LMFDB - Embedded newform 400.2.bi.d.223.9

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)

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")

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);

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			223.9
Character	$\chi$	$=$	400.223
Dual form			400.2.bi.d.287.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13079 + 2.21930i) q^{3} +(-0.139160 - 2.23173i) q^{5} +(-0.125831 - 0.125831i) q^{7} +(-1.88325 + 2.59207i) q^{9} +(3.73866 + 5.14582i) q^{11} +(0.413421 + 2.61024i) q^{13} +(4.79553 - 2.83246i) q^{15} +(3.67632 + 1.87318i) q^{17} +(-0.529169 - 1.62861i) q^{19} +(0.136968 - 0.421546i) q^{21} +(0.203992 - 1.28795i) q^{23} +(-4.96127 + 0.621135i) q^{25} +(-0.501815 - 0.0794796i) q^{27} +(-8.12566 - 2.64019i) q^{29} +(1.69590 - 0.551033i) q^{31} +(-7.19248 + 14.1160i) q^{33} +(-0.263311 + 0.298332i) q^{35} +(6.42016 - 1.01685i) q^{37} +(-5.32541 + 3.86914i) q^{39} +(-8.51041 - 6.18317i) q^{41} +(2.70230 - 2.70230i) q^{43} +(6.04689 + 3.84221i) q^{45} +(-9.15432 + 4.66436i) q^{47} -6.96833i q^{49} +10.2770i q^{51} +(8.64413 - 4.40440i) q^{53} +(10.9638 - 9.05978i) q^{55} +(3.01600 - 3.01600i) q^{57} +(-4.80977 - 3.49451i) q^{59} +(6.89430 - 5.00901i) q^{61} +(0.563135 - 0.0891919i) q^{63} +(5.76783 - 1.28589i) q^{65} +(1.50776 - 2.95914i) q^{67} +(3.08903 - 1.00369i) q^{69} +(-7.64731 - 2.48476i) q^{71} +(-1.62013 - 0.256603i) q^{73} +(-6.98864 - 10.3082i) q^{75} +(0.177065 - 1.11794i) q^{77} +(-2.78770 + 8.57966i) q^{79} +(2.57920 + 7.93795i) q^{81} +(9.56955 + 4.87593i) q^{83} +(3.66884 - 8.46524i) q^{85} +(-3.32905 - 21.0188i) q^{87} +(0.221905 + 0.305426i) q^{89} +(0.276428 - 0.380471i) q^{91} +(3.14062 + 3.14062i) q^{93} +(-3.56099 + 1.40760i) q^{95} +(-4.08577 - 8.01878i) q^{97} -20.3792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$	$-1$

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
$3$	1.13079	+	2.21930i	0.652862	+	1.28131i	0.945666	+	0.325141i	$0.105412\pi$
$3$	1.13079	+	2.21930i	0.652862	+	1.28131i	−0.292804	+	0.956173i	$0.594588\pi$
$4$		0			0
$5$	−0.139160	−	2.23173i	−0.0622341	−	0.998062i
$5$	−0.139160	−	2.23173i	−0.0622341	−	0.998062i
$6$		0			0
$7$	−0.125831	−	0.125831i	−0.0475597	−	0.0475597i	0.682927	−	0.730487i	$-0.260707\pi$
$7$	−0.125831	−	0.125831i	−0.0475597	−	0.0475597i	−0.730487	+	0.682927i	$0.760707\pi$
$8$		0			0
$9$	−1.88325	+	2.59207i	−0.627751	+	0.864025i
$10$		0			0
$11$	3.73866	+	5.14582i	1.12725	+	1.55152i	0.793194	+	0.608969i	$0.208417\pi$
$11$	3.73866	+	5.14582i	1.12725	+	1.55152i	0.334054	+	0.942554i	$0.391583\pi$
$12$		0			0
$13$	0.413421	+	2.61024i	0.114662	+	0.723950i	0.976299	+	0.216425i	$0.0694396\pi$
$13$	0.413421	+	2.61024i	0.114662	+	0.723950i	−0.861637	+	0.507525i	$0.830560\pi$
$14$		0			0
$15$	4.79553	−	2.83246i	1.23820	−	0.731338i
$16$		0			0
$17$	3.67632	+	1.87318i	0.891639	+	0.454313i	0.838894	−	0.544295i	$-0.183203\pi$
$17$	3.67632	+	1.87318i	0.891639	+	0.454313i	0.0527450	+	0.998608i	$0.483203\pi$
$18$		0			0
$19$	−0.529169	−	1.62861i	−0.121400	−	0.373630i	0.871828	−	0.489812i	$-0.162934\pi$
$19$	−0.529169	−	1.62861i	−0.121400	−	0.373630i	−0.993228	+	0.116182i	$0.962934\pi$
$20$		0			0
$21$	0.136968	−	0.421546i	0.0298890	−	0.0919888i
$22$		0			0
$23$	0.203992	−	1.28795i	0.0425353	−	0.268557i	−0.957250	−	0.289261i	$-0.906591\pi$
$23$	0.203992	−	1.28795i	0.0425353	−	0.268557i	0.999786	+	0.0207035i	$0.00659060\pi$
$24$		0			0
$25$	−4.96127	+	0.621135i	−0.992254	+	0.124227i
$26$		0			0
$27$	−0.501815	−	0.0794796i	−0.0965743	−	0.0152959i
$28$		0			0
$29$	−8.12566	−	2.64019i	−1.50890	−	0.490270i	−0.566299	−	0.824200i	$-0.691625\pi$
$29$	−8.12566	−	2.64019i	−1.50890	−	0.490270i	−0.942598	+	0.333929i	$0.891625\pi$
$30$		0			0
$31$	1.69590	−	0.551033i	0.304593	−	0.0989684i	−0.152733	−	0.988268i	$-0.548807\pi$
$31$	1.69590	−	0.551033i	0.304593	−	0.0989684i	0.457326	+	0.889299i	$0.348807\pi$
$32$		0			0
$33$	−7.19248	+	14.1160i	−1.25205	+	2.45729i
$34$		0			0
$35$	−0.263311	+	0.298332i	−0.0445077	+	0.0504273i
$36$		0			0
$37$	6.42016	−	1.01685i	1.05547	−	0.167170i	0.395501	−	0.918465i	$-0.370571\pi$
$37$	6.42016	−	1.01685i	1.05547	−	0.167170i	0.659966	+	0.751296i	$0.270571\pi$
$38$		0			0
$39$	−5.32541	+	3.86914i	−0.852748	+	0.619558i
$40$		0			0
$41$	−8.51041	−	6.18317i	−1.32910	−	0.965650i	−0.999770	−	0.0214356i	$-0.993176\pi$
$41$	−8.51041	−	6.18317i	−1.32910	−	0.965650i	−0.329332	−	0.944214i	$-0.606824\pi$
$42$		0			0
$43$	2.70230	−	2.70230i	0.412098	−	0.412098i	−0.470371	−	0.882469i	$-0.655880\pi$
$43$	2.70230	−	2.70230i	0.412098	−	0.412098i	0.882469	+	0.470371i	$0.155880\pi$
$44$		0			0
$45$	6.04689	+	3.84221i	0.901418	+	0.572762i
$46$		0			0
$47$	−9.15432	+	4.66436i	−1.33530	+	0.680367i	−0.968285	−	0.249850i	$-0.919619\pi$
$47$	−9.15432	+	4.66436i	−1.33530	+	0.680367i	−0.367010	+	0.930217i	$0.619619\pi$
$48$		0			0
$49$		−	6.96833i		−	0.995476i
$50$		0			0
$51$			10.2770i			1.43907i
$52$		0			0
$53$	8.64413	−	4.40440i	1.18736	−	0.604991i	0.255149	−	0.966902i	$-0.417875\pi$
$53$	8.64413	−	4.40440i	1.18736	−	0.604991i	0.932213	+	0.361910i	$0.117875\pi$
$54$		0			0
$55$	10.9638	−	9.05978i	1.47836	−	1.22162i
$56$		0			0
$57$	3.01600	−	3.01600i	0.399480	−	0.399480i
$58$		0			0
$59$	−4.80977	−	3.49451i	−0.626179	−	0.454946i	0.228895	−	0.973451i	$-0.426489\pi$
$59$	−4.80977	−	3.49451i	−0.626179	−	0.454946i	−0.855074	+	0.518505i	$0.826489\pi$
$60$		0			0
$61$	6.89430	−	5.00901i	0.882725	−	0.641337i	−0.0512458	−	0.998686i	$-0.516319\pi$
$61$	6.89430	−	5.00901i	0.882725	−	0.641337i	0.933971	+	0.357349i	$0.116319\pi$
$62$		0			0
$63$	0.563135	−	0.0891919i	0.0709484	−	0.0112371i
$64$		0			0
$65$	5.76783	−	1.28589i	0.715411	−	0.159495i
$66$		0			0
$67$	1.50776	−	2.95914i	0.184202	−	0.361516i	−0.780378	−	0.625308i	$-0.784973\pi$
$67$	1.50776	−	2.95914i	0.184202	−	0.361516i	0.964580	+	0.263792i	$0.0849732\pi$
$68$		0			0
$69$	3.08903	−	1.00369i	0.371875	−	0.120830i
$70$		0			0
$71$	−7.64731	−	2.48476i	−0.907568	−	0.294887i	−0.182211	−	0.983259i	$-0.558325\pi$
$71$	−7.64731	−	2.48476i	−0.907568	−	0.294887i	−0.725357	+	0.688373i	$0.758325\pi$
$72$		0			0
$73$	−1.62013	−	0.256603i	−0.189621	−	0.0300331i	0.0609013	−	0.998144i	$-0.480603\pi$
$73$	−1.62013	−	0.256603i	−0.189621	−	0.0300331i	−0.250523	+	0.968111i	$0.580603\pi$
$74$		0			0
$75$	−6.98864	−	10.3082i	−0.806978	−	1.19029i
$76$		0			0
$77$	0.177065	−	1.11794i	0.0201784	−	0.127402i
$78$		0			0
$79$	−2.78770	+	8.57966i	−0.313641	+	0.965288i	0.662669	+	0.748912i	$0.269424\pi$
$79$	−2.78770	+	8.57966i	−0.313641	+	0.965288i	−0.976310	+	0.216375i	$0.930576\pi$
$80$		0			0
$81$	2.57920	+	7.93795i	0.286577	+	0.881994i
$82$		0			0
$83$	9.56955	+	4.87593i	1.05039	+	0.535203i	0.891936	−	0.452163i	$-0.149347\pi$
$83$	9.56955	+	4.87593i	1.05039	+	0.535203i	0.158459	+	0.987365i	$0.449347\pi$
$84$		0			0
$85$	3.66884	−	8.46524i	0.397942	−	0.918184i
$86$		0			0
$87$	−3.32905	−	21.0188i	−0.356911	−	2.25345i
$88$		0			0
$89$	0.221905	+	0.305426i	0.0235219	+	0.0323751i	0.820616	−	0.571480i	$-0.193631\pi$
$89$	0.221905	+	0.305426i	0.0235219	+	0.0323751i	−0.797094	+	0.603855i	$0.793631\pi$
$90$		0			0
$91$	0.276428	−	0.380471i	0.0289775	−	0.0398842i
$92$		0			0
$93$	3.14062	+	3.14062i	0.325667	+	0.325667i
$94$		0			0
$95$	−3.56099	+	1.40760i	−0.365350	+	0.144417i
$96$		0			0
$97$	−4.08577	−	8.01878i	−0.414848	−	0.814184i	−0.999995	−	0.00325706i	$-0.998963\pi$
$97$	−4.08577	−	8.01878i	−0.414848	−	0.814184i	0.585147	−	0.810927i	$-0.301037\pi$
$98$		0			0
$99$	−20.3792			−2.04819
$100$		0			0
$101$	−5.70850			−0.568017			−0.284009	−	0.958822i	$-0.591664\pi$
$101$	−5.70850			−0.568017			−0.284009	+	0.958822i	$0.591664\pi$
$102$		0			0
$103$	7.62445	+	14.9638i	0.751259	+	1.47443i	0.876037	+	0.482244i	$0.160178\pi$
$103$	7.62445	+	14.9638i	0.751259	+	1.47443i	−0.124778	+	0.992185i	$0.539822\pi$
$104$		0			0
$105$	−0.959838	−	0.247015i	−0.0936706	−	0.0241062i
$106$		0			0
$107$	−7.70566	−	7.70566i	−0.744934	−	0.744934i	0.228589	−	0.973523i	$-0.426589\pi$
$107$	−7.70566	−	7.70566i	−0.744934	−	0.744934i	−0.973523	+	0.228589i	$0.926589\pi$
$108$		0			0
$109$	2.68570	−	3.69656i	0.257244	−	0.354066i	−0.660788	−	0.750573i	$-0.729778\pi$
$109$	2.68570	−	3.69656i	0.257244	−	0.354066i	0.918032	+	0.396507i	$0.129778\pi$
$110$		0			0
$111$	9.51655	+	13.0984i	0.903271	+	1.24325i
$112$		0			0
$113$	−2.92518	−	18.4689i	−0.275178	−	1.73741i	−0.607571	−	0.794265i	$-0.707856\pi$
$113$	−2.92518	−	18.4689i	−0.275178	−	1.73741i	0.332393	−	0.943141i	$-0.392144\pi$
$114$		0			0
$115$	−2.90276	−	0.276024i	−0.270684	−	0.0257394i
$116$		0			0
$117$	−7.54451	−	3.84412i	−0.697490	−	0.355389i
$118$		0			0
$119$	−0.226891	−	0.698300i	−0.0207991	−	0.0640130i
$120$		0			0
$121$	−9.10272	+	28.0153i	−0.827520	+	2.54685i
$122$		0			0
$123$	4.09884	−	25.8790i	0.369580	−	2.33343i
$124$		0			0
$125$	2.07662	+	10.9858i	0.185738	+	0.982599i
$126$		0			0
$127$	−14.8014	−	2.34431i	−1.31341	−	0.208024i	−0.539859	−	0.841756i	$-0.681522\pi$
$127$	−14.8014	−	2.34431i	−1.31341	−	0.208024i	−0.773553	+	0.633732i	$0.781522\pi$
$128$		0			0
$129$	9.05296	+	2.94149i	0.797069	+	0.258983i
$130$		0			0
$131$	−15.4334	+	5.01462i	−1.34842	+	0.438129i	−0.892162	−	0.451716i	$-0.850812\pi$
$131$	−15.4334	+	5.01462i	−1.34842	+	0.438129i	−0.456262	+	0.889846i	$0.650812\pi$
$132$		0			0
$133$	−0.138344	+	0.271516i	−0.0119960	+	0.0235434i
$134$		0			0
$135$	−0.107545	+	1.13098i	−0.00925600	+	0.0973390i
$136$		0			0
$137$	−2.01101	+	0.318513i	−0.171812	+	0.0272124i	−0.241748	−	0.970339i	$-0.577721\pi$
$137$	−2.01101	+	0.318513i	−0.171812	+	0.0272124i	0.0699356	+	0.997552i	$0.477721\pi$
$138$		0			0
$139$	7.81925	−	5.68102i	0.663220	−	0.481858i	−0.204529	−	0.978861i	$-0.565566\pi$
$139$	7.81925	−	5.68102i	0.663220	−	0.481858i	0.867749	+	0.497003i	$0.165566\pi$
$140$		0			0
$141$	−20.7032	−	15.0418i	−1.74353	−	1.26675i
$142$		0			0
$143$	−11.8862	+	11.8862i	−0.993972	+	0.993972i
$144$		0			0
$145$	−4.76143	+	18.5017i	−0.395415	+	1.53648i
$146$		0			0
$147$	15.4648	−	7.87972i	1.27552	−	0.649908i
$148$		0			0
$149$		−	11.3895i		−	0.933064i	−0.884504	−	0.466532i	$-0.845503\pi$
$149$		−	11.3895i		−	0.933064i	0.884504	−	0.466532i	$-0.154497\pi$
$150$		0			0
$151$		−	9.52316i		−	0.774984i	−0.921873	−	0.387492i	$-0.873342\pi$
$151$		−	9.52316i		−	0.774984i	0.921873	−	0.387492i	$-0.126658\pi$
$152$		0			0
$153$	−11.7789	+	6.00163i	−0.952264	+	0.485203i
$154$		0			0
$155$	−1.46576	−	3.70812i	−0.117733	−	0.297844i
$156$		0			0
$157$	−1.63588	+	1.63588i	−0.130557	+	0.130557i	−0.769366	−	0.638808i	$-0.779428\pi$
$157$	−1.63588	+	1.63588i	−0.130557	+	0.130557i	0.638808	+	0.769366i	$0.279428\pi$
$158$		0			0
$159$	19.5494	+	14.2035i	1.55037	+	1.12641i
$160$		0			0
$161$	−0.187733	+	0.136396i	−0.0147955	+	0.0107495i
$162$		0			0
$163$	16.7141	−	2.64726i	1.30915	−	0.207349i	0.537430	−	0.843309i	$-0.319395\pi$
$163$	16.7141	−	2.64726i	1.30915	−	0.207349i	0.771723	+	0.635959i	$0.219395\pi$
$164$		0			0
$165$	32.5042	+	14.0873i	2.53045	+	1.09670i
$166$		0			0
$167$	1.25180	−	2.45679i	0.0968671	−	0.190112i	−0.837488	−	0.546456i	$-0.815977\pi$
$167$	1.25180	−	2.45679i	0.0968671	−	0.190112i	0.934355	+	0.356343i	$0.115977\pi$
$168$		0			0
$169$	5.72130	−	1.85896i	0.440100	−	0.142997i
$170$		0			0
$171$	5.21805	+	1.69545i	0.399034	+	0.129654i
$172$		0			0
$173$	−0.737946	−	0.116879i	−0.0561050	−	0.00888616i	0.128319	−	0.991733i	$-0.459042\pi$
$173$	−0.737946	−	0.116879i	−0.0561050	−	0.00888616i	−0.184424	+	0.982847i	$0.559042\pi$
$174$		0			0
$175$	0.702440	+	0.546124i	0.0530995	+	0.0412831i
$176$		0			0
$177$	2.31651	−	14.6259i	0.174120	−	1.09935i
$178$		0			0
$179$	−5.49888	+	16.9238i	−0.411006	+	1.26495i	0.504769	+	0.863254i	$0.331578\pi$
$179$	−5.49888	+	16.9238i	−0.411006	+	1.26495i	−0.915775	+	0.401692i	$0.868422\pi$
$180$		0			0
$181$	0.00113146	+	0.00348228i	8.41008e−5	+	0.000258836i	0.951099	−	0.308888i	$-0.0999567\pi$
$181$	0.00113146	+	0.00348228i	8.41008e−5	+	0.000258836i	−0.951014	+	0.309146i	$0.899957\pi$
$182$		0			0
$183$	18.9125	+	9.63640i	1.39805	+	0.712343i
$184$		0			0
$185$	−3.16277	−	14.1866i	−0.232532	−	1.04302i
$186$		0			0
$187$	4.10546	+	25.9209i	0.300221	+	1.89552i
$188$		0			0
$189$	0.0531429	+	0.0731449i	0.00386558	+	0.00532051i
$190$		0			0
$191$	4.46083	−	6.13980i	0.322774	−	0.444260i	−0.616538	−	0.787326i	$-0.711465\pi$
$191$	4.46083	−	6.13980i	0.322774	−	0.444260i	0.939312	+	0.343065i	$0.111465\pi$
$192$		0			0
$193$	12.7046	+	12.7046i	0.914499	+	0.914499i	0.996622	−	0.0821232i	$-0.0261701\pi$
$193$	12.7046	+	12.7046i	0.914499	+	0.914499i	−0.0821232	+	0.996622i	$0.526170\pi$
$194$		0			0
$195$	9.37597	+	11.3465i	0.671427	+	0.812538i
$196$		0			0
$197$	6.83642	+	13.4172i	0.487075	+	0.955938i	0.995494	+	0.0948281i	$0.0302301\pi$
$197$	6.83642	+	13.4172i	0.487075	+	0.955938i	−0.508419	+	0.861110i	$0.669770\pi$
$198$		0			0
$199$	−4.50843			−0.319594			−0.159797	−	0.987150i	$-0.551084\pi$
$199$	−4.50843			−0.319594			−0.159797	+	0.987150i	$0.551084\pi$
$200$		0			0
$201$	8.27218			0.583474
$202$		0			0
$203$	0.690243	+	1.35468i	0.0484456	+	0.0950798i
$204$		0			0
$205$	−12.6149	+	19.8534i	−0.881062	+	1.38662i
$206$		0			0
$207$	2.95431	+	2.95431i	0.205338	+	0.205338i
$208$		0			0
$209$	6.40217	−	8.81184i	0.442848	−	0.609527i
$210$		0			0
$211$	−2.31031	−	3.17988i	−0.159049	−	0.218912i	0.722054	−	0.691837i	$-0.243198\pi$
$211$	−2.31031	−	3.17988i	−0.159049	−	0.218912i	−0.881103	+	0.472925i	$0.843198\pi$
$212$		0			0
$213$	−3.13307	−	19.7814i	−0.214674	−	1.35540i
$214$		0			0
$215$	−6.40687	−	5.65477i	−0.436945	−	0.385652i
$216$		0			0
$217$	−0.282735	−	0.144060i	−0.0191933	−	0.00977946i
$218$		0			0
$219$	−1.26254	−	3.88571i	−0.0853148	−	0.262572i
$220$		0			0
$221$	−3.36958	+	10.3705i	−0.226662	+	0.697594i
$222$		0			0
$223$	3.34198	−	21.1004i	0.223795	−	1.41299i	−0.578315	−	0.815813i	$-0.696290\pi$
$223$	3.34198	−	21.1004i	0.223795	−	1.41299i	0.802111	−	0.597175i	$-0.203710\pi$
$224$		0			0
$225$	7.73329	−	14.0297i	0.515553	−	0.935316i
$226$		0			0
$227$	11.7534	+	1.86155i	0.780099	+	0.123556i	0.533769	−	0.845630i	$-0.320775\pi$
$227$	11.7534	+	1.86155i	0.780099	+	0.123556i	0.246330	+	0.969186i	$0.420775\pi$
$228$		0			0
$229$	−9.25382	−	3.00675i	−0.611509	−	0.198691i	−0.0131425	−	0.999914i	$-0.504184\pi$
$229$	−9.25382	−	3.00675i	−0.611509	−	0.198691i	−0.598367	+	0.801222i	$0.704184\pi$
$230$		0			0
$231$	2.68128	−	0.871200i	0.176415	−	0.0573207i
$232$		0			0
$233$	−4.31029	+	8.45942i	−0.282377	+	0.554195i	−0.988011	−	0.154380i	$-0.950662\pi$
$233$	−4.31029	+	8.45942i	−0.282377	+	0.554195i	0.705635	+	0.708576i	$0.250662\pi$
$234$		0			0
$235$	11.6835	+	19.7809i	0.762149	+	1.29036i
$236$		0			0
$237$	−22.1932	+	3.51505i	−1.44160	+	0.228327i
$238$		0			0
$239$	4.87560	−	3.54233i	0.315376	−	0.229134i	−0.418824	−	0.908068i	$-0.637557\pi$
$239$	4.87560	−	3.54233i	0.315376	−	0.229134i	0.734200	+	0.678933i	$0.237557\pi$
$240$		0			0
$241$	−0.0577124	−	0.0419305i	−0.00371758	−	0.00270098i	0.585925	−	0.810365i	$-0.300731\pi$
$241$	−0.0577124	−	0.0419305i	−0.00371758	−	0.00270098i	−0.589642	+	0.807664i	$0.700731\pi$
$242$		0			0
$243$	−15.7779	+	15.7779i	−1.01216	+	1.01216i
$244$		0			0
$245$	−15.5515	+	0.969711i	−0.993546	+	0.0619526i
$246$		0			0
$247$	4.03230	−	2.05456i	0.256569	−	0.130729i
$248$		0			0
$249$			26.7514i			1.69530i
$250$		0			0
$251$			21.9664i			1.38651i	0.720694	+	0.693253i	$0.243823\pi$
$251$			21.9664i			1.38651i	−0.720694	+	0.693253i	$0.756177\pi$
$252$		0			0
$253$	7.39024	−	3.76551i	0.464620	−	0.236736i
$254$		0			0
$255$	22.9356	−	1.43015i	1.43628	−	0.0895594i
$256$		0			0
$257$	3.27612	−	3.27612i	0.204359	−	0.204359i	−0.597506	−	0.801865i	$-0.703841\pi$
$257$	3.27612	−	3.27612i	0.204359	−	0.204359i	0.801865	+	0.597506i	$0.203841\pi$
$258$		0			0
$259$	−0.935807	−	0.679904i	−0.0581482	−	0.0422472i
$260$		0			0
$261$	22.1462	−	16.0902i	1.37082	−	0.995957i
$262$		0			0
$263$	−26.6919	+	4.22759i	−1.64589	+	0.260684i	−0.909450	−	0.415814i	$-0.863497\pi$
$263$	−26.6919	+	4.22759i	−1.64589	+	0.260684i	−0.736445	+	0.676498i	$0.763497\pi$
$264$		0			0
$265$	−11.0324	−	18.6785i	−0.677713	−	1.14741i
$266$		0			0
$267$	−0.426904	+	0.837846i	−0.0261261	+	0.0512753i
$268$		0			0
$269$	−14.0309	+	4.55892i	−0.855480	+	0.277962i	−0.703740	−	0.710458i	$-0.748488\pi$
$269$	−14.0309	+	4.55892i	−0.855480	+	0.277962i	−0.151741	+	0.988420i	$0.548488\pi$
$270$		0			0
$271$	−5.10891	−	1.65999i	−0.310344	−	0.100837i	0.149704	−	0.988731i	$-0.452168\pi$
$271$	−5.10891	−	1.65999i	−0.310344	−	0.100837i	−0.460048	+	0.887894i	$0.652168\pi$
$272$		0			0
$273$	1.15696	+	0.183245i	0.0700224	+	0.0110905i
$274$		0			0
$275$	−21.7447	−	23.2076i	−1.31126	−	1.39947i
$276$		0			0
$277$	−4.52419	+	28.5646i	−0.271832	+	1.71628i	0.353088	+	0.935590i	$0.385132\pi$
$277$	−4.52419	+	28.5646i	−0.271832	+	1.71628i	−0.624920	+	0.780689i	$0.714868\pi$
$278$		0			0
$279$	−1.76550	+	5.43364i	−0.105698	+	0.325304i
$280$		0			0
$281$	4.79558	+	14.7593i	0.286080	+	0.880464i	0.986073	+	0.166314i	$0.0531866\pi$
$281$	4.79558	+	14.7593i	0.286080	+	0.880464i	−0.699993	+	0.714150i	$0.746813\pi$
$282$		0			0
$283$	9.47029	+	4.82535i	0.562950	+	0.286838i	0.712217	−	0.701959i	$-0.247691\pi$
$283$	9.47029	+	4.82535i	0.562950	+	0.286838i	−0.149267	+	0.988797i	$0.547691\pi$
$284$		0			0
$285$	−7.15062	−	6.31121i	−0.423566	−	0.373844i
$286$		0			0
$287$	0.292839	+	1.84891i	0.0172857	+	0.109138i
$288$		0			0
$289$	0.0141820	+	0.0195199i	0.000834236	+	0.00114823i
$290$		0			0
$291$	13.1759	−	18.1351i	0.772387	−	1.06310i
$292$		0			0
$293$	4.30366	+	4.30366i	0.251423	+	0.251423i	0.821554	−	0.570131i	$-0.193108\pi$
$293$	4.30366	+	4.30366i	0.251423	+	0.251423i	−0.570131	+	0.821554i	$0.693108\pi$
$294$		0			0
$295$	−7.12948	+	11.2204i	−0.415094	+	0.653279i
$296$		0			0
$297$	−1.46713	−	2.87940i	−0.0851312	−	0.167079i
$298$		0			0
$299$	3.44620			0.199299
$300$		0			0
$301$	−0.680068			−0.0391985
$302$		0			0
$303$	−6.45512	−	12.6689i	−0.370837	−	0.727808i
$304$		0			0
$305$	−12.1382	−	14.6892i	−0.695030	−	0.841101i
$306$		0			0
$307$	−10.4311	−	10.4311i	−0.595333	−	0.595333i	0.343734	−	0.939067i	$-0.388308\pi$
$307$	−10.4311	−	10.4311i	−0.595333	−	0.595333i	−0.939067	+	0.343734i	$0.888308\pi$
$308$		0			0
$309$	−24.5876	+	33.8419i	−1.39874	+	1.92520i
$310$		0			0
$311$	−8.76260	−	12.0607i	−0.496881	−	0.683899i	0.484757	−	0.874649i	$-0.338908\pi$
$311$	−8.76260	−	12.0607i	−0.496881	−	0.683899i	−0.981639	+	0.190750i	$0.938908\pi$
$312$		0			0
$313$	−0.730700	−	4.61346i	−0.0413016	−	0.260768i	0.958394	−	0.285449i	$-0.0921428\pi$
$313$	−0.730700	−	4.61346i	−0.0413016	−	0.260768i	−0.999695	+	0.0246815i	$0.992143\pi$
$314$		0			0
$315$	−0.277418	−	1.24436i	−0.0156308	−	0.0701115i
$316$		0			0
$317$	9.20580	+	4.69059i	0.517049	+	0.263450i	0.692985	−	0.720952i	$-0.256295\pi$
$317$	9.20580	+	4.69059i	0.517049	+	0.263450i	−0.175936	+	0.984402i	$0.556295\pi$
$318$		0			0
$319$	−16.7931	−	51.6839i	−0.940235	−	2.89375i
$320$		0			0
$321$	8.38769	−	25.8147i	0.468155	−	1.44083i
$322$		0			0
$323$	1.10529	−	6.97853i	0.0615000	−	0.388296i
$324$		0			0
$325$	−3.67240	−	12.6933i	−0.203708	−	0.704098i
$326$		0			0
$327$	11.2407	+	1.78036i	0.621614	+	0.0984540i
$328$		0			0
$329$	1.73882	+	0.564977i	0.0958643	+	0.0311482i
$330$		0			0
$331$	9.14170	−	2.97032i	0.502473	−	0.163263i	−0.0468032	−	0.998904i	$-0.514903\pi$
$331$	9.14170	−	2.97032i	0.502473	−	0.163263i	0.549277	+	0.835641i	$0.314903\pi$
$332$		0			0
$333$	−9.45502	+	18.5565i	−0.518132	+	1.01689i
$334$		0			0
$335$	−6.81383	−	2.95312i	−0.372279	−	0.161346i
$336$		0			0
$337$	30.0736	−	4.76320i	1.63822	−	0.259468i	0.731696	−	0.681631i	$-0.238729\pi$
$337$	30.0736	−	4.76320i	1.63822	−	0.259468i	0.906520	+	0.422164i	$0.138729\pi$
$338$		0			0
$339$	37.6802	−	27.3763i	2.04651	−	1.48688i
$340$		0			0
$341$	9.17592	+	6.66669i	0.496904	+	0.361022i
$342$		0			0
$343$	−1.75765	+	1.75765i	−0.0949042	+	0.0949042i
$344$		0			0
$345$	−2.66983	−	6.75422i	−0.143739	−	0.363635i
$346$		0			0
$347$	−19.5032	+	9.93735i	−1.04698	+	0.533465i	−0.890863	−	0.454273i	$-0.849899\pi$
$347$	−19.5032	+	9.93735i	−1.04698	+	0.533465i	−0.156121	+	0.987738i	$0.549899\pi$
$348$		0			0
$349$		−	19.2942i		−	1.03279i	−0.856349	−	0.516397i	$-0.827273\pi$
$349$		−	19.2942i		−	1.03279i	0.856349	−	0.516397i	$-0.172727\pi$
$350$		0			0
$351$		−	1.34271i		−	0.0716688i
$352$		0			0
$353$	−6.76681	+	3.44786i	−0.360161	+	0.183511i	−0.624702	−	0.780863i	$-0.714780\pi$
$353$	−6.76681	+	3.44786i	−0.360161	+	0.183511i	0.264541	+	0.964374i	$0.414780\pi$
$354$		0			0
$355$	−4.48113	+	17.4125i	−0.237833	+	0.924161i
$356$		0			0
$357$	1.29317	−	1.29317i	0.0684418	−	0.0684418i
$358$		0			0
$359$	18.0610	+	13.1221i	0.953225	+	0.692559i	0.951567	−	0.307440i	$-0.0994724\pi$
$359$	18.0610	+	13.1221i	0.953225	+	0.692559i	0.00165758	+	0.999999i	$0.499472\pi$
$360$		0			0
$361$	12.9990	−	9.44430i	0.684156	−	0.497068i
$362$		0			0
$363$	−72.4676	+	11.4777i	−3.80356	+	0.602425i
$364$		0			0
$365$	−0.347213	+	3.65140i	−0.0181740	+	0.191123i
$366$		0			0
$367$	−15.1432	+	29.7202i	−0.790469	+	1.55138i	0.0431661	+	0.999068i	$0.486256\pi$
$367$	−15.1432	+	29.7202i	−0.790469	+	1.55138i	−0.833635	+	0.552315i	$0.813744\pi$
$368$		0			0
$369$	32.0545	−	10.4151i	1.66869	−	0.542190i
$370$		0			0
$371$	−1.64191	−	0.533489i	−0.0852438	−	0.0276974i
$372$		0			0
$373$	31.7514	+	5.02893i	1.64402	+	0.260388i	0.908738	−	0.417368i	$-0.137047\pi$
$373$	31.7514	+	5.02893i	1.64402	+	0.260388i	0.735287	+	0.677756i	$0.237047\pi$
$374$		0			0
$375$	−22.0326	+	17.0313i	−1.13776	+	0.879490i
$376$		0			0
$377$	3.53220	−	22.3014i	0.181917	−	1.14858i
$378$		0			0
$379$	3.99140	−	12.2843i	0.205025	−	0.631001i	−0.794688	−	0.607018i	$-0.792365\pi$
$379$	3.99140	−	12.2843i	0.205025	−	0.631001i	0.999712	−	0.0239825i	$-0.00763459\pi$
$380$		0			0
$381$	−11.5345	−	35.4997i	−0.590933	−	1.81870i
$382$		0			0
$383$	−16.9707	−	8.64699i	−0.867161	−	0.441841i	−0.0369680	−	0.999316i	$-0.511770\pi$
$383$	−16.9707	−	8.64699i	−0.867161	−	0.441841i	−0.830193	+	0.557476i	$0.811770\pi$
$384$		0			0
$385$	−2.51959	−	0.239589i	−0.128410	−	0.0122106i
$386$		0			0
$387$	1.91545	+	12.0937i	0.0973679	+	0.614757i
$388$		0			0
$389$	11.2986	+	15.5512i	0.572860	+	0.788475i	0.992890	−	0.119036i	$-0.0379803\pi$
$389$	11.2986	+	15.5512i	0.572860	+	0.788475i	−0.420030	+	0.907510i	$0.637980\pi$
$390$		0			0
$391$	3.16251	−	4.35282i	0.159935	−	0.220132i
$392$		0			0
$393$	−28.5809	−	28.5809i	−1.44172	−	1.44172i
$394$		0			0
$395$	19.5355	+	5.02746i	0.982936	+	0.252959i
$396$		0			0
$397$	4.05205	+	7.95261i	0.203367	+	0.399130i	0.970053	−	0.242892i	$-0.0780960\pi$
$397$	4.05205	+	7.95261i	0.203367	+	0.399130i	−0.766687	+	0.642022i	$0.778096\pi$
$398$		0			0
$399$	−0.759015			−0.0379983
$400$		0			0
$401$	14.5424			0.726212			0.363106	−	0.931748i	$-0.381716\pi$
$401$	14.5424			0.726212			0.363106	+	0.931748i	$0.381716\pi$
$402$		0			0
$403$	2.13945	+	4.19891i	0.106574	+	0.209162i
$404$		0			0
$405$	17.3565	−	6.86072i	0.862450	−	0.340912i
$406$		0			0
$407$	29.2353	+	29.2353i	1.44914	+	1.44914i
$408$		0			0
$409$	−2.87699	+	3.95984i	−0.142258	+	0.195801i	−0.874201	−	0.485565i	$-0.838614\pi$
$409$	−2.87699	+	3.95984i	−0.142258	+	0.195801i	0.731943	+	0.681366i	$0.238614\pi$
$410$		0			0
$411$	−2.98090	−	4.10286i	−0.147037	−	0.202379i
$412$		0			0
$413$	0.165502	+	1.04494i	0.00814381	+	0.0514180i
$414$		0			0
$415$	9.55008	−	22.0352i	0.468795	−	1.08167i
$416$		0			0
$417$	21.4498	+	10.9292i	1.05040	+	0.535207i
$418$		0			0
$419$	6.49932	+	20.0028i	0.317512	+	0.977203i	0.974708	+	0.223483i	$0.0717426\pi$
$419$	6.49932	+	20.0028i	0.317512	+	0.977203i	−0.657195	+	0.753720i	$0.728257\pi$
$420$		0			0
$421$	5.16907	−	15.9088i	0.251925	−	0.775346i	−0.742495	−	0.669852i	$-0.766358\pi$
$421$	5.16907	−	15.9088i	0.251925	−	0.775346i	0.994420	−	0.105494i	$-0.0336423\pi$
$422$		0			0
$423$	5.14953	−	32.5129i	0.250379	−	1.58083i
$424$		0			0
$425$	−19.4027	−	7.00985i	−0.941170	−	0.340028i
$426$		0			0
$427$	−1.49781	−	0.237229i	−0.0724840	−	0.0114803i
$428$		0			0
$429$	−39.8198	−	12.9382i	−1.92252	−	0.624664i
$430$		0			0
$431$	−10.8757	+	3.53373i	−0.523864	+	0.170214i	−0.558998	−	0.829169i	$-0.688814\pi$
$431$	−10.8757	+	3.53373i	−0.523864	+	0.170214i	0.0351342	+	0.999383i	$0.488814\pi$
$432$		0			0
$433$	−9.11703	+	17.8932i	−0.438137	+	0.859891i	0.561341	+	0.827584i	$0.310285\pi$
$433$	−9.11703	+	17.8932i	−0.438137	+	0.859891i	−0.999478	+	0.0323072i	$0.989715\pi$
$434$		0			0
$435$	−46.4450	+	10.3545i	−2.22687	+	0.496461i
$436$		0			0
$437$	−2.20553	+	0.349321i	−0.105505	+	0.0167103i
$438$		0			0
$439$	−18.7617	+	13.6312i	−0.895447	+	0.650580i	−0.937292	−	0.348544i	$-0.886676\pi$
$439$	−18.7617	+	13.6312i	−0.895447	+	0.650580i	0.0418458	+	0.999124i	$0.486676\pi$
$440$		0			0
$441$	18.0624	+	13.1231i	0.860116	+	0.624911i
$442$		0			0
$443$	−2.11481	+	2.11481i	−0.100478	+	0.100478i	−0.755559	−	0.655081i	$-0.772634\pi$
$443$	−2.11481	+	2.11481i	−0.100478	+	0.100478i	0.655081	+	0.755559i	$0.272634\pi$
$444$		0			0
$445$	0.650749	−	0.537735i	0.0308484	−	0.0254911i
$446$		0			0
$447$	25.2767	−	12.8791i	1.19555	−	0.609162i
$448$		0			0
$449$		−	23.8537i		−	1.12573i	−0.826550	−	0.562863i	$-0.809700\pi$
$449$		−	23.8537i		−	1.12573i	0.826550	−	0.562863i	$-0.190300\pi$
$450$		0			0
$451$		−	66.9098i		−	3.15066i
$452$		0			0
$453$	21.1348	−	10.7687i	0.992997	−	0.505957i
$454$		0			0
$455$	−0.887577	−	0.563968i	−0.0416102	−	0.0264392i
$456$		0			0
$457$	−12.8793	+	12.8793i	−0.602468	+	0.602468i	−0.940967	−	0.338499i	$-0.890081\pi$
$457$	−12.8793	+	12.8793i	−0.602468	+	0.602468i	0.338499	+	0.940967i	$0.390081\pi$
$458$		0			0
$459$	−1.69595	−	1.23218i	−0.0791603	−	0.0575133i
$460$		0			0
$461$	−14.1365	+	10.2707i	−0.658400	+	0.478356i	−0.866122	−	0.499832i	$-0.833395\pi$
$461$	−14.1365	+	10.2707i	−0.658400	+	0.478356i	0.207722	+	0.978188i	$0.433395\pi$
$462$		0			0
$463$	−4.19053	+	0.663714i	−0.194750	+	0.0308454i	−0.253048	−	0.967454i	$-0.581433\pi$
$463$	−4.19053	+	0.663714i	−0.194750	+	0.0308454i	0.0582972	+	0.998299i	$0.481433\pi$
$464$		0			0
$465$	6.57198	−	7.44607i	0.304768	−	0.345303i
$466$		0			0
$467$	13.3260	−	26.1537i	0.616652	−	1.21025i	−0.345675	−	0.938354i	$-0.612350\pi$
$467$	13.3260	−	26.1537i	0.616652	−	1.21025i	0.962327	−	0.271894i	$-0.0876499\pi$
$468$		0			0
$469$	−0.562075	+	0.182629i	−0.0259542	+	0.00843303i
$470$		0			0
$471$	−5.48034	−	1.78067i	−0.252521	−	0.0820490i
$472$		0			0
$473$	24.0086	+	3.80258i	1.10391	+	0.174843i
$474$		0			0
$475$	3.63694	+	7.75131i	0.166874	+	0.355654i
$476$		0			0
$477$	−4.86253	+	30.7008i	−0.222640	+	1.40569i
$478$		0			0
$479$	6.33663	−	19.5021i	0.289528	−	0.891076i	−0.695477	−	0.718549i	$-0.744807\pi$
$479$	6.33663	−	19.5021i	0.289528	−	0.891076i	0.985005	−	0.172527i	$-0.0551932\pi$
$480$		0			0
$481$	5.30846	+	16.3378i	0.242045	+	0.744937i
$482$		0			0
$483$	−0.514991	−	0.262401i	−0.0234329	−	0.0119397i
$484$		0			0
$485$	−17.3272	+	10.2343i	−0.786788	+	0.464713i
$486$		0			0
$487$	2.55341	+	16.1216i	0.115706	+	0.730540i	0.975517	+	0.219926i	$0.0705816\pi$
$487$	2.55341	+	16.1216i	0.115706	+	0.730540i	−0.859810	+	0.510613i	$0.829418\pi$
$488$		0			0
$489$	24.7752	+	34.1002i	1.12038	+	1.54206i
$490$		0			0
$491$	−5.12475	+	7.05361i	−0.231277	+	0.318325i	−0.908844	−	0.417135i	$-0.863034\pi$
$491$	−5.12475	+	7.05361i	−0.231277	+	0.318325i	0.677568	+	0.735460i	$0.263034\pi$
$492$		0			0
$493$	−24.9270	−	24.9270i	−1.12265	−	1.12265i
$494$		0			0
$495$	2.83596	+	45.4809i	0.127467	+	2.04421i
$496$		0			0
$497$	0.649609	+	1.27493i	0.0291389	+	0.0571884i
$498$		0			0
$499$	−6.73434			−0.301470			−0.150735	−	0.988574i	$-0.548164\pi$
$499$	−6.73434			−0.301470			−0.150735	+	0.988574i	$0.548164\pi$
$500$		0			0
$501$	6.86788			0.306834
$502$		0			0
$503$	0.0480014	+	0.0942081i	0.00214028	+	0.00420053i	0.892074	−	0.451889i	$-0.149250\pi$
$503$	0.0480014	+	0.0942081i	0.00214028	+	0.00420053i	−0.889934	+	0.456090i	$0.849250\pi$
$504$		0			0
$505$	0.794394	+	12.7399i	0.0353501	+	0.566916i
$506$		0			0
$507$	10.5952	+	10.5952i	0.470549	+	0.470549i
$508$		0			0
$509$	−9.06764	+	12.4805i	−0.401916	+	0.553190i	−0.961224	−	0.275770i	$-0.911067\pi$
$509$	−9.06764	+	12.4805i	−0.401916	+	0.553190i	0.559308	+	0.828960i	$0.311067\pi$
$510$		0			0
$511$	0.171574	+	0.236151i	0.00758998	+	0.0104467i
$512$		0			0
$513$	0.136103	+	0.859320i	0.00600909	+	0.0379399i
$514$		0			0
$515$	32.3342	−	19.0981i	1.42482	−	0.841563i
$516$		0			0
$517$	−58.2268	−	29.6681i	−2.56081	−	1.30480i
$518$		0			0
$519$	−0.575072	−	1.76989i	−0.0252429	−	0.0776896i
$520$		0			0
$521$	4.86323	−	14.9675i	0.213062	−	0.655737i	−0.786224	−	0.617942i	$-0.787967\pi$
$521$	4.86323	−	14.9675i	0.213062	−	0.655737i	0.999286	−	0.0377948i	$-0.0120333\pi$
$522$		0			0
$523$	0.816953	−	5.15804i	0.0357228	−	0.225545i	−0.963368	−	0.268184i	$-0.913576\pi$
$523$	0.816953	−	5.15804i	0.0357228	−	0.225545i	0.999091	+	0.0426388i	$0.0135765\pi$
$524$		0			0
$525$	−0.417701	+	2.17648i	−0.0182300	+	0.0949893i
$526$		0			0
$527$	7.26687	+	1.15096i	0.316550	+	0.0501366i
$528$		0			0
$529$	20.2571	+	6.58193i	0.880743	+	0.286171i
$530$		0			0
$531$	18.1160	−	5.88626i	0.786169	−	0.255442i
$532$		0			0
$533$	12.6212	−	24.7705i	0.546684	−	1.07293i
$534$		0			0
$535$	−16.1247	+	18.2693i	−0.697130	+	0.789851i
$536$		0			0
$537$	−43.7771	+	6.93362i	−1.88912	+	0.299208i
$538$		0			0
$539$	35.8578	−	26.0522i	1.54450	−	1.12215i
$540$		0			0
$541$	29.5506	+	21.4698i	1.27048	+	0.923059i	0.999222	−	0.0394478i	$-0.0125599\pi$
$541$	29.5506	+	21.4698i	1.27048	+	0.923059i	0.271259	+	0.962506i	$0.412560\pi$
$542$		0			0
$543$	−0.00644877	+	0.00644877i	−0.000276743	+	0.000276743i
$544$		0			0
$545$	−8.62347	−	5.47937i	−0.369389	−	0.234710i
$546$		0			0
$547$	−28.1881	+	14.3625i	−1.20523	+	0.614098i	−0.937025	−	0.349263i	$-0.886432\pi$
$547$	−28.1881	+	14.3625i	−1.20523	+	0.614098i	−0.268210	+	0.963360i	$0.586432\pi$
$548$		0			0
$549$			27.3038i			1.16530i
$550$		0			0
$551$			14.6307i			0.623287i
$552$		0			0
$553$	1.43037	−	0.728809i	0.0608255	−	0.0309921i
$554$		0			0
$555$	27.9078	−	23.0612i	1.18462	−	0.978892i
$556$		0			0
$557$	−15.4577	+	15.4577i	−0.654962	+	0.654962i	−0.954184	−	0.299222i	$-0.903273\pi$
$557$	−15.4577	+	15.4577i	−0.654962	+	0.654962i	0.299222	+	0.954184i	$0.403273\pi$
$558$		0			0
$559$	8.17085	+	5.93647i	0.345590	+	0.251086i
$560$		0			0
$561$	−52.8838	+	38.4223i	−2.23275	+	1.62219i
$562$		0			0
$563$	−10.3341	+	1.63676i	−0.435532	+	0.0689814i	−0.370351	−	0.928892i	$-0.620762\pi$
$563$	−10.3341	+	1.63676i	−0.435532	+	0.0689814i	−0.0651809	+	0.997873i	$0.520762\pi$
$564$		0			0
$565$	−40.8106	+	9.09835i	−1.71691	+	0.382771i
$566$		0			0
$567$	0.674298	−	1.32338i	0.0283178	−	0.0555769i
$568$		0			0
$569$	0.0426009	−	0.0138419i	0.00178592	−	0.000580282i	−0.308124	−	0.951346i	$-0.599701\pi$
$569$	0.0426009	−	0.0138419i	0.00178592	−	0.000580282i	0.309910	+	0.950766i	$0.399701\pi$
$570$		0			0
$571$	−25.2657	−	8.20931i	−1.05733	−	0.343549i	−0.271792	−	0.962356i	$-0.587616\pi$
$571$	−25.2657	−	8.20931i	−1.05733	−	0.343549i	−0.785543	+	0.618807i	$0.787616\pi$
$572$		0			0
$573$	18.6703	+	2.95709i	0.779964	+	0.123534i
$574$		0			0
$575$	−0.212066	+	6.51659i	−0.00884376	+	0.271761i
$576$		0			0
$577$	1.99167	−	12.5749i	0.0829141	−	0.523499i	−0.910917	−	0.412591i	$-0.864624\pi$
$577$	1.99167	−	12.5749i	0.0829141	−	0.523499i	0.993831	−	0.110908i	$-0.0353760\pi$
$578$		0			0
$579$	−13.8291	+	42.5616i	−0.574719	+	1.76880i
$580$		0			0
$581$	−0.590604	−	1.81769i	−0.0245024	−	0.0754106i
$582$		0			0
$583$	54.9817	+	28.0146i	2.27711	+	1.16025i
$584$		0			0
$585$	−7.52916	+	17.3723i	−0.311292	+	0.718256i
$586$		0			0
$587$	−4.96985	−	31.3784i	−0.205128	−	1.29513i	−0.848346	−	0.529443i	$-0.822401\pi$
$587$	−4.96985	−	31.3784i	−0.205128	−	1.29513i	0.643218	−	0.765683i	$-0.277599\pi$
$588$		0			0
$589$	−1.79484	−	2.47038i	−0.0739550	−	0.101790i
$590$		0			0
$591$	−22.0463	+	30.3441i	−0.906864	+	1.24819i
$592$		0			0
$593$	−25.9959	−	25.9959i	−1.06752	−	1.06752i	−0.997549	−	0.0699739i	$-0.977708\pi$
$593$	−25.9959	−	25.9959i	−1.06752	−	1.06752i	−0.0699739	−	0.997549i	$-0.522292\pi$
$594$		0			0
$595$	−1.52684	+	0.603536i	−0.0625945	+	0.0247426i
$596$		0			0
$597$	−5.09809	−	10.0056i	−0.208651	−	0.409500i
$598$		0			0
$599$	21.2644			0.868840			0.434420	−	0.900710i	$-0.356953\pi$
$599$	21.2644			0.868840			0.434420	+	0.900710i	$0.356953\pi$
$600$		0			0
$601$	−6.84047			−0.279028			−0.139514	−	0.990220i	$-0.544554\pi$
$601$	−6.84047			−0.279028			−0.139514	+	0.990220i	$0.544554\pi$
$602$		0			0
$603$	4.83082	+	9.48103i	0.196726	+	0.386097i
$604$		0			0
$605$	63.7894	+	16.4162i	2.59341	+	0.667415i
$606$		0			0
$607$	9.28593	+	9.28593i	0.376904	+	0.376904i	0.869984	−	0.493080i	$-0.164129\pi$
$607$	9.28593	+	9.28593i	0.376904	+	0.376904i	−0.493080	+	0.869984i	$0.664129\pi$
$608$		0			0
$609$	−2.22592	+	3.06371i	−0.0901988	+	0.124148i
$610$		0			0
$611$	−15.9597	−	21.9666i	−0.645660	−	0.888674i
$612$		0			0
$613$	−1.76691	−	11.1558i	−0.0713648	−	0.450579i	−0.997333	−	0.0729792i	$-0.976749\pi$
$613$	−1.76691	−	11.1558i	−0.0713648	−	0.450579i	0.925969	−	0.377600i	$-0.123251\pi$
$614$		0			0
$615$	−58.3255	−	5.54619i	−2.35191	−	0.223644i
$616$		0			0
$617$	15.4849	+	7.88996i	0.623399	+	0.317638i	0.737004	−	0.675888i	$-0.236240\pi$
$617$	15.4849	+	7.88996i	0.623399	+	0.317638i	−0.113605	+	0.993526i	$0.536240\pi$
$618$		0			0
$619$	9.41145	+	28.9654i	0.378278	+	1.16422i	0.941240	+	0.337737i	$0.109662\pi$
$619$	9.41145	+	28.9654i	0.378278	+	1.16422i	−0.562963	+	0.826482i	$0.690338\pi$
$620$		0			0
$621$	−0.204732	+	0.630101i	−0.00821562	+	0.0252851i
$622$		0			0
$623$	0.0105095	−	0.0663546i	0.000421056	−	0.00265844i
$624$		0			0
$625$	24.2284	−	6.16323i	0.969135	−	0.246529i
$626$		0			0
$627$	26.7956	+	4.24401i	1.07011	+	0.169489i
$628$		0			0
$629$	25.5073	+	8.28782i	1.01704	+	0.330457i
$630$		0			0
$631$	32.8585	−	10.6764i	1.30808	−	0.425019i	0.429692	−	0.902976i	$-0.358622\pi$
$631$	32.8585	−	10.6764i	1.30808	−	0.425019i	0.878384	+	0.477956i	$0.158622\pi$
$632$		0			0
$633$	4.44462	−	8.72305i	0.176658	−	0.346710i
$634$		0			0
$635$	−3.17212	+	33.3590i	−0.125882	+	1.32381i
$636$		0			0
$637$	18.1890	−	2.88086i	0.720675	−	0.114144i
$638$		0			0
$639$	20.8425	−	15.1430i	0.824516	−	0.599046i
$640$		0			0
$641$	−5.23406	−	3.80277i	−0.206733	−	0.150200i	0.479601	−	0.877487i	$-0.340781\pi$
$641$	−5.23406	−	3.80277i	−0.206733	−	0.150200i	−0.686334	+	0.727286i	$0.740781\pi$
$642$		0			0
$643$	5.21671	−	5.21671i	0.205727	−	0.205727i	−0.596722	−	0.802448i	$-0.703530\pi$
$643$	5.21671	−	5.21671i	0.205727	−	0.205727i	0.802448	+	0.596722i	$0.203530\pi$
$644$		0			0
$645$	5.30481	−	20.6131i	0.208877	−	0.811641i
$646$		0			0
$647$	28.4031	−	14.4721i	1.11664	−	0.568957i	0.204514	−	0.978864i	$-0.434439\pi$
$647$	28.4031	−	14.4721i	1.11664	−	0.568957i	0.912128	+	0.409906i	$0.134439\pi$
$648$		0			0
$649$		−	37.8150i		−	1.48437i
$650$		0			0
$651$		−	0.790375i		−	0.0309772i
$652$		0			0
$653$	−14.8891	+	7.58636i	−0.582655	+	0.296877i	−0.720365	−	0.693595i	$-0.756026\pi$
$653$	−14.8891	+	7.58636i	−0.582655	+	0.296877i	0.137710	+	0.990473i	$0.456026\pi$
$654$		0			0
$655$	13.3390	+	33.7454i	0.521198	+	1.31854i
$656$		0			0
$657$	3.71624	−	3.71624i	0.144984	−	0.144984i
$658$		0			0
$659$	29.9138	+	21.7337i	1.16528	+	0.846623i	0.990436	−	0.137974i	$-0.0440589\pi$
$659$	29.9138	+	21.7337i	1.16528	+	0.846623i	0.174841	+	0.984597i	$0.444059\pi$
$660$		0			0
$661$	−6.77525	+	4.92251i	−0.263527	+	0.191463i	−0.711700	−	0.702483i	$-0.752075\pi$
$661$	−6.77525	+	4.92251i	−0.263527	+	0.191463i	0.448174	+	0.893947i	$0.352075\pi$
$662$		0			0
$663$	−26.8255	+	4.24874i	−1.04182	+	0.165007i
$664$		0			0
$665$	0.625204	+	0.270964i	0.0242444	+	0.0105075i
$666$		0			0
$667$	−5.05801	+	9.92690i	−0.195847	+	0.384371i
$668$		0			0
$669$	50.6072	−	16.4433i	1.95659	−	0.635734i
$670$		0			0
$671$	51.5509	+	16.7499i	1.99010	+	0.646623i
$672$		0			0
$673$	2.59214	+	0.410555i	0.0999197	+	0.0158257i	0.206194	−	0.978511i	$-0.433892\pi$
$673$	2.59214	+	0.410555i	0.0999197	+	0.0158257i	−0.106274	+	0.994337i	$0.533892\pi$
$674$		0			0
$675$	2.53901	+	0.0826254i	0.0977264	+	0.00318025i
$676$		0			0
$677$	−1.71212	+	10.8099i	−0.0658021	+	0.415458i	0.932696	+	0.360664i	$0.117450\pi$
$677$	−1.71212	+	10.8099i	−0.0658021	+	0.415458i	−0.998498	+	0.0547935i	$0.982550\pi$
$678$		0			0
$679$	−0.494895	+	1.52313i	−0.0189923	+	0.0584524i
$680$		0			0
$681$	9.15926	+	28.1893i	0.350983	+	1.08022i
$682$		0			0
$683$	25.0034	+	12.7399i	0.956729	+	0.487478i	0.861377	−	0.507966i	$-0.169602\pi$
$683$	25.0034	+	12.7399i	0.956729	+	0.487478i	0.0953520	+	0.995444i	$0.469602\pi$
$684$		0			0
$685$	0.990687	+	4.44371i	0.0378522	+	0.169786i
$686$		0			0
$687$	−3.79125	−	23.9370i	−0.144645	−	0.913254i
$688$		0			0
$689$	15.0702	+	20.7424i	0.574129	+	0.790221i
$690$		0			0
$691$	−10.3065	+	14.1857i	−0.392079	+	0.539650i	−0.958734	−	0.284305i	$-0.908237\pi$
$691$	−10.3065	+	14.1857i	−0.392079	+	0.539650i	0.566655	+	0.823955i	$0.308237\pi$
$692$		0			0
$693$	2.56434	+	2.56434i	0.0974111	+	0.0974111i
$694$		0			0
$695$	−13.7666	−	16.6599i	−0.522198	−	0.631947i
$696$		0			0
$697$	−19.7048	−	38.6728i	−0.746373	−	1.46484i
$698$		0			0
$699$	−23.6480			−0.894451
$700$		0			0
$701$	−42.6580			−1.61117			−0.805584	−	0.592481i	$-0.798149\pi$
$701$	−42.6580			−1.61117			−0.805584	+	0.592481i	$0.798149\pi$
$702$		0			0
$703$	−5.05341	−	9.91787i	−0.190593	−	0.374059i
$704$		0			0
$705$	−30.6882	+	48.2973i	−1.15578	+	1.81898i
$706$		0			0
$707$	0.718308	+	0.718308i	0.0270147	+	0.0270147i
$708$		0			0
$709$	24.8028	−	34.1382i	0.931491	−	1.28209i	−0.0277848	−	0.999614i	$-0.508845\pi$
$709$	24.8028	−	34.1382i	0.931491	−	1.28209i	0.959275	−	0.282473i	$-0.0911547\pi$
$710$		0			0
$711$	−16.9892	−	23.3836i	−0.637144	−	0.876954i
$712$		0			0
$713$	−0.363754	−	2.29665i	−0.0136227	−	0.0860103i
$714$		0			0
$715$	28.1809	+	24.8727i	1.05390	+	0.930187i
$716$		0			0
$717$	13.3748	+	6.81479i	0.499490	+	0.254503i
$718$		0			0
$719$	−16.1889	−	49.8242i	−0.603743	−	1.85813i	−0.505211	−	0.862996i	$-0.668585\pi$
$719$	−16.1889	−	49.8242i	−0.603743	−	1.85813i	−0.0985321	−	0.995134i	$-0.531415\pi$
$720$		0			0
$721$	0.923522	−	2.84231i	0.0343937	−	0.105853i
$722$		0			0
$723$	0.0277958	−	0.175496i	0.00103374	−	0.00652676i
$724$		0			0
$725$	41.9535	+	8.05155i	1.55811	+	0.299027i
$726$		0			0
$727$	−20.4633	−	3.24107i	−0.758942	−	0.120205i	−0.235043	−	0.971985i	$-0.575523\pi$
$727$	−20.4633	−	3.24107i	−0.758942	−	0.120205i	−0.523899	+	0.851780i	$0.675523\pi$
$728$		0			0
$729$	−29.0437	−	9.43686i	−1.07569	−	0.349513i
$730$		0			0
$731$	14.9964	−	4.87264i	0.554663	−	0.180221i
$732$		0			0
$733$	1.41356	−	2.77427i	0.0522111	−	0.102470i	−0.863427	−	0.504474i	$-0.831686\pi$
$733$	1.41356	−	2.77427i	0.0522111	−	0.102470i	0.915638	+	0.402004i	$0.131686\pi$
$734$		0			0
$735$	−19.7375	−	33.4168i	−0.728029	−	1.23260i
$736$		0			0
$737$	20.8642	−	3.30456i	0.768542	−	0.121725i
$738$		0			0
$739$	−13.0090	+	9.45162i	−0.478545	+	0.347683i	−0.800762	−	0.598982i	$-0.795572\pi$
$739$	−13.0090	+	9.45162i	−0.478545	+	0.347683i	0.322217	+	0.946666i	$0.395572\pi$
$740$		0			0
$741$	9.11937	+	6.62561i	0.335009	+	0.243398i
$742$		0			0
$743$	13.2634	−	13.2634i	0.486589	−	0.486589i	−0.420639	−	0.907228i	$-0.638194\pi$
$743$	13.2634	−	13.2634i	0.486589	−	0.486589i	0.907228	+	0.420639i	$0.138194\pi$
$744$		0			0
$745$	−25.4183	+	1.58496i	−0.931255	+	0.0580684i
$746$		0			0
$747$	−30.6607	+	15.6224i	−1.12181	+	0.571593i
$748$		0			0
$749$			1.93922i			0.0708577i
$750$		0			0
$751$			0.966648i			0.0352735i	0.999844	+	0.0176367i	$0.00561424\pi$
$751$			0.966648i			0.0352735i	−0.999844	+	0.0176367i	$0.994386\pi$
$752$		0			0
$753$	−48.7500	+	24.8394i	−1.77655	+	0.905197i
$754$		0			0
$755$	−21.2532	+	1.32524i	−0.773482	+	0.0482304i
$756$		0			0
$757$	9.27361	−	9.27361i	0.337055	−	0.337055i	−0.518203	−	0.855258i	$-0.673399\pi$
$757$	9.27361	−	9.27361i	0.337055	−	0.337055i	0.855258	+	0.518203i	$0.173399\pi$
$758$		0			0
$759$	16.7136	+	12.1432i	0.606666	+	0.440768i
$760$		0			0
$761$	−15.0872	+	10.9615i	−0.546909	+	0.397353i	−0.826644	−	0.562725i	$-0.809753\pi$
$761$	−15.0872	+	10.9615i	−0.546909	+	0.397353i	0.279736	+	0.960077i	$0.409753\pi$
$762$		0			0
$763$	−0.803087	+	0.127196i	−0.0290737	+	0.00460482i
$764$		0			0
$765$	15.0332	+	25.4521i	0.543526	+	0.920222i
$766$		0			0
$767$	7.13303	−	13.9994i	0.257559	−	0.505488i
$768$		0			0
$769$	−25.3127	+	8.22461i	−0.912801	+	0.296587i	−0.727510	−	0.686097i	$-0.759323\pi$
$769$	−25.3127	+	8.22461i	−0.912801	+	0.296587i	−0.185290	+	0.982684i	$0.559323\pi$
$770$		0			0
$771$	10.9753	+	3.56610i	0.395266	+	0.128430i
$772$		0			0
$773$	25.6051	+	4.05545i	0.920951	+	0.145864i	0.598869	−	0.800847i	$-0.295617\pi$
$773$	25.6051	+	4.05545i	0.920951	+	0.145864i	0.322083	+	0.946712i	$0.395617\pi$
$774$		0			0
$775$	−8.07157	+	3.78721i	−0.289939	+	0.136040i
$776$		0			0
$777$	0.450709	−	2.84567i	0.0161691	−	0.102088i
$778$		0			0
$779$	−5.56656	+	17.1321i	−0.199443	+	0.613822i
$780$		0			0
$781$	−15.8045	−	48.6413i	−0.565530	−	1.74052i
$782$		0			0
$783$	3.86773	+	1.97071i	0.138222	+	0.0704274i
$784$		0			0
$785$	3.87850	+	3.42320i	0.138429	+	0.122179i
$786$		0			0
$787$	−0.230310	−	1.45412i	−0.00820966	−	0.0518338i	0.983243	−	0.182297i	$-0.0583534\pi$
$787$	−0.230310	−	1.45412i	−0.00820966	−	0.0518338i	−0.991453	+	0.130464i	$0.958353\pi$
$788$		0			0
$789$	−39.5652	−	54.4569i	−1.40856	−	1.93872i
$790$		0			0
$791$	−1.95588	+	2.69204i	−0.0695431	+	0.0957179i
$792$		0			0
$793$	15.9250	+	15.9250i	0.565512	+	0.565512i
$794$		0			0
$795$	28.9779	−	45.6056i	1.02774	−	1.61746i
$796$		0			0
$797$	10.1976	+	20.0140i	0.361219	+	0.708933i	0.998073	−	0.0620520i	$-0.0197645\pi$
$797$	10.1976	+	20.0140i	0.361219	+	0.708933i	−0.636854	+	0.770985i	$0.719764\pi$
$798$		0			0
$799$	−42.3914			−1.49970
$800$		0			0
$801$	−1.20959			−0.0427387
$802$		0			0
$803$	−4.73667	−	9.29623i	−0.167153	−	0.328057i
$804$		0			0
$805$	0.330525	+	0.399990i	0.0116495	+	0.0140978i
$806$		0			0
$807$	−25.9836	−	25.9836i	−0.914667	−	0.914667i
$808$		0			0
$809$	−11.7267	+	16.1404i	−0.412290	+	0.567468i	−0.963775	−	0.266717i	$-0.914061\pi$
$809$	−11.7267	+	16.1404i	−0.412290	+	0.567468i	0.551485	+	0.834185i	$0.314061\pi$
$810$		0			0
$811$	−9.47694	−	13.0439i	−0.332780	−	0.458033i	0.609535	−	0.792759i	$-0.291356\pi$
$811$	−9.47694	−	13.0439i	−0.332780	−	0.458033i	−0.942315	+	0.334726i	$0.891356\pi$
$812$		0			0
$813$	−2.09310	−	13.2153i	−0.0734082	−	0.463481i
$814$		0			0
$815$	−8.23391	−	36.9331i	−0.288421	−	1.29371i
$816$		0			0
$817$	−5.83098	−	2.97103i	−0.204000	−	0.103943i
$818$		0			0
$819$	0.465624	+	1.43304i	0.0162702	+	0.0500746i
$820$		0			0
$821$	3.77328	−	11.6130i	0.131688	−	0.405295i	−0.863372	−	0.504568i	$-0.831652\pi$
$821$	3.77328	−	11.6130i	0.131688	−	0.405295i	0.995060	+	0.0992731i	$0.0316517\pi$
$822$		0			0
$823$	3.98600	−	25.1666i	0.138943	−	0.877252i	−0.815478	−	0.578788i	$-0.803526\pi$
$823$	3.98600	−	25.1666i	0.138943	−	0.877252i	0.954421	−	0.298464i	$-0.0964742\pi$
$824$		0			0
$825$	26.9159	−	74.5010i	0.937091	−	2.59379i
$826$		0			0
$827$	11.8326	+	1.87411i	0.411461	+	0.0651691i	0.358734	−	0.933440i	$-0.383209\pi$
$827$	11.8326	+	1.87411i	0.411461	+	0.0651691i	0.0527274	+	0.998609i	$0.483209\pi$
$828$		0			0
$829$	22.5198	+	7.31711i	0.782144	+	0.254134i	0.672755	−	0.739865i	$-0.265111\pi$
$829$	22.5198	+	7.31711i	0.782144	+	0.254134i	0.109388	+	0.993999i	$0.465111\pi$
$830$		0			0
$831$	−68.5093	+	22.2600i	−2.37656	+	0.772192i
$832$		0			0
$833$	13.0529	−	25.6178i	0.452257	−	0.887605i
$834$		0			0
$835$	−5.65711	−	2.45179i	−0.195772	−	0.0848478i
$836$		0			0
$837$	−0.894825	+	0.141726i	−0.0309297	+	0.00489878i
$838$		0			0
$839$	−38.4811	+	27.9581i	−1.32851	+	0.965222i	−0.328731	+	0.944424i	$0.606621\pi$
$839$	−38.4811	+	27.9581i	−1.32851	+	0.965222i	−0.999784	+	0.0207988i	$0.993379\pi$
$840$		0			0
$841$	35.5943	+	25.8607i	1.22739	+	0.891750i
$842$		0			0
$843$	−27.3325	+	27.3325i	−0.941380	+	0.941380i
$844$		0			0
$845$	−4.94489	−	12.5097i	−0.170109	−	0.430348i
$846$		0			0
$847$	4.67060	−	2.37979i	0.160484	−	0.0817706i
$848$		0			0
$849$			26.4739i			0.908581i
$850$		0			0
$851$		−	8.47630i		−	0.290564i
$852$		0			0
$853$	−47.7453	+	24.3274i	−1.63477	+	0.832955i	−0.636679	+	0.771129i	$0.719693\pi$
$853$	−47.7453	+	24.3274i	−1.63477	+	0.832955i	−0.998087	+	0.0618264i	$0.980307\pi$
$854$		0			0
$855$	3.05764	−	11.8812i	0.104569	−	0.406329i
$856$		0			0
$857$	−36.5766	+	36.5766i	−1.24943	+	1.24943i	−0.293461	+	0.955971i	$0.594807\pi$
$857$	−36.5766	+	36.5766i	−1.24943	+	1.24943i	−0.955971	+	0.293461i	$0.905193\pi$
$858$		0			0
$859$	−40.5206	−	29.4399i	−1.38254	−	1.00448i	−0.996637	−	0.0819401i	$-0.973888\pi$
$859$	−40.5206	−	29.4399i	−1.38254	−	1.00448i	−0.385908	−	0.922537i	$-0.626112\pi$
$860$		0			0
$861$	−3.77215	+	2.74063i	−0.128554	+	0.0934003i
$862$		0			0
$863$	24.2136	−	3.83506i	0.824240	−	0.130547i	0.269954	−	0.962873i	$-0.412991\pi$
$863$	24.2136	−	3.83506i	0.824240	−	0.130547i	0.554286	+	0.832326i	$0.312991\pi$
$864$		0			0
$865$	−0.158151	+	1.66316i	−0.00537729	+	0.0565493i
$866$		0			0
$867$	−0.0272836	+	0.0535470i	−0.000926599	+	0.00181855i
$868$		0			0
$869$	−54.5717	+	17.7314i	−1.85122	+	0.601497i
$870$		0			0
$871$	8.34740	+	2.71223i	0.282841	+	0.0919006i
$872$		0			0
$873$	28.4798	+	4.51076i	0.963896	+	0.152666i
$874$		0			0
$875$	1.12105	−	1.64366i	0.0378985	−	0.0555658i
$876$		0			0
$877$	5.58262	−	35.2473i	0.188512	−	1.19022i	−0.694018	−	0.719958i	$-0.744161\pi$
$877$	5.58262	−	35.2473i	0.188512	−	1.19022i	0.882529	−	0.470258i	$-0.155839\pi$
$878$		0			0
$879$	−4.68458	+	14.4177i	−0.158007	+	0.486296i
$880$		0			0
$881$	−15.0314	−	46.2618i	−0.506420	−	1.55860i	−0.798370	−	0.602167i	$-0.794304\pi$
$881$	−15.0314	−	46.2618i	−0.506420	−	1.55860i	0.291950	−	0.956434i	$-0.405696\pi$
$882$		0			0
$883$	15.6464	+	7.97222i	0.526542	+	0.268286i	0.696991	−	0.717080i	$-0.254522\pi$
$883$	15.6464	+	7.97222i	0.526542	+	0.268286i	−0.170449	+	0.985366i	$0.554522\pi$
$884$		0			0
$885$	−32.9634	−	3.13451i	−1.10805	−	0.105365i
$886$		0			0
$887$	2.16807	+	13.6887i	0.0727967	+	0.459620i	0.996979	+	0.0776691i	$0.0247478\pi$
$887$	2.16807	+	13.6887i	0.0727967	+	0.459620i	−0.924182	+	0.381951i	$0.875252\pi$
$888$		0			0
$889$	1.56749	+	2.15746i	0.0525719	+	0.0723590i
$890$		0			0
$891$	−31.2045	+	42.9493i	−1.04539	+	1.43886i
$892$		0			0
$893$	12.4406	+	12.4406i	0.416309	+	0.416309i
$894$		0			0
$895$	38.5347	+	9.91693i	1.28807	+	0.331486i
$896$		0			0
$897$	3.89693	+	7.64816i	0.130115	+	0.255365i
$898$		0			0
$899$	−15.2352			−0.508121
$900$		0			0
$901$	40.0288			1.33355
$902$		0			0
$903$	−0.769014	−	1.50928i	−0.0255912	−	0.0502255i
$904$		0			0
$905$	0.00761406	−	0.00300971i	0.000253100	−	0.000100046i
$906$		0			0
$907$	−33.7582	−	33.7582i	−1.12092	−	1.12092i	−0.991603	−	0.129320i	$-0.958720\pi$
$907$	−33.7582	−	33.7582i	−1.12092	−	1.12092i	−0.129320	−	0.991603i	$-0.541280\pi$
$908$		0			0
$909$	10.7506	−	14.7969i	0.356573	−	0.490781i
$910$		0			0
$911$	18.1771	+	25.0186i	0.602233	+	0.828902i	0.995910	−	0.0903464i	$-0.0287974\pi$
$911$	18.1771	+	25.0186i	0.602233	+	0.828902i	−0.393678	+	0.919249i	$0.628797\pi$
$912$		0			0
$913$	10.6866	+	67.4726i	0.353675	+	2.23302i
$914$		0			0
$915$	18.8740	−	43.5487i	0.623956	−	1.43967i
$916$		0			0
$917$	2.57300	+	1.31101i	0.0849679	+	0.0432933i
$918$		0			0
$919$	−13.9477	−	42.9267i	−0.460093	−	1.41602i	−0.865050	−	0.501686i	$-0.832713\pi$
$919$	−13.9477	−	42.9267i	−0.460093	−	1.41602i	0.404957	−	0.914336i	$-0.367287\pi$
$920$		0			0
$921$	11.3543	−	34.9450i	0.374138	−	1.15148i
$922$		0			0
$923$	3.32426	−	20.9885i	0.109419	−	0.690846i
$924$		0			0
$925$	−31.2205	+	9.03266i	−1.02652	+	0.296992i
$926$		0			0
$927$	−53.1461	−	8.41751i	−1.74555	−	0.276467i
$928$		0			0
$929$	−26.7906	−	8.70480i	−0.878971	−	0.285595i	−0.165441	−	0.986220i	$-0.552905\pi$
$929$	−26.7906	−	8.70480i	−0.878971	−	0.285595i	−0.713530	+	0.700625i	$0.752905\pi$
$930$		0			0
$931$	−11.3487	+	3.68742i	−0.371939	+	0.120850i
$932$		0			0
$933$	16.8576	−	33.0849i	0.551894	−	1.08315i
$934$		0			0
$935$	57.2771	−	12.7694i	1.87316	−	0.417605i
$936$		0			0
$937$	−19.2471	+	3.04844i	−0.628776	+	0.0995883i	−0.462686	−	0.886522i	$-0.653114\pi$
$937$	−19.2471	+	3.04844i	−0.628776	+	0.0995883i	−0.166090	+	0.986111i	$0.553114\pi$
$938$		0			0
$939$	9.41238	−	6.83849i	0.307161	−	0.223166i
$940$		0			0
$941$	22.6739	+	16.4735i	0.739147	+	0.537022i	0.892444	−	0.451158i	$-0.148989\pi$
$941$	22.6739	+	16.4735i	0.739147	+	0.537022i	−0.153297	+	0.988180i	$0.548989\pi$
$942$		0			0
$943$	−9.69970	+	9.69970i	−0.315866	+	0.315866i
$944$		0			0
$945$	0.155845	−	0.128780i	0.00506963	−	0.00418920i
$946$		0			0
$947$	−19.1883	+	9.77694i	−0.623537	+	0.317708i	−0.737060	−	0.675827i	$-0.763786\pi$
$947$	−19.1883	+	9.77694i	−0.623537	+	0.317708i	0.113523	+	0.993535i	$0.463786\pi$
$948$		0			0
$949$		−	4.33500i		−	0.140720i
$950$		0			0
$951$			25.7345i			0.834498i
$952$		0			0
$953$	15.7156	−	8.00749i	0.509078	−	0.259388i	−0.180532	−	0.983569i	$-0.557782\pi$
$953$	15.7156	−	8.00749i	0.509078	−	0.259388i	0.689610	+	0.724181i	$0.257782\pi$
$954$		0			0
$955$	−14.3232	−	9.10096i	−0.463487	−	0.294500i
$956$		0			0
$957$	95.7127	−	95.7127i	3.09395	−	3.09395i
$958$		0			0
$959$	0.293126	+	0.212969i	0.00946554	+	0.00687712i
$960$		0			0
$961$	−22.5071	+	16.3523i	−0.726035	+	0.527495i
$962$		0			0
$963$	34.4853	−	5.46194i	1.11127	−	0.176009i
$964$		0			0
$965$	26.5854	−	30.1213i	0.855813	−	0.969639i
$966$		0			0
$967$	−12.3062	+	24.1523i	−0.395741	+	0.776685i	−0.999795	−	0.0202581i	$-0.993551\pi$
$967$	−12.3062	+	24.1523i	−0.395741	+	0.776685i	0.604054	+	0.796944i	$0.293551\pi$
$968$		0			0
$969$	16.7373	−	5.43828i	0.537680	−	0.174703i
$970$		0			0
$971$	34.4150	+	11.1821i	1.10443	+	0.358851i	0.803806	−	0.594891i	$-0.202805\pi$
$971$	34.4150	+	11.1821i	1.10443	+	0.358851i	0.300624	+	0.953743i	$0.402805\pi$
$972$		0			0
$973$	−1.69875	−	0.269056i	−0.0544596	−	0.00862555i
$974$		0			0
$975$	24.0175	−	22.5036i	0.769177	−	0.720693i
$976$		0			0
$977$	1.34979	−	8.52225i	0.0431836	−	0.272651i	−0.956643	−	0.291263i	$-0.905925\pi$
$977$	1.34979	−	8.52225i	0.0431836	−	0.272651i	0.999827	+	0.0186118i	$0.00592466\pi$
$978$		0			0
$979$	−0.742040	+	2.28376i	−0.0237157	+	0.0729894i
$980$		0			0
$981$	4.52389	+	13.9231i	0.144437	+	0.444530i
$982$		0			0
$983$	8.11314	+	4.13385i	0.258769	+	0.131849i	0.578563	−	0.815638i	$-0.303614\pi$
$983$	8.11314	+	4.13385i	0.258769	+	0.131849i	−0.319794	+	0.947487i	$0.603614\pi$
$984$		0			0
$985$	28.9923	−	17.1242i	0.923772	−	0.545622i
$986$		0			0
$987$	0.712387	+	4.49784i	0.0226755	+	0.143168i
$988$		0			0
$989$	−2.92920	−	4.03169i	−0.0931430	−	0.128200i
$990$		0			0
$991$	17.9533	−	24.7106i	0.570306	−	0.784959i	−0.422285	−	0.906463i	$-0.638772\pi$
$991$	17.9533	−	24.7106i	0.570306	−	0.784959i	0.992591	+	0.121504i	$0.0387718\pi$
$992$		0			0
$993$	16.9294	+	16.9294i	0.537237	+	0.537237i
$994$		0			0
$995$	0.627391	+	10.0616i	0.0198896	+	0.318975i
$996$		0			0
$997$	12.7518	+	25.0269i	0.403855	+	0.792609i	0.999947	−	0.0103065i	$-0.00328073\pi$
$997$	12.7518	+	25.0269i	0.403855	+	0.792609i	−0.596092	+	0.802916i	$0.703281\pi$
$998$		0			0
$999$	−3.30255			−0.104488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.223.9	yes	80
4.3	odd	2	inner	400.2.bi.d.223.2	✓	80
25.12	odd	20	inner	400.2.bi.d.287.2	yes	80
100.87	even	20	inner	400.2.bi.d.287.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.223.2	✓	80	4.3	odd	2	inner
400.2.bi.d.223.9	yes	80	1.1	even	1	trivial
400.2.bi.d.287.2	yes	80	25.12	odd	20	inner
400.2.bi.d.287.9	yes	80	100.87	even	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)

\(f(q)\)	\(=\)	\(q+(1.13079 + 2.21930i) q^{3} +(-0.139160 - 2.23173i) q^{5} +(-0.125831 - 0.125831i) q^{7} +(-1.88325 + 2.59207i) q^{9} +(3.73866 + 5.14582i) q^{11} +(0.413421 + 2.61024i) q^{13} +(4.79553 - 2.83246i) q^{15} +(3.67632 + 1.87318i) q^{17} +(-0.529169 - 1.62861i) q^{19} +(0.136968 - 0.421546i) q^{21} +(0.203992 - 1.28795i) q^{23} +(-4.96127 + 0.621135i) q^{25} +(-0.501815 - 0.0794796i) q^{27} +(-8.12566 - 2.64019i) q^{29} +(1.69590 - 0.551033i) q^{31} +(-7.19248 + 14.1160i) q^{33} +(-0.263311 + 0.298332i) q^{35} +(6.42016 - 1.01685i) q^{37} +(-5.32541 + 3.86914i) q^{39} +(-8.51041 - 6.18317i) q^{41} +(2.70230 - 2.70230i) q^{43} +(6.04689 + 3.84221i) q^{45} +(-9.15432 + 4.66436i) q^{47} -6.96833i q^{49} +10.2770i q^{51} +(8.64413 - 4.40440i) q^{53} +(10.9638 - 9.05978i) q^{55} +(3.01600 - 3.01600i) q^{57} +(-4.80977 - 3.49451i) q^{59} +(6.89430 - 5.00901i) q^{61} +(0.563135 - 0.0891919i) q^{63} +(5.76783 - 1.28589i) q^{65} +(1.50776 - 2.95914i) q^{67} +(3.08903 - 1.00369i) q^{69} +(-7.64731 - 2.48476i) q^{71} +(-1.62013 - 0.256603i) q^{73} +(-6.98864 - 10.3082i) q^{75} +(0.177065 - 1.11794i) q^{77} +(-2.78770 + 8.57966i) q^{79} +(2.57920 + 7.93795i) q^{81} +(9.56955 + 4.87593i) q^{83} +(3.66884 - 8.46524i) q^{85} +(-3.32905 - 21.0188i) q^{87} +(0.221905 + 0.305426i) q^{89} +(0.276428 - 0.380471i) q^{91} +(3.14062 + 3.14062i) q^{93} +(-3.56099 + 1.40760i) q^{95} +(-4.08577 - 8.01878i) q^{97} -20.3792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) \) 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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