LMFDB - Embedded newform 980.2.x.m.863.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] 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("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$980 = 2^{2} \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	980.x (of order $12$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			863.17
Character	$\chi$	$=$	980.863
Dual form			980.2.x.m.67.17

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28076 + 0.599707i) q^{2} +(-0.551941 - 0.147892i) q^{3} +(1.28070 + 1.53616i) q^{4} +(-1.08510 + 1.95513i) q^{5} +(-0.618214 - 0.520418i) q^{6} +(0.719030 + 2.73551i) q^{8} +(-2.31531 - 1.33674i) q^{9} +(-2.56227 + 1.85332i) q^{10} +(-3.42960 + 1.98008i) q^{11} +(-0.479687 - 1.03728i) q^{12} +(-2.04987 - 2.04987i) q^{13} +(0.888062 - 0.918641i) q^{15} +(-0.719595 + 3.93474i) q^{16} +(-0.580528 - 0.155552i) q^{17} +(-2.16371 - 3.10056i) q^{18} +(-1.00269 + 1.73671i) q^{19} +(-4.39310 + 0.837053i) q^{20} +(-5.57997 + 0.479259i) q^{22} +(0.640717 + 2.39119i) q^{23} +(0.00769773 - 1.61618i) q^{24} +(-2.64510 - 4.24305i) q^{25} +(-1.39608 - 3.85472i) q^{26} +(2.29237 + 2.29237i) q^{27} -7.25964i q^{29} +(1.68831 - 0.643984i) q^{30} +(-2.83005 + 1.63393i) q^{31} +(-3.28132 + 4.60792i) q^{32} +(2.18578 - 0.585677i) q^{33} +(-0.650233 - 0.547372i) q^{34} +(-0.911768 - 5.26867i) q^{36} +(2.49187 + 9.29977i) q^{37} +(-2.32572 + 1.62299i) q^{38} +(0.828248 + 1.43457i) q^{39} +(-6.12850 - 1.56251i) q^{40} +3.35439 q^{41} +(3.31777 - 3.31777i) q^{43} +(-7.43403 - 2.73253i) q^{44} +(5.12586 - 3.07624i) q^{45} +(-0.613406 + 3.44679i) q^{46} +(-12.1147 + 3.24611i) q^{47} +(0.979091 - 2.06532i) q^{48} +(-0.843164 - 7.02062i) q^{50} +(0.297413 + 0.171711i) q^{51} +(0.523658 - 5.77421i) q^{52} +(-0.779134 + 2.90777i) q^{53} +(1.56123 + 4.31073i) q^{54} +(-0.149853 - 8.85392i) q^{55} +(0.810271 - 0.810271i) q^{57} +(4.35366 - 9.29788i) q^{58} +(7.41735 + 12.8472i) q^{59} +(2.54853 + 0.187702i) q^{60} +(2.11676 - 3.66633i) q^{61} +(-4.60450 + 0.395476i) q^{62} +(-6.96599 + 3.93382i) q^{64} +(6.23209 - 1.78345i) q^{65} +(3.15069 + 0.560711i) q^{66} +(-0.984566 + 3.67445i) q^{67} +(-0.504532 - 1.09100i) q^{68} -1.41455i q^{69} +4.86004i q^{71} +(1.99190 - 7.29470i) q^{72} +(2.53197 - 9.44944i) q^{73} +(-2.38565 + 13.4052i) q^{74} +(0.832427 + 2.73310i) q^{75} +(-3.95201 + 0.683915i) q^{76} +(0.200469 + 2.33405i) q^{78} +(-3.45719 + 5.98803i) q^{79} +(-6.91211 - 5.67650i) q^{80} +(3.08400 + 5.34165i) q^{81} +(4.29618 + 2.01165i) q^{82} +(-5.46792 + 5.46792i) q^{83} +(0.934058 - 0.966221i) q^{85} +(6.23896 - 2.25958i) q^{86} +(-1.07364 + 4.00690i) q^{87} +(-7.88251 - 7.95796i) q^{88} +(-3.35292 - 1.93581i) q^{89} +(8.40985 - 0.865911i) q^{90} +(-2.85269 + 4.04665i) q^{92} +(1.80367 - 0.483291i) q^{93} +(-17.4627 - 3.10774i) q^{94} +(-2.30748 - 3.84490i) q^{95} +(2.49257 - 2.05802i) q^{96} +(-1.11914 + 1.11914i) q^{97} +10.5874 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100})$ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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

)

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

$2$	1.28076	+	0.599707i	0.905636	+	0.424057i
$2$	1.28076	+	0.599707i	0.905636	+	0.424057i
$3$	−0.551941	−	0.147892i	−0.318663	−	0.0853856i	0.0959419	−	0.995387i	$-0.469414\pi$
$3$	−0.551941	−	0.147892i	−0.318663	−	0.0853856i	−0.414605	+	0.910001i	$0.636080\pi$
$4$	1.28070	+	1.53616i	0.640352	+	0.768082i
$5$	−1.08510	+	1.95513i	−0.485273	+	0.874363i
$5$	−1.08510	+	1.95513i	−0.485273	+	0.874363i
$6$	−0.618214	−	0.520418i	−0.252385	−	0.212460i
$7$		0			0
$7$		0			0
$8$	0.719030	+	2.73551i	0.254216	+	0.967148i
$9$	−2.31531	−	1.33674i	−0.771770	−	0.445581i
$10$	−2.56227	+	1.85332i	−0.810260	+	0.586071i
$11$	−3.42960	+	1.98008i	−1.03406	+	0.597017i	−0.918146	−	0.396242i	$-0.870314\pi$
$11$	−3.42960	+	1.98008i	−1.03406	+	0.597017i	−0.115917	+	0.993259i	$0.536981\pi$
$12$	−0.479687	−	1.03728i	−0.138474	−	0.299436i
$13$	−2.04987	−	2.04987i	−0.568532	−	0.568532i	0.363185	−	0.931717i	$-0.381689\pi$
$13$	−2.04987	−	2.04987i	−0.568532	−	0.568532i	−0.931717	+	0.363185i	$0.881689\pi$
$14$		0			0
$15$	0.888062	−	0.918641i	0.229297	−	0.237192i
$16$	−0.719595	+	3.93474i	−0.179899	+	0.983685i
$17$	−0.580528	−	0.155552i	−0.140799	−	0.0377269i	0.187731	−	0.982220i	$-0.439887\pi$
$17$	−0.580528	−	0.155552i	−0.140799	−	0.0377269i	−0.328530	+	0.944493i	$0.606553\pi$
$18$	−2.16371	−	3.10056i	−0.509990	−	0.730809i
$19$	−1.00269	+	1.73671i	−0.230033	+	0.398428i	−0.957817	−	0.287377i	$-0.907217\pi$
$19$	−1.00269	+	1.73671i	−0.230033	+	0.398428i	0.727785	+	0.685805i	$0.240550\pi$
$20$	−4.39310	+	0.837053i	−0.982327	+	0.187171i
$21$		0			0
$22$	−5.57997	+	0.479259i	−1.18965	+	0.102178i
$23$	0.640717	+	2.39119i	0.133599	+	0.498597i	1.00000		0.000751542i	$-0.000239223\pi$
$23$	0.640717	+	2.39119i	0.133599	+	0.498597i	−0.866401	+	0.499349i	$0.833573\pi$
$24$	0.00769773	−	1.61618i	0.00157129	−	0.329901i
$25$	−2.64510	−	4.24305i	−0.529020	−	0.848609i
$26$	−1.39608	−	3.85472i	−0.273793	−	0.755972i
$27$	2.29237	+	2.29237i	0.441166	+	0.441166i
$28$		0			0
$29$		−	7.25964i		−	1.34808i	−0.738694	−	0.674041i	$-0.764557\pi$
$29$		−	7.25964i		−	1.34808i	0.738694	−	0.674041i	$-0.235443\pi$
$30$	1.68831	−	0.643984i	0.308242	−	0.117575i
$31$	−2.83005	+	1.63393i	−0.508292	+	0.293462i	−0.732131	−	0.681164i	$-0.761474\pi$
$31$	−2.83005	+	1.63393i	−0.508292	+	0.293462i	0.223840	+	0.974626i	$0.428141\pi$
$32$	−3.28132	+	4.60792i	−0.580061	+	0.814573i
$33$	2.18578	−	0.585677i	0.380495	−	0.101953i
$34$	−0.650233	−	0.547372i	−0.111514	−	0.0938735i
$35$		0			0
$36$	−0.911768	−	5.26867i	−0.151961	−	0.878111i
$37$	2.49187	+	9.29977i	0.409660	+	1.52887i	0.795295	+	0.606222i	$0.207316\pi$
$37$	2.49187	+	9.29977i	0.409660	+	1.52887i	−0.385635	+	0.922651i	$0.626018\pi$
$38$	−2.32572	+	1.62299i	−0.377282	+	0.263284i
$39$	0.828248	+	1.43457i	0.132626	+	0.229715i
$40$	−6.12850	−	1.56251i	−0.969002	−	0.247054i
$41$	3.35439			0.523868			0.261934	−	0.965086i	$-0.415640\pi$
$41$	3.35439			0.523868			0.261934	+	0.965086i	$0.415640\pi$
$42$		0			0
$43$	3.31777	−	3.31777i	0.505955	−	0.505955i	−0.407327	−	0.913282i	$-0.633539\pi$
$43$	3.31777	−	3.31777i	0.505955	−	0.505955i	0.913282	+	0.407327i	$0.133539\pi$
$44$	−7.43403	−	2.73253i	−1.12072	−	0.411944i
$45$	5.12586	−	3.07624i	0.764119	−	0.458578i
$46$	−0.613406	+	3.44679i	−0.0904417	+	0.508201i
$47$	−12.1147	+	3.24611i	−1.76710	+	0.473494i	−0.988137	−	0.153572i	$-0.950922\pi$
$47$	−12.1147	+	3.24611i	−1.76710	+	0.473494i	−0.778966	+	0.627066i	$0.784256\pi$
$48$	0.979091	−	2.06532i	0.141320	−	0.298104i
$49$		0			0
$50$	−0.843164	−	7.02062i	−0.119241	−	0.992865i
$51$	0.297413	+	0.171711i	0.0416461	+	0.0240444i
$52$	0.523658	−	5.77421i	0.0726183	−	0.800739i
$53$	−0.779134	+	2.90777i	−0.107022	+	0.399413i	−0.998567	−	0.0535205i	$-0.982956\pi$
$53$	−0.779134	+	2.90777i	−0.107022	+	0.399413i	0.891544	+	0.452933i	$0.149622\pi$
$54$	1.56123	+	4.31073i	0.212456	+	0.586615i
$55$	−0.149853	−	8.85392i	−0.0202062	−	1.19386i
$56$		0			0
$57$	0.810271	−	0.810271i	0.107323	−	0.107323i
$58$	4.35366	−	9.29788i	0.571663	−	1.22087i
$59$	7.41735	+	12.8472i	0.965657	+	1.67257i	0.707839	+	0.706374i	$0.249670\pi$
$59$	7.41735	+	12.8472i	0.965657	+	1.67257i	0.257818	+	0.966193i	$0.416996\pi$
$60$	2.54853	+	0.187702i	0.329013	+	0.0242322i
$61$	2.11676	−	3.66633i	0.271023	−	0.469426i	−0.698101	−	0.715999i	$-0.745971\pi$
$61$	2.11676	−	3.66633i	0.271023	−	0.469426i	0.969124	+	0.246574i	$0.0793047\pi$
$62$	−4.60450	+	0.395476i	−0.584772	+	0.0502255i
$63$		0			0
$64$	−6.96599	+	3.93382i	−0.870749	+	0.491728i
$65$	6.23209	−	1.78345i	0.772996	−	0.221210i
$66$	3.15069	+	0.560711i	0.387824	+	0.0690188i
$67$	−0.984566	+	3.67445i	−0.120284	+	0.448906i	−0.999628	−	0.0272817i	$-0.991315\pi$
$67$	−0.984566	+	3.67445i	−0.120284	+	0.448906i	0.879344	+	0.476187i	$0.157982\pi$
$68$	−0.504532	−	1.09100i	−0.0611834	−	0.132303i
$69$		−	1.41455i		−	0.170292i
$70$		0			0
$71$			4.86004i			0.576781i	0.957513	+	0.288390i	$0.0931201\pi$
$71$			4.86004i			0.576781i	−0.957513	+	0.288390i	$0.906880\pi$
$72$	1.99190	−	7.29470i	0.234747	−	0.859689i
$73$	2.53197	−	9.44944i	0.296345	−	1.10597i	−0.643799	−	0.765195i	$-0.722643\pi$
$73$	2.53197	−	9.44944i	0.296345	−	1.10597i	0.940143	−	0.340779i	$-0.110691\pi$
$74$	−2.38565	+	13.4052i	−0.277326	+	1.55832i
$75$	0.832427	+	2.73310i	0.0961204	+	0.315591i
$76$	−3.95201	+	0.683915i	−0.453327	+	0.0784504i
$77$		0			0
$78$	0.200469	+	2.33405i	0.0226987	+	0.264279i
$79$	−3.45719	+	5.98803i	−0.388965	+	0.673706i	−0.992311	−	0.123773i	$-0.960500\pi$
$79$	−3.45719	+	5.98803i	−0.388965	+	0.673706i	0.603346	+	0.797480i	$0.293834\pi$
$80$	−6.91211	−	5.67650i	−0.772798	−	0.634652i
$81$	3.08400	+	5.34165i	0.342667	+	0.593517i
$82$	4.29618	+	2.01165i	0.474433	+	0.222150i
$83$	−5.46792	+	5.46792i	−0.600182	+	0.600182i	−0.940361	−	0.340179i	$-0.889512\pi$
$83$	−5.46792	+	5.46792i	−0.600182	+	0.600182i	0.340179	+	0.940361i	$0.389512\pi$
$84$		0			0
$85$	0.934058	−	0.966221i	0.101313	−	0.104801i
$86$	6.23896	−	2.25958i	0.672764	−	0.243657i
$87$	−1.07364	+	4.00690i	−0.115107	+	0.429584i
$88$	−7.88251	−	7.95796i	−0.840278	−	0.848321i
$89$	−3.35292	−	1.93581i	−0.355409	−	0.205195i	0.311656	−	0.950195i	$-0.399116\pi$
$89$	−3.35292	−	1.93581i	−0.355409	−	0.205195i	−0.667065	+	0.745000i	$0.732450\pi$
$90$	8.40985	−	0.865911i	0.886476	−	0.0912750i
$91$		0			0
$92$	−2.85269	+	4.04665i	−0.297413	+	0.421893i
$93$	1.80367	−	0.483291i	0.187031	−	0.0501149i
$94$	−17.4627	−	3.10774i	−1.80114	−	0.320539i
$95$	−2.30748	−	3.84490i	−0.236742	−	0.394478i
$96$	2.49257	−	2.05802i	0.254397	−	0.210046i
$97$	−1.11914	+	1.11914i	−0.113632	+	0.113632i	−0.761636	−	0.648005i	$-0.775604\pi$
$97$	−1.11914	+	1.11914i	−0.113632	+	0.113632i	0.648005	+	0.761636i	$0.275604\pi$
$98$		0			0
$99$	10.5874			1.06408
$100$	3.13042	−	9.49739i	0.313042	−	0.949739i
$101$	8.93266	+	15.4718i	0.888833	+	1.53950i	0.841257	+	0.540636i	$0.181816\pi$
$101$	8.93266	+	15.4718i	0.888833	+	1.53950i	0.0475759	+	0.998868i	$0.484850\pi$
$102$	0.277938	+	0.398282i	0.0275200	+	0.0394357i
$103$	−2.90309	−	10.8345i	−0.286050	−	1.06755i	−0.948069	−	0.318066i	$-0.896967\pi$
$103$	−2.90309	−	10.8345i	−0.286050	−	1.06755i	0.662019	−	0.749487i	$-0.269700\pi$
$104$	4.13352	−	7.08135i	0.405325	−	0.694384i
$105$		0			0
$106$	−2.74169	+	3.25691i	−0.266297	+	0.316339i
$107$	−7.59541	+	2.03518i	−0.734276	+	0.196749i	−0.606533	−	0.795059i	$-0.707440\pi$
$107$	−7.59541	+	2.03518i	−0.734276	+	0.196749i	−0.127743	+	0.991807i	$0.540773\pi$
$108$	−0.585606	+	6.45729i	−0.0563500	+	0.621353i
$109$	0.350133	−	0.202149i	0.0335366	−	0.0193624i	−0.483138	−	0.875544i	$-0.660503\pi$
$109$	0.350133	−	0.202149i	0.0335366	−	0.0193624i	0.516675	+	0.856182i	$0.327170\pi$
$110$	5.11783	−	11.4296i	0.487966	−	1.08977i
$111$		−	5.50146i		−	0.522175i
$112$		0			0
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	0.518834	−	0.854875i	$-0.326366\pi$
$113$	−3.57217	−	3.57217i	−0.336041	−	0.336041i	−0.854875	+	0.518834i	$0.826366\pi$
$114$	1.52369	−	0.551839i	0.142707	−	0.0516845i
$115$	−5.37034	−	1.34200i	−0.500787	−	0.125142i
$116$	11.1520	−	9.29746i	1.03544	−	0.863247i
$117$	2.00593	+	7.48624i	0.185448	+	0.692103i
$118$	1.79530	+	20.9025i	0.165270	+	1.92423i
$119$		0			0
$120$	3.15149	+	1.76877i	0.287691	+	0.161466i
$121$	2.34144	−	4.05549i	0.212858	−	0.368681i
$122$	4.90979	−	3.42627i	0.444511	−	0.310200i
$123$	−1.85143	−	0.496088i	−0.166937	−	0.0447308i
$124$	−6.13444	−	2.25484i	−0.550889	−	0.202490i
$125$	11.1659	−	0.567387i	0.998711	−	0.0507486i
$126$		0			0
$127$	4.80151	+	4.80151i	0.426065	+	0.426065i	0.887286	−	0.461221i	$-0.152588\pi$
$127$	4.80151	+	4.80151i	0.426065	+	0.426065i	−0.461221	+	0.887286i	$0.652588\pi$
$128$	−11.2809	+	0.860741i	−0.997102	+	0.0760795i
$129$	−2.32188	+	1.34054i	−0.204431	+	0.118028i
$130$	9.05138	+	1.45325i	0.793858	+	0.127459i
$131$	13.1564	+	7.59586i	1.14948	+	0.663653i	0.948761	−	0.315996i	$-0.102339\pi$
$131$	13.1564	+	7.59586i	1.14948	+	0.663653i	0.200720	+	0.979649i	$0.435672\pi$
$132$	3.69903	+	2.60763i	0.321959	+	0.226965i
$133$		0			0
$134$	−3.46459	+	4.11565i	−0.299295	+	0.355538i
$135$	−6.96934	+	1.99443i	−0.599825	+	0.171653i
$136$	0.00809642	−	1.69989i	0.000694263	−	0.145764i
$137$	−4.42171	−	1.18479i	−0.377772	−	0.101224i	0.0649361	−	0.997889i	$-0.479316\pi$
$137$	−4.42171	−	1.18479i	−0.377772	−	0.101224i	−0.442708	+	0.896666i	$0.645982\pi$
$138$	0.848317	−	1.81171i	0.0722135	−	0.154223i
$139$	11.1198			0.943167			0.471583	−	0.881821i	$-0.343683\pi$
$139$	11.1198			0.943167			0.471583	+	0.881821i	$0.343683\pi$
$140$		0			0
$141$	7.16665			0.603541
$142$	−2.91460	+	6.22456i	−0.244588	+	0.522353i
$143$	11.0891	+	2.97133i	0.927321	+	0.248475i
$144$	6.92583	−	8.14823i	0.577152	−	0.679019i
$145$	14.1936	+	7.87746i	1.17871	+	0.654188i
$146$	8.90975	−	10.5841i	0.737376	−	0.875942i
$147$		0			0
$148$	−11.0946	+	15.7382i	−0.911973	+	1.29367i
$149$	4.24169	+	2.44894i	0.347493	+	0.200625i	0.663580	−	0.748105i	$-0.269036\pi$
$149$	4.24169	+	2.44894i	0.347493	+	0.200625i	−0.316088	+	0.948730i	$0.602369\pi$
$150$	−0.572918	+	3.99967i	−0.0467785	+	0.326571i
$151$	12.7632	−	7.36881i	1.03865	−	0.599666i	0.119200	−	0.992870i	$-0.461967\pi$
$151$	12.7632	−	7.36881i	1.03865	−	0.599666i	0.919451	+	0.393205i	$0.128634\pi$
$152$	−5.47174	−	1.49412i	−0.443817	−	0.121189i
$153$	1.13617	+	1.13617i	0.0918538	+	0.0918538i
$154$		0			0
$155$	−0.123656	−	7.30611i	−0.00993233	−	0.586841i
$156$	−1.14299	+	3.10958i	−0.0915124	+	0.248966i
$157$	10.7377	+	2.87717i	0.856964	+	0.229623i	0.660442	−	0.750877i	$-0.270369\pi$
$157$	10.7377	+	2.87717i	0.856964	+	0.229623i	0.196522	+	0.980499i	$0.437035\pi$
$158$	−8.01890	+	5.59595i	−0.637950	+	0.445190i
$159$	0.860073	−	1.48969i	0.0682082	−	0.118140i
$160$	−5.44854	−	11.4155i	−0.430745	−	0.902474i
$161$		0			0
$162$	0.746452	+	8.69088i	0.0586468	+	0.682820i
$163$	−4.75254	−	17.7367i	−0.372248	−	1.38925i	−0.857324	−	0.514776i	$-0.827875\pi$
$163$	−4.75254	−	17.7367i	−0.372248	−	1.38925i	0.485077	−	0.874472i	$-0.338792\pi$
$164$	4.29598	+	5.15289i	0.335460	+	0.402373i
$165$	−1.22672	+	4.90901i	−0.0954997	+	0.382166i
$166$	−10.2822	+	3.72396i	−0.798057	+	0.289035i
$167$	13.1233	+	13.1233i	1.01551	+	1.01551i	0.999878	+	0.0156336i	$0.00497655\pi$
$167$	13.1233	+	13.1233i	1.01551	+	1.01551i	0.0156336	+	0.999878i	$0.495023\pi$
$168$		0			0
$169$		−	4.59606i		−	0.353543i
$170$	1.77576	−	0.677338i	0.136194	−	0.0519495i
$171$	4.64307	−	2.68068i	0.355064	−	0.204996i
$172$	9.34571	+	0.847554i	0.712604	+	0.0646254i
$173$	−7.49083	+	2.00716i	−0.569517	+	0.152602i	−0.532075	−	0.846697i	$-0.678588\pi$
$173$	−7.49083	+	2.00716i	−0.569517	+	0.152602i	−0.0374420	+	0.999299i	$0.511921\pi$
$174$	−3.77805	+	4.48801i	−0.286413	+	0.340235i
$175$		0			0
$176$	−5.32318	−	14.9194i	−0.401250	−	1.12460i
$177$	−2.19394	−	8.18789i	−0.164906	−	0.615439i
$178$	−3.13338	−	4.49008i	−0.234856	−	0.336546i
$179$	2.56434	+	4.44157i	0.191668	+	0.331979i	0.945803	−	0.324741i	$-0.105277\pi$
$179$	2.56434	+	4.44157i	0.191668	+	0.331979i	−0.754135	+	0.656719i	$0.771944\pi$
$180$	11.2903	+	3.93442i	0.841530	+	0.293254i
$181$	−18.1294			−1.34755			−0.673774	−	0.738938i	$-0.735328\pi$
$181$	−18.1294			−1.34755			−0.673774	+	0.738938i	$0.735328\pi$
$182$		0			0
$183$	−1.71055	+	1.71055i	−0.126447	+	0.126447i
$184$	−6.08042	+	3.47202i	−0.448254	+	0.255961i
$185$	−20.8862	−	5.21928i	−1.53559	−	0.383729i
$186$	2.59990	+	0.462690i	0.190634	+	0.0339260i
$187$	2.29899	−	0.616011i	0.168118	−	0.0450472i
$188$	−20.5018	−	14.4528i	−1.49525	−	1.05408i
$189$		0			0
$190$	−0.649518	−	6.30821i	−0.0471210	−	0.457646i
$191$	13.5825	+	7.84185i	0.982794	+	0.567416i	0.903112	−	0.429404i	$-0.141276\pi$
$191$	13.5825	+	7.84185i	0.982794	+	0.567416i	0.0796814	+	0.996820i	$0.474610\pi$
$192$	4.42660	−	1.14102i	0.319462	−	0.0823463i
$193$	2.00899	−	7.49764i	0.144610	−	0.539692i	−0.855162	−	0.518360i	$-0.826543\pi$
$193$	2.00899	−	7.49764i	0.144610	−	0.539692i	0.999772	−	0.0213318i	$-0.00679064\pi$
$194$	−2.10451	+	0.762199i	−0.151095	+	0.0547227i
$195$	−3.70351	+	0.0626822i	−0.265214	+	0.00448876i
$196$		0			0
$197$	4.22983	−	4.22983i	0.301363	−	0.301363i	−0.540184	−	0.841547i	$-0.681645\pi$
$197$	4.22983	−	4.22983i	0.301363	−	0.301363i	0.841547	+	0.540184i	$0.181645\pi$
$198$	13.5600	+	6.34936i	0.963667	+	0.451230i
$199$	−7.04403	−	12.2006i	−0.499338	−	0.864879i	0.500661	−	0.865643i	$-0.333090\pi$
$199$	−7.04403	−	12.2006i	−0.499338	−	0.864879i	−1.00000		0.000763945i	$0.999757\pi$
$200$	9.70497	−	10.2866i	0.686245	−	0.727370i
$201$	1.08685	−	1.88247i	0.0766601	−	0.132779i
$202$	2.16206	+	25.1727i	0.152122	+	1.77114i
$203$		0			0
$204$	0.117121	+	0.676785i	0.00820011	+	0.0473845i
$205$	−3.63986	+	6.55828i	−0.254219	+	0.458050i
$206$	2.77934	−	15.6174i	0.193646	−	1.08812i
$207$	1.71295	−	6.39282i	0.119058	−	0.444332i
$208$	9.54078	−	6.59063i	0.661534	−	0.456978i
$209$		−	7.94162i		−	0.549333i
$210$		0			0
$211$			17.2435i			1.18709i	0.804799	+	0.593547i	$0.202273\pi$
$211$			17.2435i			1.18709i	−0.804799	+	0.593547i	$0.797727\pi$
$212$	−5.46465	+	2.52711i	−0.375314	+	0.173563i
$213$	0.718762	−	2.68246i	0.0492488	−	0.183799i
$214$	−10.9484	−	1.94843i	−0.748419	−	0.133192i
$215$	2.88656	+	10.0868i	0.196862	+	0.687914i
$216$	−4.62250	+	7.91907i	−0.314522	+	0.538824i
$217$		0			0
$218$	0.569667	−	0.0489282i	0.0385827	−	0.00331383i
$219$	−2.79500	+	4.84108i	−0.188868	+	0.327130i
$220$	13.4092	−	11.5695i	0.904045	−	0.780012i
$221$	0.871146	+	1.50887i	0.0585996	+	0.101498i
$222$	3.29926	−	7.04606i	0.221432	−	0.472900i
$223$	−11.5356	+	11.5356i	−0.772484	+	0.772484i	−0.978540	−	0.206056i	$-0.933937\pi$
$223$	−11.5356	+	11.5356i	−0.772484	+	0.772484i	0.206056	+	0.978540i	$0.433937\pi$
$224$		0			0
$225$	0.452361	+	13.3598i	0.0301574	+	0.890653i
$226$	−2.43284	−	6.71735i	−0.161830	−	0.446831i
$227$	3.12892	−	11.6773i	0.207674	−	0.775049i	−0.780944	−	0.624601i	$-0.785262\pi$
$227$	3.12892	−	11.6773i	0.207674	−	0.775049i	0.988618	−	0.150448i	$-0.0480717\pi$
$228$	2.28242	+	0.206991i	0.151157	+	0.0137083i
$229$	1.89994	+	1.09693i	0.125552	+	0.0724873i	0.561460	−	0.827504i	$-0.310240\pi$
$229$	1.89994	+	1.09693i	0.125552	+	0.0724873i	−0.435909	+	0.899991i	$0.643573\pi$
$230$	−6.07332	−	4.93941i	−0.400463	−	0.325695i
$231$		0			0
$232$	19.8588	−	5.21990i	1.30379	−	0.342703i
$233$	−1.08868	+	0.291712i	−0.0713220	+	0.0191107i	−0.294304	−	0.955712i	$-0.595088\pi$
$233$	−1.08868	+	0.291712i	−0.0713220	+	0.0191107i	0.222982	+	0.974823i	$0.428421\pi$
$234$	−1.92042	+	10.7911i	−0.125542	+	0.705434i
$235$	6.79907	−	27.2081i	0.443522	−	1.77486i
$236$	−10.2360	+	27.8478i	−0.666308	+	1.81274i
$237$	2.79375	−	2.79375i	0.181474	−	0.181474i
$238$		0			0
$239$	19.8536			1.28422			0.642111	−	0.766612i	$-0.278059\pi$
$239$	19.8536			1.28422			0.642111	+	0.766612i	$0.278059\pi$
$240$	2.97557	+	4.15534i	0.192072	+	0.268226i
$241$	−4.32744	−	7.49535i	−0.278755	−	0.482818i	0.692321	−	0.721590i	$-0.256588\pi$
$241$	−4.32744	−	7.49535i	−0.278755	−	0.482818i	−0.971076	+	0.238772i	$0.923255\pi$
$242$	5.43093	−	3.78994i	0.349113	−	0.243627i
$243$	−3.42939	−	12.7987i	−0.219996	−	0.821035i
$244$	8.34302	−	1.44380i	0.534107	−	0.0924299i
$245$		0			0
$246$	−2.07373	−	1.74568i	−0.132216	−	0.111301i
$247$	5.61541	−	1.50464i	0.357300	−	0.0957382i
$248$	−6.50451	−	6.56677i	−0.413037	−	0.416990i
$249$	3.82663	−	2.20931i	0.242503	−	0.140009i
$250$	14.6412	+	5.96960i	0.925989	+	0.377550i
$251$		−	1.55623i		−	0.0982283i	−0.998793	−	0.0491141i	$-0.984360\pi$
$251$		−	1.55623i		−	0.0982283i	0.998793	−	0.0491141i	$-0.0156398\pi$
$252$		0			0
$253$	−6.93215	−	6.93215i	−0.435821	−	0.435821i
$254$	3.27009	+	9.02909i	0.205184	+	0.566535i
$255$	−0.658442	+	0.395157i	−0.0412332	+	0.0247457i
$256$	−14.9644	−	5.66284i	−0.935273	−	0.353927i
$257$	−4.60489	−	17.1857i	−0.287245	−	1.07201i	−0.947183	−	0.320693i	$-0.896084\pi$
$257$	−4.60489	−	17.1857i	−0.287245	−	1.07201i	0.659938	−	0.751320i	$-0.270582\pi$
$258$	−3.77771	+	0.324464i	−0.235190	+	0.0202003i
$259$		0			0
$260$	10.7211	+	7.28944i	0.664897	+	0.452072i
$261$	−9.70429	+	16.8083i	−0.600680	+	1.04041i
$262$	12.2949	+	17.6185i	0.759584	+	1.08847i
$263$	−18.5489	−	4.97016i	−1.14377	−	0.306473i	−0.363306	−	0.931670i	$-0.618352\pi$
$263$	−18.5489	−	4.97016i	−1.14377	−	0.306473i	−0.780467	+	0.625197i	$0.785019\pi$
$264$	3.17376	+	5.55809i	0.195332	+	0.342077i
$265$	−4.83964	−	4.67854i	−0.297297	−	0.287401i
$266$		0			0
$267$	1.56432	+	1.56432i	0.0957350	+	0.0957350i
$268$	−6.90549	+	3.19343i	−0.421820	+	0.195070i
$269$	12.4257	−	7.17398i	0.757608	−	0.437405i	−0.0708284	−	0.997489i	$-0.522564\pi$
$269$	12.4257	−	7.17398i	0.757608	−	0.437405i	0.828436	+	0.560083i	$0.189231\pi$
$270$	−10.1221	−	1.62517i	−0.616014	−	0.0989046i
$271$	17.9057	+	10.3379i	1.08770	+	0.627981i	0.932962	−	0.359975i	$-0.117215\pi$
$271$	17.9057	+	10.3379i	1.08770	+	0.627981i	0.154733	+	0.987956i	$0.450548\pi$
$272$	1.02980	−	2.17229i	0.0624409	−	0.131715i
$273$		0			0
$274$	−4.95263	−	4.16917i	−0.299199	−	0.251869i
$275$	17.4732	+	9.31444i	1.05367	+	0.561682i
$276$	2.17298	−	1.81162i	0.130798	−	0.109047i
$277$	−4.70760	−	1.26140i	−0.282853	−	0.0757901i	0.114604	−	0.993411i	$-0.463440\pi$
$277$	−4.70760	−	1.26140i	−0.282853	−	0.0757901i	−0.397456	+	0.917621i	$0.630107\pi$
$278$	14.2418	+	6.66860i	0.854166	+	0.399956i
$279$	8.73658			0.523045
$280$		0			0
$281$	−9.71163			−0.579347			−0.289674	−	0.957125i	$-0.593547\pi$
$281$	−9.71163			−0.579347			−0.289674	+	0.957125i	$0.593547\pi$
$282$	9.17878	+	4.29789i	0.546588	+	0.255935i
$283$	−1.36959	−	0.366980i	−0.0814136	−	0.0218147i	0.217882	−	0.975975i	$-0.430085\pi$
$283$	−1.36959	−	0.366980i	−0.0814136	−	0.0218147i	−0.299296	+	0.954160i	$0.596752\pi$
$284$	−7.46581	+	6.22427i	−0.443015	+	0.369343i
$285$	0.704961	+	2.46342i	0.0417583	+	0.145920i
$286$	12.4206	+	10.4558i	0.734447	+	0.618264i
$287$		0			0
$288$	13.7569	−	6.28248i	0.810632	−	0.370199i
$289$	−14.4096	−	8.31940i	−0.847624	−	0.489376i
$290$	13.4544	+	18.6011i	0.790072	+	1.09230i
$291$	0.783214	−	0.452189i	0.0459128	−	0.0265078i
$292$	17.7586	−	8.21242i	1.03924	−	0.480596i
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	0.860880	−	0.508809i	$-0.169914\pi$
$293$	6.02648	+	6.02648i	0.352071	+	0.352071i	−0.508809	+	0.860880i	$0.669914\pi$
$294$		0			0
$295$	−33.1667	+	0.561349i	−1.93104	+	0.0326830i
$296$	−23.6479	+	13.5033i	−1.37450	+	0.784866i
$297$	−12.4010	−	3.32283i	−0.719578	−	0.192810i
$298$	3.96395	+	5.68028i	0.229625	+	0.329050i
$299$	3.58824	−	6.21502i	0.207513	−	0.359424i
$300$	−3.13240	+	4.77904i	−0.180849	+	0.275918i
$301$		0			0
$302$	20.7657	−	1.78355i	1.19493	−	0.102632i
$303$	−2.64214	−	9.86060i	−0.151787	−	0.566477i
$304$	−6.11196	−	5.19504i	−0.350545	−	0.297956i
$305$	4.87127	+	8.11690i	0.278928	+	0.464772i
$306$	0.773794	+	2.13653i	0.0442349	+	0.122137i
$307$	−11.0030	−	11.0030i	−0.627975	−	0.627975i	0.319583	−	0.947558i	$-0.396457\pi$
$307$	−11.0030	−	11.0030i	−0.627975	−	0.627975i	−0.947558	+	0.319583i	$0.896457\pi$
$308$		0			0
$309$			6.40934i			0.364615i
$310$	4.22315	−	9.43154i	0.239859	−	0.535676i
$311$	−21.9956	+	12.6992i	−1.24726	+	0.720104i	−0.970561	−	0.240854i	$-0.922572\pi$
$311$	−21.9956	+	12.6992i	−1.24726	+	0.720104i	−0.276695	+	0.960958i	$0.589239\pi$
$312$	−3.32873	+	3.29718i	−0.188452	+	0.186666i
$313$	−25.0624	+	6.71544i	−1.41661	+	0.379579i	−0.884280	−	0.466958i	$-0.845350\pi$
$313$	−25.0624	+	6.71544i	−1.41661	+	0.379579i	−0.532330	+	0.846537i	$0.678683\pi$
$314$	12.0270	+	10.1245i	0.678724	+	0.571356i
$315$		0			0
$316$	−13.6262	+	2.35809i	−0.766536	+	0.132653i
$317$	0.0554686	+	0.207012i	0.00311543	+	0.0116269i	0.967466	−	0.253001i	$-0.0814176\pi$
$317$	0.0554686	+	0.207012i	0.00311543	+	0.0116269i	−0.964351	+	0.264628i	$0.914751\pi$
$318$	1.99493	−	1.39215i	0.111870	−	0.0780677i
$319$	14.3747	+	24.8977i	0.804828	+	1.39400i
$320$	−0.132333	−	17.8881i	−0.00739763	−	0.999973i
$321$	4.49321			0.250786
$322$		0			0
$323$	0.852238	−	0.852238i	0.0474198	−	0.0474198i
$324$	−4.25595	+	11.5786i	−0.236442	+	0.643256i
$325$	−3.27558	+	14.1198i	−0.181696	+	0.783226i
$326$	4.54996	−	25.5667i	0.251999	−	1.41601i
$327$	−0.223149	+	0.0597926i	−0.0123402	+	0.00330654i
$328$	2.41191	+	9.17595i	0.133175	+	0.506657i
$329$		0			0
$330$	−4.51509	+	5.55160i	−0.248548	+	0.305606i
$331$	−1.84066	−	1.06270i	−0.101172	−	0.0584115i	0.448560	−	0.893753i	$-0.351937\pi$
$331$	−1.84066	−	1.06270i	−0.101172	−	0.0584115i	−0.549732	+	0.835341i	$0.685270\pi$
$332$	−15.4024	−	1.39683i	−0.845316	−	0.0766610i
$333$	6.66198	−	24.8628i	0.365074	−	1.36248i
$334$	8.93770	+	24.6780i	0.489049	+	1.35032i
$335$	−6.11569	−	5.91212i	−0.334136	−	0.323013i
$336$		0			0
$337$	−22.4528	+	22.4528i	−1.22308	+	1.22308i	−0.256552	+	0.966530i	$0.582586\pi$
$337$	−22.4528	+	22.4528i	−1.22308	+	1.22308i	−0.966530	+	0.256552i	$0.917414\pi$
$338$	2.75629	−	5.88646i	0.149922	−	0.320181i
$339$	1.44333	+	2.49992i	0.0783909	+	0.135777i
$340$	2.68053	+	0.197423i	0.145372	+	0.0107068i
$341$	6.47062	−	11.2074i	0.350404	−	0.606917i
$342$	7.55429	−	0.648831i	0.408489	−	0.0350848i
$343$		0			0
$344$	11.4613	+	6.69020i	0.617955	+	0.360711i
$345$	2.76564	+	1.53494i	0.148897	+	0.0826382i
$346$	−10.7977	−	1.92160i	−0.580487	−	0.103306i
$347$	−4.72717	+	17.6420i	−0.253768	+	0.947074i	0.715004	+	0.699120i	$0.246425\pi$
$347$	−4.72717	+	17.6420i	−0.253768	+	0.947074i	−0.968772	+	0.247954i	$0.920242\pi$
$348$	−7.53027	+	3.48236i	−0.403665	+	0.186674i
$349$			21.6072i			1.15661i	0.815821	+	0.578304i	$0.196285\pi$
$349$			21.6072i			1.15661i	−0.815821	+	0.578304i	$0.803715\pi$
$350$		0			0
$351$		−	9.39811i		−	0.501634i
$352$	2.12956	−	22.3006i	0.113506	−	1.18863i
$353$	−4.39216	+	16.3918i	−0.233771	+	0.872446i	0.744928	+	0.667145i	$0.232484\pi$
$353$	−4.39216	+	16.3918i	−0.233771	+	0.872446i	−0.978699	+	0.205301i	$0.934183\pi$
$354$	2.10042	−	11.8025i	0.111636	−	0.627293i
$355$	−9.50203	−	5.27365i	−0.504315	−	0.279896i
$356$	−1.32038	−	7.62983i	−0.0699799	−	0.404380i
$357$		0			0
$358$	0.620673	+	7.22645i	0.0328036	+	0.381930i
$359$	4.43990	−	7.69014i	0.234329	−	0.405870i	−0.724748	−	0.689014i	$-0.758044\pi$
$359$	4.43990	−	7.69014i	0.234329	−	0.405870i	0.959078	+	0.283144i	$0.0913773\pi$
$360$	12.1007	+	11.8099i	0.637764	+	0.622438i
$361$	7.48923	+	12.9717i	0.394170	+	0.682723i
$362$	−23.2195	−	10.8723i	−1.22039	−	0.571436i
$363$	−1.89211	+	1.89211i	−0.0993101	+	0.0993101i
$364$		0			0
$365$	15.7275	+	15.2040i	0.823214	+	0.795812i
$366$	−3.21663	+	1.16498i	−0.168136	+	0.0608944i
$367$	5.62655	−	20.9986i	0.293704	−	1.09612i	−0.648538	−	0.761182i	$-0.724619\pi$
$367$	5.62655	−	20.9986i	0.293704	−	1.09612i	0.942241	−	0.334934i	$-0.108714\pi$
$368$	−9.86977	+	0.800369i	−0.514497	+	0.0417221i
$369$	−7.76645	−	4.48396i	−0.404305	−	0.233426i
$370$	−23.6203	−	19.2103i	−1.22796	−	0.998695i
$371$		0			0
$372$	3.05237	+	2.15177i	0.158258	+	0.111564i
$373$	0.472145	−	0.126511i	0.0244467	−	0.00655048i	−0.246575	−	0.969124i	$-0.579305\pi$
$373$	0.472145	−	0.126511i	0.0244467	−	0.00655048i	0.271022	+	0.962573i	$0.412638\pi$
$374$	3.31388	+	0.589753i	0.171357	+	0.0304954i
$375$	−6.24685	−	1.33819i	−0.322586	−	0.0691039i
$376$	−17.5906	−	30.8057i	−0.907164	−	1.58868i
$377$	−14.8813	+	14.8813i	−0.766427	+	0.766427i
$378$		0			0
$379$	−27.8315			−1.42961			−0.714805	−	0.699324i	$-0.753484\pi$
$379$	−27.8315			−1.42961			−0.714805	+	0.699324i	$0.753484\pi$
$380$	2.95120	−	8.46884i	0.151393	−	0.434442i
$381$	−1.94004	−	3.36026i	−0.0993915	−	0.172151i
$382$	12.6931	+	18.1890i	0.649437	+	0.930633i
$383$	−1.33854	−	4.99551i	−0.0683964	−	0.255259i	0.923259	−	0.384179i	$-0.125516\pi$
$383$	−1.33854	−	4.99551i	−0.0683964	−	0.255259i	−0.991655	+	0.128920i	$0.958849\pi$
$384$	6.35370	+	1.19328i	0.324236	+	0.0608944i
$385$		0			0
$386$	7.06942	−	8.39789i	0.359824	−	0.427441i
$387$	−12.1167	+	3.24665i	−0.615925	+	0.165037i
$388$	−3.15248	−	0.285895i	−0.160043	−	0.0145141i
$389$	−10.5873	+	6.11259i	−0.536798	+	0.309921i	−0.743780	−	0.668424i	$-0.766969\pi$
$389$	−10.5873	+	6.11259i	−0.536798	+	0.309921i	0.206982	+	0.978345i	$0.433636\pi$
$390$	−4.78090	−	2.14074i	−0.242090	−	0.108400i
$391$		−	1.48782i		−	0.0752422i
$392$		0			0
$393$	−6.13820	−	6.13820i	−0.309631	−	0.309631i
$394$	7.95407	−	2.88075i	0.400720	−	0.145130i
$395$	−7.95600	−	13.2569i	−0.400310	−	0.667028i
$396$	13.5594	+	16.2640i	0.681385	+	0.817299i
$397$	4.52602	+	16.8913i	0.227154	+	0.847751i	0.981530	+	0.191308i	$0.0612730\pi$
$397$	4.52602	+	16.8913i	0.227154	+	0.847751i	−0.754376	+	0.656443i	$0.772060\pi$
$398$	−1.70494	−	19.8505i	−0.0854608	−	0.995013i
$399$		0			0
$400$	18.5987	−	7.35452i	0.929934	−	0.367726i
$401$	15.5612	−	26.9528i	0.777089	−	1.34596i	−0.156524	−	0.987674i	$-0.550029\pi$
$401$	15.5612	−	26.9528i	0.777089	−	1.34596i	0.933613	−	0.358284i	$-0.116638\pi$
$402$	2.52092	−	1.75921i	0.125732	−	0.0877414i
$403$	9.15057	+	2.45189i	0.455823	+	0.122137i
$404$	−12.3271	+	33.5368i	−0.613298	+	1.66852i
$405$	−13.7901	+	0.233399i	−0.685236	+	0.0115977i
$406$		0			0
$407$	−26.9604	−	26.9604i	−1.33638	−	1.33638i
$408$	−0.255869	+	0.937040i	−0.0126674	+	0.0463904i
$409$	4.43457	−	2.56030i	0.219275	−	0.126599i	−0.386339	−	0.922357i	$-0.626261\pi$
$409$	4.43457	−	2.56030i	0.219275	−	0.126599i	0.605615	+	0.795758i	$0.292927\pi$
$410$	−8.59484	+	6.21675i	−0.424469	+	0.307024i
$411$	2.26530	+	1.30787i	0.111739	+	0.0645126i
$412$	12.9255	−	18.3354i	0.636795	−	0.903319i
$413$		0			0
$414$	6.02770	−	7.16041i	0.296245	−	0.351915i
$415$	−4.75726	−	16.6238i	−0.233525	−	0.816028i
$416$	16.1719	−	2.71936i	0.792894	−	0.133328i
$417$	−6.13746	−	1.64453i	−0.300553	−	0.0805329i
$418$	4.76264	−	10.1713i	0.232948	−	0.497496i
$419$	−14.0529			−0.686531			−0.343266	−	0.939238i	$-0.611533\pi$
$419$	−14.0529			−0.686531			−0.343266	+	0.939238i	$0.611533\pi$
$420$		0			0
$421$	37.5305			1.82913			0.914563	−	0.404443i	$-0.132535\pi$
$421$	37.5305			1.82913			0.914563	+	0.404443i	$0.132535\pi$
$422$	−10.3411	+	22.0849i	−0.503395	+	1.07508i
$423$	32.3884	+	8.67844i	1.57478	+	0.421960i
$424$	−8.51444	−	0.0405536i	−0.413498	−	0.00196946i
$425$	0.875542	+	2.87466i	0.0424700	+	0.139441i
$426$	2.52925	−	3.00454i	0.122543	−	0.145571i
$427$		0			0
$428$	−12.8538	−	9.06132i	−0.621314	−	0.437995i
$429$	−5.68112	−	3.28000i	−0.274287	−	0.158360i
$430$	−2.35212	+	14.6499i	−0.113429	+	0.706480i
$431$	−21.0173	+	12.1344i	−1.01237	+	0.584492i	−0.911885	−	0.410447i	$-0.865373\pi$
$431$	−21.0173	+	12.1344i	−1.01237	+	0.584492i	−0.100485	+	0.994939i	$0.532039\pi$
$432$	−10.6694	+	7.37030i	−0.513334	+	0.354604i
$433$	−0.0253628	−	0.0253628i	−0.00121886	−	0.00121886i	0.706497	−	0.707716i	$-0.250274\pi$
$433$	−0.0253628	−	0.0253628i	−0.00121886	−	0.00121886i	−0.707716	+	0.706497i	$0.750274\pi$
$434$		0			0
$435$	−6.66901	−	6.44702i	−0.319754	−	0.309111i
$436$	0.758950	+	0.278968i	0.0363471	+	0.0133601i
$437$	−4.79524	−	1.28488i	−0.229387	−	0.0614641i
$438$	−6.48296	+	4.52409i	−0.309768	+	0.216169i
$439$	7.62951	−	13.2147i	0.364137	−	0.630703i	−0.624500	−	0.781024i	$-0.714697\pi$
$439$	7.62951	−	13.2147i	0.364137	−	0.630703i	0.988637	+	0.150321i	$0.0480307\pi$
$440$	24.1122	−	6.77616i	1.14950	−	0.323041i
$441$		0			0
$442$	0.210852	+	2.45494i	0.0100292	+	0.116769i
$443$	3.09446	+	11.5487i	0.147022	+	0.548695i	0.999657	+	0.0261872i	$0.00833660\pi$
$443$	3.09446	+	11.5487i	0.147022	+	0.548695i	−0.852635	+	0.522507i	$0.824997\pi$
$444$	8.45113	−	7.04574i	0.401073	−	0.334376i
$445$	7.42303	−	4.45486i	0.351885	−	0.211180i
$446$	−21.6924	+	7.85641i	−1.02717	+	0.372012i
$447$	−1.97898	−	1.97898i	−0.0936027	−	0.0936027i
$448$		0			0
$449$			13.7142i			0.647213i	0.946192	+	0.323607i	$0.104895\pi$
$449$			13.7142i			0.647213i	−0.946192	+	0.323607i	$0.895105\pi$
$450$	−7.43259	+	17.3820i	−0.350375	+	0.819395i
$451$	−11.5042	+	6.64196i	−0.541712	+	0.312758i
$452$	0.912543	−	10.0623i	0.0429224	−	0.473292i
$453$	−8.13430	+	2.17958i	−0.382183	+	0.102406i
$454$	11.0104	−	13.0794i	0.516741	−	0.613847i
$455$		0			0
$456$	2.79911	+	1.63389i	0.131080	+	0.0765140i
$457$	−3.61073	−	13.4754i	−0.168903	−	0.630354i	−0.997510	−	0.0705235i	$-0.977533\pi$
$457$	−3.61073	−	13.4754i	−0.168903	−	0.630354i	0.828607	−	0.559830i	$-0.189134\pi$
$458$	1.77554	+	2.54432i	0.0829653	+	0.118888i
$459$	−0.974202	−	1.68737i	−0.0454718	−	0.0787595i
$460$	−4.81629	−	9.96842i	−0.224561	−	0.464780i
$461$	27.6588			1.28820			0.644100	−	0.764941i	$-0.277232\pi$
$461$	27.6588			1.28820			0.644100	+	0.764941i	$0.277232\pi$
$462$		0			0
$463$	−4.03783	+	4.03783i	−0.187654	+	0.187654i	−0.794681	−	0.607027i	$-0.792362\pi$
$463$	−4.03783	+	4.03783i	−0.187654	+	0.187654i	0.607027	+	0.794681i	$0.292362\pi$
$464$	28.5648	+	5.22400i	1.32609	+	0.242518i
$465$	−1.01226	+	4.05083i	−0.0469427	+	0.187853i
$466$	−1.56929	−	0.279277i	−0.0726958	−	0.0129373i
$467$	−11.8626	+	3.17857i	−0.548935	+	0.147087i	−0.522618	−	0.852567i	$-0.675045\pi$
$467$	−11.8626	+	3.17857i	−0.548935	+	0.147087i	−0.0263172	+	0.999654i	$0.508378\pi$
$468$	−8.93108	+	12.6691i	−0.412839	+	0.585629i
$469$		0			0
$470$	25.0249	−	30.7697i	1.15431	−	1.41930i
$471$	−5.50108	−	3.17605i	−0.253477	−	0.146345i
$472$	−29.8104	+	29.5278i	−1.37213	+	1.35913i
$473$	−4.80917	+	17.9481i	−0.221126	+	0.825253i
$474$	5.25356	−	1.90270i	0.241304	−	0.0873939i
$475$	10.0211	−	0.339315i	0.459802	−	0.0155688i
$476$		0			0
$477$	5.69088	−	5.69088i	0.260568	−	0.260568i
$478$	25.4277	+	11.9063i	1.16304	+	0.544583i
$479$	−12.0422	−	20.8577i	−0.550223	−	0.953014i	−0.998258	−	0.0589981i	$-0.981209\pi$
$479$	−12.0422	−	20.8577i	−0.550223	−	0.953014i	0.448035	−	0.894016i	$-0.352124\pi$
$480$	1.31901	+	7.10648i	0.0602042	+	0.324365i
$481$	13.9553	−	24.1713i	0.636308	−	1.10212i
$482$	−1.04741	−	12.1950i	−0.0477084	−	0.555465i
$483$		0			0
$484$	9.22859	−	1.59705i	0.419481	−	0.0725932i
$485$	−0.973689	−	3.40246i	−0.0442130	−	0.154498i
$486$	3.28321	−	18.4487i	0.148929	−	0.836850i
$487$	−0.888247	+	3.31498i	−0.0402503	+	0.150216i	−0.983126	−	0.182927i	$-0.941443\pi$
$487$	−0.888247	+	3.31498i	−0.0402503	+	0.150216i	0.942876	+	0.333144i	$0.108109\pi$
$488$	11.5513	+	3.15420i	0.522902	+	0.142784i
$489$			10.4925i			0.474487i
$490$		0			0
$491$			3.54370i			0.159925i	0.996798	+	0.0799626i	$0.0254801\pi$
$491$			3.54370i			0.159925i	−0.996798	+	0.0799626i	$0.974520\pi$
$492$	−1.60906	−	3.47943i	−0.0725419	−	0.156865i
$493$	−1.12925	+	4.21443i	−0.0508590	+	0.189808i
$494$	8.09435	+	1.44051i	0.364182	+	0.0648114i
$495$	−11.4885	+	20.6999i	−0.516368	+	0.930391i
$496$	−4.39260	−	12.3113i	−0.197234	−	0.552792i
$497$		0			0
$498$	6.22594	−	0.534740i	0.278991	−	0.0239623i
$499$	15.1647	−	26.2660i	0.678864	−	1.17583i	−0.296460	−	0.955045i	$-0.595806\pi$
$499$	15.1647	−	26.2660i	0.678864	−	1.17583i	0.975323	−	0.220781i	$-0.0708606\pi$
$500$	15.1719	+	16.4260i	0.678506	+	0.734595i
$501$	−5.30246	−	9.18412i	−0.236896	−	0.410316i
$502$	0.933280	−	1.99316i	0.0416543	−	0.0889590i
$503$	−6.85172	+	6.85172i	−0.305503	+	0.305503i	−0.843162	−	0.537659i	$-0.819309\pi$
$503$	−6.85172	+	6.85172i	−0.305503	+	0.305503i	0.537659	+	0.843162i	$0.319309\pi$
$504$		0			0
$505$	−39.9423	+	0.676027i	−1.77741	+	0.0300828i
$506$	−4.72118	−	13.0357i	−0.209882	−	0.579507i
$507$	−0.679722	+	2.53676i	−0.0301875	+	0.112661i
$508$	−1.22659	+	13.5252i	−0.0544211	+	0.600084i
$509$	−8.23953	−	4.75709i	−0.365211	−	0.210854i	0.306153	−	0.951982i	$-0.400958\pi$
$509$	−8.23953	−	4.75709i	−0.365211	−	0.210854i	−0.671364	+	0.741128i	$0.734291\pi$
$510$	−1.08029	+	0.111230i	−0.0478359	+	0.00492537i
$511$		0			0
$512$	−15.7698	−	16.2270i	−0.696931	−	0.717138i
$513$	−6.27970	+	1.68264i	−0.277256	+	0.0742904i
$514$	4.40860	−	24.7723i	0.194455	−	1.09266i
$515$	24.3330	+	6.08060i	1.07224	+	0.267943i
$516$	−5.03294	−	1.84996i	−0.221563	−	0.0814399i
$517$	35.1209	−	35.1209i	1.54461	−	1.54461i
$518$		0			0
$519$	4.43134			0.194514
$520$	9.35970	+	15.7656i	0.410450	+	0.691366i
$521$	−2.30406	−	3.99075i	−0.100943	−	0.174838i	0.811131	−	0.584865i	$-0.198853\pi$
$521$	−2.30406	−	3.99075i	−0.100943	−	0.174838i	−0.912073	+	0.410027i	$0.865519\pi$
$522$	−22.5089	+	15.7077i	−0.985190	+	0.687509i
$523$	−8.89583	−	33.1997i	−0.388987	−	1.45172i	−0.831784	−	0.555099i	$-0.812680\pi$
$523$	−8.89583	−	33.1997i	−0.388987	−	1.45172i	0.442797	−	0.896622i	$-0.353986\pi$
$524$	5.18099	+	29.9384i	0.226333	+	1.30787i
$525$		0			0
$526$	−20.7761	−	17.4895i	−0.905880	−	0.762578i
$527$	1.89708	−	0.508322i	0.0826383	−	0.0221429i
$528$	0.731614	+	9.02191i	0.0318394	+	0.392628i
$529$	14.6113	−	8.43585i	0.635275	−	0.366776i
$530$	−3.39267	−	8.89446i	−0.147368	−	0.386351i
$531$		−	39.6604i		−	1.72112i
$532$		0			0
$533$	−6.87606	−	6.87606i	−0.297835	−	0.297835i
$534$	1.06539	+	2.94166i	0.0461040	+	0.127298i
$535$	4.26275	−	17.0584i	0.184295	−	0.737500i
$536$	−10.7594	−	0.0512463i	−0.464736	−	0.00221350i
$537$	−0.758493	−	2.83073i	−0.0327314	−	0.122155i
$538$	20.2166	−	1.73639i	0.871601	−	0.0748610i
$539$		0			0
$540$	−11.9894	−	8.15177i	−0.515943	−	0.350796i
$541$	7.78637	−	13.4864i	0.334762	−	0.579825i	−0.648677	−	0.761064i	$-0.724677\pi$
$541$	7.78637	−	13.4864i	0.334762	−	0.579825i	0.983439	+	0.181239i	$0.0580107\pi$
$542$	16.7333	+	23.9785i	0.718756	+	1.02997i
$543$	10.0064	+	2.68120i	0.429414	+	0.115061i
$544$	2.62167	−	2.16461i	0.112403	−	0.0928070i
$545$	0.0152987	+	0.903909i	0.000655326	+	0.0387192i
$546$		0			0
$547$	−6.09970	−	6.09970i	−0.260804	−	0.260804i	0.564577	−	0.825381i	$-0.309039\pi$
$547$	−6.09970	−	6.09970i	−0.260804	−	0.260804i	−0.825381	+	0.564577i	$0.809039\pi$
$548$	−3.84287	−	8.30984i	−0.164159	−	0.354979i
$549$	−9.80190	+	5.65913i	−0.418335	+	0.241526i
$550$	16.7931	+	22.4084i	0.716060	+	0.955497i
$551$	12.6079	+	7.27916i	0.537114	+	0.310103i
$552$	3.86952	−	1.01711i	0.164698	−	0.0432909i
$553$		0			0
$554$	−5.27285	−	4.43873i	−0.224022	−	0.188584i
$555$	10.7561	+	5.96965i	0.456570	+	0.253397i
$556$	14.2411	+	17.0818i	0.603959	+	0.724429i
$557$	12.5982	+	3.37568i	0.533804	+	0.143032i	0.515644	−	0.856803i	$-0.327553\pi$
$557$	12.5982	+	3.37568i	0.533804	+	0.143032i	0.0181595	+	0.999835i	$0.494219\pi$
$558$	11.1895	+	5.23939i	0.473689	+	0.221801i
$559$	−13.6020			−0.575303
$560$		0			0
$561$	−1.36001			−0.0574196
$562$	−12.4383	−	5.82413i	−0.524678	−	0.245676i
$563$	−20.1494	−	5.39902i	−0.849197	−	0.227542i	−0.192126	−	0.981370i	$-0.561538\pi$
$563$	−20.1494	−	5.39902i	−0.849197	−	0.227542i	−0.657071	+	0.753829i	$0.728205\pi$
$564$	9.17836	+	11.0091i	0.386479	+	0.463569i
$565$	10.8602	−	3.10790i	0.456894	−	0.130750i
$566$	−1.53404	−	1.29137i	−0.0644804	−	0.0542801i
$567$		0			0
$568$	−13.2947	+	3.49451i	−0.557832	+	0.146627i
$569$	6.92763	+	3.99967i	0.290422	+	0.167675i	0.638132	−	0.769927i	$-0.279707\pi$
$569$	6.92763	+	3.99967i	0.290422	+	0.167675i	−0.347710	+	0.937602i	$0.613041\pi$
$570$	−0.574439	+	3.57782i	−0.0240606	+	0.149858i
$571$	−28.4622	+	16.4326i	−1.19110	+	0.687684i	−0.958557	−	0.284901i	$-0.908039\pi$
$571$	−28.4622	+	16.4326i	−1.19110	+	0.687684i	−0.232547	+	0.972585i	$0.574706\pi$
$572$	9.63747	+	20.8401i	0.402963	+	0.871369i
$573$	−6.33698	−	6.33698i	−0.264731	−	0.264731i
$574$		0			0
$575$	8.45116	−	9.04353i	0.352438	−	0.377141i
$576$	21.3869	+	0.203733i	0.891123	+	0.00848889i
$577$	−37.4537	−	10.0357i	−1.55922	−	0.417791i	−0.626802	−	0.779178i	$-0.715637\pi$
$577$	−37.4537	−	10.0357i	−1.55922	−	0.417791i	−0.932416	+	0.361387i	$0.882303\pi$
$578$	−13.4661	−	19.2967i	−0.560116	−	0.802637i
$579$	−2.21768	+	3.84114i	−0.0921638	+	0.159632i
$580$	6.07671	+	31.8924i	0.252321	+	1.32426i
$581$		0			0
$582$	1.27429	−	0.109448i	0.0528211	−	0.00453675i
$583$	−3.08550	−	11.5152i	−0.127788	−	0.476912i
$584$	27.6696	+	0.131788i	1.14498	+	0.00545343i
$585$	−16.8132	−	4.20147i	−0.695142	−	0.173710i
$586$	4.10437	+	11.3326i	0.169550	+	0.468146i
$587$	6.10922	+	6.10922i	0.252155	+	0.252155i	0.821854	−	0.569699i	$-0.192940\pi$
$587$	6.10922	+	6.10922i	0.252155	+	0.252155i	−0.569699	+	0.821854i	$0.692940\pi$
$588$		0			0
$589$		−	6.55329i		−	0.270023i
$590$	−42.8153	−	19.1713i	−1.76268	−	0.789271i
$591$	−2.96018	+	1.70906i	−0.121765	+	0.0703013i
$592$	−38.3853	+	3.11278i	−1.57763	+	0.127935i
$593$	41.4359	−	11.1027i	1.70157	−	0.455934i	0.728236	−	0.685327i	$-0.240341\pi$
$593$	41.4359	−	11.1027i	1.70157	−	0.455934i	0.973334	+	0.229392i	$0.0736739\pi$
$594$	−13.8900	−	11.6927i	−0.569913	−	0.479757i
$595$		0			0
$596$	1.67038	+	9.65229i	0.0684212	+	0.395373i
$597$	2.08351	+	7.77578i	0.0852726	+	0.318242i
$598$	8.32287	−	5.80807i	0.340347	−	0.237509i
$599$	−5.01596	−	8.68789i	−0.204946	−	0.354978i	0.745169	−	0.666875i	$-0.232369\pi$
$599$	−5.01596	−	8.68789i	−0.204946	−	0.354978i	−0.950116	+	0.311898i	$0.899035\pi$
$600$	−6.87788	+	4.24229i	−0.280788	+	0.173191i
$601$	−24.3587			−0.993613			−0.496806	−	0.867861i	$-0.665494\pi$
$601$	−24.3587			−0.993613			−0.496806	+	0.867861i	$0.665494\pi$
$602$		0			0
$603$	7.19138	−	7.19138i	0.292855	−	0.292855i
$604$	27.6655	+	10.1690i	1.12569	+	0.413772i
$605$	5.38833	+	8.97845i	0.219067	+	0.365026i
$606$	2.52952	−	14.2136i	0.102755	−	0.577388i
$607$	−24.1790	+	6.47873i	−0.981394	+	0.262964i	−0.713632	−	0.700521i	$-0.752951\pi$
$607$	−24.1790	+	6.47873i	−0.981394	+	0.262964i	−0.267762	+	0.963485i	$0.586284\pi$
$608$	−4.71247	−	10.3190i	−0.191116	−	0.418491i
$609$		0			0
$610$	1.37118	+	13.3171i	0.0555177	+	0.539196i
$611$	31.4876	+	18.1794i	1.27385	+	0.735458i
$612$	−0.290245	+	3.20044i	−0.0117325	+	0.129370i
$613$	−2.42522	+	9.05103i	−0.0979535	+	0.365568i	−0.997451	−	0.0713590i	$-0.977266\pi$
$613$	−2.42522	+	9.05103i	−0.0979535	+	0.365568i	0.899497	+	0.436927i	$0.143933\pi$
$614$	−7.49366	−	20.6908i	−0.302420	−	0.835013i
$615$	2.97891	−	3.08148i	0.120121	−	0.124257i
$616$		0			0
$617$	−16.6913	+	16.6913i	−0.671965	+	0.671965i	−0.958169	−	0.286204i	$-0.907606\pi$
$617$	−16.6913	+	16.6913i	−0.671965	+	0.671965i	0.286204	+	0.958169i	$0.407606\pi$
$618$	−3.84372	+	8.20884i	−0.154617	+	0.330208i
$619$	14.8926	+	25.7947i	0.598582	+	1.03677i	0.993031	+	0.117857i	$0.0376023\pi$
$619$	14.8926	+	25.7947i	0.598582	+	1.03677i	−0.394448	+	0.918918i	$0.629064\pi$
$620$	11.0650	−	9.54692i	0.444381	−	0.383413i
$621$	−4.01273	+	6.95024i	−0.161025	+	0.278904i
$622$	−35.7869	+	3.07371i	−1.43492	+	0.123244i
$623$		0			0
$624$	−6.24065	+	2.22663i	−0.249826	+	0.0891367i
$625$	−11.0069	+	22.4466i	−0.440275	+	0.897863i
$626$	−36.1262	−	6.42919i	−1.44390	−	0.256962i
$627$	−1.17450	+	4.38331i	−0.0469051	+	0.175052i
$628$	9.33206	+	20.1797i	0.372390	+	0.805258i
$629$		−	5.78640i		−	0.230719i
$630$		0			0
$631$			9.29850i			0.370167i	0.982723	+	0.185084i	$0.0592556\pi$
$631$			9.29850i			0.370167i	−0.982723	+	0.185084i	$0.940744\pi$
$632$	−18.8661	−	5.15160i	−0.750454	−	0.204920i
$633$	2.55019	−	9.51742i	0.101361	−	0.378284i
$634$	−0.0531042	+	0.298398i	−0.00210904	+	0.0118509i
$635$	−14.5977	+	4.17746i	−0.579293	+	0.165778i
$636$	3.38991	−	0.586639i	0.134418	−	0.0232618i
$637$		0			0
$638$	3.47925	+	40.5086i	0.137745	+	1.60375i
$639$	6.49663	−	11.2525i	0.257003	−	0.445142i
$640$	10.5581	−	22.9897i	0.417345	−	0.908748i
$641$	1.37174	+	2.37592i	0.0541805	+	0.0938434i	0.891844	−	0.452344i	$-0.149412\pi$
$641$	1.37174	+	2.37592i	0.0541805	+	0.0938434i	−0.837663	+	0.546187i	$0.816079\pi$
$642$	5.75473	+	2.69461i	0.227121	+	0.106348i
$643$	4.45513	−	4.45513i	0.175693	−	0.175693i	−0.613782	−	0.789475i	$-0.710353\pi$
$643$	4.45513	−	4.45513i	0.175693	−	0.175693i	0.789475	+	0.613782i	$0.210353\pi$
$644$		0			0
$645$	−0.101453	−	5.99422i	−0.00399470	−	0.236022i
$646$	1.60261	−	0.580421i	0.0630537	−	0.0228364i
$647$	−5.58856	+	20.8568i	−0.219709	+	0.819964i	0.764747	+	0.644331i	$0.222864\pi$
$647$	−5.58856	+	20.8568i	−0.219709	+	0.819964i	−0.984456	+	0.175633i	$0.943803\pi$
$648$	−12.3946	+	12.2771i	−0.486907	+	0.482291i
$649$	−50.8771	−	29.3739i	−1.99710	−	1.15303i
$650$	−12.6630	+	16.1197i	−0.496683	+	0.632268i
$651$		0			0
$652$	21.1599	−	30.0162i	0.828686	−	1.17552i
$653$	−28.1634	+	7.54635i	−1.10212	+	0.295311i	−0.763627	−	0.645658i	$-0.776583\pi$
$653$	−28.1634	+	7.54635i	−1.10212	+	0.295311i	−0.338491	+	0.940970i	$0.609916\pi$
$654$	−0.321659	−	0.0572438i	−0.0125779	−	0.00223841i
$655$	−29.1270	+	17.4803i	−1.13809	+	0.683010i
$656$	−2.41380	+	13.1987i	−0.0942431	+	0.515321i
$657$	−18.4938	+	18.4938i	−0.721511	+	0.721511i
$658$		0			0
$659$	8.28576			0.322768			0.161384	−	0.986892i	$-0.448404\pi$
$659$	8.28576			0.322768			0.161384	+	0.986892i	$0.448404\pi$
$660$	−9.11209	+	4.40255i	−0.354688	+	0.171369i
$661$	10.4781	+	18.1487i	0.407553	+	0.705902i	0.994615	−	0.103640i	$-0.0330490\pi$
$661$	10.4781	+	18.1487i	0.407553	+	0.705902i	−0.587062	+	0.809542i	$0.699716\pi$
$662$	−1.72013	−	2.46493i	−0.0668549	−	0.0958021i
$663$	−0.257671	−	0.961643i	−0.0100071	−	0.0373471i
$664$	−18.8891	−	11.0259i	−0.733040	−	0.427889i
$665$		0			0
$666$	23.4428	−	27.8482i	0.908391	−	1.07909i
$667$	17.3592	−	4.65138i	0.672150	−	0.180102i
$668$	−3.35247	+	36.9666i	−0.129711	+	1.43028i
$669$	8.07303	−	4.66096i	0.312121	−	0.180203i
$670$	−4.28721	−	11.2396i	−0.165629	−	0.434225i
$671$			16.7654i			0.647221i
$672$		0			0
$673$	29.0523	+	29.0523i	1.11988	+	1.11988i	0.991758	+	0.128125i	$0.0408958\pi$
$673$	29.0523	+	29.0523i	1.11988	+	1.11988i	0.128125	+	0.991758i	$0.459104\pi$
$674$	−42.2218	+	15.2916i	−1.62632	+	0.589011i
$675$	3.66307	−	15.7902i	0.140992	−	0.607764i
$676$	7.06030	−	5.88620i	0.271550	−	0.226392i
$677$	10.1358	+	37.8274i	0.389551	+	1.45383i	0.830866	+	0.556473i	$0.187846\pi$
$677$	10.1358	+	37.8274i	0.389551	+	1.45383i	−0.441314	+	0.897353i	$0.645488\pi$
$678$	0.349344	+	4.06738i	0.0134165	+	0.156207i
$679$		0			0
$680$	3.31472	+	1.86038i	0.127114	+	0.0713424i
$681$	−3.45396	+	5.98243i	−0.132356	+	0.229247i
$682$	15.0085	−	10.4736i	0.574705	−	0.401055i
$683$	11.4729	+	3.07415i	0.438998	+	0.117629i	0.471547	−	0.881841i	$-0.343696\pi$
$683$	11.4729	+	3.07415i	0.438998	+	0.117629i	−0.0325489	+	0.999470i	$0.510362\pi$
$684$	10.0644	+	3.69936i	0.384820	+	0.141448i
$685$	7.11444	−	7.35942i	0.271829	−	0.281189i
$686$		0			0
$687$	−0.886428	−	0.886428i	−0.0338193	−	0.0338193i
$688$	10.6671	+	15.4420i	0.406680	+	0.588721i
$689$	7.55767	−	4.36343i	0.287924	−	0.166233i
$690$	2.62162	+	3.62446i	0.0998033	+	0.137981i
$691$	−6.84816	−	3.95379i	−0.260516	−	0.150409i	0.364054	−	0.931378i	$-0.381392\pi$
$691$	−6.84816	−	3.95379i	−0.260516	−	0.150409i	−0.624570	+	0.780969i	$0.714726\pi$
$692$	−12.6769	−	8.93656i	−0.481902	−	0.339717i
$693$		0			0
$694$	−16.6344	+	19.7603i	−0.631434	+	0.750092i
$695$	−12.0661	+	21.7407i	−0.457693	+	0.824670i
$696$	−11.7329	−	0.0558828i	−0.444733	−	0.00211823i
$697$	−1.94732	−	0.521782i	−0.0737599	−	0.0197639i
$698$	−12.9580	+	27.6737i	−0.490467	+	1.04747i
$699$	0.644031			0.0243595
$700$		0			0
$701$	29.1974			1.10277			0.551386	−	0.834250i	$-0.314099\pi$
$701$	29.1974			1.10277			0.551386	+	0.834250i	$0.314099\pi$
$702$	5.63611	−	12.0367i	0.212721	−	0.454298i
$703$	−18.6496	−	4.99713i	−0.703381	−	0.188470i
$704$	16.1013	−	27.2847i	0.606840	−	1.02833i
$705$	−7.77656	+	14.0118i	−0.292882	+	0.527714i
$706$	−15.4556	+	18.3600i	−0.581678	+	0.690986i
$707$		0			0
$708$	9.76814	−	13.8565i	0.367109	−	0.520759i
$709$	23.6133	+	13.6331i	0.886816	+	0.512003i	0.872900	−	0.487900i	$-0.162237\pi$
$709$	23.6133	+	13.6331i	0.886816	+	0.512003i	0.0139163	+	0.999903i	$0.495570\pi$
$710$	−9.00720	−	12.4527i	−0.338034	−	0.467342i
$711$	16.0089	−	9.24277i	0.600382	−	0.346631i
$712$	2.88457	−	10.5638i	0.108104	−	0.395897i
$713$	−5.72029	−	5.72029i	−0.214227	−	0.214227i
$714$		0			0
$715$	−17.8422	+	18.4566i	−0.667261	+	0.690237i
$716$	−3.53882	+	9.62759i	−0.132252	+	0.359800i
$717$	−10.9580	−	2.93619i	−0.409234	−	0.109654i
$718$	10.2983	−	7.18660i	0.384329	−	0.268202i
$719$	17.9745	−	31.1327i	0.670335	−	1.16105i	−0.307474	−	0.951557i	$-0.599484\pi$
$719$	17.9745	−	31.1327i	0.670335	−	1.16105i	0.977809	−	0.209498i	$-0.0671831\pi$
$720$	8.41564	+	22.3826i	0.313632	+	0.834150i
$721$		0			0
$722$	1.81269	+	21.1050i	0.0674615	+	0.785448i
$723$	1.27999	+	4.77699i	0.0476033	+	0.177658i
$724$	−23.2184	−	27.8497i	−0.862905	−	1.03503i
$725$	−30.8030	+	19.2025i	−1.14399	+	0.713163i
$726$	−3.55806	+	1.28863i	−0.132052	+	0.0478257i
$727$	−5.64012	−	5.64012i	−0.209180	−	0.209180i	0.594739	−	0.803919i	$-0.297256\pi$
$727$	−5.64012	−	5.64012i	−0.209180	−	0.209180i	−0.803919	+	0.594739i	$0.797256\pi$
$728$		0			0
$729$		−	10.9327i		−	0.404916i
$730$	11.0252	+	28.9045i	0.408063	+	1.06981i
$731$	−2.44214	+	1.40997i	−0.0903260	+	0.0521497i
$732$	−4.81839	−	0.436975i	−0.178093	−	0.0161511i
$733$	−15.5419	+	4.16444i	−0.574053	+	0.153817i	−0.534155	−	0.845387i	$-0.679370\pi$
$733$	−15.5419	+	4.16444i	−0.574053	+	0.153817i	−0.0398983	+	0.999204i	$0.512703\pi$
$734$	19.7993	−	23.5199i	0.730804	−	0.868136i
$735$		0			0
$736$	−13.1208	−	4.89388i	−0.483640	−	0.180391i
$737$	−3.89904	−	14.5514i	−0.143623	−	0.536008i
$738$	−7.25791	−	10.4005i	−0.267168	−	0.382847i
$739$	−11.4543	−	19.8395i	−0.421355	−	0.729808i	0.574717	−	0.818352i	$-0.305112\pi$
$739$	−11.4543	−	19.8395i	−0.421355	−	0.729808i	−0.996072	+	0.0885439i	$0.971779\pi$
$740$	−18.7314	−	38.7690i	−0.688581	−	1.42518i
$741$	−3.32190			−0.122033
$742$		0			0
$743$	21.3493	−	21.3493i	0.783229	−	0.783229i	−0.197145	−	0.980374i	$-0.563167\pi$
$743$	21.3493	−	21.3493i	0.783229	−	0.783229i	0.980374	+	0.197145i	$0.0631669\pi$
$744$	2.61893	+	4.58644i	0.0960148	+	0.168147i
$745$	−9.39067	+	5.63572i	−0.344048	+	0.206477i
$746$	0.680575	+	0.121118i	0.0249176	+	0.00443445i
$747$	19.9691	−	5.35071i	0.730632	−	0.195772i
$748$	3.89061	+	2.74269i	0.142255	+	0.100283i
$749$		0			0
$750$	−7.19821	−	5.46018i	−0.262841	−	0.199378i
$751$	−31.7774	−	18.3467i	−1.15958	−	0.669481i	−0.208373	−	0.978049i	$-0.566817\pi$
$751$	−31.7774	−	18.3467i	−1.15958	−	0.669481i	−0.951202	+	0.308568i	$0.900150\pi$
$752$	−4.05497	−	50.0039i	−0.147869	−	1.82345i
$753$	−0.230154	+	0.858946i	−0.00838728	+	0.0313017i
$754$	−27.9839	+	10.1350i	−1.01911	+	0.369095i
$755$	0.557675	+	32.9496i	0.0202959	+	1.19916i
$756$		0			0
$757$	23.2904	−	23.2904i	0.846504	−	0.846504i	−0.143191	−	0.989695i	$-0.545736\pi$
$757$	23.2904	−	23.2904i	0.846504	−	0.846504i	0.989695	+	0.143191i	$0.0457363\pi$
$758$	−35.6456	−	16.6907i	−1.29471	−	0.606235i
$759$	2.80093	+	4.85135i	0.101667	+	0.176093i
$760$	8.85860	−	9.07671i	0.321335	−	0.329247i
$761$	3.80960	−	6.59842i	0.138098	−	0.239192i	−0.788679	−	0.614806i	$-0.789234\pi$
$761$	3.80960	−	6.59842i	0.138098	−	0.239192i	0.926777	+	0.375613i	$0.122568\pi$
$762$	−0.469568	−	5.46715i	−0.0170107	−	0.198054i
$763$		0			0
$764$	5.34878	+	30.9080i	0.193512	+	1.11821i
$765$	−3.45422	+	0.988503i	−0.124888	+	0.0357394i
$766$	1.28149	−	7.20080i	0.0463020	−	0.260175i
$767$	11.1305	−	41.5398i	0.401901	−	1.49991i
$768$	7.42196	+	5.33867i	0.267817	+	0.192643i
$769$			30.3461i			1.09431i	0.837031	+	0.547155i	$0.184289\pi$
$769$			30.3461i			1.09431i	−0.837031	+	0.547155i	$0.815711\pi$
$770$		0			0
$771$			10.1665i			0.366138i
$772$	14.0905	−	6.51613i	0.507129	−	0.234521i
$773$	6.78186	−	25.3103i	0.243927	−	0.910347i	−0.729993	−	0.683454i	$-0.760477\pi$
$773$	6.78186	−	25.3103i	0.243927	−	0.910347i	0.973920	−	0.226892i	$-0.0728565\pi$
$774$	−17.4656	−	3.10826i	−0.627788	−	0.111724i
$775$	14.4186	+	7.68611i	0.517931	+	0.276093i
$776$	−3.86612	−	2.25673i	−0.138786	−	0.0810117i
$777$		0			0
$778$	−17.2256	+	1.47949i	−0.617568	+	0.0530423i
$779$	−3.36341	+	5.82559i	−0.120507	+	0.208724i
$780$	−4.83939	−	5.60891i	−0.173278	−	0.200831i
$781$	−9.62327	−	16.6680i	−0.344348	−	0.596428i
$782$	0.892254	−	1.90554i	0.0319070	−	0.0681420i
$783$	16.6418	−	16.6418i	0.594728	−	0.594728i
$784$		0			0
$785$	−17.2768	+	17.8717i	−0.616635	+	0.637868i
$786$	−4.18045	−	11.5427i	−0.149112	−	0.411714i
$787$	2.88594	−	10.7705i	0.102873	−	0.383926i	−0.895222	−	0.445619i	$-0.852983\pi$
$787$	2.88594	−	10.7705i	0.102873	−	0.383926i	0.998095	+	0.0616935i	$0.0196501\pi$
$788$	11.9149	+	1.08055i	0.424450	+	0.0384930i
$789$	9.50285	+	5.48647i	0.338310	+	0.195324i
$790$	−2.23949	−	21.7502i	−0.0796773	−	0.773838i
$791$		0			0
$792$	7.61269	+	28.9620i	0.270505	+	1.02912i
$793$	−11.8546	+	3.17643i	−0.420969	+	0.112798i
$794$	−4.33309	+	24.3480i	−0.153775	+	0.864080i
$795$	1.97928	+	3.29803i	0.0701977	+	0.116969i
$796$	9.72083	−	26.4462i	0.344546	−	0.937360i
$797$	−9.45111	+	9.45111i	−0.334775	+	0.334775i	−0.854397	−	0.519621i	$-0.826073\pi$
$797$	−9.45111	+	9.45111i	−0.334775	+	0.334775i	0.519621	+	0.854397i	$0.326073\pi$
$798$		0			0
$799$	7.53784			0.266670
$800$	28.2310	+	1.73437i	0.998118	+	0.0613192i
$801$	5.17536	+	8.96399i	0.182863	+	0.316727i
$802$	36.0940	−	25.1880i	1.27452	−	0.889418i
$803$	10.0270	+	37.4213i	0.353846	+	1.32057i
$804$	4.28371	−	0.741317i	0.151075	−	0.0261442i
$805$		0			0
$806$	10.2493	+	8.62795i	0.361016	+	0.303906i
$807$	−7.91923	+	2.12195i	−0.278770	+	0.0746962i
$808$	−35.9004	+	35.5600i	−1.26297	+	1.25100i
$809$	28.2738	−	16.3239i	0.994055	−	0.573918i	0.0875707	−	0.996158i	$-0.472090\pi$
$809$	28.2738	−	16.3239i	0.994055	−	0.573918i	0.906484	+	0.422241i	$0.138756\pi$
$810$	−17.8018	−	7.97109i	−0.625492	−	0.280076i
$811$			38.0037i			1.33449i	0.744838	+	0.667245i	$0.232527\pi$
$811$			38.0037i			1.33449i	−0.744838	+	0.667245i	$0.767473\pi$
$812$		0			0
$813$	−8.35402	−	8.35402i	−0.292988	−	0.292988i
$814$	−18.3615	−	50.6982i	−0.643572	−	1.77697i
$815$	39.8347	+	9.95433i	1.39535	+	0.348685i
$816$	−0.889656	+	1.04668i	−0.0311442	+	0.0366411i
$817$	2.43530	+	9.08868i	0.0852005	+	0.317973i
$818$	7.21506	−	0.619695i	0.252269	−	0.0216671i
$819$		0			0
$820$	−14.7362	+	2.80780i	−0.514610	+	0.0980527i
$821$	5.78912	−	10.0271i	0.202042	−	0.349947i	−0.747144	−	0.664662i	$-0.768576\pi$
$821$	5.78912	−	10.0271i	0.202042	−	0.349947i	0.949186	+	0.314715i	$0.101909\pi$
$822$	2.11697	+	3.03359i	0.0738380	+	0.105809i
$823$	32.4334	+	8.69051i	1.13056	+	0.302932i	0.775149	−	0.631779i	$-0.217675\pi$
$823$	32.4334	+	8.69051i	1.13056	+	0.302932i	0.355409	+	0.934711i	$0.384341\pi$
$824$	27.5504	−	15.7317i	0.959763	−	0.548041i
$825$	−8.26665	−	7.72517i	−0.287808	−	0.268956i
$826$		0			0
$827$	4.77258	+	4.77258i	0.165959	+	0.165959i	0.785200	−	0.619242i	$-0.212560\pi$
$827$	4.77258	+	4.77258i	0.165959	+	0.165959i	−0.619242	+	0.785200i	$0.712560\pi$
$828$	12.0142	−	5.55594i	0.417522	−	0.193082i
$829$	29.2731	−	16.9008i	1.01670	−	0.586989i	0.103550	−	0.994624i	$-0.466980\pi$
$829$	29.2731	−	16.9008i	1.01670	−	0.586989i	0.913145	+	0.407635i	$0.133646\pi$
$830$	3.87647	−	24.1440i	0.134554	−	0.838052i
$831$	2.41177	+	1.39244i	0.0836634	+	0.0483031i
$832$	22.3432	+	6.21555i	0.774611	+	0.215485i
$833$		0			0
$834$	−6.87439	−	5.78693i	−0.238041	−	0.200385i
$835$	−39.8980	+	11.4177i	−1.38073	+	0.395125i
$836$	12.1996	−	10.1709i	0.421933	−	0.351767i
$837$	−10.2331	−	2.74194i	−0.353707	−	0.0947755i
$838$	−17.9985	−	8.42764i	−0.621747	−	0.291128i
$839$	−3.12360			−0.107839			−0.0539193	−	0.998545i	$-0.517171\pi$
$839$	−3.12360			−0.107839			−0.0539193	+	0.998545i	$0.517171\pi$
$840$		0			0
$841$	−23.7024			−0.817325
$842$	48.0677	+	22.5073i	1.65652	+	0.775653i
$843$	5.36025	+	1.43627i	0.184617	+	0.0494679i
$844$	−26.4889	+	22.0839i	−0.911785	+	0.760158i
$845$	8.98592	+	4.98720i	0.309125	+	0.171565i
$846$	36.2773	+	30.5386i	1.24724	+	1.04994i
$847$		0			0
$848$	−10.8807	−	5.15811i	−0.373643	−	0.177130i
$849$	0.701659	+	0.405103i	0.0240809	+	0.0139031i
$850$	−0.602591	+	4.20682i	−0.0206687	+	0.144293i
$851$	−20.6409	+	11.9171i	−0.707562	+	0.408511i
$852$	5.04121	−	2.33130i	0.172709	−	0.0798689i
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	0.760202	−	0.649686i	$-0.225100\pi$
$853$	3.22775	+	3.22775i	0.110516	+	0.110516i	−0.649686	+	0.760202i	$0.725100\pi$
$854$		0			0
$855$	0.202875	+	11.9866i	0.00693817	+	0.409934i
$856$	−11.0286	−	19.3139i	−0.376949	−	0.660137i
$857$	37.2336	+	9.97671i	1.27187	+	0.340798i	0.830749	−	0.556647i	$-0.187913\pi$
$857$	37.2336	+	9.97671i	1.27187	+	0.340798i	0.441126	+	0.897445i	$0.354579\pi$
$858$	−5.30913	−	7.60790i	−0.181251	−	0.259729i
$859$	−6.97976	+	12.0893i	−0.238146	+	0.412482i	−0.960182	−	0.279374i	$-0.909873\pi$
$859$	−6.97976	+	12.0893i	−0.238146	+	0.412482i	0.722036	+	0.691855i	$0.243206\pi$
$860$	−11.7981	+	17.3524i	−0.402313	+	0.591713i
$861$		0			0
$862$	−34.1953	+	2.93700i	−1.16470	+	0.100035i
$863$	10.7069	+	39.9587i	0.364467	+	1.36021i	0.868142	+	0.496316i	$0.165314\pi$
$863$	10.7069	+	39.9587i	0.364467	+	1.36021i	−0.503675	+	0.863893i	$0.668019\pi$
$864$	−18.0850	+	3.04106i	−0.615266	+	0.103459i
$865$	4.20405	−	16.8236i	0.142942	−	0.572018i
$866$	−0.0172735	−	0.0476940i	−0.000586977	−	0.00162071i
$867$	6.72289	+	6.72289i	0.228321	+	0.228321i
$868$		0			0
$869$		−	27.3821i		−	0.928873i
$870$	−4.67509	−	12.2565i	−0.158501	−	0.415536i
$871$	9.55038	−	5.51391i	0.323602	−	0.186832i
$872$	0.804736	+	0.812439i	0.0272518	+	0.0275126i
$873$	4.08717	−	1.09515i	0.138330	−	0.0370653i
$874$	−5.37101	−	4.52136i	−0.181677	−	0.152937i
$875$		0			0
$876$	−11.0163	+	1.90642i	−0.372205	+	0.0644118i
$877$	8.94885	+	33.3976i	0.302181	+	1.12776i	0.935345	+	0.353737i	$0.115089\pi$
$877$	8.94885	+	33.3976i	0.302181	+	1.12776i	−0.633164	+	0.774018i	$0.718244\pi$
$878$	17.6965	−	12.3494i	0.597229	−	0.416773i
$879$	−2.43499	−	4.21753i	−0.0821303	−	0.142254i
$880$	34.9457	+	5.78160i	1.17802	+	0.194898i
$881$	9.22163			0.310685			0.155342	−	0.987861i	$-0.450352\pi$
$881$	9.22163			0.310685			0.155342	+	0.987861i	$0.450352\pi$
$882$		0			0
$883$	18.1891	−	18.1891i	0.612111	−	0.612111i	−0.331385	−	0.943496i	$-0.607516\pi$
$883$	18.1891	−	18.1891i	0.612111	−	0.612111i	0.943496	+	0.331385i	$0.107516\pi$
$884$	−1.20219	+	3.27064i	−0.0404340	+	0.110003i
$885$	18.3891	+	4.59526i	0.618142	+	0.154468i
$886$	−2.96255	+	16.6469i	−0.0995289	+	0.559263i
$887$	19.5218	−	5.23085i	0.655477	−	0.175635i	0.0842733	−	0.996443i	$-0.473143\pi$
$887$	19.5218	−	5.23085i	0.655477	−	0.175635i	0.571204	+	0.820808i	$0.306476\pi$
$888$	15.0493	−	3.95571i	0.505020	−	0.132745i
$889$		0			0
$890$	12.1787	−	1.25397i	0.408233	−	0.0420332i
$891$	−21.1538	−	12.2132i	−0.708679	−	0.409156i
$892$	−32.4944	−	2.94689i	−1.08799	−	0.0986690i
$893$	6.50968	−	24.2944i	0.217838	−	0.812983i
$894$	−1.34780	−	3.72142i	−0.0450771	−	0.124463i
$895$	−11.4664	+	0.194071i	−0.383281	+	0.00648706i
$896$		0			0
$897$	−2.89965	+	2.89965i	−0.0968165	+	0.0968165i
$898$	−8.22450	+	17.5646i	−0.274455	+	0.586139i
$899$	11.8617	+	20.5451i	0.395611	+	0.685219i
$900$	−19.9435	+	17.8048i	−0.664782	+	0.593494i
$901$	0.904619	−	1.56685i	0.0301372	−	0.0521992i
$902$	−18.7174	+	1.60762i	−0.623221	+	0.0535279i
$903$		0			0
$904$	7.20319	−	12.3402i	0.239574	−	0.410428i
$905$	19.6723	−	35.4454i	0.653928	−	1.17825i
$906$	−11.7252	−	2.08667i	−0.389544	−	0.0693250i
$907$	10.9408	−	40.8315i	0.363282	−	1.35579i	−0.506452	−	0.862268i	$-0.669043\pi$
$907$	10.9408	−	40.8315i	0.363282	−	1.35579i	0.869734	−	0.493520i	$-0.164290\pi$
$908$	21.9454	−	10.1486i	0.728285	−	0.336794i
$909$		−	47.7627i		−	1.58419i
$910$		0			0
$911$			47.4291i			1.57140i	0.618610	+	0.785698i	$0.287696\pi$
$911$			47.4291i			1.57140i	−0.618610	+	0.785698i	$0.712304\pi$
$912$	2.60514	+	3.77127i	0.0862647	+	0.124879i
$913$	7.92585	−	29.5797i	0.262307	−	0.978945i
$914$	3.45682	−	19.4242i	0.114341	−	0.642495i
$915$	−1.48823	−	5.20047i	−0.0491994	−	0.171922i
$916$	0.748196	+	4.32346i	0.0247211	+	0.142851i
$917$		0			0
$918$	−0.235796	−	2.74535i	−0.00778242	−	0.0906101i
$919$	−15.8502	+	27.4533i	−0.522849	+	0.905601i	0.476797	+	0.879013i	$0.341798\pi$
$919$	−15.8502	+	27.4533i	−0.522849	+	0.905601i	−0.999646	+	0.0265881i	$0.991536\pi$
$920$	−0.190390	−	15.6555i	−0.00627697	−	0.516148i
$921$	4.44575	+	7.70027i	0.146493	+	0.253733i
$922$	35.4244	+	16.5872i	1.16664	+	0.546270i
$923$	9.96245	−	9.96245i	0.327918	−	0.327918i
$924$		0			0
$925$	32.8681	−	35.1720i	1.08070	−	1.15645i
$926$	−7.59302	+	2.74999i	−0.249522	+	0.0903703i
$927$	−7.76138	+	28.9659i	−0.254917	+	0.951364i
$928$	33.4519	+	23.8212i	1.09811	+	0.781970i
$929$	37.2981	+	21.5341i	1.22371	+	0.706509i	0.965707	−	0.259635i	$-0.0836021\pi$
$929$	37.2981	+	21.5341i	1.22371	+	0.706509i	0.258003	+	0.966144i	$0.416935\pi$
$930$	−3.72578	+	4.58109i	−0.122173	+	0.150220i
$931$		0			0
$932$	−1.84240	−	1.29880i	−0.0603498	−	0.0425436i
$933$	14.0184	−	3.75622i	0.458941	−	0.122973i
$934$	−17.0994	−	3.04308i	−0.559509	−	0.0995726i
$935$	−1.29025	+	5.16326i	−0.0421958	+	0.168857i
$936$	−19.0363	+	10.8701i	−0.622222	+	0.355299i
$937$	11.9105	−	11.9105i	0.389100	−	0.389100i	−0.485266	−	0.874366i	$-0.661277\pi$
$937$	11.9105	−	11.9105i	0.389100	−	0.389100i	0.874366	+	0.485266i	$0.161277\pi$
$938$		0			0
$939$	14.8261			0.483832
$940$	50.5037	−	24.4011i	1.64725	−	0.795876i
$941$	14.1264	+	24.4676i	0.460507	+	0.797622i	0.998986	−	0.0450169i	$-0.0143342\pi$
$941$	14.1264	+	24.4676i	0.460507	+	0.797622i	−0.538479	+	0.842639i	$0.681001\pi$
$942$	−5.14088	−	7.36681i	−0.167499	−	0.240023i
$943$	2.14922	+	8.02098i	0.0699881	+	0.261199i
$944$	−55.8880	+	19.9406i	−1.81900	+	0.649010i
$945$		0			0
$946$	−16.9230	+	20.1031i	−0.550213	+	0.653609i
$947$	−23.9653	+	6.42148i	−0.778767	+	0.208670i	−0.626241	−	0.779629i	$-0.715408\pi$
$947$	−23.9653	+	6.42148i	−0.778767	+	0.208670i	−0.152526	+	0.988299i	$0.548741\pi$
$948$	7.86962	+	0.713689i	0.255593	+	0.0231796i
$949$	−24.5603	+	14.1799i	−0.797263	+	0.460300i
$950$	13.0382	+	5.57516i	0.423015	+	0.180882i
$951$		−	0.122462i		−	0.00397109i
$952$		0			0
$953$	−19.4338	−	19.4338i	−0.629523	−	0.629523i	0.318425	−	0.947948i	$-0.396846\pi$
$953$	−19.4338	−	19.4338i	−0.629523	−	0.629523i	−0.947948	+	0.318425i	$0.896846\pi$
$954$	10.7015	−	3.87581i	0.346475	−	0.125484i
$955$	−30.0703	+	18.0464i	−0.973051	+	0.583967i
$956$	25.4266	+	30.4983i	0.822354	+	0.986387i
$957$	−4.25181	−	15.8680i	−0.137441	−	0.512938i
$958$	−2.91470	−	33.9356i	−0.0941696	−	1.09641i
$959$		0			0
$960$	−2.57246	+	9.89272i	−0.0830259	+	0.319286i
$961$	−10.1606	+	17.5986i	−0.327760	+	0.567697i
$962$	32.3692	−	22.5886i	1.04362	−	0.728287i
$963$	20.3062	+	5.44104i	0.654359	+	0.175335i
$964$	5.97191	−	16.2470i	0.192342	−	0.523280i
$965$	12.4789	+	12.0636i	0.401711	+	0.388339i
$966$		0			0
$967$	34.9483	+	34.9483i	1.12386	+	1.12386i	0.991155	+	0.132706i	$0.0423665\pi$
$967$	34.9483	+	34.9483i	1.12386	+	1.12386i	0.132706	+	0.991155i	$0.457633\pi$
$968$	12.7774	+	3.48900i	0.410681	+	0.112141i
$969$	−0.596424	+	0.344346i	−0.0191599	+	0.0110620i
$970$	0.793414	−	4.94167i	0.0254750	−	0.158667i
$971$	42.2275	+	24.3801i	1.35515	+	0.782393i	0.988965	−	0.148150i	$-0.0473320\pi$
$971$	42.2275	+	24.3801i	1.35515	+	0.782393i	0.366180	+	0.930544i	$0.380665\pi$
$972$	15.2688	−	21.6594i	0.489747	−	0.694726i
$973$		0			0
$974$	−3.12565	+	3.71302i	−0.100152	+	0.118973i
$975$	3.89614	−	7.30887i	0.124776	−	0.234071i
$976$	12.9029	+	10.9672i	0.413010	+	0.351050i
$977$	42.7841	+	11.4640i	1.36879	+	0.366765i	0.867035	−	0.498248i	$-0.166023\pi$
$977$	42.7841	+	11.4640i	1.36879	+	0.366765i	0.501750	+	0.865012i	$0.332690\pi$
$978$	−6.29242	+	13.4384i	−0.201209	+	0.429712i
$979$	15.3322			0.490020
$980$		0			0
$981$	−1.08089			−0.0345101
$982$	−2.12518	+	4.53864i	−0.0678173	+	0.144834i
$983$	−6.04477	−	1.61969i	−0.192798	−	0.0516601i	0.161128	−	0.986934i	$-0.448487\pi$
$983$	−6.04477	−	1.61969i	−0.192798	−	0.0516601i	−0.353926	+	0.935273i	$0.615154\pi$
$984$	0.0258212	−	5.42129i	0.000823149	−	0.172824i
$985$	3.68009	+	12.8597i	0.117257	+	0.409744i
$986$	−3.97373	+	4.72046i	−0.126549	+	0.150330i
$987$		0			0
$988$	9.50305	+	6.69918i	0.302332	+	0.213129i
$989$	10.0592	+	5.80766i	0.319863	+	0.184673i
$990$	−27.1279	+	19.6219i	−0.862180	+	0.623625i
$991$	23.9504	−	13.8278i	0.760809	−	0.439253i	−0.0687769	−	0.997632i	$-0.521910\pi$
$991$	23.9504	−	13.8278i	0.760809	−	0.439253i	0.829586	+	0.558379i	$0.188576\pi$
$992$	1.75728	−	18.4021i	0.0557936	−	0.584267i
$993$	0.858769	+	0.858769i	0.0272522	+	0.0272522i
$994$		0			0
$995$	31.4974	−	0.533095i	0.998534	−	0.0169003i
$996$	8.29463	+	3.04886i	0.262826	+	0.0966069i
$997$	8.67546	+	2.32458i	0.274755	+	0.0736203i	0.393565	−	0.919297i	$-0.371242\pi$
$997$	8.67546	+	2.32458i	0.274755	+	0.0736203i	−0.118811	+	0.992917i	$0.537908\pi$
$998$	35.1742	−	24.5461i	1.11342	−	0.776994i
$999$	−15.6062	+	27.0308i	−0.493759	+	0.855216i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.863.17		72
4.3	odd	2	inner	980.2.x.m.863.6		72
5.2	odd	4	inner	980.2.x.m.667.7		72
7.2	even	3		980.2.k.j.883.9		36
7.3	odd	6		140.2.w.b.123.3	yes	72
7.4	even	3	inner	980.2.x.m.263.3		72
7.5	odd	6		980.2.k.k.883.9		36
7.6	odd	2		140.2.w.b.23.17	yes	72
20.7	even	4	inner	980.2.x.m.667.3		72
28.3	even	6		140.2.w.b.123.7	yes	72
28.11	odd	6	inner	980.2.x.m.263.7		72
28.19	even	6		980.2.k.k.883.17		36
28.23	odd	6		980.2.k.j.883.17		36
28.27	even	2		140.2.w.b.23.6	✓	72
35.2	odd	12		980.2.k.j.687.17		36
35.3	even	12		700.2.be.e.207.13		72
35.12	even	12		980.2.k.k.687.17		36
35.13	even	4		700.2.be.e.107.12		72
35.17	even	12		140.2.w.b.67.6	yes	72
35.24	odd	6		700.2.be.e.543.16		72
35.27	even	4		140.2.w.b.107.7	yes	72
35.32	odd	12	inner	980.2.x.m.67.6		72
35.34	odd	2		700.2.be.e.443.2		72
140.3	odd	12		700.2.be.e.207.2		72
140.27	odd	4		140.2.w.b.107.3	yes	72
140.47	odd	12		980.2.k.k.687.9		36
140.59	even	6		700.2.be.e.543.12		72
140.67	even	12	inner	980.2.x.m.67.17		72
140.83	odd	4		700.2.be.e.107.16		72
140.87	odd	12		140.2.w.b.67.17	yes	72
140.107	even	12		980.2.k.j.687.9		36
140.139	even	2		700.2.be.e.443.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.6	✓	72	28.27	even	2
140.2.w.b.23.17	yes	72	7.6	odd	2
140.2.w.b.67.6	yes	72	35.17	even	12
140.2.w.b.67.17	yes	72	140.87	odd	12
140.2.w.b.107.3	yes	72	140.27	odd	4
140.2.w.b.107.7	yes	72	35.27	even	4
140.2.w.b.123.3	yes	72	7.3	odd	6
140.2.w.b.123.7	yes	72	28.3	even	6
700.2.be.e.107.12		72	35.13	even	4
700.2.be.e.107.16		72	140.83	odd	4
700.2.be.e.207.2		72	140.3	odd	12
700.2.be.e.207.13		72	35.3	even	12
700.2.be.e.443.2		72	35.34	odd	2
700.2.be.e.443.13		72	140.139	even	2
700.2.be.e.543.12		72	140.59	even	6
700.2.be.e.543.16		72	35.24	odd	6
980.2.k.j.687.9		36	140.107	even	12
980.2.k.j.687.17		36	35.2	odd	12
980.2.k.j.883.9		36	7.2	even	3
980.2.k.j.883.17		36	28.23	odd	6
980.2.k.k.687.9		36	140.47	odd	12
980.2.k.k.687.17		36	35.12	even	12
980.2.k.k.883.9		36	7.5	odd	6
980.2.k.k.883.17		36	28.19	even	6
980.2.x.m.67.6		72	35.32	odd	12	inner
980.2.x.m.67.17		72	140.67	even	12	inner
980.2.x.m.263.3		72	7.4	even	3	inner
980.2.x.m.263.7		72	28.11	odd	6	inner
980.2.x.m.667.3		72	20.7	even	4	inner
980.2.x.m.667.7		72	5.2	odd	4	inner
980.2.x.m.863.6		72	4.3	odd	2	inner
980.2.x.m.863.17		72	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	980.2.x.m.863.17

Level	$980$
Weight	$2$
Character	980.863
Analytic conductor	$7.825$
Analytic rank	$0$
Dimension	$72$
Inner twists	$8$