LMFDB - Embedded newform 605.2.j.k.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.1
Character	$\chi$	$=$	605.124
Dual form			605.2.j.k.444.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53281 - 2.10973i) q^{2} +(-2.03508 + 0.661236i) q^{3} +(-1.48342 + 4.56549i) q^{4} +(1.27403 + 1.83762i) q^{5} +(4.51440 + 3.27991i) q^{6} +(0.940480 + 0.305580i) q^{7} +(6.94547 - 2.25672i) q^{8} +(1.27725 - 0.927974i) q^{9} +O(q^{10})$	\(q+(-1.53281 - 2.10973i) q^{2} +(-2.03508 + 0.661236i) q^{3} +(-1.48342 + 4.56549i) q^{4} +(1.27403 + 1.83762i) q^{5} +(4.51440 + 3.27991i) q^{6} +(0.940480 + 0.305580i) q^{7} +(6.94547 - 2.25672i) q^{8} +(1.27725 - 0.927974i) q^{9} +(1.92403 - 5.50457i) q^{10} -10.2720i q^{12} +(1.80817 + 2.48873i) q^{13} +(-0.796882 - 2.45255i) q^{14} +(-3.80785 - 2.89726i) q^{15} +(-7.63983 - 5.55066i) q^{16} +(-0.951558 + 1.30971i) q^{17} +(-3.91554 - 1.27224i) q^{18} +(-2.03412 - 6.26038i) q^{19} +(-10.2796 + 3.09063i) q^{20} -2.11601 q^{21} +5.18097i q^{23} +(-12.6423 + 9.18518i) q^{24} +(-1.75368 + 4.68237i) q^{25} +(2.47897 - 7.62949i) q^{26} +(1.78755 - 2.46036i) q^{27} +(-2.79025 + 3.84045i) q^{28} +(-2.25958 + 6.95428i) q^{29} +(-0.275722 + 12.4745i) q^{30} +(2.13816 - 1.55347i) q^{31} +10.0203i q^{32} +4.22168 q^{34} +(0.636661 + 2.11756i) q^{35} +(2.34197 + 7.20783i) q^{36} +(-2.66676 - 0.866482i) q^{37} +(-10.0898 + 13.8874i) q^{38} +(-5.32540 - 3.86913i) q^{39} +(12.9957 + 9.88799i) q^{40} +(0.428423 + 1.31855i) q^{41} +(3.24343 + 4.46420i) q^{42} -3.18585i q^{43} +(3.33252 + 1.16482i) q^{45} +(10.9304 - 7.94143i) q^{46} +(-2.03508 + 0.661236i) q^{47} +(19.2179 + 6.24429i) q^{48} +(-4.87200 - 3.53971i) q^{49} +(12.5666 - 3.47737i) q^{50} +(1.07047 - 3.29456i) q^{51} +(-14.0446 + 4.56335i) q^{52} +(1.39715 + 1.92302i) q^{53} -7.93065 q^{54} +7.22168 q^{56} +(8.27918 + 11.3953i) q^{57} +(18.1351 - 5.89246i) q^{58} +(-3.78354 + 11.6445i) q^{59} +(18.8760 - 13.0869i) q^{60} +(0.810998 + 0.589225i) q^{61} +(-6.55478 - 2.12978i) q^{62} +(1.48480 - 0.482439i) q^{63} +(5.86035 - 4.25780i) q^{64} +(-2.26967 + 6.49345i) q^{65} +9.84499i q^{67} +(-4.56790 - 6.28717i) q^{68} +(-3.42585 - 10.5437i) q^{69} +(3.49160 - 4.58899i) q^{70} +(0.197235 + 0.143300i) q^{71} +(6.77690 - 9.32760i) q^{72} +(-12.9998 - 4.22390i) q^{73} +(2.25958 + 6.95428i) q^{74} +(0.472729 - 10.6886i) q^{75} +31.5992 q^{76} +17.1658i q^{78} +(6.22629 - 4.52366i) q^{79} +(0.466611 - 21.1108i) q^{80} +(-3.47452 + 10.6935i) q^{81} +(2.12509 - 2.92494i) q^{82} +(3.50035 - 4.81781i) q^{83} +(3.13892 - 9.66061i) q^{84} +(-3.61906 - 0.0799918i) q^{85} +(-6.72127 + 4.88329i) q^{86} -15.6466i q^{87} -9.00000 q^{89} +(-2.65064 - 8.81615i) q^{90} +(0.940039 + 2.89314i) q^{91} +(-23.6537 - 7.68555i) q^{92} +(-3.32411 + 4.57525i) q^{93} +(4.51440 + 3.27991i) q^{94} +(8.91266 - 11.7139i) q^{95} +(-6.62576 - 20.3920i) q^{96} +(7.48775 + 10.3060i) q^{97} +15.7043i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.53281	−	2.10973i	−1.08386	−	1.49180i	−0.855202	−	0.518295i	$-0.826567\pi$
$2$	−1.53281	−	2.10973i	−1.08386	−	1.49180i	−0.228656	−	0.973507i	$-0.573433\pi$
$3$	−2.03508	+	0.661236i	−1.17495	+	0.381765i	−0.830489	−	0.557035i	$-0.811939\pi$
$3$	−2.03508	+	0.661236i	−1.17495	+	0.381765i	−0.344462	+	0.938800i	$0.611939\pi$
$4$	−1.48342	+	4.56549i	−0.741709	+	2.28275i
$5$	1.27403	+	1.83762i	0.569764	+	0.821808i
$5$	1.27403	+	1.83762i	0.569764	+	0.821808i
$6$	4.51440	+	3.27991i	1.84300	+	1.33902i
$7$	0.940480	+	0.305580i	0.355468	+	0.115499i	0.481307	−	0.876552i	$-0.340162\pi$
$7$	0.940480	+	0.305580i	0.355468	+	0.115499i	−0.125839	+	0.992051i	$0.540162\pi$
$8$	6.94547	−	2.25672i	2.45559	−	0.797871i
$9$	1.27725	−	0.927974i	0.425749	−	0.309325i
$10$	1.92403	−	5.50457i	0.608431	−	1.74070i
$11$		0			0
$11$		0			0
$12$		−	10.2720i		−	2.96527i
$13$	1.80817	+	2.48873i	0.501496	+	0.690250i	0.982456	−	0.186492i	$-0.0597119\pi$
$13$	1.80817	+	2.48873i	0.501496	+	0.690250i	−0.480960	+	0.876742i	$0.659712\pi$
$14$	−0.796882	−	2.45255i	−0.212976	−	0.655472i
$15$	−3.80785	−	2.89726i	−0.983183	−	0.748068i
$16$	−7.63983	−	5.55066i	−1.90996	−	1.38767i
$17$	−0.951558	+	1.30971i	−0.230787	+	0.317651i	−0.908667	−	0.417522i	$-0.862899\pi$
$17$	−0.951558	+	1.30971i	−0.230787	+	0.317651i	0.677880	+	0.735172i	$0.262899\pi$
$18$	−3.91554	−	1.27224i	−0.922903	−	0.299869i
$19$	−2.03412	−	6.26038i	−0.466660	−	1.43623i	−0.856883	−	0.515511i	$-0.827602\pi$
$19$	−2.03412	−	6.26038i	−0.466660	−	1.43623i	0.390224	−	0.920720i	$-0.372398\pi$
$20$	−10.2796	+	3.09063i	−2.29858	+	0.691085i
$21$	−2.11601			−0.461751
$22$		0			0
$23$			5.18097i			1.08031i	0.841566	+	0.540154i	$0.181634\pi$
$23$			5.18097i			1.08031i	−0.841566	+	0.540154i	$0.818366\pi$
$24$	−12.6423	+	9.18518i	−2.58060	+	1.87492i
$25$	−1.75368	+	4.68237i	−0.350737	+	0.936474i
$26$	2.47897	−	7.62949i	0.486166	−	1.49627i
$27$	1.78755	−	2.46036i	0.344015	−	0.473496i
$28$	−2.79025	+	3.84045i	−0.527307	+	0.725776i
$29$	−2.25958	+	6.95428i	−0.419594	+	1.29138i	0.488483	+	0.872573i	$0.337550\pi$
$29$	−2.25958	+	6.95428i	−0.419594	+	1.29138i	−0.908077	+	0.418804i	$0.862450\pi$
$30$	−0.275722	+	12.4745i	−0.0503398	+	2.27751i
$31$	2.13816	−	1.55347i	0.384025	−	0.279011i	−0.378978	−	0.925406i	$-0.623724\pi$
$31$	2.13816	−	1.55347i	0.384025	−	0.279011i	0.763003	+	0.646395i	$0.223724\pi$
$32$			10.0203i			1.77135i
$33$		0			0
$34$	4.22168			0.724012
$35$	0.636661	+	2.11756i	0.107615	+	0.357933i
$36$	2.34197	+	7.20783i	0.390328	+	1.20131i
$37$	−2.66676	−	0.866482i	−0.438412	−	0.142449i	0.0814908	−	0.996674i	$-0.474032\pi$
$37$	−2.66676	−	0.866482i	−0.438412	−	0.142449i	−0.519903	+	0.854225i	$0.674032\pi$
$38$	−10.0898	+	13.8874i	−1.63678	+	2.25283i
$39$	−5.32540	−	3.86913i	−0.852747	−	0.619557i
$40$	12.9957	+	9.88799i	2.05481	+	1.56343i
$41$	0.428423	+	1.31855i	0.0669084	+	0.205923i	0.978921	−	0.204239i	$-0.0654721\pi$
$41$	0.428423	+	1.31855i	0.0669084	+	0.205923i	−0.912013	+	0.410162i	$0.865472\pi$
$42$	3.24343	+	4.46420i	0.500472	+	0.688841i
$43$		−	3.18585i		−	0.485837i	−0.970047	−	0.242919i	$-0.921895\pi$
$43$		−	3.18585i		−	0.485837i	0.970047	−	0.242919i	$-0.0781048\pi$
$44$		0			0
$45$	3.33252	+	1.16482i	0.496782	+	0.173642i
$46$	10.9304	−	7.94143i	1.61160	−	1.17090i
$47$	−2.03508	+	0.661236i	−0.296846	+	0.0964512i	−0.453654	−	0.891178i	$-0.649880\pi$
$47$	−2.03508	+	0.661236i	−0.296846	+	0.0964512i	0.156808	+	0.987629i	$0.449880\pi$
$48$	19.2179	+	6.24429i	2.77387	+	0.901285i
$49$	−4.87200	−	3.53971i	−0.695999	−	0.505673i
$50$	12.5666	−	3.47737i	1.77718	−	0.491774i
$51$	1.07047	−	3.29456i	0.149895	−	0.461330i
$52$	−14.0446	+	4.56335i	−1.94763	+	0.632823i
$53$	1.39715	+	1.92302i	0.191914	+	0.264146i	0.894120	−	0.447827i	$-0.147802\pi$
$53$	1.39715	+	1.92302i	0.191914	+	0.264146i	−0.702207	+	0.711973i	$0.747802\pi$
$54$	−7.93065			−1.07923
$55$		0			0
$56$	7.22168			0.965037
$57$	8.27918	+	11.3953i	1.09660	+	1.50935i
$58$	18.1351	−	5.89246i	2.38126	−	0.773718i
$59$	−3.78354	+	11.6445i	−0.492575	+	1.51599i	0.328127	+	0.944634i	$0.393583\pi$
$59$	−3.78354	+	11.6445i	−0.492575	+	1.51599i	−0.820702	+	0.571357i	$0.806417\pi$
$60$	18.8760	−	13.0869i	2.43689	−	1.68951i
$61$	0.810998	+	0.589225i	0.103838	+	0.0754425i	0.638492	−	0.769628i	$-0.279558\pi$
$61$	0.810998	+	0.589225i	0.103838	+	0.0754425i	−0.534655	+	0.845071i	$0.679558\pi$
$62$	−6.55478	−	2.12978i	−0.832457	−	0.270482i
$63$	1.48480	−	0.482439i	0.187067	−	0.0607816i
$64$	5.86035	−	4.25780i	0.732544	−	0.532225i
$65$	−2.26967	+	6.49345i	−0.281519	+	0.805414i
$66$		0			0
$67$			9.84499i			1.20276i	0.798964	+	0.601379i	$0.205382\pi$
$67$			9.84499i			1.20276i	−0.798964	+	0.601379i	$0.794618\pi$
$68$	−4.56790	−	6.28717i	−0.553939	−	0.762432i
$69$	−3.42585	−	10.5437i	−0.412423	−	1.26931i
$70$	3.49160	−	4.58899i	0.417326	−	0.548490i
$71$	0.197235	+	0.143300i	0.0234075	+	0.0170066i	0.599428	−	0.800429i	$-0.295395\pi$
$71$	0.197235	+	0.143300i	0.0234075	+	0.0170066i	−0.576020	+	0.817436i	$0.695395\pi$
$72$	6.77690	−	9.32760i	0.798665	−	1.09927i
$73$	−12.9998	−	4.22390i	−1.52152	−	0.494370i	−0.575310	−	0.817936i	$-0.695119\pi$
$73$	−12.9998	−	4.22390i	−1.52152	−	0.494370i	−0.946206	+	0.323565i	$0.895119\pi$
$74$	2.25958	+	6.95428i	0.262671	+	0.808418i
$75$	0.472729	−	10.6886i	0.0545860	−	1.23421i
$76$	31.5992			3.62467
$77$		0			0
$78$			17.1658i			1.94364i
$79$	6.22629	−	4.52366i	0.700512	−	0.508952i	−0.179587	−	0.983742i	$-0.557476\pi$
$79$	6.22629	−	4.52366i	0.700512	−	0.508952i	0.880099	+	0.474790i	$0.157476\pi$
$80$	0.466611	−	21.1108i	0.0521687	−	2.36026i
$81$	−3.47452	+	10.6935i	−0.386058	+	1.18817i
$82$	2.12509	−	2.92494i	0.234677	−	0.323005i
$83$	3.50035	−	4.81781i	0.384213	−	0.528824i	−0.572482	−	0.819918i	$-0.694019\pi$
$83$	3.50035	−	4.81781i	0.384213	−	0.528824i	0.956695	+	0.291094i	$0.0940192\pi$
$84$	3.13892	−	9.66061i	0.342485	−	1.05406i
$85$	−3.61906	−	0.0799918i	−0.392542	−	0.00867633i
$86$	−6.72127	+	4.88329i	−0.724773	+	0.526578i
$87$		−	15.6466i		−	1.67749i
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	−2.65064	−	8.81615i	−0.279402	−	0.929304i
$91$	0.940039	+	2.89314i	0.0985429	+	0.303284i
$92$	−23.6537	−	7.68555i	−2.46607	−	0.801274i
$93$	−3.32411	+	4.57525i	−0.344694	+	0.474431i
$94$	4.51440	+	3.27991i	0.465625	+	0.338296i
$95$	8.91266	−	11.7139i	0.914420	−	1.20182i
$96$	−6.62576	−	20.3920i	−0.676239	−	2.08125i
$97$	7.48775	+	10.3060i	0.760266	+	1.04642i	0.997192	+	0.0748885i	$0.0238601\pi$
$97$	7.48775	+	10.3060i	0.760266	+	1.04642i	−0.236926	+	0.971528i	$0.576140\pi$
$98$			15.7043i			1.58637i
$99$		0			0
$100$	−18.7759	−	14.9523i	−1.87759	−	1.49523i
$101$	−12.3627	+	8.98202i	−1.23013	+	0.893744i	−0.996900	−	0.0786766i	$-0.974931\pi$
$101$	−12.3627	+	8.98202i	−1.23013	+	0.893744i	−0.233233	+	0.972421i	$0.574931\pi$
$102$	−8.59143	+	2.79153i	−0.850678	+	0.276402i
$103$	7.73418	+	2.51299i	0.762072	+	0.247612i	0.664168	−	0.747584i	$-0.268786\pi$
$103$	7.73418	+	2.51299i	0.762072	+	0.247612i	0.0979042	+	0.995196i	$0.468786\pi$
$104$	18.1749	+	13.2049i	1.78220	+	1.29484i
$105$	−2.69586	−	3.88841i	−0.263089	−	0.379470i
$106$	1.91547	−	5.89522i	0.186047	−	0.572594i
$107$	−6.29691	+	2.04599i	−0.608745	+	0.197793i	−0.597137	−	0.802139i	$-0.703695\pi$
$107$	−6.29691	+	2.04599i	−0.608745	+	0.197793i	−0.0116082	+	0.999933i	$0.503695\pi$
$108$	8.58105	+	11.8108i	0.825711	+	1.13649i
$109$	−2.84561			−0.272560			−0.136280	−	0.990670i	$-0.543515\pi$
$109$	−2.84561			−0.272560			−0.136280	+	0.990670i	$0.543515\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$	−5.48893	−	7.55487i	−0.518656	−	0.713868i
$113$	−16.8718	+	5.48197i	−1.58716	+	0.515700i	−0.963889	−	0.266304i	$-0.914197\pi$
$113$	−16.8718	+	5.48197i	−1.58716	+	0.515700i	−0.623273	+	0.782004i	$0.714197\pi$
$114$	11.3506	−	34.9336i	1.06308	−	3.27183i
$115$	−9.52065	+	6.60072i	−0.887805	+	0.615521i
$116$	−28.3978	−	20.6322i	−2.63667	−	1.91565i
$117$	4.61896	+	1.50079i	0.427023	+	0.138748i
$118$	30.3662	−	9.86659i	2.79544	−	0.908293i
$119$	−1.29514	+	0.940975i	−0.118725	+	0.0862591i
$120$	−32.9856	−	11.5295i	−3.01116	−	1.05250i
$121$		0			0
$122$		−	2.61415i		−	0.236674i
$123$	−1.74375	−	2.40006i	−0.157228	−	0.216406i
$124$	3.92055	+	12.0662i	0.352075	+	1.08358i
$125$	−10.8387	+	2.74289i	−0.969439	+	0.245331i
$126$	−3.29372	−	2.39303i	−0.293428	−	0.213188i
$127$	−10.1518	+	13.9727i	−0.900825	+	1.23988i	0.0693797	+	0.997590i	$0.477898\pi$
$127$	−10.1518	+	13.9727i	−0.900825	+	1.23988i	−0.970204	+	0.242288i	$0.922102\pi$
$128$	1.09411	+	0.355496i	0.0967061	+	0.0314217i
$129$	2.10660	+	6.48344i	0.185476	+	0.570835i
$130$	17.1784	−	5.16481i	1.50664	−	0.452984i
$131$	−5.12335			−0.447629			−0.223815	−	0.974632i	$-0.571851\pi$
$131$	−5.12335			−0.447629			−0.223815	+	0.974632i	$0.571851\pi$
$132$		0			0
$133$		−	6.50935i		−	0.564432i
$134$	20.7702	−	15.0905i	1.79428	−	1.30362i
$135$	6.79860	+	0.150269i	0.585130	+	0.0129331i
$136$	−3.65337	+	11.2439i	−0.313274	+	0.964158i
$137$	4.27800	−	5.88816i	0.365494	−	0.503060i	−0.586175	−	0.810184i	$-0.699367\pi$
$137$	4.27800	−	5.88816i	0.365494	−	0.503060i	0.951669	+	0.307125i	$0.0993669\pi$
$138$	−16.9931	+	23.3890i	−1.44655	+	1.99100i
$139$	−3.55551	+	10.9427i	−0.301574	+	0.928150i	0.679359	+	0.733806i	$0.262258\pi$
$139$	−3.55551	+	10.9427i	−0.301574	+	0.928150i	−0.980933	+	0.194344i	$0.937742\pi$
$140$	−10.6121	−	0.234560i	−0.896890	−	0.0198239i
$141$	3.70430	−	2.69133i	0.311958	−	0.226651i
$142$		−	0.635763i		−	0.0533521i
$143$		0			0
$144$	−14.9088			−1.24240
$145$	−15.6581	+	4.70772i	−1.30033	+	0.390955i
$146$	11.0149	+	33.9005i	0.911604	+	2.80563i
$147$	12.2555	+	3.98204i	1.01081	+	0.328433i
$148$	7.91183	−	10.8897i	0.650348	−	0.895128i
$149$	8.34866	+	6.06565i	0.683949	+	0.496918i	0.874665	−	0.484727i	$-0.161081\pi$
$149$	8.34866	+	6.06565i	0.683949	+	0.496918i	−0.190717	+	0.981645i	$0.561081\pi$
$150$	−23.2746	+	15.3862i	−1.90036	+	1.25628i
$151$	−4.62597	−	14.2373i	−0.376456	−	1.15861i	−0.942491	−	0.334232i	$-0.891523\pi$
$151$	−4.62597	−	14.2373i	−0.376456	−	1.15861i	0.566034	−	0.824382i	$-0.308477\pi$
$152$	−28.2559	−	38.8908i	−2.29185	−	3.15446i
$153$			2.55584i			0.206627i
$154$		0			0
$155$	5.57876	+	1.94996i	0.448097	+	0.156625i
$156$	25.5643	−	18.5735i	2.04678	−	1.48707i
$157$	17.1829	−	5.58305i	1.37134	−	0.445576i	0.471528	−	0.881851i	$-0.343703\pi$
$157$	17.1829	−	5.58305i	1.37134	−	0.445576i	0.899813	+	0.436275i	$0.143703\pi$
$158$	−19.0874	−	6.20187i	−1.51851	−	0.493394i
$159$	−4.11488	−	2.98963i	−0.326331	−	0.237093i
$160$	−18.4134	+	12.7661i	−1.45571	+	1.00925i
$161$	−1.58320	+	4.87260i	−0.124774	+	0.384015i
$162$	27.8861	−	9.06074i	2.19094	−	0.711879i
$163$	−12.5802	−	17.3152i	−0.985360	−	1.35623i	−0.933891	−	0.357557i	$-0.883610\pi$
$163$	−12.5802	−	17.3152i	−0.985360	−	1.35623i	−0.0514684	−	0.998675i	$-0.516390\pi$
$164$	−6.65536			−0.519696
$165$		0			0
$166$	−15.5296			−1.20533
$167$	−7.39205	−	10.1743i	−0.572014	−	0.787310i	0.420778	−	0.907164i	$-0.361757\pi$
$167$	−7.39205	−	10.1743i	−0.572014	−	0.787310i	−0.992792	+	0.119854i	$0.961757\pi$
$168$	−14.6967	+	4.77523i	−1.13387	+	0.368417i
$169$	1.09291	−	3.36363i	0.0840701	−	0.258741i
$170$	5.37855	+	7.75783i	0.412516	+	0.594999i
$171$	−8.40755	−	6.10844i	−0.642942	−	0.467124i
$172$	14.5450	+	4.72594i	1.10904	+	0.360350i
$173$	−9.42560	+	3.06256i	−0.716615	+	0.232842i	−0.644555	−	0.764558i	$-0.722957\pi$
$173$	−9.42560	+	3.06256i	−0.716615	+	0.232842i	−0.0720600	+	0.997400i	$0.522957\pi$
$174$	−33.0100	+	23.9832i	−2.50248	+	1.81816i
$175$	−3.08015	+	3.86778i	−0.232837	+	0.292377i
$176$		0			0
$177$		−	26.1993i		−	1.96926i
$178$	13.7953	+	18.9875i	1.03400	+	1.42318i
$179$	0.755038	+	2.32377i	0.0564342	+	0.173687i	0.975300	−	0.220883i	$-0.0708938\pi$
$179$	0.755038	+	2.32377i	0.0564342	+	0.173687i	−0.918866	+	0.394569i	$0.870894\pi$
$180$	−10.2615	+	13.4867i	−0.764848	+	1.00524i
$181$	11.4895	+	8.34759i	0.854006	+	0.620471i	0.926248	−	0.376916i	$-0.123015\pi$
$181$	11.4895	+	8.34759i	0.854006	+	0.620471i	−0.0722420	+	0.997387i	$0.523015\pi$
$182$	4.66284	−	6.41785i	0.345633	−	0.475723i
$183$	−2.04006	−	0.662855i	−0.150805	−	0.0489997i
$184$	11.6920	+	35.9843i	0.861945	+	2.65280i
$185$	−1.80527	−	6.00441i	−0.132726	−	0.441453i
$186$	14.7477			1.08136
$187$		0			0
$188$		−	10.2720i		−	0.749163i
$189$	2.43299	−	1.76767i	0.176974	−	0.128579i
$190$	−38.3744	−	0.848188i	−2.78398	−	0.0615341i
$191$	5.37730	−	16.5496i	0.389088	−	1.19749i	−0.544383	−	0.838837i	$-0.683236\pi$
$191$	5.37730	−	16.5496i	0.389088	−	1.19749i	0.933471	−	0.358653i	$-0.116764\pi$
$192$	−9.11085	+	12.5400i	−0.657519	+	0.904998i
$193$	6.47101	−	8.90659i	0.465794	−	0.641110i	−0.509904	−	0.860231i	$-0.670319\pi$
$193$	6.47101	−	8.90659i	0.465794	−	0.641110i	0.975698	+	0.219121i	$0.0703190\pi$
$194$	10.2656	−	31.5942i	0.737026	−	2.26833i
$195$	0.325255	−	14.7155i	0.0232920	−	1.05380i
$196$	23.3877	−	16.9922i	1.67055	−	1.21373i
$197$			3.49279i			0.248851i	0.992229	+	0.124426i	$0.0397088\pi$
$197$			3.49279i			0.248851i	−0.992229	+	0.124426i	$0.960291\pi$
$198$		0			0
$199$	−2.84247			−0.201498			−0.100749	−	0.994912i	$-0.532124\pi$
$199$	−2.84247			−0.201498			−0.100749	+	0.994912i	$0.532124\pi$
$200$	−1.61337	+	36.4788i	−0.114082	+	2.57944i
$201$	−6.50986	−	20.0353i	−0.459170	−	1.41318i
$202$	37.8992	+	12.3142i	2.66658	+	0.866424i
$203$	−4.25018	+	5.84987i	−0.298304	+	0.410581i
$204$	13.4533	+	9.77441i	0.941921	+	0.684345i
$205$	−1.87717	+	2.46715i	−0.131107	+	0.172313i
$206$	−6.55329	−	20.1689i	−0.456589	−	1.40524i
$207$	4.80781	+	6.61738i	0.334166	+	0.459940i
$208$		−	29.0500i		−	2.01426i
$209$		0			0
$210$	−4.07126	+	11.6477i	−0.280944	+	0.803769i
$211$	−2.52288	+	1.83298i	−0.173682	+	0.126188i	−0.671230	−	0.741249i	$-0.734234\pi$
$211$	−2.52288	+	1.83298i	−0.173682	+	0.126188i	0.497548	+	0.867437i	$0.334234\pi$
$212$	−10.8521	+	3.52605i	−0.745323	+	0.242170i
$213$	−0.496144	−	0.161207i	−0.0339952	−	0.0110457i
$214$	13.9684	+	10.1487i	0.954861	+	0.693747i
$215$	5.85437	−	4.05887i	0.399265	−	0.276813i
$216$	6.86306	−	21.1223i	0.466972	−	1.43719i
$217$	2.48561	−	0.807622i	0.168734	−	0.0548250i
$218$	4.36177	+	6.00346i	0.295416	+	0.406606i
$219$	29.2486			1.97644
$220$		0			0
$221$	−4.98009			−0.334997
$222$	−9.19684	−	12.6584i	−0.617251	−	0.849574i
$223$	11.7638	−	3.82229i	0.787763	−	0.255960i	0.112612	−	0.993639i	$-0.464078\pi$
$223$	11.7638	−	3.82229i	0.787763	−	0.255960i	0.675151	+	0.737679i	$0.264078\pi$
$224$	−3.06200	+	9.42386i	−0.204588	+	0.629658i
$225$	2.10523	+	7.60792i	0.140349	+	0.507194i
$226$	37.4266	+	27.1920i	2.48958	+	1.80879i
$227$	12.9505	+	4.20786i	0.859552	+	0.279285i	0.705441	−	0.708768i	$-0.250749\pi$
$227$	12.9505	+	4.20786i	0.859552	+	0.279285i	0.154110	+	0.988054i	$0.450749\pi$
$228$	−64.3067	+	20.8945i	−4.25882	+	1.38377i
$229$	4.72666	−	3.43412i	0.312346	−	0.226933i	−0.420556	−	0.907266i	$-0.638165\pi$
$229$	4.72666	−	3.43412i	0.312346	−	0.226933i	0.732903	+	0.680334i	$0.238165\pi$
$230$	28.5190	+	9.96834i	1.88049	+	0.657293i
$231$		0			0
$232$			53.3999i			3.50588i
$233$	−13.7776	−	18.9632i	−0.902600	−	1.24232i	−0.969631	−	0.244571i	$-0.921353\pi$
$233$	−13.7776	−	18.9632i	−0.902600	−	1.24232i	0.0670313	−	0.997751i	$-0.478647\pi$
$234$	−3.91371	−	12.0452i	−0.255847	−	0.787417i
$235$	−3.80785	−	2.89726i	−0.248397	−	0.188996i
$236$	−47.5505	−	34.5474i	−3.09527	−	2.24885i
$237$	−9.67976	+	13.3230i	−0.628768	+	0.865425i
$238$	3.97040	+	1.29006i	0.257363	+	0.0836223i
$239$	−2.03412	−	6.26038i	−0.131576	−	0.404951i	0.863465	−	0.504408i	$-0.168289\pi$
$239$	−2.03412	−	6.26038i	−0.131576	−	0.404951i	−0.995042	+	0.0994575i	$0.968289\pi$
$240$	13.0096	+	43.2707i	0.839769	+	2.79311i
$241$	−12.1627			−0.783466			−0.391733	−	0.920079i	$-0.628124\pi$
$241$	−12.1627			−0.783466			−0.391733	+	0.920079i	$0.628124\pi$
$242$		0			0
$243$		−	14.9360i		−	0.958146i
$244$	−3.89315	+	2.82854i	−0.249233	+	0.181079i
$245$	0.297563	−	13.4626i	0.0190106	−	0.860093i
$246$	−2.39065	+	7.35765i	−0.152422	+	0.469107i
$247$	11.9024	−	16.3822i	0.757330	−	1.04238i
$248$	11.3448	−	15.6148i	0.720395	−	0.991539i
$249$	−3.93776	+	12.1192i	−0.249545	+	0.768021i
$250$	22.4003	+	18.6623i	1.41672	+	1.18031i
$251$	0.878809	−	0.638492i	0.0554700	−	0.0403013i	−0.559705	−	0.828692i	$-0.689085\pi$
$251$	0.878809	−	0.638492i	0.0554700	−	0.0403013i	0.615175	+	0.788391i	$0.289085\pi$
$252$			7.49448i			0.472108i
$253$		0			0
$254$	45.0393			2.82602
$255$	7.41795	−	2.23026i	0.464530	−	0.139664i
$256$	−5.40396	−	16.6317i	−0.337748	−	1.03948i
$257$	23.0625	+	7.49347i	1.43860	+	0.467430i	0.921461	−	0.388471i	$-0.126997\pi$
$257$	23.0625	+	7.49347i	1.43860	+	0.467430i	0.517140	+	0.855901i	$0.326997\pi$
$258$	10.4493	−	14.3822i	0.650544	−	0.895397i
$259$	−2.24325	−	1.62982i	−0.139389	−	0.101272i
$260$	−26.2789	−	19.9947i	−1.62975	−	1.24002i
$261$	3.56735	+	10.9792i	0.220813	+	0.679593i
$262$	7.85311	+	10.8089i	0.485167	+	0.667775i
$263$			2.49816i			0.154043i	0.997029	+	0.0770216i	$0.0245410\pi$
$263$			2.49816i			0.154043i	−0.997029	+	0.0770216i	$0.975459\pi$
$264$		0			0
$265$	−1.75375	+	5.01742i	−0.107732	+	0.308217i
$266$	−13.7330	+	9.97757i	−0.842021	+	0.611764i
$267$	18.3157	−	5.95112i	1.12090	−	0.364203i
$268$	−44.9472	−	14.6042i	−2.74559	−	0.892096i
$269$	13.0141	+	9.45527i	0.793482	+	0.576498i	0.908995	−	0.416808i	$-0.136851\pi$
$269$	13.0141	+	9.45527i	0.793482	+	0.576498i	−0.115513	+	0.993306i	$0.536851\pi$
$270$	−10.1039	−	14.5735i	−0.614904	−	0.886916i
$271$	0.619547	−	1.90677i	0.0376348	−	0.115828i	−0.930474	−	0.366358i	$-0.880605\pi$
$271$	0.619547	−	1.90677i	0.0376348	−	0.115828i	0.968109	+	0.250529i	$0.0806047\pi$
$272$	14.5395	−	4.72417i	0.881586	−	0.286445i
$273$	−3.82610	−	5.26618i	−0.231566	−	0.318723i
$274$	−18.9798			−1.14661
$275$		0			0
$276$	53.2190			3.20341
$277$	11.3787	+	15.6614i	0.683680	+	0.941004i	0.999971	−	0.00765777i	$-0.00243757\pi$
$277$	11.3787	+	15.6614i	0.683680	+	0.941004i	−0.316291	+	0.948662i	$0.602438\pi$
$278$	28.5361	−	9.27193i	1.71148	−	0.556093i
$279$	1.28938	−	3.96832i	0.0771934	−	0.237577i
$280$	9.20065	+	13.2707i	0.549844	+	0.793075i
$281$	2.36104	+	1.71540i	0.140848	+	0.102332i	0.655978	−	0.754780i	$-0.272256\pi$
$281$	2.36104	+	1.71540i	0.140848	+	0.102332i	−0.515130	+	0.857112i	$0.672256\pi$
$282$	−11.3559	−	3.68977i	−0.676236	−	0.219723i
$283$	−0.544316	+	0.176859i	−0.0323562	+	0.0105132i	−0.325150	−	0.945662i	$-0.605415\pi$
$283$	−0.544316	+	0.176859i	−0.0323562	+	0.0105132i	0.292794	+	0.956175i	$0.405415\pi$
$284$	−0.946816	+	0.687902i	−0.0561832	+	0.0408195i
$285$	−10.3923	+	29.7320i	−0.615587	+	1.76117i
$286$		0			0
$287$			1.37099i			0.0809268i
$288$	9.29855	+	12.7984i	0.547922	+	0.754150i
$289$	4.44342	+	13.6754i	0.261378	+	0.804437i
$290$	33.9328	+	25.8183i	1.99260	+	1.51610i
$291$	−22.0528	−	16.0223i	−1.29276	−	0.939245i
$292$	38.5684	−	53.0848i	2.25704	−	3.10655i
$293$	8.87581	+	2.88393i	0.518530	+	0.168481i	0.556578	−	0.830795i	$-0.312114\pi$
$293$	8.87581	+	2.88393i	0.518530	+	0.168481i	−0.0380479	+	0.999276i	$0.512114\pi$
$294$	−10.3842	−	31.9594i	−0.605621	−	1.86391i
$295$	−26.2186	+	7.88281i	−1.52650	+	0.458955i
$296$	−20.4773			−1.19022
$297$		0			0
$298$		−	26.9109i		−	1.55890i
$299$	−12.8941	+	9.36808i	−0.745682	+	0.541770i
$300$	48.0973	+	18.0139i	2.77690	+	1.04003i
$301$	0.973533	−	2.99623i	0.0561135	−	0.172700i
$302$	−22.9461	+	31.5825i	−1.32040	+	1.81737i
$303$	19.2198	−	26.4537i	1.10415	−	1.51973i
$304$	−19.2089	+	59.1190i	−1.10171	+	3.39071i
$305$	−0.0495326	+	2.24100i	−0.00283623	+	0.128319i
$306$	5.39212	−	3.91761i	0.308247	−	0.223955i
$307$		−	6.34982i		−	0.362404i	−0.983446	−	0.181202i	$-0.942001\pi$
$307$		−	6.34982i		−	0.362404i	0.983446	−	0.181202i	$-0.0579987\pi$
$308$		0			0
$309$	−17.4013			−0.989927
$310$	−4.43728	−	14.7586i	−0.252020	−	0.838231i
$311$	6.97107	+	21.4547i	0.395293	+	1.21659i	0.928733	+	0.370749i	$0.120899\pi$
$311$	6.97107	+	21.4547i	0.395293	+	1.21659i	−0.533440	+	0.845838i	$0.679101\pi$
$312$	−45.7189	−	14.8550i	−2.58832	−	0.840998i
$313$	15.0342	−	20.6928i	0.849785	−	1.16963i	−0.134126	−	0.990964i	$-0.542823\pi$
$313$	15.0342	−	20.6928i	0.849785	−	1.16963i	0.983910	−	0.178664i	$-0.0571774\pi$
$314$	−38.1167	−	27.6934i	−2.15105	−	1.56283i
$315$	2.77822	+	2.11384i	0.156535	+	0.119102i
$316$	11.4166	+	35.1366i	0.642232	+	1.97659i
$317$	14.5910	+	20.0827i	0.819510	+	1.12796i	0.989786	+	0.142562i	$0.0455341\pi$
$317$	14.5910	+	20.0827i	0.819510	+	1.12796i	−0.170276	+	0.985396i	$0.554466\pi$
$318$			13.2638i			0.743797i
$319$		0			0
$320$	15.2905	+	5.34453i	0.854764	+	0.298768i
$321$	11.4618	−	8.32749i	0.639735	−	0.464795i
$322$	12.7066	−	4.12862i	0.708111	−	0.230079i
$323$	10.1349	+	3.29301i	0.563918	+	0.183228i
$324$	−43.6668	−	31.7258i	−2.42594	−	1.76255i
$325$	−14.8241	+	4.10207i	−0.822295	+	0.227542i
$326$	−17.2473	+	53.0817i	−0.955239	+	2.93992i
$327$	5.79103	−	1.88162i	0.320245	−	0.104054i
$328$	5.95119	+	8.19111i	0.328600	+	0.452278i
$329$	−2.11601			−0.116659
$330$		0			0
$331$	−5.80044			−0.318821			−0.159411	−	0.987212i	$-0.550959\pi$
$331$	−5.80044			−0.318821			−0.159411	+	0.987212i	$0.550959\pi$
$332$	16.8032	+	23.1276i	0.922196	+	1.26929i
$333$	−4.21018	+	1.36797i	−0.230716	+	0.0749643i
$334$	−10.1344	+	31.1904i	−0.554529	+	1.70666i
$335$	−18.0913	+	12.5428i	−0.988435	+	0.685288i
$336$	16.1659	+	11.7452i	0.881925	+	0.640756i
$337$	−0.0439103	−	0.0142673i	−0.00239195	−	0.000777190i	0.307821	−	0.951444i	$-0.400400\pi$
$337$	−0.0439103	−	0.0142673i	−0.00239195	−	0.000777190i	−0.310213	+	0.950667i	$0.600400\pi$
$338$	−8.77157	+	2.85005i	−0.477110	+	0.155023i
$339$	30.7104	−	22.3124i	1.66796	−	1.21184i
$340$	5.73378	−	16.4041i	0.310958	−	0.889638i
$341$		0			0
$342$			27.1007i			1.46544i
$343$	−7.56909	−	10.4180i	−0.408692	−	0.562517i
$344$	−7.18956	−	22.1272i	−0.387635	−	1.19302i
$345$	15.0106	−	19.7284i	0.808144	−	1.06214i
$346$	20.9088	+	15.1911i	1.12406	+	0.816680i
$347$	−18.5530	+	25.5361i	−0.995980	+	1.37085i	−0.0682199	+	0.997670i	$0.521732\pi$
$347$	−18.5530	+	25.5361i	−0.995980	+	1.37085i	−0.927760	+	0.373178i	$0.878268\pi$
$348$	71.4344	+	23.2104i	3.82928	+	1.24421i
$349$	9.37060	+	28.8397i	0.501597	+	1.54376i	0.806418	+	0.591346i	$0.201403\pi$
$349$	9.37060	+	28.8397i	0.501597	+	1.54376i	−0.304822	+	0.952409i	$0.598597\pi$
$350$	12.8812	+	0.569704i	0.688531	+	0.0304520i
$351$	9.35537			0.499353
$352$		0			0
$353$			19.1157i			1.01743i	0.860936	+	0.508714i	$0.169879\pi$
$353$			19.1157i			1.01743i	−0.860936	+	0.508714i	$0.830121\pi$
$354$	−55.2734	+	40.1585i	−2.93775	+	2.13440i
$355$	−0.0120464	+	0.545012i	−0.000639355	+	0.0289262i
$356$	13.3508	−	41.0894i	0.707589	−	2.17773i
$357$	2.01350	−	2.77135i	0.106566	−	0.146675i
$358$	3.74519	−	5.15481i	0.197939	−	0.272440i
$359$	8.31197	−	25.5816i	0.438689	−	1.35015i	−0.450570	−	0.892741i	$-0.648779\pi$
$359$	8.31197	−	25.5816i	0.438689	−	1.35015i	0.889259	−	0.457405i	$-0.151221\pi$
$360$	25.7746	+	0.569694i	1.35844	+	0.0300255i
$361$	−19.6834	+	14.3009i	−1.03597	+	0.752676i
$362$		−	37.0349i		−	1.94651i
$363$		0			0
$364$	−14.6031			−0.765410
$365$	−8.80028	−	29.2701i	−0.460628	−	1.53207i
$366$	1.72857	+	5.31999i	0.0903538	+	0.278081i
$367$	−7.64865	−	2.48520i	−0.399256	−	0.129726i	0.102505	−	0.994733i	$-0.467314\pi$
$367$	−7.64865	−	2.48520i	−0.399256	−	0.129726i	−0.501761	+	0.865006i	$0.667314\pi$
$368$	28.7578	−	39.5818i	1.49911	−	2.06334i
$369$	1.77078	+	1.28655i	0.0921832	+	0.0669750i
$370$	−9.90053	+	13.0122i	−0.514704	+	0.676473i
$371$	0.726358	+	2.23550i	0.0377106	+	0.116061i
$372$	−15.9572	−	21.9632i	−0.827343	−	1.13874i
$373$			27.7542i			1.43706i	0.695496	+	0.718530i	$0.255185\pi$
$373$			27.7542i			1.43706i	−0.695496	+	0.718530i	$0.744815\pi$
$374$		0			0
$375$	20.2438	−	12.7489i	1.04539	−	0.658350i
$376$	−12.6423	+	9.18518i	−0.651978	+	0.473690i
$377$	−21.3930	+	6.95102i	−1.10180	+	0.357996i
$378$	−7.45862	−	2.42345i	−0.383630	−	0.124649i
$379$	−14.8172	−	10.7653i	−0.761108	−	0.552977i	0.138142	−	0.990412i	$-0.455887\pi$
$379$	−14.8172	−	10.7653i	−0.761108	−	0.552977i	−0.899250	+	0.437435i	$0.855887\pi$
$380$	40.2584	+	58.0672i	2.06521	+	2.97879i
$381$	11.4204	−	35.1483i	0.585083	−	1.80070i
$382$	−43.1576	+	14.0228i	−2.20813	+	0.717466i
$383$	10.2629	+	14.1256i	0.524408	+	0.721786i	0.986265	−	0.165168i	$-0.0528167\pi$
$383$	10.2629	+	14.1256i	0.524408	+	0.721786i	−0.461857	+	0.886954i	$0.652817\pi$
$384$	−2.46165			−0.125621
$385$		0			0
$386$	−28.7093			−1.46126
$387$	−2.95639	−	4.06911i	−0.150281	−	0.206845i
$388$	−58.1594	+	18.8971i	−2.95260	+	0.959357i
$389$	−4.18992	+	12.8952i	−0.212437	+	0.653814i	0.786888	+	0.617095i	$0.211691\pi$
$389$	−4.18992	+	12.8952i	−0.212437	+	0.653814i	−0.999326	+	0.0367191i	$0.988309\pi$
$390$	−31.5441	+	21.8697i	−1.59730	+	1.10742i
$391$	−6.78556	−	4.92999i	−0.343160	−	0.249321i
$392$	−41.8264	−	13.5902i	−2.11255	−	0.686410i
$393$	10.4264	−	3.38775i	0.525943	−	0.170889i
$394$	7.36884	−	5.35378i	0.371237	−	0.269719i
$395$	16.2453	+	5.67825i	0.817388	+	0.285704i
$396$		0			0
$397$			2.42431i			0.121673i	0.998148	+	0.0608363i	$0.0193767\pi$
$397$			2.42431i			0.121673i	−0.998148	+	0.0608363i	$0.980623\pi$
$398$	4.35696	+	5.99684i	0.218395	+	0.300594i
$399$	4.30422	+	13.2470i	0.215480	+	0.663180i
$400$	39.3881	−	26.0384i	1.96941	−	1.30192i
$401$	13.2793	+	9.64798i	0.663137	+	0.481797i	0.867721	−	0.497052i	$-0.165584\pi$
$401$	13.2793	+	9.64798i	0.663137	+	0.481797i	−0.204584	+	0.978849i	$0.565584\pi$
$402$	−32.2906	+	44.4443i	−1.61051	+	2.21668i
$403$	7.73232	+	2.51238i	0.385174	+	0.125151i
$404$	−22.6683	−	69.7658i	−1.12779	−	3.47098i
$405$	−24.0772	+	7.23899i	−1.19641	+	0.359708i
$406$	18.8563			0.935824
$407$		0			0
$408$		−	25.2980i		−	1.25244i
$409$	−15.7555	+	11.4470i	−0.779058	+	0.566018i	−0.904696	−	0.426058i	$-0.859902\pi$
$409$	−15.7555	+	11.4470i	−0.779058	+	0.566018i	0.125638	+	0.992076i	$0.459902\pi$
$410$	8.08235	+	0.178644i	0.399159	+	0.00882259i
$411$	−4.81259	+	14.8116i	−0.237387	+	0.730603i
$412$	−22.9461	+	31.5825i	−1.13047	+	1.55596i
$413$	−7.11669	+	9.79528i	−0.350189	+	0.481994i
$414$	6.59143	−	20.2863i	0.323951	−	0.997018i
$415$	13.3129	+	0.294253i	0.653503	+	0.0144443i
$416$	−24.9378	+	18.1183i	−1.22267	+	0.888325i
$417$		−	24.6203i		−	1.20566i
$418$		0			0
$419$	1.84468			0.0901185			0.0450592	−	0.998984i	$-0.485652\pi$
$419$	1.84468			0.0901185			0.0450592	+	0.998984i	$0.485652\pi$
$420$	21.7516	−	6.53979i	1.06137	−	0.319109i
$421$	−6.55102	−	20.1620i	−0.319277	−	0.982635i	−0.973958	−	0.226729i	$-0.927197\pi$
$421$	−6.55102	−	20.1620i	−0.319277	−	0.982635i	0.654681	−	0.755906i	$-0.272803\pi$
$422$	7.73418	+	2.51299i	0.376494	+	0.122330i
$423$	−1.98568	+	2.73306i	−0.0965472	+	0.132886i
$424$	14.0436	+	10.2033i	0.682017	+	0.495514i
$425$	−4.46380	−	6.75236i	−0.216526	−	0.327538i
$426$	0.420390	+	1.29383i	0.0203679	+	0.0626861i
$427$	0.582672	+	0.801979i	0.0281975	+	0.0388105i
$428$		−	31.7835i		−	1.53632i
$429$		0			0
$430$	−17.5367	−	6.12966i	−0.845696	−	0.295599i
$431$	21.3016	−	15.4765i	1.02606	−	0.745478i	0.0585454	−	0.998285i	$-0.481354\pi$
$431$	21.3016	−	15.4765i	1.02606	−	0.745478i	0.967517	+	0.252807i	$0.0813538\pi$
$432$	−27.3132	+	8.87460i	−1.31411	+	0.426980i
$433$	−8.68645	−	2.82240i	−0.417444	−	0.135636i	0.0927614	−	0.995688i	$-0.470431\pi$
$433$	−8.68645	−	2.82240i	−0.417444	−	0.135636i	−0.510205	+	0.860053i	$0.670431\pi$
$434$	−5.51381	−	4.00602i	−0.264672	−	0.192295i
$435$	28.7525	−	19.9343i	1.37858	−	0.955775i
$436$	4.22123	−	12.9916i	0.202160	−	0.622185i
$437$	32.4349	−	10.5387i	1.55157	−	0.504136i
$438$	−44.8325	−	61.7066i	−2.14218	−	2.94846i
$439$	11.0836			0.528991			0.264496	−	0.964387i	$-0.414795\pi$
$439$	11.0836			0.528991			0.264496	+	0.964387i	$0.414795\pi$
$440$		0			0
$441$	−9.50750			−0.452738
$442$	7.63351	+	10.5066i	0.363089	+	0.499749i
$443$	−16.8173	+	5.46426i	−0.799012	+	0.259615i	−0.679937	−	0.733270i	$-0.737993\pi$
$443$	−16.8173	+	5.46426i	−0.799012	+	0.259615i	−0.119075	+	0.992885i	$0.537993\pi$
$444$	−8.90051	+	27.3929i	−0.422399	+	1.30001i
$445$	−11.4663	−	16.5386i	−0.543554	−	0.784003i
$446$	−26.0956	−	18.9596i	−1.23566	−	0.897763i
$447$	−21.0010	−	6.82363i	−0.993312	−	0.322747i
$448$	6.81264	−	2.21356i	0.321867	−	0.104581i
$449$	13.6956	−	9.95046i	0.646337	−	0.469591i	−0.215684	−	0.976463i	$-0.569198\pi$
$449$	13.6956	−	9.95046i	0.646337	−	0.469591i	0.862021	+	0.506872i	$0.169198\pi$
$450$	12.8237	−	16.1029i	0.604516	−	0.759099i
$451$		0			0
$452$		−	85.1599i		−	4.00559i
$453$	18.8284	+	25.9151i	0.884636	+	1.21760i
$454$	−10.9731	−	33.7717i	−0.514993	−	1.58499i
$455$	−4.11885	+	5.41339i	−0.193095	+	0.253784i
$456$	83.2188	+	60.4620i	3.89708	+	2.83139i
$457$	19.1682	−	26.3828i	0.896650	−	1.23413i	−0.0748738	−	0.997193i	$-0.523855\pi$
$457$	19.1682	−	26.3828i	0.896650	−	1.23413i	0.971524	−	0.236940i	$-0.0761446\pi$
$458$	−14.4901	−	4.70812i	−0.677078	−	0.219996i
$459$	1.52139	+	4.68234i	0.0710122	+	0.218553i
$460$	−16.0124	−	53.2581i	−0.746584	−	2.48317i
$461$	7.96896			0.371152			0.185576	−	0.982630i	$-0.440585\pi$
$461$	7.96896			0.371152			0.185576	+	0.982630i	$0.440585\pi$
$462$		0			0
$463$		−	25.3879i		−	1.17988i	−0.807449	−	0.589938i	$-0.799152\pi$
$463$		−	25.3879i		−	1.17988i	0.807449	−	0.589938i	$-0.200848\pi$
$464$	55.8637	−	40.5873i	2.59341	−	1.88422i
$465$	−12.6426	−	0.279438i	−0.586286	−	0.0129586i
$466$	−18.8889	+	58.1339i	−0.875009	+	2.69300i
$467$	9.58502	−	13.1926i	0.443542	−	0.610483i	−0.527453	−	0.849584i	$-0.676853\pi$
$467$	9.58502	−	13.1926i	0.443542	−	0.610483i	0.970995	+	0.239101i	$0.0768528\pi$
$468$	−13.7037	+	18.8615i	−0.633453	+	0.871874i
$469$	−3.00844	+	9.25901i	−0.138917	+	0.427541i
$470$	−0.275722	+	12.4745i	−0.0127181	+	0.575404i
$471$	−31.2767	+	22.7239i	−1.44115	+	1.04706i
$472$			89.4152i			4.11567i
$473$		0			0
$474$	42.9452			1.97254
$475$	32.8806	+	1.45423i	1.50867	+	0.0667246i
$476$	−2.37478	−	7.30882i	−0.108848	−	0.334999i
$477$	3.56902	+	1.15964i	0.163414	+	0.0530965i
$478$	−10.0898	+	13.8874i	−0.461496	+	0.635195i
$479$	28.1491	+	20.4516i	1.28617	+	0.934455i	0.999721	−	0.0236408i	$-0.00752581\pi$
$479$	28.1491	+	20.4516i	1.28617	+	0.934455i	0.286447	+	0.958096i	$0.407526\pi$
$480$	29.0313	−	38.1557i	1.32509	−	1.74156i
$481$	−2.66551	−	8.20359i	−0.121537	−	0.374052i
$482$	18.6430	+	25.6599i	0.849166	+	1.16878i
$483$		−	10.9630i		−	0.498833i
$484$		0			0
$485$	−9.39887	+	26.8898i	−0.426781	+	1.22100i
$486$	−31.5109	+	22.8940i	−1.42936	+	1.03849i
$487$	2.40067	−	0.780025i	0.108785	−	0.0353463i	−0.254119	−	0.967173i	$-0.581785\pi$
$487$	2.40067	−	0.780025i	0.108785	−	0.0353463i	0.362904	+	0.931827i	$0.381785\pi$
$488$	6.96247	+	2.26224i	0.315176	+	0.102407i
$489$	37.0512	+	26.9192i	1.67551	+	1.21733i
$490$	−28.8585	+	20.0077i	−1.30369	+	0.903858i
$491$	−5.97188	+	18.3796i	−0.269507	+	0.829458i	0.721114	+	0.692817i	$0.243631\pi$
$491$	−5.97188	+	18.3796i	−0.269507	+	0.829458i	−0.990621	+	0.136641i	$0.956369\pi$
$492$	13.5442	−	4.40076i	0.610617	−	0.198402i
$493$	−6.95794	−	9.57679i	−0.313370	−	0.431317i
$494$	−52.8061			−2.37586
$495$		0			0
$496$	−24.9580			−1.12065
$497$	0.141706	+	0.195042i	0.00635639	+	0.00874882i
$498$	31.6040	−	10.2687i	1.41621	−	0.460154i
$499$	−0.357696	+	1.10087i	−0.0160127	+	0.0492819i	−0.958744	−	0.284272i	$-0.908248\pi$
$499$	−0.357696	+	1.10087i	−0.0160127	+	0.0492819i	0.942731	+	0.333554i	$0.108248\pi$
$500$	3.55565	−	53.5527i	0.159013	−	2.39495i
$501$	21.7710	+	15.8175i	0.972656	+	0.706676i
$502$	−2.69409	−	0.875363i	−0.120243	−	0.0390693i
$503$	−17.1085	+	5.55890i	−0.762832	+	0.247859i	−0.664494	−	0.747294i	$-0.731353\pi$
$503$	−17.1085	+	5.55890i	−0.762832	+	0.247859i	−0.0983382	+	0.995153i	$0.531353\pi$
$504$	9.22387	−	6.70153i	0.410864	−	0.298510i
$505$	−32.2560	−	11.2745i	−1.43537	−	0.501710i
$506$		0			0
$507$			7.56792i			0.336103i
$508$	−48.7330	−	67.0752i	−2.16218	−	2.97598i
$509$	3.50734	+	10.7945i	0.155460	+	0.478456i	0.998207	−	0.0598530i	$-0.0190632\pi$
$509$	3.50734	+	10.7945i	0.155460	+	0.478456i	−0.842747	+	0.538309i	$0.819063\pi$
$510$	−16.0755	−	12.2313i	−0.711836	−	0.541610i
$511$	−10.9353	−	7.94499i	−0.483751	−	0.351466i
$512$	−25.4527	+	35.0326i	−1.12486	+	1.54824i
$513$	−19.0389	−	6.18611i	−0.840587	−	0.273123i
$514$	−19.5412	−	60.1417i	−0.861926	−	2.65273i
$515$	5.23568	+	17.4141i	0.230712	+	0.767357i
$516$	−32.7251			−1.44064
$517$		0			0
$518$			7.23084i			0.317705i
$519$	17.1567	−	12.4651i	0.753097	−	0.547157i
$520$	−1.11006	+	50.2221i	−0.0486792	+	2.20238i
$521$	5.56982	−	17.1422i	0.244018	−	0.751011i	−0.751778	−	0.659416i	$-0.770803\pi$
$521$	5.56982	−	17.1422i	0.244018	−	0.751011i	0.995796	−	0.0915950i	$-0.0291965\pi$
$522$	17.6950	−	24.3551i	0.774488	−	1.06599i
$523$	−10.6042	+	14.5954i	−0.463688	+	0.638212i	−0.975269	−	0.221023i	$-0.929060\pi$
$523$	−10.6042	+	14.5954i	−0.463688	+	0.638212i	0.511580	+	0.859235i	$0.329060\pi$
$524$	7.60007	−	23.3906i	0.332011	−	1.02182i
$525$	3.71081	−	9.90793i	0.161953	−	0.432417i
$526$	5.27043	−	3.82919i	0.229802	−	0.166961i
$527$			4.27858i			0.186378i
$528$		0			0
$529$	−3.84247			−0.167064
$530$	13.2735	−	3.99079i	0.576566	−	0.173349i
$531$	5.97332	+	18.3840i	0.259220	+	0.797797i
$532$	29.7184	+	9.65609i	1.28846	+	0.418645i
$533$	−2.50686	+	3.45039i	−0.108584	+	0.149453i
$534$	−40.6296	−	29.5192i	−1.75822	−	1.27742i
$535$	−11.7822	−	8.96466i	−0.509389	−	0.387576i
$536$	22.2174	+	68.3780i	0.959644	+	2.95348i
$537$	−3.07312	−	4.22979i	−0.132615	−	0.182529i
$538$		−	41.9492i		−	1.80856i
$539$		0			0
$540$	−10.7712	+	30.8160i	−0.463519	+	1.32611i
$541$	5.13566	−	3.73127i	0.220799	−	0.160420i	−0.471887	−	0.881659i	$-0.656427\pi$
$541$	5.13566	−	3.73127i	0.220799	−	0.160420i	0.692686	+	0.721239i	$0.256427\pi$
$542$	−4.97241	+	1.61563i	−0.213583	+	0.0693974i
$543$	−28.9017	−	9.39072i	−1.24029	−	0.402994i
$544$	−13.1236	−	9.53486i	−0.562670	−	0.408804i
$545$	−3.62540	−	5.22915i	−0.155295	−	0.223992i
$546$	−5.24552	+	16.1441i	−0.224488	+	0.690902i
$547$	−14.4846	+	4.70634i	−0.619318	+	0.201229i	−0.601838	−	0.798619i	$-0.705565\pi$
$547$	−14.4846	+	4.70634i	−0.619318	+	0.201229i	−0.0174806	+	0.999847i	$0.505565\pi$
$548$	20.5363	+	28.2658i	0.877267	+	1.20745i
$549$	1.58263			0.0675450
$550$		0			0
$551$	48.1327			2.05052
$552$	−47.5882	−	65.4995i	−2.02549	−	2.78784i
$553$	7.23804	−	2.35178i	0.307793	−	0.100008i
$554$	15.6000	−	48.0119i	0.662781	−	2.03983i
$555$	7.64419	+	11.0257i	0.324478	+	0.468015i
$556$	−44.6846	−	32.4653i	−1.89505	−	1.37683i
$557$	38.9007	+	12.6396i	1.64828	+	0.535558i	0.978366	−	0.206883i	$-0.0663320\pi$
$557$	38.9007	+	12.6396i	1.64828	+	0.535558i	0.669912	+	0.742441i	$0.266332\pi$
$558$	−10.3484	+	3.36241i	−0.438085	+	0.142342i
$559$	7.92872	−	5.76055i	0.335349	−	0.243646i
$560$	6.88989	−	19.7117i	0.291151	−	0.832972i
$561$		0			0
$562$		−	7.61053i		−	0.321031i
$563$	10.5797	+	14.5618i	0.445883	+	0.613705i	0.971507	−	0.237012i	$-0.0761680\pi$
$563$	10.5797	+	14.5618i	0.445883	+	0.613705i	−0.525624	+	0.850717i	$0.676168\pi$
$564$	6.79222	+	20.9043i	0.286004	+	0.880230i
$565$	−31.5689	−	24.0197i	−1.32811	−	1.01051i
$566$	1.20745	+	0.877267i	0.0507531	+	0.0368743i
$567$	−6.53544	+	8.99526i	−0.274463	+	0.377765i
$568$	1.69328	+	0.550179i	0.0710484	+	0.0230850i
$569$	12.5832	+	38.7270i	0.527514	+	1.62352i	0.759290	+	0.650753i	$0.225546\pi$
$569$	12.5832	+	38.7270i	0.527514	+	1.62352i	−0.231776	+	0.972769i	$0.574454\pi$
$570$	78.6557	−	23.6484i	3.29453	−	0.990524i
$571$	13.2417			0.554149			0.277075	−	0.960848i	$-0.410635\pi$
$571$	13.2417			0.554149			0.277075	+	0.960848i	$0.410635\pi$
$572$		0			0
$573$			37.2354i			1.55553i
$574$	2.89241	−	2.10146i	0.120727	−	0.0877131i
$575$	−24.2592	−	9.08579i	−1.01168	−	0.378904i
$576$	3.53399	−	10.8765i	0.147250	−	0.453188i
$577$	−0.387625	+	0.533520i	−0.0161370	+	0.0222107i	−0.817009	−	0.576625i	$-0.804370\pi$
$577$	−0.387625	+	0.533520i	−0.0161370	+	0.0222107i	0.800872	+	0.598835i	$0.204370\pi$
$578$	22.0405	−	30.3362i	0.916765	−	1.26182i
$579$	−7.27964	+	22.4044i	−0.302532	+	0.931097i
$580$	1.73443	−	78.4704i	0.0720181	−	3.25831i
$581$	4.76423	−	3.46142i	0.197654	−	0.143604i
$582$			71.0846i			2.94655i
$583$		0			0
$584$	−99.8221			−4.13067
$585$	3.12682	+	10.3999i	0.129278	+	0.429985i
$586$	−7.52060	−	23.1460i	−0.310673	−	0.956154i
$587$	−11.4838	−	3.73130i	−0.473985	−	0.154007i	0.0622764	−	0.998059i	$-0.480164\pi$
$587$	−11.4838	−	3.73130i	−0.473985	−	0.154007i	−0.536262	+	0.844052i	$0.680164\pi$
$588$	−36.3600	+	50.0452i	−1.49946	+	2.06383i
$589$	−14.0746	−	10.2258i	−0.579933	−	0.421346i
$590$	56.8186	+	43.2312i	2.33918	+	1.77980i
$591$	−2.30956	−	7.10810i	−0.0950026	−	0.292388i
$592$	15.5640	+	21.4221i	0.639678	+	0.880441i
$593$		−	38.3249i		−	1.57382i	−0.617070	−	0.786908i	$-0.711680\pi$
$593$		−	38.3249i		−	1.57382i	0.617070	−	0.786908i	$-0.288320\pi$
$594$		0			0
$595$	−3.37921	−	1.18114i	−0.138534	−	0.0484222i
$596$	−40.0772	+	29.1178i	−1.64163	+	1.19271i
$597$	5.78464	−	1.87954i	0.236750	−	0.0769246i
$598$	39.5282	+	12.8435i	1.61643	+	0.525209i
$599$	−3.46909	−	2.52044i	−0.141743	−	0.102983i	0.514654	−	0.857398i	$-0.327920\pi$
$599$	−3.46909	−	2.52044i	−0.141743	−	0.102983i	−0.656397	+	0.754416i	$0.727920\pi$
$600$	−20.8378	−	75.3039i	−0.850699	−	3.07427i
$601$	−8.94335	+	27.5248i	−0.364807	+	1.12276i	0.585295	+	0.810821i	$0.300979\pi$
$601$	−8.94335	+	27.5248i	−0.364807	+	1.12276i	−0.950102	+	0.311940i	$0.899021\pi$
$602$	−7.81345	+	2.53874i	−0.318453	+	0.103472i
$603$	9.13590	+	12.5745i	0.372042	+	0.512073i
$604$	71.8624			2.92404
$605$		0			0
$606$	−85.2703			−3.46387
$607$	6.49815	+	8.94394i	0.263752	+	0.363023i	0.920268	−	0.391289i	$-0.127971\pi$
$607$	6.49815	+	8.94394i	0.263752	+	0.363023i	−0.656516	+	0.754312i	$0.727971\pi$
$608$	62.7307	−	20.3824i	2.54407	−	0.826617i
$609$	4.78129	−	14.7153i	0.193748	−	0.596294i
$610$	4.80381	−	3.33051i	0.194501	−	0.134848i
$611$	−5.32540	−	3.86913i	−0.215443	−	0.156528i
$612$	−11.6687	−	3.79138i	−0.471678	−	0.153257i
$613$	10.0534	−	3.26653i	0.406051	−	0.131934i	−0.0988682	−	0.995101i	$-0.531522\pi$
$613$	10.0534	−	3.26653i	0.406051	−	0.131934i	0.504919	+	0.863167i	$0.331522\pi$
$614$	−13.3964	+	9.73305i	−0.540634	+	0.392794i
$615$	2.18881	−	6.26209i	0.0882612	−	0.252512i
$616$		0			0
$617$		−	1.60816i		−	0.0647421i	−0.999476	−	0.0323710i	$-0.989694\pi$
$617$		−	1.60816i		−	0.0647421i	0.999476	−	0.0323710i	$-0.0103058\pi$
$618$	26.6729	+	36.7120i	1.07294	+	1.47677i
$619$	11.4123	+	35.1234i	0.458699	+	1.41173i	0.866737	+	0.498765i	$0.166213\pi$
$619$	11.4123	+	35.1234i	0.458699	+	1.41173i	−0.408039	+	0.912965i	$0.633787\pi$
$620$	−17.1782	+	22.5772i	−0.689892	+	0.906722i
$621$	12.7470	+	9.26126i	0.511521	+	0.371642i
$622$	34.5783	−	47.5930i	1.38647	−	1.90831i
$623$	−8.46432	−	2.75022i	−0.339116	−	0.110185i
$624$	19.2089	+	59.1190i	0.768973	+	2.36666i
$625$	−18.8492	−	16.4228i	−0.753967	−	0.656912i
$626$	−66.7008			−2.66590
$627$		0			0
$628$			86.7302i			3.46091i
$629$	3.67241	−	2.66816i	0.146429	−	0.106387i
$630$	0.201168	−	9.10139i	0.00801471	−	0.362608i
$631$	13.2924	−	40.9097i	0.529161	−	1.62859i	−0.226777	−	0.973947i	$-0.572819\pi$
$631$	13.2924	−	40.9097i	0.529161	−	1.62859i	0.755938	−	0.654643i	$-0.227181\pi$
$632$	33.0358	−	45.4699i	1.31410	−	1.80870i
$633$	3.92222	−	5.39848i	0.155894	−	0.214570i
$634$	20.0040	−	61.5659i	0.794459	−	2.44509i
$635$	−38.6102	−	0.853400i	−1.53220	−	0.0338661i
$636$	19.7532	−	14.3516i	0.783266	−	0.569076i
$637$		−	18.5255i		−	0.734007i
$638$		0			0
$639$	0.384897			0.0152263
$640$	0.740658	+	2.46346i	0.0292771	+	0.0973769i
$641$	−6.89285	−	21.2140i	−0.272251	−	0.837903i	−0.989934	−	0.141533i	$-0.954797\pi$
$641$	−6.89285	−	21.2140i	−0.272251	−	0.837903i	0.717682	−	0.696371i	$-0.245203\pi$
$642$	−35.1374	−	11.4168i	−1.38676	−	0.450587i
$643$	−19.1728	+	26.3891i	−0.756102	+	1.04069i	0.241426	+	0.970419i	$0.422385\pi$
$643$	−19.1728	+	26.3891i	−0.756102	+	1.04069i	−0.997528	+	0.0702661i	$0.977615\pi$
$644$	−19.8973	−	14.4562i	−0.784062	−	0.569654i
$645$	−9.23022	+	12.1312i	−0.363440	+	0.477667i
$646$	−8.58741	−	26.4293i	−0.337867	−	1.03985i
$647$	5.75892	+	7.92647i	0.226407	+	0.311622i	0.907074	−	0.420970i	$-0.138310\pi$
$647$	5.75892	+	7.92647i	0.226407	+	0.311622i	−0.680668	+	0.732592i	$0.738310\pi$
$648$			82.1123i			3.22567i
$649$		0			0
$650$	31.3768	+	24.9872i	1.23070	+	0.980078i
$651$	−4.52437	+	3.28714i	−0.177324	+	0.128833i
$652$	97.7142	−	31.7493i	3.82678	−	1.24340i
$653$	−26.8666	−	8.72948i	−1.05137	−	0.341611i	−0.268165	−	0.963373i	$-0.586417\pi$
$653$	−26.8666	−	8.72948i	−1.05137	−	0.341611i	−0.783206	+	0.621762i	$0.786417\pi$
$654$	−12.8462	−	9.33333i	−0.502327	−	0.364962i
$655$	−6.52732	−	9.41477i	−0.255043	−	0.367865i
$656$	4.04575	−	12.4515i	0.157960	−	0.486151i
$657$	−20.5237	+	6.66855i	−0.800705	+	0.260165i
$658$	3.24343	+	4.46420i	0.126442	+	0.174033i
$659$	35.4089			1.37934			0.689668	−	0.724126i	$-0.257756\pi$
$659$	35.4089			1.37934			0.689668	+	0.724126i	$0.257756\pi$
$660$		0			0
$661$	34.3615			1.33651			0.668254	−	0.743933i	$-0.267042\pi$
$661$	34.3615			1.33651			0.668254	+	0.743933i	$0.267042\pi$
$662$	8.89095	+	12.2373i	0.345557	+	0.475618i
$663$	10.1349	−	3.29301i	0.393605	−	0.127890i
$664$	13.4391	−	41.3613i	0.521538	−	1.60513i
$665$	11.9617	−	8.29312i	0.463855	−	0.321593i
$666$	9.33943	+	6.78550i	0.361896	+	0.262933i
$667$	−36.0299	−	11.7068i	−1.39508	−	0.453290i
$668$	57.4161	−	18.6556i	2.22150	−	0.721808i
$669$	−21.4128	+	15.5573i	−0.827867	+	0.601480i
$670$	54.1925	+	18.9420i	2.09364	+	0.731795i
$671$		0			0
$672$		−	21.2030i		−	0.817922i
$673$	−16.9863	−	23.3797i	−0.654775	−	0.901221i	0.344519	−	0.938779i	$-0.388042\pi$
$673$	−16.9863	−	23.3797i	−0.654775	−	0.901221i	−0.999294	+	0.0375586i	$0.988042\pi$
$674$	0.0372058	+	0.114508i	0.00143311	+	0.00441067i
$675$	8.38549	+	12.6847i	0.322758	+	0.488233i
$676$	13.7354	+	9.97935i	0.528284	+	0.383821i
$677$	11.5075	−	15.8388i	0.442271	−	0.608734i	−0.528444	−	0.848968i	$-0.677224\pi$
$677$	11.5075	−	15.8388i	0.442271	−	0.608734i	0.970715	+	0.240234i	$0.0772243\pi$
$678$	−94.1463	−	30.5900i	−3.61567	−	1.17480i
$679$	3.89276	+	11.9807i	0.149391	+	0.459777i
$680$	−25.3166	+	7.61161i	−0.970846	+	0.291892i
$681$	−29.1375			−1.11655
$682$		0			0
$683$			6.84643i			0.261971i	0.991384	+	0.130986i	$0.0418142\pi$
$683$			6.84643i			0.261971i	−0.991384	+	0.130986i	$0.958186\pi$
$684$	40.3600	−	29.3232i	1.54320	−	1.12120i
$685$	16.2705	+	0.359626i	0.621664	+	0.0137406i
$686$	−10.3771	+	31.9374i	−0.396199	+	1.21938i
$687$	−7.34834	+	10.1141i	−0.280357	+	0.385878i
$688$	−17.6836	+	24.3394i	−0.674180	+	0.927929i
$689$	−2.25958	+	6.95428i	−0.0860832	+	0.264937i
$690$	−64.6298	−	1.42851i	−2.46041	−	0.0543824i
$691$	28.7799	−	20.9098i	1.09484	−	0.795446i	0.114628	−	0.993409i	$-0.463432\pi$
$691$	28.7799	−	20.9098i	1.09484	−	0.795446i	0.980210	+	0.197963i	$0.0634325\pi$
$692$		−	47.5755i		−	1.80855i
$693$		0			0
$694$	82.3124			3.12453
$695$	−24.6384	+	7.40772i	−0.934587	+	0.280991i
$696$	−35.3100	−	108.673i	−1.33842	−	4.11923i
$697$	−2.13458	−	0.693568i	−0.0808531	−	0.0262708i
$698$	46.4806	−	63.9751i	1.75932	−	2.42149i
$699$	40.5776	+	29.4814i	1.53479	+	1.11509i
$700$	−13.0892	−	19.7999i	−0.494725	−	0.748366i
$701$	0.0949717	+	0.292293i	0.00358703	+	0.0110397i	0.952834	−	0.303492i	$-0.0981525\pi$
$701$	0.0949717	+	0.292293i	0.00358703	+	0.0110397i	−0.949247	+	0.314532i	$0.898153\pi$
$702$	−14.3400	−	19.7373i	−0.541227	−	0.744935i
$703$			18.4575i			0.696136i
$704$		0			0
$705$	9.66503	+	3.37825i	0.364006	+	0.127232i
$706$	40.3290	−	29.3007i	1.51780	−	1.10275i
$707$	−14.3716	+	4.66961i	−0.540499	+	0.175619i
$708$	119.613	+	38.8646i	4.49532	+	1.46062i
$709$	−3.35597	−	2.43826i	−0.126036	−	0.0915707i	0.522981	−	0.852344i	$-0.324820\pi$
$709$	−3.35597	−	2.43826i	−0.126036	−	0.0915707i	−0.649017	+	0.760774i	$0.724820\pi$
$710$	1.16829	−	0.809983i	0.0438452	−	0.0303981i
$711$	3.75467	−	11.5557i	0.140811	−	0.433372i
$712$	−62.5092	+	20.3105i	−2.34263	+	0.761167i
$713$	8.04846	+	11.0778i	0.301417	+	0.414865i
$714$	−8.93310			−0.334313
$715$		0			0
$716$	−11.7292			−0.438340
$717$	8.27918	+	11.3953i	0.309192	+	0.425566i
$718$	−66.7108	+	21.6757i	−2.48963	+	0.808929i
$719$	0.888086	−	2.73325i	0.0331200	−	0.101933i	−0.933130	−	0.359539i	$-0.882934\pi$
$719$	0.888086	−	2.73325i	0.0331200	−	0.101933i	0.966250	+	0.257606i	$0.0829338\pi$
$720$	−18.9943	−	27.3967i	−0.707877	−	1.02102i
$721$	6.50592	+	4.72683i	0.242293	+	0.176036i
$722$	60.3418	+	19.6062i	2.24569	+	0.729668i
$723$	24.7519	−	8.04239i	0.920535	−	0.299100i
$724$	−55.1545	+	40.0721i	−2.04980	+	1.48927i
$725$	−28.5999	−	22.7758i	−1.06217	−	0.845872i
$726$		0			0
$727$			27.5703i			1.02253i	0.859424	+	0.511263i	$0.170822\pi$
$727$			27.5703i			1.02253i	−0.859424	+	0.511263i	$0.829178\pi$
$728$	13.0580	+	17.9728i	0.483962	+	0.666117i
$729$	−0.547335	−	1.68452i	−0.0202717	−	0.0623897i
$730$	−48.2628	+	63.4316i	−1.78629	+	2.34771i
$731$	4.17253	+	3.03152i	0.154327	+	0.112125i
$732$	6.05252	−	8.33058i	0.223708	−	0.307907i
$733$	35.1729	+	11.4284i	1.29914	+	0.422116i	0.875282	−	0.483613i	$-0.160676\pi$
$733$	35.1729	+	11.4284i	1.29914	+	0.422116i	0.423858	+	0.905729i	$0.360676\pi$
$734$	6.48081	+	19.9459i	0.239211	+	0.736216i
$735$	8.29638	+	27.5941i	0.306017	+	1.01782i
$736$	−51.9147			−1.91360
$737$		0			0
$738$		−	5.70789i		−	0.210110i
$739$	36.3769	−	26.4294i	1.33815	−	0.972220i	0.338637	−	0.940917i	$-0.390034\pi$
$739$	36.3769	−	26.4294i	1.33815	−	0.972220i	0.999510	−	0.0313032i	$-0.00996574\pi$
$740$	30.0910	+	0.665101i	1.10617	+	0.0244496i
$741$	−13.3897	+	41.2093i	−0.491884	+	1.51386i
$742$	3.60293	−	4.95900i	0.132268	−	0.182051i
$743$	−15.6645	+	21.5603i	−0.574674	+	0.790970i	−0.993099	−	0.117281i	$-0.962582\pi$
$743$	−15.6645	+	21.5603i	−0.574674	+	0.790970i	0.418425	+	0.908251i	$0.362582\pi$
$744$	−12.7625	+	39.2788i	−0.467895	+	1.44003i
$745$	−0.509904	+	23.0695i	−0.0186814	+	0.845200i
$746$	58.5538	−	42.5418i	2.14381	−	1.55757i
$747$		−	9.40177i		−	0.343993i
$748$		0			0
$749$	−6.54733			−0.239234
$750$	−57.9265	−	23.1673i	−2.11518	−	0.845950i
$751$	10.3969	+	31.9984i	0.379389	+	1.16764i	0.940470	+	0.339878i	$0.110386\pi$
$751$	10.3969	+	31.9984i	0.379389	+	1.16764i	−0.561081	+	0.827761i	$0.689614\pi$
$752$	19.2179	+	6.24429i	0.700806	+	0.227706i
$753$	−1.36625	+	1.88048i	−0.0497889	+	0.0685285i
$754$	47.4561	+	34.4789i	1.72825	+	1.25565i
$755$	20.2691	−	26.6395i	0.737667	−	0.969512i
$756$	4.46115	+	13.7300i	0.162250	+	0.499356i
$757$	0.789437	+	1.08657i	0.0286926	+	0.0394919i	0.823122	−	0.567864i	$-0.192230\pi$
$757$	0.789437	+	1.08657i	0.0286926	+	0.0394919i	−0.794430	+	0.607356i	$0.792230\pi$
$758$			47.7614i			1.73477i
$759$		0			0
$760$	35.4677	−	101.472i	1.28655	−	3.68076i
$761$	−1.31137	+	0.952765i	−0.0475371	+	0.0345377i	−0.611300	−	0.791399i	$-0.709353\pi$
$761$	−1.31137	+	0.952765i	−0.0475371	+	0.0345377i	0.563763	+	0.825937i	$0.309353\pi$
$762$	−91.6584	+	29.7816i	−3.32043	+	1.07887i
$763$	−2.67624	−	0.869562i	−0.0968863	−	0.0314803i
$764$	67.5805	+	49.1001i	2.44498	+	1.77638i
$765$	−4.69666	+	3.25622i	−0.169808	+	0.117729i
$766$	14.0702	−	43.3037i	0.508378	−	1.56463i
$767$	−35.8214	+	11.6391i	−1.29344	+	0.420263i
$768$	21.9949	+	30.2734i	0.793674	+	1.09240i
$769$	−3.62584			−0.130751			−0.0653755	−	0.997861i	$-0.520825\pi$
$769$	−3.62584			−0.130751			−0.0653755	+	0.997861i	$0.520825\pi$
$770$		0			0
$771$	−51.8889			−1.86873
$772$	31.0637	+	42.7555i	1.11801	+	1.53881i
$773$	21.0180	−	6.82915i	0.755964	−	0.245627i	0.0944183	−	0.995533i	$-0.469901\pi$
$773$	21.0180	−	6.82915i	0.755964	−	0.245627i	0.661545	+	0.749905i	$0.269901\pi$
$774$	−4.05316	+	12.4743i	−0.145688	+	0.448380i
$775$	3.52424	+	12.7360i	0.126594	+	0.457489i
$776$	75.2637	+	54.6823i	2.70181	+	1.96298i
$777$	5.64288	+	1.83348i	0.202437	+	0.0657758i
$778$	33.6277	−	10.9263i	1.20561	−	0.391727i
$779$	7.38316	−	5.36418i	0.264529	−	0.192192i
$780$	66.7008	+	23.3141i	2.38827	+	0.834779i
$781$		0			0
$782$			21.8724i			0.782155i
$783$	13.0709	+	17.9905i	0.467115	+	0.642929i
$784$	17.5735	+	54.0856i	0.627625	+	1.93163i
$785$	32.1510	+	24.4626i	1.14752	+	0.873106i
$786$	−23.1289	−	16.8041i	−0.824980	−	0.599383i
$787$	−1.08379	+	1.49171i	−0.0386330	+	0.0531737i	−0.827896	−	0.560881i	$-0.810463\pi$
$787$	−1.08379	+	1.49171i	−0.0386330	+	0.0531737i	0.789264	+	0.614055i	$0.210463\pi$
$788$	−15.9463	−	5.18127i	−0.568064	−	0.184575i
$789$	−1.65187	−	5.08394i	−0.0588082	−	0.180993i
$790$	−12.9213	−	42.9767i	−0.459718	−	1.52904i
$791$	−17.5427			−0.623748
$792$		0			0
$793$			3.08377i			0.109508i
$794$	5.11463	−	3.71599i	0.181511	−	0.131876i
$795$	0.251321	−	11.3705i	0.00891343	−	0.403269i
$796$	4.21657	−	12.9773i	0.149453	−	0.459968i
$797$	−28.4846	+	39.2057i	−1.00898	+	1.38874i	−0.0893229	+	0.996003i	$0.528470\pi$
$797$	−28.4846	+	39.2057i	−1.00898	+	1.38874i	−0.919653	+	0.392733i	$0.871530\pi$
$798$	21.3501	−	29.3858i	0.755784	−	1.04025i
$799$	1.07047	−	3.29456i	0.0378704	−	0.116553i
$800$	−46.9186	−	17.5724i	−1.65882	−	0.621278i
$801$	−11.4952	+	8.35177i	−0.406164	+	0.295095i
$802$		−	42.8042i		−	1.51147i
$803$		0			0
$804$	101.128			3.56650
$805$	−10.9710	+	3.29852i	−0.386678	+	0.116258i
$806$	−6.55171	−	20.1641i	−0.230774	−	0.710249i
$807$	−32.7368	−	10.6368i	−1.15239	−	0.374434i
$808$	−65.5947	+	90.2834i	−2.30761	+	3.17616i
$809$	−13.3913	−	9.72937i	−0.470814	−	0.342066i	0.326944	−	0.945044i	$-0.393981\pi$
$809$	−13.3913	−	9.72937i	−0.470814	−	0.342066i	−0.797758	+	0.602977i	$0.793981\pi$
$810$	52.1780	+	39.7003i	1.83335	+	1.39493i
$811$	4.55730	+	14.0259i	0.160029	+	0.492517i	0.998636	−	0.0522195i	$-0.0166295\pi$
$811$	4.55730	+	14.0259i	0.160029	+	0.492517i	−0.838607	+	0.544737i	$0.816630\pi$
$812$	−20.4027	−	28.0820i	−0.715996	−	0.985484i
$813$			4.29009i			0.150460i
$814$		0			0
$815$	15.7911	−	45.1778i	0.553139	−	1.58251i
$816$	−26.4652	+	19.2281i	−0.926466	+	0.673117i
$817$	−19.9446	+	6.48040i	−0.697774	+	0.226721i
$818$	48.3001	+	15.6937i	1.68878	+	0.548716i
$819$	3.88542	+	2.82293i	0.135768	+	0.0986410i
$820$	−8.47914	−	12.2300i	−0.296104	−	0.427090i
$821$	12.7281	−	39.1731i	0.444215	−	1.36715i	−0.439128	−	0.898425i	$-0.644713\pi$
$821$	12.7281	−	39.1731i	0.444215	−	1.36715i	0.883343	−	0.468728i	$-0.155287\pi$
$822$	38.6252	−	12.5501i	1.34721	−	0.437735i
$823$	1.43083	+	1.96937i	0.0498757	+	0.0686480i	0.833226	−	0.552932i	$-0.186491\pi$
$823$	1.43083	+	1.96937i	0.0498757	+	0.0686480i	−0.783351	+	0.621580i	$0.786491\pi$
$824$	59.3886			2.06890
$825$		0			0
$826$	31.5739			1.09860
$827$	−24.6971	−	33.9927i	−0.858803	−	1.18204i	−0.981854	−	0.189641i	$-0.939268\pi$
$827$	−24.6971	−	33.9927i	−0.858803	−	1.18204i	0.123050	−	0.992400i	$-0.460732\pi$
$828$	−37.3436	+	12.1337i	−1.29778	+	0.421674i
$829$	4.00887	−	12.3380i	0.139234	−	0.428518i	−0.856991	−	0.515332i	$-0.827669\pi$
$829$	4.00887	−	12.3380i	0.139234	−	0.428518i	0.996225	+	0.0868142i	$0.0276687\pi$
$830$	−19.7852	−	28.5375i	−0.686756	−	0.990552i
$831$	−33.5124	−	24.3482i	−1.16253	−	0.844629i
$832$	21.1930	+	6.88603i	0.734736	+	0.238730i
$833$	9.27197	−	3.01265i	0.321255	−	0.104382i
$834$	−51.9421	+	37.7381i	−1.79861	+	1.30677i
$835$	9.27875	−	26.5461i	0.321104	−	0.918667i
$836$		0			0
$837$		−	8.03754i		−	0.277818i
$838$	−2.82754	−	3.89177i	−0.0976756	−	0.134439i
$839$	−9.42118	−	28.9954i	−0.325255	−	1.00103i	−0.971325	−	0.237755i	$-0.923589\pi$
$839$	−9.42118	−	28.9954i	−0.325255	−	1.00103i	0.646070	−	0.763278i	$-0.276411\pi$
$840$	−27.4991	−	20.9231i	−0.948808	−	0.721914i
$841$	−19.7948	−	14.3817i	−0.682578	−	0.495922i
$842$	−32.4948	+	44.7253i	−1.11985	+	1.54133i
$843$	−5.93918	−	1.92976i	−0.204556	−	0.0664644i
$844$	−4.62597	−	14.2373i	−0.159233	−	0.490067i
$845$	7.57348	−	2.27702i	0.260536	−	0.0783320i
$846$	8.80968			0.302883
$847$		0			0
$848$		−	22.4466i		−	0.770821i
$849$	0.990778	−	0.719842i	0.0340034	−	0.0247049i
$850$	−7.40349	+	19.7675i	−0.253938	+	0.678018i
$851$	4.48922	−	13.8164i	0.153888	−	0.473620i
$852$	1.47198	−	2.02600i	0.0504291	−	0.0694097i
$853$	−23.9599	+	32.9780i	−0.820371	+	1.12914i	0.169269	+	0.985570i	$0.445859\pi$
$853$	−23.9599	+	32.9780i	−0.820371	+	1.12914i	−0.989640	+	0.143574i	$0.954141\pi$
$854$	0.798833	−	2.45856i	0.0273355	−	0.0841300i
$855$	0.513501	−	23.2322i	0.0175614	−	0.794525i
$856$	−39.1177	+	28.4207i	−1.33702	+	0.971400i
$857$		−	5.21553i		−	0.178159i	−0.996025	−	0.0890796i	$-0.971607\pi$
$857$		−	5.21553i		−	0.178159i	0.996025	−	0.0890796i	$-0.0283925\pi$
$858$		0			0
$859$	−43.2632			−1.47612			−0.738061	−	0.674734i	$-0.764258\pi$
$859$	−43.2632			−1.47612			−0.738061	+	0.674734i	$0.764258\pi$
$860$	9.84626	+	32.7491i	0.335755	+	1.11674i
$861$	−0.906546	−	2.79006i	−0.0308950	−	0.0950850i
$862$	−65.3025	−	21.2181i	−2.22421	−	0.722690i
$863$	−16.8026	+	23.1268i	−0.571967	+	0.787245i	−0.992786	−	0.119900i	$-0.961743\pi$
$863$	−16.8026	+	23.1268i	−0.571967	+	0.787245i	0.420819	+	0.907145i	$0.361743\pi$
$864$	24.6534	+	17.9118i	0.838727	+	0.609370i
$865$	−17.6363	−	13.4189i	−0.599653	−	0.456255i
$866$	7.36015	+	22.6522i	0.250108	+	0.769754i
$867$	−18.0854	−	24.8924i	−0.614212	−	0.845390i
$868$			12.5461i			0.425841i
$869$		0			0
$870$	−86.1278	−	30.1045i	−2.92001	−	1.02064i
$871$	−24.5015	+	17.8014i	−0.830203	+	0.603178i
$872$	−19.7641	+	6.42174i	−0.669296	+	0.217468i
$873$	19.1274	+	6.21487i	0.647365	+	0.210342i
$874$	−71.9502	−	52.2749i	−2.43375	−	1.76822i
$875$	−11.0317	−	0.732454i	−0.372940	−	0.0247615i
$876$	−43.3880	+	133.534i	−1.46594	+	4.51171i
$877$	24.0748	−	7.82238i	0.812948	−	0.264143i	0.127102	−	0.991890i	$-0.459432\pi$
$877$	24.0748	−	7.82238i	0.812948	−	0.264143i	0.685846	+	0.727747i	$0.259432\pi$
$878$	−16.9890	−	23.3834i	−0.573351	−	0.789150i
$879$	−19.9699			−0.673568
$880$		0			0
$881$	−0.716380			−0.0241355			−0.0120677	−	0.999927i	$-0.503841\pi$
$881$	−0.716380			−0.0241355			−0.0120677	+	0.999927i	$0.503841\pi$
$882$	14.5732	+	20.0582i	0.490704	+	0.675396i
$883$	27.3537	−	8.88777i	0.920527	−	0.299097i	0.189844	−	0.981814i	$-0.439202\pi$
$883$	27.3537	−	8.88777i	0.920527	−	0.299097i	0.730683	+	0.682717i	$0.239202\pi$
$884$	7.38755	−	22.7365i	0.248470	−	0.764713i
$885$	48.1444	−	33.3788i	1.61836	−	1.12202i
$886$	37.3057	+	27.1042i	1.25331	+	0.910583i
$887$	−46.1667	−	15.0005i	−1.55013	−	0.503667i	−0.595978	−	0.803001i	$-0.703235\pi$
$887$	−46.1667	−	15.0005i	−1.55013	−	0.503667i	−0.954148	+	0.299334i	$0.903235\pi$
$888$	41.6728	−	13.5403i	1.39845	−	0.454383i
$889$	−13.8173	+	10.0389i	−0.463418	+	0.336693i
$890$	−17.3163	+	49.5412i	−0.580442	+	1.66062i
$891$		0			0
$892$			59.3776i			1.98811i
$893$	8.27918	+	11.3953i	0.277052	+	0.381330i
$894$	17.7944	+	54.7656i	0.595135	+	1.83164i
$895$	−3.30826	+	4.34803i	−0.110583	+	0.145339i
$896$	0.920351	+	0.668674i	0.0307468	+	0.0223388i
$897$	20.0459	−	27.5908i	0.669312	−	0.921228i
$898$	−41.9855	−	13.6419i	−1.40107	−	0.455237i
$899$	5.97188	+	18.3796i	0.199173	+	0.612992i
$900$	−37.8568	−	1.67431i	−1.26189	−	0.0558104i
$901$	−3.84806			−0.128197
$902$		0			0
$903$			6.74128i			0.224336i
$904$	−104.811	+	76.1496i	−3.48596	+	2.53270i
$905$	−0.701732	+	31.7484i	−0.0233264	+	1.05535i
$906$	25.8134	−	79.4456i	0.857594	−	2.63940i
$907$	19.3960	−	26.6963i	0.644033	−	0.886436i	−0.354789	−	0.934946i	$-0.615447\pi$
$907$	19.3960	−	26.6963i	0.644033	−	0.886436i	0.998823	+	0.0485104i	$0.0154474\pi$
$908$	−38.4219	+	52.8832i	−1.27507	+	1.75499i
$909$	−7.45512	+	22.9445i	−0.247271	+	0.761021i
$910$	17.7342	+	0.391978i	0.587882	+	0.0129939i
$911$	−18.5837	+	13.5019i	−0.615707	+	0.447337i	−0.851419	−	0.524486i	$-0.824258\pi$
$911$	−18.5837	+	13.5019i	−0.615707	+	0.447337i	0.235712	+	0.971823i	$0.424258\pi$
$912$		−	133.013i		−	4.40451i
$913$		0			0
$914$	−85.0415			−2.81292
$915$	−1.38102	−	4.59335i	−0.0456553	−	0.151851i
$916$	8.66683	+	26.6738i	0.286360	+	0.881326i
$917$	−4.81841	−	1.56560i	−0.159118	−	0.0517005i
$918$	7.54647	−	10.3868i	0.249071	−	0.342816i
$919$	−44.2431	−	32.1445i	−1.45945	−	1.06035i	−0.983507	−	0.180872i	$-0.942108\pi$
$919$	−44.2431	−	32.1445i	−1.45945	−	1.06035i	−0.475940	−	0.879478i	$-0.657892\pi$
$920$	−51.2294	+	67.3305i	−1.68898	+	2.21982i
$921$	4.19873	+	12.9224i	0.138353	+	0.425807i
$922$	−12.2149	−	16.8123i	−0.402275	−	0.553685i
$923$			0.749976i			0.0246858i
$924$		0			0
$925$	8.73384	−	10.9672i	0.287167	−	0.360600i
$926$	−53.5615	+	38.9147i	−1.76014	+	1.27882i
$927$	12.2105	−	3.96742i	0.401044	−	0.130307i
$928$	−69.6837	−	22.6416i	−2.28748	−	0.743247i
$929$	−38.1151	−	27.6922i	−1.25051	−	0.908552i	−0.252263	−	0.967659i	$-0.581175\pi$
$929$	−38.1151	−	27.6922i	−1.25051	−	0.908552i	−0.998252	+	0.0591068i	$0.981175\pi$
$930$	18.7891	+	27.1007i	0.616119	+	0.888668i
$931$	−12.2497	+	37.7008i	−0.401469	+	1.23559i
$932$	107.014	−	34.7711i	3.50537	−	1.13896i
$933$	−28.3733	−	39.0525i	−0.928900	−	1.27852i
$934$	−42.5249			−1.39146
$935$		0			0
$936$	35.4677			1.15930
$937$	17.3200	+	23.8390i	0.565821	+	0.778786i	0.992052	−	0.125829i	$-0.0401590\pi$
$937$	17.3200	+	23.8390i	0.565821	+	0.778786i	−0.426231	+	0.904614i	$0.640159\pi$
$938$	24.1453	−	7.84529i	0.788373	−	0.256158i
$939$	−16.9129	+	52.0526i	−0.551933	+	1.69867i
$940$	18.8760	−	13.0869i	0.615668	−	0.426846i
$941$	32.8502	+	23.8671i	1.07089	+	0.778044i	0.976071	−	0.217451i	$-0.0697742\pi$
$941$	32.8502	+	23.8671i	1.07089	+	0.778044i	0.0948147	+	0.995495i	$0.469774\pi$
$942$	95.8822	+	31.1540i	3.12401	+	1.01505i
$943$	−6.83137	+	2.21965i	−0.222460	+	0.0722816i
$944$	93.5406	−	67.9612i	3.04449	−	2.21195i
$945$	6.34802	+	2.21884i	0.206501	+	0.0721789i
$946$		0			0
$947$		−	12.2120i		−	0.396837i	−0.980117	−	0.198418i	$-0.936420\pi$
$947$		−	12.2120i		−	0.396837i	0.980117	−	0.198418i	$-0.0635805\pi$
$948$	−46.4671	−	63.9565i	−1.50918	−	2.07721i
$949$	−12.9937	−	39.9906i	−0.421795	−	1.29815i
$950$	−47.3316	−	71.5982i	−1.53564	−	2.32295i
$951$	−42.9731	−	31.2218i	−1.39350	−	1.01244i
$952$	−6.87184	+	9.45828i	−0.222718	+	0.306545i
$953$	−5.91607	−	1.92225i	−0.191640	−	0.0622677i	0.211624	−	0.977351i	$-0.432125\pi$
$953$	−5.91607	−	1.92225i	−0.191640	−	0.0622677i	−0.403265	+	0.915083i	$0.632125\pi$
$954$	−3.02408	−	9.30716i	−0.0979082	−	0.301330i
$955$	37.2628	−	11.2033i	1.20580	−	0.362532i
$956$	31.5992			1.02199
$957$		0			0
$958$		−	90.7353i		−	2.93152i
$959$	5.82268	−	4.23042i	0.188024	−	0.136608i
$960$	−34.6513	−	0.765895i	−1.11837	−	0.0247192i
$961$	−7.42105	+	22.8396i	−0.239389	+	0.736762i
$962$	−13.2216	+	18.1980i	−0.426282	+	0.586727i
$963$	−6.14408	+	8.45660i	−0.197990	+	0.272510i
$964$	18.0423	−	55.5285i	0.581104	−	1.78845i
$965$	24.6112	+	0.543980i	0.792262	+	0.0175113i
$966$	−23.1289	+	16.8041i	−0.744160	+	0.540664i
$967$			51.2195i			1.64711i	0.567238	+	0.823554i	$0.308012\pi$
$967$			51.2195i			1.64711i	−0.567238	+	0.823554i	$0.691988\pi$
$968$		0			0
$969$	−22.8026			−0.732527
$970$	71.1368	−	21.3878i	2.28406	−	0.686721i
$971$	5.24426	+	16.1402i	0.168296	+	0.517962i	0.999264	−	0.0383580i	$-0.0122127\pi$
$971$	5.24426	+	16.1402i	0.168296	+	0.517962i	−0.830968	+	0.556320i	$0.812213\pi$
$972$	68.1903	+	22.1564i	2.18720	+	0.710666i
$973$	−6.68776	+	9.20492i	−0.214400	+	0.295096i
$974$	−5.32540	−	3.86913i	−0.170637	−	0.123975i
$975$	27.4558	−	18.1503i	0.879289	−	0.581274i
$976$	−2.92530	−	9.00316i	−0.0936367	−	0.288184i
$977$	−7.73874	−	10.6515i	−0.247584	−	0.340771i	0.667079	−	0.744987i	$-0.267544\pi$
$977$	−7.73874	−	10.6515i	−0.247584	−	0.340771i	−0.914663	+	0.404216i	$0.867544\pi$
$978$		−	119.430i		−	3.81894i
$979$		0			0
$980$	61.0219	+	21.3292i	1.94927	+	0.681335i
$981$	−3.63455	+	2.64065i	−0.116042	+	0.0843095i
$982$	47.9296	−	15.5733i	1.52949	−	0.496963i
$983$	12.1699	+	3.95425i	0.388160	+	0.126121i	0.496594	−	0.867983i	$-0.334584\pi$
$983$	12.1699	+	3.95425i	0.388160	+	0.126121i	−0.108434	+	0.994104i	$0.534584\pi$
$984$	−17.5274	−	12.7344i	−0.558752	−	0.405957i
$985$	−6.41842	+	4.44993i	−0.204508	+	0.141787i
$986$	−9.53922	+	29.3587i	−0.303791	+	0.934972i
$987$	4.30623	−	1.39918i	0.137069	−	0.0445364i
$988$	57.1367	+	78.6419i	1.81776	+	2.50193i
$989$	16.5058			0.524854
$990$		0			0
$991$	2.32786			0.0739468			0.0369734	−	0.999316i	$-0.488228\pi$
$991$	2.32786			0.0739468			0.0369734	+	0.999316i	$0.488228\pi$
$992$	15.5661	+	21.4250i	0.494225	+	0.680243i
$993$	11.8043	−	3.83546i	0.374599	−	0.121715i
$994$	0.194277	−	0.597923i	0.00616209	−	0.0189650i
$995$	−3.62140	−	5.22338i	−0.114806	−	0.165592i
$996$	−49.4886	−	35.9556i	−1.56811	−	1.13930i
$997$	18.2234	+	5.92115i	0.577142	+	0.187525i	0.583020	−	0.812458i	$-0.301871\pi$
$997$	18.2234	+	5.92115i	0.577142	+	0.187525i	−0.00587774	+	0.999983i	$0.501871\pi$
$998$	2.87082	−	0.932787i	0.0908743	−	0.0295269i
$999$	−6.89882	+	5.01229i	−0.218269	+	0.158582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.k.124.1		48
5.4	even	2	inner	605.2.j.k.124.12		48
11.2	odd	10		605.2.b.h.364.2	yes	12
11.3	even	5	inner	605.2.j.k.269.2		48
11.4	even	5	inner	605.2.j.k.444.12		48
11.5	even	5	inner	605.2.j.k.9.11		48
11.6	odd	10	inner	605.2.j.k.9.1		48
11.7	odd	10	inner	605.2.j.k.444.2		48
11.8	odd	10	inner	605.2.j.k.269.12		48
11.9	even	5		605.2.b.h.364.12	yes	12
11.10	odd	2	inner	605.2.j.k.124.11		48
55.2	even	20		3025.2.a.bo.1.12		12
55.4	even	10	inner	605.2.j.k.444.1		48
55.9	even	10		605.2.b.h.364.1	✓	12
55.13	even	20		3025.2.a.bo.1.1		12
55.14	even	10	inner	605.2.j.k.269.11		48
55.19	odd	10	inner	605.2.j.k.269.1		48
55.24	odd	10		605.2.b.h.364.11	yes	12
55.29	odd	10	inner	605.2.j.k.444.11		48
55.39	odd	10	inner	605.2.j.k.9.12		48
55.42	odd	20		3025.2.a.bo.1.2		12
55.49	even	10	inner	605.2.j.k.9.2		48
55.53	odd	20		3025.2.a.bo.1.11		12
55.54	odd	2	inner	605.2.j.k.124.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.1	✓	12	55.9	even	10
605.2.b.h.364.2	yes	12	11.2	odd	10
605.2.b.h.364.11	yes	12	55.24	odd	10
605.2.b.h.364.12	yes	12	11.9	even	5
605.2.j.k.9.1		48	11.6	odd	10	inner
605.2.j.k.9.2		48	55.49	even	10	inner
605.2.j.k.9.11		48	11.5	even	5	inner
605.2.j.k.9.12		48	55.39	odd	10	inner
605.2.j.k.124.1		48	1.1	even	1	trivial
605.2.j.k.124.2		48	55.54	odd	2	inner
605.2.j.k.124.11		48	11.10	odd	2	inner
605.2.j.k.124.12		48	5.4	even	2	inner
605.2.j.k.269.1		48	55.19	odd	10	inner
605.2.j.k.269.2		48	11.3	even	5	inner
605.2.j.k.269.11		48	55.14	even	10	inner
605.2.j.k.269.12		48	11.8	odd	10	inner
605.2.j.k.444.1		48	55.4	even	10	inner
605.2.j.k.444.2		48	11.7	odd	10	inner
605.2.j.k.444.11		48	55.29	odd	10	inner
605.2.j.k.444.12		48	11.4	even	5	inner
3025.2.a.bo.1.1		12	55.13	even	20
3025.2.a.bo.1.2		12	55.42	odd	20
3025.2.a.bo.1.11		12	55.53	odd	20
3025.2.a.bo.1.12		12	55.2	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53281 - 2.10973i) q^{2} +(-2.03508 + 0.661236i) q^{3} +(-1.48342 + 4.56549i) q^{4} +(1.27403 + 1.83762i) q^{5} +(4.51440 + 3.27991i) q^{6} +(0.940480 + 0.305580i) q^{7} +(6.94547 - 2.25672i) q^{8} +(1.27725 - 0.927974i) q^{9} +O(q^{10})\)	\(q+(-1.53281 - 2.10973i) q^{2} +(-2.03508 + 0.661236i) q^{3} +(-1.48342 + 4.56549i) q^{4} +(1.27403 + 1.83762i) q^{5} +(4.51440 + 3.27991i) q^{6} +(0.940480 + 0.305580i) q^{7} +(6.94547 - 2.25672i) q^{8} +(1.27725 - 0.927974i) q^{9} +(1.92403 - 5.50457i) q^{10} -10.2720i q^{12} +(1.80817 + 2.48873i) q^{13} +(-0.796882 - 2.45255i) q^{14} +(-3.80785 - 2.89726i) q^{15} +(-7.63983 - 5.55066i) q^{16} +(-0.951558 + 1.30971i) q^{17} +(-3.91554 - 1.27224i) q^{18} +(-2.03412 - 6.26038i) q^{19} +(-10.2796 + 3.09063i) q^{20} -2.11601 q^{21} +5.18097i q^{23} +(-12.6423 + 9.18518i) q^{24} +(-1.75368 + 4.68237i) q^{25} +(2.47897 - 7.62949i) q^{26} +(1.78755 - 2.46036i) q^{27} +(-2.79025 + 3.84045i) q^{28} +(-2.25958 + 6.95428i) q^{29} +(-0.275722 + 12.4745i) q^{30} +(2.13816 - 1.55347i) q^{31} +10.0203i q^{32} +4.22168 q^{34} +(0.636661 + 2.11756i) q^{35} +(2.34197 + 7.20783i) q^{36} +(-2.66676 - 0.866482i) q^{37} +(-10.0898 + 13.8874i) q^{38} +(-5.32540 - 3.86913i) q^{39} +(12.9957 + 9.88799i) q^{40} +(0.428423 + 1.31855i) q^{41} +(3.24343 + 4.46420i) q^{42} -3.18585i q^{43} +(3.33252 + 1.16482i) q^{45} +(10.9304 - 7.94143i) q^{46} +(-2.03508 + 0.661236i) q^{47} +(19.2179 + 6.24429i) q^{48} +(-4.87200 - 3.53971i) q^{49} +(12.5666 - 3.47737i) q^{50} +(1.07047 - 3.29456i) q^{51} +(-14.0446 + 4.56335i) q^{52} +(1.39715 + 1.92302i) q^{53} -7.93065 q^{54} +7.22168 q^{56} +(8.27918 + 11.3953i) q^{57} +(18.1351 - 5.89246i) q^{58} +(-3.78354 + 11.6445i) q^{59} +(18.8760 - 13.0869i) q^{60} +(0.810998 + 0.589225i) q^{61} +(-6.55478 - 2.12978i) q^{62} +(1.48480 - 0.482439i) q^{63} +(5.86035 - 4.25780i) q^{64} +(-2.26967 + 6.49345i) q^{65} +9.84499i q^{67} +(-4.56790 - 6.28717i) q^{68} +(-3.42585 - 10.5437i) q^{69} +(3.49160 - 4.58899i) q^{70} +(0.197235 + 0.143300i) q^{71} +(6.77690 - 9.32760i) q^{72} +(-12.9998 - 4.22390i) q^{73} +(2.25958 + 6.95428i) q^{74} +(0.472729 - 10.6886i) q^{75} +31.5992 q^{76} +17.1658i q^{78} +(6.22629 - 4.52366i) q^{79} +(0.466611 - 21.1108i) q^{80} +(-3.47452 + 10.6935i) q^{81} +(2.12509 - 2.92494i) q^{82} +(3.50035 - 4.81781i) q^{83} +(3.13892 - 9.66061i) q^{84} +(-3.61906 - 0.0799918i) q^{85} +(-6.72127 + 4.88329i) q^{86} -15.6466i q^{87} -9.00000 q^{89} +(-2.65064 - 8.81615i) q^{90} +(0.940039 + 2.89314i) q^{91} +(-23.6537 - 7.68555i) q^{92} +(-3.32411 + 4.57525i) q^{93} +(4.51440 + 3.27991i) q^{94} +(8.91266 - 11.7139i) q^{95} +(-6.62576 - 20.3920i) q^{96} +(7.48775 + 10.3060i) q^{97} +15.7043i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

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