LMFDB - Embedded newform 980.2.x.j.667.10

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 = [64,4,0,0,0,0,0,16,0,0,0] 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:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.10
Character	$\chi$	$=$	980.667
Dual form			980.2.x.j.263.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.479962 - 1.33028i) q^{2} +(0.298008 - 1.11218i) q^{3} +(-1.53927 - 1.27696i) q^{4} +(-0.308165 + 2.21473i) q^{5} +(-1.33648 - 0.930237i) q^{6} +(-2.43751 + 1.43477i) q^{8} +(1.44994 + 0.837123i) q^{9} +(2.79830 + 1.47293i) q^{10} +(-1.59056 + 0.918308i) q^{11} +(-1.87893 + 1.33140i) q^{12} +(-2.24767 + 2.24767i) q^{13} +(2.37135 + 1.00274i) q^{15} +(0.738725 + 3.93119i) q^{16} +(-1.27350 + 4.75278i) q^{17} +(1.80952 - 1.52703i) q^{18} +(-3.96687 + 6.87082i) q^{19} +(3.30248 - 3.01556i) q^{20} +(0.458198 + 2.55663i) q^{22} +(-5.12402 + 1.37298i) q^{23} +(0.869322 + 3.13852i) q^{24} +(-4.81007 - 1.36501i) q^{25} +(1.91123 + 4.06882i) q^{26} +(3.80564 - 3.80564i) q^{27} -5.07030i q^{29} +(2.47208 - 2.67327i) q^{30} +(3.36913 - 1.94517i) q^{31} +(5.58414 + 0.904114i) q^{32} +(0.547326 + 2.04265i) q^{33} +(5.71128 + 3.97527i) q^{34} +(-1.16288 - 3.14008i) q^{36} +(-0.389468 + 0.104358i) q^{37} +(7.23615 + 8.57477i) q^{38} +(1.82999 + 3.16964i) q^{39} +(-2.42647 - 5.84057i) q^{40} +1.61265 q^{41} +(-5.11964 - 5.11964i) q^{43} +(3.62095 + 0.617556i) q^{44} +(-2.30082 + 2.95325i) q^{45} +(-0.632894 + 7.47534i) q^{46} +(2.87295 + 10.7220i) q^{47} +(4.59234 + 0.349931i) q^{48} +(-4.12448 + 5.74357i) q^{50} +(4.90644 + 2.83273i) q^{51} +(6.32997 - 0.589584i) q^{52} +(3.65309 + 0.978842i) q^{53} +(-3.23600 - 6.88912i) q^{54} +(-1.54365 - 3.80564i) q^{55} +(6.45944 + 6.45944i) q^{57} +(-6.74491 - 2.43355i) q^{58} +(-2.83588 - 4.91188i) q^{59} +(-2.36968 - 4.57162i) q^{60} +(1.16755 - 2.02226i) q^{61} +(-0.970559 - 5.41548i) q^{62} +(3.88289 - 6.99451i) q^{64} +(-4.28533 - 5.67063i) q^{65} +(2.97998 + 0.252298i) q^{66} +(5.24841 + 1.40631i) q^{67} +(8.02940 - 5.68961i) q^{68} +6.10799i q^{69} +4.56057i q^{71} +(-4.73531 + 0.0398294i) q^{72} +(-4.59251 - 1.23056i) q^{73} +(-0.0481052 + 0.568188i) q^{74} +(-2.95157 + 4.94288i) q^{75} +(14.8799 - 5.51052i) q^{76} +(5.09482 - 0.913089i) q^{78} +(5.67209 - 9.82435i) q^{79} +(-8.93419 + 0.424620i) q^{80} +(-0.587082 - 1.01686i) q^{81} +(0.774011 - 2.14527i) q^{82} +(-0.898867 - 0.898867i) q^{83} +(-10.1337 - 4.28511i) q^{85} +(-9.26778 + 4.35331i) q^{86} +(-5.63909 - 1.51099i) q^{87} +(2.55944 - 4.52046i) q^{88} +(13.2459 + 7.64755i) q^{89} +(2.82434 + 4.47818i) q^{90} +(9.64050 + 4.42980i) q^{92} +(-1.15935 - 4.32676i) q^{93} +(15.6421 + 1.32433i) q^{94} +(-13.9946 - 10.9029i) q^{95} +(2.66965 - 5.94113i) q^{96} +(8.82518 + 8.82518i) q^{97} -3.07495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 16 q^{8} - 8 q^{16} + 40 q^{18} - 72 q^{22} - 32 q^{25} + 36 q^{30} - 16 q^{32} - 176 q^{36} + 48 q^{37} + 56 q^{50} - 16 q^{53} - 32 q^{57} - 36 q^{58} + 80 q^{60} - 64 q^{65} - 56 q^{72}+ \cdots - 32 q^{93}+O(q^{100}) $ 64 * q + 4 * q^2 + 16 * q^8 - 8 * q^16 + 40 * q^18 - 72 * q^22 - 32 * q^25 + 36 * q^30 - 16 * q^32 - 176 * q^36 + 48 * q^37 + 56 * q^50 - 16 * q^53 - 32 * q^57 - 36 * q^58 + 80 * q^60 - 64 * q^65 - 56 * q^72 + 56 * q^78 - 56 * q^86 - 88 * q^88 + 272 * q^92 - 32 * q^93

Character values

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

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

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 $

$2$	0.479962	−	1.33028i	0.339384	−	0.940648i
$2$	0.479962	−	1.33028i	0.339384	−	0.940648i
$3$	0.298008	−	1.11218i	0.172055	−	0.642118i	−0.824980	−	0.565162i	$-0.808813\pi$
$3$	0.298008	−	1.11218i	0.172055	−	0.642118i	0.997035	−	0.0769553i	$-0.0245199\pi$
$4$	−1.53927	−	1.27696i	−0.769637	−	0.638482i
$5$	−0.308165	+	2.21473i	−0.137816	+	0.990458i
$5$	−0.308165	+	2.21473i	−0.137816	+	0.990458i
$6$	−1.33648	−	0.930237i	−0.545614	−	0.379768i
$7$		0			0
$7$		0			0
$8$	−2.43751	+	1.43477i	−0.861789	+	0.507266i
$9$	1.44994	+	0.837123i	0.483313	+	0.279041i
$10$	2.79830	+	1.47293i	0.884900	+	0.465782i
$11$	−1.59056	+	0.918308i	−0.479571	+	0.276880i	−0.720237	−	0.693728i	$-0.755967\pi$
$11$	−1.59056	+	0.918308i	−0.479571	+	0.276880i	0.240667	+	0.970608i	$0.422634\pi$
$12$	−1.87893	+	1.33140i	−0.542400	+	0.384343i
$13$	−2.24767	+	2.24767i	−0.623391	+	0.623391i	−0.946397	−	0.323006i	$-0.895307\pi$
$13$	−2.24767	+	2.24767i	−0.623391	+	0.623391i	0.323006	+	0.946397i	$0.395307\pi$
$14$		0			0
$15$	2.37135	+	1.00274i	0.612279	+	0.258907i
$16$	0.738725	+	3.93119i	0.184681	+	0.982798i
$17$	−1.27350	+	4.75278i	−0.308870	+	1.15272i	0.620692	+	0.784054i	$0.286852\pi$
$17$	−1.27350	+	4.75278i	−0.308870	+	1.15272i	−0.929562	+	0.368665i	$0.879815\pi$
$18$	1.80952	−	1.52703i	0.426508	−	0.359925i
$19$	−3.96687	+	6.87082i	−0.910063	+	1.57628i	−0.0960899	+	0.995373i	$0.530634\pi$
$19$	−3.96687	+	6.87082i	−0.910063	+	1.57628i	−0.813973	+	0.580903i	$0.802700\pi$
$20$	3.30248	−	3.01556i	0.738458	−	0.674300i
$21$		0			0
$22$	0.458198	+	2.55663i	0.0976881	+	0.545076i
$23$	−5.12402	+	1.37298i	−1.06843	+	0.286285i	−0.749848	−	0.661610i	$-0.769874\pi$
$23$	−5.12402	+	1.37298i	−1.06843	+	0.286285i	−0.318583	+	0.947895i	$0.603207\pi$
$24$	0.869322	+	3.13852i	0.177450	+	0.640648i
$25$	−4.81007	−	1.36501i	−0.962014	−	0.273001i
$26$	1.91123	+	4.06882i	0.374822	+	0.797960i
$27$	3.80564	−	3.80564i	0.732396	−	0.732396i
$28$		0			0
$29$		−	5.07030i		−	0.941532i	−0.882258	−	0.470766i	$-0.843978\pi$
$29$		−	5.07030i		−	0.941532i	0.882258	−	0.470766i	$-0.156022\pi$
$30$	2.47208	−	2.67327i	0.451338	−	0.488070i
$31$	3.36913	−	1.94517i	0.605114	−	0.349363i	−0.165937	−	0.986136i	$-0.553065\pi$
$31$	3.36913	−	1.94517i	0.605114	−	0.349363i	0.771051	+	0.636774i	$0.219731\pi$
$32$	5.58414	+	0.904114i	0.987145	+	0.159826i
$33$	0.547326	+	2.04265i	0.0952772	+	0.355579i
$34$	5.71128	+	3.97527i	0.979477	+	0.681753i
$35$		0			0
$36$	−1.16288	−	3.14008i	−0.193813	−	0.523347i
$37$	−0.389468	+	0.104358i	−0.0640281	+	0.0171563i	−0.290691	−	0.956817i	$-0.593885\pi$
$37$	−0.389468	+	0.104358i	−0.0640281	+	0.0171563i	0.226663	+	0.973973i	$0.427218\pi$
$38$	7.23615	+	8.57477i	1.17386	+	1.39101i
$39$	1.82999	+	3.16964i	0.293033	+	0.507548i
$40$	−2.42647	−	5.84057i	−0.383658	−	0.923475i
$41$	1.61265			0.251854			0.125927	−	0.992040i	$-0.459809\pi$
$41$	1.61265			0.251854			0.125927	+	0.992040i	$0.459809\pi$
$42$		0			0
$43$	−5.11964	−	5.11964i	−0.780738	−	0.780738i	0.199217	−	0.979955i	$-0.436160\pi$
$43$	−5.11964	−	5.11964i	−0.780738	−	0.780738i	−0.979955	+	0.199217i	$0.936160\pi$
$44$	3.62095	+	0.617556i	0.545878	+	0.0931001i
$45$	−2.30082	+	2.95325i	−0.342986	+	0.440245i
$46$	−0.632894	+	7.47534i	−0.0933151	+	1.10218i
$47$	2.87295	+	10.7220i	0.419063	+	1.56396i	0.776556	+	0.630049i	$0.216965\pi$
$47$	2.87295	+	10.7220i	0.419063	+	1.56396i	−0.357492	+	0.933916i	$0.616368\pi$
$48$	4.59234	+	0.349931i	0.662848	+	0.0505082i
$49$		0			0
$50$	−4.12448	+	5.74357i	−0.583290	+	0.812264i
$51$	4.90644	+	2.83273i	0.687039	+	0.396662i
$52$	6.32997	−	0.589584i	0.877809	−	0.0817606i
$53$	3.65309	+	0.978842i	0.501790	+	0.134454i	0.500831	−	0.865545i	$-0.333028\pi$
$53$	3.65309	+	0.978842i	0.501790	+	0.134454i	0.000959479		1.00000i	$0.499695\pi$
$54$	−3.23600	−	6.88912i	−0.440363	−	0.937491i
$55$	−1.54365	−	3.80564i	−0.208146	−	0.513153i
$56$		0			0
$57$	6.45944	+	6.45944i	0.855573	+	0.855573i
$58$	−6.74491	−	2.43355i	−0.885650	−	0.319541i
$59$	−2.83588	−	4.91188i	−0.369200	−	0.639473i	0.620241	−	0.784411i	$-0.287035\pi$
$59$	−2.83588	−	4.91188i	−0.369200	−	0.639473i	−0.989441	+	0.144939i	$0.953701\pi$
$60$	−2.36968	−	4.57162i	−0.305925	−	0.590193i
$61$	1.16755	−	2.02226i	0.149489	−	0.258923i	−0.781549	−	0.623843i	$-0.785570\pi$
$61$	1.16755	−	2.02226i	0.149489	−	0.258923i	0.931039	+	0.364920i	$0.118904\pi$
$62$	−0.970559	−	5.41548i	−0.123261	−	0.687767i
$63$		0			0
$64$	3.88289	−	6.99451i	0.485362	−	0.874313i
$65$	−4.28533	−	5.67063i	−0.531530	−	0.703356i
$66$	2.97998	+	0.252298i	0.366810	+	0.0310557i
$67$	5.24841	+	1.40631i	0.641195	+	0.171808i	0.564745	−	0.825266i	$-0.308975\pi$
$67$	5.24841	+	1.40631i	0.641195	+	0.171808i	0.0764503	+	0.997073i	$0.475641\pi$
$68$	8.02940	−	5.68961i	0.973708	−	0.689967i
$69$			6.10799i			0.735315i
$70$		0			0
$71$			4.56057i			0.541240i	0.962686	+	0.270620i	$0.0872287\pi$
$71$			4.56057i			0.541240i	−0.962686	+	0.270620i	$0.912771\pi$
$72$	−4.73531	+	0.0398294i	−0.558062	+	0.00469394i
$73$	−4.59251	−	1.23056i	−0.537512	−	0.144026i	−0.0201571	−	0.999797i	$-0.506417\pi$
$73$	−4.59251	−	1.23056i	−0.537512	−	0.144026i	−0.517355	+	0.855771i	$0.673083\pi$
$74$	−0.0481052	+	0.568188i	−0.00559211	+	0.0660505i
$75$	−2.95157	+	4.94288i	−0.340818	+	0.570755i
$76$	14.8799	−	5.51052i	1.70684	−	0.632100i
$77$		0			0
$78$	5.09482	−	0.913089i	0.576875	−	0.103387i
$79$	5.67209	−	9.82435i	0.638160	−	1.10533i	−0.347676	−	0.937615i	$-0.613029\pi$
$79$	5.67209	−	9.82435i	0.638160	−	1.10533i	0.985836	−	0.167711i	$-0.0536375\pi$
$80$	−8.93419	+	0.424620i	−0.998872	+	0.0474740i
$81$	−0.587082	−	1.01686i	−0.0652313	−	0.112984i
$82$	0.774011	−	2.14527i	0.0854753	−	0.236906i
$83$	−0.898867	−	0.898867i	−0.0986635	−	0.0986635i	0.656052	−	0.754716i	$-0.272225\pi$
$83$	−0.898867	−	0.898867i	−0.0986635	−	0.0986635i	−0.754716	+	0.656052i	$0.772225\pi$
$84$		0			0
$85$	−10.1337	−	4.28511i	−1.09915	−	0.464785i
$86$	−9.26778	+	4.35331i	−0.999370	+	0.469429i
$87$	−5.63909	−	1.51099i	−0.604574	−	0.161995i
$88$	2.55944	−	4.52046i	0.272837	−	0.481882i
$89$	13.2459	+	7.64755i	1.40407	+	0.810639i	0.994807	−	0.101779i	$-0.0324534\pi$
$89$	13.2459	+	7.64755i	1.40407	+	0.810639i	0.409260	+	0.912418i	$0.365787\pi$
$90$	2.82434	+	4.47818i	0.297711	+	0.472042i
$91$		0			0
$92$	9.64050	+	4.42980i	1.00509	+	0.461839i
$93$	−1.15935	−	4.32676i	−0.120219	−	0.448664i
$94$	15.6421	+	1.32433i	1.61336	+	0.136594i
$95$	−13.9946	−	10.9029i	−1.43581	−	1.11861i
$96$	2.66965	−	5.94113i	0.272470	−	0.606365i
$97$	8.82518	+	8.82518i	0.896061	+	0.896061i	0.995085	−	0.0990238i	$-0.0315720\pi$
$97$	8.82518	+	8.82518i	0.896061	+	0.896061i	−0.0990238	+	0.995085i	$0.531572\pi$
$98$		0			0
$99$	−3.07495			−0.309044
$100$	5.66095	+	8.24340i	0.566095	+	0.824340i
$101$	−6.80706	−	11.7902i	−0.677328	−	1.17317i	−0.975783	−	0.218743i	$-0.929804\pi$
$101$	−6.80706	−	11.7902i	−0.677328	−	1.17317i	0.298454	−	0.954424i	$-0.403529\pi$
$102$	6.12322	−	5.16732i	0.606289	−	0.511641i
$103$	−18.2607	+	4.89293i	−1.79928	+	0.482115i	−0.993865	−	0.110601i	$-0.964722\pi$
$103$	−18.2607	+	4.89293i	−1.79928	+	0.482115i	−0.805412	+	0.592716i	$0.798056\pi$
$104$	2.25383	−	8.70359i	0.221006	−	0.853457i
$105$		0			0
$106$	3.05547	−	4.38981i	0.296774	−	0.426376i
$107$	−1.33965	−	4.99963i	−0.129508	−	0.483332i	0.870452	−	0.492254i	$-0.163827\pi$
$107$	−1.33965	−	4.99963i	−0.129508	−	0.483332i	−0.999960	+	0.00892166i	$0.997160\pi$
$108$	−10.7176	+	0.998255i	−1.03130	+	0.0960571i
$109$	7.67494	−	4.43113i	0.735125	−	0.424425i	−0.0851688	−	0.996367i	$-0.527143\pi$
$109$	7.67494	−	4.43113i	0.735125	−	0.424425i	0.820294	+	0.571942i	$0.193810\pi$
$110$	−5.80345	+	0.226920i	−0.553337	+	0.0216360i
$111$			0.464258i			0.0440654i
$112$		0			0
$113$	−9.25139	+	9.25139i	−0.870297	+	0.870297i	−0.992505	−	0.122207i	$-0.961003\pi$
$113$	−9.25139	+	9.25139i	−0.870297	+	0.870297i	0.122207	+	0.992505i	$0.461003\pi$
$114$	11.6931	−	5.49256i	1.09516	−	0.514425i
$115$	−1.46173	−	11.7714i	−0.136307	−	1.09769i
$116$	−6.47459	+	7.80458i	−0.601151	+	0.724637i
$117$	−5.14056	+	1.37741i	−0.475245	+	0.127341i
$118$	−7.89528	+	1.41499i	−0.726819	+	0.130260i
$119$		0			0
$120$	−7.21887	+	0.958132i	−0.658990	+	0.0874651i
$121$	−3.81342	+	6.60504i	−0.346675	+	0.600458i
$122$	−2.12978	−	2.52377i	−0.192821	−	0.228491i
$123$	0.480583	−	1.79356i	0.0433327	−	0.161720i
$124$	−7.66992	−	1.30811i	−0.688780	−	0.117472i
$125$	4.50542	−	10.2324i	0.402977	−	0.915210i
$126$		0			0
$127$	7.20294	−	7.20294i	0.639157	−	0.639157i	−0.311190	−	0.950348i	$-0.600728\pi$
$127$	7.20294	−	7.20294i	0.639157	−	0.639157i	0.950348	+	0.311190i	$0.100728\pi$
$128$	−7.44099	−	8.52242i	−0.657697	−	0.753283i
$129$	−7.21966	+	4.16827i	−0.635656	+	0.366996i
$130$	−9.60031	+	2.97899i	−0.842003	+	0.261274i
$131$	−2.54112	−	1.46712i	−0.222019	−	0.128183i	0.384866	−	0.922972i	$-0.374248\pi$
$131$	−2.54112	−	1.46712i	−0.222019	−	0.128183i	−0.606885	+	0.794790i	$0.707581\pi$
$132$	1.76590	−	3.84311i	0.153702	−	0.334500i
$133$		0			0
$134$	4.38981	−	6.30686i	0.379222	−	0.544830i
$135$	7.25571	+	9.60124i	0.624472	+	0.826343i
$136$	−3.71495	−	13.4121i	−0.318554	−	1.15008i
$137$	−3.19819	+	11.9358i	−0.273240	+	1.01975i	0.683771	+	0.729696i	$0.260339\pi$
$137$	−3.19819	+	11.9358i	−0.273240	+	1.01975i	−0.957012	+	0.290050i	$0.906328\pi$
$138$	8.12532	+	2.93160i	0.691673	+	0.249554i
$139$	−13.2830			−1.12665			−0.563326	−	0.826235i	$-0.690479\pi$
$139$	−13.2830			−1.12665			−0.563326	+	0.826235i	$0.690479\pi$
$140$		0			0
$141$	12.7810			1.07635
$142$	6.06682	+	2.18890i	0.509116	+	0.183688i
$143$	1.51099	−	5.63909i	0.126355	−	0.471565i
$144$	−2.21979	+	6.31840i	−0.184982	+	0.526533i
$145$	11.2294	+	1.56249i	0.932547	+	0.129758i
$146$	−3.84121	+	5.51868i	−0.317901	+	0.456729i
$147$		0			0
$148$	0.732758	+	0.336702i	0.0602324	+	0.0276767i
$149$	19.2841	+	11.1337i	1.57982	+	0.912107i	0.994884	+	0.101024i	$0.0322120\pi$
$149$	19.2841	+	11.1337i	1.57982	+	0.912107i	0.584932	+	0.811083i	$0.301121\pi$
$150$	5.15876	+	6.29880i	0.421211	+	0.514295i
$151$	15.3338	−	8.85297i	1.24785	−	0.720444i	0.277166	−	0.960822i	$-0.410605\pi$
$151$	15.3338	−	8.85297i	1.24785	−	0.720444i	0.970679	+	0.240378i	$0.0772713\pi$
$152$	−0.188739	−	22.4392i	−0.0153088	−	1.82006i
$153$	−5.82517	+	5.82517i	−0.470937	+	0.470937i
$154$		0			0
$155$	3.26978	+	8.06115i	0.262635	+	0.647487i
$156$	1.23066	−	7.21577i	0.0985314	−	0.577724i
$157$	0.322272	−	1.20274i	0.0257201	−	0.0959889i	−0.951873	−	0.306494i	$-0.900844\pi$
$157$	0.322272	−	1.20274i	0.0257201	−	0.0959889i	0.977593	+	0.210505i	$0.0675108\pi$
$158$	−10.3467	−	12.2608i	−0.823141	−	0.975414i
$159$	2.17730	−	3.77119i	0.172671	−	0.299075i
$160$	−3.72321	+	12.0887i	−0.294345	+	0.955699i
$161$		0			0
$162$	−1.63448	+	0.292930i	−0.128417	+	0.0230147i
$163$	−21.9570	+	5.88335i	−1.71980	+	0.460820i	−0.977794	−	0.209570i	$-0.932794\pi$
$163$	−21.9570	+	5.88335i	−1.71980	+	0.460820i	−0.742009	+	0.670390i	$0.766127\pi$
$164$	−2.48231	−	2.05930i	−0.193836	−	0.160804i
$165$	−4.69258	+	0.582707i	−0.365317	+	0.0453637i
$166$	−1.62716	+	0.764320i	−0.126292	+	0.0593228i
$167$	−9.64678	+	9.64678i	−0.746491	+	0.746491i	−0.973818	−	0.227328i	$-0.927001\pi$
$167$	−9.64678	+	9.64678i	−0.746491	+	0.746491i	0.227328	+	0.973818i	$0.427001\pi$
$168$		0			0
$169$			2.89597i			0.222767i
$170$	−10.5642	+	11.4239i	−0.810234	+	0.876174i
$171$	−11.5034	+	6.64152i	−0.879691	+	0.507890i
$172$	1.34293	+	14.4181i	0.102397	+	1.09937i
$173$	1.10903	+	4.13894i	0.0843176	+	0.314678i	0.995184	−	0.0980235i	$-0.0312520\pi$
$173$	1.10903	+	4.13894i	0.0843176	+	0.314678i	−0.910866	+	0.412701i	$0.864585\pi$
$174$	−4.71658	+	6.77634i	−0.357563	+	0.513713i
$175$		0			0
$176$	−4.78503	−	5.57441i	−0.360685	−	0.420187i
$177$	−6.30801	+	1.69023i	−0.474139	+	0.127045i
$178$	16.5309	−	13.9502i	1.23904	−	1.04562i
$179$	11.7768	+	20.3979i	0.880236	+	1.52461i	0.851078	+	0.525039i	$0.175949\pi$
$179$	11.7768	+	20.3979i	0.880236	+	1.52461i	0.0291582	+	0.999575i	$0.490717\pi$
$180$	7.31279	−	1.60780i	0.545064	−	0.119838i
$181$	−12.4326			−0.924106			−0.462053	−	0.886852i	$-0.652887\pi$
$181$	−12.4326			−0.924106			−0.462053	+	0.886852i	$0.652887\pi$
$182$		0			0
$183$	−1.90117	−	1.90117i	−0.140539	−	0.140539i
$184$	10.5199	−	10.6984i	0.775540	−	0.788697i
$185$	−0.111104	−	0.894726i	−0.00816850	−	0.0657816i
$186$	−6.31223	−	0.534420i	−0.462835	−	0.0391856i
$187$	−2.33894	−	8.72903i	−0.171040	−	0.638330i
$188$	9.26935	−	20.1727i	0.676037	−	1.47125i
$189$		0			0
$190$	−21.2207	+	13.3837i	−1.53951	+	0.970955i
$191$	11.3842	+	6.57268i	0.823733	+	0.475582i	0.851702	−	0.524026i	$-0.175571\pi$
$191$	11.3842	+	6.57268i	0.823733	+	0.475582i	−0.0279691	+	0.999609i	$0.508904\pi$
$192$	−6.62202	−	6.40290i	−0.477903	−	0.462089i
$193$	15.1129	+	4.04948i	1.08785	+	0.291488i	0.757807	−	0.652479i	$-0.226271\pi$
$193$	15.1129	+	4.04948i	1.08785	+	0.291488i	0.330041	+	0.943967i	$0.392938\pi$
$194$	15.9757	−	7.50418i	1.14699	−	0.538769i
$195$	−7.58383	+	3.07616i	−0.543089	+	0.220289i
$196$		0			0
$197$	−7.35541	−	7.35541i	−0.524051	−	0.524051i	0.394741	−	0.918792i	$-0.370834\pi$
$197$	−7.35541	−	7.35541i	−0.524051	−	0.524051i	−0.918792	+	0.394741i	$0.870834\pi$
$198$	−1.47586	+	4.09053i	−0.104885	+	0.290701i
$199$	−3.80564	−	6.59157i	−0.269775	−	0.467264i	0.699029	−	0.715094i	$-0.253616\pi$
$199$	−3.80564	−	6.59157i	−0.269775	−	0.467264i	−0.968804	+	0.247830i	$0.920283\pi$
$200$	13.6830	−	3.57411i	0.967537	−	0.252728i
$201$	3.12813	−	5.41809i	0.220641	−	0.382162i
$202$	−18.9513	+	3.39644i	−1.33341	+	0.238973i
$203$		0			0
$204$	−3.93505	−	10.6257i	−0.275509	−	0.743947i
$205$	−0.496963	+	3.57159i	−0.0347094	+	0.249451i
$206$	−2.25547	+	26.6402i	−0.157146	+	1.85611i
$207$	−8.57886	−	2.29870i	−0.596272	−	0.159771i
$208$	−10.4964	−	7.17561i	−0.727796	−	0.497539i
$209$		−	14.5712i		−	1.00791i
$210$		0			0
$211$			19.7336i			1.35852i	0.733899	+	0.679259i	$0.237699\pi$
$211$			19.7336i			1.35852i	−0.733899	+	0.679259i	$0.762301\pi$
$212$	−4.37315	−	6.17157i	−0.300349	−	0.423865i
$213$	5.07218	+	1.35909i	0.347540	+	0.0931230i
$214$	−7.29387	−	0.617530i	−0.498598	−	0.0422135i
$215$	12.9163	−	9.76094i	0.880886	−	0.665690i
$216$	−3.81608	+	14.7365i	−0.259651	+	1.00269i
$217$		0			0
$218$	−2.21095	−	12.3366i	−0.149744	−	0.835537i
$219$	−2.73721	+	4.74098i	−0.184963	+	0.320366i
$220$	−2.48357	+	7.82911i	−0.167442	+	0.527839i
$221$	−7.82026	−	13.5451i	−0.526048	−	0.911141i
$222$	0.617592	+	0.222826i	0.0414500	+	0.0149551i
$223$	−0.871411	−	0.871411i	−0.0583540	−	0.0583540i	0.677328	−	0.735682i	$-0.263138\pi$
$223$	−0.871411	−	0.871411i	−0.0583540	−	0.0583540i	−0.735682	+	0.677328i	$0.763138\pi$
$224$		0			0
$225$	−5.83163	−	6.00579i	−0.388775	−	0.400386i
$226$	7.86659	+	16.7472i	0.523278	+	1.11401i
$227$	11.9499	+	3.20196i	0.793141	+	0.212522i	0.632570	−	0.774503i	$-0.282000\pi$
$227$	11.9499	+	3.20196i	0.793141	+	0.212522i	0.160571	+	0.987024i	$0.448667\pi$
$228$	−1.69437	−	18.1913i	−0.112212	−	1.20475i
$229$	−14.0935	−	8.13689i	−0.931326	−	0.537701i	−0.0440950	−	0.999027i	$-0.514040\pi$
$229$	−14.0935	−	8.13689i	−0.931326	−	0.537701i	−0.887231	+	0.461326i	$0.847374\pi$
$230$	−16.3608	−	3.70533i	−1.07880	−	0.244322i
$231$		0			0
$232$	7.27470	+	12.3589i	0.477607	+	0.811402i
$233$	−1.56599	−	5.84434i	−0.102591	−	0.382875i	0.895470	−	0.445123i	$-0.146840\pi$
$233$	−1.56599	−	5.84434i	−0.102591	−	0.382875i	−0.998061	+	0.0622473i	$0.980173\pi$
$234$	−0.634937	+	7.49947i	−0.0415071	+	0.490256i
$235$	−24.6317	+	3.05867i	−1.60679	+	0.199526i
$236$	−1.90711	+	11.1820i	−0.124142	+	0.727889i
$237$	−9.23612	−	9.23612i	−0.599951	−	0.599951i
$238$		0			0
$239$	−1.65449			−0.107020			−0.0535102	−	0.998567i	$-0.517041\pi$
$239$	−1.65449			−0.107020			−0.0535102	+	0.998567i	$0.517041\pi$
$240$	−2.19020	+	10.0630i	−0.141377	+	0.649562i
$241$	12.9251	+	22.3870i	0.832581	+	1.44207i	0.895985	+	0.444085i	$0.146471\pi$
$241$	12.9251	+	22.3870i	0.832581	+	1.44207i	−0.0634039	+	0.997988i	$0.520196\pi$
$242$	6.95624	+	8.24307i	0.447164	+	0.529885i
$243$	14.2899	−	3.82898i	0.916700	−	0.245629i
$244$	−4.37953	+	1.62189i	−0.280370	+	0.103831i
$245$		0			0
$246$	−2.15527	−	1.50015i	−0.137415	−	0.0956460i
$247$	−6.52712	−	24.3595i	−0.415311	−	1.54996i
$248$	−5.42142	+	9.57528i	−0.344261	+	0.608031i
$249$	−1.26757	+	0.731833i	−0.0803291	+	0.0463780i
$250$	−11.4494	−	10.9046i	−0.724127	−	0.689667i
$251$			19.7964i			1.24954i	0.780809	+	0.624769i	$0.214807\pi$
$251$			19.7964i			1.24954i	−0.780809	+	0.624769i	$0.785193\pi$
$252$		0			0
$253$	6.88922	−	6.88922i	0.433121	−	0.433121i
$254$	−6.12477	−	13.0390i	−0.384302	−	0.818142i
$255$	−7.78573	+	9.99349i	−0.487562	+	0.625817i
$256$	−14.9086	+	5.80814i	−0.931786	+	0.363009i
$257$	11.9768	−	3.20918i	0.747094	−	0.200183i	0.134865	−	0.990864i	$-0.456940\pi$
$257$	11.9768	−	3.20918i	0.747094	−	0.200183i	0.612229	+	0.790681i	$0.290273\pi$
$258$	2.07980	+	11.6048i	0.129482	+	0.722481i
$259$		0			0
$260$	−0.644905	+	14.2009i	−0.0399953	+	0.880700i
$261$	4.24447	−	7.35163i	0.262726	−	0.455055i
$262$	−3.17131	+	2.67623i	−0.195924	+	0.165338i
$263$	0.738908	−	2.75764i	0.0455630	−	0.170044i	−0.939395	−	0.342836i	$-0.888612\pi$
$263$	0.738908	−	2.75764i	0.0455630	−	0.170044i	0.984958	+	0.172793i	$0.0552791\pi$
$264$	−4.26483	−	4.19369i	−0.262482	−	0.258104i
$265$	−3.29363	+	7.78896i	−0.202326	+	0.478472i
$266$		0			0
$267$	12.4529	−	12.4529i	0.762102	−	0.762102i
$268$	−6.28293	−	8.86672i	−0.383791	−	0.541621i
$269$	18.3499	−	10.5943i	1.11881	−	0.645946i	0.177713	−	0.984082i	$-0.443130\pi$
$269$	18.3499	−	10.5943i	1.11881	−	0.645946i	0.941097	+	0.338137i	$0.109797\pi$
$270$	16.2548	−	5.04387i	0.989234	−	0.306960i
$271$	−11.3233	−	6.53753i	−0.687843	−	0.397127i	0.114960	−	0.993370i	$-0.463326\pi$
$271$	−11.3233	−	6.53753i	−0.687843	−	0.397127i	−0.802804	+	0.596244i	$0.796659\pi$
$272$	−19.6249	−	1.49539i	−1.18993	−	0.0906715i
$273$		0			0
$274$	14.3429	+	9.98322i	0.866488	+	0.603108i
$275$	8.90418	−	2.24601i	0.536942	−	0.135439i
$276$	7.79968	−	9.40186i	0.469486	−	0.565926i
$277$	−1.81778	+	6.78406i	−0.109220	+	0.407615i	−0.998790	−	0.0491848i	$-0.984338\pi$
$277$	−1.81778	+	6.78406i	−0.109220	+	0.407615i	0.889570	+	0.456800i	$0.151004\pi$
$278$	−6.37535	+	17.6701i	−0.382368	+	1.05978i
$279$	6.51338			0.389946
$280$		0			0
$281$	20.2107			1.20567			0.602836	−	0.797865i	$-0.294037\pi$
$281$	20.2107			1.20567			0.602836	+	0.797865i	$0.294037\pi$
$282$	6.13437	−	17.0022i	0.365297	−	1.01247i
$283$	−1.77800	+	6.63558i	−0.105691	+	0.394444i	−0.998423	−	0.0561446i	$-0.982119\pi$
$283$	−1.77800	+	6.63558i	−0.105691	+	0.394444i	0.892732	+	0.450589i	$0.148786\pi$
$284$	5.82368	−	7.01996i	0.345572	−	0.416558i
$285$	−16.2965	+	12.3153i	−0.965321	+	0.729498i
$286$	−6.77634	−	4.71658i	−0.400693	−	0.278897i
$287$		0			0
$288$	7.33980	+	5.98552i	0.432502	+	0.352700i
$289$	−6.24469	−	3.60537i	−0.367335	−	0.212081i
$290$	7.46821	−	14.1882i	0.438548	−	0.833161i
$291$	12.4452	−	7.18522i	0.729549	−	0.421205i
$292$	5.49774	+	7.75863i	0.321731	+	0.454039i
$293$	3.07808	−	3.07808i	0.179823	−	0.179823i	−0.611456	−	0.791279i	$-0.709416\pi$
$293$	3.07808	−	3.07808i	0.179823	−	0.179823i	0.791279	+	0.611456i	$0.209416\pi$
$294$		0			0
$295$	11.7524	−	4.76703i	0.684252	−	0.277547i
$296$	0.799603	−	0.813168i	0.0464760	−	0.0472644i
$297$	−2.55834	+	9.54784i	−0.148450	+	0.554022i
$298$	24.0665	−	20.3095i	1.39414	−	1.17650i
$299$	8.43109	−	14.6031i	0.487583	−	0.844518i
$300$	10.8552	−	3.83940i	0.626723	−	0.221668i
$301$		0			0
$302$	−4.41726	−	24.6473i	−0.254185	−	1.41829i
$303$	−15.1414	+	4.05712i	−0.869849	+	0.233075i
$304$	−29.9410	−	10.5189i	−1.71723	−	0.603300i
$305$	4.11896	+	3.20900i	0.235851	+	0.183747i
$306$	4.95323	+	10.5449i	0.283157	+	0.602814i
$307$	8.11427	−	8.11427i	0.463106	−	0.463106i	−0.436566	−	0.899672i	$-0.643806\pi$
$307$	8.11427	−	8.11427i	0.463106	−	0.463106i	0.899672	+	0.436566i	$0.143806\pi$
$308$		0			0
$309$			21.7673i			1.23830i
$310$	12.2929	−	0.480664i	0.698192	−	0.0272999i
$311$	9.27501	−	5.35493i	0.525938	−	0.303650i	−0.213423	−	0.976960i	$-0.568461\pi$
$311$	9.27501	−	5.35493i	0.525938	−	0.303650i	0.739361	+	0.673310i	$0.235128\pi$
$312$	−9.00830	−	5.10041i	−0.509995	−	0.288754i
$313$	−4.58621	−	17.1160i	−0.259228	−	0.967451i	−0.965689	−	0.259700i	$-0.916376\pi$
$313$	−4.58621	−	17.1160i	−0.259228	−	0.967451i	0.706462	−	0.707751i	$-0.250290\pi$
$314$	−1.44530	−	1.00598i	−0.0815627	−	0.0567707i
$315$		0			0
$316$	−21.2762	+	7.87930i	−1.19688	+	0.443245i
$317$	−1.69997	+	0.455506i	−0.0954800	+	0.0255838i	−0.306243	−	0.951953i	$-0.599072\pi$
$317$	−1.69997	+	0.455506i	−0.0954800	+	0.0255838i	0.210763	+	0.977537i	$0.432405\pi$
$318$	−3.97171	−	4.70644i	−0.222722	−	0.263924i
$319$	4.65610	+	8.06460i	0.260691	+	0.451531i
$320$	14.2944	+	10.7550i	0.799080	+	0.601224i
$321$	−5.95971			−0.332639
$322$		0			0
$323$	−27.6037	−	27.6037i	−1.53591	−	1.53591i
$324$	−0.394809	+	2.31490i	−0.0219338	+	0.128606i
$325$	13.8795	−	7.74336i	0.769897	−	0.429524i
$326$	−2.71202	+	32.0326i	−0.150205	+	1.77412i
$327$	−2.64102	−	9.85642i	−0.146049	−	0.545062i
$328$	−3.93085	+	2.31378i	−0.217045	+	0.127757i
$329$		0			0
$330$	−1.47710	+	6.52211i	−0.0813116	+	0.359030i
$331$	21.3433	+	12.3226i	1.17314	+	0.677310i	0.954417	−	0.298478i	$-0.0964788\pi$
$331$	21.3433	+	12.3226i	1.17314	+	0.677310i	0.218719	+	0.975788i	$0.429812\pi$
$332$	0.235781	+	2.53142i	0.0129402	+	0.138930i
$333$	−0.652065	−	0.174720i	−0.0357329	−	0.00957461i
$334$	8.20281	+	17.4630i	0.448838	+	0.955532i
$335$	−4.73197	+	11.1904i	−0.258535	+	0.611399i
$336$		0			0
$337$	−10.1880	−	10.1880i	−0.554976	−	0.554976i	0.372897	−	0.927873i	$-0.378365\pi$
$337$	−10.1880	−	10.1880i	−0.554976	−	0.554976i	−0.927873	+	0.372897i	$0.878365\pi$
$338$	3.85245	+	1.38996i	0.209546	+	0.0756037i
$339$	7.53223	+	13.0462i	0.409094	+	0.708572i
$340$	10.1266	+	19.5363i	0.549191	+	1.05951i
$341$	−3.57253	+	6.18780i	−0.193463	+	0.335088i
$342$	3.31384	+	18.4904i	0.179192	+	0.999849i
$343$		0			0
$344$	19.8247	+	5.13368i	1.06887	+	0.276790i
$345$	−13.5276	−	1.88227i	−0.728299	−	0.101338i
$346$	6.03822	+	0.511222i	0.324617	+	0.0274834i
$347$	2.02424	+	0.542394i	0.108667	+	0.0291172i	0.312743	−	0.949838i	$-0.398752\pi$
$347$	2.02424	+	0.542394i	0.108667	+	0.0291172i	−0.204076	+	0.978955i	$0.565419\pi$
$348$	6.75062	+	9.52675i	0.361871	+	0.510687i
$349$		−	12.1094i		−	0.648203i	−0.946022	−	0.324102i	$-0.894938\pi$
$349$		−	12.1094i		−	0.648203i	0.946022	−	0.324102i	$-0.105062\pi$
$350$		0			0
$351$			17.1076i			0.913139i
$352$	−9.71213	+	3.68991i	−0.517658	+	0.196673i
$353$	−15.2177	−	4.07757i	−0.809956	−	0.217027i	−0.170005	−	0.985443i	$-0.554378\pi$
$353$	−15.2177	−	4.07757i	−0.809956	−	0.217027i	−0.639951	+	0.768416i	$0.721045\pi$
$354$	−0.779135	+	9.20265i	−0.0414106	+	0.489115i
$355$	−10.1004	−	1.40541i	−0.536076	−	0.0745913i
$356$	−10.6235	−	28.6863i	−0.563044	−	1.52037i
$357$		0			0
$358$	32.7873	−	5.87612i	1.73286	−	0.310562i
$359$	−0.0778098	+	0.134770i	−0.00410664	+	0.00711291i	−0.868071	−	0.496439i	$-0.834641\pi$
$359$	−0.0778098	+	0.134770i	−0.00410664	+	0.00711291i	0.863965	+	0.503552i	$0.167974\pi$
$360$	1.37105	−	10.4997i	0.0722605	−	0.553384i
$361$	−21.9722	−	38.0569i	−1.15643	−	2.00299i
$362$	−5.96716	+	16.5388i	−0.313627	+	0.869258i
$363$	6.20957	+	6.20957i	0.325918	+	0.325918i
$364$		0			0
$365$	4.14061	−	9.79195i	0.216729	−	0.512534i
$366$	−3.44158	+	1.61660i	−0.179894	+	0.0845009i
$367$	−4.12393	−	1.10500i	−0.215267	−	0.0576807i	0.149573	−	0.988751i	$-0.452210\pi$
$367$	−4.12393	−	1.10500i	−0.215267	−	0.0576807i	−0.364841	+	0.931070i	$0.618877\pi$
$368$	−9.18267	−	19.1292i	−0.478680	−	0.997181i
$369$	2.33825	+	1.34999i	0.121724	+	0.0702776i
$370$	−1.24356	−	0.281636i	−0.0646496	−	0.0146415i
$371$		0			0
$372$	−3.74056	+	8.14051i	−0.193939	+	0.422066i
$373$	−0.912560	−	3.40572i	−0.0472506	−	0.176342i	0.938268	−	0.345909i	$-0.112430\pi$
$373$	−0.912560	−	3.40572i	−0.0472506	−	0.176342i	−0.985519	+	0.169568i	$0.945763\pi$
$374$	−12.7346	−	1.07817i	−0.658492	−	0.0557507i
$375$	−10.0376	−	8.06016i	−0.518339	−	0.416225i
$376$	−22.3864	−	22.0130i	−1.15449	−	1.13523i
$377$	11.3964	+	11.3964i	0.586942	+	0.586942i
$378$		0			0
$379$	−22.4354			−1.15243			−0.576214	−	0.817299i	$-0.695470\pi$
$379$	−22.4354			−1.15243			−0.576214	+	0.817299i	$0.695470\pi$
$380$	7.61886	+	34.6531i	0.390839	+	1.77767i
$381$	−5.86444	−	10.1575i	−0.300444	−	0.520384i
$382$	14.2075	−	11.9895i	0.726918	−	0.613437i
$383$	29.8482	−	7.99781i	1.52517	−	0.408669i	0.603733	−	0.797187i	$-0.293679\pi$
$383$	29.8482	−	7.99781i	1.52517	−	0.408669i	0.921441	+	0.388518i	$0.127013\pi$
$384$	−11.6959	+	5.73598i	−0.596856	+	0.292713i
$385$		0			0
$386$	12.6405	−	18.1607i	0.643386	−	0.924355i
$387$	−3.13740	−	11.7089i	−0.159483	−	0.595199i
$388$	−2.31493	−	24.8538i	−0.117523	−	1.26176i
$389$	5.32729	−	3.07571i	0.270104	−	0.155945i	−0.358831	−	0.933403i	$-0.616824\pi$
$389$	5.32729	−	3.07571i	0.270104	−	0.155945i	0.628935	+	0.777458i	$0.283491\pi$
$390$	0.452202	+	11.5650i	0.0228982	+	0.585618i
$391$		−	26.1018i		−	1.32003i
$392$		0			0
$393$	−2.38897	+	2.38897i	−0.120508	+	0.120508i
$394$	−13.3151	+	6.25442i	−0.670803	+	0.315093i
$395$	20.0104	+	15.5897i	1.00683	+	0.784402i
$396$	4.73318	+	3.92659i	0.237851	+	0.197319i
$397$	−33.6444	+	9.01500i	−1.68857	+	0.452450i	−0.970019	−	0.243028i	$-0.921859\pi$
$397$	−33.6444	+	9.01500i	−1.68857	+	0.452450i	−0.718547	+	0.695478i	$0.755193\pi$
$398$	−10.5952	+	1.89886i	−0.531088	+	0.0951812i
$399$		0			0
$400$	1.81278	−	19.9177i	0.0906392	−	0.995884i
$401$	9.01829	−	15.6201i	0.450352	−	0.780032i	−0.548056	−	0.836442i	$-0.684632\pi$
$401$	9.01829	−	15.6201i	0.450352	−	0.780032i	0.998408	+	0.0564094i	$0.0179652\pi$
$402$	−5.70617	−	6.76176i	−0.284598	−	0.337246i
$403$	−3.20060	+	11.9448i	−0.159433	+	0.595012i
$404$	−4.57771	+	26.8407i	−0.227749	+	1.33537i
$405$	2.43298	−	0.986869i	0.120896	−	0.0490379i
$406$		0			0
$407$	0.523638	−	0.523638i	0.0259558	−	0.0259558i
$408$	−16.0238	+	0.134778i	−0.793296	+	0.00667252i
$409$	−10.4110	+	6.01082i	−0.514793	+	0.297216i	−0.734802	−	0.678282i	$-0.762725\pi$
$409$	−10.4110	+	6.01082i	−0.514793	+	0.297216i	0.220009	+	0.975498i	$0.429391\pi$
$410$	4.51268	+	2.37533i	0.222865	+	0.117309i
$411$	12.3217	+	7.11394i	0.607785	+	0.350905i
$412$	34.3562	+	15.7867i	1.69261	+	0.777753i
$413$		0			0
$414$	−7.17543	+	10.3090i	−0.352653	+	0.506658i
$415$	2.26775	−	1.71375i	0.111319	−	0.0841247i
$416$	−14.5834	+	10.5191i	−0.715012	+	0.515743i
$417$	−3.95845	+	14.7731i	−0.193846	+	0.723444i
$418$	−19.3838	−	6.99364i	−0.948092	−	0.342070i
$419$	17.7521			0.867247			0.433624	−	0.901094i	$-0.357235\pi$
$419$	17.7521			0.867247			0.433624	+	0.901094i	$0.357235\pi$
$420$		0			0
$421$	−15.9892			−0.779265			−0.389632	−	0.920970i	$-0.627398\pi$
$421$	−15.9892			−0.779265			−0.389632	+	0.920970i	$0.627398\pi$
$422$	26.2512	+	9.47137i	1.27789	+	0.461059i
$423$	−4.81003	+	17.9513i	−0.233872	+	0.872820i
$424$	−10.3088	+	2.85539i	−0.500642	+	0.138670i
$425$	12.6132	−	21.1229i	0.611831	−	1.02461i
$426$	4.24241	−	6.09509i	0.205546	−	0.295308i
$427$		0			0
$428$	−4.32226	+	9.40647i	−0.208924	+	0.454679i
$429$	−5.82140	−	3.36099i	−0.281060	−	0.162270i
$430$	−6.78541	−	21.8672i	−0.327221	−	1.05453i
$431$	3.12747	−	1.80565i	0.150645	−	0.0869750i	−0.422783	−	0.906231i	$-0.638947\pi$
$431$	3.12747	−	1.80565i	0.150645	−	0.0869750i	0.573428	+	0.819256i	$0.305613\pi$
$432$	17.7720	+	12.1494i	0.855058	+	0.584538i
$433$	15.7262	−	15.7262i	0.755753	−	0.755753i	−0.219793	−	0.975546i	$-0.570538\pi$
$433$	15.7262	−	15.7262i	0.755753	−	0.755753i	0.975546	+	0.219793i	$0.0705383\pi$
$434$		0			0
$435$	5.08421	−	12.0234i	0.243769	−	0.576480i
$436$	−17.4722	−	2.97990i	−0.836767	−	0.142711i
$437$	10.8928	−	40.6526i	0.521075	−	1.94468i
$438$	4.99306	+	5.91673i	0.238578	+	0.282712i
$439$	0.322459	−	0.558515i	0.0153901	−	0.0266565i	−0.858228	−	0.513269i	$-0.828434\pi$
$439$	0.322459	−	0.558515i	0.0153901	−	0.0266565i	0.873618	+	0.486613i	$0.161768\pi$
$440$	9.22287	+	7.06151i	0.439683	+	0.336644i
$441$		0			0
$442$	−21.7721	+	3.90199i	−1.03560	+	0.185599i
$443$	−1.72706	+	0.462763i	−0.0820549	+	0.0219865i	−0.299613	−	0.954061i	$-0.596858\pi$
$443$	−1.72706	+	0.462763i	−0.0820549	+	0.0219865i	0.217558	+	0.976047i	$0.430191\pi$
$444$	0.592841	−	0.714620i	0.0281350	−	0.0339144i
$445$	−21.0192	+	26.9795i	−0.996406	+	1.27895i
$446$	−1.57746	+	0.740974i	−0.0746950	+	0.0350861i
$447$	18.1295	−	18.1295i	0.857495	−	0.857495i
$448$		0			0
$449$			9.76729i			0.460947i	0.973079	+	0.230473i	$0.0740275\pi$
$449$			9.76729i			0.460947i	−0.973079	+	0.230473i	$0.925973\pi$
$450$	−10.7883	+	4.87513i	−0.508567	+	0.229816i
$451$	−2.56501	+	1.48091i	−0.120782	+	0.0697334i
$452$	26.0541	−	2.42672i	1.22548	−	0.114143i
$453$	−5.27651	−	19.6922i	−0.247912	−	0.925220i
$454$	9.99498	−	14.3598i	0.469088	−	0.673940i
$455$		0			0
$456$	−25.0127	−	6.47715i	−1.17133	−	0.303321i
$457$	26.2642	−	7.03747i	1.22859	−	0.329199i	0.414558	−	0.910023i	$-0.363936\pi$
$457$	26.2642	−	7.03747i	1.22859	−	0.329199i	0.814029	+	0.580824i	$0.197270\pi$
$458$	−17.5887	+	14.8429i	−0.821865	+	0.693562i
$459$	13.2409	+	22.9339i	0.618032	+	1.07046i
$460$	−12.7817	+	19.9860i	−0.595949	+	0.931853i
$461$	22.8494			1.06420			0.532101	−	0.846681i	$-0.321403\pi$
$461$	22.8494			1.06420			0.532101	+	0.846681i	$0.321403\pi$
$462$		0			0
$463$	0.390203	+	0.390203i	0.0181343	+	0.0181343i	0.716116	−	0.697982i	$-0.245918\pi$
$463$	0.390203	+	0.390203i	0.0181343	+	0.0181343i	−0.697982	+	0.716116i	$0.745918\pi$
$464$	19.9323	−	3.74556i	0.925336	−	0.173883i
$465$	9.93988	−	1.23430i	0.460951	−	0.0572391i
$466$	−8.52620	−	0.721864i	−0.394969	−	0.0334397i
$467$	3.14593	+	11.7408i	0.145576	+	0.543299i	0.999729	+	0.0232762i	$0.00740972\pi$
$467$	3.14593	+	11.7408i	0.145576	+	0.543299i	−0.854153	+	0.520022i	$0.825924\pi$
$468$	9.67162	+	4.44410i	0.447071	+	0.205429i
$469$		0			0
$470$	−7.75340	+	34.2350i	−0.357637	+	1.57914i
$471$	−1.24162	−	0.716850i	−0.0572109	−	0.0330307i
$472$	13.9599	+	7.90393i	0.642555	+	0.363808i
$473$	12.8445	+	3.44167i	0.590590	+	0.158248i
$474$	−16.7196	+	7.85361i	−0.767956	+	0.360728i
$475$	28.4596	−	27.6343i	1.30582	−	1.26795i
$476$		0			0
$477$	4.47734	+	4.47734i	0.205004	+	0.205004i
$478$	−0.794094	+	2.20094i	−0.0363210	+	0.100668i
$479$	18.5696	+	32.1635i	0.848466	+	1.46959i	0.882577	+	0.470169i	$0.155807\pi$
$479$	18.5696	+	32.1635i	0.848466	+	1.46959i	−0.0341102	+	0.999418i	$0.510860\pi$
$480$	12.3353	+	7.74342i	0.563028	+	0.353437i
$481$	0.640833	−	1.10996i	0.0292195	−	0.0506096i
$482$	35.9845	−	6.44911i	1.63905	−	0.293749i
$483$		0			0
$484$	14.3043	−	5.29736i	0.650195	−	0.240789i
$485$	−22.2650	+	16.8258i	−1.01100	+	0.764020i
$486$	1.76502	−	20.8473i	0.0800631	−	0.945654i
$487$	−13.3781	−	3.58465i	−0.606220	−	0.162436i	−0.0573644	−	0.998353i	$-0.518270\pi$
$487$	−13.3781	−	3.58465i	−0.606220	−	0.162436i	−0.548856	+	0.835917i	$0.684936\pi$
$488$	0.0555508	+	6.60443i	0.00251466	+	0.298968i
$489$			26.1734i			1.18360i
$490$		0			0
$491$			24.4541i			1.10360i	0.833977	+	0.551799i	$0.186059\pi$
$491$			24.4541i			1.10360i	−0.833977	+	0.551799i	$0.813941\pi$
$492$	−3.03006	+	2.14709i	−0.136606	+	0.0967984i
$493$	24.0980	+	6.45705i	1.08532	+	0.290811i
$494$	−35.5377	−	3.00877i	−1.59892	−	0.135371i
$495$	0.947591	−	6.81018i	0.0425910	−	0.306095i
$496$	10.1357	+	11.8078i	0.455106	+	0.530184i
$497$		0			0
$498$	0.365154	+	2.03747i	0.0163630	+	0.0913014i
$499$	0.190365	−	0.329722i	0.00852191	−	0.0147604i	−0.861733	−	0.507362i	$-0.830621\pi$
$499$	0.190365	−	0.329722i	0.00852191	−	0.0147604i	0.870255	+	0.492602i	$0.163954\pi$
$500$	−20.0014	+	9.99715i	−0.894491	+	0.447086i
$501$	7.85415	+	13.6038i	0.350897	+	0.607772i
$502$	26.3347	+	9.50153i	1.17538	+	0.424074i
$503$	20.9903	+	20.9903i	0.935911	+	0.935911i	0.998066	−	0.0621557i	$-0.0197975\pi$
$503$	20.9903	+	20.9903i	0.935911	+	0.935911i	−0.0621557	+	0.998066i	$0.519798\pi$
$504$		0			0
$505$	28.2098	−	11.4425i	1.25532	−	0.509184i
$506$	−5.85801	−	12.4711i	−0.260420	−	0.554409i
$507$	3.22085	+	0.863023i	0.143043	+	0.0383282i
$508$	−20.2852	+	1.88940i	−0.900009	+	0.0838284i
$509$	−30.3506	−	17.5230i	−1.34527	−	0.776691i	−0.357693	−	0.933839i	$-0.616437\pi$
$509$	−30.3506	−	17.5230i	−1.34527	−	0.776691i	−0.987575	+	0.157148i	$0.949770\pi$
$510$	9.55725	+	15.1537i	0.423202	+	0.671016i
$511$		0			0
$512$	0.570893	+	22.6202i	0.0252301	+	0.999682i
$513$	11.0514	+	41.2444i	0.487931	+	1.82099i
$514$	1.47932	−	17.4728i	0.0652500	−	0.770691i
$515$	−5.20923	−	41.9503i	−0.229546	−	1.84855i
$516$	16.4358	+	2.80314i	0.723544	+	0.123401i
$517$	−14.4157	−	14.4157i	−0.634001	−	0.634001i
$518$		0			0
$519$	4.93374			0.216567
$520$	18.5816	+	7.67378i	0.814855	+	0.336517i
$521$	−0.375226	−	0.649910i	−0.0164389	−	0.0284731i	0.857689	−	0.514169i	$-0.171900\pi$
$521$	−0.375226	−	0.649910i	−0.0164389	−	0.0284731i	−0.874128	+	0.485696i	$0.838566\pi$
$522$	−7.74252	−	9.17482i	−0.338881	−	0.401571i
$523$	−3.16813	+	0.848897i	−0.138533	+	0.0371197i	−0.327419	−	0.944879i	$-0.606179\pi$
$523$	−3.16813	+	0.848897i	−0.138533	+	0.0371197i	0.188886	+	0.981999i	$0.439512\pi$
$524$	2.03802	+	5.50321i	0.0890314	+	0.240409i
$525$		0			0
$526$	−3.31378	−	2.30652i	−0.144488	−	0.100569i
$527$	4.95436	+	18.4899i	0.215815	+	0.805434i
$528$	−7.62572	+	3.66060i	−0.331867	+	0.159307i
$529$	4.45189	−	2.57030i	0.193561	−	0.111752i
$530$	8.78066	+	8.11984i	0.381408	+	0.352703i
$531$		−	9.49591i		−	0.412087i
$532$		0			0
$533$	−3.62471	+	3.62471i	−0.157003	+	0.157003i
$534$	−10.5888	−	22.5426i	−0.458224	−	0.975515i
$535$	11.4857	−	1.42624i	0.496568	−	0.0616619i
$536$	−14.8108	+	4.10235i	−0.639727	+	0.177195i
$537$	26.1958	−	7.01913i	1.13043	−	0.302898i
$538$	−5.28612	−	29.4952i	−0.227901	−	1.27163i
$539$		0			0
$540$	1.09192	−	24.0442i	0.0469888	−	1.03470i
$541$	5.10537	−	8.84276i	0.219497	−	0.380180i	−0.735157	−	0.677897i	$-0.762892\pi$
$541$	5.10537	−	8.84276i	0.219497	−	0.380180i	0.954654	+	0.297717i	$0.0962250\pi$
$542$	−14.1315	+	11.9254i	−0.606999	+	0.512240i
$543$	−3.70501	+	13.8273i	−0.158997	+	0.593385i
$544$	−11.4085	+	25.3888i	−0.489134	+	1.08854i
$545$	7.44861	+	18.3634i	0.319063	+	0.786603i
$546$		0			0
$547$	2.16488	−	2.16488i	0.0925637	−	0.0925637i	−0.659309	−	0.751872i	$-0.729151\pi$
$547$	2.16488	−	2.16488i	0.0925637	−	0.0925637i	0.751872	+	0.659309i	$0.229151\pi$
$548$	20.1645	−	14.2885i	0.861385	−	0.610375i
$549$	3.38575	−	1.95477i	0.144500	−	0.0834274i
$550$	1.28586	−	12.9230i	0.0548290	−	0.551039i
$551$	34.8372	+	20.1132i	1.48411	+	0.856853i
$552$	−8.76353	−	14.8883i	−0.373001	−	0.633687i
$553$		0			0
$554$	8.15221	+	5.67425i	0.346354	+	0.241076i
$555$	−1.02821	−	0.143068i	−0.0436449	−	0.00607290i
$556$	20.4462	+	16.9620i	0.867113	+	0.719348i
$557$	7.69590	−	28.7215i	0.326086	−	1.21697i	−0.587130	−	0.809493i	$-0.699742\pi$
$557$	7.69590	−	28.7215i	0.326086	−	1.21697i	0.913216	−	0.407476i	$-0.133591\pi$
$558$	3.12617	−	8.66460i	0.132342	−	0.366802i
$559$	23.0145			0.973410
$560$		0			0
$561$	−10.4053			−0.439311
$562$	9.70038	−	26.8859i	0.409186	−	1.13411i
$563$	0.153105	−	0.571395i	0.00645259	−	0.0240814i	−0.962624	−	0.270840i	$-0.912699\pi$
$563$	0.153105	−	0.571395i	0.00645259	−	0.0240814i	0.969077	+	0.246758i	$0.0793654\pi$
$564$	−19.6734	−	16.3208i	−0.828399	−	0.687231i
$565$	−17.6384	−	23.3403i	−0.742052	−	0.981933i
$566$	7.97378	+	5.55005i	0.335163	+	0.233286i
$567$		0			0
$568$	−6.54335	−	11.1164i	−0.274553	−	0.466435i
$569$	2.88252	+	1.66422i	0.120842	+	0.0697679i	0.559202	−	0.829031i	$-0.311107\pi$
$569$	2.88252	+	1.66422i	0.120842	+	0.0697679i	−0.438361	+	0.898799i	$0.644441\pi$
$570$	8.56113	+	27.5897i	0.358586	+	1.15561i
$571$	23.9165	−	13.8082i	1.00087	−	0.577855i	0.0923679	−	0.995725i	$-0.470556\pi$
$571$	23.9165	−	13.8082i	1.00087	−	0.577855i	0.908507	+	0.417870i	$0.137223\pi$
$572$	−9.52675	+	6.75062i	−0.398333	+	0.282258i
$573$	10.7026	−	10.7026i	0.447107	−	0.447107i
$574$		0			0
$575$	26.5210	+	0.390203i	1.10600	+	0.0162726i
$576$	11.4852	−	6.89115i	0.478551	−	0.287131i
$577$	−5.40191	+	20.1602i	−0.224885	+	0.839281i	0.757566	+	0.652759i	$0.226388\pi$
$577$	−5.40191	+	20.1602i	−0.224885	+	0.839281i	−0.982451	+	0.186522i	$0.940278\pi$
$578$	−7.79335	+	6.57672i	−0.324161	+	0.273556i
$579$	9.00750	−	15.6015i	0.374339	−	0.648374i
$580$	−15.2898	−	16.7446i	−0.634875	−	0.695281i
$581$		0			0
$582$	−3.58513	−	20.0041i	−0.148608	−	0.829199i
$583$	−6.70932	+	1.79776i	−0.277871	+	0.0744554i
$584$	12.9598	−	3.58967i	0.536282	−	0.148542i
$585$	−1.46645	−	11.8094i	−0.0606302	−	0.488259i
$586$	−2.61733	−	5.57205i	−0.108121	−	0.230179i
$587$	−14.6462	+	14.6462i	−0.604512	+	0.604512i	−0.941507	−	0.336995i	$-0.890590\pi$
$587$	−14.6462	+	14.6462i	−0.604512	+	0.604512i	0.336995	+	0.941507i	$0.390590\pi$
$588$		0			0
$589$			30.8649i			1.27177i
$590$	−0.700764	−	17.9220i	−0.0288500	−	0.737835i
$591$	−10.3725	+	5.98858i	−0.426668	+	0.246337i
$592$	−0.697960	−	1.45398i	−0.0286860	−	0.0597583i
$593$	4.35728	+	16.2616i	0.178932	+	0.667783i	0.995848	+	0.0910271i	$0.0290150\pi$
$593$	4.35728	+	16.2616i	0.178932	+	0.667783i	−0.816916	+	0.576756i	$0.804318\pi$
$594$	11.4734	+	7.98589i	0.470758	+	0.327665i
$595$		0			0
$596$	−15.4662	−	41.7629i	−0.633520	−	1.71067i
$597$	−8.46512	+	2.26822i	−0.346454	+	0.0928322i
$598$	−15.3795	−	18.2246i	−0.628916	−	0.745260i
$599$	2.35363	+	4.07660i	0.0961666	+	0.166565i	0.910095	−	0.414400i	$-0.136008\pi$
$599$	2.35363	+	4.07660i	0.0961666	+	0.166565i	−0.813928	+	0.580965i	$0.802675\pi$
$600$	0.102601	−	16.2831i	0.00418867	−	0.664756i
$601$	8.52304			0.347662			0.173831	−	0.984775i	$-0.444385\pi$
$601$	8.52304			0.347662			0.173831	+	0.984775i	$0.444385\pi$
$602$		0			0
$603$	6.43262	+	6.43262i	0.261957	+	0.261957i
$604$	−34.9078	−	5.95356i	−1.42038	−	0.242247i
$605$	−13.4532	−	10.4811i	−0.546951	−	0.426119i
$606$	−1.87019	+	22.0895i	−0.0759712	+	0.897324i
$607$	−4.06498	−	15.1707i	−0.164993	−	0.615761i	−0.998041	−	0.0625608i	$-0.980073\pi$
$607$	−4.06498	−	15.1707i	−0.164993	−	0.615761i	0.833049	−	0.553200i	$-0.186593\pi$
$608$	−28.3636	+	34.7811i	−1.15029	+	1.41056i
$609$		0			0
$610$	6.24580	−	3.93915i	0.252885	−	0.159492i
$611$	−30.5569	−	17.6421i	−1.23620	−	0.713721i
$612$	16.4051	−	1.52799i	0.663135	−	0.0617655i
$613$	33.9787	+	9.10458i	1.37239	+	0.367730i	0.868351	−	0.495951i	$-0.165180\pi$
$613$	33.9787	+	9.10458i	1.37239	+	0.367730i	0.504038	+	0.863681i	$0.331847\pi$
$614$	−6.89969	−	14.6888i	−0.278449	−	0.592790i
$615$	3.82416	+	1.61707i	0.154205	+	0.0652068i
$616$		0			0
$617$	−24.4754	−	24.4754i	−0.985343	−	0.985343i	0.0145509	−	0.999894i	$-0.495368\pi$
$617$	−24.4754	−	24.4754i	−0.985343	−	0.985343i	−0.999894	+	0.0145509i	$0.995368\pi$
$618$	28.9565	+	10.4475i	1.16480	+	0.420259i
$619$	−9.34362	−	16.1836i	−0.375552	−	0.650475i	0.614858	−	0.788638i	$-0.289213\pi$
$619$	−9.34362	−	16.1836i	−0.375552	−	0.650475i	−0.990409	+	0.138163i	$0.955880\pi$
$620$	5.26072	−	16.5837i	0.211276	−	0.666018i
$621$	−14.2751	+	24.7252i	−0.572841	+	0.992189i
$622$	−2.67189	−	14.9085i	−0.107133	−	0.597776i
$623$		0			0
$624$	−11.1086	+	9.53553i	−0.444700	+	0.381727i
$625$	21.2735	+	13.1315i	0.850941	+	0.525262i
$626$	−24.9702	−	2.11408i	−0.998008	−	0.0844956i
$627$	−16.2058	−	4.34234i	−0.647199	−	0.173416i
$628$	−2.03192	+	1.43981i	−0.0810823	+	0.0574547i
$629$		−	1.98396i		−	0.0791055i
$630$		0			0
$631$			8.42486i			0.335388i	0.985839	+	0.167694i	$0.0536321\pi$
$631$			8.42486i			0.335388i	−0.985839	+	0.167694i	$0.946368\pi$
$632$	0.269872	+	32.0851i	0.0107349	+	1.27627i
$633$	21.9473	+	5.88077i	0.872328	+	0.233740i
$634$	−0.209972	+	2.48006i	−0.00833907	+	0.0984958i
$635$	13.7329	+	18.1723i	0.544973	+	0.721144i
$636$	−8.16713	+	3.02456i	−0.323848	+	0.119932i
$637$		0			0
$638$	12.9629	−	2.32320i	0.513206	−	0.0919764i
$639$	−3.81776	+	6.61255i	−0.151028	+	0.261588i
$640$	21.1679	−	13.8535i	0.836736	−	0.547607i
$641$	0.919839	+	1.59321i	0.0363315	+	0.0629280i	0.883619	−	0.468206i	$-0.155099\pi$
$641$	0.919839	+	1.59321i	0.0363315	+	0.0629280i	−0.847288	+	0.531134i	$0.821766\pi$
$642$	−2.86043	+	7.92807i	−0.112892	+	0.312896i
$643$	−23.6593	−	23.6593i	−0.933032	−	0.933032i	0.0648624	−	0.997894i	$-0.479339\pi$
$643$	−23.6593	−	23.6593i	−0.933032	−	0.933032i	−0.997894	+	0.0648624i	$0.979339\pi$
$644$		0			0
$645$	−7.00676	−	17.2741i	−0.275891	−	0.680168i
$646$	−49.9693	+	23.4718i	−1.96602	+	0.923487i
$647$	26.3555	+	7.06194i	1.03614	+	0.277633i	0.736514	−	0.676423i	$-0.236471\pi$
$647$	26.3555	+	7.06194i	1.03614	+	0.277633i	0.299628	+	0.954056i	$0.403137\pi$
$648$	2.88997	+	1.63627i	0.113529	+	0.0642787i
$649$	9.02124	+	5.20841i	0.354115	+	0.204448i
$650$	−3.63917	−	22.1801i	−0.142740	−	0.869976i
$651$		0			0
$652$	41.3106	+	18.9822i	1.61785	+	0.743400i
$653$	−0.130030	−	0.485279i	−0.00508847	−	0.0189904i	0.963335	−	0.268302i	$-0.0864624\pi$
$653$	−0.130030	−	0.485279i	−0.00508847	−	0.0189904i	−0.968423	+	0.249311i	$0.919796\pi$
$654$	−14.3794	−	1.21742i	−0.562278	−	0.0476048i
$655$	4.03235	−	5.17578i	0.157557	−	0.202235i
$656$	1.19131	+	6.33965i	0.0465127	+	0.247522i
$657$	−5.62873	−	5.62873i	−0.219598	−	0.219598i
$658$		0			0
$659$	34.0104			1.32486			0.662428	−	0.749126i	$-0.269526\pi$
$659$	34.0104			1.32486			0.662428	+	0.749126i	$0.269526\pi$
$660$	7.96726	+	5.09531i	0.310125	+	0.198335i
$661$	4.28987	+	7.43027i	0.166856	+	0.289004i	0.937313	−	0.348489i	$-0.113305\pi$
$661$	4.28987	+	7.43027i	0.166856	+	0.289004i	−0.770457	+	0.637493i	$0.779972\pi$
$662$	26.6364	−	22.4782i	1.03525	−	0.873639i
$663$	−17.3951	+	4.66100i	−0.675569	+	0.181018i
$664$	3.48066	+	0.901332i	0.135076	+	0.0349785i
$665$		0			0
$666$	−0.545393	+	0.783568i	−0.0211335	+	0.0303626i
$667$	6.96140	+	25.9803i	0.269547	+	1.00596i
$668$	27.1676	−	2.53044i	1.05115	−	0.0979057i
$669$	−1.22885	+	0.709479i	−0.0475102	+	0.0274300i
$670$	12.6152	+	11.6658i	0.487368	+	0.450689i
$671$			4.28868i			0.165563i
$672$		0			0
$673$	−8.24869	+	8.24869i	−0.317964	+	0.317964i	−0.847985	−	0.530021i	$-0.822184\pi$
$673$	−8.24869	+	8.24869i	−0.317964	+	0.317964i	0.530021	+	0.847985i	$0.322184\pi$
$674$	−18.4427	+	8.66302i	−0.710387	+	0.333687i
$675$	−23.5001	+	13.1107i	−0.904520	+	0.504630i
$676$	3.69806	−	4.45770i	0.142233	−	0.171450i
$677$	−18.8259	+	5.04438i	−0.723538	+	0.193871i	−0.601750	−	0.798685i	$-0.705530\pi$
$677$	−18.8259	+	5.04438i	−0.723538	+	0.193871i	−0.121788	+	0.992556i	$0.538863\pi$
$678$	20.9702	−	3.75827i	0.805357	−	0.144335i
$679$		0			0
$680$	30.8491	−	4.09447i	1.18301	−	0.157016i
$681$	7.12232	−	12.3362i	0.272928	−	0.472725i
$682$	6.51681	+	7.72236i	0.249541	+	0.295704i
$683$	−9.56315	+	35.6902i	−0.365924	+	1.36565i	0.500241	+	0.865886i	$0.333245\pi$
$683$	−9.56315	+	35.6902i	−0.365924	+	1.36565i	−0.866164	+	0.499759i	$0.833422\pi$
$684$	26.1879	+	4.46638i	1.00132	+	0.170776i
$685$	−25.4491	−	10.7613i	−0.972359	−	0.411170i
$686$		0			0
$687$	−13.2497	+	13.2497i	−0.505507	+	0.505507i
$688$	16.3443	−	23.9083i	0.623121	−	0.911496i
$689$	−10.4110	+	6.01082i	−0.396629	+	0.228994i
$690$	−8.99665	+	17.0920i	−0.342497	+	0.650680i
$691$	−35.2631	−	20.3592i	−1.34147	−	0.774499i	−0.354449	−	0.935076i	$-0.615331\pi$
$691$	−35.2631	−	20.3592i	−1.34147	−	0.774499i	−0.987023	+	0.160576i	$0.948665\pi$
$692$	3.57818	−	7.78714i	0.136022	−	0.296023i
$693$		0			0
$694$	1.69309	−	2.43247i	0.0642689	−	0.0923354i
$695$	4.09337	−	29.4184i	0.155270	−	1.11590i
$696$	15.9133	−	4.40773i	0.603190	−	0.167074i
$697$	−2.05372	+	7.66458i	−0.0777902	+	0.290317i
$698$	−16.1089	−	5.81207i	−0.609731	−	0.219990i
$699$	−6.96664			−0.263502
$700$		0			0
$701$	17.3238			0.654312			0.327156	−	0.944970i	$-0.393910\pi$
$701$	17.3238			0.654312			0.327156	+	0.944970i	$0.393910\pi$
$702$	22.7579	+	8.21102i	0.858942	+	0.309905i
$703$	0.827947	−	3.08994i	0.0312266	−	0.116539i
$704$	0.247151	+	14.6908i	0.00931485	+	0.553682i
$705$	−3.93865	+	28.3064i	−0.148338	+	1.06608i
$706$	−12.7282	+	18.2867i	−0.479032	+	0.688228i
$707$		0			0
$708$	11.8681	+	5.45339i	0.446031	+	0.204951i
$709$	−36.5248	−	21.0876i	−1.37172	−	0.791963i	−0.380575	−	0.924750i	$-0.624274\pi$
$709$	−36.5248	−	21.0876i	−1.37172	−	0.791963i	−0.991145	+	0.132788i	$0.957607\pi$
$710$	−6.71741	+	12.7618i	−0.252100	+	0.478943i
$711$	16.4484	−	9.49647i	0.616862	−	0.356146i
$712$	−43.2595	+	0.363862i	−1.62122	+	0.0136363i
$713$	−14.5928	+	14.5928i	−0.546505	+	0.546505i
$714$		0			0
$715$	12.0234	+	5.08421i	0.449651	+	0.190139i
$716$	7.91979	−	46.4365i	0.295977	−	1.73541i
$717$	−0.493053	+	1.84010i	−0.0184134	+	0.0687197i
$718$	0.141936	+	0.168193i	0.00529702	+	0.00627692i
$719$	−18.5696	+	32.1635i	−0.692529	+	1.19950i	0.278478	+	0.960443i	$0.410170\pi$
$719$	−18.5696	+	32.1635i	−0.692529	+	1.19950i	−0.971007	+	0.239053i	$0.923163\pi$
$720$	−13.3095	−	6.86334i	−0.496015	−	0.255782i
$721$		0			0
$722$	−61.1720	+	10.9632i	−2.27659	+	0.408008i
$723$	28.7502	−	7.70358i	1.06923	−	0.286499i
$724$	19.1371	+	15.8760i	0.711226	+	0.590025i
$725$	−6.92099	+	24.3885i	−0.257039	+	0.905766i
$726$	11.2408	−	5.28009i	0.417185	−	0.195963i
$727$	−13.9553	+	13.9553i	−0.517573	+	0.517573i	−0.916836	−	0.399264i	$-0.869266\pi$
$727$	−13.9553	+	13.9553i	−0.517573	+	0.517573i	0.399264	+	0.916836i	$0.369266\pi$
$728$		0			0
$729$		−	20.5565i		−	0.761353i
$730$	−11.0387	−	10.2079i	−0.408560	−	0.377812i
$731$	30.8524	−	17.8127i	1.14112	−	0.658825i
$732$	0.498696	+	5.35416i	0.0184323	+	0.197895i
$733$	8.95786	+	33.4312i	0.330866	+	1.23481i	0.908282	+	0.418359i	$0.137394\pi$
$733$	8.95786	+	33.4312i	0.330866	+	1.23481i	−0.577416	+	0.816450i	$0.695939\pi$
$734$	−3.44929	+	4.95561i	−0.127316	+	0.182915i
$735$		0			0
$736$	−29.8545	+	3.03419i	−1.10045	+	0.111842i
$737$	−9.63930	+	2.58284i	−0.355068	+	0.0951403i
$738$	2.91813	−	2.46257i	0.107418	−	0.0906486i
$739$	−10.0489	−	17.4052i	−0.369656	−	0.640262i	0.619856	−	0.784716i	$-0.287191\pi$
$739$	−10.0489	−	17.4052i	−0.369656	−	0.640262i	−0.989512	+	0.144453i	$0.953858\pi$
$740$	−0.971514	+	1.51910i	−0.0357136	+	0.0558434i
$741$	−29.0373			−1.06671
$742$		0			0
$743$	−24.1904	−	24.1904i	−0.887460	−	0.887460i	0.106819	−	0.994279i	$-0.465934\pi$
$743$	−24.1904	−	24.1904i	−0.887460	−	0.887460i	−0.994279	+	0.106819i	$0.965934\pi$
$744$	9.03381	+	8.88311i	0.331196	+	0.325671i
$745$	−30.6008	+	39.2781i	−1.12113	+	1.43904i
$746$	−4.96855	−	0.420658i	−0.181911	−	0.0154014i
$747$	−0.550841	−	2.05577i	−0.0201542	−	0.0752165i
$748$	−7.54640	+	16.4231i	−0.275924	+	0.600488i
$749$		0			0
$750$	−15.5399	+	9.48420i	−0.567437	+	0.346314i
$751$	34.6221	+	19.9891i	1.26338	+	0.729411i	0.973726	−	0.227721i	$-0.0731274\pi$
$751$	34.6221	+	19.9891i	1.26338	+	0.729411i	0.289651	+	0.957132i	$0.406461\pi$
$752$	−40.0279	+	19.2147i	−1.45967	+	0.700690i
$753$	22.0172	+	5.89949i	0.802351	+	0.214989i
$754$	20.6301	−	9.69050i	0.751305	−	0.352907i
$755$	14.8816	+	36.6884i	0.541597	+	1.33523i
$756$		0			0
$757$	17.5230	+	17.5230i	0.636884	+	0.636884i	0.949785	−	0.312902i	$-0.101301\pi$
$757$	17.5230	+	17.5230i	0.636884	+	0.636884i	−0.312902	+	0.949785i	$0.601301\pi$
$758$	−10.7681	+	29.8453i	−0.391116	+	1.08403i
$759$	−5.60901	−	9.71509i	−0.203594	−	0.352636i
$760$	49.7550	+	6.49698i	1.80480	+	0.235670i
$761$	17.5004	−	30.3116i	0.634390	−	1.09880i	−0.352254	−	0.935904i	$-0.614585\pi$
$761$	17.5004	−	30.3116i	0.634390	−	1.09880i	0.986644	−	0.162891i	$-0.0520819\pi$
$762$	−16.3270	+	2.92611i	−0.591465	+	0.106002i
$763$		0			0
$764$	−9.13034	−	24.6544i	−0.330324	−	0.891964i
$765$	−11.1061	−	14.6963i	−0.401541	−	0.531345i
$766$	3.68671	−	43.5451i	0.133206	−	1.57335i
$767$	17.4144	+	4.66617i	0.628797	+	0.168486i
$768$	2.01683	+	18.3119i	0.0727761	+	0.660774i
$769$			3.82958i			0.138098i	0.997613	+	0.0690490i	$0.0219965\pi$
$769$			3.82958i			0.138098i	−0.997613	+	0.0690490i	$0.978004\pi$
$770$		0			0
$771$		−	14.2768i		−	0.514165i
$772$	−18.0918	−	25.5318i	−0.651138	−	0.918911i
$773$	−29.4658	−	7.89534i	−1.05981	−	0.283976i	−0.313511	−	0.949585i	$-0.601505\pi$
$773$	−29.4658	−	7.89534i	−1.05981	−	0.283976i	−0.746301	+	0.665609i	$0.768172\pi$
$774$	−17.0820	−	1.44623i	−0.613999	−	0.0519837i
$775$	−18.8609	+	4.75751i	−0.677504	+	0.170895i
$776$	−34.1735	−	8.84938i	−1.22676	−	0.317674i
$777$		0			0
$778$	−1.53465	−	8.56300i	−0.0550200	−	0.306998i
$779$	−6.39719	+	11.0803i	−0.229203	+	0.396991i
$780$	15.6017	+	4.94922i	0.558632	+	0.177211i
$781$	−4.18801	−	7.25384i	−0.149859	−	0.259563i
$782$	−34.7226	−	12.5279i	−1.24168	−	0.447996i
$783$	−19.2958	−	19.2958i	−0.689574	−	0.689574i
$784$		0			0
$785$	2.56443	+	1.08439i	0.0915283	+	0.0387035i
$786$	2.03138	+	4.32461i	0.0724569	+	0.154254i
$787$	−24.7805	−	6.63993i	−0.883331	−	0.236688i	−0.211487	−	0.977381i	$-0.567831\pi$
$787$	−24.7805	−	6.63993i	−0.883331	−	0.236688i	−0.671844	+	0.740693i	$0.734497\pi$
$788$	1.92939	+	20.7146i	0.0687318	+	0.737927i
$789$	−2.84680	−	1.64360i	−0.101349	−	0.0585137i
$790$	30.3428	−	19.1369i	1.07955	−	0.680859i
$791$		0			0
$792$	7.49520	−	4.41183i	0.266331	−	0.156767i
$793$	1.92110	+	7.16963i	0.0682201	+	0.254601i
$794$	−4.15560	+	49.0833i	−0.147477	+	1.74190i
$795$	7.68121	+	5.98428i	0.272424	+	0.212240i
$796$	−2.55927	+	15.0059i	−0.0907109	+	0.531870i
$797$	−1.67208	−	1.67208i	−0.0592281	−	0.0592281i	0.676872	−	0.736100i	$-0.263335\pi$
$797$	−1.67208	−	1.67208i	−0.0592281	−	0.0592281i	−0.736100	+	0.676872i	$0.763335\pi$
$798$		0			0
$799$	−54.6180			−1.93225
$800$	−25.6260	−	11.9712i	−0.906014	−	0.423247i
$801$	12.8039	+	22.1770i	0.452403	+	0.783585i
$802$	−16.4507	−	19.4939i	−0.580893	−	0.688353i
$803$	8.43467	−	2.26006i	0.297653	−	0.0797558i
$804$	−11.7338	+	4.34540i	−0.413818	+	0.153250i
$805$		0			0
$806$	14.3537	+	9.99072i	0.505588	+	0.351908i
$807$	−6.31437	−	23.5655i	−0.222276	−	0.829546i
$808$	33.5084	+	18.9721i	1.17882	+	0.667437i
$809$	2.42574	−	1.40050i	0.0852846	−	0.0492391i	−0.456751	−	0.889594i	$-0.650987\pi$
$809$	2.42574	−	1.40050i	0.0852846	−	0.0492391i	0.542036	+	0.840355i	$0.317654\pi$
$810$	−0.145072	−	3.71020i	−0.00509730	−	0.130363i
$811$			0.896541i			0.0314818i	0.999876	+	0.0157409i	$0.00501069\pi$
$811$			0.896541i			0.0314818i	−0.999876	+	0.0157409i	$0.994989\pi$
$812$		0			0
$813$	−10.6454	+	10.6454i	−0.373349	+	0.373349i
$814$	−0.445257	−	0.947910i	−0.0156063	−	0.0332242i
$815$	−6.26367	−	50.4418i	−0.219407	−	1.76690i
$816$	−7.51151	+	21.3808i	−0.262956	+	0.748476i
$817$	55.4851	−	14.8672i	1.94118	−	0.520137i
$818$	2.99915	+	16.7345i	0.104863	+	0.585109i
$819$		0			0
$820$	5.32576	−	4.86305i	0.185983	−	0.169825i
$821$	−4.15294	+	7.19310i	−0.144939	+	0.251041i	−0.929350	−	0.369200i	$-0.879632\pi$
$821$	−4.15294	+	7.19310i	−0.144939	+	0.251041i	0.784411	+	0.620241i	$0.212965\pi$
$822$	15.3775	−	12.9769i	0.536350	−	0.452620i
$823$	−3.81103	+	14.2230i	−0.132844	+	0.495781i	−0.999997	−	0.00226005i	$-0.999281\pi$
$823$	−3.81103	+	14.2230i	−0.132844	+	0.495781i	0.867153	+	0.498041i	$0.165947\pi$
$824$	37.4903	−	38.1263i	1.30604	−	1.32819i
$825$	0.155551	−	10.5724i	0.00541560	−	0.368083i
$826$		0			0
$827$	−18.6287	+	18.6287i	−0.647784	+	0.647784i	−0.952457	−	0.304673i	$-0.901453\pi$
$827$	−18.6287	+	18.6287i	−0.647784	+	0.647784i	0.304673	+	0.952457i	$0.401453\pi$
$828$	10.2699	+	14.4932i	0.356902	+	0.503674i
$829$	38.7234	−	22.3570i	1.34492	−	0.776490i	0.357396	−	0.933953i	$-0.383665\pi$
$829$	38.7234	−	22.3570i	1.34492	−	0.776490i	0.987525	+	0.157463i	$0.0503315\pi$
$830$	−1.19133	−	3.83927i	−0.0413516	−	0.133263i
$831$	7.00339	+	4.04341i	0.242945	+	0.140264i
$832$	6.99387	+	24.4488i	0.242469	+	0.847609i
$833$		0			0
$834$	17.7525	+	12.3564i	0.614717	+	0.427866i
$835$	−18.3922	−	24.3378i	−0.636489	−	0.842246i
$836$	−18.6069	+	22.4291i	−0.643535	+	0.775727i
$837$	5.41909	−	20.2243i	0.187311	−	0.699055i
$838$	8.52034	−	23.6152i	0.294330	−	0.815774i
$839$	−30.2098			−1.04296			−0.521480	−	0.853264i	$-0.674620\pi$
$839$	−30.2098			−1.04296			−0.521480	+	0.853264i	$0.674620\pi$
$840$		0			0
$841$	3.29203			0.113518
$842$	−7.67419	+	21.2700i	−0.264470	+	0.733014i
$843$	6.02296	−	22.4780i	0.207442	−	0.774183i
$844$	25.1991	−	30.3754i	0.867389	−	1.04556i
$845$	−6.41381	−	0.892438i	−0.220642	−	0.0307008i
$846$	21.5715	+	15.0146i	0.741644	+	0.516212i
$847$		0			0
$848$	−1.14939	+	15.0841i	−0.0394702	+	0.517990i
$849$	6.85010	+	3.95491i	0.235095	+	0.135732i
$850$	−22.0454	−	26.9172i	−0.756151	−	0.923254i
$851$	1.85236	−	1.06946i	0.0634981	−	0.0366606i
$852$	−6.07196	−	8.56899i	−0.208022	−	0.293569i
$853$	−27.6893	+	27.6893i	−0.948062	+	0.948062i	−0.998716	−	0.0506542i	$-0.983869\pi$
$853$	−27.6893	+	27.6893i	−0.948062	+	0.948062i	0.0506542	+	0.998716i	$0.483869\pi$
$854$		0			0
$855$	−11.1642	−	27.5237i	−0.381808	−	0.941292i
$856$	10.4387	+	10.2646i	0.356787	+	0.350835i
$857$	−1.90672	+	7.11598i	−0.0651324	+	0.243077i	−0.990815	−	0.135223i	$-0.956825\pi$
$857$	−1.90672	+	7.11598i	−0.0651324	+	0.243077i	0.925683	+	0.378301i	$0.123491\pi$
$858$	−7.26509	+	6.13093i	−0.248026	+	0.209307i
$859$	−2.48596	+	4.30581i	−0.0848199	+	0.146912i	−0.905314	−	0.424742i	$-0.860365\pi$
$859$	−2.48596	+	4.30581i	−0.0848199	+	0.146912i	0.820495	+	0.571654i	$0.193698\pi$
$860$	−32.3461	−	1.46894i	−1.10299	−	0.0500903i
$861$		0			0
$862$	−0.900944	−	5.02705i	−0.0306863	−	0.171222i
$863$	11.4731	−	3.07421i	0.390549	−	0.104647i	−0.0582005	−	0.998305i	$-0.518536\pi$
$863$	11.4731	−	3.07421i	0.390549	−	0.104647i	0.448749	+	0.893658i	$0.351870\pi$
$864$	24.6920	−	17.8105i	0.840038	−	0.605925i
$865$	−9.50840	+	1.18072i	−0.323295	+	0.0401456i
$866$	−13.3722	−	28.4682i	−0.454407	−	0.967388i
$867$	−5.87079	+	5.87079i	−0.199382	+	0.199382i
$868$		0			0
$869$			20.8349i			0.706775i
$870$	−13.5543	−	12.5342i	−0.459533	−	0.424949i
$871$	−14.9576	+	8.63577i	−0.506819	+	0.292612i
$872$	−12.3501	+	21.8126i	−0.418227	+	0.738669i
$873$	5.40822	+	20.1837i	0.183040	+	0.683116i
$874$	−48.8511	−	34.0022i	−1.65241	−	1.15014i
$875$		0			0
$876$	10.2674	−	3.80235i	0.346902	−	0.128469i
$877$	18.4355	−	4.93977i	0.622521	−	0.166804i	0.0662475	−	0.997803i	$-0.478897\pi$
$877$	18.4355	−	4.93977i	0.622521	−	0.166804i	0.556274	+	0.830999i	$0.312231\pi$
$878$	−0.588211	−	0.697025i	−0.0198512	−	0.0235235i
$879$	−2.50608	−	4.34067i	−0.0845281	−	0.146407i
$880$	13.8204	−	8.87971i	0.465885	−	0.299335i
$881$	47.6130			1.60412			0.802062	−	0.597241i	$-0.203736\pi$
$881$	47.6130			1.60412			0.802062	+	0.597241i	$0.203736\pi$
$882$		0			0
$883$	23.0077	+	23.0077i	0.774271	+	0.774271i	0.978850	−	0.204579i	$-0.0655827\pi$
$883$	23.0077	+	23.0077i	0.774271	+	0.774271i	−0.204579	+	0.978850i	$0.565583\pi$
$884$	−5.25907	+	30.8358i	−0.176882	+	1.03712i
$885$	−1.79949	−	14.4914i	−0.0604892	−	0.487124i
$886$	−0.213318	+	2.51957i	−0.00716654	+	0.0846466i
$887$	−5.86578	−	21.8914i	−0.196954	−	0.735041i	−0.991752	−	0.128168i	$-0.959090\pi$
$887$	−5.86578	−	21.8914i	−0.196954	−	0.735041i	0.794799	−	0.606873i	$-0.207576\pi$
$888$	−0.666102	−	1.13163i	−0.0223529	−	0.0379751i
$889$		0			0
$890$	25.8018	+	40.9105i	0.864878	+	1.37132i
$891$	1.86757	+	1.07824i	0.0625660	+	0.0361225i
$892$	0.228579	+	2.45410i	0.00765340	+	0.0821694i
$893$	−85.0656	−	22.7933i	−2.84661	−	0.762748i
$894$	−15.4158	−	32.8187i	−0.515581	−	1.09762i
$895$	−48.8051	+	19.7964i	−1.63138	+	0.661721i
$896$		0			0
$897$	−13.7287	−	13.7287i	−0.458389	−	0.458389i
$898$	12.9932	+	4.68792i	0.433589	+	0.156438i
$899$	−9.86259	−	17.0825i	−0.328936	−	0.569734i
$900$	1.30729	+	16.6913i	0.0435763	+	0.556378i
$901$	−9.30444	+	16.1158i	−0.309976	+	0.536894i
$902$	0.738913	+	4.12296i	0.0246031	+	0.137279i
$903$		0			0
$904$	9.27676	−	35.8239i	0.308540	−	1.19149i
$905$	3.83129	−	27.5348i	0.127356	−	0.915288i
$906$	−28.7286	−	2.43228i	−0.954443	−	0.0808072i
$907$	−39.2529	−	10.5178i	−1.30337	−	0.349237i	−0.460647	−	0.887584i	$-0.652382\pi$
$907$	−39.2529	−	10.5178i	−1.30337	−	0.349237i	−0.842724	+	0.538347i	$0.819049\pi$
$908$	−14.3053	−	20.1883i	−0.474739	−	0.669971i
$909$		−	22.7934i		−	0.756009i
$910$		0			0
$911$		−	7.34646i		−	0.243399i	−0.992567	−	0.121700i	$-0.961166\pi$
$911$		−	7.34646i		−	0.243399i	0.992567	−	0.121700i	$-0.0388344\pi$
$912$	−20.6216	+	30.1651i	−0.682848	+	0.998865i
$913$	2.25513	+	0.604261i	0.0746341	+	0.0199981i
$914$	3.24403	−	38.3164i	0.107303	−	1.26739i
$915$	4.79647	−	3.62472i	0.158566	−	0.119829i
$916$	11.3032	+	30.5218i	0.373470	+	1.00847i
$917$		0			0
$918$	36.8635	−	6.60666i	1.21668	−	0.218052i
$919$	−24.9086	+	43.1429i	−0.821657	+	1.42315i	0.0827899	+	0.996567i	$0.473617\pi$
$919$	−24.9086	+	43.1429i	−0.821657	+	1.42315i	−0.904447	+	0.426585i	$0.859716\pi$
$920$	20.4522	+	26.5957i	0.674289	+	0.876834i
$921$	−6.60642	−	11.4427i	−0.217689	−	0.377048i
$922$	10.9668	−	30.3960i	0.361174	−	1.00104i
$923$	−10.2506	−	10.2506i	−0.337404	−	0.337404i
$924$		0			0
$925$	2.01582	+	0.0296587i	0.0662796	+	0.000975171i
$926$	0.706360	−	0.331795i	0.0232124	−	0.0109035i
$927$	−30.5728	−	8.19197i	−1.00414	−	0.269060i
$928$	4.58413	−	28.3133i	0.150482	−	0.929428i
$929$	34.1784	+	19.7329i	1.12136	+	0.647416i	0.941747	−	0.336322i	$-0.109183\pi$
$929$	34.1784	+	19.7329i	1.12136	+	0.647416i	0.179610	+	0.983738i	$0.442516\pi$
$930$	3.12881	−	13.8152i	0.102598	−	0.453018i
$931$		0			0
$932$	−5.05253	+	10.9957i	−0.165501	+	0.360178i
$933$	−3.19162	−	11.9113i	−0.104489	−	0.389958i
$934$	17.1284	+	1.45016i	0.560459	+	0.0474508i
$935$	20.0532	−	2.49013i	0.655811	−	0.0814361i
$936$	10.5539	−	10.7329i	0.344965	−	0.350817i
$937$	−23.2697	−	23.2697i	−0.760188	−	0.760188i	0.216168	−	0.976356i	$-0.430644\pi$
$937$	−23.2697	−	23.2697i	−0.760188	−	0.760188i	−0.976356	+	0.216168i	$0.930644\pi$
$938$		0			0
$939$	−20.4028			−0.665819
$940$	41.8207	+	26.7457i	1.36404	+	0.872347i
$941$	−15.7701	−	27.3146i	−0.514091	−	0.890431i	−0.999866	−	0.0163476i	$-0.994796\pi$
$941$	−15.7701	−	27.3146i	−0.514091	−	0.890431i	0.485776	−	0.874083i	$-0.338537\pi$
$942$	−1.54954	+	1.30764i	−0.0504867	+	0.0426052i
$943$	−8.26326	+	2.21413i	−0.269089	+	0.0721021i
$944$	17.2146	−	14.7769i	0.560288	−	0.480947i
$945$		0			0
$946$	10.7432	−	15.4348i	0.349293	−	0.501830i
$947$	−0.789132	−	2.94508i	−0.0256433	−	0.0957023i	0.951918	−	0.306352i	$-0.0991086\pi$
$947$	−0.789132	−	2.94508i	−0.0256433	−	0.0957023i	−0.977562	+	0.210650i	$0.932442\pi$
$948$	2.42272	+	26.0111i	0.0786863	+	0.844802i
$949$	13.0883	−	7.55654i	0.424865	−	0.245296i
$950$	−23.1018	−	51.1226i	−0.749521	−	1.65864i
$951$			2.02642i			0.0657112i
$952$		0			0
$953$	−13.5860	+	13.5860i	−0.440095	+	0.440095i	−0.892044	−	0.451949i	$-0.850729\pi$
$953$	−13.5860	+	13.5860i	−0.440095	+	0.440095i	0.451949	+	0.892044i	$0.350729\pi$
$954$	8.10506	−	3.80715i	0.262411	−	0.123261i
$955$	−18.0649	+	23.1875i	−0.584568	+	0.750330i
$956$	2.54672	+	2.11273i	0.0823668	+	0.0683306i
$957$	10.3568	−	2.77511i	0.334789	−	0.0897065i
$958$	51.6990	−	9.26546i	1.67032	−	0.299353i
$959$		0			0
$960$	16.2214	−	12.6928i	0.523543	−	0.409660i
$961$	−7.93264	+	13.7397i	−0.255892	+	0.443217i
$962$	−1.16897	−	1.38522i	−0.0376892	−	0.0446614i
$963$	2.24290	−	8.37060i	0.0722763	−	0.269739i
$964$	8.69207	−	50.9646i	0.279953	−	1.64146i
$965$	−13.6258	+	32.2230i	−0.438629	+	1.03730i
$966$		0			0
$967$	31.0170	−	31.0170i	0.997439	−	0.997439i	−0.00255725	−	0.999997i	$-0.500814\pi$
$967$	31.0170	−	31.0170i	0.997439	−	0.997439i	0.999997	+	0.00255725i	$0.000813998\pi$
$968$	−0.181438	−	21.5712i	−0.00583165	−	0.693325i
$969$	−38.9264	+	22.4742i	−1.25050	+	0.721975i
$970$	11.6966	+	37.6944i	0.375555	+	1.21029i
$971$	−16.3303	−	9.42832i	−0.524065	−	0.302569i	0.214531	−	0.976717i	$-0.431178\pi$
$971$	−16.3303	−	9.42832i	−0.524065	−	0.302569i	−0.738596	+	0.674148i	$0.764511\pi$
$972$	−26.8856	−	12.3539i	−0.862355	−	0.396251i
$973$		0			0
$974$	−11.1896	+	16.0761i	−0.358537	+	0.515111i
$975$	−4.47581	−	17.7441i	−0.143341	−	0.568266i
$976$	8.81238	+	3.09597i	0.282077	+	0.0990997i
$977$	−6.44200	+	24.0419i	−0.206098	+	0.769168i	0.783014	+	0.622004i	$0.213681\pi$
$977$	−6.44200	+	24.0419i	−0.206098	+	0.769168i	−0.989112	+	0.147164i	$0.952985\pi$
$978$	34.8179	+	12.5622i	1.11335	+	0.401696i
$979$	−28.0912			−0.897799
$980$		0			0
$981$	14.8376			0.473728
$982$	32.5307	+	11.7370i	1.03810	+	0.374544i
$983$	3.87495	−	14.4615i	0.123592	−	0.461251i	−0.876194	−	0.481959i	$-0.839925\pi$
$983$	3.87495	−	14.4615i	0.123592	−	0.461251i	0.999786	+	0.0207081i	$0.00659205\pi$
$984$	1.40191	+	5.06134i	0.0446914	+	0.161350i
$985$	18.5569	−	14.0236i	0.591273	−	0.446828i
$986$	20.1558	−	28.9579i	0.641892	−	0.922208i
$987$		0			0
$988$	−21.0592	+	45.8309i	−0.669984	+	1.45808i
$989$	33.2623	+	19.2040i	1.05768	+	0.610651i
$990$	−8.60461	−	4.52918i	−0.273473	−	0.143947i
$991$	−6.50073	+	3.75320i	−0.206503	+	0.119224i	−0.599685	−	0.800236i	$-0.704707\pi$
$991$	−6.50073	+	3.75320i	−0.206503	+	0.119224i	0.393182	+	0.919460i	$0.371374\pi$
$992$	20.5723	−	7.81601i	0.653173	−	0.248159i
$993$	20.0654	−	20.0654i	0.636757	−	0.636757i
$994$		0			0
$995$	15.7713	−	6.39719i	0.499984	−	0.202804i
$996$	2.88566	+	0.492153i	0.0914358	+	0.0155945i
$997$	4.16779	−	15.5544i	0.131995	−	0.492613i	−0.867997	−	0.496570i	$-0.834593\pi$
$997$	4.16779	−	15.5544i	0.131995	−	0.492613i	0.999992	+	0.00395652i	$0.00125940\pi$
$998$	−0.347254	−	0.411492i	−0.0109921	−	0.0130256i
$999$	−1.08503	+	1.87932i	−0.0343288	+	0.0594592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.j.667.10		64
4.3	odd	2	inner	980.2.x.j.667.11		64
5.3	odd	4	inner	980.2.x.j.863.2		64
7.2	even	3		980.2.k.i.687.2	yes	32
7.3	odd	6	inner	980.2.x.j.67.12		64
7.4	even	3	inner	980.2.x.j.67.11		64
7.5	odd	6		980.2.k.i.687.1	✓	32
7.6	odd	2	inner	980.2.x.j.667.9		64
20.3	even	4	inner	980.2.x.j.863.11		64
28.3	even	6	inner	980.2.x.j.67.1		64
28.11	odd	6	inner	980.2.x.j.67.2		64
28.19	even	6		980.2.k.i.687.10	yes	32
28.23	odd	6		980.2.k.i.687.9	yes	32
28.27	even	2	inner	980.2.x.j.667.12		64
35.3	even	12	inner	980.2.x.j.263.12		64
35.13	even	4	inner	980.2.x.j.863.1		64
35.18	odd	12	inner	980.2.x.j.263.11		64
35.23	odd	12		980.2.k.i.883.9	yes	32
35.33	even	12		980.2.k.i.883.10	yes	32
140.3	odd	12	inner	980.2.x.j.263.9		64
140.23	even	12		980.2.k.i.883.2	yes	32
140.83	odd	4	inner	980.2.x.j.863.12		64
140.103	odd	12		980.2.k.i.883.1	yes	32
140.123	even	12	inner	980.2.x.j.263.10		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.i.687.1	✓	32	7.5	odd	6
980.2.k.i.687.2	yes	32	7.2	even	3
980.2.k.i.687.9	yes	32	28.23	odd	6
980.2.k.i.687.10	yes	32	28.19	even	6
980.2.k.i.883.1	yes	32	140.103	odd	12
980.2.k.i.883.2	yes	32	140.23	even	12
980.2.k.i.883.9	yes	32	35.23	odd	12
980.2.k.i.883.10	yes	32	35.33	even	12
980.2.x.j.67.1		64	28.3	even	6	inner
980.2.x.j.67.2		64	28.11	odd	6	inner
980.2.x.j.67.11		64	7.4	even	3	inner
980.2.x.j.67.12		64	7.3	odd	6	inner
980.2.x.j.263.9		64	140.3	odd	12	inner
980.2.x.j.263.10		64	140.123	even	12	inner
980.2.x.j.263.11		64	35.18	odd	12	inner
980.2.x.j.263.12		64	35.3	even	12	inner
980.2.x.j.667.9		64	7.6	odd	2	inner
980.2.x.j.667.10		64	1.1	even	1	trivial
980.2.x.j.667.11		64	4.3	odd	2	inner
980.2.x.j.667.12		64	28.27	even	2	inner
980.2.x.j.863.1		64	35.13	even	4	inner
980.2.x.j.863.2		64	5.3	odd	4	inner
980.2.x.j.863.11		64	20.3	even	4	inner
980.2.x.j.863.12		64	140.83	odd	4	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(0.479962 - 1.33028i) q^{2} +(0.298008 - 1.11218i) q^{3} +(-1.53927 - 1.27696i) q^{4} +(-0.308165 + 2.21473i) q^{5} +(-1.33648 - 0.930237i) q^{6} +(-2.43751 + 1.43477i) q^{8} +(1.44994 + 0.837123i) q^{9} +(2.79830 + 1.47293i) q^{10} +(-1.59056 + 0.918308i) q^{11} +(-1.87893 + 1.33140i) q^{12} +(-2.24767 + 2.24767i) q^{13} +(2.37135 + 1.00274i) q^{15} +(0.738725 + 3.93119i) q^{16} +(-1.27350 + 4.75278i) q^{17} +(1.80952 - 1.52703i) q^{18} +(-3.96687 + 6.87082i) q^{19} +(3.30248 - 3.01556i) q^{20} +(0.458198 + 2.55663i) q^{22} +(-5.12402 + 1.37298i) q^{23} +(0.869322 + 3.13852i) q^{24} +(-4.81007 - 1.36501i) q^{25} +(1.91123 + 4.06882i) q^{26} +(3.80564 - 3.80564i) q^{27} -5.07030i q^{29} +(2.47208 - 2.67327i) q^{30} +(3.36913 - 1.94517i) q^{31} +(5.58414 + 0.904114i) q^{32} +(0.547326 + 2.04265i) q^{33} +(5.71128 + 3.97527i) q^{34} +(-1.16288 - 3.14008i) q^{36} +(-0.389468 + 0.104358i) q^{37} +(7.23615 + 8.57477i) q^{38} +(1.82999 + 3.16964i) q^{39} +(-2.42647 - 5.84057i) q^{40} +1.61265 q^{41} +(-5.11964 - 5.11964i) q^{43} +(3.62095 + 0.617556i) q^{44} +(-2.30082 + 2.95325i) q^{45} +(-0.632894 + 7.47534i) q^{46} +(2.87295 + 10.7220i) q^{47} +(4.59234 + 0.349931i) q^{48} +(-4.12448 + 5.74357i) q^{50} +(4.90644 + 2.83273i) q^{51} +(6.32997 - 0.589584i) q^{52} +(3.65309 + 0.978842i) q^{53} +(-3.23600 - 6.88912i) q^{54} +(-1.54365 - 3.80564i) q^{55} +(6.45944 + 6.45944i) q^{57} +(-6.74491 - 2.43355i) q^{58} +(-2.83588 - 4.91188i) q^{59} +(-2.36968 - 4.57162i) q^{60} +(1.16755 - 2.02226i) q^{61} +(-0.970559 - 5.41548i) q^{62} +(3.88289 - 6.99451i) q^{64} +(-4.28533 - 5.67063i) q^{65} +(2.97998 + 0.252298i) q^{66} +(5.24841 + 1.40631i) q^{67} +(8.02940 - 5.68961i) q^{68} +6.10799i q^{69} +4.56057i q^{71} +(-4.73531 + 0.0398294i) q^{72} +(-4.59251 - 1.23056i) q^{73} +(-0.0481052 + 0.568188i) q^{74} +(-2.95157 + 4.94288i) q^{75} +(14.8799 - 5.51052i) q^{76} +(5.09482 - 0.913089i) q^{78} +(5.67209 - 9.82435i) q^{79} +(-8.93419 + 0.424620i) q^{80} +(-0.587082 - 1.01686i) q^{81} +(0.774011 - 2.14527i) q^{82} +(-0.898867 - 0.898867i) q^{83} +(-10.1337 - 4.28511i) q^{85} +(-9.26778 + 4.35331i) q^{86} +(-5.63909 - 1.51099i) q^{87} +(2.55944 - 4.52046i) q^{88} +(13.2459 + 7.64755i) q^{89} +(2.82434 + 4.47818i) q^{90} +(9.64050 + 4.42980i) q^{92} +(-1.15935 - 4.32676i) q^{93} +(15.6421 + 1.32433i) q^{94} +(-13.9946 - 10.9029i) q^{95} +(2.66965 - 5.94113i) q^{96} +(8.82518 + 8.82518i) q^{97} -3.07495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 16 q^{8} - 8 q^{16} + 40 q^{18} - 72 q^{22} - 32 q^{25} + 36 q^{30} - 16 q^{32} - 176 q^{36} + 48 q^{37} + 56 q^{50} - 16 q^{53} - 32 q^{57} - 36 q^{58} + 80 q^{60} - 64 q^{65} - 56 q^{72}+ \cdots - 32 q^{93}+O(q^{100}) \) 64 * q + 4 * q^2 + 16 * q^8 - 8 * q^16 + 40 * q^18 - 72 * q^22 - 32 * q^25 + 36 * q^30 - 16 * q^32 - 176 * q^36 + 48 * q^37 + 56 * q^50 - 16 * q^53 - 32 * q^57 - 36 * q^58 + 80 * q^60 - 64 * q^65 - 56 * q^72 + 56 * q^78 - 56 * q^86 - 88 * q^88 + 272 * q^92 - 32 * q^93

Introduction

L-functions

Modular forms

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