LMFDB - Embedded newform 930.2.j.h.497.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.5
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.404727 - 1.68410i) q^{3} -1.00000i q^{4} +(-2.01952 + 0.959968i) q^{5} +(1.47702 + 0.904654i) q^{6} +(-2.95632 - 2.95632i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.67239 + 1.36320i) q^{9} +(0.749217 - 2.10682i) q^{10} +4.99639i q^{11} +(-1.68410 + 0.404727i) q^{12} +(-0.576660 + 0.576660i) q^{13} +4.18087 q^{14} +(2.43404 + 3.01255i) q^{15} -1.00000 q^{16} +(1.92786 - 1.92786i) q^{17} +(0.925735 - 2.85360i) q^{18} +2.28957i q^{19} +(0.959968 + 2.01952i) q^{20} +(-3.78224 + 6.17525i) q^{21} +(-3.53298 - 3.53298i) q^{22} +(-2.35823 - 2.35823i) q^{23} +(0.904654 - 1.47702i) q^{24} +(3.15692 - 3.87735i) q^{25} -0.815520i q^{26} +(3.37736 + 3.94885i) q^{27} +(-2.95632 + 2.95632i) q^{28} +7.87675 q^{29} +(-3.85132 - 0.409070i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(8.41443 - 2.02218i) q^{33} +2.72641i q^{34} +(8.80833 + 3.13238i) q^{35} +(1.36320 + 2.67239i) q^{36} +(5.67026 + 5.67026i) q^{37} +(-1.61897 - 1.61897i) q^{38} +(1.20454 + 0.737763i) q^{39} +(-2.10682 - 0.749217i) q^{40} -6.89238i q^{41} +(-1.69211 - 7.04101i) q^{42} +(7.51778 - 7.51778i) q^{43} +4.99639 q^{44} +(4.08832 - 5.31843i) q^{45} +3.33504 q^{46} +(-4.39924 + 4.39924i) q^{47} +(0.404727 + 1.68410i) q^{48} +10.4797i q^{49} +(0.509417 + 4.97398i) q^{50} +(-4.02697 - 2.46645i) q^{51} +(0.576660 + 0.576660i) q^{52} +(-3.78705 - 3.78705i) q^{53} +(-5.18042 - 0.404103i) q^{54} +(-4.79637 - 10.0903i) q^{55} -4.18087i q^{56} +(3.85586 - 0.926650i) q^{57} +(-5.56971 + 5.56971i) q^{58} -8.23302 q^{59} +(3.01255 - 2.43404i) q^{60} +2.57501 q^{61} +(0.707107 - 0.707107i) q^{62} +(11.9305 + 3.87038i) q^{63} +1.00000i q^{64} +(0.611001 - 1.71815i) q^{65} +(-4.52000 + 7.37979i) q^{66} +(8.10538 + 8.10538i) q^{67} +(-1.92786 - 1.92786i) q^{68} +(-3.01706 + 4.92594i) q^{69} +(-8.44335 + 4.01350i) q^{70} +0.808470i q^{71} +(-2.85360 - 0.925735i) q^{72} +(6.98002 - 6.98002i) q^{73} -8.01896 q^{74} +(-7.80754 - 3.74731i) q^{75} +2.28957 q^{76} +(14.7709 - 14.7709i) q^{77} +(-1.37342 + 0.330063i) q^{78} +6.04015i q^{79} +(2.01952 - 0.959968i) q^{80} +(5.28335 - 7.28603i) q^{81} +(4.87365 + 4.87365i) q^{82} +(5.46968 + 5.46968i) q^{83} +(6.17525 + 3.78224i) q^{84} +(-2.04267 + 5.74404i) q^{85} +10.6317i q^{86} +(-3.18794 - 13.2652i) q^{87} +(-3.53298 + 3.53298i) q^{88} +13.0671 q^{89} +(0.869819 + 6.65157i) q^{90} +3.40958 q^{91} +(-2.35823 + 2.35823i) q^{92} +(0.404727 + 1.68410i) q^{93} -6.22147i q^{94} +(-2.19791 - 4.62383i) q^{95} +(-1.47702 - 0.904654i) q^{96} +(9.00142 + 9.00142i) q^{97} +(-7.41025 - 7.41025i) q^{98} +(-6.81110 - 13.3523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.404727	−	1.68410i	−0.233670	−	0.972316i
$3$	−0.404727	−	1.68410i	−0.233670	−	0.972316i
$4$		−	1.00000i		−	0.500000i
$5$	−2.01952	+	0.959968i	−0.903157	+	0.429311i
$5$	−2.01952	+	0.959968i	−0.903157	+	0.429311i
$6$	1.47702	+	0.904654i	0.602993	+	0.369323i
$7$	−2.95632	−	2.95632i	−1.11738	−	1.11738i	−0.992124	−	0.125261i	$-0.960023\pi$
$7$	−2.95632	−	2.95632i	−1.11738	−	1.11738i	−0.125261	−	0.992124i	$-0.539977\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.67239	+	1.36320i	−0.890797	+	0.454401i
$10$	0.749217	−	2.10682i	0.236923	−	0.666234i
$11$			4.99639i			1.50647i	0.657752	+	0.753234i	$0.271507\pi$
$11$			4.99639i			1.50647i	−0.657752	+	0.753234i	$0.728493\pi$
$12$	−1.68410	+	0.404727i	−0.486158	+	0.116835i
$13$	−0.576660	+	0.576660i	−0.159937	+	0.159937i	−0.782539	−	0.622602i	$-0.786076\pi$
$13$	−0.576660	+	0.576660i	−0.159937	+	0.159937i	0.622602	+	0.782539i	$0.286076\pi$
$14$	4.18087			1.11738
$15$	2.43404	+	3.01255i	0.628466	+	0.777837i
$16$	−1.00000			−0.250000
$17$	1.92786	−	1.92786i	0.467575	−	0.467575i	−0.433553	−	0.901128i	$-0.642740\pi$
$17$	1.92786	−	1.92786i	0.467575	−	0.467575i	0.901128	+	0.433553i	$0.142740\pi$
$18$	0.925735	−	2.85360i	0.218198	−	0.672599i
$19$			2.28957i			0.525263i	0.964896	+	0.262631i	$0.0845903\pi$
$19$			2.28957i			0.525263i	−0.964896	+	0.262631i	$0.915410\pi$
$20$	0.959968	+	2.01952i	0.214655	+	0.451578i
$21$	−3.78224	+	6.17525i	−0.825352	+	1.34755i
$22$	−3.53298	−	3.53298i	−0.753234	−	0.753234i
$23$	−2.35823	−	2.35823i	−0.491725	−	0.491725i	0.417124	−	0.908849i	$-0.363038\pi$
$23$	−2.35823	−	2.35823i	−0.491725	−	0.491725i	−0.908849	+	0.417124i	$0.863038\pi$
$24$	0.904654	−	1.47702i	0.184662	−	0.301496i
$25$	3.15692	−	3.87735i	0.631385	−	0.775470i
$26$		−	0.815520i		−	0.159937i
$27$	3.37736	+	3.94885i	0.649974	+	0.759957i
$28$	−2.95632	+	2.95632i	−0.558692	+	0.558692i
$29$	7.87675			1.46268			0.731338	−	0.682015i	$-0.238896\pi$
$29$	7.87675			1.46268			0.731338	+	0.682015i	$0.238896\pi$
$30$	−3.85132	−	0.409070i	−0.703152	−	0.0746857i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	8.41443	−	2.02218i	1.46476	−	0.352016i
$34$			2.72641i			0.467575i
$35$	8.80833	+	3.13238i	1.48888	+	0.529469i
$36$	1.36320	+	2.67239i	0.227201	+	0.445399i
$37$	5.67026	+	5.67026i	0.932186	+	0.932186i	0.997842	−	0.0656566i	$-0.0209142\pi$
$37$	5.67026	+	5.67026i	0.932186	+	0.932186i	−0.0656566	+	0.997842i	$0.520914\pi$
$38$	−1.61897	−	1.61897i	−0.262631	−	0.262631i
$39$	1.20454	+	0.737763i	0.192881	+	0.118137i
$40$	−2.10682	−	0.749217i	−0.333117	−	0.118462i
$41$		−	6.89238i		−	1.07641i	−0.842814	−	0.538204i	$-0.819103\pi$
$41$		−	6.89238i		−	1.07641i	0.842814	−	0.538204i	$-0.180897\pi$
$42$	−1.69211	−	7.04101i	−0.261099	−	1.08645i
$43$	7.51778	−	7.51778i	1.14645	−	1.14645i	0.159205	−	0.987245i	$-0.449107\pi$
$43$	7.51778	−	7.51778i	1.14645	−	1.14645i	0.987245	−	0.159205i	$-0.0508932\pi$
$44$	4.99639			0.753234
$45$	4.08832	−	5.31843i	0.609450	−	0.792824i
$46$	3.33504			0.491725
$47$	−4.39924	+	4.39924i	−0.641696	+	0.641696i	−0.950972	−	0.309276i	$-0.899913\pi$
$47$	−4.39924	+	4.39924i	−0.641696	+	0.641696i	0.309276	+	0.950972i	$0.399913\pi$
$48$	0.404727	+	1.68410i	0.0584174	+	0.243079i
$49$			10.4797i			1.49710i
$50$	0.509417	+	4.97398i	0.0720425	+	0.703427i
$51$	−4.02697	−	2.46645i	−0.563889	−	0.345373i
$52$	0.576660	+	0.576660i	0.0799683	+	0.0799683i
$53$	−3.78705	−	3.78705i	−0.520191	−	0.520191i	0.397438	−	0.917629i	$-0.369899\pi$
$53$	−3.78705	−	3.78705i	−0.520191	−	0.520191i	−0.917629	+	0.397438i	$0.869899\pi$
$54$	−5.18042	−	0.404103i	−0.704965	−	0.0549914i
$55$	−4.79637	−	10.0903i	−0.646743	−	1.36058i
$56$		−	4.18087i		−	0.558692i
$57$	3.85586	−	0.926650i	0.510721	−	0.122738i
$58$	−5.56971	+	5.56971i	−0.731338	+	0.731338i
$59$	−8.23302			−1.07185			−0.535924	−	0.844266i	$-0.680037\pi$
$59$	−8.23302			−1.07185			−0.535924	+	0.844266i	$0.680037\pi$
$60$	3.01255	−	2.43404i	0.388919	−	0.314233i
$61$	2.57501			0.329696			0.164848	−	0.986319i	$-0.447287\pi$
$61$	2.57501			0.329696			0.164848	+	0.986319i	$0.447287\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	11.9305	+	3.87038i	1.50310	+	0.487622i
$64$			1.00000i			0.125000i
$65$	0.611001	−	1.71815i	0.0757854	−	0.213110i
$66$	−4.52000	+	7.37979i	−0.556374	+	0.908390i
$67$	8.10538	+	8.10538i	0.990230	+	0.990230i	0.999953	−	0.00972284i	$-0.00309492\pi$
$67$	8.10538	+	8.10538i	0.990230	+	0.990230i	−0.00972284	+	0.999953i	$0.503095\pi$
$68$	−1.92786	−	1.92786i	−0.233788	−	0.233788i
$69$	−3.01706	+	4.92594i	−0.363211	+	0.593013i
$70$	−8.44335	+	4.01350i	−1.00917	+	0.479705i
$71$			0.808470i			0.0959477i	0.998849	+	0.0479739i	$0.0152764\pi$
$71$			0.808470i			0.0959477i	−0.998849	+	0.0479739i	$0.984724\pi$
$72$	−2.85360	−	0.925735i	−0.336300	−	0.109099i
$73$	6.98002	−	6.98002i	0.816949	−	0.816949i	−0.168716	−	0.985665i	$-0.553962\pi$
$73$	6.98002	−	6.98002i	0.816949	−	0.816949i	0.985665	+	0.168716i	$0.0539620\pi$
$74$	−8.01896			−0.932186
$75$	−7.80754	−	3.74731i	−0.901537	−	0.432702i
$76$	2.28957			0.262631
$77$	14.7709	−	14.7709i	1.68330	−	1.68330i
$78$	−1.37342	+	0.330063i	−0.155509	+	0.0373723i
$79$			6.04015i			0.679570i	0.940503	+	0.339785i	$0.110354\pi$
$79$			6.04015i			0.679570i	−0.940503	+	0.339785i	$0.889646\pi$
$80$	2.01952	−	0.959968i	0.225789	−	0.107328i
$81$	5.28335	−	7.28603i	0.587039	−	0.809559i
$82$	4.87365	+	4.87365i	0.538204	+	0.538204i
$83$	5.46968	+	5.46968i	0.600375	+	0.600375i	0.940412	−	0.340037i	$-0.110440\pi$
$83$	5.46968	+	5.46968i	0.600375	+	0.600375i	−0.340037	+	0.940412i	$0.610440\pi$
$84$	6.17525	+	3.78224i	0.673775	+	0.412676i
$85$	−2.04267	+	5.74404i	−0.221559	+	0.623029i
$86$			10.6317i			1.14645i
$87$	−3.18794	−	13.2652i	−0.341783	−	1.42218i
$88$	−3.53298	+	3.53298i	−0.376617	+	0.376617i
$89$	13.0671			1.38511			0.692553	−	0.721367i	$-0.256486\pi$
$89$	13.0671			1.38511			0.692553	+	0.721367i	$0.256486\pi$
$90$	0.869819	+	6.65157i	0.0916870	+	0.701137i
$91$	3.40958			0.357421
$92$	−2.35823	+	2.35823i	−0.245862	+	0.245862i
$93$	0.404727	+	1.68410i	0.0419683	+	0.174633i
$94$		−	6.22147i		−	0.641696i
$95$	−2.19791	−	4.62383i	−0.225501	−	0.474394i
$96$	−1.47702	−	0.904654i	−0.150748	−	0.0923308i
$97$	9.00142	+	9.00142i	0.913955	+	0.913955i	0.996581	−	0.0826253i	$-0.0263305\pi$
$97$	9.00142	+	9.00142i	0.913955	+	0.913955i	−0.0826253	+	0.996581i	$0.526330\pi$
$98$	−7.41025	−	7.41025i	−0.748549	−	0.748549i
$99$	−6.81110	−	13.3523i	−0.684541	−	1.34196i
$100$	−3.87735	−	3.15692i	−0.387735	−	0.315692i
$101$			15.8353i			1.57567i	0.615885	+	0.787836i	$0.288799\pi$
$101$			15.8353i			1.57567i	−0.615885	+	0.787836i	$0.711201\pi$
$102$	4.59155	−	1.10345i	0.454631	−	0.109258i
$103$	−10.6610	+	10.6610i	−1.05046	+	1.05046i	−0.0517992	+	0.998658i	$0.516496\pi$
$103$	−10.6610	+	10.6610i	−1.05046	+	1.05046i	−0.998658	+	0.0517992i	$0.983504\pi$
$104$	−0.815520			−0.0799683
$105$	1.71027	−	16.1019i	0.166905	−	1.57138i
$106$	5.35569			0.520191
$107$	−9.39588	+	9.39588i	−0.908334	+	0.908334i	−0.996138	−	0.0878038i	$-0.972015\pi$
$107$	−9.39588	+	9.39588i	−0.908334	+	0.908334i	0.0878038	+	0.996138i	$0.472015\pi$
$108$	3.94885	−	3.37736i	0.379978	−	0.324987i
$109$			15.6740i			1.50129i	0.660703	+	0.750647i	$0.270258\pi$
$109$			15.6740i			1.50129i	−0.660703	+	0.750647i	$0.729742\pi$
$110$	10.5265	+	3.74338i	1.00366	+	0.356917i
$111$	7.25438	−	11.8442i	0.688556	−	1.12420i
$112$	2.95632	+	2.95632i	0.279346	+	0.279346i
$113$	6.71657	+	6.71657i	0.631842	+	0.631842i	0.948530	−	0.316688i	$-0.102571\pi$
$113$	6.71657	+	6.71657i	0.631842	+	0.631842i	−0.316688	+	0.948530i	$0.602571\pi$
$114$	−2.07126	+	3.38175i	−0.193992	+	0.316730i
$115$	7.02632	+	2.49867i	0.655208	+	0.233002i
$116$		−	7.87675i		−	0.731338i
$117$	0.754955	−	2.32716i	0.0697957	−	0.215146i
$118$	5.82162	−	5.82162i	0.535924	−	0.535924i
$119$	−11.3988			−1.04492
$120$	−0.409070	+	3.85132i	−0.0373428	+	0.351576i
$121$	−13.9639			−1.26945
$122$	−1.82081	+	1.82081i	−0.164848	+	0.164848i
$123$	−11.6075	+	2.78953i	−1.04661	+	0.251524i
$124$			1.00000i			0.0898027i
$125$	−2.65334	+	10.8609i	−0.237322	+	0.971431i
$126$	−11.1729	+	5.69938i	−0.995363	+	0.507741i
$127$	−5.28171	−	5.28171i	−0.468676	−	0.468676i	0.432809	−	0.901486i	$-0.357522\pi$
$127$	−5.28171	−	5.28171i	−0.468676	−	0.468676i	−0.901486	+	0.432809i	$0.857522\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−15.7034	−	9.61805i	−1.38260	−	0.846822i
$130$	0.782873	+	1.64696i	0.0686625	+	0.144448i
$131$		−	6.57780i		−	0.574705i	−0.957825	−	0.287352i	$-0.907225\pi$
$131$		−	6.57780i		−	0.574705i	0.957825	−	0.287352i	$-0.0927751\pi$
$132$	−2.02218	−	8.41443i	−0.176008	−	0.732382i
$133$	6.76869	−	6.76869i	0.586920	−	0.586920i
$134$	−11.4627			−0.990230
$135$	−10.6114	−	4.73262i	−0.913286	−	0.407319i
$136$	2.72641			0.233788
$137$	6.79419	−	6.79419i	0.580467	−	0.580467i	−0.354565	−	0.935031i	$-0.615371\pi$
$137$	6.79419	−	6.79419i	0.580467	−	0.580467i	0.935031	+	0.354565i	$0.115371\pi$
$138$	−1.34978	−	5.61655i	−0.114901	−	0.478112i
$139$		−	1.63608i		−	0.138771i	−0.997590	−	0.0693853i	$-0.977896\pi$
$139$		−	1.63608i		−	0.138771i	0.997590	−	0.0693853i	$-0.0221038\pi$
$140$	3.13238	−	8.80833i	0.264734	−	0.744439i
$141$	9.18927	+	5.62828i	0.773876	+	0.473986i
$142$	−0.571674	−	0.571674i	−0.0479739	−	0.0479739i
$143$	−2.88122	−	2.88122i	−0.240939	−	0.240939i
$144$	2.67239	−	1.36320i	0.222699	−	0.113600i
$145$	−15.9073	+	7.56143i	−1.32103	+	0.627943i
$146$			9.87123i			0.816949i
$147$	17.6488	−	4.24141i	1.45565	−	0.349826i
$148$	5.67026	−	5.67026i	0.466093	−	0.466093i
$149$	12.8062			1.04913			0.524564	−	0.851371i	$-0.324228\pi$
$149$	12.8062			1.04913			0.524564	+	0.851371i	$0.324228\pi$
$150$	8.17051	−	2.87102i	0.667119	−	0.234418i
$151$	4.04968			0.329558			0.164779	−	0.986330i	$-0.447309\pi$
$151$	4.04968			0.329558			0.164779	+	0.986330i	$0.447309\pi$
$152$	−1.61897	+	1.61897i	−0.131316	+	0.131316i
$153$	−2.52393	+	7.78007i	−0.204048	+	0.628981i
$154$			20.8893i			1.68330i
$155$	2.01952	−	0.959968i	0.162212	−	0.0771065i
$156$	0.737763	−	1.20454i	0.0590683	−	0.0964406i
$157$	−15.9477	−	15.9477i	−1.27277	−	1.27277i	−0.944629	−	0.328140i	$-0.893578\pi$
$157$	−15.9477	−	15.9477i	−1.27277	−	1.27277i	−0.328140	−	0.944629i	$-0.606422\pi$
$158$	−4.27103	−	4.27103i	−0.339785	−	0.339785i
$159$	−4.84505	+	7.91049i	−0.384237	+	0.627343i
$160$	−0.749217	+	2.10682i	−0.0592308	+	0.166558i
$161$			13.9434i			1.09889i
$162$	1.41611	+	8.88789i	0.111260	+	0.698299i
$163$	−7.39856	+	7.39856i	−0.579500	+	0.579500i	−0.934766	−	0.355265i	$-0.884391\pi$
$163$	−7.39856	+	7.39856i	−0.579500	+	0.579500i	0.355265	+	0.934766i	$0.384391\pi$
$164$	−6.89238			−0.538204
$165$	−15.0519	+	12.1614i	−1.17179	+	0.946764i
$166$	−7.73529			−0.600375
$167$	−2.63668	+	2.63668i	−0.204032	+	0.204032i	−0.801725	−	0.597693i	$-0.796084\pi$
$167$	−2.63668	+	2.63668i	−0.204032	+	0.204032i	0.597693	+	0.801725i	$0.296084\pi$
$168$	−7.04101	+	1.69211i	−0.543226	+	0.130549i
$169$			12.3349i			0.948841i
$170$	−2.61726	−	5.50604i	−0.200735	−	0.422294i
$171$	−3.12115	−	6.11862i	−0.238680	−	0.467902i
$172$	−7.51778	−	7.51778i	−0.573225	−	0.573225i
$173$	12.1778	+	12.1778i	0.925862	+	0.925862i	0.997435	−	0.0715734i	$-0.0228020\pi$
$173$	12.1778	+	12.1778i	0.925862	+	0.925862i	−0.0715734	+	0.997435i	$0.522802\pi$
$174$	11.6342	+	7.12573i	0.881983	+	0.540201i
$175$	−20.7956	+	2.12981i	−1.57200	+	0.160998i
$176$		−	4.99639i		−	0.376617i
$177$	3.33213	+	13.8652i	0.250458	+	1.04217i
$178$	−9.23980	+	9.23980i	−0.692553	+	0.692553i
$179$	17.0570			1.27490			0.637448	−	0.770493i	$-0.279990\pi$
$179$	17.0570			1.27490			0.637448	+	0.770493i	$0.279990\pi$
$180$	−5.31843	−	4.08832i	−0.396412	−	0.304725i
$181$	−13.7882			−1.02487			−0.512434	−	0.858726i	$-0.671256\pi$
$181$	−13.7882			−1.02487			−0.512434	+	0.858726i	$0.671256\pi$
$182$	−2.41094	+	2.41094i	−0.178711	+	0.178711i
$183$	−1.04218	−	4.33658i	−0.0770400	−	0.320569i
$184$		−	3.33504i		−	0.245862i
$185$	−16.8945	−	6.00794i	−1.24211	−	0.441713i
$186$	−1.47702	−	0.904654i	−0.108301	−	0.0663324i
$187$	9.63235	+	9.63235i	0.704387	+	0.704387i
$188$	4.39924	+	4.39924i	0.320848	+	0.320848i
$189$	1.68950	−	21.6586i	0.122893	−	1.57543i
$190$	4.82370	+	1.71538i	0.349948	+	0.124447i
$191$		−	20.9450i		−	1.51553i	−0.652528	−	0.757765i	$-0.726291\pi$
$191$		−	20.9450i		−	1.51553i	0.652528	−	0.757765i	$-0.273709\pi$
$192$	1.68410	−	0.404727i	0.121540	−	0.0292087i
$193$	8.68054	−	8.68054i	0.624839	−	0.624839i	−0.321926	−	0.946765i	$-0.604330\pi$
$193$	8.68054	−	8.68054i	0.624839	−	0.624839i	0.946765	+	0.321926i	$0.104330\pi$
$194$	−12.7299			−0.913955
$195$	−3.14083	−	0.333605i	−0.224919	−	0.0238899i
$196$	10.4797			0.748549
$197$	10.8415	−	10.8415i	0.772428	−	0.772428i	−0.206102	−	0.978530i	$-0.566078\pi$
$197$	10.8415	−	10.8415i	0.772428	−	0.772428i	0.978530	+	0.206102i	$0.0660780\pi$
$198$	14.2577	+	4.62534i	1.01325	+	0.328708i
$199$			14.2096i			1.00729i	0.863911	+	0.503645i	$0.168008\pi$
$199$			14.2096i			1.00729i	−0.863911	+	0.503645i	$0.831992\pi$
$200$	4.97398	−	0.509417i	0.351714	−	0.0360212i
$201$	10.3698	−	16.9307i	0.731430	−	1.19420i
$202$	−11.1973	−	11.1973i	−0.787836	−	0.787836i
$203$	−23.2862	−	23.2862i	−1.63437	−	1.63437i
$204$	−2.46645	+	4.02697i	−0.172686	+	0.281944i
$205$	6.61646	+	13.9193i	0.462114	+	0.972166i
$206$		−	15.0769i		−	1.05046i
$207$	9.51686	+	3.08737i	0.661468	+	0.214587i
$208$	0.576660	−	0.576660i	0.0399841	−	0.0399841i
$209$	−11.4396			−0.791291
$210$	10.1764	+	12.5951i	0.702238	+	0.869143i
$211$	3.57614			0.246192			0.123096	−	0.992395i	$-0.460718\pi$
$211$	3.57614			0.246192			0.123096	+	0.992395i	$0.460718\pi$
$212$	−3.78705	+	3.78705i	−0.260095	+	0.260095i
$213$	1.36154	−	0.327210i	0.0932915	−	0.0224201i
$214$		−	13.2878i		−	0.908334i
$215$	−7.96548	+	22.3991i	−0.543241	+	1.52761i
$216$	−0.404103	+	5.18042i	−0.0274957	+	0.352483i
$217$	2.95632	+	2.95632i	0.200688	+	0.200688i
$218$	−11.0832	−	11.0832i	−0.750647	−	0.750647i
$219$	−14.5801	−	8.93005i	−0.985229	−	0.603437i
$220$	−10.0903	+	4.79637i	−0.680289	+	0.323371i
$221$			2.22344i			0.149565i
$222$	3.24550	+	13.5047i	0.217823	+	0.906379i
$223$	8.25222	−	8.25222i	0.552609	−	0.552609i	−0.374584	−	0.927193i	$-0.622214\pi$
$223$	8.25222	−	8.25222i	0.552609	−	0.552609i	0.927193	+	0.374584i	$0.122214\pi$
$224$	−4.18087			−0.279346
$225$	−3.15092	+	14.6653i	−0.210061	+	0.977688i
$226$	−9.49866			−0.631842
$227$	3.91654	−	3.91654i	0.259950	−	0.259950i	−0.565084	−	0.825034i	$-0.691156\pi$
$227$	3.91654	−	3.91654i	0.259950	−	0.259950i	0.825034	+	0.565084i	$0.191156\pi$
$228$	−0.926650	−	3.85586i	−0.0613689	−	0.255361i
$229$			4.19731i			0.277366i	0.990337	+	0.138683i	$0.0442869\pi$
$229$			4.19731i			0.277366i	−0.990337	+	0.138683i	$0.955713\pi$
$230$	−6.73518	+	3.20153i	−0.444105	+	0.211103i
$231$	−30.8540	−	18.8975i	−2.03004	−	1.24337i
$232$	5.56971	+	5.56971i	0.365669	+	0.365669i
$233$	−21.2882	−	21.2882i	−1.39464	−	1.39464i	−0.814560	−	0.580079i	$-0.803022\pi$
$233$	−21.2882	−	21.2882i	−1.39464	−	1.39464i	−0.580079	−	0.814560i	$-0.696978\pi$
$234$	1.11172	+	2.17939i	0.0726754	+	0.142471i
$235$	4.66123	−	13.1075i	0.304065	−	0.855039i
$236$			8.23302i			0.535924i
$237$	10.1722	−	2.44461i	0.660756	−	0.158795i
$238$	8.06014	−	8.06014i	0.522461	−	0.522461i
$239$	8.28057			0.535625			0.267813	−	0.963471i	$-0.413699\pi$
$239$	8.28057			0.535625			0.267813	+	0.963471i	$0.413699\pi$
$240$	−2.43404	−	3.01255i	−0.157116	−	0.194459i
$241$	−7.96980			−0.513380			−0.256690	−	0.966494i	$-0.582632\pi$
$241$	−7.96980			−0.513380			−0.256690	+	0.966494i	$0.582632\pi$
$242$	9.87398	−	9.87398i	0.634724	−	0.634724i
$243$	−14.4087	−	5.94884i	−0.924320	−	0.381618i
$244$		−	2.57501i		−	0.164848i
$245$	−10.0602	−	21.1639i	−0.642720	−	1.35211i
$246$	6.23521	−	10.1802i	0.397543	−	0.649067i
$247$	−1.32030	−	1.32030i	−0.0840087	−	0.0840087i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	6.99776	−	11.4252i	0.443465	−	0.724044i
$250$	−5.80364	−	9.55603i	−0.367054	−	0.604377i
$251$			2.76165i			0.174314i	0.996195	+	0.0871568i	$0.0277781\pi$
$251$			2.76165i			0.174314i	−0.996195	+	0.0871568i	$0.972222\pi$
$252$	3.87038	−	11.9305i	0.243811	−	0.751552i
$253$	11.7826	−	11.7826i	0.740768	−	0.740768i
$254$	7.46947			0.468676
$255$	10.5003	+	1.11529i	0.657552	+	0.0698423i
$256$	1.00000			0.0625000
$257$	−9.84769	+	9.84769i	−0.614282	+	0.614282i	−0.944059	−	0.329777i	$-0.893026\pi$
$257$	−9.84769	+	9.84769i	−0.614282	+	0.614282i	0.329777	+	0.944059i	$0.393026\pi$
$258$	17.9049	−	4.30296i	1.11471	−	0.267891i
$259$		−	33.5263i		−	2.08322i
$260$	−1.71815	−	0.611001i	−0.106555	−	0.0378927i
$261$	−21.0498	+	10.7376i	−1.30295	+	0.664642i
$262$	4.65120	+	4.65120i	0.287352	+	0.287352i
$263$	15.0377	+	15.0377i	0.927266	+	0.927266i	0.997529	−	0.0702629i	$-0.0223838\pi$
$263$	15.0377	+	15.0377i	0.927266	+	0.927266i	−0.0702629	+	0.997529i	$0.522384\pi$
$264$	7.37979	+	4.52000i	0.454195	+	0.278187i
$265$	11.2835	+	4.01258i	0.693138	+	0.246491i
$266$			9.57238i			0.586920i
$267$	−5.28860	−	22.0062i	−0.323657	−	1.34676i
$268$	8.10538	−	8.10538i	0.495115	−	0.495115i
$269$	1.89009			0.115241			0.0576205	−	0.998339i	$-0.481649\pi$
$269$	1.89009			0.115241			0.0576205	+	0.998339i	$0.481649\pi$
$270$	10.8499	−	4.15694i	0.660303	−	0.252983i
$271$	−0.428031			−0.0260011			−0.0130005	−	0.999915i	$-0.504138\pi$
$271$	−0.428031			−0.0260011			−0.0130005	+	0.999915i	$0.504138\pi$
$272$	−1.92786	+	1.92786i	−0.116894	+	0.116894i
$273$	−1.37995	−	5.74208i	−0.0835185	−	0.347527i
$274$			9.60844i			0.580467i
$275$	19.3727	+	15.7732i	1.16822	+	0.951161i
$276$	4.92594	+	3.01706i	0.296507	+	0.181605i
$277$	−1.06863	−	1.06863i	−0.0642080	−	0.0642080i	0.674274	−	0.738482i	$-0.264457\pi$
$277$	−1.06863	−	1.06863i	−0.0642080	−	0.0642080i	−0.738482	+	0.674274i	$0.764457\pi$
$278$	1.15688	+	1.15688i	0.0693853	+	0.0693853i
$279$	2.67239	−	1.36320i	0.159992	−	0.0816129i
$280$	4.01350	+	8.44335i	0.239853	+	0.504587i
$281$			4.19370i			0.250175i	0.992146	+	0.125088i	$0.0399212\pi$
$281$			4.19370i			0.250175i	−0.992146	+	0.125088i	$0.960079\pi$
$282$	−10.4776	+	2.51800i	−0.623931	+	0.149945i
$283$	20.3038	−	20.3038i	1.20694	−	1.20694i	0.234921	−	0.972015i	$-0.424517\pi$
$283$	20.3038	−	20.3038i	1.20694	−	1.20694i	0.972015	−	0.234921i	$-0.0754831\pi$
$284$	0.808470			0.0479739
$285$	−6.89743	+	5.57289i	−0.408569	+	0.330110i
$286$	4.07466			0.240939
$287$	−20.3761	+	20.3761i	−1.20276	+	1.20276i
$288$	−0.925735	+	2.85360i	−0.0545495	+	0.168150i
$289$			9.56670i			0.562747i
$290$	5.90140	−	16.5949i	0.346542	−	0.974485i
$291$	11.5162	−	18.8024i	0.675090	−	1.10222i
$292$	−6.98002	−	6.98002i	−0.408475	−	0.408475i
$293$	−21.7801	−	21.7801i	−1.27241	−	1.27241i	−0.944820	−	0.327589i	$-0.893764\pi$
$293$	−21.7801	−	21.7801i	−1.27241	−	1.27241i	−0.327589	−	0.944820i	$-0.606236\pi$
$294$	−9.48048	+	15.4787i	−0.552913	+	0.902739i
$295$	16.6267	−	7.90343i	0.968047	−	0.460156i
$296$			8.01896i			0.466093i
$297$	−19.7300	+	16.8746i	−1.14485	+	0.979165i
$298$	−9.05537	+	9.05537i	−0.524564	+	0.524564i
$299$	2.71979			0.157290
$300$	−3.74731	+	7.80754i	−0.216351	+	0.450769i
$301$	−44.4500			−2.56205
$302$	−2.86356	+	2.86356i	−0.164779	+	0.164779i
$303$	26.6683	−	6.40898i	1.53205	−	0.368187i
$304$		−	2.28957i		−	0.131316i
$305$	−5.20029	+	2.47193i	−0.297767	+	0.141542i
$306$	−3.71665	−	7.28603i	−0.212467	−	0.416515i
$307$	−1.13245	−	1.13245i	−0.0646323	−	0.0646323i	0.674052	−	0.738684i	$-0.264552\pi$
$307$	−1.13245	−	1.13245i	−0.0646323	−	0.0646323i	−0.738684	+	0.674052i	$0.764552\pi$
$308$	−14.7709	−	14.7709i	−0.841652	−	0.841652i
$309$	22.2689	+	13.6394i	1.26684	+	0.775916i
$310$	−0.749217	+	2.10682i	−0.0425527	+	0.119659i
$311$		−	10.7037i		−	0.606949i	−0.952840	−	0.303475i	$-0.901853\pi$
$311$		−	10.7037i		−	0.606949i	0.952840	−	0.303475i	$-0.0981467\pi$
$312$	0.330063	+	1.37342i	0.0186862	+	0.0777545i
$313$	−10.1742	+	10.1742i	−0.575077	+	0.575077i	−0.933543	−	0.358466i	$-0.883300\pi$
$313$	−10.1742	+	10.1742i	−0.575077	+	0.575077i	0.358466	+	0.933543i	$0.383300\pi$
$314$	22.5535			1.27277
$315$	−27.8094	+	3.63660i	−1.56688	+	0.204899i
$316$	6.04015			0.339785
$317$	−4.80017	+	4.80017i	−0.269604	+	0.269604i	−0.828941	−	0.559336i	$-0.811056\pi$
$317$	−4.80017	+	4.80017i	−0.269604	+	0.269604i	0.559336	+	0.828941i	$0.311056\pi$
$318$	−2.16760	−	9.01953i	−0.121553	−	0.505790i
$319$			39.3553i			2.20348i
$320$	−0.959968	−	2.01952i	−0.0536638	−	0.112895i
$321$	19.6264	+	12.0208i	1.09544	+	0.670938i
$322$	−9.85946	−	9.85946i	−0.549446	−	0.549446i
$323$	4.41397	+	4.41397i	0.245600	+	0.245600i
$324$	−7.28603	−	5.28335i	−0.404779	−	0.293519i
$325$	0.415440	+	4.05638i	0.0230444	+	0.225007i
$326$		−	10.4632i		−	0.579500i
$327$	26.3966	−	6.34369i	1.45973	−	0.350807i
$328$	4.87365	−	4.87365i	0.269102	−	0.269102i
$329$	26.0112			1.43404
$330$	2.04387	−	19.2427i	0.112512	−	1.05928i
$331$	−2.51109			−0.138022			−0.0690111	−	0.997616i	$-0.521984\pi$
$331$	−2.51109			−0.138022			−0.0690111	+	0.997616i	$0.521984\pi$
$332$	5.46968	−	5.46968i	0.300188	−	0.300188i
$333$	−22.8829	−	7.42344i	−1.25397	−	0.406802i
$334$		−	3.72882i		−	0.204032i
$335$	−24.1499	−	8.58808i	−1.31945	−	0.469217i
$336$	3.78224	−	6.17525i	0.206338	−	0.336887i
$337$	1.40334	+	1.40334i	0.0764449	+	0.0764449i	0.744295	−	0.667851i	$-0.232785\pi$
$337$	1.40334	+	1.40334i	0.0764449	+	0.0764449i	−0.667851	+	0.744295i	$0.732785\pi$
$338$	−8.72211	−	8.72211i	−0.474420	−	0.474420i
$339$	8.59300	−	14.0298i	0.466708	−	0.761992i
$340$	5.74404	+	2.04267i	0.311514	+	0.110779i
$341$		−	4.99639i		−	0.270570i
$342$	6.53350	+	2.11953i	0.353291	+	0.114611i
$343$	10.2871	−	10.2871i	0.555449	−	0.555449i
$344$	10.6317			0.573225
$345$	1.36427	−	12.8443i	0.0734496	−	0.691514i
$346$	−17.2220			−0.925862
$347$	−3.40897	+	3.40897i	−0.183003	+	0.183003i	−0.792663	−	0.609660i	$-0.791306\pi$
$347$	−3.40897	+	3.40897i	−0.183003	+	0.183003i	0.609660	+	0.792663i	$0.291306\pi$
$348$	−13.2652	+	3.18794i	−0.711092	+	0.170891i
$349$		−	7.29774i		−	0.390639i	−0.980740	−	0.195320i	$-0.937426\pi$
$349$		−	7.29774i		−	0.390639i	0.980740	−	0.195320i	$-0.0625744\pi$
$350$	13.1987	−	16.2107i	0.705500	−	0.866498i
$351$	−4.22473	−	0.329554i	−0.225499	−	0.0175903i
$352$	3.53298	+	3.53298i	0.188309	+	0.188309i
$353$	9.35024	+	9.35024i	0.497663	+	0.497663i	0.910710	−	0.413047i	$-0.135535\pi$
$353$	9.35024	+	9.35024i	0.497663	+	0.497663i	−0.413047	+	0.910710i	$0.635535\pi$
$354$	−12.1604	−	7.44803i	−0.646316	−	0.395858i
$355$	−0.776105	−	1.63272i	−0.0411914	−	0.0866558i
$356$		−	13.0671i		−	0.692553i
$357$	4.61339	+	19.1967i	0.244167	+	1.01599i
$358$	−12.0611	+	12.0611i	−0.637448	+	0.637448i
$359$	18.8780			0.996341			0.498170	−	0.867079i	$-0.334005\pi$
$359$	18.8780			0.996341			0.498170	+	0.867079i	$0.334005\pi$
$360$	6.65157	−	0.869819i	0.350569	−	0.0458435i
$361$	13.7579			0.724099
$362$	9.74973	−	9.74973i	0.512434	−	0.512434i
$363$	5.65158	+	23.5166i	0.296631	+	1.23430i
$364$		−	3.40958i		−	0.178711i
$365$	−7.39569	+	20.7969i	−0.387108	+	1.08856i
$366$	3.80335	+	2.32949i	0.198804	+	0.121765i
$367$	−1.50038	−	1.50038i	−0.0783192	−	0.0783192i	0.666862	−	0.745181i	$-0.267637\pi$
$367$	−1.50038	−	1.50038i	−0.0783192	−	0.0783192i	−0.745181	+	0.666862i	$0.767637\pi$
$368$	2.35823	+	2.35823i	0.122931	+	0.122931i
$369$	9.39571	+	18.4191i	0.489121	+	0.958862i
$370$	16.1945	−	7.69795i	0.841910	−	0.400197i
$371$			22.3915i			1.16251i
$372$	1.68410	−	0.404727i	0.0873166	−	0.0209841i
$373$	−0.674075	+	0.674075i	−0.0349023	+	0.0349023i	−0.724343	−	0.689440i	$-0.757857\pi$
$373$	−0.674075	+	0.674075i	−0.0349023	+	0.0349023i	0.689440	+	0.724343i	$0.257857\pi$
$374$	−13.6222			−0.704387
$375$	19.3648	+	0.0727794i	0.999993	+	0.00375831i
$376$	−6.22147			−0.320848
$377$	−4.54221	+	4.54221i	−0.233935	+	0.233935i
$378$	14.1203	+	16.5096i	0.726271	+	0.849164i
$379$			5.42438i			0.278631i	0.990248	+	0.139316i	$0.0444903\pi$
$379$			5.42438i			0.278631i	−0.990248	+	0.139316i	$0.955510\pi$
$380$	−4.62383	+	2.19791i	−0.237197	+	0.112750i
$381$	−6.75728	+	11.0326i	−0.346186	+	0.565217i
$382$	14.8104	+	14.8104i	0.757765	+	0.757765i
$383$	−5.48189	−	5.48189i	−0.280112	−	0.280112i	0.553042	−	0.833153i	$-0.313467\pi$
$383$	−5.48189	−	5.48189i	−0.280112	−	0.280112i	−0.833153	+	0.553042i	$0.813467\pi$
$384$	−0.904654	+	1.47702i	−0.0461654	+	0.0753741i
$385$	−15.6506	+	44.0098i	−0.797628	+	2.24295i
$386$			12.2761i			0.624839i
$387$	−9.84219	+	30.3387i	−0.500306	+	1.54220i
$388$	9.00142	−	9.00142i	0.456978	−	0.456978i
$389$	32.9134			1.66877			0.834387	−	0.551179i	$-0.185822\pi$
$389$	32.9134			1.66877			0.834387	+	0.551179i	$0.185822\pi$
$390$	2.45679	−	1.98501i	0.124405	−	0.100515i
$391$	−9.09268			−0.459837
$392$	−7.41025	+	7.41025i	−0.374274	+	0.374274i
$393$	−11.0777	+	2.66222i	−0.558795	+	0.134291i
$394$			15.3323i			0.772428i
$395$	−5.79835	−	12.1982i	−0.291746	−	0.613758i
$396$	−13.3523	+	6.81110i	−0.670979	+	0.342271i
$397$	−8.17263	−	8.17263i	−0.410173	−	0.410173i	0.471626	−	0.881799i	$-0.343667\pi$
$397$	−8.17263	−	8.17263i	−0.410173	−	0.410173i	−0.881799	+	0.471626i	$0.843667\pi$
$398$	−10.0477	−	10.0477i	−0.503645	−	0.503645i
$399$	−14.1386	−	8.65969i	−0.707817	−	0.433527i
$400$	−3.15692	+	3.87735i	−0.157846	+	0.193867i
$401$			18.6503i			0.931350i	0.884956	+	0.465675i	$0.154188\pi$
$401$			18.6503i			0.931350i	−0.884956	+	0.465675i	$0.845812\pi$
$402$	4.63929	+	19.3044i	0.231387	+	0.962816i
$403$	0.576660	−	0.576660i	0.0287255	−	0.0287255i
$404$	15.8353			0.787836
$405$	−3.67548	+	19.7861i	−0.182636	+	0.983181i
$406$	32.9317			1.63437
$407$	−28.3309	+	28.3309i	−1.40431	+	1.40431i
$408$	−1.10345	−	4.59155i	−0.0546290	−	0.227315i
$409$			31.5379i			1.55945i	0.626123	+	0.779725i	$0.284641\pi$
$409$			31.5379i			1.55945i	−0.626123	+	0.779725i	$0.715359\pi$
$410$	−14.5210	−	5.16388i	−0.717140	−	0.255026i
$411$	−14.1919	−	8.69231i	−0.700035	−	0.428760i
$412$	10.6610	+	10.6610i	0.525228	+	0.525228i
$413$	24.3395	+	24.3395i	1.19767	+	1.19767i
$414$	−8.91253	+	4.54634i	−0.438027	+	0.223440i
$415$	−16.2968	−	5.79541i	−0.799981	−	0.284486i
$416$			0.815520i			0.0399841i
$417$	−2.75532	+	0.662167i	−0.134929	+	0.0324264i
$418$	8.08900	−	8.08900i	0.395646	−	0.395646i
$419$	−2.11671			−0.103408			−0.0517040	−	0.998662i	$-0.516465\pi$
$419$	−2.11671			−0.103408			−0.0517040	+	0.998662i	$0.516465\pi$
$420$	−16.1019	−	1.71027i	−0.785691	−	0.0834526i
$421$	−10.2753			−0.500788			−0.250394	−	0.968144i	$-0.580560\pi$
$421$	−10.2753			−0.500788			−0.250394	+	0.968144i	$0.580560\pi$
$422$	−2.52871	+	2.52871i	−0.123096	+	0.123096i
$423$	5.75944	−	17.7536i	0.280033	−	0.863208i
$424$		−	5.35569i		−	0.260095i
$425$	−1.38888	−	13.5611i	−0.0673705	−	0.657810i
$426$	−0.731385	+	1.19413i	−0.0354357	+	0.0578558i
$427$	−7.61256	−	7.61256i	−0.368398	−	0.368398i
$428$	9.39588	+	9.39588i	0.454167	+	0.454167i
$429$	−3.68615	+	6.01837i	−0.177969	+	0.290569i
$430$	−10.2061	−	21.4710i	−0.492184	−	1.03543i
$431$			8.73526i			0.420763i	0.977619	+	0.210381i	$0.0674706\pi$
$431$			8.73526i			0.420763i	−0.977619	+	0.210381i	$0.932529\pi$
$432$	−3.37736	−	3.94885i	−0.162493	−	0.189989i
$433$	13.6650	−	13.6650i	0.656696	−	0.656696i	−0.297901	−	0.954597i	$-0.596286\pi$
$433$	13.6650	−	13.6650i	0.656696	−	0.656696i	0.954597	+	0.297901i	$0.0962864\pi$
$434$	−4.18087			−0.200688
$435$	19.1723	+	23.7291i	0.919242	+	1.13772i
$436$	15.6740			0.750647
$437$	5.39932	−	5.39932i	0.258285	−	0.258285i
$438$	16.6242	−	3.99516i	0.794333	−	0.190896i
$439$		−	25.3349i		−	1.20917i	−0.796541	−	0.604584i	$-0.793339\pi$
$439$		−	25.3349i		−	1.20917i	0.796541	−	0.604584i	$-0.206661\pi$
$440$	3.74338	−	10.5265i	0.178459	−	0.501830i
$441$	−14.2859	−	28.0058i	−0.680283	−	1.33361i
$442$	−1.57221	−	1.57221i	−0.0747824	−	0.0747824i
$443$	15.2217	+	15.2217i	0.723207	+	0.723207i	0.969257	−	0.246050i	$-0.0791329\pi$
$443$	15.2217	+	15.2217i	0.723207	+	0.723207i	−0.246050	+	0.969257i	$0.579133\pi$
$444$	−11.8442	−	7.25438i	−0.562101	−	0.344278i
$445$	−26.3892	+	12.5440i	−1.25097	+	0.594640i
$446$			11.6704i			0.552609i
$447$	−5.18303	−	21.5670i	−0.245149	−	1.02008i
$448$	2.95632	−	2.95632i	0.139673	−	0.139673i
$449$	37.0053			1.74639			0.873195	−	0.487371i	$-0.162044\pi$
$449$	37.0053			1.74639			0.873195	+	0.487371i	$0.162044\pi$
$450$	−8.14191	−	12.5980i	−0.383813	−	0.593875i
$451$	34.4370			1.62158
$452$	6.71657	−	6.71657i	0.315921	−	0.315921i
$453$	−1.63902	−	6.82007i	−0.0770077	−	0.320435i
$454$			5.53883i			0.259950i
$455$	−6.88572	+	3.27309i	−0.322808	+	0.153445i
$456$	3.38175	+	2.07126i	0.158365	+	0.0969958i
$457$	27.8953	+	27.8953i	1.30488	+	1.30488i	0.925057	+	0.379827i	$0.124017\pi$
$457$	27.8953	+	27.8953i	1.30488	+	1.30488i	0.379827	+	0.925057i	$0.375983\pi$
$458$	−2.96795	−	2.96795i	−0.138683	−	0.138683i
$459$	14.1239	+	1.10175i	0.659248	+	0.0514252i
$460$	2.49867	−	7.02632i	0.116501	−	0.327604i
$461$			29.3150i			1.36534i	0.730729	+	0.682668i	$0.239180\pi$
$461$			29.3150i			1.36534i	−0.730729	+	0.682668i	$0.760820\pi$
$462$	35.1796	−	8.45446i	1.63670	−	0.393337i
$463$	−9.85332	+	9.85332i	−0.457922	+	0.457922i	−0.897973	−	0.440051i	$-0.854961\pi$
$463$	−9.85332	+	9.85332i	−0.457922	+	0.457922i	0.440051	+	0.897973i	$0.354961\pi$
$464$	−7.87675			−0.365669
$465$	−2.43404	−	3.01255i	−0.112876	−	0.139704i
$466$	30.1061			1.39464
$467$	−1.63018	+	1.63018i	−0.0754357	+	0.0754357i	−0.743818	−	0.668382i	$-0.766987\pi$
$467$	−1.63018	+	1.63018i	−0.0754357	+	0.0754357i	0.668382	+	0.743818i	$0.266987\pi$
$468$	−2.32716	−	0.754955i	−0.107573	−	0.0348978i
$469$		−	47.9242i		−	2.21294i
$470$	5.97241	+	12.5644i	0.275487	+	0.579552i
$471$	−20.4031	+	33.3121i	−0.940126	+	1.53494i
$472$	−5.82162	−	5.82162i	−0.267962	−	0.267962i
$473$	37.5618	+	37.5618i	1.72709	+	1.72709i
$474$	−5.46424	+	8.92145i	−0.250981	+	0.409776i
$475$	8.87745	+	7.22799i	0.407325	+	0.331643i
$476$			11.3988i			0.522461i
$477$	15.2830	+	4.95796i	0.699760	+	0.227009i
$478$	−5.85525	+	5.85525i	−0.267813	+	0.267813i
$479$	−18.6347			−0.851442			−0.425721	−	0.904854i	$-0.639980\pi$
$479$	−18.6347			−0.851442			−0.425721	+	0.904854i	$0.639980\pi$
$480$	3.85132	+	0.409070i	0.175788	+	0.0186714i
$481$	−6.53962			−0.298181
$482$	5.63550	−	5.63550i	0.256690	−	0.256690i
$483$	23.4820	−	5.64327i	1.06847	−	0.256778i
$484$			13.9639i			0.634724i
$485$	−26.8196	−	9.53747i	−1.21782	−	0.433074i
$486$	14.3950	−	5.98204i	0.652969	−	0.271351i
$487$	−16.5699	−	16.5699i	−0.750852	−	0.750852i	0.223786	−	0.974638i	$-0.428158\pi$
$487$	−16.5699	−	16.5699i	−0.750852	−	0.750852i	−0.974638	+	0.223786i	$0.928158\pi$
$488$	1.82081	+	1.82081i	0.0824241	+	0.0824241i
$489$	15.4543	+	9.46553i	0.698869	+	0.428046i
$490$	22.0788	+	7.85155i	0.997417	+	0.354697i
$491$		−	5.39841i		−	0.243627i	−0.992553	−	0.121814i	$-0.961129\pi$
$491$		−	5.39841i		−	0.243627i	0.992553	−	0.121814i	$-0.0388710\pi$
$492$	2.78953	+	11.6075i	0.125762	+	0.523305i
$493$	15.1853	−	15.1853i	0.683911	−	0.683911i
$494$	1.86719			0.0840087
$495$	26.5729	+	20.4268i	1.19436	+	0.918118i
$496$	1.00000			0.0449013
$497$	2.39010	−	2.39010i	0.107211	−	0.107211i
$498$	3.13069	+	13.0270i	0.140289	+	0.583754i
$499$		−	30.3229i		−	1.35744i	−0.734398	−	0.678719i	$-0.762535\pi$
$499$		−	30.3229i		−	1.35744i	0.734398	−	0.678719i	$-0.237465\pi$
$500$	10.8609	+	2.65334i	0.485716	+	0.118661i
$501$	5.50757	+	3.37329i	0.246060	+	0.150708i
$502$	−1.95278	−	1.95278i	−0.0871568	−	0.0871568i
$503$	5.28566	+	5.28566i	0.235676	+	0.235676i	0.815057	−	0.579381i	$-0.196706\pi$
$503$	5.28566	+	5.28566i	0.235676	+	0.235676i	−0.579381	+	0.815057i	$0.696706\pi$
$504$	5.69938	+	11.1729i	0.253871	+	0.497682i
$505$	−15.2014	−	31.9797i	−0.676453	−	1.42308i
$506$			16.6632i			0.740768i
$507$	20.7733	−	4.99228i	0.922573	−	0.221715i
$508$	−5.28171	+	5.28171i	−0.234338	+	0.234338i
$509$	−8.19904			−0.363416			−0.181708	−	0.983353i	$-0.558163\pi$
$509$	−8.19904			−0.363416			−0.181708	+	0.983353i	$0.558163\pi$
$510$	−8.21344	+	6.63618i	−0.363697	+	0.293855i
$511$	−41.2704			−1.82569
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−9.04115	+	7.73270i	−0.399177	+	0.341407i
$514$		−	13.9267i		−	0.614282i
$515$	11.2959	−	31.7642i	0.497755	−	1.39970i
$516$	−9.61805	+	15.7034i	−0.423411	+	0.691302i
$517$	−21.9803	−	21.9803i	−0.966694	−	0.966694i
$518$	23.7066	+	23.7066i	1.04161	+	1.04161i
$519$	15.5800	−	25.4374i	0.683885	−	1.11658i
$520$	1.64696	−	0.782873i	0.0722239	−	0.0343312i
$521$			37.7000i			1.65167i	0.563914	+	0.825834i	$0.309295\pi$
$521$			37.7000i			1.65167i	−0.563914	+	0.825834i	$0.690705\pi$
$522$	7.29179	−	22.4771i	0.319153	−	0.983795i
$523$	−5.19328	+	5.19328i	−0.227086	+	0.227086i	−0.811474	−	0.584388i	$-0.801335\pi$
$523$	−5.19328	+	5.19328i	−0.227086	+	0.227086i	0.584388	+	0.811474i	$0.301335\pi$
$524$	−6.57780			−0.287352
$525$	12.0034	+	34.1599i	0.523869	+	1.49086i
$526$	−21.2665			−0.927266
$527$	−1.92786	+	1.92786i	−0.0839790	+	0.0839790i
$528$	−8.41443	+	2.02218i	−0.366191	+	0.0880039i
$529$		−	11.8775i		−	0.516413i
$530$	−10.8159	+	5.14129i	−0.469814	+	0.223324i
$531$	22.0018	−	11.2233i	0.954799	−	0.487049i
$532$	−6.76869	−	6.76869i	−0.293460	−	0.293460i
$533$	3.97455	+	3.97455i	0.172157	+	0.172157i
$534$	19.3004	+	11.8212i	0.835208	+	0.511552i
$535$	9.95543	−	27.9949i	0.430411	−	1.21033i
$536$			11.4627i			0.495115i
$537$	−6.90342	−	28.7256i	−0.297905	−	1.23960i
$538$	−1.33650	+	1.33650i	−0.0576205	+	0.0576205i
$539$	−52.3606			−2.25533
$540$	−4.73262	+	10.6114i	−0.203660	+	0.456643i
$541$	−3.17281			−0.136410			−0.0682048	−	0.997671i	$-0.521727\pi$
$541$	−3.17281			−0.136410			−0.0682048	+	0.997671i	$0.521727\pi$
$542$	0.302664	−	0.302664i	0.0130005	−	0.0130005i
$543$	5.58046	+	23.2207i	0.239481	+	0.996496i
$544$		−	2.72641i		−	0.116894i
$545$	−15.0465	−	31.6539i	−0.644522	−	1.35590i
$546$	5.03604	+	3.08449i	0.215523	+	0.132004i
$547$	15.3100	+	15.3100i	0.654610	+	0.654610i	0.954100	−	0.299489i	$-0.0968164\pi$
$547$	15.3100	+	15.3100i	0.654610	+	0.654610i	−0.299489	+	0.954100i	$0.596816\pi$
$548$	−6.79419	−	6.79419i	−0.290233	−	0.290233i
$549$	−6.88144	+	3.51026i	−0.293693	+	0.149814i
$550$	−24.8520	+	2.54525i	−1.05969	+	0.108530i
$551$			18.0344i			0.768289i
$552$	−5.61655	+	1.34978i	−0.239056	+	0.0574506i
$553$	17.8566	−	17.8566i	0.759341	−	0.759341i
$554$	1.51128			0.0642080
$555$	−3.28032	+	30.8836i	−0.139242	+	1.31094i
$556$	−1.63608			−0.0693853
$557$	27.0364	−	27.0364i	1.14557	−	1.14557i	0.158153	−	0.987415i	$-0.449446\pi$
$557$	27.0364	−	27.0364i	1.14557	−	1.14557i	0.987415	−	0.158153i	$-0.0505538\pi$
$558$	−0.925735	+	2.85360i	−0.0391895	+	0.120802i
$559$			8.67040i			0.366719i
$560$	−8.80833	−	3.13238i	−0.372220	−	0.132367i
$561$	12.3234	−	20.1203i	0.520293	−	0.849481i
$562$	−2.96539	−	2.96539i	−0.125088	−	0.125088i
$563$	20.1083	+	20.1083i	0.847464	+	0.847464i	0.989816	−	0.142352i	$-0.0454665\pi$
$563$	20.1083	+	20.1083i	0.847464	+	0.847464i	−0.142352	+	0.989816i	$0.545466\pi$
$564$	5.62828	−	9.18927i	0.236993	−	0.386938i
$565$	−20.0119	−	7.11656i	−0.841909	−	0.299396i
$566$			28.7139i			1.20694i
$567$	−37.1591	+	5.92056i	−1.56054	+	0.248640i
$568$	−0.571674	+	0.571674i	−0.0239869	+	0.0239869i
$569$	15.4858			0.649199			0.324600	−	0.945851i	$-0.394770\pi$
$569$	15.4858			0.649199			0.324600	+	0.945851i	$0.394770\pi$
$570$	0.936593	−	8.81785i	0.0392296	−	0.369339i
$571$	−4.91936			−0.205869			−0.102934	−	0.994688i	$-0.532823\pi$
$571$	−4.91936			−0.205869			−0.102934	+	0.994688i	$0.532823\pi$
$572$	−2.88122	+	2.88122i	−0.120470	+	0.120470i
$573$	−35.2736	+	8.47703i	−1.47357	+	0.354133i
$574$		−	28.8161i		−	1.20276i
$575$	−16.5884	+	1.69893i	−0.691785	+	0.0708502i
$576$	−1.36320	−	2.67239i	−0.0568002	−	0.111350i
$577$	26.8827	+	26.8827i	1.11914	+	1.11914i	0.991868	+	0.127272i	$0.0406222\pi$
$577$	26.8827	+	26.8827i	1.11914	+	1.11914i	0.127272	+	0.991868i	$0.459378\pi$
$578$	−6.76468	−	6.76468i	−0.281374	−	0.281374i
$579$	−18.1322	−	11.1057i	−0.753547	−	0.461535i
$580$	7.56143	+	15.9073i	0.313971	+	0.660513i
$581$		−	32.3403i		−	1.34170i
$582$	5.15215	+	21.4385i	0.213564	+	0.888653i
$583$	18.9216	−	18.9216i	0.783651	−	0.783651i
$584$	9.87123			0.408475
$585$	0.709355	+	5.42449i	0.0293282	+	0.224275i
$586$	30.8018			1.27241
$587$	−6.99920	+	6.99920i	−0.288888	+	0.288888i	−0.836640	−	0.547753i	$-0.815484\pi$
$587$	−6.99920	+	6.99920i	−0.288888	+	0.288888i	0.547753	+	0.836640i	$0.315484\pi$
$588$	−4.24141	−	17.6488i	−0.174913	−	0.727826i
$589$		−	2.28957i		−	0.0943399i
$590$	−6.16831	+	17.3455i	−0.253946	+	0.714101i
$591$	−22.6461	−	13.8704i	−0.931537	−	0.570551i
$592$	−5.67026	−	5.67026i	−0.233046	−	0.233046i
$593$	−6.70624	−	6.70624i	−0.275392	−	0.275392i	0.555874	−	0.831266i	$-0.312384\pi$
$593$	−6.70624	−	6.70624i	−0.275392	−	0.275392i	−0.831266	+	0.555874i	$0.812384\pi$
$594$	2.01905	−	25.8834i	0.0828428	−	1.06201i
$595$	23.0200	−	10.9424i	0.943729	−	0.448596i
$596$		−	12.8062i		−	0.524564i
$597$	23.9304	−	5.75101i	0.979405	−	0.235373i
$598$	−1.92318	+	1.92318i	−0.0786448	+	0.0786448i
$599$	−22.2127			−0.907586			−0.453793	−	0.891107i	$-0.649929\pi$
$599$	−22.2127			−0.907586			−0.453793	+	0.891107i	$0.649929\pi$
$600$	−2.87102	−	8.17051i	−0.117209	−	0.333560i
$601$	3.14003			0.128084			0.0640422	−	0.997947i	$-0.479601\pi$
$601$	3.14003			0.128084			0.0640422	+	0.997947i	$0.479601\pi$
$602$	31.4309	−	31.4309i	1.28103	−	1.28103i
$603$	−32.7100	−	10.6115i	−1.33206	−	0.432132i
$604$		−	4.04968i		−	0.164779i
$605$	28.2004	−	13.4049i	1.14651	−	0.544987i
$606$	−14.3255	+	23.3891i	−0.581932	+	0.950119i
$607$	−0.107997	−	0.107997i	−0.00438348	−	0.00438348i	0.704912	−	0.709295i	$-0.250987\pi$
$607$	−0.107997	−	0.107997i	−0.00438348	−	0.00438348i	−0.709295	+	0.704912i	$0.750987\pi$
$608$	1.61897	+	1.61897i	0.0656578	+	0.0656578i
$609$	−29.7918	+	48.6409i	−1.20722	+	1.97103i
$610$	1.92924	−	5.42507i	0.0781127	−	0.219655i
$611$		−	5.07373i		−	0.205261i
$612$	7.78007	+	2.52393i	0.314491	+	0.102024i
$613$	1.98258	−	1.98258i	0.0800755	−	0.0800755i	−0.665935	−	0.746010i	$-0.731967\pi$
$613$	1.98258	−	1.98258i	0.0800755	−	0.0800755i	0.746010	+	0.665935i	$0.231967\pi$
$614$	1.60152			0.0646323
$615$	20.7636	−	16.7763i	0.837270	−	0.676486i
$616$	20.8893			0.841652
$617$	−3.76135	+	3.76135i	−0.151426	+	0.151426i	−0.778755	−	0.627329i	$-0.784148\pi$
$617$	−3.76135	+	3.76135i	−0.151426	+	0.151426i	0.627329	+	0.778755i	$0.284148\pi$
$618$	−25.3910	+	6.10203i	−1.02138	+	0.245460i
$619$		−	31.0020i		−	1.24608i	−0.782191	−	0.623038i	$-0.785898\pi$
$619$		−	31.0020i		−	1.24608i	0.782191	−	0.623038i	$-0.214102\pi$
$620$	−0.959968	−	2.01952i	−0.0385532	−	0.0811059i
$621$	1.34770	−	17.2769i	0.0540813	−	0.693298i
$622$	7.56863	+	7.56863i	0.303475	+	0.303475i
$623$	−38.6304	−	38.6304i	−1.54770	−	1.54770i
$624$	−1.20454	−	0.737763i	−0.0482203	−	0.0295342i
$625$	−5.06766	−	24.4810i	−0.202707	−	0.979240i
$626$		−	14.3884i		−	0.575077i
$627$	4.62991	+	19.2654i	0.184901	+	0.769385i
$628$	−15.9477	+	15.9477i	−0.636384	+	0.636384i
$629$	21.8630			0.871734
$630$	17.0927	−	22.2357i	0.680990	−	0.885890i
$631$	33.0603			1.31611			0.658055	−	0.752970i	$-0.271379\pi$
$631$	33.0603			1.31611			0.658055	+	0.752970i	$0.271379\pi$
$632$	−4.27103	+	4.27103i	−0.169892	+	0.169892i
$633$	−1.44736	−	6.02258i	−0.0575275	−	0.239376i
$634$		−	6.78847i		−	0.269604i
$635$	15.7368	+	5.59625i	0.624496	+	0.222080i
$636$	7.91049	+	4.84505i	0.313671	+	0.192119i
$637$	−6.04321	−	6.04321i	−0.239441	−	0.239441i
$638$	−27.8284	−	27.8284i	−1.10174	−	1.10174i
$639$	−1.10211	−	2.16055i	−0.0435988	−	0.0854699i
$640$	2.10682	+	0.749217i	0.0832792	+	0.0296154i
$641$		−	7.32059i		−	0.289146i	−0.989494	−	0.144573i	$-0.953819\pi$
$641$		−	7.32059i		−	0.289146i	0.989494	−	0.144573i	$-0.0461808\pi$
$642$	−22.3780	+	5.37793i	−0.883188	+	0.212250i
$643$	−13.0557	+	13.0557i	−0.514867	+	0.514867i	−0.916014	−	0.401147i	$-0.868612\pi$
$643$	−13.0557	+	13.0557i	−0.514867	+	0.514867i	0.401147	+	0.916014i	$0.368612\pi$
$644$	13.9434			0.549446
$645$	40.9463	+	4.34913i	1.61226	+	0.171247i
$646$	−6.24229			−0.245600
$647$	−28.1848	+	28.1848i	−1.10806	+	1.10806i	−0.114651	+	0.993406i	$0.536575\pi$
$647$	−28.1848	+	28.1848i	−1.10806	+	1.10806i	−0.993406	+	0.114651i	$0.963425\pi$
$648$	8.88789	−	1.41611i	0.349149	−	0.0556299i
$649$		−	41.1354i		−	1.61470i
$650$	−3.16205	−	2.57453i	−0.124026	−	0.100982i
$651$	3.78224	−	6.17525i	0.148238	−	0.242027i
$652$	7.39856	+	7.39856i	0.289750	+	0.289750i
$653$	−31.2557	−	31.2557i	−1.22313	−	1.22313i	−0.966513	−	0.256617i	$-0.917392\pi$
$653$	−31.2557	−	31.2557i	−1.22313	−	1.22313i	−0.256617	−	0.966513i	$-0.582608\pi$
$654$	−14.1795	+	23.1508i	−0.554463	+	0.905270i
$655$	6.31447	+	13.2840i	0.246727	+	0.519049i
$656$			6.89238i			0.269102i
$657$	−9.13815	+	28.1685i	−0.356513	+	1.09896i
$658$	−18.3927	+	18.3927i	−0.717021	+	0.717021i
$659$	2.80641			0.109322			0.0546611	−	0.998505i	$-0.482592\pi$
$659$	2.80641			0.109322			0.0546611	+	0.998505i	$0.482592\pi$
$660$	12.1614	+	15.0519i	0.473382	+	0.585894i
$661$	45.6312			1.77485			0.887423	−	0.460955i	$-0.152493\pi$
$661$	45.6312			1.77485			0.887423	+	0.460955i	$0.152493\pi$
$662$	1.77561	−	1.77561i	0.0690111	−	0.0690111i
$663$	3.74450	−	0.899887i	0.145424	−	0.0349487i
$664$			7.73529i			0.300188i
$665$	−7.17179	+	20.1672i	−0.278110	+	0.782052i
$666$	21.4298	−	10.9315i	0.830388	−	0.423586i
$667$	−18.5752	−	18.5752i	−0.719235	−	0.719235i
$668$	2.63668	+	2.63668i	0.102016	+	0.102016i
$669$	−17.2375	−	10.5577i	−0.666439	−	0.408183i
$670$	23.1492	−	11.0039i	0.894333	−	0.425116i
$671$			12.8658i			0.496677i
$672$	1.69211	+	7.04101i	0.0652747	+	0.271613i
$673$	−29.8688	+	29.8688i	−1.15136	+	1.15136i	−0.165076	+	0.986281i	$0.552787\pi$
$673$	−29.8688	+	29.8688i	−1.15136	+	1.15136i	−0.986281	+	0.165076i	$0.947213\pi$
$674$	−1.98462			−0.0764449
$675$	25.9731	−	0.628993i	0.999707	−	0.0242099i
$676$	12.3349			0.474420
$677$	−14.3828	+	14.3828i	−0.552775	+	0.552775i	−0.927241	−	0.374466i	$-0.877826\pi$
$677$	−14.3828	+	14.3828i	−0.552775	+	0.552775i	0.374466	+	0.927241i	$0.377826\pi$
$678$	3.84437	+	15.9967i	0.147642	+	0.614350i
$679$		−	53.2222i		−	2.04248i
$680$	−5.50604	+	2.61726i	−0.211147	+	0.100367i
$681$	−8.18099	−	5.01072i	−0.313496	−	0.192011i
$682$	3.53298	+	3.53298i	0.135285	+	0.135285i
$683$	3.20982	+	3.20982i	0.122820	+	0.122820i	0.765845	−	0.643025i	$-0.222321\pi$
$683$	3.20982	+	3.20982i	0.122820	+	0.122820i	−0.643025	+	0.765845i	$0.722321\pi$
$684$	−6.11862	+	3.12115i	−0.233951	+	0.119340i
$685$	−7.19880	+	20.2432i	−0.275052	+	0.773453i
$686$			14.5481i			0.555449i
$687$	7.06870	−	1.69877i	0.269688	−	0.0648120i
$688$	−7.51778	+	7.51778i	−0.286613	+	0.286613i
$689$	4.36767			0.166395
$690$	8.11762	+	10.0470i	0.309032	+	0.382482i
$691$	25.4174			0.966922			0.483461	−	0.875366i	$-0.339379\pi$
$691$	25.4174			0.966922			0.483461	+	0.875366i	$0.339379\pi$
$692$	12.1778	−	12.1778i	0.462931	−	0.462931i
$693$	−19.3379	+	59.6095i	−0.734587	+	2.26438i
$694$		−	4.82101i		−	0.183003i
$695$	1.57058	+	3.30410i	0.0595757	+	0.125332i
$696$	7.12573	−	11.6342i	0.270100	−	0.440992i
$697$	−13.2875	−	13.2875i	−0.503302	−	0.503302i
$698$	5.16028	+	5.16028i	0.195320	+	0.195320i
$699$	−27.2356	+	44.4675i	−1.03015	+	1.68191i
$700$	2.12981	+	20.7956i	0.0804991	+	0.785999i
$701$		−	8.72209i		−	0.329429i	−0.986341	−	0.164714i	$-0.947330\pi$
$701$		−	8.72209i		−	0.329429i	0.986341	−	0.164714i	$-0.0526702\pi$
$702$	3.22037	−	2.75431i	0.121545	−	0.103955i
$703$	−12.9824	+	12.9824i	−0.489642	+	0.489642i
$704$	−4.99639			−0.188309
$705$	−23.9609	−	2.54502i	−0.902419	−	0.0958509i
$706$	−13.2232			−0.497663
$707$	46.8143	−	46.8143i	1.76063	−	1.76063i
$708$	13.8652	−	3.33213i	0.521087	−	0.125229i
$709$			0.835634i			0.0313829i	0.999877	+	0.0156915i	$0.00499495\pi$
$709$			0.835634i			0.0313829i	−0.999877	+	0.0156915i	$0.995005\pi$
$710$	1.70330	+	0.605719i	0.0639236	+	0.0227322i
$711$	−8.23395	−	16.1416i	−0.308797	−	0.605359i
$712$	9.23980	+	9.23980i	0.346276	+	0.346276i
$713$	2.35823	+	2.35823i	0.0883164	+	0.0883164i
$714$	−16.8362	−	10.3119i	−0.630081	−	0.385914i
$715$	8.58455	+	3.05280i	0.321044	+	0.114168i
$716$		−	17.0570i		−	0.637448i
$717$	−3.35137	−	13.9453i	−0.125159	−	0.520797i
$718$	−13.3487	+	13.3487i	−0.498170	+	0.498170i
$719$	48.0542			1.79212			0.896060	−	0.443933i	$-0.146417\pi$
$719$	48.0542			1.79212			0.896060	+	0.443933i	$0.146417\pi$
$720$	−4.08832	+	5.31843i	−0.152363	+	0.198206i
$721$	63.0345			2.34753
$722$	−9.72829	+	9.72829i	−0.362050	+	0.362050i
$723$	3.22560	+	13.4219i	0.119961	+	0.499167i
$724$			13.7882i			0.512434i
$725$	24.8663	−	30.5409i	0.923512	−	1.13426i
$726$	−20.6251	−	12.6325i	−0.765467	−	0.468836i
$727$	−37.9208	−	37.9208i	−1.40641	−	1.40641i	−0.777405	−	0.629001i	$-0.783464\pi$
$727$	−37.9208	−	37.9208i	−1.40641	−	1.40641i	−0.629001	−	0.777405i	$-0.716536\pi$
$728$	2.41094	+	2.41094i	0.0893553	+	0.0893553i
$729$	−4.18684	+	26.6734i	−0.155068	+	0.987904i
$730$	−9.47607	−	19.9352i	−0.350725	−	0.737833i
$731$		−	28.9865i		−	1.07210i
$732$	−4.33658	+	1.04218i	−0.160285	+	0.0385200i
$733$	−4.28209	+	4.28209i	−0.158162	+	0.158162i	−0.781752	−	0.623589i	$-0.785674\pi$
$733$	−4.28209	+	4.28209i	−0.158162	+	0.158162i	0.623589	+	0.781752i	$0.285674\pi$
$734$	2.12186			0.0783192
$735$	−31.5706	+	25.5079i	−1.16450	+	0.940874i
$736$	−3.33504			−0.122931
$737$	−40.4976	+	40.4976i	−1.49175	+	1.49175i
$738$	−19.6681	−	6.38052i	−0.723991	−	0.234870i
$739$			53.9288i			1.98380i	0.127010	+	0.991901i	$0.459462\pi$
$739$			53.9288i			1.98380i	−0.127010	+	0.991901i	$0.540538\pi$
$740$	−6.00794	+	16.8945i	−0.220856	+	0.621054i
$741$	−1.68916	+	2.75788i	−0.0620527	+	0.101313i
$742$	−15.8332	−	15.8332i	−0.581253	−	0.581253i
$743$	−2.06424	−	2.06424i	−0.0757295	−	0.0757295i	0.668227	−	0.743957i	$-0.267053\pi$
$743$	−2.06424	−	2.06424i	−0.0757295	−	0.0757295i	−0.743957	+	0.668227i	$0.767053\pi$
$744$	−0.904654	+	1.47702i	−0.0331662	+	0.0541504i
$745$	−25.8624	+	12.2936i	−0.947527	+	0.450401i
$746$		−	0.953286i		−	0.0349023i
$747$	−22.0734	−	7.16084i	−0.807624	−	0.262001i
$748$	9.63235	−	9.63235i	0.352194	−	0.352194i
$749$	55.5545			2.02992
$750$	−13.7444	+	13.6415i	−0.501876	+	0.498117i
$751$	−9.57235			−0.349300			−0.174650	−	0.984631i	$-0.555879\pi$
$751$	−9.57235			−0.349300			−0.174650	+	0.984631i	$0.555879\pi$
$752$	4.39924	−	4.39924i	0.160424	−	0.160424i
$753$	4.65089	−	1.11771i	0.169488	−	0.0407318i
$754$		−	6.42365i		−	0.233935i
$755$	−8.17841	+	3.88756i	−0.297643	+	0.141483i
$756$	−21.6586	−	1.68950i	−0.787717	−	0.0614466i
$757$	34.0638	+	34.0638i	1.23807	+	1.23807i	0.960788	+	0.277283i	$0.0894340\pi$
$757$	34.0638	+	34.0638i	1.23807	+	1.23807i	0.277283	+	0.960788i	$0.410566\pi$
$758$	−3.83561	−	3.83561i	−0.139316	−	0.139316i
$759$	−24.6119	−	15.0744i	−0.893356	−	0.547166i
$760$	1.71538	−	4.82370i	0.0622234	−	0.174974i
$761$		−	33.3780i		−	1.20995i	−0.796244	−	0.604976i	$-0.793183\pi$
$761$		−	33.3780i		−	1.20995i	0.796244	−	0.604976i	$-0.206817\pi$
$762$	−3.02310	−	12.5793i	−0.109515	−	0.455701i
$763$	46.3373	−	46.3373i	1.67752	−	1.67752i
$764$	−20.9450			−0.757765
$765$	−2.37148	−	18.1349i	−0.0857411	−	0.655669i
$766$	7.75257			0.280112
$767$	4.74765	−	4.74765i	0.171428	−	0.171428i
$768$	−0.404727	−	1.68410i	−0.0146043	−	0.0607698i
$769$			20.8747i			0.752762i	0.926465	+	0.376381i	$0.122832\pi$
$769$			20.8747i			0.752762i	−0.926465	+	0.376381i	$0.877168\pi$
$770$	−20.0530	−	42.1863i	−0.722661	−	1.52029i
$771$	20.5701	+	12.5989i	0.740815	+	0.453737i
$772$	−8.68054	−	8.68054i	−0.312419	−	0.312419i
$773$	−17.7160	−	17.7160i	−0.637200	−	0.637200i	0.312663	−	0.949864i	$-0.398779\pi$
$773$	−17.7160	−	17.7160i	−0.637200	−	0.637200i	−0.949864	+	0.312663i	$0.898779\pi$
$774$	−14.4932	−	28.4122i	−0.520949	−	1.02126i
$775$	−3.15692	+	3.87735i	−0.113400	+	0.139278i
$776$			12.7299i			0.456978i
$777$	−56.4616	+	13.5690i	−2.02555	+	0.486785i
$778$	−23.2733	+	23.2733i	−0.834387	+	0.834387i
$779$	15.7806			0.565397
$780$	−0.333605	+	3.14083i	−0.0119450	+	0.112460i
$781$	−4.03943			−0.144542
$782$	6.42950	−	6.42950i	0.229918	−	0.229918i
$783$	26.6027	+	31.1041i	0.950701	+	1.11157i
$784$		−	10.4797i		−	0.374274i
$785$	47.5161	+	16.8975i	1.69592	+	0.603097i
$786$	5.95063	−	9.71557i	0.212252	−	0.346543i
$787$	−0.361367	−	0.361367i	−0.0128813	−	0.0128813i	0.700637	−	0.713518i	$-0.252899\pi$
$787$	−0.361367	−	0.361367i	−0.0128813	−	0.0128813i	−0.713518	+	0.700637i	$0.752899\pi$
$788$	−10.8415	−	10.8415i	−0.386214	−	0.386214i
$789$	19.2389	−	31.4112i	0.684922	−	1.11827i
$790$	12.7255	+	4.52538i	0.452752	+	0.161006i
$791$		−	39.7127i		−	1.41202i
$792$	4.62534	−	14.2577i	0.164354	−	0.506625i
$793$	−1.48490	+	1.48490i	−0.0527305	+	0.0527305i
$794$	11.5578			0.410173
$795$	2.19085	−	20.6265i	0.0777016	−	0.731546i
$796$	14.2096			0.503645
$797$	−22.9014	+	22.9014i	−0.811210	+	0.811210i	−0.984815	−	0.173605i	$-0.944458\pi$
$797$	−22.9014	+	22.9014i	−0.811210	+	0.811210i	0.173605	+	0.984815i	$0.444458\pi$
$798$	16.1209	−	3.87421i	0.570672	−	0.137145i
$799$			16.9623i			0.600082i
$800$	−0.509417	−	4.97398i	−0.0180106	−	0.175857i
$801$	−34.9203	+	17.8131i	−1.23385	+	0.629394i
$802$	−13.1877	−	13.1877i	−0.465675	−	0.465675i
$803$	34.8749	+	34.8749i	1.23071	+	1.23071i
$804$	−16.9307	−	10.3698i	−0.597101	−	0.365715i
$805$	−13.3852	−	28.1589i	−0.471766	−	0.992472i
$806$			0.815520i			0.0287255i
$807$	−0.764972	−	3.18310i	−0.0269283	−	0.112051i
$808$	−11.1973	+	11.1973i	−0.393918	+	0.393918i
$809$	−22.4949			−0.790878			−0.395439	−	0.918492i	$-0.629408\pi$
$809$	−22.4949			−0.790878			−0.395439	+	0.918492i	$0.629408\pi$
$810$	−11.3919	−	16.5899i	−0.400272	−	0.582908i
$811$	−10.7028			−0.375827			−0.187913	−	0.982186i	$-0.560172\pi$
$811$	−10.7028			−0.375827			−0.187913	+	0.982186i	$0.560172\pi$
$812$	−23.2862	+	23.2862i	−0.817186	+	0.817186i
$813$	0.173236	+	0.720848i	0.00607566	+	0.0252812i
$814$		−	40.0659i		−	1.40431i
$815$	7.83917	−	22.0439i	0.274594	−	0.772165i
$816$	4.02697	+	2.46645i	0.140972	+	0.0863432i
$817$	17.2125	+	17.2125i	0.602188	+	0.602188i
$818$	−22.3007	−	22.3007i	−0.779725	−	0.779725i
$819$	−9.11174	+	4.64796i	−0.318390	+	0.162413i
$820$	13.9193	−	6.61646i	0.486083	−	0.231057i
$821$		−	13.9115i		−	0.485513i	−0.970087	−	0.242757i	$-0.921948\pi$
$821$		−	13.9115i		−	0.485513i	0.970087	−	0.242757i	$-0.0780517\pi$
$822$	16.1816	−	3.88880i	0.564397	−	0.135637i
$823$	−32.6557	+	32.6557i	−1.13831	+	1.13831i	−0.149554	+	0.988754i	$0.547784\pi$
$823$	−32.6557	+	32.6557i	−1.13831	+	1.13831i	−0.988754	+	0.149554i	$0.952216\pi$
$824$	−15.0769			−0.525228
$825$	18.7230	−	39.0095i	0.651852	−	1.35814i
$826$	−34.4212			−1.19767
$827$	4.27320	−	4.27320i	0.148594	−	0.148594i	−0.628896	−	0.777490i	$-0.716493\pi$
$827$	4.27320	−	4.27320i	0.148594	−	0.148594i	0.777490	+	0.628896i	$0.216493\pi$
$828$	3.08737	−	9.51686i	0.107293	−	0.330734i
$829$		−	35.5611i		−	1.23509i	−0.786536	−	0.617544i	$-0.788128\pi$
$829$		−	35.5611i		−	1.23509i	0.786536	−	0.617544i	$-0.211872\pi$
$830$	15.6216	−	7.42563i	0.542233	−	0.257747i
$831$	−1.36718	+	2.23219i	−0.0474270	+	0.0774339i
$832$	−0.576660	−	0.576660i	−0.0199921	−	0.0199921i
$833$	20.2034	+	20.2034i	0.700005	+	0.700005i
$834$	1.48009	−	2.41653i	0.0512512	−	0.0836776i
$835$	2.79370	−	7.85595i	0.0966799	−	0.271866i
$836$			11.4396i			0.395646i
$837$	−3.37736	−	3.94885i	−0.116739	−	0.136492i
$838$	1.49674	−	1.49674i	0.0517040	−	0.0517040i
$839$	21.6006			0.745734			0.372867	−	0.927885i	$-0.378375\pi$
$839$	21.6006			0.745734			0.372867	+	0.927885i	$0.378375\pi$
$840$	12.5951	−	10.1764i	0.434572	−	0.351119i
$841$	33.0433			1.13942
$842$	7.26575	−	7.26575i	0.250394	−	0.250394i
$843$	7.06262	−	1.69731i	0.243249	−	0.0584583i
$844$		−	3.57614i		−	0.123096i
$845$	−11.8411	−	24.9106i	−0.407347	−	0.856952i
$846$	8.48113	+	16.6262i	0.291587	+	0.571621i
$847$	41.2818	+	41.2818i	1.41846	+	1.41846i
$848$	3.78705	+	3.78705i	0.130048	+	0.130048i
$849$	−42.4111	−	25.9761i	−1.45555	−	0.891499i
$850$	10.5712	+	8.60706i	0.362590	+	0.295220i
$851$		−	26.7436i		−	0.916758i
$852$	−0.327210	−	1.36154i	−0.0112100	−	0.0466458i
$853$	11.1150	−	11.1150i	0.380570	−	0.380570i	−0.490737	−	0.871308i	$-0.663273\pi$
$853$	11.1150	−	11.1150i	0.380570	−	0.380570i	0.871308	+	0.490737i	$0.163273\pi$
$854$	10.7658			0.368398
$855$	12.1769	+	9.36047i	0.416441	+	0.320121i
$856$	−13.2878			−0.454167
$857$	14.3136	−	14.3136i	0.488944	−	0.488944i	−0.419029	−	0.907973i	$-0.637629\pi$
$857$	14.3136	−	14.3136i	0.488944	−	0.488944i	0.907973	+	0.419029i	$0.137629\pi$
$858$	−1.64912	−	6.86213i	−0.0563002	−	0.234269i
$859$		−	6.23636i		−	0.212782i	−0.994324	−	0.106391i	$-0.966071\pi$
$859$		−	6.23636i		−	0.212782i	0.994324	−	0.106391i	$-0.0339295\pi$
$860$	22.3991	+	7.96548i	0.763804	+	0.271621i
$861$	42.5621	+	26.0686i	1.45051	+	0.888416i
$862$	−6.17676	−	6.17676i	−0.210381	−	0.210381i
$863$	−11.6148	−	11.6148i	−0.395374	−	0.395374i	0.481224	−	0.876598i	$-0.340192\pi$
$863$	−11.6148	−	11.6148i	−0.395374	−	0.395374i	−0.876598	+	0.481224i	$0.840192\pi$
$864$	5.18042	+	0.404103i	0.176241	+	0.0137479i
$865$	−36.2836	−	12.9030i	−1.23368	−	0.438716i
$866$			19.3252i			0.656696i
$867$	16.1113	−	3.87191i	0.547168	−	0.131497i
$868$	2.95632	−	2.95632i	0.100344	−	0.100344i
$869$	−30.1789			−1.02375
$870$	−30.3359	−	3.22215i	−1.02848	−	0.109241i
$871$	−9.34809			−0.316748
$872$	−11.0832	+	11.0832i	−0.375324	+	0.375324i
$873$	−36.3261	−	11.7845i	−1.22945	−	0.398846i
$874$			7.63580i			0.258285i
$875$	39.9525	−	24.2643i	1.35064	−	0.820282i
$876$	−8.93005	+	14.5801i	−0.301718	+	0.492614i
$877$	−11.3836	−	11.3836i	−0.384397	−	0.384397i	0.488286	−	0.872683i	$-0.337622\pi$
$877$	−11.3836	−	11.3836i	−0.384397	−	0.384397i	−0.872683	+	0.488286i	$0.837622\pi$
$878$	17.9145	+	17.9145i	0.604584	+	0.604584i
$879$	−27.8649	+	45.4950i	−0.939861	+	1.53451i
$880$	4.79637	+	10.0903i	0.161686	+	0.340144i
$881$		−	54.8586i		−	1.84823i	−0.382112	−	0.924116i	$-0.624803\pi$
$881$		−	54.8586i		−	1.84823i	0.382112	−	0.924116i	$-0.375197\pi$
$882$	29.9048	+	9.70141i	1.00695	+	0.326663i
$883$	36.7348	−	36.7348i	1.23622	−	1.23622i	0.274693	−	0.961532i	$-0.411424\pi$
$883$	36.7348	−	36.7348i	1.23622	−	1.23622i	0.961532	−	0.274693i	$-0.0885761\pi$
$884$	2.22344			0.0747824
$885$	−20.0395	−	24.8024i	−0.673620	−	0.833723i
$886$	−21.5268			−0.723207
$887$	−21.7550	+	21.7550i	−0.730462	+	0.730462i	−0.970711	−	0.240249i	$-0.922771\pi$
$887$	−21.7550	+	21.7550i	−0.730462	+	0.730462i	0.240249	+	0.970711i	$0.422771\pi$
$888$	13.5047	−	3.24550i	0.453190	−	0.108912i
$889$			31.2289i			1.04738i
$890$	9.79006	−	27.5299i	0.328163	−	0.922804i
$891$	36.4038	+	26.3977i	1.21957	+	0.884356i
$892$	−8.25222	−	8.25222i	−0.276305	−	0.276305i
$893$	−10.0724	−	10.0724i	−0.337059	−	0.337059i
$894$	18.9151	+	11.5852i	0.632616	+	0.387467i
$895$	−34.4469	+	16.3741i	−1.15143	+	0.547327i
$896$			4.18087i			0.139673i
$897$	−1.10077	−	4.58040i	−0.0367538	−	0.152935i
$898$	−26.1667	+	26.1667i	−0.873195	+	0.873195i
$899$	−7.87675			−0.262704
$900$	14.6653	+	3.15092i	0.488844	+	0.105031i
$901$	−14.6018			−0.486457
$902$	−24.3506	+	24.3506i	−0.810788	+	0.810788i
$903$	17.9901	+	74.8582i	0.598674	+	2.49113i
$904$			9.49866i			0.315921i
$905$	27.8455	−	13.2362i	0.925617	−	0.439987i
$906$	5.98148	+	3.66356i	0.198721	+	0.121714i
$907$	−13.1411	−	13.1411i	−0.436344	−	0.436344i	0.454436	−	0.890780i	$-0.349841\pi$
$907$	−13.1411	−	13.1411i	−0.436344	−	0.436344i	−0.890780	+	0.454436i	$0.849841\pi$
$908$	−3.91654	−	3.91654i	−0.129975	−	0.129975i
$909$	−21.5868	−	42.3181i	−0.715987	−	1.40360i
$910$	2.55452	−	7.18336i	0.0846814	−	0.238126i
$911$		−	14.0057i		−	0.464029i	−0.972712	−	0.232014i	$-0.925468\pi$
$911$		−	14.0057i		−	0.464029i	0.972712	−	0.232014i	$-0.0745317\pi$
$912$	−3.85586	+	0.926650i	−0.127680	+	0.0306845i
$913$	−27.3287	+	27.3287i	−0.904446	+	0.904446i
$914$	−39.4498			−1.30488
$915$	6.26767	+	7.75735i	0.207203	+	0.256450i
$916$	4.19731			0.138683
$917$	−19.4461	+	19.4461i	−0.642166	+	0.642166i
$918$	−10.7662	+	9.20807i	−0.355337	+	0.303912i
$919$			20.4283i			0.673866i	0.941529	+	0.336933i	$0.109390\pi$
$919$			20.4283i			0.673866i	−0.941529	+	0.336933i	$0.890610\pi$
$920$	3.20153	+	6.73518i	0.105551	+	0.222052i
$921$	−1.44883	+	2.36549i	−0.0477404	+	0.0779456i
$922$	−20.7288	−	20.7288i	−0.682668	−	0.682668i
$923$	−0.466212	−	0.466212i	−0.0153455	−	0.0153455i
$924$	−18.8975	+	30.8540i	−0.621684	+	1.01502i
$925$	39.8862	−	4.08500i	1.31145	−	0.134314i
$926$		−	13.9347i		−	0.457922i
$927$	13.9572	−	43.0234i	0.458415	−	1.41307i
$928$	5.56971	−	5.56971i	0.182835	−	0.182835i
$929$	0.520712			0.0170840			0.00854200	−	0.999964i	$-0.497281\pi$
$929$	0.520712			0.0170840			0.00854200	+	0.999964i	$0.497281\pi$
$930$	3.85132	+	0.409070i	0.126290	+	0.0134139i
$931$	−23.9939			−0.786369
$932$	−21.2882	+	21.2882i	−0.697320	+	0.697320i
$933$	−18.0261	+	4.33207i	−0.590146	+	0.141826i
$934$		−	2.30542i		−	0.0754357i
$935$	−28.6995	−	10.2060i	−0.938573	−	0.333771i
$936$	2.17939	−	1.11172i	0.0712355	−	0.0363377i
$937$	19.5964	+	19.5964i	0.640186	+	0.640186i	0.950601	−	0.310415i	$-0.100468\pi$
$937$	19.5964	+	19.5964i	0.640186	+	0.640186i	−0.310415	+	0.950601i	$0.600468\pi$
$938$	33.8875	+	33.8875i	1.10647	+	1.10647i
$939$	21.2521	+	13.0165i	0.693535	+	0.424779i
$940$	−13.1075	−	4.66123i	−0.427519	−	0.152033i
$941$		−	30.2185i		−	0.985094i	−0.870286	−	0.492547i	$-0.836066\pi$
$941$		−	30.2185i		−	0.985094i	0.870286	−	0.492547i	$-0.163934\pi$
$942$	−9.12803	−	37.9824i	−0.297407	−	1.23753i
$943$	−16.2538	+	16.2538i	−0.529297	+	0.529297i
$944$	8.23302			0.267962
$945$	17.3796	+	45.3619i	0.565359	+	1.47562i
$946$	−53.1204			−1.72709
$947$	−27.3560	+	27.3560i	−0.888951	+	0.888951i	−0.994422	−	0.105471i	$-0.966365\pi$
$947$	−27.3560	+	27.3560i	−0.888951	+	0.888951i	0.105471	+	0.994422i	$0.466365\pi$
$948$	−2.44461	−	10.1722i	−0.0793974	−	0.330378i
$949$			8.05019i			0.261320i
$950$	−11.3883	+	1.16634i	−0.369484	+	0.0378412i
$951$	10.0267	+	6.14121i	0.325139	+	0.199142i
$952$	−8.06014	−	8.06014i	−0.261231	−	0.261231i
$953$	−14.6735	−	14.6735i	−0.475322	−	0.475322i	0.428310	−	0.903632i	$-0.359109\pi$
$953$	−14.6735	−	14.6735i	−0.475322	−	0.475322i	−0.903632	+	0.428310i	$0.859109\pi$
$954$	−14.3125	+	7.30090i	−0.463385	+	0.236375i
$955$	20.1066	+	42.2989i	0.650633	+	1.36876i
$956$		−	8.28057i		−	0.267813i
$957$	66.2784	−	15.9282i	2.14248	−	0.514885i
$958$	13.1767	−	13.1767i	0.425721	−	0.425721i
$959$	−40.1716			−1.29721
$960$	−3.01255	+	2.43404i	−0.0972296	+	0.0785582i
$961$	1.00000			0.0322581
$962$	4.62421	−	4.62421i	0.149091	−	0.149091i
$963$	12.3010	−	37.9180i	0.396393	−	1.22189i
$964$			7.96980i			0.256690i
$965$	−9.19749	+	25.8636i	−0.296078	+	0.832577i
$966$	−12.6139	+	20.5947i	−0.405846	+	0.662624i
$967$	−40.3911	−	40.3911i	−1.29889	−	1.29889i	−0.929125	−	0.369767i	$-0.879438\pi$
$967$	−40.3911	−	40.3911i	−1.29889	−	1.29889i	−0.369767	−	0.929125i	$-0.620562\pi$
$968$	−9.87398	−	9.87398i	−0.317362	−	0.317362i
$969$	5.64711	−	9.22002i	0.181411	−	0.296190i
$970$	25.7083	−	12.2203i	0.825445	−	0.392371i
$971$			15.8339i			0.508134i	0.967187	+	0.254067i	$0.0817684\pi$
$971$			15.8339i			0.508134i	−0.967187	+	0.254067i	$0.918232\pi$
$972$	−5.94884	+	14.4087i	−0.190809	+	0.462160i
$973$	−4.83678	+	4.83678i	−0.155060	+	0.155060i
$974$	23.4333			0.750852
$975$	6.66321	−	2.34137i	0.213394	−	0.0749839i
$976$	−2.57501			−0.0824241
$977$	−22.7765	+	22.7765i	−0.728685	+	0.728685i	−0.970358	−	0.241673i	$-0.922304\pi$
$977$	−22.7765	+	22.7765i	−0.728685	+	0.728685i	0.241673	+	0.970358i	$0.422304\pi$
$978$	−17.6210	+	4.23472i	−0.563457	+	0.135412i
$979$			65.2881i			2.08662i
$980$	−21.1639	+	10.0602i	−0.676057	+	0.321360i
$981$	−21.3668	−	41.8870i	−0.682190	−	1.33735i
$982$	3.81726	+	3.81726i	0.121814	+	0.121814i
$983$	−12.0930	−	12.0930i	−0.385706	−	0.385706i	0.487447	−	0.873153i	$-0.337928\pi$
$983$	−12.0930	−	12.0930i	−0.385706	−	0.385706i	−0.873153	+	0.487447i	$0.837928\pi$
$984$	−10.1802	−	6.23521i	−0.324533	−	0.198771i
$985$	−11.4872	+	32.3023i	−0.366012	+	1.02924i
$986$			21.4752i			0.683911i
$987$	−10.5274	−	43.8054i	−0.335092	−	1.39434i
$988$	−1.32030	+	1.32030i	−0.0420043	+	0.0420043i
$989$	−35.4573			−1.12748
$990$	−33.2339	+	4.34596i	−1.05624	+	0.138124i
$991$	21.8197			0.693127			0.346563	−	0.938027i	$-0.387349\pi$
$991$	21.8197			0.693127			0.346563	+	0.938027i	$0.387349\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	1.01631	+	4.22894i	0.0322516	+	0.134201i
$994$			3.38011i			0.107211i
$995$	−13.6407	−	28.6965i	−0.432441	−	0.909741i
$996$	−11.4252	−	6.99776i	−0.362022	−	0.221733i
$997$	8.43753	+	8.43753i	0.267219	+	0.267219i	0.827979	−	0.560759i	$-0.189491\pi$
$997$	8.43753	+	8.43753i	0.267219	+	0.267219i	−0.560759	+	0.827979i	$0.689491\pi$
$998$	21.4415	+	21.4415i	0.678719	+	0.678719i
$999$	−3.24049	+	41.5416i	−0.102524	+	1.31432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.5	✓	40
3.2	odd	2	inner	930.2.j.h.497.19	yes	40
5.3	odd	4	inner	930.2.j.h.683.19	yes	40
15.8	even	4	inner	930.2.j.h.683.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.5	✓	40	1.1	even	1	trivial
930.2.j.h.497.19	yes	40	3.2	odd	2	inner
930.2.j.h.683.5	yes	40	15.8	even	4	inner
930.2.j.h.683.19	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.404727 - 1.68410i) q^{3} -1.00000i q^{4} +(-2.01952 + 0.959968i) q^{5} +(1.47702 + 0.904654i) q^{6} +(-2.95632 - 2.95632i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.67239 + 1.36320i) q^{9} +(0.749217 - 2.10682i) q^{10} +4.99639i q^{11} +(-1.68410 + 0.404727i) q^{12} +(-0.576660 + 0.576660i) q^{13} +4.18087 q^{14} +(2.43404 + 3.01255i) q^{15} -1.00000 q^{16} +(1.92786 - 1.92786i) q^{17} +(0.925735 - 2.85360i) q^{18} +2.28957i q^{19} +(0.959968 + 2.01952i) q^{20} +(-3.78224 + 6.17525i) q^{21} +(-3.53298 - 3.53298i) q^{22} +(-2.35823 - 2.35823i) q^{23} +(0.904654 - 1.47702i) q^{24} +(3.15692 - 3.87735i) q^{25} -0.815520i q^{26} +(3.37736 + 3.94885i) q^{27} +(-2.95632 + 2.95632i) q^{28} +7.87675 q^{29} +(-3.85132 - 0.409070i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(8.41443 - 2.02218i) q^{33} +2.72641i q^{34} +(8.80833 + 3.13238i) q^{35} +(1.36320 + 2.67239i) q^{36} +(5.67026 + 5.67026i) q^{37} +(-1.61897 - 1.61897i) q^{38} +(1.20454 + 0.737763i) q^{39} +(-2.10682 - 0.749217i) q^{40} -6.89238i q^{41} +(-1.69211 - 7.04101i) q^{42} +(7.51778 - 7.51778i) q^{43} +4.99639 q^{44} +(4.08832 - 5.31843i) q^{45} +3.33504 q^{46} +(-4.39924 + 4.39924i) q^{47} +(0.404727 + 1.68410i) q^{48} +10.4797i q^{49} +(0.509417 + 4.97398i) q^{50} +(-4.02697 - 2.46645i) q^{51} +(0.576660 + 0.576660i) q^{52} +(-3.78705 - 3.78705i) q^{53} +(-5.18042 - 0.404103i) q^{54} +(-4.79637 - 10.0903i) q^{55} -4.18087i q^{56} +(3.85586 - 0.926650i) q^{57} +(-5.56971 + 5.56971i) q^{58} -8.23302 q^{59} +(3.01255 - 2.43404i) q^{60} +2.57501 q^{61} +(0.707107 - 0.707107i) q^{62} +(11.9305 + 3.87038i) q^{63} +1.00000i q^{64} +(0.611001 - 1.71815i) q^{65} +(-4.52000 + 7.37979i) q^{66} +(8.10538 + 8.10538i) q^{67} +(-1.92786 - 1.92786i) q^{68} +(-3.01706 + 4.92594i) q^{69} +(-8.44335 + 4.01350i) q^{70} +0.808470i q^{71} +(-2.85360 - 0.925735i) q^{72} +(6.98002 - 6.98002i) q^{73} -8.01896 q^{74} +(-7.80754 - 3.74731i) q^{75} +2.28957 q^{76} +(14.7709 - 14.7709i) q^{77} +(-1.37342 + 0.330063i) q^{78} +6.04015i q^{79} +(2.01952 - 0.959968i) q^{80} +(5.28335 - 7.28603i) q^{81} +(4.87365 + 4.87365i) q^{82} +(5.46968 + 5.46968i) q^{83} +(6.17525 + 3.78224i) q^{84} +(-2.04267 + 5.74404i) q^{85} +10.6317i q^{86} +(-3.18794 - 13.2652i) q^{87} +(-3.53298 + 3.53298i) q^{88} +13.0671 q^{89} +(0.869819 + 6.65157i) q^{90} +3.40958 q^{91} +(-2.35823 + 2.35823i) q^{92} +(0.404727 + 1.68410i) q^{93} -6.22147i q^{94} +(-2.19791 - 4.62383i) q^{95} +(-1.47702 - 0.904654i) q^{96} +(9.00142 + 9.00142i) q^{97} +(-7.41025 - 7.41025i) q^{98} +(-6.81110 - 13.3523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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