LMFDB - Embedded newform 980.2.s.g.19.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(19,980)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("980.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.27
Character	$\chi$	$=$	980.19
Dual form			980.2.s.g.619.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.142436 + 1.40702i) q^{2} +(-1.31926 + 0.761677i) q^{3} +(-1.95942 + 0.400822i) q^{4} +(-1.88631 - 1.20076i) q^{5} +(-1.25961 - 1.74774i) q^{6} +(-0.843059 - 2.69986i) q^{8} +(-0.339697 + 0.588372i) q^{9} +(1.42082 - 2.82511i) q^{10} +(-3.94956 + 2.28028i) q^{11} +(2.27970 - 2.02124i) q^{12} +2.19514 q^{13} +(3.40313 + 0.147364i) q^{15} +(3.67868 - 1.57076i) q^{16} +(-3.11101 - 5.38842i) q^{17} +(-0.876237 - 0.394155i) q^{18} +(1.91698 - 3.32031i) q^{19} +(4.17737 + 1.59673i) q^{20} +(-3.77097 - 5.23233i) q^{22} +(-0.215130 + 0.372617i) q^{23} +(3.16864 + 2.91969i) q^{24} +(2.11633 + 4.53003i) q^{25} +(0.312667 + 3.08861i) q^{26} -5.60502i q^{27} -0.473706 q^{29} +(0.277386 + 4.80928i) q^{30} +(3.79890 + 6.57988i) q^{31} +(2.73407 + 4.95226i) q^{32} +(3.47367 - 6.01658i) q^{33} +(7.13851 - 5.14477i) q^{34} +(0.429777 - 1.28903i) q^{36} +(7.31192 + 4.22154i) q^{37} +(4.94479 + 2.22430i) q^{38} +(-2.89596 + 1.67199i) q^{39} +(-1.65162 + 6.10509i) q^{40} +1.45831i q^{41} +8.58232 q^{43} +(6.82488 - 6.05111i) q^{44} +(1.34727 - 0.701957i) q^{45} +(-0.554922 - 0.249619i) q^{46} +(-3.88753 - 2.24446i) q^{47} +(-3.65674 + 4.87421i) q^{48} +(-6.07240 + 3.62297i) q^{50} +(8.20848 + 4.73917i) q^{51} +(-4.30120 + 0.879860i) q^{52} +(8.00130 - 4.61955i) q^{53} +(7.88639 - 0.798358i) q^{54} +(10.1882 + 0.441172i) q^{55} +5.84048i q^{57} +(-0.0674729 - 0.666515i) q^{58} +(-1.56800 - 2.71586i) q^{59} +(-6.72725 + 1.07530i) q^{60} +(-4.94644 - 2.85583i) q^{61} +(-8.71694 + 6.28235i) q^{62} +(-6.57850 + 4.55228i) q^{64} +(-4.14071 - 2.63584i) q^{65} +(8.96024 + 4.03056i) q^{66} +(-7.47296 - 12.9435i) q^{67} +(8.25558 + 9.31125i) q^{68} -0.655439i q^{69} +4.57799i q^{71} +(1.87491 + 0.421102i) q^{72} +(6.13574 + 10.6274i) q^{73} +(-4.89832 + 10.8893i) q^{74} +(-6.24242 - 4.36433i) q^{75} +(-2.42532 + 7.27425i) q^{76} +(-2.76501 - 3.83653i) q^{78} +(-5.37297 - 3.10208i) q^{79} +(-8.82525 - 1.45429i) q^{80} +(3.25012 + 5.62938i) q^{81} +(-2.05188 + 0.207717i) q^{82} -7.69966i q^{83} +(-0.601895 + 13.8998i) q^{85} +(1.22243 + 12.0755i) q^{86} +(0.624943 - 0.360811i) q^{87} +(9.48615 + 8.74086i) q^{88} +(8.07509 + 4.66216i) q^{89} +(1.17957 + 1.79565i) q^{90} +(0.272178 - 0.816343i) q^{92} +(-10.0235 - 5.78706i) q^{93} +(2.60429 - 5.78953i) q^{94} +(-7.60292 + 3.96129i) q^{95} +(-7.37898 - 4.45085i) q^{96} +9.05280 q^{97} -3.09841i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) $ 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.142436	+	1.40702i	0.100718	+	0.994915i
$2$	0.142436	+	1.40702i	0.100718	+	0.994915i
$3$	−1.31926	+	0.761677i	−0.761677	+	0.439754i	−0.829898	−	0.557916i	$-0.811601\pi$
$3$	−1.31926	+	0.761677i	−0.761677	+	0.439754i	0.0682206	+	0.997670i	$0.478268\pi$
$4$	−1.95942	+	0.400822i	−0.979712	+	0.200411i
$5$	−1.88631	−	1.20076i	−0.843584	−	0.536998i
$5$	−1.88631	−	1.20076i	−0.843584	−	0.536998i
$6$	−1.25961	−	1.74774i	−0.514233	−	0.713513i
$7$		0			0
$7$		0			0
$8$	−0.843059	−	2.69986i	−0.298066	−	0.954545i
$9$	−0.339697	+	0.588372i	−0.113232	+	0.196124i
$10$	1.42082	−	2.82511i	0.449303	−	0.893379i
$11$	−3.94956	+	2.28028i	−1.19084	+	0.687530i	−0.958497	−	0.285104i	$-0.907972\pi$
$11$	−3.94956	+	2.28028i	−1.19084	+	0.687530i	−0.232341	+	0.972634i	$0.574638\pi$
$12$	2.27970	−	2.02124i	0.658092	−	0.583481i
$13$	2.19514			0.608822			0.304411	−	0.952541i	$-0.401540\pi$
$13$	2.19514			0.608822			0.304411	+	0.952541i	$0.401540\pi$
$14$		0			0
$15$	3.40313	+	0.147364i	0.878685	+	0.0380491i
$16$	3.67868	−	1.57076i	0.919671	−	0.392690i
$17$	−3.11101	−	5.38842i	−0.754530	−	1.30688i	−0.945607	−	0.325310i	$-0.894531\pi$
$17$	−3.11101	−	5.38842i	−0.754530	−	1.30688i	0.191077	−	0.981575i	$-0.438802\pi$
$18$	−0.876237	−	0.394155i	−0.206531	−	0.0929033i
$19$	1.91698	−	3.32031i	0.439785	−	0.761730i	−0.557887	−	0.829917i	$-0.688388\pi$
$19$	1.91698	−	3.32031i	0.439785	−	0.761730i	0.997673	+	0.0681862i	$0.0217212\pi$
$20$	4.17737	+	1.59673i	0.934089	+	0.357040i
$21$		0			0
$22$	−3.77097	−	5.23233i	−0.803973	−	1.11554i
$23$	−0.215130	+	0.372617i	−0.0448578	+	0.0776959i	−0.887583	−	0.460649i	$-0.847617\pi$
$23$	−0.215130	+	0.372617i	−0.0448578	+	0.0776959i	0.842725	+	0.538345i	$0.180950\pi$
$24$	3.16864	+	2.91969i	0.646796	+	0.595979i
$25$	2.11633	+	4.53003i	0.423267	+	0.906005i
$26$	0.312667	+	3.08861i	0.0613191	+	0.605726i
$27$		−	5.60502i		−	1.07869i
$28$		0			0
$29$	−0.473706			−0.0879650			−0.0439825	−	0.999032i	$-0.514005\pi$
$29$	−0.473706			−0.0879650			−0.0439825	+	0.999032i	$0.514005\pi$
$30$	0.277386	+	4.80928i	0.0506435	+	0.878049i
$31$	3.79890	+	6.57988i	0.682302	+	1.18178i	0.974277	+	0.225356i	$0.0723544\pi$
$31$	3.79890	+	6.57988i	0.682302	+	1.18178i	−0.291975	+	0.956426i	$0.594312\pi$
$32$	2.73407	+	4.95226i	0.483320	+	0.875443i
$33$	3.47367	−	6.01658i	0.604689	−	1.04735i
$34$	7.13851	−	5.14477i	1.22424	−	0.882320i
$35$		0			0
$36$	0.429777	−	1.28903i	0.0716295	−	0.214838i
$37$	7.31192	+	4.22154i	1.20207	+	0.694017i	0.961016	−	0.276494i	$-0.0891726\pi$
$37$	7.31192	+	4.22154i	1.20207	+	0.694017i	0.241057	+	0.970511i	$0.422506\pi$
$38$	4.94479	+	2.22430i	0.802151	+	0.360829i
$39$	−2.89596	+	1.67199i	−0.463725	+	0.267732i
$40$	−1.65162	+	6.10509i	−0.261145	+	0.965300i
$41$			1.45831i			0.227750i	0.993495	+	0.113875i	$0.0363264\pi$
$41$			1.45831i			0.227750i	−0.993495	+	0.113875i	$0.963674\pi$
$42$		0			0
$43$	8.58232			1.30879			0.654396	−	0.756152i	$-0.272923\pi$
$43$	8.58232			1.30879			0.654396	+	0.756152i	$0.272923\pi$
$44$	6.82488	−	6.05111i	1.02889	−	0.912239i
$45$	1.34727	−	0.701957i	0.200839	−	0.104641i
$46$	−0.554922	−	0.249619i	−0.0818188	−	0.0368043i
$47$	−3.88753	−	2.24446i	−0.567054	−	0.327389i	0.188918	−	0.981993i	$-0.439502\pi$
$47$	−3.88753	−	2.24446i	−0.567054	−	0.327389i	−0.755972	+	0.654604i	$0.772835\pi$
$48$	−3.65674	+	4.87421i	−0.527805	+	0.703532i
$49$		0			0
$50$	−6.07240	+	3.62297i	−0.858768	+	0.512365i
$51$	8.20848	+	4.73917i	1.14942	+	0.663616i
$52$	−4.30120	+	0.879860i	−0.596470	+	0.122015i
$53$	8.00130	−	4.61955i	1.09906	−	0.634544i	0.163088	−	0.986611i	$-0.447854\pi$
$53$	8.00130	−	4.61955i	1.09906	−	0.634544i	0.935975	+	0.352067i	$0.114521\pi$
$54$	7.88639	−	0.798358i	1.07320	−	0.108643i
$55$	10.1882	+	0.441172i	1.37377	+	0.0594876i
$56$		0			0
$57$			5.84048i			0.773590i
$58$	−0.0674729	−	0.666515i	−0.00885963	−	0.0875177i
$59$	−1.56800	−	2.71586i	−0.204137	−	0.353575i	0.745721	−	0.666259i	$-0.232105\pi$
$59$	−1.56800	−	2.71586i	−0.204137	−	0.353575i	−0.949857	+	0.312684i	$0.898772\pi$
$60$	−6.72725	+	1.07530i	−0.868484	+	0.138821i
$61$	−4.94644	−	2.85583i	−0.633326	−	0.365651i	0.148713	−	0.988880i	$-0.452487\pi$
$61$	−4.94644	−	2.85583i	−0.633326	−	0.365651i	−0.782039	+	0.623229i	$0.785820\pi$
$62$	−8.71694	+	6.28235i	−1.10705	+	0.797859i
$63$		0			0
$64$	−6.57850	+	4.55228i	−0.822313	+	0.569035i
$65$	−4.14071	−	2.63584i	−0.513592	−	0.326936i
$66$	8.96024	+	4.03056i	1.10293	+	0.496127i
$67$	−7.47296	−	12.9435i	−0.912967	−	1.58131i	−0.809850	−	0.586636i	$-0.800452\pi$
$67$	−7.47296	−	12.9435i	−0.912967	−	1.58131i	−0.103117	−	0.994669i	$-0.532882\pi$
$68$	8.25558	+	9.31125i	1.00114	+	1.12915i
$69$		−	0.655439i		−	0.0789056i
$70$		0			0
$71$			4.57799i			0.543308i	0.962395	+	0.271654i	$0.0875706\pi$
$71$			4.57799i			0.543308i	−0.962395	+	0.271654i	$0.912429\pi$
$72$	1.87491	+	0.421102i	0.220960	+	0.0496273i
$73$	6.13574	+	10.6274i	0.718134	+	1.24384i	0.961738	+	0.273969i	$0.0883367\pi$
$73$	6.13574	+	10.6274i	0.718134	+	1.24384i	−0.243605	+	0.969875i	$0.578330\pi$
$74$	−4.89832	+	10.8893i	−0.569418	+	1.26586i
$75$	−6.24242	−	4.36433i	−0.720812	−	0.503950i
$76$	−2.42532	+	7.27425i	−0.278204	+	0.834414i
$77$		0			0
$78$	−2.76501	−	3.83653i	−0.313076	−	0.434402i
$79$	−5.37297	−	3.10208i	−0.604506	−	0.349012i	0.166306	−	0.986074i	$-0.446816\pi$
$79$	−5.37297	−	3.10208i	−0.604506	−	0.349012i	−0.770812	+	0.637062i	$0.780149\pi$
$80$	−8.82525	−	1.45429i	−0.986693	−	0.162594i
$81$	3.25012	+	5.62938i	0.361125	+	0.625486i
$82$	−2.05188	+	0.207717i	−0.226592	+	0.0229385i
$83$		−	7.69966i		−	0.845148i	−0.906329	−	0.422574i	$-0.861127\pi$
$83$		−	7.69966i		−	0.845148i	0.906329	−	0.422574i	$-0.138873\pi$
$84$		0			0
$85$	−0.601895	+	13.8998i	−0.0652847	+	1.50765i
$86$	1.22243	+	12.0755i	0.131818	+	1.30214i
$87$	0.624943	−	0.360811i	0.0670009	−	0.0386830i
$88$	9.48615	+	8.74086i	1.01123	+	0.931778i
$89$	8.07509	+	4.66216i	0.855958	+	0.494188i	0.862657	−	0.505790i	$-0.168799\pi$
$89$	8.07509	+	4.66216i	0.855958	+	0.494188i	−0.00669845	+	0.999978i	$0.502132\pi$
$90$	1.17957	+	1.79565i	0.124337	+	0.189278i
$91$		0			0
$92$	0.272178	−	0.816343i	0.0283766	−	0.0851096i
$93$	−10.0235	−	5.78706i	−1.03939	−	0.600091i
$94$	2.60429	−	5.78953i	0.268612	−	0.597144i
$95$	−7.60292	+	3.96129i	−0.780043	+	0.406420i
$96$	−7.37898	−	4.45085i	−0.753114	−	0.454263i
$97$	9.05280			0.919172			0.459586	−	0.888133i	$-0.347998\pi$
$97$	9.05280			0.919172			0.459586	+	0.888133i	$0.347998\pi$
$98$		0			0
$99$		−	3.09841i		−	0.311402i
$100$	−5.96253	−	8.02797i	−0.596253	−	0.802797i
$101$	6.92648	−	3.99901i	0.689211	−	0.397916i	−0.114105	−	0.993469i	$-0.536400\pi$
$101$	6.92648	−	3.99901i	0.689211	−	0.397916i	0.803316	+	0.595552i	$0.203067\pi$
$102$	−5.49893	+	12.2245i	−0.544475	+	1.21041i
$103$	−10.8268	−	6.25084i	−1.06679	−	0.615914i	−0.139490	−	0.990223i	$-0.544546\pi$
$103$	−10.8268	−	6.25084i	−1.06679	−	0.615914i	−0.927304	+	0.374310i	$0.877880\pi$
$104$	−1.85063	−	5.92657i	−0.181469	−	0.581148i
$105$		0			0
$106$	7.63949	+	10.6000i	0.742013	+	1.02956i
$107$	7.23338	−	12.5286i	0.699277	−	1.21118i	−0.269441	−	0.963017i	$-0.586839\pi$
$107$	7.23338	−	12.5286i	0.699277	−	1.21118i	0.968718	−	0.248166i	$-0.0798279\pi$
$108$	2.24662	+	10.9826i	0.216181	+	1.05680i
$109$	−9.14811	−	15.8450i	−0.876230	−	1.51768i	−0.855446	−	0.517892i	$-0.826717\pi$
$109$	−9.14811	−	15.8450i	−0.876230	−	1.51768i	−0.0207841	−	0.999784i	$-0.506616\pi$
$110$	0.830427	+	14.3978i	0.0791781	+	1.37278i
$111$	−12.8618			−1.22079
$112$		0			0
$113$			1.13588i			0.106854i	0.998572	+	0.0534272i	$0.0170145\pi$
$113$			1.13588i			0.106854i	−0.998572	+	0.0534272i	$0.982986\pi$
$114$	−8.21768	+	0.831896i	−0.769656	+	0.0779142i
$115$	0.853227	−	0.444550i	0.0795638	−	0.0414545i
$116$	0.928191	−	0.189872i	0.0861804	−	0.0176292i
$117$	−0.745681	+	1.29156i	−0.0689382	+	0.119404i
$118$	3.59794	−	2.59305i	0.331217	−	0.238710i
$119$		0			0
$120$	−2.47118	−	9.31223i	−0.225587	−	0.850086i
$121$	4.89935	−	8.48593i	0.445396	−	0.771448i
$122$	3.31366	−	7.36652i	0.300005	−	0.666934i
$123$	−1.11076	−	1.92390i	−0.100154	−	0.173472i
$124$	−10.0810	−	11.3701i	−0.905302	−	1.02106i
$125$	1.44742	−	11.0863i	0.129462	−	0.991584i
$126$		0			0
$127$	8.33473			0.739588			0.369794	−	0.929114i	$-0.379428\pi$
$127$	8.33473			0.739588			0.369794	+	0.929114i	$0.379428\pi$
$128$	−7.34218	−	8.60769i	−0.648963	−	0.760820i
$129$	−11.3223	+	6.53695i	−0.996876	+	0.575547i
$130$	3.11890	−	6.20151i	0.273546	−	0.543909i
$131$	−2.84101	+	4.92078i	−0.248220	+	0.429930i	−0.963032	−	0.269387i	$-0.913179\pi$
$131$	−2.84101	+	4.92078i	−0.248220	+	0.429930i	0.714812	+	0.699317i	$0.246512\pi$
$132$	−4.39482	+	13.1814i	−0.382520	+	1.14729i
$133$		0			0
$134$	17.1474	−	12.3583i	1.48131	−	1.06759i
$135$	−6.73030	+	10.5728i	−0.579252	+	0.909962i
$136$	−11.9252	+	12.9421i	−1.02258	+	1.10977i
$137$	12.8039	−	7.39231i	1.09391	−	0.631567i	0.159293	−	0.987231i	$-0.449079\pi$
$137$	12.8039	−	7.39231i	1.09391	−	0.631567i	0.934614	+	0.355664i	$0.115745\pi$
$138$	0.922218	−	0.0933583i	0.0785044	−	0.00794719i
$139$	1.11362			0.0944558			0.0472279	−	0.998884i	$-0.484961\pi$
$139$	1.11362			0.0944558			0.0472279	+	0.998884i	$0.484961\pi$
$140$		0			0
$141$	6.83823			0.575883
$142$	−6.44134	+	0.652073i	−0.540545	+	0.0547207i
$143$	−8.66983	+	5.00553i	−0.725007	+	0.418583i
$144$	−0.325445	+	2.69802i	−0.0271204	+	0.224835i
$145$	0.893557	+	0.568809i	0.0742058	+	0.0472370i
$146$	−14.0790	+	10.1468i	−1.16519	+	0.839759i
$147$		0			0
$148$	−16.0192	−	5.34101i	−1.31677	−	0.439028i
$149$	−3.43905	+	5.95661i	−0.281738	+	0.487985i	−0.971813	−	0.235753i	$-0.924244\pi$
$149$	−3.43905	+	5.95661i	−0.281738	+	0.487985i	0.690075	+	0.723738i	$0.257578\pi$
$150$	5.25157	−	9.40486i	0.428789	−	0.767904i
$151$	18.3926	−	10.6190i	1.49677	−	0.864161i	0.496778	−	0.867878i	$-0.334516\pi$
$151$	18.3926	−	10.6190i	1.49677	−	0.864161i	0.999993	+	0.00371622i	$0.00118291\pi$
$152$	−10.5805	−	2.37637i	−0.858191	−	0.192749i
$153$	4.22720			0.341748
$154$		0			0
$155$	0.734983	−	16.9733i	0.0590352	−	1.36333i
$156$	5.00425	−	4.43689i	0.400661	−	0.355236i
$157$	−1.16371	−	2.01560i	−0.0928741	−	0.160863i	0.815845	−	0.578270i	$-0.196272\pi$
$157$	−1.16371	−	2.01560i	−0.0928741	−	0.160863i	−0.908719	+	0.417408i	$0.862939\pi$
$158$	3.59940	−	8.00174i	0.286353	−	0.636584i
$159$	−7.03721	+	12.1888i	−0.558087	+	0.966636i
$160$	0.789176	−	12.6245i	0.0623898	−	0.998052i
$161$		0			0
$162$	−7.45773	+	5.37482i	−0.585934	+	0.422286i
$163$	−1.53342	+	2.65595i	−0.120106	+	0.208030i	−0.919809	−	0.392365i	$-0.871657\pi$
$163$	−1.53342	+	2.65595i	−0.120106	+	0.208030i	0.799703	+	0.600396i	$0.204990\pi$
$164$	−0.584525	−	2.85746i	−0.0456437	−	0.223130i
$165$	−13.7769	+	7.17808i	−1.07253	+	0.558812i
$166$	10.8336	−	1.09671i	0.840850	−	0.0851213i
$167$		−	13.0431i		−	1.00930i	−0.863323	−	0.504652i	$-0.831621\pi$
$167$		−	13.0431i		−	1.00930i	0.863323	−	0.504652i	$-0.168379\pi$
$168$		0			0
$169$	−8.18137			−0.629336
$170$	−19.6431	+	1.13296i	−1.50656	+	0.0868941i
$171$	1.30238	+	2.25579i	0.0995957	+	0.172505i
$172$	−16.8164	+	3.43998i	−1.28224	+	0.262296i
$173$	5.53012	−	9.57846i	0.420448	−	0.728237i	−0.575536	−	0.817777i	$-0.695206\pi$
$173$	5.53012	−	9.57846i	0.420448	−	0.728237i	0.995983	+	0.0895401i	$0.0285397\pi$
$174$	0.596684	+	0.827916i	0.0452345	+	0.0627642i
$175$		0			0
$176$	−10.9474	+	14.5922i	−0.825192	+	1.09993i
$177$	4.13722	+	2.38862i	0.310972	+	0.179540i
$178$	−5.40957	+	12.0259i	−0.405465	+	0.901379i
$179$	19.0915	−	11.0225i	1.42697	−	0.823860i	0.430087	−	0.902788i	$-0.358483\pi$
$179$	19.0915	−	11.0225i	1.42697	−	0.823860i	0.996880	+	0.0789277i	$0.0251496\pi$
$180$	−2.35851	+	1.91545i	−0.175793	+	0.142769i
$181$		−	2.49964i		−	0.185797i	−0.995676	−	0.0928984i	$-0.970387\pi$
$181$		−	2.49964i		−	0.185797i	0.995676	−	0.0928984i	$-0.0296132\pi$
$182$		0			0
$183$	8.70087			0.643187
$184$	1.18738	+	0.266684i	0.0875349	+	0.0196602i
$185$	−8.72348	−	16.7430i	−0.641363	−	1.23097i
$186$	6.71482	−	14.9276i	0.492355	−	1.09454i
$187$	24.5742	+	14.1879i	1.79705	+	1.03752i
$188$	8.51694	+	2.83965i	0.621162	+	0.207103i
$189$		0			0
$190$	−6.65655	−	10.1332i	−0.482917	−	0.735143i
$191$	6.72093	+	3.88033i	0.486309	+	0.280771i	0.723042	−	0.690804i	$-0.242743\pi$
$191$	6.72093	+	3.88033i	0.486309	+	0.280771i	−0.236733	+	0.971575i	$0.576077\pi$
$192$	5.21141	−	11.0164i	0.376101	−	0.795037i
$193$	−5.22832	+	3.01857i	−0.376342	+	0.217281i	−0.676226	−	0.736695i	$-0.736386\pi$
$193$	−5.22832	+	3.01857i	−0.376342	+	0.217281i	0.299883	+	0.953976i	$0.403052\pi$
$194$	1.28945	+	12.7375i	0.0925769	+	0.914498i
$195$	7.47035	+	0.323483i	0.534963	+	0.0231651i
$196$		0			0
$197$		−	9.74467i		−	0.694279i	−0.937813	−	0.347140i	$-0.887153\pi$
$197$		−	9.74467i		−	0.694279i	0.937813	−	0.347140i	$-0.112847\pi$
$198$	4.35954	−	0.441326i	0.309819	−	0.0313637i
$199$	−8.62676	−	14.9420i	−0.611535	−	1.05921i	−0.990982	−	0.133996i	$-0.957219\pi$
$199$	−8.62676	−	14.9420i	−0.611535	−	1.05921i	0.379447	−	0.925214i	$-0.376114\pi$
$200$	10.4462	−	9.53289i	0.738661	−	0.674077i
$201$	19.7176	+	11.3840i	1.39077	+	0.802963i
$202$	6.61328	+	9.17612i	0.465309	+	0.645629i
$203$		0			0
$204$	−17.9834	−	5.99590i	−1.25909	−	0.419797i
$205$	1.75109	−	2.75083i	0.122301	−	0.192127i
$206$	7.25295	−	16.1239i	0.505337	−	1.12340i
$207$	−0.146158	−	0.253153i	−0.0101587	−	0.0175954i
$208$	8.07521	−	3.44804i	0.559915	−	0.239078i
$209$			17.4850i			1.20946i
$210$		0			0
$211$			26.8147i			1.84600i	0.384796	+	0.923002i	$0.374272\pi$
$211$			26.8147i			1.84600i	−0.384796	+	0.923002i	$0.625728\pi$
$212$	−13.8263	+	12.2588i	−0.949596	+	0.841935i
$213$	−3.48695	−	6.03958i	−0.238922	−	0.413825i
$214$	18.6583	+	8.39300i	1.27545	+	0.573734i
$215$	−16.1889	−	10.3053i	−1.10407	−	0.702818i
$216$	−15.1328	+	4.72536i	−1.02965	+	0.321520i
$217$		0			0
$218$	20.9912	−	15.1285i	1.42171	−	1.02463i
$219$	−16.1893	−	9.34690i	−1.09397	−	0.631605i
$220$	−20.1398	+	3.21920i	−1.35782	+	0.217039i
$221$	−6.82909	−	11.8283i	−0.459374	−	0.795660i
$222$	−1.83199	−	18.0968i	−0.122955	−	1.21458i
$223$			17.6054i			1.17894i	0.807789	+	0.589472i	$0.200664\pi$
$223$			17.6054i			1.17894i	−0.807789	+	0.589472i	$0.799336\pi$
$224$		0			0
$225$	−3.38425	−	0.293642i	−0.225617	−	0.0195762i
$226$	−1.59820	+	0.161790i	−0.106311	+	0.0107621i
$227$	−7.61360	+	4.39572i	−0.505333	+	0.291754i	−0.730913	−	0.682471i	$-0.760905\pi$
$227$	−7.61360	+	4.39572i	−0.505333	+	0.291754i	0.225580	+	0.974225i	$0.427572\pi$
$228$	−2.34099	−	11.4440i	−0.155036	−	0.757895i
$229$	−14.7950	−	8.54191i	−0.977683	−	0.564466i	−0.0761132	−	0.997099i	$-0.524251\pi$
$229$	−14.7950	−	8.54191i	−0.977683	−	0.564466i	−0.901570	+	0.432634i	$0.857584\pi$
$230$	0.747022	+	1.13719i	0.0492572	+	0.0749840i
$231$		0			0
$232$	0.399362	+	1.27894i	0.0262194	+	0.0839666i
$233$	12.2822	+	7.09116i	0.804636	+	0.464557i	0.845090	−	0.534624i	$-0.179547\pi$
$233$	12.2822	+	7.09116i	0.804636	+	0.464557i	−0.0404533	+	0.999181i	$0.512880\pi$
$234$	−1.92346	−	0.865225i	−0.125741	−	0.0565615i
$235$	4.63801	+	8.90176i	0.302550	+	0.580686i
$236$	4.16096	+	4.69303i	0.270855	+	0.305490i
$237$	9.45115			0.613918
$238$		0			0
$239$		−	13.6734i		−	0.884456i	−0.896903	−	0.442228i	$-0.854188\pi$
$239$		−	13.6734i		−	0.884456i	0.896903	−	0.442228i	$-0.145812\pi$
$240$	12.7505	−	4.80340i	0.823043	−	0.310058i
$241$	2.90930	−	1.67968i	0.187404	−	0.108198i	−0.403362	−	0.915040i	$-0.632159\pi$
$241$	2.90930	−	1.67968i	0.187404	−	0.108198i	0.590767	+	0.806842i	$0.298825\pi$
$242$	12.6377	+	5.68479i	0.812384	+	0.365432i
$243$	5.98673	+	3.45644i	0.384049	+	0.221731i
$244$	10.8368	+	3.61313i	0.693758	+	0.231307i
$245$		0			0
$246$	2.54876	−	1.83690i	0.162503	−	0.117117i
$247$	4.20803	−	7.28853i	0.267751	−	0.463758i
$248$	14.5621	−	15.8037i	0.924693	−	1.00354i
$249$	5.86465	+	10.1579i	0.371657	+	0.643729i
$250$	15.8048	+	0.457473i	0.999581	+	0.0289331i
$251$	−26.2007			−1.65377			−0.826887	−	0.562368i	$-0.809890\pi$
$251$	−26.2007			−1.65377			−0.826887	+	0.562368i	$0.809890\pi$
$252$		0			0
$253$		−	1.96223i		−	0.123364i
$254$	1.18717	+	11.7272i	0.0744896	+	0.735827i
$255$	−9.79312	−	18.7960i	−0.613269	−	1.17705i
$256$	11.0654	−	11.5567i	0.691589	−	0.722291i
$257$	−11.1405	+	19.2959i	−0.694926	+	1.20365i	0.275279	+	0.961364i	$0.411230\pi$
$257$	−11.1405	+	19.2959i	−0.694926	+	1.20365i	−0.970205	+	0.242284i	$0.922104\pi$
$258$	−10.8104	−	14.9997i	−0.673023	−	0.933839i
$259$		0			0
$260$	9.16991	+	3.50504i	0.568694	+	0.217373i
$261$	0.160916	−	0.278715i	0.00996047	−	0.0172520i
$262$	−7.32831	−	3.29647i	−0.452744	−	0.203657i
$263$	6.89188	+	11.9371i	0.424972	+	0.736073i	0.996418	−	0.0845669i	$-0.0269507\pi$
$263$	6.89188	+	11.9371i	0.424972	+	0.736073i	−0.571446	+	0.820640i	$0.693617\pi$
$264$	−19.1724	−	4.30611i	−1.17998	−	0.265023i
$265$	−20.6399	−	0.893757i	−1.26790	−	0.0549031i
$266$		0			0
$267$	−14.2042			−0.869285
$268$	19.8308	+	22.3666i	1.21136	+	1.36626i
$269$	−5.07627	+	2.93078i	−0.309506	+	0.178693i	−0.646705	−	0.762740i	$-0.723854\pi$
$269$	−5.07627	+	2.93078i	−0.309506	+	0.178693i	0.337200	+	0.941433i	$0.390520\pi$
$270$	−15.8348	−	7.96373i	−0.963676	−	0.484657i
$271$	8.69911	−	15.0673i	0.528433	−	0.915273i	−0.471017	−	0.882124i	$-0.656113\pi$
$271$	8.69911	−	15.0673i	0.528433	−	0.915273i	0.999450	−	0.0331491i	$-0.0105536\pi$
$272$	−19.9083	−	14.9357i	−1.20712	−	0.905607i
$273$		0			0
$274$	12.2249	+	16.9624i	0.738532	+	1.02473i
$275$	−18.6883	−	13.0658i	−1.12695	−	0.787896i
$276$	0.262715	+	1.28428i	0.0158136	+	0.0773048i
$277$	3.47314	−	2.00522i	0.208681	−	0.120482i	−0.392017	−	0.919958i	$-0.628223\pi$
$277$	3.47314	−	2.00522i	0.208681	−	0.120482i	0.600698	+	0.799476i	$0.294889\pi$
$278$	0.158620	+	1.56688i	0.00951337	+	0.0939755i
$279$	−5.16189			−0.309034
$280$		0			0
$281$	−11.7101			−0.698566			−0.349283	−	0.937017i	$-0.613575\pi$
$281$	−11.7101			−0.698566			−0.349283	+	0.937017i	$0.613575\pi$
$282$	0.974012	+	9.62154i	0.0580016	+	0.572954i
$283$	15.2454	−	8.80194i	0.906245	−	0.523221i	0.0270241	−	0.999635i	$-0.491397\pi$
$283$	15.2454	−	8.80194i	0.906245	−	0.523221i	0.879221	+	0.476414i	$0.158064\pi$
$284$	−1.83496	−	8.97023i	−0.108885	−	0.532285i
$285$	7.01303	−	11.0170i	0.415416	−	0.652588i
$286$	−8.27779	−	11.4857i	−0.489476	−	0.679162i
$287$		0			0
$288$	−3.84252	−	0.0736129i	−0.226423	−	0.00433768i
$289$	−10.8567	+	18.8044i	−0.638632	+	1.10614i
$290$	−0.673052	+	1.33827i	−0.0395230	+	0.0785861i
$291$	−11.9430	+	6.89531i	−0.700112	+	0.404210i
$292$	−16.2822	−	18.3643i	−0.952844	−	1.07469i
$293$	−23.5436			−1.37543			−0.687715	−	0.725980i	$-0.741386\pi$
$293$	−23.5436			−1.37543			−0.687715	+	0.725980i	$0.741386\pi$
$294$		0			0
$295$	−0.303366	+	7.00576i	−0.0176626	+	0.407891i
$296$	5.23319	−	23.3002i	0.304173	−	1.35430i
$297$	12.7810	+	22.1374i	0.741629	+	1.28454i
$298$	−8.87094	−	3.99039i	−0.513879	−	0.231157i
$299$	−0.472241	+	0.817945i	−0.0273104	+	0.0473030i
$300$	13.9809	+	6.04948i	0.807185	+	0.349267i
$301$		0			0
$302$	17.5609	+	24.3663i	1.01052	+	1.40212i
$303$	−6.09190	+	10.5515i	−0.349971	+	0.606167i
$304$	1.83655	−	15.2255i	0.105334	−	0.873241i
$305$	5.90135	+	11.3265i	0.337910	+	0.648552i
$306$	0.602106	+	5.94776i	0.0344201	+	0.340011i
$307$		−	11.0383i		−	0.629989i	−0.949093	−	0.314995i	$-0.897997\pi$
$307$		−	11.0383i		−	0.629989i	0.949093	−	0.314995i	$-0.102003\pi$
$308$		0			0
$309$	19.0445			1.08340
$310$	23.9865	−	1.38347i	1.36234	−	0.0785760i
$311$	10.8332	+	18.7637i	0.614297	+	1.06399i	0.990507	+	0.137459i	$0.0438936\pi$
$311$	10.8332	+	18.7637i	0.614297	+	1.06399i	−0.376211	+	0.926534i	$0.622773\pi$
$312$	6.95560	+	6.40912i	0.393783	+	0.362845i
$313$	1.91184	−	3.31141i	0.108064	−	0.187172i	−0.806922	−	0.590658i	$-0.798868\pi$
$313$	1.91184	−	3.31141i	0.108064	−	0.187172i	0.914986	+	0.403486i	$0.132202\pi$
$314$	2.67025	−	1.92446i	0.150691	−	0.108604i
$315$		0			0
$316$	11.7713	+	3.92469i	0.662188	+	0.220781i
$317$	7.56807	+	4.36943i	0.425065	+	0.245411i	0.697242	−	0.716836i	$-0.254410\pi$
$317$	7.56807	+	4.36943i	0.425065	+	0.245411i	−0.272177	+	0.962247i	$0.587744\pi$
$318$	−18.1523	−	8.16539i	−1.01793	−	0.457892i
$319$	1.87093	−	1.08018i	0.104752	−	0.0604786i
$320$	17.8753	−	0.687794i	0.999261	−	0.0384489i
$321$			22.0380i			1.23004i
$322$		0			0
$323$	−23.8550			−1.32733
$324$	−8.62475	−	9.72762i	−0.479153	−	0.540423i
$325$	4.64565	+	9.94403i	0.257694	+	0.551595i
$326$	−3.95540	−	1.77925i	−0.219069	−	0.0985433i
$327$	24.1375	+	13.9358i	1.33481	+	0.770652i
$328$	3.93725	−	1.22944i	0.217398	−	0.0678847i
$329$		0			0
$330$	−12.0620	−	18.3620i	−0.663994	−	1.01080i
$331$	8.38437	+	4.84072i	0.460847	+	0.266070i	0.712400	−	0.701773i	$-0.247608\pi$
$331$	8.38437	+	4.84072i	0.460847	+	0.266070i	−0.251553	+	0.967843i	$0.580941\pi$
$332$	3.08619	+	15.0869i	0.169377	+	0.828001i
$333$	−4.96767	+	2.86809i	−0.272227	+	0.157170i
$334$	18.3519	−	1.85781i	1.00417	−	0.101655i
$335$	−1.44581	+	33.3888i	−0.0789932	+	1.82422i
$336$		0			0
$337$		−	9.54187i		−	0.519779i	−0.965638	−	0.259889i	$-0.916314\pi$
$337$		−	9.54187i		−	0.519779i	0.965638	−	0.259889i	$-0.0836861\pi$
$338$	−1.16532	−	11.5114i	−0.0633853	−	0.626136i
$339$	−0.865171	−	1.49852i	−0.0469897	−	0.0813885i
$340$	−4.39199	−	27.4769i	−0.238189	−	1.49014i
$341$	−30.0079	−	17.3251i	−1.62502	−	0.938207i
$342$	−2.98844	+	2.15379i	−0.161597	+	0.116464i
$343$		0			0
$344$	−7.23540	−	23.1711i	−0.390106	−	1.24930i
$345$	−0.787027	+	1.23636i	−0.0423721	+	0.0665635i
$346$	14.2648	+	6.41669i	0.766880	+	0.344963i
$347$	−12.0894	−	20.9394i	−0.648991	−	1.12409i	−0.983364	−	0.181645i	$-0.941858\pi$
$347$	−12.0894	−	20.9394i	−0.648991	−	1.12409i	0.334373	−	0.942441i	$-0.391476\pi$
$348$	−1.07991	+	0.957472i	−0.0578891	+	0.0513259i
$349$		−	8.31416i		−	0.445047i	−0.974927	−	0.222523i	$-0.928571\pi$
$349$		−	8.31416i		−	0.445047i	0.974927	−	0.222523i	$-0.0714294\pi$
$350$		0			0
$351$		−	12.3038i		−	0.656727i
$352$	−22.0909	−	13.3248i	−1.17745	−	0.710213i
$353$	−5.26427	−	9.11798i	−0.280189	−	0.485301i	0.691242	−	0.722623i	$-0.257064\pi$
$353$	−5.26427	−	9.11798i	−0.280189	−	0.485301i	−0.971431	+	0.237322i	$0.923730\pi$
$354$	−2.77156	+	6.16138i	−0.147307	+	0.327474i
$355$	5.49709	−	8.63552i	0.291755	−	0.458326i
$356$	−17.6912	−	5.89847i	−0.937633	−	0.312618i
$357$		0			0
$358$	18.2282	+	25.2922i	0.963391	+	1.33673i
$359$	9.61689	+	5.55231i	0.507560	+	0.293040i	0.731830	−	0.681487i	$-0.238666\pi$
$359$	9.61689	+	5.55231i	0.507560	+	0.293040i	−0.224270	+	0.974527i	$0.572000\pi$
$360$	−3.03101	−	3.04565i	−0.159748	−	0.160520i
$361$	2.15038	+	3.72456i	0.113178	+	0.196030i
$362$	3.51705	−	0.356039i	0.184852	−	0.0187130i
$363$			14.9269i			0.783459i
$364$		0			0
$365$	1.18710	−	27.4142i	0.0621355	−	1.43492i
$366$	1.23932	+	12.2423i	0.0647803	+	0.639916i
$367$	20.2509	−	11.6918i	1.05709	−	0.610309i	0.132461	−	0.991188i	$-0.457712\pi$
$367$	20.2509	−	11.6918i	1.05709	−	0.610309i	0.924625	+	0.380879i	$0.124379\pi$
$368$	−0.206105	+	1.70866i	−0.0107439	+	0.0890699i
$369$	−0.858031	−	0.495384i	−0.0446673	−	0.0257887i
$370$	22.3153	−	14.6590i	1.16012	−	0.762083i
$371$		0			0
$372$	21.9598	+	7.32168i	1.13857	+	0.379611i
$373$	−7.44109	−	4.29611i	−0.385285	−	0.222444i	0.294830	−	0.955550i	$-0.404737\pi$
$373$	−7.44109	−	4.29611i	−0.385285	−	0.222444i	−0.680115	+	0.733105i	$0.738070\pi$
$374$	−16.4625	+	36.5974i	−0.851255	+	1.89241i
$375$	6.53461	+	15.7282i	0.337446	+	0.812198i
$376$	−2.78233	+	12.3880i	−0.143488	+	0.638862i
$377$	−1.03985			−0.0535550
$378$		0			0
$379$			5.57279i			0.286255i	0.989704	+	0.143128i	$0.0457159\pi$
$379$			5.57279i			0.286255i	−0.989704	+	0.143128i	$0.954284\pi$
$380$	13.3096	−	10.8093i	0.682767	−	0.554504i
$381$	−10.9957	+	6.34837i	−0.563327	+	0.325237i
$382$	−4.50241	+	10.0092i	−0.230363	+	0.512115i
$383$	−10.5951	−	6.11706i	−0.541383	−	0.312567i	0.204257	−	0.978917i	$-0.434522\pi$
$383$	−10.5951	−	6.11706i	−0.541383	−	0.312567i	−0.745639	+	0.666350i	$0.767856\pi$
$384$	16.2426	+	5.76344i	0.828874	+	0.294114i
$385$		0			0
$386$	−4.99190	−	6.92640i	−0.254081	−	0.352545i
$387$	−2.91538	+	5.04959i	−0.148197	+	0.256685i
$388$	−17.7383	+	3.62856i	−0.900524	+	0.184212i
$389$	1.99215	+	3.45051i	0.101006	+	0.174948i	0.912099	−	0.409969i	$-0.134461\pi$
$389$	1.99215	+	3.45051i	0.101006	+	0.174948i	−0.811093	+	0.584917i	$0.801127\pi$
$390$	0.608900	+	10.5570i	0.0308328	+	0.534575i
$391$	2.67709			0.135386
$392$		0			0
$393$		−	8.65574i		−	0.436624i
$394$	13.7110	−	1.38800i	0.690749	−	0.0699262i
$395$	6.41022	+	12.3032i	0.322533	+	0.619039i
$396$	1.24191	+	6.07110i	0.0624084	+	0.305084i
$397$	−19.8903	+	34.4509i	−0.998263	+	1.72904i	−0.448112	+	0.893977i	$0.647903\pi$
$397$	−19.8903	+	34.4509i	−0.998263	+	1.72904i	−0.550151	+	0.835065i	$0.685430\pi$
$398$	19.7950	−	14.2663i	0.992231	−	0.715107i
$399$		0			0
$400$	14.9009	+	13.3403i	0.745046	+	0.667014i
$401$	−0.215963	+	0.374058i	−0.0107847	+	0.0186796i	−0.871367	−	0.490631i	$-0.836766\pi$
$401$	−0.215963	+	0.374058i	−0.0107847	+	0.0186796i	0.860583	+	0.509311i	$0.170100\pi$
$402$	−13.2090	+	29.3646i	−0.658804	+	1.46457i
$403$	8.33910	+	14.4437i	0.415400	+	0.719494i
$404$	−11.9690	+	10.6120i	−0.595481	+	0.527969i
$405$	0.628810	−	14.5214i	0.0312458	−	0.721573i
$406$		0			0
$407$	−38.5052			−1.90863
$408$	5.87486	−	26.1571i	0.290849	−	1.29497i
$409$	15.9076	−	9.18424i	0.786579	−	0.454132i	−0.0521779	−	0.998638i	$-0.516616\pi$
$409$	15.9076	−	9.18424i	0.786579	−	0.454132i	0.838757	+	0.544506i	$0.183283\pi$
$410$	4.11990	+	2.07200i	0.203468	+	0.102329i
$411$	−11.2611	+	19.5048i	−0.555469	+	0.962101i
$412$	23.7197	+	7.90844i	1.16859	+	0.389621i
$413$		0			0
$414$	0.335374	−	0.241706i	0.0164827	−	0.0118792i
$415$	−9.24547	+	14.5240i	−0.453842	+	0.712953i
$416$	6.00167	+	10.8709i	0.294256	+	0.532989i
$417$	−1.46915	+	0.848217i	−0.0719448	+	0.0415373i
$418$	−24.6018	+	2.49050i	−1.20331	+	0.121814i
$419$	23.3512			1.14078			0.570389	−	0.821375i	$-0.306792\pi$
$419$	23.3512			1.14078			0.570389	+	0.821375i	$0.306792\pi$
$420$		0			0
$421$	35.7600			1.74283			0.871417	−	0.490543i	$-0.163201\pi$
$421$	35.7600			1.74283			0.871417	+	0.490543i	$0.163201\pi$
$422$	−37.7289	+	3.81939i	−1.83662	+	0.185925i
$423$	2.64116	−	1.52487i	0.128418	−	0.0741419i
$424$	−19.2177	−	17.7078i	−0.933295	−	0.859969i
$425$	17.8258	−	25.4967i	0.864677	−	1.23677i
$426$	8.00116	−	5.76648i	0.387657	−	0.279387i
$427$		0			0
$428$	−9.15152	+	27.4481i	−0.442355	+	1.32675i
$429$	7.62519	−	13.2072i	0.368148	−	0.637650i
$430$	12.1939	−	24.2460i	0.588044	−	1.16925i
$431$	−12.6651	+	7.31218i	−0.610054	+	0.352215i	−0.772987	−	0.634422i	$-0.781238\pi$
$431$	−12.6651	+	7.31218i	−0.610054	+	0.352215i	0.162932	+	0.986637i	$0.447905\pi$
$432$	−8.80414	−	20.6191i	−0.423589	−	0.992036i
$433$	−2.12837			−0.102283			−0.0511414	−	0.998691i	$-0.516286\pi$
$433$	−2.12837			−0.102283			−0.0511414	+	0.998691i	$0.516286\pi$
$434$		0			0
$435$	−1.61208	−	0.0698070i	−0.0772936	−	0.00334699i
$436$	24.2761	+	27.3803i	1.16261	+	1.31128i
$437$	0.824801	+	1.42860i	0.0394556	+	0.0683391i
$438$	10.8453	−	24.1100i	0.518211	−	1.15202i
$439$	12.3385	−	21.3709i	0.588884	−	1.01998i	−0.405494	−	0.914098i	$-0.632901\pi$
$439$	12.3385	−	21.3709i	0.588884	−	1.01998i	0.994379	−	0.105880i	$-0.0337660\pi$
$440$	−7.39813	−	27.8786i	−0.352692	−	1.32906i
$441$		0			0
$442$	15.6700	−	11.2935i	0.745347	−	0.537175i
$443$	8.07022	−	13.9780i	0.383427	−	0.664116i	−0.608122	−	0.793843i	$-0.708077\pi$
$443$	8.07022	−	13.9780i	0.383427	−	0.664116i	0.991550	+	0.129728i	$0.0414103\pi$
$444$	25.2017	−	5.15529i	1.19602	−	0.244659i
$445$	−9.63399	−	18.4906i	−0.456695	−	0.876536i
$446$	−24.7712	+	2.50765i	−1.17295	+	0.118741i
$447$		−	10.4778i		−	0.495582i
$448$		0			0
$449$	−28.5162			−1.34576			−0.672882	−	0.739750i	$-0.734944\pi$
$449$	−28.5162			−1.34576			−0.672882	+	0.739750i	$0.734944\pi$
$450$	−0.0688785	−	4.80354i	−0.00324697	−	0.226441i
$451$	−3.32536	−	5.75970i	−0.156585	−	0.271214i
$452$	−0.455285	−	2.22566i	−0.0214148	−	0.104686i
$453$	−16.1765	+	28.0185i	−0.760037	+	1.31642i
$454$	−7.26932	−	10.0864i	−0.341166	−	0.473378i
$455$		0			0
$456$	15.7685	−	4.92386i	0.738427	−	0.230581i
$457$	−20.2500	−	11.6914i	−0.947256	−	0.546899i	−0.0550288	−	0.998485i	$-0.517525\pi$
$457$	−20.2500	−	11.6914i	−0.947256	−	0.546899i	−0.892228	+	0.451586i	$0.850858\pi$
$458$	9.91132	−	22.0336i	0.463125	−	1.02956i
$459$	−30.2022	+	17.4373i	−1.40972	+	0.813901i
$460$	−1.49365	+	1.21305i	−0.0696417	+	0.0565589i
$461$		−	9.92550i		−	0.462277i	−0.972921	−	0.231138i	$-0.925755\pi$
$461$		−	9.92550i		−	0.462277i	0.972921	−	0.231138i	$-0.0742450\pi$
$462$		0			0
$463$	−16.8887			−0.784887			−0.392443	−	0.919776i	$-0.628370\pi$
$463$	−16.8887			−0.784887			−0.392443	+	0.919776i	$0.628370\pi$
$464$	−1.74261	+	0.744079i	−0.0808988	+	0.0345430i
$465$	11.9585	+	22.9520i	0.554563	+	1.06438i
$466$	−8.22798	+	18.2914i	−0.381154	+	0.847334i
$467$	26.6366	+	15.3786i	1.23259	+	0.711638i	0.967570	−	0.252604i	$-0.0812869\pi$
$467$	26.6366	+	15.3786i	1.23259	+	0.711638i	0.265024	+	0.964242i	$0.414620\pi$
$468$	0.943420	−	2.82959i	0.0436096	−	0.130798i
$469$		0			0
$470$	−11.8643	+	7.79372i	−0.547262	+	0.359497i
$471$	3.07048	+	1.77274i	0.141480	+	0.0816836i
$472$	−6.01053	+	6.52302i	−0.276657	+	0.300246i
$473$	−33.8964	+	19.5701i	−1.55856	+	0.899833i
$474$	1.34619	+	13.2980i	0.0618324	+	0.610796i
$475$	19.0980	+	1.65709i	0.876278	+	0.0760324i
$476$		0			0
$477$			6.27698i			0.287403i
$478$	19.2387	−	1.94758i	0.879958	−	0.0890803i
$479$	7.87671	+	13.6429i	0.359896	+	0.623358i	0.987943	−	0.154817i	$-0.0494788\pi$
$479$	7.87671	+	13.6429i	0.359896	+	0.623358i	−0.628047	+	0.778175i	$0.716145\pi$
$480$	8.57464	+	17.2561i	0.391377	+	0.787629i
$481$	16.0507	+	9.26686i	0.731848	+	0.422532i
$482$	2.77774	+	3.85420i	0.126523	+	0.175554i
$483$		0			0
$484$	−6.19856	+	18.5913i	−0.281753	+	0.845059i
$485$	−17.0764	−	10.8703i	−0.775399	−	0.493593i
$486$	−4.01056	+	8.91578i	−0.181923	+	0.404428i
$487$	6.75242	+	11.6955i	0.305981	+	0.529975i	0.977479	−	0.211031i	$-0.0676821\pi$
$487$	6.75242	+	11.6955i	0.305981	+	0.529975i	−0.671498	+	0.741006i	$0.734349\pi$
$488$	−3.54020	+	15.7623i	−0.160257	+	0.713527i
$489$		−	4.67187i		−	0.211269i
$490$		0			0
$491$			3.87067i			0.174681i	0.996179	+	0.0873404i	$0.0278368\pi$
$491$			3.87067i			0.174681i	−0.996179	+	0.0873404i	$0.972163\pi$
$492$	2.94760	+	3.32452i	0.132888	+	0.149881i
$493$	1.47370	+	2.55253i	0.0663723	+	0.114960i
$494$	10.8545	+	4.88265i	0.488367	+	0.219681i
$495$	−3.72046	+	5.84457i	−0.167222	+	0.262694i
$496$	24.3104	+	18.2381i	1.09157	+	0.818917i
$497$		0			0
$498$	−13.4570	+	9.69855i	−0.603024	+	0.434602i
$499$	21.1045	+	12.1847i	0.944767	+	0.545462i	0.891452	−	0.453116i	$-0.149688\pi$
$499$	21.1045	+	12.1847i	0.944767	+	0.545462i	0.0533157	+	0.998578i	$0.483021\pi$
$500$	1.60750	+	22.3028i	0.0718895	+	0.997413i
$501$	9.93461	+	17.2072i	0.443846	+	0.768763i
$502$	−3.73193	−	36.8650i	−0.166564	−	1.64536i
$503$			11.2245i			0.500475i	0.968184	+	0.250238i	$0.0805087\pi$
$503$			11.2245i			0.500475i	−0.968184	+	0.250238i	$0.919491\pi$
$504$		0			0
$505$	−17.8674	−	0.773699i	−0.795087	−	0.0344291i
$506$	2.76090	−	0.279493i	0.122737	−	0.0124250i
$507$	10.7934	−	6.23156i	0.479351	−	0.276753i
$508$	−16.3313	+	3.34075i	−0.724583	+	0.148222i
$509$	12.4520	+	7.18916i	0.551925	+	0.318654i	0.749898	−	0.661554i	$-0.230103\pi$
$509$	12.4520	+	7.18916i	0.551925	+	0.318654i	−0.197973	+	0.980207i	$0.563436\pi$
$510$	25.0515	−	16.4564i	1.10930	−	0.728700i
$511$		0			0
$512$	17.8366	+	13.9232i	0.788274	+	0.615325i
$513$	−18.6104	−	10.7447i	−0.821668	−	0.474390i
$514$	−28.7366	−	12.9265i	−1.26752	−	0.570164i
$515$	12.9169	+	24.7914i	0.569186	+	1.09244i
$516$	19.5651	−	17.3469i	0.861305	−	0.763655i
$517$	20.4720			0.900359
$518$		0			0
$519$			16.8487i			0.739575i
$520$	−3.62554	+	13.4015i	−0.158991	+	0.587695i
$521$	22.3540	−	12.9061i	0.979347	−	0.565426i	0.0772742	−	0.997010i	$-0.475378\pi$
$521$	22.3540	−	12.9061i	0.979347	−	0.565426i	0.902073	+	0.431584i	$0.142045\pi$
$522$	0.415079	+	0.186714i	0.0181675	+	0.00817224i
$523$	−3.83258	−	2.21274i	−0.167587	−	0.0967563i	0.413861	−	0.910340i	$-0.364180\pi$
$523$	−3.83258	−	2.21274i	−0.167587	−	0.0967563i	−0.581447	+	0.813584i	$0.697513\pi$
$524$	3.59439	−	10.7806i	0.157022	−	0.470954i
$525$		0			0
$526$	−15.8141	+	11.3973i	−0.689528	+	0.496946i
$527$	23.6368	−	40.9401i	1.02964	−	1.78338i
$528$	3.32794	−	27.5894i	0.144830	−	1.20067i
$529$	11.4074	+	19.7583i	0.495976	+	0.859055i
$530$	−1.68234	−	29.1681i	−0.0730761	−	1.26698i
$531$	2.13058			0.0924593
$532$		0			0
$533$			3.20120i			0.138659i
$534$	−2.02320	−	19.9857i	−0.0875524	−	0.864865i
$535$	−28.6882	+	14.9472i	−1.24030	+	0.646224i
$536$	−28.6456	+	31.0881i	−1.23730	+	1.34280i
$537$	−16.7912	+	29.0831i	−0.724592	+	1.25503i
$538$	−4.84672	−	6.72497i	−0.208957	−	0.289934i
$539$		0			0
$540$	8.94970	−	23.4143i	0.385134	−	1.00759i
$541$	−2.05080	+	3.55209i	−0.0881708	+	0.152716i	−0.906738	−	0.421695i	$-0.861435\pi$
$541$	−2.05080	+	3.55209i	−0.0881708	+	0.152716i	0.818567	+	0.574411i	$0.194769\pi$
$542$	22.4391	+	10.0937i	0.963842	+	0.433562i
$543$	1.90392	+	3.29768i	0.0817049	+	0.141517i
$544$	18.1791	−	30.1389i	0.779424	−	1.29219i
$545$	−1.76991	+	40.8733i	−0.0758146	+	1.75082i
$546$		0			0
$547$	−4.16833			−0.178225			−0.0891125	−	0.996022i	$-0.528403\pi$
$547$	−4.16833			−0.178225			−0.0891125	+	0.996022i	$0.528403\pi$
$548$	−22.1252	+	19.6167i	−0.945140	+	0.837985i
$549$	3.36058	−	1.94023i	0.143426	−	0.0828070i
$550$	15.7219	−	28.1559i	0.670386	−	1.20057i
$551$	−0.908085	+	1.57285i	−0.0386857	+	0.0670056i
$552$	−1.76959	+	0.552574i	−0.0753190	+	0.0235191i
$553$		0			0
$554$	3.31609	+	4.60117i	0.140887	+	0.195485i
$555$	24.2613	+	15.4440i	1.02984	+	0.655560i
$556$	−2.18205	+	0.446362i	−0.0925395	+	0.0189300i
$557$	10.5286	−	6.07868i	0.446110	−	0.257562i	−0.260076	−	0.965588i	$-0.583748\pi$
$557$	10.5286	−	6.07868i	0.446110	−	0.257562i	0.706186	+	0.708026i	$0.250414\pi$
$558$	−0.735240	−	7.26289i	−0.0311252	−	0.307463i
$559$	18.8394			0.796820
$560$		0			0
$561$	−43.2265			−1.82502
$562$	−1.66794	−	16.4764i	−0.0703579	−	0.695014i
$563$	−21.5664	+	12.4514i	−0.908915	+	0.524762i	−0.880082	−	0.474822i	$-0.842513\pi$
$563$	−21.5664	+	12.4514i	−0.908915	+	0.524762i	−0.0288333	+	0.999584i	$0.509179\pi$
$564$	−13.3990	+	2.74091i	−0.564199	+	0.115413i
$565$	1.36392	−	2.14262i	0.0573805	−	0.0901406i
$566$	14.5560	+	20.1969i	0.611835	+	0.848939i
$567$		0			0
$568$	12.3600	−	3.85952i	0.518612	−	0.161942i
$569$	14.7938	−	25.6235i	0.620187	−	1.07419i	−0.369264	−	0.929325i	$-0.620390\pi$
$569$	14.7938	−	25.6235i	0.620187	−	1.07419i	0.989451	−	0.144870i	$-0.0462765\pi$
$570$	16.5000	+	8.29828i	0.691109	+	0.347577i
$571$	21.2328	−	12.2588i	0.888565	−	0.513013i	0.0150919	−	0.999886i	$-0.495196\pi$
$571$	21.2328	−	12.2588i	0.888565	−	0.513013i	0.873473	+	0.486873i	$0.161863\pi$
$572$	14.9815	−	13.2830i	0.626410	−	0.555390i
$573$	−11.8222			−0.493881
$574$		0			0
$575$	−2.14325	−	0.185964i	−0.0893797	−	0.00775524i
$576$	−0.443740	−	5.41700i	−0.0184892	−	0.225708i
$577$	−6.77379	−	11.7325i	−0.281997	−	0.488432i	0.689880	−	0.723924i	$-0.257663\pi$
$577$	−6.77379	−	11.7325i	−0.281997	−	0.488432i	−0.971876	+	0.235492i	$0.924330\pi$
$578$	−28.0047	−	12.5973i	−1.16484	−	0.523977i
$579$	4.59835	−	7.96458i	0.191101	−	0.330996i
$580$	−1.97885	−	0.756380i	−0.0821672	−	0.0314070i
$581$		0			0
$582$	−11.4030	−	15.8220i	−0.472668	−	0.655841i
$583$	−21.0677	+	36.4904i	−0.872537	+	1.51128i
$584$	23.5197	−	25.5252i	0.973254	−	1.05624i
$585$	2.95744	−	1.54089i	0.122275	−	0.0637080i
$586$	−3.35346	−	33.1263i	−0.138530	−	1.36844i
$587$			26.8772i			1.10934i	0.832070	+	0.554671i	$0.187156\pi$
$587$			26.8772i			1.10934i	−0.832070	+	0.554671i	$0.812844\pi$
$588$		0			0
$589$	29.1296			1.20027
$590$	−9.90047	+	0.571032i	−0.407596	+	0.0235090i
$591$	7.42229	+	12.8558i	0.305312	+	0.528817i
$592$	33.5293	+	4.04443i	1.37804	+	0.166225i
$593$	−0.473574	+	0.820254i	−0.0194473	+	0.0336838i	−0.875585	−	0.483064i	$-0.839524\pi$
$593$	−0.473574	+	0.820254i	−0.0194473	+	0.0336838i	0.856138	+	0.516747i	$0.172857\pi$
$594$	−29.3273	+	21.1363i	−1.20331	+	0.867234i
$595$		0			0
$596$	4.35102	−	13.0500i	0.178225	−	0.534548i
$597$	22.7619	+	13.1416i	0.931584	+	0.537850i
$598$	−1.21813	−	0.547948i	−0.0498131	−	0.0224073i
$599$	−19.1138	+	11.0354i	−0.780970	+	0.450893i	−0.836774	−	0.547549i	$-0.815561\pi$
$599$	−19.1138	+	11.0354i	−0.780970	+	0.450893i	0.0558040	+	0.998442i	$0.482228\pi$
$600$	−6.52037	+	20.5331i	−0.266193	+	0.838258i
$601$		−	20.5283i		−	0.837367i	−0.908132	−	0.418684i	$-0.862492\pi$
$601$		−	20.5283i		−	0.837367i	0.908132	−	0.418684i	$-0.137508\pi$
$602$		0			0
$603$	10.1542			0.413509
$604$	−31.7826	+	28.1793i	−1.29322	+	1.14660i
$605$	−19.4313	+	10.1241i	−0.789994	+	0.411604i
$606$	−15.7139	−	7.06853i	−0.638333	−	0.287139i
$607$	21.6917	+	12.5237i	0.880438	+	0.508321i	0.870803	−	0.491632i	$-0.163600\pi$
$607$	21.6917	+	12.5237i	0.880438	+	0.508321i	0.00963521	+	0.999954i	$0.496933\pi$
$608$	21.6842	+	0.415413i	0.879409	+	0.0168472i
$609$		0			0
$610$	−15.0960	+	9.91663i	−0.611221	+	0.401512i
$611$	−8.53365	−	4.92691i	−0.345235	−	0.199321i
$612$	−8.28287	+	1.69435i	−0.334815	+	0.0684902i
$613$	−20.2822	+	11.7100i	−0.819192	+	0.472961i	−0.850138	−	0.526560i	$-0.823481\pi$
$613$	−20.2822	+	11.7100i	−0.819192	+	0.472961i	0.0309457	+	0.999521i	$0.490148\pi$
$614$	15.5311	−	1.57225i	0.626786	−	0.0634510i
$615$	−0.214903	+	4.96284i	−0.00866571	+	0.200121i
$616$		0			0
$617$		−	16.7405i		−	0.673948i	−0.941514	−	0.336974i	$-0.890597\pi$
$617$		−	16.7405i		−	0.673948i	0.941514	−	0.336974i	$-0.109403\pi$
$618$	2.71263	+	26.7960i	0.109118	+	1.07789i
$619$	13.6919	+	23.7151i	0.550326	+	0.953192i	0.998251	+	0.0591208i	$0.0188297\pi$
$619$	13.6919	+	23.7151i	0.550326	+	0.953192i	−0.447925	+	0.894071i	$0.647837\pi$
$620$	5.36312	+	33.5524i	0.215388	+	1.34750i
$621$	2.08852	+	1.20581i	0.0838095	+	0.0483875i
$622$	−24.8579	+	17.9153i	−0.996712	+	0.718336i
$623$		0			0
$624$	−8.02704	+	10.6996i	−0.321339	+	0.428326i
$625$	−16.0423	+	19.1741i	−0.641690	+	0.766964i
$626$	4.93155	+	2.21834i	0.197104	+	0.0886628i
$627$	−13.3179	−	23.0673i	−0.531867	−	0.921220i
$628$	3.08810	+	3.48298i	0.123229	+	0.138986i
$629$		−	52.5330i		−	2.09463i
$630$		0			0
$631$		−	3.77099i		−	0.150121i	−0.997179	−	0.0750604i	$-0.976085\pi$
$631$		−	3.77099i		−	0.150121i	0.997179	−	0.0750604i	$-0.0239150\pi$
$632$	−3.84547	+	17.1215i	−0.152965	+	0.681057i
$633$	−20.4242	−	35.3757i	−0.811788	−	1.40606i
$634$	−5.06991	+	11.2708i	−0.201352	+	0.447621i
$635$	−15.7219	−	10.0080i	−0.623904	−	0.397157i
$636$	8.90334	−	26.7037i	0.353040	−	1.05887i
$637$		0			0
$638$	1.78633	+	2.47858i	0.0707214	+	0.0981281i
$639$	−2.69356	−	1.55513i	−0.106556	−	0.0615200i
$640$	3.51384	+	25.0530i	0.138897	+	0.990307i
$641$	−12.5584	−	21.7517i	−0.496026	−	0.859142i	0.503964	−	0.863725i	$-0.331874\pi$
$641$	−12.5584	−	21.7517i	−0.496026	−	0.859142i	−0.999989	+	0.00458317i	$0.998541\pi$
$642$	−31.0079	+	3.13901i	−1.22379	+	0.123887i
$643$		−	12.8390i		−	0.506319i	−0.967424	−	0.253160i	$-0.918530\pi$
$643$		−	12.8390i		−	0.506319i	0.967424	−	0.253160i	$-0.0814698\pi$
$644$		0			0
$645$	29.2068	+	1.26472i	1.15002	+	0.0497984i
$646$	−3.39781	−	33.5645i	−0.133685	−	1.32058i
$647$	−3.84568	+	2.22030i	−0.151189	+	0.0872892i	−0.573686	−	0.819075i	$-0.694487\pi$
$647$	−3.84568	+	2.22030i	−0.151189	+	0.0872892i	0.422497	+	0.906364i	$0.361154\pi$
$648$	12.4585	−	13.5208i	0.489416	−	0.531146i
$649$	12.3858	+	7.15097i	0.486187	+	0.280700i
$650$	−13.3298	+	7.95292i	−0.522836	+	0.311939i
$651$		0			0
$652$	1.94005	−	5.81877i	0.0759781	−	0.227880i
$653$	32.8985	+	18.9940i	1.28742	+	0.743291i	0.978193	−	0.207698i	$-0.0665971\pi$
$653$	32.8985	+	18.9940i	1.28742	+	0.743291i	0.309225	+	0.950989i	$0.399930\pi$
$654$	−16.1699	+	35.9470i	−0.632295	+	1.40564i
$655$	11.2677	−	5.87073i	0.440266	−	0.229389i
$656$	2.29066	+	5.36468i	0.0894354	+	0.209455i
$657$	−8.33715			−0.325263
$658$		0			0
$659$		−	19.5420i		−	0.761248i	−0.924730	−	0.380624i	$-0.875709\pi$
$659$		−	19.5420i		−	0.761248i	0.924730	−	0.380624i	$-0.124291\pi$
$660$	24.1177	−	19.5870i	0.938779	−	0.762422i
$661$	−19.8065	+	11.4353i	−0.770382	+	0.444780i	−0.833011	−	0.553257i	$-0.813385\pi$
$661$	−19.8065	+	11.4353i	−0.770382	+	0.444780i	0.0626290	+	0.998037i	$0.480052\pi$
$662$	−5.61676	+	12.4865i	−0.218302	+	0.485301i
$663$	18.0187	+	10.4031i	0.699790	+	0.404024i
$664$	−20.7880	+	6.49127i	−0.806731	+	0.251910i
$665$		0			0
$666$	−4.74304	−	6.58110i	−0.183789	−	0.255013i
$667$	0.101909	−	0.176511i	0.00394591	−	0.00683452i
$668$	5.22795	+	25.5569i	0.202276	+	0.988827i
$669$	−13.4096	−	23.2262i	−0.518446	−	0.897975i
$670$	−47.1847	+	2.72149i	−1.82290	+	0.105140i
$671$	26.0483			1.00559
$672$		0			0
$673$			23.0022i			0.886670i	0.896356	+	0.443335i	$0.146205\pi$
$673$			23.0022i			0.886670i	−0.896356	+	0.443335i	$0.853795\pi$
$674$	13.4256	−	1.35911i	0.517135	−	0.0523509i
$675$	25.3909	−	11.8621i	0.977295	−	0.456572i
$676$	16.0308	−	3.27927i	0.616568	−	0.126126i
$677$	20.3832	−	35.3047i	0.783388	−	1.35687i	−0.146569	−	0.989200i	$-0.546823\pi$
$677$	20.3832	−	35.3047i	0.783388	−	1.35687i	0.929957	−	0.367668i	$-0.119844\pi$
$678$	1.98522	−	1.43076i	0.0762419	−	0.0549480i
$679$		0			0
$680$	38.0350	−	10.0933i	1.45858	−	0.387062i
$681$	6.69623	−	11.5982i	0.256600	−	0.444444i
$682$	20.1026	−	44.6896i	0.769767	−	1.71125i
$683$	5.45020	+	9.44002i	0.208546	+	0.361212i	0.951257	−	0.308400i	$-0.0997935\pi$
$683$	5.45020	+	9.44002i	0.208546	+	0.361212i	−0.742711	+	0.669612i	$0.766460\pi$
$684$	−3.45609	−	3.89803i	−0.132147	−	0.149045i
$685$	−33.0284	−	1.43021i	−1.26195	−	0.0546455i
$686$		0			0
$687$	26.0247			0.992905
$688$	31.5716	−	13.4808i	1.20366	−	0.513949i
$689$	17.5640	−	10.1406i	0.669133	−	0.386324i
$690$	−1.85169	−	0.931262i	−0.0704926	−	0.0354525i
$691$	8.00675	−	13.8681i	0.304591	−	0.527568i	−0.672579	−	0.740025i	$-0.734813\pi$
$691$	8.00675	−	13.8681i	0.304591	−	0.527568i	0.977170	+	0.212458i	$0.0681468\pi$
$692$	−6.99660	+	20.9849i	−0.265971	+	0.797724i
$693$		0			0
$694$	27.7402	−	19.9925i	1.05301	−	0.758907i
$695$	−2.10063	−	1.33719i	−0.0796814	−	0.0507225i
$696$	−1.50100	−	1.38307i	−0.0568954	−	0.0524253i
$697$	7.85802	−	4.53683i	0.297644	−	0.171845i
$698$	11.6982	−	1.18424i	0.442784	−	0.0448241i
$699$	−21.6047			−0.817164
$700$		0			0
$701$	22.0640			0.833346			0.416673	−	0.909057i	$-0.363196\pi$
$701$	22.0640			0.833346			0.416673	+	0.909057i	$0.363196\pi$
$702$	17.3117	−	1.75251i	0.653388	−	0.0661441i
$703$	28.0336	−	16.1852i	1.05731	−	0.610437i
$704$	15.6017	−	32.9804i	0.588012	−	1.24299i
$705$	−12.8990	−	8.21109i	−0.485805	−	0.309248i
$706$	12.0794	−	8.70567i	0.454613	−	0.327642i
$707$		0			0
$708$	−9.06398	−	3.02204i	−0.340645	−	0.113575i
$709$	18.5954	−	32.2081i	0.698364	−	1.20960i	−0.270669	−	0.962672i	$-0.587245\pi$
$709$	18.5954	−	32.2081i	0.698364	−	1.20960i	0.969033	−	0.246930i	$-0.0794217\pi$
$710$	12.9334	+	6.50451i	0.485380	+	0.244110i
$711$	3.65036	−	2.10753i	0.136899	−	0.0790387i
$712$	5.77940	−	25.7321i	0.216592	−	0.964352i
$713$	−3.26903			−0.122426
$714$		0			0
$715$	22.3644	+	0.968433i	0.836383	+	0.0362173i
$716$	−32.9903	+	29.2500i	−1.23291	+	1.09313i
$717$	10.4147	+	18.0388i	0.388943	+	0.673670i
$718$	−6.44244	+	14.3220i	−0.240430	+	0.534493i
$719$	−18.1858	+	31.4988i	−0.678218	+	1.17471i	0.297300	+	0.954784i	$0.403914\pi$
$719$	−18.1858	+	31.4988i	−0.678218	+	1.17471i	−0.975517	+	0.219923i	$0.929419\pi$
$720$	3.85357	−	4.69851i	0.143614	−	0.175103i
$721$		0			0
$722$	−4.93425	+	3.55614i	−0.183634	+	0.132346i
$723$	−2.55875	+	4.43189i	−0.0951611	+	0.164824i
$724$	1.00191	+	4.89785i	0.0372357	+	0.182027i
$725$	−1.00252	−	2.14590i	−0.0372327	−	0.0796967i
$726$	−21.0025	+	2.12613i	−0.779475	+	0.0789082i
$727$		−	34.1872i		−	1.26793i	−0.773360	−	0.633967i	$-0.781425\pi$
$727$		−	34.1872i		−	1.26793i	0.773360	−	0.633967i	$-0.218575\pi$
$728$		0			0
$729$	−30.0315			−1.11228
$730$	38.7414	−	2.23450i	1.43388	−	0.0827025i
$731$	−26.6997	−	46.2452i	−0.987523	−	1.71044i
$732$	−17.0487	+	3.48750i	−0.630138	+	0.128902i
$733$	11.2674	−	19.5158i	0.416172	−	0.720832i	−0.579378	−	0.815059i	$-0.696705\pi$
$733$	11.2674	−	19.5158i	0.416172	−	0.720832i	0.995551	+	0.0942270i	$0.0300379\pi$
$734$	19.3351	+	26.8281i	0.713673	+	0.990242i
$735$		0			0
$736$	−2.43348	−	0.0466191i	−0.0896991	−	0.00171840i
$737$	59.0298	+	34.0809i	2.17439	+	1.25539i
$738$	0.574802	−	1.27783i	0.0211588	−	0.0470375i
$739$	−6.08695	+	3.51430i	−0.223912	+	0.129276i	−0.607760	−	0.794120i	$-0.707932\pi$
$739$	−6.08695	+	3.51430i	−0.223912	+	0.129276i	0.383848	+	0.923396i	$0.374599\pi$
$740$	23.8040	+	29.3101i	0.875052	+	1.07746i
$741$			12.8206i			0.470978i
$742$		0			0
$743$	−0.0257779			−0.000945701			−0.000472850	−	1.00000i	$-0.500151\pi$
$743$	−0.0257779			−0.000945701			−0.000472850		1.00000i	$0.500151\pi$
$744$	−7.17388	+	31.9409i	−0.263007	+	1.17101i
$745$	13.6396	−	7.10654i	0.499716	−	0.260363i
$746$	4.98485	−	11.0817i	0.182508	−	0.405730i
$747$	4.53026	+	2.61555i	0.165754	+	0.0956979i
$748$	−53.8382	−	17.9503i	−1.96852	−	0.656328i
$749$		0			0
$750$	−21.1991	+	11.4346i	−0.774082	+	0.417533i
$751$	−8.96782	−	5.17757i	−0.327240	−	0.188932i	0.327375	−	0.944895i	$-0.393836\pi$
$751$	−8.96782	−	5.17757i	−0.327240	−	0.188932i	−0.654615	+	0.755962i	$0.727169\pi$
$752$	−17.8265	−	2.15030i	−0.650065	−	0.0784134i
$753$	34.5656	−	19.9565i	1.25964	−	0.727254i
$754$	−0.148112	−	1.46309i	−0.00539393	−	0.0532827i
$755$	−47.4451	−	2.05448i	−1.72670	−	0.0747703i
$756$		0			0
$757$		−	36.2159i		−	1.31629i	−0.752892	−	0.658145i	$-0.771342\pi$
$757$		−	36.2159i		−	1.31629i	0.752892	−	0.658145i	$-0.228658\pi$
$758$	−7.84105	+	0.793768i	−0.284800	+	0.0288310i
$759$	1.49458	+	2.58870i	0.0542500	+	0.0939637i
$760$	17.1046	+	17.1872i	0.620451	+	0.623446i
$761$	22.3558	+	12.9071i	0.810396	+	0.467883i	0.847094	−	0.531444i	$-0.178350\pi$
$761$	22.3558	+	12.9071i	0.810396	+	0.467883i	−0.0366971	+	0.999326i	$0.511684\pi$
$762$	−10.4985	−	14.5670i	−0.380320	−	0.527706i
$763$		0			0
$764$	−14.7245	−	4.90931i	−0.532713	−	0.177613i
$765$	−7.97380	−	5.07586i	−0.288293	−	0.183518i
$766$	7.09772	−	15.7788i	0.256451	−	0.570111i
$767$	−3.44198	−	5.96169i	−0.124283	−	0.215264i
$768$	−5.79576	+	23.6746i	−0.209136	+	0.854282i
$769$			17.9643i			0.647810i	0.946090	+	0.323905i	$0.104996\pi$
$769$			17.9643i			0.647810i	−0.946090	+	0.323905i	$0.895004\pi$
$770$		0			0
$771$		−	33.9419i		−	1.22239i
$772$	9.03458	−	8.01028i	0.325162	−	0.288296i
$773$	−2.13236	−	3.69336i	−0.0766958	−	0.132841i	0.825127	−	0.564948i	$-0.191104\pi$
$773$	−2.13236	−	3.69336i	−0.0766958	−	0.132841i	−0.901822	+	0.432107i	$0.857770\pi$
$774$	−7.52015	−	3.38276i	−0.270306	−	0.121591i
$775$	−21.7673	+	31.1343i	−0.781904	+	1.11838i
$776$	−7.63204	−	24.4413i	−0.273974	−	0.877392i
$777$		0			0
$778$	−4.57118	+	3.29448i	−0.163885	+	0.118113i
$779$	4.84205	+	2.79556i	0.173484	+	0.100161i
$780$	−14.7672	+	2.36044i	−0.528752	+	0.0845173i
$781$	−10.4391	−	18.0811i	−0.373541	−	0.646991i
$782$	0.381315	+	3.76672i	0.0136358	+	0.134698i
$783$			2.65513i			0.0948866i
$784$		0			0
$785$	−0.225146	+	5.19939i	−0.00803580	+	0.185574i
$786$	12.1788	−	1.23289i	0.434404	−	0.0439758i
$787$	−32.6392	+	18.8442i	−1.16346	+	0.671725i	−0.952131	−	0.305690i	$-0.901113\pi$
$787$	−32.6392	+	18.8442i	−1.16346	+	0.671725i	−0.211331	+	0.977415i	$0.567780\pi$
$788$	3.90588	+	19.0939i	0.139141	+	0.680194i
$789$	−18.1844	−	10.4988i	−0.647382	−	0.373766i
$790$	−16.3978	+	10.7717i	−0.583407	+	0.383241i
$791$		0			0
$792$	−8.36529	+	2.61214i	−0.297247	+	0.0928185i
$793$	−10.8581	−	6.26893i	−0.385583	−	0.222616i
$794$	−51.3063	−	23.0790i	−1.82079	−	0.819042i
$795$	27.9102	−	14.5419i	0.989875	−	0.515746i
$796$	22.8926	+	25.8199i	0.811406	+	0.915162i
$797$	−12.2918			−0.435398			−0.217699	−	0.976016i	$-0.569855\pi$
$797$	−12.2918			−0.435398			−0.217699	+	0.976016i	$0.569855\pi$
$798$		0			0
$799$			27.9302i			0.988099i
$800$	−16.6476	+	22.8661i	−0.588583	+	0.808437i
$801$	−5.48616	+	3.16744i	−0.193844	+	0.111916i
$802$	−0.557069	−	0.250585i	−0.0196708	−	0.00884845i
$803$	−48.4669	−	27.9824i	−1.71036	−	0.987477i
$804$	−43.1981	−	14.4028i	−1.52348	−	0.507946i
$805$		0			0
$806$	−19.1349	+	13.7906i	−0.673997	+	0.485754i
$807$	4.46462	−	7.73295i	0.157162	−	0.272213i
$808$	−16.6362	−	15.3292i	−0.585260	−	0.539278i
$809$	13.5524	+	23.4734i	0.476476	+	0.825281i	0.999637	−	0.0269532i	$-0.00858050\pi$
$809$	13.5524	+	23.4734i	0.476476	+	0.825281i	−0.523160	+	0.852234i	$0.675247\pi$
$810$	20.5215	−	1.18362i	0.721051	−	0.0415883i
$811$	41.9273			1.47227			0.736133	−	0.676837i	$-0.236650\pi$
$811$	41.9273			1.47227			0.736133	+	0.676837i	$0.236650\pi$
$812$		0			0
$813$			26.5036i			0.929523i
$814$	−5.48453	−	54.1776i	−0.192233	−	1.89893i
$815$	6.08167	−	3.16868i	0.213032	−	0.110994i
$816$	37.6405	+	4.54034i	1.31768	+	0.158944i
$817$	16.4521	−	28.4959i	0.575587	−	0.996946i
$818$	15.1882	+	21.0741i	0.531045	+	0.736840i
$819$		0			0
$820$	−2.32853	+	6.09192i	−0.0813159	+	0.212739i
$821$	−18.2126	+	31.5451i	−0.635623	+	1.10093i	0.350760	+	0.936466i	$0.385923\pi$
$821$	−18.2126	+	31.5451i	−0.635623	+	1.10093i	−0.986383	+	0.164466i	$0.947410\pi$
$822$	−29.0477	−	13.0664i	−1.01315	−	0.455744i
$823$	−19.8907	−	34.4517i	−0.693346	−	1.20091i	−0.970735	−	0.240153i	$-0.922802\pi$
$823$	−19.8907	−	34.4517i	−0.693346	−	1.20091i	0.277388	−	0.960758i	$-0.410531\pi$
$824$	−7.74880	+	34.5006i	−0.269942	+	1.20189i
$825$	34.6067	+	3.00273i	1.20485	+	0.104542i
$826$		0			0
$827$	1.33392			0.0463851			0.0231925	−	0.999731i	$-0.492617\pi$
$827$	1.33392			0.0463851			0.0231925	+	0.999731i	$0.492617\pi$
$828$	0.387855	+	0.437451i	0.0134789	+	0.0152025i
$829$	−11.6133	+	6.70492i	−0.403345	+	0.232872i	−0.687926	−	0.725780i	$-0.741479\pi$
$829$	−11.6133	+	6.70492i	−0.403345	+	0.232872i	0.284581	+	0.958652i	$0.408146\pi$
$830$	−21.7524	−	10.9398i	−0.755037	−	0.379728i
$831$	−3.05466	+	5.29082i	−0.105965	+	0.183537i
$832$	−14.4407	+	9.99289i	−0.500642	+	0.346441i
$833$		0			0
$834$	−1.40272	−	1.94632i	−0.0485722	−	0.0673954i
$835$	−15.6616	+	24.6033i	−0.541994	+	0.851432i
$836$	−7.00837	−	34.2605i	−0.242390	−	1.18493i
$837$	36.8804	−	21.2929i	1.27477	−	0.735990i
$838$	3.32605	+	32.8556i	0.114897	+	1.13498i
$839$	−14.3910			−0.496834			−0.248417	−	0.968653i	$-0.579910\pi$
$839$	−14.3910			−0.496834			−0.248417	+	0.968653i	$0.579910\pi$
$840$		0			0
$841$	−28.7756			−0.992262
$842$	5.09352	+	50.3151i	0.175534	+	1.73397i
$843$	15.4487	−	8.91931i	0.532082	−	0.307197i
$844$	−10.7479	−	52.5415i	−0.369959	−	1.80855i
$845$	15.4326	+	9.82389i	0.530898	+	0.337952i
$846$	2.52173	+	3.49897i	0.0866988	+	0.120297i
$847$		0			0
$848$	22.1780	−	29.5620i	0.761597	−	1.01516i
$849$	−13.4085	+	23.2241i	−0.460177	+	0.797051i
$850$	38.4134	+	21.4496i	1.31757	+	0.735715i
$851$	−3.14603	+	1.81636i	−0.107845	+	0.0622641i
$852$	9.25322	+	10.4364i	0.317010	+	0.357547i
$853$	33.2591			1.13877			0.569385	−	0.822071i	$-0.307181\pi$
$853$	33.2591			1.13877			0.569385	+	0.822071i	$0.307181\pi$
$854$		0			0
$855$	0.251975	−	5.81898i	0.00861738	−	0.199005i
$856$	−39.9236	−	8.96679i	−1.36456	−	0.306479i
$857$	−0.864161	−	1.49677i	−0.0295192	−	0.0511287i	0.850888	−	0.525346i	$-0.176064\pi$
$857$	−0.864161	−	1.49677i	−0.0295192	−	0.0511287i	−0.880408	+	0.474218i	$0.842731\pi$
$858$	19.6690	+	8.84763i	0.671487	+	0.302053i
$859$	8.78624	−	15.2182i	0.299783	−	0.519239i	−0.676304	−	0.736623i	$-0.736419\pi$
$859$	8.78624	−	15.2182i	0.299783	−	0.519239i	0.976086	+	0.217385i	$0.0697526\pi$
$860$	35.8516	+	13.7036i	1.22253	+	0.467290i
$861$		0			0
$862$	−12.0924	−	16.7785i	−0.411867	−	0.571478i
$863$	20.8154	−	36.0532i	0.708563	−	1.22727i	−0.256827	−	0.966457i	$-0.582677\pi$
$863$	20.8154	−	36.0532i	0.708563	−	1.22727i	0.965390	−	0.260810i	$-0.0839895\pi$
$864$	27.7575	−	15.3245i	0.944329	−	0.521351i
$865$	−21.9330	+	11.4276i	−0.745744	+	0.388549i
$866$	−0.303157	−	2.99466i	−0.0103017	−	0.101763i
$867$		−	33.0773i		−	1.12337i
$868$		0			0
$869$	28.2945			0.959825
$870$	−0.131399	−	2.27818i	−0.00445485	−	0.0772376i
$871$	−16.4042	−	28.4129i	−0.555834	−	0.962733i
$872$	−35.0669	+	38.0569i	−1.18752	+	1.28877i
$873$	−3.07520	+	5.32641i	−0.104080	+	0.180272i
$874$	−1.89259	+	1.36400i	−0.0640177	+	0.0461379i
$875$		0			0
$876$	35.4681	+	11.8255i	1.19836	+	0.399547i
$877$	−38.4695	−	22.2104i	−1.29902	−	0.749991i	−0.318787	−	0.947826i	$-0.603276\pi$
$877$	−38.4695	−	22.2104i	−1.29902	−	0.749991i	−0.980235	+	0.197835i	$0.936609\pi$
$878$	31.8268	+	14.3166i	1.07410	+	0.483160i
$879$	31.0602	−	17.9326i	1.04763	−	0.604852i
$880$	38.1720	−	14.3803i	1.28678	−	0.484758i
$881$			25.0886i			0.845257i	0.906303	+	0.422628i	$0.138892\pi$
$881$			25.0886i			0.845257i	−0.906303	+	0.422628i	$0.861108\pi$
$882$		0			0
$883$	7.23066			0.243331			0.121666	−	0.992571i	$-0.461176\pi$
$883$	7.23066			0.243331			0.121666	+	0.992571i	$0.461176\pi$
$884$	18.1221	+	20.4395i	0.609514	+	0.687454i
$885$	−4.93590	−	9.47350i	−0.165919	−	0.318448i
$886$	20.8169	+	9.36400i	0.699357	+	0.314590i
$887$	−33.0990	−	19.1097i	−1.11136	−	0.641642i	−0.172176	−	0.985066i	$-0.555080\pi$
$887$	−33.0990	−	19.1097i	−1.11136	−	0.641642i	−0.939180	+	0.343424i	$0.888413\pi$
$888$	10.8433	+	34.7251i	0.363876	+	1.16530i
$889$		0			0
$890$	24.6444	−	16.1890i	0.826082	−	0.542655i
$891$	−25.6731	−	14.8224i	−0.860082	−	0.496568i
$892$	−7.05663	−	34.4964i	−0.236274	−	1.15503i
$893$	−14.9046	+	8.60518i	−0.498764	+	0.287962i
$894$	14.7425	−	1.49242i	0.493062	−	0.0499139i
$895$	−49.2479	−	2.13255i	−1.64618	−	0.0712833i
$896$		0			0
$897$		−	1.43878i		−	0.0480394i
$898$	−4.06175	−	40.1230i	−0.135542	−	1.33892i
$899$	−1.79956	−	3.11693i	−0.0600187	−	0.103955i
$900$	6.74888	−	0.781112i	0.224963	−	0.0260371i
$901$	−49.7842	−	28.7429i	−1.65855	−	0.957566i
$902$	7.63038	−	5.49925i	0.254064	−	0.183105i
$903$		0			0
$904$	3.06671	−	0.957611i	0.101997	−	0.0318497i
$905$	−3.00148	+	4.71510i	−0.0997724	+	0.156735i
$906$	−41.7268	−	18.7698i	−1.38628	−	0.623586i
$907$	−9.24702	−	16.0163i	−0.307042	−	0.531813i	0.670672	−	0.741754i	$-0.266006\pi$
$907$	−9.24702	−	16.0163i	−0.307042	−	0.531813i	−0.977714	+	0.209942i	$0.932673\pi$
$908$	13.1564	−	11.6648i	0.436610	−	0.387109i
$909$			5.43380i			0.180228i
$910$		0			0
$911$			14.7738i			0.489477i	0.969589	+	0.244739i	$0.0787022\pi$
$911$			14.7738i			0.489477i	−0.969589	+	0.244739i	$0.921298\pi$
$912$	9.17399	+	21.4853i	0.303781	+	0.711448i
$913$	17.5574	+	30.4103i	0.581064	+	1.00643i
$914$	13.5657	−	30.1575i	0.448712	−	0.997522i
$915$	−16.4125	−	10.4477i	−0.542582	−	0.345390i
$916$	32.4135	+	10.8071i	1.07097	+	0.357075i
$917$		0			0
$918$	−28.8365	−	40.0115i	−0.951746	−	1.32058i
$919$	−24.3953	−	14.0846i	−0.804726	−	0.464609i	0.0403951	−	0.999184i	$-0.487138\pi$
$919$	−24.3953	−	14.0846i	−0.804726	−	0.464609i	−0.845121	+	0.534575i	$0.820472\pi$
$920$	−1.91954	−	1.92881i	−0.0632855	−	0.0635911i
$921$	8.40762	+	14.5624i	0.277040	+	0.479848i
$922$	13.9654	−	1.41375i	0.459926	−	0.0465594i
$923$			10.0493i			0.330778i
$924$		0			0
$925$	−3.64921	+	42.0574i	−0.119985	+	1.38284i
$926$	−2.40557	−	23.7628i	−0.0790519	−	0.780895i
$927$	7.35564	−	4.24678i	0.241591	−	0.139483i
$928$	−1.29515	−	2.34591i	−0.0425153	−	0.0770084i
$929$	−9.20660	−	5.31543i	−0.302059	−	0.174394i	0.341309	−	0.939951i	$-0.389130\pi$
$929$	−9.20660	−	5.31543i	−0.302059	−	0.174394i	−0.643367	+	0.765558i	$0.722463\pi$
$930$	−30.5907	+	20.0951i	−1.00311	+	0.658945i
$931$		0			0
$932$	−26.9084	−	8.97159i	−0.881414	−	0.293874i
$933$	−28.5838	−	16.5029i	−0.935791	−	0.540279i
$934$	−17.8441	+	39.6687i	−0.583876	+	1.29800i
$935$	−29.3183	−	56.2707i	−0.958810	−	1.84025i
$936$	4.11568	+	0.924376i	0.134525	+	0.0302142i
$937$	58.4711			1.91017			0.955084	−	0.296334i	$-0.0957641\pi$
$937$	58.4711			1.91017			0.955084	+	0.296334i	$0.0957641\pi$
$938$		0			0
$939$			5.82483i			0.190086i
$940$	−12.6558	−	15.5833i	−0.412788	−	0.508271i
$941$	−38.8240	+	22.4151i	−1.26563	+	0.730710i	−0.974157	−	0.225870i	$-0.927478\pi$
$941$	−38.8240	+	22.4151i	−1.26563	+	0.730710i	−0.291470	+	0.956580i	$0.594144\pi$
$942$	−2.05694	+	4.57273i	−0.0670187	+	0.148988i
$943$	−0.543392	−	0.313728i	−0.0176953	−	0.0102164i
$944$	−10.0342	−	7.52783i	−0.326584	−	0.245010i
$945$		0			0
$946$	−32.3636	−	44.9055i	−1.05223	−	1.46000i
$947$	−7.20958	+	12.4874i	−0.234280	+	0.405784i	−0.959063	−	0.283192i	$-0.908607\pi$
$947$	−7.20958	+	12.4874i	−0.234280	+	0.405784i	0.724783	+	0.688977i	$0.241940\pi$
$948$	−18.5188	+	3.78823i	−0.601463	+	0.123036i
$949$	13.4688	+	23.3286i	0.437215	+	0.757279i
$950$	0.388696	+	27.1074i	0.0126110	+	0.879480i
$951$	−13.3124			−0.431683
$952$		0			0
$953$			3.56629i			0.115523i	0.998330	+	0.0577617i	$0.0183964\pi$
$953$			3.56629i			0.115523i	−0.998330	+	0.0577617i	$0.981604\pi$
$954$	−8.83186	+	0.894070i	−0.285942	+	0.0289466i
$955$	−8.01840	−	15.3897i	−0.259469	−	0.498001i
$956$	5.48058	+	26.7919i	0.177255	+	0.866512i
$957$	−1.64550	+	2.85009i	−0.0531915	+	0.0921303i
$958$	−18.0739	+	13.0259i	−0.583941	+	0.420849i
$959$		0			0
$960$	−23.0584	+	14.5226i	−0.744206	+	0.468715i
$961$	−13.3632	+	23.1458i	−0.431072	+	0.746639i
$962$	−10.7525	+	23.9036i	−0.346674	+	0.770683i
$963$	4.91431	+	8.51183i	0.158361	+	0.274290i
$964$	−5.02729	+	4.45733i	−0.161918	+	0.143561i
$965$	13.4868	+	0.584011i	0.434156	+	0.0188000i
$966$		0			0
$967$	17.8167			0.572946			0.286473	−	0.958088i	$-0.407517\pi$
$967$	17.8167			0.572946			0.286473	+	0.958088i	$0.407517\pi$
$968$	−27.0413	−	6.07344i	−0.869139	−	0.195208i
$969$	31.4710	−	18.1698i	1.01099	−	0.583697i
$970$	12.8624	−	25.5752i	0.412987	−	0.821170i
$971$	13.2409	−	22.9339i	0.424921	−	0.735984i	−0.571492	−	0.820607i	$-0.693635\pi$
$971$	13.2409	−	22.9339i	0.424921	−	0.735984i	0.996413	+	0.0846230i	$0.0269686\pi$
$972$	−13.1160	−	4.37302i	−0.420694	−	0.140265i
$973$		0			0
$974$	−15.4941	+	11.1667i	−0.496463	+	0.357803i
$975$	−13.7030	−	9.58031i	−0.438846	−	0.306815i
$976$	−22.6822	−	2.73601i	−0.726040	−	0.0875776i
$977$	7.99273	−	4.61461i	0.255710	−	0.147634i	−0.366666	−	0.930353i	$-0.619501\pi$
$977$	7.99273	−	4.61461i	0.255710	−	0.147634i	0.622376	+	0.782718i	$0.286167\pi$
$978$	6.57343	−	0.665444i	0.210195	−	0.0212785i
$979$	−42.5241			−1.35908
$980$		0			0
$981$	12.4303			0.396870
$982$	−5.44612	+	0.551324i	−0.173793	+	0.0175934i
$983$	−39.9458	+	23.0627i	−1.27407	+	0.735587i	−0.975752	−	0.218878i	$-0.929760\pi$
$983$	−39.9458	+	23.0627i	−1.27407	+	0.735587i	−0.298322	+	0.954465i	$0.596427\pi$
$984$	−4.25782	+	4.62087i	−0.135734	+	0.147308i
$985$	−11.7010	+	18.3815i	−0.372826	+	0.585683i
$986$	−3.38156	+	2.43711i	−0.107691	+	0.0776133i
$987$		0			0
$988$	−5.32392	+	15.9680i	−0.169376	+	0.508009i
$989$	−1.84632	+	3.19791i	−0.0587094	+	0.101688i
$990$	−8.75337	−	4.40229i	−0.278200	−	0.139914i
$991$	−7.63170	+	4.40617i	−0.242429	+	0.139966i	−0.616293	−	0.787517i	$-0.711366\pi$
$991$	−7.63170	+	4.40617i	−0.242429	+	0.139966i	0.373864	+	0.927484i	$0.378033\pi$
$992$	−22.1988	+	36.8030i	−0.704813	+	1.16850i
$993$	−14.7483			−0.468022
$994$		0			0
$995$	−1.66904	+	38.5439i	−0.0529122	+	1.22193i
$996$	−15.5628	−	17.5529i	−0.493128	−	0.556185i
$997$	−16.9620	−	29.3791i	−0.537192	−	0.930444i	−0.999054	−	0.0434919i	$-0.986152\pi$
$997$	−16.9620	−	29.3791i	−0.537192	−	0.930444i	0.461862	−	0.886952i	$-0.347182\pi$
$998$	−14.1381	+	31.4300i	−0.447533	+	0.994901i
$999$	23.6618	−	40.9834i	0.748626	−	1.29666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.g.19.27		96
4.3	odd	2	inner	980.2.s.g.19.44		96
5.4	even	2	inner	980.2.s.g.19.22		96
7.2	even	3		980.2.c.e.979.33	yes	48
7.3	odd	6	inner	980.2.s.g.619.5		96
7.4	even	3	inner	980.2.s.g.619.6		96
7.5	odd	6		980.2.c.e.979.34	yes	48
7.6	odd	2	inner	980.2.s.g.19.28		96
20.19	odd	2	inner	980.2.s.g.19.5		96
28.3	even	6	inner	980.2.s.g.619.22		96
28.11	odd	6	inner	980.2.s.g.619.21		96
28.19	even	6		980.2.c.e.979.13	✓	48
28.23	odd	6		980.2.c.e.979.14	yes	48
28.27	even	2	inner	980.2.s.g.19.43		96
35.4	even	6	inner	980.2.s.g.619.43		96
35.9	even	6		980.2.c.e.979.16	yes	48
35.19	odd	6		980.2.c.e.979.15	yes	48
35.24	odd	6	inner	980.2.s.g.619.44		96
35.34	odd	2	inner	980.2.s.g.19.21		96
140.19	even	6		980.2.c.e.979.36	yes	48
140.39	odd	6	inner	980.2.s.g.619.28		96
140.59	even	6	inner	980.2.s.g.619.27		96
140.79	odd	6		980.2.c.e.979.35	yes	48
140.139	even	2	inner	980.2.s.g.19.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.13	✓	48	28.19	even	6
980.2.c.e.979.14	yes	48	28.23	odd	6
980.2.c.e.979.15	yes	48	35.19	odd	6
980.2.c.e.979.16	yes	48	35.9	even	6
980.2.c.e.979.33	yes	48	7.2	even	3
980.2.c.e.979.34	yes	48	7.5	odd	6
980.2.c.e.979.35	yes	48	140.79	odd	6
980.2.c.e.979.36	yes	48	140.19	even	6
980.2.s.g.19.5		96	20.19	odd	2	inner
980.2.s.g.19.6		96	140.139	even	2	inner
980.2.s.g.19.21		96	35.34	odd	2	inner
980.2.s.g.19.22		96	5.4	even	2	inner
980.2.s.g.19.27		96	1.1	even	1	trivial
980.2.s.g.19.28		96	7.6	odd	2	inner
980.2.s.g.19.43		96	28.27	even	2	inner
980.2.s.g.19.44		96	4.3	odd	2	inner
980.2.s.g.619.5		96	7.3	odd	6	inner
980.2.s.g.619.6		96	7.4	even	3	inner
980.2.s.g.619.21		96	28.11	odd	6	inner
980.2.s.g.619.22		96	28.3	even	6	inner
980.2.s.g.619.27		96	140.59	even	6	inner
980.2.s.g.619.28		96	140.39	odd	6	inner
980.2.s.g.619.43		96	35.4	even	6	inner
980.2.s.g.619.44		96	35.24	odd	6	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.142436 + 1.40702i) q^{2} +(-1.31926 + 0.761677i) q^{3} +(-1.95942 + 0.400822i) q^{4} +(-1.88631 - 1.20076i) q^{5} +(-1.25961 - 1.74774i) q^{6} +(-0.843059 - 2.69986i) q^{8} +(-0.339697 + 0.588372i) q^{9} +(1.42082 - 2.82511i) q^{10} +(-3.94956 + 2.28028i) q^{11} +(2.27970 - 2.02124i) q^{12} +2.19514 q^{13} +(3.40313 + 0.147364i) q^{15} +(3.67868 - 1.57076i) q^{16} +(-3.11101 - 5.38842i) q^{17} +(-0.876237 - 0.394155i) q^{18} +(1.91698 - 3.32031i) q^{19} +(4.17737 + 1.59673i) q^{20} +(-3.77097 - 5.23233i) q^{22} +(-0.215130 + 0.372617i) q^{23} +(3.16864 + 2.91969i) q^{24} +(2.11633 + 4.53003i) q^{25} +(0.312667 + 3.08861i) q^{26} -5.60502i q^{27} -0.473706 q^{29} +(0.277386 + 4.80928i) q^{30} +(3.79890 + 6.57988i) q^{31} +(2.73407 + 4.95226i) q^{32} +(3.47367 - 6.01658i) q^{33} +(7.13851 - 5.14477i) q^{34} +(0.429777 - 1.28903i) q^{36} +(7.31192 + 4.22154i) q^{37} +(4.94479 + 2.22430i) q^{38} +(-2.89596 + 1.67199i) q^{39} +(-1.65162 + 6.10509i) q^{40} +1.45831i q^{41} +8.58232 q^{43} +(6.82488 - 6.05111i) q^{44} +(1.34727 - 0.701957i) q^{45} +(-0.554922 - 0.249619i) q^{46} +(-3.88753 - 2.24446i) q^{47} +(-3.65674 + 4.87421i) q^{48} +(-6.07240 + 3.62297i) q^{50} +(8.20848 + 4.73917i) q^{51} +(-4.30120 + 0.879860i) q^{52} +(8.00130 - 4.61955i) q^{53} +(7.88639 - 0.798358i) q^{54} +(10.1882 + 0.441172i) q^{55} +5.84048i q^{57} +(-0.0674729 - 0.666515i) q^{58} +(-1.56800 - 2.71586i) q^{59} +(-6.72725 + 1.07530i) q^{60} +(-4.94644 - 2.85583i) q^{61} +(-8.71694 + 6.28235i) q^{62} +(-6.57850 + 4.55228i) q^{64} +(-4.14071 - 2.63584i) q^{65} +(8.96024 + 4.03056i) q^{66} +(-7.47296 - 12.9435i) q^{67} +(8.25558 + 9.31125i) q^{68} -0.655439i q^{69} +4.57799i q^{71} +(1.87491 + 0.421102i) q^{72} +(6.13574 + 10.6274i) q^{73} +(-4.89832 + 10.8893i) q^{74} +(-6.24242 - 4.36433i) q^{75} +(-2.42532 + 7.27425i) q^{76} +(-2.76501 - 3.83653i) q^{78} +(-5.37297 - 3.10208i) q^{79} +(-8.82525 - 1.45429i) q^{80} +(3.25012 + 5.62938i) q^{81} +(-2.05188 + 0.207717i) q^{82} -7.69966i q^{83} +(-0.601895 + 13.8998i) q^{85} +(1.22243 + 12.0755i) q^{86} +(0.624943 - 0.360811i) q^{87} +(9.48615 + 8.74086i) q^{88} +(8.07509 + 4.66216i) q^{89} +(1.17957 + 1.79565i) q^{90} +(0.272178 - 0.816343i) q^{92} +(-10.0235 - 5.78706i) q^{93} +(2.60429 - 5.78953i) q^{94} +(-7.60292 + 3.96129i) q^{95} +(-7.37898 - 4.45085i) q^{96} +9.05280 q^{97} -3.09841i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 16 q^{4} + 64 q^{9} - 16 q^{16} + 16 q^{25} - 96 q^{29} + 8 q^{30} + 352 q^{36} + 48 q^{44} + 32 q^{46} + 64 q^{50} - 24 q^{60} - 160 q^{64} + 16 q^{65} + 112 q^{74} + 48 q^{81} - 128 q^{85} + 112 q^{86}+O(q^{100}) \) 96 * q - 16 * q^4 + 64 * q^9 - 16 * q^16 + 16 * q^25 - 96 * q^29 + 8 * q^30 + 352 * q^36 + 48 * q^44 + 32 * q^46 + 64 * q^50 - 24 * q^60 - 160 * q^64 + 16 * q^65 + 112 * q^74 + 48 * q^81 - 128 * q^85 + 112 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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