LMFDB - Embedded newform 961.2.g.p.844.2

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 = [16,4,0,-36,0,0,-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			844.2
Root			$-1.38331 + 0.294032i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.p.846.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 2.48990i) q^{2} +(0.854932 - 0.181721i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(1.14412 + 1.98168i) q^{6} +(-0.913545 - 0.406737i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(-2.04275 + 0.909491i) q^{9} +(-5.72618 - 1.21714i) q^{10} +(-0.443477 - 4.21940i) q^{11} +(-2.83888 + 3.15290i) q^{12} +(-1.75452 - 1.94860i) q^{13} +(0.273659 - 2.60369i) q^{14} +(-0.603941 + 1.85874i) q^{15} +(3.04508 - 9.37181i) q^{16} +(-0.387012 + 3.68218i) q^{17} +(-3.91716 - 4.35045i) q^{18} +(0.669131 - 0.743145i) q^{19} +(-1.13456 - 10.7946i) q^{20} +(-0.854932 - 0.181721i) q^{21} +(10.1471 - 4.51778i) q^{22} +(2.12132 + 1.54123i) q^{23} +(-5.96626 - 2.65635i) q^{24} +(3.43237 - 5.94504i) q^{26} +(-3.70246 + 2.68999i) q^{27} +(4.74803 - 1.00922i) q^{28} +(-0.166925 - 0.513743i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(-1.14590 - 3.52671i) q^{33} +(-9.48135 + 2.01532i) q^{34} +(1.80902 - 1.31433i) q^{35} +(5.42705 - 9.39993i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(2.39169 + 1.06485i) q^{38} +(-1.85410 - 1.34708i) q^{39} +(15.2637 - 6.79584i) q^{40} +(1.43997 + 0.306074i) q^{41} +(-0.239187 - 2.27571i) q^{42} +(-6.48599 + 7.20342i) q^{43} +(13.7802 + 15.3045i) q^{44} +(0.522642 - 4.97261i) q^{45} +(-2.12132 + 6.52875i) q^{46} +(-3.00000 + 9.23305i) q^{47} +(0.900283 - 8.56562i) q^{48} +(-4.01478 - 4.45887i) q^{49} +(0.338261 + 3.21834i) q^{51} +(12.4498 + 2.64628i) q^{52} +(-12.5425 + 5.58428i) q^{53} +(-9.69316 - 7.04250i) q^{54} +(8.66665 + 3.85864i) q^{55} +(3.73607 + 6.47106i) q^{56} +(0.437016 - 0.756934i) q^{57} +(1.14412 - 0.831254i) q^{58} +(-11.6833 + 2.48335i) q^{59} +(-2.93159 - 9.02251i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(2.69098 + 8.28199i) q^{64} +(5.73506 - 1.21902i) q^{65} +(7.85410 - 5.70634i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.98606 - 15.5643i) q^{68} +(2.09366 + 0.932157i) q^{69} +(4.73607 + 3.44095i) q^{70} +(-1.34486 + 0.598772i) q^{71} +(16.3431 + 3.47383i) q^{72} +(-0.443477 - 4.21940i) q^{73} +(7.43229 - 8.25439i) q^{74} +(-0.507392 + 4.82751i) q^{76} +(-1.31105 + 4.03499i) q^{77} +(1.85410 - 5.70634i) q^{78} +(0.169393 - 1.61167i) q^{79} +(14.7439 + 16.3748i) q^{80} +(1.81214 - 2.01259i) q^{81} +(0.402863 + 3.83299i) q^{82} +(3.09317 + 0.657474i) q^{83} +(3.87585 - 1.72564i) q^{84} +(-6.69781 - 4.86624i) q^{85} +(-23.1831 - 10.3218i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(-15.8508 + 27.4544i) q^{88} +(12.4184 - 9.02251i) q^{89} +(12.8041 - 2.72160i) q^{90} +(0.810272 + 2.49376i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(0.690983 + 2.12663i) q^{95} +(9.27952 - 1.97242i) q^{96} +(5.66312 - 4.11450i) q^{97} +(7.85410 - 13.6037i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 36 q^{4} - 2 q^{7} - 52 q^{8} - 10 q^{9} - 10 q^{10} - 8 q^{14} + 4 q^{16} + 10 q^{18} + 2 q^{19} + 30 q^{20} + 12 q^{28} + 120 q^{32} - 72 q^{33} + 20 q^{35} + 60 q^{36} + 8 q^{38} + 24 q^{39}+ \cdots + 72 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 36 * q^4 - 2 * q^7 - 52 * q^8 - 10 * q^9 - 10 * q^10 - 8 * q^14 + 4 * q^16 + 10 * q^18 + 2 * q^19 + 30 * q^20 + 12 * q^28 + 120 * q^32 - 72 * q^33 + 20 * q^35 + 60 * q^36 + 8 * q^38 + 24 * q^39 + 50 * q^40 + 26 * q^41 - 10 * q^45 - 48 * q^47 - 12 * q^49 - 12 * q^51 + 24 * q^56 - 34 * q^59 + 52 * q^64 + 72 * q^66 - 48 * q^67 - 12 * q^69 + 40 * q^70 - 14 * q^71 + 10 * q^72 + 18 * q^76 - 24 * q^78 - 50 * q^80 - 38 * q^81 - 16 * q^82 + 32 * q^87 + 10 * 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	0.645974	+	0.763359i	$0.276451\pi$
$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	−0.0739128	+	0.997265i	$0.523549\pi$
$3$	0.854932	−	0.181721i	0.493595	−	0.104917i	0.0456128	−	0.998959i	$-0.485476\pi$
$3$	0.854932	−	0.181721i	0.493595	−	0.104917i	0.447983	+	0.894042i	$0.352143\pi$
$4$	−3.92705	+	2.85317i	−1.96353	+	1.42658i
$5$	−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
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	0.226764	−	0.973950i	$-0.427186\pi$
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	−0.572051	+	0.820218i	$0.693852\pi$
$8$	−6.04508	−	4.39201i	−2.13726	−	1.55281i
$9$	−2.04275	+	0.909491i	−0.680917	+	0.303164i
$10$	−5.72618	−	1.21714i	−1.81078	−	0.384892i
$11$	−0.443477	−	4.21940i	−0.133713	−	1.27220i	−0.831352	−	0.555747i	$-0.812432\pi$
$11$	−0.443477	−	4.21940i	−0.133713	−	1.27220i	0.697638	−	0.716450i	$-0.254234\pi$
$12$	−2.83888	+	3.15290i	−0.819514	+	0.910163i
$13$	−1.75452	−	1.94860i	−0.486618	−	0.540444i	0.448966	−	0.893549i	$-0.351792\pi$
$13$	−1.75452	−	1.94860i	−0.486618	−	0.540444i	−0.935584	+	0.353105i	$0.885126\pi$
$14$	0.273659	−	2.60369i	0.0731385	−	0.695866i
$15$	−0.603941	+	1.85874i	−0.155937	+	0.479925i
$16$	3.04508	−	9.37181i	0.761271	−	2.34295i
$17$	−0.387012	+	3.68218i	−0.0938643	+	0.893059i	0.841710	+	0.539930i	$0.181549\pi$
$17$	−0.387012	+	3.68218i	−0.0938643	+	0.893059i	−0.935574	+	0.353129i	$0.885118\pi$
$18$	−3.91716	−	4.35045i	−0.923283	−	1.02541i
$19$	0.669131	−	0.743145i	0.153509	−	0.170489i	−0.661485	−	0.749958i	$-0.730073\pi$
$19$	0.669131	−	0.743145i	0.153509	−	0.170489i	0.814994	+	0.579469i	$0.196740\pi$
$20$	−1.13456	−	10.7946i	−0.253696	−	2.41376i
$21$	−0.854932	−	0.181721i	−0.186562	−	0.0396549i
$22$	10.1471	−	4.51778i	2.16337	−	0.963193i
$23$	2.12132	+	1.54123i	0.442326	+	0.321369i	0.786558	−	0.617516i	$-0.211861\pi$
$23$	2.12132	+	1.54123i	0.442326	+	0.321369i	−0.344233	+	0.938884i	$0.611861\pi$
$24$	−5.96626	−	2.65635i	−1.21786	−	0.542225i
$25$		0			0
$26$	3.43237	−	5.94504i	0.673143	−	1.16592i
$27$	−3.70246	+	2.68999i	−0.712539	+	0.517690i
$28$	4.74803	−	1.00922i	0.897293	−	0.190726i
$29$	−0.166925	−	0.513743i	−0.0309972	−	0.0953997i	0.934361	−	0.356328i	$-0.115971\pi$
$29$	−0.166925	−	0.513743i	−0.0309972	−	0.0953997i	−0.965358	+	0.260928i	$0.915971\pi$
$30$	−5.11667			−0.934172
$31$		0			0
$31$		0			0
$32$	10.8541			1.91875
$33$	−1.14590	−	3.52671i	−0.199475	−	0.613922i
$34$	−9.48135	+	2.01532i	−1.62604	+	0.345625i
$35$	1.80902	−	1.31433i	0.305780	−	0.222162i
$36$	5.42705	−	9.39993i	0.904508	−	1.56665i
$37$	−2.12132	−	3.67423i	−0.348743	−	0.604040i	0.637284	−	0.770629i	$-0.280058\pi$
$37$	−2.12132	−	3.67423i	−0.348743	−	0.604040i	−0.986026	+	0.166589i	$0.946725\pi$
$38$	2.39169	+	1.06485i	0.387984	+	0.172742i
$39$	−1.85410	−	1.34708i	−0.296894	−	0.215706i
$40$	15.2637	−	6.79584i	2.41340	−	1.07452i
$41$	1.43997	+	0.306074i	0.224885	+	0.0478008i	0.318976	−	0.947763i	$-0.396661\pi$
$41$	1.43997	+	0.306074i	0.224885	+	0.0478008i	−0.0940909	+	0.995564i	$0.529994\pi$
$42$	−0.239187	−	2.27571i	−0.0369073	−	0.351150i
$43$	−6.48599	+	7.20342i	−0.989105	+	1.09851i	0.00602946	+	0.999982i	$0.498081\pi$
$43$	−6.48599	+	7.20342i	−0.989105	+	1.09851i	−0.995134	+	0.0985301i	$0.968586\pi$
$44$	13.7802	+	15.3045i	2.07745	+	2.30724i
$45$	0.522642	−	4.97261i	0.0779109	−	0.741273i
$46$	−2.12132	+	6.52875i	−0.312772	+	0.962612i
$47$	−3.00000	+	9.23305i	−0.437595	+	1.34678i	0.452809	+	0.891608i	$0.350422\pi$
$47$	−3.00000	+	9.23305i	−0.437595	+	1.34678i	−0.890404	+	0.455171i	$0.849578\pi$
$48$	0.900283	−	8.56562i	0.129945	−	1.23634i
$49$	−4.01478	−	4.45887i	−0.573541	−	0.636981i
$50$		0			0
$51$	0.338261	+	3.21834i	0.0473660	+	0.450658i
$52$	12.4498	+	2.64628i	1.72647	+	0.366974i
$53$	−12.5425	+	5.58428i	−1.72284	+	0.767060i	−0.725999	+	0.687696i	$0.758622\pi$
$53$	−12.5425	+	5.58428i	−1.72284	+	0.767060i	−0.996846	+	0.0793640i	$0.974711\pi$
$54$	−9.69316	−	7.04250i	−1.31907	−	0.958362i
$55$	8.66665	+	3.85864i	1.16861	+	0.520299i
$56$	3.73607	+	6.47106i	0.499253	+	0.864732i
$57$	0.437016	−	0.756934i	0.0578842	−	0.100258i
$58$	1.14412	−	0.831254i	0.150231	−	0.109149i
$59$	−11.6833	+	2.48335i	−1.52103	+	0.323305i	−0.891266	−	0.453481i	$-0.850182\pi$
$59$	−11.6833	+	2.48335i	−1.52103	+	0.323305i	−0.629765	+	0.776786i	$0.716849\pi$
$60$	−2.93159	−	9.02251i	−0.378467	−	1.16480i
$61$	13.9358			1.78430			0.892148	−	0.451742i	$-0.149197\pi$
$61$	13.9358			1.78430			0.892148	+	0.451742i	$0.149197\pi$
$62$		0			0
$63$	2.23607			0.281718
$64$	2.69098	+	8.28199i	0.336373	+	1.03525i
$65$	5.73506	−	1.21902i	0.711347	−	0.151201i
$66$	7.85410	−	5.70634i	0.966773	−	0.702402i
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	−8.98606	−	15.5643i	−1.08972	−	1.88745i
$69$	2.09366	+	0.932157i	0.252047	+	0.112219i
$70$	4.73607	+	3.44095i	0.566068	+	0.411273i
$71$	−1.34486	+	0.598772i	−0.159606	+	0.0710611i	−0.484985	−	0.874523i	$-0.661175\pi$
$71$	−1.34486	+	0.598772i	−0.159606	+	0.0710611i	0.325379	+	0.945584i	$0.394508\pi$
$72$	16.3431	+	3.47383i	1.92605	+	0.409395i
$73$	−0.443477	−	4.21940i	−0.0519050	−	0.493843i	−0.989334	−	0.145666i	$-0.953467\pi$
$73$	−0.443477	−	4.21940i	−0.0519050	−	0.493843i	0.937429	−	0.348177i	$-0.113199\pi$
$74$	7.43229	−	8.25439i	0.863986	−	0.959553i
$75$		0			0
$76$	−0.507392	+	4.82751i	−0.0582018	+	0.553753i
$77$	−1.31105	+	4.03499i	−0.149408	+	0.459830i
$78$	1.85410	−	5.70634i	0.209936	−	0.646116i
$79$	0.169393	−	1.61167i	0.0190582	−	0.181327i	−0.980852	−	0.194757i	$-0.937608\pi$
$79$	0.169393	−	1.61167i	0.0190582	−	0.181327i	0.999910	+	0.0134299i	$0.00427498\pi$
$80$	14.7439	+	16.3748i	1.64842	+	1.83076i
$81$	1.81214	−	2.01259i	0.201349	−	0.223621i
$82$	0.402863	+	3.83299i	0.0444888	+	0.423283i
$83$	3.09317	+	0.657474i	0.339520	+	0.0721672i	0.374517	−	0.927220i	$-0.377809\pi$
$83$	3.09317	+	0.657474i	0.339520	+	0.0721672i	−0.0349966	+	0.999387i	$0.511142\pi$
$84$	3.87585	−	1.72564i	0.422889	−	0.188282i
$85$	−6.69781	−	4.86624i	−0.726480	−	0.527818i
$86$	−23.1831	−	10.3218i	−2.49990	−	1.11302i
$87$	−0.236068	−	0.408882i	−0.0253091	−	0.0438367i
$88$	−15.8508	+	27.4544i	−1.68970	+	2.92665i
$89$	12.4184	−	9.02251i	1.31635	−	0.956385i	0.316381	−	0.948632i	$-0.397532\pi$
$89$	12.4184	−	9.02251i	1.31635	−	0.956385i	0.999970	−	0.00775224i	$-0.00246764\pi$
$90$	12.8041	−	2.72160i	1.34967	−	0.286882i
$91$	0.810272	+	2.49376i	0.0849396	+	0.261417i
$92$	−12.7279			−1.32698
$93$		0			0
$94$	−25.4164			−2.62150
$95$	0.690983	+	2.12663i	0.0708934	+	0.218187i
$96$	9.27952	−	1.97242i	0.947087	−	0.201310i
$97$	5.66312	−	4.11450i	0.575003	−	0.417764i	−0.261916	−	0.965091i	$-0.584354\pi$
$97$	5.66312	−	4.11450i	0.575003	−	0.417764i	0.836919	+	0.547327i	$0.184354\pi$
$98$	7.85410	−	13.6037i	0.793384	−	1.37418i
$99$	4.74342	+	8.21584i	0.476731	+	0.825723i
$100$		0			0
$101$	−1.80902	−	1.31433i	−0.180004	−	0.130781i	0.494135	−	0.869385i	$-0.335485\pi$
$101$	−1.80902	−	1.31433i	−0.180004	−	0.130781i	−0.674139	+	0.738605i	$0.735485\pi$
$102$	−7.73968	+	3.44593i	−0.766343	+	0.341198i
$103$	−10.4742	−	2.22636i	−1.03205	−	0.219370i	−0.339402	−	0.940642i	$-0.610225\pi$
$103$	−10.4742	−	2.22636i	−1.03205	−	0.219370i	−0.692652	+	0.721272i	$0.743558\pi$
$104$	2.04799	+	19.4853i	0.200822	+	1.91069i
$105$	1.30775	−	1.45240i	0.127623	−	0.141740i
$106$	−24.0514	−	26.7118i	−2.33608	−	2.59448i
$107$	−0.153880	+	1.46407i	−0.0148762	+	0.141537i	−0.999439	−	0.0334949i	$-0.989336\pi$
$107$	−0.153880	+	1.46407i	−0.0148762	+	0.141537i	0.984563	+	0.175032i	$0.0560029\pi$
$108$	6.86474	−	21.1275i	0.660560	−	2.03299i
$109$	−0.399187	+	1.22857i	−0.0382352	+	0.117676i	−0.968352	−	0.249587i	$-0.919705\pi$
$109$	−0.399187	+	1.22857i	−0.0382352	+	0.117676i	0.930117	+	0.367263i	$0.119705\pi$
$110$	−2.59616	+	24.7008i	−0.247534	+	2.35513i
$111$	−2.48127	−	2.75573i	−0.235512	−	0.261563i
$112$	−6.59368	+	7.32302i	−0.623044	+	0.691961i
$113$	1.02061	+	9.71044i	0.0960108	+	0.913482i	0.931443	+	0.363888i	$0.118551\pi$
$113$	1.02061	+	9.71044i	0.0960108	+	0.913482i	−0.835432	+	0.549594i	$0.814782\pi$
$114$	2.23824	+	0.475753i	0.209631	+	0.0445584i
$115$	−5.35629	+	2.38477i	−0.499476	+	0.222381i
$116$	2.12132	+	1.54123i	0.196960	+	0.143100i
$117$	5.35629	+	2.38477i	0.495189	+	0.220472i
$118$	−15.6353	−	27.0811i	−1.43934	−	2.49301i
$119$	1.85123	−	3.20642i	0.169702	−	0.293932i
$120$	11.8145	−	8.58373i	1.07851	−	0.783583i
$121$	−6.84703	+	1.45538i	−0.622458	+	0.132307i
$122$	11.2743	+	34.6987i	1.02073	+	3.14148i
$123$	1.28669			0.116017
$124$		0			0
$125$	−11.1803			−1.00000
$126$	1.80902	+	5.56758i	0.161160	+	0.496000i
$127$	9.27952	−	1.97242i	0.823425	−	0.175024i	0.223115	−	0.974792i	$-0.428377\pi$
$127$	9.27952	−	1.97242i	0.823425	−	0.175024i	0.600309	+	0.799768i	$0.295044\pi$
$128$	−0.881966	+	0.640786i	−0.0779555	+	0.0566380i
$129$	−4.23607	+	7.33708i	−0.372965	+	0.645994i
$130$	7.67501	+	13.2935i	0.673143	+	1.16592i
$131$	6.77523	+	3.01652i	0.591954	+	0.263555i	0.680775	−	0.732493i	$-0.261643\pi$
$131$	6.77523	+	3.01652i	0.591954	+	0.263555i	−0.0888207	+	0.996048i	$0.528310\pi$
$132$	14.5623	+	10.5801i	1.26749	+	0.920883i
$133$	−0.913545	+	0.406737i	−0.0792144	+	0.0352685i
$134$	−15.3649	−	3.26592i	−1.32733	−	0.282132i
$135$	−1.06968	−	10.1773i	−0.0920630	−	0.875921i
$136$	18.5117	−	20.5593i	1.58736	−	1.76295i
$137$	−1.75452	−	1.94860i	−0.149899	−	0.166480i	0.663519	−	0.748160i	$-0.269062\pi$
$137$	−1.75452	−	1.94860i	−0.149899	−	0.166480i	−0.813418	+	0.581680i	$0.802396\pi$
$138$	−0.627171	+	5.96713i	−0.0533883	+	0.507956i
$139$	−5.55369	+	17.0925i	−0.471058	+	1.44977i	0.380144	+	0.924927i	$0.375875\pi$
$139$	−5.55369	+	17.0925i	−0.471058	+	1.44977i	−0.851201	+	0.524839i	$0.824125\pi$
$140$	−3.35410	+	10.3229i	−0.283473	+	0.872441i
$141$	−0.886953	+	8.43880i	−0.0746950	+	0.710675i
$142$	−2.57890	−	2.86416i	−0.216416	−	0.240355i
$143$	−7.44382	+	8.26720i	−0.622483	+	0.691338i
$144$	2.30323	+	21.9137i	0.191936	+	1.82614i
$145$	1.18149	+	0.251133i	0.0981172	+	0.0208555i
$146$	10.1471	−	4.51778i	0.839779	−	0.373894i
$147$	−4.24264	−	3.08246i	−0.349927	−	0.254237i
$148$	18.8137	+	8.37642i	1.54648	+	0.688537i
$149$	6.70820	+	11.6190i	0.549557	+	0.951861i	0.998305	+	0.0582028i	$0.0185370\pi$
$149$	6.70820	+	11.6190i	0.549557	+	0.951861i	−0.448747	+	0.893659i	$0.648130\pi$
$150$		0			0
$151$	−10.1302	+	7.36001i	−0.824382	+	0.598949i	−0.917964	−	0.396663i	$-0.870168\pi$
$151$	−10.1302	+	7.36001i	−0.824382	+	0.598949i	0.0935821	+	0.995612i	$0.470168\pi$
$152$	−7.30885	+	1.55354i	−0.592826	+	0.126009i
$153$	−2.55834	−	7.87375i	−0.206829	−	0.636555i
$154$	−11.1074			−0.895058
$155$		0			0
$156$	11.1246			0.890682
$157$	2.69098	+	8.28199i	0.214764	+	0.660975i	0.999170	+	0.0407279i	$0.0129677\pi$
$157$	2.69098	+	8.28199i	0.214764	+	0.660975i	−0.784406	+	0.620247i	$0.787032\pi$
$158$	4.14993	−	0.882095i	0.330151	−	0.0701757i
$159$	−9.70820	+	7.05342i	−0.769911	+	0.559373i
$160$	−12.1353	+	21.0189i	−0.959376	+	1.66169i
$161$	−1.31105	−	2.27080i	−0.103325	−	0.178964i
$162$	6.47719	+	2.88383i	0.508896	+	0.226575i
$163$	−11.6631	−	8.47375i	−0.913526	−	0.663715i	0.0283782	−	0.999597i	$-0.490966\pi$
$163$	−11.6631	−	8.47375i	−0.913526	−	0.663715i	−0.941904	+	0.335882i	$0.890966\pi$
$164$	−6.52810	+	2.90650i	−0.509759	+	0.226959i
$165$	8.11060	+	1.72396i	0.631409	+	0.134210i
$166$	0.865386	+	8.23360i	0.0671670	+	0.639051i
$167$	−0.722904	+	0.802866i	−0.0559400	+	0.0621277i	−0.770465	−	0.637482i	$-0.779976\pi$
$167$	−0.722904	+	0.802866i	−0.0559400	+	0.0621277i	0.714525	+	0.699610i	$0.246643\pi$
$168$	4.37002	+	4.85339i	0.337154	+	0.374448i
$169$	0.640196	−	6.09106i	0.0492459	−	0.468543i
$170$	6.69781	−	20.6137i	0.513699	−	1.58100i
$171$	−0.690983	+	2.12663i	−0.0528408	+	0.162627i
$172$	4.91823	−	46.7939i	0.375012	−	3.56800i
$173$	12.0444	+	13.3766i	0.915715	+	1.01700i	0.999789	+	0.0205451i	$0.00654016\pi$
$173$	12.0444	+	13.3766i	0.915715	+	1.01700i	−0.0840739	+	0.996460i	$0.526793\pi$
$174$	0.827091	−	0.918578i	0.0627016	−	0.0696372i
$175$		0			0
$176$	−40.8938	−	8.69225i	−3.08249	−	0.655203i
$177$	−9.53712	+	4.24620i	−0.716854	+	0.319164i
$178$	32.5119	+	23.6212i	2.43687	+	1.77049i
$179$	12.1210	+	5.39662i	0.905967	+	0.403363i	0.806197	−	0.591648i	$-0.201522\pi$
$179$	12.1210	+	5.39662i	0.905967	+	0.403363i	0.0997707	+	0.995010i	$0.468189\pi$
$180$	12.1353	+	21.0189i	0.904508	+	1.56665i
$181$	−4.34581	+	7.52716i	−0.323021	+	0.559489i	−0.981110	−	0.193451i	$-0.938032\pi$
$181$	−4.34581	+	7.52716i	−0.323021	+	0.559489i	0.658089	+	0.752940i	$0.271365\pi$
$182$	−5.55369	+	4.03499i	−0.411667	+	0.299093i
$183$	11.9142	−	2.53244i	0.880721	−	0.187203i
$184$	−6.05446	−	18.6337i	−0.446341	−	1.37370i
$185$	9.48683			0.697486
$186$		0			0
$187$	15.7082			1.14870
$188$	−14.5623	−	44.8182i	−1.06207	−	3.26870i
$189$	4.47648	−	0.951506i	0.325616	−	0.0692119i
$190$	−4.73607	+	3.44095i	−0.343590	+	0.249633i
$191$	−4.88197	+	8.45581i	−0.353247	+	0.611841i	−0.986816	−	0.161845i	$-0.948256\pi$
$191$	−4.88197	+	8.45581i	−0.353247	+	0.611841i	0.633570	+	0.773686i	$0.281589\pi$
$192$	3.80562	+	6.59154i	0.274647	+	0.475703i
$193$	−18.9179	−	8.42279i	−1.36174	−	0.606285i	−0.409688	−	0.912226i	$-0.634363\pi$
$193$	−18.9179	−	8.42279i	−1.36174	−	0.606285i	−0.952051	+	0.305940i	$0.901029\pi$
$194$	14.8262	+	10.7719i	1.06446	+	0.773377i
$195$	4.68157	−	2.08437i	0.335254	−	0.149265i
$196$	28.4882	+	6.05535i	2.03487	+	0.432525i
$197$	0.112929	+	1.07444i	0.00804584	+	0.0765510i	0.997808	−	0.0661755i	$-0.0210797\pi$
$197$	0.112929	+	1.07444i	0.00804584	+	0.0765510i	−0.989762	+	0.142727i	$0.954413\pi$
$198$	−16.6191	+	18.4574i	−1.18107	+	1.31171i
$199$	15.5347	+	17.2531i	1.10123	+	1.22304i	0.972880	+	0.231309i	$0.0743009\pi$
$199$	15.5347	+	17.2531i	1.10123	+	1.22304i	0.128348	+	0.991729i	$0.459032\pi$
$200$		0			0
$201$	−1.62054	+	4.98752i	−0.114304	+	0.351793i
$202$	1.80902	−	5.56758i	0.127282	−	0.391734i
$203$	−0.0564643	+	0.537222i	−0.00396302	+	0.0377056i
$204$	−10.5108	−	11.6735i	−0.735906	−	0.817306i
$205$	−2.20264	+	2.44628i	−0.153839	+	0.170856i
$206$	−2.93040	−	27.8809i	−0.204170	−	1.94255i
$207$	−5.73506	−	1.21902i	−0.398614	−	0.0847281i
$208$	−23.6046	+	10.5094i	−1.63668	+	0.728698i
$209$	−3.43237	−	2.49376i	−0.237422	−	0.172497i
$210$	4.67431	+	2.08114i	0.322558	+	0.143612i
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	33.3221	−	57.7156i	2.28857	−	3.96393i
$213$	−1.04096	+	0.756300i	−0.0713252	+	0.0518208i
$214$	−3.76988	+	0.801313i	−0.257704	+	0.0547766i
$215$	−6.69781	−	20.6137i	−0.456787	−	1.40585i
$216$	34.1962			2.32675
$217$		0			0
$218$	−3.38197			−0.229056
$219$	−1.14590	−	3.52671i	−0.0774326	−	0.238313i
$220$	−45.0438	+	9.57434i	−3.03685	+	0.645502i
$221$	7.85410	−	5.70634i	0.528324	−	0.383850i
$222$	4.85410	−	8.40755i	0.325786	−	0.564278i
$223$	−8.07262	−	13.9822i	−0.540583	−	0.936316i	−0.998871	−	0.0475128i	$-0.984871\pi$
$223$	−8.07262	−	13.9822i	−0.540583	−	0.936316i	0.458288	−	0.888804i	$-0.348463\pi$
$224$	−9.91572	−	4.41476i	−0.662522	−	0.294974i
$225$		0			0
$226$	−23.3523	+	10.3971i	−1.55337	+	0.691607i
$227$	−2.24171	−	0.476491i	−0.148788	−	0.0316258i	0.132916	−	0.991127i	$-0.457566\pi$
$227$	−2.24171	−	0.476491i	−0.148788	−	0.0316258i	−0.281703	+	0.959502i	$0.590899\pi$
$228$	0.443477	+	4.21940i	0.0293700	+	0.279437i
$229$	2.83888	−	3.15290i	0.187599	−	0.208349i	−0.642008	−	0.766698i	$-0.721898\pi$
$229$	2.83888	−	3.15290i	0.187599	−	0.208349i	0.829606	+	0.558349i	$0.188565\pi$
$230$	−10.2712	−	11.4073i	−0.677261	−	0.752174i
$231$	−0.387613	+	3.68789i	−0.0255031	+	0.242645i
$232$	−1.24729	+	3.83876i	−0.0818885	+	0.252027i
$233$	−4.16312	+	12.8128i	−0.272735	+	0.839392i	0.717075	+	0.696996i	$0.245481\pi$
$233$	−4.16312	+	12.8128i	−0.272735	+	0.839392i	−0.989810	+	0.142396i	$0.954519\pi$
$234$	−1.60451	+	15.2659i	−0.104890	+	0.997965i
$235$	−14.5256	−	16.1323i	−0.947547	−	1.05236i
$236$	38.7953	−	43.0866i	2.52536	−	2.80470i
$237$	−0.148055	−	1.40865i	−0.00961720	−	0.0915016i
$238$	9.48135	+	2.01532i	0.614584	+	0.130634i
$239$	11.0621	−	4.92515i	0.715545	−	0.318581i	−0.0164750	−	0.999864i	$-0.505244\pi$
$239$	11.0621	−	4.92515i	0.715545	−	0.318581i	0.732020	+	0.681283i	$0.238578\pi$
$240$	15.5807	+	11.3200i	1.00573	+	0.730706i
$241$	−21.2092	−	9.44292i	−1.36620	−	0.608272i	−0.413034	−	0.910716i	$-0.635531\pi$
$241$	−21.2092	−	9.44292i	−1.36620	−	0.608272i	−0.953167	+	0.302443i	$0.902198\pi$
$242$	−9.16312	−	15.8710i	−0.589028	−	1.02023i
$243$	8.04827	−	13.9400i	0.516296	−	0.894252i
$244$	−54.7266	+	39.7612i	−3.50351	+	2.54545i
$245$	13.1232	−	2.78943i	0.838412	−	0.178210i
$246$	1.04096	+	3.20374i	0.0663690	+	0.204263i
$247$	−2.62210			−0.166840
$248$		0			0
$249$	2.76393			0.175157
$250$	−9.04508	−	27.8379i	−0.572061	−	1.76062i
$251$	−10.7876	+	2.29297i	−0.680905	+	0.144731i	−0.535364	−	0.844621i	$-0.679826\pi$
$251$	−10.7876	+	2.29297i	−0.680905	+	0.144731i	−0.145541	+	0.989352i	$0.546492\pi$
$252$	−8.78115	+	6.37988i	−0.553161	+	0.401895i
$253$	5.56231	−	9.63420i	0.349699	−	0.605697i
$254$	12.4184	+	21.5093i	0.779201	+	1.34962i
$255$	−6.61048	−	2.94317i	−0.413964	−	0.184309i
$256$	11.7812	+	8.55951i	0.736322	+	0.534969i
$257$	5.53218	−	2.46309i	0.345088	−	0.153643i	−0.226872	−	0.973925i	$-0.572850\pi$
$257$	5.53218	−	2.46309i	0.345088	−	0.153643i	0.571960	+	0.820281i	$0.306183\pi$
$258$	−21.6956	−	4.61155i	−1.35071	−	0.287103i
$259$	0.443477	+	4.21940i	0.0275563	+	0.262181i
$260$	−19.0438	+	21.1503i	−1.18105	+	1.31168i
$261$	0.808231	+	0.897632i	0.0500283	+	0.0555620i
$262$	−2.02957	+	19.3100i	−0.125387	+	1.19298i
$263$	5.72061	−	17.6062i	0.352748	−	1.08565i	−0.604555	−	0.796563i	$-0.706649\pi$
$263$	5.72061	−	17.6062i	0.352748	−	1.08565i	0.957304	−	0.289084i	$-0.0933508\pi$
$264$	−8.56231	+	26.3521i	−0.526973	+	1.62186i
$265$	3.20903	−	30.5319i	0.197129	−	1.87556i
$266$	−1.75181	−	1.94558i	−0.107410	−	0.119291i
$267$	8.97733	−	9.97033i	0.549404	−	0.610175i
$268$	−3.04435	−	28.9651i	−0.185963	−	1.76932i
$269$	−2.11351	−	0.449240i	−0.128863	−	0.0273907i	0.143029	−	0.989719i	$-0.454316\pi$
$269$	−2.11351	−	0.449240i	−0.128863	−	0.0273907i	−0.271892	+	0.962328i	$0.587649\pi$
$270$	24.4750	−	10.8970i	1.48950	−	0.663169i
$271$	15.0405	+	10.9276i	0.913647	+	0.663803i	0.941934	−	0.335797i	$-0.109006\pi$
$271$	15.0405	+	10.9276i	0.913647	+	0.663803i	−0.0282879	+	0.999600i	$0.509006\pi$
$272$	33.3302	+	14.8395i	2.02094	+	0.899780i
$273$	1.14590	+	1.98475i	0.0693529	+	0.120123i
$274$	3.43237	−	5.94504i	0.207357	−	0.359153i
$275$		0			0
$276$	−10.8815	+	2.31294i	−0.654990	+	0.139222i
$277$	3.12287	+	9.61121i	0.187635	+	0.577482i	0.999984	−	0.00569038i	$-0.00181131\pi$
$277$	3.12287	+	9.61121i	0.187635	+	0.577482i	−0.812349	+	0.583172i	$0.801811\pi$
$278$	−47.0516			−2.82197
$279$		0			0
$280$	−16.7082			−0.998506
$281$	4.12868	+	12.7068i	0.246296	+	0.758022i	0.995421	+	0.0955924i	$0.0304745\pi$
$281$	4.12868	+	12.7068i	0.246296	+	0.758022i	−0.749124	+	0.662429i	$0.769525\pi$
$282$	−21.7293	+	4.61871i	−1.29396	+	0.275040i
$283$	−19.4164	+	14.1068i	−1.15419	+	0.838565i	−0.989032	−	0.147703i	$-0.952812\pi$
$283$	−19.4164	+	14.1068i	−1.15419	+	0.838565i	−0.165154	+	0.986268i	$0.552812\pi$
$284$	3.57295	−	6.18853i	0.212016	−	0.367222i
$285$	0.977198	+	1.69256i	0.0578842	+	0.100258i
$286$	−26.6067	−	11.8460i	−1.57328	−	0.700471i
$287$	−1.19098	−	0.865300i	−0.0703015	−	0.0510770i
$288$	−22.1722	+	9.87171i	−1.30651	+	0.581696i
$289$	3.21986	+	0.684403i	0.189404	+	0.0402590i
$290$	0.330548	+	3.14495i	0.0194104	+	0.184678i
$291$	4.09389	−	4.54673i	0.239988	−	0.266534i
$292$	13.7802	+	15.3045i	0.806426	+	0.895627i
$293$	0.239558	−	2.27924i	0.0139951	−	0.133155i	−0.985293	−	0.170871i	$-0.945342\pi$
$293$	0.239558	−	2.27924i	0.0139951	−	0.133155i	0.999288	+	0.0377166i	$0.0120084\pi$
$294$	4.24264	−	13.0575i	0.247436	−	0.761529i
$295$	8.25329	−	25.4010i	0.480525	−	1.47890i
$296$	−3.31372	+	31.5279i	−0.192606	+	1.83252i
$297$	12.9921	+	14.4292i	0.753879	+	0.837267i
$298$	−23.5030	+	26.1027i	−1.36149	+	1.51209i
$299$	−0.718674	−	6.83772i	−0.0415620	−	0.395436i
$300$		0			0
$301$	8.85515	−	3.94256i	0.510402	−	0.227246i
$302$	−26.5212	−	19.2687i	−1.52612	−	1.10879i
$303$	−1.78543	−	0.794924i	−0.102570	−	0.0456672i
$304$	−4.92705	−	8.53390i	−0.282586	−	0.489453i
$305$	−15.5807	+	26.9866i	−0.892148	+	1.54525i
$306$	17.5351	−	12.7400i	1.00241	−	0.728297i
$307$	−23.5974	+	5.01579i	−1.34678	+	0.286266i	−0.824187	−	0.566318i	$-0.808367\pi$
$307$	−23.5974	+	5.01579i	−1.34678	+	0.286266i	−0.522590	+	0.852584i	$0.675034\pi$
$308$	−6.36396	−	19.5863i	−0.362620	−	1.11603i
$309$	−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	$0.243133\pi$
$312$	5.29180	+	16.2865i	0.299589	+	0.922040i
$313$	11.2683	−	2.39515i	0.636922	−	0.135382i	0.121877	−	0.992545i	$-0.461109\pi$
$313$	11.2683	−	2.39515i	0.636922	−	0.135382i	0.515045	+	0.857163i	$0.327775\pi$
$314$	−18.4443	+	13.4005i	−1.04087	+	0.756237i
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	3.93314	+	6.81241i	0.221257	+	0.383228i
$317$	23.9678	+	10.6712i	1.34617	+	0.599353i	0.948091	−	0.317999i	$-0.103011\pi$
$317$	23.9678	+	10.6712i	1.34617	+	0.599353i	0.398077	+	0.917352i	$0.369678\pi$
$318$	−25.4164	−	18.4661i	−1.42528	−	1.03553i
$319$	−2.09366	+	0.932157i	−0.117222	+	0.0521908i
$320$	−19.0466	−	4.04848i	−1.06474	−	0.226317i
$321$	0.134496	+	1.27965i	0.00750684	+	0.0714228i
$322$	4.59341	−	5.10149i	0.255980	−	0.284295i
$323$	2.47743	+	2.75146i	0.137848	+	0.153096i
$324$	−1.37412	+	13.0739i	−0.0763400	+	0.726327i
$325$		0			0
$326$	11.6631	−	35.8954i	0.645960	−	1.98806i
$327$	−0.118020	+	1.12289i	−0.00652652	+	0.0620957i
$328$	−7.36044	−	8.17459i	−0.406412	−	0.451366i
$329$	6.49606	−	7.21460i	0.358139	−	0.397754i
$330$	2.26913	+	21.5893i	0.124911	+	1.18845i
$331$	−30.6052	−	6.50533i	−1.68221	−	0.357565i	−0.734975	−	0.678095i	$-0.762806\pi$
$331$	−30.6052	−	6.50533i	−1.68221	−	0.357565i	−0.947239	+	0.320529i	$0.896139\pi$
$332$	−14.0229	+	6.24341i	−0.769609	+	0.342652i
$333$	7.67501	+	5.57622i	0.420588	+	0.305575i
$334$	−2.58390	−	1.15042i	−0.141385	−	0.0629485i
$335$	−6.70820	−	11.6190i	−0.366508	−	0.634811i
$336$	−4.30640	+	7.45890i	−0.234933	+	0.406917i
$337$	12.4184	−	9.02251i	0.676475	−	0.491488i	−0.195712	−	0.980662i	$-0.562702\pi$
$337$	12.4184	−	9.02251i	0.676475	−	0.491488i	0.872186	+	0.489174i	$0.162702\pi$
$338$	15.6841	−	3.33375i	0.853100	−	0.181332i
$339$	2.63715	+	8.11631i	0.143230	+	0.440817i
$340$	40.1869			2.17944
$341$		0			0
$342$	−5.85410			−0.316554
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	70.8459	−	15.0588i	3.81975	−	0.811914i
$345$	−4.14590	+	3.01217i	−0.223208	+	0.162170i
$346$	−23.5623	+	40.8111i	−1.26672	+	2.19402i
$347$	10.7979	+	18.7025i	0.579661	+	1.00400i	0.995518	+	0.0945718i	$0.0301482\pi$
$347$	10.7979	+	18.7025i	0.579661	+	1.00400i	−0.415857	+	0.909430i	$0.636518\pi$
$348$	2.09366	+	0.932157i	0.112232	+	0.0499689i
$349$	−4.85410	−	3.52671i	−0.259834	−	0.188781i	0.450240	−	0.892908i	$-0.351338\pi$
$349$	−4.85410	−	3.52671i	−0.259834	−	0.188781i	−0.710074	+	0.704127i	$0.751338\pi$
$350$		0			0
$351$	11.7378	+	2.49494i	0.626516	+	0.133170i
$352$	−4.81354	−	45.7978i	−0.256563	−	2.44103i
$353$	6.40067	−	7.10866i	0.340673	−	0.378356i	−0.548326	−	0.836265i	$-0.684735\pi$
$353$	6.40067	−	7.10866i	0.340673	−	0.378356i	0.888999	+	0.457909i	$0.151401\pi$
$354$	−18.2883	−	20.3112i	−0.972012	−	1.07953i
$355$	0.344086	−	3.27376i	0.0182622	−	0.173753i
$356$	−23.0250	+	70.8637i	−1.22032	+	3.75577i
$357$	1.00000	−	3.07768i	0.0529256	−	0.162888i
$358$	−3.63094	+	34.5461i	−0.191901	+	1.82582i
$359$	9.52579	+	10.5795i	0.502752	+	0.558363i	0.940086	−	0.340936i	$-0.110744\pi$
$359$	9.52579	+	10.5795i	0.502752	+	0.558363i	−0.437334	+	0.899299i	$0.644077\pi$
$360$	−24.9992	+	27.7644i	−1.31757	+	1.46331i
$361$	1.88151	+	17.9014i	0.0990270	+	0.942179i
$362$	−22.2577	−	4.73102i	−1.16984	−	0.248657i
$363$	−5.58928	+	2.48851i	−0.293361	+	0.130613i
$364$	−10.2971	−	7.48128i	−0.539715	−	0.392126i
$365$	8.66665	+	3.85864i	0.453633	+	0.201971i
$366$	15.9443	+	27.6163i	0.833420	+	1.44353i
$367$	−3.32920	+	5.76635i	−0.173783	+	0.301001i	−0.939739	−	0.341892i	$-0.888932\pi$
$367$	−3.32920	+	5.76635i	−0.173783	+	0.301001i	0.765956	+	0.642892i	$0.222266\pi$
$368$	20.9037	−	15.1874i	1.08968	−	0.791700i
$369$	−3.21986	+	0.684403i	−0.167619	+	0.0356286i
$370$	7.67501	+	23.6212i	0.399005	+	1.22801i
$371$	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	$0.577330\pi$
$374$	12.7082	+	39.1118i	0.657126	+	2.02242i
$375$	−9.55843	+	2.03171i	−0.493595	+	0.104917i
$376$	58.6869	−	42.6385i	3.02655	−	2.19891i
$377$	−0.708204	+	1.22665i	−0.0364744	+	0.0631754i
$378$	5.99070	+	10.3762i	0.308129	+	0.533694i
$379$	6.77523	+	3.01652i	0.348020	+	0.154948i	0.573300	−	0.819346i	$-0.305663\pi$
$379$	6.77523	+	3.01652i	0.348020	+	0.154948i	−0.225280	+	0.974294i	$0.572330\pi$
$380$	−8.78115	−	6.37988i	−0.450464	−	0.327281i
$381$	7.57493	−	3.37258i	0.388076	−	0.172782i
$382$	−25.0037	−	5.31470i	−1.27930	−	0.271924i
$383$	0.669334	+	6.36829i	0.0342014	+	0.325404i	0.998223	+	0.0595820i	$0.0189768\pi$
$383$	0.669334	+	6.36829i	0.0342014	+	0.325404i	−0.964022	+	0.265822i	$0.914357\pi$
$384$	−0.637577	+	0.708101i	−0.0325362	+	0.0361351i
$385$	−6.34793	−	7.05009i	−0.323520	−	0.359306i
$386$	5.66699	−	53.9178i	0.288442	−	2.74434i
$387$	6.69781	−	20.6137i	0.340469	−	1.04786i
$388$	−10.5000	+	32.3157i	−0.533057	+	1.64058i
$389$	1.75743	−	16.7208i	0.0891053	−	0.847780i	−0.855109	−	0.518448i	$-0.826510\pi$
$389$	1.75743	−	16.7208i	0.0891053	−	0.847780i	0.944214	−	0.329332i	$-0.106823\pi$
$390$	8.97733	+	9.97033i	0.454585	+	0.504867i
$391$	−6.49606	+	7.21460i	−0.328520	+	0.364858i
$392$	4.68631	+	44.5872i	0.236694	+	2.25199i
$393$	6.34053	+	1.34772i	0.319837	+	0.0679835i
$394$	−2.58390	+	1.15042i	−0.130175	+	0.0579576i
$395$	2.93159	+	2.12993i	0.147504	+	0.107168i
$396$	−42.0688	−	18.7302i	−2.11404	−	0.941230i
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	0.620332	−	0.784339i	$-0.286998\pi$
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	−0.989424	+	0.145054i	$0.953665\pi$
$398$	−30.3905	+	52.6380i	−1.52334	+	2.63850i
$399$	−0.707107	+	0.513743i	−0.0353996	+	0.0257193i
$400$		0			0
$401$	−0.166925	−	0.513743i	−0.00833585	−	0.0256551i	0.946802	−	0.321816i	$-0.104293\pi$
$401$	−0.166925	−	0.513743i	−0.00833585	−	0.0256551i	−0.955138	+	0.296161i	$0.904293\pi$
$402$	−13.7295			−0.684764
$403$		0			0
$404$	10.8541			0.540012
$405$	1.87132	+	5.75934i	0.0929868	+	0.286184i
$406$	−1.38331	+	0.294032i	−0.0686525	+	0.0145925i
$407$	−14.5623	+	10.5801i	−0.721827	+	0.524438i
$408$	12.0902	−	20.9408i	0.598553	−	1.03672i
$409$	−15.0405	−	26.0509i	−0.743706	−	1.28814i	−0.950797	−	0.309815i	$-0.899733\pi$
$409$	−15.0405	−	26.0509i	−0.743706	−	1.28814i	0.207091	−	0.978322i	$-0.433600\pi$
$410$	−7.87297	−	3.50527i	−0.388818	−	0.173113i
$411$	−1.85410	−	1.34708i	−0.0914561	−	0.0664468i
$412$	47.4849	−	21.1416i	2.33941	−	1.04157i
$413$	11.6833	+	2.48335i	0.574896	+	0.122198i
$414$	−1.60451	−	15.2659i	−0.0788576	−	0.750279i
$415$	−4.73147	+	5.25483i	−0.232259	+	0.257949i
$416$	−19.0438	−	21.1503i	−0.933699	−	1.03698i
$417$	−1.64195	+	15.6222i	−0.0804069	+	0.765020i
$418$	3.43237	−	10.5637i	0.167883	−	0.516690i
$419$	9.45492	−	29.0992i	0.461903	−	1.42159i	−0.400933	−	0.916107i	$-0.631314\pi$
$419$	9.45492	−	29.0992i	0.461903	−	1.42159i	0.862836	−	0.505484i	$-0.168686\pi$
$420$	−0.991644	+	9.43486i	−0.0483873	+	0.460374i
$421$	17.6760	+	19.6312i	0.861477	+	0.956767i	0.999433	−	0.0336714i	$-0.0107200\pi$
$421$	17.6760	+	19.6312i	0.861477	+	0.956767i	−0.137956	+	0.990438i	$0.544053\pi$
$422$	−8.75903	+	9.72789i	−0.426383	+	0.473546i
$423$	−2.26913	−	21.5893i	−0.110329	−	1.04971i
$424$	100.347	+	21.3293i	4.87327	+	1.03584i
$425$		0			0
$426$	−2.72526	−	1.98002i	−0.132039	−	0.0959322i
$427$	−12.7310	−	5.66820i	−0.616096	−	0.274304i
$428$	−3.57295	−	6.18853i	−0.172705	−	0.299134i
$429$	−4.86163	+	8.42060i	−0.234722	+	0.406550i
$430$	45.9075	−	33.3537i	2.21386	−	1.60846i
$431$	35.1043	−	7.46165i	1.69091	−	0.359415i	0.740899	−	0.671617i	$-0.234400\pi$
$431$	35.1043	−	7.46165i	1.69091	−	0.359415i	0.950016	+	0.312202i	$0.101067\pi$
$432$	13.9358	+	42.8900i	0.670487	+	2.06355i
$433$	−25.8384			−1.24171			−0.620857	−	0.783924i	$-0.713215\pi$
$433$	−25.8384			−1.24171			−0.620857	+	0.783924i	$0.713215\pi$
$434$		0			0
$435$	1.05573			0.0506183
$436$	−1.93769	−	5.96361i	−0.0927987	−	0.285605i
$437$	2.56480	−	0.545164i	0.122691	−	0.0260788i
$438$	7.85410	−	5.70634i	0.375284	−	0.272659i
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	−35.4435	−	61.3899i	−1.68970	−	2.92665i
$441$	12.2565	+	5.45694i	0.583643	+	0.259855i
$442$	20.5623	+	14.9394i	0.978049	+	0.710594i
$443$	5.53218	−	2.46309i	0.262842	−	0.117025i	−0.271085	−	0.962555i	$-0.587382\pi$
$443$	5.53218	−	2.46309i	0.262842	−	0.117025i	0.533927	+	0.845531i	$0.320716\pi$
$444$	17.6067	+	3.74241i	0.835575	+	0.177607i
$445$	3.58780	+	34.1357i	0.170078	+	1.61819i
$446$	28.2833	−	31.4118i	1.33925	−	1.48739i
$447$	7.84647	+	8.71439i	0.371125	+	0.412177i
$448$	0.910255	−	8.66050i	0.0430055	−	0.409170i
$449$	10.4153	−	32.0551i	0.491529	−	1.51277i	−0.330767	−	0.943713i	$-0.607307\pi$
$449$	10.4153	−	32.0551i	0.491529	−	1.51277i	0.822296	−	0.569060i	$-0.192693\pi$
$450$		0			0
$451$	0.652858	−	6.21153i	0.0307419	−	0.292489i
$452$	−31.7135	−	35.2214i	−1.49168	−	1.65668i
$453$	−7.32315	+	8.13318i	−0.344071	+	0.382130i
$454$	−0.627171	−	5.96713i	−0.0294346	−	0.280051i
$455$	−5.73506	−	1.21902i	−0.268864	−	0.0571488i
$456$	−5.96626	+	2.65635i	−0.279396	+	0.124395i
$457$	−9.15298	−	6.65003i	−0.428158	−	0.311075i	0.352754	−	0.935716i	$-0.385245\pi$
$457$	−9.15298	−	6.65003i	−0.428158	−	0.311075i	−0.780912	+	0.624641i	$0.785245\pi$
$458$	10.1471	+	4.51778i	0.474143	+	0.211102i
$459$	−8.47214	−	14.6742i	−0.395445	−	0.684932i
$460$	14.2302	−	24.6475i	0.663489	−	1.14920i
$461$	−4.17888	+	3.03613i	−0.194630	+	0.141407i	−0.680832	−	0.732439i	$-0.738382\pi$
$461$	−4.17888	+	3.03613i	−0.194630	+	0.141407i	0.486202	+	0.873846i	$0.338382\pi$
$462$	−9.49606	+	2.01845i	−0.441797	+	0.0939068i
$463$	−1.18353	−	3.64253i	−0.0550032	−	0.169283i	0.919781	−	0.392432i	$-0.128366\pi$
$463$	−1.18353	−	3.64253i	−0.0550032	−	0.169283i	−0.974784	+	0.223150i	$0.928366\pi$
$464$	−5.32300			−0.247114
$465$		0			0
$466$	−35.2705			−1.63387
$467$	−4.83688	−	14.8864i	−0.223824	−	0.688860i	−0.998409	−	0.0563897i	$-0.982041\pi$
$467$	−4.83688	−	14.8864i	−0.223824	−	0.688860i	0.774585	−	0.632470i	$-0.217959\pi$
$468$	−27.8386	+	5.91727i	−1.28684	+	0.273526i
$469$	4.85410	−	3.52671i	0.224142	−	0.162848i
$470$	28.4164	−	49.2187i	1.31075	−	2.27029i
$471$	3.80562	+	6.59154i	0.175354	+	0.303722i
$472$	81.5332	+	36.3009i	3.75287	+	1.67089i
$473$	33.2705	+	24.1724i	1.52978	+	1.11145i
$474$	3.38761	−	1.50826i	0.155598	−	0.0692768i
$475$		0			0
$476$	1.87860	+	17.8737i	0.0861054	+	0.819238i
$477$	20.5423	−	22.8146i	0.940569	−	1.04461i
$478$	21.2125	+	23.5589i	0.970237	+	1.07756i
$479$	−1.72763	+	16.4373i	−0.0789375	+	0.751040i	0.881432	+	0.472311i	$0.156580\pi$
$479$	−1.72763	+	16.4373i	−0.0789375	+	0.751040i	−0.960370	+	0.278730i	$0.910087\pi$
$480$	−6.55524	+	20.1750i	−0.299204	+	0.920857i
$481$	−3.43769	+	10.5801i	−0.156745	+	0.482413i
$482$	6.35335	−	60.4481i	0.289387	−	2.75334i
$483$	−1.53351	−	1.70314i	−0.0697772	−	0.0774954i
$484$	22.7362	−	25.2511i	1.03346	−	1.14778i
$485$	1.63613	+	15.5667i	0.0742928	+	0.706849i
$486$	41.2204	+	8.76166i	1.86979	+	0.397437i
$487$	25.6505	−	11.4203i	1.16233	−	0.517504i	0.267349	−	0.963600i	$-0.413852\pi$
$487$	25.6505	−	11.4203i	1.16233	−	0.517504i	0.894985	+	0.446095i	$0.147186\pi$
$488$	−84.2431	−	61.2062i	−3.81351	−	2.77068i
$489$	−11.5110	−	5.12505i	−0.520547	−	0.231763i
$490$	17.5623	+	30.4188i	0.793384	+	1.37418i
$491$	7.94510	−	13.7613i	0.358557	−	0.621040i	−0.629163	−	0.777274i	$-0.716602\pi$
$491$	7.94510	−	13.7613i	0.358557	−	0.621040i	0.987720	+	0.156234i	$0.0499354\pi$
$492$	−5.05291	+	3.67116i	−0.227803	+	0.165509i
$493$	1.95630	−	0.415823i	0.0881071	−	0.0187277i
$494$	−2.12132	−	6.52875i	−0.0954427	−	0.293742i
$495$	−21.2132			−0.953463
$496$		0			0
$497$	1.47214			0.0660343
$498$	2.23607	+	6.88191i	0.100201	+	0.308386i
$499$	−17.9830	+	3.82241i	−0.805031	+	0.171115i	−0.592007	−	0.805933i	$-0.701664\pi$
$499$	−17.9830	+	3.82241i	−0.805031	+	0.171115i	−0.213023	+	0.977047i	$0.568331\pi$
$500$	43.9058	−	31.8994i	1.96353	−	1.42658i
$501$	−0.472136	+	0.817763i	−0.0210935	+	0.0365350i
$502$	−14.4366	−	25.0049i	−0.644336	−	1.11602i
$503$	−30.0452	−	13.3770i	−1.33965	−	0.596450i	−0.393244	−	0.919434i	$-0.628647\pi$
$503$	−30.0452	−	13.3770i	−1.33965	−	0.596450i	−0.946404	+	0.322984i	$0.895314\pi$
$504$	−13.5172	−	9.82084i	−0.602105	−	0.437455i
$505$	4.56773	−	2.03368i	0.203261	−	0.0904977i
$506$	28.4882	+	6.05535i	1.26645	+	0.269193i
$507$	−0.559552	−	5.32378i	−0.0248506	−	0.236437i
$508$	−30.8135	+	34.2219i	−1.36713	+	1.51835i
$509$	−5.31631	−	5.90436i	−0.235641	−	0.261706i	0.613713	−	0.789529i	$-0.289675\pi$
$509$	−5.31631	−	5.90436i	−0.235641	−	0.261706i	−0.849354	+	0.527823i	$0.823008\pi$
$510$	1.98022	−	18.8405i	0.0876854	−	0.834271i
$511$	−1.31105	+	4.03499i	−0.0579974	+	0.178497i
$512$	−12.4549	+	38.3323i	−0.550435	+	1.69406i
$513$	−0.478374	+	4.55142i	−0.0211207	+	0.200950i
$514$	10.6085	+	11.7819i	0.467919	+	0.519677i
$515$	16.0218	−	17.7941i	0.706007	−	0.784100i
$516$	−4.29869	−	40.8993i	−0.189239	−	1.80049i
$517$	40.2884	+	8.56355i	1.77188	+	0.376625i
$518$	−10.1471	+	4.51778i	−0.445838	+	0.198500i
$519$	12.7279	+	9.24738i	0.558694	+	0.405915i
$520$	−40.0229	−	17.8193i	−1.75512	−	0.781430i
$521$	6.70820	+	11.6190i	0.293892	+	0.509035i	0.974726	−	0.223402i	$-0.0717161\pi$
$521$	6.70820	+	11.6190i	0.293892	+	0.509035i	−0.680835	+	0.732437i	$0.738383\pi$
$522$	−1.58114	+	2.73861i	−0.0692046	+	0.119866i
$523$	−0.500776	+	0.363835i	−0.0218974	+	0.0159094i	−0.598680	−	0.800988i	$-0.704308\pi$
$523$	−0.500776	+	0.363835i	−0.0218974	+	0.0159094i	0.576783	+	0.816898i	$0.304308\pi$
$524$	−35.2133	+	7.48482i	−1.53830	+	0.326976i
$525$		0			0
$526$	48.4658			2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	−4.98278	−	15.3354i	−0.216643	−	0.666757i
$530$	78.6174	−	16.7106i	3.41492	−	0.725864i
$531$	21.6074	−	15.6987i	0.937681	−	0.681265i
$532$	2.42705	−	4.20378i	0.105226	−	0.182257i
$533$	−1.93004	−	3.34293i	−0.0835994	−	0.144798i
$534$	32.0879	+	14.2865i	1.38858	+	0.618236i
$535$	−2.66312	−	1.93487i	−0.115137	−	0.0836517i
$536$	40.9568	−	18.2351i	1.76906	−	0.787638i
$537$	11.3433	+	2.41110i	0.489501	+	0.104047i
$538$	−0.591302	−	5.62587i	−0.0254929	−	0.242548i
$539$	−17.0333	+	18.9174i	−0.733675	+	0.814829i
$540$	33.2382	+	36.9148i	1.43034	+	1.58856i
$541$	−2.70026	+	25.6913i	−0.116093	+	1.10456i	0.769034	+	0.639207i	$0.220737\pi$
$541$	−2.70026	+	25.6913i	−0.116093	+	1.10456i	−0.885128	+	0.465348i	$0.845929\pi$
$542$	−15.0405	+	46.2900i	−0.646046	+	1.98832i
$543$	−2.34752	+	7.22494i	−0.100742	+	0.310052i
$544$	−4.20067	+	39.9667i	−0.180102	+	1.71356i
$545$	−1.93281	−	2.14661i	−0.0827926	−	0.0919505i
$546$	−4.01478	+	4.45887i	−0.171817	+	0.190822i
$547$	−0.252583	−	2.40317i	−0.0107997	−	0.102752i	0.987794	−	0.155765i	$-0.0497842\pi$
$547$	−0.252583	−	2.40317i	−0.0107997	−	0.102752i	−0.998594	+	0.0530128i	$0.983118\pi$
$548$	12.4498	+	2.64628i	0.531829	+	0.113044i
$549$	−28.4674	+	12.6745i	−1.21496	+	0.540934i
$550$		0			0
$551$	−0.493480	−	0.219712i	−0.0210230	−	0.00936003i
$552$	−8.56231	−	14.8303i	−0.364436	−	0.631222i
$553$	−0.810272	+	1.40343i	−0.0344563	+	0.0596800i
$554$	−21.4045	+	15.5513i	−0.909389	+	0.660710i
$555$	8.11060	−	1.72396i	0.344276	−	0.0731781i
$556$	−26.9582	−	82.9687i	−1.14328	−	3.51866i
$557$	−10.6460			−0.451086			−0.225543	−	0.974233i	$-0.572416\pi$
$557$	−10.6460			−0.451086			−0.225543	+	0.974233i	$0.572416\pi$
$558$		0			0
$559$	25.4164			1.07500
$560$	−6.80902	−	20.9560i	−0.287733	−	0.885553i
$561$	13.4295	−	2.85452i	0.566992	−	0.120518i
$562$	−28.2984	+	20.5600i	−1.19369	+	0.867270i
$563$	−4.88197	+	8.45581i	−0.205750	+	0.356370i	−0.950372	−	0.311117i	$-0.899297\pi$
$563$	−4.88197	+	8.45581i	−0.205750	+	0.356370i	0.744621	+	0.667487i	$0.232630\pi$
$564$	−20.5942	−	35.6702i	−0.867173	−	1.50199i
$565$	−19.9453	−	8.88021i	−0.839104	−	0.373593i
$566$	−50.8328	−	36.9322i	−2.13666	−	1.55238i
$567$	−2.47407	+	1.10153i	−0.103901	+	0.0462597i
$568$	10.7596	+	2.28703i	0.451464	+	0.0959616i
$569$	1.22574	+	11.6621i	0.0513857	+	0.488902i	0.989704	+	0.143129i	$0.0457165\pi$
$569$	1.22574	+	11.6621i	0.0513857	+	0.488902i	−0.938318	+	0.345773i	$0.887617\pi$
$570$	−3.42372	+	3.80243i	−0.143404	+	0.159266i
$571$	−1.75452	−	1.94860i	−0.0734246	−	0.0815463i	0.705313	−	0.708896i	$-0.250806\pi$
$571$	−1.75452	−	1.94860i	−0.0734246	−	0.0815463i	−0.778738	+	0.627350i	$0.784140\pi$
$572$	5.64454	−	53.7042i	0.236010	−	2.24548i
$573$	−2.63715	+	8.11631i	−0.110168	+	0.339064i
$574$	1.19098	−	3.66547i	0.0497107	−	0.152994i
$575$		0			0
$576$	−13.0294	−	14.4706i	−0.542892	−	0.602942i
$577$	−20.0739	+	22.2943i	−0.835688	+	0.928126i	−0.998283	−	0.0585671i	$-0.981347\pi$
$577$	−20.0739	+	22.2943i	−0.835688	+	0.928126i	0.162595	+	0.986693i	$0.448013\pi$
$578$	0.900830	+	8.57082i	0.0374696	+	0.356499i
$579$	−17.7041	−	3.76313i	−0.735758	−	0.156390i
$580$	−5.35629	+	2.38477i	−0.222408	+	0.0990223i
$581$	−2.55834	−	1.85874i	−0.106138	−	0.0771135i
$582$	14.6329	+	6.51499i	0.606554	+	0.270055i
$583$	29.1246	+	50.4453i	1.20622	+	2.08923i
$584$	−15.8508	+	27.4544i	−0.655911	+	1.13607i
$585$	−10.6066	+	7.70615i	−0.438529	+	0.318610i
$586$	5.86889	−	1.24747i	0.242441	−	0.0515325i
$587$	−4.86163	−	14.9626i	−0.200661	−	0.617571i	−0.999864	−	0.0165096i	$-0.994745\pi$
$587$	−4.86163	−	14.9626i	−0.200661	−	0.617571i	0.799203	−	0.601062i	$-0.205255\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	69.9230			2.87868
$591$	0.291796	+	0.898056i	0.0120029	+	0.0369411i
$592$	−40.8938	+	8.69225i	−1.68073	+	0.357249i
$593$	−4.19098	+	3.04493i	−0.172103	+	0.125040i	−0.670502	−	0.741907i	$-0.733921\pi$
$593$	−4.19098	+	3.04493i	−0.172103	+	0.125040i	0.498399	+	0.866948i	$0.333921\pi$
$594$	−25.4164	+	44.0225i	−1.04285	+	1.80627i
$595$	4.13948	+	7.16978i	0.169702	+	0.293932i
$596$	−59.4943	−	26.4886i	−2.43698	−	1.08501i
$597$	16.4164	+	11.9272i	0.671879	+	0.488149i
$598$	16.4438	−	7.32126i	0.672438	−	0.299389i
$599$	−5.92340	−	1.25906i	−0.242023	−	0.0514437i	0.0853028	−	0.996355i	$-0.472814\pi$
$599$	−5.92340	−	1.25906i	−0.242023	−	0.0514437i	−0.327326	+	0.944911i	$0.606148\pi$
$600$		0			0
$601$	12.1638	−	13.5092i	0.496170	−	0.551052i	−0.442096	−	0.896968i	$-0.645765\pi$
$601$	12.1638	−	13.5092i	0.496170	−	0.551052i	0.938266	+	0.345915i	$0.112432\pi$
$602$	16.9805	+	18.8588i	0.692076	+	0.768628i
$603$	1.40240	−	13.3429i	0.0571100	−	0.543365i
$604$	18.7824	−	57.8062i	0.764244	−	2.35210i
$605$	4.83688	−	14.8864i	0.196647	−	0.605218i
$606$	0.534838	−	5.08864i	0.0217263	−	0.206712i
$607$	10.1203	+	11.2398i	0.410772	+	0.456208i	0.912657	−	0.408726i	$-0.134027\pi$
$607$	10.1203	+	11.2398i	0.410772	+	0.456208i	−0.501885	+	0.864934i	$0.667360\pi$
$608$	7.26281	−	8.06617i	0.294546	−	0.327126i
$609$	0.0493516	+	0.469550i	0.00199983	+	0.0190271i
$610$	−79.7989	−	16.9618i	−3.23096	−	0.686762i
$611$	23.2551	−	10.3538i	0.940799	−	0.418871i
$612$	32.5119	+	23.6212i	1.31421	+	0.954832i
$613$	0.537977	+	0.239523i	0.0217287	+	0.00967424i	0.417572	−	0.908644i	$-0.362881\pi$
$613$	0.537977	+	0.239523i	0.0217287	+	0.00967424i	−0.395844	+	0.918318i	$0.629548\pi$
$614$	−31.5795	−	54.6973i	−1.27445	−	2.20741i
$615$	−1.43857	+	2.49167i	−0.0580086	+	0.100474i
$616$	25.6471	−	18.6337i	1.03335	−	0.750774i
$617$	6.72514	−	1.42947i	0.270744	−	0.0575484i	−0.0705389	−	0.997509i	$-0.522472\pi$
$617$	6.72514	−	1.42947i	0.270744	−	0.0575484i	0.341283	+	0.939961i	$0.389139\pi$
$618$	−7.57184	−	23.3037i	−0.304584	−	0.937414i
$619$	25.8384			1.03853			0.519267	−	0.854612i	$-0.326205\pi$
$619$	25.8384			1.03853			0.519267	+	0.854612i	$0.326205\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	20.6074	+	63.4230i	0.826281	+	2.54303i
$623$	−15.0146	+	3.19145i	−0.601547	+	0.127863i
$624$	−18.2705	+	13.2743i	−0.731406	+	0.531397i
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	15.0799	+	26.1192i	0.602715	+	1.04393i
$627$	−3.38761	−	1.50826i	−0.135288	−	0.0602342i
$628$	−34.1976	−	24.8460i	−1.36463	−	0.991463i
$629$	14.3502	−	6.38910i	0.572178	−	0.254750i
$630$	−12.8041	−	2.72160i	−0.510128	−	0.108431i
$631$	2.46990	+	23.4995i	0.0983252	+	0.935501i	0.926820	+	0.375505i	$0.122531\pi$
$631$	2.46990	+	23.4995i	0.0983252	+	0.935501i	−0.828495	+	0.559996i	$0.810803\pi$
$632$	−8.10246	+	8.99869i	−0.322298	+	0.357949i
$633$	2.92421	+	3.24766i	0.116227	+	0.129083i
$634$	−7.17974	+	68.3106i	−0.285144	+	2.71296i
$635$	−6.55524	+	20.1750i	−0.260137	+	0.800619i
$636$	18.0000	−	55.3983i	0.713746	−	2.19669i
$637$	−1.64450	+	15.6464i	−0.0651575	+	0.619933i
$638$	−4.01478	−	4.45887i	−0.158947	−	0.176528i
$639$	2.20264	−	2.44628i	0.0871352	−	0.0967734i
$640$	−0.254808	−	2.42434i	−0.0100722	−	0.0958305i
$641$	8.29986	+	1.76419i	0.327825	+	0.0696813i	0.368884	−	0.929475i	$-0.379740\pi$
$641$	8.29986	+	1.76419i	0.327825	+	0.0696813i	−0.0410594	+	0.999157i	$0.513073\pi$
$642$	−3.07738	+	1.37014i	−0.121454	+	0.0540750i
$643$	3.76622	+	2.73632i	0.148525	+	0.107910i	0.659566	−	0.751646i	$-0.270740\pi$
$643$	3.76622	+	2.73632i	0.148525	+	0.107910i	−0.511041	+	0.859556i	$0.670740\pi$
$644$	11.6275	+	5.17691i	0.458189	+	0.203999i
$645$	−9.47214	−	16.4062i	−0.372965	−	0.645994i
$646$	−4.84658	+	8.39453i	−0.190686	+	0.330278i
$647$	−25.7109	+	18.6801i	−1.01080	+	0.734389i	−0.964377	−	0.264533i	$-0.914782\pi$
$647$	−25.7109	+	18.6801i	−1.01080	+	0.734389i	−0.0464226	+	0.998922i	$0.514782\pi$
$648$	−19.7939	+	4.20732i	−0.777576	+	0.165279i
$649$	15.6595	+	48.1950i	0.614690	+	1.89182i
$650$		0			0
$651$		0			0
$652$	69.9787			2.74058
$653$	7.61803	+	23.4459i	0.298117	+	0.917509i	0.982157	+	0.188064i	$0.0602214\pi$
$653$	7.61803	+	23.4459i	0.298117	+	0.917509i	−0.684040	+	0.729445i	$0.739779\pi$
$654$	−2.89135	+	0.614576i	−0.113061	+	0.0240318i
$655$	−13.4164	+	9.74759i	−0.524222	+	0.380870i
$656$	7.25329	−	12.5631i	0.283193	−	0.490505i
$657$	4.74342	+	8.21584i	0.185058	+	0.320530i
$658$	23.2190	+	10.3378i	0.905173	+	0.403009i
$659$	−20.0795	−	14.5886i	−0.782187	−	0.568292i	0.123447	−	0.992351i	$-0.460605\pi$
$659$	−20.0795	−	14.5886i	−0.782187	−	0.568292i	−0.905635	+	0.424059i	$0.860605\pi$
$660$	−36.7695	+	16.3708i	−1.43125	+	0.637234i
$661$	−7.66165	−	1.62853i	−0.298004	−	0.0633426i	0.0564835	−	0.998404i	$-0.482011\pi$
$661$	−7.66165	−	1.62853i	−0.298004	−	0.0633426i	−0.354487	+	0.935061i	$0.615345\pi$
$662$	−8.56250	−	81.4667i	−0.332791	−	3.16629i
$663$	5.67776	−	6.30579i	0.220506	−	0.244897i
$664$	−15.8109	−	17.5597i	−0.613581	−	0.681450i
$665$	0.233733	−	2.22382i	0.00906377	−	0.0862360i
$666$	−7.67501	+	23.6212i	−0.297401	+	0.915305i
$667$	0.437694	−	1.34708i	0.0169476	−	0.0521593i
$668$	0.548167	−	5.21546i	0.0212092	−	0.201792i
$669$	−9.44241	−	10.4869i	−0.365065	−	0.405445i
$670$	23.5030	−	26.1027i	0.907998	−	1.00843i
$671$	−6.18020	−	58.8007i	−0.238584	−	2.26998i
$672$	−9.27952	−	1.97242i	−0.357965	−	0.0760879i
$673$	36.5240	−	16.2615i	1.40790	−	0.626837i	0.444712	−	0.895673i	$-0.353306\pi$
$673$	36.5240	−	16.2615i	1.40790	−	0.626837i	0.963186	+	0.268837i	$0.0866392\pi$
$674$	32.5119	+	23.6212i	1.25231	+	0.909857i
$675$		0			0
$676$	14.8647	+	25.7465i	0.571721	+	0.990250i
$677$	10.6066	−	18.3712i	0.407645	−	0.706062i	−0.586981	−	0.809601i	$-0.699683\pi$
$677$	10.6066	−	18.3712i	0.407645	−	0.706062i	0.994625	+	0.103540i	$0.0330168\pi$
$678$	−18.0753	+	13.1325i	−0.694177	+	0.504349i
$679$	−6.84703	+	1.45538i	−0.262765	+	0.0558524i
$680$	19.1162	+	58.8337i	0.733074	+	2.25617i
$681$	−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	$0.788811\pi$
$684$	−3.35410	−	10.3229i	−0.128247	−	0.394705i
$685$	5.73506	−	1.21902i	0.219125	−	0.0465765i
$686$	−27.5344	+	20.0049i	−1.05127	+	0.763792i
$687$	1.85410	−	3.21140i	0.0707384	−	0.122523i
$688$	47.7587	+	82.7205i	1.82078	+	3.15369i
$689$	32.8876	+	14.6425i	1.25292	+	0.557836i
$690$	−10.8541	−	7.88597i	−0.413209	−	0.300214i
$691$	−44.2306	+	19.6927i	−1.68261	+	0.749147i	−0.682783	+	0.730622i	$0.739230\pi$
$691$	−44.2306	+	19.6927i	−1.68261	+	0.749147i	−0.999828	+	0.0185250i	$0.994103\pi$
$692$	−85.4645	−	18.1660i	−3.24887	−	0.690569i
$693$	−0.991644	−	9.43486i	−0.0376694	−	0.358401i
$694$	−37.8316	+	42.0162i	−1.43607	+	1.59491i
$695$	−26.8903	−	29.8647i	−1.02001	−	1.13283i
$696$	−0.368762	+	3.50854i	−0.0139779	+	0.132991i
$697$	−1.68430	+	5.18376i	−0.0637976	+	0.196349i
$698$	4.85410	−	14.9394i	0.183730	−	0.565464i
$699$	−1.23083	+	11.7106i	−0.0465543	+	0.442935i
$700$		0			0
$701$	−2.44398	+	2.71432i	−0.0923080	+	0.102518i	−0.787529	−	0.616278i	$-0.788640\pi$
$701$	−2.44398	+	2.71432i	−0.0923080	+	0.102518i	0.695221	+	0.718796i	$0.255307\pi$
$702$	3.28391	+	31.2443i	0.123943	+	1.17924i
$703$	−4.14993	−	0.882095i	−0.156518	−	0.0332688i
$704$	33.7516	−	15.0272i	1.27206	−	0.566359i
$705$	−15.3500	−	11.1524i	−0.578115	−	0.420025i
$706$	22.8781	+	10.1860i	0.861028	+	0.383354i
$707$	1.11803	+	1.93649i	0.0420480	+	0.0728293i
$708$	25.3376	−	43.8861i	0.952246	−	1.64934i
$709$	33.3221	−	24.2099i	1.25144	−	0.909224i	0.253134	−	0.967431i	$-0.418538\pi$
$709$	33.3221	−	24.2099i	1.25144	−	0.909224i	0.998305	+	0.0582075i	$0.0185385\pi$
$710$	8.42971	−	1.79179i	0.316361	−	0.0672447i
$711$	1.11977	+	3.44629i	0.0419946	+	0.129246i
$712$	−114.697			−4.29847
$713$		0			0
$714$	8.47214			0.317062
$715$	−7.68692	−	23.6579i	−0.287474	−	0.884755i
$716$	−62.9973	+	13.3905i	−2.35432	+	0.500426i
$717$	8.56231	−	6.22088i	0.319765	−	0.232323i
$718$	−18.6353	+	32.2772i	−0.695462	+	1.20457i
$719$	18.7824	+	32.5320i	0.700465	+	1.21324i	0.968303	+	0.249777i	$0.0803573\pi$
$719$	18.7824	+	32.5320i	0.700465	+	1.21324i	−0.267839	+	0.963464i	$0.586309\pi$
$720$	−45.0109	−	20.0401i	−1.67746	−	0.746851i
$721$	8.66312	+	6.29412i	0.322631	+	0.234405i
$722$	−43.0505	+	19.1673i	−1.60217	+	0.713333i
$723$	−19.8484	−	4.21890i	−0.738169	−	0.156903i
$724$	−4.41005	−	41.9589i	−0.163898	−	1.55939i
$725$		0			0
$726$	−10.7179	−	11.9035i	−0.397780	−	0.441780i
$727$	3.17938	−	30.2498i	0.117917	−	1.12190i	−0.762265	−	0.647265i	$-0.775913\pi$
$727$	3.17938	−	30.2498i	0.117917	−	1.12190i	0.880182	−	0.474637i	$-0.157421\pi$
$728$	6.05446	−	18.6337i	0.224393	−	0.690612i
$729$	1.83688	−	5.65334i	0.0680326	−	0.209383i
$730$	−2.59616	+	24.7008i	−0.0960881	+	0.914217i
$731$	−24.0141	−	26.6704i	−0.888194	−	0.986440i
$732$	−39.5621	+	43.9381i	−1.46226	+	1.62400i
$733$	1.50692	+	14.3374i	0.0556595	+	0.529565i	0.986456	+	0.164027i	$0.0524484\pi$
$733$	1.50692	+	14.3374i	0.0556595	+	0.529565i	−0.930796	+	0.365538i	$0.880885\pi$
$734$	−17.0510	−	3.62430i	−0.629364	−	0.133775i
$735$	10.7126	−	4.76954i	0.395139	−	0.175927i
$736$	23.0250	+	16.7287i	0.848714	+	0.616627i
$737$	23.2551	+	10.3538i	0.856612	+	0.381388i
$738$	−4.30902	−	7.46344i	−0.158617	−	0.274733i
$739$	17.5745	−	30.4399i	0.646489	−	1.11975i	−0.337467	−	0.941337i	$-0.609570\pi$
$739$	17.5745	−	30.4399i	0.646489	−	1.11975i	0.983956	−	0.178414i	$-0.0570965\pi$
$740$	−37.2553	+	27.0675i	−1.36953	+	0.995023i
$741$	−2.24171	+	0.476491i	−0.0823515	+	0.0175043i
$742$	11.1074	+	34.1850i	0.407765	+	1.25497i
$743$	−36.4844			−1.33848			−0.669242	−	0.743045i	$-0.733381\pi$
$743$	−36.4844			−1.33848			−0.669242	+	0.743045i	$0.733381\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−7.51722	−	23.1356i	−0.275225	−	0.847055i
$747$	−6.91655	+	1.47016i	−0.253063	+	0.0537903i
$748$	−61.6869	+	44.8182i	−2.25550	+	1.63871i
$749$	0.736068	−	1.27491i	0.0268953	−	0.0465841i
$750$	−12.7917	−	22.1558i	−0.467086	−	0.809017i
$751$	−34.2954	−	15.2693i	−1.25146	−	0.557185i	−0.329383	−	0.944196i	$-0.606841\pi$
$751$	−34.2954	−	15.2693i	−1.25146	−	0.557185i	−0.922075	+	0.387011i	$0.873507\pi$
$752$	77.3951	+	56.2308i	2.82231	+	2.05053i
$753$	−8.80596	+	3.92066i	−0.320907	+	0.142877i
$754$	−3.62717	−	0.770979i	−0.132094	−	0.0280774i
$755$	−2.92671	−	27.8457i	−0.106514	−	1.01341i
$756$	−14.8646	+	16.5088i	−0.540619	+	0.600419i
$757$	6.20987	+	6.89676i	0.225701	+	0.250667i	0.845350	−	0.534212i	$-0.179392\pi$
$757$	6.20987	+	6.89676i	0.225701	+	0.250667i	−0.619649	+	0.784879i	$0.712725\pi$
$758$	−2.02957	+	19.3100i	−0.0737172	+	0.701372i
$759$	3.00465	−	9.24738i	0.109062	−	0.335659i
$760$	5.16312	−	15.8904i	0.187286	−	0.576407i
$761$	−4.20067	+	39.9667i	−0.152274	+	1.44879i	0.605276	+	0.796016i	$0.293063\pi$
$761$	−4.20067	+	39.9667i	−0.152274	+	1.44879i	−0.757550	+	0.652777i	$0.773604\pi$
$762$	14.5256	+	16.1323i	0.526208	+	0.584413i
$763$	0.864380	−	0.959992i	0.0312927	−	0.0347540i
$764$	−4.95414	−	47.1355i	−0.179234	−	1.70530i
$765$	18.1078	+	3.84892i	0.654687	+	0.139158i
$766$	−15.3149	+	6.81863i	−0.553349	+	0.246367i
$767$	25.3376	+	18.4089i	0.914889	+	0.664706i
$768$	11.6275	+	5.17691i	0.419573	+	0.186806i
$769$	−27.0623	−	46.8733i	−0.975892	−	1.69029i	−0.676960	−	0.736019i	$-0.736703\pi$
$769$	−27.0623	−	46.8733i	−0.975892	−	1.69029i	−0.298931	−	0.954275i	$-0.596630\pi$
$770$	12.4184	−	21.5093i	0.447529	−	0.775143i
$771$	4.28205	−	3.11109i	0.154214	−	0.112043i
$772$	98.3231	−	20.8992i	3.53873	−	0.752180i
$773$	−3.45672	−	10.6387i	−0.124330	−	0.382647i	0.869449	−	0.494023i	$-0.164474\pi$
$773$	−3.45672	−	10.6387i	−0.124330	−	0.382647i	−0.993778	+	0.111376i	$0.964474\pi$
$774$	56.7448			2.03965
$775$		0			0
$776$	−52.3050			−1.87764
$777$	1.14590	+	3.52671i	0.0411089	+	0.126520i
$778$	43.0550	−	9.15162i	1.54360	−	0.328101i
$779$	1.19098	−	0.865300i	0.0426714	−	0.0310026i
$780$	−12.4377	+	21.5427i	−0.445341	+	0.771353i
$781$	3.12287	+	5.40897i	0.111745	+	0.193548i
$782$	−23.2190	−	10.3378i	−0.830311	−	0.369678i
$783$	2.00000	+	1.45309i	0.0714742	+	0.0519290i
$784$	−54.0130	+	24.0481i	−1.92904	+	0.858862i
$785$	−19.0466	−	4.04848i	−0.679803	−	0.144497i
$786$	1.77391	+	16.8776i	0.0632732	+	0.602004i
$787$	−25.1357	+	27.9161i	−0.895992	+	0.995100i	0.104008	+	0.994577i	$0.466833\pi$
$787$	−25.1357	+	27.9161i	−0.895992	+	0.995100i	−1.00000		0.000523804i	$0.999833\pi$
$788$	−3.50905	−	3.89719i	−0.125005	−	0.138832i
$789$	1.69131	−	16.0917i	0.0602121	−	0.572880i
$790$	−2.93159	+	9.02251i	−0.104301	+	0.321007i
$791$	3.01722	−	9.28605i	0.107280	−	0.330174i
$792$	7.40970	−	70.4986i	0.263292	−	2.50506i
$793$	−24.4507	−	27.1553i	−0.868270	−	0.964312i
$794$	25.7659	−	28.6160i	0.914399	−	1.01554i
$795$	−2.80479	−	26.6858i	−0.0994758	−	0.946449i
$796$	−110.232	−	23.4305i	−3.90706	−	0.830471i
$797$	−12.5425	+	5.58428i	−0.444278	+	0.197805i	−0.616668	−	0.787223i	$-0.711518\pi$
$797$	−12.5425	+	5.58428i	−0.444278	+	0.197805i	0.172390	+	0.985029i	$0.444851\pi$
$798$	−1.85123	−	1.34500i	−0.0655328	−	0.0476124i
$799$	−32.8367	−	14.6198i	−1.16168	−	0.517213i
$800$		0			0
$801$	−17.1618	+	29.7252i	−0.606384	+	1.05029i
$802$	1.14412	−	0.831254i	0.0404004	−	0.0293526i
$803$	−17.6067	+	3.74241i	−0.621325	+	0.132067i
$804$	−7.86629	−	24.2099i	−0.277423	−	0.853819i
$805$	5.86319			0.206650
$806$		0			0
$807$	−1.88854			−0.0664799
$808$	5.16312	+	15.8904i	0.181638	+	0.559024i
$809$	−46.4747	+	9.87850i	−1.63396	+	0.347310i	−0.931311	−	0.364224i	$-0.881334\pi$
$809$	−46.4747	+	9.87850i	−1.63396	+	0.347310i	−0.702652	+	0.711534i	$0.748001\pi$
$810$	−12.8262	+	9.31881i	−0.450668	+	0.327430i
$811$	8.29180	−	14.3618i	0.291164	−	0.504311i	−0.682921	−	0.730492i	$-0.739291\pi$
$811$	8.29180	−	14.3618i	0.291164	−	0.504311i	0.974085	+	0.226181i	$0.0726240\pi$
$812$	−1.31105	−	2.27080i	−0.0460088	−	0.0796895i
$813$	14.8444	+	6.60915i	0.520616	+	0.231793i
$814$	−38.1246	−	27.6992i	−1.33627	−	0.970855i
$815$	29.4491	−	13.1116i	1.03156	−	0.459279i
$816$	31.1917	+	6.63000i	1.09193	+	0.232096i
$817$	1.01321	+	9.64006i	0.0354478	+	0.337263i
$818$	52.6962	−	58.5250i	1.84248	−	2.04628i
$819$	−3.92324	−	4.35720i	−0.137089	−	0.152253i
$820$	1.67023	−	15.8912i	0.0583270	−	0.554944i
$821$	7.36551	−	22.6687i	0.257058	−	0.791144i	−0.736359	−	0.676591i	$-0.763457\pi$
$821$	7.36551	−	22.6687i	0.257058	−	0.791144i	0.993417	−	0.114553i	$-0.0365435\pi$
$822$	1.85410	−	5.70634i	0.0646692	−	0.199031i
$823$	1.41355	−	13.4491i	0.0492734	−	0.468805i	−0.941867	−	0.335986i	$-0.890931\pi$
$823$	1.41355	−	13.4491i	0.0492734	−	0.468805i	0.991140	−	0.132819i	$-0.0424028\pi$
$824$	53.5393	+	59.4614i	1.86513	+	2.07143i
$825$		0			0
$826$	3.26866	+	31.0992i	0.113731	+	1.08208i
$827$	17.9536	+	3.81615i	0.624307	+	0.132701i	0.509194	−	0.860652i	$-0.329944\pi$
$827$	17.9536	+	3.81615i	0.624307	+	0.132701i	0.115113	+	0.993352i	$0.463277\pi$
$828$	26.0000	−	11.5759i	0.903561	−	0.402291i
$829$	−41.3310	−	30.0287i	−1.43548	−	1.04294i	−0.988962	−	0.148168i	$-0.952662\pi$
$829$	−41.3310	−	30.0287i	−1.43548	−	1.04294i	−0.446523	−	0.894772i	$-0.647338\pi$
$830$	−16.9118	−	7.52963i	−0.587018	−	0.261357i
$831$	4.41641	+	7.64944i	0.153203	+	0.265356i
$832$	11.4169	−	19.7746i	0.395809	−	0.685561i
$833$	17.9721	−	13.0575i	0.622697	−	0.452416i
$834$	−40.2259	+	8.55029i	−1.39291	+	0.296072i
$835$	−0.746512	−	2.29753i	−0.0258341	−	0.0795093i
$836$	20.5942			0.712266
$837$		0			0
$838$	80.1033			2.76712
$839$	−6.00000	−	18.4661i	−0.207143	−	0.637521i	−0.999619	−	0.0276170i	$-0.991208\pi$
$839$	−6.00000	−	18.4661i	−0.207143	−	0.637521i	0.792476	−	0.609904i	$-0.208792\pi$
$840$	−14.2844	+	3.03624i	−0.492858	+	0.104760i
$841$	23.2254	−	16.8743i	0.800877	−	0.581871i
$842$	−34.5795	+	59.8935i	−1.19169	+	2.06407i
$843$	5.83883	+	10.1132i	0.201100	+	0.348315i
$844$	−22.1722	−	9.87171i	−0.763199	−	0.339798i
$845$	11.0795	+	8.04975i	0.381147	+	0.276920i
$846$	51.9194	−	23.1160i	1.78502	−	0.794744i
$847$	6.84703	+	1.45538i	0.235267	+	0.0500075i
$848$	14.1418	+	134.550i	0.485632	+	4.62048i
$849$	−14.0362	+	15.5888i	−0.481721	+	0.535005i
$850$		0			0
$851$	1.16284	−	11.0637i	0.0398616	−	0.379258i
$852$	1.93004	−	5.94006i	0.0661221	−	0.203503i
$853$	−9.97871	+	30.7113i	−0.341665	+	1.05154i	0.621681	+	0.783271i	$0.286450\pi$
$853$	−9.97871	+	30.7113i	−0.341665	+	1.05154i	−0.963345	+	0.268265i	$0.913550\pi$
$854$	3.81366	−	36.2845i	0.130501	−	1.24163i
$855$	−3.34565	−	3.71572i	−0.114419	−	0.127075i
$856$	7.36044	−	8.17459i	0.251575	−	0.279402i
$857$	0.627171	+	5.96713i	0.0214237	+	0.203833i	0.999998	−	0.00206149i	$-0.000656192\pi$
$857$	0.627171	+	5.96713i	0.0214237	+	0.203833i	−0.978574	+	0.205895i	$0.933990\pi$
$858$	−24.8996	−	5.29257i	−0.850057	−	0.180685i
$859$	−38.0045	+	16.9207i	−1.29670	+	0.577326i	−0.934893	−	0.354928i	$-0.884505\pi$
$859$	−38.0045	+	16.9207i	−1.29670	+	0.577326i	−0.361803	+	0.932255i	$0.617839\pi$
$860$	85.1172	+	61.8412i	2.90247	+	2.10877i
$861$	−1.17545	−	0.523346i	−0.0400593	−	0.0178356i
$862$	46.9787	+	81.3695i	1.60010	+	2.77146i
$863$	15.5413	−	26.9183i	0.529032	−	0.916310i	−0.470395	−	0.882456i	$-0.655889\pi$
$863$	15.5413	−	26.9183i	0.529032	−	0.916310i	0.999427	−	0.0338541i	$-0.0107782\pi$
$864$	−40.1869	+	29.1975i	−1.36719	+	0.993318i
$865$	−39.3697	+	8.36828i	−1.33861	+	0.284530i
$866$	−20.9037	−	64.3350i	−0.710337	−	2.18619i
$867$	2.87714			0.0977126
$868$		0			0
$869$	−6.87539			−0.233232
$870$	0.854102	+	2.62866i	0.0289568	+	0.0891198i
$871$	15.3888	−	3.27099i	0.521429	−	0.110833i
$872$	7.80902	−	5.67358i	0.264447	−	0.192132i
$873$	−7.82624	+	13.5554i	−0.264878	+	0.458782i
$874$	3.43237	+	5.94504i	0.116102	+	0.201094i
$875$	10.2137	+	4.54745i	0.345288	+	0.153732i
$876$	14.5623	+	10.5801i	0.492015	+	0.357470i
$877$	−26.2262	+	11.6767i	−0.885598	+	0.394293i	−0.798563	−	0.601912i	$-0.794406\pi$
$877$	−26.2262	+	11.6767i	−0.885598	+	0.394293i	−0.0870350	+	0.996205i	$0.527739\pi$
$878$	64.0206	+	13.6080i	2.16059	+	0.459248i
$879$	−0.209381	−	1.99213i	−0.00706226	−	0.0671929i
$880$	62.5532	−	69.4723i	2.10867	−	2.34191i
$881$	4.84939	+	5.38579i	0.163380	+	0.181452i	0.819276	−	0.573399i	$-0.194376\pi$
$881$	4.84939	+	5.38579i	0.163380	+	0.181452i	−0.655896	+	0.754851i	$0.727709\pi$
$882$	−3.67152	+	34.9322i	−0.123627	+	1.17623i
$883$	−10.4884	+	32.2799i	−0.352962	+	1.08631i	0.604219	+	0.796818i	$0.293485\pi$
$883$	−10.4884	+	32.2799i	−0.352962	+	1.08631i	−0.957182	+	0.289488i	$0.906515\pi$
$884$	−14.5623	+	44.8182i	−0.489783	+	1.50740i
$885$	2.44009	−	23.2159i	0.0820229	−	0.780395i
$886$	10.6085	+	11.7819i	0.356398	+	0.395820i
$887$	16.9696	−	18.8467i	0.569784	−	0.632809i	−0.387531	−	0.921857i	$-0.626672\pi$
$887$	16.9696	−	18.8467i	0.569784	−	0.632809i	0.957315	+	0.289048i	$0.0933387\pi$
$888$	2.89630	+	27.5564i	0.0971933	+	0.924733i
$889$	−9.27952	−	1.97242i	−0.311225	−	0.0661530i
$890$	−82.0917	+	36.5496i	−2.75172	+	1.22514i
$891$	−9.29555	−	6.75362i	−0.311413	−	0.226255i
$892$	71.5951	+	31.8762i	2.39718	+	1.06729i
$893$	4.85410	+	8.40755i	0.162436	+	0.281348i
$894$	−15.3500	+	26.5870i	−0.513381	+	0.889203i
$895$	−24.0022	+	17.4386i	−0.802306	+	0.582909i
$896$	1.06635	−	0.226659i	0.0356242	−	0.00757215i
$897$	−1.85698	−	5.71519i	−0.0620027	−	0.190825i
$898$	88.2400			2.94461
$899$		0			0
$900$		0			0
$901$	−15.7082	−	48.3449i	−0.523316	−	1.61060i
$902$	15.9942	−	3.39968i	0.532550	−	0.113197i
$903$	6.85410	−	4.97980i	0.228090	−	0.165717i
$904$	36.4787	−	63.1830i	1.21326	−	2.10143i
$905$	−9.71752	−	16.8312i	−0.323021	−	0.559489i
$906$	−26.1753	−	11.6540i	−0.869617	−	0.387179i
$907$	−9.33688	−	6.78364i	−0.310026	−	0.225247i	0.421882	−	0.906651i	$-0.361370\pi$
$907$	−9.33688	−	6.78364i	−0.310026	−	0.225247i	−0.731908	+	0.681404i	$0.761370\pi$
$908$	10.1628	−	4.52479i	0.337266	−	0.150160i
$909$	4.89074	+	1.03956i	0.162216	+	0.0344800i
$910$	−1.60451	−	15.2659i	−0.0531891	−	0.506061i
$911$	−18.0122	+	20.0045i	−0.596770	+	0.662780i	−0.963550	−	0.267528i	$-0.913793\pi$
$911$	−18.0122	+	20.0045i	−0.596770	+	0.662780i	0.366780	+	0.930308i	$0.380460\pi$
$912$	−5.76309	−	6.40056i	−0.190835	−	0.211944i
$913$	1.40240	−	13.3429i	0.0464125	−	0.441586i
$914$	9.15298	−	28.1700i	0.302754	−	0.931780i
$915$	−8.41641	+	25.9030i	−0.278238	+	0.856328i
$916$	−2.15268	+	20.4814i	−0.0711266	+	0.676724i
$917$	−4.96255	−	5.51147i	−0.163878	−	0.182005i
$918$	29.6831	−	32.9664i	0.979688	−	1.08805i
$919$	4.44675	+	42.3080i	0.146685	+	1.39561i	0.781961	+	0.623327i	$0.214219\pi$
$919$	4.44675	+	42.3080i	0.146685	+	1.39561i	−0.635277	+	0.772285i	$0.719114\pi$
$920$	42.8532	+	9.10872i	1.41283	+	0.300306i
$921$	−19.2627	+	8.57632i	−0.634729	+	0.282599i
$922$	−10.9405	−	7.94870i	−0.360305	−	0.261777i
$923$	3.52636	+	1.57004i	0.116072	+	0.0516784i
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$		0			0
$926$	8.11203	−	5.89373i	0.266578	−	0.193680i
$927$	23.4210	−	4.97829i	0.769248	−	0.163509i
$928$	−1.81182	−	5.57622i	−0.0594760	−	0.183048i
$929$	10.6460			0.349284			0.174642	−	0.984632i	$-0.444123\pi$
$929$	10.6460			0.349284			0.174642	+	0.984632i	$0.444123\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	−20.2082	−	62.1945i	−0.661942	−	2.03725i
$933$	21.7770	−	4.62883i	0.712945	−	0.151541i
$934$	33.1525	−	24.0867i	1.08478	−	0.788140i
$935$	−17.5623	+	30.4188i	−0.574349	+	0.994801i
$936$	−21.9053	−	37.9410i	−0.715996	−	1.24014i
$937$	22.1528	+	9.86305i	0.723699	+	0.322212i	0.735319	−	0.677721i	$-0.237032\pi$
$937$	22.1528	+	9.86305i	0.723699	+	0.322212i	−0.0116200	+	0.999932i	$0.503699\pi$
$938$	12.7082	+	9.23305i	0.414938	+	0.301470i
$939$	9.19838	−	4.09538i	0.300178	−	0.133648i
$940$	103.071	+	21.9085i	3.36181	+	0.714575i
$941$	−2.66910	−	25.3948i	−0.0870101	−	0.827846i	−0.947796	−	0.318878i	$-0.896694\pi$
$941$	−2.66910	−	25.3948i	−0.0870101	−	0.827846i	0.860786	−	0.508968i	$-0.169973\pi$
$942$	−13.3334	+	14.8083i	−0.434427	+	0.482480i
$943$	2.58290	+	2.86860i	0.0841108	+	0.0934145i
$944$	−12.3030	+	117.055i	−0.400429	+	3.80983i
$945$	−3.16228	+	9.73249i	−0.102869	+	0.316598i
$946$	−33.2705	+	102.396i	−1.08172	+	3.32918i
$947$	−4.20067	+	39.9667i	−0.136503	+	1.29874i	0.685001	+	0.728542i	$0.259802\pi$
$947$	−4.20067	+	39.9667i	−0.136503	+	1.29874i	−0.821505	+	0.570202i	$0.806865\pi$
$948$	4.60053	+	5.10941i	0.149418	+	0.165946i
$949$	−7.44382	+	8.26720i	−0.241637	+	0.268365i
$950$		0			0
$951$	22.4301	+	4.76766i	0.727345	+	0.154602i
$952$	−25.2735	+	11.2525i	−0.819118	+	0.364695i
$953$	−15.1043	−	10.9739i	−0.489276	−	0.355480i	0.315630	−	0.948882i	$-0.397784\pi$
$953$	−15.1043	−	10.9739i	−0.489276	−	0.355480i	−0.804906	+	0.593403i	$0.797784\pi$
$954$	73.4251	+	32.6909i	2.37722	+	1.05841i
$955$	−10.9164	−	18.9078i	−0.353247	−	0.611841i
$956$	−29.3890	+	50.9032i	−0.950508	+	1.64633i
$957$	−1.62054	+	1.17739i	−0.0523848	+	0.0380598i
$958$	−42.3249	+	8.99644i	−1.36746	+	0.290662i
$959$	0.810272	+	2.49376i	0.0261651	+	0.0805278i
$960$	−17.0193			−0.549295
$961$		0			0
$962$	−29.1246			−0.939015
$963$	−1.01722	−	3.13068i	−0.0327795	−	0.100885i
$964$	110.232	−	23.4305i	3.55032	−	0.754645i
$965$	37.4615	−	27.2174i	1.20593	−	0.876158i
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	−22.0084	−	38.1197i	−0.707743	−	1.22585i	−0.965692	−	0.259689i	$-0.916380\pi$
$967$	−22.0084	−	38.1197i	−0.707743	−	1.22585i	0.257949	−	0.966158i	$-0.416953\pi$
$968$	47.7830	+	21.2743i	1.53580	+	0.683783i
$969$	2.61803	+	1.90211i	0.0841034	+	0.0611047i
$970$	−37.4359	+	16.6675i	−1.20199	+	0.535163i
$971$	−52.7109	−	11.2041i	−1.69157	−	0.359555i	−0.741350	−	0.671119i	$-0.765814\pi$
$971$	−52.7109	−	11.2041i	−1.69157	−	0.359555i	−0.950225	+	0.311564i	$0.899147\pi$
$972$	8.16725	+	77.7062i	0.261965	+	2.49243i
$973$	12.0257	−	13.3559i	0.385526	−	0.428170i
$974$	49.1871	+	54.6278i	1.57606	+	1.75039i
$975$		0			0
$976$	42.4357	−	130.604i	1.35833	−	4.18052i
$977$	−13.1287	+	40.4059i	−0.420024	+	1.29270i	0.487656	+	0.873036i	$0.337852\pi$
$977$	−13.1287	+	40.4059i	−0.420024	+	1.29270i	−0.907680	+	0.419664i	$0.862148\pi$
$978$	3.44821	−	32.8076i	0.110262	−	1.04907i
$979$	−43.5769	−	48.3970i	−1.39272	−	1.54678i
$980$	−43.5769	+	48.3970i	−1.39201	+	1.54599i
$981$	−0.301935	−	2.87272i	−0.00964004	−	0.0917189i
$982$	40.6920	+	8.64935i	1.29853	+	0.276012i
$983$	49.2550	−	21.9298i	1.57099	−	0.699450i	0.577825	−	0.816160i	$-0.303901\pi$
$983$	49.2550	−	21.9298i	1.57099	−	0.699450i	0.993166	+	0.116710i	$0.0372348\pi$
$984$	−7.77817	−	5.65117i	−0.247959	−	0.180153i
$985$	−2.20691	−	0.982580i	−0.0703180	−	0.0313076i
$986$	2.61803	+	4.53457i	0.0833752	+	0.144410i
$987$	4.24264	−	7.34847i	0.135045	−	0.233904i
$988$	10.2971	−	7.48128i	0.327595	−	0.238011i
$989$	−24.8610	+	5.28437i	−0.790534	+	0.168033i
$990$	−17.1618	−	52.8187i	−0.545439	−	1.67869i
$991$	−13.9358			−0.442685			−0.221343	−	0.975196i	$-0.571044\pi$
$991$	−13.9358			−0.442685			−0.221343	+	0.975196i	$0.571044\pi$
$992$		0			0
$993$	−27.3475			−0.867847
$994$	1.19098	+	3.66547i	0.0377757	+	0.116262i
$995$	−50.7788	+	10.7934i	−1.60980	+	0.342173i
$996$	−10.8541	+	7.88597i	−0.343925	+	0.249876i
$997$	29.3328	−	50.8059i	0.928980	−	1.60904i	0.143947	−	0.989585i	$-0.454021\pi$
$997$	29.3328	−	50.8059i	0.928980	−	1.60904i	0.785033	−	0.619454i	$-0.212646\pi$
$998$	−24.0660	−	41.6835i	−0.761795	−	1.31947i
$999$	17.7378	+	7.89736i	0.561198	+	0.249862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.p.844.2		16
31.2	even	5		961.2.g.i.338.2		16
31.3	odd	30		961.2.a.h.1.4	yes	4
31.4	even	5		961.2.g.i.732.1		16
31.5	even	3	inner	961.2.g.p.547.1		16
31.6	odd	6		961.2.d.j.531.2		8
31.7	even	15		961.2.d.h.374.2		8
31.8	even	5	inner	961.2.g.p.448.1		16
31.9	even	15	inner	961.2.g.p.846.2		16
31.10	even	15		961.2.g.i.235.1		16
31.11	odd	30		961.2.g.i.816.1		16
31.12	odd	30		961.2.d.h.388.1		8
31.13	odd	30		961.2.c.h.439.3		8
31.14	even	15		961.2.d.j.628.1		8
31.15	odd	10		961.2.c.h.521.3		8
31.16	even	5		961.2.c.h.521.4		8
31.17	odd	30		961.2.d.j.628.2		8
31.18	even	15		961.2.c.h.439.4		8
31.19	even	15		961.2.d.h.388.2		8
31.20	even	15		961.2.g.i.816.2		16
31.21	odd	30		961.2.g.i.235.2		16
31.22	odd	30	inner	961.2.g.p.846.1		16
31.23	odd	10	inner	961.2.g.p.448.2		16
31.24	odd	30		961.2.d.h.374.1		8
31.25	even	3		961.2.d.j.531.1		8
31.26	odd	6	inner	961.2.g.p.547.2		16
31.27	odd	10		961.2.g.i.732.2		16
31.28	even	15		961.2.a.h.1.3	✓	4
31.29	odd	10		961.2.g.i.338.1		16
31.30	odd	2	inner	961.2.g.p.844.1		16
93.59	odd	30		8649.2.a.r.1.1		4
93.65	even	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	31.28	even	15
961.2.a.h.1.4	yes	4	31.3	odd	30
961.2.c.h.439.3		8	31.13	odd	30
961.2.c.h.439.4		8	31.18	even	15
961.2.c.h.521.3		8	31.15	odd	10
961.2.c.h.521.4		8	31.16	even	5
961.2.d.h.374.1		8	31.24	odd	30
961.2.d.h.374.2		8	31.7	even	15
961.2.d.h.388.1		8	31.12	odd	30
961.2.d.h.388.2		8	31.19	even	15
961.2.d.j.531.1		8	31.25	even	3
961.2.d.j.531.2		8	31.6	odd	6
961.2.d.j.628.1		8	31.14	even	15
961.2.d.j.628.2		8	31.17	odd	30
961.2.g.i.235.1		16	31.10	even	15
961.2.g.i.235.2		16	31.21	odd	30
961.2.g.i.338.1		16	31.29	odd	10
961.2.g.i.338.2		16	31.2	even	5
961.2.g.i.732.1		16	31.4	even	5
961.2.g.i.732.2		16	31.27	odd	10
961.2.g.i.816.1		16	31.11	odd	30
961.2.g.i.816.2		16	31.20	even	15
961.2.g.p.448.1		16	31.8	even	5	inner
961.2.g.p.448.2		16	31.23	odd	10	inner
961.2.g.p.547.1		16	31.5	even	3	inner
961.2.g.p.547.2		16	31.26	odd	6	inner
961.2.g.p.844.1		16	31.30	odd	2	inner
961.2.g.p.844.2		16	1.1	even	1	trivial
961.2.g.p.846.1		16	31.22	odd	30	inner
961.2.g.p.846.2		16	31.9	even	15	inner
8649.2.a.r.1.1		4	93.59	odd	30
8649.2.a.r.1.2		4	93.65	even	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+(0.809017 + 2.48990i) q^{2} +(0.854932 - 0.181721i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(1.14412 + 1.98168i) q^{6} +(-0.913545 - 0.406737i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(-2.04275 + 0.909491i) q^{9} +(-5.72618 - 1.21714i) q^{10} +(-0.443477 - 4.21940i) q^{11} +(-2.83888 + 3.15290i) q^{12} +(-1.75452 - 1.94860i) q^{13} +(0.273659 - 2.60369i) q^{14} +(-0.603941 + 1.85874i) q^{15} +(3.04508 - 9.37181i) q^{16} +(-0.387012 + 3.68218i) q^{17} +(-3.91716 - 4.35045i) q^{18} +(0.669131 - 0.743145i) q^{19} +(-1.13456 - 10.7946i) q^{20} +(-0.854932 - 0.181721i) q^{21} +(10.1471 - 4.51778i) q^{22} +(2.12132 + 1.54123i) q^{23} +(-5.96626 - 2.65635i) q^{24} +(3.43237 - 5.94504i) q^{26} +(-3.70246 + 2.68999i) q^{27} +(4.74803 - 1.00922i) q^{28} +(-0.166925 - 0.513743i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(-1.14590 - 3.52671i) q^{33} +(-9.48135 + 2.01532i) q^{34} +(1.80902 - 1.31433i) q^{35} +(5.42705 - 9.39993i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(2.39169 + 1.06485i) q^{38} +(-1.85410 - 1.34708i) q^{39} +(15.2637 - 6.79584i) q^{40} +(1.43997 + 0.306074i) q^{41} +(-0.239187 - 2.27571i) q^{42} +(-6.48599 + 7.20342i) q^{43} +(13.7802 + 15.3045i) q^{44} +(0.522642 - 4.97261i) q^{45} +(-2.12132 + 6.52875i) q^{46} +(-3.00000 + 9.23305i) q^{47} +(0.900283 - 8.56562i) q^{48} +(-4.01478 - 4.45887i) q^{49} +(0.338261 + 3.21834i) q^{51} +(12.4498 + 2.64628i) q^{52} +(-12.5425 + 5.58428i) q^{53} +(-9.69316 - 7.04250i) q^{54} +(8.66665 + 3.85864i) q^{55} +(3.73607 + 6.47106i) q^{56} +(0.437016 - 0.756934i) q^{57} +(1.14412 - 0.831254i) q^{58} +(-11.6833 + 2.48335i) q^{59} +(-2.93159 - 9.02251i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(2.69098 + 8.28199i) q^{64} +(5.73506 - 1.21902i) q^{65} +(7.85410 - 5.70634i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.98606 - 15.5643i) q^{68} +(2.09366 + 0.932157i) q^{69} +(4.73607 + 3.44095i) q^{70} +(-1.34486 + 0.598772i) q^{71} +(16.3431 + 3.47383i) q^{72} +(-0.443477 - 4.21940i) q^{73} +(7.43229 - 8.25439i) q^{74} +(-0.507392 + 4.82751i) q^{76} +(-1.31105 + 4.03499i) q^{77} +(1.85410 - 5.70634i) q^{78} +(0.169393 - 1.61167i) q^{79} +(14.7439 + 16.3748i) q^{80} +(1.81214 - 2.01259i) q^{81} +(0.402863 + 3.83299i) q^{82} +(3.09317 + 0.657474i) q^{83} +(3.87585 - 1.72564i) q^{84} +(-6.69781 - 4.86624i) q^{85} +(-23.1831 - 10.3218i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(-15.8508 + 27.4544i) q^{88} +(12.4184 - 9.02251i) q^{89} +(12.8041 - 2.72160i) q^{90} +(0.810272 + 2.49376i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(0.690983 + 2.12663i) q^{95} +(9.27952 - 1.97242i) q^{96} +(5.66312 - 4.11450i) q^{97} +(7.85410 - 13.6037i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 36 q^{4} - 2 q^{7} - 52 q^{8} - 10 q^{9} - 10 q^{10} - 8 q^{14} + 4 q^{16} + 10 q^{18} + 2 q^{19} + 30 q^{20} + 12 q^{28} + 120 q^{32} - 72 q^{33} + 20 q^{35} + 60 q^{36} + 8 q^{38} + 24 q^{39}+ \cdots + 72 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 36 * q^4 - 2 * q^7 - 52 * q^8 - 10 * q^9 - 10 * q^10 - 8 * q^14 + 4 * q^16 + 10 * q^18 + 2 * q^19 + 30 * q^20 + 12 * q^28 + 120 * q^32 - 72 * q^33 + 20 * q^35 + 60 * q^36 + 8 * q^38 + 24 * q^39 + 50 * q^40 + 26 * q^41 - 10 * q^45 - 48 * q^47 - 12 * q^49 - 12 * q^51 + 24 * q^56 - 34 * q^59 + 52 * q^64 + 72 * q^66 - 48 * q^67 - 12 * q^69 + 40 * q^70 - 14 * q^71 + 10 * q^72 + 18 * q^76 - 24 * q^78 - 50 * q^80 - 38 * q^81 - 16 * q^82 + 32 * q^87 + 10 * q^90 - 192 * q^94 + 20 * q^95 + 28 * q^97 + 72 * q^98

Introduction

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