LMFDB - Embedded newform 176.2.j.a.45.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [176,2,Mod(45,176)] 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("176.45"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(176, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$176 = 2^{4} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	176.j (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.40536707557$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			45.18
Character	$\chi$	$=$	176.45
Dual form			176.2.j.a.133.18

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28704 + 0.586108i) q^{2} +(0.586507 + 0.586507i) q^{3} +(1.31295 + 1.50869i) q^{4} +(-1.32116 + 1.32116i) q^{5} +(0.411103 + 1.09862i) q^{6} -1.42100i q^{7} +(0.805572 + 2.71128i) q^{8} -2.31202i q^{9} +(-2.47473 + 0.926044i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.114801 + 1.65492i) q^{12} +(-1.74014 - 1.74014i) q^{13} +(0.832862 - 1.82889i) q^{14} -1.54974 q^{15} +(-0.552299 + 3.96169i) q^{16} +6.99932 q^{17} +(1.35509 - 2.97566i) q^{18} +(-3.48148 - 3.48148i) q^{19} +(-3.72784 - 0.258599i) q^{20} +(0.833429 - 0.833429i) q^{21} +(-1.32452 + 0.495635i) q^{22} -4.79814i q^{23} +(-1.11771 + 2.06266i) q^{24} +1.50909i q^{25} +(-1.21972 - 3.25954i) q^{26} +(3.11554 - 3.11554i) q^{27} +(2.14386 - 1.86571i) q^{28} +(3.38802 + 3.38802i) q^{29} +(-1.99458 - 0.908313i) q^{30} -8.04642 q^{31} +(-3.03281 + 4.77515i) q^{32} -0.829447 q^{33} +(9.00842 + 4.10236i) q^{34} +(1.87737 + 1.87737i) q^{35} +(3.48812 - 3.03558i) q^{36} +(-4.09290 + 4.09290i) q^{37} +(-2.44029 - 6.52133i) q^{38} -2.04121i q^{39} +(-4.64632 - 2.51774i) q^{40} -5.85993i q^{41} +(1.56114 - 0.584179i) q^{42} +(-3.09144 + 3.09144i) q^{43} +(-1.99521 - 0.138407i) q^{44} +(3.05454 + 3.05454i) q^{45} +(2.81223 - 6.17540i) q^{46} -8.12503 q^{47} +(-2.64749 + 1.99963i) q^{48} +4.98075 q^{49} +(-0.884489 + 1.94226i) q^{50} +(4.10515 + 4.10515i) q^{51} +(0.340609 - 4.91006i) q^{52} +(0.759064 - 0.759064i) q^{53} +(5.83587 - 2.18379i) q^{54} -1.86840i q^{55} +(3.85274 - 1.14472i) q^{56} -4.08382i q^{57} +(2.37478 + 6.34627i) q^{58} +(-0.513380 + 0.513380i) q^{59} +(-2.03473 - 2.33807i) q^{60} +(0.211703 + 0.211703i) q^{61} +(-10.3561 - 4.71607i) q^{62} -3.28539 q^{63} +(-6.70211 + 4.36827i) q^{64} +4.59800 q^{65} +(-1.06753 - 0.486145i) q^{66} +(0.116562 + 0.116562i) q^{67} +(9.18979 + 10.5598i) q^{68} +(2.81414 - 2.81414i) q^{69} +(1.31591 + 3.51659i) q^{70} +9.46083i q^{71} +(6.26853 - 1.86250i) q^{72} +7.55709i q^{73} +(-7.66661 + 2.86885i) q^{74} +(-0.885092 + 0.885092i) q^{75} +(0.681452 - 9.82349i) q^{76} +(1.00480 + 1.00480i) q^{77} +(1.19637 - 2.62712i) q^{78} +8.55815 q^{79} +(-4.50434 - 5.96368i) q^{80} -3.28148 q^{81} +(3.43455 - 7.54198i) q^{82} +(7.36953 + 7.36953i) q^{83} +(2.35164 + 0.163133i) q^{84} +(-9.24720 + 9.24720i) q^{85} +(-5.79072 + 2.16689i) q^{86} +3.97420i q^{87} +(-2.48679 - 1.34754i) q^{88} -2.68256i q^{89} +(2.14103 + 5.72161i) q^{90} +(-2.47275 + 2.47275i) q^{91} +(7.23891 - 6.29974i) q^{92} +(-4.71928 - 4.71928i) q^{93} +(-10.4573 - 4.76214i) q^{94} +9.19915 q^{95} +(-4.57943 + 1.02190i) q^{96} -15.2448 q^{97} +(6.41043 + 2.91926i) q^{98} +(1.63484 + 1.63484i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q - 12 q^{6} - 12 q^{8} - 4 q^{10} - 12 q^{12} + 8 q^{14} - 16 q^{15} - 8 q^{16} - 20 q^{18} - 16 q^{19} - 20 q^{20} + 28 q^{24} + 24 q^{27} + 20 q^{28} + 12 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34}+ \cdots + 72 q^{98}+O(q^{100})$ 40 * q - 12 * q^6 - 12 * q^8 - 4 * q^10 - 12 * q^12 + 8 * q^14 - 16 * q^15 - 8 * q^16 - 20 * q^18 - 16 * q^19 - 20 * q^20 + 28 * q^24 + 24 * q^27 + 20 * q^28 + 12 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 20 * q^36 + 48 * q^38 - 8 * q^40 - 8 * q^44 - 52 * q^46 - 40 * q^47 - 40 * q^49 + 64 * q^50 - 24 * q^51 - 36 * q^52 + 32 * q^54 - 8 * q^56 + 40 * q^58 - 8 * q^59 + 12 * q^60 + 32 * q^61 - 24 * q^64 - 16 * q^65 - 20 * q^66 - 24 * q^67 + 4 * q^68 + 32 * q^69 - 8 * q^70 - 20 * q^72 - 56 * q^74 - 56 * q^75 + 4 * q^76 + 64 * q^78 + 32 * q^79 + 32 * q^80 - 40 * q^81 + 24 * q^82 + 40 * q^83 + 76 * q^84 - 32 * q^85 - 16 * q^86 + 20 * q^90 - 16 * q^91 + 12 * q^92 - 48 * q^93 + 16 * q^94 - 48 * q^95 + 36 * q^96 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$ .

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.28704	+	0.586108i	0.910076	+	0.414441i
$2$	1.28704	+	0.586108i	0.910076	+	0.414441i
$3$	0.586507	+	0.586507i	0.338620	+	0.338620i	0.855848	−	0.517228i	$-0.173036\pi$
$3$	0.586507	+	0.586507i	0.338620	+	0.338620i	−0.517228	+	0.855848i	$0.673036\pi$
$4$	1.31295	+	1.50869i	0.656477	+	0.754346i
$5$	−1.32116	+	1.32116i	−0.590839	+	0.590839i	−0.937858	−	0.347019i	$-0.887194\pi$
$5$	−1.32116	+	1.32116i	−0.590839	+	0.590839i	0.347019	+	0.937858i	$0.387194\pi$
$6$	0.411103	+	1.09862i	0.167832	+	0.448508i
$7$		−	1.42100i		−	0.537089i	−0.963267	−	0.268544i	$-0.913457\pi$
$7$		−	1.42100i		−	0.537089i	0.963267	−	0.268544i	$-0.0865426\pi$
$8$	0.805572	+	2.71128i	0.284813	+	0.958583i
$9$		−	2.31202i		−	0.770673i
$10$	−2.47473	+	0.926044i	−0.782577	+	0.292841i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−0.114801	+	1.65492i	−0.0331402	+	0.477733i
$13$	−1.74014	−	1.74014i	−0.482628	−	0.482628i	0.423342	−	0.905970i	$-0.360857\pi$
$13$	−1.74014	−	1.74014i	−0.482628	−	0.482628i	−0.905970	+	0.423342i	$0.860857\pi$
$14$	0.832862	−	1.82889i	0.222592	−	0.488792i
$15$	−1.54974			−0.400140
$16$	−0.552299	+	3.96169i	−0.138075	+	0.990422i
$17$	6.99932			1.69758			0.848792	−	0.528726i	$-0.177330\pi$
$17$	6.99932			1.69758			0.848792	+	0.528726i	$0.177330\pi$
$18$	1.35509	−	2.97566i	0.319398	−	0.701371i
$19$	−3.48148	−	3.48148i	−0.798705	−	0.798705i	0.184186	−	0.982891i	$-0.441035\pi$
$19$	−3.48148	−	3.48148i	−0.798705	−	0.798705i	−0.982891	+	0.184186i	$0.941035\pi$
$20$	−3.72784	−	0.258599i	−0.833570	−	0.0578244i
$21$	0.833429	−	0.833429i	0.181869	−	0.181869i
$22$	−1.32452	+	0.495635i	−0.282388	+	0.105670i
$23$		−	4.79814i		−	1.00048i	−0.865887	−	0.500240i	$-0.833245\pi$
$23$		−	4.79814i		−	1.00048i	0.865887	−	0.500240i	$-0.166755\pi$
$24$	−1.11771	+	2.06266i	−0.228152	+	0.421039i
$25$			1.50909i			0.301818i
$26$	−1.21972	−	3.25954i	−0.239207	−	0.639249i
$27$	3.11554	−	3.11554i	0.599586	−	0.599586i
$28$	2.14386	−	1.86571i	0.405151	−	0.352587i
$29$	3.38802	+	3.38802i	0.629140	+	0.629140i	0.947852	−	0.318712i	$-0.103250\pi$
$29$	3.38802	+	3.38802i	0.629140	+	0.629140i	−0.318712	+	0.947852i	$0.603250\pi$
$30$	−1.99458	−	0.908313i	−0.364158	−	0.165835i
$31$	−8.04642			−1.44518			−0.722590	−	0.691277i	$-0.757048\pi$
$31$	−8.04642			−1.44518			−0.722590	+	0.691277i	$0.757048\pi$
$32$	−3.03281	+	4.77515i	−0.536130	+	0.844135i
$33$	−0.829447			−0.144388
$34$	9.00842	+	4.10236i	1.54493	+	0.703549i
$35$	1.87737	+	1.87737i	0.317333	+	0.317333i
$36$	3.48812	−	3.03558i	0.581354	−	0.505929i
$37$	−4.09290	+	4.09290i	−0.672868	+	0.672868i	−0.958376	−	0.285508i	$-0.907838\pi$
$37$	−4.09290	+	4.09290i	−0.672868	+	0.672868i	0.285508	+	0.958376i	$0.407838\pi$
$38$	−2.44029	−	6.52133i	−0.395867	−	1.05790i
$39$		−	2.04121i		−	0.326855i
$40$	−4.64632	−	2.51774i	−0.734647	−	0.398090i
$41$		−	5.85993i		−	0.915167i	−0.889167	−	0.457584i	$-0.848715\pi$
$41$		−	5.85993i		−	0.915167i	0.889167	−	0.457584i	$-0.151285\pi$
$42$	1.56114	−	0.584179i	0.240889	−	0.0901408i
$43$	−3.09144	+	3.09144i	−0.471440	+	0.471440i	−0.902380	−	0.430941i	$-0.858182\pi$
$43$	−3.09144	+	3.09144i	−0.471440	+	0.471440i	0.430941	+	0.902380i	$0.358182\pi$
$44$	−1.99521	−	0.138407i	−0.300788	−	0.0208656i
$45$	3.05454	+	3.05454i	0.455344	+	0.455344i
$46$	2.81223	−	6.17540i	0.414640	−	0.910514i
$47$	−8.12503			−1.18516			−0.592579	−	0.805513i	$-0.701890\pi$
$47$	−8.12503			−1.18516			−0.592579	+	0.805513i	$0.701890\pi$
$48$	−2.64749	+	1.99963i	−0.382132	+	0.288622i
$49$	4.98075			0.711535
$50$	−0.884489	+	1.94226i	−0.125086	+	0.274677i
$51$	4.10515	+	4.10515i	0.574837	+	0.574837i
$52$	0.340609	−	4.91006i	0.0472339	−	0.680903i
$53$	0.759064	−	0.759064i	0.104265	−	0.104265i	−0.653050	−	0.757315i	$-0.726511\pi$
$53$	0.759064	−	0.759064i	0.104265	−	0.104265i	0.757315	+	0.653050i	$0.226511\pi$
$54$	5.83587	−	2.18379i	0.794161	−	0.297176i
$55$		−	1.86840i		−	0.251935i
$56$	3.85274	−	1.14472i	0.514844	−	0.152970i
$57$		−	4.08382i		−	0.540915i
$58$	2.37478	+	6.34627i	0.311824	+	0.833307i
$59$	−0.513380	+	0.513380i	−0.0668364	+	0.0668364i	−0.739735	−	0.672898i	$-0.765049\pi$
$59$	−0.513380	+	0.513380i	−0.0668364	+	0.0668364i	0.672898	+	0.739735i	$0.265049\pi$
$60$	−2.03473	−	2.33807i	−0.262683	−	0.301844i
$61$	0.211703	+	0.211703i	0.0271058	+	0.0271058i	0.720530	−	0.693424i	$-0.243899\pi$
$61$	0.211703	+	0.211703i	0.0271058	+	0.0271058i	−0.693424	+	0.720530i	$0.743899\pi$
$62$	−10.3561	−	4.71607i	−1.31522	−	0.598941i
$63$	−3.28539			−0.413920
$64$	−6.70211	+	4.36827i	−0.837763	+	0.546033i
$65$	4.59800			0.570311
$66$	−1.06753	−	0.486145i	−0.131404	−	0.0598404i
$67$	0.116562	+	0.116562i	0.0142404	+	0.0142404i	0.714191	−	0.699951i	$-0.246795\pi$
$67$	0.116562	+	0.116562i	0.0142404	+	0.0142404i	−0.699951	+	0.714191i	$0.746795\pi$
$68$	9.18979	+	10.5598i	1.11443	+	1.28057i
$69$	2.81414	−	2.81414i	0.338783	−	0.338783i
$70$	1.31591	+	3.51659i	0.157282	+	0.420313i
$71$			9.46083i			1.12279i	0.827547	+	0.561397i	$0.189736\pi$
$71$			9.46083i			1.12279i	−0.827547	+	0.561397i	$0.810264\pi$
$72$	6.26853	−	1.86250i	0.738754	−	0.219497i
$73$			7.55709i			0.884491i	0.896894	+	0.442245i	$0.145818\pi$
$73$			7.55709i			0.884491i	−0.896894	+	0.442245i	$0.854182\pi$
$74$	−7.66661	+	2.86885i	−0.891226	+	0.333497i
$75$	−0.885092	+	0.885092i	−0.102202	+	0.102202i
$76$	0.681452	−	9.82349i	0.0781679	−	1.12683i
$77$	1.00480	+	1.00480i	0.114508	+	0.114508i
$78$	1.19637	−	2.62712i	0.135462	−	0.297463i
$79$	8.55815			0.962867			0.481433	−	0.876483i	$-0.340116\pi$
$79$	8.55815			0.962867			0.481433	+	0.876483i	$0.340116\pi$
$80$	−4.50434	−	5.96368i	−0.503600	−	0.666760i
$81$	−3.28148			−0.364609
$82$	3.43455	−	7.54198i	0.379283	−	0.832872i
$83$	7.36953	+	7.36953i	0.808911	+	0.808911i	0.984469	−	0.175558i	$-0.0561729\pi$
$83$	7.36953	+	7.36953i	0.808911	+	0.808911i	−0.175558	+	0.984469i	$0.556173\pi$
$84$	2.35164	+	0.163133i	0.256585	+	0.0177992i
$85$	−9.24720	+	9.24720i	−1.00300	+	1.00300i
$86$	−5.79072	+	2.16689i	−0.624430	+	0.233662i
$87$			3.97420i			0.426079i
$88$	−2.48679	−	1.34754i	−0.265093	−	0.143648i
$89$		−	2.68256i		−	0.284350i	−0.989842	−	0.142175i	$-0.954590\pi$
$89$		−	2.68256i		−	0.284350i	0.989842	−	0.142175i	$-0.0454096\pi$
$90$	2.14103	+	5.72161i	0.225684	+	0.603111i
$91$	−2.47275	+	2.47275i	−0.259214	+	0.259214i
$92$	7.23891	−	6.29974i	0.754708	−	0.656793i
$93$	−4.71928	−	4.71928i	−0.489367	−	0.489367i
$94$	−10.4573	−	4.76214i	−1.07858	−	0.491178i
$95$	9.19915			0.943813
$96$	−4.57943	+	1.02190i	−0.467386	+	0.104297i
$97$	−15.2448			−1.54787			−0.773935	−	0.633265i	$-0.781714\pi$
$97$	−15.2448			−1.54787			−0.773935	+	0.633265i	$0.781714\pi$
$98$	6.41043	+	2.91926i	0.647552	+	0.294889i
$99$	1.63484	+	1.63484i	0.164308	+	0.164308i
$100$	−2.27675	+	1.98137i	−0.227675	+	0.198137i
$101$	−3.79328	+	3.79328i	−0.377446	+	0.377446i	−0.870180	−	0.492734i	$-0.835997\pi$
$101$	−3.79328	+	3.79328i	−0.377446	+	0.377446i	0.492734	+	0.870180i	$0.335997\pi$
$102$	2.87744	+	7.68957i	0.284909	+	0.761381i
$103$		−	11.9670i		−	1.17915i	−0.807714	−	0.589574i	$-0.799296\pi$
$103$		−	11.9670i		−	1.17915i	0.807714	−	0.589574i	$-0.200704\pi$
$104$	3.31620	−	6.11982i	0.325180	−	0.600098i
$105$			2.20218i			0.214911i
$106$	1.42184	−	0.532054i	0.138101	−	0.0516776i
$107$	−4.62971	+	4.62971i	−0.447570	+	0.447570i	−0.894546	−	0.446976i	$-0.852501\pi$
$107$	−4.62971	+	4.62971i	−0.447570	+	0.447570i	0.446976	+	0.894546i	$0.352501\pi$
$108$	8.79095	+	0.609824i	0.845909	+	0.0586804i
$109$	13.4758	+	13.4758i	1.29075	+	1.29075i	0.934326	+	0.356421i	$0.116003\pi$
$109$	13.4758	+	13.4758i	1.29075	+	1.29075i	0.356421	+	0.934326i	$0.383997\pi$
$110$	1.09508	−	2.40471i	0.104412	−	0.229280i
$111$	−4.80103			−0.455694
$112$	5.62957	+	0.784819i	0.531945	+	0.0741584i
$113$	19.4488			1.82959			0.914797	−	0.403914i	$-0.132351\pi$
$113$	19.4488			1.82959			0.914797	+	0.403914i	$0.132351\pi$
$114$	2.39356	−	5.25605i	0.224178	−	0.492274i
$115$	6.33909	+	6.33909i	0.591123	+	0.591123i
$116$	−0.663160	+	9.55980i	−0.0615728	+	0.887605i
$117$	−4.02323	+	4.02323i	−0.371948	+	0.371948i
$118$	−0.961638	+	0.359846i	−0.0885259	+	0.0331265i
$119$		−	9.94606i		−	0.911754i
$120$	−1.24842	−	4.20177i	−0.113965	−	0.383568i
$121$		−	1.00000i		−	0.0909091i
$122$	0.148390	+	0.396552i	0.0134346	+	0.0359022i
$123$	3.43689	−	3.43689i	0.309894	−	0.309894i
$124$	−10.5646	−	12.1396i	−0.948727	−	1.09016i
$125$	−8.59953	−	8.59953i	−0.769165	−	0.769165i
$126$	−4.22843	−	1.92559i	−0.376699	−	0.171545i
$127$	−0.942302			−0.0836158			−0.0418079	−	0.999126i	$-0.513312\pi$
$127$	−0.942302			−0.0836158			−0.0418079	+	0.999126i	$0.513312\pi$
$128$	−11.1862	+	1.69399i	−0.988727	+	0.149729i
$129$	−3.62630			−0.319278
$130$	5.91781	+	2.69492i	0.519027	+	0.236360i
$131$	7.37782	+	7.37782i	0.644603	+	0.644603i	0.951684	−	0.307080i	$-0.0993521\pi$
$131$	7.37782	+	7.37782i	0.644603	+	0.644603i	−0.307080	+	0.951684i	$0.599352\pi$
$132$	−1.08903	−	1.25138i	−0.0947876	−	0.108919i
$133$	−4.94719	+	4.94719i	−0.428976	+	0.428976i
$134$	0.0817026	+	0.218339i	0.00705803	+	0.0188616i
$135$			8.23223i			0.708517i
$136$	5.63846	+	18.9771i	0.483494	+	1.62728i
$137$			3.24428i			0.277178i	0.990350	+	0.138589i	$0.0442566\pi$
$137$			3.24428i			0.277178i	−0.990350	+	0.138589i	$0.955743\pi$
$138$	5.27131	−	1.97253i	0.448724	−	0.167913i
$139$	9.85522	−	9.85522i	0.835909	−	0.835909i	−0.152409	−	0.988318i	$-0.548703\pi$
$139$	9.85522	−	9.85522i	0.835909	−	0.835909i	0.988318	+	0.152409i	$0.0487030\pi$
$140$	−0.367470	+	5.29727i	−0.0310569	+	0.447701i
$141$	−4.76539	−	4.76539i	−0.401318	−	0.401318i
$142$	−5.54507	+	12.1765i	−0.465332	+	1.02183i
$143$	2.46093			0.205793
$144$	9.15949	+	1.27693i	0.763291	+	0.106410i
$145$	−8.95222			−0.743441
$146$	−4.42927	+	9.72630i	−0.366569	+	0.804954i
$147$	2.92125	+	2.92125i	0.240940	+	0.240940i
$148$	−11.5487	−	0.801130i	−0.949298	−	0.0658524i
$149$	9.59464	−	9.59464i	0.786024	−	0.786024i	−0.194816	−	0.980840i	$-0.562411\pi$
$149$	9.59464	−	9.59464i	0.786024	−	0.786024i	0.980840	+	0.194816i	$0.0624110\pi$
$150$	−1.65791	+	0.620391i	−0.135368	+	0.0506547i
$151$		−	4.32591i		−	0.352037i	−0.984387	−	0.176019i	$-0.943678\pi$
$151$		−	4.32591i		−	0.352037i	0.984387	−	0.176019i	$-0.0563219\pi$
$152$	6.63468	−	12.2438i	0.538144	−	0.993107i
$153$		−	16.1826i		−	1.30828i
$154$	0.704300	+	1.88214i	0.0567541	+	0.151667i
$155$	10.6306	−	10.6306i	0.853869	−	0.853869i
$156$	3.07956	−	2.68002i	0.246562	−	0.214573i
$157$	−11.9627	−	11.9627i	−0.954724	−	0.954724i	0.0442940	−	0.999019i	$-0.485896\pi$
$157$	−11.9627	−	11.9627i	−0.954724	−	0.954724i	−0.999019	+	0.0442940i	$0.985896\pi$
$158$	11.0147	+	5.01600i	0.876282	+	0.399051i
$159$	0.890393			0.0706128
$160$	−2.30191	−	10.3155i	−0.181982	−	0.815515i
$161$	−6.81817			−0.537347
$162$	−4.22341	−	1.92330i	−0.331822	−	0.151109i
$163$	−8.79291	−	8.79291i	−0.688714	−	0.688714i	0.273234	−	0.961948i	$-0.411907\pi$
$163$	−8.79291	−	8.79291i	−0.688714	−	0.688714i	−0.961948	+	0.273234i	$0.911907\pi$
$164$	8.84082	−	7.69382i	0.690352	−	0.600787i
$165$	1.09583	−	1.09583i	0.0853102	−	0.0853102i
$166$	5.16556	+	13.8042i	0.400925	+	1.07142i
$167$		−	9.14511i		−	0.707670i	−0.935308	−	0.353835i	$-0.884877\pi$
$167$		−	9.14511i		−	0.707670i	0.935308	−	0.353835i	$-0.115123\pi$
$168$	2.93105	+	1.58827i	0.226135	+	0.122538i
$169$		−	6.94383i		−	0.534141i
$170$	−17.3214	+	6.48168i	−1.32849	+	0.497122i
$171$	−8.04923	+	8.04923i	−0.615540	+	0.615540i
$172$	−8.72294	−	0.605107i	−0.665118	−	0.0461390i
$173$	−5.50400	−	5.50400i	−0.418461	−	0.418461i	0.466212	−	0.884673i	$-0.345618\pi$
$173$	−5.50400	−	5.50400i	−0.418461	−	0.418461i	−0.884673	+	0.466212i	$0.845618\pi$
$174$	−2.32931	+	5.11496i	−0.176585	+	0.387764i
$175$	2.14442			0.162103
$176$	−2.41080	−	3.19187i	−0.181721	−	0.240596i
$177$	−0.602202			−0.0452643
$178$	1.57227	−	3.45256i	0.117846	−	0.258780i
$179$	−12.8845	−	12.8845i	−0.963032	−	0.963032i	0.0363088	−	0.999341i	$-0.488440\pi$
$179$	−12.8845	−	12.8845i	−0.963032	−	0.963032i	−0.999341	+	0.0363088i	$0.988440\pi$
$180$	−0.597885	+	8.61883i	−0.0445637	+	0.642410i
$181$	−4.66839	+	4.66839i	−0.346999	+	0.346999i	−0.858990	−	0.511992i	$-0.828908\pi$
$181$	−4.66839	+	4.66839i	−0.346999	+	0.346999i	0.511992	+	0.858990i	$0.328908\pi$
$182$	−4.63182	+	1.73323i	−0.343334	+	0.128476i
$183$			0.248331i			0.0183572i
$184$	13.0091	−	3.86524i	0.959044	−	0.284950i
$185$		−	10.8147i		−	0.795114i
$186$	−3.30791	−	8.83992i	−0.242547	−	0.648175i
$187$	−4.94927	+	4.94927i	−0.361926	+	0.361926i
$188$	−10.6678	−	12.2582i	−0.778029	−	0.894018i
$189$	−4.42719	−	4.42719i	−0.322031	−	0.322031i
$190$	11.8397	+	5.39170i	0.858942	+	0.391155i
$191$	13.5156			0.977954			0.488977	−	0.872297i	$-0.337370\pi$
$191$	13.5156			0.977954			0.488977	+	0.872297i	$0.337370\pi$
$192$	−6.49286	−	1.36881i	−0.468582	−	0.0987857i
$193$	−21.1416			−1.52180			−0.760902	−	0.648867i	$-0.775243\pi$
$193$	−21.1416			−1.52180			−0.760902	+	0.648867i	$0.775243\pi$
$194$	−19.6206	−	8.93507i	−1.40868	−	0.641501i
$195$	2.69676	+	2.69676i	0.193119	+	0.193119i
$196$	6.53950	+	7.51441i	0.467107	+	0.536744i
$197$	15.9144	−	15.9144i	1.13385	−	1.13385i	0.144323	−	0.989531i	$-0.453900\pi$
$197$	15.9144	−	15.9144i	1.13385	−	1.13385i	0.989531	−	0.144323i	$-0.0461004\pi$
$198$	1.14592	+	3.06231i	0.0814368	+	0.217629i
$199$			18.6480i			1.32193i	0.750419	+	0.660963i	$0.229852\pi$
$199$			18.6480i			1.32193i	−0.750419	+	0.660963i	$0.770148\pi$
$200$	−4.09157	+	1.21568i	−0.289317	+	0.0859615i
$201$			0.136729i			0.00964415i
$202$	−7.10538	+	2.65884i	−0.499933	+	0.187075i
$203$	4.81439	−	4.81439i	0.337904	−	0.337904i
$204$	−0.803528	+	11.5833i	−0.0562582	+	0.810993i
$205$	7.74189	+	7.74189i	0.540717	+	0.540717i
$206$	7.01398	−	15.4021i	0.488687	−	1.07311i
$207$	−11.0934			−0.771043
$208$	7.85497	−	5.93281i	0.544644	−	0.411366i
$209$	4.92355			0.340569
$210$	−1.29072	+	2.83430i	−0.0890679	+	0.195585i
$211$	−9.48129	−	9.48129i	−0.652719	−	0.652719i	0.300928	−	0.953647i	$-0.402704\pi$
$211$	−9.48129	−	9.48129i	−0.652719	−	0.652719i	−0.953647	+	0.300928i	$0.902704\pi$
$212$	2.14181	+	0.148576i	0.147100	+	0.0102043i
$213$	−5.54885	+	5.54885i	−0.380201	+	0.380201i
$214$	−8.67213	+	3.24512i	−0.592815	+	0.221832i
$215$		−	8.16854i		−	0.557090i
$216$	10.9569	+	5.93731i	0.745522	+	0.403983i
$217$			11.4340i			0.776190i
$218$	9.44564	+	25.2422i	0.639739	+	1.70962i
$219$	−4.43229	+	4.43229i	−0.299506	+	0.299506i
$220$	2.81884	−	2.45312i	0.190046	−	0.165389i
$221$	−12.1798	−	12.1798i	−0.819302	−	0.819302i
$222$	−6.17913	−	2.81392i	−0.414716	−	0.188858i
$223$	−0.598134			−0.0400540			−0.0200270	−	0.999799i	$-0.506375\pi$
$223$	−0.598134			−0.0400540			−0.0200270	+	0.999799i	$0.506375\pi$
$224$	6.78551	+	4.30963i	0.453376	+	0.287949i
$225$	3.48904			0.232603
$226$	25.0315	+	11.3991i	1.66507	+	0.758258i
$227$	9.18505	+	9.18505i	0.609633	+	0.609633i	0.942850	−	0.333217i	$-0.108134\pi$
$227$	9.18505	+	9.18505i	0.609633	+	0.609633i	−0.333217	+	0.942850i	$0.608134\pi$
$228$	6.16123	−	5.36187i	0.408037	−	0.355099i
$229$	15.3308	−	15.3308i	1.01309	−	1.01309i	0.0131724	−	0.999913i	$-0.495807\pi$
$229$	15.3308	−	15.3308i	1.01309	−	1.01309i	0.999913	−	0.0131724i	$-0.00419302\pi$
$230$	4.44329	+	11.8741i	0.292982	+	0.782953i
$231$			1.17865i			0.0775493i
$232$	−6.45659	+	11.9152i	−0.423896	+	0.782270i
$233$			23.3441i			1.52932i	0.644433	+	0.764661i	$0.277093\pi$
$233$			23.3441i			1.52932i	−0.644433	+	0.764661i	$0.722907\pi$
$234$	−7.53612	+	2.82002i	−0.492652	+	0.184351i
$235$	10.7344	−	10.7344i	0.700238	−	0.700238i
$236$	−1.44858	−	0.100487i	−0.0942943	−	0.00654116i
$237$	5.01942	+	5.01942i	0.326046	+	0.326046i
$238$	5.82947	−	12.8010i	0.377868	−	0.829766i
$239$	29.0564			1.87950			0.939751	−	0.341860i	$-0.111057\pi$
$239$	29.0564			1.87950			0.939751	+	0.341860i	$0.111057\pi$
$240$	0.855918	−	6.13957i	0.0552493	−	0.396308i
$241$	4.84732			0.312244			0.156122	−	0.987738i	$-0.450101\pi$
$241$	4.84732			0.312244			0.156122	+	0.987738i	$0.450101\pi$
$242$	0.586108	−	1.28704i	0.0376764	−	0.0827342i
$243$	−11.2712	−	11.2712i	−0.723050	−	0.723050i
$244$	−0.0414381	+	0.597352i	−0.00265280	+	0.0382416i
$245$	−6.58035	+	6.58035i	−0.420403	+	0.420403i
$246$	6.43781	−	2.40903i	0.410460	−	0.153594i
$247$			12.1165i			0.770955i
$248$	−6.48197	−	21.8161i	−0.411605	−	1.38532i
$249$			8.64457i			0.547827i
$250$	−6.02770	−	16.1082i	−0.381225	−	1.01877i
$251$	−17.2032	+	17.2032i	−1.08585	+	1.08585i	−0.0899035	+	0.995950i	$0.528656\pi$
$251$	−17.2032	+	17.2032i	−1.08585	+	1.08585i	−0.995950	+	0.0899035i	$0.971344\pi$
$252$	−4.31356	−	4.95663i	−0.271729	−	0.312239i
$253$	3.39279	+	3.39279i	0.213303	+	0.213303i
$254$	−1.21278	−	0.552291i	−0.0760967	−	0.0346538i
$255$	−10.8471			−0.679272
$256$	−15.3899	−	4.37607i	−0.961871	−	0.273505i
$257$	−6.16863			−0.384788			−0.192394	−	0.981318i	$-0.561625\pi$
$257$	−6.16863			−0.384788			−0.192394	+	0.981318i	$0.561625\pi$
$258$	−4.66720	−	2.12540i	−0.290567	−	0.132322i
$259$	5.81602	+	5.81602i	0.361390	+	0.361390i
$260$	6.03696	+	6.93696i	0.374396	+	0.430212i
$261$	7.83317	−	7.83317i	0.484861	−	0.484861i
$262$	5.17137	+	13.8198i	0.319488	+	0.853788i
$263$			13.0343i			0.803731i	0.915699	+	0.401866i	$0.131638\pi$
$263$			13.0343i			0.803731i	−0.915699	+	0.401866i	$0.868362\pi$
$264$	−0.668179	−	2.24886i	−0.0411236	−	0.138408i
$265$			2.00568i			0.123208i
$266$	−9.26683	+	3.46765i	−0.568186	+	0.212616i
$267$	1.57334	−	1.57334i	0.0962868	−	0.0962868i
$268$	−0.0228155	+	0.328898i	−0.00139368	+	0.0200906i
$269$	8.25994	+	8.25994i	0.503618	+	0.503618i	0.912560	−	0.408943i	$-0.134102\pi$
$269$	8.25994	+	8.25994i	0.503618	+	0.503618i	−0.408943	+	0.912560i	$0.634102\pi$
$270$	−4.82498	+	10.5952i	−0.293639	+	0.644805i
$271$	19.0405			1.15663			0.578314	−	0.815814i	$-0.303711\pi$
$271$	19.0405			1.15663			0.578314	+	0.815814i	$0.303711\pi$
$272$	−3.86572	+	27.7291i	−0.234394	+	1.68133i
$273$	−2.90057			−0.175550
$274$	−1.90150	+	4.17553i	−0.114874	+	0.252253i
$275$	−1.06709	−	1.06709i	−0.0643477	−	0.0643477i
$276$	7.94051	+	0.550830i	0.477963	+	0.0331561i
$277$	1.85762	−	1.85762i	0.111614	−	0.111614i	−0.649094	−	0.760708i	$-0.724852\pi$
$277$	1.85762	−	1.85762i	0.111614	−	0.111614i	0.760708	+	0.649094i	$0.224852\pi$
$278$	18.4603	−	6.90786i	1.10718	−	0.414306i
$279$			18.6035i			1.11376i
$280$	−3.57772	+	6.60243i	−0.213810	+	0.394571i
$281$		−	0.0999892i		−	0.00596486i	−0.999996	−	0.00298243i	$-0.999051\pi$
$281$		−	0.0999892i		−	0.00596486i	0.999996	−	0.00298243i	$-0.000949338\pi$
$282$	−3.34022	−	8.92629i	−0.198907	−	0.531553i
$283$	21.0147	−	21.0147i	1.24920	−	1.24920i	0.293120	−	0.956076i	$-0.405306\pi$
$283$	21.0147	−	21.0147i	1.24920	−	1.24920i	0.956076	−	0.293120i	$-0.0946937\pi$
$284$	−14.2735	+	12.4216i	−0.846975	+	0.737089i
$285$	5.39537	+	5.39537i	0.319594	+	0.319594i
$286$	3.16732	+	1.44237i	0.187288	+	0.0852891i
$287$	−8.32698			−0.491526
$288$	11.0402	+	7.01191i	0.650552	+	0.413181i
$289$	31.9905			1.88179
$290$	−11.5219	−	5.24697i	−0.676588	−	0.308112i
$291$	−8.94116	−	8.94116i	−0.524140	−	0.524140i
$292$	−11.4013	+	9.92212i	−0.667212	+	0.580648i
$293$	−3.60771	+	3.60771i	−0.210765	+	0.210765i	−0.804592	−	0.593828i	$-0.797616\pi$
$293$	−3.60771	+	3.60771i	−0.210765	+	0.210765i	0.593828	+	0.804592i	$0.297616\pi$
$294$	2.04760	+	5.47193i	0.119419	+	0.319130i
$295$		−	1.35651i		−	0.0789791i
$296$	−14.3941	−	7.79988i	−0.836642	−	0.453359i
$297$			4.40604i			0.255664i
$298$	17.9722	−	6.72521i	1.04110	−	0.389581i
$299$	−8.34943	+	8.34943i	−0.482860	+	0.482860i
$300$	−2.49742	−	0.173245i	−0.144188	−	0.0100023i
$301$	4.39294	+	4.39294i	0.253205	+	0.253205i
$302$	2.53545	−	5.56762i	0.145899	−	0.320381i
$303$	−4.44957			−0.255621
$304$	15.7153	−	11.8697i	0.901336	−	0.680774i
$305$	−0.559387			−0.0320304
$306$	9.48473	−	20.8276i	0.542206	−	1.19064i
$307$	−19.0162	−	19.0162i	−1.08531	−	1.08531i	−0.996004	−	0.0893081i	$-0.971534\pi$
$307$	−19.0162	−	19.0162i	−1.08531	−	1.08531i	−0.0893081	−	0.996004i	$-0.528466\pi$
$308$	−0.196676	+	2.83519i	−0.0112067	+	0.161550i
$309$	7.01876	−	7.01876i	0.399283	−	0.399283i
$310$	19.9127	−	7.45134i	1.13096	−	0.423207i
$311$			30.8664i			1.75027i	0.483876	+	0.875137i	$0.339229\pi$
$311$			30.8664i			1.75027i	−0.483876	+	0.875137i	$0.660771\pi$
$312$	5.53430	−	1.64434i	0.313318	−	0.0930925i
$313$			11.0251i			0.623175i	0.950218	+	0.311587i	$0.100861\pi$
$313$			11.0251i			0.623175i	−0.950218	+	0.311587i	$0.899139\pi$
$314$	−8.38504	−	22.4079i	−0.473195	−	1.26455i
$315$	4.34051	−	4.34051i	0.244560	−	0.244560i
$316$	11.2365	+	12.9116i	0.632100	+	0.726335i
$317$	16.5248	+	16.5248i	0.928127	+	0.928127i	0.997585	−	0.0694577i	$-0.0221269\pi$
$317$	16.5248	+	16.5248i	0.928127	+	0.928127i	−0.0694577	+	0.997585i	$0.522127\pi$
$318$	1.14597	+	0.521867i	0.0642630	+	0.0292648i
$319$	−4.79139			−0.268266
$320$	3.08337	−	14.6257i	0.172366	−	0.817602i
$321$	−5.43071			−0.303113
$322$	−8.77527	−	3.99618i	−0.489027	−	0.222699i
$323$	−24.3680	−	24.3680i	−1.35587	−	1.35587i
$324$	−4.30844	−	4.95074i	−0.239358	−	0.275041i
$325$	2.62602	−	2.62602i	0.145666	−	0.145666i
$326$	−6.16325	−	16.4704i	−0.341351	−	0.912214i
$327$			15.8073i			0.874146i
$328$	15.8879	−	4.72060i	0.877264	−	0.260651i
$329$			11.5457i			0.636535i
$330$	2.05265	−	0.768104i	0.112995	−	0.0422827i
$331$	−12.4849	+	12.4849i	−0.686231	+	0.686231i	−0.961397	−	0.275166i	$-0.911267\pi$
$331$	−12.4849	+	12.4849i	−0.686231	+	0.686231i	0.275166	+	0.961397i	$0.411267\pi$
$332$	−1.44249	+	20.7942i	−0.0791667	+	1.14123i
$333$	9.46285	+	9.46285i	0.518561	+	0.518561i
$334$	5.36002	−	11.7701i	0.293287	−	0.644033i
$335$	−0.307995			−0.0168275
$336$	2.84148	+	3.76209i	0.155016	+	0.205239i
$337$	−22.9216			−1.24862			−0.624309	−	0.781178i	$-0.714619\pi$
$337$	−22.9216			−1.24862			−0.624309	+	0.781178i	$0.714619\pi$
$338$	4.06983	−	8.93700i	0.221370	−	0.486109i
$339$	11.4069	+	11.4069i	0.619537	+	0.619537i
$340$	−26.0923	−	1.81001i	−1.41506	−	0.0981618i
$341$	5.68968	−	5.68968i	0.308113	−	0.308113i
$342$	−15.0774	+	5.64198i	−0.815294	+	0.305084i
$343$		−	17.0247i		−	0.919247i
$344$	−10.8721	−	5.89138i	−0.586186	−	0.317642i
$345$			7.43585i			0.400333i
$346$	−3.85794	−	10.3098i	−0.207404	−	0.554259i
$347$	−13.5193	+	13.5193i	−0.725752	+	0.725752i	−0.969770	−	0.244019i	$-0.921534\pi$
$347$	−13.5193	+	13.5193i	−0.725752	+	0.725752i	0.244019	+	0.969770i	$0.421534\pi$
$348$	−5.99584	+	5.21795i	−0.321411	+	0.279711i
$349$	−8.95887	−	8.95887i	−0.479557	−	0.479557i	0.425433	−	0.904990i	$-0.360122\pi$
$349$	−8.95887	−	8.95887i	−0.479557	−	0.479557i	−0.904990	+	0.425433i	$0.860122\pi$
$350$	2.75996	+	1.25686i	0.147526	+	0.0671821i
$351$	−10.8429			−0.578753
$352$	−1.23202	−	5.52106i	−0.0656670	−	0.294274i
$353$	−17.2404			−0.917615			−0.458808	−	0.888536i	$-0.651723\pi$
$353$	−17.2404			−0.917615			−0.458808	+	0.888536i	$0.651723\pi$
$354$	−0.775060	−	0.352956i	−0.0411940	−	0.0187594i
$355$	−12.4992	−	12.4992i	−0.663391	−	0.663391i
$356$	4.04715	−	3.52207i	0.214498	−	0.186670i
$357$	5.83344	−	5.83344i	0.308738	−	0.308738i
$358$	−9.03118	−	24.1346i	−0.477313	−	1.27555i
$359$		−	16.9641i		−	0.895331i	−0.894201	−	0.447665i	$-0.852256\pi$
$359$		−	16.9641i		−	0.895331i	0.894201	−	0.447665i	$-0.147744\pi$
$360$	−5.82107	+	10.7424i	−0.306797	+	0.566173i
$361$			5.24135i			0.275860i
$362$	−8.74460	+	3.27224i	−0.459606	+	0.171985i
$363$	0.586507	−	0.586507i	0.0307837	−	0.0307837i
$364$	−6.97721	−	0.484006i	−0.365705	−	0.0253688i
$365$	−9.98411	−	9.98411i	−0.522592	−	0.522592i
$366$	−0.145549	+	0.319613i	−0.00760796	+	0.0167064i
$367$	4.27144			0.222968			0.111484	−	0.993766i	$-0.464440\pi$
$367$	4.27144			0.222968			0.111484	+	0.993766i	$0.464440\pi$
$368$	19.0087	+	2.65001i	0.990898	+	0.138141i
$369$	−13.5483			−0.705294
$370$	6.33859	−	13.9190i	0.329528	−	0.723614i
$371$	−1.07863	−	1.07863i	−0.0559998	−	0.0559998i
$372$	0.923736	−	13.3161i	0.0478935	−	0.690410i
$373$	−9.23365	+	9.23365i	−0.478100	+	0.478100i	−0.904524	−	0.426423i	$-0.859773\pi$
$373$	−9.23365	+	9.23365i	−0.478100	+	0.478100i	0.426423	+	0.904524i	$0.359773\pi$
$374$	−9.27072	+	3.46911i	−0.479378	+	0.179383i
$375$		−	10.0874i		−	0.520910i
$376$	−6.54530	−	22.0293i	−0.337548	−	1.13607i
$377$		−	11.7913i		−	0.607281i
$378$	−3.10317	−	8.29279i	−0.159610	−	0.426535i
$379$	13.2658	−	13.2658i	0.681416	−	0.681416i	−0.278903	−	0.960319i	$-0.589971\pi$
$379$	13.2658	−	13.2658i	0.681416	−	0.681416i	0.960319	+	0.278903i	$0.0899708\pi$
$380$	12.0781	+	13.8787i	0.619592	+	0.711961i
$381$	−0.552667	−	0.552667i	−0.0283140	−	0.0283140i
$382$	17.3951	+	7.92160i	0.890013	+	0.405304i
$383$	6.34374			0.324150			0.162075	−	0.986778i	$-0.448181\pi$
$383$	6.34374			0.324150			0.162075	+	0.986778i	$0.448181\pi$
$384$	−7.55431	−	5.56724i	−0.385504	−	0.284102i
$385$	−2.65500			−0.135311
$386$	−27.2101	−	12.3912i	−1.38496	−	0.630698i
$387$	7.14746	+	7.14746i	0.363326	+	0.363326i
$388$	−20.0157	−	22.9996i	−1.01614	−	1.16763i
$389$	−0.596988	+	0.596988i	−0.0302685	+	0.0302685i	−0.722079	−	0.691811i	$-0.756813\pi$
$389$	−0.596988	+	0.596988i	−0.0302685	+	0.0302685i	0.691811	+	0.722079i	$0.256813\pi$
$390$	1.89025	+	5.05143i	0.0957165	+	0.255789i
$391$		−	33.5837i		−	1.69840i
$392$	4.01235	+	13.5042i	0.202654	+	0.682066i
$393$			8.65429i			0.436551i
$394$	29.8100	−	11.1549i	1.50181	−	0.561978i
$395$	−11.3067	+	11.3067i	−0.568900	+	0.568900i
$396$	−0.319999	+	4.61295i	−0.0160805	+	0.231809i
$397$	11.1072	+	11.1072i	0.557454	+	0.557454i	0.928582	−	0.371128i	$-0.121029\pi$
$397$	11.1072	+	11.1072i	0.557454	+	0.557454i	−0.371128	+	0.928582i	$0.621029\pi$
$398$	−10.9298	+	24.0008i	−0.547860	+	1.20305i
$399$	−5.80313			−0.290520
$400$	−5.97854	−	0.833468i	−0.298927	−	0.0416734i
$401$	33.9036			1.69306			0.846531	−	0.532339i	$-0.178687\pi$
$401$	33.9036			1.69306			0.846531	+	0.532339i	$0.178687\pi$
$402$	−0.0801382	+	0.175977i	−0.00399693	+	0.00877691i
$403$	14.0019	+	14.0019i	0.697484	+	0.697484i
$404$	−10.7033	−	0.742483i	−0.532509	−	0.0369399i
$405$	4.33535	−	4.33535i	0.215425	−	0.215425i
$406$	9.01808	−	3.37457i	0.447560	−	0.167477i
$407$		−	5.78823i		−	0.286912i
$408$	−7.82323	+	14.4372i	−0.387308	+	0.714749i
$409$		−	8.06105i		−	0.398593i	−0.979939	−	0.199297i	$-0.936134\pi$
$409$		−	8.06105i		−	0.398593i	0.979939	−	0.199297i	$-0.0638657\pi$
$410$	5.42655	+	14.5017i	0.267998	+	0.716189i
$411$	−1.90279	+	1.90279i	−0.0938580	+	0.0938580i
$412$	18.0546	−	15.7122i	0.889485	−	0.774084i
$413$	0.729515	+	0.729515i	0.0358971	+	0.0358971i
$414$	−14.2776	−	6.50192i	−0.701708	−	0.319552i
$415$	−19.4726			−0.955873
$416$	13.5869	−	3.03192i	0.666155	−	0.148652i
$417$	11.5603			0.566111
$418$	6.33682	+	2.88573i	0.309944	+	0.141146i
$419$	6.49585	+	6.49585i	0.317343	+	0.317343i	0.847746	−	0.530403i	$-0.177959\pi$
$419$	6.49585	+	6.49585i	0.317343	+	0.317343i	−0.530403	+	0.847746i	$0.677959\pi$
$420$	−3.32241	+	2.89137i	−0.162117	+	0.141084i
$421$	20.0150	−	20.0150i	0.975472	−	0.975472i	−0.0242342	−	0.999706i	$-0.507715\pi$
$421$	20.0150	−	20.0150i	0.975472	−	0.975472i	0.999706	+	0.0242342i	$0.00771473\pi$
$422$	−6.64576	−	17.7599i	−0.323511	−	0.864537i
$423$			18.7852i			0.913368i
$424$	2.66952	+	1.44656i	0.129643	+	0.0702510i
$425$			10.5626i			0.512361i
$426$	−10.3938	+	3.88938i	−0.503582	+	0.188441i
$427$	0.300831	−	0.300831i	0.0145582	−	0.0145582i
$428$	−13.0634	−	0.906202i	−0.631443	−	0.0438029i
$429$	1.44335	+	1.44335i	0.0696858	+	0.0696858i
$430$	4.78765	−	10.5133i	0.230881	−	0.506994i
$431$	17.7166			0.853378			0.426689	−	0.904398i	$-0.359680\pi$
$431$	17.7166			0.853378			0.426689	+	0.904398i	$0.359680\pi$
$432$	10.6221	+	14.0635i	0.511055	+	0.676630i
$433$	5.96757			0.286783			0.143392	−	0.989666i	$-0.454199\pi$
$433$	5.96757			0.286783			0.143392	+	0.989666i	$0.454199\pi$
$434$	−6.70155	+	14.7160i	−0.321685	+	0.706392i
$435$	−5.25054	−	5.25054i	−0.251744	−	0.251744i
$436$	−2.63770	+	38.0239i	−0.126323	+	1.82101i
$437$	−16.7046	+	16.7046i	−0.799089	+	0.799089i
$438$	−8.30235	+	3.10674i	−0.396701	+	0.148446i
$439$			1.64838i			0.0786727i	0.999226	+	0.0393364i	$0.0125244\pi$
$439$			1.64838i			0.0786727i	−0.999226	+	0.0393364i	$0.987476\pi$
$440$	5.06576	−	1.50513i	0.241500	−	0.0717542i
$441$		−	11.5156i		−	0.548361i
$442$	−8.53724	−	22.8146i	−0.406075	−	1.08518i
$443$	−24.5367	+	24.5367i	−1.16578	+	1.16578i	−0.182586	+	0.983190i	$0.558447\pi$
$443$	−24.5367	+	24.5367i	−1.16578	+	1.16578i	−0.983190	+	0.182586i	$0.941553\pi$
$444$	−6.30354	−	7.24327i	−0.299153	−	0.343751i
$445$	3.54408	+	3.54408i	0.168005	+	0.168005i
$446$	−0.769824	−	0.350571i	−0.0364522	−	0.0166000i
$447$	11.2547			0.532327
$448$	6.20732	+	9.52372i	0.293269	+	0.449953i
$449$	−9.19478			−0.433928			−0.216964	−	0.976180i	$-0.569615\pi$
$449$	−9.19478			−0.433928			−0.216964	+	0.976180i	$0.569615\pi$
$450$	4.49054	+	2.04495i	0.211686	+	0.0964001i
$451$	4.14360	+	4.14360i	0.195114	+	0.195114i
$452$	25.5355	+	29.3423i	1.20109	+	1.38015i
$453$	2.53718	−	2.53718i	0.119207	−	0.119207i
$454$	6.43811	+	17.2050i	0.302156	+	0.807469i
$455$		−	6.53377i		−	0.306308i
$456$	11.0724	−	3.28981i	0.518512	−	0.154060i
$457$			15.0004i			0.701689i	0.936434	+	0.350845i	$0.114105\pi$
$457$			15.0004i			0.701689i	−0.936434	+	0.350845i	$0.885895\pi$
$458$	28.7168	−	10.7459i	1.34185	−	0.502121i
$459$	21.8067	−	21.8067i	1.01785	−	1.01785i
$460$	−1.24079	+	17.8867i	−0.0578522	+	0.833970i
$461$	−28.5907	−	28.5907i	−1.33160	−	1.33160i	−0.903938	−	0.427664i	$-0.859337\pi$
$461$	−28.5907	−	28.5907i	−1.33160	−	1.33160i	−0.427664	−	0.903938i	$-0.640663\pi$
$462$	−0.690814	+	1.51697i	−0.0321396	+	0.0705757i
$463$	−15.7577			−0.732324			−0.366162	−	0.930551i	$-0.619328\pi$
$463$	−15.7577			−0.732324			−0.366162	+	0.930551i	$0.619328\pi$
$464$	−15.2935	+	11.5511i	−0.709982	+	0.536246i
$465$	12.4698			0.578274
$466$	−13.6822	+	30.0448i	−0.633813	+	1.39180i
$467$	−12.8486	−	12.8486i	−0.594564	−	0.594564i	0.344296	−	0.938861i	$-0.388117\pi$
$467$	−12.8486	−	12.8486i	−0.594564	−	0.594564i	−0.938861	+	0.344296i	$0.888117\pi$
$468$	−11.3521	−	0.787494i	−0.524753	−	0.0364019i
$469$	0.165636	−	0.165636i	0.00764834	−	0.00764834i
$470$	20.1072	−	7.52413i	0.927477	−	0.347062i
$471$		−	14.0324i		−	0.646578i
$472$	−1.80548	−	0.978354i	−0.0831041	−	0.0450324i
$473$		−	4.37195i		−	0.201022i
$474$	3.51828	+	9.40212i	0.161600	+	0.431854i
$475$	5.25385	−	5.25385i	0.241063	−	0.241063i
$476$	15.0055	−	13.0587i	0.687778	−	0.598546i
$477$	−1.75497	−	1.75497i	−0.0803545	−	0.0803545i
$478$	37.3968	+	17.0302i	1.71049	+	0.778942i
$479$	20.9000			0.954946			0.477473	−	0.878646i	$-0.341553\pi$
$479$	20.9000			0.954946			0.477473	+	0.878646i	$0.341553\pi$
$480$	4.70006	−	7.40023i	0.214527	−	0.337773i
$481$	14.2444			0.649490
$482$	6.23871	+	2.84106i	0.284165	+	0.129407i
$483$	−3.99891	−	3.99891i	−0.181957	−	0.181957i
$484$	1.50869	−	1.31295i	0.0685769	−	0.0596798i
$485$	20.1407	−	20.1407i	0.914543	−	0.914543i
$486$	−7.90039	−	21.1127i	−0.358369	−	0.957692i
$487$			16.1394i			0.731348i	0.930743	+	0.365674i	$0.119162\pi$
$487$			16.1394i			0.731348i	−0.930743	+	0.365674i	$0.880838\pi$
$488$	−0.403445	+	0.744530i	−0.0182631	+	0.0337033i
$489$		−	10.3142i		−	0.466425i
$490$	−12.3260	+	4.61239i	−0.556831	+	0.208367i
$491$	−22.9759	+	22.9759i	−1.03689	+	1.03689i	−0.0375963	+	0.999293i	$0.511970\pi$
$491$	−22.9759	+	22.9759i	−1.03689	+	1.03689i	−0.999293	+	0.0375963i	$0.988030\pi$
$492$	9.69769	+	0.672725i	0.437206	+	0.0303288i
$493$	23.7139	+	23.7139i	1.06802	+	1.06802i
$494$	−7.10158	+	15.5945i	−0.319515	+	0.701628i
$495$	−4.31977			−0.194159
$496$	4.44403	−	31.8774i	0.199543	−	1.43134i
$497$	13.4439			0.603040
$498$	−5.06665	+	11.1259i	−0.227042	+	0.498565i
$499$	4.73566	+	4.73566i	0.211997	+	0.211997i	0.805115	−	0.593118i	$-0.202103\pi$
$499$	4.73566	+	4.73566i	0.211997	+	0.211997i	−0.593118	+	0.805115i	$0.702103\pi$
$500$	1.68324	−	24.2648i	0.0752768	−	1.08516i
$501$	5.36367	−	5.36367i	0.239631	−	0.239631i
$502$	−32.2241	+	12.0583i	−1.43823	+	0.538188i
$503$			9.37937i			0.418205i	0.977894	+	0.209103i	$0.0670543\pi$
$503$			9.37937i			0.418205i	−0.977894	+	0.209103i	$0.932946\pi$
$504$	−2.64662	−	8.90761i	−0.117890	−	0.396777i
$505$		−	10.0230i		−	0.446019i
$506$	2.37813	+	6.35521i	0.105721	+	0.282524i
$507$	4.07261	−	4.07261i	0.180871	−	0.180871i
$508$	−1.23720	−	1.42164i	−0.0548919	−	0.0630752i
$509$	−14.7869	−	14.7869i	−0.655418	−	0.655418i	0.298874	−	0.954292i	$-0.403389\pi$
$509$	−14.7869	−	14.7869i	−0.655418	−	0.655418i	−0.954292	+	0.298874i	$0.903389\pi$
$510$	−13.9607	−	6.35758i	−0.618189	−	0.281518i
$511$	10.7387			0.475050
$512$	−17.2426	−	14.6524i	−0.762024	−	0.647549i
$513$	−21.6933			−0.957784
$514$	−7.93928	−	3.61548i	−0.350187	−	0.159472i
$515$	15.8103	+	15.8103i	0.696687	+	0.696687i
$516$	−4.76117	−	5.47097i	−0.209599	−	0.240846i
$517$	5.74526	−	5.74526i	0.252676	−	0.252676i
$518$	4.07665	+	10.8943i	0.179118	+	0.478667i
$519$		−	6.45627i		−	0.283399i
$520$	3.70402	+	12.4665i	0.162432	+	0.546691i
$521$			24.6463i			1.07977i	0.841738	+	0.539887i	$0.181533\pi$
$521$			24.6463i			1.07977i	−0.841738	+	0.539887i	$0.818467\pi$
$522$	14.6727	−	5.49054i	0.642207	−	0.240314i
$523$	4.14744	−	4.14744i	0.181355	−	0.181355i	−0.610591	−	0.791946i	$-0.709068\pi$
$523$	4.14744	−	4.14744i	0.181355	−	0.181355i	0.791946	+	0.610591i	$0.209068\pi$
$524$	−1.44411	+	20.8176i	−0.0630862	+	0.909421i
$525$	1.25772	+	1.25772i	0.0548913	+	0.0548913i
$526$	−7.63952	+	16.7757i	−0.333099	+	0.731457i
$527$	−56.3195			−2.45331
$528$	0.458103	−	3.28601i	0.0199364	−	0.143005i
$529$	−0.0221102			−0.000961313
$530$	−1.17555	+	2.58140i	−0.0510625	+	0.112129i
$531$	1.18694	+	1.18694i	0.0515090	+	0.0515090i
$532$	−13.9592	−	0.968346i	−0.605209	−	0.0419831i
$533$	−10.1971	+	10.1971i	−0.441685	+	0.441685i
$534$	2.94710	−	1.10281i	0.127533	−	0.0477231i
$535$		−	12.2331i		−	0.528885i
$536$	−0.222134	+	0.409933i	−0.00959474	+	0.0177064i
$537$		−	15.1137i		−	0.652204i
$538$	5.78967	+	15.4721i	0.249611	+	0.667050i
$539$	−3.52192	+	3.52192i	−0.151700	+	0.151700i
$540$	−12.4199	+	10.8085i	−0.534467	+	0.465126i
$541$	−2.33025	−	2.33025i	−0.100185	−	0.100185i	0.655238	−	0.755423i	$-0.272569\pi$
$541$	−2.33025	−	2.33025i	−0.100185	−	0.100185i	−0.755423	+	0.655238i	$0.772569\pi$
$542$	24.5059	+	11.1598i	1.05262	+	0.479354i
$543$	−5.47609			−0.235002
$544$	−21.2276	+	33.4228i	−0.910126	+	1.43299i
$545$	−35.6073			−1.52525
$546$	−3.73315	−	1.70005i	−0.159764	−	0.0727552i
$547$	−6.13182	−	6.13182i	−0.262178	−	0.262178i	0.563761	−	0.825938i	$-0.309354\pi$
$547$	−6.13182	−	6.13182i	−0.262178	−	0.262178i	−0.825938	+	0.563761i	$0.809354\pi$
$548$	−4.89462	+	4.25959i	−0.209088	+	0.181961i
$549$	0.489462	−	0.489462i	0.0208897	−	0.0208897i
$550$	−0.747957	−	1.99881i	−0.0318930	−	0.0852297i
$551$		−	23.5906i		−	1.00499i
$552$	9.89693	+	5.36294i	0.421241	+	0.228262i
$553$		−	12.1612i		−	0.517145i
$554$	3.47960	−	1.30207i	0.147834	−	0.0553197i
$555$	6.34291	−	6.34291i	0.269242	−	0.269242i
$556$	27.8079	+	1.92903i	1.17932	+	0.0818089i
$557$	−8.18063	−	8.18063i	−0.346624	−	0.346624i	0.512226	−	0.858851i	$-0.328821\pi$
$557$	−8.18063	−	8.18063i	−0.346624	−	0.346624i	−0.858851	+	0.512226i	$0.828821\pi$
$558$	−10.9036	+	23.9434i	−0.461588	+	1.01361i
$559$	10.7591			0.455060
$560$	−8.47442	+	6.40068i	−0.358110	+	0.270478i
$561$	−5.80556			−0.245111
$562$	0.0586045	−	0.128690i	0.00247208	−	0.00542847i
$563$	3.13659	+	3.13659i	0.132191	+	0.132191i	0.770107	−	0.637915i	$-0.220203\pi$
$563$	3.13659	+	3.13659i	0.132191	+	0.132191i	−0.637915	+	0.770107i	$0.720203\pi$
$564$	0.932761	−	13.4462i	0.0392763	−	0.566189i
$565$	−25.6950	+	25.6950i	−1.08100	+	1.08100i
$566$	39.3637	−	14.7299i	1.65458	−	0.619146i
$567$			4.66300i			0.195828i
$568$	−25.6510	+	7.62138i	−1.07629	+	0.319786i
$569$		−	7.90270i		−	0.331298i	−0.986185	−	0.165649i	$-0.947028\pi$
$569$		−	7.90270i		−	0.331298i	0.986185	−	0.165649i	$-0.0529719\pi$
$570$	3.78180	+	10.1063i	0.158402	+	0.423308i
$571$	5.24769	−	5.24769i	0.219609	−	0.219609i	−0.588725	−	0.808334i	$-0.700370\pi$
$571$	5.24769	−	5.24769i	0.219609	−	0.219609i	0.808334	+	0.588725i	$0.200370\pi$
$572$	3.23109	+	3.71278i	0.135099	+	0.155239i
$573$	7.92700	+	7.92700i	0.331155	+	0.331155i
$574$	−10.7172	−	4.88051i	−0.447326	−	0.203709i
$575$	7.24081			0.301963
$576$	10.0995	+	15.4954i	0.420813	+	0.645641i
$577$	−17.9331			−0.746565			−0.373282	−	0.927718i	$-0.621768\pi$
$577$	−17.9331			−0.746565			−0.373282	+	0.927718i	$0.621768\pi$
$578$	41.1731	+	18.7499i	1.71258	+	0.779893i
$579$	−12.3997	−	12.3997i	−0.515314	−	0.515314i
$580$	−11.7539	−	13.5061i	−0.488052	−	0.560812i
$581$	10.4721	−	10.4721i	0.434457	−	0.434457i
$582$	−6.26717	−	16.7481i	−0.259782	−	0.694233i
$583$			1.07348i			0.0444589i
$584$	−20.4894	+	6.08778i	−0.847858	+	0.251914i
$585$		−	10.6306i		−	0.439523i
$586$	−6.75778	+	2.52877i	−0.279161	+	0.104462i
$587$	24.5007	−	24.5007i	1.01125	−	1.01125i	0.0113171	−	0.999936i	$-0.496398\pi$
$587$	24.5007	−	24.5007i	1.01125	−	1.01125i	0.999936	−	0.0113171i	$-0.00360241\pi$
$588$	−0.571794	+	8.24272i	−0.0235804	+	0.339924i
$589$	28.0134	+	28.0134i	1.15427	+	1.15427i
$590$	0.795062	−	1.74589i	0.0327322	−	0.0718770i
$591$	18.6678			0.767891
$592$	−13.9543	−	18.4753i	−0.573517	−	0.759330i
$593$	14.1320			0.580333			0.290166	−	0.956976i	$-0.406289\pi$
$593$	14.1320			0.580333			0.290166	+	0.956976i	$0.406289\pi$
$594$	−2.58241	+	5.67075i	−0.105958	+	0.232674i
$595$	13.1403	+	13.1403i	0.538700	+	0.538700i
$596$	27.0727	+	1.87802i	1.10894	+	0.0769268i
$597$	−10.9372	+	10.9372i	−0.447631	+	0.447631i
$598$	−15.6397	+	5.85240i	−0.639556	+	0.239322i
$599$		−	24.3432i		−	0.994635i	−0.867569	−	0.497318i	$-0.834318\pi$
$599$		−	24.3432i		−	0.994635i	0.867569	−	0.497318i	$-0.165682\pi$
$600$	−3.11274	−	1.68673i	−0.127077	−	0.0688604i
$601$		−	41.6105i		−	1.69733i	−0.528932	−	0.848664i	$-0.677407\pi$
$601$		−	41.6105i		−	1.69733i	0.528932	−	0.848664i	$-0.322593\pi$
$602$	3.07916	+	8.22864i	0.125497	+	0.335374i
$603$	0.269494	−	0.269494i	0.0109747	−	0.0109747i
$604$	6.52646	−	5.67972i	0.265558	−	0.231105i
$605$	1.32116	+	1.32116i	0.0537127	+	0.0537127i
$606$	−5.72679	−	2.60793i	−0.232635	−	0.105940i
$607$	−4.60294			−0.186828			−0.0934138	−	0.995627i	$-0.529778\pi$
$607$	−4.60294			−0.186828			−0.0934138	+	0.995627i	$0.529778\pi$
$608$	27.1832	−	6.06592i	1.10243	−	0.246006i
$609$	5.64735			0.228842
$610$	−0.719954	−	0.327861i	−0.0291501	−	0.0132747i
$611$	14.1387	+	14.1387i	0.571990	+	0.571990i
$612$	24.4145	−	21.2470i	0.986897	−	0.858858i
$613$	−24.5982	+	24.5982i	−0.993513	+	0.993513i	−0.999979	−	0.00646627i	$-0.997942\pi$
$613$	−24.5982	+	24.5982i	−0.993513	+	0.993513i	0.00646627	+	0.999979i	$0.497942\pi$
$614$	−13.3291	−	35.6202i	−0.537919	−	1.43751i
$615$			9.08135i			0.366195i
$616$	−1.91486	+	3.53374i	−0.0771519	+	0.142378i
$617$			4.80269i			0.193349i	0.995316	+	0.0966745i	$0.0308206\pi$
$617$			4.80269i			0.193349i	−0.995316	+	0.0966745i	$0.969179\pi$
$618$	13.1472	−	4.91969i	0.528858	−	0.197899i
$619$	24.6248	−	24.6248i	0.989756	−	0.989756i	−0.0101923	−	0.999948i	$-0.503244\pi$
$619$	24.6248	−	24.6248i	0.989756	−	0.989756i	0.999948	+	0.0101923i	$0.00324436\pi$
$620$	29.9957	+	2.08079i	1.20466	+	0.0835666i
$621$	−14.9488	−	14.9488i	−0.599874	−	0.599874i
$622$	−18.0910	+	39.7264i	−0.725385	+	1.59288i
$623$	−3.81192			−0.152721
$624$	8.08663	+	1.12736i	0.323724	+	0.0451305i
$625$	15.1772			0.607088
$626$	−6.46189	+	14.1897i	−0.258269	+	0.567136i
$627$	2.88770	+	2.88770i	0.115324	+	0.115324i
$628$	2.34153	−	33.7544i	0.0934372	−	1.34695i
$629$	−28.6475	+	28.6475i	−1.14225	+	1.14225i
$630$	8.13043	−	3.04241i	0.323924	−	0.121213i
$631$			46.1535i			1.83734i	0.395022	+	0.918672i	$0.370737\pi$
$631$			46.1535i			1.83734i	−0.395022	+	0.918672i	$0.629263\pi$
$632$	6.89421	+	23.2036i	0.274237	+	0.922988i
$633$		−	11.1217i		−	0.442048i
$634$	11.5828	+	30.9535i	0.460013	+	1.22932i
$635$	1.24493	−	1.24493i	0.0494035	−	0.0494035i
$636$	1.16905	+	1.34333i	0.0463557	+	0.0532664i
$637$	−8.66720	−	8.66720i	−0.343407	−	0.343407i
$638$	−6.16672	−	2.80827i	−0.244143	−	0.111180i
$639$	21.8736			0.865307
$640$	12.5407	−	17.0167i	0.495713	−	0.672644i
$641$	19.7346			0.779472			0.389736	−	0.920927i	$-0.372566\pi$
$641$	19.7346			0.779472			0.389736	+	0.920927i	$0.372566\pi$
$642$	−6.98956	−	3.18298i	−0.275856	−	0.125622i
$643$	−4.28037	−	4.28037i	−0.168801	−	0.168801i	0.617651	−	0.786452i	$-0.288084\pi$
$643$	−4.28037	−	4.28037i	−0.168801	−	0.168801i	−0.786452	+	0.617651i	$0.788084\pi$
$644$	−8.95195	−	10.2865i	−0.352756	−	0.405345i
$645$	4.79091	−	4.79091i	0.188642	−	0.188642i
$646$	−17.0803	−	45.6449i	−0.672017	−	1.79587i
$647$		−	9.28642i		−	0.365087i	−0.983198	−	0.182543i	$-0.941567\pi$
$647$		−	9.28642i		−	0.365087i	0.983198	−	0.182543i	$-0.0584330\pi$
$648$	−2.64347	−	8.89703i	−0.103845	−	0.349508i
$649$		−	0.726029i		−	0.0284991i
$650$	4.91894	−	1.84067i	0.192937	−	0.0721970i
$651$	−6.70612	+	6.70612i	−0.262833	+	0.262833i
$652$	1.72109	−	24.8105i	0.0674032	−	0.971654i
$653$	−25.3273	−	25.3273i	−0.991133	−	0.991133i	0.00882792	−	0.999961i	$-0.497190\pi$
$653$	−25.3273	−	25.3273i	−0.991133	−	0.991133i	−0.999961	+	0.00882792i	$0.997190\pi$
$654$	−9.26478	+	20.3447i	−0.362282	+	0.795539i
$655$	−19.4945			−0.761714
$656$	23.2152	+	3.23643i	0.906401	+	0.126362i
$657$	17.4721			0.681653
$658$	−6.76703	+	14.8598i	−0.263806	+	0.579295i
$659$	1.52170	+	1.52170i	0.0592771	+	0.0592771i	0.736124	−	0.676847i	$-0.236654\pi$
$659$	1.52170	+	1.52170i	0.0592771	+	0.0592771i	−0.676847	+	0.736124i	$0.736654\pi$
$660$	3.09204	+	0.214494i	0.120358	+	0.00834916i
$661$	−11.4634	+	11.4634i	−0.445873	+	0.445873i	−0.893980	−	0.448107i	$-0.852098\pi$
$661$	−11.4634	+	11.4634i	−0.445873	+	0.445873i	0.448107	+	0.893980i	$0.352098\pi$
$662$	−23.3861	+	8.75108i	−0.908925	+	0.340120i
$663$		−	14.2871i		−	0.554864i
$664$	−14.0442	+	25.9176i	−0.545020	+	1.00580i
$665$		−	13.0720i		−	0.506912i
$666$	6.63284	+	17.7253i	0.257017	+	0.686843i
$667$	16.2562	−	16.2562i	0.629442	−	0.629442i
$668$	13.7971	−	12.0071i	0.533828	−	0.464569i
$669$	−0.350810	−	0.350810i	−0.0135631	−	0.0135631i
$670$	−0.396402	−	0.180518i	−0.0153143	−	0.00697402i
$671$	−0.299394			−0.0115580
$672$	1.45212	+	6.50738i	0.0560167	+	0.251028i
$673$	−37.7519			−1.45523			−0.727615	−	0.685986i	$-0.759371\pi$
$673$	−37.7519			−1.45523			−0.727615	+	0.685986i	$0.759371\pi$
$674$	−29.5010	−	13.4345i	−1.13634	−	0.517478i
$675$	4.70162	+	4.70162i	0.180966	+	0.180966i
$676$	10.4761	−	9.11693i	0.402927	−	0.350651i
$677$	26.3575	−	26.3575i	1.01300	−	1.01300i	0.0130883	−	0.999914i	$-0.495834\pi$
$677$	26.3575	−	26.3575i	1.01300	−	1.01300i	0.999914	−	0.0130883i	$-0.00416624\pi$
$678$	7.99548	+	21.3668i	0.307065	+	0.820588i
$679$			21.6629i			0.831344i
$680$	−32.5211	−	17.6225i	−1.24713	−	0.675792i
$681$			10.7742i			0.412868i
$682$	10.6576	−	3.98809i	0.408101	−	0.152712i
$683$	−8.32750	+	8.32750i	−0.318643	+	0.318643i	−0.848246	−	0.529603i	$-0.822341\pi$
$683$	−8.32750	+	8.32750i	−0.318643	+	0.318643i	0.529603	+	0.848246i	$0.322341\pi$
$684$	−22.7121	−	1.57553i	−0.868419	−	0.0602419i
$685$	−4.28620	−	4.28620i	−0.163767	−	0.163767i
$686$	9.97831	−	21.9115i	0.380973	−	0.836585i
$687$	17.9832			0.686103
$688$	−10.5399	−	13.9547i	−0.401830	−	0.532018i
$689$	−2.64175			−0.100643
$690$	−4.35821	+	9.57025i	−0.165914	+	0.364333i
$691$	22.8400	+	22.8400i	0.868874	+	0.868874i	0.992348	−	0.123474i	$-0.0394035\pi$
$691$	22.8400	+	22.8400i	0.868874	+	0.868874i	−0.123474	+	0.992348i	$0.539403\pi$
$692$	1.07733	−	15.5303i	0.0409541	−	0.590375i
$693$	2.32312	−	2.32312i	0.0882480	−	0.0882480i
$694$	−25.3236	+	9.47611i	−0.961270	+	0.359708i
$695$			26.0406i			0.987776i
$696$	−10.7752	+	3.20150i	−0.408432	+	0.121353i
$697$		−	41.0155i		−	1.55357i
$698$	−6.27958	−	16.7813i	−0.237686	−	0.635182i
$699$	−13.6915	+	13.6915i	−0.517859	+	0.517859i
$700$	2.81553	+	3.23527i	0.106417	+	0.122282i
$701$	−26.9975	−	26.9975i	−1.01968	−	1.01968i	−0.999802	−	0.0198805i	$-0.993671\pi$
$701$	−26.9975	−	26.9975i	−1.01968	−	1.01968i	−0.0198805	−	0.999802i	$-0.506329\pi$
$702$	−13.9553	−	6.35514i	−0.526710	−	0.239859i
$703$	28.4987			1.07485
$704$	1.65027	−	7.82794i	0.0621970	−	0.295026i
$705$	12.5917			0.474229
$706$	−22.1891	−	10.1047i	−0.835100	−	0.380297i
$707$	5.39027	+	5.39027i	0.202722	+	0.202722i
$708$	−0.790665	−	0.908538i	−0.0297150	−	0.0341449i
$709$	−31.2791	+	31.2791i	−1.17471	+	1.17471i	−0.193640	+	0.981073i	$0.562030\pi$
$709$	−31.2791	+	31.2791i	−1.17471	+	1.17471i	−0.981073	+	0.193640i	$0.937970\pi$
$710$	−8.76115	−	23.4130i	−0.328800	−	0.878673i
$711$		−	19.7866i		−	0.742055i
$712$	7.27317	−	2.16099i	0.272573	−	0.0809866i
$713$			38.6078i			1.44587i
$714$	10.9269	−	4.08886i	0.408929	−	0.153022i
$715$	−3.25127	+	3.25127i	−0.121591	+	0.121591i
$716$	2.52196	−	36.3555i	0.0942502	−	1.35867i
$717$	17.0418	+	17.0418i	0.636437	+	0.636437i
$718$	9.94279	−	21.8335i	0.371062	−	0.814819i
$719$	−10.0611			−0.375215			−0.187608	−	0.982244i	$-0.560073\pi$
$719$	−10.0611			−0.375215			−0.187608	+	0.982244i	$0.560073\pi$
$720$	−13.7881	+	10.4141i	−0.513854	+	0.388111i
$721$	−17.0052			−0.633307
$722$	−3.07199	+	6.74583i	−0.114328	+	0.251054i
$723$	2.84299	+	2.84299i	0.105732	+	0.105732i
$724$	−13.1726	−	0.913775i	−0.489554	−	0.0339602i
$725$	−5.11283	+	5.11283i	−0.189886	+	0.189886i
$726$	1.09862	−	0.411103i	0.0407735	−	0.0152575i
$727$			42.1900i			1.56474i	0.622813	+	0.782371i	$0.285990\pi$
$727$			42.1900i			1.56474i	−0.622813	+	0.782371i	$0.714010\pi$
$728$	−8.69629	−	4.71234i	−0.322306	−	0.174651i
$729$		−	3.37687i		−	0.125069i
$730$	−6.99820	−	18.7017i	−0.259015	−	0.692182i
$731$	−21.6380	+	21.6380i	−0.800309	+	0.800309i
$732$	−0.374655	+	0.326048i	−0.0138477	+	0.0120511i
$733$	−14.3230	−	14.3230i	−0.529032	−	0.529032i	0.391251	−	0.920284i	$-0.372042\pi$
$733$	−14.3230	−	14.3230i	−0.529032	−	0.529032i	−0.920284	+	0.391251i	$0.872042\pi$
$734$	5.49753	+	2.50353i	0.202917	+	0.0924069i
$735$	−7.71885			−0.284714
$736$	22.9118	+	14.5518i	0.844541	+	0.536388i
$737$	−0.164844			−0.00607211
$738$	−17.4372	−	7.94074i	−0.641872	−	0.292303i
$739$	31.2002	+	31.2002i	1.14772	+	1.14772i	0.987000	+	0.160718i	$0.0513810\pi$
$739$	31.2002	+	31.2002i	1.14772	+	1.14772i	0.160718	+	0.987000i	$0.448619\pi$
$740$	16.3161	−	14.1992i	0.599791	−	0.521975i
$741$	−7.10642	+	7.10642i	−0.261061	+	0.261061i
$742$	−0.756050	−	2.02044i	−0.0277555	−	0.0741727i
$743$		−	47.0259i		−	1.72521i	−0.505875	−	0.862607i	$-0.668830\pi$
$743$		−	47.0259i		−	1.72521i	0.505875	−	0.862607i	$-0.331170\pi$
$744$	8.99359	−	16.5970i	0.329721	−	0.608477i
$745$			25.3521i			0.928827i
$746$	−17.2960	+	6.47218i	−0.633252	+	0.236963i
$747$	17.0385	−	17.0385i	0.623406	−	0.623406i
$748$	−13.9651	−	0.968752i	−0.510614	−	0.0354211i
$749$	6.57883	+	6.57883i	0.240385	+	0.240385i
$750$	5.91229	−	12.9829i	0.215886	−	0.474068i
$751$	−33.8187			−1.23406			−0.617031	−	0.786939i	$-0.711665\pi$
$751$	−33.8187			−1.23406			−0.617031	+	0.786939i	$0.711665\pi$
$752$	4.48745	−	32.1888i	0.163640	−	1.17381i
$753$	−20.1796			−0.735384
$754$	6.91095	−	15.1759i	0.251682	−	0.552672i
$755$	5.71520	+	5.71520i	0.207997	+	0.207997i
$756$	0.866563	−	12.4920i	0.0315166	−	0.454328i
$757$	20.5218	−	20.5218i	0.745876	−	0.745876i	−0.227826	−	0.973702i	$-0.573162\pi$
$757$	20.5218	−	20.5218i	0.745876	−	0.745876i	0.973702	+	0.227826i	$0.0731617\pi$
$758$	24.8488	−	9.29842i	0.902547	−	0.337734i
$759$			3.97980i			0.144458i
$760$	7.41058	+	24.9415i	0.268810	+	0.904723i
$761$			8.04344i			0.291574i	0.989316	+	0.145787i	$0.0465715\pi$
$761$			8.04344i			0.291574i	−0.989316	+	0.145787i	$0.953429\pi$
$762$	−0.387383	−	1.03523i	−0.0140334	−	0.0375024i
$763$	19.1491	−	19.1491i	0.693245	−	0.693245i
$764$	17.7454	+	20.3909i	0.642005	+	0.737715i
$765$	21.3797	+	21.3797i	0.772985	+	0.772985i
$766$	8.16466	+	3.71812i	0.295001	+	0.134341i
$767$	1.78671			0.0645142
$768$	−6.45971	−	11.5929i	−0.233095	−	0.418323i
$769$	−4.15624			−0.149878			−0.0749390	−	0.997188i	$-0.523876\pi$
$769$	−4.15624			−0.149878			−0.0749390	+	0.997188i	$0.523876\pi$
$770$	−3.41710	−	1.55612i	−0.123144	−	0.0560786i
$771$	−3.61795	−	3.61795i	−0.130297	−	0.130297i
$772$	−27.7579	−	31.8961i	−0.999030	−	1.14797i
$773$	−31.8173	+	31.8173i	−1.14439	+	1.14439i	−0.156751	+	0.987638i	$0.550102\pi$
$773$	−31.8173	+	31.8173i	−1.14439	+	1.14439i	−0.987638	+	0.156751i	$0.949898\pi$
$774$	5.00990	+	13.3883i	0.180077	+	0.481231i
$775$		−	12.1428i		−	0.436181i
$776$	−12.2808	−	41.3328i	−0.440853	−	1.48376i
$777$			6.82228i			0.244748i
$778$	−1.11825	+	0.418450i	−0.0400912	+	0.0150021i
$779$	−20.4012	+	20.4012i	−0.730949	+	0.730949i
$780$	−0.527854	+	7.60930i	−0.0189002	+	0.272457i
$781$	−6.68982	−	6.68982i	−0.239381	−	0.239381i
$782$	19.6837	−	43.2236i	0.703887	−	1.54567i
$783$	21.1110			0.754446
$784$	−2.75086	+	19.7322i	−0.0982451	+	0.704720i
$785$	31.6091			1.12818
$786$	−5.07235	+	11.1384i	−0.180925	+	0.397295i
$787$	25.6142	+	25.6142i	0.913049	+	0.913049i	0.996511	−	0.0834618i	$-0.0265976\pi$
$787$	25.6142	+	25.6142i	0.913049	+	0.913049i	−0.0834618	+	0.996511i	$0.526598\pi$
$788$	44.9048	+	3.11503i	1.59967	+	0.110968i
$789$	−7.64473	+	7.64473i	−0.272160	+	0.272160i
$790$	−21.1791	+	7.92522i	−0.753517	+	0.281967i
$791$		−	27.6369i		−	0.982654i
$792$	−3.11554	+	5.74951i	−0.110706	+	0.204300i
$793$		−	0.736787i		−	0.0261641i
$794$	7.78542	+	20.8055i	0.276294	+	0.738358i
$795$	−1.17635	+	1.17635i	−0.0417208	+	0.0417208i
$796$	−28.1341	+	24.4840i	−0.997188	+	0.867814i
$797$	−24.3166	−	24.3166i	−0.861340	−	0.861340i	0.130154	−	0.991494i	$-0.458453\pi$
$797$	−24.3166	−	24.3166i	−0.861340	−	0.861340i	−0.991494	+	0.130154i	$0.958453\pi$
$798$	−7.46887	−	3.40126i	−0.264395	−	0.120403i
$799$	−56.8697			−2.01191
$800$	−7.20613	−	4.57678i	−0.254775	−	0.161813i
$801$	−6.20212			−0.219141
$802$	43.6353	+	19.8711i	1.54082	+	0.701674i
$803$	−5.34367	−	5.34367i	−0.188574	−	0.188574i
$804$	−0.206283	+	0.179520i	−0.00727502	+	0.00633117i
$805$	9.00787	−	9.00787i	0.317486	−	0.317486i
$806$	9.81440	+	26.2276i	0.345698	+	0.923829i
$807$			9.68903i			0.341070i
$808$	−13.3404	−	7.22889i	−0.469314	−	0.254312i
$809$		−	44.5194i		−	1.56522i	−0.622512	−	0.782610i	$-0.713888\pi$
$809$		−	44.5194i		−	1.56522i	0.622512	−	0.782610i	$-0.286112\pi$
$810$	8.12077	−	3.03880i	0.285335	−	0.106772i
$811$	−15.6962	+	15.6962i	−0.551169	+	0.551169i	−0.926778	−	0.375609i	$-0.877433\pi$
$811$	−15.6962	+	15.6962i	−0.551169	+	0.551169i	0.375609	+	0.926778i	$0.377433\pi$
$812$	13.5845	+	0.942352i	0.476723	+	0.0330701i
$813$	11.1674	+	11.1674i	0.391658	+	0.391658i
$814$	3.39253	−	7.44970i	0.118908	−	0.261112i
$815$	23.2336			0.813839
$816$	−18.5306	+	13.9961i	−0.648701	+	0.489960i
$817$	21.5255			0.753082
$818$	4.72464	−	10.3749i	0.165193	−	0.362750i
$819$	5.71703	+	5.71703i	0.199769	+	0.199769i
$820$	−1.51537	+	21.8449i	−0.0529190	+	0.762856i
$821$	−12.4920	+	12.4920i	−0.435976	+	0.435976i	−0.890655	−	0.454680i	$-0.849754\pi$
$821$	−12.4920	+	12.4920i	−0.435976	+	0.435976i	0.454680	+	0.890655i	$0.349754\pi$
$822$	−3.56422	+	1.33373i	−0.124316	+	0.0465193i
$823$		−	47.6794i		−	1.66200i	−0.556272	−	0.831000i	$-0.687769\pi$
$823$		−	47.6794i		−	1.66200i	0.556272	−	0.831000i	$-0.312231\pi$
$824$	32.4460	−	9.64032i	1.13031	−	0.335836i
$825$		−	1.25171i		−	0.0435789i
$826$	0.511342	+	1.36649i	0.0177919	+	0.0475463i
$827$	19.1401	−	19.1401i	0.665566	−	0.665566i	−0.291120	−	0.956686i	$-0.594028\pi$
$827$	19.1401	−	19.1401i	0.665566	−	0.665566i	0.956686	+	0.291120i	$0.0940280\pi$
$828$	−14.5651	−	16.7365i	−0.506172	−	0.581633i
$829$	−1.83741	−	1.83741i	−0.0638159	−	0.0638159i	0.674479	−	0.738294i	$-0.264369\pi$
$829$	−1.83741	−	1.83741i	−0.0638159	−	0.0638159i	−0.738294	+	0.674479i	$0.764369\pi$
$830$	−25.0621	−	11.4131i	−0.869917	−	0.396153i
$831$	2.17902			0.0755893
$832$	19.2640	+	4.06121i	0.667859	+	0.140797i
$833$	34.8619			1.20789
$834$	14.8786	+	6.77560i	0.515204	+	0.234620i
$835$	12.0821	+	12.0821i	0.418119	+	0.418119i
$836$	6.46440	+	7.42812i	0.223576	+	0.256907i
$837$	−25.0689	+	25.0689i	−0.866508	+	0.866508i
$838$	4.55316	+	12.1677i	0.157286	+	0.420326i
$839$			42.4031i			1.46392i	0.681350	+	0.731958i	$0.261393\pi$
$839$			42.4031i			1.46392i	−0.681350	+	0.731958i	$0.738607\pi$
$840$	−5.97074	+	1.77402i	−0.206010	+	0.0612094i
$841$		−	6.04261i		−	0.208366i
$842$	37.4911	−	14.0292i	1.29203	−	0.483478i
$843$	0.0586444	−	0.0586444i	0.00201982	−	0.00201982i
$844$	1.85583	−	26.7528i	0.0638805	−	0.920871i
$845$	9.17389	+	9.17389i	0.315591	+	0.315591i
$846$	−11.0102	+	24.1774i	−0.378537	+	0.831235i
$847$	−1.42100			−0.0488263
$848$	2.58794	+	3.42640i	0.0888703	+	0.117663i
$849$	24.6506			0.846006
$850$	−6.19082	+	13.5945i	−0.212343	+	0.466288i
$851$	19.6383	+	19.6383i	0.673192	+	0.673192i
$852$	−15.6569	−	1.08611i	−0.536396	−	0.0372096i
$853$	−4.22753	+	4.22753i	−0.144748	+	0.144748i	−0.775767	−	0.631019i	$-0.782637\pi$
$853$	−4.22753	+	4.22753i	−0.144748	+	0.144748i	0.631019	+	0.775767i	$0.282637\pi$
$854$	0.563502	−	0.210863i	0.0192826	−	0.00721558i
$855$		−	21.2686i		−	0.727371i
$856$	−16.2820	−	8.82288i	−0.556507	−	0.301560i
$857$			15.7549i			0.538177i	0.963115	+	0.269088i	$0.0867224\pi$
$857$			15.7549i			0.538177i	−0.963115	+	0.269088i	$0.913278\pi$
$858$	1.01170	+	2.70362i	0.0345387	+	0.0923000i
$859$	−21.9613	+	21.9613i	−0.749311	+	0.749311i	−0.974350	−	0.225039i	$-0.927749\pi$
$859$	−21.9613	+	21.9613i	−0.749311	+	0.749311i	0.225039	+	0.974350i	$0.427749\pi$
$860$	12.3238	−	10.7249i	0.420238	−	0.365717i
$861$	−4.88384	−	4.88384i	−0.166441	−	0.166441i
$862$	22.8020	+	10.3838i	0.776639	+	0.353675i
$863$	−32.7635			−1.11528			−0.557642	−	0.830082i	$-0.688294\pi$
$863$	−32.7635			−1.11528			−0.557642	+	0.830082i	$0.688294\pi$
$864$	5.42833	+	24.3260i	0.184676	+	0.827587i
$865$	14.5433			0.494487
$866$	7.68052	+	3.49764i	0.260995	+	0.118855i
$867$	18.7627	+	18.7627i	0.637214	+	0.637214i
$868$	−17.2504	+	15.0123i	−0.585515	+	0.509551i
$869$	−6.05153	+	6.05153i	−0.205284	+	0.205284i
$870$	−3.68028	−	9.83505i	−0.124773	−	0.333440i
$871$		−	0.405670i		−	0.0137456i
$872$	−25.6809	+	47.3924i	−0.869667	+	1.60491i
$873$			35.2462i			1.19290i
$874$	−31.2902	+	11.7088i	−1.05841	+	0.396057i
$875$	−12.2200	+	12.2200i	−0.413110	+	0.413110i
$876$	−12.5064	−	0.867561i	−0.422551	−	0.0293122i
$877$	26.3914	+	26.3914i	0.891173	+	0.891173i	0.994634	−	0.103460i	$-0.0329915\pi$
$877$	26.3914	+	26.3914i	0.891173	+	0.891173i	−0.103460	+	0.994634i	$0.532992\pi$
$878$	−0.966127	+	2.12153i	−0.0326052	+	0.0715982i
$879$	−4.23189			−0.142738
$880$	7.40201	+	1.03191i	0.249522	+	0.0347858i
$881$	35.9400			1.21085			0.605424	−	0.795903i	$-0.293004\pi$
$881$	35.9400			1.21085			0.605424	+	0.795903i	$0.293004\pi$
$882$	6.74937	−	14.8210i	0.227263	−	0.499050i
$883$	−32.1645	−	32.1645i	−1.08242	−	1.08242i	−0.996283	−	0.0861387i	$-0.972547\pi$
$883$	−32.1645	−	32.1645i	−1.08242	−	1.08242i	−0.0861387	−	0.996283i	$-0.527453\pi$
$884$	2.38403	−	34.3671i	0.0801836	−	1.15589i
$885$	0.795604	−	0.795604i	0.0267439	−	0.0267439i
$886$	−45.9610	+	17.1986i	−1.54409	+	0.577800i
$887$			0.678766i			0.0227907i	0.999935	+	0.0113954i	$0.00362733\pi$
$887$			0.678766i			0.0227907i	−0.999935	+	0.0113954i	$0.996373\pi$
$888$	−3.86758	−	13.0169i	−0.129787	−	0.436820i
$889$			1.33901i			0.0449091i
$890$	2.48416	+	6.63859i	0.0832694	+	0.222526i
$891$	2.32036	−	2.32036i	0.0777349	−	0.0777349i
$892$	−0.785323	−	0.902400i	−0.0262946	−	0.0302146i
$893$	28.2871	+	28.2871i	0.946591	+	0.946591i
$894$	14.4852	+	6.59644i	0.484458	+	0.220618i
$895$	34.0449			1.13799
$896$	2.40716	+	15.8956i	0.0804176	+	0.531034i
$897$	−9.79400			−0.327012
$898$	−11.8341	−	5.38913i	−0.394908	−	0.179838i
$899$	−27.2614	−	27.2614i	−0.909220	−	0.909220i
$900$	4.58095	+	5.26388i	0.152698	+	0.175463i
$901$	5.31293	−	5.31293i	0.176999	−	0.176999i
$902$	2.90439	+	7.76158i	0.0967055	+	0.258432i
$903$			5.15299i			0.171481i
$904$	15.6674	+	52.7313i	0.521092	+	1.75382i
$905$		−	12.3354i		−	0.410041i
$906$	4.75251	−	1.77839i	0.157892	−	0.0590832i
$907$	2.84441	−	2.84441i	0.0944470	−	0.0944470i	−0.658305	−	0.752752i	$-0.728726\pi$
$907$	2.84441	−	2.84441i	0.0944470	−	0.0944470i	0.752752	+	0.658305i	$0.228726\pi$
$908$	−1.79785	+	25.9170i	−0.0596637	+	0.860084i
$909$	8.77013	+	8.77013i	0.290887	+	0.290887i
$910$	3.82949	−	8.40924i	0.126946	−	0.278763i
$911$	−2.56191			−0.0848797			−0.0424399	−	0.999099i	$-0.513513\pi$
$911$	−2.56191			−0.0848797			−0.0424399	+	0.999099i	$0.513513\pi$
$912$	16.1788	+	2.25549i	0.535735	+	0.0746868i
$913$	−10.4221			−0.344921
$914$	−8.79185	+	19.3061i	−0.290809	+	0.638591i
$915$	−0.328085	−	0.328085i	−0.0108461	−	0.0108461i
$916$	43.2580	+	3.00079i	1.42928	+	0.0991489i
$917$	10.4839	−	10.4839i	0.346209	−	0.346209i
$918$	40.8471	−	15.2850i	1.34816	−	0.504481i
$919$		−	38.8243i		−	1.28070i	−0.768085	−	0.640348i	$-0.778790\pi$
$919$		−	38.8243i		−	1.28070i	0.768085	−	0.640348i	$-0.221210\pi$
$920$	−12.0805	+	22.2937i	−0.398281	+	0.735000i
$921$		−	22.3063i		−	0.735017i
$922$	−20.0402	−	53.5547i	−0.659989	−	1.76373i
$923$	16.4632	−	16.4632i	0.541892	−	0.541892i
$924$	−1.77821	+	1.54751i	−0.0584990	+	0.0509093i
$925$	−6.17655	−	6.17655i	−0.203084	−	0.203084i
$926$	−20.2809	−	9.23573i	−0.666470	−	0.303505i
$927$	−27.6680			−0.908737
$928$	−26.4535	+	5.90310i	−0.868380	+	0.193779i
$929$	−13.4329			−0.440718			−0.220359	−	0.975419i	$-0.570723\pi$
$929$	−13.4329			−0.440718			−0.220359	+	0.975419i	$0.570723\pi$
$930$	16.0492	+	7.30866i	0.526274	+	0.239661i
$931$	−17.3404	−	17.3404i	−0.568307	−	0.568307i
$932$	−35.2190	+	30.6497i	−1.15364	+	1.00396i
$933$	−18.1034	+	18.1034i	−0.592678	+	0.592678i
$934$	−9.00606	−	24.0674i	−0.294687	−	0.787511i
$935$		−	13.0775i		−	0.427681i
$936$	−14.1491	−	7.66712i	−0.462479	−	0.250608i
$937$		−	6.57052i		−	0.214649i	−0.994224	−	0.107325i	$-0.965772\pi$
$937$		−	6.57052i		−	0.214649i	0.994224	−	0.107325i	$-0.0342284\pi$
$938$	0.310260	−	0.116100i	0.0101304	−	0.00379079i
$939$	−6.46629	+	6.46629i	−0.211020	+	0.211020i
$940$	30.2888	+	2.10112i	0.987911	+	0.0685310i
$941$	2.12185	+	2.12185i	0.0691702	+	0.0691702i	0.740846	−	0.671675i	$-0.234425\pi$
$941$	2.12185	+	2.12185i	0.0691702	+	0.0691702i	−0.671675	+	0.740846i	$0.734425\pi$
$942$	8.22449	−	18.0603i	0.267968	−	0.588435i
$943$	−28.1167			−0.915607
$944$	−1.75031	−	2.31739i	−0.0569678	−	0.0754246i
$945$	11.6980			0.380537
$946$	2.56243	−	5.62688i	0.0833119	−	0.182946i
$947$	8.47091	+	8.47091i	0.275268	+	0.275268i	0.831216	−	0.555949i	$-0.187645\pi$
$947$	8.47091	+	8.47091i	0.275268	+	0.275268i	−0.555949	+	0.831216i	$0.687645\pi$
$948$	−0.982483	+	14.1630i	−0.0319096	+	0.459994i
$949$	13.1504	−	13.1504i	0.426880	−	0.426880i
$950$	9.84126	−	3.68261i	0.319293	−	0.119480i
$951$			19.3839i			0.628565i
$952$	26.9666	−	8.01227i	0.873992	−	0.259679i
$953$			27.4440i			0.888998i	0.895779	+	0.444499i	$0.146618\pi$
$953$			27.4440i			0.888998i	−0.895779	+	0.444499i	$0.853382\pi$
$954$	−1.23012	−	3.28732i	−0.0398265	−	0.106431i
$955$	−17.8562	+	17.8562i	−0.577814	+	0.577814i
$956$	38.1497	+	43.8371i	1.23385	+	1.41779i
$957$	−2.81018	−	2.81018i	−0.0908403	−	0.0908403i
$958$	26.8992	+	12.2497i	0.869073	+	0.395769i
$959$	4.61014			0.148869
$960$	10.3865	−	6.76966i	0.335223	−	0.218490i
$961$	33.7448			1.08854
$962$	18.3332	+	8.34877i	0.591085	+	0.269175i
$963$	10.7040	+	10.7040i	0.344930	+	0.344930i
$964$	6.36432	+	7.31312i	0.204981	+	0.235540i
$965$	27.9313	−	27.9313i	0.899142	−	0.899142i
$966$	−2.80297	−	7.49055i	−0.0901841	−	0.241005i
$967$			20.9785i			0.674624i	0.941393	+	0.337312i	$0.109518\pi$
$967$			20.9785i			0.674624i	−0.941393	+	0.337312i	$0.890482\pi$
$968$	2.71128	−	0.805572i	0.0871439	−	0.0258921i
$969$		−	28.5840i		−	0.918250i
$970$	37.7266	−	14.1173i	1.21133	−	0.453280i
$971$	17.1622	−	17.1622i	0.550761	−	0.550761i	−0.375899	−	0.926660i	$-0.622666\pi$
$971$	17.1622	−	17.1622i	0.550761	−	0.550761i	0.926660	+	0.375899i	$0.122666\pi$
$972$	2.20619	−	31.8034i	0.0707636	−	1.02010i
$973$	−14.0043	−	14.0043i	−0.448957	−	0.448957i
$974$	−9.45946	+	20.7722i	−0.303101	+	0.665583i
$975$	3.08037			0.0986507
$976$	−0.955626	+	0.721779i	−0.0305889	+	0.0231036i
$977$	−44.2995			−1.41727			−0.708634	−	0.705577i	$-0.750688\pi$
$977$	−44.2995			−1.41727			−0.708634	+	0.705577i	$0.750688\pi$
$978$	6.04525	−	13.2748i	0.193306	−	0.424482i
$979$	1.89685	+	1.89685i	0.0606237	+	0.0606237i
$980$	−18.5674	−	1.28801i	−0.593115	−	0.0411441i
$981$	31.1563	−	31.1563i	0.994743	−	0.994743i
$982$	−43.0374	+	16.1046i	−1.37338	+	0.513919i
$983$			0.162242i			0.00517472i	0.999997	+	0.00258736i	$0.000823583\pi$
$983$			0.162242i			0.00517472i	−0.999997	+	0.00258736i	$0.999176\pi$
$984$	12.0870	+	6.54972i	0.385321	+	0.208797i
$985$			42.0508i			1.33985i
$986$	16.6219	+	44.4196i	0.529348	+	1.41461i
$987$	−6.77164	+	6.77164i	−0.215544	+	0.215544i
$988$	−18.2801	+	15.9084i	−0.581567	+	0.506115i
$989$	14.8331	+	14.8331i	0.471666	+	0.471666i
$990$	−5.55973	−	2.53185i	−0.176700	−	0.0804675i
$991$	6.44898			0.204859			0.102429	−	0.994740i	$-0.467338\pi$
$991$	6.44898			0.204859			0.102429	+	0.994740i	$0.467338\pi$
$992$	24.4032	−	38.4229i	0.774804	−	1.21993i
$993$	−14.6449			−0.464743
$994$	17.3028	+	7.87956i	0.548813	+	0.249925i
$995$	−24.6370	−	24.6370i	−0.781045	−	0.781045i
$996$	−13.0420	+	11.3499i	−0.413251	+	0.359636i
$997$	18.6908	−	18.6908i	0.591944	−	0.591944i	−0.346212	−	0.938156i	$-0.612532\pi$
$997$	18.6908	−	18.6908i	0.591944	−	0.591944i	0.938156	+	0.346212i	$0.112532\pi$
$998$	3.31939	+	8.87061i	0.105073	+	0.280794i
$999$			25.5032i			0.806884i

Display

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.2.j.a.45.18	✓	40
4.3	odd	2		704.2.j.a.529.8		40
8.3	odd	2		1408.2.j.b.1057.13		40
8.5	even	2		1408.2.j.a.1057.8		40
16.3	odd	4		1408.2.j.b.353.13		40
16.5	even	4	inner	176.2.j.a.133.18	yes	40
16.11	odd	4		704.2.j.a.177.8		40
16.13	even	4		1408.2.j.a.353.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.j.a.45.18	✓	40	1.1	even	1	trivial
176.2.j.a.133.18	yes	40	16.5	even	4	inner
704.2.j.a.177.8		40	16.11	odd	4
704.2.j.a.529.8		40	4.3	odd	2
1408.2.j.a.353.8		40	16.13	even	4
1408.2.j.a.1057.8		40	8.5	even	2
1408.2.j.b.353.13		40	16.3	odd	4
1408.2.j.b.1057.13		40	8.3	odd	2

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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

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L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	176.2.j.a.45.18

Level	$176$
Weight	$2$
Character	176.45
Analytic conductor	$1.405$
Analytic rank	$0$
Dimension	$40$
Inner twists	$2$