LMFDB - Embedded newform 961.2.g.p.547.1

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			547.1
Root			$0.946294 + 1.05097i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.p.448.1

$q$-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} +(-0.584842 - 0.649532i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(1.14412 - 1.98168i) q^{6} +(0.104528 + 0.994522i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(0.233733 - 2.22382i) q^{9} +(3.91716 - 4.35045i) q^{10} +(3.87585 + 1.72564i) q^{11} +(4.14993 + 0.882095i) q^{12} +(2.56480 - 0.545164i) q^{13} +(-2.39169 + 1.06485i) q^{14} +(-0.603941 + 1.85874i) q^{15} +(3.04508 - 9.37181i) q^{16} +(3.38236 - 1.50593i) q^{17} +(5.72618 - 1.21714i) q^{18} +(-0.978148 - 0.207912i) q^{19} +(9.91572 + 4.41476i) q^{20} +(0.584842 - 0.649532i) q^{21} +(-1.16104 + 11.0465i) q^{22} +(2.12132 + 1.54123i) q^{23} +(0.682664 + 6.49511i) q^{24} +(3.43237 + 5.94504i) q^{26} +(-3.70246 + 2.68999i) q^{27} +(-3.24803 - 3.60730i) q^{28} +(-0.166925 - 0.513743i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(-1.14590 - 3.52671i) q^{33} +(6.48599 + 7.20342i) q^{34} +(1.80902 - 1.31433i) q^{35} +(5.42705 + 9.39993i) q^{36} +(-2.12132 + 3.67423i) q^{37} +(-0.273659 - 2.60369i) q^{38} +(-1.85410 - 1.34708i) q^{39} +(-1.74648 + 16.6167i) q^{40} +(-0.985051 + 1.09401i) q^{41} +(2.09042 + 0.930713i) q^{42} +(9.48135 + 2.01532i) q^{43} +(-20.1442 + 4.28178i) q^{44} +(-4.56773 + 2.03368i) q^{45} +(-2.12132 + 6.52875i) q^{46} +(-3.00000 + 9.23305i) q^{47} +(-7.86819 + 3.50314i) q^{48} +(5.86889 - 1.24747i) q^{49} +(-2.95630 - 1.31623i) q^{51} +(-8.51664 + 9.45869i) q^{52} +(1.43512 - 13.6543i) q^{53} +(-9.69316 - 7.04250i) q^{54} +(-0.991644 - 9.43486i) q^{55} +(3.73607 - 6.47106i) q^{56} +(0.437016 + 0.756934i) q^{57} +(1.14412 - 0.831254i) q^{58} +(7.99228 + 8.87632i) q^{59} +(-2.93159 - 9.02251i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(2.69098 + 8.28199i) q^{64} +(-3.92324 - 4.35720i) q^{65} +(7.85410 - 5.70634i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-8.98606 + 15.5643i) q^{68} +(-0.239558 - 2.27924i) q^{69} +(4.73607 + 3.44095i) q^{70} +(0.153880 - 1.46407i) q^{71} +(-11.1800 + 12.4166i) q^{72} +(3.87585 + 1.72564i) q^{73} +(-10.8647 - 2.30935i) q^{74} +(4.43444 - 1.97434i) q^{76} +(-1.31105 + 4.03499i) q^{77} +(1.85410 - 5.70634i) q^{78} +(-1.48044 + 0.659135i) q^{79} +(-21.5529 + 4.58122i) q^{80} +(-2.64902 - 0.563067i) q^{81} +(-3.52090 - 1.56760i) q^{82} +(-2.11598 + 2.35003i) q^{83} +(-0.443477 + 4.21940i) q^{84} +(-6.69781 - 4.86624i) q^{85} +(2.65262 + 25.2380i) q^{86} +(-0.236068 + 0.408882i) q^{87} +(-15.8508 - 27.4544i) q^{88} +(12.4184 - 9.02251i) q^{89} +(-8.75903 - 9.72789i) q^{90} +(0.810272 + 2.49376i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(0.690983 + 2.12663i) q^{95} +(-6.34793 - 7.05009i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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	$0.523549\pi$
$3$	−0.584842	−	0.649532i	−0.337658	−	0.375008i	0.550272	−	0.834985i	$-0.314524\pi$
$3$	−0.584842	−	0.649532i	−0.337658	−	0.375008i	−0.887930	+	0.459978i	$0.847857\pi$
$4$	−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
$7$	0.104528	+	0.994522i	0.0395080	+	0.375894i	0.996355	+	0.0853021i	$0.0271855\pi$
$7$	0.104528	+	0.994522i	0.0395080	+	0.375894i	−0.956847	+	0.290592i	$0.906148\pi$
$8$	−6.04508	−	4.39201i	−2.13726	−	1.55281i
$9$	0.233733	−	2.22382i	0.0779109	−	0.741273i
$10$	3.91716	−	4.35045i	1.23871	−	1.37573i
$11$	3.87585	+	1.72564i	1.16861	+	0.520299i	0.896967	−	0.442098i	$-0.145766\pi$
$11$	3.87585	+	1.72564i	1.16861	+	0.520299i	0.271645	+	0.962398i	$0.412432\pi$
$12$	4.14993	+	0.882095i	1.19798	+	0.254639i
$13$	2.56480	−	0.545164i	0.711347	−	0.151201i	0.161994	−	0.986792i	$-0.448208\pi$
$13$	2.56480	−	0.545164i	0.711347	−	0.151201i	0.549353	+	0.835590i	$0.314874\pi$
$14$	−2.39169	+	1.06485i	−0.639207	+	0.284593i
$15$	−0.603941	+	1.85874i	−0.155937	+	0.479925i
$16$	3.04508	−	9.37181i	0.761271	−	2.34295i
$17$	3.38236	−	1.50593i	0.820344	−	0.365241i	0.0467376	−	0.998907i	$-0.485118\pi$
$17$	3.38236	−	1.50593i	0.820344	−	0.365241i	0.773606	+	0.633667i	$0.218451\pi$
$18$	5.72618	−	1.21714i	1.34967	−	0.286882i
$19$	−0.978148	−	0.207912i	−0.224402	−	0.0476982i	0.0943381	−	0.995540i	$-0.469927\pi$
$19$	−0.978148	−	0.207912i	−0.224402	−	0.0476982i	−0.318741	+	0.947842i	$0.603260\pi$
$20$	9.91572	+	4.41476i	2.21722	+	0.987171i
$21$	0.584842	−	0.649532i	0.127623	−	0.141740i
$22$	−1.16104	+	11.0465i	−0.247534	+	2.35513i
$23$	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	$0.611861\pi$
$24$	0.682664	+	6.49511i	0.139348	+	1.32581i
$25$		0			0
$26$	3.43237	+	5.94504i	0.673143	+	1.16592i
$27$	−3.70246	+	2.68999i	−0.712539	+	0.517690i
$28$	−3.24803	−	3.60730i	−0.613820	−	0.681716i
$29$	−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
$34$	6.48599	+	7.20342i	1.11234	+	1.23538i
$35$	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	$-0.946725\pi$
$37$	−2.12132	+	3.67423i	−0.348743	+	0.604040i	0.637284	+	0.770629i	$0.280058\pi$
$38$	−0.273659	−	2.60369i	−0.0443934	−	0.422375i
$39$	−1.85410	−	1.34708i	−0.296894	−	0.215706i
$40$	−1.74648	+	16.6167i	−0.276143	+	2.62733i
$41$	−0.985051	+	1.09401i	−0.153839	+	0.170856i	−0.815138	−	0.579267i	$-0.803339\pi$
$41$	−0.985051	+	1.09401i	−0.153839	+	0.170856i	0.661299	+	0.750123i	$0.270006\pi$
$42$	2.09042	+	0.930713i	0.322558	+	0.143612i
$43$	9.48135	+	2.01532i	1.44589	+	0.307334i	0.862995	−	0.505213i	$-0.168586\pi$
$43$	9.48135	+	2.01532i	1.44589	+	0.307334i	0.582897	+	0.812546i	$0.301919\pi$
$44$	−20.1442	+	4.28178i	−3.03685	+	0.645502i
$45$	−4.56773	+	2.03368i	−0.680917	+	0.303164i
$46$	−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	$0.849578\pi$
$48$	−7.86819	+	3.50314i	−1.13567	+	0.505635i
$49$	5.86889	−	1.24747i	0.838412	−	0.178210i
$50$		0			0
$51$	−2.95630	−	1.31623i	−0.413964	−	0.184309i
$52$	−8.51664	+	9.45869i	−1.18105	+	1.31168i
$53$	1.43512	−	13.6543i	0.197129	−	1.87556i	−0.232563	−	0.972581i	$-0.574711\pi$
$53$	1.43512	−	13.6543i	0.197129	−	1.87556i	0.429692	−	0.902976i	$-0.358622\pi$
$54$	−9.69316	−	7.04250i	−1.31907	−	0.958362i
$55$	−0.991644	−	9.43486i	−0.133713	−	1.27220i
$56$	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
$59$	7.99228	+	8.87632i	1.04051	+	1.15560i	0.987599	+	0.157000i	$0.0501821\pi$
$59$	7.99228	+	8.87632i	1.04051	+	1.15560i	0.0529073	+	0.998599i	$0.483151\pi$
$60$	−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
$65$	−3.92324	−	4.35720i	−0.486618	−	0.540444i
$66$	7.85410	−	5.70634i	0.966773	−	0.702402i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	−8.98606	+	15.5643i	−1.08972	+	1.88745i
$69$	−0.239558	−	2.27924i	−0.0288394	−	0.274388i
$70$	4.73607	+	3.44095i	0.566068	+	0.411273i
$71$	0.153880	−	1.46407i	0.0182622	−	0.173753i	−0.981589	−	0.191006i	$-0.938825\pi$
$71$	0.153880	−	1.46407i	0.0182622	−	0.173753i	0.999851	+	0.0172522i	$0.00549182\pi$
$72$	−11.1800	+	12.4166i	−1.31757	+	1.46331i
$73$	3.87585	+	1.72564i	0.453633	+	0.201971i	0.620818	−	0.783955i	$-0.286801\pi$
$73$	3.87585	+	1.72564i	0.453633	+	0.201971i	−0.167184	+	0.985926i	$0.553467\pi$
$74$	−10.8647	−	2.30935i	−1.26299	−	0.268457i
$75$		0			0
$76$	4.43444	−	1.97434i	0.508665	−	0.226472i
$77$	−1.31105	+	4.03499i	−0.149408	+	0.459830i
$78$	1.85410	−	5.70634i	0.209936	−	0.646116i
$79$	−1.48044	+	0.659135i	−0.166563	+	0.0741585i	−0.488324	−	0.872662i	$-0.662392\pi$
$79$	−1.48044	+	0.659135i	−0.166563	+	0.0741585i	0.321762	+	0.946821i	$0.395725\pi$
$80$	−21.5529	+	4.58122i	−2.40969	+	0.512196i
$81$	−2.64902	−	0.563067i	−0.294336	−	0.0625630i
$82$	−3.52090	−	1.56760i	−0.388818	−	0.173113i
$83$	−2.11598	+	2.35003i	−0.232259	+	0.257949i	−0.847997	−	0.530002i	$-0.822191\pi$
$83$	−2.11598	+	2.35003i	−0.232259	+	0.257949i	0.615738	+	0.787951i	$0.288858\pi$
$84$	−0.443477	+	4.21940i	−0.0483873	+	0.460374i
$85$	−6.69781	−	4.86624i	−0.726480	−	0.527818i
$86$	2.65262	+	25.2380i	0.286040	+	2.72149i
$87$	−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	$-0.00246764\pi$
$90$	−8.75903	−	9.72789i	−0.923283	−	1.02541i
$91$	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
$96$	−6.34793	−	7.05009i	−0.647883	−	0.719547i
$97$	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	$0.735485\pi$
$102$	0.885579	−	8.42572i	0.0876854	−	0.834271i
$103$	7.16519	−	7.95775i	0.706007	−	0.784100i	−0.278313	−	0.960490i	$-0.589775\pi$
$103$	7.16519	−	7.95775i	0.706007	−	0.784100i	0.984320	+	0.176390i	$0.0564421\pi$
$104$	−17.8988	−	7.96905i	−1.75512	−	0.781430i
$105$	−1.91169	−	0.406342i	−0.186562	−	0.0396549i
$106$	35.1588	−	7.47323i	3.41492	−	0.725864i
$107$	1.34486	−	0.598772i	0.130013	−	0.0578854i	−0.340699	−	0.940172i	$-0.610664\pi$
$107$	1.34486	−	0.598772i	0.130013	−	0.0578854i	0.470712	+	0.882287i	$0.343997\pi$
$108$	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	$0.119705\pi$
$110$	22.6896	−	10.1021i	2.16337	−	0.963193i
$111$	3.62717	−	0.770979i	0.344276	−	0.0731781i
$112$	9.63877	+	2.04878i	0.910778	+	0.193592i
$113$	−8.91980	−	3.97135i	−0.839104	−	0.373593i	−0.0582463	−	0.998302i	$-0.518551\pi$
$113$	−8.91980	−	3.97135i	−0.839104	−	0.373593i	−0.780858	+	0.624709i	$0.785218\pi$
$114$	−1.53114	+	1.70050i	−0.143404	+	0.159266i
$115$	0.612870	−	5.83107i	0.0571504	−	0.543750i
$116$	2.12132	+	1.54123i	0.196960	+	0.143100i
$117$	−0.612870	−	5.83107i	−0.0566598	−	0.539082i
$118$	−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
$121$	4.68391	+	5.20201i	0.425810	+	0.472910i
$122$	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
$127$	−6.34793	−	7.05009i	−0.563288	−	0.625594i	0.392465	−	0.919767i	$-0.371623\pi$
$127$	−6.34793	−	7.05009i	−0.563288	−	0.625594i	−0.955752	+	0.294173i	$0.904956\pi$
$128$	−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
$131$	−0.775226	−	7.37578i	−0.0677318	−	0.644425i	−0.974745	−	0.223322i	$-0.928310\pi$
$131$	−0.775226	−	7.37578i	−0.0677318	−	0.644425i	0.907013	−	0.421103i	$-0.138357\pi$
$132$	14.5623	+	10.5801i	1.26749	+	0.920883i
$133$	0.104528	−	0.994522i	0.00906377	−	0.0862360i
$134$	10.5108	−	11.6735i	0.907998	−	1.00843i
$135$	9.34863	+	4.16228i	0.804602	+	0.358232i
$136$	−27.0607	−	5.75193i	−2.32044	−	0.493224i
$137$	2.56480	−	0.545164i	0.219125	−	0.0465765i	−0.0970406	−	0.995280i	$-0.530938\pi$
$137$	2.56480	−	0.545164i	0.219125	−	0.0465765i	0.316166	+	0.948704i	$0.397604\pi$
$138$	5.48127	−	2.44042i	0.466597	−	0.207742i
$139$	−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
$141$	7.75169	−	3.45127i	0.652810	−	0.290650i
$142$	3.76988	−	0.801313i	0.316361	−	0.0672447i
$143$	10.8815	+	2.31294i	0.909958	+	0.193417i
$144$	−20.1295	−	8.96221i	−1.67746	−	0.746851i
$145$	−0.808231	+	0.897632i	−0.0671199	+	0.0745443i
$146$	−1.16104	+	11.0465i	−0.0960881	+	0.914217i
$147$	−4.24264	−	3.08246i	−0.349927	−	0.254237i
$148$	−2.15268	−	20.4814i	−0.176949	−	1.68356i
$149$	6.70820	−	11.6190i	0.549557	−	0.951861i	−0.448747	−	0.893659i	$-0.648130\pi$
$149$	6.70820	−	11.6190i	0.549557	−	0.951861i	0.998305	−	0.0582028i	$-0.0185370\pi$
$150$		0			0
$151$	−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	$0.470168\pi$
$152$	4.99983	+	5.55288i	0.405540	+	0.450398i
$153$	−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	$0.787032\pi$
$158$	−2.83888	−	3.15290i	−0.225849	−	0.250831i
$159$	−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
$162$	−0.741125	−	7.05133i	−0.0582282	−	0.554005i
$163$	−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	$0.890966\pi$
$164$	0.746950	−	7.10675i	0.0583270	−	0.554944i
$165$	−5.54829	+	6.16201i	−0.431934	+	0.479711i
$166$	−7.56320	−	3.36735i	−0.587018	−	0.261357i
$167$	1.05675	+	0.224620i	0.0817741	+	0.0173816i	0.248617	−	0.968602i	$-0.420024\pi$
$167$	1.05675	+	0.224620i	0.0817741	+	0.0173816i	−0.166843	+	0.985983i	$0.553357\pi$
$168$	−6.38817	+	1.35785i	−0.492858	+	0.104760i
$169$	−5.59511	+	2.49110i	−0.430393	+	0.191623i
$170$	6.69781	−	20.6137i	0.513699	−	1.58100i
$171$	−0.690983	+	2.12663i	−0.0528408	+	0.162627i
$172$	−42.9838	+	19.1376i	−3.27748	+	1.45923i
$173$	−17.6067	+	3.74241i	−1.33861	+	0.284530i	−0.820922	−	0.571040i	$-0.806540\pi$
$173$	−17.6067	+	3.74241i	−1.33861	+	0.284530i	−0.517687	+	0.855570i	$0.673207\pi$
$174$	−1.20906	−	0.256993i	−0.0916584	−	0.0194826i
$175$		0			0
$176$	27.9746	−	31.0690i	2.10867	−	2.34191i
$177$	1.09124	−	10.3825i	0.0820229	−	0.780395i
$178$	32.5119	+	23.6212i	2.43687	+	1.77049i
$179$	−1.38689	−	13.1954i	−0.103661	−	0.986272i	−0.915480	−	0.402363i	$-0.868189\pi$
$179$	−1.38689	−	13.1954i	−0.103661	−	0.986272i	0.811819	−	0.583909i	$-0.198478\pi$
$180$	12.1353	−	21.0189i	0.904508	−	1.56665i
$181$	−4.34581	−	7.52716i	−0.323021	−	0.559489i	0.658089	−	0.752940i	$-0.271365\pi$
$181$	−4.34581	−	7.52716i	−0.323021	−	0.559489i	−0.981110	+	0.193451i	$0.938032\pi$
$182$	−5.55369	+	4.03499i	−0.411667	+	0.299093i
$183$	−8.15024	−	9.05176i	−0.602483	−	0.669125i
$184$	−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
$189$	−3.06227	−	3.40100i	−0.222747	−	0.247386i
$190$	−4.73607	+	3.44095i	−0.343590	+	0.249633i
$191$	−4.88197	−	8.45581i	−0.353247	−	0.611841i	0.633570	−	0.773686i	$-0.281589\pi$
$191$	−4.88197	−	8.45581i	−0.353247	−	0.611841i	−0.986816	+	0.161845i	$0.948256\pi$
$192$	3.80562	−	6.59154i	0.274647	−	0.475703i
$193$	2.16460	+	20.5948i	0.155811	+	1.48244i	0.740977	+	0.671530i	$0.234363\pi$
$193$	2.16460	+	20.5948i	0.155811	+	1.48244i	−0.585166	+	0.810913i	$0.698971\pi$
$194$	14.8262	+	10.7719i	1.06446	+	0.773377i
$195$	−0.535668	+	5.09654i	−0.0383600	+	0.364971i
$196$	−19.4882	+	21.6438i	−1.39201	+	1.54599i
$197$	−0.986961	−	0.439423i	−0.0703180	−	0.0313076i	0.371276	−	0.928522i	$-0.378920\pi$
$197$	−0.986961	−	0.439423i	−0.0703180	−	0.0313076i	−0.441594	+	0.897215i	$0.645587\pi$
$198$	24.2941	+	5.16387i	1.72651	+	0.366980i
$199$	−22.7090	+	4.82694i	−1.60980	+	0.342173i	−0.923037	−	0.384712i	$-0.874301\pi$
$199$	−22.7090	+	4.82694i	−1.60980	+	0.342173i	−0.686760	+	0.726884i	$0.740968\pi$
$200$		0			0
$201$	−1.62054	+	4.98752i	−0.114304	+	0.351793i
$202$	1.80902	−	5.56758i	0.127282	−	0.391734i
$203$	0.493480	−	0.219712i	0.0346355	−	0.0154207i
$204$	15.3649	−	3.26592i	1.07576	−	0.228660i
$205$	3.21986	+	0.684403i	0.224885	+	0.0478008i
$206$	25.6107	+	11.4026i	1.78438	+	0.794459i
$207$	3.92324	−	4.35720i	0.272684	−	0.302846i
$208$	2.70085	−	25.6969i	0.187270	−	1.78176i
$209$	−3.43237	−	2.49376i	−0.237422	−	0.172497i
$210$	−0.534838	−	5.08864i	−0.0369073	−	0.351150i
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	33.3221	+	57.7156i	2.28857	+	3.96393i
$213$	−1.04096	+	0.756300i	−0.0713252	+	0.0518208i
$214$	2.57890	+	2.86416i	0.176290	+	0.195790i
$215$	−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
$220$	30.8135	+	34.2219i	2.07745	+	2.30724i
$221$	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	0.458288	+	0.888804i	$0.348463\pi$
$223$	−8.07262	+	13.9822i	−0.540583	+	0.936316i	−0.998871	+	0.0475128i	$0.984871\pi$
$224$	1.13456	+	10.7946i	0.0758062	+	0.721247i
$225$		0			0
$226$	2.67199	−	25.4223i	0.177738	−	1.69106i
$227$	1.53351	−	1.70314i	0.101783	−	0.113041i	−0.690101	−	0.723713i	$-0.742434\pi$
$227$	1.53351	−	1.70314i	0.101783	−	0.113041i	0.791884	+	0.610672i	$0.209101\pi$
$228$	−3.87585	−	1.72564i	−0.256684	−	0.114283i
$229$	−4.14993	−	0.882095i	−0.274235	−	0.0582905i	0.0687412	−	0.997635i	$-0.478102\pi$
$229$	−4.14993	−	0.882095i	−0.274235	−	0.0582905i	−0.342976	+	0.939344i	$0.611435\pi$
$230$	15.0146	−	3.19145i	0.990032	−	0.210438i
$231$	3.38761	−	1.50826i	0.222889	−	0.0992364i
$232$	−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	$0.954519\pi$
$234$	14.0229	−	6.24341i	0.916708	−	0.408145i
$235$	21.2338	−	4.51339i	1.38514	−	0.294421i
$236$	−56.7117	−	12.0545i	−3.69162	−	0.784678i
$237$	1.29395	+	0.576105i	0.0840513	+	0.0374220i
$238$	−6.48599	+	7.20342i	−0.420424	+	0.466929i
$239$	−1.26573	+	12.0426i	−0.0818731	+	0.778971i	0.874145	+	0.485664i	$0.161422\pi$
$239$	−1.26573	+	12.0426i	−0.0818731	+	0.778971i	−0.956018	+	0.293306i	$0.905244\pi$
$240$	15.5807	+	11.3200i	1.00573	+	0.730706i
$241$	2.42676	+	23.0891i	0.156322	+	1.48730i	0.738507	+	0.674245i	$0.235531\pi$
$241$	2.42676	+	23.0891i	0.156322	+	1.48730i	−0.582186	+	0.813056i	$0.697802\pi$
$242$	−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
$245$	−8.97733	−	9.97033i	−0.573541	−	0.636981i
$246$	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
$251$	7.37955	+	8.19582i	0.465793	+	0.517316i	0.929575	−	0.368634i	$-0.120174\pi$
$251$	7.37955	+	8.19582i	0.465793	+	0.517316i	−0.463782	+	0.885950i	$0.653508\pi$
$252$	−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
$255$	0.756375	+	7.19643i	0.0473660	+	0.450658i
$256$	11.7812	+	8.55951i	0.736322	+	0.534969i
$257$	−0.632996	+	6.02255i	−0.0394852	+	0.375677i	0.956879	+	0.290485i	$0.0938168\pi$
$257$	−0.632996	+	6.02255i	−0.0394852	+	0.375677i	−0.996365	+	0.0851912i	$0.972850\pi$
$258$	14.8415	−	16.4832i	0.923994	−	1.02620i
$259$	−3.87585	−	1.72564i	−0.240833	−	0.107226i
$260$	27.8386	+	5.91727i	1.72647	+	0.366974i
$261$	−1.18149	+	0.251133i	−0.0731322	+	0.0155447i
$262$	17.7378	−	7.89736i	1.09584	−	0.487901i
$263$	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
$265$	−28.0459	+	12.4868i	−1.72284	+	0.767060i
$266$	2.56082	−	0.544320i	0.157014	−	0.0333744i
$267$	−13.1232	−	2.78943i	−0.803128	−	0.170710i
$268$	26.6067	+	11.8460i	1.62526	+	0.723612i
$269$	1.44581	−	1.60573i	0.0881525	−	0.0979032i	−0.697455	−	0.716629i	$-0.745684\pi$
$269$	1.44581	−	1.60573i	0.0881525	−	0.0979032i	0.785607	+	0.618726i	$0.212351\pi$
$270$	−2.80045	+	26.6445i	−0.170430	+	1.62153i
$271$	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	$0.509006\pi$
$272$	−3.81366	−	36.2845i	−0.231237	−	2.20007i
$273$	1.14590	−	1.98475i	0.0693529	−	0.120123i
$274$	3.43237	+	5.94504i	0.207357	+	0.359153i
$275$		0			0
$276$	7.44382	+	8.26720i	0.448065	+	0.497627i
$277$	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	$0.769525\pi$
$282$	14.8646	+	16.5088i	0.885172	+	0.983084i
$283$	−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
$286$	3.04435	+	28.9651i	0.180016	+	1.71274i
$287$	−1.19098	−	0.865300i	−0.0703015	−	0.0510770i
$288$	2.53696	−	24.1376i	0.149492	−	1.42232i
$289$	−2.20264	+	2.44628i	−0.129567	+	0.143899i
$290$	−2.88888	−	1.28621i	−0.169641	−	0.0755291i
$291$	−5.98453	−	1.27205i	−0.350819	−	0.0745689i
$292$	−20.1442	+	4.28178i	−1.17885	+	0.250572i
$293$	−2.09366	+	0.932157i	−0.122313	+	0.0544572i	−0.466981	−	0.884268i	$-0.654658\pi$
$293$	−2.09366	+	0.932157i	−0.122313	+	0.0544572i	0.344668	+	0.938725i	$0.387992\pi$
$294$	4.24264	−	13.0575i	0.247436	−	0.761529i
$295$	8.25329	−	25.4010i	0.480525	−	1.47890i
$296$	28.9608	−	12.8942i	1.68331	−	0.749460i
$297$	−18.9921	+	4.03690i	−1.10203	+	0.234245i
$298$	34.3571	+	7.30282i	1.99025	+	0.423041i
$299$	6.28098	+	2.79647i	0.363238	+	0.161724i
$300$		0			0
$301$	−1.01321	+	9.64006i	−0.0584005	+	0.555644i
$302$	−26.5212	−	19.2687i	−1.52612	−	1.10879i
$303$	0.204290	+	1.94369i	0.0117361	+	0.111662i
$304$	−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
$307$	16.1425	+	17.9281i	0.921302	+	1.02321i	0.999655	+	0.0262839i	$0.00836738\pi$
$307$	16.1425	+	17.9281i	0.921302	+	1.02321i	−0.0783525	+	0.996926i	$0.524966\pi$
$308$	−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
$313$	−7.70841	−	8.56106i	−0.435705	−	0.483900i	0.484803	−	0.874624i	$-0.338891\pi$
$313$	−7.70841	−	8.56106i	−0.435705	−	0.483900i	−0.920508	+	0.390724i	$0.872225\pi$
$314$	−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
$317$	−2.74242	−	26.0923i	−0.154029	−	1.46549i	−0.749441	−	0.662071i	$-0.769678\pi$
$317$	−2.74242	−	26.0923i	−0.154029	−	1.46549i	0.595412	−	0.803421i	$-0.296989\pi$
$318$	−25.4164	−	18.4661i	−1.42528	−	1.03553i
$319$	0.239558	−	2.27924i	0.0134127	−	0.127613i
$320$	13.0294	−	14.4706i	0.728366	−	0.808932i
$321$	−1.17545	−	0.523346i	−0.0656074	−	0.0292103i
$322$	−6.71473	−	1.42726i	−0.374197	−	0.0795380i
$323$	−3.62155	+	0.769785i	−0.201509	+	0.0428320i
$324$	12.0094	−	5.34692i	0.667188	−	0.297051i
$325$		0			0
$326$	11.6631	−	35.8954i	0.645960	−	1.98806i
$327$	1.03146	−	0.459235i	0.0570397	−	0.0253957i
$328$	10.7596	−	2.28703i	0.594101	−	0.126280i
$329$	−9.49606	−	2.01845i	−0.523535	−	0.111281i
$330$	−19.8314	−	8.82952i	−1.09168	−	0.486049i
$331$	20.9364	−	23.2522i	1.15077	−	1.27806i	0.196033	−	0.980597i	$-0.437194\pi$
$331$	20.9364	−	23.2522i	1.15077	−	1.27806i	0.954734	−	0.297459i	$-0.0961393\pi$
$332$	1.60451	−	15.2659i	0.0880591	−	0.837827i
$333$	7.67501	+	5.57622i	0.420588	+	0.305575i
$334$	0.295651	+	2.81293i	0.0161773	+	0.153917i
$335$	−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	$0.162702\pi$
$338$	−10.7291	−	11.9159i	−0.583588	−	0.648140i
$339$	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
$344$	−48.4642	−	53.8250i	−2.61302	−	2.90205i
$345$	−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	−0.415857	−	0.909430i	$-0.636518\pi$
$347$	10.7979	−	18.7025i	0.579661	−	1.00400i	0.995518	−	0.0945718i	$-0.0301482\pi$
$348$	−0.239558	−	2.27924i	−0.0128417	−	0.122180i
$349$	−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
$351$	−8.02957	+	8.91774i	−0.428587	+	0.475994i
$352$	42.0688	+	18.7302i	2.24228	+	0.998325i
$353$	−9.35661	−	1.98881i	−0.498002	−	0.105854i	−0.0479389	−	0.998850i	$-0.515265\pi$
$353$	−9.35661	−	1.98881i	−0.498002	−	0.105854i	−0.450063	+	0.892997i	$0.648599\pi$
$354$	26.7342	−	5.68252i	1.42091	−	0.302023i
$355$	−3.00721	+	1.33889i	−0.159606	+	0.0710611i
$356$	−23.0250	+	70.8637i	−1.22032	+	3.75577i
$357$	1.00000	−	3.07768i	0.0529256	−	0.162888i
$358$	31.7332	−	14.1285i	1.67715	−	0.746717i
$359$	−13.9250	+	2.95984i	−0.734932	+	0.156215i	−0.560148	−	0.828392i	$-0.689256\pi$
$359$	−13.9250	+	2.95984i	−0.734932	+	0.156215i	−0.174784	+	0.984607i	$0.555923\pi$
$360$	36.5443	+	7.76772i	1.92605	+	0.409395i
$361$	−16.4438	−	7.32126i	−0.865464	−	0.385329i
$362$	15.2260	−	16.9102i	0.800262	−	0.888781i
$363$	0.639529	−	6.08471i	0.0335665	−	0.319364i
$364$	−10.2971	−	7.48128i	−0.539715	−	0.392126i
$365$	−0.991644	−	9.43486i	−0.0519050	−	0.493843i
$366$	15.9443	−	27.6163i	0.833420	−	1.44353i
$367$	−3.32920	−	5.76635i	−0.173783	−	0.301001i	0.765956	−	0.642892i	$-0.222266\pi$
$367$	−3.32920	−	5.76635i	−0.173783	−	0.301001i	−0.939739	+	0.341892i	$0.888932\pi$
$368$	20.9037	−	15.1874i	1.08968	−	0.791700i
$369$	2.20264	+	2.44628i	0.114665	+	0.127348i
$370$	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
$375$	6.53873	+	7.26199i	0.337658	+	0.375008i
$376$	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
$379$	−0.775226	−	7.37578i	−0.0398207	−	0.378868i	−0.996224	−	0.0868195i	$-0.972330\pi$
$379$	−0.775226	−	7.37578i	−0.0398207	−	0.378868i	0.956403	−	0.292049i	$-0.0943370\pi$
$380$	−8.78115	−	6.37988i	−0.450464	−	0.327281i
$381$	−0.866729	+	8.24637i	−0.0444039	+	0.422474i
$382$	17.1045	−	18.9965i	0.875143	−	0.971945i
$383$	−5.84977	−	2.60448i	−0.298909	−	0.133083i	0.251802	−	0.967779i	$-0.418977\pi$
$383$	−5.84977	−	2.60448i	−0.298909	−	0.133083i	−0.550711	+	0.834696i	$0.685643\pi$
$384$	0.932022	+	0.198107i	0.0475620	+	0.0101096i
$385$	9.27952	−	1.97242i	0.472928	−	0.100524i
$386$	−49.5277	+	22.0511i	−2.52089	+	1.12237i
$387$	6.69781	−	20.6137i	0.340469	−	1.04786i
$388$	−10.5000	+	32.3157i	−0.533057	+	1.64058i
$389$	−15.3594	+	6.83844i	−0.778752	+	0.346723i	−0.757317	−	0.653048i	$-0.773490\pi$
$389$	−15.3594	+	6.83844i	−0.778752	+	0.346723i	−0.0214349	+	0.999770i	$0.506823\pi$
$390$	−13.1232	+	2.78943i	−0.664520	+	0.141248i
$391$	9.49606	+	2.01845i	0.480236	+	0.102077i
$392$	−40.9568	−	18.2351i	−2.06863	−	0.921014i
$393$	−4.33742	+	4.81720i	−0.218794	+	0.242995i
$394$	0.295651	−	2.81293i	0.0148947	−	0.141714i
$395$	2.93159	+	2.12993i	0.147504	+	0.107168i
$396$	4.81354	+	45.7978i	0.241890	+	2.30143i
$397$	−7.35410	+	12.7377i	−0.369092	+	0.639286i	−0.989424	−	0.145054i	$-0.953665\pi$
$397$	−7.35410	+	12.7377i	−0.369092	+	0.639286i	0.620332	+	0.784339i	$0.286998\pi$
$398$	−30.3905	−	52.6380i	−1.52334	−	2.63850i
$399$	−0.707107	+	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
$406$	0.946294	+	1.05097i	0.0469638	+	0.0521585i
$407$	−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	0.207091	+	0.978322i	$0.433600\pi$
$409$	−15.0405	+	26.0509i	−0.743706	+	1.28814i	−0.950797	+	0.309815i	$0.899733\pi$
$410$	0.900830	+	8.57082i	0.0444888	+	0.423283i
$411$	−1.85410	−	1.34708i	−0.0914561	−	0.0664468i
$412$	−5.43326	+	51.6940i	−0.267677	+	2.54678i
$413$	−7.99228	+	8.87632i	−0.393274	+	0.436775i
$414$	14.0229	+	6.24341i	0.689190	+	0.306847i
$415$	6.91655	+	1.47016i	0.339520	+	0.0721672i
$416$	27.8386	−	5.91727i	1.36490	−	0.290118i
$417$	14.3502	−	6.38910i	0.702730	−	0.312876i
$418$	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	$-0.168686\pi$
$420$	8.66665	−	3.85864i	0.422889	−	0.188282i
$421$	−25.8391	+	5.49228i	−1.25932	+	0.267677i	−0.788767	−	0.614693i	$-0.789280\pi$
$421$	−25.8391	+	5.49228i	−1.25932	+	0.267677i	−0.470556	+	0.882370i	$0.655947\pi$
$422$	12.8041	+	2.72160i	0.623295	+	0.132485i
$423$	19.8314	+	8.82952i	0.964237	+	0.429306i
$424$	−68.6451	+	76.2381i	−3.33370	+	3.70245i
$425$		0			0
$426$	−2.72526	−	1.98002i	−0.132039	−	0.0959322i
$427$	1.45669	+	13.8595i	0.0704941	+	0.670706i
$428$	−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
$431$	−24.0141	−	26.6704i	−1.15672	−	1.28467i	−0.952087	−	0.305829i	$-0.901067\pi$
$431$	−24.0141	−	26.6704i	−1.15672	−	1.28467i	−0.204633	−	0.978839i	$-0.565600\pi$
$432$	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
$437$	−1.75452	−	1.94860i	−0.0839303	−	0.0932140i
$438$	7.85410	−	5.70634i	0.375284	−	0.272659i
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	−35.4435	+	61.3899i	−1.68970	+	2.92665i
$441$	−1.40240	−	13.3429i	−0.0667808	−	0.635377i
$442$	20.5623	+	14.9394i	0.978049	+	0.710594i
$443$	−0.632996	+	6.02255i	−0.0300745	+	0.286140i	0.969140	+	0.246511i	$0.0792842\pi$
$443$	−0.632996	+	6.02255i	−0.0300745	+	0.286140i	−0.999214	+	0.0396289i	$0.987382\pi$
$444$	−12.0444	+	13.3766i	−0.571600	+	0.634826i
$445$	−31.3562	−	13.9607i	−1.48643	−	0.661801i
$446$	−41.3451	−	8.78817i	−1.95775	−	0.416132i
$447$	−11.4701	+	2.43805i	−0.542518	+	0.115316i
$448$	−7.95534	+	3.54195i	−0.375854	+	0.167341i
$449$	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
$451$	−5.70577	+	2.54037i	−0.268674	+	0.119621i
$452$	46.3594	−	9.85400i	2.18056	−	0.463493i
$453$	10.7051	+	2.27544i	0.502970	+	0.106910i
$454$	5.48127	+	2.44042i	0.257249	+	0.114535i
$455$	3.92324	−	4.35720i	0.183924	−	0.204268i
$456$	0.682664	−	6.49511i	0.0319686	−	0.304161i
$457$	−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	$0.785245\pi$
$458$	−1.16104	−	11.0465i	−0.0542517	−	0.516170i
$459$	−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	$0.338382\pi$
$462$	6.49606	+	7.21460i	0.302224	+	0.335654i
$463$	−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	$-0.217959\pi$
$468$	19.0438	+	21.1503i	0.880300	+	0.977672i
$469$	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
$472$	−9.32908	−	88.7603i	−0.429406	−	4.08552i
$473$	33.2705	+	24.1724i	1.52978	+	1.11145i
$474$	−0.387613	+	3.68789i	−0.0178036	+	0.169390i
$475$		0			0
$476$	−16.4183	−	7.30992i	−0.752534	−	0.335050i
$477$	−30.0292	−	6.38290i	−1.37494	−	0.292253i
$478$	−31.0088	+	6.59113i	−1.41831	+	0.301471i
$479$	15.0990	−	6.72249i	0.689889	−	0.307158i	−0.0316829	−	0.999498i	$-0.510087\pi$
$479$	15.0990	−	6.72249i	0.689889	−	0.307158i	0.721572	+	0.692340i	$0.243420\pi$
$480$	−6.55524	+	20.1750i	−0.299204	+	0.920857i
$481$	−3.43769	+	10.5801i	−0.156745	+	0.482413i
$482$	−55.5263	+	24.7219i	−2.52915	+	1.12605i
$483$	2.24171	−	0.476491i	0.102002	−	0.0216811i
$484$	−33.2362	−	7.06457i	−1.51074	−	0.321117i
$485$	−14.2992	−	6.36644i	−0.649295	−	0.289085i
$486$	−28.1980	+	31.3171i	−1.27909	+	1.42057i
$487$	−2.93494	+	27.9241i	−0.132995	+	1.26536i	0.700828	+	0.713331i	$0.252814\pi$
$487$	−2.93494	+	27.9241i	−0.132995	+	1.26536i	−0.833823	+	0.552032i	$0.813852\pi$
$488$	−84.2431	−	61.2062i	−3.81351	−	2.77068i
$489$	1.31710	+	12.5314i	0.0595614	+	0.566688i
$490$	17.5623	−	30.4188i	0.793384	−	1.37418i
$491$	7.94510	+	13.7613i	0.358557	+	0.621040i	0.987720	−	0.156234i	$-0.0499354\pi$
$491$	7.94510	+	13.7613i	0.358557	+	0.621040i	−0.629163	+	0.777274i	$0.716602\pi$
$492$	−5.05291	+	3.67116i	−0.227803	+	0.165509i
$493$	−1.33826	−	1.48629i	−0.0602723	−	0.0669391i
$494$	−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
$499$	12.3018	+	13.6626i	0.550705	+	0.611620i	0.952659	−	0.304040i	$-0.0983356\pi$
$499$	12.3018	+	13.6626i	0.550705	+	0.611620i	−0.401954	+	0.915660i	$0.631669\pi$
$500$	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
$503$	3.43779	+	32.7084i	0.153283	+	1.45839i	0.752915	+	0.658118i	$0.228647\pi$
$503$	3.43779	+	32.7084i	0.153283	+	1.45839i	−0.599631	+	0.800276i	$0.704686\pi$
$504$	−13.5172	−	9.82084i	−0.602105	−	0.437455i
$505$	−0.522642	+	4.97261i	−0.0232573	+	0.221278i
$506$	−19.4882	+	21.6438i	−0.866355	+	0.962184i
$507$	4.89031	+	2.17730i	0.217186	+	0.0966975i
$508$	45.0438	+	9.57434i	1.99849	+	0.424793i
$509$	7.77148	−	1.65188i	0.344465	−	0.0732183i	−0.0324308	−	0.999474i	$-0.510325\pi$
$509$	7.77148	−	1.65188i	0.344465	−	0.0732183i	0.376896	+	0.926256i	$0.376992\pi$
$510$	−17.3065	+	7.70533i	−0.766343	+	0.341198i
$511$	−1.31105	+	4.03499i	−0.0579974	+	0.178497i
$512$	−12.4549	+	38.3323i	−0.550435	+	1.69406i
$513$	4.18083	−	1.86143i	0.184588	−	0.0821840i
$514$	−15.5077	+	3.29625i	−0.684013	+	0.145391i
$515$	−23.4210	−	4.97829i	−1.03205	−	0.219370i
$516$	37.5692	+	16.7269i	1.65389	+	0.736360i
$517$	−27.5604	+	30.6090i	−1.21211	+	1.34618i
$518$	1.16104	−	11.0465i	0.0510130	−	0.485357i
$519$	12.7279	+	9.24738i	0.558694	+	0.405915i
$520$	4.57945	+	43.5705i	0.200822	+	1.91069i
$521$	6.70820	−	11.6190i	0.293892	−	0.509035i	−0.680835	−	0.732437i	$-0.738383\pi$
$521$	6.70820	−	11.6190i	0.293892	−	0.509035i	0.974726	+	0.223402i	$0.0717161\pi$
$522$	−1.58114	−	2.73861i	−0.0692046	−	0.119866i
$523$	−0.500776	+	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	$0.304308\pi$
$524$	24.0887	+	26.7532i	1.05232	+	1.16872i
$525$		0			0
$526$	48.4658			2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	−4.98278	−	15.3354i	−0.216643	−	0.666757i
$530$	−53.7805	−	59.7293i	−2.33608	−	2.59448i
$531$	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
$534$	−3.67152	−	34.9322i	−0.158882	−	1.51166i
$535$	−2.66312	−	1.93487i	−0.115137	−	0.0836517i
$536$	−4.68631	+	44.5872i	−0.202418	+	1.92587i
$537$	−7.75974	+	8.61806i	−0.334857	+	0.371897i
$538$	5.16779	+	2.30085i	0.222799	+	0.0991967i
$539$	24.8996	+	5.29257i	1.07250	+	0.227967i
$540$	−48.5882	+	10.3277i	−2.09090	+	0.444435i
$541$	23.5995	−	10.5072i	1.01462	−	0.451738i	0.169053	−	0.985607i	$-0.445929\pi$
$541$	23.5995	−	10.5072i	1.01462	−	0.451738i	0.845567	+	0.533869i	$0.179263\pi$
$542$	−15.0405	+	46.2900i	−0.646046	+	1.98832i
$543$	−2.34752	+	7.22494i	−0.100742	+	0.310052i
$544$	36.7125	−	16.3455i	1.57404	−	0.700806i
$545$	2.82542	−	0.600562i	0.121028	−	0.0257253i
$546$	5.86889	+	1.24747i	0.251165	+	0.0533868i
$547$	2.20750	+	0.982842i	0.0943858	+	0.0420233i	0.453386	−	0.891314i	$-0.350216\pi$
$547$	2.20750	+	0.982842i	0.0943858	+	0.0420233i	−0.359001	+	0.933337i	$0.616882\pi$
$548$	−8.51664	+	9.45869i	−0.363813	+	0.404055i
$549$	3.25725	−	30.9907i	0.139016	−	1.32265i
$550$		0			0
$551$	0.0564643	+	0.537222i	0.00240546	+	0.0228864i
$552$	−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
$555$	−5.54829	−	6.16201i	−0.235512	−	0.261563i
$556$	−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
$561$	−9.18681	−	10.2030i	−0.387867	−	0.430770i
$562$	−28.2984	+	20.5600i	−1.19369	+	0.867270i
$563$	−4.88197	−	8.45581i	−0.205750	−	0.356370i	0.744621	−	0.667487i	$-0.232630\pi$
$563$	−4.88197	−	8.45581i	−0.205750	−	0.356370i	−0.950372	+	0.311117i	$0.899297\pi$
$564$	−20.5942	+	35.6702i	−0.867173	+	1.50199i
$565$	2.28215	+	21.7132i	0.0960108	+	0.913482i
$566$	−50.8328	−	36.9322i	−2.13666	−	1.55238i
$567$	0.283084	−	2.69337i	0.0118884	−	0.113111i
$568$	−7.36044	+	8.17459i	−0.308837	+	0.342998i
$569$	−10.7126	−	4.76954i	−0.449094	−	0.199950i	0.169711	−	0.985494i	$-0.445716\pi$
$569$	−10.7126	−	4.76954i	−0.449094	−	0.199950i	−0.618806	+	0.785544i	$0.712383\pi$
$570$	5.00486	+	1.06382i	0.209631	+	0.0445584i
$571$	2.56480	−	0.545164i	0.107333	−	0.0228144i	−0.153932	−	0.988081i	$-0.549194\pi$
$571$	2.56480	−	0.545164i	0.107333	−	0.0228144i	0.261265	+	0.965267i	$0.415860\pi$
$572$	−49.3315	+	21.9638i	−2.06265	+	0.918352i
$573$	−2.63715	+	8.11631i	−0.110168	+	0.339064i
$574$	1.19098	−	3.66547i	0.0497107	−	0.152994i
$575$		0			0
$576$	19.0466	−	4.04848i	0.793609	−	0.168687i
$577$	29.3444	+	6.23735i	1.22162	+	0.259664i	0.773203	−	0.634158i	$-0.218653\pi$
$577$	29.3444	+	6.23735i	1.22162	+	0.259664i	0.448421	+	0.893822i	$0.351987\pi$
$578$	−7.87297	−	3.50527i	−0.327472	−	0.145800i
$579$	12.1110	−	13.4506i	0.503317	−	0.558990i
$580$	0.612870	−	5.83107i	0.0254480	−	0.242122i
$581$	−2.55834	−	1.85874i	−0.106138	−	0.0771135i
$582$	−1.67431	−	15.9300i	−0.0694023	−	0.660319i
$583$	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
$586$	−4.01478	−	4.45887i	−0.165849	−	0.184194i
$587$	−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
$592$	27.9746	+	31.0690i	1.14975	+	1.27693i
$593$	−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
$596$	6.80738	+	64.7679i	0.278841	+	2.65299i
$597$	16.4164	+	11.9272i	0.671879	+	0.488149i
$598$	−1.88151	+	17.9014i	−0.0769408	+	0.732042i
$599$	4.05207	−	4.50028i	0.165563	−	0.183877i	−0.654654	−	0.755928i	$-0.727186\pi$
$599$	4.05207	−	4.50028i	0.165563	−	0.183877i	0.820217	+	0.572052i	$0.193852\pi$
$600$		0			0
$601$	−17.7812	−	3.77951i	−0.725310	−	0.154169i	−0.169561	−	0.985520i	$-0.554235\pi$
$601$	−17.7812	−	3.77951i	−0.725310	−	0.154169i	−0.555749	+	0.831350i	$0.687568\pi$
$602$	−24.8225	+	5.27618i	−1.01169	+	0.215041i
$603$	−12.2565	+	5.45694i	−0.499123	+	0.222224i
$604$	18.7824	−	57.8062i	0.764244	−	2.35210i
$605$	4.83688	−	14.8864i	0.196647	−	0.605218i
$606$	−4.67431	+	2.08114i	−0.189881	+	0.0845405i
$607$	−14.7941	+	3.14458i	−0.600474	+	0.127635i	−0.498112	−	0.867113i	$-0.665973\pi$
$607$	−14.7941	+	3.14458i	−0.600474	+	0.127635i	−0.102362	+	0.994747i	$0.532640\pi$
$608$	−10.6169	−	2.25669i	−0.430573	−	0.0915211i
$609$	−0.431318	−	0.192035i	−0.0174779	−	0.00778165i
$610$	54.5888	−	60.6270i	2.21023	−	2.45471i
$611$	−2.66086	+	25.3164i	−0.107647	+	1.02419i
$612$	32.5119	+	23.6212i	1.31421	+	0.954832i
$613$	−0.0615557	−	0.585664i	−0.00248621	−	0.0236547i	0.993208	−	0.116348i	$-0.0371189\pi$
$613$	−0.0615557	−	0.585664i	−0.00248621	−	0.0236547i	−0.995695	+	0.0926937i	$0.970452\pi$
$614$	−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
$617$	−4.60053	−	5.10941i	−0.185210	−	0.205697i	0.643388	−	0.765540i	$-0.277528\pi$
$617$	−4.60053	−	5.10941i	−0.185210	−	0.205697i	−0.828599	+	0.559843i	$0.810861\pi$
$618$	−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
$623$	10.2712	+	11.4073i	0.411506	+	0.457023i
$624$	−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
$627$	0.387613	+	3.68789i	0.0154798	+	0.147280i
$628$	−34.1976	−	24.8460i	−1.36463	−	0.991463i
$629$	−1.64195	+	15.6222i	−0.0654690	+	0.622896i
$630$	8.75903	−	9.72789i	0.348968	−	0.387568i
$631$	−21.5861	−	9.61077i	−0.859331	−	0.382599i	−0.0707234	−	0.997496i	$-0.522531\pi$
$631$	−21.5861	−	9.61077i	−0.859331	−	0.382599i	−0.788607	+	0.614897i	$0.789197\pi$
$632$	11.8443	+	2.51759i	0.471142	+	0.100144i
$633$	−4.27466	+	0.908607i	−0.169903	+	0.0361139i
$634$	62.7486	−	27.9375i	2.49207	−	1.10954i
$635$	−6.55524	+	20.1750i	−0.260137	+	0.800619i
$636$	18.0000	−	55.3983i	0.713746	−	2.19669i
$637$	14.3724	−	6.39902i	0.569456	−	0.253538i
$638$	5.86889	−	1.24747i	0.232351	−	0.0493878i
$639$	−3.21986	−	0.684403i	−0.127376	−	0.0270746i
$640$	2.22694	+	0.991500i	0.0880277	+	0.0391925i
$641$	−5.67776	+	6.30579i	−0.224258	+	0.249064i	−0.844765	−	0.535137i	$-0.820260\pi$
$641$	−5.67776	+	6.30579i	−0.224258	+	0.249064i	0.620507	+	0.784201i	$0.286927\pi$
$642$	0.352115	−	3.35016i	0.0138969	−	0.132220i
$643$	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	$0.670740\pi$
$644$	−1.33043	−	12.6582i	−0.0524263	−	0.498803i
$645$	−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	$0.514782\pi$
$648$	13.5406	+	15.0383i	0.531924	+	0.590761i
$649$	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	$0.739779\pi$
$654$	1.97791	+	2.19670i	0.0773426	+	0.0858976i
$655$	−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
$658$	−2.65674	−	25.2772i	−0.103570	−	0.985407i
$659$	−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	$0.860605\pi$
$660$	4.20719	−	40.0287i	0.163765	−	1.55812i
$661$	5.24118	−	5.82092i	0.203858	−	0.226407i	−0.632543	−	0.774525i	$-0.717989\pi$
$661$	5.24118	−	5.82092i	0.203858	−	0.226407i	0.836401	+	0.548118i	$0.184655\pi$
$662$	74.8335	+	33.3180i	2.90849	+	1.29494i
$663$	−8.29986	−	1.76419i	−0.322340	−	0.0685154i
$664$	23.1126	−	4.91274i	0.896944	−	0.190651i
$665$	−2.04275	+	0.909491i	−0.0792144	+	0.0352685i
$666$	−7.67501	+	23.6212i	−0.297401	+	0.915305i
$667$	0.437694	−	1.34708i	0.0169476	−	0.0521593i
$668$	−4.79081	+	2.13301i	−0.185362	+	0.0825284i
$669$	13.8031	−	2.93394i	0.533658	−	0.113433i
$670$	−34.3571	−	7.30282i	−1.32733	−	0.282132i
$671$	54.0130	+	24.0481i	2.08515	+	0.928368i
$672$	6.34793	−	7.05009i	0.244877	−	0.271963i
$673$	−4.17910	+	39.7615i	−0.161093	+	1.53269i	0.553320	+	0.832969i	$0.313361\pi$
$673$	−4.17910	+	39.7615i	−0.161093	+	1.53269i	−0.714412	+	0.699725i	$0.753306\pi$
$674$	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	$-0.0330168\pi$
$677$	10.6066	+	18.3712i	0.407645	+	0.706062i	−0.586981	+	0.809601i	$0.699683\pi$
$678$	−18.0753	+	13.1325i	−0.694177	+	0.504349i
$679$	4.68391	+	5.20201i	0.179752	+	0.199635i
$680$	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
$685$	−3.92324	−	4.35720i	−0.149899	−	0.166480i
$686$	−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
$689$	−3.76302	−	35.8028i	−0.143360	−	1.36398i
$690$	−10.8541	−	7.88597i	−0.413209	−	0.300214i
$691$	5.06089	−	48.1512i	0.192525	−	1.83176i	−0.291346	−	0.956618i	$-0.594103\pi$
$691$	5.06089	−	48.1512i	0.192525	−	1.83176i	0.483871	−	0.875139i	$-0.339230\pi$
$692$	58.4645	−	64.9314i	2.22249	−	2.46832i
$693$	8.66665	+	3.85864i	0.329219	+	0.146578i
$694$	55.3029	+	11.7550i	2.09927	+	0.446214i
$695$	39.3087	−	8.35532i	1.49106	−	0.316935i
$696$	3.22286	−	1.43491i	0.122162	−	0.0543902i
$697$	−1.68430	+	5.18376i	−0.0637976	+	0.196349i
$698$	4.85410	−	14.9394i	0.183730	−	0.565464i
$699$	10.7571	−	4.78936i	0.406870	−	0.181150i
$700$		0			0
$701$	3.57266	+	0.759392i	0.134938	+	0.0286819i	0.274885	−	0.961477i	$-0.411360\pi$
$701$	3.57266	+	0.759392i	0.134938	+	0.0286819i	−0.139948	+	0.990159i	$0.544693\pi$
$702$	−28.7003	−	12.7782i	−1.08322	−	0.482282i
$703$	2.83888	−	3.15290i	0.107070	−	0.118914i
$704$	−3.86189	+	36.7434i	−0.145550	+	1.38482i
$705$	−15.3500	−	11.1524i	−0.578115	−	0.420025i
$706$	−2.61773	−	24.9060i	−0.0985194	−	0.937349i
$707$	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	$0.0185385\pi$
$710$	−5.76659	−	6.40445i	−0.216416	−	0.240355i
$711$	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
$716$	43.0952	+	47.8620i	1.61054	+	1.78869i
$717$	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	−0.267839	−	0.963464i	$-0.586309\pi$
$719$	18.7824	−	32.5320i	0.700465	−	1.21324i	0.968303	−	0.249777i	$-0.0803573\pi$
$720$	5.15017	+	49.0006i	0.191936	+	1.82614i
$721$	8.66312	+	6.29412i	0.322631	+	0.234405i
$722$	4.92586	−	46.8665i	0.183322	−	1.74419i
$723$	13.5779	−	15.0797i	0.504966	−	0.560822i
$724$	38.5425	+	17.1602i	1.43242	+	0.637754i
$725$		0			0
$726$	15.6677	−	3.33027i	0.581483	−	0.123598i
$727$	−27.7868	+	12.3715i	−1.03055	+	0.458832i	−0.851139	−	0.524941i	$-0.824087\pi$
$727$	−27.7868	+	12.3715i	−1.03055	+	0.458832i	−0.179416	+	0.983773i	$0.557421\pi$
$728$	6.05446	−	18.6337i	0.224393	−	0.690612i
$729$	1.83688	−	5.65334i	0.0680326	−	0.209383i
$730$	22.6896	−	10.1021i	0.839779	−	0.373894i
$731$	35.1043	−	7.46165i	1.29838	−	0.275979i
$732$	57.8326	+	12.2927i	2.13755	+	0.454351i
$733$	−13.1700	−	5.86368i	−0.486447	−	0.216580i	0.148833	−	0.988862i	$-0.452448\pi$
$733$	−13.1700	−	5.86368i	−0.486447	−	0.216580i	−0.635279	+	0.772282i	$0.719115\pi$
$734$	11.6642	−	12.9545i	0.430535	−	0.478158i
$735$	−1.22574	+	11.6621i	−0.0452121	+	0.430164i
$736$	23.0250	+	16.7287i	0.848714	+	0.616627i
$737$	−2.66086	−	25.3164i	−0.0980140	−	0.932541i
$738$	−4.30902	+	7.46344i	−0.158617	+	0.274733i
$739$	17.5745	+	30.4399i	0.646489	+	1.11975i	0.983956	+	0.178414i	$0.0570965\pi$
$739$	17.5745	+	30.4399i	0.646489	+	1.11975i	−0.337467	+	0.941337i	$0.609570\pi$
$740$	−37.2553	+	27.0675i	−1.36953	+	0.995023i
$741$	1.53351	+	1.70314i	0.0563349	+	0.0625663i
$742$	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
$747$	4.73147	+	5.25483i	0.173115	+	0.192264i
$748$	−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
$751$	3.92411	+	37.3354i	0.143193	+	1.36239i	0.796199	+	0.605035i	$0.206841\pi$
$751$	3.92411	+	37.3354i	0.143193	+	1.36239i	−0.653007	+	0.757352i	$0.726493\pi$
$752$	77.3951	+	56.2308i	2.82231	+	2.05053i
$753$	1.00758	−	9.58652i	0.0367184	−	0.349352i
$754$	2.48127	−	2.75573i	0.0903626	−	0.100358i
$755$	25.5785	+	11.3883i	0.930896	+	0.414462i
$756$	21.7293	+	4.61871i	0.790287	+	0.167981i
$757$	−9.07770	+	1.92952i	−0.329935	+	0.0701298i	−0.369901	−	0.929071i	$-0.620608\pi$
$757$	−9.07770	+	1.92952i	−0.329935	+	0.0701298i	0.0399661	+	0.999201i	$0.487275\pi$
$758$	17.7378	−	7.89736i	0.644265	−	0.286845i
$759$	3.00465	−	9.24738i	0.109062	−	0.335659i
$760$	5.16312	−	15.8904i	0.187286	−	0.576407i
$761$	36.7125	−	16.3455i	1.33083	−	0.592523i	0.386732	−	0.922192i	$-0.373604\pi$
$761$	36.7125	−	16.3455i	1.33083	−	0.592523i	0.944096	+	0.329669i	$0.106937\pi$
$762$	−21.2338	+	4.51339i	−0.769220	+	0.163503i
$763$	−1.26357	−	0.268580i	−0.0457442	−	0.00972323i
$764$	43.2976	+	19.2773i	1.56645	+	0.697429i
$765$	−12.3871	+	13.7573i	−0.447858	+	0.497397i
$766$	1.75234	−	16.6724i	0.0633146	−	0.602398i
$767$	25.3376	+	18.4089i	0.914889	+	0.664706i
$768$	−1.33043	−	12.6582i	−0.0480078	−	0.456763i
$769$	−27.0623	+	46.8733i	−0.975892	+	1.69029i	−0.298931	+	0.954275i	$0.596630\pi$
$769$	−27.0623	+	46.8733i	−0.975892	+	1.69029i	−0.676960	+	0.736019i	$0.736703\pi$
$770$	12.4184	+	21.5093i	0.447529	+	0.775143i
$771$	4.28205	−	3.11109i	0.154214	−	0.112043i
$772$	−67.2608	−	74.7007i	−2.42077	−	2.68854i
$773$	−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
$778$	−29.4530	−	32.7109i	−1.05594	−	1.17274i
$779$	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
$782$	2.65674	+	25.2772i	0.0950048	+	0.903910i
$783$	2.00000	+	1.45309i	0.0714742	+	0.0519290i
$784$	6.18020	−	58.8007i	0.220722	−	2.10003i
$785$	13.0294	−	14.4706i	0.465039	−	0.516478i
$786$	−15.5034	−	6.90255i	−0.552987	−	0.246206i
$787$	36.7439	+	7.81016i	1.30978	+	0.278402i	0.809325	−	0.587361i	$-0.199833\pi$
$787$	36.7439	+	7.81016i	1.30978	+	0.278402i	0.500454	+	0.865763i	$0.333167\pi$
$788$	5.12959	−	1.09033i	0.182734	−	0.0388414i
$789$	−14.7815	+	6.58114i	−0.526234	+	0.234295i
$790$	−2.93159	+	9.02251i	−0.104301	+	0.321007i
$791$	3.01722	−	9.28605i	0.107280	−	0.330174i
$792$	−64.7584	+	28.8323i	−2.30109	+	1.02451i
$793$	35.7425	−	7.59731i	1.26925	−	0.269788i
$794$	−37.6651	−	8.00597i	−1.33668	−	0.284121i
$795$	24.5130	+	10.9139i	0.869386	+	0.387076i
$796$	75.4072	−	83.7482i	2.67274	−	2.96838i
$797$	1.43512	−	13.6543i	0.0508346	−	0.483659i	−0.939255	−	0.343221i	$-0.888482\pi$
$797$	1.43512	−	13.6543i	0.0508346	−	0.483659i	0.990089	−	0.140438i	$-0.0448512\pi$
$798$	−1.85123	−	1.34500i	−0.0655328	−	0.0476124i
$799$	3.75719	+	35.7473i	0.132920	+	1.26465i
$800$		0			0
$801$	−17.1618	−	29.7252i	−0.606384	−	1.05029i
$802$	1.14412	−	0.831254i	0.0404004	−	0.0293526i
$803$	12.0444	+	13.3766i	0.425036	+	0.472050i
$804$	−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
$809$	31.7924	+	35.3090i	1.11776	+	1.24140i	0.967532	+	0.252748i	$0.0813343\pi$
$809$	31.7924	+	35.3090i	1.11776	+	1.24140i	0.150229	+	0.988651i	$0.451999\pi$
$810$	−12.8262	+	9.31881i	−0.450668	+	0.327430i
$811$	8.29180	+	14.3618i	0.291164	+	0.504311i	0.974085	−	0.226181i	$-0.0726240\pi$
$811$	8.29180	+	14.3618i	0.291164	+	0.504311i	−0.682921	+	0.730492i	$0.739291\pi$
$812$	−1.31105	+	2.27080i	−0.0460088	+	0.0796895i
$813$	−1.69851	−	16.1602i	−0.0595692	−	0.566763i
$814$	−38.1246	−	27.6992i	−1.33627	−	0.970855i
$815$	−3.36959	+	32.0595i	−0.118031	+	1.12299i
$816$	−21.3376	+	23.6978i	−0.746965	+	0.829589i
$817$	−8.85515	−	3.94256i	−0.309802	−	0.137933i
$818$	−77.0322	−	16.3737i	−2.69337	−	0.572493i
$819$	5.73506	−	1.21902i	0.200399	−	0.0425962i
$820$	−14.5973	+	6.49913i	−0.509759	+	0.226959i
$821$	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
$823$	−12.3540	+	5.50036i	−0.430634	+	0.191730i	−0.610595	−	0.791943i	$-0.709069\pi$
$823$	−12.3540	+	5.50036i	−0.430634	+	0.191730i	0.179961	+	0.983674i	$0.442403\pi$
$824$	−78.2647	+	16.6357i	−2.72648	+	0.579531i
$825$		0			0
$826$	−28.5670	−	12.7189i	−0.993974	−	0.442546i
$827$	−12.2817	+	13.6402i	−0.427076	+	0.474316i	−0.917825	−	0.396985i	$-0.870056\pi$
$827$	−12.2817	+	13.6402i	−0.427076	+	0.474316i	0.490749	+	0.871301i	$0.336723\pi$
$828$	−2.97493	+	28.3046i	−0.103386	+	0.983652i
$829$	−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	$-0.647338\pi$
$830$	1.93506	+	18.4109i	0.0671670	+	0.639051i
$831$	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
$834$	27.5177	+	30.5615i	0.952861	+	1.05826i
$835$	−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	$-0.208792\pi$
$840$	9.77165	+	10.8525i	0.337154	+	0.374448i
$841$	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
$844$	2.53696	+	24.1376i	0.0873257	+	0.830849i
$845$	11.0795	+	8.04975i	0.381147	+	0.276920i
$846$	−5.94065	+	56.5215i	−0.204244	+	1.94325i
$847$	−4.68391	+	5.20201i	−0.160941	+	0.178743i
$848$	−123.595	−	55.0281i	−4.24427	−	1.88967i
$849$	20.5184	+	4.36132i	0.704189	+	0.149680i
$850$		0			0
$851$	−10.1628	+	4.52479i	−0.348378	+	0.155108i
$852$	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	$0.913550\pi$
$854$	−33.3302	+	14.8395i	−1.14053	+	0.507799i
$855$	4.89074	−	1.03956i	0.167260	−	0.0355521i
$856$	−10.7596	−	2.28703i	−0.367756	−	0.0781690i
$857$	−5.48127	−	2.44042i	−0.187237	−	0.0833632i	0.310977	−	0.950417i	$-0.399344\pi$
$857$	−5.48127	−	2.44042i	−0.187237	−	0.0833632i	−0.498214	+	0.867054i	$0.666010\pi$
$858$	17.0333	−	18.9174i	0.581507	−	0.645829i
$859$	4.34850	−	41.3732i	0.148369	−	1.41163i	−0.626455	−	0.779458i	$-0.715495\pi$
$859$	4.34850	−	41.3732i	0.148369	−	1.41163i	0.774824	−	0.632177i	$-0.217839\pi$
$860$	85.1172	+	61.8412i	2.90247	+	2.10877i
$861$	0.134496	+	1.27965i	0.00458362	+	0.0436102i
$862$	46.9787	−	81.3695i	1.60010	−	2.77146i
$863$	15.5413	+	26.9183i	0.529032	+	0.916310i	0.999427	+	0.0338541i	$0.0107782\pi$
$863$	15.5413	+	26.9183i	0.529032	+	0.916310i	−0.470395	+	0.882456i	$0.655889\pi$
$864$	−40.1869	+	29.1975i	−1.36719	+	0.993318i
$865$	26.9320	+	29.9110i	0.915715	+	1.01700i
$866$	−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
$871$	−10.5271	−	11.6916i	−0.356699	−	0.396154i
$872$	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
$875$	−1.16866	−	11.1191i	−0.0395080	−	0.375894i
$876$	14.5623	+	10.5801i	0.492015	+	0.357470i
$877$	3.00082	−	28.5509i	0.101331	−	0.964097i	−0.819222	−	0.573477i	$-0.805594\pi$
$877$	3.00082	−	28.5509i	0.101331	−	0.964097i	0.920552	−	0.390620i	$-0.127739\pi$
$878$	−43.7952	+	48.6395i	−1.47802	+	1.64150i
$879$	1.82993	+	0.814735i	0.0617219	+	0.0274803i
$880$	−91.4414	−	19.4365i	−3.08249	−	0.655203i
$881$	−7.08892	+	1.50680i	−0.238832	+	0.0507653i	−0.325772	−	0.945448i	$-0.605624\pi$
$881$	−7.08892	+	1.50680i	−0.238832	+	0.0507653i	0.0869405	+	0.996214i	$0.472291\pi$
$882$	32.0879	−	14.2865i	1.08046	−	0.481050i
$883$	−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
$885$	−21.3256	+	9.49479i	−0.716854	+	0.319164i
$886$	−15.5077	+	3.29625i	−0.520990	+	0.110740i
$887$	−24.8065	−	5.27278i	−0.832920	−	0.177043i	−0.228335	−	0.973583i	$-0.573328\pi$
$887$	−24.8065	−	5.27278i	−0.832920	−	0.177043i	−0.604586	+	0.796540i	$0.706661\pi$
$888$	−25.3127	−	11.2699i	−0.849439	−	0.378194i
$889$	6.34793	−	7.05009i	0.212903	−	0.236452i
$890$	9.39299	−	89.3683i	0.314854	−	2.99563i
$891$	−9.29555	−	6.75362i	−0.311413	−	0.226255i
$892$	−8.19196	−	77.9413i	−0.274287	−	2.60967i
$893$	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
$896$	−0.729466	−	0.810154i	−0.0243698	−	0.0270654i
$897$	−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
$902$	−10.9413	−	12.1516i	−0.364307	−	0.404604i
$903$	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
$906$	2.99500	+	28.4955i	0.0995022	+	0.946700i
$907$	−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	$0.761370\pi$
$908$	−1.16284	+	11.0637i	−0.0385902	+	0.367161i
$909$	−3.34565	+	3.71572i	−0.110968	+	0.123243i
$910$	14.0229	+	6.24341i	0.464856	+	0.206967i
$911$	26.3305	+	5.59673i	0.872369	+	0.185428i	0.622280	−	0.782795i	$-0.286207\pi$
$911$	26.3305	+	5.59673i	0.872369	+	0.185428i	0.250089	+	0.968223i	$0.419540\pi$
$912$	8.42459	−	1.79070i	0.278966	−	0.0592961i
$913$	−12.2565	+	5.45694i	−0.405631	+	0.180599i
$914$	9.15298	−	28.1700i	0.302754	−	0.931780i
$915$	−8.41641	+	25.9030i	−0.278238	+	0.856328i
$916$	18.8137	−	8.37642i	0.621624	−	0.276765i
$917$	7.25434	−	1.54196i	0.239559	−	0.0509199i
$918$	−43.3913	−	9.22310i	−1.43213	−	0.304408i
$919$	−38.8632	−	17.3030i	−1.28198	−	0.570773i	−0.351180	−	0.936308i	$-0.614219\pi$
$919$	−38.8632	−	17.3030i	−1.28198	−	0.570773i	−0.930798	+	0.365535i	$0.880886\pi$
$920$	−29.3150	+	32.5576i	−0.966486	+	1.07339i
$921$	2.20405	−	20.9702i	0.0726261	−	0.690991i
$922$	−10.9405	−	7.94870i	−0.360305	−	0.261777i
$923$	−0.403488	−	3.83894i	−0.0132810	−	0.126360i
$924$	−9.00000	+	15.5885i	−0.296078	+	0.512823i
$925$		0			0
$926$	8.11203	−	5.89373i	0.266578	−	0.193680i
$927$	−16.0218	−	17.7941i	−0.526226	−	0.584434i
$928$	−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
$933$	−14.8972	−	16.5450i	−0.487711	−	0.541658i
$934$	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
$937$	−2.53473	−	24.1164i	−0.0828062	−	0.787848i	−0.954583	−	0.297945i	$-0.903699\pi$
$937$	−2.53473	−	24.1164i	−0.0828062	−	0.787848i	0.871777	−	0.489903i	$-0.162968\pi$
$938$	12.7082	+	9.23305i	0.414938	+	0.301470i
$939$	−1.05248	+	10.0137i	−0.0343465	+	0.326786i
$940$	−70.5089	+	78.3080i	−2.29975	+	2.55413i
$941$	23.3271	+	10.3859i	0.760441	+	0.338570i	0.750054	−	0.661376i	$-0.230027\pi$
$941$	23.3271	+	10.3859i	0.760441	+	0.338570i	0.0103862	+	0.999946i	$0.496694\pi$
$942$	19.4911	+	4.14295i	0.635053	+	0.134985i
$943$	−3.77573	+	0.802556i	−0.122955	+	0.0261348i
$944$	107.524	−	47.8729i	3.49962	−	1.55813i
$945$	−3.16228	+	9.73249i	−0.102869	+	0.316598i
$946$	−33.2705	+	102.396i	−1.08172	+	3.32918i
$947$	36.7125	−	16.3455i	1.19300	−	0.531156i	0.288435	−	0.957499i	$-0.406865\pi$
$947$	36.7125	−	16.3455i	1.19300	−	0.531156i	0.904562	+	0.426343i	$0.140198\pi$
$948$	−6.72514	+	1.42947i	−0.218423	+	0.0464271i
$949$	10.8815	+	2.31294i	0.353229	+	0.0750811i
$950$		0			0
$951$	−15.3439	+	17.0412i	−0.497561	+	0.552598i
$952$	2.89181	−	27.5137i	0.0937241	−	0.891725i
$953$	−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	$0.797784\pi$
$954$	−8.40134	−	79.9334i	−0.272004	−	2.58794i
$955$	−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
$958$	28.9536	+	32.1563i	0.935449	+	1.03892i
$959$	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
$964$	−75.4072	−	83.7482i	−2.42870	−	2.69735i
$965$	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	0.257949	+	0.966158i	$0.416953\pi$
$967$	−22.0084	+	38.1197i	−0.707743	+	1.22585i	−0.965692	+	0.259689i	$0.916380\pi$
$968$	−5.46736	−	52.0184i	−0.175727	−	1.67194i
$969$	2.61803	+	1.90211i	0.0841034	+	0.0611047i
$970$	4.28344	−	40.7542i	0.137533	−	1.30854i
$971$	36.0585	−	40.0470i	1.15717	−	1.28517i	0.205291	−	0.978701i	$-0.434186\pi$
$971$	36.0585	−	40.0470i	1.15717	−	1.28517i	0.951881	−	0.306468i	$-0.0991473\pi$
$972$	−71.3791	−	31.7800i	−2.28949	−	1.01935i
$973$	−17.5794	−	3.73661i	−0.563569	−	0.119790i
$974$	−71.9027	+	15.2834i	−2.30391	+	0.489711i
$975$		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	$0.862148\pi$
$978$	−30.1363	+	13.4175i	−0.963652	+	0.429046i
$979$	63.7015	−	13.5402i	2.03591	−	0.432746i
$980$	63.7015	+	13.5402i	2.03487	+	0.432525i
$981$	2.63882	+	1.17488i	0.0842509	+	0.0375109i
$982$	−27.8366	+	30.9156i	−0.888300	+	0.986557i
$983$	−5.63579	+	53.6210i	−0.179754	+	1.71024i	0.417903	+	0.908492i	$0.362765\pi$
$983$	−5.63579	+	53.6210i	−0.179754	+	1.71024i	−0.597657	+	0.801752i	$0.703901\pi$
$984$	−7.77817	−	5.65117i	−0.247959	−	0.180153i
$985$	0.252516	+	2.40253i	0.00804584	+	0.0765510i
$986$	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
$989$	17.0069	+	18.8881i	0.540788	+	0.600606i
$990$	−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
$995$	34.7367	+	38.5791i	1.10123	+	1.22304i
$996$	−10.8541	+	7.88597i	−0.343925	+	0.249876i
$997$	29.3328	+	50.8059i	0.928980	+	1.60904i	0.785033	+	0.619454i	$0.212646\pi$
$997$	29.3328	+	50.8059i	0.928980	+	1.60904i	0.143947	+	0.989585i	$0.454021\pi$
$998$	−24.0660	+	41.6835i	−0.761795	+	1.31947i
$999$	−2.02957	−	19.3100i	−0.0642127	−	0.610943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.p.547.1		16
31.2	even	5		961.2.g.i.235.1		16
31.3	odd	30		961.2.c.h.521.3		8
31.4	even	5		961.2.g.i.816.2		16
31.5	even	3		961.2.d.j.531.1		8
31.6	odd	6	inner	961.2.g.p.844.1		16
31.7	even	15		961.2.g.i.732.1		16
31.8	even	5	inner	961.2.g.p.846.2		16
31.9	even	15		961.2.d.j.628.1		8
31.10	even	15		961.2.d.h.388.2		8
31.11	odd	30		961.2.d.h.374.1		8
31.12	odd	30		961.2.g.i.338.1		16
31.13	odd	30		961.2.a.h.1.4	yes	4
31.14	even	15	inner	961.2.g.p.448.1		16
31.15	odd	10		961.2.c.h.439.3		8
31.16	even	5		961.2.c.h.439.4		8
31.17	odd	30	inner	961.2.g.p.448.2		16
31.18	even	15		961.2.a.h.1.3	✓	4
31.19	even	15		961.2.g.i.338.2		16
31.20	even	15		961.2.d.h.374.2		8
31.21	odd	30		961.2.d.h.388.1		8
31.22	odd	30		961.2.d.j.628.2		8
31.23	odd	10	inner	961.2.g.p.846.1		16
31.24	odd	30		961.2.g.i.732.2		16
31.25	even	3	inner	961.2.g.p.844.2		16
31.26	odd	6		961.2.d.j.531.2		8
31.27	odd	10		961.2.g.i.816.1		16
31.28	even	15		961.2.c.h.521.4		8
31.29	odd	10		961.2.g.i.235.2		16
31.30	odd	2	inner	961.2.g.p.547.2		16
93.44	even	30		8649.2.a.r.1.2		4
93.80	odd	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	31.18	even	15
961.2.a.h.1.4	yes	4	31.13	odd	30
961.2.c.h.439.3		8	31.15	odd	10
961.2.c.h.439.4		8	31.16	even	5
961.2.c.h.521.3		8	31.3	odd	30
961.2.c.h.521.4		8	31.28	even	15
961.2.d.h.374.1		8	31.11	odd	30
961.2.d.h.374.2		8	31.20	even	15
961.2.d.h.388.1		8	31.21	odd	30
961.2.d.h.388.2		8	31.10	even	15
961.2.d.j.531.1		8	31.5	even	3
961.2.d.j.531.2		8	31.26	odd	6
961.2.d.j.628.1		8	31.9	even	15
961.2.d.j.628.2		8	31.22	odd	30
961.2.g.i.235.1		16	31.2	even	5
961.2.g.i.235.2		16	31.29	odd	10
961.2.g.i.338.1		16	31.12	odd	30
961.2.g.i.338.2		16	31.19	even	15
961.2.g.i.732.1		16	31.7	even	15
961.2.g.i.732.2		16	31.24	odd	30
961.2.g.i.816.1		16	31.27	odd	10
961.2.g.i.816.2		16	31.4	even	5
961.2.g.p.448.1		16	31.14	even	15	inner
961.2.g.p.448.2		16	31.17	odd	30	inner
961.2.g.p.547.1		16	1.1	even	1	trivial
961.2.g.p.547.2		16	31.30	odd	2	inner
961.2.g.p.844.1		16	31.6	odd	6	inner
961.2.g.p.844.2		16	31.25	even	3	inner
961.2.g.p.846.1		16	31.23	odd	10	inner
961.2.g.p.846.2		16	31.8	even	5	inner
8649.2.a.r.1.1		4	93.80	odd	30
8649.2.a.r.1.2		4	93.44	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} +(-0.584842 - 0.649532i) q^{3} +(-3.92705 + 2.85317i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(1.14412 - 1.98168i) q^{6} +(0.104528 + 0.994522i) q^{7} +(-6.04508 - 4.39201i) q^{8} +(0.233733 - 2.22382i) q^{9} +(3.91716 - 4.35045i) q^{10} +(3.87585 + 1.72564i) q^{11} +(4.14993 + 0.882095i) q^{12} +(2.56480 - 0.545164i) q^{13} +(-2.39169 + 1.06485i) q^{14} +(-0.603941 + 1.85874i) q^{15} +(3.04508 - 9.37181i) q^{16} +(3.38236 - 1.50593i) q^{17} +(5.72618 - 1.21714i) q^{18} +(-0.978148 - 0.207912i) q^{19} +(9.91572 + 4.41476i) q^{20} +(0.584842 - 0.649532i) q^{21} +(-1.16104 + 11.0465i) q^{22} +(2.12132 + 1.54123i) q^{23} +(0.682664 + 6.49511i) q^{24} +(3.43237 + 5.94504i) q^{26} +(-3.70246 + 2.68999i) q^{27} +(-3.24803 - 3.60730i) q^{28} +(-0.166925 - 0.513743i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(-1.14590 - 3.52671i) q^{33} +(6.48599 + 7.20342i) q^{34} +(1.80902 - 1.31433i) q^{35} +(5.42705 + 9.39993i) q^{36} +(-2.12132 + 3.67423i) q^{37} +(-0.273659 - 2.60369i) q^{38} +(-1.85410 - 1.34708i) q^{39} +(-1.74648 + 16.6167i) q^{40} +(-0.985051 + 1.09401i) q^{41} +(2.09042 + 0.930713i) q^{42} +(9.48135 + 2.01532i) q^{43} +(-20.1442 + 4.28178i) q^{44} +(-4.56773 + 2.03368i) q^{45} +(-2.12132 + 6.52875i) q^{46} +(-3.00000 + 9.23305i) q^{47} +(-7.86819 + 3.50314i) q^{48} +(5.86889 - 1.24747i) q^{49} +(-2.95630 - 1.31623i) q^{51} +(-8.51664 + 9.45869i) q^{52} +(1.43512 - 13.6543i) q^{53} +(-9.69316 - 7.04250i) q^{54} +(-0.991644 - 9.43486i) q^{55} +(3.73607 - 6.47106i) q^{56} +(0.437016 + 0.756934i) q^{57} +(1.14412 - 0.831254i) q^{58} +(7.99228 + 8.87632i) q^{59} +(-2.93159 - 9.02251i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(2.69098 + 8.28199i) q^{64} +(-3.92324 - 4.35720i) q^{65} +(7.85410 - 5.70634i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-8.98606 + 15.5643i) q^{68} +(-0.239558 - 2.27924i) q^{69} +(4.73607 + 3.44095i) q^{70} +(0.153880 - 1.46407i) q^{71} +(-11.1800 + 12.4166i) q^{72} +(3.87585 + 1.72564i) q^{73} +(-10.8647 - 2.30935i) q^{74} +(4.43444 - 1.97434i) q^{76} +(-1.31105 + 4.03499i) q^{77} +(1.85410 - 5.70634i) q^{78} +(-1.48044 + 0.659135i) q^{79} +(-21.5529 + 4.58122i) q^{80} +(-2.64902 - 0.563067i) q^{81} +(-3.52090 - 1.56760i) q^{82} +(-2.11598 + 2.35003i) q^{83} +(-0.443477 + 4.21940i) q^{84} +(-6.69781 - 4.86624i) q^{85} +(2.65262 + 25.2380i) q^{86} +(-0.236068 + 0.408882i) q^{87} +(-15.8508 - 27.4544i) q^{88} +(12.4184 - 9.02251i) q^{89} +(-8.75903 - 9.72789i) q^{90} +(0.810272 + 2.49376i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(0.690983 + 2.12663i) q^{95} +(-6.34793 - 7.05009i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more