LMFDB - Embedded newform 961.2.g.i.816.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] 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("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-16,0,24,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			816.1
Root			$1.29195 + 0.575212i$ of defining polynomial
Character	$\chi$	$=$	961.816
Dual form			961.2.g.i.338.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.11803 - 1.53884i) q^{2} +(-0.0913612 - 0.869244i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-1.14412 + 1.98168i) q^{6} +(0.978148 + 0.207912i) q^{7} +(2.30902 - 7.10642i) q^{8} +(2.18720 - 0.464905i) q^{9} +(-0.611920 + 5.82203i) q^{10} +(-2.83888 + 3.15290i) q^{11} +(3.87585 - 1.72564i) q^{12} +(2.39540 + 1.06650i) q^{13} +(-1.75181 - 1.94558i) q^{14} +(-1.58114 + 1.14876i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(-2.47743 - 2.75146i) q^{17} +(-5.34799 - 2.38108i) q^{18} +(0.913545 - 0.406737i) q^{19} +(7.26281 - 8.06617i) q^{20} +(0.0913612 - 0.869244i) q^{21} +(10.8647 - 2.30935i) q^{22} +(0.810272 - 2.49376i) q^{23} +(-6.38817 - 1.35785i) q^{24} +(-3.43237 - 5.94504i) q^{26} +(-1.41421 - 4.35250i) q^{27} +(0.507392 + 4.82751i) q^{28} +(-0.437016 - 0.317511i) q^{29} +5.11667 q^{30} +10.8541 q^{32} +(3.00000 + 2.17963i) q^{33} +(1.01321 + 9.64006i) q^{34} +(-0.690983 - 2.12663i) q^{35} +(5.42705 + 9.39993i) q^{36} +(2.12132 - 3.67423i) q^{37} +(-2.56082 - 0.544320i) q^{38} +(0.708204 - 2.17963i) q^{39} +(-16.3431 + 3.47383i) q^{40} +(0.153880 - 1.46407i) q^{41} +(-1.53114 + 1.70050i) q^{42} +(8.85515 - 3.94256i) q^{43} +(-18.8137 - 8.37642i) q^{44} +(-3.34565 - 3.71572i) q^{45} +(-5.55369 + 4.03499i) q^{46} +(7.85410 - 5.70634i) q^{47} +(5.76309 + 6.40056i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(-2.16535 + 2.40487i) q^{51} +(-1.33043 + 12.6582i) q^{52} +(-13.4295 + 2.85452i) q^{53} +(-3.70246 + 11.3950i) q^{54} +(9.27952 + 1.97242i) q^{55} +(3.73607 - 6.47106i) q^{56} +(-0.437016 - 0.756934i) q^{57} +(0.437016 + 1.34500i) q^{58} +(-1.24852 - 11.8788i) q^{59} +(-7.67501 - 5.57622i) q^{60} -13.9358 q^{61} +2.23607 q^{63} +(-7.04508 - 5.11855i) q^{64} +(-0.612870 - 5.83107i) q^{65} +(-3.00000 - 9.23305i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(8.98606 - 15.5643i) q^{68} +(-2.24171 - 0.476491i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(1.43997 - 0.306074i) q^{71} +(1.74648 - 16.6167i) q^{72} +(-2.83888 + 3.15290i) q^{73} +(-10.1471 + 4.51778i) q^{74} +(3.24803 + 3.60730i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(1.08436 + 1.20430i) q^{79} +(20.1295 + 8.96221i) q^{80} +(2.47407 - 1.10153i) q^{81} +(-2.57890 + 2.86416i) q^{82} +(-0.330548 + 3.14495i) q^{83} +(4.14993 - 0.882095i) q^{84} +(-2.55834 + 7.87375i) q^{85} +(-24.8225 - 5.27618i) q^{86} +(-0.236068 + 0.408882i) q^{87} +(15.8508 + 27.4544i) q^{88} +(4.74342 + 14.5987i) q^{89} +(1.36830 + 13.0185i) q^{90} +(2.12132 + 1.54123i) q^{91} +12.7279 q^{92} -25.4164 q^{94} +(-1.80902 - 1.31433i) q^{95} +(-0.991644 - 9.43486i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(7.85410 + 13.6037i) q^{98} +(-4.74342 + 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 24 q^{4} - 2 q^{7} + 28 q^{8} + 10 q^{9} + 20 q^{10} + 2 q^{14} - 56 q^{16} - 20 q^{18} + 2 q^{19} - 18 q^{28} + 120 q^{32} + 48 q^{33} - 20 q^{35} + 60 q^{36} - 2 q^{38} - 96 q^{39} - 10 q^{40}+ \cdots + 72 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 24 * q^4 - 2 * q^7 + 28 * q^8 + 10 * q^9 + 20 * q^10 + 2 * q^14 - 56 * q^16 - 20 * q^18 + 2 * q^19 - 18 * q^28 + 120 * q^32 + 48 * q^33 - 20 * q^35 + 60 * q^36 - 2 * q^38 - 96 * q^39 - 10 * q^40 - 14 * q^41 - 10 * q^45 + 72 * q^47 - 12 * q^49 + 8 * q^51 + 24 * q^56 + 46 * q^59 - 68 * q^64 - 48 * q^66 - 48 * q^67 + 48 * q^69 - 20 * q^70 + 26 * q^71 - 50 * q^72 - 12 * q^76 - 24 * q^78 + 80 * q^80 + 22 * q^81 + 14 * q^82 + 32 * q^87 - 40 * q^90 - 192 * q^94 - 20 * q^95 + 28 * q^97 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.971295	−	0.237877i	$-0.923549\pi$
$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.526381	−	0.850249i	$-0.676451\pi$
$3$	−0.0913612	−	0.869244i	−0.0527474	−	0.501858i	−0.988719	−	0.149783i	$-0.952143\pi$
$3$	−0.0913612	−	0.869244i	−0.0527474	−	0.501858i	0.935972	−	0.352076i	$-0.114524\pi$
$4$	1.50000	+	4.61653i	0.750000	+	2.30826i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i	−1.00000			$\pi$
$6$	−1.14412	+	1.98168i	−0.467086	+	0.809017i
$7$	0.978148	+	0.207912i	0.369705	+	0.0785832i	0.389018	−	0.921230i	$-0.372814\pi$
$7$	0.978148	+	0.207912i	0.369705	+	0.0785832i	−0.0193127	+	0.999813i	$0.506148\pi$
$8$	2.30902	−	7.10642i	0.816361	−	2.51250i
$9$	2.18720	−	0.464905i	0.729068	−	0.154968i
$10$	−0.611920	+	5.82203i	−0.193506	+	1.84109i
$11$	−2.83888	+	3.15290i	−0.855955	+	0.950634i	−0.999237	−	0.0390478i	$-0.987568\pi$
$11$	−2.83888	+	3.15290i	−0.855955	+	0.950634i	0.143283	+	0.989682i	$0.454234\pi$
$12$	3.87585	−	1.72564i	1.11886	−	0.498149i
$13$	2.39540	+	1.06650i	0.664366	+	0.295795i	0.711077	−	0.703114i	$-0.248208\pi$
$13$	2.39540	+	1.06650i	0.664366	+	0.295795i	−0.0467118	+	0.998908i	$0.514874\pi$
$14$	−1.75181	−	1.94558i	−0.468190	−	0.519978i
$15$	−1.58114	+	1.14876i	−0.408248	+	0.296610i
$16$	−7.97214	+	5.79210i	−1.99303	+	1.44802i
$17$	−2.47743	−	2.75146i	−0.600865	−	0.667328i	0.363595	−	0.931557i	$-0.381549\pi$
$17$	−2.47743	−	2.75146i	−0.600865	−	0.667328i	−0.964460	+	0.264229i	$0.914882\pi$
$18$	−5.34799	−	2.38108i	−1.26053	−	0.561225i
$19$	0.913545	−	0.406737i	0.209582	−	0.0933118i	−0.299261	−	0.954171i	$-0.596740\pi$
$19$	0.913545	−	0.406737i	0.209582	−	0.0933118i	0.508843	+	0.860859i	$0.330073\pi$
$20$	7.26281	−	8.06617i	1.62401	−	1.80365i
$21$	0.0913612	−	0.869244i	0.0199367	−	0.189685i
$22$	10.8647	−	2.30935i	2.31635	−	0.492356i
$23$	0.810272	−	2.49376i	0.168953	−	0.519985i	−0.830352	−	0.557239i	$-0.811861\pi$
$23$	0.810272	−	2.49376i	0.168953	−	0.519985i	0.999306	+	0.0372534i	$0.0118609\pi$
$24$	−6.38817	−	1.35785i	−1.30398	−	0.277169i
$25$		0			0
$26$	−3.43237	−	5.94504i	−0.673143	−	1.16592i
$27$	−1.41421	−	4.35250i	−0.272166	−	0.837639i
$28$	0.507392	+	4.82751i	0.0958880	+	0.912314i
$29$	−0.437016	−	0.317511i	−0.0811518	−	0.0589603i	0.546470	−	0.837479i	$-0.315971\pi$
$29$	−0.437016	−	0.317511i	−0.0811518	−	0.0589603i	−0.627621	+	0.778519i	$0.715971\pi$
$30$	5.11667			0.934172
$31$		0			0
$31$		0			0
$32$	10.8541			1.91875
$33$	3.00000	+	2.17963i	0.522233	+	0.379424i
$34$	1.01321	+	9.64006i	0.173764	+	1.65326i
$35$	−0.690983	−	2.12663i	−0.116797	−	0.359466i
$36$	5.42705	+	9.39993i	0.904508	+	1.56665i
$37$	2.12132	−	3.67423i	0.348743	−	0.604040i	−0.637284	−	0.770629i	$-0.719942\pi$
$37$	2.12132	−	3.67423i	0.348743	−	0.604040i	0.986026	+	0.166589i	$0.0532753\pi$
$38$	−2.56082	−	0.544320i	−0.415420	−	0.0883003i
$39$	0.708204	−	2.17963i	0.113403	−	0.349020i
$40$	−16.3431	+	3.47383i	−2.58407	+	0.549261i
$41$	0.153880	−	1.46407i	0.0240320	−	0.228650i	−0.975913	−	0.218160i	$-0.929994\pi$
$41$	0.153880	−	1.46407i	0.0240320	−	0.228650i	0.999945	−	0.0104893i	$-0.00333889\pi$
$42$	−1.53114	+	1.70050i	−0.236259	+	0.262393i
$43$	8.85515	−	3.94256i	1.35040	−	0.601236i	0.401221	−	0.915981i	$-0.368586\pi$
$43$	8.85515	−	3.94256i	1.35040	−	0.601236i	0.949176	+	0.314746i	$0.101919\pi$
$44$	−18.8137	−	8.37642i	−2.83628	−	1.26279i
$45$	−3.34565	−	3.71572i	−0.498741	−	0.553907i
$46$	−5.55369	+	4.03499i	−0.818847	+	0.594927i
$47$	7.85410	−	5.70634i	1.14564	−	0.832355i	0.157744	−	0.987480i	$-0.449578\pi$
$47$	7.85410	−	5.70634i	1.14564	−	0.832355i	0.987895	+	0.155125i	$0.0495780\pi$
$48$	5.76309	+	6.40056i	0.831830	+	0.923841i
$49$	−5.48127	−	2.44042i	−0.783039	−	0.348631i
$50$		0			0
$51$	−2.16535	+	2.40487i	−0.303210	+	0.336749i
$52$	−1.33043	+	12.6582i	−0.184497	+	1.75538i
$53$	−13.4295	+	2.85452i	−1.84468	+	0.392098i	−0.991563	−	0.129626i	$-0.958622\pi$
$53$	−13.4295	+	2.85452i	−1.84468	+	0.392098i	−0.853114	+	0.521724i	$0.825289\pi$
$54$	−3.70246	+	11.3950i	−0.503841	+	1.55066i
$55$	9.27952	+	1.97242i	1.25125	+	0.265962i
$56$	3.73607	−	6.47106i	0.499253	−	0.864732i
$57$	−0.437016	−	0.756934i	−0.0578842	−	0.100258i
$58$	0.437016	+	1.34500i	0.0573830	+	0.176607i
$59$	−1.24852	−	11.8788i	−0.162543	−	1.54649i	−0.706702	−	0.707511i	$-0.749818\pi$
$59$	−1.24852	−	11.8788i	−0.162543	−	1.54649i	0.544159	−	0.838982i	$-0.316849\pi$
$60$	−7.67501	−	5.57622i	−0.990839	−	0.719887i
$61$	−13.9358			−1.78430			−0.892148	−	0.451742i	$-0.850803\pi$
$61$	−13.9358			−1.78430			−0.892148	+	0.451742i	$0.850803\pi$
$62$		0			0
$63$	2.23607			0.281718
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	−0.612870	−	5.83107i	−0.0760171	−	0.723255i
$66$	−3.00000	−	9.23305i	−0.369274	−	1.13651i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	8.98606	−	15.5643i	1.08972	−	1.88745i
$69$	−2.24171	−	0.476491i	−0.269871	−	0.0573628i
$70$	−1.80902	+	5.56758i	−0.216219	+	0.665453i
$71$	1.43997	−	0.306074i	0.170893	−	0.0363243i	−0.121671	−	0.992571i	$-0.538825\pi$
$71$	1.43997	−	0.306074i	0.170893	−	0.0363243i	0.292563	+	0.956246i	$0.405492\pi$
$72$	1.74648	−	16.6167i	0.205825	−	1.95829i
$73$	−2.83888	+	3.15290i	−0.332266	+	0.369019i	−0.886008	−	0.463669i	$-0.846533\pi$
$73$	−2.83888	+	3.15290i	−0.332266	+	0.369019i	0.553742	+	0.832688i	$0.313199\pi$
$74$	−10.1471	+	4.51778i	−1.17958	+	0.525181i
$75$		0			0
$76$	3.24803	+	3.60730i	0.372574	+	0.413786i
$77$	−3.43237	+	2.49376i	−0.391155	+	0.284191i
$78$	−4.85410	+	3.52671i	−0.549619	+	0.399321i
$79$	1.08436	+	1.20430i	0.122000	+	0.135494i	0.801050	−	0.598597i	$-0.204275\pi$
$79$	1.08436	+	1.20430i	0.122000	+	0.135494i	−0.679051	+	0.734091i	$0.737608\pi$
$80$	20.1295	+	8.96221i	2.25054	+	1.00201i
$81$	2.47407	−	1.10153i	0.274896	−	0.122392i
$82$	−2.57890	+	2.86416i	−0.284792	+	0.316293i
$83$	−0.330548	+	3.14495i	−0.0362824	+	0.345204i	0.961288	+	0.275544i	$0.0888580\pi$
$83$	−0.330548	+	3.14495i	−0.0362824	+	0.345204i	−0.997571	+	0.0696596i	$0.977809\pi$
$84$	4.14993	−	0.882095i	0.452794	−	0.0962444i
$85$	−2.55834	+	7.87375i	−0.277491	+	0.854028i
$86$	−24.8225	−	5.27618i	−2.67668	−	0.568945i
$87$	−0.236068	+	0.408882i	−0.0253091	+	0.0438367i
$88$	15.8508	+	27.4544i	1.68970	+	2.92665i
$89$	4.74342	+	14.5987i	0.502801	+	1.54746i	0.804436	+	0.594039i	$0.202468\pi$
$89$	4.74342	+	14.5987i	0.502801	+	1.54746i	−0.301635	+	0.953424i	$0.597532\pi$
$90$	1.36830	+	13.0185i	0.144231	+	1.37227i
$91$	2.12132	+	1.54123i	0.222375	+	0.161565i
$92$	12.7279			1.32698
$93$		0			0
$94$	−25.4164			−2.62150
$95$	−1.80902	−	1.31433i	−0.185601	−	0.134847i
$96$	−0.991644	−	9.43486i	−0.101209	−	0.962942i
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	−0.998792	−	0.0491321i	$-0.984354\pi$
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	0.779161	−	0.626824i	$-0.215646\pi$
$98$	7.85410	+	13.6037i	0.793384	+	1.37418i
$99$	−4.74342	+	8.21584i	−0.476731	+	0.825723i
$100$		0			0
$101$	0.690983	−	2.12663i	0.0687554	−	0.211607i	−0.910775	−	0.412902i	$-0.864515\pi$
$101$	0.690983	−	2.12663i	0.0687554	−	0.211607i	0.979531	+	0.201295i	$0.0645150\pi$
$102$	8.28700	−	1.76146i	0.820535	−	0.174410i
$103$	−1.11931	+	10.6495i	−0.110289	+	1.04933i	0.789722	+	0.613464i	$0.210225\pi$
$103$	−1.11931	+	10.6495i	−0.110289	+	1.04933i	−0.900011	+	0.435866i	$0.856442\pi$
$104$	13.1100	−	14.5602i	1.28555	−	1.42774i
$105$	−1.78543	+	0.794924i	−0.174240	+	0.0775766i
$106$	32.8367	+	14.6198i	3.18938	+	1.42000i
$107$	0.985051	+	1.09401i	0.0952285	+	0.105762i	0.788875	−	0.614553i	$-0.210664\pi$
$107$	0.985051	+	1.09401i	0.0952285	+	0.105762i	−0.693647	+	0.720315i	$0.743997\pi$
$108$	17.9721	−	13.0575i	1.72937	−	1.25646i
$109$	1.04508	−	0.759299i	0.100101	−	0.0727276i	−0.536609	−	0.843831i	$-0.680295\pi$
$109$	1.04508	−	0.759299i	0.100101	−	0.0727276i	0.636710	+	0.771103i	$0.280295\pi$
$110$	−16.6191	−	18.4574i	−1.58457	−	1.75984i
$111$	−3.38761	−	1.50826i	−0.321538	−	0.143158i
$112$	−9.00217	+	4.00802i	−0.850625	+	0.378723i
$113$	−6.53335	+	7.25602i	−0.614605	+	0.682589i	−0.967441	−	0.253097i	$-0.918551\pi$
$113$	−6.53335	+	7.25602i	−0.614605	+	0.682589i	0.352835	+	0.935685i	$0.385218\pi$
$114$	−0.239187	+	2.27571i	−0.0224019	+	0.213140i
$115$	−5.73506	+	1.21902i	−0.534797	+	0.113675i
$116$	0.810272	−	2.49376i	0.0752319	−	0.231540i
$117$	5.73506	+	1.21902i	0.530207	+	0.112699i
$118$	−15.6353	+	27.0811i	−1.43934	+	2.49301i
$119$	−1.85123	−	3.20642i	−0.169702	−	0.293932i
$120$	4.51273	+	13.8888i	0.411954	+	1.26786i
$121$	−0.731699	−	6.96165i	−0.0665181	−	0.632878i
$122$	29.5165	+	21.4450i	2.67230	+	1.94154i
$123$	−1.28669			−0.116017
$124$		0			0
$125$	−11.1803			−1.00000
$126$	−4.73607	−	3.44095i	−0.421922	−	0.306545i
$127$	−0.991644	−	9.43486i	−0.0879942	−	0.837209i	−0.946130	−	0.323786i	$-0.895044\pi$
$127$	−0.991644	−	9.43486i	−0.0879942	−	0.837209i	0.858136	−	0.513422i	$-0.171623\pi$
$128$	0.336881	+	1.03681i	0.0297764	+	0.0916422i
$129$	−4.23607	−	7.33708i	−0.372965	−	0.645994i
$130$	−7.67501	+	13.2935i	−0.673143	+	1.16592i
$131$	−7.25434	−	1.54196i	−0.633815	−	0.134721i	−0.120210	−	0.992748i	$-0.538357\pi$
$131$	−7.25434	−	1.54196i	−0.633815	−	0.134721i	−0.513605	+	0.858027i	$0.671690\pi$
$132$	−5.56231	+	17.1190i	−0.484137	+	1.49002i
$133$	0.978148	−	0.207912i	0.0848162	−	0.0180282i
$134$	−1.64195	+	15.6222i	−0.141843	+	1.34955i
$135$	−6.84744	+	7.60486i	−0.589334	+	0.654522i
$136$	−25.2735	+	11.2525i	−2.16718	+	0.964892i
$137$	2.39540	+	1.06650i	0.204653	+	0.0911175i	0.506504	−	0.862238i	$-0.330938\pi$
$137$	2.39540	+	1.06650i	0.204653	+	0.0911175i	−0.301850	+	0.953355i	$0.597604\pi$
$138$	4.01478	+	4.45887i	0.341761	+	0.379564i
$139$	−14.5397	+	10.5637i	−1.23325	+	0.896005i	−0.997129	−	0.0757198i	$-0.975875\pi$
$139$	−14.5397	+	10.5637i	−1.23325	+	0.896005i	−0.236116	+	0.971725i	$0.575875\pi$
$140$	8.78115	−	6.37988i	0.742143	−	0.539198i
$141$	−5.67776	−	6.30579i	−0.478154	−	0.531044i
$142$	−3.52090	−	1.56760i	−0.295467	−	0.131550i
$143$	−10.1628	+	4.52479i	−0.849859	+	0.378382i
$144$	−14.7439	+	16.3748i	−1.22866	+	1.36457i
$145$	−0.126258	+	1.20127i	−0.0104852	+	0.0997597i
$146$	10.8647	−	2.30935i	0.899165	−	0.191123i
$147$	−1.62054	+	4.98752i	−0.133660	+	0.411364i
$148$	20.1442	+	4.28178i	1.65584	+	0.351960i
$149$	6.70820	−	11.6190i	0.549557	−	0.951861i	−0.448747	−	0.893659i	$-0.648130\pi$
$149$	6.70820	−	11.6190i	0.549557	−	0.951861i	0.998305	−	0.0582028i	$-0.0185370\pi$
$150$		0			0
$151$	−3.86938	−	11.9087i	−0.314886	−	0.969120i	−0.975801	−	0.218659i	$-0.929832\pi$
$151$	−3.86938	−	11.9087i	−0.314886	−	0.969120i	0.660915	−	0.750461i	$-0.270168\pi$
$152$	−0.781051	−	7.43120i	−0.0633516	−	0.602750i
$153$	−6.69781	−	4.86624i	−0.541486	−	0.393413i
$154$	11.1074			0.895058
$155$		0			0
$156$	11.1246			0.890682
$157$	−7.04508	−	5.11855i	−0.562259	−	0.408505i	0.270026	−	0.962853i	$-0.412968\pi$
$157$	−7.04508	−	5.11855i	−0.562259	−	0.408505i	−0.832285	+	0.554348i	$0.812968\pi$
$158$	−0.443477	−	4.21940i	−0.0352811	−	0.335677i
$159$	3.70820	+	11.4127i	0.294080	+	0.905084i
$160$	−12.1353	−	21.0189i	−0.959376	−	1.66169i
$161$	1.31105	−	2.27080i	0.103325	−	0.178964i
$162$	−6.93523	−	1.47413i	−0.544883	−	0.115819i
$163$	4.45492	−	13.7108i	0.348936	−	1.07391i	−0.610507	−	0.792011i	$-0.709034\pi$
$163$	4.45492	−	13.7108i	0.348936	−	1.07391i	0.959443	−	0.281903i	$-0.0909657\pi$
$164$	6.98974	−	1.48572i	0.545807	−	0.116015i
$165$	0.866729	−	8.24637i	0.0674747	−	0.641979i
$166$	5.53970	−	6.15246i	0.429964	−	0.477523i
$167$	0.986961	−	0.439423i	0.0763733	−	0.0340036i	−0.368194	−	0.929749i	$-0.620024\pi$
$167$	0.986961	−	0.439423i	0.0763733	−	0.0340036i	0.444568	+	0.895745i	$0.353357\pi$
$168$	−5.96626	−	2.65635i	−0.460307	−	0.204942i
$169$	−4.09817	−	4.55147i	−0.315243	−	0.350113i
$170$	17.5351	−	12.7400i	1.34488	−	0.977113i
$171$	1.80902	−	1.31433i	0.138339	−	0.100509i
$172$	31.4837	+	34.9662i	2.40061	+	2.66614i
$173$	16.4438	+	7.32126i	1.25020	+	0.556625i	0.921709	−	0.387882i	$-0.126793\pi$
$173$	16.4438	+	7.32126i	1.25020	+	0.556625i	0.328491	+	0.944507i	$0.393460\pi$
$174$	1.12920	−	0.502754i	0.0856048	−	0.0381137i
$175$		0			0
$176$	4.37006	−	41.5784i	0.329406	−	3.13409i
$177$	−10.2115	+	2.17053i	−0.767547	+	0.163147i
$178$	12.4184	−	38.2200i	0.930800	−	2.86471i
$179$	12.9782	+	2.75859i	0.970033	+	0.206187i	0.665569	−	0.746337i	$-0.268189\pi$
$179$	12.9782	+	2.75859i	0.970033	+	0.206187i	0.304465	+	0.952524i	$0.401522\pi$
$180$	12.1353	−	21.0189i	0.904508	−	1.56665i
$181$	4.34581	+	7.52716i	0.323021	+	0.559489i	0.981110	−	0.193451i	$-0.0619681\pi$
$181$	4.34581	+	7.52716i	0.323021	+	0.559489i	−0.658089	+	0.752940i	$0.728635\pi$
$182$	−2.12132	−	6.52875i	−0.157243	−	0.483943i
$183$	1.27319	+	12.1136i	0.0941171	+	0.895464i
$184$	−15.8508	−	11.5163i	−1.16854	−	0.848991i
$185$	−9.48683			−0.697486
$186$		0			0
$187$	15.7082			1.14870
$188$	38.1246	+	27.6992i	2.78052	+	2.02017i
$189$	−0.478374	−	4.55142i	−0.0347966	−	0.331067i
$190$	1.80902	+	5.56758i	0.131240	+	0.403915i
$191$	−4.88197	−	8.45581i	−0.353247	−	0.611841i	0.633570	−	0.773686i	$-0.281589\pi$
$191$	−4.88197	−	8.45581i	−0.353247	−	0.611841i	−0.986816	+	0.161845i	$0.948256\pi$
$192$	−3.80562	+	6.59154i	−0.274647	+	0.475703i
$193$	20.2557	+	4.30548i	1.45804	+	0.309915i	0.867638	−	0.497197i	$-0.165637\pi$
$193$	20.2557	+	4.30548i	1.45804	+	0.309915i	0.590398	+	0.807112i	$0.298971\pi$
$194$	−5.66312	+	17.4293i	−0.406588	+	1.25135i
$195$	−5.01263	+	1.06547i	−0.358962	+	0.0762997i
$196$	3.04435	−	28.9651i	0.217454	−	2.06893i
$197$	0.722904	−	0.802866i	0.0515048	−	0.0572018i	−0.716842	−	0.697236i	$-0.754413\pi$
$197$	0.722904	−	0.802866i	0.0515048	−	0.0572018i	0.768347	+	0.640034i	$0.221080\pi$
$198$	22.6896	−	10.1021i	1.61248	−	0.717922i
$199$	−21.2092	−	9.44292i	−1.50348	−	0.669391i	−0.520625	−	0.853786i	$-0.674301\pi$
$199$	−21.2092	−	9.44292i	−1.50348	−	0.669391i	−0.982852	+	0.184395i	$0.940968\pi$
$200$		0			0
$201$	−4.24264	+	3.08246i	−0.299253	+	0.217420i
$202$	−4.73607	+	3.44095i	−0.333229	+	0.242105i
$203$	−0.361452	−	0.401433i	−0.0253690	−	0.0281751i
$204$	−14.3502	−	6.38910i	−1.00471	−	0.447327i
$205$	−3.00721	+	1.33889i	−0.210032	+	0.0935124i
$206$	18.7587	−	20.8337i	1.30698	−	1.45155i
$207$	0.612870	−	5.83107i	0.0425974	−	0.405287i
$208$	−25.2738	+	5.37211i	−1.75242	+	0.372489i
$209$	−1.31105	+	4.03499i	−0.0906871	+	0.279106i
$210$	5.00486	+	1.06382i	0.345368	+	0.0734103i
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	−33.3221	−	57.7156i	−2.28857	−	3.96393i
$213$	−0.397610	−	1.22372i	−0.0272438	−	0.0838478i
$214$	−0.402863	−	3.83299i	−0.0275392	−	0.262018i
$215$	−17.5351	−	12.7400i	−1.19588	−	0.868860i
$216$	−34.1962			−2.32675
$217$		0			0
$218$	−3.38197			−0.229056
$219$	3.00000	+	2.17963i	0.202721	+	0.147286i
$220$	4.81354	+	45.7978i	0.324529	+	3.08769i
$221$	−3.00000	−	9.23305i	−0.201802	−	0.621082i
$222$	4.85410	+	8.40755i	0.325786	+	0.564278i
$223$	8.07262	−	13.9822i	0.540583	−	0.936316i	−0.458288	−	0.888804i	$-0.651537\pi$
$223$	8.07262	−	13.9822i	0.540583	−	0.936316i	0.998871	−	0.0475128i	$-0.0151295\pi$
$224$	10.6169	+	2.25669i	0.709372	+	0.150782i
$225$		0			0
$226$	25.0037	−	5.31470i	1.66322	−	0.353529i
$227$	−0.239558	+	2.27924i	−0.0159000	+	0.151279i	−0.999591	−	0.0285864i	$-0.990899\pi$
$227$	−0.239558	+	2.27924i	−0.0159000	+	0.151279i	0.983691	+	0.179865i	$0.0575661\pi$
$228$	2.83888	−	3.15290i	0.188009	−	0.208806i
$229$	−3.87585	+	1.72564i	−0.256123	+	0.114033i	−0.530782	−	0.847508i	$-0.678102\pi$
$229$	−3.87585	+	1.72564i	−0.256123	+	0.114033i	0.274659	+	0.961542i	$0.411435\pi$
$230$	14.0229	+	6.24341i	0.924645	+	0.411679i
$231$	2.48127	+	2.75573i	0.163256	+	0.181314i
$232$	−3.26544	+	2.37248i	−0.214387	+	0.155761i
$233$	10.8992	−	7.91872i	0.714029	−	0.518773i	−0.170442	−	0.985368i	$-0.554519\pi$
$233$	10.8992	−	7.91872i	0.714029	−	0.518773i	0.884471	+	0.466595i	$0.154519\pi$
$234$	−10.2712	−	11.4073i	−0.671447	−	0.745718i
$235$	−19.8314	−	8.82952i	−1.29366	−	0.575975i
$236$	52.9662	−	23.5821i	3.44781	−	1.53506i
$237$	0.947762	−	1.05260i	0.0615637	−	0.0683735i
$238$	−1.01321	+	9.64006i	−0.0656767	+	0.624873i
$239$	11.8443	−	2.51759i	0.766145	−	0.162849i	0.191768	−	0.981440i	$-0.438578\pi$
$239$	11.8443	−	2.51759i	0.766145	−	0.162849i	0.574377	+	0.818591i	$0.305244\pi$
$240$	5.95130	−	18.3162i	0.384155	−	1.18231i
$241$	−22.7090	−	4.82694i	−1.46281	−	0.310931i	−0.593357	−	0.804940i	$-0.702198\pi$
$241$	−22.7090	−	4.82694i	−1.46281	−	0.310931i	−0.869457	+	0.494009i	$0.835531\pi$
$242$	−9.16312	+	15.8710i	−0.589028	+	1.02023i
$243$	−8.04827	−	13.9400i	−0.516296	−	0.894252i
$244$	−20.9037	−	64.3350i	−1.33822	−	4.11863i
$245$	1.40240	+	13.3429i	0.0895958	+	0.852447i
$246$	2.72526	+	1.98002i	0.173756	+	0.126241i
$247$	2.62210			0.166840
$248$		0			0
$249$	2.76393			0.175157
$250$	23.6803	+	17.2048i	1.49768	+	1.08813i
$251$	1.15280	+	10.9682i	0.0727640	+	0.692304i	0.968719	+	0.248159i	$0.0798256\pi$
$251$	1.15280	+	10.9682i	0.0727640	+	0.692304i	−0.895955	+	0.444144i	$0.853508\pi$
$252$	3.35410	+	10.3229i	0.211289	+	0.650279i
$253$	5.56231	+	9.63420i	0.349699	+	0.605697i
$254$	−12.4184	+	21.5093i	−0.779201	+	1.34962i
$255$	7.07794	+	1.50446i	0.443238	+	0.0942131i
$256$	−4.50000	+	13.8496i	−0.281250	+	0.865598i
$257$	−5.92340	+	1.25906i	−0.369491	+	0.0785378i	−0.388915	−	0.921274i	$-0.627150\pi$
$257$	−5.92340	+	1.25906i	−0.369491	+	0.0785378i	0.0194240	+	0.999811i	$0.493817\pi$
$258$	−2.31848	+	22.0588i	−0.144342	+	1.37332i
$259$	2.83888	−	3.15290i	0.176399	−	0.195911i
$260$	26.0000	−	11.5759i	1.61245	−	0.717909i
$261$	−1.10346	−	0.491290i	−0.0683022	−	0.0304101i
$262$	12.9921	+	14.4292i	0.802655	+	0.891439i
$263$	14.9768	−	10.8813i	0.923507	−	0.670967i	−0.0208877	−	0.999782i	$-0.506649\pi$
$263$	14.9768	−	10.8813i	0.923507	−	0.670967i	0.944394	+	0.328815i	$0.106649\pi$
$264$	22.4164	−	16.2865i	1.37963	−	1.00236i
$265$	20.5423	+	22.8146i	1.26191	+	1.40149i
$266$	−2.39169	−	1.06485i	−0.146644	−	0.0652902i
$267$	12.2565	−	5.45694i	0.750086	−	0.333960i
$268$	19.4882	−	21.6438i	1.19043	−	1.32211i
$269$	0.225857	−	2.14889i	0.0137708	−	0.131020i	−0.985477	−	0.169811i	$-0.945684\pi$
$269$	0.225857	−	2.14889i	0.0137708	−	0.131020i	0.999247	+	0.0387914i	$0.0123508\pi$
$270$	26.2058	−	5.57021i	1.59483	−	0.338992i
$271$	5.74497	−	17.6812i	0.348982	−	1.07406i	−0.610435	−	0.792066i	$-0.709006\pi$
$271$	5.74497	−	17.6812i	0.348982	−	1.07406i	0.959417	−	0.281990i	$-0.0909945\pi$
$272$	35.6871	+	7.58554i	2.16385	+	0.459941i
$273$	1.14590	−	1.98475i	0.0693529	−	0.120123i
$274$	−3.43237	−	5.94504i	−0.207357	−	0.359153i
$275$		0			0
$276$	−1.16284	−	11.0637i	−0.0699947	−	0.665955i
$277$	8.17578	+	5.94006i	0.491235	+	0.356903i	0.805659	−	0.592379i	$-0.201811\pi$
$277$	8.17578	+	5.94006i	0.491235	+	0.356903i	−0.314424	+	0.949283i	$0.601811\pi$
$278$	47.0516			2.82197
$279$		0			0
$280$	−16.7082			−0.998506
$281$	−10.8090	−	7.85321i	−0.644812	−	0.468483i	0.216688	−	0.976241i	$-0.430475\pi$
$281$	−10.8090	−	7.85321i	−0.644812	−	0.468483i	−0.861500	+	0.507758i	$0.830475\pi$
$282$	2.32207	+	22.0931i	0.138278	+	1.31562i
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	0.886961	+	0.461844i	$0.152812\pi$
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	−0.446101	+	0.894982i	$0.647188\pi$
$284$	3.57295	+	6.18853i	0.212016	+	0.367222i
$285$	−0.977198	+	1.69256i	−0.0578842	+	0.100258i
$286$	28.4882	+	6.05535i	1.68454	+	0.358060i
$287$	0.454915	−	1.40008i	0.0268528	−	0.0826444i
$288$	23.7401	−	5.04612i	1.39890	−	0.297346i
$289$	0.344086	−	3.27376i	0.0202404	−	0.192574i
$290$	2.11598	−	2.35003i	0.124254	−	0.137999i
$291$	−5.58928	+	2.48851i	−0.327649	+	0.145879i
$292$	−18.8137	−	8.37642i	−1.10099	−	0.490193i
$293$	−1.53351	−	1.70314i	−0.0895887	−	0.0994983i	0.696683	−	0.717379i	$-0.254658\pi$
$293$	−1.53351	−	1.70314i	−0.0895887	−	0.0994983i	−0.786272	+	0.617880i	$0.787992\pi$
$294$	11.1074	−	8.06998i	0.647795	−	0.470651i
$295$	−21.6074	+	15.6987i	−1.25803	+	0.914013i
$296$	−21.2125	−	23.5589i	−1.23295	−	1.36933i
$297$	17.7378	+	7.89736i	1.02925	+	0.458252i
$298$	−32.0879	+	14.2865i	−1.85880	+	0.827593i
$299$	4.60053	−	5.10941i	0.266056	−	0.295485i
$300$		0			0
$301$	9.48135	−	2.01532i	0.546496	−	0.116161i
$302$	−10.1302	+	31.1775i	−0.582926	+	1.79406i
$303$	−1.91169	−	0.406342i	−0.109824	−	0.0233437i
$304$	−4.92705	+	8.53390i	−0.282586	+	0.489453i
$305$	15.5807	+	26.9866i	0.892148	+	1.54525i
$306$	6.69781	+	20.6137i	0.382888	+	1.17841i
$307$	−2.52171	−	23.9925i	−0.143922	−	1.36932i	−0.793288	−	0.608846i	$-0.791633\pi$
$307$	−2.52171	−	23.9925i	−0.143922	−	1.36932i	0.649367	−	0.760475i	$-0.275034\pi$
$308$	−16.6611	−	12.1050i	−0.949352	−	0.689745i
$309$	9.35931			0.532433
$310$		0			0
$311$	25.4721			1.44439			0.722196	−	0.691688i	$-0.243133\pi$
$311$	25.4721			1.44439			0.722196	+	0.691688i	$0.243133\pi$
$312$	−13.8541	−	10.0656i	−0.784334	−	0.569852i
$313$	−1.20417	−	11.4569i	−0.0680638	−	0.647584i	−0.974368	−	0.224959i	$-0.927775\pi$
$313$	−1.20417	−	11.4569i	−0.0680638	−	0.647584i	0.906304	−	0.422625i	$-0.138891\pi$
$314$	7.04508	+	21.6825i	0.397577	+	1.22362i
$315$	−2.50000	−	4.33013i	−0.140859	−	0.243975i
$316$	−3.93314	+	6.81241i	−0.221257	+	0.383228i
$317$	−25.6627	−	5.45479i	−1.44136	−	0.306371i	−0.580106	−	0.814541i	$-0.696989\pi$
$317$	−25.6627	−	5.45479i	−1.44136	−	0.306371i	−0.861257	+	0.508169i	$0.830322\pi$
$318$	9.70820	−	29.8788i	0.544409	−	1.67552i
$319$	2.24171	−	0.476491i	0.125512	−	0.0266784i
$320$	−2.03539	+	19.3655i	−0.113782	+	1.08256i
$321$	0.860966	−	0.956200i	0.0480545	−	0.0533699i
$322$	−6.27125	+	2.79214i	−0.349483	+	0.155600i
$323$	−3.38236	−	1.50593i	−0.188200	−	0.0837920i
$324$	8.79632	+	9.76931i	0.488685	+	0.542739i
$325$		0			0
$326$	−30.5344	+	22.1846i	−1.69115	+	1.22869i
$327$	−0.755496	−	0.839063i	−0.0417790	−	0.0464003i
$328$	−10.0490	−	4.47410i	−0.554863	−	0.247041i
$329$	8.86889	−	3.94868i	0.488957	−	0.217698i
$330$	−14.5256	+	16.1323i	−0.799609	+	0.888056i
$331$	3.27058	−	31.1175i	0.179768	−	1.71037i	−0.417787	−	0.908545i	$-0.637194\pi$
$331$	3.27058	−	31.1175i	0.179768	−	1.71037i	0.597554	−	0.801829i	$-0.296139\pi$
$332$	−15.0146	+	3.19145i	−0.824032	+	0.175153i
$333$	2.93159	−	9.02251i	0.160650	−	0.494431i
$334$	−2.76662	−	0.588063i	−0.151383	−	0.0321774i
$335$	−6.70820	+	11.6190i	−0.366508	+	0.634811i
$336$	4.30640	+	7.45890i	0.234933	+	0.406917i
$337$	4.74342	+	14.5987i	0.258390	+	0.795244i	0.993143	+	0.116908i	$0.0372984\pi$
$337$	4.74342	+	14.5987i	0.258390	+	0.795244i	−0.734752	+	0.678335i	$0.762702\pi$
$338$	1.67606	+	15.9466i	0.0911654	+	0.867381i
$339$	6.90414	+	5.01615i	0.374982	+	0.272440i
$340$	−40.1869			−2.17944
$341$		0			0
$342$	−5.85410			−0.316554
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	−7.57085	−	72.0319i	−0.408193	−	3.88370i
$345$	1.58359	+	4.87380i	0.0852577	+	0.262396i
$346$	−23.5623	−	40.8111i	−1.26672	−	2.19402i
$347$	−10.7979	+	18.7025i	−0.579661	+	1.00400i	0.415857	+	0.909430i	$0.363482\pi$
$347$	−10.7979	+	18.7025i	−0.579661	+	1.00400i	−0.995518	+	0.0945718i	$0.969852\pi$
$348$	−2.24171	−	0.476491i	−0.120169	−	0.0255426i
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	−0.889090	−	0.457733i	$-0.848662\pi$
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	0.988337	+	0.152280i	$0.0486615\pi$
$350$		0			0
$351$	1.25434	−	11.9343i	0.0669518	−	0.637004i
$352$	−30.8135	+	34.2219i	−1.64237	+	1.82403i
$353$	−8.73865	+	3.89070i	−0.465111	+	0.207081i	−0.625893	−	0.779909i	$-0.715265\pi$
$353$	−8.73865	+	3.89070i	−0.465111	+	0.207081i	0.160781	+	0.986990i	$0.448599\pi$
$354$	24.9685	+	11.1167i	1.32706	+	0.590846i
$355$	−2.20264	−	2.44628i	−0.116904	−	0.129835i
$356$	−60.2803	+	43.7962i	−3.19485	+	2.32119i
$357$	−2.61803	+	1.90211i	−0.138561	+	0.100670i
$358$	−23.2432	−	25.8141i	−1.22844	−	1.36432i
$359$	13.0053	+	5.79033i	0.686393	+	0.305602i	0.720140	−	0.693828i	$-0.244077\pi$
$359$	13.0053	+	5.79033i	0.686393	+	0.305602i	−0.0337471	+	0.999430i	$0.510744\pi$
$360$	−34.1307	+	15.1960i	−1.79884	+	0.800897i
$361$	−12.0444	+	13.3766i	−0.633913	+	0.704032i
$362$	2.37854	−	22.6303i	0.125013	−	1.18942i
$363$	−5.98453	+	1.27205i	−0.314106	+	0.0667653i
$364$	−3.93314	+	12.1050i	−0.206153	+	0.634473i
$365$	9.27952	+	1.97242i	0.485712	+	0.103241i
$366$	15.9443	−	27.6163i	0.833420	−	1.44353i
$367$	3.32920	+	5.76635i	0.173783	+	0.301001i	0.939739	−	0.341892i	$-0.111068\pi$
$367$	3.32920	+	5.76635i	0.173783	+	0.301001i	−0.765956	+	0.642892i	$0.777734\pi$
$368$	7.98451	+	24.5738i	0.416221	+	1.28100i
$369$	−0.344086	−	3.27376i	−0.0179124	−	0.170425i
$370$	20.0934	+	14.5987i	1.04461	+	0.758952i
$371$	−13.7295			−0.712799
$372$		0			0
$373$	−9.29180			−0.481111			−0.240555	−	0.970635i	$-0.577330\pi$
$373$	−9.29180			−0.481111			−0.240555	+	0.970635i	$0.577330\pi$
$374$	−33.2705	−	24.1724i	−1.72038	−	1.24993i
$375$	1.02145	+	9.71844i	0.0527474	+	0.501858i
$376$	−22.4164	−	68.9906i	−1.15604	−	3.55792i
$377$	−0.708204	−	1.22665i	−0.0364744	−	0.0631754i
$378$	−5.99070	+	10.3762i	−0.308129	+	0.533694i
$379$	−7.25434	−	1.54196i	−0.372630	−	0.0792051i	0.0177899	−	0.999842i	$-0.494337\pi$
$379$	−7.25434	−	1.54196i	−0.372630	−	0.0792051i	−0.390420	+	0.920637i	$0.627670\pi$
$380$	3.35410	−	10.3229i	0.172062	−	0.529552i
$381$	−8.11060	+	1.72396i	−0.415519	+	0.0883212i
$382$	−2.67199	+	25.4223i	−0.136711	+	1.30072i
$383$	4.28469	−	4.75863i	0.218937	−	0.243155i	−0.623664	−	0.781693i	$-0.714357\pi$
$383$	4.28469	−	4.75863i	0.218937	−	0.243155i	0.842601	+	0.538538i	$0.181023\pi$
$384$	0.870466	−	0.387556i	0.0444208	−	0.0197774i
$385$	8.66665	+	3.85864i	0.441694	+	0.196655i
$386$	−36.2768	−	40.2894i	−1.84644	−	2.05068i
$387$	17.5351	−	12.7400i	0.891359	−	0.647610i
$388$	27.4894	−	19.9722i	1.39556	−	1.01393i
$389$	11.2501	+	12.4944i	0.570400	+	0.633494i	0.957462	−	0.288560i	$-0.0931765\pi$
$389$	11.2501	+	12.4944i	0.570400	+	0.633494i	−0.387061	+	0.922054i	$0.626510\pi$
$390$	12.2565	+	5.45694i	0.620632	+	0.276323i
$391$	−8.86889	+	3.94868i	−0.448519	+	0.199693i
$392$	−29.9990	+	33.3173i	−1.51518	+	1.68278i
$393$	−0.677572	+	6.44667i	−0.0341790	+	0.325191i
$394$	−2.76662	+	0.588063i	−0.139380	+	0.0296262i
$395$	1.11977	−	3.44629i	0.0563417	−	0.173402i
$396$	−45.0438	−	9.57434i	−2.26353	−	0.481129i
$397$	−7.35410	+	12.7377i	−0.369092	+	0.639286i	−0.989424	−	0.145054i	$-0.953665\pi$
$397$	−7.35410	+	12.7377i	−0.369092	+	0.639286i	0.620332	+	0.784339i	$0.286998\pi$
$398$	30.3905	+	52.6380i	1.52334	+	2.63850i
$399$	−0.270091	−	0.831254i	−0.0135215	−	0.0416147i
$400$		0			0
$401$	−0.437016	−	0.317511i	−0.0218235	−	0.0158557i	0.576820	−	0.816871i	$-0.304293\pi$
$401$	−0.437016	−	0.317511i	−0.0218235	−	0.0158557i	−0.598644	+	0.801016i	$0.704293\pi$
$402$	13.7295			0.684764
$403$		0			0
$404$	10.8541			0.540012
$405$	−4.89919	−	3.55947i	−0.243443	−	0.176871i
$406$	0.147826	+	1.40647i	0.00733646	+	0.0698018i
$407$	5.56231	+	17.1190i	0.275713	+	0.848558i
$408$	12.0902	+	20.9408i	0.598553	+	1.03672i
$409$	15.0405	−	26.0509i	0.743706	−	1.28814i	−0.207091	−	0.978322i	$-0.566400\pi$
$409$	15.0405	−	26.0509i	0.743706	−	1.28814i	0.950797	−	0.309815i	$-0.100267\pi$
$410$	8.42971	+	1.79179i	0.416314	+	0.0884902i
$411$	0.708204	−	2.17963i	0.0349331	−	0.107513i
$412$	−50.8429	+	10.8070i	−2.50485	+	0.532422i
$413$	1.24852	−	11.8788i	0.0614355	−	0.584520i
$414$	−10.2712	+	11.4073i	−0.504800	+	0.560638i
$415$	6.45974	−	2.87606i	0.317096	−	0.141180i
$416$	26.0000	+	11.5759i	1.27475	+	0.567557i
$417$	10.5108	+	11.6735i	0.514718	+	0.571652i
$418$	8.98606	−	6.52875i	0.439522	−	0.319332i
$419$	−24.7533	+	17.9843i	−1.20928	+	0.878591i	−0.995165	−	0.0982177i	$-0.968686\pi$
$419$	−24.7533	+	17.9843i	−1.20928	+	0.878591i	−0.214112	+	0.976809i	$0.568686\pi$
$420$	−6.34793	−	7.05009i	−0.309747	−	0.344009i
$421$	24.1326	+	10.7445i	1.17615	+	0.523656i	0.899332	−	0.437266i	$-0.144053\pi$
$421$	24.1326	+	10.7445i	1.17615	+	0.523656i	0.276818	+	0.960922i	$0.410720\pi$
$422$	−11.9585	+	5.32425i	−0.582129	+	0.259181i
$423$	14.5256	−	16.1323i	0.706260	−	0.784381i
$424$	−10.7234	+	102.027i	−0.520775	+	4.95485i
$425$		0			0
$426$	−1.04096	+	3.20374i	−0.0504345	+	0.155222i
$427$	−13.6313	−	2.89742i	−0.659664	−	0.140216i
$428$	−3.57295	+	6.18853i	−0.172705	+	0.299134i
$429$	4.86163	+	8.42060i	0.234722	+	0.406550i
$430$	17.5351	+	53.9675i	0.845618	+	2.60254i
$431$	3.75137	+	35.6919i	0.180697	+	1.71922i	0.590493	+	0.807043i	$0.298933\pi$
$431$	3.75137	+	35.6919i	0.180697	+	1.71922i	−0.409795	+	0.912177i	$0.634400\pi$
$432$	36.4844	+	26.5075i	1.75536	+	1.27534i
$433$	25.8384			1.24171			0.620857	−	0.783924i	$-0.286785\pi$
$433$	25.8384			1.24171			0.620857	+	0.783924i	$0.286785\pi$
$434$		0			0
$435$	1.05573			0.0506183
$436$	5.07295	+	3.68571i	0.242950	+	0.176514i
$437$	−0.274084	−	2.60773i	−0.0131112	−	0.124745i
$438$	−3.00000	−	9.23305i	−0.143346	−	0.441172i
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	35.4435	−	61.3899i	1.68970	−	2.92665i
$441$	−13.1232	−	2.78943i	−0.624916	−	0.132830i
$442$	−7.85410	+	24.1724i	−0.373582	+	1.14977i
$443$	−5.92340	+	1.25906i	−0.281429	+	0.0598196i	−0.346464	−	0.938063i	$-0.612618\pi$
$443$	−5.92340	+	1.25906i	−0.281429	+	0.0598196i	0.0650345	+	0.997883i	$0.479284\pi$
$444$	1.88151	−	17.9014i	0.0892926	−	0.849563i
$445$	22.9670	−	25.5075i	1.08874	−	1.20917i
$446$	−38.6145	+	17.1923i	−1.82845	+	0.814077i
$447$	−10.7126	−	4.76954i	−0.506687	−	0.225592i
$448$	−5.82693	−	6.47146i	−0.275296	−	0.305748i
$449$	27.2677	−	19.8111i	1.28684	−	0.934945i	0.287104	−	0.957899i	$-0.407307\pi$
$449$	27.2677	−	19.8111i	1.28684	−	0.934945i	0.999737	+	0.0229547i	$0.00730736\pi$
$450$		0			0
$451$	4.17922	+	4.64149i	0.196792	+	0.218559i
$452$	−43.2976	−	19.2773i	−2.03655	−	0.906729i
$453$	−9.99809	+	4.45144i	−0.469751	+	0.209147i
$454$	4.01478	−	4.45887i	0.188423	−	0.209265i
$455$	0.612870	−	5.83107i	0.0287318	−	0.273365i
$456$	−6.38817	+	1.35785i	−0.299154	+	0.0635870i
$457$	−3.49613	+	10.7600i	−0.163542	+	0.503330i	−0.998926	−	0.0463365i	$-0.985245\pi$
$457$	−3.49613	+	10.7600i	−0.163542	+	0.503330i	0.835384	+	0.549667i	$0.185245\pi$
$458$	10.8647	+	2.30935i	0.507672	+	0.107909i
$459$	−8.47214	+	14.6742i	−0.395445	+	0.684932i
$460$	−14.2302	−	24.6475i	−0.663489	−	1.14920i
$461$	−1.59619	−	4.91257i	−0.0743420	−	0.228801i	0.906980	−	0.421174i	$-0.138382\pi$
$461$	−1.59619	−	4.91257i	−0.0743420	−	0.228801i	−0.981322	+	0.192373i	$0.938382\pi$
$462$	−1.01478	−	9.65502i	−0.0472120	−	0.449192i
$463$	−3.09852	−	2.25121i	−0.144000	−	0.104622i	0.513453	−	0.858118i	$-0.328366\pi$
$463$	−3.09852	−	2.25121i	−0.144000	−	0.104622i	−0.657453	+	0.753496i	$0.728366\pi$
$464$	5.32300			0.247114
$465$		0			0
$466$	−35.2705			−1.63387
$467$	12.6631	+	9.20029i	0.585979	+	0.425739i	0.840875	−	0.541230i	$-0.182041\pi$
$467$	12.6631	+	9.20029i	0.585979	+	0.425739i	−0.254895	+	0.966969i	$0.582041\pi$
$468$	2.97493	+	28.3046i	0.137516	+	1.30838i
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	28.4164	+	49.2187i	1.31075	+	2.27029i
$471$	−3.80562	+	6.59154i	−0.175354	+	0.303722i
$472$	−87.2989	−	18.5560i	−4.01826	−	0.854107i
$473$	−12.7082	+	39.1118i	−0.584324	+	1.79836i
$474$	−3.62717	+	0.770979i	−0.166601	+	0.0354122i
$475$		0			0
$476$	12.0257	−	13.3559i	0.551197	−	0.612166i
$477$	−28.0459	+	12.4868i	−1.28413	+	0.571733i
$478$	−28.9608	−	12.8942i	−1.32464	−	0.589767i
$479$	11.0593	+	12.2826i	0.505312	+	0.561206i	0.940789	−	0.338994i	$-0.110087\pi$
$479$	11.0593	+	12.2826i	0.505312	+	0.561206i	−0.435476	+	0.900200i	$0.643420\pi$
$480$	−17.1618	+	12.4688i	−0.783327	+	0.569121i
$481$	9.00000	−	6.53888i	0.410365	−	0.298147i
$482$	40.6705	+	45.1691i	1.85249	+	2.05740i
$483$	−2.09366	−	0.932157i	−0.0952648	−	0.0424146i
$484$	31.0411	−	13.8204i	1.41096	−	0.628199i
$485$	−10.4736	+	11.6321i	−0.475579	+	0.528184i
$486$	−4.40496	+	41.9104i	−0.199813	+	1.90109i
$487$	27.4644	−	5.83773i	1.24453	−	0.264533i	0.461850	−	0.886958i	$-0.347186\pi$
$487$	27.4644	−	5.83773i	1.24453	−	0.264533i	0.782679	+	0.622425i	$0.213852\pi$
$488$	−32.1780	+	99.0337i	−1.45663	+	4.48305i
$489$	−12.3251	−	2.61977i	−0.557358	−	0.118470i
$490$	17.5623	−	30.4188i	0.793384	−	1.37418i
$491$	−7.94510	−	13.7613i	−0.358557	−	0.621040i	0.629163	−	0.777274i	$-0.283398\pi$
$491$	−7.94510	−	13.7613i	−0.358557	−	0.621040i	−0.987720	+	0.156234i	$0.950065\pi$
$492$	−1.93004	−	5.94006i	−0.0870130	−	0.267798i
$493$	0.209057	+	1.98904i	0.00941545	+	0.0895820i
$494$	−5.55369	−	4.03499i	−0.249872	−	0.181543i
$495$	21.2132			0.953463
$496$		0			0
$497$	1.47214			0.0660343
$498$	−5.85410	−	4.25325i	−0.262329	−	0.190593i
$499$	1.92173	+	18.2841i	0.0860286	+	0.818507i	0.949428	+	0.313986i	$0.101664\pi$
$499$	1.92173	+	18.2841i	0.0860286	+	0.818507i	−0.863399	+	0.504521i	$0.831669\pi$
$500$	−16.7705	−	51.6143i	−0.750000	−	2.30826i
$501$	−0.472136	−	0.817763i	−0.0210935	−	0.0365350i
$502$	14.4366	−	25.0049i	0.644336	−	1.11602i
$503$	32.1699	+	6.83791i	1.43438	+	0.304887i	0.858571	−	0.512695i	$-0.171353\pi$
$503$	32.1699	+	6.83791i	1.43438	+	0.304887i	0.575812	+	0.817582i	$0.304686\pi$
$504$	5.16312	−	15.8904i	0.229984	−	0.707817i
$505$	−4.89074	+	1.03956i	−0.217635	+	0.0462597i
$506$	3.04435	−	28.9651i	0.135338	−	1.28765i
$507$	−3.58193	+	3.97813i	−0.159079	+	0.176675i
$508$	42.0688	−	18.7302i	1.86650	−	0.831020i
$509$	7.25821	+	3.23156i	0.321714	+	0.143237i	0.561239	−	0.827654i	$-0.310325\pi$
$509$	7.25821	+	3.23156i	0.321714	+	0.143237i	−0.239524	+	0.970890i	$0.576992\pi$
$510$	−12.6762	−	14.0783i	−0.561311	−	0.623399i
$511$	−3.43237	+	2.49376i	−0.151839	+	0.110318i
$512$	32.6074	−	23.6907i	1.44106	−	1.04699i
$513$	−3.06227	−	3.40100i	−0.135203	−	0.150158i
$514$	14.4834	+	6.44844i	0.638837	+	0.284429i
$515$	21.8742	−	9.73901i	0.963892	−	0.429152i
$516$	27.5177	−	30.5615i	1.21140	−	1.34540i
$517$	−4.30536	+	40.9628i	−0.189350	+	1.80154i
$518$	−10.8647	+	2.30935i	−0.477366	+	0.101467i
$519$	4.86163	−	14.9626i	0.213402	−	0.656784i
$520$	−42.8532	−	9.10872i	−1.87924	−	0.399444i
$521$	6.70820	−	11.6190i	0.293892	−	0.509035i	−0.680835	−	0.732437i	$-0.738383\pi$
$521$	6.70820	−	11.6190i	0.293892	−	0.509035i	0.974726	+	0.223402i	$0.0717161\pi$
$522$	1.58114	+	2.73861i	0.0692046	+	0.119866i
$523$	−0.191279	−	0.588697i	−0.00836406	−	0.0257419i	0.946787	−	0.321860i	$-0.104308\pi$
$523$	−0.191279	−	0.588697i	−0.00836406	−	0.0257419i	−0.955151	+	0.296118i	$0.904308\pi$
$524$	−3.76302	−	35.8028i	−0.164388	−	1.56405i
$525$		0			0
$526$	−48.4658			−2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	13.0451	+	9.47781i	0.567178	+	0.412079i
$530$	−8.40134	−	79.9334i	−0.364931	−	3.47209i
$531$	−8.25329	−	25.4010i	−0.358162	−	1.10231i
$532$	2.42705	+	4.20378i	0.105226	+	0.182257i
$533$	1.93004	−	3.34293i	0.0835994	−	0.144798i
$534$	−34.3571	−	7.30282i	−1.48678	−	0.316024i
$535$	1.01722	−	3.13068i	0.0439783	−	0.135351i
$536$	−43.8531	+	9.32127i	−1.89417	+	0.402617i
$537$	1.21219	−	11.5332i	0.0523099	−	0.497695i
$538$	−3.78517	+	4.20386i	−0.163190	+	0.181241i
$539$	23.2551	−	10.3538i	1.00167	−	0.445971i
$540$	−45.3792	−	20.2041i	−1.95281	−	0.869447i
$541$	17.2855	+	19.1975i	0.743163	+	0.825366i	0.989608	−	0.143791i	$-0.0459292\pi$
$541$	17.2855	+	19.1975i	0.743163	+	0.825366i	−0.246445	+	0.969157i	$0.579263\pi$
$542$	−39.3766	+	28.6088i	−1.69137	+	1.22885i
$543$	6.14590	−	4.46526i	0.263746	−	0.191622i
$544$	−26.8903	−	29.8647i	−1.15291	−	1.28044i
$545$	−2.63882	−	1.17488i	−0.113034	−	0.0503262i
$546$	−5.48127	+	2.44042i	−0.234577	+	0.104440i
$547$	1.61689	−	1.79574i	0.0691333	−	0.0767803i	−0.707586	−	0.706627i	$-0.750216\pi$
$547$	1.61689	−	1.79574i	0.0691333	−	0.0767803i	0.776719	+	0.629847i	$0.216882\pi$
$548$	−1.33043	+	12.6582i	−0.0568332	+	0.540731i
$549$	−30.4805	+	6.47882i	−1.30087	+	0.276509i
$550$		0			0
$551$	−0.528377	−	0.112310i	−0.0225096	−	0.00478457i
$552$	−8.56231	+	14.8303i	−0.364436	+	0.631222i
$553$	0.810272	+	1.40343i	0.0344563	+	0.0596800i
$554$	−8.17578	−	25.1625i	−0.347356	−	1.06905i
$555$	0.866729	+	8.24637i	0.0367906	+	0.350039i
$556$	−70.5774	−	51.2775i	−2.99315	−	2.17465i
$557$	10.6460			0.451086			0.225543	−	0.974233i	$-0.427584\pi$
$557$	10.6460			0.451086			0.225543	+	0.974233i	$0.427584\pi$
$558$		0			0
$559$	25.4164			1.07500
$560$	17.8262	+	12.9515i	0.753296	+	0.547302i
$561$	−1.43512	−	13.6543i	−0.0605908	−	0.576483i
$562$	10.8090	+	33.2667i	0.455951	+	1.40327i
$563$	−4.88197	−	8.45581i	−0.205750	−	0.356370i	0.744621	−	0.667487i	$-0.232630\pi$
$563$	−4.88197	−	8.45581i	−0.205750	−	0.356370i	−0.950372	+	0.311117i	$0.899297\pi$
$564$	20.5942	−	35.6702i	0.867173	−	1.50199i
$565$	21.3557	+	4.53930i	0.898442	+	0.190970i
$566$	19.4164	−	59.7576i	0.816132	−	2.51180i
$567$	2.64902	−	0.563067i	0.111249	−	0.0236466i
$568$	1.14981	−	10.9397i	0.0482451	−	0.459021i
$569$	7.84647	−	8.71439i	0.328941	−	0.365326i	−0.555875	−	0.831266i	$-0.687617\pi$
$569$	7.84647	−	8.71439i	0.328941	−	0.365326i	0.884817	+	0.465939i	$0.154284\pi$
$570$	4.67431	−	2.08114i	0.195785	−	0.0871693i
$571$	2.39540	+	1.06650i	0.100245	+	0.0446317i	0.456246	−	0.889854i	$-0.349194\pi$
$571$	2.39540	+	1.06650i	0.100245	+	0.0446317i	−0.356002	+	0.934485i	$0.615860\pi$
$572$	−36.1331	−	40.1298i	−1.51080	−	1.67791i
$573$	−6.90414	+	5.01615i	−0.288425	+	0.209553i
$574$	−3.11803	+	2.26538i	−0.130144	+	0.0945553i
$575$		0			0
$576$	−17.7887	−	7.92003i	−0.741195	−	0.330001i
$577$	−27.4064	+	12.2021i	−1.14094	+	0.507980i	−0.888156	−	0.459542i	$-0.848013\pi$
$577$	−27.4064	+	12.2021i	−1.14094	+	0.507980i	−0.252786	+	0.967522i	$0.581347\pi$
$578$	−5.76659	+	6.40445i	−0.239859	+	0.266390i
$579$	1.89193	−	18.0005i	0.0786258	−	0.748075i
$580$	−5.73506	+	1.21902i	−0.238135	+	0.0506172i
$581$	−0.977198	+	3.00750i	−0.0405410	+	0.124772i
$582$	15.6677	+	3.33027i	0.649447	+	0.138044i
$583$	29.1246	−	50.4453i	1.20622	−	2.08923i
$584$	15.8508	+	27.4544i	0.655911	+	1.13607i
$585$	−4.05136	−	12.4688i	−0.167503	−	0.515522i
$586$	0.627171	+	5.96713i	0.0259082	+	0.246500i
$587$	−12.7279	−	9.24738i	−0.525338	−	0.381680i	0.293273	−	0.956029i	$-0.405255\pi$
$587$	−12.7279	−	9.24738i	−0.525338	−	0.381680i	−0.818611	+	0.574349i	$0.805255\pi$
$588$	−25.4558			−1.04978
$589$		0			0
$590$	69.9230			2.87868
$591$	−0.763932	−	0.555029i	−0.0314240	−	0.0228308i
$592$	4.37006	+	41.5784i	0.179609	+	1.70886i
$593$	1.60081	+	4.92680i	0.0657375	+	0.202319i	0.978530	−	0.206104i	$-0.0660786\pi$
$593$	1.60081	+	4.92680i	0.0657375	+	0.202319i	−0.912793	+	0.408424i	$0.866079\pi$
$594$	−25.4164	−	44.0225i	−1.04285	−	1.80627i
$595$	−4.13948	+	7.16978i	−0.169702	+	0.293932i
$596$	63.7015	+	13.5402i	2.60931	+	0.554627i
$597$	−6.27051	+	19.2986i	−0.256635	+	0.789841i
$598$	−17.6067	+	3.74241i	−0.719990	+	0.153039i
$599$	−0.632996	+	6.02255i	−0.0258635	+	0.246075i	0.973950	+	0.226763i	$0.0728142\pi$
$599$	−0.632996	+	6.02255i	−0.0258635	+	0.246075i	−0.999814	+	0.0193120i	$0.993852\pi$
$600$		0			0
$601$	−16.6068	+	7.39384i	−0.677407	+	0.301601i	−0.716452	−	0.697636i	$-0.754235\pi$
$601$	−16.6068	+	7.39384i	−0.677407	+	0.301601i	0.0390450	+	0.999237i	$0.487568\pi$
$602$	−23.1831	−	10.3218i	−0.944872	−	0.420684i
$603$	−8.97733	−	9.97033i	−0.365585	−	0.406023i
$604$	49.1729	−	35.7262i	2.00082	−	1.45368i
$605$	−12.6631	+	9.20029i	−0.514829	+	0.374045i
$606$	3.42372	+	3.80243i	0.139079	+	0.154463i
$607$	13.8170	+	6.15173i	0.560816	+	0.249691i	0.667510	−	0.744601i	$-0.267360\pi$
$607$	13.8170	+	6.15173i	0.560816	+	0.249691i	−0.106695	+	0.994292i	$0.534027\pi$
$608$	9.91572	−	4.41476i	0.402135	−	0.179042i
$609$	−0.315921	+	0.350865i	−0.0128017	+	0.0142178i
$610$	8.52760	−	81.1347i	0.345272	−	3.28505i
$611$	24.8996	−	5.29257i	1.00733	−	0.214114i
$612$	12.4184	−	38.2200i	0.501985	−	1.54495i
$613$	0.576021	+	0.122437i	0.0232653	+	0.00494519i	0.219530	−	0.975606i	$-0.429548\pi$
$613$	0.576021	+	0.122437i	0.0232653	+	0.00494519i	−0.196264	+	0.980551i	$0.562881\pi$
$614$	−31.5795	+	54.6973i	−1.27445	+	2.20741i
$615$	1.43857	+	2.49167i	0.0580086	+	0.100474i
$616$	9.79633	+	30.1500i	0.394705	+	1.21478i
$617$	0.718674	+	6.83772i	0.0289327	+	0.275276i	0.999418	+	0.0341156i	$0.0108614\pi$
$617$	0.718674	+	6.83772i	0.0289327	+	0.275276i	−0.970485	+	0.241161i	$0.922472\pi$
$618$	−19.8233	−	14.4025i	−0.797412	−	0.579354i
$619$	−25.8384			−1.03853			−0.519267	−	0.854612i	$-0.673795\pi$
$619$	−25.8384			−1.03853			−0.519267	+	0.854612i	$0.673795\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	−53.9508	−	39.1976i	−2.16323	−	1.57168i
$623$	1.60451	+	15.2659i	0.0642835	+	0.611617i
$624$	6.97871	+	21.4783i	0.279372	+	0.859819i
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	−15.0799	+	26.1192i	−0.602715	+	1.04393i
$627$	3.62717	+	0.770979i	0.144855	+	0.0307899i
$628$	13.0623	−	40.2016i	0.521243	−	1.60422i
$629$	−15.3649	+	3.26592i	−0.612640	+	0.130221i
$630$	−1.36830	+	13.0185i	−0.0545142	+	0.518668i
$631$	15.8109	−	17.5597i	0.629421	−	0.699042i	−0.341109	−	0.940024i	$-0.610803\pi$
$631$	15.8109	−	17.5597i	0.629421	−	0.699042i	0.970530	+	0.240981i	$0.0774692\pi$
$632$	11.0621	−	4.92515i	0.440025	−	0.195912i
$633$	−3.99234	−	1.77750i	−0.158681	−	0.0706495i
$634$	45.9605	+	51.0443i	1.82533	+	2.02723i
$635$	−17.1618	+	12.4688i	−0.681047	+	0.494810i
$636$	−47.1246	+	34.2380i	−1.86861	+	1.35763i
$637$	−10.5271	−	11.6916i	−0.417101	−	0.463237i
$638$	−5.48127	−	2.44042i	−0.217006	−	0.0966171i
$639$	3.00721	−	1.33889i	0.118963	−	0.0529658i
$640$	1.63114	−	1.81156i	0.0644763	−	0.0716082i
$641$	−0.886953	+	8.43880i	−0.0350326	+	0.333312i	0.962943	+	0.269707i	$0.0869267\pi$
$641$	−0.886953	+	8.43880i	−0.0350326	+	0.333312i	−0.997975	+	0.0636059i	$0.979740\pi$
$642$	−3.29500	+	0.700373i	−0.130043	+	0.0276415i
$643$	1.43857	−	4.42746i	0.0567316	−	0.174602i	−0.918675	−	0.395013i	$-0.870740\pi$
$643$	1.43857	−	4.42746i	0.0567316	−	0.174602i	0.975407	+	0.220411i	$0.0707400\pi$
$644$	12.4498	+	2.64628i	0.490590	+	0.104278i
$645$	−9.47214	+	16.4062i	−0.372965	+	0.645994i
$646$	4.84658	+	8.39453i	0.190686	+	0.330278i
$647$	−9.82068	−	30.2250i	−0.386091	−	1.18827i	−0.935686	−	0.352834i	$-0.885218\pi$
$647$	−9.82068	−	30.2250i	−0.386091	−	1.18827i	0.549595	−	0.835431i	$-0.314782\pi$
$648$	−2.11525	−	20.1252i	−0.0830947	−	0.790593i
$649$	40.9971	+	29.7862i	1.60928	+	1.16921i
$650$		0			0
$651$		0			0
$652$	69.9787			2.74058
$653$	−19.9443	−	14.4904i	−0.780480	−	0.567052i	0.124643	−	0.992202i	$-0.460221\pi$
$653$	−19.9443	−	14.4904i	−0.780480	−	0.567052i	−0.905123	+	0.425150i	$0.860221\pi$
$654$	0.308981	+	2.93975i	0.0120821	+	0.114953i
$655$	5.12461	+	15.7719i	0.200235	+	0.616260i
$656$	7.25329	+	12.5631i	0.283193	+	0.490505i
$657$	−4.74342	+	8.21584i	−0.185058	+	0.320530i
$658$	−24.8610	−	5.28437i	−0.969183	−	0.206006i
$659$	7.66970	−	23.6049i	0.298769	−	0.919516i	−0.683160	−	0.730268i	$-0.739395\pi$
$659$	7.66970	−	23.6049i	0.298769	−	0.919516i	0.981929	−	0.189248i	$-0.0606050\pi$
$660$	39.3697	−	8.36828i	1.53246	−	0.325735i
$661$	−0.818752	+	7.78991i	−0.0318458	+	0.302992i	0.966993	+	0.254805i	$0.0820112\pi$
$661$	−0.818752	+	7.78991i	−0.0318458	+	0.302992i	−0.998838	+	0.0481876i	$0.984655\pi$
$662$	−54.8121	+	60.8751i	−2.13033	+	2.36598i
$663$	−7.75169	+	3.45127i	−0.301051	+	0.134036i
$664$	21.5861	+	9.61077i	0.837705	+	0.372970i
$665$	−1.49622	−	1.66172i	−0.0580210	−	0.0644388i
$666$	−20.0934	+	14.5987i	−0.778605	+	0.565689i
$667$	−1.14590	+	0.832544i	−0.0443693	+	0.0322362i
$668$	3.50905	+	3.89719i	0.135769	+	0.150787i
$669$	−12.8915	−	5.73965i	−0.498413	−	0.221908i
$670$	32.0879	−	14.2865i	1.23966	−	0.551934i
$671$	39.5621	−	43.9381i	1.52728	−	1.69621i
$672$	0.991644	−	9.43486i	0.0382535	−	0.363958i
$673$	39.1069	−	8.31242i	1.50746	−	0.320420i	0.621215	−	0.783640i	$-0.286639\pi$
$673$	39.1069	−	8.31242i	1.50746	−	0.320420i	0.886244	+	0.463220i	$0.153306\pi$
$674$	12.4184	−	38.2200i	0.478340	−	1.47218i
$675$		0			0
$676$	14.8647	−	25.7465i	0.571721	−	0.990250i
$677$	−10.6066	−	18.3712i	−0.407645	−	0.706062i	0.586981	−	0.809601i	$-0.300317\pi$
$677$	−10.6066	−	18.3712i	−0.407645	−	0.706062i	−0.994625	+	0.103540i	$0.966983\pi$
$678$	−6.90414	−	21.2488i	−0.265152	−	0.816054i
$679$	−0.731699	−	6.96165i	−0.0280800	−	0.267164i
$680$	50.0470	+	36.3612i	1.91921	+	1.39439i
$681$	2.00310			0.0767591
$682$		0			0
$683$	−41.1803			−1.57572			−0.787861	−	0.615853i	$-0.788811\pi$
$683$	−41.1803			−1.57572			−0.787861	+	0.615853i	$0.788811\pi$
$684$	8.78115	+	6.37988i	0.335756	+	0.243941i
$685$	−0.612870	−	5.83107i	−0.0234165	−	0.222794i
$686$	10.5172	+	32.3687i	0.401549	+	1.23584i
$687$	1.85410	+	3.21140i	0.0707384	+	0.122523i
$688$	−47.7587	+	82.7205i	−1.82078	+	3.15369i
$689$	−35.2133	−	7.48482i	−1.34152	−	0.285149i
$690$	4.14590	−	12.7598i	0.157832	−	0.485756i
$691$	47.3584	−	10.0663i	1.80160	−	0.382942i	0.819767	−	0.572697i	$-0.194103\pi$
$691$	47.3584	−	10.0663i	1.80160	−	0.382942i	0.981831	+	0.189756i	$0.0607696\pi$
$692$	−9.13305	+	86.8952i	−0.347187	+	3.30326i
$693$	−6.34793	+	7.05009i	−0.241138	+	0.267811i
$694$	51.6504	−	22.9963i	1.96062	−	0.872926i
$695$	36.7125	+	16.3455i	1.39259	+	0.620019i
$696$	2.36060	+	2.62171i	0.0894784	+	0.0993758i
$697$	−4.40957	+	3.20374i	−0.167024	+	0.121350i
$698$	−12.7082	+	9.23305i	−0.481013	+	0.349476i
$699$	−7.87907	−	8.75059i	−0.298014	−	0.330978i
$700$		0			0
$701$	−3.33670	+	1.48560i	−0.126026	+	0.0561102i	−0.468781	−	0.883315i	$-0.655307\pi$
$701$	−3.33670	+	1.48560i	−0.126026	+	0.0561102i	0.342755	+	0.939425i	$0.388640\pi$
$702$	−21.0217	+	23.3469i	−0.793412	+	0.881174i
$703$	0.443477	−	4.21940i	0.0167260	−	0.159138i
$704$	36.1384	−	7.68146i	1.36202	−	0.289506i
$705$	−5.86319	+	18.0450i	−0.220820	+	0.679615i
$706$	24.4959	+	5.20677i	0.921916	+	0.195959i
$707$	1.11803	−	1.93649i	0.0420480	−	0.0728293i
$708$	−25.3376	−	43.8861i	−0.952246	−	1.64934i
$709$	12.7279	+	39.1725i	0.478007	+	1.47115i	0.841859	+	0.539698i	$0.181462\pi$
$709$	12.7279	+	39.1725i	0.478007	+	1.47115i	−0.363852	+	0.931457i	$0.618538\pi$
$710$	0.900830	+	8.57082i	0.0338075	+	0.321657i
$711$	2.93159	+	2.12993i	0.109943	+	0.0798785i
$712$	114.697			4.29847
$713$		0			0
$714$	8.47214			0.317062
$715$	20.1246	+	14.6214i	0.752618	+	0.546809i
$716$	6.73213	+	64.0519i	0.251591	+	2.39373i
$717$	−3.27051	−	10.0656i	−0.122139	−	0.375907i
$718$	−18.6353	−	32.2772i	−0.695462	−	1.20457i
$719$	−18.7824	+	32.5320i	−0.700465	+	1.21324i	0.267839	+	0.963464i	$0.413691\pi$
$719$	−18.7824	+	32.5320i	−0.700465	+	1.21324i	−0.968303	+	0.249777i	$0.919643\pi$
$720$	48.1938	+	10.2439i	1.79608	+	0.381768i
$721$	−3.30902	+	10.1841i	−0.123234	+	0.379276i
$722$	46.0948	−	9.79776i	1.71547	−	0.364635i
$723$	−2.12107	+	20.1806i	−0.0788835	+	0.750526i
$724$	−28.2306	+	31.3533i	−1.04918	+	1.16523i
$725$		0			0
$726$	14.6329	+	6.51499i	0.543078	+	0.241794i
$727$	−20.3525	−	22.6038i	−0.754834	−	0.838328i	0.236232	−	0.971697i	$-0.424087\pi$
$727$	−20.3525	−	22.6038i	−0.754834	−	0.838328i	−0.991067	+	0.133368i	$0.957421\pi$
$728$	15.8508	−	11.5163i	0.587470	−	0.426822i
$729$	−4.80902	+	3.49396i	−0.178112	+	0.129406i
$730$	−16.6191	−	18.4574i	−0.615100	−	0.683138i
$731$	−32.7858	−	14.5972i	−1.21263	−	0.539896i
$732$	−54.0130	+	24.0481i	−1.99638	+	0.888845i
$733$	−9.64646	+	10.7135i	−0.356300	+	0.395711i	−0.894472	−	0.447124i	$-0.852448\pi$
$733$	−9.64646	+	10.7135i	−0.356300	+	0.395711i	0.538172	+	0.842835i	$0.319115\pi$
$734$	1.82213	−	17.3364i	0.0672562	−	0.639900i
$735$	11.4701	−	2.43805i	0.423082	−	0.0899288i
$736$	8.79478	−	27.0675i	0.324180	−	0.997723i
$737$	24.8996	+	5.29257i	0.917188	+	0.194954i
$738$	−4.30902	+	7.46344i	−0.158617	+	0.274733i
$739$	−17.5745	−	30.4399i	−0.646489	−	1.11975i	−0.983956	−	0.178414i	$-0.942903\pi$
$739$	−17.5745	−	30.4399i	−0.646489	−	1.11975i	0.337467	−	0.941337i	$-0.390430\pi$
$740$	−14.2302	−	43.7962i	−0.523114	−	1.60998i
$741$	−0.239558	−	2.27924i	−0.00880038	−	0.0837300i
$742$	29.0795	+	21.1275i	1.06754	+	0.775614i
$743$	36.4844			1.33848			0.669242	−	0.743045i	$-0.266619\pi$
$743$	36.4844			1.33848			0.669242	+	0.743045i	$0.266619\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	19.6803	+	14.2986i	0.720548	+	0.523509i
$747$	0.739128	+	7.03233i	0.0270433	+	0.257300i
$748$	23.5623	+	72.5173i	0.861523	+	2.65150i
$749$	0.736068	+	1.27491i	0.0268953	+	0.0465841i
$750$	12.7917	−	22.1558i	0.467086	−	0.809017i
$751$	36.7207	+	7.80522i	1.33996	+	0.284816i	0.821461	−	0.570264i	$-0.193159\pi$
$751$	36.7207	+	7.80522i	1.33996	+	0.284816i	0.518495	+	0.855081i	$0.326493\pi$
$752$	−29.5623	+	90.9834i	−1.07803	+	3.31782i
$753$	9.42868	−	2.00413i	0.343600	−	0.0730345i
$754$	−0.387613	+	3.68789i	−0.0141160	+	0.134305i
$755$	−18.7351	+	20.8074i	−0.681839	+	0.757259i
$756$	20.2942	−	9.03555i	0.738093	−	0.328620i
$757$	−8.47816	−	3.77472i	−0.308144	−	0.137195i	0.246838	−	0.969057i	$-0.420608\pi$
$757$	−8.47816	−	3.77472i	−0.308144	−	0.137195i	−0.554982	+	0.831862i	$0.687275\pi$
$758$	12.9921	+	14.4292i	0.471895	+	0.524092i
$759$	7.86629	−	5.71519i	0.285528	−	0.207448i
$760$	−13.5172	+	9.82084i	−0.490321	+	0.356239i
$761$	−26.8903	−	29.8647i	−0.974771	−	1.08259i	−0.996564	−	0.0828307i	$-0.973604\pi$
$761$	−26.8903	−	29.8647i	−0.974771	−	1.08259i	0.0217923	−	0.999763i	$-0.493063\pi$
$762$	19.8314	+	8.82952i	0.718417	+	0.319860i
$763$	1.18011	−	0.525421i	0.0427230	−	0.0190215i
$764$	31.7135	−	35.2214i	1.14736	−	1.27427i
$765$	−1.93506	+	18.4109i	−0.0699623	+	0.665647i
$766$	−16.3979	+	3.48548i	−0.592480	+	0.125936i
$767$	9.67811	−	29.7862i	0.349456	−	1.07552i
$768$	12.4498	+	2.64628i	0.449243	+	0.0954895i
$769$	−27.0623	+	46.8733i	−0.975892	+	1.69029i	−0.298931	+	0.954275i	$0.596630\pi$
$769$	−27.0623	+	46.8733i	−0.975892	+	1.69029i	−0.676960	+	0.736019i	$0.736703\pi$
$770$	−12.4184	−	21.5093i	−0.447529	−	0.775143i
$771$	1.63560	+	5.03385i	0.0589046	+	0.181290i
$772$	10.5072	+	99.9691i	0.378161	+	3.59797i
$773$	−9.04982	−	6.57508i	−0.325499	−	0.236489i	0.413019	−	0.910722i	$-0.364474\pi$
$773$	−9.04982	−	6.57508i	−0.325499	−	0.236489i	−0.738518	+	0.674233i	$0.764474\pi$
$774$	−56.7448			−2.03965
$775$		0			0
$776$	−52.3050			−1.87764
$777$	−3.00000	−	2.17963i	−0.107624	−	0.0781937i
$778$	−4.60101	−	43.7757i	−0.164954	−	1.56944i
$779$	−0.454915	−	1.40008i	−0.0162990	−	0.0501632i
$780$	−12.4377	−	21.5427i	−0.445341	−	0.771353i
$781$	−3.12287	+	5.40897i	−0.111745	+	0.193548i
$782$	24.8610	+	5.28437i	0.889027	+	0.188969i
$783$	−0.763932	+	2.35114i	−0.0273007	+	0.0840229i
$784$	57.8326	−	12.2927i	2.06545	−	0.439025i
$785$	−2.03539	+	19.3655i	−0.0726463	+	0.691183i
$786$	11.3555	−	12.6116i	0.405038	−	0.449840i
$787$	34.3171	−	15.2790i	1.22327	−	0.544636i	0.309515	−	0.950895i	$-0.399833\pi$
$787$	34.3171	−	15.2790i	1.22327	−	0.544636i	0.913758	+	0.406258i	$0.133167\pi$
$788$	4.79081	+	2.13301i	0.170665	+	0.0759852i
$789$	−10.8268	−	12.0243i	−0.385443	−	0.428078i
$790$	−7.67501	+	5.57622i	−0.273065	+	0.198393i
$791$	−7.89919	+	5.73910i	−0.280863	+	0.204059i
$792$	47.4326	+	52.6792i	1.68544	+	1.87188i
$793$	−33.3819	−	14.8626i	−1.18543	−	0.527785i
$794$	35.1775	−	15.6620i	1.24840	−	0.555825i
$795$	17.9547	−	19.9407i	0.636786	−	0.707223i
$796$	11.7798	−	112.077i	0.417523	−	3.97246i
$797$	−13.4295	+	2.85452i	−0.475696	+	0.101112i	−0.439519	−	0.898233i	$-0.644851\pi$
$797$	−13.4295	+	2.85452i	−0.475696	+	0.101112i	−0.0361764	+	0.999345i	$0.511518\pi$
$798$	−0.707107	+	2.17625i	−0.0250313	+	0.0770384i
$799$	−35.1588	−	7.47323i	−1.24383	−	0.264384i
$800$		0			0
$801$	17.1618	+	29.7252i	0.606384	+	1.05029i
$802$	0.437016	+	1.34500i	0.0154316	+	0.0474935i
$803$	−1.88151	−	17.9014i	−0.0663971	−	0.631726i
$804$	−20.5942	−	14.9626i	−0.726302	−	0.527689i
$805$	−5.86319			−0.206650
$806$		0			0
$807$	−1.88854			−0.0664799
$808$	−13.5172	−	9.82084i	−0.475534	−	0.345496i
$809$	4.96646	+	47.2527i	0.174611	+	1.66132i	0.634189	+	0.773178i	$0.281334\pi$
$809$	4.96646	+	47.2527i	0.174611	+	1.66132i	−0.459577	+	0.888138i	$0.651999\pi$
$810$	4.89919	+	15.0781i	0.172140	+	0.529792i
$811$	8.29180	+	14.3618i	0.291164	+	0.504311i	0.974085	−	0.226181i	$-0.0726240\pi$
$811$	8.29180	+	14.3618i	0.291164	+	0.504311i	−0.682921	+	0.730492i	$0.739291\pi$
$812$	1.31105	−	2.27080i	0.0460088	−	0.0796895i
$813$	−15.8941	−	3.37840i	−0.557432	−	0.118486i
$814$	14.5623	−	44.8182i	0.510409	−	1.57088i
$815$	−31.5316	+	6.70226i	−1.10450	+	0.234770i
$816$	3.33326	−	31.7139i	0.116687	−	1.11021i
$817$	6.48599	−	7.20342i	0.226916	−	0.252016i
$818$	−71.9446	+	32.0318i	−2.51548	+	1.11997i
$819$	5.35629	+	2.38477i	0.187164	+	0.0833307i
$820$	−10.6918	−	11.8745i	−0.373375	−	0.414675i
$821$	19.2832	−	14.0100i	0.672987	−	0.488954i	−0.198037	−	0.980195i	$-0.563457\pi$
$821$	19.2832	−	14.0100i	0.672987	−	0.488954i	0.871024	+	0.491241i	$0.163457\pi$
$822$	−4.85410	+	3.52671i	−0.169306	+	0.123008i
$823$	9.04875	+	10.0497i	0.315420	+	0.350309i	0.879918	−	0.475125i	$-0.157597\pi$
$823$	9.04875	+	10.0497i	0.315420	+	0.350309i	−0.564499	+	0.825434i	$0.690931\pi$
$824$	73.0957	+	32.5443i	2.54641	+	1.13373i
$825$		0			0
$826$	−20.9241	+	23.2385i	−0.728041	+	0.808571i
$827$	−1.91859	+	18.2541i	−0.0667158	+	0.634758i	0.909162	+	0.416442i	$0.136723\pi$
$827$	−1.91859	+	18.2541i	−0.0667158	+	0.634758i	−0.975878	+	0.218316i	$0.929944\pi$
$828$	27.8386	−	5.91727i	0.967457	−	0.205639i
$829$	−15.7870	+	48.5875i	−0.548306	+	1.68751i	0.164690	+	0.986345i	$0.447338\pi$
$829$	−15.7870	+	48.5875i	−0.548306	+	1.68751i	−0.712996	+	0.701168i	$0.752662\pi$
$830$	−18.1078	−	3.84892i	−0.628529	−	0.133598i
$831$	4.41641	−	7.64944i	0.153203	−	0.265356i
$832$	−11.4169	−	19.7746i	−0.395809	−	0.685561i
$833$	6.86474	+	21.1275i	0.237849	+	0.732024i
$834$	−4.29869	−	40.8993i	−0.148852	−	1.41623i
$835$	−1.95440	−	1.41995i	−0.0676346	−	0.0491394i
$836$	−20.5942			−0.712266
$837$		0			0
$838$	80.1033			2.76712
$839$	15.7082	+	11.4127i	0.542307	+	0.394009i	0.824941	−	0.565218i	$-0.191208\pi$
$839$	15.7082	+	11.4127i	0.542307	+	0.394009i	−0.282634	+	0.959228i	$0.591208\pi$
$840$	1.52648	+	14.5235i	0.0526686	+	0.501109i
$841$	−8.87132	−	27.3031i	−0.305908	−	0.941487i
$842$	−34.5795	−	59.8935i	−1.19169	−	2.06407i
$843$	−5.83883	+	10.1132i	−0.201100	+	0.348315i
$844$	23.7401	+	5.04612i	0.817169	+	0.173695i
$845$	−4.23200	+	13.0248i	−0.145585	+	0.448066i
$846$	−55.5909	+	11.8162i	−1.91125	+	0.406250i
$847$	0.731699	−	6.96165i	0.0251415	−	0.239205i
$848$	90.5278	−	100.541i	3.10874	−	3.45260i
$849$	19.1632	−	8.53202i	0.657680	−	0.292818i
$850$		0			0
$851$	−7.44382	−	8.26720i	−0.255171	−	0.283396i
$852$	5.05291	−	3.67116i	0.173110	−	0.125772i
$853$	26.1246	−	18.9806i	0.894490	−	0.649885i	−0.0425551	−	0.999094i	$-0.513550\pi$
$853$	26.1246	−	18.9806i	0.894490	−	0.649885i	0.937045	+	0.349209i	$0.113550\pi$
$854$	24.4128	+	27.1132i	0.835390	+	0.927795i
$855$	−4.56773	−	2.03368i	−0.156213	−	0.0695505i
$856$	10.0490	−	4.47410i	0.343468	−	0.152922i
$857$	−4.01478	+	4.45887i	−0.137142	+	0.152312i	−0.807804	−	0.589452i	$-0.799344\pi$
$857$	−4.01478	+	4.45887i	−0.137142	+	0.152312i	0.670661	+	0.741764i	$0.266010\pi$
$858$	2.66086	−	25.3164i	0.0908403	−	0.864287i
$859$	−40.6920	+	8.64935i	−1.38839	+	0.295112i	−0.840670	−	0.541548i	$-0.817839\pi$
$859$	−40.6920	+	8.64935i	−1.38839	+	0.295112i	−0.547723	+	0.836660i	$0.684505\pi$
$860$	32.5119	−	100.061i	1.10865	−	3.41206i
$861$	−1.25858	−	0.267519i	−0.0428922	−	0.00911701i
$862$	46.9787	−	81.3695i	1.60010	−	2.77146i
$863$	−15.5413	−	26.9183i	−0.529032	−	0.916310i	−0.999427	−	0.0338541i	$-0.989222\pi$
$863$	−15.5413	−	26.9183i	−0.529032	−	0.916310i	0.470395	−	0.882456i	$-0.344111\pi$
$864$	−15.3500	−	47.2425i	−0.522218	−	1.60722i
$865$	−4.20719	−	40.0287i	−0.143049	−	1.36102i
$866$	−54.7266	−	39.7612i	−1.85969	−	1.35114i
$867$	−2.87714			−0.0977126
$868$		0			0
$869$	−6.87539			−0.233232
$870$	−2.23607	−	1.62460i	−0.0758098	−	0.0550790i
$871$	−1.64450	−	15.6464i	−0.0557218	−	0.530158i
$872$	−2.98278	−	9.18005i	−0.101010	−	0.310876i
$873$	−7.82624	−	13.5554i	−0.264878	−	0.458782i
$874$	−3.43237	+	5.94504i	−0.116102	+	0.201094i
$875$	−10.9360	−	2.32452i	−0.369705	−	0.0785832i
$876$	−5.56231	+	17.1190i	−0.187933	+	0.578398i
$877$	28.0809	−	5.96877i	0.948223	−	0.201551i	0.292256	−	0.956340i	$-0.405594\pi$
$877$	28.0809	−	5.96877i	0.948223	−	0.201551i	0.655968	+	0.754789i	$0.272261\pi$
$878$	6.84148	−	65.0923i	0.230889	−	2.19676i
$879$	−1.34034	+	1.48860i	−0.0452085	+	0.0502091i
$880$	−85.4021	+	38.0235i	−2.87890	+	1.28177i
$881$	−6.62073	−	2.94774i	−0.223058	−	0.0993119i	0.292165	−	0.956368i	$-0.405624\pi$
$881$	−6.62073	−	2.94774i	−0.223058	−	0.0993119i	−0.515223	+	0.857056i	$0.672291\pi$
$882$	23.5030	+	26.1027i	0.791386	+	0.878923i
$883$	−27.4589	+	19.9501i	−0.924067	+	0.671374i	−0.944533	−	0.328416i	$-0.893485\pi$
$883$	−27.4589	+	19.9501i	−0.924067	+	0.671374i	0.0204659	+	0.999791i	$0.493485\pi$
$884$	38.1246	−	27.6992i	1.28227	−	0.931623i
$885$	15.6201	+	17.3478i	0.525063	+	0.583141i
$886$	14.4834	+	6.44844i	0.486581	+	0.216640i
$887$	23.1681	−	10.3151i	0.777910	−	0.346348i	0.0209257	−	0.999781i	$-0.493339\pi$
$887$	23.1681	−	10.3151i	0.777910	−	0.346348i	0.756984	+	0.653433i	$0.226672\pi$
$888$	−18.5404	+	20.5912i	−0.622175	+	0.690996i
$889$	0.991644	−	9.43486i	0.0332587	−	0.316435i
$890$	−87.8969	+	18.6831i	−2.94631	+	0.626258i
$891$	−3.55059	+	10.9276i	−0.118949	+	0.366088i
$892$	76.6580	+	16.2942i	2.56670	+	0.545569i
$893$	4.85410	−	8.40755i	0.162436	−	0.281348i
$894$	15.3500	+	26.5870i	0.513381	+	0.889203i
$895$	−9.16803	−	28.2163i	−0.306454	−	0.943167i
$896$	0.113954	+	1.08420i	0.00380693	+	0.0362205i
$897$	−4.86163	−	3.53218i	−0.162325	−	0.117936i
$898$	−88.2400			−2.94461
$899$		0			0
$900$		0			0
$901$	41.1246	+	29.8788i	1.37006	+	0.995406i
$902$	−1.70920	−	16.2620i	−0.0569103	−	0.541465i
$903$	−2.61803	−	8.05748i	−0.0871227	−	0.268136i
$904$	36.4787	+	63.1830i	1.21326	+	2.10143i
$905$	9.71752	−	16.8312i	0.323021	−	0.559489i
$906$	28.0264	+	5.95718i	0.931113	+	0.197914i
$907$	3.56637	−	10.9762i	0.118419	−	0.364457i	−0.874225	−	0.485520i	$-0.838630\pi$
$907$	3.56637	−	10.9762i	0.118419	−	0.364457i	0.992645	+	0.121063i	$0.0386302\pi$
$908$	−10.8815	+	2.31294i	−0.361116	+	0.0767575i
$909$	0.522642	−	4.97261i	0.0173350	−	0.164931i
$910$	−10.2712	+	11.4073i	−0.340486	+	0.378148i
$911$	24.5915	−	10.9488i	0.814753	−	0.362752i	0.0433196	−	0.999061i	$-0.486207\pi$
$911$	24.5915	−	10.9488i	0.814753	−	0.362752i	0.771434	+	0.636310i	$0.219540\pi$
$912$	7.86819	+	3.50314i	0.260542	+	0.116001i
$913$	−8.97733	−	9.97033i	−0.297106	−	0.329970i
$914$	23.9628	−	17.4100i	0.792620	−	0.575872i
$915$	22.0344	−	16.0090i	0.728436	−	0.529240i
$916$	−13.7802	−	15.3045i	−0.455311	−	0.505674i
$917$	−6.77523	−	3.01652i	−0.223738	−	0.0996144i
$918$	40.5255	−	18.0431i	1.33754	−	0.595511i
$919$	−28.4655	+	31.6141i	−0.938990	+	1.04285i	0.0600123	+	0.998198i	$0.480886\pi$
$919$	−28.4655	+	31.6141i	−0.938990	+	1.04285i	−0.999002	+	0.0446566i	$0.985781\pi$
$920$	−4.57945	+	43.5705i	−0.150980	+	1.43648i
$921$	−20.6249	+	4.38396i	−0.679614	+	0.144456i
$922$	−4.17888	+	12.8613i	−0.137624	+	0.423563i
$923$	3.77573	+	0.802556i	0.124280	+	0.0264165i
$924$	−9.00000	+	15.5885i	−0.296078	+	0.512823i
$925$		0			0
$926$	3.09852	+	9.53626i	0.101824	+	0.313381i
$927$	2.50286	+	23.8131i	0.0822046	+	0.782125i
$928$	−4.74342	−	3.44629i	−0.155710	−	0.113130i
$929$	−10.6460			−0.349284			−0.174642	−	0.984632i	$-0.555877\pi$
$929$	−10.6460			−0.349284			−0.174642	+	0.984632i	$0.555877\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	52.9058	+	38.4383i	1.73299	+	1.25909i
$933$	−2.32717	−	22.1415i	−0.0761880	−	0.724880i
$934$	−12.6631	−	38.9731i	−0.414350	−	1.27524i
$935$	−17.5623	−	30.4188i	−0.574349	−	0.994801i
$936$	21.9053	−	37.9410i	0.715996	−	1.24014i
$937$	−23.7193	−	5.04170i	−0.774876	−	0.164705i	−0.196532	−	0.980497i	$-0.562968\pi$
$937$	−23.7193	−	5.04170i	−0.774876	−	0.164705i	−0.578345	+	0.815792i	$0.696301\pi$
$938$	−4.85410	+	14.9394i	−0.158492	+	0.487788i
$939$	−9.84885	+	2.09344i	−0.321405	+	0.0683168i
$940$	11.0146	−	104.797i	0.359256	−	3.41809i
$941$	−17.0860	+	18.9759i	−0.556988	+	0.618598i	−0.954215	−	0.299122i	$-0.903306\pi$
$941$	−17.0860	+	18.9759i	−0.556988	+	0.618598i	0.397226	+	0.917721i	$0.369973\pi$
$942$	18.2038	−	8.10484i	0.593111	−	0.264070i
$943$	−3.52636	−	1.57004i	−0.114834	−	0.0511274i
$944$	78.7567	+	87.4682i	2.56331	+	2.84685i
$945$	−8.27895	+	6.01501i	−0.269314	+	0.195668i
$946$	87.1033	−	63.2843i	2.83197	−	2.05755i
$947$	−26.8903	−	29.8647i	−0.873816	−	0.970471i	0.125951	−	0.992036i	$-0.459802\pi$
$947$	−26.8903	−	29.8647i	−0.873816	−	0.970471i	−0.999767	+	0.0215652i	$0.993135\pi$
$948$	6.28098	+	2.79647i	0.203997	+	0.0908252i
$949$	−10.1628	+	4.52479i	−0.329900	+	0.146881i
$950$		0			0
$951$	−2.39696	+	22.8055i	−0.0777267	+	0.739520i
$952$	−27.0607	+	5.75193i	−0.877043	+	0.186421i
$953$	−5.76932	+	17.7561i	−0.186887	+	0.575178i	−0.999976	−	0.00696122i	$-0.997784\pi$
$953$	−5.76932	+	17.7561i	−0.186887	+	0.575178i	0.813089	+	0.582139i	$0.197784\pi$
$954$	78.6174	+	16.7106i	2.54533	+	0.541027i
$955$	−10.9164	+	18.9078i	−0.353247	+	0.611841i
$956$	29.3890	+	50.9032i	0.950508	+	1.64633i
$957$	−0.618993	−	1.90506i	−0.0200092	−	0.0615820i
$958$	−4.52300	−	43.0335i	−0.146131	−	1.39035i
$959$	2.12132	+	1.54123i	0.0685010	+	0.0497689i
$960$	17.0193			0.549295
$961$		0			0
$962$	−29.1246			−0.939015
$963$	2.66312	+	1.93487i	0.0858178	+	0.0623503i
$964$	−11.7798	−	112.077i	−0.379401	−	3.60976i
$965$	−14.3090	−	44.0386i	−0.460624	−	1.41765i
$966$	3.00000	+	5.19615i	0.0965234	+	0.167183i
$967$	22.0084	−	38.1197i	0.707743	−	1.22585i	−0.257949	−	0.966158i	$-0.583047\pi$
$967$	22.0084	−	38.1197i	0.707743	−	1.22585i	0.965692	−	0.259689i	$-0.0836200\pi$
$968$	−51.1620	−	10.8748i	−1.64441	−	0.349530i
$969$	−1.00000	+	3.07768i	−0.0321246	+	0.0988694i
$970$	40.0832	−	8.51995i	1.28699	−	0.273559i
$971$	−5.63289	+	53.5933i	−0.180768	+	1.71989i	0.409183	+	0.912453i	$0.365814\pi$
$971$	−5.63289	+	53.5933i	−0.180768	+	1.71989i	−0.589950	+	0.807439i	$0.700853\pi$
$972$	52.2820	−	58.0650i	1.67695	−	1.86244i
$973$	−16.4183	+	7.30992i	−0.526348	+	0.234345i
$974$	−67.1538	−	29.8988i	−2.15175	−	0.958019i
$975$		0			0
$976$	111.098	−	80.7175i	3.55616	−	2.58370i
$977$	34.3713	−	24.9722i	1.09964	−	0.798932i	0.118636	−	0.992938i	$-0.462148\pi$
$977$	34.3713	−	24.9722i	1.09964	−	0.798932i	0.981000	+	0.194006i	$0.0621480\pi$
$978$	22.0735	+	24.5151i	0.705832	+	0.783906i
$979$	−59.4943	−	26.4886i	−1.90145	−	0.846578i
$980$	−59.4943	+	26.4886i	−1.90048	+	0.846146i
$981$	1.93281	−	2.14661i	0.0617100	−	0.0685359i
$982$	−4.34850	+	41.3732i	−0.138766	+	1.32027i
$983$	52.7381	−	11.2098i	1.68209	−	0.357538i	0.734888	−	0.678189i	$-0.237235\pi$
$983$	52.7381	−	11.2098i	1.68209	−	0.357538i	0.947198	+	0.320650i	$0.103901\pi$
$984$	−2.97100	+	9.14379i	−0.0947120	+	0.291493i
$985$	−2.36297	−	0.502266i	−0.0752906	−	0.0160035i
$986$	2.61803	−	4.53457i	0.0833752	−	0.144410i
$987$	−4.24264	−	7.34847i	−0.135045	−	0.233904i
$988$	3.93314	+	12.1050i	0.125130	+	0.385111i
$989$	−2.65674	−	25.2772i	−0.0844794	−	0.803767i
$990$	−44.9303	−	32.6438i	−1.42798	−	1.03749i
$991$	13.9358			0.442685			0.221343	−	0.975196i	$-0.428956\pi$
$991$	13.9358			0.442685			0.221343	+	0.975196i	$0.428956\pi$
$992$		0			0
$993$	−27.3475			−0.867847
$994$	−3.11803	−	2.26538i	−0.0988980	−	0.0718536i
$995$	5.42641	+	51.6289i	0.172029	+	1.63674i
$996$	4.14590	+	12.7598i	0.131368	+	0.404309i
$997$	29.3328	+	50.8059i	0.928980	+	1.60904i	0.785033	+	0.619454i	$0.212646\pi$
$997$	29.3328	+	50.8059i	0.928980	+	1.60904i	0.143947	+	0.989585i	$0.454021\pi$
$998$	24.0660	−	41.6835i	0.761795	−	1.31947i
$999$	−18.9921	−	4.03690i	−0.600884	−	0.127722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.i.816.1		16
31.2	even	5		961.2.g.p.846.1		16
31.3	odd	30	inner	961.2.g.i.338.2		16
31.4	even	5		961.2.c.h.439.3		8
31.5	even	3		961.2.d.h.374.1		8
31.6	odd	6	inner	961.2.g.i.732.1		16
31.7	even	15		961.2.c.h.521.3		8
31.8	even	5		961.2.g.p.547.2		16
31.9	even	15		961.2.d.j.531.2		8
31.10	even	15		961.2.d.j.628.2		8
31.11	odd	30		961.2.a.h.1.3	✓	4
31.12	odd	30		961.2.g.p.448.1		16
31.13	odd	30		961.2.d.h.388.2		8
31.14	even	15		961.2.g.p.844.1		16
31.15	odd	10	inner	961.2.g.i.235.1		16
31.16	even	5	inner	961.2.g.i.235.2		16
31.17	odd	30		961.2.g.p.844.2		16
31.18	even	15		961.2.d.h.388.1		8
31.19	even	15		961.2.g.p.448.2		16
31.20	even	15		961.2.a.h.1.4	yes	4
31.21	odd	30		961.2.d.j.628.1		8
31.22	odd	30		961.2.d.j.531.1		8
31.23	odd	10		961.2.g.p.547.1		16
31.24	odd	30		961.2.c.h.521.4		8
31.25	even	3	inner	961.2.g.i.732.2		16
31.26	odd	6		961.2.d.h.374.2		8
31.27	odd	10		961.2.c.h.439.4		8
31.28	even	15	inner	961.2.g.i.338.1		16
31.29	odd	10		961.2.g.p.846.2		16
31.30	odd	2	inner	961.2.g.i.816.2		16
93.11	even	30		8649.2.a.r.1.1		4
93.20	odd	30		8649.2.a.r.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.3	✓	4	31.11	odd	30
961.2.a.h.1.4	yes	4	31.20	even	15
961.2.c.h.439.3		8	31.4	even	5
961.2.c.h.439.4		8	31.27	odd	10
961.2.c.h.521.3		8	31.7	even	15
961.2.c.h.521.4		8	31.24	odd	30
961.2.d.h.374.1		8	31.5	even	3
961.2.d.h.374.2		8	31.26	odd	6
961.2.d.h.388.1		8	31.18	even	15
961.2.d.h.388.2		8	31.13	odd	30
961.2.d.j.531.1		8	31.22	odd	30
961.2.d.j.531.2		8	31.9	even	15
961.2.d.j.628.1		8	31.21	odd	30
961.2.d.j.628.2		8	31.10	even	15
961.2.g.i.235.1		16	31.15	odd	10	inner
961.2.g.i.235.2		16	31.16	even	5	inner
961.2.g.i.338.1		16	31.28	even	15	inner
961.2.g.i.338.2		16	31.3	odd	30	inner
961.2.g.i.732.1		16	31.6	odd	6	inner
961.2.g.i.732.2		16	31.25	even	3	inner
961.2.g.i.816.1		16	1.1	even	1	trivial
961.2.g.i.816.2		16	31.30	odd	2	inner
961.2.g.p.448.1		16	31.12	odd	30
961.2.g.p.448.2		16	31.19	even	15
961.2.g.p.547.1		16	31.23	odd	10
961.2.g.p.547.2		16	31.8	even	5
961.2.g.p.844.1		16	31.14	even	15
961.2.g.p.844.2		16	31.17	odd	30
961.2.g.p.846.1		16	31.2	even	5
961.2.g.p.846.2		16	31.29	odd	10
8649.2.a.r.1.1		4	93.11	even	30
8649.2.a.r.1.2		4	93.20	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.11803 - 1.53884i) q^{2} +(-0.0913612 - 0.869244i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-1.14412 + 1.98168i) q^{6} +(0.978148 + 0.207912i) q^{7} +(2.30902 - 7.10642i) q^{8} +(2.18720 - 0.464905i) q^{9} +(-0.611920 + 5.82203i) q^{10} +(-2.83888 + 3.15290i) q^{11} +(3.87585 - 1.72564i) q^{12} +(2.39540 + 1.06650i) q^{13} +(-1.75181 - 1.94558i) q^{14} +(-1.58114 + 1.14876i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(-2.47743 - 2.75146i) q^{17} +(-5.34799 - 2.38108i) q^{18} +(0.913545 - 0.406737i) q^{19} +(7.26281 - 8.06617i) q^{20} +(0.0913612 - 0.869244i) q^{21} +(10.8647 - 2.30935i) q^{22} +(0.810272 - 2.49376i) q^{23} +(-6.38817 - 1.35785i) q^{24} +(-3.43237 - 5.94504i) q^{26} +(-1.41421 - 4.35250i) q^{27} +(0.507392 + 4.82751i) q^{28} +(-0.437016 - 0.317511i) q^{29} +5.11667 q^{30} +10.8541 q^{32} +(3.00000 + 2.17963i) q^{33} +(1.01321 + 9.64006i) q^{34} +(-0.690983 - 2.12663i) q^{35} +(5.42705 + 9.39993i) q^{36} +(2.12132 - 3.67423i) q^{37} +(-2.56082 - 0.544320i) q^{38} +(0.708204 - 2.17963i) q^{39} +(-16.3431 + 3.47383i) q^{40} +(0.153880 - 1.46407i) q^{41} +(-1.53114 + 1.70050i) q^{42} +(8.85515 - 3.94256i) q^{43} +(-18.8137 - 8.37642i) q^{44} +(-3.34565 - 3.71572i) q^{45} +(-5.55369 + 4.03499i) q^{46} +(7.85410 - 5.70634i) q^{47} +(5.76309 + 6.40056i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(-2.16535 + 2.40487i) q^{51} +(-1.33043 + 12.6582i) q^{52} +(-13.4295 + 2.85452i) q^{53} +(-3.70246 + 11.3950i) q^{54} +(9.27952 + 1.97242i) q^{55} +(3.73607 - 6.47106i) q^{56} +(-0.437016 - 0.756934i) q^{57} +(0.437016 + 1.34500i) q^{58} +(-1.24852 - 11.8788i) q^{59} +(-7.67501 - 5.57622i) q^{60} -13.9358 q^{61} +2.23607 q^{63} +(-7.04508 - 5.11855i) q^{64} +(-0.612870 - 5.83107i) q^{65} +(-3.00000 - 9.23305i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(8.98606 - 15.5643i) q^{68} +(-2.24171 - 0.476491i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(1.43997 - 0.306074i) q^{71} +(1.74648 - 16.6167i) q^{72} +(-2.83888 + 3.15290i) q^{73} +(-10.1471 + 4.51778i) q^{74} +(3.24803 + 3.60730i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(1.08436 + 1.20430i) q^{79} +(20.1295 + 8.96221i) q^{80} +(2.47407 - 1.10153i) q^{81} +(-2.57890 + 2.86416i) q^{82} +(-0.330548 + 3.14495i) q^{83} +(4.14993 - 0.882095i) q^{84} +(-2.55834 + 7.87375i) q^{85} +(-24.8225 - 5.27618i) q^{86} +(-0.236068 + 0.408882i) q^{87} +(15.8508 + 27.4544i) q^{88} +(4.74342 + 14.5987i) q^{89} +(1.36830 + 13.0185i) q^{90} +(2.12132 + 1.54123i) q^{91} +12.7279 q^{92} -25.4164 q^{94} +(-1.80902 - 1.31433i) q^{95} +(-0.991644 - 9.43486i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(7.85410 + 13.6037i) q^{98} +(-4.74342 + 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 24 q^{4} - 2 q^{7} + 28 q^{8} + 10 q^{9} + 20 q^{10} + 2 q^{14} - 56 q^{16} - 20 q^{18} + 2 q^{19} - 18 q^{28} + 120 q^{32} + 48 q^{33} - 20 q^{35} + 60 q^{36} - 2 q^{38} - 96 q^{39} - 10 q^{40}+ \cdots + 72 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 24 * q^4 - 2 * q^7 + 28 * q^8 + 10 * q^9 + 20 * q^10 + 2 * q^14 - 56 * q^16 - 20 * q^18 + 2 * q^19 - 18 * q^28 + 120 * q^32 + 48 * q^33 - 20 * q^35 + 60 * q^36 - 2 * q^38 - 96 * q^39 - 10 * q^40 - 14 * q^41 - 10 * q^45 + 72 * q^47 - 12 * q^49 + 8 * q^51 + 24 * q^56 + 46 * q^59 - 68 * q^64 - 48 * q^66 - 48 * q^67 + 48 * q^69 - 20 * q^70 + 26 * q^71 - 50 * q^72 - 12 * q^76 - 24 * q^78 + 80 * q^80 + 22 * q^81 + 14 * q^82 + 32 * q^87 - 40 * q^90 - 192 * q^94 - 20 * q^95 + 28 * q^97 + 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more