LMFDB - Embedded newform 925.2.t.b.643.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.14
Character	$\chi$	$=$	925.643
Dual form			925.2.t.b.82.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.993536 - 1.72086i) q^{2} +(-2.35179 - 0.630160i) q^{3} +(-0.974229 - 1.68741i) q^{4} +(-3.42100 + 3.42100i) q^{6} +(2.62941 + 0.704548i) q^{7} +0.102418 q^{8} +(2.53574 + 1.46401i) q^{9} +1.67944i q^{11} +(1.22784 + 4.58237i) q^{12} +(-2.78351 - 4.82119i) q^{13} +(3.82484 - 3.82484i) q^{14} +(2.05021 - 3.55107i) q^{16} +(-6.03425 - 3.48387i) q^{17} +(5.03870 - 2.90910i) q^{18} +(1.39201 - 5.19504i) q^{19} +(-5.73984 - 3.31390i) q^{21} +(2.89007 + 1.66858i) q^{22} -2.29976 q^{23} +(-0.240865 - 0.0645396i) q^{24} -11.0621 q^{26} +(0.123920 + 0.123920i) q^{27} +(-1.37278 - 5.12329i) q^{28} +(-0.561787 + 0.561787i) q^{29} +(-0.512854 - 0.512854i) q^{31} +(-3.97151 - 6.87885i) q^{32} +(1.05832 - 3.94969i) q^{33} +(-11.9905 + 6.92271i) q^{34} -5.70513i q^{36} +(-0.400637 + 6.06955i) q^{37} +(-7.55690 - 7.55690i) q^{38} +(3.50812 + 13.0925i) q^{39} +(7.49700 - 4.32839i) q^{41} +(-11.4055 + 6.58496i) q^{42} -4.49647 q^{43} +(2.83391 - 1.63616i) q^{44} +(-2.28490 + 3.95756i) q^{46} +(3.51508 - 3.51508i) q^{47} +(-7.05942 + 7.05942i) q^{48} +(0.355227 + 0.205090i) q^{49} +(11.9959 + 11.9959i) q^{51} +(-5.42356 + 9.39388i) q^{52} +(0.122101 - 0.0327168i) q^{53} +(0.336369 - 0.0901297i) q^{54} +(0.269298 + 0.0721582i) q^{56} +(-6.54742 + 11.3405i) q^{57} +(0.408598 + 1.52491i) q^{58} +(-9.18809 + 2.46194i) q^{59} +(-1.77087 + 6.60897i) q^{61} +(-1.39209 + 0.373008i) q^{62} +(5.63603 + 5.63603i) q^{63} -7.58249 q^{64} +(-5.74537 - 5.74537i) q^{66} +(2.26393 - 8.44910i) q^{67} +13.5764i q^{68} +(5.40856 + 1.44922i) q^{69} +(-4.91365 - 8.51069i) q^{71} +(0.259705 + 0.149941i) q^{72} +(-0.804857 + 0.804857i) q^{73} +(10.0468 + 6.71976i) q^{74} +(-10.1223 + 2.71227i) q^{76} +(-1.18324 + 4.41593i) q^{77} +(26.0157 + 6.97089i) q^{78} +(2.57773 - 9.62023i) q^{79} +(-4.60538 - 7.97675i) q^{81} -17.2017i q^{82} +(-7.05316 + 1.88989i) q^{83} +12.9140i q^{84} +(-4.46741 + 7.73777i) q^{86} +(1.67522 - 0.967189i) q^{87} +0.172004i q^{88} +(-1.12526 - 4.19952i) q^{89} +(-3.92224 - 14.6380i) q^{91} +(2.24050 + 3.88065i) q^{92} +(0.882945 + 1.52931i) q^{93} +(-2.55659 - 9.54131i) q^{94} +(5.00537 + 18.6803i) q^{96} -9.54307i q^{97} +(0.705861 - 0.407529i) q^{98} +(-2.45872 + 4.25862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.993536	−	1.72086i	0.702536	−	1.21683i	−0.265037	−	0.964238i	$-0.585384\pi$
$2$	0.993536	−	1.72086i	0.702536	−	1.21683i	0.967573	−	0.252590i	$-0.0812825\pi$
$3$	−2.35179	−	0.630160i	−1.35781	−	0.363823i	−0.494796	−	0.869009i	$-0.664757\pi$
$3$	−2.35179	−	0.630160i	−1.35781	−	0.363823i	−0.863011	+	0.505186i	$0.831424\pi$
$4$	−0.974229	−	1.68741i	−0.487115	−	0.843707i
$5$		0			0
$5$		0			0
$6$	−3.42100	+	3.42100i	−1.39662	+	1.39662i
$7$	2.62941	+	0.704548i	0.993823	+	0.266294i	0.718856	−	0.695159i	$-0.244666\pi$
$7$	2.62941	+	0.704548i	0.993823	+	0.266294i	0.274968	+	0.961453i	$0.411333\pi$
$8$	0.102418			0.0362101
$9$	2.53574	+	1.46401i	0.845247	+	0.488004i
$10$		0			0
$11$			1.67944i			0.506370i	0.967418	+	0.253185i	$0.0814781\pi$
$11$			1.67944i			0.506370i	−0.967418	+	0.253185i	$0.918522\pi$
$12$	1.22784	+	4.58237i	0.354447	+	1.32281i
$13$	−2.78351	−	4.82119i	−0.772008	−	1.33716i	−0.936461	−	0.350772i	$-0.885919\pi$
$13$	−2.78351	−	4.82119i	−0.772008	−	1.33716i	0.164453	−	0.986385i	$-0.447414\pi$
$14$	3.82484	−	3.82484i	1.02223	−	1.02223i
$15$		0			0
$16$	2.05021	−	3.55107i	0.512553	−	0.887769i
$17$	−6.03425	−	3.48387i	−1.46352	−	0.844964i	−0.464348	−	0.885653i	$-0.653711\pi$
$17$	−6.03425	−	3.48387i	−1.46352	−	0.844964i	−0.999172	+	0.0406892i	$0.987045\pi$
$18$	5.03870	−	2.90910i	1.18763	−	0.685680i
$19$	1.39201	−	5.19504i	0.319348	−	1.19182i	−0.600524	−	0.799606i	$-0.705041\pi$
$19$	1.39201	−	5.19504i	0.319348	−	1.19182i	0.919873	−	0.392217i	$-0.128292\pi$
$20$		0			0
$21$	−5.73984	−	3.31390i	−1.25254	−	0.723152i
$22$	2.89007	+	1.66858i	0.616165	+	0.355743i
$23$	−2.29976			−0.479534			−0.239767	−	0.970830i	$-0.577071\pi$
$23$	−2.29976			−0.479534			−0.239767	+	0.970830i	$0.577071\pi$
$24$	−0.240865	−	0.0645396i	−0.0491664	−	0.0131741i
$25$		0			0
$26$	−11.0621			−2.16945
$27$	0.123920	+	0.123920i	0.0238485	+	0.0238485i
$28$	−1.37278	−	5.12329i	−0.259431	−	0.968211i
$29$	−0.561787	+	0.561787i	−0.104321	+	0.104321i	−0.757341	−	0.653020i	$-0.773502\pi$
$29$	−0.561787	+	0.561787i	−0.104321	+	0.104321i	0.653020	+	0.757341i	$0.273502\pi$
$30$		0			0
$31$	−0.512854	−	0.512854i	−0.0921113	−	0.0921113i	0.659550	−	0.751661i	$-0.270747\pi$
$31$	−0.512854	−	0.512854i	−0.0921113	−	0.0921113i	−0.751661	+	0.659550i	$0.770747\pi$
$32$	−3.97151	−	6.87885i	−0.702070	−	1.21602i
$33$	1.05832	−	3.94969i	0.184229	−	0.687552i
$34$	−11.9905	+	6.92271i	−2.05635	+	1.18724i
$35$		0			0
$36$		−	5.70513i		−	0.950854i
$37$	−0.400637	+	6.06955i	−0.0658643	+	0.997829i
$37$	−0.400637	+	6.06955i	−0.0658643	+	0.997829i
$38$	−7.55690	−	7.55690i	−1.22589	−	1.22589i
$39$	3.50812	+	13.0925i	0.561749	+	2.09648i
$40$		0			0
$41$	7.49700	−	4.32839i	1.17083	−	0.675982i	0.216958	−	0.976181i	$-0.430387\pi$
$41$	7.49700	−	4.32839i	1.17083	−	0.675982i	0.953877	+	0.300199i	$0.0970532\pi$
$42$	−11.4055	+	6.58496i	−1.75990	+	1.01608i
$43$	−4.49647			−0.685705			−0.342853	−	0.939389i	$-0.611393\pi$
$43$	−4.49647			−0.685705			−0.342853	+	0.939389i	$0.611393\pi$
$44$	2.83391	−	1.63616i	0.427228	−	0.246660i
$45$		0			0
$46$	−2.28490	+	3.95756i	−0.336890	+	0.583510i
$47$	3.51508	−	3.51508i	0.512728	−	0.512728i	−0.402634	−	0.915361i	$-0.631905\pi$
$47$	3.51508	−	3.51508i	0.512728	−	0.512728i	0.915361	+	0.402634i	$0.131905\pi$
$48$	−7.05942	+	7.05942i	−1.01894	+	1.01894i
$49$	0.355227	+	0.205090i	0.0507467	+	0.0292986i
$50$		0			0
$51$	11.9959	+	11.9959i	1.67976	+	1.67976i
$52$	−5.42356	+	9.39388i	−0.752112	+	1.30270i
$53$	0.122101	−	0.0327168i	0.0167718	−	0.00449400i	−0.250423	−	0.968136i	$-0.580570\pi$
$53$	0.122101	−	0.0327168i	0.0167718	−	0.00449400i	0.267195	+	0.963642i	$0.413903\pi$
$54$	0.336369	−	0.0901297i	0.0457740	−	0.0122651i
$55$		0			0
$56$	0.269298	+	0.0721582i	0.0359865	+	0.00964254i
$57$	−6.54742	+	11.3405i	−0.867227	+	1.50208i
$58$	0.408598	+	1.52491i	0.0536516	+	0.200230i
$59$	−9.18809	+	2.46194i	−1.19619	+	0.320517i	−0.801329	−	0.598224i	$-0.795873\pi$
$59$	−9.18809	+	2.46194i	−1.19619	+	0.320517i	−0.394859	+	0.918742i	$0.629206\pi$
$60$		0			0
$61$	−1.77087	+	6.60897i	−0.226736	+	0.846192i	0.754965	+	0.655765i	$0.227654\pi$
$61$	−1.77087	+	6.60897i	−0.226736	+	0.846192i	−0.981701	+	0.190427i	$0.939013\pi$
$62$	−1.39209	+	0.373008i	−0.176795	+	0.0473721i
$63$	5.63603	+	5.63603i	0.710074	+	0.710074i
$64$	−7.58249			−0.947811
$65$		0			0
$66$	−5.74537	−	5.74537i	−0.707206	−	0.707206i
$67$	2.26393	−	8.44910i	0.276583	−	1.03222i	−0.678190	−	0.734886i	$-0.737235\pi$
$67$	2.26393	−	8.44910i	0.276583	−	1.03222i	0.954773	−	0.297335i	$-0.0960979\pi$
$68$			13.5764i			1.64638i
$69$	5.40856	+	1.44922i	0.651114	+	0.174466i
$70$		0			0
$71$	−4.91365	−	8.51069i	−0.583143	−	1.01003i	−0.995104	−	0.0988320i	$-0.968489\pi$
$71$	−4.91365	−	8.51069i	−0.583143	−	1.01003i	0.411961	−	0.911201i	$-0.364844\pi$
$72$	0.259705	+	0.149941i	0.0306065	+	0.0176707i
$73$	−0.804857	+	0.804857i	−0.0942014	+	0.0942014i	−0.752637	−	0.658436i	$-0.771218\pi$
$73$	−0.804857	+	0.804857i	−0.0942014	+	0.0942014i	0.658436	+	0.752637i	$0.271218\pi$
$74$	10.0468	+	6.71976i	1.16791	+	0.781156i
$75$		0			0
$76$	−10.1223	+	2.71227i	−1.16111	+	0.311118i
$77$	−1.18324	+	4.41593i	−0.134843	+	0.503242i
$78$	26.0157	+	6.97089i	2.94570	+	0.789298i
$79$	2.57773	−	9.62023i	0.290018	−	1.08236i	−0.655076	−	0.755563i	$-0.727364\pi$
$79$	2.57773	−	9.62023i	0.290018	−	1.08236i	0.945094	−	0.326798i	$-0.105970\pi$
$80$		0			0
$81$	−4.60538	−	7.97675i	−0.511709	−	0.886305i
$82$		−	17.2017i		−	1.89961i
$83$	−7.05316	+	1.88989i	−0.774185	+	0.207442i	−0.624219	−	0.781249i	$-0.714583\pi$
$83$	−7.05316	+	1.88989i	−0.774185	+	0.207442i	−0.149965	+	0.988691i	$0.547916\pi$
$84$			12.9140i			1.40903i
$85$		0			0
$86$	−4.46741	+	7.73777i	−0.481733	+	0.834386i
$87$	1.67522	−	0.967189i	0.179603	−	0.103694i
$88$			0.172004i			0.0183357i
$89$	−1.12526	−	4.19952i	−0.119277	−	0.445148i	0.880294	−	0.474428i	$-0.157345\pi$
$89$	−1.12526	−	4.19952i	−0.119277	−	0.445148i	−0.999571	+	0.0292801i	$0.990679\pi$
$90$		0			0
$91$	−3.92224	−	14.6380i	−0.411162	−	1.53448i
$92$	2.24050	+	3.88065i	0.233588	+	0.404586i
$93$	0.882945	+	1.52931i	0.0915571	+	0.158582i
$94$	−2.55659	−	9.54131i	−0.263692	−	0.984111i
$95$		0			0
$96$	5.00537	+	18.6803i	0.510859	+	1.90655i
$97$		−	9.54307i		−	0.968952i	−0.874805	−	0.484476i	$-0.839010\pi$
$97$		−	9.54307i		−	0.968952i	0.874805	−	0.484476i	$-0.160990\pi$
$98$	0.705861	−	0.407529i	0.0713027	−	0.0411667i
$99$	−2.45872	+	4.25862i	−0.247110	+	0.428007i
$100$		0			0
$101$			16.8321i			1.67486i	0.546548	+	0.837428i	$0.315941\pi$
$101$			16.8321i			1.67486i	−0.546548	+	0.837428i	$0.684059\pi$
$102$	32.5615	−	8.72484i	3.22407	−	0.863888i
$103$		−	7.86111i		−	0.774579i	−0.921958	−	0.387289i	$-0.873411\pi$
$103$		−	7.86111i		−	0.774579i	0.921958	−	0.387289i	$-0.126589\pi$
$104$	−0.285081	−	0.493775i	−0.0279545	−	0.0484186i
$105$		0			0
$106$	0.0650107	−	0.242623i	0.00631440	−	0.0235657i
$107$	2.78611	+	0.746535i	0.269343	+	0.0721703i	0.390963	−	0.920407i	$-0.372142\pi$
$107$	2.78611	+	0.746535i	0.269343	+	0.0721703i	−0.121620	+	0.992577i	$0.538809\pi$
$108$	0.0883782	−	0.329832i	0.00850419	−	0.0317381i
$109$	−0.520227	+	0.139395i	−0.0498288	+	0.0133516i	−0.283647	−	0.958929i	$-0.591544\pi$
$109$	−0.520227	+	0.139395i	−0.0498288	+	0.0133516i	0.233819	+	0.972280i	$0.424878\pi$
$110$		0			0
$111$	4.76701	−	14.0219i	0.452464	−	1.33090i
$112$	7.89275	−	7.89275i	0.745795	−	0.745795i
$113$	14.3608	+	8.29122i	1.35095	+	0.779973i	0.988383	−	0.151984i	$-0.0485663\pi$
$113$	14.3608	+	8.29122i	1.35095	+	0.779973i	0.362569	+	0.931957i	$0.381900\pi$
$114$	13.0102	+	22.5343i	1.21852	+	2.11053i
$115$		0			0
$116$	1.49528	+	0.400658i	0.138833	+	0.0372002i
$117$		−	16.3004i		−	1.50697i
$118$	−4.89206	+	18.2574i	−0.450350	+	1.68073i
$119$	−13.4119	−	13.4119i	−1.22947	−	1.22947i
$120$		0			0
$121$	8.17949			0.743590
$122$	9.61366	+	9.61366i	0.870380	+	0.870380i
$123$	−20.3590	+	5.45517i	−1.83571	+	0.491876i
$124$	−0.365760	+	1.36503i	−0.0328462	+	0.122584i
$125$		0			0
$126$	15.2984	−	4.09920i	1.36289	−	0.365185i
$127$	4.85902	+	18.1341i	0.431168	+	1.60914i	0.750073	+	0.661355i	$0.230018\pi$
$127$	4.85902	+	18.1341i	0.431168	+	1.60914i	−0.318904	+	0.947787i	$0.603315\pi$
$128$	0.409535	−	0.709335i	0.0361981	−	0.0626970i
$129$	10.5748	+	2.83350i	0.931055	+	0.249475i
$130$		0			0
$131$	6.02317	−	1.61390i	0.526247	−	0.141007i	0.0140923	−	0.999901i	$-0.495514\pi$
$131$	6.02317	−	1.61390i	0.526247	−	0.141007i	0.512155	+	0.858893i	$0.328847\pi$
$132$	−7.69580	+	2.06208i	−0.669833	+	0.179481i
$133$	7.32031	−	12.6791i	0.634751	−	1.09942i
$134$	−12.2904	−	12.2904i	−1.06173	−	1.06173i
$135$		0			0
$136$	−0.618014	−	0.356810i	−0.0529942	−	0.0305962i
$137$	−6.73698	+	6.73698i	−0.575579	+	0.575579i	−0.933682	−	0.358103i	$-0.883424\pi$
$137$	−6.73698	+	6.73698i	−0.575579	+	0.575579i	0.358103	+	0.933682i	$0.383424\pi$
$138$	7.86750	−	7.86750i	0.669726	−	0.669726i
$139$	6.78219	−	11.7471i	0.575258	−	0.996376i	−0.420756	−	0.907174i	$-0.638235\pi$
$139$	6.78219	−	11.7471i	0.575258	−	0.996376i	0.996014	−	0.0892018i	$-0.0284316\pi$
$140$		0			0
$141$	−10.4818	+	6.05167i	−0.882727	+	0.509643i
$142$	−19.5276			−1.63872
$143$	8.09689	−	4.67474i	0.677096	−	0.390921i
$144$	10.3976	−	6.00307i	0.866468	−	0.500256i
$145$		0			0
$146$	0.585388	+	2.18470i	0.0484470	+	0.180807i
$147$	−0.706179	−	0.706179i	−0.0582447	−	0.0582447i
$148$	10.6322	−	5.23710i	0.873958	−	0.430487i
$149$			6.46606i			0.529721i	0.964287	+	0.264860i	$0.0853259\pi$
$149$			6.46606i			0.529721i	−0.964287	+	0.264860i	$0.914674\pi$
$150$		0			0
$151$	9.73455	−	5.62024i	0.792186	−	0.457369i	−0.0485454	−	0.998821i	$-0.515459\pi$
$151$	9.73455	−	5.62024i	0.792186	−	0.457369i	0.840732	+	0.541452i	$0.182125\pi$
$152$	0.142566	−	0.532064i	0.0115636	−	0.0431561i
$153$	−10.2009	−	17.6684i	−0.824691	−	1.42841i
$154$	6.42358	+	6.42358i	0.517627	+	0.517627i
$155$		0			0
$156$	18.6747	−	18.6747i	1.49518	−	1.49518i
$157$	−2.47810	−	9.24841i	−0.197774	−	0.738103i	−0.991531	−	0.129868i	$-0.958545\pi$
$157$	−2.47810	−	9.24841i	−0.197774	−	0.738103i	0.793757	−	0.608235i	$-0.208122\pi$
$158$	−13.9940	−	13.9940i	−1.11330	−	1.11330i
$159$	−0.307772			−0.0244079
$160$		0			0
$161$	−6.04702	−	1.62029i	−0.476572	−	0.127697i
$162$	−18.3024			−1.43798
$163$	8.55394	+	4.93862i	0.669997	+	0.386823i	0.796075	−	0.605198i	$-0.206906\pi$
$163$	8.55394	+	4.93862i	0.669997	+	0.386823i	−0.126079	+	0.992020i	$0.540239\pi$
$164$	−14.6076	−	8.43369i	−1.14066	−	0.658561i
$165$		0			0
$166$	−3.75534	+	14.0151i	−0.291471	+	1.08779i
$167$	14.4757	−	8.35752i	1.12016	−	0.646725i	0.178718	−	0.983900i	$-0.442805\pi$
$167$	14.4757	−	8.35752i	1.12016	−	0.646725i	0.941442	+	0.337176i	$0.109472\pi$
$168$	−0.587861	−	0.339402i	−0.0453545	−	0.0261854i
$169$	−8.99590	+	15.5814i	−0.691992	+	1.19857i
$170$		0			0
$171$	11.1354	−	11.1354i	0.851542	−	0.851542i
$172$	4.38059	+	7.58741i	0.334017	+	0.578534i
$173$	5.00685	+	18.6858i	0.380664	+	1.42066i	0.844890	+	0.534940i	$0.179666\pi$
$173$	5.00685	+	18.6858i	0.380664	+	1.42066i	−0.464226	+	0.885717i	$0.653668\pi$
$174$		−	3.84375i		−	0.291394i
$175$		0			0
$176$	5.96381	+	3.44321i	0.449539	+	0.259542i
$177$	23.1599			1.74080
$178$	−8.34475	−	2.23597i	−0.625465	−	0.167593i
$179$	−0.796965	+	0.796965i	−0.0595680	+	0.0595680i	−0.736263	−	0.676695i	$-0.763411\pi$
$179$	−0.796965	+	0.796965i	−0.0595680	+	0.0595680i	0.676695	+	0.736263i	$0.263411\pi$
$180$		0			0
$181$	3.50696	+	6.07423i	0.260670	+	0.451494i	0.966420	−	0.256967i	$-0.0827232\pi$
$181$	3.50696	+	6.07423i	0.260670	+	0.451494i	−0.705750	+	0.708461i	$0.749390\pi$
$182$	−29.0868	−	7.79377i	−2.15605	−	0.577713i
$183$	8.32942	−	14.4270i	0.615729	−	1.06647i
$184$	−0.235536			−0.0173640
$185$		0			0
$186$	3.50895			0.257289
$187$	5.85095	−	10.1341i	0.427864	−	0.741082i
$188$	−9.35590	−	2.50691i	−0.682349	−	0.182835i
$189$	0.238530	+	0.413145i	0.0173505	+	0.0300519i
$190$		0			0
$191$	8.62975	−	8.62975i	0.624427	−	0.624427i	−0.322233	−	0.946660i	$-0.604434\pi$
$191$	8.62975	−	8.62975i	0.624427	−	0.624427i	0.946660	+	0.322233i	$0.104434\pi$
$192$	17.8324	+	4.77818i	1.28694	+	0.344836i
$193$	−9.26626			−0.667000			−0.333500	−	0.942750i	$-0.608230\pi$
$193$	−9.26626			−0.667000			−0.333500	+	0.942750i	$0.608230\pi$
$194$	−16.4222	−	9.48138i	−1.17905	−	0.680724i
$195$		0			0
$196$		−	0.799219i		−	0.0570871i
$197$	5.47729	+	20.4415i	0.390241	+	1.45640i	0.829737	+	0.558154i	$0.188490\pi$
$197$	5.47729	+	20.4415i	0.390241	+	1.45640i	−0.439496	+	0.898244i	$0.644843\pi$
$198$	4.88565	+	8.46219i	0.347208	+	0.601382i
$199$	10.0796	−	10.0796i	0.714524	−	0.714524i	−0.252954	−	0.967478i	$-0.581402\pi$
$199$	10.0796	−	10.0796i	0.714524	−	0.714524i	0.967478	+	0.252954i	$0.0814022\pi$
$200$		0			0
$201$	−10.6486	+	18.4439i	−0.751092	+	1.30093i
$202$	28.9656	+	16.7233i	2.03801	+	1.17665i
$203$	−1.87297	+	1.08136i	−0.131457	+	0.0758967i
$204$	8.55529	−	31.9288i	0.598990	−	2.23546i
$205$		0			0
$206$	−13.5278	−	7.81030i	−0.942529	−	0.544170i
$207$	−5.83160	−	3.36688i	−0.405324	−	0.234014i
$208$	−22.8272			−1.58278
$209$	8.72475	+	2.33779i	0.603503	+	0.161708i
$210$		0			0
$211$	9.16134			0.630693			0.315346	−	0.948977i	$-0.397879\pi$
$211$	9.16134			0.630693			0.315346	+	0.948977i	$0.397879\pi$
$212$	−0.174161	−	0.174161i	−0.0119614	−	0.0119614i
$213$	6.19278	+	23.1118i	0.424322	+	1.58359i
$214$	4.05278	−	4.05278i	0.277042	−	0.277042i
$215$		0			0
$216$	0.0126916	+	0.0126916i	0.000863557	+	0.000863557i
$217$	−0.987173	−	1.70983i	−0.0670136	−	0.116071i
$218$	−0.276987	+	1.03373i	−0.0187599	+	0.0700130i
$219$	2.40004	−	1.38567i	0.162180	−	0.0936346i
$220$		0			0
$221$			38.7897i			2.60927i
$222$	−19.3934	−	22.1346i	−1.30160	−	1.48557i
$223$	7.67262	+	7.67262i	0.513796	+	0.513796i	0.915688	−	0.401891i	$-0.131647\pi$
$223$	7.67262	+	7.67262i	0.513796	+	0.513796i	−0.401891	+	0.915688i	$0.631647\pi$
$224$	−5.59623	−	20.8854i	−0.373914	−	1.39547i
$225$		0			0
$226$	28.5360	−	16.4753i	1.89819	−	1.09592i
$227$	−10.5642	+	6.09924i	−0.701171	+	0.404821i	−0.807783	−	0.589480i	$-0.799333\pi$
$227$	−10.5642	+	6.09924i	−0.701171	+	0.404821i	0.106613	+	0.994301i	$0.466000\pi$
$228$	25.5147			1.68975
$229$	6.92938	−	4.00068i	0.457906	−	0.264372i	−0.253257	−	0.967399i	$-0.581502\pi$
$229$	6.92938	−	4.00068i	0.457906	−	0.264372i	0.711163	+	0.703027i	$0.248169\pi$
$230$		0			0
$231$	5.56549	−	9.63971i	0.366182	−	0.634246i
$232$	−0.0575369	+	0.0575369i	−0.00377748	+	0.00377748i
$233$	12.4980	−	12.4980i	0.818769	−	0.818769i	−0.167160	−	0.985930i	$-0.553460\pi$
$233$	12.4980	−	12.4980i	0.818769	−	0.818769i	0.985930	+	0.167160i	$0.0534598\pi$
$234$	−28.0506	−	16.1950i	−1.83372	−	1.05870i
$235$		0			0
$236$	13.1056	+	13.1056i	0.853103	+	0.853103i
$237$	−12.1246	+	21.0004i	−0.787576	+	1.36412i
$238$	−36.4053	+	9.75477i	−2.35980	+	0.632308i
$239$	−21.0290	+	5.63471i	−1.36025	+	0.364479i	−0.863910	−	0.503647i	$-0.831991\pi$
$239$	−21.0290	+	5.63471i	−1.36025	+	0.364479i	−0.496344	+	0.868126i	$0.665325\pi$
$240$		0			0
$241$	2.79110	+	0.747874i	0.179791	+	0.0481748i	0.347591	−	0.937646i	$-0.387000\pi$
$241$	2.79110	+	0.747874i	0.179791	+	0.0481748i	−0.167800	+	0.985821i	$0.553666\pi$
$242$	8.12662	−	14.0757i	0.522399	−	0.904821i
$243$	5.66818	+	21.1539i	0.363614	+	1.35703i
$244$	12.8773	−	3.45046i	0.824385	−	0.220893i
$245$		0			0
$246$	−10.8398	+	40.4547i	−0.691121	+	2.57930i
$247$	−28.9209	+	7.74934i	−1.84019	+	0.493079i
$248$	−0.0525253	−	0.0525253i	−0.00333536	−	0.00333536i
$249$	17.7785			1.12667
$250$		0			0
$251$	−8.78658	−	8.78658i	−0.554604	−	0.554604i	0.373162	−	0.927766i	$-0.378273\pi$
$251$	−8.78658	−	8.78658i	−0.554604	−	0.554604i	−0.927766	+	0.373162i	$0.878273\pi$
$252$	4.01954	−	15.0011i	0.253207	−	0.944981i
$253$		−	3.86231i		−	0.242821i
$254$	36.0338	+	9.65523i	2.26096	+	0.605823i
$255$		0			0
$256$	−8.39626	−	14.5428i	−0.524766	−	0.908922i
$257$	13.9589	+	8.05916i	0.870731	+	0.502717i	0.867591	−	0.497279i	$-0.165667\pi$
$257$	13.9589	+	8.05916i	0.870731	+	0.502717i	0.00313967	+	0.999995i	$0.499001\pi$
$258$	15.3824	−	15.3824i	0.957669	−	0.957669i
$259$	−5.32973	+	15.6771i	−0.331173	+	0.974126i
$260$		0			0
$261$	−2.24701	+	0.602084i	−0.139086	+	0.0372681i
$262$	3.20695	−	11.9685i	0.198126	−	0.739415i
$263$	8.62681	+	2.31155i	0.531952	+	0.142536i	0.514789	−	0.857317i	$-0.327870\pi$
$263$	8.62681	+	2.31155i	0.531952	+	0.142536i	0.0171624	+	0.999853i	$0.494537\pi$
$264$	0.108390	−	0.404518i	0.00667096	−	0.0248964i
$265$		0			0
$266$	−14.5460	−	25.1944i	−0.891872	−	1.54477i
$267$			10.5855i			0.647821i
$268$	−16.4627	+	4.41117i	−1.00562	+	0.269455i
$269$		−	4.45940i		−	0.271895i	−0.990716	−	0.135947i	$-0.956592\pi$
$269$		−	4.45940i		−	0.271895i	0.990716	−	0.135947i	$-0.0434078\pi$
$270$		0			0
$271$	12.8742	−	22.2987i	0.782050	−	1.35455i	−0.148696	−	0.988883i	$-0.547507\pi$
$271$	12.8742	−	22.2987i	0.782050	−	1.35455i	0.930746	−	0.365667i	$-0.119159\pi$
$272$	−24.7430	+	14.2854i	−1.50026	+	0.866178i
$273$			36.8971i			2.23312i
$274$	4.89993	+	18.2868i	0.296016	+	1.10475i
$275$		0			0
$276$	−2.82374	−	10.5384i	−0.169969	−	0.634334i
$277$	−14.5025	−	25.1190i	−0.871368	−	1.50925i	−0.860582	−	0.509312i	$-0.829900\pi$
$277$	−14.5025	−	25.1190i	−0.871368	−	1.50925i	−0.0107863	−	0.999942i	$-0.503433\pi$
$278$	−13.4767	−	23.3423i	−0.808279	−	1.39998i
$279$	−0.549641	−	2.05129i	−0.0329062	−	0.122807i
$280$		0			0
$281$	1.36182	+	5.08238i	0.0812394	+	0.303190i	0.994576	−	0.104017i	$-0.0331696\pi$
$281$	1.36182	+	5.08238i	0.0812394	+	0.303190i	−0.913336	+	0.407207i	$0.866503\pi$
$282$			24.0502i			1.43217i
$283$	13.7819	−	7.95697i	0.819248	−	0.472993i	−0.0309093	−	0.999522i	$-0.509840\pi$
$283$	13.7819	−	7.95697i	0.819248	−	0.472993i	0.850157	+	0.526529i	$0.176507\pi$
$284$	−9.57404	+	16.5827i	−0.568115	+	0.984004i
$285$		0			0
$286$		−	18.5781i		−	1.09855i
$287$	22.7622	−	6.09912i	1.34361	−	0.360020i
$288$		−	23.2573i		−	1.37045i
$289$	15.7748	+	27.3227i	0.927927	+	1.60722i
$290$		0			0
$291$	−6.01366	+	22.4433i	−0.352527	+	1.31565i
$292$	2.14224	+	0.574012i	0.125365	+	0.0335915i
$293$	5.48481	−	20.4696i	0.320426	−	1.19585i	−0.598405	−	0.801194i	$-0.704199\pi$
$293$	5.48481	−	20.4696i	0.320426	−	1.19585i	0.918831	−	0.394651i	$-0.129135\pi$
$294$	−1.91685	+	0.513617i	−0.111793	+	0.0299548i
$295$		0			0
$296$	−0.0410323	+	0.621630i	−0.00238495	+	0.0361315i
$297$	−0.208117	+	0.208117i	−0.0120762	+	0.0120762i
$298$	11.1272	+	6.42427i	0.644579	+	0.372148i
$299$	6.40142	+	11.0876i	0.370204	+	0.641212i
$300$		0			0
$301$	−11.8231	−	3.16798i	−0.681470	−	0.182599i
$302$		−	22.3357i		−	1.28527i
$303$	10.6069	−	39.5855i	0.609351	−	2.27413i
$304$	−15.5941	−	15.5941i	−0.894381	−	0.894381i
$305$		0			0
$306$	−40.5397			−2.31750
$307$	−18.3419	−	18.3419i	−1.04683	−	1.04683i	−0.998848	−	0.0479805i	$-0.984721\pi$
$307$	−18.3419	−	18.3419i	−1.04683	−	1.04683i	−0.0479805	−	0.998848i	$-0.515279\pi$
$308$	8.60425	−	2.30550i	0.490273	−	0.131368i
$309$	−4.95376	+	18.4877i	−0.281810	+	1.05173i
$310$		0			0
$311$	−5.37036	+	1.43898i	−0.304525	+	0.0815973i	−0.407846	−	0.913051i	$-0.633720\pi$
$311$	−5.37036	+	1.43898i	−0.304525	+	0.0815973i	0.103321	+	0.994648i	$0.467053\pi$
$312$	0.359294	+	1.34090i	0.0203410	+	0.0759136i
$313$	3.05709	−	5.29504i	0.172797	−	0.299294i	−0.766600	−	0.642125i	$-0.778053\pi$
$313$	3.05709	−	5.29504i	0.172797	−	0.299294i	0.939397	+	0.342832i	$0.111386\pi$
$314$	−18.3773	−	4.92417i	−1.03709	−	0.277887i
$315$		0			0
$316$	−18.7446	+	5.02261i	−1.05447	+	0.282544i
$317$	−26.0909	+	6.99103i	−1.46541	+	0.392655i	−0.901354	−	0.433082i	$-0.857426\pi$
$317$	−26.0909	+	6.99103i	−1.46541	+	0.392655i	−0.564055	+	0.825737i	$0.690759\pi$
$318$	−0.305783	+	0.529632i	−0.0171475	+	0.0297003i
$319$	−0.943486	−	0.943486i	−0.0528251	−	0.0528251i
$320$		0			0
$321$	−6.08190	−	3.51139i	−0.339459	−	0.195987i
$322$	−8.79622	+	8.79622i	−0.490194	+	0.490194i
$323$	−26.4986	+	26.4986i	−1.47442	+	1.47442i
$324$	−8.97338	+	15.5424i	−0.498521	+	0.863464i
$325$		0			0
$326$	16.9973	−	9.81340i	0.941394	−	0.543514i
$327$	1.31131			0.0725154
$328$	0.767825	−	0.443304i	0.0423961	−	0.0244774i
$329$	11.7191	−	6.76605i	0.646097	−	0.373024i
$330$		0			0
$331$	−2.23150	−	8.32808i	−0.122655	−	0.457753i	0.877091	−	0.480325i	$-0.159481\pi$
$331$	−2.23150	−	8.32808i	−0.122655	−	0.457753i	−0.999745	+	0.0225719i	$0.992815\pi$
$332$	10.0604	+	10.0604i	0.552137	+	0.552137i
$333$	−9.90180	+	14.8043i	−0.542615	+	0.811270i
$334$		−	33.2140i		−	1.81739i
$335$		0			0
$336$	−23.5358	+	13.5884i	−1.28398	+	0.741308i
$337$	−0.414161	+	1.54567i	−0.0225608	+	0.0841979i	−0.976288	−	0.216474i	$-0.930544\pi$
$337$	−0.414161	+	1.54567i	−0.0225608	+	0.0841979i	0.953728	+	0.300672i	$0.0972110\pi$
$338$	17.8755	+	30.9613i	0.972300	+	1.68407i
$339$	−28.5488	−	28.5488i	−1.55056	−	1.55056i
$340$		0			0
$341$	0.861307	−	0.861307i	0.0466424	−	0.0466424i
$342$	−8.09896	−	30.2257i	−0.437942	−	1.63442i
$343$	−12.6845	−	12.6845i	−0.684898	−	0.684898i
$344$	−0.460518			−0.0248295
$345$		0			0
$346$	37.1301	+	9.94898i	1.99613	+	0.534860i
$347$	17.9655			0.964438			0.482219	−	0.876051i	$-0.339831\pi$
$347$	17.9655			0.964438			0.482219	+	0.876051i	$0.339831\pi$
$348$	−3.26410	−	1.88453i	−0.174974	−	0.101021i
$349$	−21.5887	−	12.4642i	−1.15562	−	0.667195i	−0.205366	−	0.978685i	$-0.565838\pi$
$349$	−21.5887	−	12.4642i	−1.15562	−	0.667195i	−0.950249	+	0.311490i	$0.899172\pi$
$350$		0			0
$351$	0.252509	−	0.942378i	0.0134780	−	0.0503004i
$352$	11.5526	−	6.66990i	0.615756	−	0.355507i
$353$	−0.344022	−	0.198621i	−0.0183104	−	0.0105715i	0.490817	−	0.871263i	$-0.336698\pi$
$353$	−0.344022	−	0.198621i	−0.0183104	−	0.0105715i	−0.509127	+	0.860691i	$0.670032\pi$
$354$	23.0102	−	39.8548i	1.22298	−	2.11826i
$355$		0			0
$356$	−5.99007	+	5.99007i	−0.317473	+	0.317473i
$357$	23.0904	+	39.9938i	1.22207	+	2.11669i
$358$	0.579648	+	2.16328i	0.0306354	+	0.114333i
$359$			26.6480i			1.40643i	0.710977	+	0.703215i	$0.248253\pi$
$359$			26.6480i			1.40643i	−0.710977	+	0.703215i	$0.751747\pi$
$360$		0			0
$361$	−8.59627	−	4.96306i	−0.452435	−	0.261214i
$362$	13.9372			0.732521
$363$	−19.2364	−	5.15439i	−1.00965	−	0.270535i
$364$	−20.8792	+	20.8792i	−1.09437	+	1.09437i
$365$		0			0
$366$	−16.5512	−	28.6675i	−0.865144	−	1.49847i
$367$	−14.7639	−	3.95597i	−0.770668	−	0.206500i	−0.148001	−	0.988987i	$-0.547284\pi$
$367$	−14.7639	−	3.95597i	−0.770668	−	0.206500i	−0.622666	+	0.782487i	$0.713951\pi$
$368$	−4.71501	+	8.16663i	−0.245787	+	0.425715i
$369$	25.3473			1.31953
$370$		0			0
$371$	0.344104			0.0178650
$372$	1.72038	−	2.97979i	0.0891976	−	0.154495i
$373$	35.2816	+	9.45368i	1.82681	+	0.489493i	0.997587	−	0.0694227i	$-0.0221157\pi$
$373$	35.2816	+	9.45368i	1.82681	+	0.489493i	0.829225	+	0.558915i	$0.188782\pi$
$374$	−11.6263	−	20.1373i	−0.601180	−	1.04127i
$375$		0			0
$376$	0.360007	−	0.360007i	0.0185659	−	0.0185659i
$377$	4.27222	+	1.14474i	0.220031	+	0.0589570i
$378$	0.947951			0.0487573
$379$	19.1447	+	11.0532i	0.983399	+	0.567765i	0.903294	−	0.429021i	$-0.141141\pi$
$379$	19.1447	+	11.0532i	0.983399	+	0.567765i	0.0801041	+	0.996787i	$0.474475\pi$
$380$		0			0
$381$		−	45.7096i		−	2.34177i
$382$	−6.27658	−	23.4245i	−0.321138	−	1.19850i
$383$	6.91250	+	11.9728i	0.353212	+	0.611781i	0.986810	−	0.161881i	$-0.0517560\pi$
$383$	6.91250	+	11.9728i	0.353212	+	0.611781i	−0.633598	+	0.773662i	$0.718423\pi$
$384$	−1.41013	+	1.41013i	−0.0719606	+	0.0719606i
$385$		0			0
$386$	−9.20636	+	15.9459i	−0.468592	+	0.811624i
$387$	−11.4019	−	6.58288i	−0.579590	−	0.334627i
$388$	−16.1031	+	9.29713i	−0.817511	+	0.471990i
$389$	−2.77714	+	10.3644i	−0.140806	+	0.525496i	0.859100	+	0.511808i	$0.171024\pi$
$389$	−2.77714	+	10.3644i	−0.140806	+	0.525496i	−0.999906	+	0.0136886i	$0.995643\pi$
$390$		0			0
$391$	13.8773	+	8.01208i	0.701807	+	0.405189i
$392$	0.0363815	+	0.0210049i	0.00183754	+	0.00106091i
$393$	−15.1823			−0.765844
$394$	40.6188	+	10.8838i	2.04635	+	0.548317i
$395$		0			0
$396$	9.58141			0.481484
$397$	16.8089	+	16.8089i	0.843614	+	0.843614i	0.989327	−	0.145713i	$-0.0465475\pi$
$397$	16.8089	+	16.8089i	0.843614	+	0.843614i	−0.145713	+	0.989327i	$0.546548\pi$
$398$	−7.33109	−	27.3600i	−0.367474	−	1.37143i
$399$	−25.2057	+	25.2057i	−1.26187	+	1.26187i
$400$		0			0
$401$	10.5045	+	10.5045i	0.524569	+	0.524569i	0.918948	−	0.394379i	$-0.129040\pi$
$401$	10.5045	+	10.5045i	0.524569	+	0.524569i	−0.394379	+	0.918948i	$0.629040\pi$
$402$	21.1595	+	36.6493i	1.05534	+	1.82790i
$403$	−1.04503	+	3.90010i	−0.0520566	+	0.194278i
$404$	28.4027	−	16.3983i	1.41309	−	0.815846i
$405$		0			0
$406$			4.29749i			0.213281i
$407$	−10.1934	−	0.672844i	−0.505270	−	0.0333517i
$408$	1.22859	+	1.22859i	0.0608243	+	0.0608243i
$409$	6.05393	+	22.5936i	0.299348	+	1.11718i	0.937703	+	0.347438i	$0.112948\pi$
$409$	6.05393	+	22.5936i	0.299348	+	1.11718i	−0.638355	+	0.769742i	$0.720385\pi$
$410$		0			0
$411$	20.0893	−	11.5986i	0.990934	−	0.572116i
$412$	−13.2650	+	7.65853i	−0.653517	+	0.377308i
$413$	−25.8938			−1.27415
$414$	−11.5878	+	6.69023i	−0.569510	+	0.328807i
$415$		0			0
$416$	−22.1095	+	38.2948i	−1.08401	+	1.87755i
$417$	−23.3528	+	23.3528i	−1.14359	+	1.14359i
$418$	12.6914	−	12.6914i	0.620754	−	0.620754i
$419$	20.0193	+	11.5582i	0.978009	+	0.564654i	0.901668	−	0.432428i	$-0.142343\pi$
$419$	20.0193	+	11.5582i	0.978009	+	0.564654i	0.0763404	+	0.997082i	$0.475676\pi$
$420$		0			0
$421$	0.796474	+	0.796474i	0.0388178	+	0.0388178i	0.726249	−	0.687431i	$-0.241262\pi$
$421$	0.796474	+	0.796474i	0.0388178	+	0.0388178i	−0.687431	+	0.726249i	$0.741262\pi$
$422$	9.10213	−	15.7654i	0.443085	−	0.767445i
$423$	14.0595	−	3.76722i	0.683594	−	0.183169i
$424$	0.0125053	−	0.00335078i	0.000607310	−	0.000162728i
$425$		0			0
$426$	45.9247	+	12.3055i	2.22506	+	0.596203i
$427$	−9.31268	+	16.1300i	−0.450672	+	0.780587i
$428$	−1.45459	−	5.42861i	−0.0703104	−	0.262402i
$429$	−21.9880	+	5.89167i	−1.06159	+	0.284453i
$430$		0			0
$431$	−6.09536	+	22.7482i	−0.293603	+	1.09574i	0.648717	+	0.761030i	$0.275306\pi$
$431$	−6.09536	+	22.7482i	−0.293603	+	1.09574i	−0.942320	+	0.334713i	$0.891361\pi$
$432$	0.694114	−	0.185987i	0.0333956	−	0.00894832i
$433$	8.35425	+	8.35425i	0.401480	+	0.401480i	0.878754	−	0.477275i	$-0.158375\pi$
$433$	8.35425	+	8.35425i	0.401480	+	0.401480i	−0.477275	+	0.878754i	$0.658375\pi$
$434$	−3.92317			−0.188318
$435$		0			0
$436$	0.742037	+	0.742037i	0.0355371	+	0.0355371i
$437$	−3.20129	+	11.9474i	−0.153138	+	0.571520i
$438$		−	5.50684i		−	0.263127i
$439$	−3.56774	−	0.955972i	−0.170279	−	0.0456261i	0.172672	−	0.984979i	$-0.444760\pi$
$439$	−3.56774	−	0.955972i	−0.170279	−	0.0456261i	−0.342951	+	0.939353i	$0.611427\pi$
$440$		0			0
$441$	0.600508	+	1.04011i	0.0285956	+	0.0495291i
$442$	66.7514	+	38.5389i	3.17504	+	1.83311i
$443$	25.0265	−	25.0265i	1.18905	−	1.18905i	0.211714	−	0.977332i	$-0.432095\pi$
$443$	25.0265	−	25.0265i	1.18905	−	1.18905i	0.977332	−	0.211714i	$-0.0679045\pi$
$444$	−28.3048	+	5.61659i	−1.34329	+	0.266551i
$445$		0			0
$446$	20.8265	−	5.58044i	0.986163	−	0.264242i
$447$	4.07466	−	15.2068i	0.192725	−	0.719258i
$448$	−19.9375	−	5.34223i	−0.941957	−	0.252397i
$449$	2.73747	−	10.2164i	0.129189	−	0.482141i	−0.870765	−	0.491699i	$-0.836376\pi$
$449$	2.73747	−	10.2164i	0.129189	−	0.482141i	0.999954	+	0.00955863i	$0.00304265\pi$
$450$		0			0
$451$	7.26927	+	12.5907i	0.342297	+	0.592875i
$452$		−	32.3102i		−	1.51974i
$453$	−26.4353	+	7.08331i	−1.24204	+	0.332803i
$454$			24.2393i			1.13761i
$455$		0			0
$456$	−0.670571	+	1.16146i	−0.0314024	+	0.0543905i
$457$	26.1013	−	15.0696i	1.22097	−	0.704927i	0.255845	−	0.966718i	$-0.417646\pi$
$457$	26.1013	−	15.0696i	1.22097	−	0.704927i	0.965125	+	0.261791i	$0.0843130\pi$
$458$		−	15.8993i		−	0.742924i
$459$	−0.316043	−	1.17949i	−0.0147516	−	0.0550538i
$460$		0			0
$461$	−3.05838	−	11.4140i	−0.142443	−	0.531605i	−0.999856	−	0.0169755i	$-0.994596\pi$
$461$	−3.05838	−	11.4140i	−0.142443	−	0.531605i	0.857413	−	0.514629i	$-0.172070\pi$
$462$	−11.0590	−	19.1548i	−0.514513	−	0.891162i
$463$	8.71241	+	15.0903i	0.404900	+	0.701307i	0.994310	−	0.106527i	$-0.0339730\pi$
$463$	8.71241	+	15.0903i	0.404900	+	0.701307i	−0.589410	+	0.807834i	$0.700640\pi$
$464$	0.843164	+	3.14673i	0.0391429	+	0.146083i
$465$		0			0
$466$	−9.09001	−	33.9244i	−0.421087	−	1.57152i
$467$		−	10.9228i		−	0.505446i	−0.967539	−	0.252723i	$-0.918674\pi$
$467$		−	10.9228i		−	0.505446i	0.967539	−	0.252723i	$-0.0813262\pi$
$468$	−27.5055	+	15.8803i	−1.27144	+	0.734067i
$469$	11.9056	−	20.6211i	0.549749	−	0.952193i
$470$		0			0
$471$			23.3119i			1.07416i
$472$	−0.941023	+	0.252146i	−0.0433141	+	0.0116060i
$473$		−	7.55154i		−	0.347220i
$474$	24.0924	+	41.7293i	1.10660	+	1.91669i
$475$		0			0
$476$	−9.56520	+	35.6978i	−0.438420	+	1.63621i
$477$	0.357514	+	0.0957956i	0.0163694	+	0.00438618i
$478$	−11.1966	+	41.7862i	−0.512119	+	1.91126i
$479$	8.05522	−	2.15839i	0.368052	−	0.0986194i	−0.0700522	−	0.997543i	$-0.522317\pi$
$479$	8.05522	−	2.15839i	0.368052	−	0.0986194i	0.438105	+	0.898924i	$0.355650\pi$
$480$		0			0
$481$	30.3776	−	14.9631i	1.38510	−	0.682261i
$482$	4.06005	−	4.06005i	0.184930	−	0.184930i
$483$	13.2003	+	7.62118i	0.600633	+	0.346776i
$484$	−7.96869	−	13.8022i	−0.362213	−	0.627372i
$485$		0			0
$486$	42.0344	+	11.2631i	1.90672	+	0.510904i
$487$		−	8.29876i		−	0.376053i	−0.982164	−	0.188026i	$-0.939791\pi$
$487$		−	8.29876i		−	0.376053i	0.982164	−	0.188026i	$-0.0602090\pi$
$488$	−0.181368	+	0.676876i	−0.00821016	+	0.0306407i
$489$	−17.0050	−	17.0050i	−0.768991	−	0.768991i
$490$		0			0
$491$	−21.4566			−0.968322			−0.484161	−	0.874979i	$-0.660875\pi$
$491$	−21.4566			−0.968322			−0.484161	+	0.874979i	$0.660875\pi$
$492$	29.0394	+	29.0394i	1.30920	+	1.30920i
$493$	5.34715	−	1.43277i	0.240824	−	0.0645285i
$494$	−15.3985	+	57.4680i	−0.692811	+	2.58561i
$495$		0			0
$496$	−2.87264	+	0.769722i	−0.128985	+	0.0345616i
$497$	−6.92381	−	25.8400i	−0.310575	−	1.15908i
$498$	17.6636	−	30.5942i	0.791523	−	1.37096i
$499$	1.94647	+	0.521555i	0.0871360	+	0.0233480i	0.302124	−	0.953269i	$-0.402304\pi$
$499$	1.94647	+	0.521555i	0.0871360	+	0.0233480i	−0.214988	+	0.976617i	$0.568971\pi$
$500$		0			0
$501$	−39.3103	+	10.5332i	−1.75625	+	0.470587i
$502$	−23.8502	+	6.39064i	−1.06449	+	0.285228i
$503$	−15.9589	+	27.6417i	−0.711574	+	1.23248i	0.252692	+	0.967547i	$0.418684\pi$
$503$	−15.9589	+	27.6417i	−0.711574	+	1.23248i	−0.964266	+	0.264936i	$0.914649\pi$
$504$	0.577230	+	0.577230i	0.0257119	+	0.0257119i
$505$		0			0
$506$	−6.64648	−	3.83735i	−0.295472	−	0.170591i
$507$	30.9752	−	30.9752i	1.37566	−	1.37566i
$508$	25.8660	−	25.8660i	1.14762	−	1.14762i
$509$	3.16251	−	5.47763i	0.140176	−	0.242792i	−0.787387	−	0.616459i	$-0.788567\pi$
$509$	3.16251	−	5.47763i	0.140176	−	0.242792i	0.927563	+	0.373667i	$0.121900\pi$
$510$		0			0
$511$	−2.68336	+	1.54924i	−0.118705	+	0.0685342i
$512$	−31.7298			−1.40227
$513$	0.816269	−	0.471273i	0.0360392	−	0.0208072i
$514$	27.7373	−	16.0141i	1.22344	−	0.706353i
$515$		0			0
$516$	−5.52095	−	20.6045i	−0.243046	−	0.907061i
$517$	5.90337	+	5.90337i	0.259630	+	0.259630i
$518$	21.6827	+	24.7474i	0.952683	+	1.08734i
$519$		−	47.1003i		−	2.06747i
$520$		0			0
$521$	−11.6555	+	6.72930i	−0.510637	+	0.294816i	−0.733095	−	0.680126i	$-0.761925\pi$
$521$	−11.6555	+	6.72930i	−0.510637	+	0.294816i	0.222459	+	0.974942i	$0.428592\pi$
$522$	−1.19638	+	4.46497i	−0.0523643	+	0.195426i
$523$	17.0666	+	29.5603i	0.746272	+	1.29258i	0.949598	+	0.313470i	$0.101492\pi$
$523$	17.0666	+	29.5603i	0.746272	+	1.29258i	−0.203326	+	0.979111i	$0.565175\pi$
$524$	−8.59127	−	8.59127i	−0.375312	−	0.375312i
$525$		0			0
$526$	12.5489	−	12.5489i	0.547158	−	0.547158i
$527$	1.30797	+	4.88141i	0.0569760	+	0.212637i
$528$	−11.8559	−	11.8559i	−0.515960	−	0.515960i
$529$	−17.7111			−0.770047
$530$		0			0
$531$	−26.9029	−	7.20862i	−1.16749	−	0.312827i
$532$	−28.5266			−1.23679
$533$	−41.7360	−	24.0963i	−1.80779	−	1.04373i
$534$	18.2161	+	10.5171i	0.788287	+	0.455118i
$535$		0			0
$536$	0.231866	−	0.865337i	0.0100151	−	0.0373769i
$537$	2.37651	−	1.37208i	0.102554	−	0.0592096i
$538$	−7.67399	−	4.43058i	−0.330849	−	0.191016i
$539$	−0.344436	+	0.596581i	−0.0148359	+	0.0256966i
$540$		0			0
$541$	−20.9871	+	20.9871i	−0.902306	+	0.902306i	−0.995635	−	0.0933293i	$-0.970249\pi$
$541$	−20.9871	+	20.9871i	−0.902306	+	0.902306i	0.0933293	+	0.995635i	$0.470249\pi$
$542$	−25.5819	−	44.3092i	−1.09884	−	1.90324i
$543$	−4.41989	−	16.4953i	−0.189676	−	0.707879i
$544$			55.3449i			2.37289i
$545$		0			0
$546$	63.4946	+	36.6586i	2.71732	+	1.56885i
$547$	−26.7961			−1.14572			−0.572859	−	0.819654i	$-0.694166\pi$
$547$	−26.7961			−1.14572			−0.572859	+	0.819654i	$0.694166\pi$
$548$	17.9314	+	4.80471i	0.765993	+	0.205247i
$549$	−14.1661	+	14.1661i	−0.604593	+	0.604593i
$550$		0			0
$551$	2.13649	+	3.70052i	0.0910177	+	0.157647i
$552$	0.553932	+	0.148426i	0.0235769	+	0.00631742i
$553$	13.5558	−	23.4794i	0.576453	−	0.998445i
$554$	−57.6349			−2.44867
$555$		0			0
$556$	−26.4296			−1.12087
$557$	−1.41789	+	2.45586i	−0.0600781	+	0.104058i	−0.894500	−	0.447068i	$-0.852468\pi$
$557$	−1.41789	+	2.45586i	−0.0600781	+	0.104058i	0.834422	+	0.551126i	$0.185802\pi$
$558$	−4.07606	−	1.09218i	−0.172553	−	0.0462355i
$559$	12.5160	+	21.6783i	0.529370	+	0.916895i
$560$		0			0
$561$	−20.1463	+	20.1463i	−0.850580	+	0.850580i
$562$	10.0991	+	2.70604i	0.426003	+	0.114147i
$563$	−18.8024			−0.792425			−0.396212	−	0.918159i	$-0.629676\pi$
$563$	−18.8024			−0.792425			−0.396212	+	0.918159i	$0.629676\pi$
$564$	20.4234	+	11.7914i	0.859979	+	0.496509i
$565$		0			0
$566$		−	31.6222i		−	1.32918i
$567$	−6.48942	−	24.2188i	−0.272530	−	1.01710i
$568$	−0.503245	−	0.871646i	−0.0211157	−	0.0365734i
$569$	−12.7829	+	12.7829i	−0.535887	+	0.535887i	−0.922318	−	0.386431i	$-0.873708\pi$
$569$	−12.7829	+	12.7829i	−0.535887	+	0.535887i	0.386431	+	0.922318i	$0.373708\pi$
$570$		0			0
$571$	−8.53388	+	14.7811i	−0.357132	+	0.618570i	−0.987480	−	0.157742i	$-0.949579\pi$
$571$	−8.53388	+	14.7811i	−0.357132	+	0.618570i	0.630349	+	0.776312i	$0.282912\pi$
$572$	−15.7764	−	9.10853i	−0.659646	−	0.380847i
$573$	−25.7335	+	14.8572i	−1.07503	+	0.620670i
$574$	12.1194	−	45.2302i	0.505854	−	1.88787i
$575$		0			0
$576$	−19.2272	−	11.1008i	−0.801134	−	0.462535i
$577$	20.8390	+	12.0314i	0.867541	+	0.500875i	0.866530	−	0.499125i	$-0.166345\pi$
$577$	20.8390	+	12.0314i	0.867541	+	0.500875i	0.00101057	+	0.999999i	$0.499678\pi$
$578$	62.6912			2.60761
$579$	21.7923	+	5.83923i	0.905657	+	0.242670i
$580$		0			0
$581$	−19.8772			−0.824643
$582$	32.6469	+	32.6469i	1.35326	+	1.35326i
$583$	0.0549459	+	0.205061i	0.00227563	+	0.00849275i
$584$	−0.0824316	+	0.0824316i	−0.00341104	+	0.00341104i
$585$		0			0
$586$	−29.7758	−	29.7758i	−1.23003	−	1.23003i
$587$	5.47950	+	9.49077i	0.226163	+	0.391726i	0.956668	−	0.291182i	$-0.0940484\pi$
$587$	5.47950	+	9.49077i	0.226163	+	0.391726i	−0.730505	+	0.682908i	$0.760715\pi$
$588$	−0.503636	+	1.87960i	−0.0207696	+	0.0775132i
$589$	−3.37819	+	1.95040i	−0.139196	+	0.0803649i
$590$		0			0
$591$		−	51.5258i		−	2.11949i
$592$	20.7320	+	13.8666i	0.852082	+	0.569913i
$593$	18.4396	+	18.4396i	0.757223	+	0.757223i	0.975816	−	0.218593i	$-0.0701468\pi$
$593$	18.4396	+	18.4396i	0.757223	+	0.757223i	−0.218593	+	0.975816i	$0.570147\pi$
$594$	0.151367	+	0.564910i	0.00621067	+	0.0231785i
$595$		0			0
$596$	10.9109	−	6.29943i	0.446929	−	0.258035i
$597$	−30.0569	+	17.3534i	−1.23015	+	0.710225i
$598$	25.4402			1.04033
$599$	14.9856	−	8.65196i	0.612297	−	0.353510i	−0.161567	−	0.986862i	$-0.551655\pi$
$599$	14.9856	−	8.65196i	0.612297	−	0.353510i	0.773864	+	0.633352i	$0.218321\pi$
$600$		0			0
$601$	−14.5641	+	25.2257i	−0.594080	+	1.02898i	0.399596	+	0.916692i	$0.369151\pi$
$601$	−14.5641	+	25.2257i	−0.594080	+	1.02898i	−0.993676	+	0.112286i	$0.964183\pi$
$602$	−17.1983	+	17.1983i	−0.700949	+	0.700949i
$603$	18.1103	−	18.1103i	0.737509	−	0.737509i
$604$	−18.9674	−	10.9508i	−0.771771	−	0.445582i
$605$		0			0
$606$	−57.5826	−	57.5826i	−2.33913	−	2.33913i
$607$	11.1067	−	19.2374i	0.450808	−	0.780822i	−0.547629	−	0.836722i	$-0.684469\pi$
$607$	11.1067	−	19.2374i	0.450808	−	0.780822i	0.998436	+	0.0558995i	$0.0178027\pi$
$608$	−41.2643	+	11.0567i	−1.67349	+	0.448409i
$609$	5.08627	−	1.36286i	0.206106	−	0.0552260i
$610$		0			0
$611$	−26.7312	−	7.16259i	−1.08143	−	0.289768i
$612$	−19.8759	+	34.4261i	−0.803437	+	1.39159i
$613$	−3.75684	−	14.0207i	−0.151737	−	0.566292i	−0.999363	−	0.0356964i	$-0.988635\pi$
$613$	−3.75684	−	14.0207i	−0.151737	−	0.566292i	0.847625	−	0.530595i	$-0.178032\pi$
$614$	−49.7872	+	13.3404i	−2.00925	+	0.538376i
$615$		0			0
$616$	−0.121185	+	0.452269i	−0.00488269	+	0.0182225i
$617$	13.4471	−	3.60314i	0.541360	−	0.145057i	0.0222308	−	0.999753i	$-0.492923\pi$
$617$	13.4471	−	3.60314i	0.541360	−	0.145057i	0.519129	+	0.854696i	$0.326256\pi$
$618$	26.8929	+	26.8929i	1.08179	+	1.08179i
$619$	4.87562			0.195968			0.0979838	−	0.995188i	$-0.468761\pi$
$619$	4.87562			0.195968			0.0979838	+	0.995188i	$0.468761\pi$
$620$		0			0
$621$	−0.284988	−	0.284988i	−0.0114362	−	0.0114362i
$622$	−2.85937	+	10.6713i	−0.114650	+	0.427880i
$623$		−	11.8351i		−	0.474161i
$624$	53.6848	+	14.3848i	2.14911	+	0.575853i
$625$		0			0
$626$	−6.07467	−	10.5216i	−0.242793	−	0.420529i
$627$	−19.0456	−	10.9960i	−0.760608	−	0.439137i
$628$	−13.1917	+	13.1917i	−0.526404	+	0.526404i
$629$	23.5631	−	35.2294i	0.939522	−	1.40469i
$630$		0			0
$631$	−12.0881	+	3.23901i	−0.481222	+	0.128943i	−0.491271	−	0.871007i	$-0.663468\pi$
$631$	−12.0881	+	3.23901i	−0.481222	+	0.128943i	0.0100498	+	0.999949i	$0.496801\pi$
$632$	0.264006	−	0.985282i	0.0105016	−	0.0391924i
$633$	−21.5456	−	5.77312i	−0.856359	−	0.229461i
$634$	−13.8917	+	51.8444i	−0.551709	+	2.05901i
$635$		0			0
$636$	0.299841	+	0.519340i	0.0118895	+	0.0205932i
$637$		−	2.28349i		−	0.0904750i
$638$	−2.56099	+	0.686216i	−0.101391	+	0.0271675i
$639$		−	28.7746i		−	1.13830i
$640$		0			0
$641$	6.83773	−	11.8433i	0.270074	−	0.467782i	−0.698806	−	0.715311i	$-0.746285\pi$
$641$	6.83773	−	11.8433i	0.270074	−	0.467782i	0.968881	+	0.247529i	$0.0796184\pi$
$642$	−12.0852	+	6.97739i	−0.476964	+	0.275375i
$643$		−	38.4862i		−	1.51775i	−0.651239	−	0.758873i	$-0.725750\pi$
$643$		−	38.4862i		−	1.51775i	0.651239	−	0.758873i	$-0.274250\pi$
$644$	3.15707	+	11.7824i	0.124406	+	0.464290i
$645$		0			0
$646$	19.2729	+	71.9275i	0.758283	+	2.82995i
$647$	7.13127	+	12.3517i	0.280359	+	0.485596i	0.971473	−	0.237150i	$-0.0762132\pi$
$647$	7.13127	+	12.3517i	0.280359	+	0.485596i	−0.691114	+	0.722746i	$0.742880\pi$
$648$	−0.471672	−	0.816960i	−0.0185290	−	0.0320932i
$649$	−4.13468	−	15.4308i	−0.162300	−	0.605713i
$650$		0			0
$651$	1.24415	+	4.64325i	0.0487622	+	0.181983i
$652$		−	19.2454i		−	0.753708i
$653$	−40.8194	+	23.5671i	−1.59739	+	0.922253i	−0.605400	+	0.795921i	$0.706987\pi$
$653$	−40.8194	+	23.5671i	−1.59739	+	0.922253i	−0.991988	+	0.126332i	$0.959680\pi$
$654$	1.30283	−	2.25657i	0.0509447	−	0.0882389i
$655$		0			0
$656$		−	35.4965i		−	1.38591i
$657$	−3.21923	+	0.862589i	−0.125594	+	0.0336528i
$658$		−	26.8893i		−	1.04825i
$659$	−15.9643	−	27.6509i	−0.621880	−	1.07713i	−0.989135	−	0.147007i	$-0.953036\pi$
$659$	−15.9643	−	27.6509i	−0.621880	−	1.07713i	0.367256	−	0.930120i	$-0.380297\pi$
$660$		0			0
$661$	0.934896	−	3.48908i	0.0363632	−	0.135709i	−0.945358	−	0.326034i	$-0.894287\pi$
$661$	0.934896	−	3.48908i	0.0363632	−	0.135709i	0.981721	+	0.190325i	$0.0609541\pi$
$662$	−16.5485	−	4.43416i	−0.643176	−	0.172338i
$663$	24.4437	−	91.2251i	0.949315	−	3.54289i
$664$	−0.722368	+	0.193558i	−0.0280333	+	0.00751151i
$665$		0			0
$666$	15.6382	+	31.7482i	0.605969	+	1.23022i
$667$	1.29198	−	1.29198i	0.0500255	−	0.0500255i
$668$	−28.2052	−	16.2843i	−1.09129	−	0.630058i
$669$	−13.2094	−	22.8794i	−0.510705	−	0.884568i
$670$		0			0
$671$	−11.0994	−	2.97406i	−0.428486	−	0.114812i
$672$			52.6447i			2.03081i
$673$	5.76709	−	21.5231i	0.222305	−	0.829654i	−0.761161	−	0.648563i	$-0.775370\pi$
$673$	5.76709	−	21.5231i	0.222305	−	0.829654i	0.983466	−	0.181091i	$-0.0579629\pi$
$674$	2.24839	+	2.24839i	0.0866047	+	0.0866047i
$675$		0			0
$676$	35.0563			1.34832
$677$	−18.0215	−	18.0215i	−0.692623	−	0.692623i	0.270185	−	0.962808i	$-0.412915\pi$
$677$	−18.0215	−	18.0215i	−0.692623	−	0.692623i	−0.962808	+	0.270185i	$0.912915\pi$
$678$	−77.4927	+	20.7641i	−2.97609	+	0.797441i
$679$	6.72355	−	25.0926i	0.258026	−	0.962967i
$680$		0			0
$681$	28.6883	−	7.68700i	1.09934	−	0.294567i
$682$	−0.626445	−	2.33792i	−0.0239878	−	0.0895237i
$683$	−9.12242	+	15.8005i	−0.349060	+	0.604589i	−0.986083	−	0.166256i	$-0.946832\pi$
$683$	−9.12242	+	15.8005i	−0.349060	+	0.604589i	0.637023	+	0.770845i	$0.280166\pi$
$684$	−29.6384	−	7.94157i	−1.13325	−	0.303654i
$685$		0			0
$686$	−34.4307	+	9.22567i	−1.31457	+	0.352238i
$687$	−18.8175	+	5.04214i	−0.717933	+	0.192370i
$688$	−9.21872	+	15.9673i	−0.351460	+	0.608747i
$689$	−0.497603	−	0.497603i	−0.0189572	−	0.0189572i
$690$		0			0
$691$	−26.8608	−	15.5081i	−1.02183	−	0.589957i	−0.107200	−	0.994237i	$-0.534189\pi$
$691$	−26.8608	−	15.5081i	−1.02183	−	0.589957i	−0.914635	+	0.404281i	$0.867522\pi$
$692$	26.6529	−	26.6529i	1.01319	−	1.01319i
$693$	−9.46537	+	9.46537i	−0.359560	+	0.359560i
$694$	17.8494	−	30.9160i	0.677553	−	1.17356i
$695$		0			0
$696$	0.171572	−	0.0990573i	0.00650343	−	0.00375476i
$697$	−60.3183			−2.28472
$698$	−42.8983	+	24.7673i	−1.62372	+	0.937457i
$699$	−37.2683	+	21.5169i	−1.40962	+	0.813843i
$700$		0			0
$701$	1.72147	+	6.42463i	0.0650192	+	0.242655i	0.990785	−	0.135442i	$-0.0432454\pi$
$701$	1.72147	+	6.42463i	0.0650192	+	0.242655i	−0.925766	+	0.378097i	$0.876579\pi$
$702$	−1.37082	−	1.37082i	−0.0517382	−	0.0517382i
$703$	30.9739	+	10.5302i	1.16820	+	0.397153i
$704$		−	12.7343i		−	0.479943i
$705$		0			0
$706$	−0.683596	+	0.394674i	−0.0257275	+	0.0148538i
$707$	−11.8590	+	44.2584i	−0.446004	+	1.66451i
$708$	−22.5630	−	39.0803i	−0.847970	−	1.46873i
$709$	−5.97248	−	5.97248i	−0.224301	−	0.224301i	0.586006	−	0.810307i	$-0.300700\pi$
$709$	−5.97248	−	5.97248i	−0.224301	−	0.224301i	−0.810307	+	0.586006i	$0.800700\pi$
$710$		0			0
$711$	20.6206	−	20.6206i	0.773333	−	0.773333i
$712$	−0.115246	−	0.430105i	−0.00431904	−	0.0161189i
$713$	1.17944	+	1.17944i	0.0441705	+	0.0441705i
$714$	91.7647			3.43421
$715$		0			0
$716$	2.12124	+	0.568384i	0.0792744	+	0.0212415i
$717$	53.0066			1.97957
$718$	45.8574	+	26.4758i	1.71138	+	0.988068i
$719$	−18.4724	−	10.6650i	−0.688904	−	0.397739i	0.114297	−	0.993447i	$-0.463538\pi$
$719$	−18.4724	−	10.6650i	−0.688904	−	0.397739i	−0.803201	+	0.595707i	$0.796872\pi$
$720$		0			0
$721$	5.53853	−	20.6701i	0.206266	−	0.769794i
$722$	−17.0814	+	9.86196i	−0.635705	+	0.367024i
$723$	−6.09281	−	3.51769i	−0.226594	−	0.130824i
$724$	6.83316	−	11.8354i	0.253952	−	0.439858i
$725$		0			0
$726$	−27.9821	+	27.9821i	−1.03851	+	1.03851i
$727$	1.94208	+	3.36379i	0.0720279	+	0.124756i	0.899790	−	0.436323i	$-0.143720\pi$
$727$	1.94208	+	3.36379i	0.0720279	+	0.124756i	−0.827762	+	0.561079i	$0.810386\pi$
$728$	−0.401707	−	1.49919i	−0.0148882	−	0.0555637i
$729$		−	25.6892i		−	0.951452i
$730$		0			0
$731$	27.1328	+	15.6651i	1.00354	+	0.579396i
$732$	−32.4591			−1.19972
$733$	−32.6370	−	8.74505i	−1.20547	−	0.323006i	−0.400489	−	0.916302i	$-0.631160\pi$
$733$	−32.6370	−	8.74505i	−1.20547	−	0.323006i	−0.804984	+	0.593296i	$0.797826\pi$
$734$	−21.4761	+	21.4761i	−0.792697	+	0.792697i
$735$		0			0
$736$	9.13352	+	15.8197i	0.336666	+	0.583123i
$737$	14.1897	+	3.80213i	0.522686	+	0.140053i
$738$	25.1834	−	43.6190i	0.927015	−	1.60564i
$739$	41.3843			1.52234			0.761172	−	0.648550i	$-0.224624\pi$
$739$	41.3843			1.52234			0.761172	+	0.648550i	$0.224624\pi$
$740$		0			0
$741$	72.8993			2.67802
$742$	0.341879	−	0.592153i	0.0125508	−	0.0217386i
$743$	10.8057	+	2.89539i	0.396424	+	0.106222i	0.451523	−	0.892259i	$-0.350881\pi$
$743$	10.8057	+	2.89539i	0.396424	+	0.106222i	−0.0550990	+	0.998481i	$0.517547\pi$
$744$	0.0904292	+	0.156628i	0.00331529	+	0.00574226i
$745$		0			0
$746$	51.3220	−	51.3220i	1.87903	−	1.87903i
$747$	−20.6518	−	5.53363i	−0.755610	−	0.202465i
$748$	−22.8007			−0.833675
$749$	6.79985	+	3.92589i	0.248461	+	0.143449i
$750$		0			0
$751$			2.77329i			0.101199i	0.998719	+	0.0505993i	$0.0161132\pi$
$751$			2.77329i			0.101199i	−0.998719	+	0.0505993i	$0.983887\pi$
$752$	−5.27565	−	19.6890i	−0.192383	−	0.717984i
$753$	15.1272	+	26.2011i	0.551267	+	0.954823i
$754$	6.21454	−	6.21454i	0.226320	−	0.226320i
$755$		0			0
$756$	0.464765	−	0.804996i	0.0169033	−	0.0292774i
$757$	23.9288	+	13.8153i	0.869705	+	0.502125i	0.867250	−	0.497872i	$-0.165885\pi$
$757$	23.9288	+	13.8153i	0.869705	+	0.502125i	0.00245512	+	0.999997i	$0.499219\pi$
$758$	38.0420	−	21.9635i	1.38175	−	0.797752i
$759$	−2.43387	+	9.08334i	−0.0883441	+	0.329704i
$760$		0			0
$761$	5.11172	+	2.95125i	0.185300	+	0.106983i	0.589780	−	0.807564i	$-0.299214\pi$
$761$	5.11172	+	2.95125i	0.185300	+	0.106983i	−0.404481	+	0.914547i	$0.632548\pi$
$762$	−78.6596	−	45.4141i	−2.84954	−	1.64518i
$763$	−1.46610			−0.0530764
$764$	−22.9693	−	6.15461i	−0.831001	−	0.222666i
$765$		0			0
$766$	27.4713			0.992577
$767$	37.4447	+	37.4447i	1.35205	+	1.35205i
$768$	10.5820	+	39.4925i	0.381845	+	1.42506i
$769$	15.6442	−	15.6442i	0.564144	−	0.564144i	−0.366338	−	0.930482i	$-0.619389\pi$
$769$	15.6442	−	15.6442i	0.564144	−	0.564144i	0.930482	+	0.366338i	$0.119389\pi$
$770$		0			0
$771$	−27.7498	−	27.7498i	−0.999384	−	0.999384i
$772$	9.02746	+	15.6360i	0.324905	+	0.562752i
$773$	−7.54766	+	28.1683i	−0.271470	+	1.01314i	0.686699	+	0.726941i	$0.259059\pi$
$773$	−7.54766	+	28.1683i	−0.271470	+	1.01314i	−0.958170	+	0.286200i	$0.907608\pi$
$774$	−22.6564	+	13.0807i	−0.814366	+	0.470175i
$775$		0			0
$776$		−	0.977379i		−	0.0350859i
$777$	22.4135	−	33.5106i	0.804079	−	1.20219i
$778$	15.0765	+	15.0765i	0.540518	+	0.540518i
$779$	−12.0503	−	44.9724i	−0.431747	−	1.61130i
$780$		0			0
$781$	14.2932	−	8.25217i	0.511450	−	0.295286i
$782$	27.5753	−	15.9206i	0.986090	−	0.569319i
$783$	−0.139234			−0.00497581
$784$	1.45658	−	0.840957i	0.0520207	−	0.0300342i
$785$		0			0
$786$	−15.0841	+	26.1265i	−0.538033	+	0.931900i
$787$	−2.72026	+	2.72026i	−0.0969667	+	0.0969667i	−0.753926	−	0.656959i	$-0.771842\pi$
$787$	−2.72026	+	2.72026i	−0.0969667	+	0.0969667i	0.656959	+	0.753926i	$0.271842\pi$
$788$	29.1572	−	29.1572i	1.03868	−	1.03868i
$789$	−18.8318	−	10.8725i	−0.670430	−	0.387073i
$790$		0			0
$791$	31.9189	+	31.9189i	1.13491	+	1.13491i
$792$	−0.251816	+	0.436158i	−0.00894789	+	0.0154982i
$793$	36.7923	−	9.85847i	1.30653	−	0.350085i
$794$	45.6259	−	12.2254i	1.61920	−	0.433864i
$795$		0			0
$796$	−26.8283	−	7.18862i	−0.950904	−	0.254794i
$797$	5.21913	−	9.03980i	0.184871	−	0.320206i	−0.758662	−	0.651484i	$-0.774147\pi$
$797$	5.21913	−	9.03980i	0.184871	−	0.320206i	0.943533	+	0.331278i	$0.107480\pi$
$798$	18.3326	+	68.4182i	0.648967	+	2.42198i
$799$	−33.4570	+	8.96477i	−1.18362	+	0.317151i
$800$		0			0
$801$	3.29478	−	12.2963i	0.116415	−	0.434468i
$802$	28.5133	−	7.64012i	1.00684	−	0.269782i
$803$	−1.35171	−	1.35171i	−0.0477007	−	0.0477007i
$804$	41.4966			1.46347
$805$		0			0
$806$	5.67324	+	5.67324i	0.199831	+	0.199831i
$807$	−2.81014	+	10.4876i	−0.0989216	+	0.369180i
$808$			1.72390i			0.0606467i
$809$	−17.2925	−	4.63351i	−0.607972	−	0.162906i	−0.0583182	−	0.998298i	$-0.518574\pi$
$809$	−17.2925	−	4.63351i	−0.607972	−	0.162906i	−0.549654	+	0.835392i	$0.685240\pi$
$810$		0			0
$811$	12.0147	+	20.8102i	0.421895	+	0.730743i	0.996125	−	0.0879507i	$-0.0280318\pi$
$811$	12.0147	+	20.8102i	0.421895	+	0.730743i	−0.574230	+	0.818694i	$0.694698\pi$
$812$	3.64941	+	2.10699i	0.128069	+	0.0739408i
$813$	−44.3291	+	44.3291i	−1.55469	+	1.55469i
$814$	−11.2854	+	16.8729i	−0.395554	+	0.591396i
$815$		0			0
$816$	67.1924	−	18.0042i	2.35220	−	0.630271i
$817$	−6.25911	+	23.3593i	−0.218979	+	0.817240i
$818$	44.8951	+	12.0296i	1.56972	+	0.420605i
$819$	11.4844	−	42.8604i	0.401297	−	1.49766i
$820$		0			0
$821$	−12.1723	−	21.0830i	−0.424815	−	0.735801i	0.571588	−	0.820541i	$-0.306327\pi$
$821$	−12.1723	−	21.0830i	−0.424815	−	0.735801i	−0.996403	+	0.0847397i	$0.972994\pi$
$822$		−	46.0945i		−	1.60773i
$823$	14.6573	−	3.92742i	0.510923	−	0.136901i	0.00585796	−	0.999983i	$-0.498135\pi$
$823$	14.6573	−	3.92742i	0.510923	−	0.136901i	0.505065	+	0.863082i	$0.331469\pi$
$824$		−	0.805117i		−	0.0280476i
$825$		0			0
$826$	−25.7264	+	44.5595i	−0.895137	+	1.55042i
$827$	−7.81135	+	4.50988i	−0.271627	+	0.156824i	−0.629627	−	0.776898i	$-0.716792\pi$
$827$	−7.81135	+	4.50988i	−0.271627	+	0.156824i	0.358000	+	0.933722i	$0.383459\pi$
$828$			13.1204i			0.455967i
$829$	5.61392	+	20.9514i	0.194979	+	0.727673i	0.992272	+	0.124080i	$0.0395981\pi$
$829$	5.61392	+	20.9514i	0.194979	+	0.727673i	−0.797293	+	0.603593i	$0.793735\pi$
$830$		0			0
$831$	18.2777	+	68.2135i	0.634048	+	2.36630i
$832$	21.1060	+	36.5566i	0.731718	+	1.26737i
$833$	−1.42902	−	2.47513i	−0.0495125	−	0.0857582i
$834$	16.9850	+	63.3888i	0.588141	+	2.19497i
$835$		0			0
$836$	−4.55508	−	16.9998i	−0.157541	−	0.587951i
$837$		−	0.127106i		−	0.00439343i
$838$	39.7799	−	22.9669i	1.37417	−	0.793379i
$839$	17.8183	−	30.8622i	0.615157	−	1.06548i	−0.375200	−	0.926944i	$-0.622426\pi$
$839$	17.8183	−	30.8622i	0.615157	−	1.06548i	0.990357	−	0.138539i	$-0.0442406\pi$
$840$		0			0
$841$			28.3688i			0.978234i
$842$	2.16194	−	0.579291i	0.0745055	−	0.0199637i
$843$		−	12.8109i		−	0.441230i
$844$	−8.92525	−	15.4590i	−0.307220	−	0.532120i
$845$		0			0
$846$	7.48574	−	27.9372i	0.257365	−	0.960500i
$847$	21.5072	+	5.76284i	0.738997	+	0.198014i
$848$	0.134153	−	0.500666i	0.00460683	−	0.0171929i
$849$	−37.4263	+	10.0283i	−1.28447	+	0.344172i
$850$		0			0
$851$	0.921369	−	13.9585i	0.0315841	−	0.478492i
$852$	32.9659	−	32.9659i	1.12939	−	1.12939i
$853$	−24.8691	−	14.3582i	−0.851501	−	0.491614i	0.00965588	−	0.999953i	$-0.496926\pi$
$853$	−24.8691	−	14.3582i	−0.851501	−	0.491614i	−0.861157	+	0.508339i	$0.830260\pi$
$854$	18.5050	+	32.0515i	0.633227	+	1.09678i
$855$		0			0
$856$	0.285347	+	0.0764584i	0.00975295	+	0.00261329i
$857$		−	6.04867i		−	0.206618i	−0.994649	−	0.103309i	$-0.967057\pi$
$857$		−	6.04867i		−	0.206618i	0.994649	−	0.103309i	$-0.0329431\pi$
$858$	−11.7072	+	43.6918i	−0.399677	+	1.49161i
$859$	−38.1045	−	38.1045i	−1.30011	−	1.30011i	−0.928316	−	0.371791i	$-0.878744\pi$
$859$	−38.1045	−	38.1045i	−1.30011	−	1.30011i	−0.371791	−	0.928316i	$-0.621256\pi$
$860$		0			0
$861$	−57.3755			−1.95535
$862$	33.0904	+	33.0904i	1.12706	+	1.12706i
$863$	11.2783	−	3.02200i	0.383917	−	0.102870i	−0.0616982	−	0.998095i	$-0.519652\pi$
$863$	11.2783	−	3.02200i	0.383917	−	0.102870i	0.445615	+	0.895225i	$0.352985\pi$
$864$	0.360279	−	1.34458i	0.0122569	−	0.0457436i
$865$		0			0
$866$	22.6767	−	6.07620i	0.770586	−	0.206478i
$867$	−19.8813	−	74.1979i	−0.675203	−	2.51989i
$868$	−1.92346	+	3.33154i	−0.0652866	+	0.113080i
$869$	16.1566	+	4.32914i	0.548075	+	0.146856i
$870$		0			0
$871$	−47.0364	+	12.6034i	−1.59377	+	0.427048i
$872$	−0.0532805	+	0.0142765i	−0.00180431	+	0.000483462i
$873$	13.9712	−	24.1987i	0.472852	−	0.819003i
$874$	17.3791	+	17.3791i	0.587856	+	0.587856i
$875$		0			0
$876$	−4.67638	−	2.69991i	−0.158000	−	0.0912216i
$877$	−25.9009	+	25.9009i	−0.874612	+	0.874612i	−0.992971	−	0.118359i	$-0.962237\pi$
$877$	−25.9009	+	25.9009i	−0.874612	+	0.874612i	0.118359	+	0.992971i	$0.462237\pi$
$878$	−5.18977	+	5.18977i	−0.175146	+	0.175146i
$879$	−25.7982	+	44.6838i	−0.870153	+	1.50715i
$880$		0			0
$881$	−19.7789	+	11.4193i	−0.666367	+	0.384727i	−0.794699	−	0.607004i	$-0.792371\pi$
$881$	−19.7789	+	11.4193i	−0.666367	+	0.384727i	0.128332	+	0.991731i	$0.459038\pi$
$882$	2.38651			0.0803579
$883$	−14.0457	+	8.10927i	−0.472674	+	0.272899i	−0.717359	−	0.696704i	$-0.754649\pi$
$883$	−14.0457	+	8.10927i	−0.472674	+	0.272899i	0.244684	+	0.969603i	$0.421316\pi$
$884$	65.4542	−	37.7900i	2.20146	−	1.27102i
$885$		0			0
$886$	−18.2023	−	67.9318i	−0.611517	−	2.28221i
$887$	9.65037	+	9.65037i	0.324028	+	0.324028i	0.850310	−	0.526282i	$-0.176414\pi$
$887$	9.65037	+	9.65037i	0.324028	+	0.324028i	−0.526282	+	0.850310i	$0.676414\pi$
$888$	0.488226	−	1.43609i	0.0163838	−	0.0481919i
$889$			51.1054i			1.71402i
$890$		0			0
$891$	13.3965	−	7.73445i	0.448798	−	0.259114i
$892$	5.47200	−	20.4218i	0.183216	−	0.683771i
$893$	−13.3680	−	23.1540i	−0.447342	−	0.774820i
$894$	−22.1204	−	22.1204i	−0.739818	−	0.739818i
$895$		0			0
$896$	1.57660	−	1.57660i	0.0526703	−	0.0526703i
$897$	−8.06785	−	30.1096i	−0.269378	−	1.00533i
$898$	−14.8611	−	14.8611i	−0.495922	−	0.495922i
$899$	0.576229			0.0192183
$900$		0			0
$901$	−0.850768	−	0.227963i	−0.0283432	−	0.00759453i
$902$	28.8891			0.961903
$903$	25.8090	+	14.9008i	0.858870	+	0.495869i
$904$	1.47080	+	0.849168i	0.0489181	+	0.0282429i
$905$		0			0
$906$	−14.0751	+	52.5288i	−0.467612	+	1.74515i
$907$	34.7453	−	20.0602i	1.15370	−	0.666089i	0.203913	−	0.978989i	$-0.434634\pi$
$907$	34.7453	−	20.0602i	1.15370	−	0.666089i	0.949786	+	0.312900i	$0.101301\pi$
$908$	20.5839	+	11.8841i	0.683101	+	0.394388i
$909$	−24.6424	+	42.6818i	−0.817335	+	1.41567i
$910$		0			0
$911$	−6.91310	+	6.91310i	−0.229041	+	0.229041i	−0.812292	−	0.583251i	$-0.801780\pi$
$911$	−6.91310	+	6.91310i	−0.229041	+	0.229041i	0.583251	+	0.812292i	$0.301780\pi$
$912$	26.8472	+	46.5007i	0.889000	+	1.53979i
$913$	−3.17395	−	11.8453i	−0.105042	−	0.392024i
$914$		−	59.8889i		−	1.98095i
$915$		0			0
$916$	−13.5016	−	7.79515i	−0.446106	−	0.257559i
$917$	16.9745			0.560546
$918$	−2.34373	−	0.628001i	−0.0773547	−	0.0207271i
$919$	−10.7644	+	10.7644i	−0.355086	+	0.355086i	−0.861998	−	0.506912i	$-0.830787\pi$
$919$	−10.7644	+	10.7644i	−0.355086	+	0.355086i	0.506912	+	0.861998i	$0.330787\pi$
$920$		0			0
$921$	31.5780	+	54.6947i	1.04053	+	1.80225i
$922$	−22.6805	−	6.07723i	−0.746943	−	0.200143i
$923$	−27.3544	+	47.3793i	−0.900382	+	1.55951i
$924$	−21.6882			−0.713491
$925$		0			0
$926$	34.6244			1.13783
$927$	11.5088	−	19.9338i	0.377997	−	0.654710i
$928$	6.09559	+	1.63331i	0.200097	+	0.0536159i
$929$	2.66910	+	4.62301i	0.0875702	+	0.151676i	0.906484	−	0.422241i	$-0.138756\pi$
$929$	2.66910	+	4.62301i	0.0875702	+	0.151676i	−0.818913	+	0.573917i	$0.805423\pi$
$930$		0			0
$931$	1.55993	−	1.55993i	0.0511246	−	0.0511246i
$932$	−33.2651	−	8.91337i	−1.08964	−	0.291967i
$933$	13.5368			0.443174
$934$	−18.7965	−	10.8522i	−0.615041	−	0.355094i
$935$		0			0
$936$		−	1.66945i		−	0.0545676i
$937$	−4.23510	−	15.8056i	−0.138355	−	0.516346i	−0.999962	−	0.00877029i	$-0.997208\pi$
$937$	−4.23510	−	15.8056i	−0.138355	−	0.516346i	0.861607	−	0.507576i	$-0.169458\pi$
$938$	−23.6573	−	40.9756i	−0.772437	−	1.33790i
$939$	−10.5264	+	10.5264i	−0.343515	+	0.343515i
$940$		0			0
$941$	15.2812	−	26.4678i	0.498152	−	0.862824i	−0.501846	−	0.864957i	$-0.667346\pi$
$941$	15.2812	−	26.4678i	0.498152	−	0.862824i	0.999998	+	0.00213282i	$0.000678897\pi$
$942$	40.1165	+	23.1612i	1.30706	+	0.754634i
$943$	−17.2413	+	9.95428i	−0.561455	+	0.324156i
$944$	−10.0950	+	37.6751i	−0.328565	+	1.22622i
$945$		0			0
$946$	−12.9951	−	7.50273i	−0.422508	−	0.243935i
$947$	−43.7794	−	25.2760i	−1.42264	−	0.821361i	−0.426115	−	0.904669i	$-0.640118\pi$
$947$	−43.7794	−	25.2760i	−1.42264	−	0.821361i	−0.996524	+	0.0833078i	$0.973452\pi$
$948$	47.2485			1.53456
$949$	6.12070	+	1.64004i	0.198686	+	0.0532378i
$950$		0			0
$951$	65.7657			2.13260
$952$	−1.37362	−	1.37362i	−0.0445193	−	0.0445193i
$953$	−9.34657	−	34.8819i	−0.302765	−	1.12994i	−0.934852	−	0.355038i	$-0.884468\pi$
$953$	−9.34657	−	34.8819i	−0.302765	−	1.12994i	0.632087	−	0.774898i	$-0.282199\pi$
$954$	0.520053	−	0.520053i	0.0168373	−	0.0168373i
$955$		0			0
$956$	29.9952	+	29.9952i	0.970113	+	0.970113i
$957$	1.62433	+	2.81343i	0.0525073	+	0.0909453i
$958$	4.28888	−	16.0063i	0.138567	−	0.517140i
$959$	−22.4608	+	12.9678i	−0.725297	+	0.418751i
$960$		0			0
$961$		−	30.4740i		−	0.983031i
$962$	4.43188	−	67.1420i	0.142889	−	2.16474i
$963$	5.97191	+	5.97191i	0.192442	+	0.192442i
$964$	−1.45720	−	5.43835i	−0.0469333	−	0.175157i
$965$		0			0
$966$	26.2299	−	15.1438i	0.843933	−	0.487245i
$967$	30.8443	−	17.8080i	0.991886	−	0.572666i	0.0860487	−	0.996291i	$-0.472576\pi$
$967$	30.8443	−	17.8080i	0.991886	−	0.572666i	0.905838	+	0.423625i	$0.139243\pi$
$968$	0.837724			0.0269255
$969$	79.0175	−	45.6208i	2.53841	−	1.46555i
$970$		0			0
$971$	16.8077	−	29.1118i	0.539386	−	0.934244i	−0.459551	−	0.888151i	$-0.651990\pi$
$971$	16.8077	−	29.1118i	0.539386	−	0.934244i	0.998937	−	0.0460924i	$-0.0146769\pi$
$972$	30.1733	−	30.1733i	0.967810	−	0.967810i
$973$	26.1095	−	26.1095i	0.837034	−	0.837034i
$974$	−14.2810	−	8.24512i	−0.457592	−	0.264191i
$975$		0			0
$976$	19.8383	+	19.8383i	0.635008	+	0.635008i
$977$	28.3165	−	49.0457i	0.905926	−	1.56911i	0.0862569	−	0.996273i	$-0.472509\pi$
$977$	28.3165	−	49.0457i	0.905926	−	1.56911i	0.819669	−	0.572837i	$-0.194157\pi$
$978$	−46.1581	+	12.3680i	−1.47597	+	0.395486i
$979$	7.05283	−	1.88980i	0.225410	−	0.0603983i
$980$		0			0
$981$	−1.52324	−	0.408150i	−0.0486332	−	0.0130312i
$982$	−21.3179	+	36.9237i	−0.680282	+	1.17828i
$983$	−9.23907	−	34.4807i	−0.294681	−	1.09976i	−0.941471	−	0.337095i	$-0.890556\pi$
$983$	−9.23907	−	34.4807i	−0.294681	−	1.09976i	0.646790	−	0.762668i	$-0.276111\pi$
$984$	−2.08512	+	0.558706i	−0.0664711	+	0.0178109i
$985$		0			0
$986$	2.84701	−	10.6252i	0.0906673	−	0.338375i
$987$	−31.8247	+	8.52739i	−1.01299	+	0.271430i
$988$	41.2520	+	41.2520i	1.31240	+	1.31240i
$989$	10.3408			0.328819
$990$		0			0
$991$	−1.29277	−	1.29277i	−0.0410661	−	0.0410661i	0.686276	−	0.727342i	$-0.259244\pi$
$991$	−1.29277	−	1.29277i	−0.0410661	−	0.0410661i	−0.727342	+	0.686276i	$0.759244\pi$
$992$	−1.49104	+	5.56465i	−0.0473407	+	0.176678i
$993$			20.9921i			0.666165i
$994$	−51.3460	−	13.7581i	−1.62859	−	0.436381i
$995$		0			0
$996$	−17.3203	−	29.9997i	−0.548815	−	0.950576i
$997$	−25.1686	−	14.5311i	−0.797098	−	0.460205i	0.0453572	−	0.998971i	$-0.485557\pi$
$997$	−25.1686	−	14.5311i	−0.797098	−	0.460205i	−0.842456	+	0.538766i	$0.818891\pi$
$998$	2.83141	−	2.83141i	0.0896267	−	0.0896267i
$999$	−0.801789	+	0.702495i	−0.0253675	+	0.0222259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.t.b.643.14		68
5.2	odd	4		925.2.y.b.532.14		68
5.3	odd	4		185.2.u.a.162.4	yes	68
5.4	even	2		185.2.p.a.88.4	yes	68
37.8	odd	12		925.2.y.b.193.14		68
185.8	even	12		185.2.p.a.82.4	✓	68
185.82	even	12	inner	925.2.t.b.82.14		68
185.119	odd	12		185.2.u.a.8.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.4	✓	68	185.8	even	12
185.2.p.a.88.4	yes	68	5.4	even	2
185.2.u.a.8.4	yes	68	185.119	odd	12
185.2.u.a.162.4	yes	68	5.3	odd	4
925.2.t.b.82.14		68	185.82	even	12	inner
925.2.t.b.643.14		68	1.1	even	1	trivial
925.2.y.b.193.14		68	37.8	odd	12
925.2.y.b.532.14		68	5.2	odd	4

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.993536 - 1.72086i) q^{2} +(-2.35179 - 0.630160i) q^{3} +(-0.974229 - 1.68741i) q^{4} +(-3.42100 + 3.42100i) q^{6} +(2.62941 + 0.704548i) q^{7} +0.102418 q^{8} +(2.53574 + 1.46401i) q^{9} +1.67944i q^{11} +(1.22784 + 4.58237i) q^{12} +(-2.78351 - 4.82119i) q^{13} +(3.82484 - 3.82484i) q^{14} +(2.05021 - 3.55107i) q^{16} +(-6.03425 - 3.48387i) q^{17} +(5.03870 - 2.90910i) q^{18} +(1.39201 - 5.19504i) q^{19} +(-5.73984 - 3.31390i) q^{21} +(2.89007 + 1.66858i) q^{22} -2.29976 q^{23} +(-0.240865 - 0.0645396i) q^{24} -11.0621 q^{26} +(0.123920 + 0.123920i) q^{27} +(-1.37278 - 5.12329i) q^{28} +(-0.561787 + 0.561787i) q^{29} +(-0.512854 - 0.512854i) q^{31} +(-3.97151 - 6.87885i) q^{32} +(1.05832 - 3.94969i) q^{33} +(-11.9905 + 6.92271i) q^{34} -5.70513i q^{36} +(-0.400637 + 6.06955i) q^{37} +(-7.55690 - 7.55690i) q^{38} +(3.50812 + 13.0925i) q^{39} +(7.49700 - 4.32839i) q^{41} +(-11.4055 + 6.58496i) q^{42} -4.49647 q^{43} +(2.83391 - 1.63616i) q^{44} +(-2.28490 + 3.95756i) q^{46} +(3.51508 - 3.51508i) q^{47} +(-7.05942 + 7.05942i) q^{48} +(0.355227 + 0.205090i) q^{49} +(11.9959 + 11.9959i) q^{51} +(-5.42356 + 9.39388i) q^{52} +(0.122101 - 0.0327168i) q^{53} +(0.336369 - 0.0901297i) q^{54} +(0.269298 + 0.0721582i) q^{56} +(-6.54742 + 11.3405i) q^{57} +(0.408598 + 1.52491i) q^{58} +(-9.18809 + 2.46194i) q^{59} +(-1.77087 + 6.60897i) q^{61} +(-1.39209 + 0.373008i) q^{62} +(5.63603 + 5.63603i) q^{63} -7.58249 q^{64} +(-5.74537 - 5.74537i) q^{66} +(2.26393 - 8.44910i) q^{67} +13.5764i q^{68} +(5.40856 + 1.44922i) q^{69} +(-4.91365 - 8.51069i) q^{71} +(0.259705 + 0.149941i) q^{72} +(-0.804857 + 0.804857i) q^{73} +(10.0468 + 6.71976i) q^{74} +(-10.1223 + 2.71227i) q^{76} +(-1.18324 + 4.41593i) q^{77} +(26.0157 + 6.97089i) q^{78} +(2.57773 - 9.62023i) q^{79} +(-4.60538 - 7.97675i) q^{81} -17.2017i q^{82} +(-7.05316 + 1.88989i) q^{83} +12.9140i q^{84} +(-4.46741 + 7.73777i) q^{86} +(1.67522 - 0.967189i) q^{87} +0.172004i q^{88} +(-1.12526 - 4.19952i) q^{89} +(-3.92224 - 14.6380i) q^{91} +(2.24050 + 3.88065i) q^{92} +(0.882945 + 1.52931i) q^{93} +(-2.55659 - 9.54131i) q^{94} +(5.00537 + 18.6803i) q^{96} -9.54307i q^{97} +(0.705861 - 0.407529i) q^{98} +(-2.45872 + 4.25862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

L-functions

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