0.803534i	$0.297049\pi$
$318$	0.226899	+	0.962442i	0.0127238	+	0.0539711i
$319$		0			0
$320$	−22.8254	−	4.19229i	−1.27598	−	0.234356i
$321$	−8.20988	−	5.96482i	−0.458231	−	0.332924i
$322$	−14.7433	−	1.22108i	−0.821612	−	0.0680479i
$323$	−10.4903	+	3.40850i	−0.583696	+	0.189654i
$324$	5.95662	−	11.4576i	0.330923	−	0.636534i
$325$	−5.25403	−	7.23155i	−0.291441	−	0.401134i
$326$	4.23029	+	6.96707i	0.234294	+	0.385870i
$327$	−2.03374	+	6.25922i	−0.112466	+	0.346136i
$328$	0.702033	+	10.5800i	0.0387633	+	0.584181i
$329$	30.8550			1.70109
$330$		0			0
$331$			21.3447i			1.17321i	0.809874	+	0.586604i	$0.199536\pi$
$331$			21.3447i			1.17321i	−0.809874	+	0.586604i	$0.800464\pi$
$332$	5.25872	−	31.5292i	0.288610	−	1.73039i
$333$	22.1212	+	7.18761i	1.21223	+	0.393879i
$334$	2.85869	−	1.73575i	0.156420	−	0.0949759i
$335$	−24.3948	+	17.7238i	−1.33283	+	0.968357i
$336$	−5.62943	−	0.0921956i	−0.307111	−	0.00502968i
$337$	−2.42159	−	7.45289i	−0.131913	−	0.405985i	0.863184	−	0.504889i	$-0.168466\pi$
$337$	−2.42159	−	7.45289i	−0.131913	−	0.405985i	−0.995097	+	0.0989036i	$0.968466\pi$
$338$	−8.66717	−	0.717836i	−0.471432	−	0.0390451i
$339$	1.68630	−	2.32099i	0.0915873	−	0.126059i
$340$	17.8584	+	35.7701i	0.968507	+	1.93991i
$341$		0			0
$342$	−5.96631	+	1.40658i	−0.322621	+	0.0760589i
$343$	−15.2059	−	11.0477i	−0.821042	−	0.596522i
$344$	−2.59574	−	6.49103i	−0.139953	−	0.349973i
$345$	−1.94576	−	5.98845i	−0.104756	−	0.322407i
$346$	2.28609	−	2.65458i	0.122901	−	0.142711i
$347$	−16.0312	−	22.0651i	−0.860601	−	1.18452i	−0.981426	−	0.191841i	$-0.938554\pi$
$347$	−16.0312	−	22.0651i	−0.860601	−	1.18452i	0.120825	−	0.992674i	$-0.461446\pi$
$348$	−1.51415	−	1.53915i	−0.0811667	−	0.0825069i
$349$	−7.12749	−	2.31586i	−0.381526	−	0.123965i	0.111974	−	0.993711i	$-0.464283\pi$
$349$	−7.12749	−	2.31586i	−0.381526	−	0.123965i	−0.493500	+	0.869746i	$0.664283\pi$
$350$	−4.86142	+	11.6019i	−0.259854	+	0.620150i
$351$	−8.07373			−0.430944
$352$		0			0
$353$	18.1327			0.965105			0.482552	−	0.875867i	$-0.339710\pi$
$353$	18.1327			0.965105			0.482552	+	0.875867i	$0.339710\pi$
$354$	0.103826	−	0.247785i	0.00551831	−	0.0131696i
$355$	9.57417	+	3.11084i	0.508144	+	0.165106i
$356$	18.4076	+	18.7115i	0.975599	+	0.991708i
$357$	5.70119	+	7.84701i	0.301739	+	0.415308i
$358$	18.8884	−	21.9330i	0.998280	−	1.15919i
$359$	1.48874	+	4.58186i	0.0785726	+	0.241821i	0.982626	−	0.185599i	$-0.0594225\pi$
$359$	1.48874	+	4.58186i	0.0785726	+	0.241821i	−0.904053	+	0.427420i	$0.859422\pi$
$360$	8.24992	+	20.6302i	0.434809	+	1.08730i
$361$	−13.2985	−	9.66196i	−0.699923	−	0.508524i
$362$	23.7364	−	5.59594i	1.24756	−	0.294116i
$363$		0			0
$364$	−6.08989	−	12.1980i	−0.319197	−	0.639348i
$365$	−2.27530	+	3.13168i	−0.119094	+	0.163920i
$366$	−2.34700	−	0.194384i	−0.122679	−	0.0101606i
$367$	−2.61034	−	8.03381i	−0.136259	−	0.419361i	0.859525	−	0.511094i	$-0.170760\pi$
$367$	−2.61034	−	8.03381i	−0.136259	−	0.419361i	−0.995784	+	0.0917325i	$0.970760\pi$
$368$	0.263079	−	16.0635i	0.0137139	−	0.837368i
$369$	8.21277	−	5.96693i	0.427540	−	0.310626i
$370$	−30.1204	+	18.2886i	−1.56589	+	0.950780i
$371$	3.20479	+	1.04130i	0.166384	+	0.0540616i
$372$	−0.921191	+	5.52309i	−0.0477615	+	0.286359i
$373$		−	27.7651i		−	1.43762i	−0.695207	−	0.718810i	$-0.744687\pi$
$373$		−	27.7651i		−	1.43762i	0.695207	−	0.718810i	$-0.255313\pi$
$374$		0			0
$375$	2.48453			0.128301
$376$	2.21852	+	33.4342i	0.114412	+	1.72424i
$377$	1.61563	−	4.97239i	0.0832090	−	0.256091i
$378$	5.89695	+	9.71197i	0.303306	+	0.499530i
$379$	9.01289	+	12.4052i	0.462961	+	0.637211i	0.975120	−	0.221680i	$-0.0711539\pi$
$379$	9.01289	+	12.4052i	0.462961	+	0.637211i	−0.512158	+	0.858891i	$0.671154\pi$
$380$	4.28367	−	8.23968i	0.219748	−	0.422687i
$381$	−5.09462	+	1.65534i	−0.261005	+	0.0848058i
$382$	−28.5790	−	2.36698i	−1.46223	−	0.121105i
$383$	9.60199	+	6.97625i	0.490639	+	0.356470i	0.805430	−	0.592691i	$-0.201934\pi$
$383$	9.60199	+	6.97625i	0.490639	+	0.356470i	−0.314791	+	0.949161i	$0.601934\pi$
$384$	−0.304863	−	6.10663i	−0.0155575	−	0.311628i
$385$		0			0
$386$	0.837687	+	3.55324i	0.0426371	+	0.180855i
$387$	−3.93405	+	5.41475i	−0.199979	+	0.275247i
$388$	2.55521	+	17.0345i	0.129721	+	0.864798i
$389$	4.31984	−	1.40360i	0.219025	−	0.0711654i	−0.197449	−	0.980313i	$-0.563266\pi$
$389$	4.31984	−	1.40360i	0.219025	−	0.0711654i	0.416474	+	0.909148i	$0.363266\pi$
$390$	3.78669	−	4.39707i	0.191747	−	0.222654i
$391$	−22.3913	+	16.2683i	−1.13238	+	0.822721i
$392$	0.326411	−	0.518257i	0.0164862	−	0.0261759i
$393$	1.90868	−	5.87431i	0.0962801	−	0.296320i
$394$	−27.4483	−	11.5013i	−1.38283	−	0.579429i
$395$		−	12.5400i		−	0.630958i
$396$		0			0
$397$		−	10.8631i		−	0.545204i	−0.962127	−	0.272602i	$-0.912116\pi$
$397$		−	10.8631i		−	0.545204i	0.962127	−	0.272602i	$-0.0878841\pi$
$398$	−4.36379	+	10.4143i	−0.218737	+	0.522022i
$399$	0.696214	−	2.14273i	0.0348543	−	0.107270i
$400$	−12.9213	−	4.43360i	−0.646066	−	0.221680i
$401$	−1.87813	+	1.36454i	−0.0937894	+	0.0681420i	−0.633692	−	0.773586i	$-0.718461\pi$
$401$	−1.87813	+	1.36454i	−0.0937894	+	0.0681420i	0.539902	+	0.841728i	$0.318461\pi$
$402$	−6.01977	−	5.18414i	−0.300239	−	0.258561i
$403$	−12.8955	+	4.19000i	−0.642370	+	0.208719i
$404$	−17.2192	+	2.58291i	−0.856687	+	0.128505i
$405$	11.0094	−	15.1532i	0.547063	−	0.752967i
$406$	−7.16136	+	1.68831i	−0.355412	+	0.0837895i
$407$		0			0
$408$	−8.09303	+	6.74197i	−0.400664	+	0.333777i
$409$	−20.4112	−	14.8296i	−1.00927	−	0.733277i	−0.0452131	−	0.998977i	$-0.514397\pi$
$409$	−20.4112	−	14.8296i	−1.00927	−	0.733277i	−0.964056	+	0.265701i	$0.914397\pi$
$410$	−1.26942	+	15.3270i	−0.0626919	+	0.756944i
$411$	0.603116	−	0.195964i	0.0297495	−	0.00966621i
$412$	1.15094	−	2.21385i	0.0567029	−	0.109069i
$413$	−0.538136	−	0.740681i	−0.0264800	−	0.0364465i
$414$	−13.1475	+	7.98294i	−0.646164	+	0.392340i
$415$	14.3270	−	44.0940i	0.703285	−	2.16449i
$416$	12.7798	−	7.47601i	0.626579	−	0.366542i
$417$	3.91349			0.191644
$418$		0			0
$419$		−	16.7174i		−	0.816696i	−0.912826	−	0.408348i	$-0.866105\pi$
$419$		−	16.7174i		−	0.816696i	0.912826	−	0.408348i	$-0.133895\pi$
$420$	−8.05502	−	1.34349i	−0.393045	−	0.0655555i
$421$	−9.03716	−	2.93635i	−0.440444	−	0.143109i	0.0803964	−	0.996763i	$-0.474381\pi$
$421$	−9.03716	−	2.93635i	−0.440444	−	0.143109i	−0.520841	+	0.853654i	$0.674381\pi$
$422$	−6.91845	−	11.3943i	−0.336785	−	0.554667i
$423$	25.9535	−	18.8563i	1.26190	−	0.916826i
$424$	−0.897914	+	3.54756i	−0.0436065	+	0.172285i
$425$	7.27247	+	22.3824i	0.352767	+	1.08570i
$426$	−0.218916	+	2.64320i	−0.0106065	+	0.128064i
$427$	−4.71725	+	6.49274i	−0.228284	+	0.314206i
$428$	−16.7752	−	33.6005i	−0.810860	−	1.62414i
$429$		0			0
$430$	−2.32670	−	9.86925i	−0.112204	−	0.475937i
$431$	−25.2075	−	18.3143i	−1.21420	−	0.882171i	−0.218598	−	0.975815i	$-0.570148\pi$
$431$	−25.2075	−	18.3143i	−1.21420	−	0.882171i	−0.995606	+	0.0936441i	$0.970148\pi$
$432$	−10.0998	+	7.08819i	−0.485927	+	0.341031i
$433$	−1.54212	−	4.74614i	−0.0741094	−	0.228085i	0.907140	−	0.420830i	$-0.138261\pi$
$433$	−1.54212	−	4.74614i	−0.0741094	−	0.228085i	−0.981249	+	0.192745i	$0.938261\pi$
$434$	14.4589	+	12.4518i	0.694048	+	0.597705i
$435$	−1.84072	−	2.53354i	−0.0882559	−	0.121474i
$436$	−17.3628	+	17.0807i	−0.831525	+	0.818018i
$437$	6.11424	+	1.98664i	0.292484	+	0.0950338i
$438$	−0.940620	−	0.394137i	−0.0449445	−	0.0188326i
$439$	−22.9729			−1.09644			−0.548219	−	0.836335i	$-0.684694\pi$
$439$	−22.9729			−1.09644			−0.548219	+	0.836335i	$0.684694\pi$
$440$		0			0
$441$	−0.586391			−0.0279234
$442$	−23.5251	−	9.85744i	−1.11897	−	0.468871i
$443$	27.0521	+	8.78977i	1.28529	+	0.417615i	0.870439	−	0.492277i	$-0.163835\pi$
$443$	27.0521	+	8.78977i	1.28529	+	0.417615i	0.414847	+	0.909891i	$0.363835\pi$
$444$	−6.51074	−	6.61824i	−0.308986	−	0.314088i
$445$	22.3778	+	30.8004i	1.06081	+	1.46008i
$446$	15.5461	+	13.3881i	0.736129	+	0.633944i
$447$	2.05251	+	6.31698i	0.0970804	+	0.298783i
$448$	−18.3271	−	9.91250i	−0.865875	−	0.468322i
$449$	−9.21473	−	6.69489i	−0.434870	−	0.315952i	0.348723	−	0.937226i	$-0.386615\pi$
$449$	−9.21473	−	6.69489i	−0.434870	−	0.315952i	−0.783593	+	0.621274i	$0.786615\pi$
$450$	3.00111	+	12.7299i	0.141473	+	0.600092i
$451$		0			0
$452$	9.49913	−	4.74248i	0.446801	−	0.223068i
$453$	4.59209	−	6.32048i	0.215755	−	0.296962i
$454$	−0.318017	+	3.83974i	−0.0149253	+	0.180208i
$455$	−6.11080	−	18.8071i	−0.286479	−	0.881691i
$456$	2.37190	+	0.600346i	0.111074	+	0.0281138i
$457$	11.2666	−	8.18567i	0.527029	−	0.382909i	−0.292216	−	0.956352i	$-0.594393\pi$
$457$	11.2666	−	8.18567i	0.527029	−	0.382909i	0.819245	+	0.573443i	$0.194393\pi$
$458$	−10.2475	−	16.8770i	−0.478832	−	0.788612i
$459$	20.2165	+	6.56875i	0.943627	+	0.306603i
$460$	3.83363	−	22.9849i	0.178744	−	1.07168i
$461$			12.8159i			0.596895i	0.954426	+	0.298447i	$0.0964687\pi$
$461$			12.8159i			0.596895i	−0.954426	+	0.298447i	$0.903531\pi$
$462$		0			0
$463$	−38.2137			−1.77594			−0.887970	−	0.459902i	$-0.847884\pi$
$463$	−38.2137			−1.77594			−0.887970	+	0.459902i	$0.847884\pi$
$464$	−2.34435	−	7.63860i	−0.108834	−	0.354613i
$465$	−2.50972	+	7.72412i	−0.116385	+	0.358198i
$466$	−15.0285	+	9.12503i	−0.696180	+	0.422709i
$467$	−19.1899	−	26.4126i	−0.888003	−	1.22223i	−0.974139	−	0.225948i	$-0.927452\pi$
$467$	−19.1899	−	26.4126i	−0.888003	−	1.22223i	0.0861364	−	0.996283i	$-0.472548\pi$
$468$	−12.5770	−	6.53857i	−0.581372	−	0.302245i
$469$	−25.7477	+	8.36594i	−1.18892	+	0.386303i
$470$	−4.01153	+	48.4353i	−0.185038	+	2.23416i
$471$	7.75891	+	5.63718i	0.357512	+	0.259747i
$472$	0.763903	−	0.636376i	0.0351615	−	0.0292916i
$473$		0			0
$474$	3.21568	−	0.758107i	0.147701	−	0.0348210i
$475$	3.21316	−	4.42253i	0.147430	−	0.202920i
$476$	5.32481	+	35.4983i	0.244062	+	1.62706i
$477$	3.33206	−	1.08265i	0.152565	−	0.0495713i
$478$	19.1325	+	16.4767i	0.875102	+	0.753625i
$479$	−21.0573	+	15.2990i	−0.962133	+	0.699031i	−0.953645	−	0.300933i	$-0.902702\pi$
$479$	−21.0573	+	15.2990i	−0.962133	+	0.699031i	−0.00848808	+	0.999964i	$0.502702\pi$
$480$	0.876623	−	8.82495i	0.0400122	−	0.402802i
$481$	6.94710	−	21.3810i	0.316761	−	0.974889i
$482$	0.390459	−	0.931844i	0.0177849	−	0.0424443i
$483$		−	5.65329i		−	0.257234i
$484$		0			0
$485$			24.9841i			1.13447i
$486$	16.6219	+	6.96488i	0.753985	+	0.315933i
$487$	1.72449	−	5.30742i	0.0781439	−	0.240502i	−0.904352	−	0.426788i	$-0.859645\pi$
$487$	1.72449	−	5.30742i	0.0781439	−	0.240502i	0.982496	+	0.186286i	$0.0596451\pi$
$488$	−7.37465	−	4.64473i	−0.333835	−	0.210257i
$489$	−2.51988	+	1.83080i	−0.113953	+	0.0827916i
$490$	0.579713	−	0.673157i	0.0261888	−	0.0304101i
$491$	−23.2786	+	7.56367i	−1.05055	+	0.341344i	−0.782883	−	0.622169i	$-0.786252\pi$
$491$	−23.2786	+	7.56367i	−1.05055	+	0.341344i	−0.267664	+	0.963512i	$0.586252\pi$
$492$	−4.00709	+	0.601070i	−0.180653	+	0.0270983i
$493$	−8.09102	+	11.1363i	−0.364401	+	0.501555i
$494$	1.35951	+	5.76667i	0.0611673	+	0.259455i
$495$		0			0
$496$	−12.4530	+	16.5628i	−0.559157	+	0.743692i
$497$	7.31216	+	5.31260i	0.327995	+	0.238303i
$498$	12.1733	+	1.00822i	0.545499	+	0.0451796i
$499$	−19.9536	+	6.48333i	−0.893248	+	0.290234i	−0.719447	−	0.694547i	$-0.755605\pi$
$499$	−19.9536	+	6.48333i	−0.893248	+	0.290234i	−0.173800	+	0.984781i	$0.555605\pi$
$500$	8.15808	+	4.24125i	0.364841	+	0.189674i
$501$	0.751203	+	1.03394i	0.0335613	+	0.0461931i
$502$	−1.10971	−	1.82764i	−0.0495289	−	0.0815715i
$503$	−7.52917	+	23.1724i	−0.335709	+	1.03321i	0.630663	+	0.776057i	$0.282783\pi$
$503$	−7.52917	+	23.1724i	−0.335709	+	1.03321i	−0.966372	+	0.257149i	$0.917217\pi$
$504$	1.32077	+	19.9047i	0.0588320	+	0.886625i
$505$	−25.2550			−1.12383
$506$		0			0
$507$		−	3.32341i		−	0.147598i
$508$	−19.5542	−	3.26143i	−0.867578	−	0.144702i
$509$	28.6859	+	9.32062i	1.27148	+	0.413129i	0.865572	−	0.500785i	$-0.166955\pi$
$509$	28.6859	+	9.32062i	1.27148	+	0.413129i	0.405909	+	0.913914i	$0.366955\pi$
$510$	−13.0593	+	7.92937i	−0.578274	+	0.351118i
$511$	−2.81171	+	2.04283i	−0.124383	+	0.0903693i
$512$	9.42335	−	20.5718i	0.416457	−	0.909155i
$513$	−1.52580	−	4.69592i	−0.0673656	−	0.207330i
$514$	25.9732	+	2.15116i	1.14563	+	0.0948838i
$515$	2.12725	−	2.92791i	0.0937379	−	0.129019i
$516$	2.39014	−	1.19329i	0.105220	−	0.0525316i
$517$		0			0
$518$	−30.7934	+	7.25965i	−1.35299	+	0.318971i
$519$	1.08307	+	0.786894i	0.0475413	+	0.0345408i
$520$	19.9398	−	7.97387i	0.874420	−	0.349677i
$521$	−7.56112	−	23.2707i	−0.331259	−	1.01951i	−0.968536	−	0.248874i	$-0.919939\pi$
$521$	−7.56112	−	23.2707i	−0.331259	−	1.01951i	0.637277	−	0.770635i	$-0.280061\pi$
$522$	−4.99197	+	5.79662i	−0.218493	+	0.253711i
$523$	−9.68546	−	13.3309i	−0.423516	−	0.582919i	0.542934	−	0.839775i	$-0.317313\pi$
$523$	−9.68546	−	13.3309i	−0.423516	−	0.582919i	−0.966450	+	0.256856i	$0.917313\pi$
$524$	16.2950	−	16.0304i	0.711852	−	0.700289i
$525$	−4.57177	−	1.48546i	−0.199529	−	0.0648308i
$526$	6.17062	−	14.7264i	0.269052	−	0.642101i
$527$	35.6991			1.55508
$528$		0			0
$529$	−6.86841			−0.298626
$530$	−2.05127	+	4.89542i	−0.0891014	+	0.212643i
$531$	−0.905301	−	0.294150i	−0.0392867	−	0.0127650i
$532$	5.94381	−	5.84727i	0.257697	−	0.253511i
$533$	−5.76726	−	7.93796i	−0.249808	−	0.343831i
$534$	−6.54540	+	7.60045i	−0.283247	+	0.328904i
$535$	−16.8328	−	51.8060i	−0.727745	−	2.23977i
$536$	−10.9166	−	27.2985i	−0.471524	−	1.17912i
$537$	8.94863	+	6.50156i	0.386162	+	0.280563i
$538$	24.2015	−	5.70558i	1.04340	−	0.245985i
$539$		0			0
$540$	−16.0123	+	7.99420i	−0.689059	+	0.344016i
$541$	8.63691	−	11.8877i	0.371330	−	0.511092i	−0.581932	−	0.813238i	$-0.697703\pi$
$541$	8.63691	−	11.8877i	0.371330	−	0.511092i	0.953262	+	0.302146i	$0.0977030\pi$
$542$	9.19870	+	0.761859i	0.395118	+	0.0327246i
$543$	2.87982	+	8.86318i	0.123585	+	0.380355i
$544$	−38.0828	+	8.32230i	−1.63279	+	0.356816i
$545$	−28.5803	+	20.7648i	−1.22424	+	0.889465i
$546$	4.45334	−	2.70400i	0.190585	−	0.115720i
$547$	−21.3069	−	6.92304i	−0.911019	−	0.296008i	−0.184241	−	0.982881i	$-0.558983\pi$
$547$	−21.3069	−	6.92304i	−0.911019	−	0.296008i	−0.726777	+	0.686873i	$0.758983\pi$
$548$	2.31489	+	0.386097i	0.0988870	+	0.0164933i
$549$			8.34418i			0.356121i
$550$		0			0
$551$	3.19741			0.136214
$552$	6.12586	−	0.406481i	0.260734	−	0.0173010i
$553$	3.47916	−	10.7078i	0.147949	−	0.455340i
$554$	−0.188121	−	0.309826i	−0.00799250	−	0.0131632i
$555$	−7.91501	−	10.8941i	−0.335973	−	0.462428i
$556$	12.8501	+	6.68056i	0.544967	+	0.283319i
$557$	3.83093	−	1.24474i	0.162322	−	0.0527415i	−0.226729	−	0.973958i	$-0.572803\pi$
$557$	3.83093	−	1.24474i	0.162322	−	0.0527415i	0.389051	+	0.921216i	$0.372803\pi$
$558$	19.7716	+	1.63753i	0.837000	+	0.0693224i
$559$	5.23357	+	3.80241i	0.221356	+	0.160825i
$560$	−24.1556	−	18.1618i	−1.02076	−	0.767476i
$561$		0			0
$562$	−8.42374	−	35.7312i	−0.355334	−	1.50723i
$563$	1.43161	−	1.97045i	0.0603353	−	0.0830444i	−0.777783	−	0.628533i	$-0.783656\pi$
$563$	1.43161	−	1.97045i	0.0603353	−	0.0830444i	0.838118	+	0.545488i	$0.183656\pi$
$564$	−12.6630	+	1.89947i	−0.533207	+	0.0799819i
$565$	14.6460	−	4.75876i	0.616160	−	0.200203i
$566$	−8.68519	+	10.0852i	−0.365066	+	0.423911i
$567$	13.6049	−	9.88457i	0.571354	−	0.415113i
$568$	−5.23093	+	8.30538i	−0.219485	+	0.348486i
$569$	1.18299	−	3.64086i	0.0495935	−	0.152633i	−0.923193	−	0.384337i	$-0.874430\pi$
$569$	1.18299	−	3.64086i	0.0495935	−	0.152633i	0.972786	+	0.231704i	$0.0744301\pi$
$570$	3.27308	+	1.37148i	0.137094	+	0.0574450i
$571$			42.5296i			1.77981i	0.456149	+	0.889903i	$0.349228\pi$
$571$			42.5296i			1.77981i	−0.456149	+	0.889903i	$0.650772\pi$
$572$		0			0
$573$		−	10.9586i		−	0.457800i
$574$	−5.33631	+	12.7353i	−0.222733	+	0.531560i
$575$	4.23874	−	13.0455i	0.176768	−	0.544035i
$576$	−21.4736	+	2.86236i	−0.894732	+	0.119265i
$577$	−14.4316	+	10.4852i	−0.600797	+	0.436505i	−0.846162	−	0.532926i	$-0.821092\pi$
$577$	−14.4316	+	10.4852i	−0.600797	+	0.436505i	0.245364	+	0.969431i	$0.421092\pi$
$578$	32.6693	+	28.1343i	1.35886	+	1.17023i
$579$	−1.32678	+	0.431097i	−0.0551390	+	0.0179158i
$580$	−1.71920	−	11.4612i	−0.0713860	−	0.475901i
$581$	24.4673	−	33.6763i	1.01507	−	1.39713i
$582$	−6.40677	+	1.51041i	−0.265569	+	0.0626087i
$583$		0			0
$584$	−2.41576	−	2.89986i	−0.0999647	−	0.119997i
$585$	−16.6336	−	12.0850i	−0.687715	−	0.499654i
$586$	−0.224052	+	2.70521i	−0.00925551	+	0.111751i
$587$	−0.553041	+	0.179694i	−0.0228265	+	0.00741676i	−0.320408	−	0.947280i	$-0.603820\pi$
$587$	−0.553041	+	0.179694i	−0.0228265	+	0.00741676i	0.297582	+	0.954696i	$0.403820\pi$
$588$	0.207666	+	0.107962i	0.00856402	+	0.00445229i
$589$	−4.87405	−	6.70855i	−0.200832	−	0.276421i
$590$	1.23267	−	0.748455i	0.0507481	−	0.0308134i
$591$	3.51435	−	10.8161i	0.144561	−	0.444914i
$592$	−10.0806	−	32.8455i	−0.414310	−	1.34994i
$593$	−8.33594			−0.342316			−0.171158	−	0.985244i	$-0.554751\pi$
$593$	−8.33594			−0.342316			−0.171158	+	0.985244i	$0.554751\pi$
$594$		0			0
$595$			52.0645i			2.13443i
$596$	−4.04394	+	24.2459i	−0.165646	+	0.993149i
$597$	−4.10378	−	1.33340i	−0.167957	−	0.0545725i
$598$	7.71582	+	12.7076i	0.315523	+	0.519651i
$599$	5.82516	−	4.23223i	0.238010	−	0.172924i	−0.462386	−	0.886679i	$-0.653007\pi$
$599$	5.82516	−	4.23223i	0.238010	−	0.172924i	0.700396	+	0.713754i	$0.253007\pi$
$600$	1.28091	−	5.06074i	0.0522930	−	0.206604i
$601$	−7.43698	−	22.8887i	−0.303361	−	0.933649i	−0.980284	−	0.197595i	$-0.936687\pi$
$601$	−7.43698	−	22.8887i	−0.303361	−	0.933649i	0.676923	−	0.736054i	$-0.263313\pi$
$602$	0.751426	−	9.07274i	0.0306258	−	0.369777i
$603$	−16.5449	+	22.7721i	−0.673761	+	0.927353i
$604$	25.8678	−	12.9146i	1.05255	−	0.525488i
$605$		0			0
$606$	−1.52679	−	6.47621i	−0.0620215	−	0.263078i
$607$	19.0386	+	13.8324i	0.772753	+	0.561438i	0.902795	−	0.430070i	$-0.141511\pi$
$607$	19.0386	+	13.8324i	0.772753	+	0.561438i	−0.130042	+	0.991508i	$0.541511\pi$
$608$	6.76342	+	6.02024i	0.274293	+	0.244153i
$609$	−0.868852	−	2.67405i	−0.0352076	−	0.108358i
$610$	−9.57883	−	8.24915i	−0.387836	−	0.333999i
$611$	−18.2254	−	25.0851i	−0.737320	−	1.01483i
$612$	26.1729	+	26.6051i	1.05798	+	1.07545i
$613$	39.1776	+	12.7296i	1.58237	+	0.514143i	0.962665	−	0.270694i	$-0.0872532\pi$
$613$	39.1776	+	12.7296i	1.58237	+	0.514143i	0.619703	+	0.784837i	$0.287253\pi$
$614$	13.3397	+	5.58957i	0.538346	+	0.225577i
$615$	−5.87709			−0.236987
$616$		0			0
$617$	14.6295			0.588961			0.294481	−	0.955657i	$-0.404853\pi$
$617$	14.6295			0.588961			0.294481	+	0.955657i	$0.404853\pi$
$618$	0.879417	+	0.368492i	0.0353754	+	0.0148229i
$619$	−19.4977	−	6.33519i	−0.783679	−	0.254633i	−0.110269	−	0.993902i	$-0.535171\pi$
$619$	−19.4977	−	6.33519i	−0.783679	−	0.254633i	−0.673410	+	0.739269i	$0.735171\pi$
$620$	−21.4263	+	21.0783i	−0.860502	+	0.846524i
$621$	−7.28239	−	10.0233i	−0.292232	−	0.402223i
$622$	−16.0305	−	13.8052i	−0.642765	−	0.553540i
$623$	10.5627	+	32.5086i	0.423185	+	1.30243i
$624$	3.25023	+	4.63118i	0.130113	+	0.185396i
$625$	24.6042	+	17.8760i	0.984166	+	0.715039i
$626$	1.57768	+	6.69210i	0.0630569	+	0.267470i
$627$		0			0
$628$	15.8538	+	31.7549i	0.632634	+	1.26716i
$629$	−34.7909	+	47.8856i	−1.38720	+	1.90932i
$630$	−2.38822	+	28.8355i	−0.0951491	+	1.14883i
$631$	−10.5080	−	32.3403i	−0.418317	−	1.28745i	−0.909250	−	0.416251i	$-0.863344\pi$
$631$	−10.5080	−	32.3403i	−0.418317	−	1.28745i	0.490932	−	0.871198i	$-0.336656\pi$
$632$	11.8530	+	3.00008i	0.471487	+	0.119337i
$633$	4.12115	−	2.99419i	0.163801	−	0.119008i
$634$	−7.84582	−	12.9217i	−0.311597	−	0.513185i
$635$	−27.3468	−	8.88552i	−1.08523	−	0.352611i
$636$	−1.37936	−	0.230062i	−0.0546951	−	0.00912254i
$637$			0.566770i			0.0224562i
$638$		0			0
$639$	9.39727			0.371750
$640$	17.9431	−	27.4807i	0.709265	−	1.08627i
$641$	−8.94090	+	27.5173i	−0.353144	+	1.08687i	0.603933	+	0.797035i	$0.293599\pi$
$641$	−8.94090	+	27.5173i	−0.353144	+	1.08687i	−0.957078	+	0.289832i	$0.906401\pi$
$642$	12.2672	−	7.44842i	0.484146	−	0.293966i
$643$	9.90117	+	13.6278i	0.390464	+	0.537428i	0.958319	−	0.285701i	$-0.0922264\pi$
$643$	9.90117	+	13.6278i	0.390464	+	0.537428i	−0.567855	+	0.823129i	$0.692226\pi$
$644$	9.65050	−	18.5629i	0.380283	−	0.731479i
$645$	3.68517	−	1.19739i	0.145104	−	0.0471470i
$646$	1.28754	−	15.5458i	0.0506575	−	0.611640i
$647$	−22.0123	−	15.9929i	−0.865393	−	0.628744i	0.0639541	−	0.997953i	$-0.479629\pi$
$647$	−22.0123	−	15.9929i	−0.865393	−	0.628744i	−0.929347	+	0.369208i	$0.879629\pi$
$648$	11.6891	+	14.0315i	0.459189	+	0.551209i
$649$		0			0
$650$	12.3039	−	2.90068i	0.482599	−	0.113774i
$651$	−4.28603	+	5.89921i	−0.167983	+	0.231208i
$652$	−11.3994	+	1.70993i	−0.446436	+	0.0669662i
$653$	16.6791	−	5.41938i	0.652705	−	0.212077i	0.0360983	−	0.999348i	$-0.488507\pi$
$653$	16.6791	−	5.41938i	0.652705	−	0.212077i	0.616606	+	0.787272i	$0.288507\pi$
$654$	−7.05260	−	6.07360i	−0.275779	−	0.237497i
$655$	26.8227	−	19.4879i	1.04805	−	0.761454i
$656$	−14.1835	−	4.86669i	−0.553773	−	0.190012i
$657$	−1.11663	+	3.43663i	−0.0435638	+	0.134076i
$658$	−16.8635	+	40.2453i	−0.657407	+	1.56892i
$659$		−	0.0398060i		−	0.00155062i	−1.00000		0.000775311i	$-0.999753\pi$
$659$		−	0.0398060i		−	0.00155062i	1.00000		0.000775311i	$-0.000246789\pi$
$660$		0			0
$661$		−	33.5882i		−	1.30643i	−0.757173	−	0.653214i	$-0.773420\pi$
$661$		−	33.5882i		−	1.30643i	0.757173	−	0.653214i	$-0.226580\pi$
$662$	−27.8406	−	11.6657i	−1.08206	−	0.453401i
$663$	3.01204	−	9.27012i	0.116978	−	0.360022i
$664$	38.2506	+	24.0911i	1.48441	+	0.934917i
$665$	9.78392	−	7.10844i	0.379404	−	0.275653i
$666$	−21.4652	+	24.9251i	−0.831759	+	0.965830i
$667$	7.63037	−	2.47926i	0.295449	−	0.0959972i
$668$	0.701610	+	4.67735i	0.0271461	+	0.180972i
$669$	−4.60831	+	6.34279i	−0.178167	+	0.245227i
$670$	−9.78512	−	41.5058i	−0.378032	−	1.60351i
$671$		0			0
$672$	3.19697	−	7.29228i	0.123326	−	0.281306i
$673$	−4.05440	−	2.94569i	−0.156286	−	0.113548i	0.506894	−	0.862008i	$-0.330794\pi$
$673$	−4.05440	−	2.94569i	−0.156286	−	0.113548i	−0.663180	+	0.748460i	$0.730794\pi$
$674$	11.0446	+	0.914739i	0.425421	+	0.0352344i
$675$	−10.0193	+	3.25548i	−0.385644	+	0.125303i
$676$	5.67326	−	10.9126i	0.218202	−	0.419715i
$677$	8.76042	+	12.0577i	0.336690	+	0.463414i	0.943471	−	0.331455i	$-0.107539\pi$
$677$	8.76042	+	12.0577i	0.336690	+	0.463414i	−0.606781	+	0.794869i	$0.707539\pi$
$678$	2.10573	+	3.46802i	0.0808699	+	0.133189i
$679$	−6.93170	+	21.3336i	−0.266014	+	0.818708i
$680$	−56.4166	+	3.74352i	−2.16348	+	0.143558i
$681$	−1.47234			−0.0564203
$682$		0			0
$683$			31.7556i			1.21510i	0.794283	+	0.607548i	$0.207847\pi$
$683$			31.7556i			1.21510i	−0.794283	+	0.607548i	$0.792153\pi$
$684$	1.42618	−	8.55083i	0.0545315	−	0.326949i
$685$	3.23740	+	1.05189i	0.123695	+	0.0401908i
$686$	22.7206	−	13.7956i	0.867477	−	0.526718i
$687$	6.10416	−	4.43493i	0.232888	−	0.169203i
$688$	9.88517	+	0.161894i	0.376869	+	0.00617214i
$689$	−1.04643	−	3.22057i	−0.0398656	−	0.122694i
$690$	8.87439	+	0.734998i	0.337842	+	0.0279809i
$691$	6.79640	−	9.35445i	0.258547	−	0.355860i	−0.659934	−	0.751323i	$-0.729416\pi$
$691$	6.79640	−	9.35445i	0.258547	−	0.355860i	0.918482	+	0.395463i	$0.129416\pi$
$692$	2.21303	+	4.43266i	0.0841266	+	0.168505i
$693$		0			0
$694$	37.5420	−	8.85064i	1.42507	−	0.335966i
$695$	16.9948	+	12.3475i	0.644651	+	0.468366i
$696$	2.83511	−	1.13375i	0.107464	−	0.0429746i
$697$	7.98287	+	24.5688i	0.302373	+	0.930608i
$698$	6.91612	−	8.03093i	0.261779	−	0.303975i
$699$	−3.94916	−	5.43556i	−0.149371	−	0.205592i
$700$	−12.4759	−	12.6819i	−0.471544	−	0.479329i
$701$	10.2311	+	3.32427i	0.386422	+	0.125556i	0.495784	−	0.868446i	$-0.334881\pi$
$701$	10.2311	+	3.32427i	0.386422	+	0.125556i	−0.109362	+	0.994002i	$0.534881\pi$
$702$	4.41262	−	10.5309i	0.166544	−	0.397462i
$703$	13.7487			0.518541
$704$		0			0
$705$	−18.5724			−0.699479
$706$	−9.91024	+	23.6511i	−0.372977	+	0.890121i
$707$	−21.5648	−	7.00684i	−0.811029	−	0.263519i
$708$	0.266450	+	0.270849i	0.0100138	+	0.0101791i
$709$	16.8294	+	23.1636i	0.632040	+	0.869929i	0.998160	−	0.0606391i	$-0.0193139\pi$
$709$	16.8294	+	23.1636i	0.632040	+	0.869929i	−0.366120	+	0.930568i	$0.619314\pi$
$710$	−9.29025	+	10.7877i	−0.348657	+	0.404857i
$711$	−3.61733	−	11.1330i	−0.135660	−	0.417520i
$712$	−34.4666	+	13.7831i	−1.29169	+	0.516542i
$713$	−16.8333	−	12.2301i	−0.630413	−	0.458022i
$714$	−13.3511	+	3.14755i	−0.499651	+	0.117794i
$715$		0			0
$716$	18.2847	+	36.6240i	0.683331	+	1.36870i
$717$	−5.67143	+	7.80606i	−0.211804	+	0.291523i
$718$	−6.78995	−	0.562360i	−0.253399	−	0.0209871i
$719$	0.968932	+	2.98206i	0.0361350	+	0.111212i	0.967497	−	0.252882i	$-0.0813785\pi$
$719$	0.968932	+	2.98206i	0.0361350	+	0.111212i	−0.931362	+	0.364094i	$0.881379\pi$
$720$	−31.4176	−	0.514539i	−1.17086	−	0.0191758i
$721$	2.62876	−	1.90991i	0.0979002	−	0.0711287i
$722$	19.8706	−	12.0651i	0.739509	−	0.449017i
$723$	0.367195	+	0.119309i	0.0136561	+	0.00443715i
$724$	−5.67394	+	34.0187i	−0.210870	+	1.26430i
$725$		−	6.82207i		−	0.253365i
$726$		0			0
$727$	43.0374			1.59617			0.798084	−	0.602546i	$-0.205847\pi$
$727$	43.0374			1.59617			0.798084	+	0.602546i	$0.205847\pi$
$728$	19.2386	−	1.27658i	0.713032	−	0.0473132i
$729$	3.85754	−	11.8723i	0.142872	−	0.439714i
$730$	−2.84122	−	4.67934i	−0.105158	−	0.173190i
$731$	−10.0112	−	13.7792i	−0.370276	−	0.509642i
$732$	1.53627	−	2.95503i	0.0567822	−	0.109221i
$733$	26.1038	−	8.48165i	0.964167	−	0.313277i	0.215708	−	0.976458i	$-0.430794\pi$
$733$	26.1038	−	8.48165i	0.964167	−	0.313277i	0.748459	+	0.663181i	$0.230794\pi$
$734$	11.9054	+	0.986037i	0.439438	+	0.0363953i
$735$	0.274647	+	0.199543i	0.0101305	+	0.00736026i
$736$	20.8084	+	9.12250i	0.767009	+	0.336260i
$737$		0			0
$738$	3.29427	+	13.9734i	0.121264	+	0.514367i
$739$	23.6352	−	32.5310i	0.869434	−	1.19667i	−0.109803	−	0.993953i	$-0.535022\pi$
$739$	23.6352	−	32.5310i	0.869434	−	1.19667i	0.979237	−	0.202720i	$-0.0649782\pi$
$740$	−7.39248	−	49.2826i	−0.271753	−	1.81166i
$741$	−2.15327	+	0.699641i	−0.0791025	+	0.0257020i
$742$	−3.10975	+	3.61101i	−0.114163	+	0.132564i
$743$	27.0459	−	19.6500i	0.992219	−	0.720890i	0.0318134	−	0.999494i	$-0.489872\pi$
$743$	27.0459	−	19.6500i	0.992219	−	0.720890i	0.960406	+	0.278604i	$0.0898718\pi$
$744$	−6.70050	−	4.22014i	−0.245652	−	0.154718i
$745$	−11.0174	+	33.9082i	−0.403647	+	1.24230i
$746$	36.2150	+	15.1747i	1.32592	+	0.555586i
$747$		−	43.2793i		−	1.58351i
$748$		0			0
$749$		−	48.9066i		−	1.78701i
$750$	−1.35790	+	3.24067i	−0.0495834	+	0.118332i
$751$	−7.55280	+	23.2451i	−0.275605	+	0.848227i	0.713453	+	0.700703i	$0.247130\pi$
$751$	−7.55280	+	23.2451i	−0.275605	+	0.848227i	−0.989059	+	0.147523i	$0.952870\pi$
$752$	−44.8219	−	15.3794i	−1.63449	−	0.560830i
$753$	0.661028	−	0.480265i	0.0240892	−	0.0175018i
$754$	5.60266	+	4.82493i	0.204037	+	0.175714i
$755$	39.8835	−	12.9589i	1.45151	−	0.471624i
$756$	−15.8906	+	2.38362i	−0.577935	+	0.0866913i
$757$	−29.7373	+	40.9299i	−1.08082	+	1.48762i	−0.222205	+	0.975000i	$0.571325\pi$
$757$	−29.7373	+	40.9299i	−1.08082	+	1.48762i	−0.858615	+	0.512621i	$0.828675\pi$
$758$	−21.1064	+	4.97591i	−0.766621	+	0.180733i
$759$		0			0
$760$	8.40612	+	10.0907i	0.304922	+	0.366027i
$761$	18.4911	+	13.4346i	0.670302	+	0.487003i	0.870126	−	0.492829i	$-0.164037\pi$
$761$	18.4911	+	13.4346i	0.670302	+	0.487003i	−0.199825	+	0.979832i	$0.564037\pi$
$762$	0.625294	−	7.54981i	0.0226520	−	0.273501i
$763$	−30.1653	+	9.80131i	−1.09206	+	0.354831i
$764$	18.7069	−	35.9830i	0.676792	−	1.30182i
$765$	31.8180	+	43.7938i	1.15038	+	1.58337i
$766$	−14.3473	+	8.71142i	−0.518388	+	0.314756i
$767$	−0.284308	+	0.875009i	−0.0102658	+	0.0315947i
$768$	8.13172	+	2.93988i	0.293428	+	0.106084i
$769$	−10.5112			−0.379044			−0.189522	−	0.981877i	$-0.560694\pi$
$769$	−10.5112			−0.379044			−0.189522	+	0.981877i	$0.560694\pi$
$770$		0			0
$771$			9.95938i			0.358678i
$772$	−5.09245	−	0.849364i	−0.183281	−	0.0305693i
$773$	−32.1287	−	10.4392i	−1.15559	−	0.375474i	−0.332343	−	0.943159i	$-0.607839\pi$
$773$	−32.1287	−	10.4392i	−1.15559	−	0.375474i	−0.823246	+	0.567685i	$0.807839\pi$
$774$	−4.91254	−	8.09071i	−0.176578	−	0.290814i
$775$	−14.3135	+	10.3994i	−0.514157	+	0.373557i
$776$	−23.6153	−	5.97721i	−0.847740	−	0.214569i
$777$	−3.73601	−	11.4983i	−0.134029	−	0.412498i
$778$	−0.530200	+	6.40165i	−0.0190086	+	0.229510i
$779$	3.52703	−	4.85455i	0.126369	−	0.173932i
$780$	3.66567	+	7.34229i	0.131252	+	0.262896i
$781$		0			0
$782$	−8.98151	−	38.0971i	−0.321178	−	1.36235i
$783$	−4.98511	−	3.62189i	−0.178153	−	0.129436i
$784$	0.497585	+	0.708998i	0.0177709	+	0.0253214i
$785$	15.9082	+	48.9603i	0.567787	+	1.74747i
$786$	6.61891	+	5.70011i	0.236089	+	0.203316i
$787$	16.6731	+	22.9485i	0.594331	+	0.818026i	0.995175	−	0.0981203i	$-0.0312830\pi$
$787$	16.6731	+	22.9485i	0.594331	+	0.818026i	−0.400844	+	0.916146i	$0.631283\pi$
$788$	30.0032	−	29.5159i	1.06882	−	1.05146i
$789$	5.80296	+	1.88550i	0.206591	+	0.0671255i
$790$	16.3564	+	6.85364i	0.581935	+	0.243842i
$791$	13.8263			0.491605
$792$		0			0
$793$	8.06497			0.286395
$794$	14.1691	+	5.93713i	0.502844	+	0.210701i
$795$	−1.92905	−	0.626787i	−0.0684164	−	0.0222298i
$796$	−11.1988	−	11.3837i	−0.396930	−	0.403484i
$797$	14.1709	+	19.5046i	0.501959	+	0.690887i	0.982538	−	0.186065i	$-0.0595734\pi$
$797$	14.1709	+	19.5046i	0.501959	+	0.690887i	−0.480579	+	0.876952i	$0.659573\pi$
$798$	2.41433	+	2.07918i	0.0854662	+	0.0736023i
$799$	25.2270	+	77.6408i	0.892468	+	2.74673i
$800$	12.8449	−	14.4306i	0.454137	−	0.510199i
$801$	28.7517	+	20.8893i	1.01589	+	0.738088i
$802$	−0.753347	−	3.19549i	−0.0266016	−	0.112837i
$803$		0			0
$804$	10.0519	−	5.01846i	0.354504	−	0.176987i
$805$	17.8367	−	24.5501i	0.628662	−	0.865279i
$806$	1.58274	−	19.1101i	0.0557497	−	0.673123i
$807$	2.93625	+	9.03685i	0.103361	+	0.318112i
$808$	6.04201	−	23.8713i	0.212557	−	0.839789i
$809$	−18.3369	+	13.3226i	−0.644693	+	0.468397i	−0.861459	−	0.507827i	$-0.830449\pi$
$809$	−18.3369	+	13.3226i	−0.644693	+	0.468397i	0.216766	+	0.976223i	$0.430449\pi$
$810$	13.7477	+	22.6418i	0.483046	+	0.795552i
$811$	−47.7662	−	15.5202i	−1.67730	−	0.544987i	−0.692913	−	0.721021i	$-0.743673\pi$
$811$	−47.7662	−	15.5202i	−1.67730	−	0.544987i	−0.984384	+	0.176034i	$0.943673\pi$
$812$	1.71185	−	10.2636i	0.0600741	−	0.360180i
$813$			3.52723i			0.123705i
$814$		0			0
$815$	−16.7193			−0.585650
$816$	−4.37063	−	14.2408i	−0.153003	−	0.498527i
$817$	−1.22254	+	3.76259i	−0.0427712	+	0.131636i
$818$	30.4983	−	18.5181i	1.06635	−	0.647470i
$819$	−10.8503	−	14.9341i	−0.379139	−	0.521841i
$820$	−19.2977	−	10.0325i	−0.673905	−	0.350352i
$821$	−21.7713	+	7.07391i	−0.759822	+	0.246881i	−0.663202	−	0.748440i	$-0.730803\pi$
$821$	−21.7713	+	7.07391i	−0.759822	+	0.246881i	−0.0966197	+	0.995321i	$0.530803\pi$
$822$	−0.0740241	+	0.893769i	−0.00258189	+	0.0311738i
$823$	−20.3029	−	14.7509i	−0.707715	−	0.514185i	0.174721	−	0.984618i	$-0.444098\pi$
$823$	−20.3029	−	14.7509i	−0.707715	−	0.514185i	−0.882436	+	0.470433i	$0.844098\pi$
$824$	2.25857	+	2.71118i	0.0786811	+	0.0944484i
$825$		0			0
$826$	1.26021	−	0.297098i	0.0438483	−	0.0103374i
$827$	−7.76904	+	10.6932i	−0.270156	+	0.371838i	−0.922442	−	0.386135i	$-0.873810\pi$
$827$	−7.76904	+	10.6932i	−0.270156	+	0.371838i	0.652286	+	0.757973i	$0.273810\pi$
$828$	−3.22680	−	21.5117i	−0.112139	−	0.747585i
$829$	−28.5459	+	9.27513i	−0.991441	+	0.322139i	−0.759440	−	0.650577i	$-0.774527\pi$
$829$	−28.5459	+	9.27513i	−0.991441	+	0.322139i	−0.232001	+	0.972716i	$0.574527\pi$
$830$	49.6831	+	42.7864i	1.72453	+	1.48514i
$831$	0.112059	−	0.0814157i	0.00388729	−	0.00282428i
$832$	2.76658	+	20.7550i	0.0959139	+	0.719552i
$833$	0.461121	−	1.41918i	0.0159769	−	0.0491718i
$834$	−2.13888	+	5.10451i	−0.0740634	+	0.176755i
$835$			6.86015i			0.237405i
$836$		0			0
$837$			15.9805i			0.552366i
$838$	21.8051	+	9.13671i	0.753243	+	0.315623i
$839$	−0.839010	+	2.58221i	−0.0289659	+	0.0891477i	−0.964494	−	0.264104i	$-0.914924\pi$
$839$	−0.839010	+	2.58221i	−0.0289659	+	0.0891477i	0.935528	+	0.353251i	$0.114924\pi$
$840$	6.15475	−	9.77218i	0.212359	−	0.337172i
$841$	−20.2333	+	14.7004i	−0.697700	+	0.506909i
$842$	8.76916	−	10.1827i	0.302205	−	0.350918i
$843$	13.3420	−	4.33509i	0.459524	−	0.149308i
$844$	18.6433	−	2.79652i	0.641727	−	0.0962602i
$845$	10.4857	−	14.4323i	0.360719	−	0.496487i
$846$	10.4103	+	44.1579i	0.357915	+	1.51818i
$847$		0			0
$848$	−4.13646	−	3.11006i	−0.142047	−	0.106800i
$849$	−4.11473	−	2.98953i	−0.141217	−	0.102600i
$850$	−33.1688	−	2.74712i	−1.13768	−	0.0942255i
$851$	32.8101	−	10.6607i	1.12472	−	0.365443i
$852$	−3.32798	−	1.73016i	−0.114015	−	0.0592742i
$853$	8.79061	+	12.0992i	0.300985	+	0.414270i	0.932543	−	0.361058i	$-0.117584\pi$
$853$	8.79061	+	12.0992i	0.300985	+	0.414270i	−0.631558	+	0.775328i	$0.717584\pi$
$854$	−5.89055	−	9.70143i	−0.201570	−	0.331976i
$855$	3.88554	−	11.9585i	0.132883	−	0.408970i
$856$	52.9947	−	3.51646i	1.81132	−	0.120190i
$857$	13.6354			0.465776			0.232888	−	0.972504i	$-0.425182\pi$
$857$	13.6354			0.465776			0.232888	+	0.972504i	$0.425182\pi$
$858$		0			0
$859$			5.59465i			0.190887i	0.995435	+	0.0954434i	$0.0304269\pi$
$859$			5.59465i			0.190887i	−0.995435	+	0.0954434i	$0.969573\pi$
$860$	14.1445	+	2.35914i	0.482322	+	0.0804460i
$861$	−5.01836	−	1.63057i	−0.171025	−	0.0555695i
$862$	37.6650	−	22.8696i	1.28288	−	0.778941i
$863$	3.60812	−	2.62145i	0.122822	−	0.0892353i	−0.524678	−	0.851300i	$-0.675814\pi$
$863$	3.60812	−	2.62145i	0.122822	−	0.0892353i	0.647500	+	0.762065i	$0.275814\pi$
$864$	−3.72543	−	17.0475i	−0.126742	−	0.579969i
$865$	2.22062	+	6.83437i	0.0755034	+	0.232376i
$866$	7.03340	+	0.582523i	0.239005	+	0.0197949i
$867$	−9.68411	+	13.3290i	−0.328889	+	0.452677i
$868$	−24.1437	+	12.0538i	−0.819490	+	0.409134i
$869$		0			0
$870$	4.31062	−	1.01624i	0.146144	−	0.0344538i
$871$	22.0101	+	15.9913i	0.745785	+	0.541845i
$872$	−12.7896	−	31.9822i	−0.433109	−	1.08305i
$873$	7.20698	+	22.1808i	0.243919	+	0.750706i
$874$	−5.93293	+	6.88925i	−0.200684	+	0.233032i
$875$	7.03804	+	9.68703i	0.237929	+	0.327481i
$876$	1.02817	−	1.01147i	0.0347388	−	0.0341745i
$877$	35.3412	+	11.4830i	1.19339	+	0.387755i	0.837324	−	0.546708i	$-0.184119\pi$
$877$	35.3412	+	11.4830i	1.19339	+	0.387755i	0.356062	+	0.934462i	$0.384119\pi$
$878$	12.5556	−	29.9644i	0.423732	−	1.01125i
$879$	−1.03731			−0.0349876
$880$		0			0
$881$	−30.4894			−1.02721			−0.513607	−	0.858025i	$-0.671691\pi$
$881$	−30.4894			−1.02721			−0.513607	+	0.858025i	$0.671691\pi$
$882$	0.320487	−	0.764851i	0.0107913	−	0.0257539i
$883$	29.5234	+	9.59272i	0.993540	+	0.322821i	0.760281	−	0.649594i	$-0.225061\pi$
$883$	29.5234	+	9.59272i	0.993540	+	0.322821i	0.233259	+	0.972415i	$0.425061\pi$
$884$	25.7148	−	25.2971i	0.864884	−	0.850835i
$885$	0.323919	+	0.445836i	0.0108884	+	0.0149866i
$886$	−26.2499	+	30.4811i	−0.881883	+	1.02403i
$887$	−10.3375	−	31.8156i	−0.347100	−	1.06826i	−0.960450	−	0.278453i	$-0.910178\pi$
$887$	−10.3375	−	31.8156i	−0.347100	−	1.06826i	0.613349	−	0.789812i	$-0.289822\pi$
$888$	12.1908	−	4.87505i	0.409096	−	0.163596i
$889$	−20.8858	−	15.1744i	−0.700488	−	0.508934i
$890$	−52.4045	+	12.3545i	−1.75660	+	0.414124i
$891$		0			0
$892$	−25.9591	+	12.9602i	−0.869176	+	0.433940i
$893$	11.1459	−	15.3410i	0.372984	−	0.513369i
$894$	−9.36124	−	0.775321i	−0.313087	−	0.0259306i
$895$	18.3475	+	56.4677i	0.613288	+	1.88751i
$896$	22.9458	−	18.4871i	0.766564	−	0.617612i
$897$	−4.59612	+	3.33928i	−0.153460	+	0.111495i
$898$	13.7686	−	8.36008i	0.459465	−	0.278979i
$899$	−9.84193	−	3.19784i	−0.328247	−	0.106654i
$900$	−18.2443	−	3.04294i	−0.608142	−	0.101431i
$901$			8.91562i			0.297023i
$902$		0			0
$903$	3.47892			0.115771
$904$	0.994131	+	14.9820i	0.0330643	+	0.498294i
$905$	−15.4583	+	47.5756i	−0.513850	+	1.58147i
$906$	5.73426	+	9.44403i	0.190508	+	0.313757i
$907$	−20.6403	−	28.4089i	−0.685348	−	0.943301i	0.314634	−	0.949213i	$-0.398118\pi$
$907$	−20.6403	−	28.4089i	−0.685348	−	0.943301i	−0.999983	+	0.00591202i	$0.998118\pi$
$908$	−4.83451	−	2.51338i	−0.160439	−	0.0834093i
$909$	−22.4212	+	7.28510i	−0.743666	+	0.241632i
$910$	27.8706	+	2.30831i	0.923901	+	0.0765197i
$911$	17.2222	+	12.5126i	0.570595	+	0.414562i	0.835321	−	0.549762i	$-0.185282\pi$
$911$	17.2222	+	12.5126i	0.570595	+	0.414562i	−0.264726	+	0.964324i	$0.585282\pi$
$912$	−2.07939	+	2.76564i	−0.0688556	+	0.0915795i
$913$		0			0
$914$	4.51921	+	19.1692i	0.149482	+	0.634062i
$915$	2.83944	−	3.90815i	0.0938690	−	0.129200i
$916$	27.6140	−	4.14215i	0.912392	−	0.136860i
$917$	28.3103	−	9.19859i	0.934890	−	0.303764i
$918$	−19.6170	+	22.7791i	−0.647458	+	0.751821i
$919$	−3.55772	+	2.58483i	−0.117358	+	0.0852658i	−0.644916	−	0.764253i	$-0.723108\pi$
$919$	−3.55772	+	2.58483i	−0.117358	+	0.0852658i	0.527558	+	0.849519i	$0.323108\pi$
$920$	27.8848	+	17.5625i	0.919335	+	0.579019i
$921$	−1.70795	+	5.25653i	−0.0562789	+	0.173209i
$922$	−16.7162	−	7.00439i	−0.550519	−	0.230677i
$923$		−	9.08282i		−	0.298965i
$924$		0			0
$925$		−	29.3345i		−	0.964513i
$926$	20.8853	−	49.8435i	0.686334	−	1.63796i
$927$	1.04397	−	3.21302i	0.0342886	−	0.105529i
$928$	11.2446	+	1.11698i	0.369122	+	0.0366665i
$929$	−16.0108	+	11.6326i	−0.525298	+	0.381652i	−0.818596	−	0.574370i	$-0.805247\pi$
$929$	−16.0108	+	11.6326i	−0.525298	+	0.381652i	0.293298	+	0.956021i	$0.405247\pi$
$930$	−8.70319	−	7.49506i	−0.285389	−	0.245773i
$931$	−0.329650	+	0.107110i	−0.0108038	+	0.00351038i
$932$	−3.68845	−	24.5894i	−0.120819	−	0.805452i
$933$	4.75190	−	6.54043i	0.155570	−	0.214124i
$934$	44.9390	−	10.5945i	1.47045	−	0.346663i
$935$		0			0
$936$	15.4023	−	12.8311i	0.503441	−	0.419396i
$937$	37.5819	+	27.3048i	1.22775	+	0.892010i	0.996719	−	0.0809370i	$-0.0257913\pi$
$937$	37.5819	+	27.3048i	1.22775	+	0.892010i	0.231028	+	0.972947i	$0.425791\pi$
$938$	3.16017	−	38.1560i	0.103183	−	1.24584i
$939$	−2.49883	+	0.811918i	−0.0815461	+	0.0264959i
$940$	−60.9835	−	31.7043i	−1.98906	−	1.03408i
$941$	27.7118	+	38.1420i	0.903379	+	1.24339i	0.969378	+	0.245575i	$0.0789768\pi$
$941$	27.7118	+	38.1420i	0.903379	+	1.24339i	−0.0659983	+	0.997820i	$0.521023\pi$
$942$	−11.5933	+	7.03928i	−0.377731	+	0.229352i
$943$	4.65280	−	14.3198i	0.151516	−	0.466318i
$944$	0.412544	+	1.34419i	0.0134272	+	0.0437497i
$945$	−23.3063			−0.758155
$946$		0			0
$947$		−	5.18884i		−	0.168615i	−0.996440	−	0.0843074i	$-0.973132\pi$
$947$		−	5.18884i		−	0.168615i	0.996440	−	0.0843074i	$-0.0268678\pi$
$948$	−0.768675	+	4.60867i	−0.0249654	+	0.149683i
$949$	3.32163	+	1.07926i	0.107825	+	0.0350344i
$950$	4.01235	+	6.60813i	0.130178	+	0.214396i
$951$	4.67356	−	3.39554i	0.151551	−	0.110108i
$952$	−49.2119	−	12.4559i	−1.59497	−	0.403699i
$953$	5.39691	+	16.6100i	0.174823	+	0.538050i	0.999625	−	0.0273715i	$-0.00871369\pi$
$953$	5.39691	+	16.6100i	0.174823	+	0.538050i	−0.824802	+	0.565421i	$0.808714\pi$
$954$	−0.408964	+	4.93784i	−0.0132407	+	0.159869i
$955$	34.5754	−	47.5889i	1.11883	−	1.53994i
$956$	−31.9478	+	15.9501i	−1.03327	+	0.515863i
$957$		0			0
$958$	−8.44641	−	35.8274i	−0.272891	−	1.15753i
$959$	2.47253	+	1.79639i	0.0798420	+	0.0580086i
$960$	11.0316	+	5.96660i	0.356043	+	0.192571i
$961$	−1.28619	−	3.95850i	−0.0414901	−	0.127693i
$962$	24.0911	+	20.7469i	0.776729	+	0.668908i
$963$	−29.8882	−	41.1375i	−0.963132	−	1.32564i
$964$	1.00204	+	1.01858i	0.0322734	+	0.0328063i
$965$	−7.12186	−	2.31403i	−0.229261	−	0.0744913i
$966$	7.37379	+	3.08975i	0.237248	+	0.0994112i
$967$	−22.0455			−0.708936			−0.354468	−	0.935068i	$-0.615338\pi$
$967$	−22.0455			−0.708936			−0.354468	+	0.935068i	$0.615338\pi$
$968$		0			0
$969$	5.96100			0.191495
$970$	−32.5877	−	13.6548i	−1.04633	−	0.438431i
$971$	−24.5153	−	7.96551i	−0.786734	−	0.255625i	−0.112021	−	0.993706i	$-0.535732\pi$
$971$	−24.5153	−	7.96551i	−0.786734	−	0.255625i	−0.674713	+	0.738080i	$0.735732\pi$
$972$	−18.1691	+	17.8740i	−0.582774	+	0.573308i
$973$	11.0859	+	15.2584i	0.355398	+	0.489163i
$974$	5.98016	+	5.15003i	0.191617	+	0.165018i
$975$	1.49277	+	4.59428i	0.0478069	+	0.147135i
$976$	10.0888	−	7.08049i	0.322936	−	0.226641i
$977$	−23.7225	−	17.2354i	−0.758951	−	0.551410i	0.139638	−	0.990203i	$-0.455406\pi$
$977$	−23.7225	−	17.2354i	−0.758951	−	0.551410i	−0.898588	+	0.438793i	$0.855406\pi$
$978$	−1.01076	−	4.28738i	−0.0323206	−	0.137095i
$979$		0			0
$980$	0.561186	+	1.12405i	0.0179264	+	0.0359064i
$981$	−19.3836	+	26.6792i	−0.618870	+	0.851802i
$982$	2.85712	−	34.4970i	0.0911744	−	1.10084i
$983$	−8.89777	−	27.3845i	−0.283795	−	0.873430i	−0.986757	−	0.162204i	$-0.948140\pi$
$983$	−8.89777	−	27.3845i	−0.283795	−	0.873430i	0.702963	−	0.711227i	$-0.251860\pi$
$984$	1.40604	−	5.55510i	0.0448228	−	0.177090i
$985$	49.3873	−	35.8820i	1.57361	−	1.14330i
$986$	−10.1034	−	16.6399i	−0.321759	−	0.529921i
$987$	−15.8587	−	5.15282i	−0.504789	−	0.164016i
$988$	−8.26471	−	1.37846i	−0.262935	−	0.0438547i
$989$			9.92707i			0.315662i
$990$		0			0
$991$	−50.7188			−1.61113			−0.805567	−	0.592504i	$-0.798139\pi$
$991$	−50.7188			−1.61113			−0.805567	+	0.592504i	$0.798139\pi$
$992$	−14.7974	−	25.2952i	−0.469818	−	0.803123i
$993$	3.56458	−	10.9707i	0.113119	−	0.348143i
$994$	−10.9258	+	6.63397i	−0.346546	+	0.210417i
$995$	−13.6142	−	18.7383i	−0.431599	−	0.594045i
$996$	−7.96827	+	15.3271i	−0.252484	+	0.485657i
$997$	12.6358	−	4.10563i	0.400181	−	0.130027i	−0.102010	−	0.994783i	$-0.532527\pi$
$997$	12.6358	−	4.10563i	0.400181	−	0.130027i	0.502191	+	0.864757i	$0.332527\pi$
$998$	2.44903	−	29.5697i	0.0775227	−	0.936011i
$999$	−21.4357	−	15.5739i	−0.678195	−	0.492738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.d.565.5		40
8.5	even	2	inner	968.2.o.d.565.9		40
11.2	odd	10		88.2.o.a.5.3	✓	40
11.3	even	5	inner	968.2.o.d.245.9		40
11.4	even	5		968.2.o.i.493.1		40
11.5	even	5		968.2.c.i.485.9		20
11.6	odd	10		968.2.c.h.485.12		20
11.7	odd	10		88.2.o.a.53.10	yes	40
11.8	odd	10		968.2.o.j.245.2		40
11.9	even	5		968.2.o.i.269.8		40
11.10	odd	2		968.2.o.j.565.6		40
33.2	even	10		792.2.br.b.181.8		40
33.29	even	10		792.2.br.b.757.1		40
44.7	even	10		352.2.w.a.273.4		40
44.27	odd	10		3872.2.c.i.1937.12		20
44.35	even	10		352.2.w.a.49.7		40
44.39	even	10		3872.2.c.h.1937.12		20
88.5	even	10		968.2.c.i.485.10		20
88.13	odd	10		88.2.o.a.5.10	yes	40
88.21	odd	2		968.2.o.j.565.2		40
88.27	odd	10		3872.2.c.i.1937.9		20
88.29	odd	10		88.2.o.a.53.3	yes	40
88.35	even	10		352.2.w.a.49.4		40
88.37	even	10		968.2.o.i.493.8		40
88.51	even	10		352.2.w.a.273.7		40
88.53	even	10		968.2.o.i.269.1		40
88.61	odd	10		968.2.c.h.485.11		20
88.69	even	10	inner	968.2.o.d.245.5		40
88.83	even	10		3872.2.c.h.1937.9		20
88.85	odd	10		968.2.o.j.245.6		40
264.29	even	10		792.2.br.b.757.8		40
264.101	even	10		792.2.br.b.181.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.3	✓	40	11.2	odd	10
88.2.o.a.5.10	yes	40	88.13	odd	10
88.2.o.a.53.3	yes	40	88.29	odd	10
88.2.o.a.53.10	yes	40	11.7	odd	10
352.2.w.a.49.4		40	88.35	even	10
352.2.w.a.49.7		40	44.35	even	10
352.2.w.a.273.4		40	44.7	even	10
352.2.w.a.273.7		40	88.51	even	10
792.2.br.b.181.1		40	264.101	even	10
792.2.br.b.181.8		40	33.2	even	10
792.2.br.b.757.1		40	33.29	even	10
792.2.br.b.757.8		40	264.29	even	10
968.2.c.h.485.11		20	88.61	odd	10
968.2.c.h.485.12		20	11.6	odd	10
968.2.c.i.485.9		20	11.5	even	5
968.2.c.i.485.10		20	88.5	even	10
968.2.o.d.245.5		40	88.69	even	10	inner
968.2.o.d.245.9		40	11.3	even	5	inner
968.2.o.d.565.5		40	1.1	even	1	trivial
968.2.o.d.565.9		40	8.5	even	2	inner
968.2.o.i.269.1		40	88.53	even	10
968.2.o.i.269.8		40	11.9	even	5
968.2.o.i.493.1		40	11.4	even	5
968.2.o.i.493.8		40	88.37	even	10
968.2.o.j.245.2		40	11.8	odd	10
968.2.o.j.245.6		40	88.85	odd	10
968.2.o.j.565.2		40	88.21	odd	2
968.2.o.j.565.6		40	11.10	odd	2
3872.2.c.h.1937.9		20	88.83	even	10
3872.2.c.h.1937.12		20	44.39	even	10
3872.2.c.i.1937.9		20	88.27	odd	10
3872.2.c.i.1937.12		20	44.27	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.546541 + 1.30434i) q^{2} +(-0.513977 - 0.167001i) q^{3} +(-1.40259 - 1.42575i) q^{4} +(-1.70510 - 2.34687i) q^{5} +(0.498735 - 0.579126i) q^{6} +(-0.804837 - 2.47703i) q^{7} +(2.62622 - 1.05022i) q^{8} +(-2.19077 - 1.59169i) q^{9} +(3.99302 - 0.941367i) q^{10} +(0.482796 + 0.967034i) q^{12} +(-1.53843 + 2.11746i) q^{13} +(3.67076 + 0.304021i) q^{14} +(0.484453 + 1.49099i) q^{15} +(-0.0655010 + 3.99946i) q^{16} +(5.57496 - 4.05044i) q^{17} +(3.27344 - 1.98758i) q^{18} +(-1.52231 - 0.494630i) q^{19} +(-0.954489 + 5.72274i) q^{20} +1.40755i q^{21} -4.01642 q^{23} +(-1.52520 + 0.101205i) q^{24} +(-1.05535 + 3.24804i) q^{25} +(-1.92107 - 3.16390i) q^{26} +(1.81316 + 2.49560i) q^{27} +(-2.40277 + 4.62175i) q^{28} +(-1.89980 + 0.617281i) q^{29} +(-2.20953 - 0.182999i) q^{30} +(4.19113 + 3.04503i) q^{31} +(-5.18085 - 2.27130i) q^{32} +(2.23620 + 9.48535i) q^{34} +(-4.44095 + 6.11245i) q^{35} +(0.803403 + 5.35596i) q^{36} +(-8.16901 + 2.65427i) q^{37} +(1.47717 - 1.71527i) q^{38} +(1.14433 - 0.831407i) q^{39} +(-6.94271 - 4.37268i) q^{40} +(-1.15845 + 3.56533i) q^{41} +(-1.83591 - 0.769281i) q^{42} -2.47162i q^{43} +7.85545i q^{45} +(2.19513 - 5.23876i) q^{46} +(-3.66085 + 11.2669i) q^{47} +(0.701581 - 2.04469i) q^{48} +(0.175189 - 0.127282i) q^{49} +(-3.65975 - 3.15172i) q^{50} +(-3.54183 + 1.15081i) q^{51} +(5.17674 - 0.776520i) q^{52} +(-0.760478 + 1.04671i) q^{53} +(-4.24606 + 1.00102i) q^{54} +(-4.71510 - 5.65999i) q^{56} +(0.699830 + 0.508456i) q^{57} +(0.233173 - 2.81534i) q^{58} +(0.334314 - 0.108625i) q^{59} +(1.44629 - 2.78195i) q^{60} +(-1.81119 - 2.49289i) q^{61} +(-6.26237 + 3.80241i) q^{62} +(-2.17945 + 6.70765i) q^{63} +(5.79409 - 5.51621i) q^{64} +7.59259 q^{65} -10.3946i q^{67} +(-13.5943 - 2.26737i) q^{68} +(2.06434 + 0.670746i) q^{69} +(-5.54553 - 9.13320i) q^{70} +(-2.80750 + 2.03977i) q^{71} +(-7.42506 - 1.87934i) q^{72} +(-0.412353 - 1.26909i) q^{73} +(1.00263 - 12.1058i) q^{74} +(1.08485 - 1.49317i) q^{75} +(1.42996 + 2.86419i) q^{76} +(0.459010 + 1.94699i) q^{78} +(3.49723 + 2.54089i) q^{79} +(9.49792 - 6.66578i) q^{80} +(1.99524 + 6.14073i) q^{81} +(-4.01725 - 3.45960i) q^{82} +(9.39420 + 12.9300i) q^{83} +(2.00680 - 1.97421i) q^{84} +(-19.0118 - 6.17729i) q^{85} +(3.22383 + 1.35084i) q^{86} +1.07954 q^{87} -13.1240 q^{89} +(-10.2461 - 4.29332i) q^{90} +(6.48321 + 2.10652i) q^{91} +(5.63337 + 5.72639i) q^{92} +(-1.64562 - 2.26500i) q^{93} +(-12.6951 - 10.9328i) q^{94} +(1.43487 + 4.41607i) q^{95} +(2.28352 + 2.03261i) q^{96} +(-6.96770 - 5.06233i) q^{97} +(0.0702709 + 0.298070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

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