LMFDB - Embedded newform 720.2.bm.h.109.20

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			109.20
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20386 - 0.742113i) q^{2} +(0.898535 - 1.78679i) q^{4} +(2.06370 + 0.860885i) q^{5} +0.707398 q^{7} +(-0.244298 - 2.81786i) q^{8} +O(q^{10})$	\(q+(1.20386 - 0.742113i) q^{2} +(0.898535 - 1.78679i) q^{4} +(2.06370 + 0.860885i) q^{5} +0.707398 q^{7} +(-0.244298 - 2.81786i) q^{8} +(3.12328 - 0.495122i) q^{10} +(-1.79993 + 1.79993i) q^{11} +(3.86348 - 3.86348i) q^{13} +(0.851604 - 0.524969i) q^{14} +(-2.38527 - 3.21100i) q^{16} +0.244884i q^{17} +(1.53863 + 1.53863i) q^{19} +(3.39254 - 2.91388i) q^{20} +(-0.831102 + 3.50260i) q^{22} -6.92280 q^{23} +(3.51775 + 3.55323i) q^{25} +(1.78393 - 7.51820i) q^{26} +(0.635622 - 1.26397i) q^{28} +(4.89882 + 4.89882i) q^{29} +7.60734 q^{31} +(-5.25444 - 2.09543i) q^{32} +(0.181732 + 0.294805i) q^{34} +(1.45986 + 0.608988i) q^{35} +(-8.47863 - 8.47863i) q^{37} +(2.99413 + 0.710450i) q^{38} +(1.92169 - 6.02554i) q^{40} -2.12118i q^{41} +(-0.684507 - 0.684507i) q^{43} +(1.59880 + 4.83340i) q^{44} +(-8.33405 + 5.13750i) q^{46} +4.47342i q^{47} -6.49959 q^{49} +(6.87176 + 1.66700i) q^{50} +(-3.43177 - 10.3747i) q^{52} +(-1.47026 - 1.47026i) q^{53} +(-5.26405 + 2.16499i) q^{55} +(-0.172815 - 1.99335i) q^{56} +(9.53295 + 2.26199i) q^{58} +(-5.86121 + 5.86121i) q^{59} +(0.0537432 + 0.0537432i) q^{61} +(9.15813 - 5.64551i) q^{62} +(-7.88064 + 1.37679i) q^{64} +(11.2991 - 4.64706i) q^{65} +(-7.85550 + 7.85550i) q^{67} +(0.437558 + 0.220037i) q^{68} +(2.20940 - 0.350248i) q^{70} +2.08595i q^{71} +9.69951 q^{73} +(-16.4992 - 3.91494i) q^{74} +(4.13173 - 1.36670i) q^{76} +(-1.27326 + 1.27326i) q^{77} -7.34690 q^{79} +(-2.15819 - 8.67999i) q^{80} +(-1.57415 - 2.55359i) q^{82} +(6.80291 - 6.80291i) q^{83} +(-0.210817 + 0.505369i) q^{85} +(-1.33203 - 0.316066i) q^{86} +(5.51166 + 4.63222i) q^{88} +3.07483i q^{89} +(2.73301 - 2.73301i) q^{91} +(-6.22038 + 12.3696i) q^{92} +(3.31978 + 5.38535i) q^{94} +(1.85069 + 4.49986i) q^{95} -1.39922i q^{97} +(-7.82456 + 4.82343i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * 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} - 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}+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

Display 100 coefficients 10 coefficients

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
$5$	2.06370	+	0.860885i	0.922917	+	0.385000i
$5$	2.06370	+	0.860885i	0.922917	+	0.385000i
$6$		0			0
$7$	0.707398			0.267371			0.133686	−	0.991024i	$-0.457319\pi$
$7$	0.707398			0.267371			0.133686	+	0.991024i	$0.457319\pi$
$8$	−0.244298	−	2.81786i	−0.0863722	−	0.996263i
$9$		0			0
$10$	3.12328	−	0.495122i	0.987667	−	0.156571i
$11$	−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	$-0.476328\pi$
$13$	3.86348	−	3.86348i	1.07154	−	1.07154i	0.997236	−	0.0742996i	$-0.0236721\pi$
$14$	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	$0.00945410\pi$
$17$			0.244884i			0.0593932i	−0.999559	+	0.0296966i	$0.990546\pi$
$18$		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	$0.669701\pi$
$20$	3.39254	−	2.91388i	0.758594	−	0.651563i
$21$		0			0
$22$	−0.831102	+	3.50260i	−0.177192	+	0.746757i
$23$	−6.92280			−1.44350			−0.721752	−	0.692152i	$-0.756663\pi$
$23$	−6.92280			−1.44350			−0.721752	+	0.692152i	$0.756663\pi$
$24$		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
$35$	1.45986	+	0.608988i	0.246761	+	0.102938i
$36$		0			0
$37$	−8.47863	−	8.47863i	−1.39388	−	1.39388i	−0.816420	−	0.577459i	$-0.804044\pi$
$37$	−8.47863	−	8.47863i	−1.39388	−	1.39388i	−0.577459	−	0.816420i	$-0.695956\pi$
$38$	2.99413	+	0.710450i	0.485712	+	0.115250i
$39$		0			0
$40$	1.92169	−	6.02554i	0.303846	−	0.952721i
$41$		−	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	0.652985	−	0.757371i	$-0.273517\pi$
$43$	−0.684507	−	0.684507i	−0.104386	−	0.104386i	−0.757371	+	0.652985i	$0.773517\pi$
$44$	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	$0.105788\pi$
$47$			4.47342i			0.652515i	−0.945281	+	0.326258i	$0.894212\pi$
$48$		0			0
$49$	−6.49959			−0.928513
$50$	6.87176	+	1.66700i	0.971814	+	0.235749i
$51$		0			0
$52$	−3.43177	−	10.3747i	−0.475901	−	1.43871i
$53$	−1.47026	−	1.47026i	−0.201956	−	0.201956i	0.598881	−	0.800838i	$-0.295612\pi$
$53$	−1.47026	−	1.47026i	−0.201956	−	0.201956i	−0.800838	+	0.598881i	$0.795612\pi$
$54$		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	−0.999219	−	0.0395170i	$-0.987418\pi$
$67$	−7.85550	+	7.85550i	−0.959702	+	0.959702i	0.0395170	+	0.999219i	$0.487418\pi$
$68$	0.437558	+	0.220037i	0.0530617	+	0.0266834i
$69$		0			0
$70$	2.20940	−	0.350248i	0.264074	−	0.0418626i
$71$			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	$-0.307864\pi$
$73$	9.69951			1.13524			0.567621	+	0.823290i	$0.307864\pi$
$74$	−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	$0.635622\pi$
$80$	−2.15819	−	8.67999i	−0.241293	−	0.970452i
$81$		0			0
$82$	−1.57415	−	2.55359i	−0.173836	−	0.281997i
$83$	6.80291	−	6.80291i	0.746716	−	0.746716i	−0.227145	−	0.973861i	$-0.572939\pi$
$83$	6.80291	−	6.80291i	0.746716	−	0.746716i	0.973861	+	0.227145i	$0.0729391\pi$
$84$		0			0
$85$	−0.210817	+	0.505369i	−0.0228663	+	0.0548149i
$86$	−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	$-0.977370\pi$
$97$		−	1.39922i		−	0.142070i	0.997474	−	0.0710348i	$-0.0226301\pi$
$98$	−7.82456	+	4.82343i	−0.790400	+	0.487240i
$99$		0			0
$100$	9.50971	−	3.09280i	0.950971	−	0.309280i
$101$	−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	$-0.463974\pi$
$103$	2.29240			0.225877			0.112938	+	0.993602i	$0.463974\pi$
$104$	−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	0.0794010	−	0.996843i	$-0.474699\pi$
$107$	−9.49009	−	9.49009i	−0.917442	−	0.917442i	−0.996843	+	0.0794010i	$0.974699\pi$
$108$		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	$0.451434\pi$
$110$	−4.73049	+	6.51285i	−0.451034	+	0.620976i
$111$		0			0
$112$	−1.68733	−	2.27145i	−0.159438	−	0.214632i
$113$		−	7.92806i		−	0.745809i	−0.927870	−	0.372904i	$-0.878362\pi$
$113$		−	7.92806i		−	0.745809i	0.927870	−	0.372904i	$-0.121638\pi$
$114$		0			0
$115$	−14.2866	−	5.95974i	−1.33223	−	0.555748i
$116$	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
$125$	4.20068	+	10.3612i	0.375721	+	0.926733i
$126$		0			0
$127$			19.4466i			1.72561i	0.505536	+	0.862806i	$0.331295\pi$
$127$			19.4466i			1.72561i	−0.505536	+	0.862806i	$0.668705\pi$
$128$	−8.46541	+	7.50578i	−0.748244	+	0.663424i
$129$		0			0
$130$	10.1538	−	13.9796i	0.890548	−	1.22609i
$131$	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	$-0.399050\pi$
$137$	7.30033			0.623709			0.311854	+	0.950130i	$0.399050\pi$
$138$		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	$0.428221\pi$
$140$	2.39987	−	2.06127i	0.202826	−	0.174209i
$141$		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
$155$	15.6993	+	6.54904i	1.26100	+	0.526032i
$156$		0			0
$157$	−2.86465	+	2.86465i	−0.228624	+	0.228624i	−0.812118	−	0.583494i	$-0.801685\pi$
$157$	−2.86465	+	2.86465i	−0.228624	+	0.228624i	0.583494	+	0.812118i	$0.301685\pi$
$158$	−8.84460	+	5.45223i	−0.703639	+	0.433756i
$159$		0			0
$160$	−9.03969	−	8.84783i	−0.714650	−	0.699482i
$161$	−4.89717			−0.385951
$162$		0			0
$163$	−5.94216	+	5.94216i	−0.465426	+	0.465426i	−0.900429	−	0.435003i	$-0.856747\pi$
$163$	−5.94216	+	5.94216i	−0.465426	+	0.465426i	0.435003	+	0.900429i	$0.356747\pi$
$164$	−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	$-0.688989\pi$
$167$	−14.4595			−1.11891			−0.559454	+	0.828861i	$0.688989\pi$
$168$		0			0
$169$		−	16.8529i		−	1.29638i
$170$	0.121247	+	0.764841i	0.00929926	+	0.0586606i
$171$		0			0
$172$	−1.83813	+	0.608020i	−0.140156	+	0.0463611i
$173$	6.65096	−	6.65096i	0.505663	−	0.505663i	−0.407529	−	0.913192i	$-0.633610\pi$
$173$	6.65096	−	6.65096i	0.505663	−	0.505663i	0.913192	+	0.407529i	$0.133610\pi$
$174$		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
$190$	5.56738	+	4.04376i	0.403900	+	0.293365i
$191$	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	$-0.787197\pi$
$193$		−	17.2222i		−	1.23968i	0.784727	−	0.619842i	$-0.212803\pi$
$194$	−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	0.968178	−	0.250263i	$-0.0805171\pi$
$197$	10.0764	+	10.0764i	0.717915	+	0.717915i	−0.250263	+	0.968178i	$0.580517\pi$
$198$		0			0
$199$		−	5.74179i		−	0.407025i	−0.979072	−	0.203513i	$-0.934764\pi$
$199$		−	5.74179i		−	0.407025i	0.979072	−	0.203513i	$-0.0652358\pi$
$200$	9.15310	−	10.7806i	0.647222	−	0.762301i
$201$		0			0
$202$	−5.44469	+	22.9461i	−0.383087	+	1.61448i
$203$	3.46541	+	3.46541i	0.243224	+	0.243224i
$204$		0			0
$205$	1.82609	−	4.37748i	0.127540	−	0.305737i
$206$	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
$220$	−0.861547	+	11.3511i	−0.0580855	+	0.765291i
$221$	0.946104	+	0.946104i	0.0636419	+	0.0636419i
$222$		0			0
$223$		−	22.1037i		−	1.48017i	−0.672511	−	0.740087i	$-0.734784\pi$
$223$		−	22.1037i		−	1.48017i	0.672511	−	0.740087i	$-0.265216\pi$
$224$	−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	−0.862095	−	0.506746i	$-0.830848\pi$
$227$	−5.35387	+	5.35387i	−0.355349	+	0.355349i	0.506746	+	0.862095i	$0.330848\pi$
$228$		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	$0.923441\pi$
$230$	−21.6218	+	3.42763i	−1.42570	+	0.226011i
$231$		0			0
$232$	12.6074	−	15.0009i	0.827716	−	0.984860i
$233$	12.0546			0.789721			0.394861	−	0.918741i	$-0.370793\pi$
$233$	12.0546			0.789721			0.394861	+	0.918741i	$0.370793\pi$
$234$		0			0
$235$	−3.85110	+	9.23182i	−0.251218	+	0.602217i
$236$	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
$245$	−13.4132	−	5.59540i	−0.856940	−	0.357477i
$246$		0			0
$247$	11.8889			0.756474
$248$	−1.85845	−	21.4364i	−0.118012	−	1.36121i
$249$		0			0
$250$	12.7462	+	9.35599i	0.806140	+	0.591725i
$251$	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	$0.0929922\pi$
$257$			9.23416i			0.576011i	−0.957629	+	0.288006i	$0.907008\pi$
$258$		0			0
$259$	−5.99776	−	5.99776i	−0.372683	−	0.372683i
$260$	1.84928	−	24.3647i	0.114687	−	1.51103i
$261$		0			0
$262$	0.688969	+	0.163479i	0.0425646	+	0.0100998i
$263$	18.5516			1.14394			0.571971	−	0.820274i	$-0.306179\pi$
$263$	18.5516			1.14394			0.571971	+	0.820274i	$0.306179\pi$
$264$		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
$275$	−12.7272	−	0.0638476i	−0.767482	−	0.00385016i
$276$		0			0
$277$	3.52269	+	3.52269i	0.211658	+	0.211658i	0.804971	−	0.593314i	$-0.202181\pi$
$277$	3.52269	+	3.52269i	0.211658	+	0.211658i	−0.593314	+	0.804971i	$0.702181\pi$
$278$	−4.08881	+	17.2319i	−0.245231	+	1.03350i
$279$		0			0
$280$	1.35940	−	4.26245i	0.0812398	−	0.254730i
$281$		−	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	0.351205	−	0.936298i	$-0.385772\pi$
$283$	−9.84279	−	9.84279i	−0.585093	−	0.585093i	−0.936298	+	0.351205i	$0.885772\pi$
$284$	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
$290$	17.7259	+	12.8749i	1.04090	+	0.756037i
$291$		0			0
$292$	8.71535	−	17.3310i	0.510027	−	1.01422i
$293$	−11.8238	−	11.8238i	−0.690755	−	0.690755i	0.271643	−	0.962398i	$-0.412433\pi$
$293$	−11.8238	−	11.8238i	−0.690755	−	0.690755i	−0.962398	+	0.271643i	$0.912433\pi$
$294$		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	−0.0500151	−	0.998748i	$-0.515927\pi$
$307$	16.6232	−	16.6232i	0.948733	−	0.948733i	0.998748	+	0.0500151i	$0.0159269\pi$
$308$	1.13099	+	3.41913i	0.0644441	+	0.194823i
$309$		0			0
$310$	23.7598	−	3.76656i	1.34947	−	0.213926i
$311$		−	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	$-0.567100\pi$
$313$	−7.40380			−0.418488			−0.209244	+	0.977864i	$0.567100\pi$
$314$	−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	−0.756032	−	0.654534i	$-0.772865\pi$
$317$	−1.80712	+	1.80712i	−0.101498	+	0.101498i	0.654534	+	0.756032i	$0.272865\pi$
$318$		0			0
$319$	−17.6350			−0.987372
$320$	−17.4486	−	3.94303i	−0.975405	−	0.220422i
$321$		0			0
$322$	−5.89549	+	3.63426i	−0.328543	+	0.202529i
$323$	−0.376786	+	0.376786i	−0.0209650	+	0.0209650i
$324$		0			0
$325$	27.3186	+	0.137046i	1.51536	+	0.00760197i
$326$	−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	$-0.755178\pi$
$337$		−	25.5357i		−	1.39102i	0.718516	−	0.695510i	$-0.244822\pi$
$338$	−12.5068	−	20.2885i	−0.680278	−	1.10355i
$339$		0			0
$340$	0.713563	+	0.830779i	0.0386984	+	0.0450553i
$341$	−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	0.0535933	−	0.998563i	$-0.482933\pi$
$347$	−17.6028	−	17.6028i	−0.944970	−	0.944970i	−0.998563	+	0.0535933i	$0.982933\pi$
$348$		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	$0.811535\pi$
$350$	4.86107	+	1.17923i	0.259835	+	0.0630325i
$351$		0			0
$352$	13.2292	−	5.68598i	0.705121	−	0.303064i
$353$			0.171535i			0.00912990i	0.999990	+	0.00456495i	$0.00145307\pi$
$353$			0.171535i			0.00912990i	−0.999990	+	0.00456495i	$0.998547\pi$
$354$		0			0
$355$	−1.79576	+	4.30479i	−0.0953093	+	0.228474i
$356$	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
$365$	20.0169	+	8.35016i	1.04773	+	0.437068i
$366$		0			0
$367$			23.3124i			1.21690i	0.793593	+	0.608450i	$0.208208\pi$
$367$			23.3124i			1.21690i	−0.793593	+	0.608450i	$0.791792\pi$
$368$	16.5127	+	22.2291i	0.860786	+	1.15877i
$369$		0			0
$370$	−30.6791	−	22.2832i	−1.59493	−	1.15845i
$371$	−1.04006	−	1.04006i	−0.0539973	−	0.0539973i
$372$		0			0
$373$	1.11817	+	1.11817i	0.0578964	+	0.0578964i	0.735462	−	0.677566i	$-0.236965\pi$
$373$	1.11817	+	1.11817i	0.0578964	+	0.0578964i	−0.677566	+	0.735462i	$0.736965\pi$
$374$	−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	$-0.0519153\pi$
$380$	9.70325	+	0.736475i	0.497766	+	0.0377804i
$381$		0			0
$382$	21.4334	−	13.2126i	1.09663	−	0.676013i
$383$		−	32.1168i		−	1.64109i	−0.571579	−	0.820547i	$-0.693669\pi$
$383$		−	32.1168i		−	1.64109i	0.571579	−	0.820547i	$-0.306331\pi$
$384$		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
$395$	−15.1618	−	6.32484i	−0.762874	−	0.318237i
$396$		0			0
$397$	−21.6530	+	21.6530i	−1.08673	+	1.08673i	−0.0908707	+	0.995863i	$0.528965\pi$
$397$	−21.6530	+	21.6530i	−1.08673	+	1.08673i	−0.995863	+	0.0908707i	$0.971035\pi$
$398$	−4.26106	−	6.91229i	−0.213588	−	0.346482i
$399$		0			0
$400$	3.01861	−	19.7709i	0.150930	−	0.988544i
$401$	−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	$-0.146442\pi$
$410$	−1.05024	−	6.62502i	−0.0518677	−	0.327187i
$411$		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
$430$	−2.47682	−	1.79899i	−0.119443	−	0.0867551i
$431$	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	$0.0309920\pi$
$433$			4.04564i			0.194421i	−0.995264	+	0.0972106i	$0.969008\pi$
$434$	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	$0.919625\pi$
$440$	7.38662	+	14.3044i	0.352143	+	0.681937i
$441$		0			0
$442$	1.84109	+	0.436856i	0.0875717	+	0.0207791i
$443$	1.81582	+	1.81582i	0.0862722	+	0.0862722i	0.748926	−	0.662654i	$-0.230570\pi$
$443$	1.81582	+	1.81582i	0.0862722	+	0.0862722i	−0.662654	+	0.748926i	$0.730570\pi$
$444$		0			0
$445$	−2.64707	+	6.34554i	−0.125483	+	0.300807i
$446$	−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	$-0.407674\pi$
$457$	12.2280			0.572000			0.286000	+	0.958230i	$0.407674\pi$
$458$	−8.45072	+	35.6148i	−0.394876	+	1.66417i
$459$		0			0
$460$	−23.4859	+	20.1722i	−1.09503	+	0.940534i
$461$	−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	$0.0402217\pi$
$463$			5.42343i			0.252048i	−0.992027	+	0.126024i	$0.959778\pi$
$464$	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	−0.328079	−	0.944650i	$-0.606401\pi$
$467$	13.3242	−	13.3242i	0.616571	−	0.616571i	0.944650	+	0.328079i	$0.106401\pi$
$468$		0			0
$469$	−5.55696	+	5.55696i	−0.256597	+	0.256597i
$470$	2.21489	+	13.9717i	0.102165	+	0.644468i
$471$		0			0
$472$	17.9479	+	15.0842i	0.826121	+	0.694306i
$473$	2.46413			0.113301
$474$		0			0
$475$	−0.0545788	+	10.8796i	−0.00250425	+	0.499191i
$476$	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
$485$	1.20457	−	2.88758i	0.0546967	−	0.131118i
$486$		0			0
$487$	15.8116			0.716491			0.358246	−	0.933627i	$-0.383375\pi$
$487$	15.8116			0.716491			0.358246	+	0.933627i	$0.383375\pi$
$488$	0.138311	−	0.164570i	0.00626106	−	0.00744974i
$489$		0			0
$490$	−20.3000	+	3.21809i	−0.917061	+	0.145378i
$491$	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	$0.448154\pi$
$500$	22.2878	+	1.80414i	0.996740	+	0.0806834i
$501$		0			0
$502$	4.18880	−	17.6533i	0.186955	−	0.787905i
$503$	−4.72004			−0.210456			−0.105228	−	0.994448i	$-0.533557\pi$
$503$	−4.72004			−0.210456			−0.105228	+	0.994448i	$0.533557\pi$
$504$		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
$515$	4.73084	+	1.97349i	0.208466	+	0.0869625i
$516$		0			0
$517$	−8.05183	−	8.05183i	−0.354119	−	0.354119i
$518$	−11.6715	−	2.76942i	−0.512815	−	0.121681i
$519$		0			0
$520$	−15.8551	−	30.7039i	−0.695292	−	1.34646i
$521$			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	0.987328	−	0.158693i	$-0.0507279\pi$
$523$	18.9502	+	18.9502i	0.828635	+	0.828635i	−0.158693	+	0.987328i	$0.550728\pi$
$524$	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
$530$	−5.32000	−	3.86408i	−0.231086	−	0.167845i
$531$		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	−0.707313	−	0.706901i	$-0.750093\pi$
$547$	−0.00963023	+	0.00963023i	−0.000411759	+	0.000411759i	0.706901	+	0.707313i	$0.250093\pi$
$548$	6.55960	−	13.0442i	0.280212	−	0.557220i
$549$		0			0
$550$	−15.3691	+	9.36820i	−0.655343	+	0.399461i
$551$			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	$0.529236\pi$
$557$	−25.6660	+	25.6660i	−1.08750	+	1.08750i	−0.995785	+	0.0917192i	$0.970764\pi$
$558$		0			0
$559$	−5.28916			−0.223707
$560$	−1.52670	−	6.14020i	−0.0645148	−	0.259471i
$561$		0			0
$562$	−21.6754	−	35.1618i	−0.914321	−	1.48321i
$563$	6.16719	−	6.16719i	0.259916	−	0.259916i	−0.565104	−	0.825020i	$-0.691164\pi$
$563$	6.16719	−	6.16719i	0.259916	−	0.259916i	0.825020	+	0.565104i	$0.191164\pi$
$564$		0			0
$565$	6.82515	−	16.3612i	0.287136	−	0.688319i
$566$	−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	$0.0695882\pi$
$577$			10.4193i			0.433761i	−0.976198	+	0.216880i	$0.930412\pi$
$578$	20.3933	−	12.5714i	0.848251	−	0.522902i
$579$		0			0
$580$	30.8940	+	2.34485i	1.28280	+	0.0973646i
$581$	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	$0.0508376\pi$
$587$	27.7728	+	27.7728i	1.14631	+	1.14631i	0.159033	+	0.987273i	$0.449162\pi$
$588$		0			0
$589$	11.7049	+	11.7049i	0.482291	+	0.482291i
$590$	−15.4042	+	21.2082i	−0.634180	+	0.873128i
$591$		0			0
$592$	−7.00104	+	47.4487i	−0.287741	+	1.95013i
$593$			25.4466i			1.04496i	0.852650	+	0.522482i	$0.174994\pi$
$593$			25.4466i			1.04496i	−0.852650	+	0.522482i	$0.825006\pi$
$594$		0			0
$595$	−0.149132	+	0.357497i	−0.00611380	+	0.0146559i
$596$	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
$605$	−3.89165	+	9.32902i	−0.158218	+	0.379279i
$606$		0			0
$607$			1.20300i			0.0488283i	0.999702	+	0.0244141i	$0.00777203\pi$
$607$			1.20300i			0.0488283i	−0.999702	+	0.0244141i	$0.992228\pi$
$608$	−4.86054	−	11.3087i	−0.197121	−	0.458630i
$609$		0			0
$610$	0.194464	+	0.141246i	0.00787363	+	0.00571886i
$611$	17.2830	+	17.2830i	0.699193	+	0.699193i
$612$		0			0
$613$	−4.84340	−	4.84340i	−0.195623	−	0.195623i	0.602498	−	0.798121i	$-0.294172\pi$
$613$	−4.84340	−	4.84340i	−0.195623	−	0.195623i	−0.798121	+	0.602498i	$0.794172\pi$
$614$	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	$-0.682683\pi$
$617$	−26.9719			−1.08585			−0.542924	+	0.839782i	$0.682683\pi$
$618$		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	$0.0584316\pi$
$620$	25.8082	−	22.1669i	1.03648	−	0.890243i
$621$		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
$635$	−16.7413	+	40.1321i	−0.664360	+	1.59260i
$636$		0			0
$637$	−25.1110	+	25.1110i	−0.994934	+	0.994934i
$638$	−21.2300	+	13.0872i	−0.840505	+	0.518127i
$639$		0			0
$640$	−23.9317	+	8.20197i	−0.945985	+	0.324211i
$641$	−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	−0.248480	−	0.968637i	$-0.579931\pi$
$643$	18.2613	−	18.2613i	0.720157	−	0.720157i	0.968637	+	0.248480i	$0.0799311\pi$
$644$	−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	$-0.566210\pi$
$647$	−10.5055			−0.413014			−0.206507	+	0.978445i	$0.566210\pi$
$648$		0			0
$649$		−	21.0995i		−	0.828228i
$650$	32.9893	−	20.1085i	1.29395	−	0.788720i
$651$		0			0
$652$	5.27818	+	15.9567i	0.206709	+	0.624911i
$653$	11.1836	−	11.1836i	0.437648	−	0.437648i	−0.453572	−	0.891220i	$-0.649850\pi$
$653$	11.1836	−	11.1836i	0.437648	−	0.437648i	0.891220	+	0.453572i	$0.149850\pi$
$654$		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
$670$	−20.6455	+	28.4243i	−0.797604	+	1.09813i
$671$	−0.193468			−0.00746874
$672$		0			0
$673$			27.1091i			1.04498i	0.852645	+	0.522490i	$0.174997\pi$
$673$			27.1091i			1.04498i	−0.852645	+	0.522490i	$0.825003\pi$
$674$	−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	0.461782	−	0.886993i	$-0.347210\pi$
$677$	−11.0637	−	11.0637i	−0.425211	−	0.425211i	−0.886993	+	0.461782i	$0.847210\pi$
$678$		0			0
$679$		−	0.989807i		−	0.0379853i
$680$	1.47556	+	0.470592i	0.0565851	+	0.0180464i
$681$		0			0
$682$	−6.32247	+	26.6455i	−0.242100	+	1.02031i
$683$	−17.4289	−	17.4289i	−0.666898	−	0.666898i	0.290098	−	0.956997i	$-0.406312\pi$
$683$	−17.4289	−	17.4289i	−0.666898	−	0.666898i	−0.956997	+	0.290098i	$0.906312\pi$
$684$		0			0
$685$	15.0657	+	6.28474i	0.575631	+	0.240128i
$686$	−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
$700$	6.72714	−	2.18784i	0.254262	−	0.0826926i
$701$	−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	$0.277717\pi$
$710$	1.03280	+	6.51500i	0.0387603	+	0.244504i
$711$		0			0
$712$	8.66443	−	0.751173i	0.324713	−	0.0281514i
$713$	−52.6641			−1.97229
$714$		0			0
$715$	−11.9732	+	28.7019i	−0.447771	+	1.07339i
$716$	−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
$725$	−0.173772	+	34.6394i	−0.00645375	+	1.28648i
$726$		0			0
$727$	−6.37077			−0.236279			−0.118139	−	0.992997i	$-0.537693\pi$
$727$	−6.37077			−0.236279			−0.118139	+	0.992997i	$0.537693\pi$
$728$	−8.36891	−	7.03357i	−0.310172	−	0.260682i
$729$		0			0
$730$	30.2942	−	4.80244i	1.12124	−	0.177746i
$731$	0.167625	−	0.167625i	0.00619984	−	0.00619984i
$732$		0			0
$733$	6.95026	−	6.95026i	0.256714	−	0.256714i	−0.567002	−	0.823716i	$-0.691897\pi$
$733$	6.95026	−	6.95026i	0.256714	−	0.256714i	0.823716	+	0.567002i	$0.191897\pi$
$734$	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	$0.749600\pi$
$740$	−53.4698	−	4.05835i	−1.96559	−	0.149188i
$741$		0			0
$742$	−2.02393	−	0.480240i	−0.0743007	−	0.0176302i
$743$	−0.148848			−0.00546069			−0.00273035	−	0.999996i	$-0.500869\pi$
$743$	−0.148848			−0.00546069			−0.00273035	+	0.999996i	$0.500869\pi$
$744$		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
$755$	0.294034	−	0.704855i	0.0107010	−	0.0256523i
$756$		0			0
$757$	26.6876	+	26.6876i	0.969977	+	0.969977i	0.999562	−	0.0295851i	$-0.00941860\pi$
$757$	26.6876	+	26.6876i	0.969977	+	0.969977i	−0.0295851	+	0.999562i	$0.509419\pi$
$758$	10.3295	−	43.5326i	0.375183	−	1.58118i
$759$		0			0
$760$	12.2279	−	6.31430i	0.443551	−	0.229044i
$761$			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	$0.652980\pi$
$770$	−3.34634	+	4.60718i	−0.120594	+	0.166031i
$771$		0			0
$772$	−30.7726	−	15.4748i	−1.10753	−	0.556950i
$773$	27.4452	+	27.4452i	0.987137	+	0.987137i	0.999918	−	0.0127818i	$-0.00406868\pi$
$773$	27.4452	+	27.4452i	0.987137	+	0.987137i	−0.0127818	+	0.999918i	$0.504069\pi$
$774$		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	−0.513675	−	0.857985i	$-0.671716\pi$
$787$	9.65912	−	9.65912i	0.344310	−	0.344310i	0.857985	+	0.513675i	$0.171716\pi$
$788$	27.0585	−	8.95047i	0.963919	−	0.318847i
$789$		0			0
$790$	−22.9464	+	3.63761i	−0.816396	+	0.129420i
$791$		−	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	−0.886916	−	0.461931i	$-0.847157\pi$
$797$	−11.9978	+	11.9978i	−0.424984	+	0.424984i	0.461931	+	0.886916i	$0.347157\pi$
$798$		0			0
$799$	−1.09547			−0.0387549
$800$	−11.0383	−	26.0414i	−0.390262	−	0.920704i
$801$		0			0
$802$	−20.6582	+	12.7347i	−0.729466	+	0.449678i
$803$	−17.4584	+	17.4584i	−0.616094	+	0.616094i
$804$		0			0
$805$	−10.1063	−	4.21590i	−0.356201	−	0.148591i
$806$	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
$820$	−6.18086	−	7.19617i	−0.215845	−	0.251301i
$821$	−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	$-0.524344\pi$
$823$	−4.38382			−0.152810			−0.0764052	+	0.997077i	$0.524344\pi$
$824$	−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	0.223895	−	0.974613i	$-0.428123\pi$
$827$	−21.5889	−	21.5889i	−0.750718	−	0.750718i	−0.974613	+	0.223895i	$0.928123\pi$
$828$		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	$0.688003\pi$
$830$	17.8791	−	24.6156i	0.620593	−	0.854421i
$831$		0			0
$832$	−25.1275	+	35.7659i	−0.871138	+	1.23996i
$833$		−	1.59165i		−	0.0551473i
$834$		0			0
$835$	−29.8401	−	12.4480i	−1.03266	−	0.430779i
$836$	−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
$845$	14.5084	−	34.7794i	0.499105	−	1.19645i
$846$		0			0
$847$			3.19781i			0.109878i
$848$	−1.21404	+	8.22799i	−0.0416902	+	0.282550i
$849$		0			0
$850$	−0.408221	+	1.68279i	−0.0140019	+	0.0577191i
$851$	58.6959	+	58.6959i	2.01207	+	2.01207i
$852$		0			0
$853$	−12.6685	−	12.6685i	−0.433763	−	0.433763i	0.456144	−	0.889906i	$-0.349230\pi$
$853$	−12.6685	−	12.6685i	−0.433763	−	0.433763i	−0.889906	+	0.456144i	$0.849230\pi$
$854$	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	$-0.526102\pi$
$857$	−4.79580			−0.163821			−0.0819106	+	0.996640i	$0.526102\pi$
$858$		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	$0.943485\pi$
$860$	−4.31679	−	0.327644i	−0.147201	−	0.0111726i
$861$		0			0
$862$	34.1946	−	21.0792i	1.16467	−	0.717960i
$863$		−	8.20297i		−	0.279232i	−0.990206	−	0.139616i	$-0.955413\pi$
$863$		−	8.20297i		−	0.279232i	0.990206	−	0.139616i	$-0.0445869\pi$
$864$		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
$875$	2.97155	+	7.32948i	0.100457	+	0.247782i
$876$		0			0
$877$	−23.9525	+	23.9525i	−0.808817	+	0.808817i	−0.984455	−	0.175638i	$-0.943801\pi$
$877$	−23.9525	+	23.9525i	−0.808817	+	0.808817i	0.175638	+	0.984455i	$0.443801\pi$
$878$	7.76922	+	12.6032i	0.262198	+	0.425338i
$879$		0			0
$880$	19.5079	+	11.7388i	0.657612	+	0.395714i
$881$	−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	−0.978552	−	0.206001i	$-0.933955\pi$
$883$	−22.9566	+	22.9566i	−0.772550	+	0.772550i	0.206001	+	0.978552i	$0.433955\pi$
$884$	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	$-0.545689\pi$
$887$	−8.52038			−0.286086			−0.143043	+	0.989716i	$0.545689\pi$
$888$		0			0
$889$			13.7565i			0.461379i
$890$	1.52241	+	9.60354i	0.0510314	+	0.321911i
$891$		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	0.261808	−	0.965120i	$-0.415681\pi$
$907$	−21.1812	−	21.1812i	−0.703312	−	0.703312i	−0.965120	+	0.261808i	$0.915681\pi$
$908$	4.75563	+	14.3769i	0.157821	+	0.477115i
$909$		0			0
$910$	7.18278	−	9.88913i	0.238107	−	0.327822i
$911$	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	$-0.0188813\pi$
$920$	−13.3035	+	41.7136i	−0.438604	+	1.37526i
$921$		0			0
$922$	−1.40781	−	0.334046i	−0.0463636	−	0.0110012i
$923$	8.05902	+	8.05902i	0.265266	+	0.265266i
$924$		0			0
$925$	0.300757	−	59.9522i	0.00988882	−	1.97122i
$926$	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	$-0.268123\pi$
$937$	40.7563			1.33145			0.665725	+	0.746198i	$0.268123\pi$
$938$	−2.56588	+	10.8137i	−0.0837790	+	0.353079i
$939$		0			0
$940$	13.0350	+	15.1762i	0.425155	+	0.494994i
$941$	−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	$-0.432995\pi$
$947$	36.5242	−	36.5242i	1.18688	−	1.18688i	0.977926	−	0.208951i	$-0.0670050\pi$
$948$		0			0
$949$	37.4738	−	37.4738i	1.21645	−	1.21645i
$950$	8.00821	+	13.1380i	0.259821	+	0.426253i
$951$		0			0
$952$	0.488139	−	0.0423198i	0.0158207	−	0.00137159i
$953$	16.0927			0.521294			0.260647	−	0.965434i	$-0.416064\pi$
$953$	16.0927			0.521294			0.260647	+	0.965434i	$0.416064\pi$
$954$		0			0
$955$	36.7421	+	15.3272i	1.18895	+	0.495975i
$956$	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
$965$	14.8264	−	35.5416i	0.477278	−	1.14413i
$966$		0			0
$967$	21.3561			0.686767			0.343384	−	0.939195i	$-0.388427\pi$
$967$	21.3561			0.686767			0.343384	+	0.939195i	$0.388427\pi$
$968$	12.7382	−	1.10435i	0.409421	−	0.0354952i
$969$		0			0
$970$	−0.692786	−	4.37016i	−0.0222440	−	0.140317i
$971$	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	$-0.853442\pi$
$977$		−	27.7769i		−	0.888661i	0.895863	−	0.444331i	$-0.146558\pi$
$978$		0			0
$979$	−5.53447	−	5.53447i	−0.176882	−	0.176882i
$980$	−22.0501	+	18.9390i	−0.704364	+	0.604985i
$981$		0			0
$982$	7.20354	−	30.3586i	0.229874	−	0.968783i
$983$	0.428090			0.0136540			0.00682698	−	0.999977i	$-0.497827\pi$
$983$	0.428090			0.0136540			0.00682698	+	0.999977i	$0.497827\pi$
$984$		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
$995$	4.94303	−	11.8494i	0.156704	−	0.375650i
$996$		0			0
$997$	−20.1044	−	20.1044i	−0.636713	−	0.636713i	0.313030	−	0.949743i	$-0.398656\pi$
$997$	−20.1044	−	20.1044i	−0.636713	−	0.636713i	−0.949743	+	0.313030i	$0.898656\pi$
$998$	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.109.20		48
3.2	odd	2		240.2.bl.a.109.5	✓	48
5.4	even	2	inner	720.2.bm.h.109.5		48
12.11	even	2		960.2.bl.a.529.15		48
15.14	odd	2		240.2.bl.a.109.20	yes	48
16.5	even	4	inner	720.2.bm.h.469.5		48
24.5	odd	2		1920.2.bl.a.289.18		48
24.11	even	2		1920.2.bl.b.289.7		48
48.5	odd	4		240.2.bl.a.229.20	yes	48
48.11	even	4		960.2.bl.a.49.9		48
48.29	odd	4		1920.2.bl.a.1249.7		48
48.35	even	4		1920.2.bl.b.1249.18		48
60.59	even	2		960.2.bl.a.529.9		48
80.69	even	4	inner	720.2.bm.h.469.20		48
120.29	odd	2		1920.2.bl.a.289.7		48
120.59	even	2		1920.2.bl.b.289.18		48
240.29	odd	4		1920.2.bl.a.1249.18		48
240.59	even	4		960.2.bl.a.49.15		48
240.149	odd	4		240.2.bl.a.229.5	yes	48
240.179	even	4		1920.2.bl.b.1249.7		48

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

\(f(q)\)	\(=\)	\(q+(1.20386 - 0.742113i) q^{2} +(0.898535 - 1.78679i) q^{4} +(2.06370 + 0.860885i) q^{5} +0.707398 q^{7} +(-0.244298 - 2.81786i) q^{8} +O(q^{10})\)	\(q+(1.20386 - 0.742113i) q^{2} +(0.898535 - 1.78679i) q^{4} +(2.06370 + 0.860885i) q^{5} +0.707398 q^{7} +(-0.244298 - 2.81786i) q^{8} +(3.12328 - 0.495122i) q^{10} +(-1.79993 + 1.79993i) q^{11} +(3.86348 - 3.86348i) q^{13} +(0.851604 - 0.524969i) q^{14} +(-2.38527 - 3.21100i) q^{16} +0.244884i q^{17} +(1.53863 + 1.53863i) q^{19} +(3.39254 - 2.91388i) q^{20} +(-0.831102 + 3.50260i) q^{22} -6.92280 q^{23} +(3.51775 + 3.55323i) q^{25} +(1.78393 - 7.51820i) q^{26} +(0.635622 - 1.26397i) q^{28} +(4.89882 + 4.89882i) q^{29} +7.60734 q^{31} +(-5.25444 - 2.09543i) q^{32} +(0.181732 + 0.294805i) q^{34} +(1.45986 + 0.608988i) q^{35} +(-8.47863 - 8.47863i) q^{37} +(2.99413 + 0.710450i) q^{38} +(1.92169 - 6.02554i) q^{40} -2.12118i q^{41} +(-0.684507 - 0.684507i) q^{43} +(1.59880 + 4.83340i) q^{44} +(-8.33405 + 5.13750i) q^{46} +4.47342i q^{47} -6.49959 q^{49} +(6.87176 + 1.66700i) q^{50} +(-3.43177 - 10.3747i) q^{52} +(-1.47026 - 1.47026i) q^{53} +(-5.26405 + 2.16499i) q^{55} +(-0.172815 - 1.99335i) q^{56} +(9.53295 + 2.26199i) q^{58} +(-5.86121 + 5.86121i) q^{59} +(0.0537432 + 0.0537432i) q^{61} +(9.15813 - 5.64551i) q^{62} +(-7.88064 + 1.37679i) q^{64} +(11.2991 - 4.64706i) q^{65} +(-7.85550 + 7.85550i) q^{67} +(0.437558 + 0.220037i) q^{68} +(2.20940 - 0.350248i) q^{70} +2.08595i q^{71} +9.69951 q^{73} +(-16.4992 - 3.91494i) q^{74} +(4.13173 - 1.36670i) q^{76} +(-1.27326 + 1.27326i) q^{77} -7.34690 q^{79} +(-2.15819 - 8.67999i) q^{80} +(-1.57415 - 2.55359i) q^{82} +(6.80291 - 6.80291i) q^{83} +(-0.210817 + 0.505369i) q^{85} +(-1.33203 - 0.316066i) q^{86} +(5.51166 + 4.63222i) q^{88} +3.07483i q^{89} +(2.73301 - 2.73301i) q^{91} +(-6.22038 + 12.3696i) q^{92} +(3.31978 + 5.38535i) q^{94} +(1.85069 + 4.49986i) q^{95} -1.39922i q^{97} +(-7.82456 + 4.82343i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) \) 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

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