LMFDB - Embedded newform 930.2.j.h.683.19

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			683.19
Character	$\chi$	$=$	930.683
Dual form			930.2.j.h.497.19

$q$-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} +(1.68410 - 0.404727i) 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} +(0.404727 + 1.68410i) q^{12} +(-0.576660 - 0.576660i) q^{13} -4.18087 q^{14} +(3.78960 + 0.799327i) q^{15} -1.00000 q^{16} +(-1.92786 - 1.92786i) q^{17} +(2.85360 + 0.925735i) 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} +(3.94885 - 3.37736i) q^{27} +(-2.95632 - 2.95632i) q^{28} -7.87675 q^{29} +(2.11444 + 3.24486i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.02218 + 8.41443i) 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} +(-7.04101 + 1.69211i) q^{42} +(7.51778 + 7.51778i) q^{43} -4.99639 q^{44} +(6.70558 - 0.187608i) q^{45} +3.33504 q^{46} +(4.39924 + 4.39924i) q^{47} +(-1.68410 + 0.404727i) 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} +(-0.926650 - 3.85586i) q^{57} +(-5.56971 - 5.56971i) q^{58} +8.23302 q^{59} +(-0.799327 + 3.78960i) q^{60} +2.57501 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-3.87038 + 11.9305i) 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} +(-0.925735 + 2.85360i) q^{72} +(6.98002 + 6.98002i) q^{73} +8.01896 q^{74} +(6.88585 + 5.25215i) q^{75} +2.28957 q^{76} +(-14.7709 - 14.7709i) q^{77} +(-0.330063 - 1.37342i) 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} +(-13.2652 + 3.18794i) q^{87} +(-3.53298 - 3.53298i) q^{88} -13.0671 q^{89} +(4.87422 + 4.60890i) q^{90} +3.40958 q^{91} +(2.35823 + 2.35823i) q^{92} +(-1.68410 + 0.404727i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	1.68410	−	0.404727i	0.972316	−	0.233670i
$3$	1.68410	−	0.404727i	0.972316	−	0.233670i
$4$			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	−0.125261	+	0.992124i	$0.539977\pi$
$7$	−2.95632	+	2.95632i	−1.11738	+	1.11738i	−0.992124	+	0.125261i	$0.960023\pi$
$8$	−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	$0.728493\pi$
$12$	0.404727	+	1.68410i	0.116835	+	0.486158i
$13$	−0.576660	−	0.576660i	−0.159937	−	0.159937i	0.622602	−	0.782539i	$-0.286076\pi$
$13$	−0.576660	−	0.576660i	−0.159937	−	0.159937i	−0.782539	+	0.622602i	$0.786076\pi$
$14$	−4.18087			−1.11738
$15$	3.78960	+	0.799327i	0.978471	+	0.206385i
$16$	−1.00000			−0.250000
$17$	−1.92786	−	1.92786i	−0.467575	−	0.467575i	0.433553	−	0.901128i	$-0.357260\pi$
$17$	−1.92786	−	1.92786i	−0.467575	−	0.467575i	−0.901128	+	0.433553i	$0.857260\pi$
$18$	2.85360	+	0.925735i	0.672599	+	0.218198i
$19$		−	2.28957i		−	0.525263i	−0.964896	−	0.262631i	$-0.915410\pi$
$19$		−	2.28957i		−	0.525263i	0.964896	−	0.262631i	$-0.0845903\pi$
$20$	−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	$-0.636962\pi$
$23$	2.35823	−	2.35823i	0.491725	−	0.491725i	0.908849	+	0.417124i	$0.136962\pi$
$24$	−0.904654	+	1.47702i	−0.184662	+	0.301496i
$25$	3.15692	+	3.87735i	0.631385	+	0.775470i
$26$		−	0.815520i		−	0.159937i
$27$	3.94885	−	3.37736i	0.759957	−	0.649974i
$28$	−2.95632	−	2.95632i	−0.558692	−	0.558692i
$29$	−7.87675			−1.46268			−0.731338	−	0.682015i	$-0.761104\pi$
$29$	−7.87675			−1.46268			−0.731338	+	0.682015i	$0.761104\pi$
$30$	2.11444	+	3.24486i	0.386043	+	0.592428i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.02218	+	8.41443i	0.352016	+	1.46476i
$34$		−	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	−0.0656566	−	0.997842i	$-0.520914\pi$
$37$	5.67026	−	5.67026i	0.932186	−	0.932186i	0.997842	+	0.0656566i	$0.0209142\pi$
$38$	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	$-0.180897\pi$
$42$	−7.04101	+	1.69211i	−1.08645	+	0.261099i
$43$	7.51778	+	7.51778i	1.14645	+	1.14645i	0.987245	+	0.159205i	$0.0508932\pi$
$43$	7.51778	+	7.51778i	1.14645	+	1.14645i	0.159205	+	0.987245i	$0.449107\pi$
$44$	−4.99639			−0.753234
$45$	6.70558	−	0.187608i	0.999609	−	0.0279670i
$46$	3.33504			0.491725
$47$	4.39924	+	4.39924i	0.641696	+	0.641696i	0.950972	−	0.309276i	$-0.100087\pi$
$47$	4.39924	+	4.39924i	0.641696	+	0.641696i	−0.309276	+	0.950972i	$0.600087\pi$
$48$	−1.68410	+	0.404727i	−0.243079	+	0.0584174i
$49$		−	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	$-0.630101\pi$
$53$	3.78705	−	3.78705i	0.520191	−	0.520191i	0.917629	+	0.397438i	$0.130101\pi$
$54$	5.18042	+	0.404103i	0.704965	+	0.0549914i
$55$	−4.79637	+	10.0903i	−0.646743	+	1.36058i
$56$		−	4.18087i		−	0.558692i
$57$	−0.926650	−	3.85586i	−0.122738	−	0.510721i
$58$	−5.56971	−	5.56971i	−0.731338	−	0.731338i
$59$	8.23302			1.07185			0.535924	−	0.844266i	$-0.319963\pi$
$59$	8.23302			1.07185			0.535924	+	0.844266i	$0.319963\pi$
$60$	−0.799327	+	3.78960i	−0.103193	+	0.489235i
$61$	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
$63$	−3.87038	+	11.9305i	−0.487622	+	1.50310i
$64$		−	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	−0.00972284	−	0.999953i	$-0.503095\pi$
$67$	8.10538	−	8.10538i	0.990230	−	0.990230i	0.999953	+	0.00972284i	$0.00309492\pi$
$68$	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	$0.984724\pi$
$72$	−0.925735	+	2.85360i	−0.109099	+	0.336300i
$73$	6.98002	+	6.98002i	0.816949	+	0.816949i	0.985665	−	0.168716i	$-0.0539620\pi$
$73$	6.98002	+	6.98002i	0.816949	+	0.816949i	−0.168716	+	0.985665i	$0.553962\pi$
$74$	8.01896			0.932186
$75$	6.88585	+	5.25215i	0.795109	+	0.606466i
$76$	2.28957			0.262631
$77$	−14.7709	−	14.7709i	−1.68330	−	1.68330i
$78$	−0.330063	−	1.37342i	−0.0373723	−	0.155509i
$79$		−	6.04015i		−	0.679570i	−0.940503	−	0.339785i	$-0.889646\pi$
$79$		−	6.04015i		−	0.679570i	0.940503	−	0.339785i	$-0.110354\pi$
$80$	−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	$-0.889560\pi$
$83$	−5.46968	+	5.46968i	−0.600375	+	0.600375i	0.340037	+	0.940412i	$0.389560\pi$
$84$	−6.17525	−	3.78224i	−0.673775	−	0.412676i
$85$	−2.04267	−	5.74404i	−0.221559	−	0.623029i
$86$			10.6317i			1.14645i
$87$	−13.2652	+	3.18794i	−1.42218	+	0.341783i
$88$	−3.53298	−	3.53298i	−0.376617	−	0.376617i
$89$	−13.0671			−1.38511			−0.692553	−	0.721367i	$-0.743514\pi$
$89$	−13.0671			−1.38511			−0.692553	+	0.721367i	$0.743514\pi$
$90$	4.87422	+	4.60890i	0.513788	+	0.485821i
$91$	3.40958			0.357421
$92$	2.35823	+	2.35823i	0.245862	+	0.245862i
$93$	−1.68410	+	0.404727i	−0.174633	+	0.0419683i
$94$			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	−0.0826253	−	0.996581i	$-0.526330\pi$
$97$	9.00142	−	9.00142i	0.913955	−	0.913955i	0.996581	+	0.0826253i	$0.0263305\pi$
$98$	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	$0.711201\pi$
$102$	−1.10345	−	4.59155i	−0.109258	−	0.454631i
$103$	−10.6610	−	10.6610i	−1.05046	−	1.05046i	−0.998658	−	0.0517992i	$-0.983504\pi$
$103$	−10.6610	−	10.6610i	−1.05046	−	1.05046i	−0.0517992	−	0.998658i	$-0.516496\pi$
$104$	0.815520			0.0799683
$105$	−13.5663	+	8.84021i	−1.32394	+	0.862716i
$106$	5.35569			0.520191
$107$	9.39588	+	9.39588i	0.908334	+	0.908334i	0.996138	−	0.0878038i	$-0.0279849\pi$
$107$	9.39588	+	9.39588i	0.908334	+	0.908334i	−0.0878038	+	0.996138i	$0.527985\pi$
$108$	3.37736	+	3.94885i	0.324987	+	0.379978i
$109$		−	15.6740i		−	1.50129i	−0.660703	−	0.750647i	$-0.729742\pi$
$109$		−	15.6740i		−	1.50129i	0.660703	−	0.750647i	$-0.270258\pi$
$110$	−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	$-0.897429\pi$
$113$	−6.71657	+	6.71657i	−0.631842	+	0.631842i	0.316688	+	0.948530i	$0.397429\pi$
$114$	2.07126	−	3.38175i	0.193992	−	0.316730i
$115$	7.02632	−	2.49867i	0.655208	−	0.233002i
$116$		−	7.87675i		−	0.731338i
$117$	−2.32716	−	0.754955i	−0.215146	−	0.0697957i
$118$	5.82162	+	5.82162i	0.535924	+	0.535924i
$119$	11.3988			1.04492
$120$	−3.24486	+	2.11444i	−0.296214	+	0.193021i
$121$	−13.9639			−1.26945
$122$	1.82081	+	1.82081i	0.164848	+	0.164848i
$123$	−2.78953	−	11.6075i	−0.251524	−	1.04661i
$124$		−	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	−0.901486	−	0.432809i	$-0.857522\pi$
$127$	−5.28171	+	5.28171i	−0.468676	+	0.468676i	0.432809	+	0.901486i	$0.357522\pi$
$128$	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	$-0.0927751\pi$
$132$	−8.41443	+	2.02218i	−0.732382	+	0.176008i
$133$	6.76869	+	6.76869i	0.586920	+	0.586920i
$134$	11.4627			0.990230
$135$	11.2169	−	3.02988i	0.965401	−	0.260771i
$136$	2.72641			0.233788
$137$	−6.79419	−	6.79419i	−0.580467	−	0.580467i	0.354565	−	0.935031i	$-0.384629\pi$
$137$	−6.79419	−	6.79419i	−0.580467	−	0.580467i	−0.935031	+	0.354565i	$0.884629\pi$
$138$	5.61655	−	1.34978i	0.478112	−	0.114901i
$139$			1.63608i			0.138771i	0.997590	+	0.0693853i	$0.0221038\pi$
$139$			1.63608i			0.138771i	−0.997590	+	0.0693853i	$0.977896\pi$
$140$	−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
$147$	−4.24141	−	17.6488i	−0.349826	−	1.45565i
$148$	5.67026	+	5.67026i	0.466093	+	0.466093i
$149$	−12.8062			−1.04913			−0.524564	−	0.851371i	$-0.675772\pi$
$149$	−12.8062			−1.04913			−0.524564	+	0.851371i	$0.675772\pi$
$150$	1.15520	+	8.58286i	0.0943215	+	0.700788i
$151$	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
$153$	−7.78007	−	2.52393i	−0.628981	−	0.204048i
$154$		−	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	−0.328140	+	0.944629i	$0.606422\pi$
$157$	−15.9477	+	15.9477i	−1.27277	+	1.27277i	−0.944629	+	0.328140i	$0.893578\pi$
$158$	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
$162$	8.88789	−	1.41611i	0.698299	−	0.111260i
$163$	−7.39856	−	7.39856i	−0.579500	−	0.579500i	0.355265	−	0.934766i	$-0.384391\pi$
$163$	−7.39856	−	7.39856i	−0.579500	−	0.579500i	−0.934766	+	0.355265i	$0.884391\pi$
$164$	6.89238			0.538204
$165$	−3.99375	+	18.9343i	−0.310913	+	1.47404i
$166$	−7.73529			−0.600375
$167$	2.63668	+	2.63668i	0.204032	+	0.204032i	0.801725	−	0.597693i	$-0.203916\pi$
$167$	2.63668	+	2.63668i	0.204032	+	0.204032i	−0.597693	+	0.801725i	$0.703916\pi$
$168$	−1.69211	−	7.04101i	−0.130549	−	0.543226i
$169$		−	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	$-0.977198\pi$
$173$	−12.1778	+	12.1778i	−0.925862	+	0.925862i	0.0715734	+	0.997435i	$0.477198\pi$
$174$	−11.6342	−	7.12573i	−0.881983	−	0.540201i
$175$	−20.7956	−	2.12981i	−1.57200	−	0.160998i
$176$		−	4.99639i		−	0.376617i
$177$	13.8652	−	3.33213i	1.04217	−	0.250458i
$178$	−9.23980	−	9.23980i	−0.692553	−	0.692553i
$179$	−17.0570			−1.27490			−0.637448	−	0.770493i	$-0.720010\pi$
$179$	−17.0570			−1.27490			−0.637448	+	0.770493i	$0.720010\pi$
$180$	0.187608	+	6.70558i	0.0139835	+	0.499804i
$181$	−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
$183$	4.33658	−	1.04218i	0.320569	−	0.0770400i
$184$			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	$-0.273709\pi$
$192$	−0.404727	−	1.68410i	−0.0292087	−	0.121540i
$193$	8.68054	+	8.68054i	0.624839	+	0.624839i	0.946765	−	0.321926i	$-0.104330\pi$
$193$	8.68054	+	8.68054i	0.624839	+	0.624839i	−0.321926	+	0.946765i	$0.604330\pi$
$194$	12.7299			0.913955
$195$	−1.72437	−	2.64625i	−0.123485	−	0.189502i
$196$	10.4797			0.748549
$197$	−10.8415	−	10.8415i	−0.772428	−	0.772428i	0.206102	−	0.978530i	$-0.433922\pi$
$197$	−10.8415	−	10.8415i	−0.772428	−	0.772428i	−0.978530	+	0.206102i	$0.933922\pi$
$198$	−4.62534	+	14.2577i	−0.328708	+	1.01325i
$199$		−	14.2096i		−	1.00729i	−0.863911	−	0.503645i	$-0.831992\pi$
$199$		−	14.2096i		−	1.00729i	0.863911	−	0.503645i	$-0.168008\pi$
$200$	−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
$207$	3.08737	−	9.51686i	0.214587	−	0.661468i
$208$	0.576660	+	0.576660i	0.0399841	+	0.0399841i
$209$	11.4396			0.791291
$210$	−15.8438	−	3.34188i	−1.09333	−	0.230612i
$211$	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
$213$	0.327210	+	1.36154i	0.0224201	+	0.0932915i
$214$			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
$222$	13.5047	−	3.24550i	0.906379	−	0.217823i
$223$	8.25222	+	8.25222i	0.552609	+	0.552609i	0.927193	−	0.374584i	$-0.122214\pi$
$223$	8.25222	+	8.25222i	0.552609	+	0.552609i	−0.374584	+	0.927193i	$0.622214\pi$
$224$	4.18087			0.279346
$225$	13.7222	+	6.05826i	0.914810	+	0.403884i
$226$	−9.49866			−0.631842
$227$	−3.91654	−	3.91654i	−0.259950	−	0.259950i	0.565084	−	0.825034i	$-0.308844\pi$
$227$	−3.91654	−	3.91654i	−0.259950	−	0.259950i	−0.825034	+	0.565084i	$0.808844\pi$
$228$	3.85586	−	0.926650i	0.255361	−	0.0613689i
$229$		−	4.19731i		−	0.277366i	−0.990337	−	0.138683i	$-0.955713\pi$
$229$		−	4.19731i		−	0.277366i	0.990337	−	0.138683i	$-0.0442869\pi$
$230$	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	0.580079	−	0.814560i	$-0.303022\pi$
$233$	21.2882	−	21.2882i	1.39464	−	1.39464i	0.814560	−	0.580079i	$-0.196978\pi$
$234$	−1.11172	−	2.17939i	−0.0726754	−	0.142471i
$235$	4.66123	+	13.1075i	0.304065	+	0.855039i
$236$			8.23302i			0.535924i
$237$	−2.44461	−	10.1722i	−0.158795	−	0.660756i
$238$	8.06014	+	8.06014i	0.522461	+	0.522461i
$239$	−8.28057			−0.535625			−0.267813	−	0.963471i	$-0.586301\pi$
$239$	−8.28057			−0.535625			−0.267813	+	0.963471i	$0.586301\pi$
$240$	−3.78960	−	0.799327i	−0.244618	−	0.0515963i
$241$	−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
$243$	5.94884	−	14.4087i	0.381618	−	0.924320i
$244$			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	$0.972222\pi$
$252$	−11.9305	−	3.87038i	−0.751552	−	0.243811i
$253$	11.7826	+	11.7826i	0.740768	+	0.740768i
$254$	−7.46947			−0.468676
$255$	−5.76483	−	8.84682i	−0.361008	−	0.554009i
$256$	1.00000			0.0625000
$257$	9.84769	+	9.84769i	0.614282	+	0.614282i	0.944059	−	0.329777i	$-0.106974\pi$
$257$	9.84769	+	9.84769i	0.614282	+	0.614282i	−0.329777	+	0.944059i	$0.606974\pi$
$258$	4.30296	+	17.9049i	0.267891	+	1.11471i
$259$			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	$-0.977616\pi$
$263$	−15.0377	+	15.0377i	−0.927266	+	0.927266i	0.0702629	+	0.997529i	$0.477616\pi$
$264$	−7.37979	−	4.52000i	−0.454195	−	0.278187i
$265$	11.2835	−	4.01258i	0.693138	−	0.246491i
$266$			9.57238i			0.586920i
$267$	−22.0062	+	5.28860i	−1.34676	+	0.323657i
$268$	8.10538	+	8.10538i	0.495115	+	0.495115i
$269$	−1.89009			−0.115241			−0.0576205	−	0.998339i	$-0.518351\pi$
$269$	−1.89009			−0.115241			−0.0576205	+	0.998339i	$0.518351\pi$
$270$	10.0740	+	5.78912i	0.613086	+	0.352315i
$271$	−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
$273$	5.74208	−	1.37995i	0.347527	−	0.0835185i
$274$		−	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	−0.738482	−	0.674274i	$-0.764457\pi$
$277$	−1.06863	+	1.06863i	−0.0642080	+	0.0642080i	0.674274	+	0.738482i	$0.264457\pi$
$278$	−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	$0.960079\pi$
$282$	2.51800	+	10.4776i	0.149945	+	0.623931i
$283$	20.3038	+	20.3038i	1.20694	+	1.20694i	0.972015	+	0.234921i	$0.0754831\pi$
$283$	20.3038	+	20.3038i	1.20694	+	1.20694i	0.234921	+	0.972015i	$0.424517\pi$
$284$	−0.808470			−0.0479739
$285$	1.83011	−	8.67654i	0.108407	−	0.513954i
$286$	4.07466			0.240939
$287$	20.3761	+	20.3761i	1.20276	+	1.20276i
$288$	−2.85360	−	0.925735i	−0.168150	−	0.0545495i
$289$		−	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	0.327589	−	0.944820i	$-0.393764\pi$
$293$	21.7801	−	21.7801i	1.27241	−	1.27241i	0.944820	−	0.327589i	$-0.106236\pi$
$294$	9.48048	−	15.4787i	0.552913	−	0.902739i
$295$	16.6267	+	7.90343i	0.968047	+	0.460156i
$296$			8.01896i			0.466093i
$297$	16.8746	+	19.7300i	0.979165	+	1.14485i
$298$	−9.05537	−	9.05537i	−0.524564	−	0.524564i
$299$	−2.71979			−0.157290
$300$	−5.25215	+	6.88585i	−0.303233	+	0.397555i
$301$	−44.4500			−2.56205
$302$	2.86356	+	2.86356i	0.164779	+	0.164779i
$303$	6.40898	+	26.6683i	0.368187	+	1.53205i
$304$			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	−0.738684	−	0.674052i	$-0.764552\pi$
$307$	−1.13245	+	1.13245i	−0.0646323	+	0.0646323i	0.674052	+	0.738684i	$0.264552\pi$
$308$	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	$-0.0981467\pi$
$312$	1.37342	−	0.330063i	0.0777545	−	0.0186862i
$313$	−10.1742	−	10.1742i	−0.575077	−	0.575077i	0.358466	−	0.933543i	$-0.383300\pi$
$313$	−10.1742	−	10.1742i	−0.575077	−	0.575077i	−0.933543	+	0.358466i	$0.883300\pi$
$314$	−22.5535			−1.27277
$315$	−19.2692	+	20.3785i	−1.08570	+	1.14820i
$316$	6.04015			0.339785
$317$	4.80017	+	4.80017i	0.269604	+	0.269604i	0.828941	−	0.559336i	$-0.188944\pi$
$317$	4.80017	+	4.80017i	0.269604	+	0.269604i	−0.559336	+	0.828941i	$0.688944\pi$
$318$	9.01953	−	2.16760i	0.505790	−	0.121553i
$319$		−	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
$327$	−6.34369	−	26.3966i	−0.350807	−	1.45973i
$328$	4.87365	+	4.87365i	0.269102	+	0.269102i
$329$	−26.0112			−1.43404
$330$	−16.2126	+	10.5646i	−0.892474	+	0.581561i
$331$	−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
$333$	7.42344	−	22.8829i	0.406802	−	1.25397i
$334$			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	−0.667851	−	0.744295i	$-0.732785\pi$
$337$	1.40334	−	1.40334i	0.0764449	−	0.0764449i	0.744295	+	0.667851i	$0.232785\pi$
$338$	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
$342$	2.11953	−	6.53350i	0.114611	−	0.353291i
$343$	10.2871	+	10.2871i	0.555449	+	0.555449i
$344$	−10.6317			−0.573225
$345$	10.8217	−	7.05175i	0.582623	−	0.379654i
$346$	−17.2220			−0.925862
$347$	3.40897	+	3.40897i	0.183003	+	0.183003i	0.792663	−	0.609660i	$-0.208694\pi$
$347$	3.40897	+	3.40897i	0.183003	+	0.183003i	−0.609660	+	0.792663i	$0.708694\pi$
$348$	−3.18794	−	13.2652i	−0.170891	−	0.711092i
$349$			7.29774i			0.390639i	0.980740	+	0.195320i	$0.0625744\pi$
$349$			7.29774i			0.390639i	−0.980740	+	0.195320i	$0.937426\pi$
$350$	−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	$-0.864465\pi$
$353$	−9.35024	+	9.35024i	−0.497663	+	0.497663i	0.413047	+	0.910710i	$0.364465\pi$
$354$	12.1604	+	7.44803i	0.646316	+	0.395858i
$355$	−0.776105	+	1.63272i	−0.0411914	+	0.0866558i
$356$		−	13.0671i		−	0.692553i
$357$	19.1967	−	4.61339i	1.01599	−	0.244167i
$358$	−12.0611	−	12.0611i	−0.637448	−	0.637448i
$359$	−18.8780			−0.996341			−0.498170	−	0.867079i	$-0.665995\pi$
$359$	−18.8780			−0.996341			−0.498170	+	0.867079i	$0.665995\pi$
$360$	−4.60890	+	4.87422i	−0.242910	+	0.256894i
$361$	13.7579			0.724099
$362$	−9.74973	−	9.74973i	−0.512434	−	0.512434i
$363$	−23.5166	+	5.65158i	−1.23430	+	0.296631i
$364$			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	−0.745181	−	0.666862i	$-0.767637\pi$
$367$	−1.50038	+	1.50038i	−0.0783192	+	0.0783192i	0.666862	+	0.745181i	$0.267637\pi$
$368$	−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
$372$	−0.404727	−	1.68410i	−0.0209841	−	0.0873166i
$373$	−0.674075	−	0.674075i	−0.0349023	−	0.0349023i	0.689440	−	0.724343i	$-0.257857\pi$
$373$	−0.674075	−	0.674075i	−0.0349023	−	0.0349023i	−0.724343	+	0.689440i	$0.757857\pi$
$374$	13.6222			0.704387
$375$	8.86421	+	17.2170i	0.457746	+	0.889083i
$376$	−6.22147			−0.320848
$377$	4.54221	+	4.54221i	0.233935	+	0.233935i
$378$	−16.5096	+	14.1203i	−0.849164	+	0.726271i
$379$		−	5.42438i		−	0.278631i	−0.990248	−	0.139316i	$-0.955510\pi$
$379$		−	5.42438i		−	0.278631i	0.990248	−	0.139316i	$-0.0444903\pi$
$380$	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	$-0.686533\pi$
$383$	5.48189	−	5.48189i	0.280112	−	0.280112i	0.833153	+	0.553042i	$0.186533\pi$
$384$	0.904654	−	1.47702i	0.0461654	−	0.0753741i
$385$	−15.6506	−	44.0098i	−0.797628	−	2.24295i
$386$			12.2761i			0.624839i
$387$	30.3387	+	9.84219i	1.54220	+	0.500306i
$388$	9.00142	+	9.00142i	0.456978	+	0.456978i
$389$	−32.9134			−1.66877			−0.834387	−	0.551179i	$-0.814178\pi$
$389$	−32.9134			−1.66877			−0.834387	+	0.551179i	$0.814178\pi$
$390$	0.651867	−	3.09049i	0.0330086	−	0.156493i
$391$	−9.09268			−0.459837
$392$	7.41025	+	7.41025i	0.374274	+	0.374274i
$393$	−2.66222	−	11.0777i	−0.134291	−	0.558795i
$394$		−	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	−0.881799	−	0.471626i	$-0.843667\pi$
$397$	−8.17263	+	8.17263i	−0.410173	+	0.410173i	0.471626	+	0.881799i	$0.343667\pi$
$398$	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	$0.845812\pi$
$402$	19.3044	−	4.63929i	0.962816	−	0.231387i
$403$	0.576660	+	0.576660i	0.0287255	+	0.0287255i
$404$	−15.8353			−0.787836
$405$	17.6642	−	9.64243i	0.877740	−	0.479136i
$406$	32.9317			1.63437
$407$	28.3309	+	28.3309i	1.40431	+	1.40431i
$408$	4.59155	−	1.10345i	0.227315	−	0.0546290i
$409$		−	31.5379i		−	1.55945i	−0.626123	−	0.779725i	$-0.715359\pi$
$409$		−	31.5379i		−	1.55945i	0.626123	−	0.779725i	$-0.284641\pi$
$410$	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
$417$	0.662167	+	2.75532i	0.0324264	+	0.134929i
$418$	8.08900	+	8.08900i	0.395646	+	0.395646i
$419$	2.11671			0.103408			0.0517040	−	0.998662i	$-0.483535\pi$
$419$	2.11671			0.103408			0.0517040	+	0.998662i	$0.483535\pi$
$420$	−8.84021	−	13.5663i	−0.431358	−	0.661970i
$421$	−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
$423$	17.7536	+	5.75944i	0.863208	+	0.280033i
$424$			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	$0.932529\pi$
$432$	−3.94885	+	3.37736i	−0.189989	+	0.162493i
$433$	13.6650	+	13.6650i	0.656696	+	0.656696i	0.954597	−	0.297901i	$-0.0962864\pi$
$433$	13.6650	+	13.6650i	0.656696	+	0.656696i	−0.297901	+	0.954597i	$0.596286\pi$
$434$	4.18087			0.200688
$435$	−29.8498	−	6.29610i	−1.43119	−	0.301875i
$436$	15.6740			0.750647
$437$	−5.39932	−	5.39932i	−0.258285	−	0.258285i
$438$	3.99516	+	16.6242i	0.190896	+	0.794333i
$439$			25.3349i			1.20917i	0.796541	+	0.604584i	$0.206661\pi$
$439$			25.3349i			1.20917i	−0.796541	+	0.604584i	$0.793339\pi$
$440$	−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	$-0.920867\pi$
$443$	−15.2217	+	15.2217i	−0.723207	+	0.723207i	0.246050	+	0.969257i	$0.420867\pi$
$444$	11.8442	+	7.25438i	0.562101	+	0.344278i
$445$	−26.3892	−	12.5440i	−1.25097	−	0.594640i
$446$			11.6704i			0.552609i
$447$	−21.5670	+	5.18303i	−1.02008	+	0.245149i
$448$	2.95632	+	2.95632i	0.139673	+	0.139673i
$449$	−37.0053			−1.74639			−0.873195	−	0.487371i	$-0.837956\pi$
$449$	−37.0053			−1.74639			−0.873195	+	0.487371i	$0.837956\pi$
$450$	5.41919	+	13.9869i	0.255463	+	0.659347i
$451$	34.4370			1.62158
$452$	−6.71657	−	6.71657i	−0.315921	−	0.315921i
$453$	6.82007	−	1.63902i	0.320435	−	0.0770077i
$454$		−	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	0.379827	−	0.925057i	$-0.375983\pi$
$457$	27.8953	−	27.8953i	1.30488	−	1.30488i	0.925057	−	0.379827i	$-0.124017\pi$
$458$	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	$0.760820\pi$
$462$	−8.45446	−	35.1796i	−0.393337	−	1.63670i
$463$	−9.85332	−	9.85332i	−0.457922	−	0.457922i	0.440051	−	0.897973i	$-0.354961\pi$
$463$	−9.85332	−	9.85332i	−0.457922	−	0.457922i	−0.897973	+	0.440051i	$0.854961\pi$
$464$	7.87675			0.365669
$465$	−3.78960	−	0.799327i	−0.175739	−	0.0370679i
$466$	30.1061			1.39464
$467$	1.63018	+	1.63018i	0.0754357	+	0.0754357i	0.743818	−	0.668382i	$-0.233013\pi$
$467$	1.63018	+	1.63018i	0.0754357	+	0.0754357i	−0.668382	+	0.743818i	$0.733013\pi$
$468$	0.754955	−	2.32716i	0.0348978	−	0.107573i
$469$			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
$477$	4.95796	−	15.2830i	0.227009	−	0.699760i
$478$	−5.85525	−	5.85525i	−0.267813	−	0.267813i
$479$	18.6347			0.851442			0.425721	−	0.904854i	$-0.360020\pi$
$479$	18.6347			0.851442			0.425721	+	0.904854i	$0.360020\pi$
$480$	−2.11444	−	3.24486i	−0.0965107	−	0.148107i
$481$	−6.53962			−0.298181
$482$	−5.63550	−	5.63550i	−0.256690	−	0.256690i
$483$	5.64327	+	23.4820i	0.256778	+	1.06847i
$484$		−	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	−0.974638	−	0.223786i	$-0.928158\pi$
$487$	−16.5699	+	16.5699i	−0.750852	+	0.750852i	0.223786	+	0.974638i	$0.428158\pi$
$488$	−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	$-0.0388710\pi$
$492$	11.6075	−	2.78953i	0.523305	−	0.125762i
$493$	15.1853	+	15.1853i	0.683911	+	0.683911i
$494$	−1.86719			−0.0840087
$495$	0.937364	+	33.5037i	0.0421314	+	1.50588i
$496$	1.00000			0.0449013
$497$	−2.39010	−	2.39010i	−0.107211	−	0.107211i
$498$	−13.0270	+	3.13069i	−0.583754	+	0.140289i
$499$			30.3229i			1.35744i	0.734398	+	0.678719i	$0.237465\pi$
$499$			30.3229i			1.35744i	−0.734398	+	0.678719i	$0.762535\pi$
$500$	−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	$-0.803294\pi$
$503$	−5.28566	+	5.28566i	−0.235676	+	0.235676i	0.579381	+	0.815057i	$0.303294\pi$
$504$	−5.69938	−	11.1729i	−0.253871	−	0.497682i
$505$	−15.2014	+	31.9797i	−0.676453	+	1.42308i
$506$			16.6632i			0.740768i
$507$	−4.99228	−	20.7733i	−0.221715	−	0.922573i
$508$	−5.28171	−	5.28171i	−0.234338	−	0.234338i
$509$	8.19904			0.363416			0.181708	−	0.983353i	$-0.441837\pi$
$509$	8.19904			0.363416			0.181708	+	0.983353i	$0.441837\pi$
$510$	2.17929	−	10.3320i	0.0965007	−	0.457509i
$511$	−41.2704			−1.82569
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−7.73270	−	9.04115i	−0.341407	−	0.399177i
$514$			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	$0.690705\pi$
$522$	−22.4771	−	7.29179i	−0.983795	−	0.319153i
$523$	−5.19328	−	5.19328i	−0.227086	−	0.227086i	0.584388	−	0.811474i	$-0.301335\pi$
$523$	−5.19328	−	5.19328i	−0.227086	−	0.227086i	−0.811474	+	0.584388i	$0.801335\pi$
$524$	6.57780			0.287352
$525$	−35.8838	+	4.82973i	−1.56610	+	0.210787i
$526$	−21.2665			−0.927266
$527$	1.92786	+	1.92786i	0.0839790	+	0.0839790i
$528$	−2.02218	−	8.41443i	−0.0880039	−	0.366191i
$529$			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
$537$	−28.7256	+	6.90342i	−1.23960	+	0.297905i
$538$	−1.33650	−	1.33650i	−0.0576205	−	0.0576205i
$539$	52.3606			2.25533
$540$	3.02988	+	11.2169i	0.130385	+	0.482700i
$541$	−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
$543$	−23.2207	+	5.58046i	−0.996496	+	0.239481i
$544$			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	−0.299489	−	0.954100i	$-0.596816\pi$
$547$	15.3100	−	15.3100i	0.654610	−	0.654610i	0.954100	+	0.299489i	$0.0968164\pi$
$548$	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
$552$	1.34978	+	5.61655i	0.0574506	+	0.239056i
$553$	17.8566	+	17.8566i	0.759341	+	0.759341i
$554$	−1.51128			−0.0642080
$555$	26.0204	−	16.9556i	1.10451	−	0.719727i
$556$	−1.63608			−0.0693853
$557$	−27.0364	−	27.0364i	−1.14557	−	1.14557i	−0.987415	−	0.158153i	$-0.949446\pi$
$557$	−27.0364	−	27.0364i	−1.14557	−	1.14557i	−0.158153	−	0.987415i	$-0.550554\pi$
$558$	−2.85360	−	0.925735i	−0.120802	−	0.0391895i
$559$		−	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	$-0.954534\pi$
$563$	−20.1083	+	20.1083i	−0.847464	+	0.847464i	0.142352	+	0.989816i	$0.454534\pi$
$564$	−5.62828	+	9.18927i	−0.236993	+	0.386938i
$565$	−20.0119	+	7.11656i	−0.841909	+	0.299396i
$566$			28.7139i			1.20694i
$567$	5.92056	+	37.1591i	0.248640	+	1.56054i
$568$	−0.571674	−	0.571674i	−0.0239869	−	0.0239869i
$569$	−15.4858			−0.649199			−0.324600	−	0.945851i	$-0.605230\pi$
$569$	−15.4858			−0.649199			−0.324600	+	0.945851i	$0.605230\pi$
$570$	7.42933	−	4.84116i	0.311180	−	0.202774i
$571$	−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
$573$	−8.47703	−	35.2736i	−0.354133	−	1.47357i
$574$			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	0.127272	−	0.991868i	$-0.459378\pi$
$577$	26.8827	−	26.8827i	1.11914	−	1.11914i	0.991868	−	0.127272i	$-0.0406222\pi$
$578$	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
$582$	21.4385	−	5.15215i	0.888653	−	0.213564i
$583$	18.9216	+	18.9216i	0.783651	+	0.783651i
$584$	−9.87123			−0.408475
$585$	−3.97502	−	3.75865i	−0.164347	−	0.155401i
$586$	30.8018			1.27241
$587$	6.99920	+	6.99920i	0.288888	+	0.288888i	0.836640	−	0.547753i	$-0.184516\pi$
$587$	6.99920	+	6.99920i	0.288888	+	0.288888i	−0.547753	+	0.836640i	$0.684516\pi$
$588$	17.6488	−	4.24141i	0.727826	−	0.174913i
$589$			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	$-0.687616\pi$
$593$	6.70624	−	6.70624i	0.275392	−	0.275392i	0.831266	+	0.555874i	$0.187616\pi$
$594$	−2.01905	+	25.8834i	−0.0828428	+	1.06201i
$595$	23.0200	+	10.9424i	0.943729	+	0.448596i
$596$		−	12.8062i		−	0.524564i
$597$	−5.75101	−	23.9304i	−0.235373	−	0.979405i
$598$	−1.92318	−	1.92318i	−0.0786448	−	0.0786448i
$599$	22.2127			0.907586			0.453793	−	0.891107i	$-0.350071\pi$
$599$	22.2127			0.907586			0.453793	+	0.891107i	$0.350071\pi$
$600$	−8.58286	+	1.15520i	−0.350394	+	0.0471607i
$601$	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
$603$	10.6115	−	32.7100i	0.432132	−	1.33206i
$604$			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	−0.709295	−	0.704912i	$-0.750987\pi$
$607$	−0.107997	+	0.107997i	−0.00438348	+	0.00438348i	0.704912	+	0.709295i	$0.250987\pi$
$608$	−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
$612$	2.52393	−	7.78007i	0.102024	−	0.314491i
$613$	1.98258	+	1.98258i	0.0800755	+	0.0800755i	0.746010	−	0.665935i	$-0.231967\pi$
$613$	1.98258	+	1.98258i	0.0800755	+	0.0800755i	−0.665935	+	0.746010i	$0.731967\pi$
$614$	−1.60152			−0.0646323
$615$	5.50926	−	26.1194i	0.222155	−	1.05323i
$616$	20.8893			0.841652
$617$	3.76135	+	3.76135i	0.151426	+	0.151426i	0.778755	−	0.627329i	$-0.215852\pi$
$617$	3.76135	+	3.76135i	0.151426	+	0.151426i	−0.627329	+	0.778755i	$0.715852\pi$
$618$	−6.10203	−	25.3910i	−0.245460	−	1.02138i
$619$			31.0020i			1.24608i	0.782191	+	0.623038i	$0.214102\pi$
$619$			31.0020i			1.24608i	−0.782191	+	0.623038i	$0.785898\pi$
$620$	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
$627$	19.2654	−	4.62991i	0.769385	−	0.184901i
$628$	−15.9477	−	15.9477i	−0.636384	−	0.636384i
$629$	−21.8630			−0.871734
$630$	−28.0352	+	0.784366i	−1.11695	+	0.0312499i
$631$	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
$633$	6.02258	−	1.44736i	0.239376	−	0.0575275i
$634$			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	$-0.0461808\pi$
$642$	5.37793	+	22.3780i	0.212250	+	0.883188i
$643$	−13.0557	−	13.0557i	−0.514867	−	0.514867i	0.401147	−	0.916014i	$-0.368612\pi$
$643$	−13.0557	−	13.0557i	−0.514867	−	0.514867i	−0.916014	+	0.401147i	$0.868612\pi$
$644$	−13.9434			−0.549446
$645$	22.4802	+	34.4986i	0.885158	+	1.35838i
$646$	−6.24229			−0.245600
$647$	28.1848	+	28.1848i	1.10806	+	1.10806i	0.993406	+	0.114651i	$0.0365751\pi$
$647$	28.1848	+	28.1848i	1.10806	+	1.10806i	0.114651	+	0.993406i	$0.463425\pi$
$648$	1.41611	+	8.88789i	0.0556299	+	0.349149i
$649$			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	0.256617	−	0.966513i	$-0.417392\pi$
$653$	31.2557	−	31.2557i	1.22313	−	1.22313i	0.966513	−	0.256617i	$-0.0826078\pi$
$654$	14.1795	−	23.1508i	0.554463	−	0.905270i
$655$	6.31447	−	13.2840i	0.246727	−	0.519049i
$656$			6.89238i			0.269102i
$657$	28.1685	+	9.13815i	1.09896	+	0.356513i
$658$	−18.3927	−	18.3927i	−0.717021	−	0.717021i
$659$	−2.80641			−0.109322			−0.0546611	−	0.998505i	$-0.517408\pi$
$659$	−2.80641			−0.109322			−0.0546611	+	0.998505i	$0.517408\pi$
$660$	−18.9343	−	3.99375i	−0.737018	−	0.155457i
$661$	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
$663$	0.899887	+	3.74450i	0.0349487	+	0.145424i
$664$		−	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
$672$	7.04101	−	1.69211i	0.271613	−	0.0652747i
$673$	−29.8688	−	29.8688i	−1.15136	−	1.15136i	−0.986281	−	0.165076i	$-0.947213\pi$
$673$	−29.8688	−	29.8688i	−1.15136	−	1.15136i	−0.165076	−	0.986281i	$-0.552787\pi$
$674$	1.98462			0.0764449
$675$	25.5614	+	4.64899i	0.983860	+	0.178940i
$676$	12.3349			0.474420
$677$	14.3828	+	14.3828i	0.552775	+	0.552775i	0.927241	−	0.374466i	$-0.122174\pi$
$677$	14.3828	+	14.3828i	0.552775	+	0.552775i	−0.374466	+	0.927241i	$0.622174\pi$
$678$	−15.9967	+	3.84437i	−0.614350	+	0.147642i
$679$			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	$-0.777679\pi$
$683$	−3.20982	+	3.20982i	−0.122820	+	0.122820i	0.643025	+	0.765845i	$0.277679\pi$
$684$	6.11862	−	3.12115i	0.233951	−	0.119340i
$685$	−7.19880	−	20.2432i	−0.275052	−	0.773453i
$686$			14.5481i			0.555449i
$687$	−1.69877	−	7.06870i	−0.0648120	−	0.269688i
$688$	−7.51778	−	7.51778i	−0.286613	−	0.286613i
$689$	−4.36767			−0.166395
$690$	12.6385	+	2.66579i	0.481139	+	0.101485i
$691$	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
$693$	−59.6095	−	19.3379i	−2.26438	−	0.734587i
$694$			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	$-0.0526702\pi$
$702$	−2.75431	−	3.22037i	−0.103955	−	0.121545i
$703$	−12.9824	−	12.9824i	−0.489642	−	0.489642i
$704$	4.99639			0.188309
$705$	13.1549	+	20.1878i	0.495444	+	0.760317i
$706$	−13.2232			−0.497663
$707$	−46.8143	−	46.8143i	−1.76063	−	1.76063i
$708$	3.33213	+	13.8652i	0.125229	+	0.521087i
$709$		−	0.835634i		−	0.0313829i	−0.999877	−	0.0156915i	$-0.995005\pi$
$709$		−	0.835634i		−	0.0313829i	0.999877	−	0.0156915i	$-0.00499495\pi$
$710$	−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
$717$	−13.9453	+	3.35137i	−0.520797	+	0.125159i
$718$	−13.3487	−	13.3487i	−0.498170	−	0.498170i
$719$	−48.0542			−1.79212			−0.896060	−	0.443933i	$-0.853583\pi$
$719$	−48.0542			−1.79212			−0.896060	+	0.443933i	$0.853583\pi$
$720$	−6.70558	+	0.187608i	−0.249902	+	0.00699175i
$721$	63.0345			2.34753
$722$	9.72829	+	9.72829i	0.362050	+	0.362050i
$723$	−13.4219	+	3.22560i	−0.499167	+	0.119961i
$724$		−	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	−0.629001	+	0.777405i	$0.716536\pi$
$727$	−37.9208	+	37.9208i	−1.40641	+	1.40641i	−0.777405	+	0.629001i	$0.783464\pi$
$728$	−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
$732$	1.04218	+	4.33658i	0.0385200	+	0.160285i
$733$	−4.28209	−	4.28209i	−0.158162	−	0.158162i	0.623589	−	0.781752i	$-0.285674\pi$
$733$	−4.28209	−	4.28209i	−0.158162	−	0.158162i	−0.781752	+	0.623589i	$0.785674\pi$
$734$	−2.12186			−0.0783192
$735$	8.37669	−	39.7138i	0.308979	−	1.46487i
$736$	−3.33504			−0.122931
$737$	40.4976	+	40.4976i	1.49175	+	1.49175i
$738$	6.38052	−	19.6681i	0.234870	−	0.723991i
$739$		−	53.9288i		−	1.98380i	−0.127010	−	0.991901i	$-0.540538\pi$
$739$		−	53.9288i		−	1.98380i	0.127010	−	0.991901i	$-0.459462\pi$
$740$	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	$-0.732947\pi$
$743$	2.06424	−	2.06424i	0.0757295	−	0.0757295i	0.743957	+	0.668227i	$0.232947\pi$
$744$	0.904654	−	1.47702i	0.0331662	−	0.0541504i
$745$	−25.8624	−	12.2936i	−0.947527	−	0.450401i
$746$		−	0.953286i		−	0.0349023i
$747$	−7.16084	+	22.0734i	−0.262001	+	0.807624i
$748$	9.63235	+	9.63235i	0.352194	+	0.352194i
$749$	−55.5545			−2.02992
$750$	−5.90633	+	18.4422i	−0.215669	+	0.673414i
$751$	−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
$753$	1.11771	+	4.65089i	0.0407318	+	0.169488i
$754$			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	0.277283	−	0.960788i	$-0.410566\pi$
$757$	34.0638	−	34.0638i	1.23807	−	1.23807i	0.960788	−	0.277283i	$-0.0894340\pi$
$758$	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	$-0.206817\pi$
$762$	−12.5793	+	3.02310i	−0.455701	+	0.109515i
$763$	46.3373	+	46.3373i	1.67752	+	1.67752i
$764$	20.9450			0.757765
$765$	−13.2891	−	12.5657i	−0.480469	−	0.454315i
$766$	7.75257			0.280112
$767$	−4.74765	−	4.74765i	−0.171428	−	0.171428i
$768$	1.68410	−	0.404727i	0.0607698	−	0.0146043i
$769$		−	20.8747i		−	0.752762i	−0.926465	−	0.376381i	$-0.877168\pi$
$769$		−	20.8747i		−	0.752762i	0.926465	−	0.376381i	$-0.122832\pi$
$770$	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	$-0.601221\pi$
$773$	17.7160	−	17.7160i	0.637200	−	0.637200i	0.949864	+	0.312663i	$0.101221\pi$
$774$	14.4932	+	28.4122i	0.520949	+	1.02126i
$775$	−3.15692	−	3.87735i	−0.113400	−	0.139278i
$776$			12.7299i			0.456978i
$777$	13.5690	+	56.4616i	0.486785	+	2.02555i
$778$	−23.2733	−	23.2733i	−0.834387	−	0.834387i
$779$	−15.7806			−0.565397
$780$	2.64625	−	1.72437i	0.0947509	−	0.0617423i
$781$	−4.03943			−0.144542
$782$	−6.42950	−	6.42950i	−0.229918	−	0.229918i
$783$	−31.1041	+	26.6027i	−1.11157	+	0.950701i
$784$			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	−0.713518	−	0.700637i	$-0.752899\pi$
$787$	−0.361367	+	0.361367i	−0.0128813	+	0.0128813i	0.700637	+	0.713518i	$0.252899\pi$
$788$	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
$792$	−14.2577	−	4.62534i	−0.506625	−	0.164354i
$793$	−1.48490	−	1.48490i	−0.0527305	−	0.0527305i
$794$	−11.5578			−0.410173
$795$	17.3785	−	11.3243i	0.616351	−	0.401632i
$796$	14.2096			0.503645
$797$	22.9014	+	22.9014i	0.811210	+	0.811210i	0.984815	−	0.173605i	$-0.0555417\pi$
$797$	22.9014	+	22.9014i	0.811210	+	0.811210i	−0.173605	+	0.984815i	$0.555542\pi$
$798$	3.87421	+	16.1209i	0.137145	+	0.570672i
$799$		−	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
$807$	−3.18310	+	0.764972i	−0.112051	+	0.0269283i
$808$	−11.1973	−	11.1973i	−0.393918	−	0.393918i
$809$	22.4949			0.790878			0.395439	−	0.918492i	$-0.370592\pi$
$809$	22.4949			0.790878			0.395439	+	0.918492i	$0.370592\pi$
$810$	19.3087	+	5.67223i	0.678438	+	0.199302i
$811$	−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
$813$	−0.720848	+	0.173236i	−0.0252812	+	0.00607566i
$814$			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	$-0.0780517\pi$
$822$	−3.88880	−	16.1816i	−0.135637	−	0.564397i
$823$	−32.6557	−	32.6557i	−1.13831	−	1.13831i	−0.988754	−	0.149554i	$-0.952216\pi$
$823$	−32.6557	−	32.6557i	−1.13831	−	1.13831i	−0.149554	−	0.988754i	$-0.547784\pi$
$824$	15.0769			0.525228
$825$	−26.2418	+	34.4044i	−0.913622	+	1.19781i
$826$	−34.4212			−1.19767
$827$	−4.27320	−	4.27320i	−0.148594	−	0.148594i	0.628896	−	0.777490i	$-0.283507\pi$
$827$	−4.27320	−	4.27320i	−0.148594	−	0.148594i	−0.777490	+	0.628896i	$0.783507\pi$
$828$	9.51686	+	3.08737i	0.330734	+	0.107293i
$829$			35.5611i			1.23509i	0.786536	+	0.617544i	$0.211872\pi$
$829$			35.5611i			1.23509i	−0.786536	+	0.617544i	$0.788128\pi$
$830$	−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
$837$	−3.94885	+	3.37736i	−0.136492	+	0.116739i
$838$	1.49674	+	1.49674i	0.0517040	+	0.0517040i
$839$	−21.6006			−0.745734			−0.372867	−	0.927885i	$-0.621625\pi$
$839$	−21.6006			−0.745734			−0.372867	+	0.927885i	$0.621625\pi$
$840$	3.34188	−	15.8438i	0.115306	−	0.546664i
$841$	33.0433			1.13942
$842$	−7.26575	−	7.26575i	−0.250394	−	0.250394i
$843$	1.69731	+	7.06262i	0.0584583	+	0.243249i
$844$			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
$852$	−1.36154	+	0.327210i	−0.0466458	+	0.0112100i
$853$	11.1150	+	11.1150i	0.380570	+	0.380570i	0.871308	−	0.490737i	$-0.163273\pi$
$853$	11.1150	+	11.1150i	0.380570	+	0.380570i	−0.490737	+	0.871308i	$0.663273\pi$
$854$	−10.7658			−0.368398
$855$	−0.429542	−	15.3529i	−0.0146900	−	0.525057i
$856$	−13.2878			−0.454167
$857$	−14.3136	−	14.3136i	−0.488944	−	0.488944i	0.419029	−	0.907973i	$-0.362371\pi$
$857$	−14.3136	−	14.3136i	−0.488944	−	0.488944i	−0.907973	+	0.419029i	$0.862371\pi$
$858$	6.86213	−	1.64912i	0.234269	−	0.0563002i
$859$			6.23636i			0.212782i	0.994324	+	0.106391i	$0.0339295\pi$
$859$			6.23636i			0.212782i	−0.994324	+	0.106391i	$0.966071\pi$
$860$	−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	$-0.659808\pi$
$863$	11.6148	−	11.6148i	0.395374	−	0.395374i	0.876598	+	0.481224i	$0.159808\pi$
$864$	−5.18042	−	0.404103i	−0.176241	−	0.0137479i
$865$	−36.2836	+	12.9030i	−1.23368	+	0.438716i
$866$			19.3252i			0.656696i
$867$	−3.87191	−	16.1113i	−0.131497	−	0.547168i
$868$	2.95632	+	2.95632i	0.100344	+	0.100344i
$869$	30.1789			1.02375
$870$	−16.6549	−	25.5590i	−0.564656	−	0.866531i
$871$	−9.34809			−0.316748
$872$	11.0832	+	11.0832i	0.375324	+	0.375324i
$873$	11.7845	−	36.3261i	0.398846	−	1.22945i
$874$		−	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	−0.872683	−	0.488286i	$-0.837622\pi$
$877$	−11.3836	+	11.3836i	−0.384397	+	0.384397i	0.488286	+	0.872683i	$0.337622\pi$
$878$	−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	$-0.375197\pi$
$882$	9.70141	−	29.9048i	0.326663	−	1.00695i
$883$	36.7348	+	36.7348i	1.23622	+	1.23622i	0.961532	+	0.274693i	$0.0885761\pi$
$883$	36.7348	+	36.7348i	1.23622	+	1.23622i	0.274693	+	0.961532i	$0.411424\pi$
$884$	−2.22344			−0.0747824
$885$	31.1999	+	6.58087i	1.04877	+	0.221214i
$886$	−21.5268			−0.723207
$887$	21.7550	+	21.7550i	0.730462	+	0.730462i	0.970711	−	0.240249i	$-0.0772292\pi$
$887$	21.7550	+	21.7550i	0.730462	+	0.730462i	−0.240249	+	0.970711i	$0.577229\pi$
$888$	3.24550	+	13.5047i	0.108912	+	0.453190i
$889$		−	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
$897$	−4.58040	+	1.10077i	−0.152935	+	0.0367538i
$898$	−26.1667	−	26.1667i	−0.873195	−	0.873195i
$899$	7.87675			0.262704
$900$	−6.05826	+	13.7222i	−0.201942	+	0.457405i
$901$	−14.6018			−0.486457
$902$	24.3506	+	24.3506i	0.810788	+	0.810788i
$903$	−74.8582	+	17.9901i	−2.49113	+	0.598674i
$904$		−	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	−0.890780	−	0.454436i	$-0.849841\pi$
$907$	−13.1411	+	13.1411i	−0.436344	+	0.436344i	0.454436	+	0.890780i	$0.349841\pi$
$908$	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	$-0.0745317\pi$
$912$	0.926650	+	3.85586i	0.0306845	+	0.127680i
$913$	−27.3287	−	27.3287i	−0.904446	−	0.904446i
$914$	39.4498			1.30488
$915$	9.75826	+	2.05828i	0.322598	+	0.0680445i
$916$	4.19731			0.138683
$917$	19.4461	+	19.4461i	0.642166	+	0.642166i
$918$	−9.20807	−	10.7662i	−0.303912	−	0.355337i
$919$		−	20.4283i		−	0.673866i	−0.941529	−	0.336933i	$-0.890610\pi$
$919$		−	20.4283i		−	0.673866i	0.941529	−	0.336933i	$-0.109390\pi$
$920$	−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
$927$	−43.0234	−	13.9572i	−1.41307	−	0.458415i
$928$	5.56971	+	5.56971i	0.182835	+	0.182835i
$929$	−0.520712			−0.0170840			−0.00854200	−	0.999964i	$-0.502719\pi$
$929$	−0.520712			−0.0170840			−0.00854200	+	0.999964i	$0.502719\pi$
$930$	−2.11444	−	3.24486i	−0.0693353	−	0.106403i
$931$	−23.9939			−0.786369
$932$	21.2882	+	21.2882i	0.697320	+	0.697320i
$933$	−4.33207	−	18.0261i	−0.141826	−	0.590146i
$934$			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	−0.310415	−	0.950601i	$-0.600468\pi$
$937$	19.5964	−	19.5964i	0.640186	−	0.640186i	0.950601	+	0.310415i	$0.100468\pi$
$938$	−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	$-0.163934\pi$
$942$	−37.9824	+	9.12803i	−1.23753	+	0.297407i
$943$	−16.2538	−	16.2538i	−0.529297	−	0.529297i
$944$	−8.23302			−0.267962
$945$	−24.2036	+	42.1182i	−0.787343	+	1.37011i
$946$	−53.1204			−1.72709
$947$	27.3560	+	27.3560i	0.888951	+	0.888951i	0.994422	−	0.105471i	$-0.0336350\pi$
$947$	27.3560	+	27.3560i	0.888951	+	0.888951i	−0.105471	+	0.994422i	$0.533635\pi$
$948$	10.1722	−	2.44461i	0.330378	−	0.0793974i
$949$		−	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	$-0.640891\pi$
$953$	14.6735	−	14.6735i	0.475322	−	0.475322i	0.903632	+	0.428310i	$0.140891\pi$
$954$	14.3125	−	7.30090i	0.463385	−	0.236375i
$955$	20.1066	−	42.2989i	0.650633	−	1.36876i
$956$		−	8.28057i		−	0.267813i
$957$	−15.9282	−	66.2784i	−0.514885	−	2.14248i
$958$	13.1767	+	13.1767i	0.425721	+	0.425721i
$959$	40.1716			1.29721
$960$	0.799327	−	3.78960i	0.0257982	−	0.122309i
$961$	1.00000			0.0322581
$962$	−4.62421	−	4.62421i	−0.149091	−	0.149091i
$963$	37.9180	+	12.3010i	1.22189	+	0.396393i
$964$		−	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	−0.369767	+	0.929125i	$0.620562\pi$
$967$	−40.3911	+	40.3911i	−1.29889	+	1.29889i	−0.929125	+	0.369767i	$0.879438\pi$
$968$	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	$0.918232\pi$
$972$	14.4087	+	5.94884i	0.462160	+	0.190809i
$973$	−4.83678	−	4.83678i	−0.155060	−	0.155060i
$974$	−23.4333			−0.750852
$975$	−0.942086	−	6.99949i	−0.0301709	−	0.224163i
$976$	−2.57501			−0.0824241
$977$	22.7765	+	22.7765i	0.728685	+	0.728685i	0.970358	−	0.241673i	$-0.0776961\pi$
$977$	22.7765	+	22.7765i	0.728685	+	0.728685i	−0.241673	+	0.970358i	$0.577696\pi$
$978$	−4.23472	−	17.6210i	−0.135412	−	0.563457i
$979$		−	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	$-0.662072\pi$
$983$	12.0930	−	12.0930i	0.385706	−	0.385706i	0.873153	+	0.487447i	$0.162072\pi$
$984$	10.1802	+	6.23521i	0.324533	+	0.198771i
$985$	−11.4872	−	32.3023i	−0.366012	−	1.02924i
$986$			21.4752i			0.683911i
$987$	−43.8054	+	10.5274i	−1.39434	+	0.335092i
$988$	−1.32030	−	1.32030i	−0.0420043	−	0.0420043i
$989$	35.4573			1.12748
$990$	−23.0279	+	24.3535i	−0.731874	+	0.774005i
$991$	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
$993$	−4.22894	+	1.01631i	−0.134201	+	0.0322516i
$994$		−	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	−0.560759	−	0.827979i	$-0.689491\pi$
$997$	8.43753	−	8.43753i	0.267219	−	0.267219i	0.827979	+	0.560759i	$0.189491\pi$
$998$	−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.683.19	yes	40
3.2	odd	2	inner	930.2.j.h.683.5	yes	40
5.2	odd	4	inner	930.2.j.h.497.5	✓	40
15.2	even	4	inner	930.2.j.h.497.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.5	✓	40	5.2	odd	4	inner
930.2.j.h.497.19	yes	40	15.2	even	4	inner
930.2.j.h.683.5	yes	40	3.2	odd	2	inner
930.2.j.h.683.19	yes	40	1.1	even	1	trivial

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} +(1.68410 - 0.404727i) 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} +(0.404727 + 1.68410i) q^{12} +(-0.576660 - 0.576660i) q^{13} -4.18087 q^{14} +(3.78960 + 0.799327i) q^{15} -1.00000 q^{16} +(-1.92786 - 1.92786i) q^{17} +(2.85360 + 0.925735i) 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} +(3.94885 - 3.37736i) q^{27} +(-2.95632 - 2.95632i) q^{28} -7.87675 q^{29} +(2.11444 + 3.24486i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.02218 + 8.41443i) 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} +(-7.04101 + 1.69211i) q^{42} +(7.51778 + 7.51778i) q^{43} -4.99639 q^{44} +(6.70558 - 0.187608i) q^{45} +3.33504 q^{46} +(4.39924 + 4.39924i) q^{47} +(-1.68410 + 0.404727i) 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} +(-0.926650 - 3.85586i) q^{57} +(-5.56971 - 5.56971i) q^{58} +8.23302 q^{59} +(-0.799327 + 3.78960i) q^{60} +2.57501 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-3.87038 + 11.9305i) 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} +(-0.925735 + 2.85360i) q^{72} +(6.98002 + 6.98002i) q^{73} +8.01896 q^{74} +(6.88585 + 5.25215i) q^{75} +2.28957 q^{76} +(-14.7709 - 14.7709i) q^{77} +(-0.330063 - 1.37342i) 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} +(-13.2652 + 3.18794i) q^{87} +(-3.53298 - 3.53298i) q^{88} -13.0671 q^{89} +(4.87422 + 4.60890i) q^{90} +3.40958 q^{91} +(2.35823 + 2.35823i) q^{92} +(-1.68410 + 0.404727i) 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

Related objects

Downloads

Learn more