LMFDB - Embedded newform 400.2.bi.d.303.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(47,400)] 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("400.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,0,4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			303.1
Character	$\chi$	$=$	400.303
Dual form			400.2.bi.d.367.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.10308 + 0.491480i) q^{3} +(-0.657061 - 2.13735i) q^{5} +(-1.48242 - 1.48242i) q^{7} +(6.53441 - 2.12316i) q^{9} +(1.78975 + 0.581525i) q^{11} +(-3.02736 + 5.94154i) q^{13} +(3.08938 + 6.30945i) q^{15} +(0.378869 - 2.39209i) q^{17} +(-2.43438 + 1.76868i) q^{19} +(5.32864 + 3.87148i) q^{21} +(2.55503 + 5.01453i) q^{23} +(-4.13654 + 2.80874i) q^{25} +(-10.8353 + 5.52089i) q^{27} +(-2.79473 + 3.84662i) q^{29} +(1.62620 + 2.23827i) q^{31} +(-5.83955 - 0.924894i) q^{33} +(-2.19440 + 4.14248i) q^{35} +(3.13777 + 1.59877i) q^{37} +(6.47402 - 19.9250i) q^{39} +(2.32964 + 7.16989i) q^{41} +(8.80325 - 8.80325i) q^{43} +(-8.83145 - 12.5713i) q^{45} +(1.05721 + 6.67497i) q^{47} -2.60489i q^{49} +7.60906i q^{51} +(1.14017 + 7.19877i) q^{53} +(0.0669477 - 4.20742i) q^{55} +(6.68480 - 6.68480i) q^{57} +(-0.807784 - 2.48610i) q^{59} +(-0.283453 + 0.872379i) q^{61} +(-12.8341 - 6.53931i) q^{63} +(14.6883 + 2.56659i) q^{65} +(-8.27337 - 1.31037i) q^{67} +(-10.3930 - 14.3048i) q^{69} +(-5.33283 + 7.34002i) q^{71} +(1.04647 - 0.533201i) q^{73} +(11.4556 - 10.7488i) q^{75} +(-1.79109 - 3.51521i) q^{77} +(4.61218 + 3.35095i) q^{79} +(14.2341 - 10.3417i) q^{81} +(0.967254 - 6.10700i) q^{83} +(-5.36167 + 0.761971i) q^{85} +(6.78175 - 13.3099i) q^{87} +(0.0514581 + 0.0167197i) q^{89} +(13.2956 - 4.32001i) q^{91} +(-6.14629 - 6.14629i) q^{93} +(5.37982 + 4.04099i) q^{95} +(-15.5905 + 2.46930i) q^{97} +12.9296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$-1$

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			0
$2$		0			0
$3$	−3.10308	+	0.491480i	−1.79157	+	0.283756i	−0.961680	−	0.274175i	$-0.911595\pi$
$3$	−3.10308	+	0.491480i	−1.79157	+	0.283756i	−0.829887	+	0.557931i	$0.811595\pi$
$4$		0			0
$5$	−0.657061	−	2.13735i	−0.293847	−	0.955853i
$5$	−0.657061	−	2.13735i	−0.293847	−	0.955853i
$6$		0			0
$7$	−1.48242	−	1.48242i	−0.560300	−	0.560300i	0.369092	−	0.929393i	$-0.379669\pi$
$7$	−1.48242	−	1.48242i	−0.560300	−	0.560300i	−0.929393	+	0.369092i	$0.879669\pi$
$8$		0			0
$9$	6.53441	−	2.12316i	2.17814	−	0.707720i
$10$		0			0
$11$	1.78975	+	0.581525i	0.539630	+	0.175336i	0.566135	−	0.824312i	$-0.308438\pi$
$11$	1.78975	+	0.581525i	0.539630	+	0.175336i	−0.0265057	+	0.999649i	$0.508438\pi$
$12$		0			0
$13$	−3.02736	+	5.94154i	−0.839640	+	1.64789i	−0.0806872	+	0.996739i	$0.525711\pi$
$13$	−3.02736	+	5.94154i	−0.839640	+	1.64789i	−0.758952	+	0.651146i	$0.774289\pi$
$14$		0			0
$15$	3.08938	+	6.30945i	0.797675	+	1.62909i
$16$		0			0
$17$	0.378869	−	2.39209i	0.0918893	−	0.580166i	−0.898185	−	0.439619i	$-0.855114\pi$
$17$	0.378869	−	2.39209i	0.0918893	−	0.580166i	0.990074	−	0.140548i	$-0.0448864\pi$
$18$		0			0
$19$	−2.43438	+	1.76868i	−0.558484	+	0.405762i	−0.830904	−	0.556416i	$-0.812176\pi$
$19$	−2.43438	+	1.76868i	−0.558484	+	0.405762i	0.272420	+	0.962179i	$0.412176\pi$
$20$		0			0
$21$	5.32864	+	3.87148i	1.16280	+	0.844827i
$22$		0			0
$23$	2.55503	+	5.01453i	0.532761	+	1.04560i	0.987887	+	0.155175i	$0.0495940\pi$
$23$	2.55503	+	5.01453i	0.532761	+	1.04560i	−0.455126	+	0.890427i	$0.650406\pi$
$24$		0			0
$25$	−4.13654	+	2.80874i	−0.827308	+	0.561748i
$26$		0			0
$27$	−10.8353	+	5.52089i	−2.08526	+	1.06250i
$28$		0			0
$29$	−2.79473	+	3.84662i	−0.518968	+	0.714299i	−0.985399	−	0.170259i	$-0.945540\pi$
$29$	−2.79473	+	3.84662i	−0.518968	+	0.714299i	0.466431	+	0.884558i	$0.345540\pi$
$30$		0			0
$31$	1.62620	+	2.23827i	0.292073	+	0.402005i	0.929686	−	0.368352i	$-0.120078\pi$
$31$	1.62620	+	2.23827i	0.292073	+	0.402005i	−0.637613	+	0.770357i	$0.720078\pi$
$32$		0			0
$33$	−5.83955	−	0.924894i	−1.01654	−	0.161003i
$34$		0			0
$35$	−2.19440	+	4.14248i	−0.370922	+	0.700207i
$36$		0			0
$37$	3.13777	+	1.59877i	0.515845	+	0.262836i	0.692476	−	0.721441i	$-0.256520\pi$
$37$	3.13777	+	1.59877i	0.515845	+	0.262836i	−0.176631	+	0.984277i	$0.556520\pi$
$38$		0			0
$39$	6.47402	−	19.9250i	1.03667	−	3.19055i
$40$		0			0
$41$	2.32964	+	7.16989i	0.363828	+	1.11975i	0.950711	+	0.310077i	$0.100355\pi$
$41$	2.32964	+	7.16989i	0.363828	+	1.11975i	−0.586883	+	0.809672i	$0.699645\pi$
$42$		0			0
$43$	8.80325	−	8.80325i	1.34248	−	1.34248i	0.448901	−	0.893581i	$-0.351816\pi$
$43$	8.80325	−	8.80325i	1.34248	−	1.34248i	0.893581	−	0.448901i	$-0.148184\pi$
$44$		0			0
$45$	−8.83145	−	12.5713i	−1.31651	−	1.87402i
$46$		0			0
$47$	1.05721	+	6.67497i	0.154210	+	0.973644i	0.936484	+	0.350710i	$0.114060\pi$
$47$	1.05721	+	6.67497i	0.154210	+	0.973644i	−0.782274	+	0.622934i	$0.785940\pi$
$48$		0			0
$49$		−	2.60489i		−	0.372127i
$50$		0			0
$51$			7.60906i			1.06548i
$52$		0			0
$53$	1.14017	+	7.19877i	0.156615	+	0.988826i	0.933342	+	0.358989i	$0.116878\pi$
$53$	1.14017	+	7.19877i	0.156615	+	0.988826i	−0.776727	+	0.629837i	$0.783122\pi$
$54$		0			0
$55$	0.0669477	−	4.20742i	0.00902723	−	0.567328i
$56$		0			0
$57$	6.68480	−	6.68480i	0.885424	−	0.885424i
$58$		0			0
$59$	−0.807784	−	2.48610i	−0.105165	−	0.323663i	0.884604	−	0.466342i	$-0.154428\pi$
$59$	−0.807784	−	2.48610i	−0.105165	−	0.323663i	−0.989769	+	0.142679i	$0.954428\pi$
$60$		0			0
$61$	−0.283453	+	0.872379i	−0.0362924	+	0.111697i	−0.967562	−	0.252635i	$-0.918703\pi$
$61$	−0.283453	+	0.872379i	−0.0362924	+	0.111697i	0.931269	+	0.364332i	$0.118703\pi$
$62$		0			0
$63$	−12.8341	−	6.53931i	−1.61695	−	0.823876i
$64$		0			0
$65$	14.6883	+	2.56659i	1.82186	+	0.318346i
$66$		0			0
$67$	−8.27337	−	1.31037i	−1.01075	−	0.160088i	−0.370972	−	0.928644i	$-0.620975\pi$
$67$	−8.27337	−	1.31037i	−1.01075	−	0.160088i	−0.639782	+	0.768557i	$0.720975\pi$
$68$		0			0
$69$	−10.3930	−	14.3048i	−1.25117	−	1.72209i
$70$		0			0
$71$	−5.33283	+	7.34002i	−0.632891	+	0.871100i	−0.998211	−	0.0597821i	$-0.980959\pi$
$71$	−5.33283	+	7.34002i	−0.632891	+	0.871100i	0.365320	+	0.930882i	$0.380959\pi$
$72$		0			0
$73$	1.04647	−	0.533201i	0.122480	−	0.0624065i	−0.391677	−	0.920103i	$-0.628105\pi$
$73$	1.04647	−	0.533201i	0.122480	−	0.0624065i	0.514157	+	0.857696i	$0.328105\pi$
$74$		0			0
$75$	11.4556	−	10.7488i	1.32278	−	1.24116i
$76$		0			0
$77$	−1.79109	−	3.51521i	−0.204114	−	0.400596i
$78$		0			0
$79$	4.61218	+	3.35095i	0.518911	+	0.377011i	0.816194	−	0.577779i	$-0.196080\pi$
$79$	4.61218	+	3.35095i	0.518911	+	0.377011i	−0.297282	+	0.954790i	$0.596080\pi$
$80$		0			0
$81$	14.2341	−	10.3417i	1.58157	−	1.14907i
$82$		0			0
$83$	0.967254	−	6.10700i	0.106170	−	0.670330i	−0.875997	−	0.482317i	$-0.839795\pi$
$83$	0.967254	−	6.10700i	0.106170	−	0.670330i	0.982167	−	0.188013i	$-0.0602047\pi$
$84$		0			0
$85$	−5.36167	+	0.761971i	−0.581555	+	0.0826474i
$86$		0			0
$87$	6.78175	−	13.3099i	0.727080	−	1.42697i
$88$		0			0
$89$	0.0514581	+	0.0167197i	0.00545454	+	0.00177229i	0.311743	−	0.950166i	$-0.399087\pi$
$89$	0.0514581	+	0.0167197i	0.00545454	+	0.00177229i	−0.306288	+	0.951939i	$0.599087\pi$
$90$		0			0
$91$	13.2956	−	4.32001i	1.39376	−	0.452860i
$92$		0			0
$93$	−6.14629	−	6.14629i	−0.637340	−	0.637340i
$94$		0			0
$95$	5.37982	+	4.04099i	0.551958	+	0.414596i
$96$		0			0
$97$	−15.5905	+	2.46930i	−1.58298	+	0.250719i	−0.885066	−	0.465465i	$-0.845887\pi$
$97$	−15.5905	+	2.46930i	−1.58298	+	0.250719i	−0.697912	+	0.716184i	$0.745887\pi$
$98$		0			0
$99$	12.9296			1.29948
$100$		0			0
$101$	−13.5714			−1.35041			−0.675203	−	0.737632i	$-0.735944\pi$
$101$	−13.5714			−1.35041			−0.675203	+	0.737632i	$0.735944\pi$
$102$		0			0
$103$	−11.5602	+	1.83096i	−1.13906	+	0.180410i	−0.697339	−	0.716742i	$-0.745633\pi$
$103$	−11.5602	+	1.83096i	−1.13906	+	0.180410i	−0.441723	+	0.897151i	$0.645633\pi$
$104$		0			0
$105$	4.77348	−	13.9330i	0.465844	−	1.35972i
$106$		0			0
$107$	0.0758596	+	0.0758596i	0.00733362	+	0.00733362i	0.710764	−	0.703430i	$-0.248349\pi$
$107$	0.0758596	+	0.0758596i	0.00733362	+	0.00733362i	−0.703430	+	0.710764i	$0.748349\pi$
$108$		0			0
$109$	1.88979	−	0.614031i	0.181009	−	0.0588135i	−0.217110	−	0.976147i	$-0.569663\pi$
$109$	1.88979	−	0.614031i	0.181009	−	0.0588135i	0.398119	+	0.917334i	$0.369663\pi$
$110$		0			0
$111$	−10.5225	−	3.41897i	−0.998753	−	0.324515i
$112$		0			0
$113$	−1.52262	+	2.98831i	−0.143236	+	0.281117i	−0.951468	−	0.307748i	$-0.900425\pi$
$113$	−1.52262	+	2.98831i	−0.143236	+	0.281117i	0.808232	+	0.588864i	$0.200425\pi$
$114$		0			0
$115$	9.03900	−	8.75585i	0.842891	−	0.816487i
$116$		0			0
$117$	−7.16722	+	45.2520i	−0.662609	+	4.18355i
$118$		0			0
$119$	−4.10771	+	2.98443i	−0.376553	+	0.273582i
$120$		0			0
$121$	−6.03416	−	4.38407i	−0.548560	−	0.398552i
$122$		0			0
$123$	−10.7529	−	21.1038i	−0.969559	−	1.90287i
$124$		0			0
$125$	8.72123	+	6.99573i	0.780050	+	0.625717i
$126$		0			0
$127$	−8.15162	+	4.15346i	−0.723339	+	0.368560i	−0.776577	−	0.630022i	$-0.783046\pi$
$127$	−8.15162	+	4.15346i	−0.723339	+	0.368560i	0.0532378	+	0.998582i	$0.483046\pi$
$128$		0			0
$129$	−22.9906	+	31.6438i	−2.02421	+	2.78609i
$130$		0			0
$131$	10.6435	+	14.6495i	0.929923	+	1.27993i	0.959890	+	0.280378i	$0.0904598\pi$
$131$	10.6435	+	14.6495i	0.929923	+	1.27993i	−0.0299669	+	0.999551i	$0.509540\pi$
$132$		0			0
$133$	6.23067	+	0.986841i	0.540268	+	0.0855700i
$134$		0			0
$135$	18.9196	+	19.5314i	1.62834	+	1.68099i
$136$		0			0
$137$	14.2013	+	7.23592i	1.21330	+	0.618206i	0.939159	−	0.343484i	$-0.111607\pi$
$137$	14.2013	+	7.23592i	1.21330	+	0.618206i	0.274139	+	0.961690i	$0.411607\pi$
$138$		0			0
$139$	−3.65431	+	11.2468i	−0.309954	+	0.953941i	0.667828	+	0.744316i	$0.267224\pi$
$139$	−3.65431	+	11.2468i	−0.309954	+	0.953941i	−0.977782	+	0.209625i	$0.932776\pi$
$140$		0			0
$141$	−6.56123	−	20.1934i	−0.552555	−	1.70059i
$142$		0			0
$143$	−8.87337	+	8.87337i	−0.742028	+	0.742028i
$144$		0			0
$145$	10.0579	+	3.44586i	0.835262	+	0.286163i
$146$		0			0
$147$	1.28025	+	8.08319i	0.105593	+	0.666690i
$148$		0			0
$149$		−	5.96489i		−	0.488663i	−0.969692	−	0.244331i	$-0.921432\pi$
$149$		−	5.96489i		−	0.488663i	0.969692	−	0.244331i	$-0.0785684\pi$
$150$		0			0
$151$		−	7.86408i		−	0.639970i	−0.947423	−	0.319985i	$-0.896322\pi$
$151$		−	7.86408i		−	0.639970i	0.947423	−	0.319985i	$-0.103678\pi$
$152$		0			0
$153$	−2.60309	−	16.4353i	−0.210448	−	1.32871i
$154$		0			0
$155$	3.71545	−	4.94643i	0.298432	−	0.397307i
$156$		0			0
$157$	8.99195	−	8.99195i	0.717635	−	0.717635i	−0.250485	−	0.968120i	$-0.580590\pi$
$157$	8.99195	−	8.99195i	0.717635	−	0.717635i	0.968120	+	0.250485i	$0.0805901\pi$
$158$		0			0
$159$	−7.07610	−	21.7780i	−0.561172	−	1.72711i
$160$		0			0
$161$	3.64600	−	11.2212i	0.287345	−	0.884357i
$162$		0			0
$163$	7.61107	+	3.87804i	0.596145	+	0.303751i	0.725906	−	0.687794i	$-0.241421\pi$
$163$	7.61107	+	3.87804i	0.596145	+	0.303751i	−0.129761	+	0.991545i	$0.541421\pi$
$164$		0			0
$165$	1.86012	+	13.0889i	0.144810	+	1.01897i
$166$		0			0
$167$	−1.62049	−	0.256660i	−0.125397	−	0.0198610i	0.0934204	−	0.995627i	$-0.470220\pi$
$167$	−1.62049	−	0.256660i	−0.125397	−	0.0198610i	−0.218818	+	0.975766i	$0.570220\pi$
$168$		0			0
$169$	−18.4957	−	25.4572i	−1.42275	−	1.95824i
$170$		0			0
$171$	−12.1520	+	16.7258i	−0.929289	+	1.27906i
$172$		0			0
$173$	7.59320	−	3.86893i	0.577300	−	0.294149i	−0.140857	−	0.990030i	$-0.544986\pi$
$173$	7.59320	−	3.86893i	0.577300	−	0.294149i	0.718157	+	0.695881i	$0.244986\pi$
$174$		0			0
$175$	10.2958	+	1.96835i	0.778289	+	0.148793i
$176$		0			0
$177$	3.72849	+	7.31758i	0.280251	+	0.550023i
$178$		0			0
$179$	11.6100	+	8.43516i	0.867772	+	0.630473i	0.929988	−	0.367589i	$-0.119817\pi$
$179$	11.6100	+	8.43516i	0.867772	+	0.630473i	−0.0622162	+	0.998063i	$0.519817\pi$
$180$		0			0
$181$	−10.2327	+	7.43451i	−0.760592	+	0.552603i	−0.899092	−	0.437760i	$-0.855772\pi$
$181$	−10.2327	+	7.43451i	−0.760592	+	0.552603i	0.138500	+	0.990362i	$0.455772\pi$
$182$		0			0
$183$	0.450822	−	2.84638i	0.0333257	−	0.210410i
$184$		0			0
$185$	1.35543	−	7.75700i	0.0996533	−	0.570306i
$186$		0			0
$187$	2.06914	−	4.06091i	0.151310	−	0.296963i
$188$		0			0
$189$	24.2467	+	7.87824i	1.76369	+	0.573058i
$190$		0			0
$191$	−25.2328	+	8.19864i	−1.82578	+	0.593233i	−0.826231	+	0.563332i	$0.809519\pi$
$191$	−25.2328	+	8.19864i	−1.82578	+	0.593233i	−0.999553	+	0.0299015i	$0.990481\pi$
$192$		0			0
$193$	12.8160	+	12.8160i	0.922513	+	0.922513i	0.997207	−	0.0746938i	$-0.0237980\pi$
$193$	12.8160	+	12.8160i	0.922513	+	0.922513i	−0.0746938	+	0.997207i	$0.523798\pi$
$194$		0			0
$195$	−46.8405	−	0.745318i	−3.35432	−	0.0533733i
$196$		0			0
$197$	2.61520	−	0.414208i	0.186326	−	0.0295111i	−0.0625742	−	0.998040i	$-0.519931\pi$
$197$	2.61520	−	0.414208i	0.186326	−	0.0295111i	0.248900	+	0.968529i	$0.419931\pi$
$198$		0			0
$199$	3.27718			0.232313			0.116157	−	0.993231i	$-0.462943\pi$
$199$	3.27718			0.232313			0.116157	+	0.993231i	$0.462943\pi$
$200$		0			0
$201$	26.3170			1.85626
$202$		0			0
$203$	9.84524	−	1.55933i	0.691000	−	0.109444i
$204$		0			0
$205$	13.7939	−	9.69031i	0.963405	−	0.676801i
$206$		0			0
$207$	27.3423	+	27.3423i	1.90042	+	1.90042i
$208$		0			0
$209$	−5.38545	+	1.74984i	−0.372519	+	0.121039i
$210$		0			0
$211$	−12.5986	−	4.09353i	−0.867323	−	0.281810i	−0.158639	−	0.987337i	$-0.550711\pi$
$211$	−12.5986	−	4.09353i	−0.867323	−	0.281810i	−0.708684	+	0.705526i	$0.750711\pi$
$212$		0			0
$213$	12.9408	−	25.3977i	0.886687	−	1.74022i
$214$		0			0
$215$	−24.5999	−	13.0314i	−1.67770	−	0.888731i
$216$		0			0
$217$	0.907343	−	5.72874i	0.0615945	−	0.388892i
$218$		0			0
$219$	−2.98522	+	2.16889i	−0.201722	+	0.146560i
$220$		0			0
$221$	13.0657	+	9.49278i	0.878894	+	0.638554i
$222$		0			0
$223$	−2.04426	−	4.01208i	−0.136893	−	0.268669i	0.812375	−	0.583135i	$-0.198174\pi$
$223$	−2.04426	−	4.01208i	−0.136893	−	0.268669i	−0.949268	+	0.314467i	$0.898174\pi$
$224$		0			0
$225$	−21.0665	+	27.1360i	−1.40443	+	1.80907i
$226$		0			0
$227$	−18.0576	+	9.20080i	−1.19852	+	0.610679i	−0.935231	−	0.354037i	$-0.884809\pi$
$227$	−18.0576	+	9.20080i	−1.19852	+	0.610679i	−0.263293	+	0.964716i	$0.584809\pi$
$228$		0			0
$229$	1.72355	−	2.37227i	0.113896	−	0.156764i	−0.748263	−	0.663402i	$-0.769112\pi$
$229$	1.72355	−	2.37227i	0.113896	−	0.156764i	0.862159	+	0.506638i	$0.169112\pi$
$230$		0			0
$231$	7.28556	+	10.0277i	0.479355	+	0.659775i
$232$		0			0
$233$	−9.06421	−	1.43563i	−0.593816	−	0.0940512i	−0.147709	−	0.989031i	$-0.547190\pi$
$233$	−9.06421	−	1.43563i	−0.593816	−	0.0940512i	−0.446107	+	0.894980i	$0.647190\pi$
$234$		0			0
$235$	13.5721	−	6.64549i	0.885346	−	0.433504i
$236$		0			0
$237$	−15.9589	−	8.13148i	−1.03664	−	0.528196i
$238$		0			0
$239$	−3.98858	+	12.2756i	−0.258000	+	0.794043i	0.735224	+	0.677825i	$0.237077\pi$
$239$	−3.98858	+	12.2756i	−0.258000	+	0.794043i	−0.993224	+	0.116218i	$0.962923\pi$
$240$		0			0
$241$	0.206055	+	0.634173i	0.0132732	+	0.0408507i	0.957474	−	0.288520i	$-0.0931633\pi$
$241$	0.206055	+	0.634173i	0.0132732	+	0.0408507i	−0.944201	+	0.329371i	$0.893163\pi$
$242$		0			0
$243$	−13.2899	+	13.2899i	−0.852548	+	0.852548i
$244$		0			0
$245$	−5.56756	+	1.71157i	−0.355698	+	0.109348i
$246$		0			0
$247$	−3.13892	−	19.8184i	−0.199725	−	1.26101i
$248$		0			0
$249$			19.4259i			1.23107i
$250$		0			0
$251$			1.24780i			0.0787607i	0.999224	+	0.0393803i	$0.0125384\pi$
$251$			1.24780i			0.0787607i	−0.999224	+	0.0393803i	$0.987462\pi$
$252$		0			0
$253$	1.65679	+	10.4606i	0.104161	+	0.657650i
$254$		0			0
$255$	16.2632	−	4.99962i	1.01844	−	0.313088i
$256$		0			0
$257$	21.6851	−	21.6851i	1.35268	−	1.35268i	0.470029	−	0.882651i	$-0.344244\pi$
$257$	21.6851	−	21.6851i	1.35268	−	1.35268i	0.882651	−	0.470029i	$-0.155756\pi$
$258$		0			0
$259$	−2.28143	−	7.02151i	−0.141761	−	0.436296i
$260$		0			0
$261$	−10.0949	+	31.0690i	−0.624861	+	1.92313i
$262$		0			0
$263$	8.68088	+	4.42313i	0.535286	+	0.272742i	0.700668	−	0.713488i	$-0.252886\pi$
$263$	8.68088	+	4.42313i	0.535286	+	0.272742i	−0.165382	+	0.986230i	$0.552886\pi$
$264$		0			0
$265$	14.6371	−	7.16698i	0.899152	−	0.440264i
$266$		0			0
$267$	−0.167896	−	0.0265921i	−0.0102751	−	0.00162741i
$268$		0			0
$269$	−8.00337	−	11.0157i	−0.487974	−	0.671639i	0.492038	−	0.870573i	$-0.336252\pi$
$269$	−8.00337	−	11.0157i	−0.487974	−	0.671639i	−0.980013	+	0.198934i	$0.936252\pi$
$270$		0			0
$271$	4.57148	−	6.29210i	0.277697	−	0.382218i	−0.647272	−	0.762259i	$-0.724090\pi$
$271$	4.57148	−	6.29210i	0.277697	−	0.382218i	0.924970	+	0.380041i	$0.124090\pi$
$272$		0			0
$273$	−39.1343	+	19.9399i	−2.36851	+	1.20682i
$274$		0			0
$275$	−9.03672	+	2.62144i	−0.544935	+	0.158079i
$276$		0			0
$277$	−2.36128	−	4.63427i	−0.141875	−	0.278446i	0.809125	−	0.587637i	$-0.199942\pi$
$277$	−2.36128	−	4.63427i	−0.141875	−	0.278446i	−0.951000	+	0.309191i	$0.899942\pi$
$278$		0			0
$279$	15.3784	+	11.1731i	0.920683	+	0.668915i
$280$		0			0
$281$	−4.54165	+	3.29970i	−0.270932	+	0.196844i	−0.714952	−	0.699173i	$-0.753552\pi$
$281$	−4.54165	+	3.29970i	−0.270932	+	0.196844i	0.444021	+	0.896017i	$0.353552\pi$
$282$		0			0
$283$	−3.02132	+	19.0758i	−0.179599	+	1.13394i	0.718948	+	0.695063i	$0.244624\pi$
$283$	−3.02132	+	19.0758i	−0.179599	+	1.13394i	−0.898547	+	0.438877i	$0.855376\pi$
$284$		0			0
$285$	−18.6801	−	9.89545i	−1.10651	−	0.586156i
$286$		0			0
$287$	7.17526	−	14.0822i	0.423542	−	0.831249i
$288$		0			0
$289$	10.5894	+	3.44071i	0.622907	+	0.202395i
$290$		0			0
$291$	47.1651	−	15.3249i	2.76487	−	0.898360i
$292$		0			0
$293$	14.3952	+	14.3952i	0.840975	+	0.840975i	0.988986	−	0.148011i	$-0.0472870\pi$
$293$	14.3952	+	14.3952i	0.840975	+	0.840975i	−0.148011	+	0.988986i	$0.547287\pi$
$294$		0			0
$295$	−4.78291	+	3.36004i	−0.278472	+	0.195629i
$296$		0			0
$297$	−22.6031	+	3.57998i	−1.31156	+	0.207731i
$298$		0			0
$299$	−37.5290			−2.17036
$300$		0			0
$301$	−26.1001			−1.50439
$302$		0			0
$303$	42.1133	−	6.67009i	2.41934	−	0.383187i
$304$		0			0
$305$	2.05083	+	0.0326324i	0.117430	+	0.00186852i
$306$		0			0
$307$	−8.19364	−	8.19364i	−0.467636	−	0.467636i	0.433512	−	0.901148i	$-0.357274\pi$
$307$	−8.19364	−	8.19364i	−0.467636	−	0.467636i	−0.901148	+	0.433512i	$0.857274\pi$
$308$		0			0
$309$	34.9724	−	11.3632i	1.98951	−	0.646432i
$310$		0			0
$311$	23.3819	+	7.59725i	1.32587	+	0.430800i	0.884506	−	0.466529i	$-0.154496\pi$
$311$	23.3819	+	7.59725i	1.32587	+	0.430800i	0.441361	+	0.897329i	$0.354496\pi$
$312$		0			0
$313$	−8.71271	+	17.0997i	−0.492471	+	0.966530i	0.502328	+	0.864677i	$0.332477\pi$
$313$	−8.71271	+	17.0997i	−0.492471	+	0.966530i	−0.994800	+	0.101852i	$0.967523\pi$
$314$		0			0
$315$	−5.54400	+	31.7278i	−0.312369	+	1.78766i
$316$		0			0
$317$	0.452132	−	2.85465i	0.0253942	−	0.160333i	−0.971732	−	0.236085i	$-0.924136\pi$
$317$	0.452132	−	2.85465i	0.0253942	−	0.160333i	0.997127	+	0.0757519i	$0.0241357\pi$
$318$		0			0
$319$	−7.23877	+	5.25927i	−0.405293	+	0.294463i
$320$		0			0
$321$	−0.272682	−	0.198115i	−0.0152196	−	0.0110577i
$322$		0			0
$323$	3.30852	+	6.49334i	0.184091	+	0.361299i
$324$		0			0
$325$	−4.16543	−	33.0805i	−0.231056	−	1.83498i
$326$		0			0
$327$	−5.56240	+	2.83419i	−0.307602	+	0.156731i
$328$		0			0
$329$	8.32785	−	11.4623i	0.459129	−	0.631937i
$330$		0			0
$331$	−17.3693	−	23.9068i	−0.954705	−	1.31404i	−0.949406	−	0.314052i	$-0.898313\pi$
$331$	−17.3693	−	23.9068i	−0.954705	−	1.31404i	−0.00529905	−	0.999986i	$-0.501687\pi$
$332$		0			0
$333$	23.8979	+	3.78506i	1.30960	+	0.207420i
$334$		0			0
$335$	2.63539	+	18.5441i	0.143986	+	1.01317i
$336$		0			0
$337$	−23.0595	−	11.7494i	−1.25613	−	0.640031i	−0.306044	−	0.952017i	$-0.599006\pi$
$337$	−23.0595	−	11.7494i	−1.25613	−	0.640031i	−0.950086	+	0.311987i	$0.899006\pi$
$338$		0			0
$339$	3.25612	−	10.0213i	0.176848	−	0.544283i
$340$		0			0
$341$	1.60888	+	4.95161i	0.0871255	+	0.268145i
$342$		0			0
$343$	−14.2384	+	14.2384i	−0.768803	+	0.768803i
$344$		0			0
$345$	−23.7455	+	31.6126i	−1.27841	+	1.70197i
$346$		0			0
$347$	1.72540	+	10.8937i	0.0926243	+	0.584807i	0.989725	+	0.142982i	$0.0456690\pi$
$347$	1.72540	+	10.8937i	0.0926243	+	0.584807i	−0.897101	+	0.441826i	$0.854331\pi$
$348$		0			0
$349$		−	1.52465i		−	0.0816125i	−0.999167	−	0.0408062i	$-0.987007\pi$
$349$		−	1.52465i		−	0.0816125i	0.999167	−	0.0408062i	$-0.0129926\pi$
$350$		0			0
$351$		−	81.0923i		−	4.32839i
$352$		0			0
$353$	−1.42534	−	8.99925i	−0.0758633	−	0.478982i	−0.996145	−	0.0877249i	$-0.972040\pi$
$353$	−1.42534	−	8.99925i	−0.0758633	−	0.478982i	0.920281	−	0.391257i	$-0.127960\pi$
$354$		0			0
$355$	19.1922	+	6.57530i	1.01862	+	0.348981i
$356$		0			0
$357$	11.2798	−	11.2798i	0.596989	−	0.596989i
$358$		0			0
$359$	2.16850	+	6.67395i	0.114449	+	0.352237i	0.991832	−	0.127554i	$-0.0407125\pi$
$359$	2.16850	+	6.67395i	0.114449	+	0.352237i	−0.877383	+	0.479791i	$0.840712\pi$
$360$		0			0
$361$	−3.07336	+	9.45882i	−0.161756	+	0.497833i
$362$		0			0
$363$	20.8792	+	10.6385i	1.09587	+	0.558375i
$364$		0			0
$365$	−1.82723	−	1.88632i	−0.0956417	−	0.0987345i
$366$		0			0
$367$	−16.7913	−	2.65948i	−0.876499	−	0.138824i	−0.298058	−	0.954548i	$-0.596339\pi$
$367$	−16.7913	−	2.65948i	−0.876499	−	0.138824i	−0.578441	+	0.815724i	$0.696339\pi$
$368$		0			0
$369$	30.4456	+	41.9048i	1.58494	+	2.18148i
$370$		0			0
$371$	8.98135	−	12.3618i	0.466289	−	0.641791i
$372$		0			0
$373$	3.92679	−	2.00080i	0.203322	−	0.103598i	−0.349365	−	0.936987i	$-0.613603\pi$
$373$	3.92679	−	2.00080i	0.203322	−	0.103598i	0.552687	+	0.833389i	$0.313603\pi$
$374$		0			0
$375$	−30.5010	−	17.4220i	−1.57506	−	0.899669i
$376$		0			0
$377$	−14.3941	−	28.2501i	−0.741336	−	1.45495i
$378$		0			0
$379$	−1.70130	−	1.23607i	−0.0873901	−	0.0634926i	0.543232	−	0.839582i	$-0.317200\pi$
$379$	−1.70130	−	1.23607i	−0.0873901	−	0.0634926i	−0.630622	+	0.776090i	$0.717200\pi$
$380$		0			0
$381$	23.2538	−	16.8949i	1.19133	−	0.865552i
$382$		0			0
$383$	4.01170	−	25.3289i	0.204988	−	1.29425i	−0.643669	−	0.765304i	$-0.722589\pi$
$383$	4.01170	−	25.3289i	0.204988	−	1.29425i	0.848658	−	0.528942i	$-0.177411\pi$
$384$		0			0
$385$	−6.33639	+	6.13790i	−0.322932	+	0.312816i
$386$		0			0
$387$	38.8334	−	76.2148i	1.97401	−	3.87421i
$388$		0			0
$389$	−3.41177	−	1.10855i	−0.172983	−	0.0562057i	0.221245	−	0.975218i	$-0.428988\pi$
$389$	−3.41177	−	1.10855i	−0.172983	−	0.0562057i	−0.394228	+	0.919013i	$0.628988\pi$
$390$		0			0
$391$	12.9632	−	4.21200i	0.655578	−	0.213010i
$392$		0			0
$393$	−40.2275	−	40.2275i	−2.02921	−	2.02921i
$394$		0			0
$395$	4.13166	−	12.0596i	0.207887	−	0.606786i
$396$		0			0
$397$	27.1780	−	4.30457i	1.36402	−	0.216040i	0.568860	−	0.822435i	$-0.307385\pi$
$397$	27.1780	−	4.30457i	1.36402	−	0.216040i	0.795164	+	0.606394i	$0.207385\pi$
$398$		0			0
$399$	−19.8193			−0.992207
$400$		0			0
$401$	−11.5819			−0.578374			−0.289187	−	0.957273i	$-0.593385\pi$
$401$	−11.5819			−0.578374			−0.289187	+	0.957273i	$0.593385\pi$
$402$		0			0
$403$	−18.2218	+	2.88605i	−0.907694	+	0.143765i
$404$		0			0
$405$	−31.4565	−	23.6281i	−1.56308	−	1.17409i
$406$		0			0
$407$	4.68609	+	4.68609i	0.232281	+	0.232281i
$408$		0			0
$409$	6.32672	−	2.05568i	0.312836	−	0.101647i	−0.148391	−	0.988929i	$-0.547409\pi$
$409$	6.32672	−	2.05568i	0.312836	−	0.101647i	0.461227	+	0.887282i	$0.347409\pi$
$410$		0			0
$411$	−47.6241	−	15.4740i	−2.34912	−	0.763277i
$412$		0			0
$413$	−2.48797	+	4.88291i	−0.122425	+	0.240272i
$414$		0			0
$415$	−13.6883	+	1.94531i	−0.671935	+	0.0954916i
$416$		0			0
$417$	5.81204	−	36.6958i	0.284617	−	1.79700i
$418$		0			0
$419$	17.1911	−	12.4901i	0.839841	−	0.610180i	−0.0824855	−	0.996592i	$-0.526286\pi$
$419$	17.1911	−	12.4901i	0.839841	−	0.610180i	0.922326	+	0.386412i	$0.126286\pi$
$420$		0			0
$421$	3.51629	+	2.55473i	0.171373	+	0.124510i	0.670166	−	0.742211i	$-0.266223\pi$
$421$	3.51629	+	2.55473i	0.171373	+	0.124510i	−0.498792	+	0.866721i	$0.666223\pi$
$422$		0			0
$423$	21.0803	+	41.3724i	1.02496	+	2.01159i
$424$		0			0
$425$	5.15155	+	10.9591i	0.249887	+	0.531595i
$426$		0			0
$427$	1.71342	−	0.873032i	0.0829183	−	0.0422490i
$428$		0			0
$429$	23.1737	−	31.8959i	1.11884	−	1.53995i
$430$		0			0
$431$	22.0143	+	30.3001i	1.06039	+	1.45950i	0.879438	+	0.476013i	$0.157919\pi$
$431$	22.0143	+	30.3001i	1.06039	+	1.45950i	0.180954	+	0.983492i	$0.442081\pi$
$432$		0			0
$433$	6.86293	+	1.08698i	0.329811	+	0.0522370i	0.319144	−	0.947706i	$-0.396605\pi$
$433$	6.86293	+	1.08698i	0.329811	+	0.0522370i	0.0106671	+	0.999943i	$0.496605\pi$
$434$		0			0
$435$	−32.9040	−	5.74954i	−1.57763	−	0.275669i
$436$		0			0
$437$	−15.0890	−	7.68822i	−0.721804	−	0.367778i
$438$		0			0
$439$	1.52930	−	4.70671i	0.0729896	−	0.224639i	−0.907906	−	0.419174i	$-0.862320\pi$
$439$	1.52930	−	4.70671i	0.0729896	−	0.224639i	0.980896	+	0.194535i	$0.0623198\pi$
$440$		0			0
$441$	−5.53059	−	17.0214i	−0.263362	−	0.810544i
$442$		0			0
$443$	25.3224	−	25.3224i	1.20310	−	1.20310i	0.229887	−	0.973217i	$-0.426164\pi$
$443$	25.3224	−	25.3224i	1.20310	−	1.20310i	0.973217	−	0.229887i	$-0.0738357\pi$
$444$		0			0
$445$	0.00192485	−	0.120970i	9.12467e−5	−	0.00573452i
$446$		0			0
$447$	2.93163	+	18.5096i	0.138661	+	0.875472i
$448$		0			0
$449$		−	4.43711i		−	0.209400i	−0.994504	−	0.104700i	$-0.966612\pi$
$449$		−	4.43711i		−	0.209400i	0.994504	−	0.104700i	$-0.0333883\pi$
$450$		0			0
$451$			14.1870i			0.668042i
$452$		0			0
$453$	3.86504	+	24.4029i	0.181595	+	1.14655i
$454$		0			0
$455$	−17.9694	−	25.5789i	−0.842420	−	1.19916i
$456$		0			0
$457$	−9.45276	+	9.45276i	−0.442182	+	0.442182i	−0.892745	−	0.450563i	$-0.851223\pi$
$457$	−9.45276	+	9.45276i	−0.442182	+	0.442182i	0.450563	+	0.892745i	$0.351223\pi$
$458$		0			0
$459$	9.10126	+	28.0108i	0.424810	+	1.30743i
$460$		0			0
$461$	−3.38937	+	10.4314i	−0.157859	+	0.485839i	−0.998439	−	0.0558473i	$-0.982214\pi$
$461$	−3.38937	+	10.4314i	−0.157859	+	0.485839i	0.840581	+	0.541686i	$0.182214\pi$
$462$		0			0
$463$	−5.23594	−	2.66785i	−0.243335	−	0.123985i	0.328071	−	0.944653i	$-0.393602\pi$
$463$	−5.23594	−	2.66785i	−0.243335	−	0.123985i	−0.571405	+	0.820668i	$0.693602\pi$
$464$		0			0
$465$	−9.09829	+	17.1753i	−0.421923	+	0.796484i
$466$		0			0
$467$	16.1066	+	2.55103i	0.745323	+	0.118048i	0.517534	−	0.855663i	$-0.326850\pi$
$467$	16.1066	+	2.55103i	0.745323	+	0.118048i	0.227789	+	0.973710i	$0.426850\pi$
$468$		0			0
$469$	10.3221	+	14.2071i	0.476628	+	0.656023i
$470$		0			0
$471$	−23.4834	+	32.3221i	−1.08206	+	1.48933i
$472$		0			0
$473$	20.8749	−	10.6363i	0.959829	−	0.489057i
$474$		0			0
$475$	5.10214	−	14.1537i	0.234102	−	0.649418i
$476$		0			0
$477$	22.7345	+	44.6189i	1.04094	+	2.04296i
$478$		0			0
$479$	−25.4775	−	18.5105i	−1.16410	−	0.845766i	−0.173807	−	0.984780i	$-0.555607\pi$
$479$	−25.4775	−	18.5105i	−1.16410	−	0.845766i	−0.990290	+	0.139014i	$0.955607\pi$
$480$		0			0
$481$	−18.9983	+	13.8031i	−0.866248	+	0.629366i
$482$		0			0
$483$	−5.79883	+	36.6124i	−0.263856	+	1.66592i
$484$		0			0
$485$	15.5217	+	31.6999i	0.704803	+	1.43942i
$486$		0			0
$487$	1.48160	−	2.90780i	0.0671376	−	0.131765i	−0.854999	−	0.518630i	$-0.826442\pi$
$487$	1.48160	−	2.90780i	0.0671376	−	0.131765i	0.922136	+	0.386865i	$0.126442\pi$
$488$		0			0
$489$	−25.5238	−	8.29318i	−1.15423	−	0.375031i
$490$		0			0
$491$	−5.87178	+	1.90786i	−0.264990	+	0.0861004i	−0.438498	−	0.898732i	$-0.644490\pi$
$491$	−5.87178	+	1.90786i	−0.264990	+	0.0861004i	0.173509	+	0.984832i	$0.444490\pi$
$492$		0			0
$493$	8.14261	+	8.14261i	0.366724	+	0.366724i
$494$		0			0
$495$	−8.49556	−	27.6352i	−0.381847	−	1.24211i
$496$		0			0
$497$	18.7864	−	2.97548i	0.842687	−	0.133468i
$498$		0			0
$499$	29.4478			1.31826			0.659132	−	0.752027i	$-0.270924\pi$
$499$	29.4478			1.31826			0.659132	+	0.752027i	$0.270924\pi$
$500$		0			0
$501$	5.15466			0.230293
$502$		0			0
$503$	4.97751	−	0.788360i	0.221936	−	0.0351512i	−0.0444760	−	0.999010i	$-0.514162\pi$
$503$	4.97751	−	0.788360i	0.221936	−	0.0351512i	0.266412	+	0.963859i	$0.414162\pi$
$504$		0			0
$505$	8.91726	+	29.0069i	0.396813	+	1.29079i
$506$		0			0
$507$	69.9054	+	69.9054i	3.10461	+	3.10461i
$508$		0			0
$509$	−40.5299	+	13.1690i	−1.79646	+	0.583704i	−0.999786	−	0.0207073i	$-0.993408\pi$
$509$	−40.5299	+	13.1690i	−1.79646	+	0.583704i	−0.796672	+	0.604412i	$0.793408\pi$
$510$		0			0
$511$	−2.34172	−	0.760872i	−0.103592	−	0.0336590i
$512$		0			0
$513$	16.6126	−	32.6041i	0.733466	−	1.43951i
$514$		0			0
$515$	11.5092	+	23.5052i	0.507155	+	1.03576i
$516$		0			0
$517$	−1.98952	+	12.5613i	−0.0874988	+	0.552446i
$518$		0			0
$519$	−21.6608	+	15.7375i	−0.950806	+	0.690801i
$520$		0			0
$521$	27.3429	+	19.8657i	1.19791	+	0.870334i	0.994078	−	0.108671i	$-0.0346595\pi$
$521$	27.3429	+	19.8657i	1.19791	+	0.870334i	0.203835	+	0.979005i	$0.434660\pi$
$522$		0			0
$523$	7.33650	+	14.3987i	0.320803	+	0.629610i	0.993942	−	0.109905i	$-0.0350547\pi$
$523$	7.33650	+	14.3987i	0.320803	+	0.629610i	−0.673140	+	0.739515i	$0.735055\pi$
$524$		0			0
$525$	−32.9161	−	1.04778i	−1.43658	−	0.0457287i
$526$		0			0
$527$	5.97025	−	3.04199i	0.260068	−	0.132511i
$528$		0			0
$529$	−5.09826	+	7.01715i	−0.221663	+	0.305094i
$530$		0			0
$531$	−10.5568	−	14.5302i	−0.458126	−	0.630556i
$532$		0			0
$533$	−49.6528	−	7.86424i	−2.15070	−	0.340638i
$534$		0			0
$535$	0.112294	−	0.211983i	0.00485490	−	0.00916482i
$536$		0			0
$537$	−40.1725	−	20.4689i	−1.73357	−	0.883299i
$538$		0			0
$539$	1.51481	−	4.66210i	0.0652474	−	0.200811i
$540$		0			0
$541$	−9.37129	−	28.8419i	−0.402903	−	1.24001i	−0.922633	−	0.385678i	$-0.873968\pi$
$541$	−9.37129	−	28.8419i	−0.402903	−	1.24001i	0.519730	−	0.854330i	$-0.326032\pi$
$542$		0			0
$543$	28.0991	−	28.0991i	1.20585	−	1.20585i
$544$		0			0
$545$	−2.55411	−	3.63569i	−0.109406	−	0.155736i
$546$		0			0
$547$	−2.71648	−	17.1512i	−0.116148	−	0.733332i	−0.975181	−	0.221411i	$-0.928934\pi$
$547$	−2.71648	−	17.1512i	−0.116148	−	0.733332i	0.859032	−	0.511921i	$-0.171066\pi$
$548$		0			0
$549$			6.30230i			0.268976i
$550$		0			0
$551$		−	14.3071i		−	0.609502i
$552$		0			0
$553$	−1.86968	−	11.8047i	−0.0795067	−	0.501986i
$554$		0			0
$555$	−0.393607	+	24.7368i	−0.0167077	+	1.05002i
$556$		0			0
$557$	−13.0360	+	13.0360i	−0.552354	+	0.552354i	−0.927120	−	0.374765i	$-0.877723\pi$
$557$	−13.0360	+	13.0360i	−0.552354	+	0.552354i	0.374765	+	0.927120i	$0.377723\pi$
$558$		0			0
$559$	25.6542	+	78.9554i	1.08506	+	3.33946i
$560$		0			0
$561$	−4.42485	+	13.6183i	−0.186817	+	0.574965i
$562$		0			0
$563$	0.756513	+	0.385463i	0.0318832	+	0.0162453i	0.469859	−	0.882741i	$-0.344305\pi$
$563$	0.756513	+	0.385463i	0.0318832	+	0.0162453i	−0.437976	+	0.898987i	$0.644305\pi$
$564$		0			0
$565$	7.38752	+	1.29087i	0.310795	+	0.0543074i
$566$		0			0
$567$	−36.4315	−	5.77018i	−1.52998	−	0.242325i
$568$		0			0
$569$	18.3379	+	25.2399i	0.768764	+	1.05811i	0.996434	+	0.0843741i	$0.0268891\pi$
$569$	18.3379	+	25.2399i	0.768764	+	1.05811i	−0.227671	+	0.973738i	$0.573111\pi$
$570$		0			0
$571$	18.6193	−	25.6273i	0.779193	−	1.07247i	−0.216177	−	0.976354i	$-0.569359\pi$
$571$	18.6193	−	25.6273i	0.779193	−	1.07247i	0.995370	−	0.0961130i	$-0.0306410\pi$
$572$		0			0
$573$	74.2702	−	37.8425i	3.10268	−	1.58089i
$574$		0			0
$575$	−24.6535	−	13.5664i	−1.02812	−	0.565757i
$576$		0			0
$577$	13.3730	+	26.2460i	0.556725	+	1.09264i	0.982230	+	0.187679i	$0.0600965\pi$
$577$	13.3730	+	26.2460i	0.556725	+	1.09264i	−0.425505	+	0.904956i	$0.639904\pi$
$578$		0			0
$579$	−46.0678	−	33.4702i	−1.91451	−	1.39097i
$580$		0			0
$581$	−10.4870	+	7.61924i	−0.435073	+	0.316099i
$582$		0			0
$583$	−2.14564	+	13.5470i	−0.0888632	+	0.561060i
$584$		0			0
$585$	101.429	−	14.4145i	4.19356	−	0.595966i
$586$		0			0
$587$	−5.17748	+	10.1614i	−0.213698	+	0.419405i	−0.972827	−	0.231535i	$-0.925625\pi$
$587$	−5.17748	+	10.1614i	−0.213698	+	0.419405i	0.759129	+	0.650940i	$0.225625\pi$
$588$		0			0
$589$	−7.91754	−	2.57257i	−0.326237	−	0.106001i
$590$		0			0
$591$	−7.91162	+	2.57064i	−0.325441	+	0.105742i
$592$		0			0
$593$	19.0653	+	19.0653i	0.782917	+	0.782917i	0.980322	−	0.197405i	$-0.0632513\pi$
$593$	19.0653	+	19.0653i	0.782917	+	0.782917i	−0.197405	+	0.980322i	$0.563251\pi$
$594$		0			0
$595$	9.07778	+	6.81867i	0.372153	+	0.279538i
$596$		0			0
$597$	−10.1694	+	1.61067i	−0.416205	+	0.0659204i
$598$		0			0
$599$	11.8002			0.482144			0.241072	−	0.970507i	$-0.422501\pi$
$599$	11.8002			0.482144			0.241072	+	0.970507i	$0.422501\pi$
$600$		0			0
$601$	−32.6525			−1.33192			−0.665962	−	0.745986i	$-0.731979\pi$
$601$	−32.6525			−1.33192			−0.665962	+	0.745986i	$0.731979\pi$
$602$		0			0
$603$	−56.8438	+	9.00317i	−2.31486	+	0.366637i
$604$		0			0
$605$	−5.40549	+	15.7777i	−0.219764	+	0.641455i
$606$		0			0
$607$	−6.42050	−	6.42050i	−0.260600	−	0.260600i	0.564698	−	0.825298i	$-0.308993\pi$
$607$	−6.42050	−	6.42050i	−0.260600	−	0.260600i	−0.825298	+	0.564698i	$0.808993\pi$
$608$		0			0
$609$	−29.7842	+	9.67748i	−1.20692	+	0.392151i
$610$		0			0
$611$	−42.8601	−	13.9261i	−1.73393	−	0.563389i
$612$		0			0
$613$	−5.69952	+	11.1859i	−0.230201	+	0.451796i	−0.976996	−	0.213259i	$-0.931592\pi$
$613$	−5.69952	+	11.1859i	−0.230201	+	0.451796i	0.746794	+	0.665055i	$0.231592\pi$
$614$		0			0
$615$	−38.0409	+	36.8493i	−1.53396	+	1.48591i
$616$		0			0
$617$	−3.28442	+	20.7370i	−0.132226	+	0.834842i	0.829034	+	0.559198i	$0.188891\pi$
$617$	−3.28442	+	20.7370i	−0.132226	+	0.834842i	−0.961260	+	0.275644i	$0.911109\pi$
$618$		0			0
$619$	−36.0389	+	26.1838i	−1.44852	+	1.05241i	−0.462350	+	0.886697i	$0.652994\pi$
$619$	−36.0389	+	26.1838i	−1.44852	+	1.05241i	−0.986173	+	0.165717i	$0.947006\pi$
$620$		0			0
$621$	−55.3693	−	40.2281i	−2.22189	−	1.61430i
$622$		0			0
$623$	−0.0514966	−	0.101068i	−0.00206317	−	0.00404920i
$624$		0			0
$625$	9.22194	−	23.2369i	0.368878	−	0.929478i
$626$		0			0
$627$	15.8515	−	8.07674i	0.633048	−	0.322554i
$628$		0			0
$629$	5.01320	−	6.90008i	0.199890	−	0.275124i
$630$		0			0
$631$	19.0878	+	26.2721i	0.759873	+	1.04588i	0.997225	+	0.0744520i	$0.0237208\pi$
$631$	19.0878	+	26.2721i	0.759873	+	1.04588i	−0.237351	+	0.971424i	$0.576279\pi$
$632$		0			0
$633$	41.1064	+	6.51062i	1.63383	+	0.258774i
$634$		0			0
$635$	14.2335	+	14.6938i	0.564840	+	0.583106i
$636$		0			0
$637$	15.4770	+	7.88595i	0.613223	+	0.312453i
$638$		0			0
$639$	−19.2629	+	59.2852i	−0.762029	+	2.34528i
$640$		0			0
$641$	−7.52983	−	23.1744i	−0.297410	−	0.915335i	−0.982401	−	0.186783i	$-0.940194\pi$
$641$	−7.52983	−	23.1744i	−0.297410	−	0.915335i	0.684991	−	0.728552i	$-0.259806\pi$
$642$		0			0
$643$	1.49712	−	1.49712i	0.0590406	−	0.0590406i	−0.676970	−	0.736011i	$-0.736707\pi$
$643$	1.49712	−	1.49712i	0.0590406	−	0.0590406i	0.736011	+	0.676970i	$0.236707\pi$
$644$		0			0
$645$	82.7402	+	28.3470i	3.25789	+	1.11616i
$646$		0			0
$647$	−5.49681	−	34.7055i	−0.216102	−	1.36441i	−0.822279	−	0.569084i	$-0.807298\pi$
$647$	−5.49681	−	34.7055i	−0.216102	−	1.36441i	0.606178	−	0.795329i	$-0.292702\pi$
$648$		0			0
$649$		−	4.91925i		−	0.193097i
$650$		0			0
$651$			18.2227i			0.714204i
$652$		0			0
$653$	−1.54836	−	9.77595i	−0.0605920	−	0.382563i	−0.999285	−	0.0378086i	$-0.987962\pi$
$653$	−1.54836	−	9.77595i	−0.0605920	−	0.382563i	0.938693	−	0.344754i	$-0.112038\pi$
$654$		0			0
$655$	24.3176	−	32.3744i	0.950168	−	1.26497i
$656$		0			0
$657$	5.70597	−	5.70597i	0.222611	−	0.222611i
$658$		0			0
$659$	−6.38389	−	19.6476i	−0.248681	−	0.765361i	−0.995009	−	0.0997831i	$-0.968185\pi$
$659$	−6.38389	−	19.6476i	−0.248681	−	0.765361i	0.746328	−	0.665578i	$-0.231815\pi$
$660$		0			0
$661$	9.13244	−	28.1068i	0.355211	−	1.09323i	−0.600676	−	0.799492i	$-0.705102\pi$
$661$	9.13244	−	28.1068i	0.355211	−	1.09323i	0.955887	−	0.293734i	$-0.0948980\pi$
$662$		0			0
$663$	−45.2095	−	23.0354i	−1.75579	−	0.894620i
$664$		0			0
$665$	−1.98471	−	13.9655i	−0.0769636	−	0.541561i
$666$		0			0
$667$	−26.4296	−	4.18604i	−1.02336	−	0.162084i
$668$		0			0
$669$	8.31536	+	11.4451i	0.321490	+	0.442493i
$670$		0			0
$671$	−1.01462	+	1.39650i	−0.0391689	+	0.0539114i
$672$		0			0
$673$	−4.71234	+	2.40106i	−0.181647	+	0.0925539i	−0.542449	−	0.840088i	$-0.682503\pi$
$673$	−4.71234	+	2.40106i	−0.181647	+	0.0925539i	0.360802	+	0.932642i	$0.382503\pi$
$674$		0			0
$675$	29.3141	−	53.2711i	1.12830	−	2.05040i
$676$		0			0
$677$	11.9354	+	23.4246i	0.458716	+	0.900281i	0.998296	+	0.0583466i	$0.0185828\pi$
$677$	11.9354	+	23.4246i	0.458716	+	0.900281i	−0.539581	+	0.841934i	$0.681417\pi$
$678$		0			0
$679$	26.7722	+	19.4511i	1.02742	+	0.746465i
$680$		0			0
$681$	51.5122	−	37.4258i	1.97395	−	1.43416i
$682$		0			0
$683$	1.48152	−	9.35392i	0.0566886	−	0.357918i	−0.942996	−	0.332804i	$-0.892005\pi$
$683$	1.48152	−	9.35392i	0.0566886	−	0.357918i	0.999685	−	0.0251137i	$-0.00799478\pi$
$684$		0			0
$685$	6.13458	−	35.1076i	0.234390	−	1.34139i
$686$		0			0
$687$	−4.18241	+	8.20844i	−0.159569	+	0.313171i
$688$		0			0
$689$	−46.2234	−	15.0189i	−1.76097	−	0.572175i
$690$		0			0
$691$	20.0943	−	6.52902i	0.764422	−	0.248376i	0.0992465	−	0.995063i	$-0.468357\pi$
$691$	20.0943	−	6.52902i	0.764422	−	0.248376i	0.665175	+	0.746687i	$0.268357\pi$
$692$		0			0
$693$	−19.1671	−	19.1671i	−0.728097	−	0.728097i
$694$		0			0
$695$	26.4395	+	0.420700i	1.00291	+	0.0159581i
$696$		0			0
$697$	18.0336	−	2.85625i	0.683073	−	0.108188i
$698$		0			0
$699$	28.8326			1.09055
$700$		0			0
$701$	−24.4373			−0.922985			−0.461492	−	0.887144i	$-0.652686\pi$
$701$	−24.4373			−0.922985			−0.461492	+	0.887144i	$0.652686\pi$
$702$		0			0
$703$	−10.4662	+	1.65768i	−0.394741	+	0.0625208i
$704$		0			0
$705$	−38.8492	+	27.2919i	−1.46315	+	1.02787i
$706$		0			0
$707$	20.1185	+	20.1185i	0.756634	+	0.756634i
$708$		0			0
$709$	10.2804	−	3.34029i	0.386087	−	0.125447i	−0.109541	−	0.993982i	$-0.534938\pi$
$709$	10.2804	−	3.34029i	0.386087	−	0.125447i	0.495628	+	0.868535i	$0.334938\pi$
$710$		0			0
$711$	37.2525	+	12.1041i	1.39708	+	0.453938i
$712$		0			0
$713$	−7.06887	+	13.8734i	−0.264731	+	0.519565i
$714$		0			0
$715$	24.7959	+	13.1352i	0.927312	+	0.491227i
$716$		0			0
$717$	6.34370	−	40.0525i	0.236910	−	1.49579i
$718$		0			0
$719$	32.1715	−	23.3740i	1.19980	−	0.871703i	0.205531	−	0.978651i	$-0.434108\pi$
$719$	32.1715	−	23.3740i	1.19980	−	0.871703i	0.994265	+	0.106948i	$0.0341077\pi$
$720$		0			0
$721$	19.8513	+	14.4228i	0.739300	+	0.537133i
$722$		0			0
$723$	−0.951091	−	1.86662i	−0.0353715	−	0.0694204i
$724$		0			0
$725$	0.756365	−	23.7614i	0.0280907	−	0.882475i
$726$		0			0
$727$	−6.89379	+	3.51256i	−0.255677	+	0.130274i	−0.577132	−	0.816651i	$-0.695828\pi$
$727$	−6.89379	+	3.51256i	−0.255677	+	0.130274i	0.321455	+	0.946925i	$0.395828\pi$
$728$		0			0
$729$	3.68298	−	5.06919i	0.136407	−	0.187748i
$730$		0			0
$731$	−17.7229	−	24.3934i	−0.655503	−	0.902223i
$732$		0			0
$733$	27.0471	+	4.28384i	0.999008	+	0.158227i	0.634459	−	0.772957i	$-0.281223\pi$
$733$	27.0471	+	4.28384i	0.999008	+	0.158227i	0.364549	+	0.931184i	$0.381223\pi$
$734$		0			0
$735$	16.4354	−	8.04750i	0.606229	−	0.296836i
$736$		0			0
$737$	−14.0452	−	7.15641i	−0.517363	−	0.263610i
$738$		0			0
$739$	−14.0319	+	43.1859i	−0.516173	+	1.58862i	0.264964	+	0.964258i	$0.414640\pi$
$739$	−14.0319	+	43.1859i	−0.516173	+	1.58862i	−0.781137	+	0.624359i	$0.785360\pi$
$740$		0			0
$741$	19.4807	+	59.9553i	0.715640	+	2.20251i
$742$		0			0
$743$	−11.6889	+	11.6889i	−0.428825	+	0.428825i	−0.888228	−	0.459403i	$-0.848063\pi$
$743$	−11.6889	+	11.6889i	−0.428825	+	0.428825i	0.459403	+	0.888228i	$0.348063\pi$
$744$		0			0
$745$	−12.7491	+	3.91930i	−0.467089	+	0.143592i
$746$		0			0
$747$	−6.64570	−	41.9593i	−0.243153	−	1.53521i
$748$		0			0
$749$		−	0.224911i		−	0.00821806i
$750$		0			0
$751$			1.17883i			0.0430162i	0.999769	+	0.0215081i	$0.00684677\pi$
$751$			1.17883i			0.0430162i	−0.999769	+	0.0215081i	$0.993153\pi$
$752$		0			0
$753$	−0.613271	−	3.87204i	−0.0223488	−	0.141105i
$754$		0			0
$755$	−16.8083	+	5.16718i	−0.611717	+	0.188053i
$756$		0			0
$757$	−30.8942	+	30.8942i	−1.12287	+	1.12287i	−0.131559	+	0.991308i	$0.541998\pi$
$757$	−30.8942	+	30.8942i	−1.12287	+	1.12287i	−0.991308	+	0.131559i	$0.958002\pi$
$758$		0			0
$759$	−10.2823	−	31.6457i	−0.373225	−	1.14867i
$760$		0			0
$761$	13.3968	−	41.2310i	0.485633	−	1.49462i	−0.345430	−	0.938444i	$-0.612267\pi$
$761$	13.3968	−	41.2310i	0.485633	−	1.49462i	0.831063	−	0.556179i	$-0.187733\pi$
$762$		0			0
$763$	−3.71171	−	1.89121i	−0.134373	−	0.0684663i
$764$		0			0
$765$	−33.4176	+	16.3627i	−1.20822	+	0.591595i
$766$		0			0
$767$	17.2167	+	2.72686i	0.621660	+	0.0984613i
$768$		0			0
$769$	29.3429	+	40.3870i	1.05813	+	1.45639i	0.881541	+	0.472107i	$0.156506\pi$
$769$	29.3429	+	40.3870i	1.05813	+	1.45639i	0.176589	+	0.984285i	$0.443494\pi$
$770$		0			0
$771$	−56.6329	+	77.9485i	−2.03959	+	2.80725i
$772$		0			0
$773$	−11.2904	+	5.75273i	−0.406086	+	0.206911i	−0.645089	−	0.764108i	$-0.723180\pi$
$773$	−11.2904	+	5.75273i	−0.406086	+	0.206911i	0.239002	+	0.971019i	$0.423180\pi$
$774$		0			0
$775$	−13.0135	−	4.69112i	−0.467460	−	0.168510i
$776$		0			0
$777$	10.5304	+	20.6671i	0.377776	+	0.741427i
$778$		0			0
$779$	−18.3524	−	13.3338i	−0.657544	−	0.477734i
$780$		0			0
$781$	−13.8128	+	10.0356i	−0.494262	+	0.359102i
$782$		0			0
$783$	9.04515	−	57.1088i	0.323247	−	2.04090i
$784$		0			0
$785$	−25.1272	−	13.3107i	−0.896829	−	0.475079i
$786$		0			0
$787$	−14.3613	+	28.1856i	−0.511924	+	1.00471i	0.479927	+	0.877308i	$0.340663\pi$
$787$	−14.3613	+	28.1856i	−0.511924	+	1.00471i	−0.991852	+	0.127399i	$0.959337\pi$
$788$		0			0
$789$	−29.1114	−	9.45887i	−1.03639	−	0.336745i
$790$		0			0
$791$	6.68707	−	2.17276i	0.237765	−	0.0772545i
$792$		0			0
$793$	−4.32515	−	4.32515i	−0.153591	−	0.153591i
$794$		0			0
$795$	−41.8978	+	29.4336i	−1.48596	+	1.04390i
$796$		0			0
$797$	−34.8296	+	5.51647i	−1.23373	+	0.195403i	−0.739037	−	0.673665i	$-0.764719\pi$
$797$	−34.8296	+	5.51647i	−1.23373	+	0.195403i	−0.494692	+	0.869069i	$0.664719\pi$
$798$		0			0
$799$	16.3676			0.579046
$800$		0			0
$801$	0.371747			0.0131350
$802$		0			0
$803$	2.18298	−	0.345750i	0.0770358	−	0.0122013i
$804$		0			0
$805$	−26.3794	−	0.419744i	−0.929750	−	0.0147940i
$806$		0			0
$807$	30.2491	+	30.2491i	1.06482	+	1.06482i
$808$		0			0
$809$	−18.8208	+	6.11524i	−0.661704	+	0.215001i	−0.620568	−	0.784153i	$-0.713098\pi$
$809$	−18.8208	+	6.11524i	−0.661704	+	0.215001i	−0.0411361	+	0.999154i	$0.513098\pi$
$810$		0			0
$811$	−18.8755	−	6.13303i	−0.662809	−	0.215360i	−0.0417556	−	0.999128i	$-0.513295\pi$
$811$	−18.8755	−	6.13303i	−0.662809	−	0.215360i	−0.621054	+	0.783768i	$0.713295\pi$
$812$		0			0
$813$	−11.0932	+	21.7717i	−0.389057	+	0.763567i
$814$		0			0
$815$	3.28778	−	18.8156i	0.115166	−	0.659083i
$816$		0			0
$817$	−5.86031	+	37.0005i	−0.205026	+	1.29448i
$818$		0			0
$819$	77.7071	−	56.4575i	2.71531	−	1.97279i
$820$		0			0
$821$	−3.09509	−	2.24872i	−0.108020	−	0.0784808i	0.532464	−	0.846453i	$-0.321266\pi$
$821$	−3.09509	−	2.24872i	−0.108020	−	0.0784808i	−0.640484	+	0.767972i	$0.721266\pi$
$822$		0			0
$823$	−5.52402	−	10.8415i	−0.192555	−	0.377911i	0.774463	−	0.632620i	$-0.218020\pi$
$823$	−5.52402	−	10.8415i	−0.192555	−	0.377911i	−0.967018	+	0.254709i	$0.918020\pi$
$824$		0			0
$825$	26.7533	−	12.5759i	0.931431	−	0.437838i
$826$		0			0
$827$	34.3578	−	17.5062i	1.19474	−	0.608750i	0.260526	−	0.965467i	$-0.416104\pi$
$827$	34.3578	−	17.5062i	1.19474	−	0.608750i	0.934213	+	0.356717i	$0.116104\pi$
$828$		0			0
$829$	24.1681	−	33.2646i	0.839394	−	1.15533i	−0.146707	−	0.989180i	$-0.546867\pi$
$829$	24.1681	−	33.2646i	0.839394	−	1.15533i	0.986101	−	0.166147i	$-0.0531327\pi$
$830$		0			0
$831$	9.60490	+	13.2200i	0.333190	+	0.458597i
$832$		0			0
$833$	−6.23112	−	0.986913i	−0.215896	−	0.0341945i
$834$		0			0
$835$	0.516187	+	3.63219i	0.0178634	+	0.125697i
$836$		0			0
$837$	−29.9776	−	15.2744i	−1.03618	−	0.527959i
$838$		0			0
$839$	10.7884	−	33.2034i	0.372458	−	1.14631i	−0.572719	−	0.819751i	$-0.694112\pi$
$839$	10.7884	−	33.2034i	0.372458	−	1.14631i	0.945178	−	0.326557i	$-0.105888\pi$
$840$		0			0
$841$	1.97555	+	6.08012i	0.0681225	+	0.209659i
$842$		0			0
$843$	12.4714	−	12.4714i	0.429537	−	0.429537i
$844$		0			0
$845$	−42.2581	+	56.2587i	−1.45372	+	1.93536i
$846$		0			0
$847$	2.44611	+	15.4441i	0.0840494	+	0.530667i
$848$		0			0
$849$		−	60.6788i		−	2.08249i
$850$		0			0
$851$			19.8193i			0.679398i
$852$		0			0
$853$	−2.54315	−	16.0568i	−0.0870760	−	0.549776i	−0.992203	−	0.124634i	$-0.960224\pi$
$853$	−2.54315	−	16.0568i	−0.0870760	−	0.549776i	0.905127	−	0.425142i	$-0.139776\pi$
$854$		0			0
$855$	43.7336	+	14.9833i	1.49566	+	0.512417i
$856$		0			0
$857$	17.7376	−	17.7376i	0.605904	−	0.605904i	−0.335969	−	0.941873i	$-0.609064\pi$
$857$	17.7376	−	17.7376i	0.605904	−	0.605904i	0.941873	+	0.335969i	$0.109064\pi$
$858$		0			0
$859$	−5.51226	−	16.9650i	−0.188076	−	0.578838i	0.811912	−	0.583780i	$-0.198427\pi$
$859$	−5.51226	−	16.9650i	−0.188076	−	0.578838i	−0.999988	+	0.00494198i	$0.998427\pi$
$860$		0			0
$861$	−15.3443	+	47.2249i	−0.522933	+	1.60942i
$862$		0			0
$863$	45.3876	+	23.1261i	1.54501	+	0.787223i	0.998730	−	0.0503786i	$-0.0160428\pi$
$863$	45.3876	+	23.1261i	1.54501	+	0.787223i	0.546282	+	0.837602i	$0.316043\pi$
$864$		0			0
$865$	−13.2585	−	13.6872i	−0.450801	−	0.465379i
$866$		0			0
$867$	−34.5509	−	5.47233i	−1.17341	−	0.185850i
$868$		0			0
$869$	6.30599	+	8.67945i	0.213916	+	0.294430i
$870$		0			0
$871$	32.8321	−	45.1896i	1.11247	−	1.53119i
$872$		0			0
$873$	−96.6322	+	49.2366i	−3.27051	+	1.66641i
$874$		0			0
$875$	−2.55791	−	23.2991i	−0.0864732	−	0.787652i
$876$		0			0
$877$	3.37829	+	6.63027i	0.114077	+	0.223888i	0.940985	−	0.338449i	$-0.109902\pi$
$877$	3.37829	+	6.63027i	0.114077	+	0.223888i	−0.826908	+	0.562337i	$0.809902\pi$
$878$		0			0
$879$	−51.7444	−	37.5945i	−1.74530	−	1.26803i
$880$		0			0
$881$	14.7119	−	10.6889i	0.495658	−	0.360117i	−0.311698	−	0.950181i	$-0.600898\pi$
$881$	14.7119	−	10.6889i	0.495658	−	0.360117i	0.807356	+	0.590065i	$0.200898\pi$
$882$		0			0
$883$	−6.72079	+	42.4334i	−0.226173	+	1.42800i	0.569361	+	0.822088i	$0.307191\pi$
$883$	−6.72079	+	42.4334i	−0.226173	+	1.42800i	−0.795533	+	0.605910i	$0.792809\pi$
$884$		0			0
$885$	13.1904	−	12.7772i	0.443390	−	0.429501i
$886$		0			0
$887$	5.10177	−	10.0128i	0.171301	−	0.336197i	−0.789356	−	0.613936i	$-0.789585\pi$
$887$	5.10177	−	10.0128i	0.171301	−	0.336197i	0.960656	+	0.277739i	$0.0895852\pi$
$888$		0			0
$889$	18.2412	+	5.92694i	0.611792	+	0.198783i
$890$		0			0
$891$	31.4894	−	10.2315i	1.05493	−	0.342769i
$892$		0			0
$893$	−14.3795	−	14.3795i	−0.481192	−	0.481192i
$894$		0			0
$895$	10.4004	−	30.3571i	0.347647	−	1.01472i
$896$		0			0
$897$	116.456	−	18.4448i	3.88834	−	0.615853i
$898$		0			0
$899$	−13.1545			−0.438728
$900$		0			0
$901$	17.6521			0.588075
$902$		0			0
$903$	80.9909	−	12.8277i	2.69521	−	0.426879i
$904$		0			0
$905$	22.6137	+	16.9860i	0.751704	+	0.564634i
$906$		0			0
$907$	−22.0214	−	22.0214i	−0.731208	−	0.731208i	0.239651	−	0.970859i	$-0.422967\pi$
$907$	−22.0214	−	22.0214i	−0.731208	−	0.731208i	−0.970859	+	0.239651i	$0.922967\pi$
$908$		0			0
$909$	−88.6813	+	28.8143i	−2.94137	+	0.955710i
$910$		0			0
$911$	−16.3818	−	5.32276i	−0.542753	−	0.176351i	0.0247935	−	0.999693i	$-0.492107\pi$
$911$	−16.3818	−	5.32276i	−0.542753	−	0.176351i	−0.567546	+	0.823342i	$0.692107\pi$
$912$		0			0
$913$	5.28251	−	10.3675i	0.174826	−	0.343115i
$914$		0			0
$915$	−6.37992	+	0.906679i	−0.210914	+	0.0299739i
$916$		0			0
$917$	5.93856	−	37.4946i	0.196109	−	1.23818i
$918$		0			0
$919$	45.1693	−	32.8174i	1.49000	−	1.08255i	0.515839	−	0.856685i	$-0.327480\pi$
$919$	45.1693	−	32.8174i	1.49000	−	1.08255i	0.974159	−	0.225862i	$-0.0725198\pi$
$920$		0			0
$921$	29.4526	+	21.3986i	0.970496	+	0.705107i
$922$		0			0
$923$	−27.4665	−	53.9061i	−0.904072	−	1.77434i
$924$		0			0
$925$	−17.4700	+	2.19979i	−0.574411	+	0.0723286i
$926$		0			0
$927$	−71.6518	+	36.5084i	−2.35335	+	1.19909i
$928$		0			0
$929$	19.9905	−	27.5145i	0.655866	−	0.902722i	−0.343470	−	0.939164i	$-0.611602\pi$
$929$	19.9905	−	27.5145i	0.655866	−	0.902722i	0.999336	+	0.0364414i	$0.0116022\pi$
$930$		0			0
$931$	4.60721	+	6.34128i	0.150995	+	0.207827i
$932$		0			0
$933$	−76.2900	−	12.0831i	−2.49762	−	0.395584i
$934$		0			0
$935$	−10.0391	−	1.75421i	−0.328315	−	0.0573687i
$936$		0			0
$937$	−16.4853	−	8.39969i	−0.538552	−	0.274406i	0.163486	−	0.986546i	$-0.447726\pi$
$937$	−16.4853	−	8.39969i	−0.538552	−	0.274406i	−0.702038	+	0.712140i	$0.747726\pi$
$938$		0			0
$939$	18.6321	−	57.3438i	0.608037	−	1.87134i
$940$		0			0
$941$	13.7612	+	42.3526i	0.448602	+	1.38066i	0.878484	+	0.477771i	$0.158555\pi$
$941$	13.7612	+	42.3526i	0.448602	+	1.38066i	−0.429882	+	0.902885i	$0.641445\pi$
$942$		0			0
$943$	−30.0013	+	30.0013i	−0.976978	+	0.976978i
$944$		0			0
$945$	0.906978	−	57.0003i	0.0295040	−	1.85422i
$946$		0			0
$947$	3.46390	+	21.8702i	0.112562	+	0.710686i	0.977834	+	0.209383i	$0.0671456\pi$
$947$	3.46390	+	21.8702i	0.112562	+	0.710686i	−0.865272	+	0.501302i	$0.832854\pi$
$948$		0			0
$949$			7.83181i			0.254231i
$950$		0			0
$951$			9.08042i			0.294453i
$952$		0			0
$953$	−4.50148	−	28.4212i	−0.145817	−	0.920654i	−0.946766	−	0.321921i	$-0.895671\pi$
$953$	−4.50148	−	28.4212i	−0.145817	−	0.920654i	0.800949	−	0.598732i	$-0.204329\pi$
$954$		0			0
$955$	34.1029	+	48.5444i	1.10354	+	1.57086i
$956$		0			0
$957$	19.8777	−	19.8777i	0.642554	−	0.642554i
$958$		0			0
$959$	−10.3256	−	31.7788i	−0.333430	−	1.02619i
$960$		0			0
$961$	7.21420	−	22.2030i	0.232716	−	0.716227i
$962$		0			0
$963$	0.656760	+	0.334636i	0.0211638	+	0.0107835i
$964$		0			0
$965$	18.9713	−	35.8131i	0.610709	−	1.15286i
$966$		0			0
$967$	−39.5249	−	6.26013i	−1.27104	−	0.201312i	−0.515768	−	0.856728i	$-0.672493\pi$
$967$	−39.5249	−	6.26013i	−1.27104	−	0.201312i	−0.755268	+	0.655416i	$0.772493\pi$
$968$		0			0
$969$	−13.4580	−	18.5233i	−0.432332	−	0.595054i
$970$		0			0
$971$	−2.20060	+	3.02886i	−0.0706206	+	0.0972009i	−0.842866	−	0.538123i	$-0.819133\pi$
$971$	−2.20060	+	3.02886i	−0.0706206	+	0.0972009i	0.772246	+	0.635324i	$0.219133\pi$
$972$		0			0
$973$	22.0896	−	11.2552i	0.708161	−	0.360826i
$974$		0			0
$975$	29.1841	+	100.604i	0.934639	+	3.22192i
$976$		0			0
$977$	−6.45251	−	12.6638i	−0.206434	−	0.405150i	0.764456	−	0.644676i	$-0.223008\pi$
$977$	−6.45251	−	12.6638i	−0.206434	−	0.405150i	−0.970890	+	0.239526i	$0.923008\pi$
$978$		0			0
$979$	0.0823740	+	0.0598482i	0.00263269	+	0.00191276i
$980$		0			0
$981$	11.0450	−	8.02466i	0.352640	−	0.256208i
$982$		0			0
$983$	3.31062	−	20.9025i	0.105593	−	0.666685i	−0.876941	−	0.480598i	$-0.840420\pi$
$983$	3.31062	−	20.9025i	0.105593	−	0.666685i	0.982533	−	0.186087i	$-0.0595805\pi$
$984$		0			0
$985$	−2.60366	−	5.31745i	−0.0829594	−	0.169428i
$986$		0			0
$987$	−20.2085	+	39.6615i	−0.643244	+	1.26244i
$988$		0			0
$989$	66.6367	+	21.6516i	2.11892	+	0.688480i
$990$		0			0
$991$	−28.1717	+	9.15355i	−0.894905	+	0.290772i	−0.720132	−	0.693837i	$-0.755919\pi$
$991$	−28.1717	+	9.15355i	−0.894905	+	0.290772i	−0.174772	+	0.984609i	$0.555919\pi$
$992$		0			0
$993$	65.6482	+	65.6482i	2.08328	+	2.08328i
$994$		0			0
$995$	−2.15331	−	7.00450i	−0.0682646	−	0.222057i
$996$		0			0
$997$	−34.8626	+	5.52170i	−1.10411	+	0.174874i	−0.681772	−	0.731564i	$-0.738791\pi$
$997$	−34.8626	+	5.52170i	−1.10411	+	0.174874i	−0.422338	+	0.906438i	$0.638791\pi$
$998$		0			0
$999$	−42.8254			−1.35494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.303.1	✓	80
4.3	odd	2	inner	400.2.bi.d.303.10	yes	80
25.17	odd	20	inner	400.2.bi.d.367.10	yes	80
100.67	even	20	inner	400.2.bi.d.367.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.303.1	✓	80	1.1	even	1	trivial
400.2.bi.d.303.10	yes	80	4.3	odd	2	inner
400.2.bi.d.367.1	yes	80	100.67	even	20	inner
400.2.bi.d.367.10	yes	80	25.17	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.10308 + 0.491480i) q^{3} +(-0.657061 - 2.13735i) q^{5} +(-1.48242 - 1.48242i) q^{7} +(6.53441 - 2.12316i) q^{9} +(1.78975 + 0.581525i) q^{11} +(-3.02736 + 5.94154i) q^{13} +(3.08938 + 6.30945i) q^{15} +(0.378869 - 2.39209i) q^{17} +(-2.43438 + 1.76868i) q^{19} +(5.32864 + 3.87148i) q^{21} +(2.55503 + 5.01453i) q^{23} +(-4.13654 + 2.80874i) q^{25} +(-10.8353 + 5.52089i) q^{27} +(-2.79473 + 3.84662i) q^{29} +(1.62620 + 2.23827i) q^{31} +(-5.83955 - 0.924894i) q^{33} +(-2.19440 + 4.14248i) q^{35} +(3.13777 + 1.59877i) q^{37} +(6.47402 - 19.9250i) q^{39} +(2.32964 + 7.16989i) q^{41} +(8.80325 - 8.80325i) q^{43} +(-8.83145 - 12.5713i) q^{45} +(1.05721 + 6.67497i) q^{47} -2.60489i q^{49} +7.60906i q^{51} +(1.14017 + 7.19877i) q^{53} +(0.0669477 - 4.20742i) q^{55} +(6.68480 - 6.68480i) q^{57} +(-0.807784 - 2.48610i) q^{59} +(-0.283453 + 0.872379i) q^{61} +(-12.8341 - 6.53931i) q^{63} +(14.6883 + 2.56659i) q^{65} +(-8.27337 - 1.31037i) q^{67} +(-10.3930 - 14.3048i) q^{69} +(-5.33283 + 7.34002i) q^{71} +(1.04647 - 0.533201i) q^{73} +(11.4556 - 10.7488i) q^{75} +(-1.79109 - 3.51521i) q^{77} +(4.61218 + 3.35095i) q^{79} +(14.2341 - 10.3417i) q^{81} +(0.967254 - 6.10700i) q^{83} +(-5.36167 + 0.761971i) q^{85} +(6.78175 - 13.3099i) q^{87} +(0.0514581 + 0.0167197i) q^{89} +(13.2956 - 4.32001i) q^{91} +(-6.14629 - 6.14629i) q^{93} +(5.37982 + 4.04099i) q^{95} +(-15.5905 + 2.46930i) q^{97} +12.9296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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