LMFDB - Embedded newform 720.2.bm.h.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20386 + 0.742113i) q^{2} +(0.898535 - 1.78679i) q^{4} +(-0.860885 - 2.06370i) q^{5} -0.707398 q^{7} +(0.244298 + 2.81786i) q^{8} +(2.56788 + 1.84553i) q^{10} +(-1.79993 + 1.79993i) q^{11} +(-3.86348 + 3.86348i) q^{13} +(0.851604 - 0.524969i) q^{14} +(-2.38527 - 3.21100i) q^{16} -0.244884i q^{17} +(1.53863 + 1.53863i) q^{19} +(-4.46095 - 0.316087i) q^{20} +(0.831102 - 3.50260i) q^{22} +6.92280 q^{23} +(-3.51775 + 3.55323i) q^{25} +(1.78393 - 7.51820i) q^{26} +(-0.635622 + 1.26397i) q^{28} +(4.89882 + 4.89882i) q^{29} +7.60734 q^{31} +(5.25444 + 2.09543i) q^{32} +(0.181732 + 0.294805i) q^{34} +(0.608988 + 1.45986i) q^{35} +(8.47863 + 8.47863i) q^{37} +(-2.99413 - 0.710450i) q^{38} +(5.60491 - 2.93001i) q^{40} -2.12118i q^{41} +(0.684507 + 0.684507i) q^{43} +(1.59880 + 4.83340i) q^{44} +(-8.33405 + 5.13750i) q^{46} -4.47342i q^{47} -6.49959 q^{49} +(1.59797 - 6.88814i) q^{50} +(3.43177 + 10.3747i) q^{52} +(1.47026 + 1.47026i) q^{53} +(5.26405 + 2.16499i) q^{55} +(-0.172815 - 1.99335i) q^{56} +(-9.53295 - 2.26199i) q^{58} +(-5.86121 + 5.86121i) q^{59} +(0.0537432 + 0.0537432i) q^{61} +(-9.15813 + 5.64551i) q^{62} +(-7.88064 + 1.37679i) q^{64} +(11.2991 + 4.64706i) q^{65} +(7.85550 - 7.85550i) q^{67} +(-0.437558 - 0.220037i) q^{68} +(-1.81651 - 1.30552i) q^{70} +2.08595i q^{71} -9.69951 q^{73} +(-16.4992 - 3.91494i) q^{74} +(4.13173 - 1.36670i) q^{76} +(1.27326 - 1.27326i) q^{77} -7.34690 q^{79} +(-4.57310 + 7.68679i) q^{80} +(1.57415 + 2.55359i) q^{82} +(-6.80291 + 6.80291i) q^{83} +(-0.505369 + 0.210817i) q^{85} +(-1.33203 - 0.316066i) q^{86} +(-5.51166 - 4.63222i) q^{88} +3.07483i q^{89} +(2.73301 - 2.73301i) q^{91} +(6.22038 - 12.3696i) q^{92} +(3.31978 + 5.38535i) q^{94} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(7.82456 - 4.82343i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64}+ \cdots + 48 q^{95}+O(q^{100}) $ 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.20386	+	0.742113i	−0.851254	+	0.524753i
$2$	−1.20386	+	0.742113i	−0.851254	+	0.524753i
$3$		0			0
$3$		0			0
$4$	0.898535	−	1.78679i	0.449268	−	0.893397i
$5$	−0.860885	−	2.06370i	−0.385000	−	0.922917i
$5$	−0.860885	−	2.06370i	−0.385000	−	0.922917i
$6$		0			0
$7$	−0.707398			−0.267371			−0.133686	−	0.991024i	$-0.542681\pi$
$7$	−0.707398			−0.267371			−0.133686	+	0.991024i	$0.542681\pi$
$8$	0.244298	+	2.81786i	0.0863722	+	0.996263i
$9$		0			0
$10$	2.56788	+	1.84553i	0.812036	+	0.583607i
$11$	−1.79993	+	1.79993i	−0.542699	+	0.542699i	−0.924319	−	0.381621i	$-0.875366\pi$
$11$	−1.79993	+	1.79993i	−0.542699	+	0.542699i	0.381621	+	0.924319i	$0.375366\pi$
$12$		0			0
$13$	−3.86348	+	3.86348i	−1.07154	+	1.07154i	−0.0742996	+	0.997236i	$0.523672\pi$
$13$	−3.86348	+	3.86348i	−1.07154	+	1.07154i	−0.997236	+	0.0742996i	$0.976328\pi$
$14$	0.851604	−	0.524969i	0.227601	−	0.140304i
$15$		0			0
$16$	−2.38527	−	3.21100i	−0.596317	−	0.802749i
$17$		−	0.244884i		−	0.0593932i	−0.999559	−	0.0296966i	$-0.990546\pi$
$17$		−	0.244884i		−	0.0593932i	0.999559	−	0.0296966i	$-0.00945410\pi$
$18$		0			0
$19$	1.53863	+	1.53863i	0.352986	+	0.352986i	0.861219	−	0.508233i	$-0.169701\pi$
$19$	1.53863	+	1.53863i	0.352986	+	0.352986i	−0.508233	+	0.861219i	$0.669701\pi$
$20$	−4.46095	−	0.316087i	−0.997499	−	0.0706791i
$21$		0			0
$22$	0.831102	−	3.50260i	0.177192	−	0.746757i
$23$	6.92280			1.44350			0.721752	−	0.692152i	$-0.243337\pi$
$23$	6.92280			1.44350			0.721752	+	0.692152i	$0.243337\pi$
$24$		0			0
$25$	−3.51775	+	3.55323i	−0.703551	+	0.710645i
$26$	1.78393	−	7.51820i	0.349857	−	1.47444i
$27$		0			0
$28$	−0.635622	+	1.26397i	−0.120121	+	0.238869i
$29$	4.89882	+	4.89882i	0.909688	+	0.909688i	0.996247	−	0.0865591i	$-0.0275871\pi$
$29$	4.89882	+	4.89882i	0.909688	+	0.909688i	−0.0865591	+	0.996247i	$0.527587\pi$
$30$		0			0
$31$	7.60734			1.36632			0.683159	−	0.730270i	$-0.260606\pi$
$31$	7.60734			1.36632			0.683159	+	0.730270i	$0.260606\pi$
$32$	5.25444	+	2.09543i	0.928863	+	0.370424i
$33$		0			0
$34$	0.181732	+	0.294805i	0.0311668	+	0.0505587i
$35$	0.608988	+	1.45986i	0.102938	+	0.246761i
$36$		0			0
$37$	8.47863	+	8.47863i	1.39388	+	1.39388i	0.816420	+	0.577459i	$0.195956\pi$
$37$	8.47863	+	8.47863i	1.39388	+	1.39388i	0.577459	+	0.816420i	$0.304044\pi$
$38$	−2.99413	−	0.710450i	−0.485712	−	0.115250i
$39$		0			0
$40$	5.60491	−	2.93001i	0.886214	−	0.463275i
$41$		−	2.12118i		−	0.331272i	−0.986187	−	0.165636i	$-0.947032\pi$
$41$		−	2.12118i		−	0.331272i	0.986187	−	0.165636i	$-0.0529677\pi$
$42$		0			0
$43$	0.684507	+	0.684507i	0.104386	+	0.104386i	0.757371	−	0.652985i	$-0.226483\pi$
$43$	0.684507	+	0.684507i	0.104386	+	0.104386i	−0.652985	+	0.757371i	$0.726483\pi$
$44$	1.59880	+	4.83340i	0.241028	+	0.728662i
$45$		0			0
$46$	−8.33405	+	5.13750i	−1.22879	+	0.757484i
$47$		−	4.47342i		−	0.652515i	−0.945281	−	0.326258i	$-0.894212\pi$
$47$		−	4.47342i		−	0.652515i	0.945281	−	0.326258i	$-0.105788\pi$
$48$		0			0
$49$	−6.49959			−0.928513
$50$	1.59797	−	6.88814i	0.225987	−	0.974130i
$51$		0			0
$52$	3.43177	+	10.3747i	0.475901	+	1.43871i
$53$	1.47026	+	1.47026i	0.201956	+	0.201956i	0.800838	−	0.598881i	$-0.204388\pi$
$53$	1.47026	+	1.47026i	0.201956	+	0.201956i	−0.598881	+	0.800838i	$0.704388\pi$
$54$		0			0
$55$	5.26405	+	2.16499i	0.709804	+	0.291927i
$56$	−0.172815	−	1.99335i	−0.0230934	−	0.266372i
$57$		0			0
$58$	−9.53295	−	2.26199i	−1.25174	−	0.297014i
$59$	−5.86121	+	5.86121i	−0.763065	+	0.763065i	−0.976875	−	0.213810i	$-0.931413\pi$
$59$	−5.86121	+	5.86121i	−0.763065	+	0.763065i	0.213810	+	0.976875i	$0.431413\pi$
$60$		0			0
$61$	0.0537432	+	0.0537432i	0.00688112	+	0.00688112i	0.710539	−	0.703658i	$-0.248451\pi$
$61$	0.0537432	+	0.0537432i	0.00688112	+	0.00688112i	−0.703658	+	0.710539i	$0.748451\pi$
$62$	−9.15813	+	5.64551i	−1.16308	+	0.716980i
$63$		0			0
$64$	−7.88064	+	1.37679i	−0.985080	+	0.172099i
$65$	11.2991	+	4.64706i	1.40148	+	0.576397i
$66$		0			0
$67$	7.85550	−	7.85550i	0.959702	−	0.959702i	−0.0395170	−	0.999219i	$-0.512582\pi$
$67$	7.85550	−	7.85550i	0.959702	−	0.959702i	0.999219	+	0.0395170i	$0.0125819\pi$
$68$	−0.437558	−	0.220037i	−0.0530617	−	0.0266834i
$69$		0			0
$70$	−1.81651	−	1.30552i	−0.217115	−	0.156040i
$71$			2.08595i			0.247557i	0.992310	+	0.123778i	$0.0395012\pi$
$71$			2.08595i			0.247557i	−0.992310	+	0.123778i	$0.960499\pi$
$72$		0			0
$73$	−9.69951			−1.13524			−0.567621	−	0.823290i	$-0.692136\pi$
$73$	−9.69951			−1.13524			−0.567621	+	0.823290i	$0.692136\pi$
$74$	−16.4992	−	3.91494i	−1.91799	−	0.455103i
$75$		0			0
$76$	4.13173	−	1.36670i	0.473942	−	0.156772i
$77$	1.27326	−	1.27326i	0.145102	−	0.145102i
$78$		0			0
$79$	−7.34690			−0.826591			−0.413295	−	0.910597i	$-0.635622\pi$
$79$	−7.34690			−0.826591			−0.413295	+	0.910597i	$0.635622\pi$
$80$	−4.57310	+	7.68679i	−0.511289	+	0.859409i
$81$		0			0
$82$	1.57415	+	2.55359i	0.173836	+	0.281997i
$83$	−6.80291	+	6.80291i	−0.746716	+	0.746716i	−0.973861	−	0.227145i	$-0.927061\pi$
$83$	−6.80291	+	6.80291i	−0.746716	+	0.746716i	0.227145	+	0.973861i	$0.427061\pi$
$84$		0			0
$85$	−0.505369	+	0.210817i	−0.0548149	+	0.0228663i
$86$	−1.33203	−	0.316066i	−0.143636	−	0.0340822i
$87$		0			0
$88$	−5.51166	−	4.63222i	−0.587545	−	0.493796i
$89$			3.07483i			0.325931i	0.986632	+	0.162966i	$0.0521060\pi$
$89$			3.07483i			0.325931i	−0.986632	+	0.162966i	$0.947894\pi$
$90$		0			0
$91$	2.73301	−	2.73301i	0.286498	−	0.286498i
$92$	6.22038	−	12.3696i	0.648520	−	1.28962i
$93$		0			0
$94$	3.31978	+	5.38535i	0.342410	+	0.555456i
$95$	1.85069	−	4.49986i	0.189877	−	0.461676i
$96$		0			0
$97$			1.39922i			0.142070i	0.997474	+	0.0710348i	$0.0226301\pi$
$97$			1.39922i			0.142070i	−0.997474	+	0.0710348i	$0.977370\pi$
$98$	7.82456	−	4.82343i	0.790400	−	0.487240i
$99$		0			0
$100$	3.18806	+	9.47820i	0.318806	+	0.947820i
$101$	−11.7916	+	11.7916i	−1.17331	+	1.17331i	−0.191895	+	0.981415i	$0.561463\pi$
$101$	−11.7916	+	11.7916i	−1.17331	+	1.17331i	−0.981415	+	0.191895i	$0.938537\pi$
$102$		0			0
$103$	−2.29240			−0.225877			−0.112938	−	0.993602i	$-0.536026\pi$
$103$	−2.29240			−0.225877			−0.112938	+	0.993602i	$0.536026\pi$
$104$	−11.8306	−	9.94289i	−1.16008	−	0.974980i
$105$		0			0
$106$	−2.86109	−	0.678882i	−0.277893	−	0.0659389i
$107$	9.49009	+	9.49009i	0.917442	+	0.917442i	0.996843	−	0.0794010i	$-0.0253008\pi$
$107$	9.49009	+	9.49009i	0.917442	+	0.917442i	−0.0794010	+	0.996843i	$0.525301\pi$
$108$		0			0
$109$	11.9058	+	11.9058i	1.14037	+	1.14037i	0.988383	+	0.151984i	$0.0485662\pi$
$109$	11.9058	+	11.9058i	1.14037	+	1.14037i	0.151984	+	0.988383i	$0.451434\pi$
$110$	−7.94382	+	1.30019i	−0.757414	+	0.123968i
$111$		0			0
$112$	1.68733	+	2.27145i	0.159438	+	0.214632i
$113$			7.92806i			0.745809i	0.927870	+	0.372904i	$0.121638\pi$
$113$			7.92806i			0.745809i	−0.927870	+	0.372904i	$0.878362\pi$
$114$		0			0
$115$	−5.95974	−	14.2866i	−0.555748	−	1.33223i
$116$	13.1549	−	4.35142i	1.22141	−	0.404019i
$117$		0			0
$118$	2.70637	−	11.4057i	0.249141	−	1.04998i
$119$			0.173231i			0.0158800i
$120$		0			0
$121$			4.52052i			0.410956i
$122$	−0.104583	−	0.0248155i	−0.00946847	−	0.00224669i
$123$		0			0
$124$	6.83546	−	13.5927i	0.613843	−	1.22066i
$125$	10.3612	+	4.20068i	0.926733	+	0.375721i
$126$		0			0
$127$		−	19.4466i		−	1.72561i	−0.505536	−	0.862806i	$-0.668705\pi$
$127$		−	19.4466i		−	1.72561i	0.505536	−	0.862806i	$-0.331295\pi$
$128$	8.46541	−	7.50578i	0.748244	−	0.663424i
$129$		0			0
$130$	−17.0511	+	2.79081i	−1.49548	+	0.244770i
$131$	0.354049	+	0.354049i	0.0309334	+	0.0309334i	0.722404	−	0.691471i	$-0.243037\pi$
$131$	0.354049	+	0.354049i	0.0309334	+	0.0309334i	−0.691471	+	0.722404i	$0.743037\pi$
$132$		0			0
$133$	−1.08842	−	1.08842i	−0.0943783	−	0.0943783i
$134$	−3.62721	+	15.2866i	−0.313343	+	1.32056i
$135$		0			0
$136$	0.690049	−	0.0598246i	0.0591712	−	0.00512992i
$137$	−7.30033			−0.623709			−0.311854	−	0.950130i	$-0.600950\pi$
$137$	−7.30033			−0.623709			−0.311854	+	0.950130i	$0.600950\pi$
$138$		0			0
$139$	−8.85519	+	8.85519i	−0.751087	+	0.751087i	−0.974682	−	0.223595i	$-0.928221\pi$
$139$	−8.85519	+	8.85519i	−0.751087	+	0.751087i	0.223595	+	0.974682i	$0.428221\pi$
$140$	3.15567	+	0.223599i	0.266702	+	0.0188976i
$141$		0			0
$142$	−1.54801	−	2.51118i	−0.129906	−	0.210734i
$143$		−	13.9080i		−	1.16304i
$144$		0			0
$145$	5.89239	−	14.3270i	0.489337	−	1.18980i
$146$	11.6768	−	7.19814i	0.966379	−	0.595722i
$147$		0			0
$148$	22.7679	−	7.53122i	1.87151	−	0.619063i
$149$	−5.41385	+	5.41385i	−0.443520	+	0.443520i	−0.893193	−	0.449673i	$-0.851540\pi$
$149$	−5.41385	+	5.41385i	−0.443520	+	0.443520i	0.449673	+	0.893193i	$0.351540\pi$
$150$		0			0
$151$		−	0.341548i		−	0.0277948i	−0.999903	−	0.0138974i	$-0.995576\pi$
$151$		−	0.341548i		−	0.0277948i	0.999903	−	0.0138974i	$-0.00442382\pi$
$152$	−3.95976	+	4.71153i	−0.321179	+	0.382155i
$153$		0			0
$154$	−0.587920	+	2.47773i	−0.0473759	+	0.199661i
$155$	−6.54904	−	15.6993i	−0.526032	−	1.26100i
$156$		0			0
$157$	2.86465	−	2.86465i	0.228624	−	0.228624i	−0.583494	−	0.812118i	$-0.698315\pi$
$157$	2.86465	−	2.86465i	0.228624	−	0.228624i	0.812118	+	0.583494i	$0.198315\pi$
$158$	8.84460	−	5.45223i	0.703639	−	0.433756i
$159$		0			0
$160$	−0.199113	−	12.6475i	−0.0157412	−	0.999876i
$161$	−4.89717			−0.385951
$162$		0			0
$163$	5.94216	−	5.94216i	0.465426	−	0.465426i	−0.435003	−	0.900429i	$-0.643253\pi$
$163$	5.94216	−	5.94216i	0.465426	−	0.465426i	0.900429	+	0.435003i	$0.143253\pi$
$164$	−3.79011	−	1.90595i	−0.295958	−	0.148830i
$165$		0			0
$166$	3.14119	−	13.2382i	0.243803	−	1.02749i
$167$	14.4595			1.11891			0.559454	−	0.828861i	$-0.311011\pi$
$167$	14.4595			1.11891			0.559454	+	0.828861i	$0.311011\pi$
$168$		0			0
$169$		−	16.8529i		−	1.29638i
$170$	0.451941	−	0.628834i	0.0346623	−	0.0482294i
$171$		0			0
$172$	1.83813	−	0.608020i	0.140156	−	0.0463611i
$173$	−6.65096	+	6.65096i	−0.505663	+	0.505663i	−0.913192	−	0.407529i	$-0.866390\pi$
$173$	−6.65096	+	6.65096i	−0.505663	+	0.505663i	0.407529	+	0.913192i	$0.366390\pi$
$174$		0			0
$175$	2.48845	−	2.51354i	0.188109	−	0.190006i
$176$	10.0729	+	1.48625i	0.759271	+	0.112030i
$177$		0			0
$178$	−2.28187	−	3.70165i	−0.171033	−	0.277450i
$179$	−17.2660	−	17.2660i	−1.29052	−	1.29052i	−0.934466	−	0.356052i	$-0.884123\pi$
$179$	−17.2660	−	17.2660i	−1.29052	−	1.29052i	−0.356052	−	0.934466i	$-0.615877\pi$
$180$		0			0
$181$	5.12242	−	5.12242i	0.380746	−	0.380746i	−0.490625	−	0.871371i	$-0.663231\pi$
$181$	5.12242	−	5.12242i	0.380746	−	0.380746i	0.871371	+	0.490625i	$0.163231\pi$
$182$	−1.26195	+	5.31836i	−0.0935417	+	0.394223i
$183$		0			0
$184$	1.69122	+	19.5075i	0.124679	+	1.43811i
$185$	10.1983	−	24.7965i	0.749791	−	1.82308i
$186$		0			0
$187$	0.440774	+	0.440774i	0.0322326	+	0.0322326i
$188$	−7.99308	−	4.01953i	−0.582955	−	0.293154i
$189$		0			0
$190$	1.11144	+	6.79061i	0.0806324	+	0.492643i
$191$	17.8040			1.28825			0.644124	−	0.764921i	$-0.277222\pi$
$191$	17.8040			1.28825			0.644124	+	0.764921i	$0.277222\pi$
$192$		0			0
$193$			17.2222i			1.23968i	0.784727	+	0.619842i	$0.212803\pi$
$193$			17.2222i			1.23968i	−0.784727	+	0.619842i	$0.787197\pi$
$194$	−1.03838	−	1.68446i	−0.0745515	−	0.120937i
$195$		0			0
$196$	−5.84011	+	11.6134i	−0.417151	+	0.829531i
$197$	−10.0764	−	10.0764i	−0.717915	−	0.717915i	0.250263	−	0.968178i	$-0.419483\pi$
$197$	−10.0764	−	10.0764i	−0.717915	−	0.717915i	−0.968178	+	0.250263i	$0.919483\pi$
$198$		0			0
$199$		−	5.74179i		−	0.407025i	−0.979072	−	0.203513i	$-0.934764\pi$
$199$		−	5.74179i		−	0.407025i	0.979072	−	0.203513i	$-0.0652358\pi$
$200$	−10.8719	−	9.04448i	−0.768757	−	0.639541i
$201$		0			0
$202$	5.44469	−	22.9461i	0.383087	−	1.61448i
$203$	−3.46541	−	3.46541i	−0.243224	−	0.243224i
$204$		0			0
$205$	−4.37748	+	1.82609i	−0.305737	+	0.127540i
$206$	2.75972	−	1.70122i	0.192279	−	0.118530i
$207$		0			0
$208$	21.6210	+	3.19018i	1.49915	+	0.221199i
$209$	−5.53885			−0.383130
$210$		0			0
$211$	−9.73318	−	9.73318i	−0.670060	−	0.670060i	0.287670	−	0.957730i	$-0.407119\pi$
$211$	−9.73318	−	9.73318i	−0.670060	−	0.670060i	−0.957730	+	0.287670i	$0.907119\pi$
$212$	3.94814	−	1.30598i	0.271160	−	0.0896947i
$213$		0			0
$214$	−18.4674	−	4.38197i	−1.26241	−	0.299545i
$215$	0.823339	−	2.00190i	0.0561512	−	0.136529i
$216$		0			0
$217$	−5.38141			−0.365314
$218$	−23.1683	−	5.49740i	−1.56915	−	0.372331i
$219$		0			0
$220$	8.59832	−	7.46046i	0.579699	−	0.502984i
$221$	0.946104	+	0.946104i	0.0636419	+	0.0636419i
$222$		0			0
$223$			22.1037i			1.48017i	0.672511	+	0.740087i	$0.265216\pi$
$223$			22.1037i			1.48017i	−0.672511	+	0.740087i	$0.734784\pi$
$224$	−3.71698	−	1.48231i	−0.248351	−	0.0990407i
$225$		0			0
$226$	−5.88352	−	9.54423i	−0.391366	−	0.634873i
$227$	5.35387	−	5.35387i	0.355349	−	0.355349i	−0.506746	−	0.862095i	$-0.669152\pi$
$227$	5.35387	−	5.35387i	0.355349	−	0.355349i	0.862095	+	0.506746i	$0.169152\pi$
$228$		0			0
$229$	−18.3018	+	18.3018i	−1.20942	+	1.20942i	−0.238204	+	0.971215i	$0.576559\pi$
$229$	−18.3018	+	18.3018i	−1.20942	+	1.20942i	−0.971215	+	0.238204i	$0.923441\pi$
$230$	17.7770	+	12.7762i	1.17218	+	0.842439i
$231$		0			0
$232$	−12.6074	+	15.0009i	−0.827716	+	0.984860i
$233$	−12.0546			−0.789721			−0.394861	−	0.918741i	$-0.629207\pi$
$233$	−12.0546			−0.789721			−0.394861	+	0.918741i	$0.629207\pi$
$234$		0			0
$235$	−9.23182	+	3.85110i	−0.602217	+	0.251218i
$236$	5.20628	+	15.7393i	0.338900	+	1.02454i
$237$		0			0
$238$	−0.128557	−	0.208544i	−0.00833309	−	0.0135179i
$239$	27.9193			1.80595			0.902974	−	0.429695i	$-0.141379\pi$
$239$	27.9193			1.80595			0.902974	+	0.429695i	$0.141379\pi$
$240$		0			0
$241$	13.7118			0.883253			0.441626	−	0.897199i	$-0.354402\pi$
$241$	13.7118			0.883253			0.441626	+	0.897199i	$0.354402\pi$
$242$	−3.35474	−	5.44205i	−0.215651	−	0.349828i
$243$		0			0
$244$	0.144318	−	0.0477379i	0.00923903	−	0.00305611i
$245$	5.59540	+	13.4132i	0.357477	+	0.856940i
$246$		0			0
$247$	−11.8889			−0.756474
$248$	1.85845	+	21.4364i	0.118012	+	1.36121i
$249$		0			0
$250$	−15.5908	+	2.63216i	−0.986046	+	0.166473i
$251$	9.07173	−	9.07173i	0.572602	−	0.572602i	−0.360252	−	0.932855i	$-0.617309\pi$
$251$	9.07173	−	9.07173i	0.572602	−	0.572602i	0.932855	+	0.360252i	$0.117309\pi$
$252$		0			0
$253$	−12.4605	+	12.4605i	−0.783388	+	0.783388i
$254$	14.4316	+	23.4110i	0.905520	+	1.46893i
$255$		0			0
$256$	−4.62099	+	15.3182i	−0.288812	+	0.957386i
$257$		−	9.23416i		−	0.576011i	−0.957629	−	0.288006i	$-0.907008\pi$
$257$		−	9.23416i		−	0.576011i	0.957629	−	0.288006i	$-0.0929922\pi$
$258$		0			0
$259$	−5.99776	−	5.99776i	−0.372683	−	0.372683i
$260$	18.4560	−	16.0136i	1.14459	−	0.993121i
$261$		0			0
$262$	−0.688969	−	0.163479i	−0.0425646	−	0.0100998i
$263$	−18.5516			−1.14394			−0.571971	−	0.820274i	$-0.693821\pi$
$263$	−18.5516			−1.14394			−0.571971	+	0.820274i	$0.693821\pi$
$264$		0			0
$265$	1.76846	−	4.29992i	0.108636	−	0.264142i
$266$	2.11804	+	0.502571i	0.129865	+	0.0308146i
$267$		0			0
$268$	−6.97772	−	21.0946i	−0.426232	−	1.28856i
$269$	−14.3977	−	14.3977i	−0.877844	−	0.877844i	0.115467	−	0.993311i	$-0.463163\pi$
$269$	−14.3977	−	14.3977i	−0.877844	−	0.877844i	−0.993311	+	0.115467i	$0.963163\pi$
$270$		0			0
$271$	19.2974			1.17224			0.586118	−	0.810226i	$-0.300656\pi$
$271$	19.2974			1.17224			0.586118	+	0.810226i	$0.300656\pi$
$272$	−0.786322	+	0.584115i	−0.0476778	+	0.0354172i
$273$		0			0
$274$	8.78854	−	5.41767i	0.530935	−	0.327293i
$275$	−0.0638476	−	12.7272i	−0.00385016	−	0.767482i
$276$		0			0
$277$	−3.52269	−	3.52269i	−0.211658	−	0.211658i	0.593314	−	0.804971i	$-0.297819\pi$
$277$	−3.52269	−	3.52269i	−0.211658	−	0.211658i	−0.804971	+	0.593314i	$0.797819\pi$
$278$	4.08881	−	17.2319i	0.245231	−	1.03350i
$279$		0			0
$280$	−3.96490	+	2.07268i	−0.236948	+	0.123866i
$281$		−	29.2076i		−	1.74238i	−0.490945	−	0.871191i	$-0.663348\pi$
$281$		−	29.2076i		−	1.74238i	0.490945	−	0.871191i	$-0.336652\pi$
$282$		0			0
$283$	9.84279	+	9.84279i	0.585093	+	0.585093i	0.936298	−	0.351205i	$-0.114228\pi$
$283$	9.84279	+	9.84279i	0.585093	+	0.585093i	−0.351205	+	0.936298i	$0.614228\pi$
$284$	3.72717	+	1.87430i	0.221167	+	0.111219i
$285$		0			0
$286$	10.3213	+	16.7432i	0.610310	+	0.990044i
$287$			1.50052i			0.0885726i
$288$		0			0
$289$	16.9400			0.996472
$290$	3.53869	+	21.6205i	0.207799	+	1.26960i
$291$		0			0
$292$	−8.71535	+	17.3310i	−0.510027	+	1.01422i
$293$	11.8238	+	11.8238i	0.690755	+	0.690755i	0.962398	−	0.271643i	$-0.0875671\pi$
$293$	11.8238	+	11.8238i	0.690755	+	0.690755i	−0.271643	+	0.962398i	$0.587567\pi$
$294$		0			0
$295$	17.1416	+	7.04998i	0.998025	+	0.410466i
$296$	−21.8203	+	25.9629i	−1.26828	+	1.50906i
$297$		0			0
$298$	2.49980	−	10.5352i	0.144810	−	0.610287i
$299$	−26.7461	+	26.7461i	−1.54677	+	1.54677i
$300$		0			0
$301$	−0.484219	−	0.484219i	−0.0279099	−	0.0279099i
$302$	0.253468	+	0.411175i	0.0145854	+	0.0236604i
$303$		0			0
$304$	1.27049	−	8.61058i	0.0728676	−	0.493851i
$305$	0.0646434	−	0.157177i	0.00370147	−	0.00899992i
$306$		0			0
$307$	−16.6232	+	16.6232i	−0.948733	+	0.948733i	−0.998748	−	0.0500151i	$-0.984073\pi$
$307$	−16.6232	+	16.6232i	−0.948733	+	0.948733i	0.0500151	+	0.998748i	$0.484073\pi$
$308$	−1.13099	−	3.41913i	−0.0644441	−	0.194823i
$309$		0			0
$310$	19.5348	+	14.0396i	1.10950	+	0.797393i
$311$		−	13.8069i		−	0.782920i	−0.920195	−	0.391460i	$-0.871970\pi$
$311$		−	13.8069i		−	0.782920i	0.920195	−	0.391460i	$-0.128030\pi$
$312$		0			0
$313$	7.40380			0.418488			0.209244	−	0.977864i	$-0.432900\pi$
$313$	7.40380			0.418488			0.209244	+	0.977864i	$0.432900\pi$
$314$	−1.32273	+	5.57452i	−0.0746459	+	0.314588i
$315$		0			0
$316$	−6.60145	+	13.1274i	−0.371360	+	0.738474i
$317$	1.80712	−	1.80712i	0.101498	−	0.101498i	−0.654534	−	0.756032i	$-0.727135\pi$
$317$	1.80712	−	1.80712i	0.101498	−	0.101498i	0.756032	+	0.654534i	$0.227135\pi$
$318$		0			0
$319$	−17.6350			−0.987372
$320$	9.62561	+	15.0780i	0.538088	+	0.842889i
$321$		0			0
$322$	5.89549	−	3.63426i	0.328543	−	0.202529i
$323$	0.376786	−	0.376786i	0.0209650	−	0.0209650i
$324$		0			0
$325$	−0.137046	−	27.3186i	−0.00760197	−	1.51536i
$326$	−2.74375	+	11.5633i	−0.151962	+	0.640430i
$327$		0			0
$328$	5.97717	−	0.518198i	0.330034	−	0.0286127i
$329$			3.16449i			0.174464i
$330$		0			0
$331$	−5.82711	+	5.82711i	−0.320287	+	0.320287i	−0.848877	−	0.528590i	$-0.822721\pi$
$331$	−5.82711	+	5.82711i	−0.320287	+	0.320287i	0.528590	+	0.848877i	$0.322721\pi$
$332$	6.04275	+	18.2681i	0.331639	+	1.00259i
$333$		0			0
$334$	−17.4071	+	10.7306i	−0.952475	+	0.587151i
$335$	−22.9741	−	9.44875i	−1.25521	−	0.516240i
$336$		0			0
$337$			25.5357i			1.39102i	0.718516	+	0.695510i	$0.244822\pi$
$337$			25.5357i			1.39102i	−0.718516	+	0.695510i	$0.755178\pi$
$338$	12.5068	+	20.2885i	0.680278	+	1.10355i
$339$		0			0
$340$	−0.0774046	+	1.09242i	−0.00419786	+	0.0592446i
$341$	−13.6927	+	13.6927i	−0.741499	+	0.741499i
$342$		0			0
$343$	9.54958			0.515629
$344$	−1.76162	+	2.09607i	−0.0949802	+	0.113012i
$345$		0			0
$346$	3.07102	−	12.9426i	0.165099	−	0.695796i
$347$	17.6028	+	17.6028i	0.944970	+	0.944970i	0.998563	−	0.0535933i	$-0.0170675\pi$
$347$	17.6028	+	17.6028i	0.944970	+	0.944970i	−0.0535933	+	0.998563i	$0.517067\pi$
$348$		0			0
$349$	−5.07562	−	5.07562i	−0.271692	−	0.271692i	0.558089	−	0.829781i	$-0.311535\pi$
$349$	−5.07562	−	5.07562i	−0.271692	−	0.271692i	−0.829781	+	0.558089i	$0.811535\pi$
$350$	−1.13040	+	4.87265i	−0.0604224	+	0.260454i
$351$		0			0
$352$	−13.2292	+	5.68598i	−0.705121	+	0.303064i
$353$		−	0.171535i		−	0.00912990i	−0.999990	−	0.00456495i	$-0.998547\pi$
$353$		−	0.171535i		−	0.00912990i	0.999990	−	0.00456495i	$-0.00145307\pi$
$354$		0			0
$355$	4.30479	−	1.79576i	0.228474	−	0.0953093i
$356$	5.49409	+	2.76284i	0.291186	+	0.146430i
$357$		0			0
$358$	33.5990	+	7.97242i	1.77576	+	0.421355i
$359$			17.1694i			0.906169i	0.891468	+	0.453084i	$0.149676\pi$
$359$			17.1694i			0.906169i	−0.891468	+	0.453084i	$0.850324\pi$
$360$		0			0
$361$		−	14.2652i		−	0.750802i
$362$	−2.36524	+	9.96807i	−0.124314	+	0.523910i
$363$		0			0
$364$	−2.42762	−	7.33904i	−0.127242	−	0.384670i
$365$	8.35016	+	20.0169i	0.437068	+	1.04773i
$366$		0			0
$367$		−	23.3124i		−	1.21690i	−0.793593	−	0.608450i	$-0.791792\pi$
$367$		−	23.3124i		−	1.21690i	0.793593	−	0.608450i	$-0.208208\pi$
$368$	−16.5127	−	22.2291i	−0.860786	−	1.15877i
$369$		0			0
$370$	6.12460	+	37.4197i	0.318403	+	1.94536i
$371$	−1.04006	−	1.04006i	−0.0539973	−	0.0539973i
$372$		0			0
$373$	−1.11817	−	1.11817i	−0.0578964	−	0.0578964i	0.677566	−	0.735462i	$-0.263035\pi$
$373$	−1.11817	−	1.11817i	−0.0578964	−	0.0578964i	−0.735462	+	0.677566i	$0.763035\pi$
$374$	−0.857732	−	0.203524i	−0.0443523	−	0.0105240i
$375$		0			0
$376$	12.6055	−	1.09285i	0.650077	−	0.0563592i
$377$	−37.8529			−1.94953
$378$		0			0
$379$	22.3707	−	22.3707i	1.14910	−	1.14910i	0.162375	−	0.986729i	$-0.448085\pi$
$379$	22.3707	−	22.3707i	1.14910	−	1.14910i	0.986729	−	0.162375i	$-0.0519153\pi$
$380$	−6.37742	−	7.35010i	−0.327155	−	0.377052i
$381$		0			0
$382$	−21.4334	+	13.2126i	−1.09663	+	0.676013i
$383$			32.1168i			1.64109i	0.571579	+	0.820547i	$0.306331\pi$
$383$			32.1168i			1.64109i	−0.571579	+	0.820547i	$0.693669\pi$
$384$		0			0
$385$	−3.72378	−	1.53151i	−0.189781	−	0.0780528i
$386$	−12.7809	−	20.7331i	−0.650529	−	1.05529i
$387$		0			0
$388$	2.50012	+	1.25725i	0.126925	+	0.0638273i
$389$	22.7409	−	22.7409i	1.15301	−	1.15301i	0.167062	−	0.985946i	$-0.446572\pi$
$389$	22.7409	−	22.7409i	1.15301	−	1.15301i	0.985946	−	0.167062i	$-0.0534280\pi$
$390$		0			0
$391$		−	1.69529i		−	0.0857342i
$392$	−1.58783	−	18.3149i	−0.0801977	−	0.925043i
$393$		0			0
$394$	19.6084	+	4.65270i	0.987857	+	0.234400i
$395$	6.32484	+	15.1618i	0.318237	+	0.762874i
$396$		0			0
$397$	21.6530	−	21.6530i	1.08673	−	1.08673i	0.0908707	−	0.995863i	$-0.471035\pi$
$397$	21.6530	−	21.6530i	1.08673	−	1.08673i	0.995863	−	0.0908707i	$-0.0289650\pi$
$398$	4.26106	+	6.91229i	0.213588	+	0.346482i
$399$		0			0
$400$	19.8002	+	2.82009i	0.990009	+	0.141005i
$401$	−17.1600			−0.856931			−0.428466	−	0.903558i	$-0.640946\pi$
$401$	−17.1600			−0.856931			−0.428466	+	0.903558i	$0.640946\pi$
$402$		0			0
$403$	−29.3908	+	29.3908i	−1.46406	+	1.46406i
$404$	10.4740	+	31.6644i	0.521102	+	1.57536i
$405$		0			0
$406$	6.74358	+	1.60013i	0.334678	+	0.0794129i
$407$	−30.5218			−1.51291
$408$		0			0
$409$		−	17.9588i		−	0.888006i	−0.896025	−	0.444003i	$-0.853558\pi$
$409$		−	17.9588i		−	0.888006i	0.896025	−	0.444003i	$-0.146442\pi$
$410$	3.91469	−	5.44694i	0.193333	−	0.269005i
$411$		0			0
$412$	−2.05980	+	4.09605i	−0.101479	+	0.201798i
$413$	4.14621	−	4.14621i	0.204022	−	0.204022i
$414$		0			0
$415$	19.8957	+	8.18267i	0.976642	+	0.401671i
$416$	−28.3961	+	12.2047i	−1.39223	+	0.598387i
$417$		0			0
$418$	6.66797	−	4.11045i	0.326141	−	0.201049i
$419$	−23.4031	−	23.4031i	−1.14332	−	1.14332i	−0.987840	−	0.155476i	$-0.950309\pi$
$419$	−23.4031	−	23.4031i	−1.14332	−	1.14332i	−0.155476	−	0.987840i	$-0.549691\pi$
$420$		0			0
$421$	−27.0016	+	27.0016i	−1.31598	+	1.31598i	−0.399043	+	0.916932i	$0.630658\pi$
$421$	−27.0016	+	27.0016i	−1.31598	+	1.31598i	−0.916932	+	0.399043i	$0.869342\pi$
$422$	18.9405	+	4.49422i	0.922007	+	0.218775i
$423$		0			0
$424$	−3.78381	+	4.50218i	−0.183758	+	0.218645i
$425$	0.870129	+	0.861442i	0.0422075	+	0.0417861i
$426$		0			0
$427$	−0.0380178	−	0.0380178i	−0.00183981	−	0.00183981i
$428$	25.4840	−	8.42966i	1.23182	−	0.407463i
$429$		0			0
$430$	0.494459	+	3.02101i	0.0238449	+	0.145686i
$431$	28.4043			1.36819			0.684093	−	0.729395i	$-0.260198\pi$
$431$	28.4043			1.36819			0.684093	+	0.729395i	$0.260198\pi$
$432$		0			0
$433$		−	4.04564i		−	0.194421i	−0.995264	−	0.0972106i	$-0.969008\pi$
$433$		−	4.04564i		−	0.194421i	0.995264	−	0.0972106i	$-0.0309920\pi$
$434$	6.47844	−	3.99362i	0.310975	−	0.191700i
$435$		0			0
$436$	31.9709	−	10.5754i	1.53113	−	0.506471i
$437$	10.6516	+	10.6516i	0.509537	+	0.509537i
$438$		0			0
$439$			10.4690i			0.499660i	0.968290	+	0.249830i	$0.0803748\pi$
$439$			10.4690i			0.499660i	−0.968290	+	0.249830i	$0.919625\pi$
$440$	−4.81463	+	15.3622i	−0.229529	+	0.732366i
$441$		0			0
$442$	−1.84109	−	0.436856i	−0.0875717	−	0.0207791i
$443$	−1.81582	−	1.81582i	−0.0862722	−	0.0862722i	0.662654	−	0.748926i	$-0.269430\pi$
$443$	−1.81582	−	1.81582i	−0.0862722	−	0.0862722i	−0.748926	+	0.662654i	$0.769430\pi$
$444$		0			0
$445$	6.34554	−	2.64707i	0.300807	−	0.125483i
$446$	−16.4035	−	26.6097i	−0.776726	−	1.26000i
$447$		0			0
$448$	5.57474	−	0.973939i	0.263382	−	0.0460143i
$449$	22.2064			1.04799			0.523993	−	0.851723i	$-0.324442\pi$
$449$	22.2064			1.04799			0.523993	+	0.851723i	$0.324442\pi$
$450$		0			0
$451$	3.81797	+	3.81797i	0.179781	+	0.179781i
$452$	14.1658	+	7.12364i	0.666303	+	0.335068i
$453$		0			0
$454$	−2.47211	+	10.4185i	−0.116022	+	0.488963i
$455$	−7.99294	−	3.28732i	−0.374715	−	0.154112i
$456$		0			0
$457$	−12.2280			−0.572000			−0.286000	−	0.958230i	$-0.592326\pi$
$457$	−12.2280			−0.572000			−0.286000	+	0.958230i	$0.592326\pi$
$458$	8.45072	−	35.6148i	0.394876	−	1.66417i
$459$		0			0
$460$	−30.8823	−	2.18820i	−1.43989	−	0.102026i
$461$	−0.723447	−	0.723447i	−0.0336943	−	0.0336943i	0.690059	−	0.723753i	$-0.257585\pi$
$461$	−0.723447	−	0.723447i	−0.0336943	−	0.0336943i	−0.723753	+	0.690059i	$0.757585\pi$
$462$		0			0
$463$		−	5.42343i		−	0.252048i	−0.992027	−	0.126024i	$-0.959778\pi$
$463$		−	5.42343i		−	0.252048i	0.992027	−	0.126024i	$-0.0402217\pi$
$464$	4.04509	−	27.4151i	0.187788	−	1.27271i
$465$		0			0
$466$	14.5120	−	8.94586i	0.672254	−	0.414409i
$467$	−13.3242	+	13.3242i	−0.616571	+	0.616571i	−0.944650	−	0.328079i	$-0.893599\pi$
$467$	−13.3242	+	13.3242i	−0.616571	+	0.616571i	0.328079	+	0.944650i	$0.393599\pi$
$468$		0			0
$469$	−5.55696	+	5.55696i	−0.256597	+	0.256597i
$470$	8.25582	−	11.4872i	0.380812	−	0.529866i
$471$		0			0
$472$	−17.9479	−	15.0842i	−0.826121	−	0.694306i
$473$	−2.46413			−0.113301
$474$		0			0
$475$	−10.8796	+	0.0545788i	−0.499191	+	0.00250425i
$476$	0.309527	+	0.155654i	0.0141872	+	0.00713438i
$477$		0			0
$478$	−33.6108	+	20.7193i	−1.53732	+	0.947678i
$479$	1.25963			0.0575541			0.0287771	−	0.999586i	$-0.490839\pi$
$479$	1.25963			0.0575541			0.0287771	+	0.999586i	$0.490839\pi$
$480$		0			0
$481$	−65.5140			−2.98718
$482$	−16.5070	+	10.1757i	−0.751873	+	0.463490i
$483$		0			0
$484$	8.07724	+	4.06185i	0.367147	+	0.184629i
$485$	2.88758	−	1.20457i	0.131118	−	0.0546967i
$486$		0			0
$487$	−15.8116			−0.716491			−0.358246	−	0.933627i	$-0.616625\pi$
$487$	−15.8116			−0.716491			−0.358246	+	0.933627i	$0.616625\pi$
$488$	−0.138311	+	0.164570i	−0.00626106	+	0.00744974i
$489$		0			0
$490$	−16.6902	−	11.9952i	−0.753986	−	0.541886i
$491$	15.6008	−	15.6008i	0.704054	−	0.704054i	−0.261224	−	0.965278i	$-0.584126\pi$
$491$	15.6008	−	15.6008i	0.704054	−	0.704054i	0.965278	+	0.261224i	$0.0841263\pi$
$492$		0			0
$493$	1.19964	−	1.19964i	0.0540292	−	0.0540292i
$494$	14.3125	−	8.82293i	0.643952	−	0.396962i
$495$		0			0
$496$	−18.1455	−	24.4271i	−0.814759	−	1.09681i
$497$		−	1.47560i		−	0.0661896i
$498$		0			0
$499$	25.6650	+	25.6650i	1.14892	+	1.14892i	0.986765	+	0.162159i	$0.0518459\pi$
$499$	25.6650	+	25.6650i	1.14892	+	1.14892i	0.162159	+	0.986765i	$0.448154\pi$
$500$	16.8157	−	14.7389i	0.752019	−	0.659142i
$501$		0			0
$502$	−4.18880	+	17.6533i	−0.186955	+	0.787905i
$503$	4.72004			0.210456			0.105228	−	0.994448i	$-0.466443\pi$
$503$	4.72004			0.210456			0.105228	+	0.994448i	$0.466443\pi$
$504$		0			0
$505$	34.4857	+	14.1832i	1.53459	+	0.631144i
$506$	5.75355	−	24.2478i	0.255777	−	1.07795i
$507$		0			0
$508$	−34.7472	−	17.4735i	−1.54166	−	0.775261i
$509$	11.8862	+	11.8862i	0.526848	+	0.526848i	0.919631	−	0.392783i	$-0.128488\pi$
$509$	11.8862	+	11.8862i	0.526848	+	0.526848i	−0.392783	+	0.919631i	$0.628488\pi$
$510$		0			0
$511$	6.86141			0.303531
$512$	−5.80482	−	21.8702i	−0.256539	−	0.966534i
$513$		0			0
$514$	6.85280	+	11.1166i	0.302264	+	0.490332i
$515$	1.97349	+	4.73084i	0.0869625	+	0.208466i
$516$		0			0
$517$	8.05183	+	8.05183i	0.354119	+	0.354119i
$518$	11.6715	+	2.76942i	0.512815	+	0.121681i
$519$		0			0
$520$	−10.3344	+	32.9745i	−0.453195	+	1.44603i
$521$			5.01467i			0.219696i	0.993948	+	0.109848i	$0.0350365\pi$
$521$			5.01467i			0.219696i	−0.993948	+	0.109848i	$0.964964\pi$
$522$		0			0
$523$	−18.9502	−	18.9502i	−0.828635	−	0.828635i	0.158693	−	0.987328i	$-0.449272\pi$
$523$	−18.9502	−	18.9502i	−0.828635	−	0.828635i	−0.987328	+	0.158693i	$0.949272\pi$
$524$	0.950739	−	0.314487i	0.0415332	−	0.0137384i
$525$		0			0
$526$	22.3335	−	13.7674i	0.973785	−	0.600287i
$527$		−	1.86292i		−	0.0811499i
$528$		0			0
$529$	24.9252			1.08370
$530$	1.06206	+	6.48888i	0.0461327	+	0.281859i
$531$		0			0
$532$	−2.92278	+	0.966802i	−0.126718	+	0.0419162i
$533$	8.19512	+	8.19512i	0.354970	+	0.354970i
$534$		0			0
$535$	11.4149	−	27.7546i	0.493508	−	1.19994i
$536$	24.0548	+	20.2166i	1.03901	+	0.873224i
$537$		0			0
$538$	28.0175	+	6.64803i	1.20792	+	0.286617i
$539$	11.6988	−	11.6988i	0.503903	−	0.503903i
$540$		0			0
$541$	−22.8366	−	22.8366i	−0.981822	−	0.981822i	0.0180153	−	0.999838i	$-0.494265\pi$
$541$	−22.8366	−	22.8366i	−0.981822	−	0.981822i	−0.999838	+	0.0180153i	$0.994265\pi$
$542$	−23.2313	+	14.3209i	−0.997870	+	0.615134i
$543$		0			0
$544$	0.513139	−	1.28673i	0.0220007	−	0.0551681i
$545$	14.3205	−	34.8195i	0.613423	−	1.49150i
$546$		0			0
$547$	0.00963023	−	0.00963023i	0.000411759	−	0.000411759i	−0.706901	−	0.707313i	$-0.749907\pi$
$547$	0.00963023	−	0.00963023i	0.000411759	−	0.000411759i	0.707313	+	0.706901i	$0.249907\pi$
$548$	−6.55960	+	13.0442i	−0.280212	+	0.557220i
$549$		0			0
$550$	9.52193	+	15.2744i	0.406016	+	0.651302i
$551$			15.0749i			0.642214i
$552$		0			0
$553$	5.19718			0.221006
$554$	6.85504	+	1.62657i	0.291243	+	0.0691064i
$555$		0			0
$556$	7.86570	+	23.7791i	0.333580	+	1.00846i
$557$	25.6660	−	25.6660i	1.08750	−	1.08750i	0.0917192	−	0.995785i	$-0.470764\pi$
$557$	25.6660	−	25.6660i	1.08750	−	1.08750i	0.995785	−	0.0917192i	$-0.0292362\pi$
$558$		0			0
$559$	−5.28916			−0.223707
$560$	3.23500	−	5.43762i	0.136704	−	0.229781i
$561$		0			0
$562$	21.6754	+	35.1618i	0.914321	+	1.48321i
$563$	−6.16719	+	6.16719i	−0.259916	+	0.259916i	−0.825020	−	0.565104i	$-0.808836\pi$
$563$	−6.16719	+	6.16719i	−0.259916	+	0.259916i	0.565104	+	0.825020i	$0.308836\pi$
$564$		0			0
$565$	16.3612	−	6.82515i	0.688319	−	0.287136i
$566$	−19.1538	−	4.54483i	−0.805093	−	0.191033i
$567$		0			0
$568$	−5.87791	+	0.509593i	−0.246632	+	0.0213820i
$569$			4.05892i			0.170159i	0.996374	+	0.0850794i	$0.0271144\pi$
$569$			4.05892i			0.170159i	−0.996374	+	0.0850794i	$0.972886\pi$
$570$		0			0
$571$	−12.9113	+	12.9113i	−0.540323	+	0.540323i	−0.923624	−	0.383301i	$-0.874787\pi$
$571$	−12.9113	+	12.9113i	−0.540323	+	0.540323i	0.383301	+	0.923624i	$0.374787\pi$
$572$	−24.8507	−	12.4968i	−1.03906	−	0.522517i
$573$		0			0
$574$	−1.11355	−	1.80640i	−0.0464788	−	0.0753978i
$575$	−24.3527	+	24.5983i	−1.01558	+	1.02582i
$576$		0			0
$577$		−	10.4193i		−	0.433761i	−0.976198	−	0.216880i	$-0.930412\pi$
$577$		−	10.4193i		−	0.433761i	0.976198	−	0.216880i	$-0.0695882\pi$
$578$	−20.3933	+	12.5714i	−0.848251	+	0.522902i
$579$		0			0
$580$	−20.3049	−	23.4018i	−0.843117	−	0.971708i
$581$	4.81236	−	4.81236i	0.199650	−	0.199650i
$582$		0			0
$583$	−5.29274			−0.219203
$584$	−2.36957	−	27.3318i	−0.0980534	−	1.13100i
$585$		0			0
$586$	−23.0088	−	5.45955i	−0.950484	−	0.225532i
$587$	−27.7728	−	27.7728i	−1.14631	−	1.14631i	−0.987273	−	0.159033i	$-0.949162\pi$
$587$	−27.7728	−	27.7728i	−1.14631	−	1.14631i	−0.159033	−	0.987273i	$-0.550838\pi$
$588$		0			0
$589$	11.7049	+	11.7049i	0.482291	+	0.482291i
$590$	−25.8679	+	4.23389i	−1.06497	+	0.174306i
$591$		0			0
$592$	7.00104	−	47.4487i	0.287741	−	1.95013i
$593$		−	25.4466i		−	1.04496i	−0.852650	−	0.522482i	$-0.825006\pi$
$593$		−	25.4466i		−	1.04496i	0.852650	−	0.522482i	$-0.174994\pi$
$594$		0			0
$595$	0.357497	−	0.149132i	0.0146559	−	0.00611380i
$596$	4.80890	+	14.5380i	0.196980	+	0.595498i
$597$		0			0
$598$	12.3498	−	52.0470i	0.505020	−	2.12836i
$599$		−	1.32051i		−	0.0539544i	−0.999636	−	0.0269772i	$-0.991412\pi$
$599$		−	1.32051i		−	0.0539544i	0.999636	−	0.0269772i	$-0.00858816\pi$
$600$		0			0
$601$			23.8236i			0.971787i	0.874018	+	0.485893i	$0.161506\pi$
$601$			23.8236i			0.971787i	−0.874018	+	0.485893i	$0.838494\pi$
$602$	0.942275	+	0.223584i	0.0384043	+	0.00911261i
$603$		0			0
$604$	−0.610277	−	0.306893i	−0.0248318	−	0.0124873i
$605$	9.32902	−	3.89165i	0.379279	−	0.158218i
$606$		0			0
$607$		−	1.20300i		−	0.0488283i	−0.999702	−	0.0244141i	$-0.992228\pi$
$607$		−	1.20300i		−	0.0488283i	0.999702	−	0.0244141i	$-0.00777203\pi$
$608$	4.86054	+	11.3087i	0.197121	+	0.458630i
$609$		0			0
$610$	0.0388218	+	0.237191i	0.00157185	+	0.00960358i
$611$	17.2830	+	17.2830i	0.699193	+	0.699193i
$612$		0			0
$613$	4.84340	+	4.84340i	0.195623	+	0.195623i	0.798121	−	0.602498i	$-0.205828\pi$
$613$	4.84340	+	4.84340i	0.195623	+	0.195623i	−0.602498	+	0.798121i	$0.705828\pi$
$614$	7.67561	−	32.3481i	0.309762	−	1.30546i
$615$		0			0
$616$	3.89893	+	3.27682i	0.157092	+	0.132027i
$617$	26.9719			1.08585			0.542924	−	0.839782i	$-0.317317\pi$
$617$	26.9719			1.08585			0.542924	+	0.839782i	$0.317317\pi$
$618$		0			0
$619$	19.9202	−	19.9202i	0.800660	−	0.800660i	−0.182539	−	0.983199i	$-0.558432\pi$
$619$	19.9202	−	19.9202i	0.800660	−	0.800660i	0.983199	+	0.182539i	$0.0584316\pi$
$620$	−33.9360	−	2.40458i	−1.36290	−	0.0965702i
$621$		0			0
$622$	10.2463	+	16.6216i	0.410840	+	0.666464i
$623$		−	2.17513i		−	0.0871446i
$624$		0			0
$625$	−0.250824	−	24.9987i	−0.0100330	−	0.999950i
$626$	−8.91310	+	5.49446i	−0.356239	+	0.219603i
$627$		0			0
$628$	−2.54455	−	7.69253i	−0.101539	−	0.306965i
$629$	2.07628	−	2.07628i	0.0827868	−	0.0827868i
$630$		0			0
$631$		−	12.7975i		−	0.509462i	−0.967012	−	0.254731i	$-0.918013\pi$
$631$		−	12.7975i		−	0.509462i	0.967012	−	0.254731i	$-0.0819870\pi$
$632$	−1.79483	−	20.7025i	−0.0713945	−	0.823502i
$633$		0			0
$634$	−0.834425	+	3.51661i	−0.0331392	+	0.139662i
$635$	−40.1321	+	16.7413i	−1.59260	+	0.664360i
$636$		0			0
$637$	25.1110	−	25.1110i	0.994934	−	0.994934i
$638$	21.2300	−	13.0872i	0.840505	−	0.518127i
$639$		0			0
$640$	−22.7775	−	11.0085i	−0.900359	−	0.435149i
$641$	−10.9406			−0.432129			−0.216064	−	0.976379i	$-0.569322\pi$
$641$	−10.9406			−0.432129			−0.216064	+	0.976379i	$0.569322\pi$
$642$		0			0
$643$	−18.2613	+	18.2613i	−0.720157	+	0.720157i	−0.968637	−	0.248480i	$-0.920069\pi$
$643$	−18.2613	+	18.2613i	−0.720157	+	0.720157i	0.248480	+	0.968637i	$0.420069\pi$
$644$	−4.40028	+	8.75024i	−0.173395	+	0.344808i
$645$		0			0
$646$	−0.173978	+	0.733215i	−0.00684508	+	0.0288479i
$647$	10.5055			0.413014			0.206507	−	0.978445i	$-0.433790\pi$
$647$	10.5055			0.413014			0.206507	+	0.978445i	$0.433790\pi$
$648$		0			0
$649$		−	21.0995i		−	0.828228i
$650$	20.4385	+	32.7859i	0.801662	+	1.28597i
$651$		0			0
$652$	−5.27818	−	15.9567i	−0.206709	−	0.624911i
$653$	−11.1836	+	11.1836i	−0.437648	+	0.437648i	−0.891220	−	0.453572i	$-0.850150\pi$
$653$	−11.1836	+	11.1836i	−0.437648	+	0.437648i	0.453572	+	0.891220i	$0.350150\pi$
$654$		0			0
$655$	0.425857	−	1.03545i	0.0166396	−	0.0404583i
$656$	−6.81109	+	5.05958i	−0.265928	+	0.197543i
$657$		0			0
$658$	−2.34841	−	3.80958i	−0.0915505	−	0.148513i
$659$	−2.60687	−	2.60687i	−0.101549	−	0.101549i	0.654507	−	0.756056i	$-0.272876\pi$
$659$	−2.60687	−	2.60687i	−0.101549	−	0.101549i	−0.756056	+	0.654507i	$0.772876\pi$
$660$		0			0
$661$	15.9084	−	15.9084i	0.618766	−	0.618766i	−0.326449	−	0.945215i	$-0.605852\pi$
$661$	15.9084	−	15.9084i	0.618766	−	0.618766i	0.945215	+	0.326449i	$0.105852\pi$
$662$	2.69062	−	11.3394i	0.104574	−	0.440717i
$663$		0			0
$664$	−20.8316	−	17.5077i	−0.808421	−	0.679430i
$665$	−1.30918	+	3.18319i	−0.0507677	+	0.123439i
$666$		0			0
$667$	33.9135	+	33.9135i	1.31314	+	1.31314i
$668$	12.9924	−	25.8361i	0.502689	−	0.999629i
$669$		0			0
$670$	34.6695	−	5.67447i	1.33940	−	0.219224i
$671$	−0.193468			−0.00746874
$672$		0			0
$673$		−	27.1091i		−	1.04498i	−0.852645	−	0.522490i	$-0.825003\pi$
$673$		−	27.1091i		−	1.04498i	0.852645	−	0.522490i	$-0.174997\pi$
$674$	−18.9504	−	30.7413i	−0.729943	−	1.18411i
$675$		0			0
$676$	−30.1127	−	15.1429i	−1.15818	−	0.582420i
$677$	11.0637	+	11.0637i	0.425211	+	0.425211i	0.886993	−	0.461782i	$-0.152790\pi$
$677$	11.0637	+	11.0637i	0.425211	+	0.425211i	−0.461782	+	0.886993i	$0.652790\pi$
$678$		0			0
$679$		−	0.989807i		−	0.0379853i
$680$	−0.717513	−	1.37255i	−0.0275154	−	0.0526351i
$681$		0			0
$682$	6.32247	−	26.6455i	0.242100	−	1.02031i
$683$	17.4289	+	17.4289i	0.666898	+	0.666898i	0.956997	−	0.290098i	$-0.0936881\pi$
$683$	17.4289	+	17.4289i	0.666898	+	0.666898i	−0.290098	+	0.956997i	$0.593688\pi$
$684$		0			0
$685$	6.28474	+	15.0657i	0.240128	+	0.575631i
$686$	−11.4963	+	7.08687i	−0.438931	+	0.270578i
$687$		0			0
$688$	0.565216	−	3.83068i	0.0215487	−	0.146043i
$689$	−11.3607			−0.432807
$690$		0			0
$691$	26.0352	+	26.0352i	0.990426	+	0.990426i	0.999955	−	0.00952887i	$-0.00303318\pi$
$691$	26.0352	+	26.0352i	0.990426	+	0.990426i	−0.00952887	+	0.999955i	$0.503033\pi$
$692$	5.90777	+	17.8600i	0.224580	+	0.678936i
$693$		0			0
$694$	−34.2546	−	8.12797i	−1.30029	−	0.308533i
$695$	25.8978	+	10.6512i	0.982359	+	0.404023i
$696$		0			0
$697$	−0.519443			−0.0196753
$698$	9.87700	+	2.34363i	0.373850	+	0.0887076i
$699$		0			0
$700$	−2.25522	−	6.70486i	−0.0852395	−	0.253420i
$701$	−2.08057	−	2.08057i	−0.0785822	−	0.0785822i	0.666723	−	0.745305i	$-0.267696\pi$
$701$	−2.08057	−	2.08057i	−0.0785822	−	0.0785822i	−0.745305	+	0.666723i	$0.767696\pi$
$702$		0			0
$703$			26.0910i			0.984039i
$704$	11.7065	−	16.6627i	0.441204	−	0.627999i
$705$		0			0
$706$	0.127299	+	0.206504i	0.00479095	+	0.00777187i
$707$	8.34137	−	8.34137i	0.313709	−	0.313709i
$708$		0			0
$709$	−3.27484	+	3.27484i	−0.122989	+	0.122989i	−0.765922	−	0.642933i	$-0.777717\pi$
$709$	−3.27484	+	3.27484i	−0.122989	+	0.122989i	0.642933	+	0.765922i	$0.277717\pi$
$710$	−3.84968	+	5.35648i	−0.144476	+	0.201025i
$711$		0			0
$712$	−8.66443	+	0.751173i	−0.324713	+	0.0281514i
$713$	52.6641			1.97229
$714$		0			0
$715$	−28.7019	+	11.9732i	−1.07339	+	0.447771i
$716$	−46.3648	+	15.3366i	−1.73273	+	0.573157i
$717$		0			0
$718$	−12.7417	−	20.6695i	−0.475515	−	0.771380i
$719$	2.03220			0.0757882			0.0378941	−	0.999282i	$-0.487935\pi$
$719$	2.03220			0.0757882			0.0378941	+	0.999282i	$0.487935\pi$
$720$		0			0
$721$	1.62164			0.0603930
$722$	10.5864	+	17.1733i	0.393986	+	0.639123i
$723$		0			0
$724$	−4.55003	−	13.7554i	−0.169101	−	0.511215i
$725$	−34.6394	+	0.173772i	−1.28648	+	0.00645375i
$726$		0			0
$727$	6.37077			0.236279			0.118139	−	0.992997i	$-0.462307\pi$
$727$	6.37077			0.236279			0.118139	+	0.992997i	$0.462307\pi$
$728$	8.36891	+	7.03357i	0.310172	+	0.260682i
$729$		0			0
$730$	−24.9072	−	17.9007i	−0.921857	−	0.662535i
$731$	0.167625	−	0.167625i	0.00619984	−	0.00619984i
$732$		0			0
$733$	−6.95026	+	6.95026i	−0.256714	+	0.256714i	−0.823716	−	0.567002i	$-0.808103\pi$
$733$	−6.95026	+	6.95026i	−0.256714	+	0.256714i	0.567002	+	0.823716i	$0.308103\pi$
$734$	17.3005	+	28.0648i	0.638572	+	1.03589i
$735$		0			0
$736$	36.3755	+	14.5063i	1.34082	+	0.534709i
$737$			28.2787i			1.04166i
$738$		0			0
$739$	0.0483355	+	0.0483355i	0.00177805	+	0.00177805i	0.707995	−	0.706217i	$-0.249600\pi$
$739$	0.0483355	+	0.0483355i	0.00177805	+	0.00177805i	−0.706217	+	0.707995i	$0.749600\pi$
$740$	−35.1428	−	40.5028i	−1.29187	−	1.48891i
$741$		0			0
$742$	2.02393	+	0.480240i	0.0743007	+	0.0176302i
$743$	0.148848			0.00546069			0.00273035	−	0.999996i	$-0.499131\pi$
$743$	0.148848			0.00546069			0.00273035	+	0.999996i	$0.499131\pi$
$744$		0			0
$745$	15.8333	+	6.51188i	0.580087	+	0.238577i
$746$	2.17592	+	0.516304i	0.0796659	+	0.0189032i
$747$		0			0
$748$	1.18362	−	0.391521i	0.0432776	−	0.0143154i
$749$	−6.71327	−	6.71327i	−0.245297	−	0.245297i
$750$		0			0
$751$	1.69304			0.0617798			0.0308899	−	0.999523i	$-0.490166\pi$
$751$	1.69304			0.0617798			0.0308899	+	0.999523i	$0.490166\pi$
$752$	−14.3641	+	10.6703i	−0.523806	+	0.389106i
$753$		0			0
$754$	45.5695	−	28.0912i	1.65954	−	1.02302i
$755$	−0.704855	+	0.294034i	−0.0256523	+	0.0107010i
$756$		0			0
$757$	−26.6876	−	26.6876i	−0.969977	−	0.969977i	0.0295851	−	0.999562i	$-0.490581\pi$
$757$	−26.6876	−	26.6876i	−0.969977	−	0.969977i	−0.999562	+	0.0295851i	$0.990581\pi$
$758$	−10.3295	+	43.5326i	−0.375183	+	1.58118i
$759$		0			0
$760$	13.1321	+	4.11569i	0.476351	+	0.149292i
$761$			17.1363i			0.621189i	0.950542	+	0.310595i	$0.100528\pi$
$761$			17.1363i			0.621189i	−0.950542	+	0.310595i	$0.899472\pi$
$762$		0			0
$763$	−8.42212	−	8.42212i	−0.304901	−	0.304901i
$764$	15.9975	−	31.8120i	0.578769	−	1.15092i
$765$		0			0
$766$	−23.8343	−	38.6640i	−0.861169	−	1.39699i
$767$		−	45.2893i		−	1.63530i
$768$		0			0
$769$	−25.6406			−0.924622			−0.462311	−	0.886718i	$-0.652980\pi$
$769$	−25.6406			−0.924622			−0.462311	+	0.886718i	$0.652980\pi$
$770$	5.61944	−	0.919751i	0.202511	−	0.0331455i
$771$		0			0
$772$	30.7726	+	15.4748i	1.10753	+	0.556950i
$773$	−27.4452	−	27.4452i	−0.987137	−	0.987137i	0.0127818	−	0.999918i	$-0.495931\pi$
$773$	−27.4452	−	27.4452i	−0.987137	−	0.987137i	−0.999918	+	0.0127818i	$0.995931\pi$
$774$		0			0
$775$	−26.7607	+	27.0306i	−0.961274	+	0.970967i
$776$	−3.94281	+	0.341827i	−0.141539	+	0.0122709i
$777$		0			0
$778$	−10.5004	+	44.2530i	−0.376458	+	1.58655i
$779$	3.26371	−	3.26371i	0.116934	−	0.116934i
$780$		0			0
$781$	−3.75456	−	3.75456i	−0.134349	−	0.134349i
$782$	1.25809	+	2.04088i	0.0449893	+	0.0729816i
$783$		0			0
$784$	15.5033	+	20.8702i	0.553688	+	0.745363i
$785$	−8.37792	−	3.44565i	−0.299021	−	0.122981i
$786$		0			0
$787$	−9.65912	+	9.65912i	−0.344310	+	0.344310i	−0.857985	−	0.513675i	$-0.828284\pi$
$787$	−9.65912	+	9.65912i	−0.344310	+	0.344310i	0.513675	+	0.857985i	$0.328284\pi$
$788$	−27.0585	+	8.95047i	−0.963919	+	0.318847i
$789$		0			0
$790$	−18.8660	−	13.5589i	−0.671221	−	0.482404i
$791$		−	5.60829i		−	0.199408i
$792$		0			0
$793$	−0.415271			−0.0147467
$794$	−9.99810	+	42.1361i	−0.354819	+	1.49535i
$795$		0			0
$796$	−10.2594	−	5.15921i	−0.363635	−	0.182863i
$797$	11.9978	−	11.9978i	0.424984	−	0.424984i	−0.461931	−	0.886916i	$-0.652843\pi$
$797$	11.9978	−	11.9978i	0.424984	−	0.424984i	0.886916	+	0.461931i	$0.152843\pi$
$798$		0			0
$799$	−1.09547			−0.0387549
$800$	−25.9294	+	11.2990i	−0.916742	+	0.399480i
$801$		0			0
$802$	20.6582	−	12.7347i	0.729466	−	0.449678i
$803$	17.4584	−	17.4584i	0.616094	−	0.616094i
$804$		0			0
$805$	4.21590	+	10.1063i	0.148591	+	0.356201i
$806$	13.5710	−	57.1935i	0.478016	−	2.01456i
$807$		0			0
$808$	−36.1078	−	30.3464i	−1.27027	−	1.06758i
$809$			36.2916i			1.27594i	0.770060	+	0.637972i	$0.220226\pi$
$809$			36.2916i			1.27594i	−0.770060	+	0.637972i	$0.779774\pi$
$810$		0			0
$811$	17.0781	−	17.0781i	0.599693	−	0.599693i	−0.340538	−	0.940231i	$-0.610609\pi$
$811$	17.0781	−	17.0781i	0.599693	−	0.599693i	0.940231	+	0.340538i	$0.110609\pi$
$812$	−9.30577	+	3.07818i	−0.326569	+	0.108023i
$813$		0			0
$814$	36.7439	−	22.6507i	1.28787	−	0.793906i
$815$	−17.3784	−	7.14735i	−0.608738	−	0.250361i
$816$		0			0
$817$			2.10641i			0.0736939i
$818$	13.3275	+	21.6198i	0.465984	+	0.755919i
$819$		0			0
$820$	−0.670476	+	9.46247i	−0.0234140	+	0.330444i
$821$	−21.9249	+	21.9249i	−0.765183	+	0.765183i	−0.977254	−	0.212071i	$-0.931979\pi$
$821$	−21.9249	+	21.9249i	−0.765183	+	0.765183i	0.212071	+	0.977254i	$0.431979\pi$
$822$		0			0
$823$	4.38382			0.152810			0.0764052	−	0.997077i	$-0.475656\pi$
$823$	4.38382			0.152810			0.0764052	+	0.997077i	$0.475656\pi$
$824$	−0.560028	−	6.45966i	−0.0195095	−	0.225033i
$825$		0			0
$826$	−1.91448	+	8.06839i	−0.0666132	+	0.280735i
$827$	21.5889	+	21.5889i	0.750718	+	0.750718i	0.974613	−	0.223895i	$-0.0718772\pi$
$827$	21.5889	+	21.5889i	0.750718	+	0.750718i	−0.223895	+	0.974613i	$0.571877\pi$
$828$		0			0
$829$	7.88066	+	7.88066i	0.273707	+	0.273707i	0.830590	−	0.556884i	$-0.188003\pi$
$829$	7.88066	+	7.88066i	0.273707	+	0.273707i	−0.556884	+	0.830590i	$0.688003\pi$
$830$	−30.0240	+	4.91413i	−1.04215	+	0.170572i
$831$		0			0
$832$	25.1275	−	35.7659i	0.871138	−	1.23996i
$833$			1.59165i			0.0551473i
$834$		0			0
$835$	−12.4480	−	29.8401i	−0.430779	−	1.03266i
$836$	−4.97685	+	9.89678i	−0.172128	+	0.342287i
$837$		0			0
$838$	45.5417	+	10.8062i	1.57321	+	0.373294i
$839$			6.03706i			0.208423i	0.994555	+	0.104211i	$0.0332318\pi$
$839$			6.03706i			0.208423i	−0.994555	+	0.104211i	$0.966768\pi$
$840$		0			0
$841$			18.9968i			0.655063i
$842$	12.4678	−	52.5442i	0.429667	−	1.81079i
$843$		0			0
$844$	−26.1368	+	8.64558i	−0.899666	+	0.297593i
$845$	−34.7794	+	14.5084i	−1.19645	+	0.499105i
$846$		0			0
$847$		−	3.19781i		−	0.109878i
$848$	1.21404	−	8.22799i	0.0416902	−	0.282550i
$849$		0			0
$850$	−1.68680	−	0.391318i	−0.0578567	−	0.0134221i
$851$	58.6959	+	58.6959i	2.01207	+	2.01207i
$852$		0			0
$853$	12.6685	+	12.6685i	0.433763	+	0.433763i	0.889906	−	0.456144i	$-0.150770\pi$
$853$	12.6685	+	12.6685i	0.433763	+	0.433763i	−0.456144	+	0.889906i	$0.650770\pi$
$854$	0.0739815	+	0.0175544i	0.00253160	+	0.000600700i
$855$		0			0
$856$	−24.4233	+	29.0601i	−0.834772	+	0.993255i
$857$	4.79580			0.163821			0.0819106	−	0.996640i	$-0.473898\pi$
$857$	4.79580			0.163821			0.0819106	+	0.996640i	$0.473898\pi$
$858$		0			0
$859$	−34.0244	+	34.0244i	−1.16090	+	1.16090i	−0.176616	+	0.984280i	$0.556515\pi$
$859$	−34.0244	+	34.0244i	−1.16090	+	1.16090i	−0.984280	+	0.176616i	$0.943485\pi$
$860$	−2.83719	−	3.26992i	−0.0967474	−	0.111503i
$861$		0			0
$862$	−34.1946	+	21.0792i	−1.16467	+	0.717960i
$863$			8.20297i			0.279232i	0.990206	+	0.139616i	$0.0445869\pi$
$863$			8.20297i			0.279232i	−0.990206	+	0.139616i	$0.955413\pi$
$864$		0			0
$865$	19.4513	+	7.99990i	0.661365	+	0.272005i
$866$	3.00233	+	4.87037i	0.102023	+	0.165502i
$867$		0			0
$868$	−4.83539	+	9.61548i	−0.164124	+	0.326371i
$869$	13.2239	−	13.2239i	0.448590	−	0.448590i
$870$		0			0
$871$			60.6991i			2.05671i
$872$	−30.6402	+	36.4573i	−1.03761	+	1.23460i
$873$		0			0
$874$	−20.7277	−	4.91831i	−0.701127	−	0.166364i
$875$	−7.32948	−	2.97155i	−0.247782	−	0.100457i
$876$		0			0
$877$	23.9525	−	23.9525i	0.808817	−	0.808817i	−0.175638	−	0.984455i	$-0.556199\pi$
$877$	23.9525	−	23.9525i	0.808817	−	0.808817i	0.984455	+	0.175638i	$0.0561987\pi$
$878$	−7.76922	−	12.6032i	−0.262198	−	0.425338i
$879$		0			0
$880$	−5.60441	−	22.0669i	−0.188924	−	0.743876i
$881$	−27.4850			−0.925993			−0.462997	−	0.886360i	$-0.653226\pi$
$881$	−27.4850			−0.925993			−0.462997	+	0.886360i	$0.653226\pi$
$882$		0			0
$883$	22.9566	−	22.9566i	0.772550	−	0.772550i	−0.206001	−	0.978552i	$-0.566045\pi$
$883$	22.9566	−	22.9566i	0.772550	−	0.772550i	0.978552	+	0.206001i	$0.0660452\pi$
$884$	2.54060	−	0.840386i	0.0854497	−	0.0282652i
$885$		0			0
$886$	3.53353	+	0.838440i	0.118711	+	0.0281679i
$887$	8.52038			0.286086			0.143043	−	0.989716i	$-0.454311\pi$
$887$	8.52038			0.286086			0.143043	+	0.989716i	$0.454311\pi$
$888$		0			0
$889$			13.7565i			0.461379i
$890$	−5.67468	+	7.89580i	−0.190216	+	0.264668i
$891$		0			0
$892$	39.4948	+	19.8610i	1.32238	+	0.664994i
$893$	6.88294	−	6.88294i	0.230329	−	0.230329i
$894$		0			0
$895$	−20.7678	+	50.4958i	−0.694192	+	1.68789i
$896$	−5.98841	+	5.30957i	−0.200059	+	0.177380i
$897$		0			0
$898$	−26.7333	+	16.4797i	−0.892102	+	0.549934i
$899$	37.2670	+	37.2670i	1.24292	+	1.24292i
$900$		0			0
$901$	0.360044	−	0.360044i	0.0119948	−	0.0119948i
$902$	−7.42964	−	1.76291i	−0.247380	−	0.0586986i
$903$		0			0
$904$	−22.3401	+	1.93680i	−0.743022	+	0.0644172i
$905$	−14.9810	−	6.16134i	−0.497984	−	0.204810i
$906$		0			0
$907$	21.1812	+	21.1812i	0.703312	+	0.703312i	0.965120	−	0.261808i	$-0.0843188\pi$
$907$	21.1812	+	21.1812i	0.703312	+	0.703312i	−0.261808	+	0.965120i	$0.584319\pi$
$908$	−4.75563	−	14.3769i	−0.157821	−	0.477115i
$909$		0			0
$910$	12.0619	−	1.97421i	0.399849	−	0.0654445i
$911$	12.3002			0.407525			0.203763	−	0.979020i	$-0.434683\pi$
$911$	12.3002			0.407525			0.203763	+	0.979020i	$0.434683\pi$
$912$		0			0
$913$		−	24.4895i		−	0.810484i
$914$	14.7207	−	9.07454i	0.486918	−	0.300159i
$915$		0			0
$916$	16.2568	+	49.1465i	0.537139	+	1.62384i
$917$	−0.250454	−	0.250454i	−0.00827070	−	0.00827070i
$918$		0			0
$919$		−	3.59430i		−	0.118565i	−0.998241	−	0.0592826i	$-0.981119\pi$
$919$		−	3.59430i		−	0.118565i	0.998241	−	0.0592826i	$-0.0188813\pi$
$920$	38.8017	−	20.2839i	1.27925	−	0.668740i
$921$		0			0
$922$	1.40781	+	0.334046i	0.0463636	+	0.0110012i
$923$	−8.05902	−	8.05902i	−0.265266	−	0.265266i
$924$		0			0
$925$	−59.9522	+	0.300757i	−1.97122	+	0.00988882i
$926$	4.02480	+	6.52903i	0.132263	+	0.214557i
$927$		0			0
$928$	15.4754	+	36.0057i	0.508005	+	1.18195i
$929$	35.8527			1.17629			0.588145	−	0.808756i	$-0.299858\pi$
$929$	35.8527			1.17629			0.588145	+	0.808756i	$0.299858\pi$
$930$		0			0
$931$	−10.0005	−	10.0005i	−0.327752	−	0.327752i
$932$	−10.8315	+	21.5390i	−0.354796	+	0.705535i
$933$		0			0
$934$	6.15234	−	25.9285i	0.201311	−	0.848406i
$935$	0.530171	−	1.28908i	0.0173385	−	0.0421575i
$936$		0			0
$937$	−40.7563			−1.33145			−0.665725	−	0.746198i	$-0.731877\pi$
$937$	−40.7563			−1.33145			−0.665725	+	0.746198i	$0.731877\pi$
$938$	2.56588	−	10.8137i	0.0837790	−	0.353079i
$939$		0			0
$940$	−1.41399	+	19.9557i	−0.0461192	+	0.650883i
$941$	−36.2143	−	36.2143i	−1.18055	−	1.18055i	−0.979602	−	0.200950i	$-0.935597\pi$
$941$	−36.2143	−	36.2143i	−1.18055	−	1.18055i	−0.200950	−	0.979602i	$-0.564403\pi$
$942$		0			0
$943$		−	14.6845i		−	0.478193i
$944$	32.8009	+	4.83976i	1.06758	+	0.157521i
$945$		0			0
$946$	2.96645	−	1.82866i	0.0964477	−	0.0594549i
$947$	−36.5242	+	36.5242i	−1.18688	+	1.18688i	−0.208951	+	0.977926i	$0.567005\pi$
$947$	−36.5242	+	36.5242i	−1.18688	+	1.18688i	−0.977926	+	0.208951i	$0.932995\pi$
$948$		0			0
$949$	37.4738	−	37.4738i	1.21645	−	1.21645i
$950$	13.0570	−	8.13962i	0.423625	−	0.264084i
$951$		0			0
$952$	−0.488139	+	0.0423198i	−0.0158207	+	0.00137159i
$953$	−16.0927			−0.521294			−0.260647	−	0.965434i	$-0.583936\pi$
$953$	−16.0927			−0.521294			−0.260647	+	0.965434i	$0.583936\pi$
$954$		0			0
$955$	−15.3272	−	36.7421i	−0.495975	−	1.18895i
$956$	25.0865	−	49.8860i	0.811354	−	1.61343i
$957$		0			0
$958$	−1.51642	+	0.934791i	−0.0489932	+	0.0302017i
$959$	5.16423			0.166762
$960$		0			0
$961$	26.8716			0.866826
$962$	78.8694	−	48.6188i	2.54285	−	1.56753i
$963$		0			0
$964$	12.3205	−	24.5001i	0.396817	−	0.789095i
$965$	35.5416	−	14.8264i	1.14413	−	0.477278i
$966$		0			0
$967$	−21.3561			−0.686767			−0.343384	−	0.939195i	$-0.611573\pi$
$967$	−21.3561			−0.686767			−0.343384	+	0.939195i	$0.611573\pi$
$968$	−12.7382	+	1.10435i	−0.409421	+	0.0354952i
$969$		0			0
$970$	−2.58230	+	3.59304i	−0.0829128	+	0.115366i
$971$	20.0626	−	20.0626i	0.643839	−	0.643839i	−0.307658	−	0.951497i	$-0.599545\pi$
$971$	20.0626	−	20.0626i	0.643839	−	0.643839i	0.951497	+	0.307658i	$0.0995454\pi$
$972$		0			0
$973$	6.26414	−	6.26414i	0.200819	−	0.200819i
$974$	19.0349	−	11.7340i	0.609916	−	0.375981i
$975$		0			0
$976$	0.0443773	−	0.300761i	0.00142048	−	0.00962714i
$977$			27.7769i			0.888661i	0.895863	+	0.444331i	$0.146558\pi$
$977$			27.7769i			0.888661i	−0.895863	+	0.444331i	$0.853442\pi$
$978$		0			0
$979$	−5.53447	−	5.53447i	−0.176882	−	0.176882i
$980$	28.9944	+	2.05443i	0.926191	+	0.0656265i
$981$		0			0
$982$	−7.20354	+	30.3586i	−0.229874	+	0.968783i
$983$	−0.428090			−0.0136540			−0.00682698	−	0.999977i	$-0.502173\pi$
$983$	−0.428090			−0.0136540			−0.00682698	+	0.999977i	$0.502173\pi$
$984$		0			0
$985$	−12.1201	+	29.4694i	−0.386179	+	0.938973i
$986$	−0.553926	+	2.33447i	−0.0176406	+	0.0743446i
$987$		0			0
$988$	−10.6826	+	21.2431i	−0.339859	+	0.675832i
$989$	4.73871	+	4.73871i	0.150682	+	0.150682i
$990$		0			0
$991$	−5.82267			−0.184963			−0.0924816	−	0.995714i	$-0.529480\pi$
$991$	−5.82267			−0.184963			−0.0924816	+	0.995714i	$0.529480\pi$
$992$	39.9723	+	15.9407i	1.26912	+	0.506117i
$993$		0			0
$994$	1.09506	+	1.77641i	0.0347332	+	0.0563442i
$995$	−11.8494	+	4.94303i	−0.375650	+	0.156704i
$996$		0			0
$997$	20.1044	+	20.1044i	0.636713	+	0.636713i	0.949743	−	0.313030i	$-0.101344\pi$
$997$	20.1044	+	20.1044i	0.636713	+	0.636713i	−0.313030	+	0.949743i	$0.601344\pi$
$998$	−49.9433	−	11.8506i	−1.58093	−	0.375125i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.5		48
3.2	odd	2		240.2.bl.a.109.20	yes	48
5.4	even	2	inner	720.2.bm.h.109.20		48
12.11	even	2		960.2.bl.a.529.9		48
15.14	odd	2		240.2.bl.a.109.5	✓	48
16.5	even	4	inner	720.2.bm.h.469.20		48
24.5	odd	2		1920.2.bl.a.289.7		48
24.11	even	2		1920.2.bl.b.289.18		48
48.5	odd	4		240.2.bl.a.229.5	yes	48
48.11	even	4		960.2.bl.a.49.15		48
48.29	odd	4		1920.2.bl.a.1249.18		48
48.35	even	4		1920.2.bl.b.1249.7		48
60.59	even	2		960.2.bl.a.529.15		48
80.69	even	4	inner	720.2.bm.h.469.5		48
120.29	odd	2		1920.2.bl.a.289.18		48
120.59	even	2		1920.2.bl.b.289.7		48
240.29	odd	4		1920.2.bl.a.1249.7		48
240.59	even	4		960.2.bl.a.49.9		48
240.149	odd	4		240.2.bl.a.229.20	yes	48
240.179	even	4		1920.2.bl.b.1249.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.5	✓	48	15.14	odd	2
240.2.bl.a.109.20	yes	48	3.2	odd	2
240.2.bl.a.229.5	yes	48	48.5	odd	4
240.2.bl.a.229.20	yes	48	240.149	odd	4
720.2.bm.h.109.5		48	1.1	even	1	trivial
720.2.bm.h.109.20		48	5.4	even	2	inner
720.2.bm.h.469.5		48	80.69	even	4	inner
720.2.bm.h.469.20		48	16.5	even	4	inner
960.2.bl.a.49.9		48	240.59	even	4
960.2.bl.a.49.15		48	48.11	even	4
960.2.bl.a.529.9		48	12.11	even	2
960.2.bl.a.529.15		48	60.59	even	2
1920.2.bl.a.289.7		48	24.5	odd	2
1920.2.bl.a.289.18		48	120.29	odd	2
1920.2.bl.a.1249.7		48	240.29	odd	4
1920.2.bl.a.1249.18		48	48.29	odd	4
1920.2.bl.b.289.7		48	120.59	even	2
1920.2.bl.b.289.18		48	24.11	even	2
1920.2.bl.b.1249.7		48	48.35	even	4
1920.2.bl.b.1249.18		48	240.179	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20386 + 0.742113i) q^{2} +(0.898535 - 1.78679i) q^{4} +(-0.860885 - 2.06370i) q^{5} -0.707398 q^{7} +(0.244298 + 2.81786i) q^{8} +(2.56788 + 1.84553i) q^{10} +(-1.79993 + 1.79993i) q^{11} +(-3.86348 + 3.86348i) q^{13} +(0.851604 - 0.524969i) q^{14} +(-2.38527 - 3.21100i) q^{16} -0.244884i q^{17} +(1.53863 + 1.53863i) q^{19} +(-4.46095 - 0.316087i) q^{20} +(0.831102 - 3.50260i) q^{22} +6.92280 q^{23} +(-3.51775 + 3.55323i) q^{25} +(1.78393 - 7.51820i) q^{26} +(-0.635622 + 1.26397i) q^{28} +(4.89882 + 4.89882i) q^{29} +7.60734 q^{31} +(5.25444 + 2.09543i) q^{32} +(0.181732 + 0.294805i) q^{34} +(0.608988 + 1.45986i) q^{35} +(8.47863 + 8.47863i) q^{37} +(-2.99413 - 0.710450i) q^{38} +(5.60491 - 2.93001i) q^{40} -2.12118i q^{41} +(0.684507 + 0.684507i) q^{43} +(1.59880 + 4.83340i) q^{44} +(-8.33405 + 5.13750i) q^{46} -4.47342i q^{47} -6.49959 q^{49} +(1.59797 - 6.88814i) q^{50} +(3.43177 + 10.3747i) q^{52} +(1.47026 + 1.47026i) q^{53} +(5.26405 + 2.16499i) q^{55} +(-0.172815 - 1.99335i) q^{56} +(-9.53295 - 2.26199i) q^{58} +(-5.86121 + 5.86121i) q^{59} +(0.0537432 + 0.0537432i) q^{61} +(-9.15813 + 5.64551i) q^{62} +(-7.88064 + 1.37679i) q^{64} +(11.2991 + 4.64706i) q^{65} +(7.85550 - 7.85550i) q^{67} +(-0.437558 - 0.220037i) q^{68} +(-1.81651 - 1.30552i) q^{70} +2.08595i q^{71} -9.69951 q^{73} +(-16.4992 - 3.91494i) q^{74} +(4.13173 - 1.36670i) q^{76} +(1.27326 - 1.27326i) q^{77} -7.34690 q^{79} +(-4.57310 + 7.68679i) q^{80} +(1.57415 + 2.55359i) q^{82} +(-6.80291 + 6.80291i) q^{83} +(-0.505369 + 0.210817i) q^{85} +(-1.33203 - 0.316066i) q^{86} +(-5.51166 - 4.63222i) q^{88} +3.07483i q^{89} +(2.73301 - 2.73301i) q^{91} +(6.22038 - 12.3696i) q^{92} +(3.31978 + 5.38535i) q^{94} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(7.82456 - 4.82343i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64}+ \cdots + 48 q^{95}+O(q^{100}) \) 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Introduction

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