LMFDB - Embedded newform 280.2.bg.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(9,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	280.9
Dual form			280.2.bg.a.249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82577 + 1.05411i) q^{3} +(1.46656 - 1.68796i) q^{5} +(-1.44930 - 2.21349i) q^{7} +(0.722285 - 1.25103i) q^{9} +O(q^{10})$	\(q+(-1.82577 + 1.05411i) q^{3} +(1.46656 - 1.68796i) q^{5} +(-1.44930 - 2.21349i) q^{7} +(0.722285 - 1.25103i) q^{9} +(-0.887326 - 1.53689i) q^{11} -1.44457i q^{13} +(-0.898317 + 4.62773i) q^{15} +(5.08189 - 2.93403i) q^{17} +(3.58102 - 6.20251i) q^{19} +(4.97934 + 2.51359i) q^{21} +(0.574733 + 0.331822i) q^{23} +(-0.698386 - 4.95099i) q^{25} -3.27918i q^{27} -6.45763 q^{29} +(5.03658 + 8.72362i) q^{31} +(3.24010 + 1.87067i) q^{33} +(-5.86176 - 0.799863i) q^{35} +(-4.34489 - 2.50852i) q^{37} +(1.52273 + 2.63745i) q^{39} -1.92363 q^{41} +5.81995i q^{43} +(-1.05241 - 3.05391i) q^{45} +(-3.20709 - 1.85161i) q^{47} +(-2.79905 + 6.41602i) q^{49} +(-6.18557 + 10.7137i) q^{51} +(-0.513002 + 0.296182i) q^{53} +(-3.89553 - 0.756185i) q^{55} +15.0991i q^{57} +(-3.79538 - 6.57379i) q^{59} +(-4.36055 + 7.55270i) q^{61} +(-3.81596 + 0.214357i) q^{63} +(-2.43837 - 2.11855i) q^{65} +(1.87782 - 1.08416i) q^{67} -1.39911 q^{69} +6.49826 q^{71} +(13.4511 - 7.76600i) q^{73} +(6.49396 + 8.30318i) q^{75} +(-2.11589 + 4.19151i) q^{77} +(-1.35360 + 2.34451i) q^{79} +(5.62346 + 9.74012i) q^{81} -6.35340i q^{83} +(2.50040 - 12.8809i) q^{85} +(11.7901 - 6.80704i) q^{87} +(2.93079 - 5.07627i) q^{89} +(-3.19754 + 2.09362i) q^{91} +(-18.3913 - 10.6182i) q^{93} +(-5.21777 - 15.1410i) q^{95} +14.7748i q^{97} -2.56361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{9}+O(q^{10}) $ 24 * q + 14 * q^9	$ 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) $ 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.82577	+	1.05411i	−1.05411	+	0.608589i	−0.923796	−	0.382884i	$-0.874931\pi$
$3$	−1.82577	+	1.05411i	−1.05411	+	0.608589i	−0.130311	+	0.991473i	$0.541598\pi$
$4$		0			0
$5$	1.46656	−	1.68796i	0.655867	−	0.754877i
$5$	1.46656	−	1.68796i	0.655867	−	0.754877i
$6$		0			0
$7$	−1.44930	−	2.21349i	−0.547784	−	0.836620i
$7$	−1.44930	−	2.21349i	−0.547784	−	0.836620i
$8$		0			0
$9$	0.722285	−	1.25103i	0.240762	−	0.417011i
$10$		0			0
$11$	−0.887326	−	1.53689i	−0.267539	−	0.463391i	0.700687	−	0.713469i	$-0.252877\pi$
$11$	−0.887326	−	1.53689i	−0.267539	−	0.463391i	−0.968226	+	0.250078i	$0.919544\pi$
$12$		0			0
$13$		−	1.44457i		−	0.400652i	−0.979729	−	0.200326i	$-0.935800\pi$
$13$		−	1.44457i		−	0.400652i	0.979729	−	0.200326i	$-0.0642001\pi$
$14$		0			0
$15$	−0.898317	+	4.62773i	−0.231945	+	1.19487i
$16$		0			0
$17$	5.08189	−	2.93403i	1.23254	−	0.711607i	0.264981	−	0.964254i	$-0.414634\pi$
$17$	5.08189	−	2.93403i	1.23254	−	0.711607i	0.967559	+	0.252647i	$0.0813010\pi$
$18$		0			0
$19$	3.58102	−	6.20251i	0.821543	−	1.42295i	−0.0829897	−	0.996550i	$-0.526447\pi$
$19$	3.58102	−	6.20251i	0.821543	−	1.42295i	0.904533	−	0.426404i	$-0.140220\pi$
$20$		0			0
$21$	4.97934	+	2.51359i	1.08658	+	0.548511i
$22$		0			0
$23$	0.574733	+	0.331822i	0.119840	+	0.0691898i	0.558722	−	0.829355i	$-0.311292\pi$
$23$	0.574733	+	0.331822i	0.119840	+	0.0691898i	−0.438882	+	0.898545i	$0.644625\pi$
$24$		0			0
$25$	−0.698386	−	4.95099i	−0.139677	−	0.990197i
$26$		0			0
$27$		−	3.27918i		−	0.631079i
$28$		0			0
$29$	−6.45763			−1.19915			−0.599576	−	0.800318i	$-0.704664\pi$
$29$	−6.45763			−1.19915			−0.599576	+	0.800318i	$0.704664\pi$
$30$		0			0
$31$	5.03658	+	8.72362i	0.904597	+	1.56681i	0.821457	+	0.570271i	$0.193162\pi$
$31$	5.03658	+	8.72362i	0.904597	+	1.56681i	0.0831406	+	0.996538i	$0.473505\pi$
$32$		0			0
$33$	3.24010	+	1.87067i	0.564029	+	0.325642i
$34$		0			0
$35$	−5.86176	−	0.799863i	−0.990818	−	0.135201i
$36$		0			0
$37$	−4.34489	−	2.50852i	−0.714295	−	0.412399i	0.0983541	−	0.995151i	$-0.468642\pi$
$37$	−4.34489	−	2.50852i	−0.714295	−	0.412399i	−0.812649	+	0.582753i	$0.801976\pi$
$38$		0			0
$39$	1.52273	+	2.63745i	0.243832	+	0.422330i
$40$		0			0
$41$	−1.92363			−0.300421			−0.150211	−	0.988654i	$-0.547995\pi$
$41$	−1.92363			−0.300421			−0.150211	+	0.988654i	$0.547995\pi$
$42$		0			0
$43$			5.81995i			0.887535i	0.896142	+	0.443767i	$0.146358\pi$
$43$			5.81995i			0.887535i	−0.896142	+	0.443767i	$0.853642\pi$
$44$		0			0
$45$	−1.05241	−	3.05391i	−0.156885	−	0.455249i
$46$		0			0
$47$	−3.20709	−	1.85161i	−0.467802	−	0.270085i	0.247517	−	0.968883i	$-0.420385\pi$
$47$	−3.20709	−	1.85161i	−0.467802	−	0.270085i	−0.715319	+	0.698798i	$0.753719\pi$
$48$		0			0
$49$	−2.79905	+	6.41602i	−0.399864	+	0.916574i
$50$		0			0
$51$	−6.18557	+	10.7137i	−0.866153	+	1.50022i
$52$		0			0
$53$	−0.513002	+	0.296182i	−0.0704662	+	0.0406837i	−0.534819	−	0.844967i	$-0.679620\pi$
$53$	−0.513002	+	0.296182i	−0.0704662	+	0.0406837i	0.464353	+	0.885650i	$0.346287\pi$
$54$		0			0
$55$	−3.89553	−	0.756185i	−0.525273	−	0.101964i
$56$		0			0
$57$			15.0991i			1.99993i
$58$		0			0
$59$	−3.79538	−	6.57379i	−0.494116	−	0.855835i	0.505861	−	0.862615i	$-0.331175\pi$
$59$	−3.79538	−	6.57379i	−0.494116	−	0.855835i	−0.999977	+	0.00678044i	$0.997842\pi$
$60$		0			0
$61$	−4.36055	+	7.55270i	−0.558312	+	0.967024i	0.439326	+	0.898328i	$0.355217\pi$
$61$	−4.36055	+	7.55270i	−0.558312	+	0.967024i	−0.997638	+	0.0686963i	$0.978116\pi$
$62$		0			0
$63$	−3.81596	+	0.214357i	−0.480765	+	0.0270065i
$64$		0			0
$65$	−2.43837	−	2.11855i	−0.302442	−	0.262774i
$66$		0			0
$67$	1.87782	−	1.08416i	0.229412	−	0.132451i	−0.380889	−	0.924621i	$-0.624382\pi$
$67$	1.87782	−	1.08416i	0.229412	−	0.132451i	0.610301	+	0.792170i	$0.291049\pi$
$68$		0			0
$69$	−1.39911			−0.168433
$70$		0			0
$71$	6.49826			0.771201			0.385601	−	0.922666i	$-0.373994\pi$
$71$	6.49826			0.771201			0.385601	+	0.922666i	$0.373994\pi$
$72$		0			0
$73$	13.4511	−	7.76600i	1.57433	−	0.908941i	0.578704	−	0.815538i	$-0.303559\pi$
$73$	13.4511	−	7.76600i	1.57433	−	0.908941i	0.995628	−	0.0934035i	$-0.0297746\pi$
$74$		0			0
$75$	6.49396	+	8.30318i	0.749858	+	0.958768i
$76$		0			0
$77$	−2.11589	+	4.19151i	−0.241128	+	0.477666i
$78$		0			0
$79$	−1.35360	+	2.34451i	−0.152292	+	0.263778i	−0.932070	−	0.362279i	$-0.881999\pi$
$79$	−1.35360	+	2.34451i	−0.152292	+	0.263778i	0.779778	+	0.626057i	$0.215332\pi$
$80$		0			0
$81$	5.62346	+	9.74012i	0.624829	+	1.08224i
$82$		0			0
$83$		−	6.35340i		−	0.697376i	−0.937239	−	0.348688i	$-0.886627\pi$
$83$		−	6.35340i		−	0.697376i	0.937239	−	0.348688i	$-0.113373\pi$
$84$		0			0
$85$	2.50040	−	12.8809i	0.271207	−	1.39713i
$86$		0			0
$87$	11.7901	−	6.80704i	1.26404	−	0.729791i
$88$		0			0
$89$	2.93079	−	5.07627i	0.310663	−	0.538084i	−0.667843	−	0.744302i	$-0.732782\pi$
$89$	2.93079	−	5.07627i	0.310663	−	0.538084i	0.978506	+	0.206218i	$0.0661157\pi$
$90$		0			0
$91$	−3.19754	+	2.09362i	−0.335193	+	0.219471i
$92$		0			0
$93$	−18.3913	−	10.6182i	−1.90709	−	1.10106i
$94$		0			0
$95$	−5.21777	−	15.1410i	−0.535332	−	1.55343i
$96$		0			0
$97$			14.7748i			1.50015i	0.661351	+	0.750076i	$0.269983\pi$
$97$			14.7748i			1.50015i	−0.661351	+	0.750076i	$0.730017\pi$
$98$		0			0
$99$	−2.56361			−0.257652
$100$		0			0
$101$	−1.74093	−	3.01538i	−0.173229	−	0.300041i	0.766318	−	0.642461i	$-0.222087\pi$
$101$	−1.74093	−	3.01538i	−0.173229	−	0.300041i	−0.939547	+	0.342420i	$0.888753\pi$
$102$		0			0
$103$	6.99628	+	4.03930i	0.689364	+	0.398004i	0.803374	−	0.595475i	$-0.203036\pi$
$103$	6.99628	+	4.03930i	0.689364	+	0.398004i	−0.114010	+	0.993480i	$0.536370\pi$
$104$		0			0
$105$	11.5454	−	4.71856i	1.12671	−	0.460484i
$106$		0			0
$107$	0.112276	+	0.0648226i	0.0108541	+	0.00626664i	0.505417	−	0.862875i	$-0.331339\pi$
$107$	0.112276	+	0.0648226i	0.0108541	+	0.00626664i	−0.494563	+	0.869142i	$0.664672\pi$
$108$		0			0
$109$	6.13241	+	10.6217i	0.587379	+	1.01737i	0.994574	+	0.104029i	$0.0331734\pi$
$109$	6.13241	+	10.6217i	0.587379	+	1.01737i	−0.407196	+	0.913341i	$0.633493\pi$
$110$		0			0
$111$	10.5770			1.00393
$112$		0			0
$113$			11.7467i			1.10503i	0.833501	+	0.552517i	$0.186333\pi$
$113$			11.7467i			1.10503i	−0.833501	+	0.552517i	$0.813667\pi$
$114$		0			0
$115$	1.40298	−	0.483486i	0.130829	−	0.0450853i
$116$		0			0
$117$	−1.80721	−	1.04339i	−0.167076	−	0.0964615i
$118$		0			0
$119$	−13.8596	−	6.99641i	−1.27051	−	0.641359i
$120$		0			0
$121$	3.92531	−	6.79883i	0.356846	−	0.618075i
$122$		0			0
$123$	3.51211	−	2.02772i	0.316676	−	0.182833i
$124$		0			0
$125$	−9.38127	−	6.08209i	−0.839086	−	0.543999i
$126$		0			0
$127$			12.6983i			1.12679i	0.826187	+	0.563395i	$0.190505\pi$
$127$			12.6983i			1.12679i	−0.826187	+	0.563395i	$0.809495\pi$
$128$		0			0
$129$	−6.13486	−	10.6259i	−0.540144	−	0.935557i
$130$		0			0
$131$	0.115466	−	0.199993i	0.0100883	−	0.0174734i	−0.860937	−	0.508711i	$-0.830122\pi$
$131$	0.115466	−	0.199993i	0.0100883	−	0.0174734i	0.871025	+	0.491238i	$0.163455\pi$
$132$		0			0
$133$	−18.9192	+	1.06276i	−1.64050	+	0.0921533i
$134$		0			0
$135$	−5.53511	−	4.80913i	−0.476386	−	0.413904i
$136$		0			0
$137$	−14.5594	+	8.40586i	−1.24389	+	0.718161i	−0.969884	−	0.243566i	$-0.921683\pi$
$137$	−14.5594	+	8.40586i	−1.24389	+	0.718161i	−0.274008	+	0.961728i	$0.588349\pi$
$138$		0			0
$139$	20.5531			1.74329			0.871644	−	0.490139i	$-0.163054\pi$
$139$	20.5531			1.74329			0.871644	+	0.490139i	$0.163054\pi$
$140$		0			0
$141$	7.80719			0.657484
$142$		0			0
$143$	−2.22015	+	1.28180i	−0.185658	+	0.107190i
$144$		0			0
$145$	−9.47053	+	10.9002i	−0.786485	+	0.905212i
$146$		0			0
$147$	−1.65276	−	14.6647i	−0.136317	−	1.20952i
$148$		0			0
$149$	10.6363	−	18.4225i	0.871356	−	1.50923i	0.0107608	−	0.999942i	$-0.496575\pi$
$149$	10.6363	−	18.4225i	0.871356	−	1.50923i	0.860595	−	0.509290i	$-0.170092\pi$
$150$		0			0
$151$	−3.23995	−	5.61176i	−0.263663	−	0.456678i	0.703549	−	0.710647i	$-0.251597\pi$
$151$	−3.23995	−	5.61176i	−0.263663	−	0.456678i	−0.967213	+	0.253968i	$0.918264\pi$
$152$		0			0
$153$		−	8.47683i		−	0.685311i
$154$		0			0
$155$	22.1116	+	4.29221i	1.77604	+	0.344759i
$156$		0			0
$157$	−4.71976	+	2.72495i	−0.376678	+	0.217475i	−0.676372	−	0.736560i	$-0.736449\pi$
$157$	−4.71976	+	2.72495i	−0.376678	+	0.217475i	0.299694	+	0.954035i	$0.403115\pi$
$158$		0			0
$159$	0.624415	−	1.08152i	0.0495193	−	0.0857699i
$160$		0			0
$161$	−0.0984771	−	1.75308i	−0.00776108	−	0.138162i
$162$		0			0
$163$	5.42930	+	3.13461i	0.425255	+	0.245521i	0.697323	−	0.716757i	$-0.254374\pi$
$163$	5.42930	+	3.13461i	0.425255	+	0.245521i	−0.272068	+	0.962278i	$0.587708\pi$
$164$		0			0
$165$	7.90942	−	2.72569i	0.615748	−	0.212194i
$166$		0			0
$167$		−	18.5728i		−	1.43720i	−0.695422	−	0.718602i	$-0.744782\pi$
$167$		−	18.5728i		−	1.43720i	0.695422	−	0.718602i	$-0.255218\pi$
$168$		0			0
$169$	10.9132			0.839478
$170$		0			0
$171$	−5.17304	−	8.95997i	−0.395592	−	0.685186i
$172$		0			0
$173$	12.0960	+	6.98361i	0.919639	+	0.530954i	0.883520	−	0.468394i	$-0.155167\pi$
$173$	12.0960	+	6.98361i	0.919639	+	0.530954i	0.0361190	+	0.999347i	$0.488500\pi$
$174$		0			0
$175$	−9.94677	+	8.72134i	−0.751905	+	0.659271i
$176$		0			0
$177$	13.8590	+	8.00148i	1.04170	+	0.601428i
$178$		0			0
$179$	3.96270	+	6.86359i	0.296186	+	0.513009i	0.975260	−	0.221061i	$-0.0709519\pi$
$179$	3.96270	+	6.86359i	0.296186	+	0.513009i	−0.679074	+	0.734070i	$0.737619\pi$
$180$		0			0
$181$	−11.6887			−0.868815			−0.434407	−	0.900717i	$-0.643042\pi$
$181$	−11.6887			−0.868815			−0.434407	+	0.900717i	$0.643042\pi$
$182$		0			0
$183$		−	18.3860i		−	1.35913i
$184$		0			0
$185$	−10.6063	+	3.65507i	−0.779793	+	0.268726i
$186$		0			0
$187$	−9.01858	−	5.20688i	−0.659504	−	0.380765i
$188$		0			0
$189$	−7.25843	+	4.75252i	−0.527973	+	0.345695i
$190$		0			0
$191$	6.48908	−	11.2394i	0.469533	−	0.813255i	−0.529860	−	0.848085i	$-0.677756\pi$
$191$	6.48908	−	11.2394i	0.469533	−	0.813255i	0.999393	+	0.0348297i	$0.0110889\pi$
$192$		0			0
$193$	18.5375	−	10.7026i	1.33436	−	0.770393i	0.348395	−	0.937348i	$-0.386727\pi$
$193$	18.5375	−	10.7026i	1.33436	−	0.770393i	0.985965	+	0.166955i	$0.0533935\pi$
$194$		0			0
$195$	6.68508	+	1.29768i	0.478728	+	0.0929289i
$196$		0			0
$197$			8.42871i			0.600521i	0.953857	+	0.300261i	$0.0970736\pi$
$197$			8.42871i			0.600521i	−0.953857	+	0.300261i	$0.902926\pi$
$198$		0			0
$199$	2.10741	+	3.65013i	0.149390	+	0.258751i	0.931002	−	0.365014i	$-0.118936\pi$
$199$	2.10741	+	3.65013i	0.149390	+	0.258751i	−0.781612	+	0.623765i	$0.785602\pi$
$200$		0			0
$201$	−2.28564	+	3.95885i	−0.161217	+	0.279236i
$202$		0			0
$203$	9.35906	+	14.2939i	0.656877	+	1.00323i
$204$		0			0
$205$	−2.82113	+	3.24701i	−0.197036	+	0.226781i
$206$		0			0
$207$	0.830243	−	0.479341i	0.0577058	−	0.0333165i
$208$		0			0
$209$	−12.7101			−0.879179
$210$		0			0
$211$	−0.629004			−0.0433025			−0.0216512	−	0.999766i	$-0.506892\pi$
$211$	−0.629004			−0.0433025			−0.0216512	+	0.999766i	$0.506892\pi$
$212$		0			0
$213$	−11.8643	+	6.84986i	−0.812929	+	0.469345i
$214$		0			0
$215$	9.82382	+	8.53533i	0.669979	+	0.582105i
$216$		0			0
$217$	12.0101	−	23.7916i	0.815298	−	1.61508i
$218$		0			0
$219$	−16.3724	+	28.3578i	−1.10634	+	1.91624i
$220$		0			0
$221$	−4.23841	−	7.34115i	−0.285107	−	0.493819i
$222$		0			0
$223$			21.4138i			1.43398i	0.697086	+	0.716988i	$0.254480\pi$
$223$			21.4138i			1.43398i	−0.697086	+	0.716988i	$0.745520\pi$
$224$		0			0
$225$	−6.69829	−	2.70232i	−0.446552	−	0.180155i
$226$		0			0
$227$	19.0953	−	11.0247i	1.26740	−	0.731732i	0.292902	−	0.956142i	$-0.405379\pi$
$227$	19.0953	−	11.0247i	1.26740	−	0.731732i	0.974495	+	0.224411i	$0.0720457\pi$
$228$		0			0
$229$	5.81797	−	10.0770i	0.384462	−	0.665908i	−0.607232	−	0.794524i	$-0.707720\pi$
$229$	5.81797	−	10.0770i	0.384462	−	0.665908i	0.991694	+	0.128616i	$0.0410535\pi$
$230$		0			0
$231$	−0.555172	−	9.88309i	−0.0365276	−	0.650260i
$232$		0			0
$233$	9.71624	+	5.60967i	0.636532	+	0.367502i	0.783277	−	0.621672i	$-0.213546\pi$
$233$	9.71624	+	5.60967i	0.636532	+	0.367502i	−0.146745	+	0.989174i	$0.546880\pi$
$234$		0			0
$235$	−7.82883	+	2.69791i	−0.510697	+	0.175992i
$236$		0			0
$237$		−	5.70737i		−	0.370733i
$238$		0			0
$239$	−22.8279			−1.47662			−0.738308	−	0.674464i	$-0.764375\pi$
$239$	−22.8279			−1.47662			−0.738308	+	0.674464i	$0.764375\pi$
$240$		0			0
$241$	−2.10135	−	3.63965i	−0.135360	−	0.234450i	0.790375	−	0.612623i	$-0.209886\pi$
$241$	−2.10135	−	3.63965i	−0.135360	−	0.234450i	−0.925735	+	0.378173i	$0.876552\pi$
$242$		0			0
$243$	−12.0147	−	6.93670i	−0.770744	−	0.444989i
$244$		0			0
$245$	6.72497	+	14.1342i	0.429643	+	0.902999i
$246$		0			0
$247$	−8.95997	−	5.17304i	−0.570109	−	0.329153i
$248$		0			0
$249$	6.69717	+	11.5998i	0.424416	+	0.735109i
$250$		0			0
$251$	−16.9587			−1.07042			−0.535211	−	0.844718i	$-0.679768\pi$
$251$	−16.9587			−1.07042			−0.535211	+	0.844718i	$0.679768\pi$
$252$		0			0
$253$		−	1.17774i		−	0.0740438i
$254$		0			0
$255$	9.01275	+	26.1533i	0.564400	+	1.63778i
$256$		0			0
$257$	−23.3223	−	13.4651i	−1.45480	−	0.839932i	−0.456056	−	0.889951i	$-0.650738\pi$
$257$	−23.3223	−	13.4651i	−1.45480	−	0.839932i	−0.998748	+	0.0500191i	$0.984072\pi$
$258$		0			0
$259$	0.744470	+	13.2530i	0.0462591	+	0.823499i
$260$		0			0
$261$	−4.66425	+	8.07872i	−0.288710	+	0.500060i
$262$		0			0
$263$	−19.0110	+	10.9760i	−1.17227	+	0.676809i	−0.954213	−	0.299127i	$-0.903304\pi$
$263$	−19.0110	+	10.9760i	−1.17227	+	0.676809i	−0.218055	+	0.975937i	$0.569971\pi$
$264$		0			0
$265$	−0.252408	+	1.30029i	−0.0155053	+	0.0798764i
$266$		0			0
$267$			12.3575i			0.756264i
$268$		0			0
$269$	12.0427	+	20.8586i	0.734256	+	1.27177i	0.955049	+	0.296448i	$0.0958023\pi$
$269$	12.0427	+	20.8586i	0.734256	+	1.27177i	−0.220793	+	0.975321i	$0.570864\pi$
$270$		0			0
$271$	−1.03365	+	1.79034i	−0.0627900	+	0.108755i	−0.895712	−	0.444636i	$-0.853333\pi$
$271$	−1.03365	+	1.79034i	−0.0627900	+	0.108755i	0.832922	+	0.553391i	$0.186666\pi$
$272$		0			0
$273$	3.63106	−	7.19301i	0.219762	−	0.435341i
$274$		0			0
$275$	−6.98944	+	5.46648i	−0.421479	+	0.329641i
$276$		0			0
$277$	14.7880	−	8.53786i	0.888525	−	0.512990i	0.0150652	−	0.999887i	$-0.495204\pi$
$277$	14.7880	−	8.53786i	0.888525	−	0.512990i	0.873460	+	0.486896i	$0.161871\pi$
$278$		0			0
$279$	14.5514			0.871169
$280$		0			0
$281$	−13.2035			−0.787655			−0.393828	−	0.919184i	$-0.628849\pi$
$281$	−13.2035			−0.787655			−0.393828	+	0.919184i	$0.628849\pi$
$282$		0			0
$283$	−23.0353	+	13.2994i	−1.36931	+	0.790570i	−0.990840	−	0.135045i	$-0.956882\pi$
$283$	−23.0353	+	13.2994i	−1.36931	+	0.790570i	−0.378468	+	0.925615i	$0.623549\pi$
$284$		0			0
$285$	25.4867	+	22.1438i	1.50970	+	1.31169i
$286$		0			0
$287$	2.78793	+	4.25794i	0.164566	+	0.251338i
$288$		0			0
$289$	8.71708	−	15.0984i	0.512769	−	0.888142i
$290$		0			0
$291$	−15.5742	−	26.9753i	−0.912977	−	1.58132i
$292$		0			0
$293$			0.472681i			0.0276143i	0.999905	+	0.0138071i	$0.00439509\pi$
$293$			0.472681i			0.0276143i	−0.999905	+	0.0138071i	$0.995605\pi$
$294$		0			0
$295$	−16.6624	−	3.23445i	−0.970124	−	0.188317i
$296$		0			0
$297$	−5.03975	+	2.90970i	−0.292436	+	0.168838i
$298$		0			0
$299$	0.479341	−	0.830243i	0.0277210	−	0.0480142i
$300$		0			0
$301$	12.8824	−	8.43487i	0.742529	−	0.486178i
$302$		0			0
$303$	6.35706	+	3.67025i	0.365204	+	0.210850i
$304$		0			0
$305$	6.35359	+	18.4369i	0.363806	+	1.05570i
$306$		0			0
$307$			15.2073i			0.867929i	0.900930	+	0.433965i	$0.142886\pi$
$307$			15.2073i			0.867929i	−0.900930	+	0.433965i	$0.857114\pi$
$308$		0			0
$309$	−17.0314			−0.968885
$310$		0			0
$311$	8.29030	+	14.3592i	0.470100	+	0.814237i	0.999415	−	0.0341882i	$-0.0108846\pi$
$311$	8.29030	+	14.3592i	0.470100	+	0.814237i	−0.529316	+	0.848425i	$0.677551\pi$
$312$		0			0
$313$	−1.02148	−	0.589752i	−0.0577375	−	0.0333348i	0.470853	−	0.882211i	$-0.343946\pi$
$313$	−1.02148	−	0.589752i	−0.0577375	−	0.0333348i	−0.528591	+	0.848877i	$0.677279\pi$
$314$		0			0
$315$	−5.23452	+	6.75553i	−0.294932	+	0.380631i
$316$		0			0
$317$	23.7540	+	13.7144i	1.33416	+	0.770278i	0.985934	−	0.167133i	$-0.0534509\pi$
$317$	23.7540	+	13.7144i	1.33416	+	0.770278i	0.348226	+	0.937411i	$0.386784\pi$
$318$		0			0
$319$	5.73002	+	9.92469i	0.320820	+	0.555676i
$320$		0			0
$321$	−0.273320			−0.0152552
$322$		0			0
$323$		−	42.0273i		−	2.33846i
$324$		0			0
$325$	−7.15204	+	1.00887i	−0.396724	+	0.0559619i
$326$		0			0
$327$	−22.3927	−	12.9284i	−1.23832	−	0.714945i
$328$		0			0
$329$	0.549515	+	9.78239i	0.0302957	+	0.539320i
$330$		0			0
$331$	−2.60580	+	4.51337i	−0.143228	+	0.248078i	−0.928710	−	0.370806i	$-0.879081\pi$
$331$	−2.60580	+	4.51337i	−0.143228	+	0.248078i	0.785483	+	0.618884i	$0.212415\pi$
$332$		0			0
$333$	−6.27649	+	3.62374i	−0.343950	+	0.198580i
$334$		0			0
$335$	0.923929	−	4.75967i	0.0504796	−	0.260048i
$336$		0			0
$337$		−	9.52496i		−	0.518858i	−0.965762	−	0.259429i	$-0.916466\pi$
$337$		−	9.52496i		−	0.518858i	0.965762	−	0.259429i	$-0.0835343\pi$
$338$		0			0
$339$	−12.3823	−	21.4467i	−0.672512	−	1.16483i
$340$		0			0
$341$	8.93818	−	15.4814i	0.484030	−	0.838364i
$342$		0			0
$343$	18.2584	−	3.10308i	0.985863	−	0.167551i
$344$		0			0
$345$	−2.05188	+	2.36163i	−0.110469	+	0.127146i
$346$		0			0
$347$	−23.6235	+	13.6390i	−1.26818	+	0.732182i	−0.974643	−	0.223767i	$-0.928165\pi$
$347$	−23.6235	+	13.6390i	−1.26818	+	0.732182i	−0.293534	+	0.955949i	$0.594831\pi$
$348$		0			0
$349$	−6.78145			−0.363003			−0.181501	−	0.983391i	$-0.558096\pi$
$349$	−6.78145			−0.363003			−0.181501	+	0.983391i	$0.558096\pi$
$350$		0			0
$351$	−4.73701			−0.252843
$352$		0			0
$353$	13.5785	−	7.83957i	0.722713	−	0.417258i	−0.0930377	−	0.995663i	$-0.529658\pi$
$353$	13.5785	−	7.83957i	0.722713	−	0.417258i	0.815750	+	0.578404i	$0.196324\pi$
$354$		0			0
$355$	9.53010	−	10.9688i	0.505805	−	0.582162i
$356$		0			0
$357$	32.6794	−	1.83573i	1.72958	−	0.0971572i
$358$		0			0
$359$	−3.16733	+	5.48598i	−0.167165	+	0.289539i	−0.937422	−	0.348195i	$-0.886795\pi$
$359$	−3.16733	+	5.48598i	−0.167165	+	0.289539i	0.770257	+	0.637734i	$0.220128\pi$
$360$		0			0
$361$	−16.1475	−	27.9682i	−0.849866	−	1.47201i
$362$		0			0
$363$			16.5508i			0.868691i
$364$		0			0
$365$	6.61823	−	34.0942i	0.346414	−	1.78457i
$366$		0			0
$367$	11.0504	−	6.37993i	0.576824	−	0.333030i	−0.183046	−	0.983104i	$-0.558596\pi$
$367$	11.0504	−	6.37993i	0.576824	−	0.333030i	0.759870	+	0.650075i	$0.225262\pi$
$368$		0			0
$369$	−1.38941	+	2.40653i	−0.0723299	+	0.125279i
$370$		0			0
$371$	1.39909	+	0.706266i	0.0726370	+	0.0366675i
$372$		0			0
$373$	−1.44553	−	0.834577i	−0.0748467	−	0.0432127i	0.462110	−	0.886823i	$-0.347093\pi$
$373$	−1.44553	−	0.834577i	−0.0748467	−	0.0432127i	−0.536956	+	0.843610i	$0.680426\pi$
$374$		0			0
$375$	23.5392	+	1.21562i	1.21556	+	0.0627742i
$376$		0			0
$377$			9.32850i			0.480442i
$378$		0			0
$379$	21.5557			1.10724			0.553621	−	0.832768i	$-0.313245\pi$
$379$	21.5557			1.10724			0.553621	+	0.832768i	$0.313245\pi$
$380$		0			0
$381$	−13.3854	−	23.1841i	−0.685753	−	1.18776i
$382$		0			0
$383$	−4.36845	−	2.52213i	−0.223217	−	0.128875i	0.384222	−	0.923241i	$-0.374470\pi$
$383$	−4.36845	−	2.52213i	−0.223217	−	0.128875i	−0.607439	+	0.794366i	$0.707803\pi$
$384$		0			0
$385$	3.97199	+	9.71864i	0.202431	+	0.495308i
$386$		0			0
$387$	7.28096	+	4.20366i	0.370112	+	0.213684i
$388$		0			0
$389$	−6.25975	−	10.8422i	−0.317382	−	0.549722i	0.662559	−	0.749010i	$-0.269470\pi$
$389$	−6.25975	−	10.8422i	−0.317382	−	0.549722i	−0.979941	+	0.199288i	$0.936137\pi$
$390$		0			0
$391$	3.89431			0.196944
$392$		0			0
$393$			0.486853i			0.0245585i
$394$		0			0
$395$	1.97228	+	5.72319i	0.0992362	+	0.287965i
$396$		0			0
$397$	−19.3934	−	11.1968i	−0.973326	−	0.561950i	−0.0730773	−	0.997326i	$-0.523282\pi$
$397$	−19.3934	−	11.1968i	−0.973326	−	0.561950i	−0.900249	+	0.435376i	$0.856615\pi$
$398$		0			0
$399$	33.4217	−	21.8832i	1.67318	−	1.09553i
$400$		0			0
$401$	7.69654	−	13.3308i	0.384347	−	0.665708i	−0.607331	−	0.794449i	$-0.707760\pi$
$401$	7.69654	−	13.3308i	0.384347	−	0.665708i	0.991678	+	0.128740i	$0.0410933\pi$
$402$		0			0
$403$	12.6019	−	7.27570i	0.627744	−	0.362428i
$404$		0			0
$405$	24.6881	+	4.79235i	1.22676	+	0.238134i
$406$		0			0
$407$			8.90351i			0.441330i
$408$		0			0
$409$	15.4851	+	26.8209i	0.765687	+	1.32621i	0.939883	+	0.341498i	$0.110934\pi$
$409$	15.4851	+	26.8209i	0.765687	+	1.32621i	−0.174196	+	0.984711i	$0.555733\pi$
$410$		0			0
$411$	17.7214	−	30.6943i	0.874130	−	1.51404i
$412$		0			0
$413$	−9.05035	+	17.9284i	−0.445339	+	0.882200i
$414$		0			0
$415$	−10.7243	−	9.31766i	−0.526433	−	0.457386i
$416$		0			0
$417$	−37.5251	+	21.6651i	−1.83761	+	1.06095i
$418$		0			0
$419$	−0.434578			−0.0212305			−0.0106153	−	0.999944i	$-0.503379\pi$
$419$	−0.434578			−0.0212305			−0.0106153	+	0.999944i	$0.503379\pi$
$420$		0			0
$421$	−27.3152			−1.33126			−0.665630	−	0.746282i	$-0.731837\pi$
$421$	−27.3152			−1.33126			−0.665630	+	0.746282i	$0.731837\pi$
$422$		0			0
$423$	−4.63286	+	2.67478i	−0.225257	+	0.130052i
$424$		0			0
$425$	−18.0755	−	23.1113i	−0.876789	−	1.12106i
$426$		0			0
$427$	23.0376	−	1.29411i	1.11487	−	0.0626263i
$428$		0			0
$429$	2.70232	−	4.68055i	0.130469	−	0.225979i
$430$		0			0
$431$	10.2637	+	17.7773i	0.494386	+	0.856302i	0.999979	−	0.00646986i	$-0.00205944\pi$
$431$	10.2637	+	17.7773i	0.494386	+	0.856302i	−0.505593	+	0.862772i	$0.668726\pi$
$432$		0			0
$433$		−	16.0082i		−	0.769304i	−0.923062	−	0.384652i	$-0.874321\pi$
$433$		−	16.0082i		−	0.769304i	0.923062	−	0.384652i	$-0.125679\pi$
$434$		0			0
$435$	5.80100	−	29.8842i	0.278137	−	1.43284i
$436$		0			0
$437$	4.11627	−	2.37653i	0.196908	−	0.113685i
$438$		0			0
$439$	4.03479	−	6.98846i	0.192570	−	0.333541i	−0.753531	−	0.657412i	$-0.771651\pi$
$439$	4.03479	−	6.98846i	0.192570	−	0.333541i	0.946101	+	0.323871i	$0.104984\pi$
$440$		0			0
$441$	6.00495	+	8.13590i	0.285950	+	0.387424i
$442$		0			0
$443$	6.22857	+	3.59607i	0.295928	+	0.170854i	0.640612	−	0.767864i	$-0.278681\pi$
$443$	6.22857	+	3.59607i	0.295928	+	0.170854i	−0.344684	+	0.938719i	$0.612014\pi$
$444$		0			0
$445$	−4.27034	−	12.3917i	−0.202433	−	0.587423i
$446$		0			0
$447$			44.8470i			2.12119i
$448$		0			0
$449$	4.16729			0.196667			0.0983334	−	0.995154i	$-0.468649\pi$
$449$	4.16729			0.196667			0.0983334	+	0.995154i	$0.468649\pi$
$450$		0			0
$451$	1.70689	+	2.95642i	0.0803743	+	0.139212i
$452$		0			0
$453$	11.8308	+	6.83051i	0.555859	+	0.320925i
$454$		0			0
$455$	−1.15546	+	8.46772i	−0.0541687	+	0.396973i
$456$		0			0
$457$	−7.94968	−	4.58975i	−0.371871	−	0.214700i	0.302405	−	0.953180i	$-0.402211\pi$
$457$	−7.94968	−	4.58975i	−0.371871	−	0.214700i	−0.674275	+	0.738480i	$0.735544\pi$
$458$		0			0
$459$	−9.62122	−	16.6644i	−0.449080	−	0.777829i
$460$		0			0
$461$	27.3537			1.27399			0.636995	−	0.770868i	$-0.280177\pi$
$461$	27.3537			1.27399			0.636995	+	0.770868i	$0.280177\pi$
$462$		0			0
$463$		−	12.8660i		−	0.597932i	−0.954264	−	0.298966i	$-0.903358\pi$
$463$		−	12.8660i		−	0.597932i	0.954264	−	0.298966i	$-0.0966418\pi$
$464$		0			0
$465$	−44.8950	+	15.4714i	−2.08196	+	0.717468i
$466$		0			0
$467$	−12.0386	−	6.95048i	−0.557079	−	0.321630i	0.194893	−	0.980824i	$-0.437564\pi$
$467$	−12.0386	−	6.95048i	−0.557079	−	0.321630i	−0.751972	+	0.659195i	$0.770897\pi$
$468$		0			0
$469$	−5.12130	−	2.58526i	−0.236480	−	0.119376i
$470$		0			0
$471$	5.74478	−	9.95026i	0.264706	−	0.458484i
$472$		0			0
$473$	8.94465	−	5.16419i	0.411275	−	0.237450i
$474$		0			0
$475$	−33.2095	−	13.3978i	−1.52376	−	0.614735i
$476$		0			0
$477$			0.855710i			0.0391803i
$478$		0			0
$479$	−0.185972	−	0.322113i	−0.00849729	−	0.0147177i	0.861745	−	0.507341i	$-0.169371\pi$
$479$	−0.185972	−	0.322113i	−0.00849729	−	0.0147177i	−0.870243	+	0.492623i	$0.836038\pi$
$480$		0			0
$481$	−3.62374	+	6.27649i	−0.165228	+	0.286184i
$482$		0			0
$483$	2.02773	+	3.09690i	0.0922648	+	0.140914i
$484$		0			0
$485$	24.9392	+	21.6682i	1.13243	+	0.983901i
$486$		0			0
$487$	−16.6572	+	9.61701i	−0.754808	+	0.435788i	−0.827428	−	0.561571i	$-0.810197\pi$
$487$	−16.6572	+	9.61701i	−0.754808	+	0.435788i	0.0726206	+	0.997360i	$0.476864\pi$
$488$		0			0
$489$	−13.2168			−0.597686
$490$		0			0
$491$	15.2267			0.687170			0.343585	−	0.939122i	$-0.388359\pi$
$491$	15.2267			0.687170			0.343585	+	0.939122i	$0.388359\pi$
$492$		0			0
$493$	−32.8170	+	18.9469i	−1.47800	+	0.853325i
$494$		0			0
$495$	−3.75969	+	4.32726i	−0.168986	+	0.194496i
$496$		0			0
$497$	−9.41793	−	14.3838i	−0.422452	−	0.645202i
$498$		0			0
$499$	6.97149	−	12.0750i	0.312087	−	0.540550i	−0.666727	−	0.745302i	$-0.732305\pi$
$499$	6.97149	−	12.0750i	0.312087	−	0.540550i	0.978814	+	0.204752i	$0.0656387\pi$
$500$		0			0
$501$	19.5777	+	33.9095i	0.874666	+	1.51497i
$502$		0			0
$503$		−	41.6394i		−	1.85661i	−0.371821	−	0.928305i	$-0.621266\pi$
$503$		−	41.6394i		−	1.85661i	0.371821	−	0.928305i	$-0.378734\pi$
$504$		0			0
$505$	−7.64300	−	1.48363i	−0.340109	−	0.0660207i
$506$		0			0
$507$	−19.9250	+	11.5037i	−0.884900	+	0.510897i
$508$		0			0
$509$	−15.5832	+	26.9908i	−0.690712	+	1.19635i	0.280893	+	0.959739i	$0.409369\pi$
$509$	−15.5832	+	26.9908i	−0.690712	+	1.19635i	−0.971605	+	0.236609i	$0.923964\pi$
$510$		0			0
$511$	−36.6846	−	18.5186i	−1.62283	−	0.819213i
$512$		0			0
$513$	−20.3392	−	11.7428i	−0.897996	−	0.518458i
$514$		0			0
$515$	17.0786	−	5.88551i	0.752575	−	0.259347i
$516$		0			0
$517$			6.57193i			0.289033i
$518$		0			0
$519$	−29.4459			−1.29253
$520$		0			0
$521$	4.95959	+	8.59026i	0.217284	+	0.376346i	0.953977	−	0.299881i	$-0.0969470\pi$
$521$	4.95959	+	8.59026i	0.217284	+	0.376346i	−0.736693	+	0.676227i	$0.763614\pi$
$522$		0			0
$523$	16.6572	+	9.61701i	0.728367	+	0.420523i	0.817824	−	0.575468i	$-0.195180\pi$
$523$	16.6572	+	9.61701i	0.728367	+	0.420523i	−0.0894577	+	0.995991i	$0.528513\pi$
$524$		0			0
$525$	8.96727	−	26.4081i	0.391364	−	1.15254i
$526$		0			0
$527$	51.1908	+	29.5550i	2.22990	+	1.28744i
$528$		0			0
$529$	−11.2798	−	19.5372i	−0.490426	−	0.849442i
$530$		0			0
$531$	−10.9654			−0.475857
$532$		0			0
$533$			2.77882i			0.120364i
$534$		0			0
$535$	0.274078	−	0.0944505i	0.0118494	−	0.00408345i
$536$		0			0
$537$	−14.4699	−	8.35421i	−0.624423	−	0.360511i
$538$		0			0
$539$	12.3444	−	1.39126i	0.531711	−	0.0599257i
$540$		0			0
$541$	1.80279	−	3.12253i	0.0775081	−	0.134248i	−0.824666	−	0.565620i	$-0.808637\pi$
$541$	1.80279	−	3.12253i	0.0775081	−	0.134248i	0.902174	+	0.431372i	$0.141970\pi$
$542$		0			0
$543$	21.3409	−	12.3212i	0.915824	−	0.528751i
$544$		0			0
$545$	26.9224	+	5.22608i	1.15323	+	0.223861i
$546$		0			0
$547$			11.1011i			0.474647i	0.971431	+	0.237324i	$0.0762702\pi$
$547$			11.1011i			0.474647i	−0.971431	+	0.237324i	$0.923730\pi$
$548$		0			0
$549$	6.29912	+	10.9104i	0.268840	+	0.465645i
$550$		0			0
$551$	−23.1249	+	40.0536i	−0.985156	+	1.70634i
$552$		0			0
$553$	7.15132	−	0.401717i	0.304105	−	0.0170828i
$554$		0			0
$555$	15.5119	−	17.8535i	0.658441	−	0.757840i
$556$		0			0
$557$	21.5074	−	12.4173i	0.911298	−	0.526138i	0.0304492	−	0.999536i	$-0.490306\pi$
$557$	21.5074	−	12.4173i	0.911298	−	0.526138i	0.880848	+	0.473398i	$0.156973\pi$
$558$		0			0
$559$	8.40733			0.355592
$560$		0			0
$561$	21.9545			0.926918
$562$		0			0
$563$	−2.44929	+	1.41410i	−0.103225	+	0.0595970i	−0.550724	−	0.834688i	$-0.685648\pi$
$563$	−2.44929	+	1.41410i	−0.103225	+	0.0595970i	0.447499	+	0.894285i	$0.352315\pi$
$564$		0			0
$565$	19.8279	+	17.2272i	0.834165	+	0.724756i
$566$		0			0
$567$	13.4095	−	26.5638i	0.563148	−	1.11558i
$568$		0			0
$569$	−12.5659	+	21.7648i	−0.526791	+	0.912429i	0.472722	+	0.881212i	$0.343272\pi$
$569$	−12.5659	+	21.7648i	−0.526791	+	0.912429i	−0.999513	+	0.0312168i	$0.990062\pi$
$570$		0			0
$571$	17.6047	+	30.4922i	0.736733	+	1.27606i	0.953959	+	0.299937i	$0.0969657\pi$
$571$	17.6047	+	30.4922i	0.736733	+	1.27606i	−0.217226	+	0.976121i	$0.569701\pi$
$572$		0			0
$573$			27.3607i			1.14301i
$574$		0			0
$575$	1.24146	−	3.07724i	0.0517726	−	0.128330i
$576$		0			0
$577$	24.1071	−	13.9182i	1.00359	−	0.579424i	0.0942822	−	0.995546i	$-0.469944\pi$
$577$	24.1071	−	13.9182i	1.00359	−	0.579424i	0.909309	+	0.416122i	$0.136611\pi$
$578$		0			0
$579$	−22.5635	+	39.0811i	−0.937705	+	1.62415i
$580$		0			0
$581$	−14.0632	+	9.20799i	−0.583439	+	0.382012i
$582$		0			0
$583$	0.910399	+	0.525619i	0.0377049	+	0.0217689i
$584$		0			0
$585$	−4.41158	+	1.52028i	−0.182396	+	0.0628560i
$586$		0			0
$587$		−	4.74640i		−	0.195905i	−0.995191	−	0.0979524i	$-0.968771\pi$
$587$		−	4.74640i		−	0.195905i	0.995191	−	0.0979524i	$-0.0312293\pi$
$588$		0			0
$589$	72.1445			2.97266
$590$		0			0
$591$	−8.88477	−	15.3889i	−0.365471	−	0.633014i
$592$		0			0
$593$	6.47860	+	3.74042i	0.266044	+	0.153601i	0.627089	−	0.778948i	$-0.284246\pi$
$593$	6.47860	+	3.74042i	0.266044	+	0.153601i	−0.361044	+	0.932549i	$0.617580\pi$
$594$		0			0
$595$	−32.1356	+	13.1338i	−1.31743	+	0.538432i
$596$		0			0
$597$	−7.69527	−	4.44286i	−0.314946	−	0.181834i
$598$		0			0
$599$	−2.28083	−	3.95051i	−0.0931920	−	0.161413i	0.815661	−	0.578531i	$-0.196374\pi$
$599$	−2.28083	−	3.95051i	−0.0931920	−	0.161413i	−0.908853	+	0.417117i	$0.863040\pi$
$600$		0			0
$601$	−4.96538			−0.202542			−0.101271	−	0.994859i	$-0.532291\pi$
$601$	−4.96538			−0.202542			−0.101271	+	0.994859i	$0.532291\pi$
$602$		0			0
$603$		−	3.13229i		−	0.127557i
$604$		0			0
$605$	−5.71941	−	16.5967i	−0.232527	−	0.674750i
$606$		0			0
$607$	−3.81333	−	2.20162i	−0.154778	−	0.0893612i	0.420611	−	0.907241i	$-0.361816\pi$
$607$	−3.81333	−	2.20162i	−0.154778	−	0.0893612i	−0.575389	+	0.817880i	$0.695149\pi$
$608$		0			0
$609$	−32.1548	−	16.2319i	−1.30298	−	0.657749i
$610$		0			0
$611$	−2.67478	+	4.63286i	−0.108210	+	0.187425i
$612$		0			0
$613$	−36.9750	+	21.3475i	−1.49340	+	0.862218i	−0.999971	−	0.00756572i	$-0.997592\pi$
$613$	−36.9750	+	21.3475i	−1.49340	+	0.862218i	−0.493434	+	0.869783i	$0.664258\pi$
$614$		0			0
$615$	1.72803	−	8.90206i	0.0696810	−	0.358966i
$616$		0			0
$617$		−	23.2135i		−	0.934541i	−0.884114	−	0.467270i	$-0.845237\pi$
$617$		−	23.2135i		−	0.934541i	0.884114	−	0.467270i	$-0.154763\pi$
$618$		0			0
$619$	−14.0067	−	24.2603i	−0.562977	−	0.975104i	−0.997235	−	0.0743159i	$-0.976323\pi$
$619$	−14.0067	−	24.2603i	−0.562977	−	0.975104i	0.434258	−	0.900789i	$-0.357011\pi$
$620$		0			0
$621$	1.08811	−	1.88465i	0.0436642	−	0.0756286i
$622$		0			0
$623$	−15.4839	+	0.869788i	−0.620348	+	0.0348473i
$624$		0			0
$625$	−24.0245	+	6.91539i	−0.960981	+	0.276616i
$626$		0			0
$627$	23.2058	−	13.3978i	0.926749	−	0.535059i
$628$		0			0
$629$	−29.4403			−1.17386
$630$		0			0
$631$	−28.8446			−1.14829			−0.574144	−	0.818755i	$-0.694665\pi$
$631$	−28.8446			−1.14829			−0.574144	+	0.818755i	$0.694665\pi$
$632$		0			0
$633$	1.14842	−	0.663038i	0.0456454	−	0.0263534i
$634$		0			0
$635$	21.4341	+	18.6228i	0.850588	+	0.739025i
$636$		0			0
$637$	9.26839	+	4.04342i	0.367227	+	0.160206i
$638$		0			0
$639$	4.69359	−	8.12954i	0.185676	−	0.321600i
$640$		0			0
$641$	20.5927	+	35.6676i	0.813363	+	1.40879i	0.910498	+	0.413514i	$0.135699\pi$
$641$	20.5927	+	35.6676i	0.813363	+	1.40879i	−0.0971347	+	0.995271i	$0.530968\pi$
$642$		0			0
$643$		−	7.64360i		−	0.301434i	−0.988577	−	0.150717i	$-0.951842\pi$
$643$		−	7.64360i		−	0.301434i	0.988577	−	0.150717i	$-0.0481583\pi$
$644$		0			0
$645$	−26.9332	−	5.22816i	−1.06049	−	0.205859i
$646$		0			0
$647$	−19.1717	+	11.0688i	−0.753717	+	0.435159i	−0.827035	−	0.562150i	$-0.809974\pi$
$647$	−19.1717	+	11.0688i	−0.753717	+	0.435159i	0.0733183	+	0.997309i	$0.476641\pi$
$648$		0			0
$649$	−6.73548	+	11.6662i	−0.264391	+	0.457938i
$650$		0			0
$651$	3.15123	+	56.0978i	0.123507	+	2.19865i
$652$		0			0
$653$	15.8506	+	9.15132i	0.620280	+	0.358119i	0.776978	−	0.629528i	$-0.216752\pi$
$653$	15.8506	+	9.15132i	0.620280	+	0.358119i	−0.156698	+	0.987647i	$0.550085\pi$
$654$		0			0
$655$	−0.168241	−	0.488203i	−0.00657371	−	0.0190757i
$656$		0			0
$657$		−	22.4370i		−	0.875353i
$658$		0			0
$659$	28.1377			1.09609			0.548044	−	0.836449i	$-0.315373\pi$
$659$	28.1377			1.09609			0.548044	+	0.836449i	$0.315373\pi$
$660$		0			0
$661$	11.6371	+	20.1560i	0.452630	+	0.783979i	0.998549	−	0.0538598i	$-0.0171524\pi$
$661$	11.6371	+	20.1560i	0.452630	+	0.783979i	−0.545918	+	0.837838i	$0.683819\pi$
$662$		0			0
$663$	15.4767	+	8.93548i	0.601066	+	0.347025i
$664$		0			0
$665$	−25.9523	+	33.4933i	−1.00639	+	1.29882i
$666$		0			0
$667$	−3.71142	−	2.14279i	−0.143707	−	0.0829691i
$668$		0			0
$669$	−22.5725	−	39.0967i	−0.872702	−	1.51156i
$670$		0			0
$671$	15.4769			0.597480
$672$		0			0
$673$		−	19.0282i		−	0.733484i	−0.930323	−	0.366742i	$-0.880473\pi$
$673$		−	19.0282i		−	0.733484i	0.930323	−	0.366742i	$-0.119527\pi$
$674$		0			0
$675$	−16.2352	+	2.29013i	−0.624892	+	0.0881472i
$676$		0			0
$677$	−35.2928	−	20.3763i	−1.35641	−	0.783124i	−0.367273	−	0.930113i	$-0.619708\pi$
$677$	−35.2928	−	20.3763i	−1.35641	−	0.783124i	−0.989138	+	0.146989i	$0.953042\pi$
$678$		0			0
$679$	32.7038	−	21.4131i	1.25506	−	0.821760i
$680$		0			0
$681$	−23.2423	+	40.2569i	−0.890648	+	1.54265i
$682$		0			0
$683$	−27.6456	+	15.9612i	−1.05783	+	0.610738i	−0.924831	−	0.380378i	$-0.875794\pi$
$683$	−27.6456	+	15.9612i	−1.05783	+	0.610738i	−0.132999	+	0.991116i	$0.542461\pi$
$684$		0			0
$685$	−7.16353	+	36.9033i	−0.273704	+	1.41000i
$686$		0			0
$687$			24.5311i			0.935918i
$688$		0			0
$689$	0.427855	+	0.741067i	0.0163000	+	0.0282324i
$690$		0			0
$691$	6.05622	−	10.4897i	0.230389	−	0.399046i	−0.727533	−	0.686072i	$-0.759333\pi$
$691$	6.05622	−	10.4897i	0.230389	−	0.399046i	0.957923	+	0.287026i	$0.0926667\pi$
$692$		0			0
$693$	3.71544	+	5.67451i	0.141138	+	0.215557i
$694$		0			0
$695$	30.1424	−	34.6927i	1.14337	−	1.31597i
$696$		0			0
$697$	−9.77570	+	5.64400i	−0.370281	+	0.213782i
$698$		0			0
$699$	−23.6528			−0.894631
$700$		0			0
$701$	−9.83067			−0.371299			−0.185650	−	0.982616i	$-0.559439\pi$
$701$	−9.83067			−0.371299			−0.185650	+	0.982616i	$0.559439\pi$
$702$		0			0
$703$	−31.1183	+	17.9662i	−1.17365	+	0.677606i
$704$		0			0
$705$	11.4497	−	13.1782i	0.431222	−	0.496319i
$706$		0			0
$707$	−4.15137	+	8.22371i	−0.156128	+	0.309284i
$708$		0			0
$709$	−4.61102	+	7.98651i	−0.173170	+	0.299940i	−0.939527	−	0.342476i	$-0.888734\pi$
$709$	−4.61102	+	7.98651i	−0.173170	+	0.299940i	0.766356	+	0.642416i	$0.222068\pi$
$710$		0			0
$711$	1.95537	+	3.38681i	0.0733322	+	0.127015i
$712$		0			0
$713$			6.68501i			0.250356i
$714$		0			0
$715$	−1.09236	+	5.62736i	−0.0408520	+	0.210451i
$716$		0			0
$717$	41.6785	−	24.0631i	1.55651	−	0.898653i
$718$		0			0
$719$	−16.2886	+	28.2128i	−0.607464	+	1.05216i	0.384193	+	0.923253i	$0.374480\pi$
$719$	−16.2886	+	28.2128i	−0.607464	+	1.05216i	−0.991657	+	0.128906i	$0.958854\pi$
$720$		0			0
$721$	−1.19877	−	21.3403i	−0.0446445	−	0.794756i
$722$		0			0
$723$	7.67316	+	4.43010i	0.285368	+	0.164757i
$724$		0			0
$725$	4.50992	+	31.9717i	0.167494	+	1.18740i
$726$		0			0
$727$		−	28.4462i		−	1.05501i	−0.849552	−	0.527505i	$-0.823128\pi$
$727$		−	28.4462i		−	1.05501i	0.849552	−	0.527505i	$-0.176872\pi$
$728$		0			0
$729$	−4.49268			−0.166396
$730$		0			0
$731$	17.0759	+	29.5764i	0.631576	+	1.09392i
$732$		0			0
$733$	−8.32604	−	4.80704i	−0.307529	−	0.177552i	0.338291	−	0.941042i	$-0.390151\pi$
$733$	−8.32604	−	4.80704i	−0.307529	−	0.177552i	−0.645820	+	0.763489i	$0.723484\pi$
$734$		0			0
$735$	−27.1772	−	18.7169i	−1.00244	−	0.690382i
$736$		0			0
$737$	−3.33248	−	1.92401i	−0.122753	−	0.0708717i
$738$		0			0
$739$	1.94205	+	3.36372i	0.0714393	+	0.123736i	0.899532	−	0.436854i	$-0.143907\pi$
$739$	1.94205	+	3.36372i	0.0714393	+	0.123736i	−0.828093	+	0.560591i	$0.810574\pi$
$740$		0			0
$741$	21.8118			0.801275
$742$		0			0
$743$			16.8174i			0.616971i	0.951229	+	0.308486i	$0.0998222\pi$
$743$			16.8174i			0.616971i	−0.951229	+	0.308486i	$0.900178\pi$
$744$		0			0
$745$	−15.4977	−	44.9713i	−0.567791	−	1.64762i
$746$		0			0
$747$	−7.94832	−	4.58897i	−0.290814	−	0.167901i
$748$		0			0
$749$	−0.0192378	−	0.342469i	−0.000702935	−	0.0125135i
$750$		0			0
$751$	16.6827	−	28.8953i	0.608760	−	1.05440i	−0.382685	−	0.923879i	$-0.625000\pi$
$751$	16.6827	−	28.8953i	0.608760	−	1.05440i	0.991445	−	0.130525i	$-0.0416662\pi$
$752$		0			0
$753$	30.9626	−	17.8763i	1.12834	−	0.651448i
$754$		0			0
$755$	−14.2240	−	2.76111i	−0.517664	−	0.100487i
$756$		0			0
$757$			31.2781i			1.13682i	0.822744	+	0.568412i	$0.192442\pi$
$757$			31.2781i			1.13682i	−0.822744	+	0.568412i	$0.807558\pi$
$758$		0			0
$759$	1.24146	+	2.15028i	0.0450622	+	0.0780501i
$760$		0			0
$761$	−1.41224	+	2.44608i	−0.0511937	+	0.0886702i	−0.890487	−	0.455009i	$-0.849636\pi$
$761$	−1.41224	+	2.44608i	−0.0511937	+	0.0886702i	0.839293	+	0.543679i	$0.182969\pi$
$762$		0			0
$763$	14.6232	−	28.9680i	0.529394	−	1.04871i
$764$		0			0
$765$	−14.3085	−	12.4318i	−0.517325	−	0.449473i
$766$		0			0
$767$	−9.49630	+	5.48269i	−0.342892	+	0.197969i
$768$		0			0
$769$	29.1637			1.05167			0.525836	−	0.850586i	$-0.323753\pi$
$769$	29.1637			1.05167			0.525836	+	0.850586i	$0.323753\pi$
$770$		0			0
$771$	56.7748			2.04469
$772$		0			0
$773$	35.3151	−	20.3892i	1.27020	−	0.733348i	0.295171	−	0.955444i	$-0.404623\pi$
$773$	35.3151	−	20.3892i	1.27020	−	0.733348i	0.975025	+	0.222096i	$0.0712899\pi$
$774$		0			0
$775$	39.6730	−	31.0285i	1.42510	−	1.11458i
$776$		0			0
$777$	−15.3293	−	23.4121i	−0.549935	−	0.839903i
$778$		0			0
$779$	−6.88858	+	11.9314i	−0.246809	+	0.427486i
$780$		0			0
$781$	−5.76607	−	9.98713i	−0.206326	−	0.357367i
$782$		0			0
$783$			21.1758i			0.756760i
$784$		0			0
$785$	−2.32222	+	11.9631i	−0.0828837	+	0.426980i
$786$		0			0
$787$	7.14650	−	4.12603i	0.254745	−	0.147077i	−0.367190	−	0.930146i	$-0.619680\pi$
$787$	7.14650	−	4.12603i	0.254745	−	0.147077i	0.621935	+	0.783069i	$0.286347\pi$
$788$		0			0
$789$	23.1398	−	40.0793i	0.823798	−	1.42686i
$790$		0			0
$791$	26.0011	−	17.0245i	0.924494	−	0.605321i
$792$		0			0
$793$	10.9104	+	6.29912i	0.387440	+	0.223688i
$794$		0			0
$795$	−0.909810	−	2.64010i	−0.0322676	−	0.0936346i
$796$		0			0
$797$		−	39.6687i		−	1.40514i	−0.711616	−	0.702569i	$-0.752036\pi$
$797$		−	39.6687i		−	1.40514i	0.711616	−	0.702569i	$-0.247964\pi$
$798$		0			0
$799$	−21.7307			−0.768779
$800$		0			0
$801$	−4.23373	−	7.33303i	−0.149591	−	0.259100i
$802$		0			0
$803$	−23.8710	−	13.7819i	−0.842390	−	0.486354i
$804$		0			0
$805$	−3.10354	−	2.40477i	−0.109385	−	0.0847571i
$806$		0			0
$807$	−43.9743	−	25.3886i	−1.54797	−	0.893721i
$808$		0			0
$809$	−16.1578	−	27.9861i	−0.568078	−	0.983940i	−0.996756	−	0.0804828i	$-0.974354\pi$
$809$	−16.1578	−	27.9861i	−0.568078	−	0.983940i	0.428678	−	0.903457i	$-0.358980\pi$
$810$		0			0
$811$	7.67248			0.269417			0.134709	−	0.990885i	$-0.456990\pi$
$811$	7.67248			0.269417			0.134709	+	0.990885i	$0.456990\pi$
$812$		0			0
$813$		−	4.35833i		−	0.152853i
$814$		0			0
$815$	13.2535	−	4.56731i	0.464249	−	0.159986i
$816$		0			0
$817$	36.0983	+	20.8414i	1.26292	+	0.729148i
$818$		0			0
$819$	0.309654	+	5.51242i	0.0108202	+	0.192619i
$820$		0			0
$821$	−8.52811	+	14.7711i	−0.297633	+	0.515515i	−0.975594	−	0.219582i	$-0.929530\pi$
$821$	−8.52811	+	14.7711i	−0.297633	+	0.515515i	0.677961	+	0.735098i	$0.262864\pi$
$822$		0			0
$823$	28.6675	−	16.5512i	0.999288	−	0.576939i	0.0912502	−	0.995828i	$-0.470914\pi$
$823$	28.6675	−	16.5512i	0.999288	−	0.576939i	0.908037	+	0.418889i	$0.137580\pi$
$824$		0			0
$825$	6.99884	−	17.3481i	0.243668	−	0.603985i
$826$		0			0
$827$			20.1051i			0.699123i	0.936913	+	0.349561i	$0.113669\pi$
$827$			20.1051i			0.699123i	−0.936913	+	0.349561i	$0.886331\pi$
$828$		0			0
$829$	9.48334	+	16.4256i	0.329370	+	0.570486i	0.982387	−	0.186858i	$-0.0598303\pi$
$829$	9.48334	+	16.4256i	0.329370	+	0.570486i	−0.653017	+	0.757343i	$0.726497\pi$
$830$		0			0
$831$	−17.9996	+	31.1763i	−0.624400	+	1.08149i
$832$		0			0
$833$	4.60033	+	40.8180i	0.159392	+	1.41426i
$834$		0			0
$835$	−31.3500	−	27.2381i	−1.08491	−	0.942614i
$836$		0			0
$837$	28.6063	−	16.5159i	0.988779	−	0.570872i
$838$		0			0
$839$	−4.15025			−0.143283			−0.0716413	−	0.997430i	$-0.522824\pi$
$839$	−4.15025			−0.143283			−0.0716413	+	0.997430i	$0.522824\pi$
$840$		0			0
$841$	12.7010			0.437967
$842$		0			0
$843$	24.1065	−	13.9179i	0.830273	−	0.479358i
$844$		0			0
$845$	16.0049	−	18.4210i	0.550586	−	0.633702i
$846$		0			0
$847$	−20.7381	+	1.16494i	−0.712569	+	0.0400278i
$848$		0			0
$849$	28.0381	−	48.5634i	0.962265	−	1.66669i
$850$		0			0
$851$	−1.66477	−	2.88346i	−0.0570675	−	0.0988439i
$852$		0			0
$853$		−	1.53140i		−	0.0524340i	−0.999656	−	0.0262170i	$-0.991654\pi$
$853$		−	1.53140i		−	0.0524340i	0.999656	−	0.0262170i	$-0.00834609\pi$
$854$		0			0
$855$	−22.7106	−	4.40850i	−0.776686	−	0.150767i
$856$		0			0
$857$	20.6317	−	11.9117i	0.704766	−	0.406897i	−0.104354	−	0.994540i	$-0.533278\pi$
$857$	20.6317	−	11.9117i	0.704766	−	0.406897i	0.809120	+	0.587643i	$0.199944\pi$
$858$		0			0
$859$	7.34165	−	12.7161i	0.250494	−	0.433868i	−0.713168	−	0.700993i	$-0.752740\pi$
$859$	7.34165	−	12.7161i	0.250494	−	0.433868i	0.963662	+	0.267125i	$0.0860737\pi$
$860$		0			0
$861$	−9.57843	−	4.83524i	−0.326432	−	0.164784i
$862$		0			0
$863$	−36.6611	−	21.1663i	−1.24796	−	0.720508i	−0.277255	−	0.960796i	$-0.589425\pi$
$863$	−36.6611	−	21.1663i	−1.24796	−	0.720508i	−0.970702	+	0.240288i	$0.922758\pi$
$864$		0			0
$865$	29.5275	−	10.1755i	1.00397	−	0.345979i
$866$		0			0
$867$			36.7549i			1.24826i
$868$		0			0
$869$	4.80434			0.162976
$870$		0			0
$871$	−1.56615	−	2.71264i	−0.0530668	−	0.0919144i
$872$		0			0
$873$	18.4838	+	10.6716i	0.625581	+	0.361179i
$874$		0			0
$875$	0.133659	+	29.5801i	0.00451849	+	0.999990i
$876$		0			0
$877$	−9.17470	−	5.29702i	−0.309808	−	0.178868i	0.337033	−	0.941493i	$-0.390577\pi$
$877$	−9.17470	−	5.29702i	−0.309808	−	0.178868i	−0.646840	+	0.762625i	$0.723910\pi$
$878$		0			0
$879$	−0.498256	−	0.863005i	−0.0168058	−	0.0291084i
$880$		0			0
$881$	27.1174			0.913609			0.456805	−	0.889567i	$-0.348994\pi$
$881$	27.1174			0.913609			0.456805	+	0.889567i	$0.348994\pi$
$882$		0			0
$883$			21.7240i			0.731072i	0.930797	+	0.365536i	$0.119114\pi$
$883$			21.7240i			0.731072i	−0.930797	+	0.365536i	$0.880886\pi$
$884$		0			0
$885$	33.8312	−	11.6586i	1.13722	−	0.391901i
$886$		0			0
$887$	18.3256	+	10.5803i	0.615312	+	0.355251i	0.775042	−	0.631910i	$-0.217729\pi$
$887$	18.3256	+	10.5803i	0.615312	+	0.355251i	−0.159729	+	0.987161i	$0.551062\pi$
$888$		0			0
$889$	28.1075	−	18.4036i	0.942695	−	0.617238i
$890$		0			0
$891$	9.97969	−	17.2853i	0.334332	−	0.579080i
$892$		0			0
$893$	−22.9693	+	13.2613i	−0.768638	+	0.443774i
$894$		0			0
$895$	17.3970	+	3.37704i	0.581517	+	0.112882i
$896$		0			0
$897$			2.02111i			0.0674828i
$898$		0			0
$899$	−32.5244	−	56.3340i	−1.08475	−	1.87884i
$900$		0			0
$901$	−1.73801	+	3.01033i	−0.0579016	+	0.100288i
$902$		0			0
$903$	−14.6290	+	28.9795i	−0.486823	+	0.964378i
$904$		0			0
$905$	−17.1422	+	19.7300i	−0.569827	+	0.655848i
$906$		0			0
$907$	−32.7913	+	18.9321i	−1.08882	+	0.628630i	−0.933262	−	0.359197i	$-0.883051\pi$
$907$	−32.7913	+	18.9321i	−1.08882	+	0.628630i	−0.155557	+	0.987827i	$0.549717\pi$
$908$		0			0
$909$	−5.02978			−0.166827
$910$		0			0
$911$	−30.1221			−0.997990			−0.498995	−	0.866605i	$-0.666297\pi$
$911$	−30.1221			−0.997990			−0.498995	+	0.866605i	$0.666297\pi$
$912$		0			0
$913$	−9.76450	+	5.63753i	−0.323158	+	0.186575i
$914$		0			0
$915$	−31.0347	−	26.9642i	−1.02597	−	0.891408i
$916$		0			0
$917$	−0.610026	+	0.0342675i	−0.0201448	+	0.00113161i
$918$		0			0
$919$	−23.0566	+	39.9352i	−0.760566	+	1.31734i	0.181993	+	0.983300i	$0.441745\pi$
$919$	−23.0566	+	39.9352i	−0.760566	+	1.31734i	−0.942559	+	0.334040i	$0.891588\pi$
$920$		0			0
$921$	−16.0302	−	27.7651i	−0.528212	−	0.914891i
$922$		0			0
$923$		−	9.38718i		−	0.308983i
$924$		0			0
$925$	−9.38525	+	23.2634i	−0.308585	+	0.764896i
$926$		0			0
$927$	10.1066	−	5.83506i	0.331945	−	0.191648i
$928$		0			0
$929$	13.7587	−	23.8308i	0.451408	−	0.781862i	−0.547066	−	0.837090i	$-0.684255\pi$
$929$	13.7587	−	23.8308i	0.451408	−	0.781862i	0.998474	+	0.0552279i	$0.0175885\pi$
$930$		0			0
$931$	29.7720	+	40.3371i	0.975738	+	1.32199i
$932$		0			0
$933$	−30.2723	−	17.4777i	−0.991071	−	0.572195i
$934$		0			0
$935$	−22.0153	+	7.58675i	−0.719978	+	0.248113i
$936$		0			0
$937$			50.4704i			1.64880i	0.566010	+	0.824399i	$0.308486\pi$
$937$			50.4704i			1.64880i	−0.566010	+	0.824399i	$0.691514\pi$
$938$		0			0
$939$	2.48665			0.0811487
$940$		0			0
$941$	−0.928314	−	1.60789i	−0.0302622	−	0.0524156i	0.850498	−	0.525979i	$-0.176301\pi$
$941$	−0.928314	−	1.60789i	−0.0302622	−	0.0524156i	−0.880760	+	0.473563i	$0.842968\pi$
$942$		0			0
$943$	−1.10558	−	0.638305i	−0.0360025	−	0.0207861i
$944$		0			0
$945$	−2.62289	+	19.2218i	−0.0853228	+	0.625284i
$946$		0			0
$947$	31.3232	+	18.0844i	1.01787	+	0.587666i	0.913485	−	0.406872i	$-0.133380\pi$
$947$	31.3232	+	18.0844i	1.01787	+	0.587666i	0.104381	+	0.994537i	$0.466714\pi$
$948$		0			0
$949$	−11.2185	−	19.4311i	−0.364169	−	0.630759i
$950$		0			0
$951$	−57.8258			−1.87513
$952$		0			0
$953$		−	17.3367i		−	0.561590i	−0.959768	−	0.280795i	$-0.909402\pi$
$953$		−	17.3367i		−	0.561590i	0.959768	−	0.280795i	$-0.0905981\pi$
$954$		0			0
$955$	−9.45498	−	27.4366i	−0.305956	−	0.887827i
$956$		0			0
$957$	−20.9234	−	12.0801i	−0.676357	−	0.390495i
$958$		0			0
$959$	39.7072	+	20.0444i	1.28221	+	0.647267i
$960$		0			0
$961$	−35.2344	+	61.0277i	−1.13659	+	1.96864i
$962$		0			0
$963$	0.162191	−	0.0936408i	0.00522652	−	0.00301753i
$964$		0			0
$965$	9.12086	−	46.9866i	0.293611	−	1.51255i
$966$		0			0
$967$			23.4618i			0.754480i	0.926116	+	0.377240i	$0.123127\pi$
$967$			23.4618i			0.754480i	−0.926116	+	0.377240i	$0.876873\pi$
$968$		0			0
$969$	44.3013	+	76.7322i	1.42316	+	2.46499i
$970$		0			0
$971$	28.2777	−	48.9783i	0.907473	−	1.57179i	0.0899104	−	0.995950i	$-0.471342\pi$
$971$	28.2777	−	48.9783i	0.907473	−	1.57179i	0.817563	−	0.575840i	$-0.195325\pi$
$972$		0			0
$973$	−29.7876	−	45.4940i	−0.954946	−	1.45847i
$974$		0			0
$975$	11.9945	−	9.38098i	0.384132	−	0.300432i
$976$		0			0
$977$	−25.0960	+	14.4892i	−0.802891	+	0.463549i	−0.844481	−	0.535585i	$-0.820091\pi$
$977$	−25.0960	+	14.4892i	−0.802891	+	0.463549i	0.0415899	+	0.999135i	$0.486758\pi$
$978$		0			0
$979$	−10.4022			−0.332457
$980$		0			0
$981$	17.7174			0.565673
$982$		0			0
$983$	35.7911	−	20.6640i	1.14156	−	0.659079i	0.194742	−	0.980854i	$-0.437613\pi$
$983$	35.7911	−	20.6640i	1.14156	−	0.659079i	0.946816	+	0.321776i	$0.104280\pi$
$984$		0			0
$985$	14.2273	+	12.3612i	0.453319	+	0.393862i
$986$		0			0
$987$	−11.3150	−	17.2811i	−0.360160	−	0.550064i
$988$		0			0
$989$	−1.93119	+	3.34492i	−0.0614083	+	0.106362i
$990$		0			0
$991$	14.5449	+	25.1924i	0.462032	+	0.800264i	0.999062	−	0.0432996i	$-0.0137870\pi$
$991$	14.5449	+	25.1924i	0.462032	+	0.800264i	−0.537030	+	0.843563i	$0.680454\pi$
$992$		0			0
$993$		−	10.9872i		−	0.348667i
$994$		0			0
$995$	9.25191	+	1.79595i	0.293305	+	0.0569353i
$996$		0			0
$997$	−18.5965	+	10.7367i	−0.588957	+	0.340035i	−0.764685	−	0.644404i	$-0.777105\pi$
$997$	−18.5965	+	10.7367i	−0.588957	+	0.340035i	0.175728	+	0.984439i	$0.443772\pi$
$998$		0			0
$999$	−8.22590	+	14.2477i	−0.260256	+	0.450777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bg.a.9.3	✓	24
4.3	odd	2		560.2.bw.f.289.10		24
5.2	odd	4		1400.2.q.o.401.5		12
5.3	odd	4		1400.2.q.n.401.2		12
5.4	even	2	inner	280.2.bg.a.9.10	yes	24
7.2	even	3		1960.2.g.f.1569.3		12
7.4	even	3	inner	280.2.bg.a.249.10	yes	24
7.5	odd	6		1960.2.g.e.1569.10		12
20.19	odd	2		560.2.bw.f.289.3		24
28.11	odd	6		560.2.bw.f.529.3		24
35.2	odd	12		9800.2.a.cv.1.2		6
35.4	even	6	inner	280.2.bg.a.249.3	yes	24
35.9	even	6		1960.2.g.f.1569.10		12
35.12	even	12		9800.2.a.cy.1.5		6
35.18	odd	12		1400.2.q.n.1201.2		12
35.19	odd	6		1960.2.g.e.1569.3		12
35.23	odd	12		9800.2.a.cx.1.5		6
35.32	odd	12		1400.2.q.o.1201.5		12
35.33	even	12		9800.2.a.cw.1.2		6
140.39	odd	6		560.2.bw.f.529.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.3	✓	24	1.1	even	1	trivial
280.2.bg.a.9.10	yes	24	5.4	even	2	inner
280.2.bg.a.249.3	yes	24	35.4	even	6	inner
280.2.bg.a.249.10	yes	24	7.4	even	3	inner
560.2.bw.f.289.3		24	20.19	odd	2
560.2.bw.f.289.10		24	4.3	odd	2
560.2.bw.f.529.3		24	28.11	odd	6
560.2.bw.f.529.10		24	140.39	odd	6
1400.2.q.n.401.2		12	5.3	odd	4
1400.2.q.n.1201.2		12	35.18	odd	12
1400.2.q.o.401.5		12	5.2	odd	4
1400.2.q.o.1201.5		12	35.32	odd	12
1960.2.g.e.1569.3		12	35.19	odd	6
1960.2.g.e.1569.10		12	7.5	odd	6
1960.2.g.f.1569.3		12	7.2	even	3
1960.2.g.f.1569.10		12	35.9	even	6
9800.2.a.cv.1.2		6	35.2	odd	12
9800.2.a.cw.1.2		6	35.33	even	12
9800.2.a.cx.1.5		6	35.23	odd	12
9800.2.a.cy.1.5		6	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82577 + 1.05411i) q^{3} +(1.46656 - 1.68796i) q^{5} +(-1.44930 - 2.21349i) q^{7} +(0.722285 - 1.25103i) q^{9} +O(q^{10})\)	\(q+(-1.82577 + 1.05411i) q^{3} +(1.46656 - 1.68796i) q^{5} +(-1.44930 - 2.21349i) q^{7} +(0.722285 - 1.25103i) q^{9} +(-0.887326 - 1.53689i) q^{11} -1.44457i q^{13} +(-0.898317 + 4.62773i) q^{15} +(5.08189 - 2.93403i) q^{17} +(3.58102 - 6.20251i) q^{19} +(4.97934 + 2.51359i) q^{21} +(0.574733 + 0.331822i) q^{23} +(-0.698386 - 4.95099i) q^{25} -3.27918i q^{27} -6.45763 q^{29} +(5.03658 + 8.72362i) q^{31} +(3.24010 + 1.87067i) q^{33} +(-5.86176 - 0.799863i) q^{35} +(-4.34489 - 2.50852i) q^{37} +(1.52273 + 2.63745i) q^{39} -1.92363 q^{41} +5.81995i q^{43} +(-1.05241 - 3.05391i) q^{45} +(-3.20709 - 1.85161i) q^{47} +(-2.79905 + 6.41602i) q^{49} +(-6.18557 + 10.7137i) q^{51} +(-0.513002 + 0.296182i) q^{53} +(-3.89553 - 0.756185i) q^{55} +15.0991i q^{57} +(-3.79538 - 6.57379i) q^{59} +(-4.36055 + 7.55270i) q^{61} +(-3.81596 + 0.214357i) q^{63} +(-2.43837 - 2.11855i) q^{65} +(1.87782 - 1.08416i) q^{67} -1.39911 q^{69} +6.49826 q^{71} +(13.4511 - 7.76600i) q^{73} +(6.49396 + 8.30318i) q^{75} +(-2.11589 + 4.19151i) q^{77} +(-1.35360 + 2.34451i) q^{79} +(5.62346 + 9.74012i) q^{81} -6.35340i q^{83} +(2.50040 - 12.8809i) q^{85} +(11.7901 - 6.80704i) q^{87} +(2.93079 - 5.07627i) q^{89} +(-3.19754 + 2.09362i) q^{91} +(-18.3913 - 10.6182i) q^{93} +(-5.21777 - 15.1410i) q^{95} +14.7748i q^{97} -2.56361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{9}+O(q^{10}) \) 24 * q + 14 * q^9	\( 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) \) 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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