LMFDB - Embedded newform 925.2.y.b.193.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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("925.193"); 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([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (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			193.14
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72086 - 0.993536i) q^{2} +(-0.630160 - 2.35179i) q^{3} +(0.974229 - 1.68741i) q^{4} +(-3.42100 - 3.42100i) q^{6} +(-0.704548 - 2.62941i) q^{7} +0.102418i q^{8} +(-2.53574 + 1.46401i) q^{9} -1.67944i q^{11} +(-4.58237 - 1.22784i) q^{12} +(-4.82119 - 2.78351i) q^{13} +(-3.82484 - 3.82484i) q^{14} +(2.05021 + 3.55107i) q^{16} +(3.48387 + 6.03425i) q^{17} +(-2.90910 + 5.03870i) q^{18} +(-1.39201 - 5.19504i) q^{19} +(-5.73984 + 3.31390i) q^{21} +(-1.66858 - 2.89007i) q^{22} -2.29976i q^{23} +(0.240865 - 0.0645396i) q^{24} -11.0621 q^{26} +(-0.123920 - 0.123920i) q^{27} +(-5.12329 - 1.37278i) q^{28} +(0.561787 + 0.561787i) q^{29} +(-0.512854 + 0.512854i) q^{31} +(6.87885 + 3.97151i) q^{32} +(-3.94969 + 1.05832i) q^{33} +(11.9905 + 6.92271i) q^{34} +5.70513i q^{36} +(-6.06955 + 0.400637i) q^{37} +(-7.55690 - 7.55690i) q^{38} +(-3.50812 + 13.0925i) q^{39} +(7.49700 + 4.32839i) q^{41} +(-6.58496 + 11.4055i) q^{42} -4.49647i 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} +(-9.39388 + 5.42356i) q^{52} +(-0.0327168 + 0.122101i) q^{53} +(-0.336369 - 0.0901297i) q^{54} +(0.269298 - 0.0721582i) q^{56} +(-11.3405 + 6.54742i) q^{57} +(1.52491 + 0.408598i) q^{58} +(9.18809 + 2.46194i) q^{59} +(-1.77087 - 6.60897i) q^{61} +(-0.373008 + 1.39209i) q^{62} +(5.63603 + 5.63603i) q^{63} +7.58249 q^{64} +(-5.74537 + 5.74537i) q^{66} +(8.44910 - 2.26393i) q^{67} +13.5764 q^{68} +(-5.40856 + 1.44922i) q^{69} +(-4.91365 + 8.51069i) q^{71} +(-0.149941 - 0.259705i) q^{72} +(0.804857 - 0.804857i) q^{73} +(-10.0468 + 6.71976i) q^{74} +(-10.1223 - 2.71227i) q^{76} +(-4.41593 + 1.18324i) q^{77} +(6.97089 + 26.0157i) q^{78} +(-2.57773 - 9.62023i) q^{79} +(-4.60538 + 7.97675i) q^{81} +17.2017 q^{82} +(1.88989 - 7.05316i) q^{83} +12.9140i q^{84} +(-4.46741 - 7.73777i) q^{86} +(0.967189 - 1.67522i) q^{87} +0.172004 q^{88} +(1.12526 - 4.19952i) q^{89} +(-3.92224 + 14.6380i) q^{91} +(-3.88065 - 2.24050i) q^{92} +(1.52931 + 0.882945i) q^{93} +(2.55659 - 9.54131i) q^{94} +(5.00537 - 18.6803i) q^{96} +9.54307 q^{97} +(-0.407529 + 0.705861i) q^{98} +(2.45872 + 4.25862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.72086	−	0.993536i	1.21683	−	0.702536i	0.252590	−	0.967573i	$-0.418718\pi$
$2$	1.72086	−	0.993536i	1.21683	−	0.702536i	0.964238	+	0.265037i	$0.0853842\pi$
$3$	−0.630160	−	2.35179i	−0.363823	−	1.35781i	−0.869009	−	0.494796i	$-0.835243\pi$
$3$	−0.630160	−	2.35179i	−0.363823	−	1.35781i	0.505186	−	0.863011i	$-0.331424\pi$
$4$	0.974229	−	1.68741i	0.487115	−	0.843707i
$5$		0			0
$5$		0			0
$6$	−3.42100	−	3.42100i	−1.39662	−	1.39662i
$7$	−0.704548	−	2.62941i	−0.266294	−	0.993823i	−0.961453	−	0.274968i	$-0.911333\pi$
$7$	−0.704548	−	2.62941i	−0.266294	−	0.993823i	0.695159	−	0.718856i	$-0.255334\pi$
$8$			0.102418i			0.0362101i
$9$	−2.53574	+	1.46401i	−0.845247	+	0.488004i
$10$		0			0
$11$		−	1.67944i		−	0.506370i	−0.967418	−	0.253185i	$-0.918522\pi$
$11$		−	1.67944i		−	0.506370i	0.967418	−	0.253185i	$-0.0814781\pi$
$12$	−4.58237	−	1.22784i	−1.32281	−	0.354447i
$13$	−4.82119	−	2.78351i	−1.33716	−	0.772008i	−0.350772	−	0.936461i	$-0.614081\pi$
$13$	−4.82119	−	2.78351i	−1.33716	−	0.772008i	−0.986385	+	0.164453i	$0.947414\pi$
$14$	−3.82484	−	3.82484i	−1.02223	−	1.02223i
$15$		0			0
$16$	2.05021	+	3.55107i	0.512553	+	0.887769i
$17$	3.48387	+	6.03425i	0.844964	+	1.46352i	0.885653	+	0.464348i	$0.153711\pi$
$17$	3.48387	+	6.03425i	0.844964	+	1.46352i	−0.0406892	+	0.999172i	$0.512955\pi$
$18$	−2.90910	+	5.03870i	−0.685680	+	1.18763i
$19$	−1.39201	−	5.19504i	−0.319348	−	1.19182i	−0.919873	−	0.392217i	$-0.871708\pi$
$19$	−1.39201	−	5.19504i	−0.319348	−	1.19182i	0.600524	−	0.799606i	$-0.294959\pi$
$20$		0			0
$21$	−5.73984	+	3.31390i	−1.25254	+	0.723152i
$22$	−1.66858	−	2.89007i	−0.355743	−	0.616165i
$23$		−	2.29976i		−	0.479534i	−0.970830	−	0.239767i	$-0.922929\pi$
$23$		−	2.29976i		−	0.479534i	0.970830	−	0.239767i	$-0.0770710\pi$
$24$	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
$28$	−5.12329	−	1.37278i	−0.968211	−	0.259431i
$29$	0.561787	+	0.561787i	0.104321	+	0.104321i	0.757341	−	0.653020i	$-0.226498\pi$
$29$	0.561787	+	0.561787i	0.104321	+	0.104321i	−0.653020	+	0.757341i	$0.726498\pi$
$30$		0			0
$31$	−0.512854	+	0.512854i	−0.0921113	+	0.0921113i	−0.751661	−	0.659550i	$-0.770747\pi$
$31$	−0.512854	+	0.512854i	−0.0921113	+	0.0921113i	0.659550	+	0.751661i	$0.270747\pi$
$32$	6.87885	+	3.97151i	1.21602	+	0.702070i
$33$	−3.94969	+	1.05832i	−0.687552	+	0.184229i
$34$	11.9905	+	6.92271i	2.05635	+	1.18724i
$35$		0			0
$36$			5.70513i			0.950854i
$37$	−6.06955	+	0.400637i	−0.997829	+	0.0658643i
$37$	−6.06955	+	0.400637i	−0.997829	+	0.0658643i
$38$	−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	0.953877	−	0.300199i	$-0.0970532\pi$
$41$	7.49700	+	4.32839i	1.17083	+	0.675982i	0.216958	+	0.976181i	$0.430387\pi$
$42$	−6.58496	+	11.4055i	−1.01608	+	1.75990i
$43$		−	4.49647i		−	0.685705i	−0.939389	−	0.342853i	$-0.888607\pi$
$43$		−	4.49647i		−	0.685705i	0.939389	−	0.342853i	$-0.111393\pi$
$44$	−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
$52$	−9.39388	+	5.42356i	−1.30270	+	0.752112i
$53$	−0.0327168	+	0.122101i	−0.00449400	+	0.0167718i	−0.968136	−	0.250423i	$-0.919430\pi$
$53$	−0.0327168	+	0.122101i	−0.00449400	+	0.0167718i	0.963642	+	0.267195i	$0.0860969\pi$
$54$	−0.336369	−	0.0901297i	−0.0457740	−	0.0122651i
$55$		0			0
$56$	0.269298	−	0.0721582i	0.0359865	−	0.00964254i
$57$	−11.3405	+	6.54742i	−1.50208	+	0.867227i
$58$	1.52491	+	0.408598i	0.200230	+	0.0536516i
$59$	9.18809	+	2.46194i	1.19619	+	0.320517i	0.801329	−	0.598224i	$-0.204127\pi$
$59$	9.18809	+	2.46194i	1.19619	+	0.320517i	0.394859	+	0.918742i	$0.370794\pi$
$60$		0			0
$61$	−1.77087	−	6.60897i	−0.226736	−	0.846192i	−0.981701	−	0.190427i	$-0.939013\pi$
$61$	−1.77087	−	6.60897i	−0.226736	−	0.846192i	0.754965	−	0.655765i	$-0.227654\pi$
$62$	−0.373008	+	1.39209i	−0.0473721	+	0.176795i
$63$	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
$67$	8.44910	−	2.26393i	1.03222	−	0.276583i	0.297335	−	0.954773i	$-0.403902\pi$
$67$	8.44910	−	2.26393i	1.03222	−	0.276583i	0.734886	+	0.678190i	$0.237235\pi$
$68$	13.5764			1.64638
$69$	−5.40856	+	1.44922i	−0.651114	+	0.174466i
$70$		0			0
$71$	−4.91365	+	8.51069i	−0.583143	+	1.01003i	0.411961	+	0.911201i	$0.364844\pi$
$71$	−4.91365	+	8.51069i	−0.583143	+	1.01003i	−0.995104	+	0.0988320i	$0.968489\pi$
$72$	−0.149941	−	0.259705i	−0.0176707	−	0.0306065i
$73$	0.804857	−	0.804857i	0.0942014	−	0.0942014i	−0.658436	−	0.752637i	$-0.728782\pi$
$73$	0.804857	−	0.804857i	0.0942014	−	0.0942014i	0.752637	+	0.658436i	$0.228782\pi$
$74$	−10.0468	+	6.71976i	−1.16791	+	0.781156i
$75$		0			0
$76$	−10.1223	−	2.71227i	−1.16111	−	0.311118i
$77$	−4.41593	+	1.18324i	−0.503242	+	0.134843i
$78$	6.97089	+	26.0157i	0.789298	+	2.94570i
$79$	−2.57773	−	9.62023i	−0.290018	−	1.08236i	−0.945094	−	0.326798i	$-0.894030\pi$
$79$	−2.57773	−	9.62023i	−0.290018	−	1.08236i	0.655076	−	0.755563i	$-0.272636\pi$
$80$		0			0
$81$	−4.60538	+	7.97675i	−0.511709	+	0.886305i
$82$	17.2017			1.89961
$83$	1.88989	−	7.05316i	0.207442	−	0.774185i	−0.781249	−	0.624219i	$-0.785417\pi$
$83$	1.88989	−	7.05316i	0.207442	−	0.774185i	0.988691	−	0.149965i	$-0.0479162\pi$
$84$			12.9140i			1.40903i
$85$		0			0
$86$	−4.46741	−	7.73777i	−0.481733	−	0.834386i
$87$	0.967189	−	1.67522i	0.103694	−	0.179603i
$88$	0.172004			0.0183357
$89$	1.12526	−	4.19952i	0.119277	−	0.445148i	−0.880294	−	0.474428i	$-0.842655\pi$
$89$	1.12526	−	4.19952i	0.119277	−	0.445148i	0.999571	+	0.0292801i	$0.00932149\pi$
$90$		0			0
$91$	−3.92224	+	14.6380i	−0.411162	+	1.53448i
$92$	−3.88065	−	2.24050i	−0.404586	−	0.233588i
$93$	1.52931	+	0.882945i	0.158582	+	0.0915571i
$94$	2.55659	−	9.54131i	0.263692	−	0.984111i
$95$		0			0
$96$	5.00537	−	18.6803i	0.510859	−	1.90655i
$97$	9.54307			0.968952			0.484476	−	0.874805i	$-0.339010\pi$
$97$	9.54307			0.968952			0.484476	+	0.874805i	$0.339010\pi$
$98$	−0.407529	+	0.705861i	−0.0411667	+	0.0713027i
$99$	2.45872	+	4.25862i	0.247110	+	0.428007i
$100$		0			0
$101$		−	16.8321i		−	1.67486i	−0.546548	−	0.837428i	$-0.684059\pi$
$101$		−	16.8321i		−	1.67486i	0.546548	−	0.837428i	$-0.315941\pi$
$102$	8.72484	−	32.5615i	0.863888	−	3.22407i
$103$	−7.86111			−0.774579			−0.387289	−	0.921958i	$-0.626589\pi$
$103$	−7.86111			−0.774579			−0.387289	+	0.921958i	$0.626589\pi$
$104$	0.285081	−	0.493775i	0.0279545	−	0.0484186i
$105$		0			0
$106$	0.0650107	+	0.242623i	0.00631440	+	0.0235657i
$107$	−0.746535	−	2.78611i	−0.0721703	−	0.269343i	0.920407	−	0.390963i	$-0.127858\pi$
$107$	−0.746535	−	2.78611i	−0.0721703	−	0.269343i	−0.992577	+	0.121620i	$0.961191\pi$
$108$	−0.329832	+	0.0883782i	−0.0317381	+	0.00850419i
$109$	0.520227	+	0.139395i	0.0498288	+	0.0133516i	0.283647	−	0.958929i	$-0.408456\pi$
$109$	0.520227	+	0.139395i	0.0498288	+	0.0133516i	−0.233819	+	0.972280i	$0.575122\pi$
$110$		0			0
$111$	4.76701	+	14.0219i	0.452464	+	1.33090i
$112$	7.89275	−	7.89275i	0.745795	−	0.745795i
$113$	8.29122	+	14.3608i	0.779973	+	1.35095i	0.931957	+	0.362569i	$0.118100\pi$
$113$	8.29122	+	14.3608i	0.779973	+	1.35095i	−0.151984	+	0.988383i	$0.548566\pi$
$114$	−13.0102	+	22.5343i	−1.21852	+	2.11053i
$115$		0			0
$116$	1.49528	−	0.400658i	0.138833	−	0.0372002i
$117$	16.3004			1.50697
$118$	18.2574	−	4.89206i	1.68073	−	0.450350i
$119$	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
$123$	5.45517	−	20.3590i	0.491876	−	1.83571i
$124$	0.365760	+	1.36503i	0.0328462	+	0.122584i
$125$		0			0
$126$	15.2984	+	4.09920i	1.36289	+	0.365185i
$127$	−18.1341	−	4.85902i	−1.60914	−	0.431168i	−0.661355	−	0.750073i	$-0.730018\pi$
$127$	−18.1341	−	4.85902i	−1.60914	−	0.431168i	−0.947787	+	0.318904i	$0.896685\pi$
$128$	−0.709335	+	0.409535i	−0.0626970	+	0.0361981i
$129$	−10.5748	+	2.83350i	−0.931055	+	0.249475i
$130$		0			0
$131$	6.02317	+	1.61390i	0.526247	+	0.141007i	0.512155	−	0.858893i	$-0.328847\pi$
$131$	6.02317	+	1.61390i	0.526247	+	0.141007i	0.0140923	+	0.999901i	$0.495514\pi$
$132$	−2.06208	+	7.69580i	−0.179481	+	0.669833i
$133$	−12.6791	+	7.32031i	−1.09942	+	0.634751i
$134$	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	−0.996014	−	0.0892018i	$-0.971568\pi$
$139$	−6.78219	−	11.7471i	−0.575258	−	0.996376i	0.420756	−	0.907174i	$-0.361765\pi$
$140$		0			0
$141$	−10.4818	−	6.05167i	−0.882727	−	0.509643i
$142$			19.5276i			1.63872i
$143$	−4.67474	+	8.09689i	−0.390921	+	0.677096i
$144$	−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
$148$	−5.23710	+	10.6322i	−0.430487	+	0.873958i
$149$			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	0.840732	−	0.541452i	$-0.182125\pi$
$151$	9.73455	+	5.62024i	0.792186	+	0.457369i	−0.0485454	+	0.998821i	$0.515459\pi$
$152$	0.532064	−	0.142566i	0.0431561	−	0.0115636i
$153$	−17.6684	−	10.2009i	−1.42841	−	0.824691i
$154$	−6.42358	+	6.42358i	−0.517627	+	0.517627i
$155$		0			0
$156$	18.6747	+	18.6747i	1.49518	+	1.49518i
$157$	9.24841	+	2.47810i	0.738103	+	0.197774i	0.608235	−	0.793757i	$-0.291878\pi$
$157$	9.24841	+	2.47810i	0.738103	+	0.197774i	0.129868	+	0.991531i	$0.458545\pi$
$158$	−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
$162$			18.3024i			1.43798i
$163$	4.93862	+	8.55394i	0.386823	+	0.669997i	0.992020	−	0.126079i	$-0.0402392\pi$
$163$	4.93862	+	8.55394i	0.386823	+	0.669997i	−0.605198	+	0.796075i	$0.706906\pi$
$164$	14.6076	−	8.43369i	1.14066	−	0.658561i
$165$		0			0
$166$	−3.75534	−	14.0151i	−0.291471	−	1.08779i
$167$	8.35752	−	14.4757i	0.646725	−	1.12016i	−0.337176	−	0.941442i	$-0.609472\pi$
$167$	8.35752	−	14.4757i	0.646725	−	1.12016i	0.983900	−	0.178718i	$-0.0571950\pi$
$168$	−0.339402	−	0.587861i	−0.0261854	−	0.0453545i
$169$	8.99590	+	15.5814i	0.691992	+	1.19857i
$170$		0			0
$171$	11.1354	+	11.1354i	0.851542	+	0.851542i
$172$	−7.58741	−	4.38059i	−0.578534	−	0.334017i
$173$	18.6858	+	5.00685i	1.42066	+	0.380664i	0.885717	−	0.464226i	$-0.153668\pi$
$173$	18.6858	+	5.00685i	1.42066	+	0.380664i	0.534940	+	0.844890i	$0.320334\pi$
$174$		−	3.84375i		−	0.291394i
$175$		0			0
$176$	5.96381	−	3.44321i	0.449539	−	0.259542i
$177$		−	23.1599i		−	1.74080i
$178$	−2.23597	−	8.34475i	−0.167593	−	0.625465i
$179$	0.796965	+	0.796965i	0.0595680	+	0.0595680i	0.736263	−	0.676695i	$-0.236589\pi$
$179$	0.796965	+	0.796965i	0.0595680	+	0.0595680i	−0.676695	+	0.736263i	$0.736589\pi$
$180$		0			0
$181$	3.50696	−	6.07423i	0.260670	−	0.451494i	−0.705750	−	0.708461i	$-0.749390\pi$
$181$	3.50696	−	6.07423i	0.260670	−	0.451494i	0.966420	+	0.256967i	$0.0827232\pi$
$182$	7.79377	+	29.0868i	0.577713	+	2.15605i
$183$	−14.4270	+	8.32942i	−1.06647	+	0.615729i
$184$	0.235536			0.0173640
$185$		0			0
$186$	3.50895			0.257289
$187$	10.1341	−	5.85095i	0.741082	−	0.427864i
$188$	−2.50691	−	9.35590i	−0.182835	−	0.682349i
$189$	−0.238530	+	0.413145i	−0.0173505	+	0.0300519i
$190$		0			0
$191$	8.62975	+	8.62975i	0.624427	+	0.624427i	0.946660	−	0.322233i	$-0.104434\pi$
$191$	8.62975	+	8.62975i	0.624427	+	0.624427i	−0.322233	+	0.946660i	$0.604434\pi$
$192$	−4.77818	−	17.8324i	−0.344836	−	1.28694i
$193$		−	9.26626i		−	0.667000i	−0.942750	−	0.333500i	$-0.891770\pi$
$193$		−	9.26626i		−	0.667000i	0.942750	−	0.333500i	$-0.108230\pi$
$194$	16.4222	−	9.48138i	1.17905	−	0.680724i
$195$		0			0
$196$			0.799219i			0.0570871i
$197$	−20.4415	−	5.47729i	−1.45640	−	0.390241i	−0.558154	−	0.829737i	$-0.688490\pi$
$197$	−20.4415	−	5.47729i	−1.45640	−	0.390241i	−0.898244	+	0.439496i	$0.855157\pi$
$198$	8.46219	+	4.88565i	0.601382	+	0.347208i
$199$	−10.0796	−	10.0796i	−0.714524	−	0.714524i	0.252954	−	0.967478i	$-0.418598\pi$
$199$	−10.0796	−	10.0796i	−0.714524	−	0.714524i	−0.967478	+	0.252954i	$0.918598\pi$
$200$		0			0
$201$	−10.6486	−	18.4439i	−0.751092	−	1.30093i
$202$	−16.7233	−	28.9656i	−1.17665	−	2.03801i
$203$	1.08136	−	1.87297i	0.0758967	−	0.131457i
$204$	−8.55529	−	31.9288i	−0.598990	−	2.23546i
$205$		0			0
$206$	−13.5278	+	7.81030i	−0.942529	+	0.544170i
$207$	3.36688	+	5.83160i	0.234014	+	0.405324i
$208$		−	22.8272i		−	1.58278i
$209$	−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
$213$	23.1118	+	6.19278i	1.58359	+	0.424322i
$214$	−4.05278	−	4.05278i	−0.277042	−	0.277042i
$215$		0			0
$216$	0.0126916	−	0.0126916i	0.000863557	−	0.000863557i
$217$	1.70983	+	0.987173i	0.116071	+	0.0670136i
$218$	1.03373	−	0.276987i	0.0700130	−	0.0187599i
$219$	−2.40004	−	1.38567i	−0.162180	−	0.0936346i
$220$		0			0
$221$		−	38.7897i		−	2.60927i
$222$	22.1346	+	19.3934i	1.48557	+	1.30160i
$223$	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
$227$	−6.09924	+	10.5642i	−0.404821	+	0.701171i	−0.994301	−	0.106613i	$-0.966000\pi$
$227$	−6.09924	+	10.5642i	−0.404821	+	0.701171i	0.589480	+	0.807783i	$0.299333\pi$
$228$			25.5147i			1.68975i
$229$	−6.92938	−	4.00068i	−0.457906	−	0.264372i	0.253257	−	0.967399i	$-0.418498\pi$
$229$	−6.92938	−	4.00068i	−0.457906	−	0.264372i	−0.711163	+	0.703027i	$0.751831\pi$
$230$		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	−0.985930	−	0.167160i	$-0.946540\pi$
$233$	−12.4980	+	12.4980i	−0.818769	+	0.818769i	0.167160	+	0.985930i	$0.446540\pi$
$234$	28.0506	−	16.1950i	1.83372	−	1.05870i
$235$		0			0
$236$	13.1056	−	13.1056i	0.853103	−	0.853103i
$237$	−21.0004	+	12.1246i	−1.36412	+	0.787576i
$238$	9.75477	−	36.4053i	0.632308	−	2.35980i
$239$	21.0290	+	5.63471i	1.36025	+	0.364479i	0.863910	−	0.503647i	$-0.168009\pi$
$239$	21.0290	+	5.63471i	1.36025	+	0.364479i	0.496344	+	0.868126i	$0.334675\pi$
$240$		0			0
$241$	2.79110	−	0.747874i	0.179791	−	0.0481748i	−0.167800	−	0.985821i	$-0.553666\pi$
$241$	2.79110	−	0.747874i	0.179791	−	0.0481748i	0.347591	+	0.937646i	$0.387000\pi$
$242$	14.0757	−	8.12662i	0.904821	−	0.522399i
$243$	21.1539	+	5.66818i	1.35703	+	0.363614i
$244$	−12.8773	−	3.45046i	−0.824385	−	0.220893i
$245$		0			0
$246$	−10.8398	−	40.4547i	−0.691121	−	2.57930i
$247$	−7.74934	+	28.9209i	−0.493079	+	1.84019i
$248$	−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	−0.927766	−	0.373162i	$-0.878273\pi$
$251$	−8.78658	+	8.78658i	−0.554604	+	0.554604i	0.373162	+	0.927766i	$0.378273\pi$
$252$	15.0011	−	4.01954i	0.944981	−	0.253207i
$253$	−3.86231			−0.242821
$254$	−36.0338	+	9.65523i	−2.26096	+	0.605823i
$255$		0			0
$256$	−8.39626	+	14.5428i	−0.524766	+	0.908922i
$257$	−8.05916	−	13.9589i	−0.502717	−	0.870731i	−0.999995	−	0.00313967i	$-0.999001\pi$
$257$	−8.05916	−	13.9589i	−0.502717	−	0.870731i	0.497279	−	0.867591i	$-0.334333\pi$
$258$	−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
$262$	11.9685	−	3.20695i	0.739415	−	0.198126i
$263$	2.31155	+	8.62681i	0.142536	+	0.531952i	0.999853	+	0.0171624i	$0.00546324\pi$
$263$	2.31155	+	8.62681i	0.142536	+	0.531952i	−0.857317	+	0.514789i	$0.827870\pi$
$264$	−0.108390	−	0.404518i	−0.00667096	−	0.0248964i
$265$		0			0
$266$	−14.5460	+	25.1944i	−0.891872	+	1.54477i
$267$	−10.5855			−0.647821
$268$	4.41117	−	16.4627i	0.269455	−	1.00562i
$269$		−	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	0.930746	+	0.365667i	$0.119159\pi$
$271$	12.8742	+	22.2987i	0.782050	+	1.35455i	−0.148696	+	0.988883i	$0.547507\pi$
$272$	−14.2854	+	24.7430i	−0.866178	+	1.50026i
$273$	36.8971			2.23312
$274$	−4.89993	+	18.2868i	−0.296016	+	1.10475i
$275$		0			0
$276$	−2.82374	+	10.5384i	−0.169969	+	0.634334i
$277$	25.1190	+	14.5025i	1.50925	+	0.871368i	0.999942	+	0.0107863i	$0.00343344\pi$
$277$	25.1190	+	14.5025i	1.50925	+	0.871368i	0.509312	+	0.860582i	$0.329900\pi$
$278$	−23.3423	−	13.4767i	−1.39998	−	0.808279i
$279$	0.549641	−	2.05129i	0.0329062	−	0.122807i
$280$		0			0
$281$	1.36182	−	5.08238i	0.0812394	−	0.303190i	−0.913336	−	0.407207i	$-0.866503\pi$
$281$	1.36182	−	5.08238i	0.0812394	−	0.303190i	0.994576	+	0.104017i	$0.0331696\pi$
$282$	−24.0502			−1.43217
$283$	−7.95697	+	13.7819i	−0.472993	+	0.819248i	−0.999522	−	0.0309093i	$-0.990160\pi$
$283$	−7.95697	+	13.7819i	−0.472993	+	0.819248i	0.526529	+	0.850157i	$0.323493\pi$
$284$	9.57404	+	16.5827i	0.568115	+	0.984004i
$285$		0			0
$286$			18.5781i			1.09855i
$287$	6.09912	−	22.7622i	0.360020	−	1.34361i
$288$	−23.2573			−1.37045
$289$	−15.7748	+	27.3227i	−0.927927	+	1.60722i
$290$		0			0
$291$	−6.01366	−	22.4433i	−0.352527	−	1.31565i
$292$	−0.574012	−	2.14224i	−0.0335915	−	0.125365i
$293$	−20.4696	+	5.48481i	−1.19585	+	0.320426i	−0.801194	−	0.598405i	$-0.795801\pi$
$293$	−20.4696	+	5.48481i	−1.19585	+	0.320426i	−0.394651	+	0.918831i	$0.629135\pi$
$294$	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
$298$	6.42427	+	11.1272i	0.372148	+	0.644579i
$299$	−6.40142	+	11.0876i	−0.370204	+	0.641212i
$300$		0			0
$301$	−11.8231	+	3.16798i	−0.681470	+	0.182599i
$302$	22.3357			1.28527
$303$	−39.5855	+	10.6069i	−2.27413	+	0.609351i
$304$	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	$0.0152785\pi$
$307$	18.3419	+	18.3419i	1.04683	+	1.04683i	0.0479805	+	0.998848i	$0.484721\pi$
$308$	−2.30550	+	8.60425i	−0.131368	+	0.490273i
$309$	4.95376	+	18.4877i	0.281810	+	1.05173i
$310$		0			0
$311$	−5.37036	−	1.43898i	−0.304525	−	0.0815973i	0.103321	−	0.994648i	$-0.467053\pi$
$311$	−5.37036	−	1.43898i	−0.304525	−	0.0815973i	−0.407846	+	0.913051i	$0.633720\pi$
$312$	−1.34090	−	0.359294i	−0.0759136	−	0.0203410i
$313$	−5.29504	+	3.05709i	−0.299294	+	0.172797i	−0.642125	−	0.766600i	$-0.721947\pi$
$313$	−5.29504	+	3.05709i	−0.299294	+	0.172797i	0.342832	+	0.939397i	$0.388614\pi$
$314$	18.3773	−	4.92417i	1.03709	−	0.277887i
$315$		0			0
$316$	−18.7446	−	5.02261i	−1.05447	−	0.282544i
$317$	−6.99103	+	26.0909i	−0.392655	+	1.46541i	0.433082	+	0.901354i	$0.357426\pi$
$317$	−6.99103	+	26.0909i	−0.392655	+	1.46541i	−0.825737	+	0.564055i	$0.809241\pi$
$318$	0.529632	−	0.305783i	0.0297003	−	0.0171475i
$319$	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
$327$		−	1.31131i		−	0.0725154i
$328$	−0.443304	+	0.767825i	−0.0244774	+	0.0423961i
$329$	−11.7191	−	6.76605i	−0.646097	−	0.373024i
$330$		0			0
$331$	−2.23150	+	8.32808i	−0.122655	+	0.457753i	−0.999745	−	0.0225719i	$-0.992815\pi$
$331$	−2.23150	+	8.32808i	−0.122655	+	0.457753i	0.877091	+	0.480325i	$0.159481\pi$
$332$	−10.0604	−	10.0604i	−0.552137	−	0.552137i
$333$	14.8043	−	9.90180i	0.811270	−	0.542615i
$334$		−	33.2140i		−	1.81739i
$335$		0			0
$336$	−23.5358	−	13.5884i	−1.28398	−	0.741308i
$337$	−1.54567	+	0.414161i	−0.0841979	+	0.0225608i	−0.300672	−	0.953728i	$-0.597211\pi$
$337$	−1.54567	+	0.414161i	−0.0841979	+	0.0225608i	0.216474	+	0.976288i	$0.430544\pi$
$338$	30.9613	+	17.8755i	1.68407	+	0.972300i
$339$	28.5488	−	28.5488i	1.55056	−	1.55056i
$340$		0			0
$341$	0.861307	+	0.861307i	0.0466424	+	0.0466424i
$342$	30.2257	+	8.09896i	1.63442	+	0.437942i
$343$	−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
$347$		−	17.9655i		−	0.964438i	−0.876051	−	0.482219i	$-0.839831\pi$
$347$		−	17.9655i		−	0.964438i	0.876051	−	0.482219i	$-0.160169\pi$
$348$	−1.88453	−	3.26410i	−0.101021	−	0.174974i
$349$	21.5887	−	12.4642i	1.15562	−	0.667195i	0.205366	−	0.978685i	$-0.434162\pi$
$349$	21.5887	−	12.4642i	1.15562	−	0.667195i	0.950249	+	0.311490i	$0.100828\pi$
$350$		0			0
$351$	0.252509	+	0.942378i	0.0134780	+	0.0503004i
$352$	6.66990	−	11.5526i	0.355507	−	0.615756i
$353$	−0.198621	−	0.344022i	−0.0105715	−	0.0183104i	0.860691	−	0.509127i	$-0.170032\pi$
$353$	−0.198621	−	0.344022i	−0.0105715	−	0.0183104i	−0.871263	+	0.490817i	$0.836698\pi$
$354$	−23.0102	−	39.8548i	−1.22298	−	2.11826i
$355$		0			0
$356$	−5.99007	−	5.99007i	−0.317473	−	0.317473i
$357$	−39.9938	−	23.0904i	−2.11669	−	1.22207i
$358$	2.16328	+	0.579648i	0.114333	+	0.0306354i
$359$			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
$362$		−	13.9372i		−	0.732521i
$363$	−5.15439	−	19.2364i	−0.270535	−	1.00965i
$364$	20.8792	+	20.8792i	1.09437	+	1.09437i
$365$		0			0
$366$	−16.5512	+	28.6675i	−0.865144	+	1.49847i
$367$	3.95597	+	14.7639i	0.206500	+	0.770668i	0.988987	+	0.148001i	$0.0472840\pi$
$367$	3.95597	+	14.7639i	0.206500	+	0.770668i	−0.782487	+	0.622666i	$0.786049\pi$
$368$	8.16663	−	4.71501i	0.425715	−	0.245787i
$369$	−25.3473			−1.31953
$370$		0			0
$371$	0.344104			0.0178650
$372$	2.97979	−	1.72038i	0.154495	−	0.0891976i
$373$	9.45368	+	35.2816i	0.489493	+	1.82681i	0.558915	+	0.829225i	$0.311218\pi$
$373$	9.45368	+	35.2816i	0.489493	+	1.82681i	−0.0694227	+	0.997587i	$0.522116\pi$
$374$	11.6263	−	20.1373i	0.601180	−	1.04127i
$375$		0			0
$376$	0.360007	+	0.360007i	0.0185659	+	0.0185659i
$377$	−1.14474	−	4.27222i	−0.0589570	−	0.220031i
$378$			0.947951i			0.0487573i
$379$	−19.1447	+	11.0532i	−0.983399	+	0.567765i	−0.903294	−	0.429021i	$-0.858859\pi$
$379$	−19.1447	+	11.0532i	−0.983399	+	0.567765i	−0.0801041	+	0.996787i	$0.525525\pi$
$380$		0			0
$381$			45.7096i			2.34177i
$382$	23.4245	+	6.27658i	1.19850	+	0.321138i
$383$	11.9728	+	6.91250i	0.611781	+	0.353212i	0.773662	−	0.633598i	$-0.218423\pi$
$383$	11.9728	+	6.91250i	0.611781	+	0.353212i	−0.161881	+	0.986810i	$0.551756\pi$
$384$	1.41013	+	1.41013i	0.0719606	+	0.0719606i
$385$		0			0
$386$	−9.20636	−	15.9459i	−0.468592	−	0.811624i
$387$	6.58288	+	11.4019i	0.334627	+	0.579590i
$388$	9.29713	−	16.1031i	0.471990	−	0.817511i
$389$	2.77714	+	10.3644i	0.140806	+	0.525496i	0.999906	+	0.0136886i	$0.00435736\pi$
$389$	2.77714	+	10.3644i	0.140806	+	0.525496i	−0.859100	+	0.511808i	$0.828976\pi$
$390$		0			0
$391$	13.8773	−	8.01208i	0.701807	−	0.405189i
$392$	−0.0210049	−	0.0363815i	−0.00106091	−	0.00183754i
$393$		−	15.1823i		−	0.765844i
$394$	−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	0.145713	−	0.989327i	$-0.453452\pi$
$397$	−16.8089	−	16.8089i	−0.843614	−	0.843614i	−0.989327	+	0.145713i	$0.953452\pi$
$398$	−27.3600	−	7.33109i	−1.37143	−	0.367474i
$399$	25.2057	+	25.2057i	1.26187	+	1.26187i
$400$		0			0
$401$	10.5045	−	10.5045i	0.524569	−	0.524569i	−0.394379	−	0.918948i	$-0.629040\pi$
$401$	10.5045	−	10.5045i	0.524569	−	0.524569i	0.918948	+	0.394379i	$0.129040\pi$
$402$	−36.6493	−	21.1595i	−1.82790	−	1.05534i
$403$	3.90010	−	1.04503i	0.194278	−	0.0520566i
$404$	−28.4027	−	16.3983i	−1.41309	−	0.815846i
$405$		0			0
$406$		−	4.29749i		−	0.213281i
$407$	0.672844	+	10.1934i	0.0333517	+	0.505270i
$408$	1.22859	+	1.22859i	0.0608243	+	0.0608243i
$409$	−6.05393	+	22.5936i	−0.299348	+	1.11718i	0.638355	+	0.769742i	$0.279615\pi$
$409$	−6.05393	+	22.5936i	−0.299348	+	1.11718i	−0.937703	+	0.347438i	$0.887052\pi$
$410$		0			0
$411$	20.0893	+	11.5986i	0.990934	+	0.572116i
$412$	−7.65853	+	13.2650i	−0.377308	+	0.653517i
$413$		−	25.8938i		−	1.27415i
$414$	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	$-0.857657\pi$
$419$	−20.0193	+	11.5582i	−0.978009	+	0.564654i	−0.0763404	+	0.997082i	$0.524324\pi$
$420$		0			0
$421$	0.796474	−	0.796474i	0.0388178	−	0.0388178i	−0.687431	−	0.726249i	$-0.741262\pi$
$421$	0.796474	−	0.796474i	0.0388178	−	0.0388178i	0.726249	+	0.687431i	$0.241262\pi$
$422$	15.7654	−	9.10213i	0.767445	−	0.443085i
$423$	−3.76722	+	14.0595i	−0.183169	+	0.683594i
$424$	−0.0125053	−	0.00335078i	−0.000607310	−	0.000162728i
$425$		0			0
$426$	45.9247	−	12.3055i	2.22506	−	0.596203i
$427$	−16.1300	+	9.31268i	−0.780587	+	0.450672i
$428$	−5.42861	−	1.45459i	−0.262402	−	0.0703104i
$429$	21.9880	+	5.89167i	1.06159	+	0.284453i
$430$		0			0
$431$	−6.09536	−	22.7482i	−0.293603	−	1.09574i	−0.942320	−	0.334713i	$-0.891361\pi$
$431$	−6.09536	−	22.7482i	−0.293603	−	1.09574i	0.648717	−	0.761030i	$-0.275306\pi$
$432$	0.185987	−	0.694114i	0.00894832	−	0.0333956i
$433$	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
$437$	−11.9474	+	3.20129i	−0.571520	+	0.153138i
$438$	−5.50684			−0.263127
$439$	3.56774	−	0.955972i	0.170279	−	0.0456261i	−0.172672	−	0.984979i	$-0.555240\pi$
$439$	3.56774	−	0.955972i	0.170279	−	0.0456261i	0.342951	+	0.939353i	$0.388573\pi$
$440$		0			0
$441$	0.600508	−	1.04011i	0.0285956	−	0.0495291i
$442$	−38.5389	−	66.7514i	−1.83311	−	3.17504i
$443$	−25.0265	+	25.0265i	−1.18905	+	1.18905i	−0.211714	+	0.977332i	$0.567905\pi$
$443$	−25.0265	+	25.0265i	−1.18905	+	1.18905i	−0.977332	+	0.211714i	$0.932095\pi$
$444$	28.3048	+	5.61659i	1.34329	+	0.266551i
$445$		0			0
$446$	20.8265	+	5.58044i	0.986163	+	0.264242i
$447$	15.2068	−	4.07466i	0.719258	−	0.192725i
$448$	−5.34223	−	19.9375i	−0.252397	−	0.941957i
$449$	−2.73747	−	10.2164i	−0.129189	−	0.482141i	0.870765	−	0.491699i	$-0.163624\pi$
$449$	−2.73747	−	10.2164i	−0.129189	−	0.482141i	−0.999954	+	0.00955863i	$0.996957\pi$
$450$		0			0
$451$	7.26927	−	12.5907i	0.342297	−	0.592875i
$452$	32.3102			1.51974
$453$	7.08331	−	26.4353i	0.332803	−	1.24204i
$454$			24.2393i			1.13761i
$455$		0			0
$456$	−0.670571	−	1.16146i	−0.0314024	−	0.0543905i
$457$	15.0696	−	26.1013i	0.704927	−	1.22097i	−0.261791	−	0.965125i	$-0.584313\pi$
$457$	15.0696	−	26.1013i	0.704927	−	1.22097i	0.966718	−	0.255845i	$-0.0823536\pi$
$458$	−15.8993			−0.742924
$459$	0.316043	−	1.17949i	0.0147516	−	0.0550538i
$460$		0			0
$461$	−3.05838	+	11.4140i	−0.142443	+	0.531605i	0.857413	+	0.514629i	$0.172070\pi$
$461$	−3.05838	+	11.4140i	−0.142443	+	0.531605i	−0.999856	+	0.0169755i	$0.994596\pi$
$462$	19.1548	+	11.0590i	0.891162	+	0.514513i
$463$	15.0903	+	8.71241i	0.701307	+	0.404900i	0.807834	−	0.589410i	$-0.200640\pi$
$463$	15.0903	+	8.71241i	0.701307	+	0.404900i	−0.106527	+	0.994310i	$0.533973\pi$
$464$	−0.843164	+	3.14673i	−0.0391429	+	0.146083i
$465$		0			0
$466$	−9.09001	+	33.9244i	−0.421087	+	1.57152i
$467$	10.9228			0.505446			0.252723	−	0.967539i	$-0.418674\pi$
$467$	10.9228			0.505446			0.252723	+	0.967539i	$0.418674\pi$
$468$	15.8803	−	27.5055i	0.734067	−	1.27144i
$469$	−11.9056	−	20.6211i	−0.549749	−	0.952193i
$470$		0			0
$471$		−	23.3119i		−	1.07416i
$472$	−0.252146	+	0.941023i	−0.0116060	+	0.0433141i
$473$	−7.55154			−0.347220
$474$	−24.0924	+	41.7293i	−1.10660	+	1.91669i
$475$		0			0
$476$	−9.56520	−	35.6978i	−0.438420	−	1.63621i
$477$	−0.0957956	−	0.357514i	−0.00438618	−	0.0163694i
$478$	41.7862	−	11.1966i	1.91126	−	0.512119i
$479$	−8.05522	−	2.15839i	−0.368052	−	0.0986194i	0.0700522	−	0.997543i	$-0.477683\pi$
$479$	−8.05522	−	2.15839i	−0.368052	−	0.0986194i	−0.438105	+	0.898924i	$0.644350\pi$
$480$		0			0
$481$	30.3776	+	14.9631i	1.38510	+	0.682261i
$482$	4.06005	−	4.06005i	0.184930	−	0.184930i
$483$	7.62118	+	13.2003i	0.346776	+	0.600633i
$484$	7.96869	−	13.8022i	0.362213	−	0.627372i
$485$		0			0
$486$	42.0344	−	11.2631i	1.90672	−	0.510904i
$487$	8.29876			0.376053			0.188026	−	0.982164i	$-0.439791\pi$
$487$	8.29876			0.376053			0.188026	+	0.982164i	$0.439791\pi$
$488$	0.676876	−	0.181368i	0.0306407	−	0.00821016i
$489$	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
$493$	−1.43277	+	5.34715i	−0.0645285	+	0.240824i
$494$	15.3985	+	57.4680i	0.692811	+	2.58561i
$495$		0			0
$496$	−2.87264	−	0.769722i	−0.128985	−	0.0345616i
$497$	25.8400	+	6.92381i	1.15908	+	0.310575i
$498$	−30.5942	+	17.6636i	−1.37096	+	0.791523i
$499$	−1.94647	+	0.521555i	−0.0871360	+	0.0233480i	−0.302124	−	0.953269i	$-0.597696\pi$
$499$	−1.94647	+	0.521555i	−0.0871360	+	0.0233480i	0.214988	+	0.976617i	$0.431029\pi$
$500$		0			0
$501$	−39.3103	−	10.5332i	−1.75625	−	0.470587i
$502$	−6.39064	+	23.8502i	−0.285228	+	1.06449i
$503$	27.6417	−	15.9589i	1.23248	−	0.711574i	0.264936	−	0.964266i	$-0.414649\pi$
$503$	27.6417	−	15.9589i	1.23248	−	0.711574i	0.967547	+	0.252692i	$0.0813159\pi$
$504$	−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	$-0.211433\pi$
$509$	−3.16251	−	5.47763i	−0.140176	−	0.242792i	−0.927563	+	0.373667i	$0.878100\pi$
$510$		0			0
$511$	−2.68336	−	1.54924i	−0.118705	−	0.0685342i
$512$			31.7298i			1.40227i
$513$	−0.471273	+	0.816269i	−0.0208072	+	0.0360392i
$514$	−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
$518$	24.7474	+	21.6827i	1.08734	+	0.952683i
$519$		−	47.1003i		−	2.06747i
$520$		0			0
$521$	−11.6555	−	6.72930i	−0.510637	−	0.294816i	0.222459	−	0.974942i	$-0.428592\pi$
$521$	−11.6555	−	6.72930i	−0.510637	−	0.294816i	−0.733095	+	0.680126i	$0.761925\pi$
$522$	−4.46497	+	1.19638i	−0.195426	+	0.0523643i
$523$	29.5603	+	17.0666i	1.29258	+	0.746272i	0.979111	−	0.203326i	$-0.0651750\pi$
$523$	29.5603	+	17.0666i	1.29258	+	0.746272i	0.313470	+	0.949598i	$0.398508\pi$
$524$	8.59127	−	8.59127i	0.375312	−	0.375312i
$525$		0			0
$526$	12.5489	+	12.5489i	0.547158	+	0.547158i
$527$	−4.88141	−	1.30797i	−0.212637	−	0.0569760i
$528$	−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
$532$			28.5266i			1.23679i
$533$	−24.0963	−	41.7360i	−1.04373	−	1.80779i
$534$	−18.2161	+	10.5171i	−0.788287	+	0.455118i
$535$		0			0
$536$	0.231866	+	0.865337i	0.0100151	+	0.0373769i
$537$	1.37208	−	2.37651i	0.0592096	−	0.102554i
$538$	−4.43058	−	7.67399i	−0.191016	−	0.330849i
$539$	0.344436	+	0.596581i	0.0148359	+	0.0256966i
$540$		0			0
$541$	−20.9871	−	20.9871i	−0.902306	−	0.902306i	0.0933293	−	0.995635i	$-0.470249\pi$
$541$	−20.9871	−	20.9871i	−0.902306	−	0.902306i	−0.995635	+	0.0933293i	$0.970249\pi$
$542$	44.3092	+	25.5819i	1.90324	+	1.09884i
$543$	−16.4953	−	4.41989i	−0.707879	−	0.189676i
$544$			55.3449i			2.37289i
$545$		0			0
$546$	63.4946	−	36.6586i	2.71732	−	1.56885i
$547$			26.7961i			1.14572i	0.819654	+	0.572859i	$0.194166\pi$
$547$			26.7961i			1.14572i	−0.819654	+	0.572859i	$0.805834\pi$
$548$	4.80471	+	17.9314i	0.205247	+	0.765993i
$549$	14.1661	+	14.1661i	0.604593	+	0.604593i
$550$		0			0
$551$	2.13649	−	3.70052i	0.0910177	−	0.157647i
$552$	−0.148426	−	0.553932i	−0.00631742	−	0.0235769i
$553$	−23.4794	+	13.5558i	−0.998445	+	0.576453i
$554$	57.6349			2.44867
$555$		0			0
$556$	−26.4296			−1.12087
$557$	−2.45586	+	1.41789i	−0.104058	+	0.0600781i	−0.551126	−	0.834422i	$-0.685802\pi$
$557$	−2.45586	+	1.41789i	−0.104058	+	0.0600781i	0.447068	+	0.894500i	$0.352468\pi$
$558$	−1.09218	−	4.07606i	−0.0462355	−	0.172553i
$559$	−12.5160	+	21.6783i	−0.529370	+	0.916895i
$560$		0			0
$561$	−20.1463	−	20.1463i	−0.850580	−	0.850580i
$562$	−2.70604	−	10.0991i	−0.114147	−	0.426003i
$563$		−	18.8024i		−	0.792425i	−0.918159	−	0.396212i	$-0.870324\pi$
$563$		−	18.8024i		−	0.792425i	0.918159	−	0.396212i	$-0.129676\pi$
$564$	−20.4234	+	11.7914i	−0.859979	+	0.496509i
$565$		0			0
$566$			31.6222i			1.32918i
$567$	24.2188	+	6.48942i	1.01710	+	0.272530i
$568$	−0.871646	−	0.503245i	−0.0365734	−	0.0211157i
$569$	12.7829	+	12.7829i	0.535887	+	0.535887i	0.922318	−	0.386431i	$-0.126292\pi$
$569$	12.7829	+	12.7829i	0.535887	+	0.535887i	−0.386431	+	0.922318i	$0.626292\pi$
$570$		0			0
$571$	−8.53388	−	14.7811i	−0.357132	−	0.618570i	0.630349	−	0.776312i	$-0.282912\pi$
$571$	−8.53388	−	14.7811i	−0.357132	−	0.618570i	−0.987480	+	0.157742i	$0.949579\pi$
$572$	9.10853	+	15.7764i	0.380847	+	0.659646i
$573$	14.8572	−	25.7335i	0.620670	−	1.07503i
$574$	−12.1194	−	45.2302i	−0.505854	−	1.88787i
$575$		0			0
$576$	−19.2272	+	11.1008i	−0.801134	+	0.462535i
$577$	−12.0314	−	20.8390i	−0.500875	−	0.867541i	−0.999999	−	0.00101057i	$-0.999678\pi$
$577$	−12.0314	−	20.8390i	−0.500875	−	0.867541i	0.499125	−	0.866530i	$-0.333655\pi$
$578$			62.6912i			2.60761i
$579$	−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
$583$	0.205061	+	0.0549459i	0.00849275	+	0.00227563i
$584$	0.0824316	+	0.0824316i	0.00341104	+	0.00341104i
$585$		0			0
$586$	−29.7758	+	29.7758i	−1.23003	+	1.23003i
$587$	−9.49077	−	5.47950i	−0.391726	−	0.226163i	0.291182	−	0.956668i	$-0.405952\pi$
$587$	−9.49077	−	5.47950i	−0.391726	−	0.226163i	−0.682908	+	0.730505i	$0.739285\pi$
$588$	1.87960	−	0.503636i	0.0775132	−	0.0207696i
$589$	3.37819	+	1.95040i	0.139196	+	0.0803649i
$590$		0			0
$591$			51.5258i			2.11949i
$592$	−13.8666	−	20.7320i	−0.569913	−	0.852082i
$593$	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
$597$	−17.3534	+	30.0569i	−0.710225	+	1.23015i
$598$			25.4402i			1.04033i
$599$	−14.9856	−	8.65196i	−0.612297	−	0.353510i	0.161567	−	0.986862i	$-0.448345\pi$
$599$	−14.9856	−	8.65196i	−0.612297	−	0.353510i	−0.773864	+	0.633352i	$0.781679\pi$
$600$		0			0
$601$	−14.5641	−	25.2257i	−0.594080	−	1.02898i	−0.993676	−	0.112286i	$-0.964183\pi$
$601$	−14.5641	−	25.2257i	−0.594080	−	1.02898i	0.399596	−	0.916692i	$-0.369151\pi$
$602$	−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
$607$	19.2374	−	11.1067i	0.780822	−	0.450808i	−0.0558995	−	0.998436i	$-0.517803\pi$
$607$	19.2374	−	11.1067i	0.780822	−	0.450808i	0.836722	+	0.547629i	$0.184469\pi$
$608$	11.0567	−	41.2643i	0.448409	−	1.67349i
$609$	−5.08627	−	1.36286i	−0.206106	−	0.0552260i
$610$		0			0
$611$	−26.7312	+	7.16259i	−1.08143	+	0.289768i
$612$	−34.4261	+	19.8759i	−1.39159	+	0.803437i
$613$	−14.0207	−	3.75684i	−0.566292	−	0.151737i	−0.0356964	−	0.999363i	$-0.511365\pi$
$613$	−14.0207	−	3.75684i	−0.566292	−	0.151737i	−0.530595	+	0.847625i	$0.678032\pi$
$614$	49.7872	+	13.3404i	2.00925	+	0.538376i
$615$		0			0
$616$	−0.121185	−	0.452269i	−0.00488269	−	0.0182225i
$617$	3.60314	−	13.4471i	0.145057	−	0.541360i	−0.854696	−	0.519129i	$-0.826256\pi$
$617$	3.60314	−	13.4471i	0.145057	−	0.541360i	0.999753	−	0.0222308i	$-0.00707688\pi$
$618$	26.8929	+	26.8929i	1.08179	+	1.08179i
$619$	−4.87562			−0.195968			−0.0979838	−	0.995188i	$-0.531239\pi$
$619$	−4.87562			−0.195968			−0.0979838	+	0.995188i	$0.531239\pi$
$620$		0			0
$621$	−0.284988	+	0.284988i	−0.0114362	+	0.0114362i
$622$	−10.6713	+	2.85937i	−0.427880	+	0.114650i
$623$	−11.8351			−0.474161
$624$	−53.6848	+	14.3848i	−2.14911	+	0.575853i
$625$		0			0
$626$	−6.07467	+	10.5216i	−0.242793	+	0.420529i
$627$	10.9960	+	19.0456i	0.439137	+	0.760608i
$628$	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	0.0100498	−	0.999949i	$-0.496801\pi$
$631$	−12.0881	−	3.23901i	−0.481222	−	0.128943i	−0.491271	+	0.871007i	$0.663468\pi$
$632$	0.985282	−	0.264006i	0.0391924	−	0.0105016i
$633$	−5.77312	−	21.5456i	−0.229461	−	0.856359i
$634$	13.8917	+	51.8444i	0.551709	+	2.05901i
$635$		0			0
$636$	0.299841	−	0.519340i	0.0118895	−	0.0205932i
$637$	2.28349			0.0904750
$638$	0.686216	−	2.56099i	0.0271675	−	0.101391i
$639$		−	28.7746i		−	1.13830i
$640$		0			0
$641$	6.83773	+	11.8433i	0.270074	+	0.467782i	0.968881	−	0.247529i	$-0.0796184\pi$
$641$	6.83773	+	11.8433i	0.270074	+	0.467782i	−0.698806	+	0.715311i	$0.746285\pi$
$642$	−6.97739	+	12.0852i	−0.275375	+	0.476964i
$643$	−38.4862			−1.51775			−0.758873	−	0.651239i	$-0.774250\pi$
$643$	−38.4862			−1.51775			−0.758873	+	0.651239i	$0.774250\pi$
$644$	−3.15707	+	11.7824i	−0.124406	+	0.464290i
$645$		0			0
$646$	19.2729	−	71.9275i	0.758283	−	2.82995i
$647$	−12.3517	−	7.13127i	−0.485596	−	0.280359i	0.237150	−	0.971473i	$-0.423787\pi$
$647$	−12.3517	−	7.13127i	−0.485596	−	0.280359i	−0.722746	+	0.691114i	$0.757120\pi$
$648$	−0.816960	−	0.471672i	−0.0320932	−	0.0185290i
$649$	4.13468	−	15.4308i	0.162300	−	0.605713i
$650$		0			0
$651$	1.24415	−	4.64325i	0.0487622	−	0.181983i
$652$	19.2454			0.753708
$653$	23.5671	−	40.8194i	0.922253	−	1.59739i	0.126332	−	0.991988i	$-0.459680\pi$
$653$	23.5671	−	40.8194i	0.922253	−	1.59739i	0.795921	−	0.605400i	$-0.206987\pi$
$654$	−1.30283	−	2.25657i	−0.0509447	−	0.0882389i
$655$		0			0
$656$			35.4965i			1.38591i
$657$	−0.862589	+	3.21923i	−0.0336528	+	0.125594i
$658$	−26.8893			−1.04825
$659$	15.9643	−	27.6509i	0.621880	−	1.07713i	−0.367256	−	0.930120i	$-0.619703\pi$
$659$	15.9643	−	27.6509i	0.621880	−	1.07713i	0.989135	−	0.147007i	$-0.0469641\pi$
$660$		0			0
$661$	0.934896	+	3.48908i	0.0363632	+	0.135709i	0.981721	−	0.190325i	$-0.0609541\pi$
$661$	0.934896	+	3.48908i	0.0363632	+	0.135709i	−0.945358	+	0.326034i	$0.894287\pi$
$662$	4.43416	+	16.5485i	0.172338	+	0.643176i
$663$	−91.2251	+	24.4437i	−3.54289	+	0.949315i
$664$	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
$668$	−16.2843	−	28.2052i	−0.630058	−	1.09129i
$669$	13.2094	−	22.8794i	0.510705	−	0.884568i
$670$		0			0
$671$	−11.0994	+	2.97406i	−0.428486	+	0.114812i
$672$	−52.6447			−2.03081
$673$	−21.5231	+	5.76709i	−0.829654	+	0.222305i	−0.648563	−	0.761161i	$-0.724630\pi$
$673$	−21.5231	+	5.76709i	−0.829654	+	0.222305i	−0.181091	+	0.983466i	$0.557963\pi$
$674$	−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	0.962808	−	0.270185i	$-0.0870849\pi$
$677$	18.0215	+	18.0215i	0.692623	+	0.692623i	−0.270185	+	0.962808i	$0.587085\pi$
$678$	20.7641	−	77.4927i	0.797441	−	2.97609i
$679$	−6.72355	−	25.0926i	−0.258026	−	0.962967i
$680$		0			0
$681$	28.6883	+	7.68700i	1.09934	+	0.294567i
$682$	2.33792	+	0.626445i	0.0895237	+	0.0239878i
$683$	15.8005	−	9.12242i	0.604589	−	0.349060i	−0.166256	−	0.986083i	$-0.553168\pi$
$683$	15.8005	−	9.12242i	0.604589	−	0.349060i	0.770845	+	0.637023i	$0.219834\pi$
$684$	29.6384	−	7.94157i	1.13325	−	0.303654i
$685$		0			0
$686$	−34.4307	−	9.22567i	−1.31457	−	0.352238i
$687$	−5.04214	+	18.8175i	−0.192370	+	0.717933i
$688$	15.9673	−	9.21872i	0.608747	−	0.351460i
$689$	0.497603	−	0.497603i	0.0189572	−	0.0189572i
$690$		0			0
$691$	−26.8608	+	15.5081i	−1.02183	+	0.589957i	−0.914635	−	0.404281i	$-0.867522\pi$
$691$	−26.8608	+	15.5081i	−1.02183	+	0.589957i	−0.107200	+	0.994237i	$0.534189\pi$
$692$	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
$697$			60.3183i			2.28472i
$698$	24.7673	−	42.8983i	0.937457	−	1.62372i
$699$	37.2683	+	21.5169i	1.40962	+	0.813843i
$700$		0			0
$701$	1.72147	−	6.42463i	0.0650192	−	0.242655i	−0.925766	−	0.378097i	$-0.876579\pi$
$701$	1.72147	−	6.42463i	0.0650192	−	0.242655i	0.990785	+	0.135442i	$0.0432454\pi$
$702$	1.37082	+	1.37082i	0.0517382	+	0.0517382i
$703$	10.5302	+	30.9739i	0.397153	+	1.16820i
$704$		−	12.7343i		−	0.479943i
$705$		0			0
$706$	−0.683596	−	0.394674i	−0.0257275	−	0.0148538i
$707$	−44.2584	+	11.8590i	−1.66451	+	0.446004i
$708$	−39.0803	−	22.5630i	−1.46873	−	0.847970i
$709$	5.97248	−	5.97248i	0.224301	−	0.224301i	−0.586006	−	0.810307i	$-0.699300\pi$
$709$	5.97248	−	5.97248i	0.224301	−	0.224301i	0.810307	+	0.586006i	$0.199300\pi$
$710$		0			0
$711$	20.6206	+	20.6206i	0.773333	+	0.773333i
$712$	0.430105	+	0.115246i	0.0161189	+	0.00431904i
$713$	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
$717$		−	53.0066i		−	1.97957i
$718$	26.4758	+	45.8574i	0.988068	+	1.71138i
$719$	18.4724	−	10.6650i	0.688904	−	0.397739i	−0.114297	−	0.993447i	$-0.536462\pi$
$719$	18.4724	−	10.6650i	0.688904	−	0.397739i	0.803201	+	0.595707i	$0.203128\pi$
$720$		0			0
$721$	5.53853	+	20.6701i	0.206266	+	0.769794i
$722$	−9.86196	+	17.0814i	−0.367024	+	0.635705i
$723$	−3.51769	−	6.09281i	−0.130824	−	0.226594i
$724$	−6.83316	−	11.8354i	−0.253952	−	0.439858i
$725$		0			0
$726$	−27.9821	−	27.9821i	−1.03851	−	1.03851i
$727$	−3.36379	−	1.94208i	−0.124756	−	0.0720279i	0.436323	−	0.899790i	$-0.356280\pi$
$727$	−3.36379	−	1.94208i	−0.124756	−	0.0720279i	−0.561079	+	0.827762i	$0.689614\pi$
$728$	−1.49919	−	0.401707i	−0.0555637	−	0.0148882i
$729$		−	25.6892i		−	0.951452i
$730$		0			0
$731$	27.1328	−	15.6651i	1.00354	−	0.579396i
$732$			32.4591i			1.19972i
$733$	−8.74505	−	32.6370i	−0.323006	−	1.20547i	−0.916302	−	0.400489i	$-0.868840\pi$
$733$	−8.74505	−	32.6370i	−0.323006	−	1.20547i	0.593296	−	0.804984i	$-0.297826\pi$
$734$	21.4761	+	21.4761i	0.792697	+	0.792697i
$735$		0			0
$736$	9.13352	−	15.8197i	0.336666	−	0.583123i
$737$	−3.80213	−	14.1897i	−0.140053	−	0.522686i
$738$	−43.6190	+	25.1834i	−1.60564	+	0.927015i
$739$	−41.3843			−1.52234			−0.761172	−	0.648550i	$-0.775376\pi$
$739$	−41.3843			−1.52234			−0.761172	+	0.648550i	$0.775376\pi$
$740$		0			0
$741$	72.8993			2.67802
$742$	0.592153	−	0.341879i	0.0217386	−	0.0125508i
$743$	2.89539	+	10.8057i	0.106222	+	0.396424i	0.998481	−	0.0550990i	$-0.0175475\pi$
$743$	2.89539	+	10.8057i	0.106222	+	0.396424i	−0.892259	+	0.451523i	$0.850881\pi$
$744$	−0.0904292	+	0.156628i	−0.00331529	+	0.00574226i
$745$		0			0
$746$	51.3220	+	51.3220i	1.87903	+	1.87903i
$747$	5.53363	+	20.6518i	0.202465	+	0.755610i
$748$		−	22.8007i		−	0.833675i
$749$	−6.79985	+	3.92589i	−0.248461	+	0.143449i
$750$		0			0
$751$		−	2.77329i		−	0.101199i	−0.998719	−	0.0505993i	$-0.983887\pi$
$751$		−	2.77329i		−	0.101199i	0.998719	−	0.0505993i	$-0.0161132\pi$
$752$	19.6890	+	5.27565i	0.717984	+	0.192383i
$753$	26.2011	+	15.1272i	0.954823	+	0.551267i
$754$	−6.21454	−	6.21454i	−0.226320	−	0.226320i
$755$		0			0
$756$	0.464765	+	0.804996i	0.0169033	+	0.0292774i
$757$	−13.8153	−	23.9288i	−0.502125	−	0.869705i	−0.999997	−	0.00245512i	$-0.999219\pi$
$757$	−13.8153	−	23.9288i	−0.502125	−	0.869705i	0.497872	−	0.867250i	$-0.334115\pi$
$758$	−21.9635	+	38.0420i	−0.797752	+	1.38175i
$759$	2.43387	+	9.08334i	0.0883441	+	0.329704i
$760$		0			0
$761$	5.11172	−	2.95125i	0.185300	−	0.106983i	−0.404481	−	0.914547i	$-0.632548\pi$
$761$	5.11172	−	2.95125i	0.185300	−	0.106983i	0.589780	+	0.807564i	$0.299214\pi$
$762$	45.4141	+	78.6596i	1.64518	+	2.84954i
$763$		−	1.46610i		−	0.0530764i
$764$	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
$768$	39.4925	+	10.5820i	1.42506	+	0.381845i
$769$	−15.6442	−	15.6442i	−0.564144	−	0.564144i	0.366338	−	0.930482i	$-0.380611\pi$
$769$	−15.6442	−	15.6442i	−0.564144	−	0.564144i	−0.930482	+	0.366338i	$0.880611\pi$
$770$		0			0
$771$	−27.7498	+	27.7498i	−0.999384	+	0.999384i
$772$	−15.6360	−	9.02746i	−0.562752	−	0.324905i
$773$	28.1683	−	7.54766i	1.01314	−	0.271470i	0.286200	−	0.958170i	$-0.407608\pi$
$773$	28.1683	−	7.54766i	1.01314	−	0.271470i	0.726941	+	0.686699i	$0.240941\pi$
$774$	22.6564	+	13.0807i	0.814366	+	0.470175i
$775$		0			0
$776$			0.977379i			0.0350859i
$777$	33.5106	−	22.4135i	1.20219	−	0.804079i
$778$	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
$782$	15.9206	−	27.5753i	0.569319	−	0.986090i
$783$		−	0.139234i		−	0.00497581i
$784$	−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
$792$	−0.436158	+	0.251816i	−0.0154982	+	0.00894789i
$793$	−9.85847	+	36.7923i	−0.350085	+	1.30653i
$794$	−45.6259	−	12.2254i	−1.61920	−	0.433864i
$795$		0			0
$796$	−26.8283	+	7.18862i	−0.950904	+	0.254794i
$797$	9.03980	−	5.21913i	0.320206	−	0.184871i	−0.331278	−	0.943533i	$-0.607480\pi$
$797$	9.03980	−	5.21913i	0.320206	−	0.184871i	0.651484	+	0.758662i	$0.274147\pi$
$798$	68.4182	+	18.3326i	2.42198	+	0.648967i
$799$	33.4570	+	8.96477i	1.18362	+	0.317151i
$800$		0			0
$801$	3.29478	+	12.2963i	0.116415	+	0.434468i
$802$	7.64012	−	28.5133i	0.269782	−	1.00684i
$803$	−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
$807$	−10.4876	+	2.81014i	−0.369180	+	0.0989216i
$808$	1.72390			0.0606467
$809$	17.2925	−	4.63351i	0.607972	−	0.162906i	0.0583182	−	0.998298i	$-0.481426\pi$
$809$	17.2925	−	4.63351i	0.607972	−	0.162906i	0.549654	+	0.835392i	$0.314760\pi$
$810$		0			0
$811$	12.0147	−	20.8102i	0.421895	−	0.730743i	−0.574230	−	0.818694i	$-0.694698\pi$
$811$	12.0147	−	20.8102i	0.421895	−	0.730743i	0.996125	+	0.0879507i	$0.0280318\pi$
$812$	−2.10699	−	3.64941i	−0.0739408	−	0.128069i
$813$	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
$817$	−23.3593	+	6.25911i	−0.817240	+	0.218979i
$818$	12.0296	+	44.8951i	0.420605	+	1.56972i
$819$	−11.4844	−	42.8604i	−0.401297	−	1.49766i
$820$		0			0
$821$	−12.1723	+	21.0830i	−0.424815	+	0.735801i	−0.996403	−	0.0847397i	$-0.972994\pi$
$821$	−12.1723	+	21.0830i	−0.424815	+	0.735801i	0.571588	+	0.820541i	$0.306327\pi$
$822$	46.0945			1.60773
$823$	−3.92742	+	14.6573i	−0.136901	+	0.510923i	0.863082	+	0.505065i	$0.168531\pi$
$823$	−3.92742	+	14.6573i	−0.136901	+	0.510923i	−0.999983	+	0.00585796i	$0.998135\pi$
$824$		−	0.805117i		−	0.0280476i
$825$		0			0
$826$	−25.7264	−	44.5595i	−0.895137	−	1.55042i
$827$	−4.50988	+	7.81135i	−0.156824	+	0.271627i	−0.933722	−	0.358000i	$-0.883459\pi$
$827$	−4.50988	+	7.81135i	−0.156824	+	0.271627i	0.776898	+	0.629627i	$0.216792\pi$
$828$	13.1204			0.455967
$829$	−5.61392	+	20.9514i	−0.194979	+	0.727673i	0.797293	+	0.603593i	$0.206265\pi$
$829$	−5.61392	+	20.9514i	−0.194979	+	0.727673i	−0.992272	+	0.124080i	$0.960402\pi$
$830$		0			0
$831$	18.2777	−	68.2135i	0.634048	−	2.36630i
$832$	−36.5566	−	21.1060i	−1.26737	−	0.731718i
$833$	−2.47513	−	1.42902i	−0.0857582	−	0.0495125i
$834$	−16.9850	+	63.3888i	−0.588141	+	2.19497i
$835$		0			0
$836$	−4.55508	+	16.9998i	−0.157541	+	0.587951i
$837$	0.127106			0.00439343
$838$	−22.9669	+	39.7799i	−0.793379	+	1.37417i
$839$	−17.8183	−	30.8622i	−0.615157	−	1.06548i	−0.990357	−	0.138539i	$-0.955759\pi$
$839$	−17.8183	−	30.8622i	−0.615157	−	1.06548i	0.375200	−	0.926944i	$-0.377574\pi$
$840$		0			0
$841$		−	28.3688i		−	0.978234i
$842$	0.579291	−	2.16194i	0.0199637	−	0.0745055i
$843$	−12.8109			−0.441230
$844$	8.92525	−	15.4590i	0.307220	−	0.532120i
$845$		0			0
$846$	7.48574	+	27.9372i	0.257365	+	0.960500i
$847$	−5.76284	−	21.5072i	−0.198014	−	0.738997i
$848$	−0.500666	+	0.134153i	−0.0171929	+	0.00460683i
$849$	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
$853$	−14.3582	−	24.8691i	−0.491614	−	0.851501i	0.508339	−	0.861157i	$-0.330260\pi$
$853$	−14.3582	−	24.8691i	−0.491614	−	0.851501i	−0.999953	+	0.00965588i	$0.996926\pi$
$854$	−18.5050	+	32.0515i	−0.633227	+	1.09678i
$855$		0			0
$856$	0.285347	−	0.0764584i	0.00975295	−	0.00261329i
$857$	6.04867			0.206618			0.103309	−	0.994649i	$-0.467057\pi$
$857$	6.04867			0.206618			0.103309	+	0.994649i	$0.467057\pi$
$858$	43.6918	−	11.7072i	1.49161	−	0.399677i
$859$	38.1045	−	38.1045i	1.30011	−	1.30011i	0.371791	−	0.928316i	$-0.378744\pi$
$859$	38.1045	−	38.1045i	1.30011	−	1.30011i	0.928316	−	0.371791i	$-0.121256\pi$
$860$		0			0
$861$	−57.3755			−1.95535
$862$	−33.0904	−	33.0904i	−1.12706	−	1.12706i
$863$	−3.02200	+	11.2783i	−0.102870	+	0.383917i	−0.998095	−	0.0616982i	$-0.980348\pi$
$863$	−3.02200	+	11.2783i	−0.102870	+	0.383917i	0.895225	+	0.445615i	$0.147015\pi$
$864$	−0.360279	−	1.34458i	−0.0122569	−	0.0457436i
$865$		0			0
$866$	22.6767	+	6.07620i	0.770586	+	0.206478i
$867$	74.1979	+	19.8813i	2.51989	+	0.675203i
$868$	3.33154	−	1.92346i	0.113080	−	0.0652866i
$869$	−16.1566	+	4.32914i	−0.548075	+	0.146856i
$870$		0			0
$871$	−47.0364	−	12.6034i	−1.59377	−	0.427048i
$872$	−0.0142765	+	0.0532805i	−0.000483462	+	0.00180431i
$873$	−24.1987	+	13.9712i	−0.819003	+	0.472852i
$874$	−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	0.128332	−	0.991731i	$-0.459038\pi$
$881$	−19.7789	−	11.4193i	−0.666367	−	0.384727i	−0.794699	+	0.607004i	$0.792371\pi$
$882$		−	2.38651i		−	0.0803579i
$883$	8.10927	−	14.0457i	0.272899	−	0.472674i	−0.696704	−	0.717359i	$-0.745351\pi$
$883$	8.10927	−	14.0457i	0.272899	−	0.472674i	0.969603	+	0.244684i	$0.0786843\pi$
$884$	−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	0.526282	−	0.850310i	$-0.323586\pi$
$887$	−9.65037	−	9.65037i	−0.324028	−	0.324028i	−0.850310	+	0.526282i	$0.823586\pi$
$888$	−1.43609	+	0.488226i	−0.0481919	+	0.0163838i
$889$			51.1054i			1.71402i
$890$		0			0
$891$	13.3965	+	7.73445i	0.448798	+	0.259114i
$892$	20.4218	−	5.47200i	0.683771	−	0.183216i
$893$	−23.1540	−	13.3680i	−0.774820	−	0.447342i
$894$	22.1204	−	22.1204i	0.739818	−	0.739818i
$895$		0			0
$896$	1.57660	+	1.57660i	0.0526703	+	0.0526703i
$897$	30.1096	+	8.06785i	1.00533	+	0.269378i
$898$	−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
$902$		−	28.8891i		−	0.961903i
$903$	14.9008	+	25.8090i	0.495869	+	0.858870i
$904$	−1.47080	+	0.849168i	−0.0489181	+	0.0282429i
$905$		0			0
$906$	−14.0751	−	52.5288i	−0.467612	−	1.74515i
$907$	20.0602	−	34.7453i	0.666089	−	1.15370i	−0.312900	−	0.949786i	$-0.601301\pi$
$907$	20.0602	−	34.7453i	0.666089	−	1.15370i	0.978989	−	0.203913i	$-0.0653661\pi$
$908$	11.8841	+	20.5839i	0.394388	+	0.683101i
$909$	24.6424	+	42.6818i	0.817335	+	1.41567i
$910$		0			0
$911$	−6.91310	−	6.91310i	−0.229041	−	0.229041i	0.583251	−	0.812292i	$-0.301780\pi$
$911$	−6.91310	−	6.91310i	−0.229041	−	0.229041i	−0.812292	+	0.583251i	$0.801780\pi$
$912$	−46.5007	−	26.8472i	−1.53979	−	0.889000i
$913$	−11.8453	−	3.17395i	−0.392024	−	0.105042i
$914$		−	59.8889i		−	1.98095i
$915$		0			0
$916$	−13.5016	+	7.79515i	−0.446106	+	0.257559i
$917$		−	16.9745i		−	0.560546i
$918$	−0.628001	−	2.34373i	−0.0207271	−	0.0773547i
$919$	10.7644	+	10.7644i	0.355086	+	0.355086i	0.861998	−	0.506912i	$-0.169213\pi$
$919$	10.7644	+	10.7644i	0.355086	+	0.355086i	−0.506912	+	0.861998i	$0.669213\pi$
$920$		0			0
$921$	31.5780	−	54.6947i	1.04053	−	1.80225i
$922$	6.07723	+	22.6805i	0.200143	+	0.746943i
$923$	47.3793	−	27.3544i	1.55951	−	0.900382i
$924$	21.6882			0.713491
$925$		0			0
$926$	34.6244			1.13783
$927$	19.9338	−	11.5088i	0.654710	−	0.377997i
$928$	1.63331	+	6.09559i	0.0536159	+	0.200097i
$929$	−2.66910	+	4.62301i	−0.0875702	+	0.151676i	−0.906484	−	0.422241i	$-0.861244\pi$
$929$	−2.66910	+	4.62301i	−0.0875702	+	0.151676i	0.818913	+	0.573917i	$0.194577\pi$
$930$		0			0
$931$	1.55993	+	1.55993i	0.0511246	+	0.0511246i
$932$	8.91337	+	33.2651i	0.291967	+	1.08964i
$933$			13.5368i			0.443174i
$934$	18.7965	−	10.8522i	0.615041	−	0.355094i
$935$		0			0
$936$			1.66945i			0.0545676i
$937$	15.8056	+	4.23510i	0.516346	+	0.138355i	0.507576	−	0.861607i	$-0.330542\pi$
$937$	15.8056	+	4.23510i	0.516346	+	0.138355i	0.00877029	+	0.999962i	$0.497208\pi$
$938$	−40.9756	−	23.6573i	−1.33790	−	0.772437i
$939$	10.5264	+	10.5264i	0.343515	+	0.343515i
$940$		0			0
$941$	15.2812	+	26.4678i	0.498152	+	0.862824i	0.999998	−	0.00213282i	$-0.000678897\pi$
$941$	15.2812	+	26.4678i	0.498152	+	0.862824i	−0.501846	+	0.864957i	$0.667346\pi$
$942$	−23.1612	−	40.1165i	−0.754634	−	1.30706i
$943$	9.95428	−	17.2413i	0.324156	−	0.561455i
$944$	10.0950	+	37.6751i	0.328565	+	1.22622i
$945$		0			0
$946$	−12.9951	+	7.50273i	−0.422508	+	0.243935i
$947$	25.2760	+	43.7794i	0.821361	+	1.42264i	0.904669	+	0.426115i	$0.140118\pi$
$947$	25.2760	+	43.7794i	0.821361	+	1.42264i	−0.0833078	+	0.996524i	$0.526548\pi$
$948$			47.2485i			1.53456i
$949$	−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
$953$	−34.8819	−	9.34657i	−1.12994	−	0.302765i	−0.355038	−	0.934852i	$-0.615532\pi$
$953$	−34.8819	−	9.34657i	−1.12994	−	0.302765i	−0.774898	+	0.632087i	$0.782199\pi$
$954$	−0.520053	−	0.520053i	−0.0168373	−	0.0168373i
$955$		0			0
$956$	29.9952	−	29.9952i	0.970113	−	0.970113i
$957$	−2.81343	−	1.62433i	−0.0909453	−	0.0525073i
$958$	−16.0063	+	4.28888i	−0.517140	+	0.138567i
$959$	22.4608	+	12.9678i	0.725297	+	0.418751i
$960$		0			0
$961$			30.4740i			0.983031i
$962$	67.1420	−	4.43188i	2.16474	−	0.142889i
$963$	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
$967$	17.8080	−	30.8443i	0.572666	−	0.991886i	−0.423625	−	0.905838i	$-0.639243\pi$
$967$	17.8080	−	30.8443i	0.572666	−	0.991886i	0.996291	−	0.0860487i	$-0.0274241\pi$
$968$			0.837724i			0.0269255i
$969$	−79.0175	−	45.6208i	−2.53841	−	1.46555i
$970$		0			0
$971$	16.8077	+	29.1118i	0.539386	+	0.934244i	0.998937	+	0.0460924i	$0.0146769\pi$
$971$	16.8077	+	29.1118i	0.539386	+	0.934244i	−0.459551	+	0.888151i	$0.651990\pi$
$972$	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
$977$	49.0457	−	28.3165i	1.56911	−	0.905926i	0.572837	−	0.819669i	$-0.305843\pi$
$977$	49.0457	−	28.3165i	1.56911	−	0.905926i	0.996273	−	0.0862569i	$-0.0274906\pi$
$978$	12.3680	−	46.1581i	0.395486	−	1.47597i
$979$	−7.05283	−	1.88980i	−0.225410	−	0.0603983i
$980$		0			0
$981$	−1.52324	+	0.408150i	−0.0486332	+	0.0130312i
$982$	−36.9237	+	21.3179i	−1.17828	+	0.680282i
$983$	−34.4807	−	9.23907i	−1.09976	−	0.294681i	−0.337095	−	0.941471i	$-0.609444\pi$
$983$	−34.4807	−	9.23907i	−1.09976	−	0.294681i	−0.762668	+	0.646790i	$0.776111\pi$
$984$	2.08512	+	0.558706i	0.0664711	+	0.0178109i
$985$		0			0
$986$	2.84701	+	10.6252i	0.0906673	+	0.338375i
$987$	−8.52739	+	31.8247i	−0.271430	+	1.01299i
$988$	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	−0.727342	−	0.686276i	$-0.759244\pi$
$991$	−1.29277	+	1.29277i	−0.0410661	+	0.0410661i	0.686276	+	0.727342i	$0.259244\pi$
$992$	−5.56465	+	1.49104i	−0.176678	+	0.0473407i
$993$	20.9921			0.666165
$994$	51.3460	−	13.7581i	1.62859	−	0.436381i
$995$		0			0
$996$	−17.3203	+	29.9997i	−0.548815	+	0.950576i
$997$	14.5311	+	25.1686i	0.460205	+	0.797098i	0.998971	−	0.0453572i	$-0.0144426\pi$
$997$	14.5311	+	25.1686i	0.460205	+	0.797098i	−0.538766	+	0.842456i	$0.681109\pi$
$998$	−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.y.b.193.14		68
5.2	odd	4		925.2.t.b.82.14		68
5.3	odd	4		185.2.p.a.82.4	✓	68
5.4	even	2		185.2.u.a.8.4	yes	68
37.14	odd	12		925.2.t.b.643.14		68
185.14	odd	12		185.2.p.a.88.4	yes	68
185.88	even	12		185.2.u.a.162.4	yes	68
185.162	even	12	inner	925.2.y.b.532.14		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.4	✓	68	5.3	odd	4
185.2.p.a.88.4	yes	68	185.14	odd	12
185.2.u.a.8.4	yes	68	5.4	even	2
185.2.u.a.162.4	yes	68	185.88	even	12
925.2.t.b.82.14		68	5.2	odd	4
925.2.t.b.643.14		68	37.14	odd	12
925.2.y.b.193.14		68	1.1	even	1	trivial
925.2.y.b.532.14		68	185.162	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.72086 - 0.993536i) q^{2} +(-0.630160 - 2.35179i) q^{3} +(0.974229 - 1.68741i) q^{4} +(-3.42100 - 3.42100i) q^{6} +(-0.704548 - 2.62941i) q^{7} +0.102418i q^{8} +(-2.53574 + 1.46401i) q^{9} -1.67944i q^{11} +(-4.58237 - 1.22784i) q^{12} +(-4.82119 - 2.78351i) q^{13} +(-3.82484 - 3.82484i) q^{14} +(2.05021 + 3.55107i) q^{16} +(3.48387 + 6.03425i) q^{17} +(-2.90910 + 5.03870i) q^{18} +(-1.39201 - 5.19504i) q^{19} +(-5.73984 + 3.31390i) q^{21} +(-1.66858 - 2.89007i) q^{22} -2.29976i q^{23} +(0.240865 - 0.0645396i) q^{24} -11.0621 q^{26} +(-0.123920 - 0.123920i) q^{27} +(-5.12329 - 1.37278i) q^{28} +(0.561787 + 0.561787i) q^{29} +(-0.512854 + 0.512854i) q^{31} +(6.87885 + 3.97151i) q^{32} +(-3.94969 + 1.05832i) q^{33} +(11.9905 + 6.92271i) q^{34} +5.70513i q^{36} +(-6.06955 + 0.400637i) q^{37} +(-7.55690 - 7.55690i) q^{38} +(-3.50812 + 13.0925i) q^{39} +(7.49700 + 4.32839i) q^{41} +(-6.58496 + 11.4055i) q^{42} -4.49647i 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} +(-9.39388 + 5.42356i) q^{52} +(-0.0327168 + 0.122101i) q^{53} +(-0.336369 - 0.0901297i) q^{54} +(0.269298 - 0.0721582i) q^{56} +(-11.3405 + 6.54742i) q^{57} +(1.52491 + 0.408598i) q^{58} +(9.18809 + 2.46194i) q^{59} +(-1.77087 - 6.60897i) q^{61} +(-0.373008 + 1.39209i) q^{62} +(5.63603 + 5.63603i) q^{63} +7.58249 q^{64} +(-5.74537 + 5.74537i) q^{66} +(8.44910 - 2.26393i) q^{67} +13.5764 q^{68} +(-5.40856 + 1.44922i) q^{69} +(-4.91365 + 8.51069i) q^{71} +(-0.149941 - 0.259705i) q^{72} +(0.804857 - 0.804857i) q^{73} +(-10.0468 + 6.71976i) q^{74} +(-10.1223 - 2.71227i) q^{76} +(-4.41593 + 1.18324i) q^{77} +(6.97089 + 26.0157i) q^{78} +(-2.57773 - 9.62023i) q^{79} +(-4.60538 + 7.97675i) q^{81} +17.2017 q^{82} +(1.88989 - 7.05316i) q^{83} +12.9140i q^{84} +(-4.46741 - 7.73777i) q^{86} +(0.967189 - 1.67522i) q^{87} +0.172004 q^{88} +(1.12526 - 4.19952i) q^{89} +(-3.92224 + 14.6380i) q^{91} +(-3.88065 - 2.24050i) q^{92} +(1.52931 + 0.882945i) q^{93} +(2.55659 - 9.54131i) q^{94} +(5.00537 - 18.6803i) q^{96} +9.54307 q^{97} +(-0.407529 + 0.705861i) q^{98} +(2.45872 + 4.25862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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