LMFDB - Embedded newform 675.2.l.h.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	675.151
Dual form			675.2.l.h.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.06784 - 1.73512i) q^{2} +(0.239124 - 1.71546i) q^{3} +(0.918006 + 5.20627i) q^{4} +(-3.47101 + 3.13239i) q^{6} +(-0.175710 + 0.996499i) q^{7} +(4.43585 - 7.68312i) q^{8} +(-2.88564 - 0.820419i) q^{9} +(-1.18249 + 0.430390i) q^{11} +(9.15069 - 0.329860i) q^{12} +(-3.17545 + 2.66452i) q^{13} +(2.09238 - 1.75572i) q^{14} +(-12.5682 + 4.57445i) q^{16} +(-1.95549 - 3.38700i) q^{17} +(4.54350 + 6.70342i) q^{18} +(0.433214 - 0.750349i) q^{19} +(1.66744 + 0.539711i) q^{21} +(3.19197 + 1.16178i) q^{22} +(0.479332 + 2.71843i) q^{23} +(-12.1194 - 9.44677i) q^{24} +11.1896 q^{26} +(-2.09743 + 4.75403i) q^{27} -5.34934 q^{28} +(6.00558 + 5.03928i) q^{29} +(0.941551 + 5.33980i) q^{31} +(17.2529 + 6.27953i) q^{32} +(0.455557 + 2.13143i) q^{33} +(-1.83323 + 10.3968i) q^{34} +(1.62229 - 15.7766i) q^{36} +(3.71964 + 6.44260i) q^{37} +(-2.19776 + 0.799919i) q^{38} +(3.81156 + 6.08452i) q^{39} +(-2.73623 + 2.29597i) q^{41} +(-2.51153 - 4.00925i) q^{42} +(-4.00634 + 1.45819i) q^{43} +(-3.32626 - 5.76125i) q^{44} +(3.72562 - 6.45296i) q^{46} +(-0.640847 + 3.63443i) q^{47} +(4.84195 + 22.6542i) q^{48} +(5.61571 + 2.04395i) q^{49} +(-6.27789 + 2.54465i) q^{51} +(-16.7873 - 14.0862i) q^{52} +0.485518 q^{53} +(12.5859 - 6.19126i) q^{54} +(6.87680 + 5.77032i) q^{56} +(-1.18360 - 0.922590i) q^{57} +(-3.67480 - 20.8408i) q^{58} +(1.47979 + 0.538599i) q^{59} +(0.286481 - 1.62472i) q^{61} +(7.31822 - 12.6755i) q^{62} +(1.32458 - 2.73138i) q^{63} +(-11.4056 - 19.7550i) q^{64} +(2.75627 - 5.19790i) q^{66} +(2.53969 - 2.13105i) q^{67} +(15.8385 - 13.2901i) q^{68} +(4.77798 - 0.172235i) q^{69} +(-4.95764 - 8.58688i) q^{71} +(-19.1036 + 18.5314i) q^{72} +(-2.63257 + 4.55975i) q^{73} +(3.48709 - 19.7763i) q^{74} +(4.30421 + 1.56660i) q^{76} +(-0.221109 - 1.25397i) q^{77} +(2.67570 - 19.1953i) q^{78} +(-6.41639 - 5.38399i) q^{79} +(7.65382 + 4.73487i) q^{81} +9.64185 q^{82} +(2.21851 + 1.86155i) q^{83} +(-1.27916 + 9.17661i) q^{84} +(10.8146 + 3.93619i) q^{86} +(10.0808 - 9.09735i) q^{87} +(-1.93860 + 10.9943i) q^{88} +(-8.03383 + 13.9150i) q^{89} +(-2.09723 - 3.63251i) q^{91} +(-13.7128 + 4.99106i) q^{92} +(9.38539 - 0.338321i) q^{93} +(7.63133 - 6.40345i) q^{94} +(14.8979 - 28.0951i) q^{96} +(-2.90290 + 1.05657i) q^{97} +(-8.06587 - 13.9705i) q^{98} +(3.76533 - 0.271815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−2.06784	−	1.73512i	−1.46218	−	1.22692i	−0.923043	−	0.384698i	$-0.874306\pi$
$2$	−2.06784	−	1.73512i	−1.46218	−	1.22692i	−0.539138	−	0.842218i	$-0.681250\pi$
$3$	0.239124	−	1.71546i	0.138059	−	0.990424i
$3$	0.239124	−	1.71546i	0.138059	−	0.990424i
$4$	0.918006	+	5.20627i	0.459003	+	2.60313i
$5$		0			0
$5$		0			0
$6$	−3.47101	+	3.13239i	−1.41703	+	1.27879i
$7$	−0.175710	+	0.996499i	−0.0664120	+	0.376641i	0.933428	+	0.358764i	$0.116802\pi$
$7$	−0.175710	+	0.996499i	−0.0664120	+	0.376641i	−0.999840	+	0.0178769i	$0.994309\pi$
$8$	4.43585	−	7.68312i	1.56831	−	2.71639i
$9$	−2.88564	−	0.820419i	−0.961880	−	0.273473i
$10$		0			0
$11$	−1.18249	+	0.430390i	−0.356533	+	0.129767i	−0.514076	−	0.857745i	$-0.671865\pi$
$11$	−1.18249	+	0.430390i	−0.356533	+	0.129767i	0.157543	+	0.987512i	$0.449643\pi$
$12$	9.15069	−	0.329860i	2.64158	−	0.0952225i
$13$	−3.17545	+	2.66452i	−0.880711	+	0.739004i	−0.966325	−	0.257324i	$-0.917159\pi$
$13$	−3.17545	+	2.66452i	−0.880711	+	0.739004i	0.0856143	+	0.996328i	$0.472715\pi$
$14$	2.09238	−	1.75572i	0.559213	−	0.469235i
$15$		0			0
$16$	−12.5682	+	4.57445i	−3.14205	+	1.14361i
$17$	−1.95549	−	3.38700i	−0.474275	−	0.821469i	0.525291	−	0.850923i	$-0.323957\pi$
$17$	−1.95549	−	3.38700i	−0.474275	−	0.821469i	−0.999566	+	0.0294538i	$0.990623\pi$
$18$	4.54350	+	6.70342i	1.07091	+	1.58001i
$19$	0.433214	−	0.750349i	0.0993861	−	0.172142i	−0.812045	−	0.583595i	$-0.801645\pi$
$19$	0.433214	−	0.750349i	0.0993861	−	0.172142i	0.911431	+	0.411454i	$0.134979\pi$
$20$		0			0
$21$	1.66744	+	0.539711i	0.363866	+	0.117775i
$22$	3.19197	+	1.16178i	0.680530	+	0.247693i
$23$	0.479332	+	2.71843i	0.0999476	+	0.566831i	0.993119	+	0.117114i	$0.0373642\pi$
$23$	0.479332	+	2.71843i	0.0999476	+	0.566831i	−0.893171	+	0.449717i	$0.851525\pi$
$24$	−12.1194	−	9.44677i	−2.47386	−	1.92831i
$25$		0			0
$26$	11.1896			2.19445
$27$	−2.09743	+	4.75403i	−0.403650	+	0.914913i
$28$	−5.34934			−1.01093
$29$	6.00558	+	5.03928i	1.11521	+	0.935771i	0.998353	−	0.0573776i	$-0.0182739\pi$
$29$	6.00558	+	5.03928i	1.11521	+	0.935771i	0.116856	+	0.993149i	$0.462718\pi$
$30$		0			0
$31$	0.941551	+	5.33980i	0.169108	+	0.959057i	0.944728	+	0.327857i	$0.106326\pi$
$31$	0.941551	+	5.33980i	0.169108	+	0.959057i	−0.775620	+	0.631200i	$0.782563\pi$
$32$	17.2529	+	6.27953i	3.04991	+	1.11008i
$33$	0.455557	+	2.13143i	0.0793024	+	0.371035i
$34$	−1.83323	+	10.3968i	−0.314397	+	1.78303i
$35$		0			0
$36$	1.62229	−	15.7766i	0.270382	−	2.62943i
$37$	3.71964	+	6.44260i	0.611504	+	1.05916i	0.990987	+	0.133958i	$0.0427687\pi$
$37$	3.71964	+	6.44260i	0.611504	+	1.05916i	−0.379483	+	0.925199i	$0.623898\pi$
$38$	−2.19776	+	0.799919i	−0.356524	+	0.129764i
$39$	3.81156	+	6.08452i	0.610338	+	0.974303i
$40$		0			0
$41$	−2.73623	+	2.29597i	−0.427327	+	0.358570i	−0.830942	−	0.556359i	$-0.812198\pi$
$41$	−2.73623	+	2.29597i	−0.427327	+	0.358570i	0.403615	+	0.914929i	$0.367754\pi$
$42$	−2.51153	−	4.00925i	−0.387538	−	0.618640i
$43$	−4.00634	+	1.45819i	−0.610962	+	0.222372i	−0.628924	−	0.777467i	$-0.716504\pi$
$43$	−4.00634	+	1.45819i	−0.610962	+	0.222372i	0.0179623	+	0.999839i	$0.494282\pi$
$44$	−3.32626	−	5.76125i	−0.501452	−	0.868540i
$45$		0			0
$46$	3.72562	−	6.45296i	0.549312	−	0.951436i
$47$	−0.640847	+	3.63443i	−0.0934772	+	0.530136i	0.901726	+	0.432308i	$0.142301\pi$
$47$	−0.640847	+	3.63443i	−0.0934772	+	0.530136i	−0.995203	+	0.0978279i	$0.968811\pi$
$48$	4.84195	+	22.6542i	0.698875	+	3.26985i
$49$	5.61571	+	2.04395i	0.802245	+	0.291993i
$50$		0			0
$51$	−6.27789	+	2.54465i	−0.879080	+	0.356323i
$52$	−16.7873	−	14.0862i	−2.32798	−	1.95340i
$53$	0.485518			0.0666910			0.0333455	−	0.999444i	$-0.489384\pi$
$53$	0.485518			0.0666910			0.0333455	+	0.999444i	$0.489384\pi$
$54$	12.5859	−	6.19126i	1.71273	−	0.842524i
$55$		0			0
$56$	6.87680	+	5.77032i	0.918951	+	0.771091i
$57$	−1.18360	−	0.922590i	−0.156772	−	0.122200i
$58$	−3.67480	−	20.8408i	−0.482525	−	2.73653i
$59$	1.47979	+	0.538599i	0.192652	+	0.0701196i	0.436544	−	0.899683i	$-0.356202\pi$
$59$	1.47979	+	0.538599i	0.192652	+	0.0701196i	−0.243892	+	0.969802i	$0.578424\pi$
$60$		0			0
$61$	0.286481	−	1.62472i	0.0366802	−	0.208023i	−0.960960	−	0.276689i	$-0.910763\pi$
$61$	0.286481	−	1.62472i	0.0366802	−	0.208023i	0.997640	+	0.0686652i	$0.0218740\pi$
$62$	7.31822	−	12.6755i	0.929415	−	1.60979i
$63$	1.32458	−	2.73138i	0.166882	−	0.344122i
$64$	−11.4056	−	19.7550i	−1.42569	−	2.46938i
$65$		0			0
$66$	2.75627	−	5.19790i	0.339274	−	0.639817i
$67$	2.53969	−	2.13105i	0.310272	−	0.260349i	−0.474332	−	0.880346i	$-0.657310\pi$
$67$	2.53969	−	2.13105i	0.310272	−	0.260349i	0.784604	+	0.619997i	$0.212866\pi$
$68$	15.8385	−	13.2901i	1.92070	−	1.61166i
$69$	4.77798	−	0.172235i	0.575202	−	0.0207346i
$70$		0			0
$71$	−4.95764	−	8.58688i	−0.588363	−	1.01907i	−0.994447	−	0.105239i	$-0.966439\pi$
$71$	−4.95764	−	8.58688i	−0.588363	−	1.01907i	0.406084	−	0.913836i	$-0.366894\pi$
$72$	−19.1036	+	18.5314i	−2.25139	+	2.18395i
$73$	−2.63257	+	4.55975i	−0.308119	+	0.533678i	−0.977951	−	0.208835i	$-0.933033\pi$
$73$	−2.63257	+	4.55975i	−0.308119	+	0.533678i	0.669832	+	0.742513i	$0.266366\pi$
$74$	3.48709	−	19.7763i	0.405366	−	2.29894i
$75$		0			0
$76$	4.30421	+	1.56660i	0.493727	+	0.179702i
$77$	−0.221109	−	1.25397i	−0.0251977	−	0.142903i
$78$	2.67570	−	19.1953i	0.302963	−	2.17344i
$79$	−6.41639	−	5.38399i	−0.721901	−	0.605747i	0.206010	−	0.978550i	$-0.433952\pi$
$79$	−6.41639	−	5.38399i	−0.721901	−	0.605747i	−0.927910	+	0.372803i	$0.878397\pi$
$80$		0			0
$81$	7.65382	+	4.73487i	0.850425	+	0.526096i
$82$	9.64185			1.06476
$83$	2.21851	+	1.86155i	0.243513	+	0.204331i	0.756373	−	0.654141i	$-0.226970\pi$
$83$	2.21851	+	1.86155i	0.243513	+	0.204331i	−0.512860	+	0.858472i	$0.671414\pi$
$84$	−1.27916	+	9.17661i	−0.139568	+	1.00125i
$85$		0			0
$86$	10.8146	+	3.93619i	1.16617	+	0.424450i
$87$	10.0808	−	9.09735i	1.08077	−	0.975338i
$88$	−1.93860	+	10.9943i	−0.206655	+	1.17200i
$89$	−8.03383	+	13.9150i	−0.851584	+	1.47499i	0.0281944	+	0.999602i	$0.491024\pi$
$89$	−8.03383	+	13.9150i	−0.851584	+	1.47499i	−0.879778	+	0.475384i	$0.842309\pi$
$90$		0			0
$91$	−2.09723	−	3.63251i	−0.219850	−	0.380791i
$92$	−13.7128	+	4.99106i	−1.42966	+	0.520354i
$93$	9.38539	−	0.338321i	0.973220	−	0.0350822i
$94$	7.63133	−	6.40345i	0.787112	−	0.660465i
$95$		0			0
$96$	14.8979	−	28.0951i	1.52051	−	2.86745i
$97$	−2.90290	+	1.05657i	−0.294745	+	0.107278i	−0.485160	−	0.874425i	$-0.661239\pi$
$97$	−2.90290	+	1.05657i	−0.294745	+	0.107278i	0.190416	+	0.981704i	$0.439016\pi$
$98$	−8.06587	−	13.9705i	−0.814776	−	1.41123i
$99$	3.76533	−	0.271815i	0.378430	−	0.0273185i
$100$		0			0
$101$	1.48218	−	8.40586i	0.147482	−	0.836415i	−0.817858	−	0.575420i	$-0.804838\pi$
$101$	1.48218	−	8.40586i	0.147482	−	0.836415i	0.965340	−	0.260994i	$-0.0840504\pi$
$102$	17.3969	+	5.63097i	1.72255	+	0.557549i
$103$	14.9916	+	5.45651i	1.47717	+	0.537646i	0.950037	−	0.312136i	$-0.101045\pi$
$103$	14.9916	+	5.45651i	1.47717	+	0.537646i	0.527134	+	0.849782i	$0.323267\pi$
$104$	6.38599	+	36.2167i	0.626198	+	3.55134i
$105$		0			0
$106$	−1.00397	−	0.842432i	−0.0975143	−	0.0818242i
$107$	−9.20342			−0.889728			−0.444864	−	0.895598i	$-0.646748\pi$
$107$	−9.20342			−0.889728			−0.444864	+	0.895598i	$0.646748\pi$
$108$	−26.6762	−	6.55554i	−2.56692	−	0.630808i
$109$	4.98029			0.477025			0.238512	−	0.971139i	$-0.423340\pi$
$109$	4.98029			0.477025			0.238512	+	0.971139i	$0.423340\pi$
$110$		0			0
$111$	11.9415	−	4.84032i	1.13344	−	0.459423i
$112$	−2.35008	−	13.3280i	−0.222062	−	1.25938i
$113$	−7.47831	−	2.72188i	−0.703500	−	0.256053i	−0.0345954	−	0.999401i	$-0.511014\pi$
$113$	−7.47831	−	2.72188i	−0.703500	−	0.256053i	−0.668904	+	0.743348i	$0.733236\pi$
$114$	0.846695	+	3.96146i	0.0793003	+	0.371025i
$115$		0			0
$116$	−20.7227	+	35.8928i	−1.92405	+	3.33256i
$117$	11.3492	−	5.08364i	1.04924	−	0.469982i
$118$	−2.12542	−	3.68134i	−0.195661	−	0.338895i
$119$	3.71874	−	1.35351i	0.340897	−	0.124076i
$120$		0			0
$121$	−7.21345	+	6.05280i	−0.655768	+	0.550255i
$122$	−3.41147	+	2.86256i	−0.308860	+	0.259164i
$123$	3.28435	+	5.24293i	0.296140	+	0.472739i
$124$	−26.9361	+	9.80394i	−2.41893	+	0.880420i
$125$		0			0
$126$	−7.47829	+	3.34974i	−0.666219	+	0.298418i
$127$	−9.29062	+	16.0918i	−0.824409	+	1.42792i	0.0779609	+	0.996956i	$0.475159\pi$
$127$	−9.29062	+	16.0918i	−0.824409	+	1.42792i	−0.902370	+	0.430962i	$0.858174\pi$
$128$	−4.31608	+	24.4777i	−0.381491	+	2.16354i
$129$	1.54346	+	7.22143i	0.135894	+	0.635812i
$130$		0			0
$131$	3.27027	+	18.5466i	0.285725	+	1.62043i	0.702685	+	0.711501i	$0.251984\pi$
$131$	3.27027	+	18.5466i	0.285725	+	1.62043i	−0.416960	+	0.908925i	$0.636905\pi$
$132$	−10.6786	+	4.32842i	−0.929453	+	0.376741i
$133$	0.671602	+	0.563541i	0.0582353	+	0.0488652i
$134$	−8.94928			−0.773100
$135$		0			0
$136$	−34.6970			−2.97524
$137$	−12.2568	−	10.2847i	−1.04717	−	0.878680i	−0.0543771	−	0.998520i	$-0.517317\pi$
$137$	−12.2568	−	10.2847i	−1.04717	−	0.878680i	−0.992793	+	0.119840i	$0.961762\pi$
$138$	−10.1789	−	7.93422i	−0.866488	−	0.675406i
$139$	−2.32924	−	13.2098i	−0.197564	−	1.12044i	−0.908720	−	0.417406i	$-0.862939\pi$
$139$	−2.32924	−	13.2098i	−0.197564	−	1.12044i	0.711156	−	0.703034i	$-0.248172\pi$
$140$		0			0
$141$	6.08149	+	1.96843i	0.512154	+	0.165772i
$142$	−4.64769	+	26.3583i	−0.390025	+	2.21194i
$143$	2.60814	−	4.51744i	0.218104	−	0.377767i
$144$	40.0203	−	2.88902i	3.33502	−	0.240752i
$145$		0			0
$146$	13.3554	−	4.86098i	1.10530	−	0.402297i
$147$	4.84918	−	9.14480i	0.399954	−	0.754250i
$148$	−30.1273	+	25.2798i	−2.47645	+	2.07798i
$149$	−2.58412	+	2.16833i	−0.211699	+	0.177637i	−0.742471	−	0.669878i	$-0.766346\pi$
$149$	−2.58412	+	2.16833i	−0.211699	+	0.177637i	0.530772	+	0.847515i	$0.321902\pi$
$150$		0			0
$151$	21.6795	−	7.89070i	1.76426	−	0.642136i	0.764259	−	0.644910i	$-0.223105\pi$
$151$	21.6795	−	7.89070i	1.76426	−	0.642136i	0.999996	+	0.00277330i	$0.000882769\pi$
$152$	−3.84335	−	6.65687i	−0.311737	−	0.539943i
$153$	2.86407	+	11.3780i	0.231546	+	0.919856i
$154$	−1.71857	+	2.97665i	−0.138487	+	0.239866i
$155$		0			0
$156$	−28.1786	+	25.4296i	−2.25610	+	2.03600i
$157$	8.58300	+	3.12396i	0.684998	+	0.249319i	0.660992	−	0.750393i	$-0.270136\pi$
$157$	8.58300	+	3.12396i	0.684998	+	0.249319i	0.0240060	+	0.999712i	$0.492358\pi$
$158$	3.92617	+	22.2664i	0.312349	+	1.77142i
$159$	0.116099	−	0.832889i	0.00920726	−	0.0660524i
$160$		0			0
$161$	−2.79313			−0.220130
$162$	−7.61129	−	23.0712i	−0.597999	−	1.81265i
$163$	7.32494			0.573734			0.286867	−	0.957970i	$-0.407386\pi$
$163$	7.32494			0.573734			0.286867	+	0.957970i	$0.407386\pi$
$164$	−14.4653	−	12.1378i	−1.12955	−	0.947806i
$165$		0			0
$166$	−1.35750	−	7.69875i	−0.105362	−	0.597539i
$167$	4.72696	+	1.72047i	0.365783	+	0.133134i	0.518371	−	0.855156i	$-0.326539\pi$
$167$	4.72696	+	1.72047i	0.365783	+	0.133134i	−0.152588	+	0.988290i	$0.548761\pi$
$168$	11.5432	−	10.4171i	0.890576	−	0.803695i
$169$	0.726391	−	4.11957i	0.0558763	−	0.316890i
$170$		0			0
$171$	−1.86570	+	1.80982i	−0.142674	+	0.138400i
$172$	−11.2696	−	19.5195i	−0.859297	−	1.48835i
$173$	−18.0111	+	6.55550i	−1.36936	+	0.498406i	−0.918935	−	0.394410i	$-0.870949\pi$
$173$	−18.0111	+	6.55550i	−1.36936	+	0.498406i	−0.450423	+	0.892815i	$0.648727\pi$
$174$	−36.6304	+	1.32044i	−2.77694	+	0.100102i
$175$		0			0
$176$	12.8929	−	10.8185i	0.971842	−	0.815472i
$177$	1.27780	−	2.40973i	0.0960454	−	0.181127i
$178$	40.7568	−	14.8343i	3.05485	−	1.11188i
$179$	−6.81005	−	11.7953i	−0.509007	−	0.881626i	−0.999946	−	0.0104315i	$-0.996679\pi$
$179$	−6.81005	−	11.7953i	−0.509007	−	0.881626i	0.490939	−	0.871194i	$-0.336654\pi$
$180$		0			0
$181$	−4.25402	+	7.36817i	−0.316198	+	0.547672i	−0.979692	−	0.200511i	$-0.935740\pi$
$181$	−4.25402	+	7.36817i	−0.316198	+	0.547672i	0.663493	+	0.748182i	$0.269073\pi$
$182$	−1.96611	+	11.1504i	−0.145738	+	0.826521i
$183$	−2.71864	−	0.879957i	−0.200967	−	0.0650483i
$184$	23.0122	+	8.37577i	1.69648	+	0.617470i
$185$		0			0
$186$	−19.9945	−	15.5852i	−1.46607	−	1.14276i
$187$	3.77007	+	3.16346i	0.275695	+	0.231335i
$188$	−19.5101			−1.42292
$189$	−4.36885	−	2.92541i	−0.317787	−	0.212792i
$190$		0			0
$191$	−9.82022	−	8.24015i	−0.710566	−	0.596236i	0.214192	−	0.976792i	$-0.431288\pi$
$191$	−9.82022	−	8.24015i	−0.710566	−	0.596236i	−0.924758	+	0.380556i	$0.875733\pi$
$192$	−36.6164	+	14.8419i	−2.64256	+	1.07112i
$193$	1.73065	+	9.81499i	0.124575	+	0.706498i	0.981560	+	0.191157i	$0.0612239\pi$
$193$	1.73065	+	9.81499i	0.124575	+	0.706498i	−0.856985	+	0.515342i	$0.827665\pi$
$194$	7.83599	+	2.85207i	0.562591	+	0.204766i
$195$		0			0
$196$	−5.48611	+	31.1133i	−0.391865	+	2.22238i
$197$	−9.82458	+	17.0167i	−0.699972	+	1.21239i	0.268503	+	0.963279i	$0.413471\pi$
$197$	−9.82458	+	17.0167i	−0.699972	+	1.21239i	−0.968475	+	0.249109i	$0.919862\pi$
$198$	−8.25772	−	5.97123i	−0.586850	−	0.424357i
$199$	−1.80778	−	3.13117i	−0.128150	−	0.221963i	0.794810	−	0.606859i	$-0.207571\pi$
$199$	−1.80778	−	3.13117i	−0.128150	−	0.221963i	−0.922960	+	0.384896i	$0.874237\pi$
$200$		0			0
$201$	−3.04844	−	4.86633i	−0.215020	−	0.343244i
$202$	−17.6501	+	14.8102i	−1.24186	+	1.04204i
$203$	−6.07688	+	5.09911i	−0.426513	+	0.357887i
$204$	−19.0113	−	30.3484i	−1.33106	−	2.12481i
$205$		0			0
$206$	−21.5326	−	37.2955i	−1.50024	−	2.59850i
$207$	0.847070	−	8.23765i	0.0588754	−	0.572556i
$208$	27.7210	−	48.0142i	1.92210	−	3.32918i
$209$	−0.189327	+	1.07373i	−0.0130960	+	0.0742714i
$210$		0			0
$211$	−17.2131	−	6.26505i	−1.18500	−	0.431304i	−0.327033	−	0.945013i	$-0.606049\pi$
$211$	−17.2131	−	6.26505i	−1.18500	−	0.431304i	−0.857964	+	0.513709i	$0.828271\pi$
$212$	0.445708	+	2.52774i	0.0306114	+	0.173606i
$213$	−15.9160	+	6.45132i	−1.09054	+	0.442037i
$214$	19.0312	+	15.9690i	1.30094	+	1.09162i
$215$		0			0
$216$	27.2219	+	37.2029i	1.85222	+	2.53134i
$217$	−5.48655			−0.372451
$218$	−10.2984	−	8.64139i	−0.697496	−	0.585269i
$219$	7.19257	+	5.60643i	0.486029	+	0.378847i
$220$		0			0
$221$	15.2343	+	5.54482i	1.02477	+	0.372985i
$222$	−33.0916	−	10.7110i	−2.22096	−	0.718873i
$223$	−1.21714	+	6.90273i	−0.0815055	+	0.462241i	0.916551	+	0.399919i	$0.130962\pi$
$223$	−1.21714	+	6.90273i	−0.0815055	+	0.462241i	−0.998056	+	0.0623220i	$0.980149\pi$
$224$	−9.28904	+	16.0891i	−0.620650	+	1.07500i
$225$		0			0
$226$	10.7411	+	18.6042i	0.714488	+	1.23753i
$227$	12.6185	−	4.59274i	0.837516	−	0.304831i	0.112576	−	0.993643i	$-0.464090\pi$
$227$	12.6185	−	4.59274i	0.837516	−	0.304831i	0.724940	+	0.688812i	$0.241868\pi$
$228$	3.71670	−	7.00911i	0.246144	−	0.464190i
$229$	−7.11646	+	5.97142i	−0.470269	+	0.394602i	−0.846893	−	0.531764i	$-0.821529\pi$
$229$	−7.11646	+	5.97142i	−0.470269	+	0.394602i	0.376624	+	0.926366i	$0.377085\pi$
$230$		0			0
$231$	−2.20401	+	0.0794494i	−0.145014	+	0.00522739i
$232$	65.3573	−	23.7881i	4.29091	−	1.56177i
$233$	5.10552	+	8.84302i	0.334474	+	0.579325i	0.983384	−	0.181540i	$-0.0581081\pi$
$233$	5.10552	+	8.84302i	0.334474	+	0.579325i	−0.648910	+	0.760865i	$0.724775\pi$
$234$	−32.2890	−	9.18013i	−2.11080	−	0.600124i
$235$		0			0
$236$	−1.44564	+	8.19861i	−0.0941029	+	0.533684i
$237$	−10.7704	+	9.71965i	−0.699611	+	0.631359i
$238$	−10.0383	−	3.65363i	−0.650683	−	0.236829i
$239$	0.450136	+	2.55285i	0.0291169	+	0.165130i	0.995899	−	0.0904719i	$-0.0288375\pi$
$239$	0.450136	+	2.55285i	0.0291169	+	0.165130i	−0.966782	+	0.255602i	$0.917726\pi$
$240$		0			0
$241$	−12.7419	−	10.6918i	−0.820781	−	0.688717i	0.132374	−	0.991200i	$-0.457740\pi$
$241$	−12.7419	−	10.6918i	−0.820781	−	0.688717i	−0.953155	+	0.302483i	$0.902185\pi$
$242$	25.4186			1.63397
$243$	9.95271	−	11.9976i	0.638467	−	0.769649i
$244$	8.72170			0.558349
$245$		0			0
$246$	2.30560	−	16.5403i	0.147000	−	1.05457i
$247$	0.623669	+	3.53700i	0.0396831	+	0.225054i
$248$	45.2029	+	16.4525i	2.87039	+	1.04474i
$249$	3.72392	−	3.36063i	0.235994	−	0.212971i
$250$		0			0
$251$	−6.10066	+	10.5667i	−0.385070	+	0.666961i	−0.991779	−	0.127963i	$-0.959156\pi$
$251$	−6.10066	+	10.5667i	−0.385070	+	0.666961i	0.606709	+	0.794924i	$0.292489\pi$
$252$	15.4363	+	4.38870i	0.972394	+	0.276462i
$253$	−1.73679	−	3.00820i	−0.109191	−	0.189124i
$254$	47.1327	−	17.1549i	2.95737	−	1.07639i
$255$		0			0
$256$	16.4481	−	13.8016i	1.02800	−	0.862597i
$257$	−6.52086	+	5.47165i	−0.406760	+	0.341312i	−0.823100	−	0.567897i	$-0.807757\pi$
$257$	−6.52086	+	5.47165i	−0.406760	+	0.341312i	0.416340	+	0.909209i	$0.363313\pi$
$258$	9.33843	−	17.6108i	0.581385	−	1.09640i
$259$	−7.07362	+	2.57459i	−0.439533	+	0.159977i
$260$		0			0
$261$	−13.1956	−	19.4686i	−0.816788	−	1.20508i
$262$	25.4182	−	44.0257i	1.57034	−	2.71992i
$263$	1.60132	−	9.08152i	0.0987415	−	0.559991i	−0.894795	−	0.446477i	$-0.852678\pi$
$263$	1.60132	−	9.08152i	0.0987415	−	0.559991i	0.993536	−	0.113514i	$-0.0362105\pi$
$264$	18.3968	+	5.95461i	1.13225	+	0.366481i
$265$		0			0
$266$	−0.410951	−	2.33062i	−0.0251970	−	0.142899i
$267$	21.9496	+	17.1092i	1.34329	+	1.04706i
$268$	13.4263	+	11.2660i	0.820140	+	0.688179i
$269$	−7.15347			−0.436155			−0.218078	−	0.975931i	$-0.569979\pi$
$269$	−7.15347			−0.436155			−0.218078	+	0.975931i	$0.569979\pi$
$270$		0			0
$271$	17.3418			1.05344			0.526721	−	0.850038i	$-0.323421\pi$
$271$	17.3418			1.05344			0.526721	+	0.850038i	$0.323421\pi$
$272$	40.0707	+	33.6233i	2.42964	+	2.03871i
$273$	−6.73294	+	2.72910i	−0.407496	+	0.165173i
$274$	7.49991	+	42.5341i	0.453086	+	2.56958i
$275$		0			0
$276$	5.28292	+	24.7174i	0.317994	+	1.48781i
$277$	−1.83081	+	10.3831i	−0.110003	+	0.623858i	0.879101	+	0.476636i	$0.158144\pi$
$277$	−1.83081	+	10.3831i	−0.110003	+	0.623858i	−0.989104	+	0.147222i	$0.952967\pi$
$278$	−18.1041	+	31.3572i	−1.08581	+	1.88068i
$279$	1.66390	−	16.1812i	0.0996150	−	0.968744i
$280$		0			0
$281$	20.1528	−	7.33501i	1.20221	−	0.437570i	0.338217	−	0.941068i	$-0.390176\pi$
$281$	20.1528	−	7.33501i	1.20221	−	0.437570i	0.863996	+	0.503498i	$0.167954\pi$
$282$	−9.16005	−	14.6225i	−0.545473	−	0.870758i
$283$	12.4408	−	10.4391i	0.739528	−	0.620538i	−0.193183	−	0.981163i	$-0.561881\pi$
$283$	12.4408	−	10.4391i	0.739528	−	0.620538i	0.932711	+	0.360625i	$0.117437\pi$
$284$	40.1545	−	33.6936i	2.38273	−	1.99935i
$285$		0			0
$286$	−13.2315	+	4.81588i	−0.782396	+	0.284769i
$287$	−1.80715	−	3.13007i	−0.106673	−	0.184762i
$288$	−44.6337	−	32.2751i	−2.63007	−	1.90183i
$289$	0.852138	−	1.47595i	0.0501257	−	0.0868203i
$290$		0			0
$291$	1.11835	+	5.23247i	0.0655589	+	0.306733i
$292$	−26.1560	−	9.52000i	−1.53066	−	0.557116i
$293$	−4.10392	−	23.2745i	−0.239753	−	1.35971i	−0.832368	−	0.554223i	$-0.813016\pi$
$293$	−4.10392	−	23.2745i	−0.239753	−	1.35971i	0.592615	−	0.805486i	$-0.298096\pi$
$294$	−25.8946	+	10.4960i	−1.51021	+	0.612141i
$295$		0			0
$296$	65.9990			3.83611
$297$	0.434093	−	6.52429i	0.0251886	−	0.378578i
$298$	9.10584			0.527487
$299$	−8.76538	−	7.35503i	−0.506915	−	0.425352i
$300$		0			0
$301$	−0.749131	−	4.24853i	−0.0431792	−	0.244881i
$302$	−58.5210	−	21.2999i	−3.36751	−	1.22567i
$303$	−14.0655	−	4.55268i	−0.808044	−	0.261544i
$304$	−2.01229	+	11.4123i	−0.115413	+	0.654538i
$305$		0			0
$306$	13.8198	−	28.4973i	0.790023	−	1.62908i
$307$	3.08468	+	5.34281i	0.176052	+	0.304931i	0.940525	−	0.339725i	$-0.110334\pi$
$307$	3.08468	+	5.34281i	0.176052	+	0.304931i	−0.764473	+	0.644656i	$0.777001\pi$
$308$	6.32553	−	2.30230i	0.360430	−	0.131186i
$309$	12.9453	−	24.4129i	0.736434	−	1.38880i
$310$		0			0
$311$	−10.4699	+	8.78527i	−0.593692	+	0.498167i	−0.889411	−	0.457108i	$-0.848885\pi$
$311$	−10.4699	+	8.78527i	−0.593692	+	0.498167i	0.295719	+	0.955275i	$0.404441\pi$
$312$	63.6556	−	2.29463i	3.60379	−	0.129908i
$313$	−7.42730	+	2.70332i	−0.419816	+	0.152800i	−0.543286	−	0.839548i	$-0.682820\pi$
$313$	−7.42730	+	2.70332i	−0.419816	+	0.152800i	0.123470	+	0.992348i	$0.460598\pi$
$314$	−12.3278	−	21.3524i	−0.695698	−	1.20498i
$315$		0			0
$316$	22.1402	−	38.3480i	1.24549	−	2.15724i
$317$	−0.976298	+	5.53686i	−0.0548344	+	0.310981i	−0.999872	−	0.0159795i	$-0.994913\pi$
$317$	−0.976298	+	5.53686i	−0.0548344	+	0.310981i	0.945038	+	0.326961i	$0.106024\pi$
$318$	−1.68524	+	1.52083i	−0.0945033	+	0.0852840i
$319$	−9.27038	−	3.37414i	−0.519042	−	0.188916i
$320$		0			0
$321$	−2.20076	+	15.7881i	−0.122835	+	0.881208i
$322$	5.77574	+	4.84642i	0.321869	+	0.270080i
$323$	−3.38858			−0.188546
$324$	−17.6247	+	44.1945i	−0.979152	+	2.45525i
$325$		0			0
$326$	−15.1468	−	12.7097i	−0.838902	−	0.703923i
$327$	1.19091	−	8.54351i	0.0658574	−	0.472457i
$328$	5.50270	+	31.2073i	0.303836	+	1.72314i
$329$	−3.50910	−	1.27721i	−0.193463	−	0.0704147i
$330$		0			0
$331$	4.33246	−	24.5706i	0.238133	−	1.35052i	−0.597780	−	0.801660i	$-0.703951\pi$
$331$	4.33246	−	24.5706i	0.238133	−	1.35052i	0.835914	−	0.548861i	$-0.184938\pi$
$332$	−7.65512	+	13.2591i	−0.420129	+	0.727685i
$333$	−5.44790	−	21.6427i	−0.298543	−	1.18601i
$334$	−6.78935	−	11.7595i	−0.371497	−	0.643451i
$335$		0			0
$336$	−23.4256	+	0.844438i	−1.27797	+	0.0460679i
$337$	−8.27238	+	6.94135i	−0.450625	+	0.378119i	−0.839668	−	0.543100i	$-0.817250\pi$
$337$	−8.27238	+	6.94135i	−0.450625	+	0.378119i	0.389043	+	0.921220i	$0.372806\pi$
$338$	−8.65001	+	7.25822i	−0.470498	+	0.394795i
$339$	−6.45754	+	12.1779i	−0.350725	+	0.661413i
$340$		0			0
$341$	−3.41157	−	5.90901i	−0.184747	−	0.319991i
$342$	6.99821	−	0.505194i	0.378420	−	0.0273178i
$343$	−6.56508	+	11.3711i	−0.354481	+	0.613979i
$344$	−6.56810	+	37.2495i	−0.354128	+	2.00836i
$345$		0			0
$346$	48.6186	+	17.6957i	2.61375	+	0.951327i
$347$	−4.49326	−	25.4825i	−0.241211	−	1.36797i	−0.829131	−	0.559055i	$-0.811164\pi$
$347$	−4.49326	−	25.4825i	−0.241211	−	1.36797i	0.587920	−	0.808919i	$-0.299947\pi$
$348$	56.6175	+	44.1319i	3.03502	+	2.36572i
$349$	−11.7162	−	9.83109i	−0.627156	−	0.526246i	0.272888	−	0.962046i	$-0.412021\pi$
$349$	−11.7162	−	9.83109i	−0.627156	−	0.526246i	−0.900044	+	0.435799i	$0.856466\pi$
$350$		0			0
$351$	−6.00692	−	20.6848i	−0.320626	−	1.10407i
$352$	−23.1039			−1.23144
$353$	26.5412	+	22.2707i	1.41265	+	1.18535i	0.955144	+	0.296142i	$0.0957001\pi$
$353$	26.5412	+	22.2707i	1.41265	+	1.18535i	0.457502	+	0.889209i	$0.348744\pi$
$354$	−6.82346	+	2.76579i	−0.362663	+	0.147000i
$355$		0			0
$356$	−79.8203	−	29.0522i	−4.23047	−	1.53976i
$357$	−1.43266	−	6.70303i	−0.0758244	−	0.354762i
$358$	−6.38429	+	36.2071i	−0.337420	+	1.91360i
$359$	4.31838	−	7.47966i	0.227915	−	0.394761i	−0.729275	−	0.684221i	$-0.760142\pi$
$359$	4.31838	−	7.47966i	0.227915	−	0.394761i	0.957190	+	0.289460i	$0.0934757\pi$
$360$		0			0
$361$	9.12465	+	15.8044i	0.480245	+	0.831808i
$362$	21.5813	−	7.85494i	1.13429	−	0.412846i
$363$	8.65846	+	13.8218i	0.454451	+	0.725456i
$364$	16.9866	−	14.2534i	0.890338	−	0.747082i
$365$		0			0
$366$	4.09486	+	6.53677i	0.214042	+	0.341682i
$367$	25.7417	−	9.36923i	1.34371	−	0.489070i	0.432729	−	0.901524i	$-0.357551\pi$
$367$	25.7417	−	9.36923i	1.34371	−	0.489070i	0.910978	+	0.412454i	$0.135328\pi$
$368$	−18.4597	−	31.9731i	−0.962276	−	1.66671i
$369$	9.77943	−	4.38048i	0.509097	−	0.228039i
$370$		0			0
$371$	−0.0853101	+	0.483818i	−0.00442908	+	0.0251186i
$372$	10.3772	+	48.5523i	0.538034	+	2.51732i
$373$	−24.5318	−	8.92883i	−1.27021	−	0.462317i	−0.383025	−	0.923738i	$-0.625118\pi$
$373$	−24.5318	−	8.92883i	−1.27021	−	0.462317i	−0.887181	+	0.461421i	$0.847340\pi$
$374$	−2.30689	−	13.0831i	−0.119287	−	0.676508i
$375$		0			0
$376$	25.0810	+	21.0455i	1.29346	+	1.08534i
$377$	−32.4977			−1.67372
$378$	3.95812	+	13.6297i	0.203583	+	0.701038i
$379$	−10.9442			−0.562163			−0.281082	−	0.959684i	$-0.590693\pi$
$379$	−10.9442			−0.562163			−0.281082	+	0.959684i	$0.590693\pi$
$380$		0			0
$381$	25.3833	+	19.7857i	1.30043	+	1.01365i
$382$	6.00896	+	34.0785i	0.307445	+	1.74361i
$383$	−2.07084	−	0.753724i	−0.105815	−	0.0385135i	0.288570	−	0.957459i	$-0.406820\pi$
$383$	−2.07084	−	0.753724i	−0.105815	−	0.0385135i	−0.394385	+	0.918945i	$0.629042\pi$
$384$	40.9586	+	13.2573i	2.09016	+	0.676534i
$385$		0			0
$386$	13.4515	−	23.2987i	0.684663	−	1.18587i
$387$	12.7572	−	0.920928i	0.648484	−	0.0468134i
$388$	−8.16566	−	14.1433i	−0.414548	−	0.718019i
$389$	−22.8822	+	8.32844i	−1.16017	+	0.422268i	−0.849159	−	0.528137i	$-0.822891\pi$
$389$	−22.8822	+	8.32844i	−1.16017	+	0.422268i	−0.311014	+	0.950405i	$0.600669\pi$
$390$		0			0
$391$	8.26999	−	6.93935i	0.418231	−	0.350938i
$392$	40.6144	−	34.0795i	2.05134	−	1.72128i
$393$	32.5981	−	1.17508i	1.64436	−	0.0592750i
$394$	49.8416	−	18.1409i	2.51098	−	0.913923i
$395$		0			0
$396$	4.87174	+	19.3538i	0.244814	+	0.972565i
$397$	−5.57711	+	9.65983i	−0.279907	+	0.484813i	−0.971361	−	0.237607i	$-0.923637\pi$
$397$	−5.57711	+	9.65983i	−0.279907	+	0.484813i	0.691454	+	0.722420i	$0.256970\pi$
$398$	−1.69476	+	9.61146i	−0.0849506	+	0.481779i
$399$	1.12733	−	1.01735i	0.0564371	−	0.0509313i
$400$		0			0
$401$	0.624022	+	3.53900i	0.0311621	+	0.176729i	0.996416	−	0.0845831i	$-0.0269558\pi$
$401$	0.624022	+	3.53900i	0.0311621	+	0.176729i	−0.965254	+	0.261312i	$0.915845\pi$
$402$	−2.13999	+	15.3522i	−0.106733	+	0.765697i
$403$	−17.2178	−	14.4475i	−0.857682	−	0.719680i
$404$	45.1238			2.24500
$405$		0			0
$406$	21.4135			1.06274
$407$	−7.17125	−	6.01739i	−0.355466	−	0.298271i
$408$	−8.29690	+	59.5215i	−0.410758	+	2.94675i
$409$	−1.50204	−	8.51848i	−0.0742710	−	0.421212i	−0.999160	−	0.0409749i	$-0.986954\pi$
$409$	−1.50204	−	8.51848i	−0.0742710	−	0.421212i	0.924889	−	0.380237i	$-0.124157\pi$
$410$		0			0
$411$	−20.5739	+	18.5668i	−1.01484	+	0.915833i
$412$	−14.6457	+	83.0597i	−0.721540	+	4.09206i
$413$	−0.796726	+	1.37997i	−0.0392043	+	0.0679039i
$414$	−16.0449	+	15.5643i	−0.788564	+	0.764945i
$415$		0			0
$416$	−71.5175	+	26.0303i	−3.50644	+	1.27624i
$417$	−23.2179	+	0.836950i	−1.13699	+	0.0409856i
$418$	2.25455	−	1.89179i	0.110273	−	0.0925304i
$419$	−28.1908	+	23.6549i	−1.37721	+	1.15562i	−0.406977	+	0.913438i	$0.633417\pi$
$419$	−28.1908	+	23.6549i	−1.37721	+	1.15562i	−0.970232	+	0.242177i	$0.922139\pi$
$420$		0			0
$421$	−34.0828	+	12.4051i	−1.66109	+	0.604588i	−0.990534	−	0.137269i	$-0.956168\pi$
$421$	−34.0828	+	12.4051i	−1.66109	+	0.604588i	−0.670558	+	0.741857i	$0.733945\pi$
$422$	24.7232	+	42.8218i	1.20351	+	2.08453i
$423$	4.83101	−	9.96188i	0.234892	−	0.484363i
$424$	2.15368	−	3.73029i	0.104592	−	0.181159i
$425$		0			0
$426$	44.1054	+	14.2759i	2.13692	+	0.691668i
$427$	1.56869	+	0.570956i	0.0759142	+	0.0276305i
$428$	−8.44879	−	47.9155i	−0.408388	−	2.31608i
$429$	−7.12583	−	5.55441i	−0.344039	−	0.268169i
$430$		0			0
$431$	−19.3566			−0.932373			−0.466187	−	0.884686i	$-0.654372\pi$
$431$	−19.3566			−0.932373			−0.466187	+	0.884686i	$0.654372\pi$
$432$	4.61381	−	69.3442i	0.221982	−	3.33633i
$433$	22.8003			1.09571			0.547855	−	0.836573i	$-0.315444\pi$
$433$	22.8003			1.09571			0.547855	+	0.836573i	$0.315444\pi$
$434$	11.3453	+	9.51981i	0.544591	+	0.456966i
$435$		0			0
$436$	4.57193	+	25.9287i	0.218956	+	1.24176i
$437$	2.24742	+	0.817994i	0.107509	+	0.0391300i
$438$	−5.14523	−	24.0731i	−0.245849	−	1.15026i
$439$	3.36657	−	19.0928i	0.160678	−	0.911248i	−0.792732	−	0.609570i	$-0.791342\pi$
$439$	3.36657	−	19.0928i	0.160678	−	0.911248i	0.953410	−	0.301678i	$-0.0975468\pi$
$440$		0			0
$441$	−14.5280	−	10.5053i	−0.691811	−	0.500255i
$442$	−21.8810	−	37.8991i	−1.04078	−	1.80268i
$443$	3.65769	−	1.33129i	0.173782	−	0.0632516i	−0.253664	−	0.967292i	$-0.581636\pi$
$443$	3.65769	−	1.33129i	0.173782	−	0.0632516i	0.427446	+	0.904041i	$0.359413\pi$
$444$	36.1624	+	57.7273i	1.71619	+	2.73962i
$445$		0			0
$446$	14.4939	−	12.1618i	0.686306	−	0.575879i
$447$	3.10177	+	4.95146i	0.146709	+	0.234196i
$448$	21.6899	−	7.89448i	1.02475	−	0.372979i
$449$	10.9458	+	18.9586i	0.516562	+	0.894712i	0.999815	+	0.0192309i	$0.00612178\pi$
$449$	10.9458	+	18.9586i	0.516562	+	0.894712i	−0.483253	+	0.875481i	$0.660545\pi$
$450$		0			0
$451$	2.24739	−	3.89260i	0.105826	−	0.183295i
$452$	7.30572	−	41.4328i	0.343632	−	1.94883i
$453$	−8.35212	−	39.0773i	−0.392417	−	1.83601i
$454$	−34.0618	−	12.3975i	−1.59860	−	0.581843i
$455$		0			0
$456$	−12.3387	+	5.00130i	−0.577811	+	0.234208i
$457$	−14.7842	−	12.4055i	−0.691578	−	0.580303i	0.227786	−	0.973711i	$-0.426851\pi$
$457$	−14.7842	−	12.4055i	−0.691578	−	0.580303i	−0.919364	+	0.393409i	$0.871296\pi$
$458$	25.0768			1.17176
$459$	20.2034	−	2.19245i	0.943014	−	0.102335i
$460$		0			0
$461$	29.2721	+	24.5622i	1.36334	+	1.14398i	0.974936	+	0.222486i	$0.0714173\pi$
$461$	29.2721	+	24.5622i	1.36334	+	1.14398i	0.388402	+	0.921490i	$0.373027\pi$
$462$	4.69539	+	3.65994i	0.218449	+	0.170276i
$463$	3.87239	+	21.9614i	0.179965	+	1.02063i	0.932255	+	0.361801i	$0.117838\pi$
$463$	3.87239	+	21.9614i	0.179965	+	1.02063i	−0.752290	+	0.658832i	$0.771051\pi$
$464$	−98.5314	−	35.8625i	−4.57421	−	1.66487i
$465$		0			0
$466$	4.78632	−	27.1446i	0.221722	−	1.25745i
$467$	15.0806	−	26.1204i	0.697847	−	1.20871i	−0.271365	−	0.962477i	$-0.587475\pi$
$467$	15.0806	−	26.1204i	0.697847	−	1.20871i	0.969212	−	0.246229i	$-0.0791917\pi$
$468$	36.8854	+	54.4203i	1.70503	+	2.51558i
$469$	1.67734	+	2.90524i	0.0774524	+	0.134152i
$470$		0			0
$471$	7.41144	−	13.9768i	0.341501	−	0.644018i
$472$	10.7022	−	8.98024i	0.492610	−	0.413349i
$473$	4.10986	−	3.44858i	0.188971	−	0.158566i
$474$	39.1361	−	1.41076i	1.79758	−	0.0647985i
$475$		0			0
$476$	10.4606	+	18.1182i	0.479460	+	0.830448i
$477$	−1.40103	−	0.398328i	−0.0641487	−	0.0182382i
$478$	3.49869	−	6.05991i	0.160026	−	0.277174i
$479$	2.47679	−	14.0466i	0.113167	−	0.641804i	−0.874474	−	0.485073i	$-0.838793\pi$
$479$	2.47679	−	14.0466i	0.113167	−	0.641804i	0.987641	−	0.156731i	$-0.0500957\pi$
$480$		0			0
$481$	−28.9779	−	10.5471i	−1.32128	−	0.480907i
$482$	7.79676	+	44.2176i	0.355133	+	2.01406i
$483$	−0.667906	+	4.79152i	−0.0303908	+	0.218022i
$484$	−38.1345	−	31.9987i	−1.73339	−	1.45448i
$485$		0			0
$486$	−41.3979	+	7.54000i	−1.87785	+	0.342021i
$487$	20.9938			0.951318			0.475659	−	0.879630i	$-0.342210\pi$
$487$	20.9938			0.951318			0.475659	+	0.879630i	$0.342210\pi$
$488$	−11.2121	−	9.40806i	−0.507548	−	0.425883i
$489$	1.75157	−	12.5657i	0.0792089	−	0.568240i
$490$		0			0
$491$	−4.84651	−	1.76398i	−0.218720	−	0.0796075i	0.230336	−	0.973111i	$-0.426017\pi$
$491$	−4.84651	−	1.76398i	−0.218720	−	0.0796075i	−0.449056	+	0.893504i	$0.648240\pi$
$492$	−24.2810	+	21.9123i	−1.09467	+	0.987882i
$493$	5.32423	−	30.1952i	0.239791	−	1.35992i
$494$	4.84748	−	8.39607i	0.218098	−	0.377757i
$495$		0			0
$496$	−36.2603	−	62.8047i	−1.62814	−	2.82001i
$497$	9.42792	−	3.43148i	0.422900	−	0.153923i
$498$	−13.5315	+	0.487780i	−0.606363	+	0.0218579i
$499$	−27.2570	+	22.8713i	−1.22019	+	1.02386i	−0.221376	+	0.975189i	$0.571055\pi$
$499$	−27.2570	+	22.8713i	−1.22019	+	1.02386i	−0.998815	+	0.0486726i	$0.984501\pi$
$500$		0			0
$501$	4.08174	−	7.69753i	0.182359	−	0.343900i
$502$	30.9496	−	11.2647i	1.38135	−	0.502769i
$503$	−1.70975	−	2.96137i	−0.0762338	−	0.132041i	0.825388	−	0.564565i	$-0.190956\pi$
$503$	−1.70975	−	2.96137i	−0.0762338	−	0.132041i	−0.901622	+	0.432525i	$0.857623\pi$
$504$	−15.1099	−	22.2929i	−0.673047	−	0.993005i
$505$		0			0
$506$	−1.62820	+	9.23400i	−0.0723825	+	0.410501i
$507$	−6.89328	−	2.23119i	−0.306141	−	0.0990906i
$508$	−92.3072	−	33.5971i	−4.09547	−	1.49063i
$509$	3.45809	+	19.6118i	0.153277	+	0.869277i	0.960344	+	0.278817i	$0.0899424\pi$
$509$	3.45809	+	19.6118i	0.153277	+	0.869277i	−0.807067	+	0.590460i	$0.798946\pi$
$510$		0			0
$511$	−4.08121	−	3.42454i	−0.180542	−	0.151493i
$512$	−8.24859			−0.364540
$513$	2.65855	+	3.63331i	0.117378	+	0.160415i
$514$	22.9780			1.01352
$515$		0			0
$516$	−36.1798	+	14.6650i	−1.59273	+	0.645590i
$517$	−0.806427	−	4.57348i	−0.0354666	−	0.201141i
$518$	19.0943	+	6.94976i	0.838955	+	0.305355i
$519$	6.93884	+	32.4650i	0.304581	+	1.42505i
$520$		0			0
$521$	−10.7424	+	18.6064i	−0.470633	+	0.815160i	−0.999436	−	0.0335849i	$-0.989308\pi$
$521$	−10.7424	+	18.6064i	−0.470633	+	0.815160i	0.528803	+	0.848744i	$0.322641\pi$
$522$	−6.49406	+	63.1539i	−0.284237	+	2.76417i
$523$	−16.5963	−	28.7457i	−0.725707	−	1.25696i	−0.958682	−	0.284479i	$-0.908180\pi$
$523$	−16.5963	−	28.7457i	−0.725707	−	1.25696i	0.232976	−	0.972483i	$-0.425154\pi$
$524$	−93.5566	+	34.0518i	−4.08704	+	1.48756i
$525$		0			0
$526$	−19.0688	+	16.0006i	−0.831439	+	0.697660i
$527$	16.2447	−	13.6310i	0.707632	−	0.593774i
$528$	−15.4757	−	24.7044i	−0.673492	−	1.07512i
$529$	14.4529	−	5.26041i	0.628385	−	0.228713i
$530$		0			0
$531$	−3.82826	−	2.76825i	−0.166132	−	0.120132i
$532$	−2.31741	+	4.01387i	−0.100473	+	0.174024i
$533$	2.57110	−	14.5815i	0.111367	−	0.631593i
$534$	−15.7017	−	73.4641i	−0.679480	−	3.17910i
$535$		0			0
$536$	−5.10744	−	28.9657i	−0.220608	−	1.25113i
$537$	−21.8629	+	8.86184i	−0.943456	+	0.382417i
$538$	14.7922	+	12.4121i	0.637737	+	0.535125i
$539$	−7.52020			−0.323918
$540$		0			0
$541$	2.83444			0.121862			0.0609309	−	0.998142i	$-0.480593\pi$
$541$	2.83444			0.121862			0.0609309	+	0.998142i	$0.480593\pi$
$542$	−35.8601	−	30.0902i	−1.54032	−	1.29248i
$543$	11.6226	+	9.05952i	0.498773	+	0.388781i
$544$	−12.4690	−	70.7151i	−0.534603	−	3.03188i
$545$		0			0
$546$	18.6579	+	6.03913i	0.798486	+	0.258451i
$547$	5.85741	−	33.2190i	0.250445	−	1.42034i	−0.557055	−	0.830475i	$-0.688069\pi$
$547$	5.85741	−	33.2190i	0.250445	−	1.42034i	0.807500	−	0.589868i	$-0.200820\pi$
$548$	42.2930	−	73.2537i	1.80667	−	3.12924i
$549$	−2.15963	+	4.45331i	−0.0921707	+	0.190063i
$550$		0			0
$551$	6.38292	−	2.32319i	0.271922	−	0.0989714i
$552$	19.8711	−	37.4738i	0.845771	−	1.59499i
$553$	6.49256	−	5.44791i	0.276092	−	0.231669i
$554$	21.8017	−	18.2938i	0.926265	−	0.777229i
$555$		0			0
$556$	66.6355	−	24.2533i	2.82598	−	1.02857i
$557$	−8.28915	−	14.3572i	−0.351222	−	0.608335i	0.635242	−	0.772314i	$-0.280901\pi$
$557$	−8.28915	−	14.3572i	−0.351222	−	0.608335i	−0.986464	+	0.163979i	$0.947567\pi$
$558$	−31.5170	+	30.5730i	−1.33422	+	1.29426i
$559$	8.83656	−	15.3054i	0.373747	−	0.647349i
$560$		0			0
$561$	6.32833	−	5.71096i	0.267182	−	0.241117i
$562$	−54.3997	−	19.7999i	−2.29471	−	0.835208i
$563$	2.34303	+	13.2880i	0.0987471	+	0.560023i	0.993535	+	0.113530i	$0.0362159\pi$
$563$	2.34303	+	13.2880i	0.0987471	+	0.560023i	−0.894787	+	0.446492i	$0.852673\pi$
$564$	−4.66534	+	33.4689i	−0.196446	+	1.40930i
$565$		0			0
$566$	−43.8385			−1.84267
$567$	−6.06314	+	6.79507i	−0.254628	+	0.285366i
$568$	−87.9653			−3.69094
$569$	14.0395	+	11.7805i	0.588565	+	0.493865i	0.887747	−	0.460331i	$-0.152269\pi$
$569$	14.0395	+	11.7805i	0.588565	+	0.493865i	−0.299182	+	0.954196i	$0.596714\pi$
$570$		0			0
$571$	1.67291	+	9.48757i	0.0700093	+	0.397043i	0.999596	+	0.0284379i	$0.00905327\pi$
$571$	1.67291	+	9.48757i	0.0700093	+	0.397043i	−0.929586	+	0.368605i	$0.879836\pi$
$572$	25.9133	+	9.43167i	1.08349	+	0.394358i
$573$	−16.4839	+	14.8758i	−0.688626	+	0.621447i
$574$	−1.69417	+	9.60809i	−0.0707131	+	0.401034i
$575$		0			0
$576$	16.7049	+	66.3631i	0.696039	+	2.76513i
$577$	−9.45304	−	16.3731i	−0.393535	−	0.681623i	0.599378	−	0.800466i	$-0.295415\pi$
$577$	−9.45304	−	16.3731i	−0.393535	−	0.681623i	−0.992913	+	0.118843i	$0.962081\pi$
$578$	−4.32302	+	1.57345i	−0.179814	+	0.0654470i
$579$	17.2511	−	0.621861i	0.716932	−	0.0258437i
$580$		0			0
$581$	−2.24484	+	1.88365i	−0.0931318	+	0.0781468i
$582$	6.76639	−	12.7604i	0.280476	−	0.528934i
$583$	−0.574118	+	0.208962i	−0.0237776	+	0.00865432i
$584$	23.3554	+	40.4527i	0.966452	+	1.67394i
$585$		0			0
$586$	−31.8978	+	55.2485i	−1.31768	+	2.28230i
$587$	−6.83405	+	38.7578i	−0.282071	+	1.59971i	0.433491	+	0.901158i	$0.357282\pi$
$587$	−6.83405	+	38.7578i	−0.282071	+	1.59971i	−0.715563	+	0.698549i	$0.753830\pi$
$588$	52.0619	+	16.8512i	2.14700	+	0.694931i
$589$	4.41461	+	1.60679i	0.181901	+	0.0662065i
$590$		0			0
$591$	26.8422	+	20.9228i	1.10414	+	0.860650i
$592$	−76.2206	−	63.9566i	−3.13265	−	2.62860i
$593$	1.34012			0.0550322			0.0275161	−	0.999621i	$-0.491240\pi$
$593$	1.34012			0.0550322			0.0275161	+	0.999621i	$0.491240\pi$
$594$	−12.2181	+	12.7380i	−0.501313	+	0.522645i
$595$		0			0
$596$	−13.6612	−	11.4631i	−0.559583	−	0.469546i
$597$	−5.80370	+	2.35245i	−0.237529	+	0.0962792i
$598$	5.36351	+	30.4180i	0.219330	+	1.24388i
$599$	30.9748	+	11.2739i	1.26559	+	0.460639i	0.885643	−	0.464367i	$-0.153718\pi$
$599$	30.9748	+	11.2739i	1.26559	+	0.460639i	0.379952	+	0.925006i	$0.375940\pi$
$600$		0			0
$601$	5.62780	−	31.9168i	0.229563	−	1.30192i	−0.624205	−	0.781261i	$-0.714577\pi$
$601$	5.62780	−	31.9168i	0.229563	−	1.30192i	0.853767	−	0.520655i	$-0.174312\pi$
$602$	−5.82264	+	10.0851i	−0.237313	+	0.411038i
$603$	−9.07697	+	4.06583i	−0.369643	+	0.165574i
$604$	60.9831	+	105.626i	2.48137	+	4.29785i
$605$		0			0
$606$	21.1858	+	33.8196i	0.860613	+	1.37383i
$607$	15.8543	−	13.3034i	0.643508	−	0.539967i	−0.261585	−	0.965180i	$-0.584245\pi$
$607$	15.8543	−	13.3034i	0.643508	−	0.539967i	0.905093	+	0.425213i	$0.139801\pi$
$608$	12.1860	−	10.2253i	0.494209	−	0.414690i
$609$	7.29421	+	11.6440i	0.295576	+	0.471838i
$610$		0			0
$611$	−7.64901	−	13.2485i	−0.309446	−	0.535976i
$612$	−56.6076	+	25.3562i	−2.28823	+	1.02496i
$613$	−16.8679	+	29.2160i	−0.681287	+	1.18002i	0.293301	+	0.956020i	$0.405246\pi$
$613$	−16.8679	+	29.2160i	−0.681287	+	1.18002i	−0.974588	+	0.224004i	$0.928087\pi$
$614$	2.89182	−	16.4003i	0.116704	−	0.661864i
$615$		0			0
$616$	−10.6152	−	3.86362i	−0.427699	−	0.155670i
$617$	5.32646	+	30.2079i	0.214435	+	1.21612i	0.881884	+	0.471467i	$0.156275\pi$
$617$	5.32646	+	30.2079i	0.214435	+	1.21612i	−0.667448	+	0.744656i	$0.732614\pi$
$618$	−69.1280	+	28.0201i	−2.78074	+	1.12713i
$619$	22.9897	+	19.2906i	0.924033	+	0.775356i	0.974737	−	0.223358i	$-0.0717018\pi$
$619$	22.9897	+	19.2906i	0.924033	+	0.775356i	−0.0507031	+	0.998714i	$0.516146\pi$
$620$		0			0
$621$	−13.9288	−	3.42294i	−0.558945	−	0.137358i
$622$	36.8935			1.47929
$623$	−12.4547	−	10.4507i	−0.498985	−	0.418698i
$624$	−75.7378	−	59.0357i	−3.03194	−	2.36332i
$625$		0			0
$626$	20.0490	+	7.29725i	0.801320	+	0.291657i
$627$	1.79667	+	0.581539i	0.0717521	+	0.0232244i
$628$	−8.38492	+	47.5532i	−0.334595	+	1.89758i
$629$	14.5474	−	25.1968i	0.580043	−	1.00466i
$630$		0			0
$631$	22.1756	+	38.4093i	0.882797	+	1.52905i	0.848218	+	0.529647i	$0.177675\pi$
$631$	22.1756	+	38.4093i	0.882797	+	1.52905i	0.0345781	+	0.999402i	$0.488991\pi$
$632$	−69.8280	+	25.4153i	−2.77761	+	1.01097i
$633$	−14.8635	+	28.0303i	−0.590772	+	1.11410i
$634$	11.6259	−	9.75533i	0.461725	−	0.387433i
$635$		0			0
$636$	4.44282	−	0.160153i	0.176169	−	0.00635048i
$637$	−23.2785	+	8.47270i	−0.922330	+	0.335701i
$638$	13.3151	+	23.0624i	0.527149	+	0.913049i
$639$	7.26111	+	28.8460i	0.287245	+	1.14113i
$640$		0			0
$641$	5.79316	−	32.8547i	0.228816	−	1.29768i	−0.626437	−	0.779472i	$-0.715488\pi$
$641$	5.79316	−	32.8547i	0.228816	−	1.29768i	0.855254	−	0.518210i	$-0.173401\pi$
$642$	31.9451	−	28.8287i	1.26077	−	1.13778i
$643$	15.2874	+	5.56415i	0.602875	+	0.219429i	0.625383	−	0.780318i	$-0.284943\pi$
$643$	15.2874	+	5.56415i	0.602875	+	0.219429i	−0.0225078	+	0.999747i	$0.507165\pi$
$644$	−2.56411	−	14.5418i	−0.101040	−	0.573027i
$645$		0			0
$646$	7.00702	+	5.87959i	0.275688	+	0.231329i
$647$	39.9222			1.56950			0.784751	−	0.619811i	$-0.212791\pi$
$647$	39.9222			1.56950			0.784751	+	0.619811i	$0.212791\pi$
$648$	70.3298	−	37.8021i	2.76281	−	1.48501i
$649$	−1.98164			−0.0777861
$650$		0			0
$651$	−1.31197	+	9.41198i	−0.0514200	+	0.368884i
$652$	6.72434	+	38.1356i	0.263345	+	1.49351i
$653$	5.23644	+	1.90591i	0.204918	+	0.0745839i	0.442440	−	0.896798i	$-0.354113\pi$
$653$	5.23644	+	1.90591i	0.204918	+	0.0745839i	−0.237522	+	0.971382i	$0.576335\pi$
$654$	−17.2866	+	15.6002i	−0.675960	+	0.610016i
$655$		0			0
$656$	23.8867	−	41.3730i	0.932619	−	1.61534i
$657$	11.3376	−	10.9980i	0.442320	−	0.429072i
$658$	5.04013	+	8.72976i	0.196485	+	0.340322i
$659$	−6.70045	+	2.43876i	−0.261012	+	0.0950007i	−0.469212	−	0.883086i	$-0.655462\pi$
$659$	−6.70045	+	2.43876i	−0.261012	+	0.0950007i	0.208199	+	0.978086i	$0.433240\pi$
$660$		0			0
$661$	−11.1617	+	9.36578i	−0.434140	+	0.364286i	−0.833511	−	0.552503i	$-0.813673\pi$
$661$	−11.1617	+	9.36578i	−0.434140	+	0.364286i	0.399371	+	0.916789i	$0.369228\pi$
$662$	−51.5917	+	43.2906i	−2.00517	+	1.68254i
$663$	13.1548	−	24.8080i	0.510892	−	0.963462i
$664$	24.1435	−	8.78750i	0.936948	−	0.341021i
$665$		0			0
$666$	−26.2873	+	54.2062i	−1.01861	+	2.10045i
$667$	−10.8202	+	18.7412i	−0.418962	+	0.725663i
$668$	−4.61787	+	26.1892i	−0.178671	+	1.01329i
$669$	11.5503	+	3.73857i	0.446562	+	0.144541i
$670$		0			0
$671$	0.360501	+	2.04450i	0.0139170	+	0.0789272i
$672$	25.3790	+	19.7823i	0.979018	+	0.763120i
$673$	−0.370154	−	0.310596i	−0.0142684	−	0.0119726i	0.635626	−	0.771998i	$-0.280742\pi$
$673$	−0.370154	−	0.310596i	−0.0142684	−	0.0119726i	−0.649894	+	0.760025i	$0.725187\pi$
$674$	29.1500			1.12282
$675$		0			0
$676$	22.1144			0.850555
$677$	29.9869	+	25.1620i	1.15249	+	0.967055i	0.999775	−	0.0212148i	$-0.00675338\pi$
$677$	29.9869	+	25.1620i	1.15249	+	0.967055i	0.152717	+	0.988270i	$0.451198\pi$
$678$	34.4832	−	13.9773i	1.32432	−	0.536795i
$679$	−0.542802	−	3.07838i	−0.0208308	−	0.118137i
$680$		0			0
$681$	−4.86131	−	22.7447i	−0.186286	−	0.871581i
$682$	−3.19828	+	18.1383i	−0.122468	+	0.694553i
$683$	0.106584	−	0.184609i	0.00407832	−	0.00706386i	−0.863979	−	0.503528i	$-0.832035\pi$
$683$	0.106584	−	0.184609i	0.00407832	−	0.00706386i	0.868057	+	0.496464i	$0.165368\pi$
$684$	−11.1351	−	8.05191i	−0.425762	−	0.307873i
$685$		0			0
$686$	33.3056	−	12.1223i	1.27162	−	0.462830i
$687$	8.54204	+	13.6359i	0.325899	+	0.520244i
$688$	43.6821	−	36.6537i	1.66537	−	1.39741i
$689$	−1.54174	+	1.29367i	−0.0587355	+	0.0492849i
$690$		0			0
$691$	20.5204	−	7.46881i	0.780633	−	0.284127i	0.0791962	−	0.996859i	$-0.474765\pi$
$691$	20.5204	−	7.46881i	0.780633	−	0.284127i	0.701436	+	0.712732i	$0.252542\pi$
$692$	−50.6640	−	87.7526i	−1.92596	−	3.33585i
$693$	−0.390741	+	3.79991i	−0.0148430	+	0.144347i
$694$	−34.9239	+	60.4900i	−1.32569	+	2.29617i
$695$		0			0
$696$	−25.1791	−	117.806i	−0.954412	−	4.46544i
$697$	13.1271	+	4.77788i	0.497225	+	0.180975i
$698$	7.16913	+	40.6582i	0.271356	+	1.53893i
$699$	16.3907	−	6.64376i	0.619955	−	0.251290i
$700$		0			0
$701$	−35.4129			−1.33753			−0.668763	−	0.743476i	$-0.733176\pi$
$701$	−35.4129			−1.33753			−0.668763	+	0.743476i	$0.733176\pi$
$702$	−23.4693	+	53.1955i	−0.885791	+	2.00774i
$703$	6.44560			0.243100
$704$	21.9893	+	18.4512i	0.828752	+	0.695405i
$705$		0			0
$706$	−16.2405	−	92.1044i	−0.611219	−	3.46639i
$707$	8.11600	+	2.95398i	0.305234	+	0.111096i
$708$	13.7187	+	4.44043i	0.515582	+	0.166882i
$709$	1.16039	−	6.58093i	0.0435795	−	0.247152i	−0.955234	−	0.295852i	$-0.904397\pi$
$709$	1.16039	−	6.58093i	0.0435795	−	0.247152i	0.998813	+	0.0486997i	$0.0155077\pi$
$710$		0			0
$711$	14.0983	+	20.8004i	0.528726	+	0.780076i
$712$	71.2737	+	123.450i	2.67110	+	4.62647i
$713$	−14.0645	+	5.11907i	−0.526721	+	0.191711i
$714$	−8.66806	+	16.3466i	−0.324394	+	0.611756i
$715$		0			0
$716$	55.1581	−	46.2831i	2.06135	−	1.72968i
$717$	4.48696	−	0.161744i	0.167569	−	0.00604044i
$718$	−21.9078	+	7.97379i	−0.817592	+	0.297579i
$719$	1.59977	+	2.77089i	0.0596614	+	0.103337i	0.894313	−	0.447441i	$-0.147665\pi$
$719$	1.59977	+	2.77089i	0.0596614	+	0.103337i	−0.834652	+	0.550778i	$0.814331\pi$
$720$		0			0
$721$	−8.07159	+	13.9804i	−0.300602	+	0.520657i
$722$	8.55418	−	48.5132i	0.318354	−	1.80547i
$723$	−21.3883	+	19.3017i	−0.795438	+	0.717838i
$724$	−42.2659	−	15.3835i	−1.57080	−	0.571724i
$725$		0			0
$726$	6.07820	−	43.6047i	0.225583	−	1.61832i
$727$	−30.2941	−	25.4198i	−1.12355	−	0.942768i	−0.124769	−	0.992186i	$-0.539819\pi$
$727$	−30.2941	−	25.4198i	−1.12355	−	0.942768i	−0.998778	+	0.0494182i	$0.984263\pi$
$728$	−37.2120			−1.37917
$729$	−18.2016	−	19.9425i	−0.674133	−	0.738610i
$730$		0			0
$731$	12.7732	+	10.7180i	0.472436	+	0.396421i
$732$	2.08557	−	14.9618i	0.0770849	−	0.553003i
$733$	−8.28983	−	47.0139i	−0.306192	−	1.73650i	−0.617842	−	0.786302i	$-0.711993\pi$
$733$	−8.28983	−	47.0139i	−0.306192	−	1.73650i	0.311650	−	0.950197i	$-0.399118\pi$
$734$	−69.4864	−	25.2910i	−2.56479	−	0.933507i
$735$		0			0
$736$	−8.80059	+	49.9106i	−0.324394	+	1.83973i
$737$	−2.08596	+	3.61299i	−0.0768374	+	0.133086i
$738$	−27.8229	−	7.91036i	−1.02418	−	0.291184i
$739$	−0.756718	−	1.31067i	−0.0278363	−	0.0482139i	0.851772	−	0.523913i	$-0.175528\pi$
$739$	−0.756718	−	1.31067i	−0.0278363	−	0.0482139i	−0.879608	+	0.475699i	$0.842195\pi$
$740$		0			0
$741$	6.21673	−	0.224098i	0.228377	−	0.00823245i
$742$	1.01589	−	0.852432i	0.0372945	−	0.0312938i
$743$	14.9554	−	12.5490i	0.548659	−	0.460380i	−0.325827	−	0.945429i	$-0.605643\pi$
$743$	14.9554	−	12.5490i	0.548659	−	0.460380i	0.874487	+	0.485049i	$0.161198\pi$
$744$	39.0328	−	73.6098i	1.43101	−	2.69867i
$745$		0			0
$746$	35.2351	+	61.0289i	1.29005	+	2.23443i
$747$	−4.87456	−	7.19186i	−0.178351	−	0.263136i
$748$	−13.0089	+	22.5321i	−0.475653	+	0.823855i
$749$	1.61713	−	9.17119i	0.0590886	−	0.335108i
$750$		0			0
$751$	−20.9890	−	7.63937i	−0.765900	−	0.278765i	−0.0706193	−	0.997503i	$-0.522498\pi$
$751$	−20.9890	−	7.63937i	−0.765900	−	0.278765i	−0.695280	+	0.718739i	$0.744720\pi$
$752$	−8.57121	−	48.6098i	−0.312560	−	1.77262i
$753$	16.6679	+	12.9922i	0.607412	+	0.473463i
$754$	67.1998	+	56.3874i	2.44727	+	2.05351i
$755$		0			0
$756$	11.2199	−	25.4309i	0.408062	−	0.924914i
$757$	−41.7562			−1.51766			−0.758828	−	0.651291i	$-0.774228\pi$
$757$	−41.7562			−1.51766			−0.758828	+	0.651291i	$0.774228\pi$
$758$	22.6307	+	18.9894i	0.821984	+	0.689727i
$759$	−5.57577	+	2.26006i	−0.202388	+	0.0820350i
$760$		0			0
$761$	31.4550	+	11.4487i	1.14024	+	0.415014i	0.842001	−	0.539476i	$-0.181378\pi$
$761$	31.4550	+	11.4487i	1.14024	+	0.415014i	0.298241	+	0.954490i	$0.403600\pi$
$762$	−18.1581	−	84.9567i	−0.657797	−	3.07766i
$763$	−0.875084	+	4.96285i	−0.0316802	+	0.179667i
$764$	33.8854	−	58.6912i	1.22593	−	2.12337i
$765$		0			0
$766$	2.97435	+	5.15173i	0.107468	+	0.186140i
$767$	−6.13410	+	2.23263i	−0.221489	+	0.0806155i
$768$	−19.7430	−	31.5163i	−0.712412	−	1.13725i
$769$	−11.6956	+	9.81375i	−0.421753	+	0.353893i	−0.828830	−	0.559501i	$-0.810993\pi$
$769$	−11.6956	+	9.81375i	−0.421753	+	0.353893i	0.407076	+	0.913394i	$0.366548\pi$
$770$		0			0
$771$	7.82713	+	12.4947i	0.281887	+	0.449986i
$772$	−49.5107	+	18.0204i	−1.78193	+	0.648570i
$773$	−13.4630	−	23.3186i	−0.484230	−	0.838711i	0.515606	−	0.856826i	$-0.327567\pi$
$773$	−13.4630	−	23.3186i	−0.484230	−	0.838711i	−0.999836	+	0.0181148i	$0.994234\pi$
$774$	−27.9777	−	20.2309i	−1.00564	−	0.727186i
$775$		0			0
$776$	−4.75908	+	26.9901i	−0.170841	+	0.968887i
$777$	2.72514	+	12.7502i	0.0977638	+	0.457411i
$778$	61.7674	+	22.4815i	2.21447	+	0.806001i
$779$	0.537404	+	3.04777i	0.0192545	+	0.109198i
$780$		0			0
$781$	9.55805	+	8.02015i	0.342014	+	0.286984i
$782$	−29.1416			−1.04210
$783$	−36.5532	+	17.9812i	−1.30630	+	0.642595i
$784$	−79.9294			−2.85462
$785$		0			0
$786$	−69.4464	−	54.1317i	−2.47707	−	1.93081i
$787$	−4.54419	−	25.7714i	−0.161983	−	0.918650i	−0.952121	−	0.305722i	$-0.901102\pi$
$787$	−4.54419	−	25.7714i	−0.161983	−	0.918650i	0.790138	−	0.612929i	$-0.210009\pi$
$788$	−97.6124	−	35.5280i	−3.47730	−	1.26563i
$789$	−15.1961	−	4.91862i	−0.540996	−	0.175107i
$790$		0			0
$791$	4.02636	−	6.97386i	0.143161	−	0.247962i
$792$	14.6141	−	30.1352i	0.519288	−	1.07081i
$793$	3.41938	+	5.92253i	0.121426	+	0.210315i
$794$	28.2935	−	10.2980i	1.00410	−	0.365462i
$795$		0			0
$796$	14.6422	−	12.2862i	0.518978	−	0.435474i
$797$	27.3057	−	22.9122i	0.967216	−	0.811591i	−0.0148959	−	0.999889i	$-0.504742\pi$
$797$	27.3057	−	22.9122i	0.967216	−	0.811591i	0.982112	+	0.188298i	$0.0602972\pi$
$798$	−4.09636	+	0.147664i	−0.145010	+	0.00522725i
$799$	13.5630	−	4.93652i	0.479824	−	0.174642i
$800$		0			0
$801$	34.5989	−	33.5626i	1.22249	−	1.18587i
$802$	4.85022	−	8.40083i	0.171267	−	0.296643i
$803$	1.15051	−	6.52487i	0.0406006	−	0.230258i
$804$	22.5369	−	20.3383i	0.794816	−	0.717277i
$805$		0			0
$806$	10.5355	+	59.7500i	0.371099	+	2.10461i
$807$	−1.71057	+	12.2715i	−0.0602149	+	0.431978i
$808$	−58.0085	−	48.6749i	−2.04073	−	1.71238i
$809$	−5.37671			−0.189035			−0.0945175	−	0.995523i	$-0.530131\pi$
$809$	−5.37671			−0.189035			−0.0945175	+	0.995523i	$0.530131\pi$
$810$		0			0
$811$	25.4236			0.892744			0.446372	−	0.894847i	$-0.352716\pi$
$811$	25.4236			0.892744			0.446372	+	0.894847i	$0.352716\pi$
$812$	−32.1259	−	26.9569i	−1.12740	−	0.946000i
$813$	4.14686	−	29.7493i	0.145437	−	1.04335i
$814$	4.38807	+	24.8860i	0.153802	+	0.872253i
$815$		0			0
$816$	67.2614	−	60.6997i	2.35462	−	2.12491i
$817$	−0.641454	+	3.63786i	−0.0224416	+	0.127273i
$818$	−11.6746	+	20.2210i	−0.408193	+	0.707012i
$819$	3.07167	+	12.2027i	0.107333	+	0.426398i
$820$		0			0
$821$	12.2590	−	4.46192i	0.427843	−	0.155722i	−0.119118	−	0.992880i	$-0.538007\pi$
$821$	12.2590	−	4.46192i	0.427843	−	0.155722i	0.546961	+	0.837158i	$0.315785\pi$
$822$	74.7591	−	2.69489i	2.60752	−	0.0939950i
$823$	26.0965	−	21.8976i	0.909668	−	0.763302i	−0.0623879	−	0.998052i	$-0.519872\pi$
$823$	26.0965	−	21.8976i	0.909668	−	0.763302i	0.972056	+	0.234750i	$0.0754272\pi$
$824$	108.424	−	90.9783i	3.77712	−	3.16938i
$825$		0			0
$826$	4.04191	−	1.47114i	0.140636	−	0.0511874i
$827$	16.0942	+	27.8760i	0.559651	+	0.969345i	0.997525	+	0.0703083i	$0.0223983\pi$
$827$	16.0942	+	27.8760i	0.559651	+	0.969345i	−0.437874	+	0.899036i	$0.644268\pi$
$828$	43.6650	−	3.15213i	1.51746	−	0.109544i
$829$	−11.4430	+	19.8198i	−0.397431	+	0.688371i	−0.993408	−	0.114630i	$-0.963432\pi$
$829$	−11.4430	+	19.8198i	−0.397431	+	0.688371i	0.595977	+	0.803001i	$0.296765\pi$
$830$		0			0
$831$	17.3740	+	5.62354i	0.602697	+	0.195079i
$832$	88.8553	+	32.3407i	3.08050	+	1.12121i
$833$	−4.05858	−	23.0174i	−0.140622	−	0.797504i
$834$	49.4631	+	38.5552i	1.71277	+	1.33506i
$835$		0			0
$836$	−5.76392			−0.199350
$837$	−27.3604	−	6.72368i	−0.945714	−	0.232404i
$838$	99.3379			3.43157
$839$	14.3141	+	12.0109i	0.494176	+	0.414663i	0.855520	−	0.517769i	$-0.173237\pi$
$839$	14.3141	+	12.0109i	0.494176	+	0.414663i	−0.361344	+	0.932433i	$0.617682\pi$
$840$		0			0
$841$	5.63686	+	31.9682i	0.194375	+	1.10235i
$842$	92.0019	+	33.4859i	3.17059	+	1.15400i
$843$	−7.76393	−	36.3254i	−0.267404	−	1.25111i
$844$	16.8158	−	95.3673i	0.578824	−	3.28268i
$845$		0			0
$846$	−27.2748	+	12.2172i	−0.937726	+	0.420034i
$847$	−4.76414	−	8.25173i	−0.163698	−	0.283533i
$848$	−6.10209	+	2.22098i	−0.209547	+	0.0762687i
$849$	−14.9329	−	23.8380i	−0.512497	−	0.818117i
$850$		0			0
$851$	−15.7308	+	13.1997i	−0.539244	+	0.452480i
$852$	−48.1983	−	76.9405i	−1.65125	−	2.63594i
$853$	20.1180	−	7.32234i	0.688826	−	0.250712i	0.0261934	−	0.999657i	$-0.491661\pi$
$853$	20.1180	−	7.32234i	0.688826	−	0.250712i	0.662632	+	0.748945i	$0.269439\pi$
$854$	−2.25311	−	3.90251i	−0.0771000	−	0.133541i
$855$		0			0
$856$	−40.8250	+	70.7109i	−1.39537	+	2.41685i
$857$	−1.04514	+	5.92728i	−0.0357013	+	0.202472i	−0.997441	−	0.0714922i	$-0.977224\pi$
$857$	−1.04514	+	5.92728i	−0.0357013	+	0.202472i	0.961740	+	0.273964i	$0.0883350\pi$
$858$	5.09749	+	23.8498i	0.174025	+	0.814218i
$859$	21.9131	+	7.97570i	0.747664	+	0.272128i	0.687623	−	0.726068i	$-0.258654\pi$
$859$	21.9131	+	7.97570i	0.747664	+	0.272128i	0.0600417	+	0.998196i	$0.480877\pi$
$860$		0			0
$861$	−5.80166	+	2.35162i	−0.197720	+	0.0801431i
$862$	40.0262	+	33.5860i	1.36330	+	1.14394i
$863$	−19.5769			−0.666405			−0.333203	−	0.942855i	$-0.608129\pi$
$863$	−19.5769			−0.666405			−0.333203	+	0.942855i	$0.608129\pi$
$864$	−66.0397	+	68.8498i	−2.24672	+	2.34232i
$865$		0			0
$866$	−47.1472	−	39.5612i	−1.60213	−	1.34434i
$867$	−2.32817	−	1.81475i	−0.0790687	−	0.0616320i
$868$	−5.03668	−	28.5644i	−0.170956	−	0.969540i
$869$	9.90452	+	3.60495i	0.335988	+	0.122290i
$870$		0			0
$871$	−2.38642	+	13.5341i	−0.0808609	+	0.458585i
$872$	22.0918	−	38.2641i	0.748123	−	1.29579i
$873$	9.24354	−	0.667282i	0.312847	−	0.0225841i
$874$	−3.22798	−	5.59102i	−0.109188	−	0.189119i
$875$		0			0
$876$	−22.5858	+	42.5932i	−0.763102	+	1.43909i
$877$	38.4239	−	32.2415i	1.29748	−	1.08872i	0.306910	−	0.951739i	$-0.400705\pi$
$877$	38.4239	−	32.2415i	1.29748	−	1.08872i	0.990574	−	0.136979i	$-0.0437394\pi$
$878$	−40.0898	+	33.6393i	−1.35296	+	1.13527i
$879$	−40.9079	+	1.47463i	−1.37979	+	0.0497380i
$880$		0			0
$881$	4.92107	+	8.52354i	0.165795	+	0.287165i	0.936937	−	0.349497i	$-0.113648\pi$
$881$	4.92107	+	8.52354i	0.165795	+	0.287165i	−0.771142	+	0.636663i	$0.780314\pi$
$882$	11.8135	+	46.9312i	0.397782	+	1.58026i
$883$	−8.11410	+	14.0540i	−0.273061	+	0.472956i	−0.969644	−	0.244520i	$-0.921369\pi$
$883$	−8.11410	+	14.0540i	−0.273061	+	0.472956i	0.696583	+	0.717476i	$0.254703\pi$
$884$	−14.8827	+	84.4039i	−0.500559	+	2.83881i
$885$		0			0
$886$	−9.87346	−	3.59365i	−0.331705	−	0.120731i
$887$	0.805833	+	4.57011i	0.0270572	+	0.153449i	0.995343	−	0.0963958i	$-0.0307315\pi$
$887$	0.805833	+	4.57011i	0.0270572	+	0.153449i	−0.968286	+	0.249845i	$0.919620\pi$
$888$	15.7820	−	113.219i	0.529608	−	3.79938i
$889$	−14.4030	−	12.0856i	−0.483062	−	0.405337i
$890$		0			0
$891$	−11.0884	−	2.30479i	−0.371475	−	0.0772133i
$892$	−37.0548			−1.24069
$893$	2.44946	+	2.05534i	0.0819682	+	0.0687795i
$894$	2.17743	−	15.6208i	0.0728241	−	0.522436i
$895$		0			0
$896$	−23.6336	−	8.60194i	−0.789544	−	0.287371i
$897$	−14.7133	+	13.2779i	−0.491263	+	0.443338i
$898$	10.2614	−	58.1955i	0.342428	−	1.94201i
$899$	−21.2542	+	36.8134i	−0.708867	+	1.22779i
$900$		0			0
$901$	−0.949424	−	1.64445i	−0.0316299	−	0.0547846i
$902$	−11.4014	+	4.14976i	−0.379624	+	0.138172i
$903$	−7.46735	+	0.269180i	−0.248498	+	0.00895774i
$904$	−54.0852	+	45.3829i	−1.79885	+	1.50941i
$905$		0			0
$906$	−50.5330	+	95.2974i	−1.67885	+	3.16604i
$907$	−8.36499	+	3.04461i	−0.277755	+	0.101094i	−0.477142	−	0.878826i	$-0.658327\pi$
$907$	−8.36499	+	3.04461i	−0.277755	+	0.101094i	0.199387	+	0.979921i	$0.436105\pi$
$908$	35.4949	+	61.4789i	1.17794	+	2.04025i
$909$	−11.1734	+	23.0403i	−0.370597	+	0.764198i
$910$		0			0
$911$	5.06913	−	28.7484i	0.167948	−	0.952478i	−0.778025	−	0.628233i	$-0.783779\pi$
$911$	5.06913	−	28.7484i	0.167948	−	0.952478i	0.945973	−	0.324245i	$-0.105110\pi$
$912$	19.0961	+	6.18096i	0.632336	+	0.204672i
$913$	−3.42455	−	1.24643i	−0.113336	−	0.0412509i
$914$	9.04643	+	51.3049i	0.299229	+	1.69701i
$915$		0			0
$916$	−37.6218	−	31.5684i	−1.24306	−	1.04305i
$917$	−19.0563			−0.629295
$918$	−45.5815	−	30.5217i	−1.50441	−	1.00737i
$919$	48.7206			1.60714			0.803572	−	0.595208i	$-0.202930\pi$
$919$	48.7206			1.60714			0.803572	+	0.595208i	$0.202930\pi$
$920$		0			0
$921$	9.90303	−	4.01405i	0.326316	−	0.132268i
$922$	−17.9115	−	101.581i	−0.589884	−	3.34540i
$923$	38.6226	+	14.0575i	1.27128	+	0.462707i
$924$	−2.43693	−	11.4018i	−0.0801692	−	0.375090i
$925$		0			0
$926$	30.0982	−	52.1316i	0.989088	−	1.71315i
$927$	−38.7839	−	28.0450i	−1.27383	−	0.921117i
$928$	71.9692	+	124.654i	2.36251	+	4.09198i
$929$	34.3831	−	12.5144i	1.12807	−	0.410585i	0.290480	−	0.956881i	$-0.406185\pi$
$929$	34.3831	−	12.5144i	1.12807	−	0.410585i	0.837592	+	0.546296i	$0.183963\pi$
$930$		0			0
$931$	3.96648	−	3.32827i	0.129996	−	0.109080i
$932$	−41.3522	+	34.6987i	−1.35454	+	1.13659i
$933$	12.5672	+	20.0615i	0.411432	+	0.656783i
$934$	−76.5061	+	27.8460i	−2.50336	+	0.911148i
$935$		0			0
$936$	11.2853	−	109.748i	0.368870	−	3.58721i
$937$	11.4630	−	19.8545i	0.374480	−	0.648618i	−0.615769	−	0.787927i	$-0.711155\pi$
$937$	11.4630	−	19.8545i	0.374480	−	0.648618i	0.990249	+	0.139308i	$0.0444880\pi$
$938$	1.57247	−	8.91795i	0.0513431	−	0.291181i
$939$	2.86140	+	13.3877i	0.0933781	+	0.436891i
$940$		0			0
$941$	2.11146	+	11.9747i	0.0688317	+	0.390364i	0.999688	+	0.0249784i	$0.00795170\pi$
$941$	2.11146	+	11.9747i	0.0688317	+	0.390364i	−0.930856	+	0.365385i	$0.880937\pi$
$942$	−39.5771	+	16.0420i	−1.28949	+	0.522677i
$943$	−7.55298	−	6.33770i	−0.245959	−	0.206384i
$944$	−21.0621			−0.685512
$945$		0			0
$946$	−14.4822			−0.470857
$947$	9.82072	+	8.24056i	0.319130	+	0.267782i	0.788254	−	0.615351i	$-0.210986\pi$
$947$	9.82072	+	8.24056i	0.319130	+	0.267782i	−0.469123	+	0.883133i	$0.655430\pi$
$948$	−60.4904	−	47.1507i	−1.96464	−	1.53138i
$949$	−3.78993	−	21.4938i	−0.123026	−	0.697717i
$950$		0			0
$951$	9.26484	+	2.99880i	0.300433	+	0.0972429i
$952$	6.09660	−	34.5755i	0.197592	−	1.12060i
$953$	−5.10838	+	8.84797i	−0.165477	+	0.286614i	−0.936824	−	0.349800i	$-0.886250\pi$
$953$	−5.10838	+	8.84797i	−0.165477	+	0.286614i	0.771348	+	0.636414i	$0.219583\pi$
$954$	2.20595	+	3.25463i	0.0714203	+	0.105373i
$955$		0			0
$956$	−12.8776	+	4.68706i	−0.416491	+	0.151590i
$957$	−8.00500	+	15.0962i	−0.258765	+	0.487990i
$958$	−29.4941	+	24.7485i	−0.952910	+	0.799586i
$959$	12.4023	−	10.4068i	0.400492	−	0.336053i
$960$		0			0
$961$	1.50350	−	0.547231i	0.0485002	−	0.0176526i
$962$	41.6211	+	72.0899i	1.34192	+	2.32427i
$963$	26.5577	+	7.55066i	0.855811	+	0.243317i
$964$	43.9670	−	76.1531i	1.41608	−	2.45273i
$965$		0			0
$966$	9.69498	−	8.74917i	0.311931	−	0.281500i
$967$	25.5290	+	9.29181i	0.820958	+	0.298804i	0.718143	−	0.695896i	$-0.244993\pi$
$967$	25.5290	+	9.29181i	0.820958	+	0.298804i	0.102816	+	0.994700i	$0.467215\pi$
$968$	14.5066	+	82.2711i	0.466260	+	2.64429i
$969$	−0.810292	+	5.81299i	−0.0260303	+	0.186740i
$970$		0			0
$971$	−7.96515			−0.255614			−0.127807	−	0.991799i	$-0.540794\pi$
$971$	−7.96515			−0.255614			−0.127807	+	0.991799i	$0.540794\pi$
$972$	71.5996	+	40.8026i	2.29656	+	1.30874i
$973$	13.5728			0.435125
$974$	−43.4117	−	36.4267i	−1.39100	−	1.16719i
$975$		0			0
$976$	3.83163	+	21.7303i	0.122648	+	0.695569i
$977$	40.4381	+	14.7183i	1.29373	+	0.470879i	0.894949	−	0.446168i	$-0.147212\pi$
$977$	40.4381	+	14.7183i	1.29373	+	0.470879i	0.398779	+	0.917047i	$0.369434\pi$
$978$	−25.4249	+	22.9446i	−0.813000	+	0.733687i
$979$	3.51102	−	19.9120i	0.112213	−	0.636390i
$980$		0			0
$981$	−14.3713	−	4.08592i	−0.458841	−	0.130453i
$982$	6.96105	+	12.0569i	0.222136	+	0.384751i
$983$	40.3135	−	14.6729i	1.28580	−	0.467993i	0.393453	−	0.919345i	$-0.371280\pi$
$983$	40.3135	−	14.6729i	1.28580	−	0.467993i	0.892346	+	0.451352i	$0.149058\pi$
$984$	54.8509	−	1.97724i	1.74858	−	0.0630322i
$985$		0			0
$986$	−63.4019	+	53.2005i	−2.01913	+	1.69425i
$987$	−3.03012	+	5.71432i	−0.0964496	+	0.181889i
$988$	−17.8420	+	6.49397i	−0.567631	+	0.206601i
$989$	−5.88435	−	10.1920i	−0.187111	−	0.324086i
$990$		0			0
$991$	18.5127	−	32.0649i	0.588075	−	1.01858i	−0.406410	−	0.913691i	$-0.633219\pi$
$991$	18.5127	−	32.0649i	0.588075	−	1.01858i	0.994484	−	0.104884i	$-0.0334473\pi$
$992$	−17.2870	+	98.0394i	−0.548863	+	3.11276i
$993$	−41.1140	−	13.3076i	−1.30471	−	0.422304i
$994$	−25.4494	−	9.26283i	−0.807206	−	0.293799i
$995$		0			0
$996$	20.9149	+	16.3027i	0.662714	+	0.516569i
$997$	−19.3849	−	16.2659i	−0.613927	−	0.515146i	0.281961	−	0.959426i	$-0.409015\pi$
$997$	−19.3849	−	16.2659i	−0.613927	−	0.515146i	−0.895888	+	0.444280i	$0.853460\pi$
$998$	96.0475			3.04033
$999$	−38.4300	+	4.17038i	−1.21587	+	0.131945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.h.151.1		96
5.2	odd	4		135.2.p.a.124.16	yes	96
5.3	odd	4		135.2.p.a.124.1	yes	96
5.4	even	2	inner	675.2.l.h.151.16		96
15.2	even	4		405.2.p.a.289.1		96
15.8	even	4		405.2.p.a.289.16		96
27.22	even	9	inner	675.2.l.h.76.1		96
135.22	odd	36		135.2.p.a.49.1	✓	96
135.32	even	36		405.2.p.a.199.16		96
135.49	even	18	inner	675.2.l.h.76.16		96
135.103	odd	36		135.2.p.a.49.16	yes	96
135.113	even	36		405.2.p.a.199.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.1	✓	96	135.22	odd	36
135.2.p.a.49.16	yes	96	135.103	odd	36
135.2.p.a.124.1	yes	96	5.3	odd	4
135.2.p.a.124.16	yes	96	5.2	odd	4
405.2.p.a.199.1		96	135.113	even	36
405.2.p.a.199.16		96	135.32	even	36
405.2.p.a.289.1		96	15.2	even	4
405.2.p.a.289.16		96	15.8	even	4
675.2.l.h.76.1		96	27.22	even	9	inner
675.2.l.h.76.16		96	135.49	even	18	inner
675.2.l.h.151.1		96	1.1	even	1	trivial
675.2.l.h.151.16		96	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06784 - 1.73512i) q^{2} +(0.239124 - 1.71546i) q^{3} +(0.918006 + 5.20627i) q^{4} +(-3.47101 + 3.13239i) q^{6} +(-0.175710 + 0.996499i) q^{7} +(4.43585 - 7.68312i) q^{8} +(-2.88564 - 0.820419i) q^{9} +(-1.18249 + 0.430390i) q^{11} +(9.15069 - 0.329860i) q^{12} +(-3.17545 + 2.66452i) q^{13} +(2.09238 - 1.75572i) q^{14} +(-12.5682 + 4.57445i) q^{16} +(-1.95549 - 3.38700i) q^{17} +(4.54350 + 6.70342i) q^{18} +(0.433214 - 0.750349i) q^{19} +(1.66744 + 0.539711i) q^{21} +(3.19197 + 1.16178i) q^{22} +(0.479332 + 2.71843i) q^{23} +(-12.1194 - 9.44677i) q^{24} +11.1896 q^{26} +(-2.09743 + 4.75403i) q^{27} -5.34934 q^{28} +(6.00558 + 5.03928i) q^{29} +(0.941551 + 5.33980i) q^{31} +(17.2529 + 6.27953i) q^{32} +(0.455557 + 2.13143i) q^{33} +(-1.83323 + 10.3968i) q^{34} +(1.62229 - 15.7766i) q^{36} +(3.71964 + 6.44260i) q^{37} +(-2.19776 + 0.799919i) q^{38} +(3.81156 + 6.08452i) q^{39} +(-2.73623 + 2.29597i) q^{41} +(-2.51153 - 4.00925i) q^{42} +(-4.00634 + 1.45819i) q^{43} +(-3.32626 - 5.76125i) q^{44} +(3.72562 - 6.45296i) q^{46} +(-0.640847 + 3.63443i) q^{47} +(4.84195 + 22.6542i) q^{48} +(5.61571 + 2.04395i) q^{49} +(-6.27789 + 2.54465i) q^{51} +(-16.7873 - 14.0862i) q^{52} +0.485518 q^{53} +(12.5859 - 6.19126i) q^{54} +(6.87680 + 5.77032i) q^{56} +(-1.18360 - 0.922590i) q^{57} +(-3.67480 - 20.8408i) q^{58} +(1.47979 + 0.538599i) q^{59} +(0.286481 - 1.62472i) q^{61} +(7.31822 - 12.6755i) q^{62} +(1.32458 - 2.73138i) q^{63} +(-11.4056 - 19.7550i) q^{64} +(2.75627 - 5.19790i) q^{66} +(2.53969 - 2.13105i) q^{67} +(15.8385 - 13.2901i) q^{68} +(4.77798 - 0.172235i) q^{69} +(-4.95764 - 8.58688i) q^{71} +(-19.1036 + 18.5314i) q^{72} +(-2.63257 + 4.55975i) q^{73} +(3.48709 - 19.7763i) q^{74} +(4.30421 + 1.56660i) q^{76} +(-0.221109 - 1.25397i) q^{77} +(2.67570 - 19.1953i) q^{78} +(-6.41639 - 5.38399i) q^{79} +(7.65382 + 4.73487i) q^{81} +9.64185 q^{82} +(2.21851 + 1.86155i) q^{83} +(-1.27916 + 9.17661i) q^{84} +(10.8146 + 3.93619i) q^{86} +(10.0808 - 9.09735i) q^{87} +(-1.93860 + 10.9943i) q^{88} +(-8.03383 + 13.9150i) q^{89} +(-2.09723 - 3.63251i) q^{91} +(-13.7128 + 4.99106i) q^{92} +(9.38539 - 0.338321i) q^{93} +(7.63133 - 6.40345i) q^{94} +(14.8979 - 28.0951i) q^{96} +(-2.90290 + 1.05657i) q^{97} +(-8.06587 - 13.9705i) q^{98} +(3.76533 - 0.271815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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