LMFDB - Embedded newform 961.2.g.p.844.1

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 = [16,4,0,-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			844.1
Root			$1.38331 - 0.294032i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.p.846.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(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	−0.447983	−	0.894042i	$-0.647857\pi$
$3$	−0.854932	+	0.181721i	−0.493595	+	0.104917i	−0.0456128	+	0.998959i	$0.514524\pi$
$4$	−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	$0.187568\pi$
$11$	0.443477	+	4.21940i	0.133713	+	1.27220i	−0.697638	+	0.716450i	$0.745766\pi$
$12$	2.83888	−	3.15290i	0.819514	−	0.910163i
$13$	1.75452	+	1.94860i	0.486618	+	0.540444i	0.935584	−	0.353105i	$-0.114874\pi$
$13$	1.75452	+	1.94860i	0.486618	+	0.540444i	−0.448966	+	0.893549i	$0.648208\pi$
$14$	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	$-0.818451\pi$
$17$	0.387012	−	3.68218i	0.0938643	−	0.893059i	0.935574	−	0.353129i	$-0.114882\pi$
$18$	−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	0.344233	−	0.938884i	$-0.388139\pi$
$23$	−2.12132	−	1.54123i	−0.442326	−	0.321369i	−0.786558	+	0.617516i	$0.788139\pi$
$24$	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	0.965358	−	0.260928i	$-0.0840286\pi$
$29$	0.166925	+	0.513743i	0.0309972	+	0.0953997i	−0.934361	+	0.356328i	$0.884029\pi$
$30$	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	0.986026	−	0.166589i	$-0.0532753\pi$
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	−0.637284	+	0.770629i	$0.719942\pi$
$38$	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	$-0.501919\pi$
$43$	6.48599	−	7.20342i	0.989105	−	1.09851i	0.995134	−	0.0985301i	$-0.0314141\pi$
$44$	−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	$-0.241378\pi$
$53$	12.5425	−	5.58428i	1.72284	−	0.767060i	0.996846	−	0.0793640i	$-0.0252890\pi$
$54$	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	$-0.850803\pi$
$61$	−13.9358			−1.78430			−0.892148	+	0.451742i	$0.850803\pi$
$62$		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	$0.0465326\pi$
$73$	0.443477	+	4.21940i	0.0519050	+	0.493843i	−0.937429	+	0.348177i	$0.886801\pi$
$74$	−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	−0.999910	−	0.0134299i	$-0.995725\pi$
$79$	−0.169393	+	1.61167i	−0.0190582	+	0.181327i	0.980852	+	0.194757i	$0.0623917\pi$
$80$	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	0.0349966	−	0.999387i	$-0.488858\pi$
$83$	−3.09317	−	0.657474i	−0.339520	−	0.0721672i	−0.374517	+	0.927220i	$0.622191\pi$
$84$	−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	$0.602468\pi$
$89$	−12.4184	+	9.02251i	−1.31635	+	0.956385i	−0.999970	+	0.00775224i	$0.997532\pi$
$90$	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	−0.600309	−	0.799768i	$-0.704956\pi$
$127$	−9.27952	+	1.97242i	−0.823425	+	0.175024i	−0.223115	+	0.974792i	$0.571623\pi$
$128$	−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	0.813418	−	0.581680i	$-0.197604\pi$
$137$	1.75452	+	1.94860i	0.149899	+	0.166480i	−0.663519	+	0.748160i	$0.730938\pi$
$138$	−0.627171	+	5.96713i	−0.0533883	+	0.507956i
$139$	5.55369	−	17.0925i	0.471058	−	1.44977i	−0.380144	−	0.924927i	$-0.624125\pi$
$139$	5.55369	−	17.0925i	0.471058	−	1.44977i	0.851201	−	0.524839i	$-0.175875\pi$
$140$	−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	−0.0935821	−	0.995612i	$-0.529832\pi$
$151$	10.1302	−	7.36001i	0.824382	−	0.598949i	0.917964	+	0.396663i	$0.129832\pi$
$152$	−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	−0.714525	−	0.699610i	$-0.753357\pi$
$167$	0.722904	−	0.802866i	0.0559400	−	0.0621277i	0.770465	+	0.637482i	$0.220024\pi$
$168$	−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	−0.0997707	−	0.995010i	$-0.531811\pi$
$179$	−12.1210	−	5.39662i	−0.905967	−	0.403363i	−0.806197	+	0.591648i	$0.798478\pi$
$180$	12.1353	+	21.0189i	0.904508	+	1.56665i
$181$	4.34581	−	7.52716i	0.323021	−	0.559489i	−0.658089	−	0.752940i	$-0.728635\pi$
$181$	4.34581	−	7.52716i	0.323021	−	0.559489i	0.981110	+	0.193451i	$0.0619681\pi$
$182$	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	0.989762	−	0.142727i	$-0.0455869\pi$
$197$	−0.112929	−	1.07444i	−0.00804584	−	0.0765510i	−0.997808	+	0.0661755i	$0.978920\pi$
$198$	16.6191	−	18.4574i	1.18107	−	1.31171i
$199$	−15.5347	−	17.2531i	−1.10123	−	1.22304i	−0.972880	−	0.231309i	$-0.925699\pi$
$199$	−15.5347	−	17.2531i	−1.10123	−	1.22304i	−0.128348	−	0.991729i	$-0.540968\pi$
$200$		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	$0.0151295\pi$
$223$	8.07262	+	13.9822i	0.540583	+	0.936316i	−0.458288	+	0.888804i	$0.651537\pi$
$224$	−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	−0.829606	−	0.558349i	$-0.811435\pi$
$229$	−2.83888	+	3.15290i	−0.187599	+	0.208349i	0.642008	+	0.766698i	$0.278102\pi$
$230$	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	−0.732020	−	0.681283i	$-0.761422\pi$
$239$	−11.0621	+	4.92515i	−0.715545	+	0.318581i	0.0164750	+	0.999864i	$0.494756\pi$
$240$	−15.5807	−	11.3200i	−1.00573	−	0.730706i
$241$	21.2092	+	9.44292i	1.36620	+	0.608272i	0.953167	−	0.302443i	$-0.0978023\pi$
$241$	21.2092	+	9.44292i	1.36620	+	0.608272i	0.413034	+	0.910716i	$0.364469\pi$
$242$	−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	0.145541	−	0.989352i	$-0.453508\pi$
$251$	10.7876	−	2.29297i	0.680905	−	0.144731i	0.535364	+	0.844621i	$0.320174\pi$
$252$	−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	$0.293351\pi$
$263$	−5.72061	+	17.6062i	−0.352748	+	1.08565i	−0.957304	+	0.289084i	$0.906649\pi$
$264$	−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	0.271892	−	0.962328i	$-0.412351\pi$
$269$	2.11351	+	0.449240i	0.128863	+	0.0273907i	−0.143029	+	0.989719i	$0.545684\pi$
$270$	−24.4750	+	10.8970i	−1.48950	+	0.663169i
$271$	−15.0405	−	10.9276i	−0.913647	−	0.663803i	0.0282879	−	0.999600i	$-0.490994\pi$
$271$	−15.0405	−	10.9276i	−0.913647	−	0.663803i	−0.941934	+	0.335797i	$0.890994\pi$
$272$	−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	0.812349	−	0.583172i	$-0.198189\pi$
$277$	−3.12287	−	9.61121i	−0.187635	−	0.577482i	−0.999984	+	0.00569038i	$0.998189\pi$
$278$	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	−0.515045	−	0.857163i	$-0.672225\pi$
$313$	−11.2683	+	2.39515i	−0.636922	+	0.135382i	−0.121877	+	0.992545i	$0.538891\pi$
$314$	−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	0.947239	−	0.320529i	$-0.103861\pi$
$331$	30.6052	+	6.50533i	1.68221	+	0.357565i	0.734975	+	0.678095i	$0.237194\pi$
$332$	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	−0.872186	−	0.489174i	$-0.837298\pi$
$337$	−12.4184	+	9.02251i	−0.676475	+	0.491488i	0.195712	+	0.980662i	$0.437298\pi$
$338$	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	$-0.969852\pi$
$347$	−10.7979	−	18.7025i	−0.579661	−	1.00400i	0.415857	−	0.909430i	$-0.363482\pi$
$348$	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	−0.888999	−	0.457909i	$-0.848599\pi$
$353$	−6.40067	+	7.10866i	−0.340673	+	0.378356i	0.548326	+	0.836265i	$0.315265\pi$
$354$	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	−0.765956	−	0.642892i	$-0.777734\pi$
$367$	3.32920	−	5.76635i	0.173783	−	0.301001i	0.939739	+	0.341892i	$0.111068\pi$
$368$	−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	$-0.981023\pi$
$383$	−0.669334	−	6.36829i	−0.0342014	−	0.325404i	0.964022	−	0.265822i	$-0.0856435\pi$
$384$	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	$0.173490\pi$
$389$	−1.75743	+	16.7208i	−0.0891053	+	0.847780i	−0.944214	+	0.329332i	$0.893177\pi$
$390$	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	0.955138	−	0.296161i	$-0.0957066\pi$
$401$	0.166925	+	0.513743i	0.00833585	+	0.0256551i	−0.946802	+	0.321816i	$0.895707\pi$
$402$	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	$0.100267\pi$
$409$	15.0405	+	26.0509i	0.743706	+	1.28814i	−0.207091	+	0.978322i	$0.566400\pi$
$410$	−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	$-0.286785\pi$
$433$	25.8384			1.24171			0.620857	+	0.783924i	$0.286785\pi$
$434$		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	$0.392693\pi$
$449$	−10.4153	+	32.0551i	−0.491529	+	1.51277i	−0.822296	+	0.569060i	$0.807307\pi$
$450$		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	0.780912	−	0.624641i	$-0.214755\pi$
$457$	9.15298	+	6.65003i	0.428158	+	0.311075i	−0.352754	+	0.935716i	$0.614755\pi$
$458$	−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	−0.486202	−	0.873846i	$-0.661618\pi$
$461$	4.17888	−	3.03613i	0.194630	−	0.141407i	0.680832	+	0.732439i	$0.261618\pi$
$462$	−9.49606	+	2.01845i	−0.441797	+	0.0939068i
$463$	1.18353	+	3.64253i	0.0550032	+	0.169283i	0.974784	−	0.223150i	$-0.0716338\pi$
$463$	1.18353	+	3.64253i	0.0550032	+	0.169283i	−0.919781	+	0.392432i	$0.871634\pi$
$464$	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	−0.894985	−	0.446095i	$-0.852814\pi$
$487$	−25.6505	+	11.4203i	−1.16233	+	0.517504i	−0.267349	+	0.963600i	$0.586148\pi$
$488$	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	−0.987720	−	0.156234i	$-0.950065\pi$
$491$	−7.94510	+	13.7613i	−0.358557	+	0.621040i	0.629163	+	0.777274i	$0.283398\pi$
$492$	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	0.213023	−	0.977047i	$-0.431669\pi$
$499$	17.9830	−	3.82241i	0.805031	−	0.171115i	0.592007	+	0.805933i	$0.298336\pi$
$500$	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	0.849354	−	0.527823i	$-0.176992\pi$
$509$	5.31631	+	5.90436i	0.235641	+	0.261706i	−0.613713	+	0.789529i	$0.710325\pi$
$510$	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	−0.576783	−	0.816898i	$-0.695692\pi$
$523$	0.500776	−	0.363835i	0.0218974	−	0.0159094i	0.598680	+	0.800988i	$0.295692\pi$
$524$	−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	$-0.427584\pi$
$557$	10.6460			0.451086			0.225543	+	0.974233i	$0.427584\pi$
$558$		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	$-0.954284\pi$
$569$	−1.22574	−	11.6621i	−0.0513857	−	0.488902i	0.938318	−	0.345773i	$-0.112383\pi$
$570$	3.42372	−	3.80243i	0.143404	−	0.159266i
$571$	1.75452	+	1.94860i	0.0734246	+	0.0815463i	0.778738	−	0.627350i	$-0.215860\pi$
$571$	1.75452	+	1.94860i	0.0734246	+	0.0815463i	−0.705313	+	0.708896i	$0.749194\pi$
$572$	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	$0.00525542\pi$
$587$	4.86163	+	14.9626i	0.200661	+	0.617571i	−0.799203	+	0.601062i	$0.794745\pi$
$588$	−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	−0.938266	−	0.345915i	$-0.887568\pi$
$601$	−12.1638	+	13.5092i	−0.496170	+	0.551052i	0.442096	+	0.896968i	$0.354235\pi$
$602$	−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	0.395844	−	0.918318i	$-0.370452\pi$
$613$	−0.537977	−	0.239523i	−0.0217287	−	0.00967424i	−0.417572	+	0.908644i	$0.637119\pi$
$614$	−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	$-0.673795\pi$
$619$	−25.8384			−1.03853			−0.519267	+	0.854612i	$0.673795\pi$
$620$		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	$-0.877469\pi$
$631$	−2.46990	−	23.4995i	−0.0983252	−	0.935501i	0.828495	−	0.559996i	$-0.189197\pi$
$632$	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	0.0410594	−	0.999157i	$-0.486927\pi$
$641$	−8.29986	−	1.76419i	−0.327825	−	0.0696813i	−0.368884	+	0.929475i	$0.620260\pi$
$642$	3.07738	−	1.37014i	0.121454	−	0.0540750i
$643$	−3.76622	−	2.73632i	−0.148525	−	0.107910i	0.511041	−	0.859556i	$-0.329260\pi$
$643$	−3.76622	−	2.73632i	−0.148525	−	0.107910i	−0.659566	+	0.751646i	$0.729260\pi$
$644$	−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	0.0464226	−	0.998922i	$-0.485218\pi$
$647$	25.7109	−	18.6801i	1.01080	−	0.734389i	0.964377	+	0.264533i	$0.0852179\pi$
$648$	−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	−0.963186	−	0.268837i	$-0.913361\pi$
$673$	−36.5240	+	16.2615i	−1.40790	+	0.626837i	−0.444712	+	0.895673i	$0.646694\pi$
$674$	−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	−0.994625	−	0.103540i	$-0.966983\pi$
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	0.586981	+	0.809601i	$0.300317\pi$
$678$	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	−0.998305	−	0.0582075i	$-0.981462\pi$
$709$	−33.3221	+	24.2099i	−1.25144	+	0.909224i	−0.253134	+	0.967431i	$0.581462\pi$
$710$	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	$-0.919643\pi$
$719$	−18.7824	−	32.5320i	−0.700465	−	1.21324i	0.267839	−	0.963464i	$-0.413691\pi$
$720$	−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	$0.390430\pi$
$739$	−17.5745	+	30.4399i	−0.646489	+	1.11975i	−0.983956	+	0.178414i	$0.942903\pi$
$740$	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	$-0.266619\pi$
$743$	36.4844			1.33848			0.669242	+	0.743045i	$0.266619\pi$
$744$		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	0.619649	−	0.784879i	$-0.287275\pi$
$757$	−6.20987	−	6.89676i	−0.225701	−	0.250667i	−0.845350	+	0.534212i	$0.820608\pi$
$758$	−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	$-0.706937\pi$
$761$	4.20067	−	39.9667i	0.152274	−	1.44879i	0.757550	−	0.652777i	$-0.226396\pi$
$762$	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	0.993778	−	0.111376i	$-0.0355258\pi$
$773$	3.45672	+	10.6387i	0.124330	+	0.382647i	−0.869449	+	0.494023i	$0.835526\pi$
$774$	−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	$-0.533167\pi$
$787$	25.1357	−	27.9161i	0.895992	−	0.995100i	1.00000		0.000523804i	$-0.000166732\pi$
$788$	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	−0.172390	−	0.985029i	$-0.555149\pi$
$797$	12.5425	−	5.58428i	0.444278	−	0.197805i	0.616668	+	0.787223i	$0.288482\pi$
$798$	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	0.702652	−	0.711534i	$-0.251999\pi$
$809$	46.4747	−	9.87850i	1.63396	−	0.347310i	0.931311	+	0.364224i	$0.118666\pi$
$810$	−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	$0.236543\pi$
$821$	−7.36551	+	22.6687i	−0.257058	+	0.791144i	−0.993417	+	0.114553i	$0.963457\pi$
$822$	1.85410	−	5.70634i	0.0646692	−	0.199031i
$823$	−1.41355	+	13.4491i	−0.0492734	+	0.468805i	0.941867	+	0.335986i	$0.109069\pi$
$823$	−1.41355	+	13.4491i	−0.0492734	+	0.468805i	−0.991140	+	0.132819i	$0.957597\pi$
$824$	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	−0.115113	−	0.993352i	$-0.536723\pi$
$827$	−17.9536	−	3.81615i	−0.624307	−	0.132701i	−0.509194	+	0.860652i	$0.670056\pi$
$828$	−26.0000	+	11.5759i	−0.903561	+	0.402291i
$829$	41.3310	+	30.0287i	1.43548	+	1.04294i	0.988962	+	0.148168i	$0.0473377\pi$
$829$	41.3310	+	30.0287i	1.43548	+	1.04294i	0.446523	+	0.894772i	$0.352662\pi$
$830$	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	0.361803	−	0.932255i	$-0.382161\pi$
$859$	38.0045	−	16.9207i	1.29670	−	0.577326i	0.934893	+	0.354928i	$0.115495\pi$
$860$	−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	$0.344111\pi$
$863$	−15.5413	+	26.9183i	−0.529032	+	0.916310i	−0.999427	+	0.0338541i	$0.989222\pi$
$864$	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	0.655896	−	0.754851i	$-0.272291\pi$
$881$	−4.84939	−	5.38579i	−0.163380	−	0.181452i	−0.819276	+	0.573399i	$0.805624\pi$
$882$	−3.67152	+	34.9322i	−0.123627	+	1.17623i
$883$	10.4884	−	32.2799i	0.352962	−	1.08631i	−0.604219	−	0.796818i	$-0.706515\pi$
$883$	10.4884	−	32.2799i	0.352962	−	1.08631i	0.957182	−	0.289488i	$-0.0934851\pi$
$884$	−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	−0.366780	−	0.930308i	$-0.619540\pi$
$911$	18.0122	−	20.0045i	0.596770	−	0.662780i	0.963550	+	0.267528i	$0.0862066\pi$
$912$	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	$-0.555877\pi$
$929$	−10.6460			−0.349284			−0.174642	+	0.984632i	$0.555877\pi$
$930$		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	$0.103306\pi$
$941$	2.66910	+	25.3948i	0.0870101	+	0.827846i	−0.860786	+	0.508968i	$0.830027\pi$
$942$	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	$-0.740198\pi$
$947$	4.20067	−	39.9667i	0.136503	−	1.29874i	0.821505	−	0.570202i	$-0.193135\pi$
$948$	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	0.804906	−	0.593403i	$-0.202216\pi$
$953$	15.1043	+	10.9739i	0.489276	+	0.355480i	−0.315630	+	0.948882i	$0.602216\pi$
$954$	−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	$0.0836200\pi$
$967$	22.0084	+	38.1197i	0.707743	+	1.22585i	−0.257949	+	0.966158i	$0.583047\pi$
$968$	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	−0.993166	−	0.116710i	$-0.962765\pi$
$983$	−49.2550	+	21.9298i	−1.57099	+	0.699450i	−0.577825	+	0.816160i	$0.696099\pi$
$984$	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	$-0.428956\pi$
$991$	13.9358			0.442685			0.221343	+	0.975196i	$0.428956\pi$
$992$		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.844.1		16
31.2	even	5		961.2.g.i.338.1		16
31.3	odd	30		961.2.a.h.1.3	✓	4
31.4	even	5		961.2.g.i.732.2		16
31.5	even	3	inner	961.2.g.p.547.2		16
31.6	odd	6		961.2.d.j.531.1		8
31.7	even	15		961.2.d.h.374.1		8
31.8	even	5	inner	961.2.g.p.448.2		16
31.9	even	15	inner	961.2.g.p.846.1		16
31.10	even	15		961.2.g.i.235.2		16
31.11	odd	30		961.2.g.i.816.2		16
31.12	odd	30		961.2.d.h.388.2		8
31.13	odd	30		961.2.c.h.439.4		8
31.14	even	15		961.2.d.j.628.2		8
31.15	odd	10		961.2.c.h.521.4		8
31.16	even	5		961.2.c.h.521.3		8
31.17	odd	30		961.2.d.j.628.1		8
31.18	even	15		961.2.c.h.439.3		8
31.19	even	15		961.2.d.h.388.1		8
31.20	even	15		961.2.g.i.816.1		16
31.21	odd	30		961.2.g.i.235.1		16
31.22	odd	30	inner	961.2.g.p.846.2		16
31.23	odd	10	inner	961.2.g.p.448.1		16
31.24	odd	30		961.2.d.h.374.2		8
31.25	even	3		961.2.d.j.531.2		8
31.26	odd	6	inner	961.2.g.p.547.1		16
31.27	odd	10		961.2.g.i.732.1		16
31.28	even	15		961.2.a.h.1.4	yes	4
31.29	odd	10		961.2.g.i.338.2		16
31.30	odd	2	inner	961.2.g.p.844.2		16
93.59	odd	30		8649.2.a.r.1.2		4
93.65	even	30		8649.2.a.r.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.3	✓	4	31.3	odd	30
961.2.a.h.1.4	yes	4	31.28	even	15
961.2.c.h.439.3		8	31.18	even	15
961.2.c.h.439.4		8	31.13	odd	30
961.2.c.h.521.3		8	31.16	even	5
961.2.c.h.521.4		8	31.15	odd	10
961.2.d.h.374.1		8	31.7	even	15
961.2.d.h.374.2		8	31.24	odd	30
961.2.d.h.388.1		8	31.19	even	15
961.2.d.h.388.2		8	31.12	odd	30
961.2.d.j.531.1		8	31.6	odd	6
961.2.d.j.531.2		8	31.25	even	3
961.2.d.j.628.1		8	31.17	odd	30
961.2.d.j.628.2		8	31.14	even	15
961.2.g.i.235.1		16	31.21	odd	30
961.2.g.i.235.2		16	31.10	even	15
961.2.g.i.338.1		16	31.2	even	5
961.2.g.i.338.2		16	31.29	odd	10
961.2.g.i.732.1		16	31.27	odd	10
961.2.g.i.732.2		16	31.4	even	5
961.2.g.i.816.1		16	31.20	even	15
961.2.g.i.816.2		16	31.11	odd	30
961.2.g.p.448.1		16	31.23	odd	10	inner
961.2.g.p.448.2		16	31.8	even	5	inner
961.2.g.p.547.1		16	31.26	odd	6	inner
961.2.g.p.547.2		16	31.5	even	3	inner
961.2.g.p.844.1		16	1.1	even	1	trivial
961.2.g.p.844.2		16	31.30	odd	2	inner
961.2.g.p.846.1		16	31.9	even	15	inner
961.2.g.p.846.2		16	31.22	odd	30	inner
8649.2.a.r.1.1		4	93.65	even	30
8649.2.a.r.1.2		4	93.59	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+(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

L-functions

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