LMFDB - Embedded newform 840.2.bj.b.517.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			517.7
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38448 + 0.288447i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.83360 - 0.798701i) q^{4} +(-1.97588 - 1.04685i) q^{5} +(0.775016 - 1.18294i) q^{6} +(0.379700 + 2.61836i) q^{7} +(-2.30820 + 1.63468i) q^{8} -1.00000i q^{9} +(3.03754 + 0.879417i) q^{10} -1.52074i q^{11} +(-0.731782 + 1.86132i) q^{12} +(-2.99475 + 2.99475i) q^{13} +(-1.28095 - 3.51556i) q^{14} +(2.13739 - 0.656920i) q^{15} +(2.72415 - 2.92899i) q^{16} +(0.848750 - 0.848750i) q^{17} +(0.288447 + 1.38448i) q^{18} +1.11033i q^{19} +(-4.45909 - 0.341372i) q^{20} +(-2.11995 - 1.58297i) q^{21} +(0.438654 + 2.10545i) q^{22} +(2.90269 - 2.90269i) q^{23} +(0.476250 - 2.78804i) q^{24} +(2.80819 + 4.13691i) q^{25} +(3.28236 - 5.01001i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.78751 + 4.49776i) q^{28} -6.35863 q^{29} +(-2.76970 + 1.52602i) q^{30} -3.55692i q^{31} +(-2.92669 + 4.84092i) q^{32} +(1.07533 + 1.07533i) q^{33} +(-0.930262 + 1.41990i) q^{34} +(1.99080 - 5.57106i) q^{35} +(-0.798701 - 1.83360i) q^{36} +(0.232865 - 0.232865i) q^{37} +(-0.320271 - 1.53723i) q^{38} -4.23521i q^{39} +(6.27201 - 0.813586i) q^{40} -6.76778i q^{41} +(3.39164 + 1.58011i) q^{42} +(-7.11664 - 7.11664i) q^{43} +(-1.21462 - 2.78843i) q^{44} +(-1.04685 + 1.97588i) q^{45} +(-3.18146 + 4.85600i) q^{46} +(-1.87781 + 1.87781i) q^{47} +(0.144842 + 3.99738i) q^{48} +(-6.71166 + 1.98839i) q^{49} +(-5.08118 - 4.91748i) q^{50} +1.20031i q^{51} +(-3.09925 + 7.88306i) q^{52} +(0.0961110 + 0.0961110i) q^{53} +(-1.18294 - 0.775016i) q^{54} +(-1.59200 + 3.00480i) q^{55} +(-5.15662 - 5.42303i) q^{56} +(-0.785121 - 0.785121i) q^{57} +(8.80343 - 1.83413i) q^{58} -11.0439i q^{59} +(3.39444 - 2.91167i) q^{60} +9.42450 q^{61} +(1.02598 + 4.92450i) q^{62} +(2.61836 - 0.379700i) q^{63} +(2.65561 - 7.54637i) q^{64} +(9.05232 - 2.78219i) q^{65} +(-1.79895 - 1.17860i) q^{66} +(11.4129 - 11.4129i) q^{67} +(0.878368 - 2.23416i) q^{68} +4.10502i q^{69} +(-1.14928 + 8.28729i) q^{70} -4.00852 q^{71} +(1.63468 + 2.30820i) q^{72} +(-10.1745 - 10.1745i) q^{73} +(-0.255229 + 0.389567i) q^{74} +(-4.91093 - 0.939546i) q^{75} +(0.886821 + 2.03590i) q^{76} +(3.98186 - 0.577426i) q^{77} +(1.22163 + 5.86359i) q^{78} -3.22206i q^{79} +(-8.44882 + 2.93554i) q^{80} -1.00000 q^{81} +(1.95215 + 9.36989i) q^{82} +(-2.36021 + 2.36021i) q^{83} +(-5.15146 - 1.20933i) q^{84} +(-2.56554 + 0.788510i) q^{85} +(11.9056 + 7.80010i) q^{86} +(4.49623 - 4.49623i) q^{87} +(2.48594 + 3.51019i) q^{88} +7.10490 q^{89} +(0.879417 - 3.03754i) q^{90} +(-8.97844 - 6.70423i) q^{91} +(3.00398 - 7.64074i) q^{92} +(2.51512 + 2.51512i) q^{93} +(2.05815 - 3.14144i) q^{94} +(1.16235 - 2.19388i) q^{95} +(-1.35356 - 5.49253i) q^{96} +(5.73370 - 5.73370i) q^{97} +(8.71864 - 4.68885i) q^{98} -1.52074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−1.38448	+	0.288447i	−0.978979	+	0.203963i
$2$	−1.38448	+	0.288447i	−0.978979	+	0.203963i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.83360	−	0.798701i	0.916798	−	0.399350i
$5$	−1.97588	−	1.04685i	−0.883640	−	0.468167i
$5$	−1.97588	−	1.04685i	−0.883640	−	0.468167i
$6$	0.775016	−	1.18294i	0.316399	−	0.482934i
$7$	0.379700	+	2.61836i	0.143513	+	0.989648i
$7$	0.379700	+	2.61836i	0.143513	+	0.989648i
$8$	−2.30820	+	1.63468i	−0.816073	+	0.577948i
$9$		−	1.00000i		−	0.333333i
$10$	3.03754	+	0.879417i	0.960553	+	0.278096i
$11$		−	1.52074i		−	0.458521i	−0.973365	−	0.229261i	$-0.926369\pi$
$11$		−	1.52074i		−	0.458521i	0.973365	−	0.229261i	$-0.0736308\pi$
$12$	−0.731782	+	1.86132i	−0.211247	+	0.537316i
$13$	−2.99475	+	2.99475i	−0.830593	+	0.830593i	−0.987598	−	0.157005i	$-0.949816\pi$
$13$	−2.99475	+	2.99475i	−0.830593	+	0.830593i	0.157005	+	0.987598i	$0.449816\pi$
$14$	−1.28095	−	3.51556i	−0.342348	−	0.939573i
$15$	2.13739	−	0.656920i	0.551873	−	0.169616i
$16$	2.72415	−	2.92899i	0.681038	−	0.732248i
$17$	0.848750	−	0.848750i	0.205852	−	0.205852i	−0.596650	−	0.802502i	$-0.703502\pi$
$17$	0.848750	−	0.848750i	0.205852	−	0.205852i	0.802502	+	0.596650i	$0.203502\pi$
$18$	0.288447	+	1.38448i	0.0679876	+	0.326326i
$19$			1.11033i			0.254727i	0.991856	+	0.127363i	$0.0406515\pi$
$19$			1.11033i			0.254727i	−0.991856	+	0.127363i	$0.959349\pi$
$20$	−4.45909	−	0.341372i	−0.997082	−	0.0763330i
$21$	−2.11995	−	1.58297i	−0.462611	−	0.345433i
$22$	0.438654	+	2.10545i	0.0935213	+	0.448883i
$23$	2.90269	−	2.90269i	0.605253	−	0.605253i	−0.336449	−	0.941702i	$-0.609226\pi$
$23$	2.90269	−	2.90269i	0.605253	−	0.605253i	0.941702	+	0.336449i	$0.109226\pi$
$24$	0.476250	−	2.78804i	0.0972141	−	0.569107i
$25$	2.80819	+	4.13691i	0.561639	+	0.827383i
$26$	3.28236	−	5.01001i	0.643723	−	0.982543i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.78751	+	4.49776i	0.526789	+	0.849996i
$29$	−6.35863			−1.18077			−0.590384	−	0.807122i	$-0.701024\pi$
$29$	−6.35863			−1.18077			−0.590384	+	0.807122i	$0.701024\pi$
$30$	−2.76970	+	1.52602i	−0.505676	+	0.278612i
$31$		−	3.55692i		−	0.638841i	−0.947613	−	0.319420i	$-0.896512\pi$
$31$		−	3.55692i		−	0.638841i	0.947613	−	0.319420i	$-0.103488\pi$
$32$	−2.92669	+	4.84092i	−0.517371	+	0.855761i
$33$	1.07533	+	1.07533i	0.187191	+	0.187191i
$34$	−0.930262	+	1.41990i	−0.159539	+	0.243511i
$35$	1.99080	−	5.57106i	0.336507	−	0.941681i
$36$	−0.798701	−	1.83360i	−0.133117	−	0.305599i
$37$	0.232865	−	0.232865i	0.0382827	−	0.0382827i	−0.687706	−	0.725989i	$-0.741382\pi$
$37$	0.232865	−	0.232865i	0.0382827	−	0.0382827i	0.725989	+	0.687706i	$0.241382\pi$
$38$	−0.320271	−	1.53723i	−0.0519548	−	0.249372i
$39$		−	4.23521i		−	0.678177i
$40$	6.27201	−	0.813586i	0.991691	−	0.128639i
$41$		−	6.76778i		−	1.05695i	−0.848949	−	0.528475i	$-0.822764\pi$
$41$		−	6.76778i		−	1.05695i	0.848949	−	0.528475i	$-0.177236\pi$
$42$	3.39164	+	1.58011i	0.523342	+	0.243816i
$43$	−7.11664	−	7.11664i	−1.08528	−	1.08528i	−0.996008	−	0.0892693i	$-0.971547\pi$
$43$	−7.11664	−	7.11664i	−1.08528	−	1.08528i	−0.0892693	−	0.996008i	$-0.528453\pi$
$44$	−1.21462	−	2.78843i	−0.183111	−	0.420372i
$45$	−1.04685	+	1.97588i	−0.156056	+	0.294547i
$46$	−3.18146	+	4.85600i	−0.469080	+	0.715978i
$47$	−1.87781	+	1.87781i	−0.273906	+	0.273906i	−0.830671	−	0.556764i	$-0.812043\pi$
$47$	−1.87781	+	1.87781i	−0.273906	+	0.273906i	0.556764	+	0.830671i	$0.312043\pi$
$48$	0.144842	+	3.99738i	0.0209061	+	0.576972i
$49$	−6.71166	+	1.98839i	−0.958808	+	0.284055i
$50$	−5.08118	−	4.91748i	−0.718588	−	0.695436i
$51$			1.20031i			0.168078i
$52$	−3.09925	+	7.88306i	−0.429789	+	1.09318i
$53$	0.0961110	+	0.0961110i	0.0132019	+	0.0132019i	0.713677	−	0.700475i	$-0.247028\pi$
$53$	0.0961110	+	0.0961110i	0.0132019	+	0.0132019i	−0.700475	+	0.713677i	$0.747028\pi$
$54$	−1.18294	−	0.775016i	−0.160978	−	0.105466i
$55$	−1.59200	+	3.00480i	−0.214665	+	0.405168i
$56$	−5.15662	−	5.42303i	−0.689083	−	0.724683i
$57$	−0.785121	−	0.785121i	−0.103992	−	0.103992i
$58$	8.80343	−	1.83413i	1.15595	−	0.240833i
$59$		−	11.0439i		−	1.43779i	−0.695117	−	0.718897i	$-0.744647\pi$
$59$		−	11.0439i		−	1.43779i	0.695117	−	0.718897i	$-0.255353\pi$
$60$	3.39444	−	2.91167i	0.438220	−	0.375894i
$61$	9.42450			1.20668			0.603342	−	0.797483i	$-0.293835\pi$
$61$	9.42450			1.20668			0.603342	+	0.797483i	$0.293835\pi$
$62$	1.02598	+	4.92450i	0.130300	+	0.625412i
$63$	2.61836	−	0.379700i	0.329883	−	0.0478377i
$64$	2.65561	−	7.54637i	0.331951	−	0.943296i
$65$	9.05232	−	2.78219i	1.12280	−	0.345089i
$66$	−1.79895	−	1.17860i	−0.221435	−	0.145076i
$67$	11.4129	−	11.4129i	1.39431	−	1.39431i	0.578947	−	0.815365i	$-0.303464\pi$
$67$	11.4129	−	11.4129i	1.39431	−	1.39431i	0.815365	−	0.578947i	$-0.196536\pi$
$68$	0.878368	−	2.23416i	0.106518	−	0.270932i
$69$			4.10502i			0.494187i
$70$	−1.14928	+	8.28729i	−0.137365	+	0.990520i
$71$	−4.00852			−0.475724			−0.237862	−	0.971299i	$-0.576447\pi$
$71$	−4.00852			−0.475724			−0.237862	+	0.971299i	$0.576447\pi$
$72$	1.63468	+	2.30820i	0.192649	+	0.272024i
$73$	−10.1745	−	10.1745i	−1.19083	−	1.19083i	−0.976834	−	0.213997i	$-0.931352\pi$
$73$	−10.1745	−	10.1745i	−1.19083	−	1.19083i	−0.213997	−	0.976834i	$-0.568648\pi$
$74$	−0.255229	+	0.389567i	−0.0296697	+	0.0452862i
$75$	−4.91093	−	0.939546i	−0.567066	−	0.108489i
$76$	0.886821	+	2.03590i	0.101725	+	0.233533i
$77$	3.98186	−	0.577426i	0.453775	−	0.0658038i
$78$	1.22163	+	5.86359i	0.138323	+	0.663920i
$79$		−	3.22206i		−	0.362510i	−0.983436	−	0.181255i	$-0.941984\pi$
$79$		−	3.22206i		−	0.362510i	0.983436	−	0.181255i	$-0.0580159\pi$
$80$	−8.44882	+	2.93554i	−0.944607	+	0.328203i
$81$	−1.00000			−0.111111
$82$	1.95215	+	9.36989i	0.215578	+	1.03473i
$83$	−2.36021	+	2.36021i	−0.259067	+	0.259067i	−0.824674	−	0.565608i	$-0.808642\pi$
$83$	−2.36021	+	2.36021i	−0.259067	+	0.259067i	0.565608	+	0.824674i	$0.308642\pi$
$84$	−5.15146	−	1.20933i	−0.562070	−	0.131949i
$85$	−2.56554	+	0.788510i	−0.278272	+	0.0855259i
$86$	11.9056	+	7.80010i	1.28382	+	0.841107i
$87$	4.49623	−	4.49623i	0.482047	−	0.482047i
$88$	2.48594	+	3.51019i	0.265002	+	0.374187i
$89$	7.10490			0.753118			0.376559	−	0.926393i	$-0.377107\pi$
$89$	7.10490			0.753118			0.376559	+	0.926393i	$0.377107\pi$
$90$	0.879417	−	3.03754i	0.0926987	−	0.320184i
$91$	−8.97844	−	6.70423i	−0.941196	−	0.702794i
$92$	3.00398	−	7.64074i	0.313187	−	0.796603i
$93$	2.51512	+	2.51512i	0.260806	+	0.260806i
$94$	2.05815	−	3.14144i	0.212282	−	0.324015i
$95$	1.16235	−	2.19388i	0.119255	−	0.225087i
$96$	−1.35356	−	5.49253i	−0.138147	−	0.560579i
$97$	5.73370	−	5.73370i	0.582169	−	0.582169i	−0.353330	−	0.935499i	$-0.614951\pi$
$97$	5.73370	−	5.73370i	0.582169	−	0.582169i	0.935499	+	0.353330i	$0.114951\pi$
$98$	8.71864	−	4.68885i	0.880716	−	0.473645i
$99$	−1.52074			−0.152840
$100$	8.45325	+	5.34252i	0.845325	+	0.534252i
$101$	−3.64826			−0.363015			−0.181508	−	0.983390i	$-0.558098\pi$
$101$	−3.64826			−0.363015			−0.181508	+	0.983390i	$0.558098\pi$
$102$	−0.346227	−	1.66182i	−0.0342816	−	0.164544i
$103$	−6.96900	−	6.96900i	−0.686676	−	0.686676i	0.274820	−	0.961496i	$-0.411382\pi$
$103$	−6.96900	−	6.96900i	−0.686676	−	0.686676i	−0.961496	+	0.274820i	$0.911382\pi$
$104$	2.01702	−	11.8080i	0.197785	−	1.15786i
$105$	2.53162	+	5.34704i	0.247061	+	0.521818i
$106$	−0.160787	−	0.105341i	−0.0156170	−	0.0102317i
$107$	10.3407	−	10.3407i	0.999676	−	0.999676i	−0.000323617	−	1.00000i	$-0.500103\pi$
$107$	10.3407	−	10.3407i	0.999676	−	0.999676i	1.00000		0.000323617i	$0.000103010\pi$
$108$	1.86132	+	0.731782i	0.179105	+	0.0704157i
$109$	5.48962			0.525810			0.262905	−	0.964822i	$-0.415319\pi$
$109$	5.48962			0.525810			0.262905	+	0.964822i	$0.415319\pi$
$110$	1.33737	−	4.61931i	0.127513	−	0.440434i
$111$			0.329321i			0.0312577i
$112$	8.70352	+	6.02069i	0.822406	+	0.568901i
$113$	−7.25806	+	7.25806i	−0.682780	+	0.682780i	−0.960626	−	0.277845i	$-0.910380\pi$
$113$	−7.25806	+	7.25806i	−0.682780	+	0.682780i	0.277845	+	0.960626i	$0.410380\pi$
$114$	1.31345	+	0.860522i	0.123016	+	0.0805953i
$115$	−8.77406	+	2.69667i	−0.818185	+	0.251466i
$116$	−11.6592	+	5.07864i	−1.08253	+	0.471540i
$117$	2.99475	+	2.99475i	0.276864	+	0.276864i
$118$	3.18558	+	15.2901i	0.293256	+	1.40757i
$119$	2.54461	+	1.90007i	0.233264	+	0.174179i
$120$	−3.85969	+	5.01027i	−0.352340	+	0.457373i
$121$	8.68734			0.789758
$122$	−13.0481	+	2.71847i	−1.18132	+	0.246119i
$123$	4.78554	+	4.78554i	0.431498	+	0.431498i
$124$	−2.84091	−	6.52195i	−0.255121	−	0.585688i
$125$	−1.21791	−	11.1138i	−0.108933	−	0.994049i
$126$	−3.51556	+	1.28095i	−0.313191	+	0.114116i
$127$	−8.26216	−	8.26216i	−0.733148	−	0.733148i	0.238094	−	0.971242i	$-0.423477\pi$
$127$	−8.26216	−	8.26216i	−0.733148	−	0.733148i	−0.971242	+	0.238094i	$0.923477\pi$
$128$	−1.49993	+	11.2138i	−0.132576	+	0.991173i
$129$	10.0644			0.886125
$130$	−11.7303	+	6.46302i	−1.02881	+	0.566844i
$131$	−9.50624			−0.830564			−0.415282	−	0.909693i	$-0.636317\pi$
$131$	−9.50624			−0.830564			−0.415282	+	0.909693i	$0.636317\pi$
$132$	2.83058	+	1.11285i	0.246371	+	0.0968614i
$133$	−2.90724	+	0.421592i	−0.252090	+	0.0365566i
$134$	−12.5090	+	19.0931i	−1.08061	+	1.64939i
$135$	−0.656920	−	2.13739i	−0.0565387	−	0.183958i
$136$	−0.571649	+	3.34653i	−0.0490185	+	0.286962i
$137$	−1.43035	−	1.43035i	−0.122203	−	0.122203i	0.643360	−	0.765564i	$-0.277540\pi$
$137$	−1.43035	−	1.43035i	−0.122203	−	0.122203i	−0.765564	+	0.643360i	$0.777540\pi$
$138$	−1.18408	−	5.68334i	−0.100796	−	0.483798i
$139$		−	8.91288i		−	0.755981i	−0.925810	−	0.377990i	$-0.876615\pi$
$139$		−	8.91288i		−	0.755981i	0.925810	−	0.377990i	$-0.123385\pi$
$140$	−0.799280	−	11.8051i	−0.0675515	−	0.997716i
$141$		−	2.65562i		−	0.223644i
$142$	5.54974	−	1.15625i	0.465723	−	0.0970300i
$143$	4.55424	+	4.55424i	0.380845	+	0.380845i
$144$	−2.92899	−	2.72415i	−0.244083	−	0.227013i
$145$	12.5639	+	6.65656i	1.04337	+	0.552797i
$146$	17.0212	+	11.1516i	1.40868	+	0.922913i
$147$	3.33986	−	6.15186i	0.275467	−	0.507397i
$148$	0.240991	−	0.612969i	0.0198093	−	0.0503858i
$149$	−18.6817			−1.53046			−0.765231	−	0.643755i	$-0.777375\pi$
$149$	−18.6817			−1.53046			−0.765231	+	0.643755i	$0.777375\pi$
$150$	7.07012	−	0.115756i	0.577273	−	0.00945142i
$151$	−23.1559			−1.88440			−0.942202	−	0.335046i	$-0.891248\pi$
$151$	−23.1559			−1.88440			−0.942202	+	0.335046i	$0.891248\pi$
$152$	−1.81504	−	2.56287i	−0.147219	−	0.207876i
$153$	−0.848750	−	0.848750i	−0.0686174	−	0.0686174i
$154$	−5.34627	+	1.94799i	−0.430814	+	0.156974i
$155$	−3.72357	+	7.02803i	−0.299084	+	0.564505i
$156$	−3.38267	−	7.76567i	−0.270830	−	0.621751i
$157$	13.4688	+	13.4688i	1.07493	+	1.07493i	0.996956	+	0.0779709i	$0.0248441\pi$
$157$	13.4688	+	13.4688i	1.07493	+	1.07493i	0.0779709	+	0.996956i	$0.475156\pi$
$158$	0.929392	+	4.46089i	0.0739385	+	0.354889i
$159$	−0.135921			−0.0107793
$160$	10.8505	−	6.50125i	0.857809	−	0.513969i
$161$	8.70245	+	6.49815i	0.685849	+	0.512126i
$162$	1.38448	−	0.288447i	0.108775	−	0.0226625i
$163$	7.46067	+	7.46067i	0.584365	+	0.584365i	0.936100	−	0.351735i	$-0.114408\pi$
$163$	7.46067	+	7.46067i	0.584365	+	0.584365i	−0.351735	+	0.936100i	$0.614408\pi$
$164$	−5.40543	−	12.4094i	−0.422093	−	0.969010i
$165$	−0.999006	−	3.25043i	−0.0777725	−	0.253046i
$166$	2.58688	−	3.94847i	0.200781	−	0.306461i
$167$	−10.9850	+	10.9850i	−0.850041	+	0.850041i	−0.990138	−	0.140097i	$-0.955259\pi$
$167$	−10.9850	+	10.9850i	−0.850041	+	0.850041i	0.140097	+	0.990138i	$0.455259\pi$
$168$	7.48094	+	0.188376i	0.577167	+	0.0145335i
$169$		−	4.93701i		−	0.379770i
$170$	3.32451	−	1.83170i	0.254979	−	0.140485i
$171$	1.11033			0.0849090
$172$	−18.7331	−	7.36498i	−1.42839	−	0.561574i
$173$	−10.0310	+	10.0310i	−0.762642	+	0.762642i	−0.976799	−	0.214157i	$-0.931300\pi$
$173$	−10.0310	+	10.0310i	−0.762642	+	0.762642i	0.214157	+	0.976799i	$0.431300\pi$
$174$	−4.92804	+	7.52189i	−0.373594	+	0.570233i
$175$	−9.76567	+	8.92366i	−0.738215	+	0.674565i
$176$	−4.45424	−	4.14274i	−0.335751	−	0.312271i
$177$	7.80922	+	7.80922i	0.586977	+	0.586977i
$178$	−9.83663	+	2.04939i	−0.737287	+	0.153608i
$179$	−9.37542			−0.700752			−0.350376	−	0.936609i	$-0.613946\pi$
$179$	−9.37542			−0.700752			−0.350376	+	0.936609i	$0.613946\pi$
$180$	−0.341372	+	4.45909i	−0.0254443	+	0.332361i
$181$	9.58152			0.712189			0.356095	−	0.934450i	$-0.384108\pi$
$181$	9.58152			0.712189			0.356095	+	0.934450i	$0.384108\pi$
$182$	14.3643	+	6.69210i	1.06475	+	0.496052i
$183$	−6.66413	+	6.66413i	−0.492627	+	0.492627i
$184$	−1.95502	+	11.4450i	−0.144126	+	0.843735i
$185$	−0.703888	+	0.216337i	−0.0517509	+	0.0159054i
$186$	−4.20762	−	2.75667i	−0.308518	−	0.202129i
$187$	−1.29073	−	1.29073i	−0.0943876	−	0.0943876i
$188$	−1.94334	+	4.94295i	−0.141732	+	0.360502i
$189$	−1.58297	+	2.11995i	−0.115144	+	0.154204i
$190$	−0.976442	+	3.37266i	−0.0708386	+	0.244679i
$191$	20.1759			1.45988			0.729940	−	0.683511i	$-0.239548\pi$
$191$	20.1759			1.45988			0.729940	+	0.683511i	$0.239548\pi$
$192$	3.45829	+	7.21389i	0.249581	+	0.520618i
$193$	−14.3672	+	14.3672i	−1.03417	+	1.03417i	−0.0347779	+	0.999395i	$0.511072\pi$
$193$	−14.3672	+	14.3672i	−1.03417	+	1.03417i	−0.999395	+	0.0347779i	$0.988928\pi$
$194$	−6.28435	+	9.59208i	−0.451190	+	0.688672i
$195$	−4.43365	+	8.36826i	−0.317500	+	0.599264i
$196$	−10.7183	+	9.00650i	−0.765596	+	0.643322i
$197$	−10.1289	+	10.1289i	−0.721653	+	0.721653i	−0.968942	−	0.247289i	$-0.920460\pi$
$197$	−10.1289	+	10.1289i	−0.721653	+	0.721653i	0.247289	+	0.968942i	$0.420460\pi$
$198$	2.10545	−	0.438654i	0.149628	−	0.0311738i
$199$	15.0599			1.06757			0.533785	−	0.845620i	$-0.320769\pi$
$199$	15.0599			1.06757			0.533785	+	0.845620i	$0.320769\pi$
$200$	−13.2444	−	4.95833i	−0.936523	−	0.350607i
$201$			16.1403i			1.13845i
$202$	5.05096	−	1.05233i	0.355384	−	0.0740416i
$203$	−2.41437	−	16.6492i	−0.169456	−	1.16855i
$204$	0.958692	+	2.20089i	0.0671218	+	0.154093i
$205$	−7.08488	+	13.3723i	−0.494829	+	0.933963i
$206$	11.6587	+	7.63828i	0.812297	+	0.532184i
$207$	−2.90269	−	2.90269i	−0.201751	−	0.201751i
$208$	0.613435	+	16.9297i	0.0425341	+	1.17387i
$209$	1.68852			0.116798
$210$	−5.04733	−	6.67266i	−0.348299	−	0.460457i
$211$			8.79652i			0.605578i	0.953058	+	0.302789i	$0.0979177\pi$
$211$			8.79652i			0.605578i	−0.953058	+	0.302789i	$0.902082\pi$
$212$	0.252993	+	0.0994649i	0.0173756	+	0.00683127i
$213$	2.83445	−	2.83445i	0.194213	−	0.194213i
$214$	−11.3338	+	17.2993i	−0.774765	+	1.18256i
$215$	6.61153	+	21.5117i	0.450903	+	1.46708i
$216$	−2.78804	−	0.476250i	−0.189702	−	0.0324047i
$217$	9.31330	−	1.35056i	0.632228	−	0.0916820i
$218$	−7.60029	+	1.58346i	−0.514757	+	0.107246i
$219$	14.3889			0.972309
$220$	−0.519139	+	6.78113i	−0.0350003	+	0.457184i
$221$			5.08358i			0.341959i
$222$	−0.0949915	−	0.455939i	−0.00637541	−	0.0306006i
$223$	−7.43822	−	7.43822i	−0.498100	−	0.498100i	0.412746	−	0.910846i	$-0.364570\pi$
$223$	−7.43822	−	7.43822i	−0.498100	−	0.498100i	−0.910846	+	0.412746i	$0.864570\pi$
$224$	−13.7865	−	5.82505i	−0.921152	−	0.389202i
$225$	4.13691	−	2.80819i	0.275794	−	0.187213i
$226$	7.95510	−	12.1422i	0.529166	−	0.807689i
$227$	4.83361	+	4.83361i	0.320818	+	0.320818i	0.849081	−	0.528263i	$-0.177156\pi$
$227$	4.83361	+	4.83361i	0.320818	+	0.320818i	−0.528263	+	0.849081i	$0.677156\pi$
$228$	−2.06667	−	0.812518i	−0.136869	−	0.0538103i
$229$		−	13.7101i		−	0.905990i	−0.891513	−	0.452995i	$-0.850355\pi$
$229$		−	13.7101i		−	0.905990i	0.891513	−	0.452995i	$-0.149645\pi$
$230$	11.3697	−	6.26435i	0.749696	−	0.413059i
$231$	−2.40730	+	3.22390i	−0.158389	+	0.212117i
$232$	14.6770	−	10.3944i	0.963593	−	0.682423i
$233$	−10.8753	+	10.8753i	−0.712467	+	0.712467i	−0.967051	−	0.254584i	$-0.918062\pi$
$233$	−10.8753	+	10.8753i	−0.712467	+	0.712467i	0.254584	+	0.967051i	$0.418062\pi$
$234$	−5.01001	−	3.28236i	−0.327514	−	0.214574i
$235$	5.67611	−	1.74453i	0.370269	−	0.113801i
$236$	−8.82078	−	20.2501i	−0.574184	−	1.31817i
$237$	2.27834	+	2.27834i	0.147994	+	0.147994i
$238$	−4.07104	−	1.89663i	−0.263886	−	0.122940i
$239$		−	6.63832i		−	0.429397i	−0.976680	−	0.214698i	$-0.931123\pi$
$239$		−	6.63832i		−	0.429397i	0.976680	−	0.214698i	$-0.0688769\pi$
$240$	3.89848	−	8.04996i	0.251646	−	0.519623i
$241$			13.6399i			0.878622i	0.898335	+	0.439311i	$0.144777\pi$
$241$			13.6399i			0.878622i	−0.898335	+	0.439311i	$0.855223\pi$
$242$	−12.0275	+	2.50584i	−0.773156	+	0.161081i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	17.2807	−	7.52736i	1.10629	−	0.481890i
$245$	15.3430	+	3.09732i	0.980226	+	0.197880i
$246$	−8.00589	−	5.24514i	−0.510437	−	0.334418i
$247$	−3.32515	−	3.32515i	−0.211574	−	0.211574i
$248$	5.81444	+	8.21009i	0.369217	+	0.521341i
$249$		−	3.33784i		−	0.211527i
$250$	4.89192	+	15.0356i	0.309392	+	0.950935i
$251$	25.6650			1.61996			0.809981	−	0.586456i	$-0.199477\pi$
$251$	25.6650			1.61996			0.809981	+	0.586456i	$0.199477\pi$
$252$	4.49776	−	2.78751i	0.283332	−	0.175596i
$253$	−4.41425	−	4.41425i	−0.277521	−	0.277521i
$254$	13.8220	+	9.05564i	0.867271	+	0.568202i
$255$	1.25655	−	2.37167i	0.0786884	−	0.148520i
$256$	−1.15797	−	15.9580i	−0.0723734	−	0.997378i
$257$	12.8605	−	12.8605i	0.802219	−	0.802219i	−0.181223	−	0.983442i	$-0.558006\pi$
$257$	12.8605	−	12.8605i	0.802219	−	0.802219i	0.983442	+	0.181223i	$0.0580056\pi$
$258$	−13.9341	+	2.90306i	−0.867497	+	0.180737i
$259$	0.698143	+	0.521306i	0.0433805	+	0.0323924i
$260$	14.3762	−	12.3315i	0.891572	−	0.764768i
$261$			6.35863i			0.393589i
$262$	13.1612	−	2.74205i	0.813104	−	0.169404i
$263$	−2.75098	+	2.75098i	−0.169633	+	0.169633i	−0.786818	−	0.617185i	$-0.788273\pi$
$263$	−2.75098	+	2.75098i	−0.169633	+	0.169633i	0.617185	+	0.786818i	$0.288273\pi$
$264$	−4.23990	−	0.724254i	−0.260948	−	0.0445748i
$265$	−0.0892895	−	0.290518i	−0.00548501	−	0.0178464i
$266$	3.90343	−	1.42227i	0.239335	−	0.0872052i
$267$	−5.02392	+	5.02392i	−0.307459	+	0.307459i
$268$	11.8112	−	30.0422i	0.721484	−	1.83512i
$269$			14.7056i			0.896618i	0.893879	+	0.448309i	$0.147974\pi$
$269$			14.7056i			0.896618i	−0.893879	+	0.448309i	$0.852026\pi$
$270$	1.52602	+	2.76970i	0.0928707	+	0.168559i
$271$		−	17.6104i		−	1.06975i	−0.844930	−	0.534877i	$-0.820358\pi$
$271$		−	17.6104i		−	1.06975i	0.844930	−	0.534877i	$-0.179642\pi$
$272$	−0.173855	−	4.79811i	−0.0105415	−	0.290928i
$273$	11.0893	−	1.60811i	0.671156	−	0.0973272i
$274$	2.39288	+	1.56772i	0.144559	+	0.0947095i
$275$	6.29118	−	4.27054i	0.379373	−	0.257523i
$276$	3.27869	+	7.52696i	0.197354	+	0.453070i
$277$	−11.1941	+	11.1941i	−0.672587	+	0.672587i	−0.958312	−	0.285724i	$-0.907766\pi$
$277$	−11.1941	+	11.1941i	−0.672587	+	0.672587i	0.285724	+	0.958312i	$0.407766\pi$
$278$	2.57089	+	12.3398i	0.154192	+	0.740089i
$279$	−3.55692			−0.212947
$280$	4.51175	+	16.1135i	0.269628	+	0.962964i
$281$	−13.1563			−0.784838			−0.392419	−	0.919787i	$-0.628362\pi$
$281$	−13.1563			−0.784838			−0.392419	+	0.919787i	$0.628362\pi$
$282$	0.766006	+	3.67667i	0.0456150	+	0.218942i
$283$	15.5270	−	15.5270i	0.922986	−	0.922986i	−0.0742535	−	0.997239i	$-0.523657\pi$
$283$	15.5270	−	15.5270i	0.922986	−	0.922986i	0.997239	+	0.0742535i	$0.0236574\pi$
$284$	−7.35001	+	3.20161i	−0.436143	+	0.189981i
$285$	0.729397	+	2.37321i	0.0432057	+	0.140577i
$286$	−7.61893	−	4.99162i	−0.450517	−	0.295161i
$287$	17.7205	−	2.56973i	1.04601	−	0.151686i
$288$	4.84092	+	2.92669i	0.285254	+	0.172457i
$289$			15.5592i			0.915250i
$290$	−19.3146	−	5.59189i	−1.13419	−	0.328367i
$291$			8.10867i			0.475339i
$292$	−26.7822	−	10.5295i	−1.56731	−	0.616193i
$293$	−3.37224	+	3.37224i	−0.197008	+	0.197008i	−0.798716	−	0.601708i	$-0.794487\pi$
$293$	−3.37224	+	3.37224i	−0.197008	+	0.197008i	0.601708	+	0.798716i	$0.294487\pi$
$294$	−2.84950	+	9.48053i	−0.166186	+	0.552915i
$295$	−11.5614	+	21.8214i	−0.673128	+	1.27049i
$296$	−0.156839	+	0.918160i	−0.00911608	+	0.0533670i
$297$	1.07533	−	1.07533i	0.0623968	−	0.0623968i
$298$	25.8645	−	5.38867i	1.49829	−	0.312157i
$299$			17.3856i			1.00544i
$300$	−9.75509	+	2.19962i	−0.563210	+	0.126995i
$301$	15.9318	−	21.3361i	0.918291	−	1.22979i
$302$	32.0590	−	6.67926i	1.84479	−	0.384348i
$303$	2.57971	−	2.57971i	0.148200	−	0.148200i
$304$	3.25214	+	3.02471i	0.186523	+	0.173479i
$305$	−18.6217	−	9.86608i	−1.06627	−	0.564930i
$306$	1.41990	+	0.930262i	0.0811703	+	0.0531795i
$307$	−6.55201	−	6.55201i	−0.373943	−	0.373943i	0.494968	−	0.868911i	$-0.335180\pi$
$307$	−6.55201	−	6.55201i	−0.373943	−	0.373943i	−0.868911	+	0.494968i	$0.835180\pi$
$308$	6.83993	−	4.23908i	0.389741	−	0.241544i
$309$	9.85565			0.560668
$310$	3.12801	−	10.8043i	0.177659	−	0.613641i
$311$			20.9167i			1.18608i	0.805175	+	0.593038i	$0.202072\pi$
$311$			20.9167i			1.18608i	−0.805175	+	0.593038i	$0.797928\pi$
$312$	6.92323	+	9.77573i	0.391951	+	0.553442i
$313$	−15.5832	−	15.5832i	−0.880813	−	0.880813i	0.112804	−	0.993617i	$-0.464017\pi$
$313$	−15.5832	−	15.5832i	−0.880813	−	0.880813i	−0.993617	+	0.112804i	$0.964017\pi$
$314$	−22.5324	−	14.7623i	−1.27158	−	0.833085i
$315$	−5.57106	−	1.99080i	−0.313894	−	0.112169i
$316$	−2.57346	−	5.90795i	−0.144768	−	0.332348i
$317$	−6.28966	+	6.28966i	−0.353263	+	0.353263i	−0.861322	−	0.508059i	$-0.830363\pi$
$317$	−6.28966	+	6.28966i	−0.353263	+	0.353263i	0.508059	+	0.861322i	$0.330363\pi$
$318$	0.188181	−	0.0392061i	0.0105527	−	0.00219857i
$319$			9.66985i			0.541407i
$320$	−13.1471	+	12.1307i	−0.734946	+	0.678126i
$321$			14.6240i			0.816232i
$322$	−13.9228	−	6.48639i	−0.775886	−	0.361472i
$323$	0.942391	+	0.942391i	0.0524361	+	0.0524361i
$324$	−1.83360	+	0.798701i	−0.101866	+	0.0443723i
$325$	−20.7988	−	3.97918i	−1.15371	−	0.220725i
$326$	−12.4812	−	8.17718i	−0.691269	−	0.452892i
$327$	−3.88175	+	3.88175i	−0.214661	+	0.214661i
$328$	11.0632	+	15.6214i	0.610862	+	0.862549i
$329$	−5.62979	−	4.20378i	−0.310380	−	0.231762i
$330$	2.32069	+	4.21201i	0.127750	+	0.231863i
$331$			18.2380i			1.00245i	0.865316	+	0.501227i	$0.167118\pi$
$331$			18.2380i			1.00245i	−0.865316	+	0.501227i	$0.832882\pi$
$332$	−2.44257	+	6.21277i	−0.134053	+	0.340970i
$333$	−0.232865	−	0.232865i	−0.0127609	−	0.0127609i
$334$	12.0399	−	18.3771i	0.658795	−	1.00555i
$335$	−34.4983	+	10.6029i	−1.88484	+	0.579298i
$336$	−10.4116	+	1.89705i	−0.567999	+	0.103493i
$337$	−16.2269	−	16.2269i	−0.883935	−	0.883935i	0.109997	−	0.993932i	$-0.464916\pi$
$337$	−16.2269	−	16.2269i	−0.883935	−	0.883935i	−0.993932	+	0.109997i	$0.964916\pi$
$338$	1.42407	+	6.83522i	0.0774590	+	0.371787i
$339$		−	10.2644i		−	0.557488i
$340$	−4.07439	+	3.49491i	−0.220965	+	0.189538i
$341$	−5.40916			−0.292922
$342$	−1.53723	+	0.320271i	−0.0831241	+	0.0173183i
$343$	−7.75473	−	16.8186i	−0.418716	−	0.908117i
$344$	28.0601	+	4.79319i	1.51290	+	0.258432i
$345$	4.29736	−	8.11103i	0.231362	−	0.436683i
$346$	10.9943	−	16.7812i	0.591060	−	0.902161i
$347$	22.7572	−	22.7572i	1.22167	−	1.22167i	0.254635	−	0.967037i	$-0.418045\pi$
$347$	22.7572	−	22.7572i	1.22167	−	1.22167i	0.967037	−	0.254635i	$-0.0819554\pi$
$348$	4.65313	−	11.8354i	0.249434	−	0.634445i
$349$		−	25.2403i		−	1.35108i	−0.737322	−	0.675542i	$-0.763910\pi$
$349$		−	25.2403i		−	1.35108i	0.737322	−	0.675542i	$-0.236090\pi$
$350$	10.9464	−	15.1715i	0.585111	−	0.810953i
$351$	−4.23521			−0.226059
$352$	7.36179	+	4.45075i	0.392385	+	0.237226i
$353$	−21.8977	−	21.8977i	−1.16549	−	1.16549i	−0.983254	−	0.182241i	$-0.941665\pi$
$353$	−21.8977	−	21.8977i	−1.16549	−	1.16549i	−0.182241	−	0.983254i	$-0.558335\pi$
$354$	−13.0643	−	8.55920i	−0.694359	−	0.454916i
$355$	7.92035	+	4.19633i	0.420369	+	0.222718i
$356$	13.0275	−	5.67469i	0.690457	−	0.300758i
$357$	−3.14286	+	0.455759i	−0.166338	+	0.0241213i
$358$	12.9801	−	2.70431i	0.686021	−	0.142927i
$359$		−	31.8415i		−	1.68053i	−0.542177	−	0.840264i	$-0.682400\pi$
$359$		−	31.8415i		−	1.68053i	0.542177	−	0.840264i	$-0.317600\pi$
$360$	−0.813586	−	6.27201i	−0.0428798	−	0.330564i
$361$	17.7672			0.935114
$362$	−13.2655	+	2.76376i	−0.697218	+	0.145260i
$363$	−6.14288	+	6.14288i	−0.322417	+	0.322417i
$364$	−21.8175	−	5.12177i	−1.14355	−	0.268453i
$365$	9.45233	+	30.7547i	0.494758	+	1.60977i
$366$	7.30414	−	11.1486i	0.381794	−	0.582749i
$367$	−14.4374	+	14.4374i	−0.753628	+	0.753628i	−0.975154	−	0.221526i	$-0.928896\pi$
$367$	−14.4374	+	14.4374i	−0.753628	+	0.753628i	0.221526	+	0.975154i	$0.428896\pi$
$368$	−0.594579	−	16.4093i	−0.0309945	−	0.855395i
$369$	−6.76778			−0.352317
$370$	0.912120	−	0.502550i	0.0474189	−	0.0261263i
$371$	−0.215160	+	0.288147i	−0.0111706	+	0.0149598i
$372$	6.62054	+	2.60289i	0.343259	+	0.134953i
$373$	−18.3750	−	18.3750i	−0.951420	−	0.951420i	0.0474534	−	0.998873i	$-0.484889\pi$
$373$	−18.3750	−	18.3750i	−0.951420	−	0.951420i	−0.998873	+	0.0474534i	$0.984889\pi$
$374$	2.15930	+	1.41469i	0.111655	+	0.0731519i
$375$	8.71984	+	6.99746i	0.450291	+	0.361347i
$376$	1.26474	−	7.40399i	0.0652240	−	0.381832i
$377$	19.0425	−	19.0425i	0.980738	−	0.980738i
$378$	1.58011	−	3.39164i	0.0812721	−	0.174447i
$379$	−26.2670			−1.34925			−0.674623	−	0.738163i	$-0.735694\pi$
$379$	−26.2670			−1.34925			−0.674623	+	0.738163i	$0.735694\pi$
$380$	0.379035	−	4.95105i	0.0194441	−	0.253984i
$381$	11.6845			0.598613
$382$	−27.9333	+	5.81969i	−1.42919	+	0.297761i
$383$	0.772551	+	0.772551i	0.0394755	+	0.0394755i	0.726569	−	0.687093i	$-0.241114\pi$
$383$	0.772551	+	0.772551i	0.0394755	+	0.0394755i	−0.687093	+	0.726569i	$0.741114\pi$
$384$	−6.86878	−	8.98999i	−0.350521	−	0.458769i
$385$	−8.47215	−	3.02750i	−0.431781	−	0.154296i
$386$	15.7470	−	24.0353i	0.801500	−	1.22337i
$387$	−7.11664	+	7.11664i	−0.361759	+	0.361759i
$388$	5.93378	−	15.0928i	0.301242	−	0.766221i
$389$	13.7206			0.695663			0.347831	−	0.937557i	$-0.386918\pi$
$389$	13.7206			0.695663			0.347831	+	0.937557i	$0.386918\pi$
$390$	3.72452	−	12.8646i	0.188598	−	0.651425i
$391$		−	4.92731i		−	0.249185i
$392$	12.2415	−	15.5610i	0.618289	−	0.785951i
$393$	6.72193	−	6.72193i	0.339076	−	0.339076i
$394$	11.1016	−	16.9449i	0.559292	−	0.853673i
$395$	−3.37302	+	6.36639i	−0.169715	+	0.320328i
$396$	−2.78843	+	1.21462i	−0.140124	+	0.0610369i
$397$	−0.780593	−	0.780593i	−0.0391768	−	0.0391768i	0.687247	−	0.726424i	$-0.258819\pi$
$397$	−0.780593	−	0.780593i	−0.0391768	−	0.0391768i	−0.726424	+	0.687247i	$0.758819\pi$
$398$	−20.8502	+	4.34399i	−1.04513	+	0.217744i
$399$	1.75762	−	2.35384i	0.0879912	−	0.117840i
$400$	19.7669	+	3.04441i	0.988347	+	0.152221i
$401$	14.9433			0.746232			0.373116	−	0.927785i	$-0.378289\pi$
$401$	14.9433			0.746232			0.373116	+	0.927785i	$0.378289\pi$
$402$	−4.65563	−	22.3460i	−0.232202	−	1.11452i
$403$	10.6521	+	10.6521i	0.530617	+	0.530617i
$404$	−6.68943	+	2.91387i	−0.332812	+	0.144970i
$405$	1.97588	+	1.04685i	0.0981822	+	0.0520186i
$406$	8.14508	+	22.3542i	0.404233	+	1.10942i
$407$	−0.354127	−	0.354127i	−0.0175534	−	0.0175534i
$408$	−1.96213	−	2.77057i	−0.0971401	−	0.137164i
$409$	−3.97129			−0.196367			−0.0981837	−	0.995168i	$-0.531303\pi$
$409$	−3.97129			−0.196367			−0.0981837	+	0.995168i	$0.531303\pi$
$410$	5.95170	−	20.5574i	0.293934	−	1.01526i
$411$	2.02283			0.0997786
$412$	−18.3445	−	7.21218i	−0.903767	−	0.355319i
$413$	28.9170	−	4.19337i	1.42291	−	0.206342i
$414$	4.85600	+	3.18146i	0.238659	+	0.156360i
$415$	7.13428	−	2.19269i	0.350208	−	0.107635i
$416$	−5.73262	−	23.2620i	−0.281065	−	1.14051i
$417$	6.30236	+	6.30236i	0.308628	+	0.308628i
$418$	−2.33774	+	0.487050i	−0.114342	+	0.0238224i
$419$		−	0.149944i		−	0.00732525i	−0.999993	−	0.00366262i	$-0.998834\pi$
$419$		−	0.149944i		−	0.00732525i	0.999993	−	0.00366262i	$-0.00116585\pi$
$420$	8.91267	+	7.78231i	0.434894	+	0.379738i
$421$			32.9588i			1.60631i	0.595767	+	0.803157i	$0.296848\pi$
$421$			32.9588i			1.60631i	−0.595767	+	0.803157i	$0.703152\pi$
$422$	−2.53733	−	12.1787i	−0.123515	−	0.592848i
$423$	1.87781	+	1.87781i	0.0913021	+	0.0913021i
$424$	−0.378955	−	0.0647326i	−0.0184037	−	0.00314369i
$425$	5.89466	+	1.12775i	0.285933	+	0.0547039i
$426$	−3.10667	+	4.74184i	−0.150518	+	0.229743i
$427$	3.57848	+	24.6768i	0.173175	+	1.19419i
$428$	10.7016	−	27.2199i	0.517280	−	1.31572i
$429$	−6.44067			−0.310958
$430$	−15.3585	−	27.8755i	−0.740655	−	1.34428i
$431$	11.1204			0.535652			0.267826	−	0.963467i	$-0.413695\pi$
$431$	11.1204			0.535652			0.267826	+	0.963467i	$0.413695\pi$
$432$	3.99738	−	0.144842i	0.192324	−	0.00696870i
$433$	7.91034	+	7.91034i	0.380147	+	0.380147i	0.871155	−	0.491008i	$-0.163371\pi$
$433$	7.91034	+	7.91034i	0.380147	+	0.380147i	−0.491008	+	0.871155i	$0.663371\pi$
$434$	−12.5046	+	4.55622i	−0.600238	+	0.218706i
$435$	−13.5909	+	4.17711i	−0.651634	+	0.200277i
$436$	10.0657	−	4.38456i	0.482062	−	0.209982i
$437$	3.22294	+	3.22294i	0.154174	+	0.154174i
$438$	−19.9212	+	4.15042i	−0.951870	+	0.198315i
$439$	−1.40457			−0.0670365			−0.0335183	−	0.999438i	$-0.510671\pi$
$439$	−1.40457			−0.0670365			−0.0335183	+	0.999438i	$0.510671\pi$
$440$	−1.23726	−	9.53811i	−0.0589839	−	0.454712i
$441$	1.98839	+	6.71166i	0.0946850	+	0.319603i
$442$	−1.46634	−	7.03814i	−0.0697468	−	0.334770i
$443$	−1.49653	−	1.49653i	−0.0711021	−	0.0711021i	0.670661	−	0.741764i	$-0.266010\pi$
$443$	−1.49653	−	1.49653i	−0.0711021	−	0.0711021i	−0.741764	+	0.670661i	$0.766010\pi$
$444$	0.263029	+	0.603841i	0.0124828	+	0.0286570i
$445$	−14.0384	−	7.43779i	−0.665485	−	0.352585i
$446$	12.4436	+	8.15257i	0.589223	+	0.386035i
$447$	13.2099	−	13.2099i	0.624809	−	0.624809i
$448$	20.7675	+	4.08800i	0.981171	+	0.193140i
$449$		−	28.3156i		−	1.33630i	−0.744028	−	0.668148i	$-0.767087\pi$
$449$		−	28.3156i		−	1.33630i	0.744028	−	0.668148i	$-0.232913\pi$
$450$	−4.91748	+	5.08118i	−0.231812	+	0.239529i
$451$	−10.2921			−0.484634
$452$	−7.51133	+	19.1054i	−0.353303	+	0.898641i
$453$	16.3737	−	16.3737i	0.769304	−	0.769304i
$454$	−8.08631	−	5.29782i	−0.379509	−	0.248639i
$455$	10.7220	+	22.6459i	0.502653	+	1.06165i
$456$	3.09564	+	0.528794i	0.144967	+	0.0247631i
$457$	−14.1475	−	14.1475i	−0.661792	−	0.661792i	0.294010	−	0.955802i	$-0.405010\pi$
$457$	−14.1475	−	14.1475i	−0.661792	−	0.661792i	−0.955802	+	0.294010i	$0.905010\pi$
$458$	3.95464	+	18.9815i	0.184788	+	0.886945i
$459$	1.20031			0.0560258
$460$	−13.9342	+	11.9525i	−0.649688	+	0.557286i
$461$	−6.65838			−0.310112			−0.155056	−	0.987906i	$-0.549556\pi$
$461$	−6.65838			−0.310112			−0.155056	+	0.987906i	$0.549556\pi$
$462$	2.40294	−	5.15782i	0.111795	−	0.239964i
$463$	8.68321	−	8.68321i	0.403543	−	0.403543i	−0.475936	−	0.879480i	$-0.657891\pi$
$463$	8.68321	−	8.68321i	0.403543	−	0.403543i	0.879480	+	0.475936i	$0.157891\pi$
$464$	−17.3219	+	18.6244i	−0.804149	+	0.864615i
$465$	−2.33661	−	7.60253i	−0.108358	−	0.352559i
$466$	11.9198	−	18.1937i	0.552173	−	0.842807i
$467$	2.12237	+	2.12237i	0.0982116	+	0.0982116i	0.754505	−	0.656294i	$-0.227877\pi$
$467$	2.12237	+	2.12237i	0.0982116	+	0.0982116i	−0.656294	+	0.754505i	$0.727877\pi$
$468$	7.88306	+	3.09925i	0.364395	+	0.143263i
$469$	34.2167	+	25.5497i	1.57998	+	1.17978i
$470$	−7.35529	+	4.05253i	−0.339274	+	0.186929i
$471$	−19.0477			−0.877674
$472$	18.0533	+	25.4916i	0.830970	+	1.17335i
$473$	−10.8226	+	10.8226i	−0.497623	+	0.497623i
$474$	−3.81150	−	2.49714i	−0.175068	−	0.114698i
$475$	−4.59333	+	3.11802i	−0.210757	+	0.143064i
$476$	6.18337	+	1.45157i	0.283414	+	0.0665328i
$477$	0.0961110	−	0.0961110i	0.00440062	−	0.00440062i
$478$	1.91480	+	9.19065i	0.0875810	+	0.420370i
$479$	25.6504			1.17200			0.585998	−	0.810312i	$-0.300703\pi$
$479$	25.6504			1.17200			0.585998	+	0.810312i	$0.300703\pi$
$480$	−3.07540	+	12.2696i	−0.140372	+	0.560026i
$481$			1.39474i			0.0635948i
$482$	−3.93438	−	18.8842i	−0.179206	−	0.860152i
$483$	−10.7484	+	1.55868i	−0.489071	+	0.0709223i
$484$	15.9291	−	6.93859i	0.724049	−	0.315390i
$485$	−17.3314	+	5.32675i	−0.786980	+	0.241875i
$486$	−0.775016	+	1.18294i	−0.0351554	+	0.0536593i
$487$	−23.7691	−	23.7691i	−1.07708	−	1.07708i	−0.996770	−	0.0803106i	$-0.974409\pi$
$487$	−23.7691	−	23.7691i	−1.07708	−	1.07708i	−0.0803106	−	0.996770i	$-0.525591\pi$
$488$	−21.7537	+	15.4061i	−0.984743	+	0.697401i
$489$	−10.5510			−0.477132
$490$	−22.1355	+	0.137446i	−0.999981	+	0.00620918i
$491$			19.2617i			0.869268i	0.900607	+	0.434634i	$0.143122\pi$
$491$			19.2617i			0.869268i	−0.900607	+	0.434634i	$0.856878\pi$
$492$	12.5970	+	4.95254i	0.567916	+	0.223278i
$493$	−5.39689	+	5.39689i	−0.243064	+	0.243064i
$494$	5.56275	+	3.64449i	0.250280	+	0.163974i
$495$	3.00480	+	1.59200i	0.135056	+	0.0715549i
$496$	−10.4182	−	9.68959i	−0.467790	−	0.435075i
$497$	−1.52203	−	10.4958i	−0.0682726	−	0.470799i
$498$	0.962789	+	4.62119i	0.0431436	+	0.207080i
$499$	18.0408			0.807618			0.403809	−	0.914843i	$-0.367686\pi$
$499$	18.0408			0.807618			0.403809	+	0.914843i	$0.367686\pi$
$500$	−11.1098	−	19.4055i	−0.496843	−	0.867840i
$501$		−	15.5351i		−	0.694056i
$502$	−35.5329	+	7.40300i	−1.58591	+	0.330412i
$503$	25.2456	+	25.2456i	1.12565	+	1.12565i	0.990877	+	0.134770i	$0.0430296\pi$
$503$	25.2456	+	25.2456i	1.12565	+	1.12565i	0.134770	+	0.990877i	$0.456970\pi$
$504$	−5.42303	+	5.15662i	−0.241561	+	0.229694i
$505$	7.20851	+	3.81919i	0.320775	+	0.169952i
$506$	7.38473	+	4.83818i	0.328291	+	0.215083i
$507$	3.49099	+	3.49099i	0.155040	+	0.155040i
$508$	−21.7485	−	8.55048i	−0.964932	−	0.379366i
$509$			36.1209i			1.60103i	0.599312	+	0.800516i	$0.295441\pi$
$509$			36.1209i			1.60103i	−0.599312	+	0.800516i	$0.704559\pi$
$510$	−1.05558	+	3.64600i	−0.0467417	+	0.161447i
$511$	22.7772	−	30.5037i	1.00760	−	1.34940i
$512$	6.20625	+	21.7597i	0.274280	+	0.961650i
$513$	−0.785121	+	0.785121i	−0.0346639	+	0.0346639i
$514$	−14.0956	+	21.5148i	−0.621732	+	0.948978i
$515$	6.47437	+	21.0654i	0.285295	+	0.928253i
$516$	18.4541	−	8.03848i	0.812398	−	0.353874i
$517$	2.85566	+	2.85566i	0.125592	+	0.125592i
$518$	−1.11694	−	0.520363i	−0.0490754	−	0.0228634i
$519$		−	14.1860i		−	0.622695i
$520$	−16.3466	+	21.2196i	−0.716845	+	0.930539i
$521$			6.42708i			0.281576i	0.990040	+	0.140788i	$0.0449635\pi$
$521$			6.42708i			0.281576i	−0.990040	+	0.140788i	$0.955036\pi$
$522$	−1.83413	−	8.80343i	−0.0802776	−	0.385316i
$523$	25.4190	−	25.4190i	1.11149	−	1.11149i	0.118546	−	0.992949i	$-0.462177\pi$
$523$	25.4190	−	25.4190i	1.11149	−	1.11149i	0.992949	−	0.118546i	$-0.0378233\pi$
$524$	−17.4306	+	7.59264i	−0.761460	+	0.331686i
$525$	0.595393	−	13.2154i	0.0259851	−	0.576765i
$526$	3.01518	−	4.60221i	0.131468	−	0.200666i
$527$	−3.01893	−	3.01893i	−0.131507	−	0.131507i
$528$	6.07898	−	0.220267i	0.264554	−	0.00958589i
$529$			6.14878i			0.267338i
$530$	0.207419	+	0.376462i	0.00900970	+	0.0163525i
$531$	−11.0439			−0.479265
$532$	−4.99399	+	3.09505i	−0.216517	+	0.134187i
$533$	20.2678	+	20.2678i	0.877895	+	0.877895i
$534$	5.50641	−	8.40468i	0.238286	−	0.363706i
$535$	−31.2573	+	9.60680i	−1.35137	+	0.415338i
$536$	−7.68683	+	44.9999i	−0.332021	+	1.94370i
$537$	6.62942	−	6.62942i	0.286081	−	0.286081i
$538$	−4.24179	−	20.3597i	−0.182877	−	0.877770i
$539$	3.02382	+	10.2067i	0.130245	+	0.439634i
$540$	−2.91167	−	3.39444i	−0.125298	−	0.146073i
$541$		−	37.0301i		−	1.59205i	−0.605265	−	0.796024i	$-0.706933\pi$
$541$		−	37.0301i		−	1.59205i	0.605265	−	0.796024i	$-0.293067\pi$
$542$	5.07965	+	24.3813i	0.218190	+	1.04727i
$543$	−6.77516	+	6.77516i	−0.290750	+	0.290750i
$544$	1.62470	+	6.59276i	0.0696584	+	0.282662i
$545$	−10.8468	−	5.74683i	−0.464627	−	0.246167i
$546$	−14.8891	+	5.42508i	−0.637197	+	0.232172i
$547$	−27.7422	+	27.7422i	−1.18617	+	1.18617i	−0.208051	+	0.978118i	$0.566712\pi$
$547$	−27.7422	+	27.7422i	−1.18617	+	1.18617i	−0.978118	+	0.208051i	$0.933288\pi$
$548$	−3.76512	−	1.48027i	−0.160838	−	0.0632339i
$549$		−	9.42450i		−	0.402228i
$550$	−7.47822	+	7.72717i	−0.318872	+	0.329488i
$551$		−	7.06017i		−	0.300773i
$552$	−6.71042	−	9.47523i	−0.285614	−	0.403293i
$553$	8.43651	−	1.22341i	0.358757	−	0.0520249i
$554$	12.2691	−	18.7269i	0.521266	−	0.795632i
$555$	0.344750	−	0.650697i	0.0146338	−	0.0276206i
$556$	−7.11873	−	16.3426i	−0.301901	−	0.693082i
$557$	29.6681	−	29.6681i	1.25708	−	1.25708i	0.304599	−	0.952481i	$-0.401478\pi$
$557$	29.6681	−	29.6681i	1.25708	−	1.25708i	0.952481	−	0.304599i	$-0.0985223\pi$
$558$	4.92450	−	1.02598i	0.208471	−	0.0434333i
$559$	42.6250			1.80285
$560$	−10.8943	−	21.0075i	−0.460369	−	0.887727i
$561$	1.82537			0.0770671
$562$	18.2147	−	3.79489i	0.768339	−	0.160078i
$563$	16.8010	−	16.8010i	0.708079	−	0.708079i	−0.258052	−	0.966131i	$-0.583081\pi$
$563$	16.8010	−	16.8010i	0.708079	−	0.708079i	0.966131	+	0.258052i	$0.0830807\pi$
$564$	−2.12105	−	4.86934i	−0.0893122	−	0.205036i
$565$	21.9392	−	6.74291i	0.922987	−	0.283677i
$566$	−17.0182	+	25.9757i	−0.715329	+	1.09184i
$567$	−0.379700	−	2.61836i	−0.0159459	−	0.109961i
$568$	9.25248	−	6.55267i	0.388226	−	0.274944i
$569$			33.4211i			1.40108i	0.713611	+	0.700542i	$0.247058\pi$
$569$			33.4211i			1.40108i	−0.713611	+	0.700542i	$0.752942\pi$
$570$	−1.69438	−	3.07528i	−0.0709700	−	0.128809i
$571$		−	23.0943i		−	0.966468i	−0.875491	−	0.483234i	$-0.839462\pi$
$571$		−	23.0943i		−	0.966468i	0.875491	−	0.483234i	$-0.160538\pi$
$572$	11.9881	+	4.71316i	0.501248	+	0.197067i
$573$	−14.2665	+	14.2665i	−0.595994	+	0.595994i
$574$	−23.7926	+	8.66918i	−0.993082	+	0.361844i
$575$	20.1595	+	3.85686i	0.840709	+	0.160842i
$576$	−7.54637	−	2.65561i	−0.314432	−	0.110650i
$577$	−31.9268	+	31.9268i	−1.32913	+	1.32913i	−0.423001	+	0.906129i	$0.639023\pi$
$577$	−31.9268	+	31.9268i	−1.32913	+	1.32913i	−0.906129	+	0.423001i	$0.860977\pi$
$578$	−4.48802	−	21.5415i	−0.186677	−	0.896010i
$579$		−	20.3183i		−	0.844399i
$580$	28.3537	+	2.17066i	1.17732	+	0.0901316i
$581$	−7.07605	−	5.28371i	−0.293564	−	0.219205i
$582$	−2.33892	−	11.2263i	−0.0969514	−	0.465347i
$583$	0.146160	−	0.146160i	0.00605333	−	0.00605333i
$584$	40.1168	+	6.85270i	1.66004	+	0.283567i
$585$	−2.78219	−	9.05232i	−0.115030	−	0.374267i
$586$	3.69610	−	5.64153i	0.152685	−	0.233049i
$587$	2.51742	+	2.51742i	0.103905	+	0.103905i	0.757148	−	0.653243i	$-0.226592\pi$
$587$	2.51742	+	2.51742i	0.103905	+	0.103905i	−0.653243	+	0.757148i	$0.726592\pi$
$588$	1.21046	−	13.9476i	0.0499184	−	0.575188i
$589$	3.94935			0.162730
$590$	9.71220	−	33.5463i	0.399845	−	1.38108i
$591$		−	14.3244i		−	0.589227i
$592$	−0.0476993	−	1.31642i	−0.00196043	−	0.0541045i
$593$	−6.85674	−	6.85674i	−0.281572	−	0.281572i	0.552163	−	0.833736i	$-0.313802\pi$
$593$	−6.85674	−	6.85674i	−0.281572	−	0.281572i	−0.833736	+	0.552163i	$0.813802\pi$
$594$	−1.17860	+	1.79895i	−0.0483585	+	0.0738118i
$595$	−3.03874	−	6.41813i	−0.124576	−	0.263118i
$596$	−34.2547	+	14.9211i	−1.40313	+	0.611191i
$597$	−10.6490	+	10.6490i	−0.435833	+	0.435833i
$598$	−5.01483	−	24.0702i	−0.205072	−	0.984302i
$599$			1.82633i			0.0746219i	0.999304	+	0.0373109i	$0.0118792\pi$
$599$			1.82633i			0.0746219i	−0.999304	+	0.0373109i	$0.988121\pi$
$600$	12.8713	−	5.85916i	0.525468	−	0.239199i
$601$			30.2963i			1.23581i	0.786252	+	0.617906i	$0.212019\pi$
$601$			30.2963i			1.23581i	−0.786252	+	0.617906i	$0.787981\pi$
$602$	−15.9029	+	34.1350i	−0.648155	+	1.39124i
$603$	−11.4129	−	11.4129i	−0.464771	−	0.464771i
$604$	−42.4586	+	18.4947i	−1.72762	+	0.752537i
$605$	−17.1651	−	9.09438i	−0.697862	−	0.369739i
$606$	−2.82746	+	4.31567i	−0.114858	+	0.175312i
$607$	22.0479	−	22.0479i	0.894897	−	0.894897i	−0.100082	−	0.994979i	$-0.531911\pi$
$607$	22.0479	−	22.0479i	0.894897	−	0.894897i	0.994979	+	0.100082i	$0.0319106\pi$
$608$	−5.37501	−	3.24959i	−0.217985	−	0.131788i
$609$	13.4800	+	10.0655i	0.546237	+	0.407877i
$610$	28.6273	+	8.28807i	1.15908	+	0.335574i
$611$		−	11.2471i		−	0.455010i
$612$	−2.23416	−	0.878368i	−0.0903107	−	0.0355059i
$613$	−2.56239	−	2.56239i	−0.103494	−	0.103494i	0.653464	−	0.756958i	$-0.273315\pi$
$613$	−2.56239	−	2.56239i	−0.103494	−	0.103494i	−0.756958	+	0.653464i	$0.773315\pi$
$614$	10.9611	+	7.18125i	0.442353	+	0.289812i
$615$	−4.44589	−	14.4654i	−0.179276	−	0.583302i
$616$	−8.24703	+	7.84190i	−0.332282	+	0.315959i
$617$	−3.74358	−	3.74358i	−0.150711	−	0.150711i	0.627725	−	0.778436i	$-0.283986\pi$
$617$	−3.74358	−	3.74358i	−0.150711	−	0.150711i	−0.778436	+	0.627725i	$0.783986\pi$
$618$	−13.6450	+	2.84283i	−0.548882	+	0.114355i
$619$			23.6429i			0.950290i	0.879907	+	0.475145i	$0.157604\pi$
$619$			23.6429i			0.950290i	−0.879907	+	0.475145i	$0.842396\pi$
$620$	−1.21423	+	15.8606i	−0.0487647	+	0.636977i
$621$	4.10502			0.164729
$622$	−6.03335	−	28.9588i	−0.241915	−	1.16114i
$623$	2.69773	+	18.6032i	0.108082	+	0.745322i
$624$	−12.4049	−	11.5374i	−0.496593	−	0.461864i
$625$	−9.22810	+	23.2345i	−0.369124	+	0.929380i
$626$	26.0696	+	17.0798i	1.04195	+	0.682644i
$627$	−1.19397	+	1.19397i	−0.0476825	+	0.0476825i
$628$	35.4539	+	13.9388i	1.41476	+	0.556218i
$629$		−	0.395288i		−	0.0157612i
$630$	8.28729	+	1.14928i	0.330173	+	0.0457885i
$631$	−23.2977			−0.927469			−0.463734	−	0.885974i	$-0.653491\pi$
$631$	−23.2977			−0.927469			−0.463734	+	0.885974i	$0.653491\pi$
$632$	5.26705	+	7.43716i	0.209512	+	0.295834i
$633$	−6.22008	−	6.22008i	−0.247226	−	0.247226i
$634$	6.89371	−	10.5222i	0.273784	−	0.417889i
$635$	7.67575	+	24.9743i	0.304603	+	0.991075i
$636$	−0.249225	+	0.108561i	−0.00988242	+	0.00430471i
$637$	14.1450	−	26.0544i	0.560445	−	1.03231i
$638$	−2.78924	−	13.3878i	−0.110427	−	0.530026i
$639$			4.00852i			0.158575i
$640$	14.7029	−	20.5870i	0.581184	−	0.813772i
$641$	−6.17239			−0.243795			−0.121897	−	0.992543i	$-0.538898\pi$
$641$	−6.17239			−0.243795			−0.121897	+	0.992543i	$0.538898\pi$
$642$	−4.21825	−	20.2467i	−0.166481	−	0.799074i
$643$	−3.57264	+	3.57264i	−0.140891	+	0.140891i	−0.774035	−	0.633143i	$-0.781764\pi$
$643$	−3.57264	+	3.57264i	−0.140891	+	0.140891i	0.633143	+	0.774035i	$0.281764\pi$
$644$	21.1469	+	4.96433i	0.833303	+	0.195622i
$645$	−19.8861	−	10.5360i	−0.783015	−	0.414855i
$646$	−1.57656	−	1.03290i	−0.0620288	−	0.0406388i
$647$	21.0908	−	21.0908i	0.829165	−	0.829165i	−0.158236	−	0.987401i	$-0.550581\pi$
$647$	21.0908	−	21.0908i	0.829165	−	0.829165i	0.987401	+	0.158236i	$0.0505808\pi$
$648$	2.30820	−	1.63468i	0.0906748	−	0.0642165i
$649$	−16.7949			−0.659259
$650$	29.9435	−	0.490250i	1.17448	−	0.0192292i
$651$	−5.63051	+	7.54049i	−0.220677	+	0.295535i
$652$	19.6387	+	7.72101i	0.769111	+	0.302378i
$653$	−2.57017	−	2.57017i	−0.100579	−	0.100579i	0.655027	−	0.755605i	$-0.272657\pi$
$653$	−2.57017	−	2.57017i	−0.100579	−	0.100579i	−0.755605	+	0.655027i	$0.772657\pi$
$654$	4.25454	−	6.49390i	0.166366	−	0.253931i
$655$	18.7832	+	9.95164i	0.733919	+	0.388843i
$656$	−19.8228	−	18.4365i	−0.773949	−	0.719824i
$657$	−10.1745	+	10.1745i	−0.396944	+	0.396944i
$658$	9.00692	+	4.19618i	0.351126	+	0.163584i
$659$	−41.6781			−1.62355			−0.811774	−	0.583971i	$-0.801498\pi$
$659$	−41.6781			−1.62355			−0.811774	+	0.583971i	$0.801498\pi$
$660$	−4.42789	−	5.16207i	−0.172356	−	0.200933i
$661$	−12.4654			−0.484849			−0.242424	−	0.970170i	$-0.577943\pi$
$661$	−12.4654			−0.484849			−0.242424	+	0.970170i	$0.577943\pi$
$662$	−5.26071	−	25.2503i	−0.204463	−	0.981381i
$663$	−3.59463	−	3.59463i	−0.139604	−	0.139604i
$664$	1.58965	−	9.30604i	0.0616902	−	0.361144i
$665$	6.18571	+	2.21045i	0.239871	+	0.0857174i
$666$	0.389567	+	0.255229i	0.0150954	+	0.00988991i
$667$	−18.4571	+	18.4571i	−0.714663	+	0.714663i
$668$	−11.3683	+	28.9157i	−0.439852	+	1.11878i
$669$	10.5192			0.406697
$670$	44.7039	−	24.6305i	1.72706	−	0.951558i
$671$		−	14.3323i		−	0.553290i
$672$	13.8675	−	5.62963i	0.534950	−	0.217168i
$673$	14.9316	−	14.9316i	0.575571	−	0.575571i	−0.358109	−	0.933680i	$-0.616578\pi$
$673$	14.9316	−	14.9316i	0.575571	−	0.575571i	0.933680	+	0.358109i	$0.116578\pi$
$674$	27.1465	+	17.7853i	1.04564	+	0.685064i
$675$	−0.939546	+	4.91093i	−0.0361632	+	0.189022i
$676$	−3.94320	−	9.05249i	−0.151661	−	0.348173i
$677$	−36.2061	−	36.2061i	−1.39151	−	1.39151i	−0.821943	−	0.569570i	$-0.807110\pi$
$677$	−36.2061	−	36.2061i	−1.39151	−	1.39151i	−0.569570	−	0.821943i	$-0.692890\pi$
$678$	2.96075	+	14.2110i	0.113707	+	0.545769i
$679$	17.1900	+	12.8358i	0.659691	+	0.492594i
$680$	4.63283	−	6.01390i	0.177661	−	0.230622i
$681$	−6.83576			−0.261947
$682$	7.48889	−	1.56025i	0.286765	−	0.0597452i
$683$	−1.81183	−	1.81183i	−0.0693279	−	0.0693279i	0.671593	−	0.740921i	$-0.265611\pi$
$683$	−1.81183	−	1.81183i	−0.0693279	−	0.0693279i	−0.740921	+	0.671593i	$0.765611\pi$
$684$	2.03590	−	0.886821i	0.0778444	−	0.0339084i
$685$	1.32883	+	4.32358i	0.0507721	+	0.165195i
$686$	15.5876	+	21.0482i	0.595136	+	0.803625i
$687$	9.69452	+	9.69452i	0.369869	+	0.369869i
$688$	−40.2314	+	1.45775i	−1.53381	+	0.0555762i
$689$	−0.575656			−0.0219307
$690$	−3.61003	+	12.4692i	−0.137431	+	0.474693i
$691$	−13.2691			−0.504779			−0.252390	−	0.967626i	$-0.581216\pi$
$691$	−13.2691			−0.504779			−0.252390	+	0.967626i	$0.581216\pi$
$692$	−10.3810	+	26.4045i	−0.394627	+	1.00375i
$693$	−0.577426	−	3.98186i	−0.0219346	−	0.151258i
$694$	−24.9428	+	38.0713i	−0.946815	+	1.44517i
$695$	−9.33049	+	17.6108i	−0.353926	+	0.668015i
$696$	−3.02830	+	17.7281i	−0.114787	+	0.671983i
$697$	−5.74415	−	5.74415i	−0.217575	−	0.217575i
$698$	7.28049	+	34.9448i	0.275571	+	1.32268i
$699$		−	15.3801i		−	0.581727i
$700$	−10.7790	+	24.1622i	−0.407407	+	0.913247i
$701$		−	29.4261i		−	1.11141i	−0.831380	−	0.555704i	$-0.812449\pi$
$701$		−	29.4261i		−	1.11141i	0.831380	−	0.555704i	$-0.187551\pi$
$702$	5.86359	−	1.22163i	0.221307	−	0.0461076i
$703$	0.258556	+	0.258556i	0.00975164	+	0.00975164i
$704$	−11.4761	−	4.03850i	−0.432522	−	0.152207i
$705$	−2.78005	+	5.24719i	−0.104703	+	0.197620i
$706$	36.6333	+	24.0007i	1.37871	+	0.903277i
$707$	−1.38524	−	9.55246i	−0.0520974	−	0.359257i
$708$	20.5562	+	8.08173i	0.772549	+	0.303730i
$709$	1.25438			0.0471093			0.0235546	−	0.999723i	$-0.492502\pi$
$709$	1.25438			0.0471093			0.0235546	+	0.999723i	$0.492502\pi$
$710$	−12.1760	−	3.52516i	−0.456958	−	0.132297i
$711$	−3.22206			−0.120837
$712$	−16.3996	+	11.6143i	−0.614600	+	0.435263i
$713$	−10.3246	−	10.3246i	−0.386660	−	0.386660i
$714$	4.21978	−	1.53754i	0.157921	−	0.0575410i
$715$	−4.23100	−	13.7663i	−0.158231	−	0.514829i
$716$	−17.1907	+	7.48816i	−0.642448	+	0.279846i
$717$	4.69400	+	4.69400i	0.175301	+	0.175301i
$718$	9.18458	+	44.0840i	0.342765	+	1.64520i
$719$	−19.9400			−0.743638			−0.371819	−	0.928305i	$-0.621266\pi$
$719$	−19.9400			−0.743638			−0.371819	+	0.928305i	$0.621266\pi$
$720$	2.93554	+	8.44882i	0.109401	+	0.314869i
$721$	15.6012	−	20.8935i	0.581020	−	0.778114i
$722$	−24.5984	+	5.12489i	−0.915457	+	0.190729i
$723$	−9.64485	−	9.64485i	−0.358696	−	0.358696i
$724$	17.5686	−	7.65277i	0.652934	−	0.284413i
$725$	−17.8563	−	26.3051i	−0.663165	−	0.976947i
$726$	6.73283	−	10.2766i	0.249879	−	0.381401i
$727$	−1.14406	+	1.14406i	−0.0424310	+	0.0424310i	−0.728004	−	0.685573i	$-0.759552\pi$
$727$	−1.14406	+	1.14406i	−0.0424310	+	0.0424310i	0.685573	+	0.728004i	$0.259552\pi$
$728$	31.6834	+	0.797811i	1.17426	+	0.0295689i
$729$			1.00000i			0.0370370i
$730$	−21.9577	−	39.8529i	−0.812691	−	1.47502i
$731$	−12.0805			−0.446813
$732$	−6.89668	+	17.5420i	−0.254909	+	0.648370i
$733$	8.00282	−	8.00282i	0.295591	−	0.295591i	−0.543693	−	0.839284i	$-0.682975\pi$
$733$	8.00282	−	8.00282i	0.295591	−	0.295591i	0.839284	+	0.543693i	$0.182975\pi$
$734$	15.8240	−	24.1529i	0.584074	−	0.891498i
$735$	−13.0392	+	8.65898i	−0.480960	+	0.319391i
$736$	5.55640	+	22.5470i	0.204812	+	0.831092i
$737$	−17.3561	−	17.3561i	−0.639322	−	0.639322i
$738$	9.36989	−	1.95215i	0.344910	−	0.0718595i
$739$	−3.79213			−0.139496			−0.0697478	−	0.997565i	$-0.522219\pi$
$739$	−3.79213			−0.139496			−0.0697478	+	0.997565i	$0.522219\pi$
$740$	−1.11786	+	0.958871i	−0.0410933	+	0.0352488i
$741$	4.70248			0.172750
$742$	0.214771	−	0.460997i	0.00788449	−	0.0169237i
$743$	−20.0768	+	20.0768i	−0.736547	+	0.736547i	−0.971908	−	0.235361i	$-0.924373\pi$
$743$	−20.0768	+	20.0768i	−0.736547	+	0.736547i	0.235361	+	0.971908i	$0.424373\pi$
$744$	−9.91684	−	1.69398i	−0.363569	−	0.0621044i
$745$	36.9127	+	19.5570i	1.35238	+	0.716513i
$746$	30.7401	+	20.1397i	1.12547	+	0.737366i
$747$	2.36021	+	2.36021i	0.0863555	+	0.0863555i
$748$	−3.39759	−	1.33577i	−0.124228	−	0.0488406i
$749$	31.0022	+	23.1494i	1.13279	+	0.845861i
$750$	−14.0909	−	7.17266i	−0.514526	−	0.261909i
$751$	14.2569			0.520241			0.260120	−	0.965576i	$-0.416238\pi$
$751$	14.2569			0.520241			0.260120	+	0.965576i	$0.416238\pi$
$752$	0.384645	+	10.6155i	0.0140266	+	0.387108i
$753$	−18.1479	+	18.1479i	−0.661347	+	0.661347i
$754$	−20.8713	+	31.8568i	−0.760088	+	1.16016i
$755$	45.7533	+	24.2409i	1.66513	+	0.882216i
$756$	−1.20933	+	5.15146i	−0.0439829	+	0.187357i
$757$	15.8680	−	15.8680i	0.576731	−	0.576731i	−0.357270	−	0.934001i	$-0.616292\pi$
$757$	15.8680	−	15.8680i	0.576731	−	0.576731i	0.934001	+	0.357270i	$0.116292\pi$
$758$	36.3663	−	7.57664i	1.32088	−	0.275196i
$759$	6.24269			0.226595
$760$	0.903348	+	6.96399i	0.0327679	+	0.252610i
$761$			48.6461i			1.76342i	0.471790	+	0.881711i	$0.343608\pi$
$761$			48.6461i			1.76342i	−0.471790	+	0.881711i	$0.656392\pi$
$762$	−16.1770	+	3.37035i	−0.586029	+	0.122095i
$763$	2.08441	+	14.3738i	0.0754606	+	0.520367i
$764$	36.9945	−	16.1145i	1.33842	−	0.583004i
$765$	0.788510	+	2.56554i	0.0285086	+	0.0927574i
$766$	−1.29243	−	0.846745i	−0.0466972	−	0.0305941i
$767$	33.0737	+	33.0737i	1.19422	+	1.19422i
$768$	12.1029	+	10.4652i	0.436724	+	0.377631i
$769$	−4.44726			−0.160372			−0.0801861	−	0.996780i	$-0.525551\pi$
$769$	−4.44726			−0.160372			−0.0801861	+	0.996780i	$0.525551\pi$
$770$	12.6028	+	1.74776i	0.454175	+	0.0629850i
$771$			18.1876i			0.655009i
$772$	−14.8685	+	37.8187i	−0.535131	+	1.36113i
$773$	−0.262925	+	0.262925i	−0.00945677	+	0.00945677i	−0.711819	−	0.702363i	$-0.752129\pi$
$773$	−0.262925	+	0.262925i	−0.00945677	+	0.00945677i	0.702363	+	0.711819i	$0.252129\pi$
$774$	7.80010	−	11.9056i	0.280369	−	0.427940i
$775$	14.7147	−	9.98851i	0.528566	−	0.358798i
$776$	−3.86176	+	22.6073i	−0.138629	+	0.811556i
$777$	−0.862281	+	0.125043i	−0.0309342	+	0.00448589i
$778$	−18.9960	+	3.95767i	−0.681039	+	0.141889i
$779$	7.51446			0.269234
$780$	−1.44578	+	18.8852i	−0.0517673	+	0.676198i
$781$			6.09593i			0.218130i
$782$	1.42127	+	6.82179i	0.0508245	+	0.243947i
$783$	−4.49623	−	4.49623i	−0.160682	−	0.160682i
$784$	−12.4596	+	25.0750i	−0.444986	+	0.895537i
$785$	−12.5128	−	40.7126i	−0.446602	−	1.45309i
$786$	−7.36749	+	11.2453i	−0.262790	+	0.401107i
$787$	22.2870	+	22.2870i	0.794445	+	0.794445i	0.982213	−	0.187769i	$-0.0601255\pi$
$787$	22.2870	+	22.2870i	0.794445	+	0.794445i	−0.187769	+	0.982213i	$0.560126\pi$
$788$	−10.4823	+	26.6622i	−0.373418	+	0.949803i
$789$		−	3.89048i		−	0.138505i
$790$	2.83353	−	9.78711i	0.100813	−	0.348210i
$791$	−21.7601	−	16.2483i	−0.773700	−	0.577725i
$792$	3.51019	−	2.48594i	0.124729	−	0.0883339i
$793$	−28.2240	+	28.2240i	−1.00226	+	1.00226i
$794$	1.30588	+	0.855559i	0.0463439	+	0.0303627i
$795$	0.268564	+	0.142290i	0.00952500	+	0.00504650i
$796$	27.6138	−	12.0284i	0.978746	−	0.426334i
$797$	−29.5432	−	29.5432i	−1.04647	−	1.04647i	−0.998866	−	0.0476063i	$-0.984841\pi$
$797$	−29.5432	−	29.5432i	−1.04647	−	1.04647i	−0.0476063	−	0.998866i	$-0.515159\pi$
$798$	−1.75444	+	3.76584i	−0.0621066	+	0.133309i
$799$			3.18758i			0.112768i
$800$	−28.2452	+	1.48677i	−0.998617	+	0.0525652i
$801$		−	7.10490i		−	0.251039i
$802$	−20.6887	+	4.31034i	−0.730545	+	0.152204i
$803$	−15.4727	+	15.4727i	−0.546021	+	0.546021i
$804$	12.8913	+	29.5949i	0.454641	+	1.04373i
$805$	−10.3924	−	21.9497i	−0.366283	−	0.773627i
$806$	−17.8202	−	11.6751i	−0.627689	−	0.411237i
$807$	−10.3984	−	10.3984i	−0.366043	−	0.366043i
$808$	8.42092	−	5.96375i	0.296247	−	0.209804i
$809$		−	4.58512i		−	0.161204i	−0.996746	−	0.0806020i	$-0.974316\pi$
$809$		−	4.58512i		−	0.161204i	0.996746	−	0.0806020i	$-0.0256843\pi$
$810$	−3.03754	−	0.879417i	−0.106728	−	0.0308996i
$811$	−37.3285			−1.31078			−0.655390	−	0.755291i	$-0.727496\pi$
$811$	−37.3285			−1.31078			−0.655390	+	0.755291i	$0.727496\pi$
$812$	−17.7247	−	28.5996i	−0.622016	−	1.00365i
$813$	12.4524	+	12.4524i	0.436725	+	0.436725i
$814$	0.592431	+	0.388137i	0.0207647	+	0.0136042i
$815$	−6.93115	−	22.5516i	−0.242787	−	0.789948i
$816$	3.51571	+	3.26984i	0.123074	+	0.114467i
$817$	7.90181	−	7.90181i	0.276449	−	0.276449i
$818$	5.49818	−	1.14551i	0.192240	−	0.0400517i
$819$	−6.70423	+	8.97844i	−0.234265	+	0.313732i
$820$	−2.31033	+	30.1781i	−0.0806802	+	1.05387i
$821$		−	18.6845i		−	0.652095i	−0.945353	−	0.326048i	$-0.894283\pi$
$821$		−	18.6845i		−	0.652095i	0.945353	−	0.326048i	$-0.105717\pi$
$822$	−2.80057	+	0.583478i	−0.0976811	+	0.0203511i
$823$	12.8034	−	12.8034i	0.446299	−	0.446299i	−0.447823	−	0.894122i	$-0.647801\pi$
$823$	12.8034	−	12.8034i	0.446299	−	0.446299i	0.894122	+	0.447823i	$0.147801\pi$
$824$	27.4780	+	4.69375i	0.957241	+	0.163515i
$825$	−1.42881	+	7.46827i	−0.0497447	+	0.260012i
$826$	−38.8255	+	14.1467i	−1.35091	+	0.492225i
$827$	−21.5163	+	21.5163i	−0.748194	+	0.748194i	−0.974140	−	0.225946i	$-0.927453\pi$
$827$	−21.5163	+	21.5163i	−0.748194	+	0.748194i	0.225946	+	0.974140i	$0.427453\pi$
$828$	−7.64074	−	3.00398i	−0.265534	−	0.104396i
$829$		−	25.4280i		−	0.883153i	−0.897224	−	0.441576i	$-0.854419\pi$
$829$		−	25.4280i		−	0.883153i	0.897224	−	0.441576i	$-0.145581\pi$
$830$	−9.24483	+	5.09361i	−0.320893	+	0.176802i
$831$		−	15.8308i		−	0.549165i
$832$	14.6466	+	30.5524i	0.507779	+	1.05921i
$833$	−4.00888	+	7.38416i	−0.138899	+	0.255846i
$834$	−10.5434	−	6.90762i	−0.365089	−	0.239191i
$835$	33.2046	−	10.2053i	1.14909	−	0.353169i
$836$	3.09607	−	1.34863i	0.107080	−	0.0466432i
$837$	2.51512	−	2.51512i	0.0869352	−	0.0869352i
$838$	0.0432509	+	0.207595i	0.00149408	+	0.00717126i
$839$	1.38408			0.0477839			0.0238919	−	0.999715i	$-0.492394\pi$
$839$	1.38408			0.0477839			0.0238919	+	0.999715i	$0.492394\pi$
$840$	−14.5842	−	8.20366i	−0.503204	−	0.283053i
$841$	11.4322			0.394214
$842$	−9.50687	−	45.6310i	−0.327628	−	1.57255i
$843$	9.30289	−	9.30289i	0.320409	−	0.320409i
$844$	7.02579	+	16.1293i	0.241838	+	0.555193i
$845$	−5.16833	+	9.75494i	−0.177796	+	0.335580i
$846$	−3.14144	−	2.05815i	−0.108005	−	0.0707606i
$847$	3.29858	+	22.7466i	0.113341	+	0.781583i
$848$	0.543329	−	0.0196871i	0.0186580	−	0.000676058i
$849$			21.9585i			0.753615i
$850$	−8.48636	+	0.138943i	−0.291080	+	0.00476572i
$851$		−	1.35187i		−	0.0463414i
$852$	2.93336	−	7.46112i	0.100495	−	0.255614i
$853$	−35.6952	+	35.6952i	−1.22218	+	1.22218i	−0.255324	+	0.966856i	$0.582182\pi$
$853$	−35.6952	+	35.6952i	−1.22218	+	1.22218i	−0.966856	+	0.255324i	$0.917818\pi$
$854$	−12.0723	−	33.1324i	−0.413106	−	1.13377i
$855$	−2.19388	−	1.16235i	−0.0750289	−	0.0397516i
$856$	−6.96468	+	40.7724i	−0.238048	+	1.39357i
$857$	13.0267	−	13.0267i	0.444983	−	0.444983i	−0.448699	−	0.893683i	$-0.648113\pi$
$857$	13.0267	−	13.0267i	0.444983	−	0.444983i	0.893683	+	0.448699i	$0.148113\pi$
$858$	8.91701	−	1.85779i	0.304422	−	0.0634239i
$859$		−	4.10179i		−	0.139951i	−0.997549	−	0.0699756i	$-0.977708\pi$
$859$		−	4.10179i		−	0.139951i	0.997549	−	0.0699756i	$-0.0222921\pi$
$860$	29.3043	+	34.1631i	0.999268	+	1.16495i
$861$	−10.7132	+	14.3474i	−0.365106	+	0.488957i
$862$	−15.3961	+	3.20765i	−0.524392	+	0.109253i
$863$	5.90515	−	5.90515i	0.201014	−	0.201014i	−0.599421	−	0.800434i	$-0.704602\pi$
$863$	5.90515	−	5.90515i	0.201014	−	0.201014i	0.800434	+	0.599421i	$0.204602\pi$
$864$	−5.49253	+	1.35356i	−0.186860	+	0.0460491i
$865$	30.3210	−	9.31904i	1.03094	−	0.316857i
$866$	−13.2335	−	8.67003i	−0.449691	−	0.294620i
$867$	−11.0020	−	11.0020i	−0.373649	−	0.373649i
$868$	15.9981	−	9.91492i	0.543012	−	0.336534i
$869$	−4.89992			−0.166218
$870$	17.6115	−	9.70340i	0.597087	−	0.328976i
$871$			68.3577i			2.31621i
$872$	−12.6712	+	8.97379i	−0.429100	+	0.303891i
$873$	−5.73370	−	5.73370i	−0.194056	−	0.194056i
$874$	−5.39176	−	3.53246i	−0.182379	−	0.119487i
$875$	28.6375	−	7.40884i	0.968126	−	0.250464i
$876$	26.3834	−	11.4924i	0.891412	−	0.388292i
$877$	−21.9317	+	21.9317i	−0.740582	+	0.740582i	−0.972690	−	0.232108i	$-0.925438\pi$
$877$	−21.9317	+	21.9317i	−0.740582	+	0.740582i	0.232108	+	0.972690i	$0.425438\pi$
$878$	1.94461	−	0.405144i	0.0656273	−	0.0136730i
$879$		−	4.76907i		−	0.160857i
$880$	4.46420	+	12.8485i	0.150488	+	0.433122i
$881$		−	43.9967i		−	1.48229i	−0.671347	−	0.741143i	$-0.734284\pi$
$881$		−	43.9967i		−	1.48229i	0.671347	−	0.741143i	$-0.265716\pi$
$882$	−4.68885	−	8.71864i	−0.157882	−	0.293572i
$883$	−9.57769	−	9.57769i	−0.322315	−	0.322315i	0.527340	−	0.849655i	$-0.323190\pi$
$883$	−9.57769	−	9.57769i	−0.322315	−	0.322315i	−0.849655	+	0.527340i	$0.823190\pi$
$884$	4.06026	+	9.32124i	0.136561	+	0.313507i
$885$	−7.25496	−	23.6052i	−0.243873	−	0.793479i
$886$	2.50359	+	1.64025i	0.0841096	+	0.0551053i
$887$	−35.7292	+	35.7292i	−1.19967	+	1.19967i	−0.225403	+	0.974266i	$0.572370\pi$
$887$	−35.7292	+	35.7292i	−1.19967	+	1.19967i	−0.974266	+	0.225403i	$0.927630\pi$
$888$	−0.538335	−	0.760139i	−0.0180653	−	0.0255086i
$889$	18.4962	−	24.7705i	0.620343	−	0.830775i
$890$	21.5814	+	6.24817i	0.723410	+	0.209439i
$891$			1.52074i			0.0509468i
$892$	−19.5796	−	7.69778i	−0.655574	−	0.257741i
$893$	−2.08498	−	2.08498i	−0.0697713	−	0.0697713i
$894$	−14.4786	+	22.0993i	−0.484237	+	0.739112i
$895$	18.5247	+	9.81470i	0.619212	+	0.328069i
$896$	−29.9314	+	0.330544i	−0.999939	+	0.0110427i
$897$	−12.2935	−	12.2935i	−0.410468	−	0.410468i
$898$	8.16755	+	39.2025i	0.272555	+	1.30821i
$899$			22.6171i			0.754323i
$900$	5.34252	−	8.45325i	0.178084	−	0.281775i
$901$	0.163148			0.00543526
$902$	14.2492	−	2.96871i	0.474446	−	0.0988473i
$903$	3.82147	+	26.3524i	0.127171	+	0.876952i
$904$	4.88844	−	28.6177i	0.162587	−	0.951811i
$905$	−18.9319	−	10.0305i	−0.629319	−	0.333424i
$906$	−17.9462	+	27.3921i	−0.596223	+	0.910042i
$907$	6.29706	−	6.29706i	0.209090	−	0.209090i	−0.594790	−	0.803881i	$-0.702765\pi$
$907$	6.29706	−	6.29706i	0.209090	−	0.209090i	0.803881	+	0.594790i	$0.202765\pi$
$908$	12.7235	+	5.00229i	0.422244	+	0.166007i
$909$			3.64826i			0.121005i
$910$	−21.3765	−	28.2601i	−0.708625	−	0.936814i
$911$	14.1662			0.469347			0.234674	−	0.972074i	$-0.424598\pi$
$911$	14.1662			0.469347			0.234674	+	0.972074i	$0.424598\pi$
$912$	−4.43840	+	0.160822i	−0.146970	+	0.00532535i
$913$	3.58927	+	3.58927i	0.118788	+	0.118788i
$914$	23.6678	+	15.5062i	0.782861	+	0.512899i
$915$	20.1439	−	6.19114i	0.665936	−	0.204673i
$916$	−10.9503	−	25.1388i	−0.361808	−	0.830610i
$917$	−3.60952	−	24.8908i	−0.119197	−	0.821966i
$918$	−1.66182	+	0.346227i	−0.0548481	+	0.0114272i
$919$		−	16.1887i		−	0.534017i	−0.963694	−	0.267009i	$-0.913965\pi$
$919$		−	16.1887i		−	0.534017i	0.963694	−	0.267009i	$-0.0860352\pi$
$920$	15.8441	−	20.5673i	0.522365	−	0.678083i
$921$	9.26595			0.305323
$922$	9.21843	−	1.92059i	0.303593	−	0.0632513i
$923$	12.0045	−	12.0045i	0.395133	−	0.395133i
$924$	−1.83908	+	7.83405i	−0.0605013	+	0.257721i
$925$	1.61727	+	0.309412i	0.0531755	+	0.0101734i
$926$	−9.51713	+	14.5264i	−0.312752	+	0.477368i
$927$	−6.96900	+	6.96900i	−0.228892	+	0.228892i
$928$	18.6097	−	30.7816i	0.610895	−	1.01046i
$929$	−52.8230			−1.73307			−0.866534	−	0.499119i	$-0.833657\pi$
$929$	−52.8230			−1.73307			−0.866534	+	0.499119i	$0.833657\pi$
$930$	5.42793	+	9.85161i	0.177989	+	0.323047i
$931$	−2.20776	−	7.45214i	−0.0723565	−	0.244234i
$932$	−11.2548	+	28.6271i	−0.368665	+	0.937713i
$933$	−14.7903	−	14.7903i	−0.484213	−	0.484213i
$934$	−3.55058	−	2.32620i	−0.116179	−	0.0761156i
$935$	1.19912	+	3.90153i	0.0392154	+	0.127594i
$936$	−11.8080	−	2.01702i	−0.385955	−	0.0659283i
$937$	−37.9230	+	37.9230i	−1.23889	+	1.23889i	−0.278437	+	0.960454i	$0.589816\pi$
$937$	−37.9230	+	37.9230i	−1.23889	+	1.23889i	−0.960454	+	0.278437i	$0.910184\pi$
$938$	−54.7423	−	25.5035i	−1.78740	−	0.832719i
$939$	22.0379			0.719181
$940$	9.01434	−	7.73228i	0.294015	−	0.252199i
$941$	−1.99271			−0.0649604			−0.0324802	−	0.999472i	$-0.510341\pi$
$941$	−1.99271			−0.0649604			−0.0324802	+	0.999472i	$0.510341\pi$
$942$	26.3713	−	5.49426i	0.859224	−	0.179013i
$943$	−19.6448	−	19.6448i	−0.639722	−	0.639722i
$944$	−32.3475	−	30.0853i	−1.05282	−	0.979193i
$945$	5.34704	−	2.53162i	0.173939	−	0.0823537i
$946$	11.8620	−	18.1054i	0.385665	−	0.588658i
$947$	18.1934	−	18.1934i	0.591207	−	0.591207i	−0.346750	−	0.937958i	$-0.612715\pi$
$947$	18.1934	−	18.1934i	0.591207	−	0.591207i	0.937958	+	0.346750i	$0.112715\pi$
$948$	5.99726	+	2.35784i	0.194782	+	0.0765791i
$949$	60.9399			1.97819
$950$	5.46002	−	5.64178i	0.177146	−	0.183044i
$951$		−	8.89492i		−	0.288438i
$952$	−8.97948	−	0.226110i	−0.291027	−	0.00732827i
$953$	−3.43956	+	3.43956i	−0.111418	+	0.111418i	−0.760618	−	0.649200i	$-0.775104\pi$
$953$	−3.43956	+	3.43956i	−0.111418	+	0.111418i	0.649200	+	0.760618i	$0.275104\pi$
$954$	−0.105341	+	0.160787i	−0.00341055	+	0.00520568i
$955$	−39.8652	−	21.1213i	−1.29001	−	0.683468i
$956$	−5.30203	−	12.1720i	−0.171480	−	0.393670i
$957$	−6.83761	−	6.83761i	−0.221029	−	0.221029i
$958$	−35.5126	+	7.39878i	−1.14736	+	0.239044i
$959$	3.20208	−	4.28829i	0.103401	−	0.138476i
$960$	0.718729	−	17.8741i	0.0231969	−	0.576884i
$961$	18.3483			0.591882
$962$	−0.402309	−	1.93100i	−0.0129710	−	0.0622579i
$963$	−10.3407	−	10.3407i	−0.333225	−	0.333225i
$964$	10.8942	+	25.0100i	0.350878	+	0.805519i
$965$	43.4282	−	13.3475i	1.39800	−	0.429670i
$966$	14.4315	−	5.25832i	0.464325	−	0.169184i
$967$	24.5418	+	24.5418i	0.789211	+	0.789211i	0.981365	−	0.192154i	$-0.0615472\pi$
$967$	24.5418	+	24.5418i	0.789211	+	0.789211i	−0.192154	+	0.981365i	$0.561547\pi$
$968$	−20.0522	+	14.2011i	−0.644501	+	0.456439i
$969$	−1.33274			−0.0428139
$970$	22.4586	−	12.3740i	0.721103	−	0.397305i
$971$	−59.2737			−1.90218			−0.951092	−	0.308907i	$-0.900037\pi$
$971$	−59.2737			−1.90218			−0.951092	+	0.308907i	$0.900037\pi$
$972$	0.731782	−	1.86132i	0.0234719	−	0.0597017i
$973$	23.3372	−	3.38422i	0.748155	−	0.108493i
$974$	39.7641	+	26.0518i	1.27412	+	0.834754i
$975$	17.5207	−	11.8933i	0.561111	−	0.380890i
$976$	25.6738	−	27.6043i	0.821798	−	0.883592i
$977$	35.3074	+	35.3074i	1.12958	+	1.12958i	0.990245	+	0.139340i	$0.0444981\pi$
$977$	35.3074	+	35.3074i	1.12958	+	1.12958i	0.139340	+	0.990245i	$0.455502\pi$
$978$	14.6077	−	3.04340i	0.467102	−	0.0973171i
$979$		−	10.8047i		−	0.345321i
$980$	30.6066	−	6.57521i	0.977693	−	0.210038i
$981$		−	5.48962i		−	0.175270i
$982$	−5.55598	−	26.6675i	−0.177298	−	0.850995i
$983$	−6.11856	−	6.11856i	−0.195152	−	0.195152i	0.602766	−	0.797918i	$-0.294065\pi$
$983$	−6.11856	−	6.11856i	−0.195152	−	0.195152i	−0.797918	+	0.602766i	$0.794065\pi$
$984$	−18.8689	−	3.22316i	−0.601518	−	0.102750i
$985$	30.6169	−	9.40998i	0.975536	−	0.299827i
$986$	5.91519	−	9.02862i	0.188378	−	0.287530i
$987$	6.95338	−	1.00834i	0.221329	−	0.0320958i
$988$	−8.75279	−	3.44119i	−0.278463	−	0.109479i
$989$	−41.3148			−1.31373
$990$	−4.61931	−	1.33737i	−0.146811	−	0.0425043i
$991$	15.7439			0.500122			0.250061	−	0.968230i	$-0.419549\pi$
$991$	15.7439			0.500122			0.250061	+	0.968230i	$0.419549\pi$
$992$	17.2187	+	10.4100i	0.546695	+	0.330518i
$993$	−12.8962	−	12.8962i	−0.409250	−	0.409250i
$994$	5.13471	+	14.0922i	0.162863	+	0.446977i
$995$	−29.7566	−	15.7655i	−0.943347	−	0.499801i
$996$	−2.66593	−	6.12025i	−0.0844734	−	0.193928i
$997$	−31.8627	−	31.8627i	−1.00910	−	1.00910i	−0.999958	−	0.00914329i	$-0.997090\pi$
$997$	−31.8627	−	31.8627i	−1.00910	−	1.00910i	−0.00914329	−	0.999958i	$-0.502910\pi$
$998$	−24.9772	+	5.20382i	−0.790641	+	0.164724i
$999$	0.329321			0.0104192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.517.7	yes	184
5.3	odd	4	inner	840.2.bj.b.13.53	yes	184
7.6	odd	2	inner	840.2.bj.b.517.8	yes	184
8.5	even	2	inner	840.2.bj.b.517.54	yes	184
35.13	even	4	inner	840.2.bj.b.13.54	yes	184
40.13	odd	4	inner	840.2.bj.b.13.8	yes	184
56.13	odd	2	inner	840.2.bj.b.517.53	yes	184
280.13	even	4	inner	840.2.bj.b.13.7	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.7	✓	184	280.13	even	4	inner
840.2.bj.b.13.8	yes	184	40.13	odd	4	inner
840.2.bj.b.13.53	yes	184	5.3	odd	4	inner
840.2.bj.b.13.54	yes	184	35.13	even	4	inner
840.2.bj.b.517.7	yes	184	1.1	even	1	trivial
840.2.bj.b.517.8	yes	184	7.6	odd	2	inner
840.2.bj.b.517.53	yes	184	56.13	odd	2	inner
840.2.bj.b.517.54	yes	184	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.38448 + 0.288447i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.83360 - 0.798701i) q^{4} +(-1.97588 - 1.04685i) q^{5} +(0.775016 - 1.18294i) q^{6} +(0.379700 + 2.61836i) q^{7} +(-2.30820 + 1.63468i) q^{8} -1.00000i q^{9} +(3.03754 + 0.879417i) q^{10} -1.52074i q^{11} +(-0.731782 + 1.86132i) q^{12} +(-2.99475 + 2.99475i) q^{13} +(-1.28095 - 3.51556i) q^{14} +(2.13739 - 0.656920i) q^{15} +(2.72415 - 2.92899i) q^{16} +(0.848750 - 0.848750i) q^{17} +(0.288447 + 1.38448i) q^{18} +1.11033i q^{19} +(-4.45909 - 0.341372i) q^{20} +(-2.11995 - 1.58297i) q^{21} +(0.438654 + 2.10545i) q^{22} +(2.90269 - 2.90269i) q^{23} +(0.476250 - 2.78804i) q^{24} +(2.80819 + 4.13691i) q^{25} +(3.28236 - 5.01001i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.78751 + 4.49776i) q^{28} -6.35863 q^{29} +(-2.76970 + 1.52602i) q^{30} -3.55692i q^{31} +(-2.92669 + 4.84092i) q^{32} +(1.07533 + 1.07533i) q^{33} +(-0.930262 + 1.41990i) q^{34} +(1.99080 - 5.57106i) q^{35} +(-0.798701 - 1.83360i) q^{36} +(0.232865 - 0.232865i) q^{37} +(-0.320271 - 1.53723i) q^{38} -4.23521i q^{39} +(6.27201 - 0.813586i) q^{40} -6.76778i q^{41} +(3.39164 + 1.58011i) q^{42} +(-7.11664 - 7.11664i) q^{43} +(-1.21462 - 2.78843i) q^{44} +(-1.04685 + 1.97588i) q^{45} +(-3.18146 + 4.85600i) q^{46} +(-1.87781 + 1.87781i) q^{47} +(0.144842 + 3.99738i) q^{48} +(-6.71166 + 1.98839i) q^{49} +(-5.08118 - 4.91748i) q^{50} +1.20031i q^{51} +(-3.09925 + 7.88306i) q^{52} +(0.0961110 + 0.0961110i) q^{53} +(-1.18294 - 0.775016i) q^{54} +(-1.59200 + 3.00480i) q^{55} +(-5.15662 - 5.42303i) q^{56} +(-0.785121 - 0.785121i) q^{57} +(8.80343 - 1.83413i) q^{58} -11.0439i q^{59} +(3.39444 - 2.91167i) q^{60} +9.42450 q^{61} +(1.02598 + 4.92450i) q^{62} +(2.61836 - 0.379700i) q^{63} +(2.65561 - 7.54637i) q^{64} +(9.05232 - 2.78219i) q^{65} +(-1.79895 - 1.17860i) q^{66} +(11.4129 - 11.4129i) q^{67} +(0.878368 - 2.23416i) q^{68} +4.10502i q^{69} +(-1.14928 + 8.28729i) q^{70} -4.00852 q^{71} +(1.63468 + 2.30820i) q^{72} +(-10.1745 - 10.1745i) q^{73} +(-0.255229 + 0.389567i) q^{74} +(-4.91093 - 0.939546i) q^{75} +(0.886821 + 2.03590i) q^{76} +(3.98186 - 0.577426i) q^{77} +(1.22163 + 5.86359i) q^{78} -3.22206i q^{79} +(-8.44882 + 2.93554i) q^{80} -1.00000 q^{81} +(1.95215 + 9.36989i) q^{82} +(-2.36021 + 2.36021i) q^{83} +(-5.15146 - 1.20933i) q^{84} +(-2.56554 + 0.788510i) q^{85} +(11.9056 + 7.80010i) q^{86} +(4.49623 - 4.49623i) q^{87} +(2.48594 + 3.51019i) q^{88} +7.10490 q^{89} +(0.879417 - 3.03754i) q^{90} +(-8.97844 - 6.70423i) q^{91} +(3.00398 - 7.64074i) q^{92} +(2.51512 + 2.51512i) q^{93} +(2.05815 - 3.14144i) q^{94} +(1.16235 - 2.19388i) q^{95} +(-1.35356 - 5.49253i) q^{96} +(5.73370 - 5.73370i) q^{97} +(8.71864 - 4.68885i) q^{98} -1.52074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more