LMFDB - Embedded newform 1920.2.bl.b.289.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, 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("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, degree $2$, not 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:	$15.3312771881$
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			289.18
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.b.1249.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-0.860885 - 2.06370i) q^{5} +0.707398 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.860885 - 2.06370i) q^{5} +0.707398 q^{7} -1.00000i q^{9} +(1.79993 - 1.79993i) q^{11} +(3.86348 - 3.86348i) q^{13} +(-2.06800 - 0.850522i) q^{15} +0.244884i q^{17} +(1.53863 + 1.53863i) q^{19} +(0.500206 - 0.500206i) q^{21} +6.92280 q^{23} +(-3.51775 + 3.55323i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(4.89882 + 4.89882i) q^{29} -7.60734 q^{31} -2.54548i q^{33} +(-0.608988 - 1.45986i) q^{35} +(-8.47863 - 8.47863i) q^{37} -5.46378i q^{39} +2.12118i q^{41} +(0.684507 + 0.684507i) q^{43} +(-2.06370 + 0.860885i) q^{45} -4.47342i q^{47} -6.49959 q^{49} +(0.173159 + 0.173159i) q^{51} +(1.47026 + 1.47026i) q^{53} +(-5.26405 - 2.16499i) q^{55} +2.17595 q^{57} +(5.86121 - 5.86121i) q^{59} +(-0.0537432 - 0.0537432i) q^{61} -0.707398i q^{63} +(-11.2991 - 4.64706i) q^{65} +(7.85550 - 7.85550i) q^{67} +(4.89516 - 4.89516i) q^{69} +2.08595i q^{71} -9.69951 q^{73} +(0.0250827 + 4.99994i) q^{75} +(1.27326 - 1.27326i) q^{77} +7.34690 q^{79} -1.00000 q^{81} +(6.80291 - 6.80291i) q^{83} +(0.505369 - 0.210817i) q^{85} +6.92797 q^{87} -3.07483i q^{89} +(2.73301 - 2.73301i) q^{91} +(-5.37920 + 5.37920i) q^{93} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(-1.79993 - 1.79993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 8 q^{19} + 48 q^{31} + 24 q^{35} + 48 q^{49} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} - 16 q^{75} + 96 q^{79} - 48 q^{81} - 32 q^{91} + 48 q^{95}+O(q^{100}) $ 48 * q + 8 * q^19 + 48 * q^31 + 24 * q^35 + 48 * q^49 + 8 * q^51 - 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 - 16 * q^75 + 96 * q^79 - 48 * q^81 - 32 * q^91 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−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	$-0.457319\pi$
$7$	0.707398			0.267371			0.133686	+	0.991024i	$0.457319\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.79993	−	1.79993i	0.542699	−	0.542699i	−0.381621	−	0.924319i	$-0.624634\pi$
$11$	1.79993	−	1.79993i	0.542699	−	0.542699i	0.924319	+	0.381621i	$0.124634\pi$
$12$		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			0
$15$	−2.06800	−	0.850522i	−0.533955	−	0.219604i
$16$		0			0
$17$			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	$0.669701\pi$
$20$		0			0
$21$	0.500206	−	0.500206i	0.109154	−	0.109154i
$22$		0			0
$23$	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
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	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	$-0.739394\pi$
$31$	−7.60734			−1.36632			−0.683159	+	0.730270i	$0.739394\pi$
$32$		0			0
$33$		−	2.54548i		−	0.443112i
$34$		0			0
$35$	−0.608988	−	1.45986i	−0.102938	−	0.246761i
$36$		0			0
$37$	−8.47863	−	8.47863i	−1.39388	−	1.39388i	−0.816420	−	0.577459i	$-0.804044\pi$
$37$	−8.47863	−	8.47863i	−1.39388	−	1.39388i	−0.577459	−	0.816420i	$-0.695956\pi$
$38$		0			0
$39$		−	5.46378i		−	0.874905i
$40$		0			0
$41$			2.12118i			0.331272i	0.986187	+	0.165636i	$0.0529677\pi$
$41$			2.12118i			0.331272i	−0.986187	+	0.165636i	$0.947032\pi$
$42$		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	$0.726483\pi$
$44$		0			0
$45$	−2.06370	+	0.860885i	−0.307639	+	0.128333i
$46$		0			0
$47$		−	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
$50$		0			0
$51$	0.173159	+	0.173159i	0.0242472	+	0.0242472i
$52$		0			0
$53$	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			0
$57$	2.17595			0.288212
$58$		0			0
$59$	5.86121	−	5.86121i	0.763065	−	0.763065i	−0.213810	−	0.976875i	$-0.568587\pi$
$59$	5.86121	−	5.86121i	0.763065	−	0.763065i	0.976875	+	0.213810i	$0.0685874\pi$
$60$		0			0
$61$	−0.0537432	−	0.0537432i	−0.00688112	−	0.00688112i	0.703658	−	0.710539i	$-0.251549\pi$
$61$	−0.0537432	−	0.0537432i	−0.00688112	−	0.00688112i	−0.710539	+	0.703658i	$0.751549\pi$
$62$		0			0
$63$		−	0.707398i		−	0.0891237i
$64$		0			0
$65$	−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			0
$69$	4.89516	−	4.89516i	0.589308	−	0.589308i
$70$		0			0
$71$			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	$0.692136\pi$
$74$		0			0
$75$	0.0250827	+	4.99994i	0.00289630	+	0.577343i
$76$		0			0
$77$	1.27326	−	1.27326i	0.145102	−	0.145102i
$78$		0			0
$79$	7.34690			0.826591			0.413295	−	0.910597i	$-0.364378\pi$
$79$	7.34690			0.826591			0.413295	+	0.910597i	$0.364378\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	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
$85$	0.505369	−	0.210817i	0.0548149	−	0.0228663i
$86$		0			0
$87$	6.92797			0.742757
$88$		0			0
$89$		−	3.07483i		−	0.325931i	−0.986632	−	0.162966i	$-0.947894\pi$
$89$		−	3.07483i		−	0.325931i	0.986632	−	0.162966i	$-0.0521060\pi$
$90$		0			0
$91$	2.73301	−	2.73301i	0.286498	−	0.286498i
$92$		0			0
$93$	−5.37920	+	5.37920i	−0.557797	+	0.557797i
$94$		0			0
$95$	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	$0.977370\pi$
$98$		0			0
$99$	−1.79993	−	1.79993i	−0.180900	−	0.180900i
$100$		0			0
$101$	−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	$0.463974\pi$
$104$		0			0
$105$	−1.46290	−	0.601657i	−0.142764	−	0.0587157i
$106$		0			0
$107$	−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	$-0.951434\pi$
$109$	−11.9058	−	11.9058i	−1.14037	−	1.14037i	−0.151984	−	0.988383i	$-0.548566\pi$
$110$		0			0
$111$	−11.9906			−1.13810
$112$		0			0
$113$		−	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
$115$	−5.95974	−	14.2866i	−0.555748	−	1.33223i
$116$		0			0
$117$	−3.86348	−	3.86348i	−0.357179	−	0.357179i
$118$		0			0
$119$			0.173231i			0.0158800i
$120$		0			0
$121$			4.52052i			0.410956i
$122$		0			0
$123$	1.49990	+	1.49990i	0.135241	+	0.135241i
$124$		0			0
$125$	10.3612	+	4.20068i	0.926733	+	0.375721i
$126$		0			0
$127$			19.4466i			1.72561i	0.505536	+	0.862806i	$0.331295\pi$
$127$			19.4466i			1.72561i	−0.505536	+	0.862806i	$0.668705\pi$
$128$		0			0
$129$	0.968040			0.0852311
$130$		0			0
$131$	−0.354049	−	0.354049i	−0.0309334	−	0.0309334i	0.691471	−	0.722404i	$-0.256963\pi$
$131$	−0.354049	−	0.354049i	−0.0309334	−	0.0309334i	−0.722404	+	0.691471i	$0.756963\pi$
$132$		0			0
$133$	1.08842	+	1.08842i	0.0943783	+	0.0943783i
$134$		0			0
$135$	−0.850522	+	2.06800i	−0.0732013	+	0.177985i
$136$		0			0
$137$	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	$0.428221\pi$
$140$		0			0
$141$	−3.16319	−	3.16319i	−0.266388	−	0.266388i
$142$		0			0
$143$		−	13.9080i		−	1.16304i
$144$		0			0
$145$	5.89239	−	14.3270i	0.489337	−	1.18980i
$146$		0			0
$147$	−4.59590	+	4.59590i	−0.379064	+	0.379064i
$148$		0			0
$149$	−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	$0.00442382\pi$
$151$			0.341548i			0.0277948i	−0.999903	+	0.0138974i	$0.995576\pi$
$152$		0			0
$153$	0.244884			0.0197977
$154$		0			0
$155$	6.54904	+	15.6993i	0.526032	+	1.26100i
$156$		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	$0.301685\pi$
$158$		0			0
$159$	2.07927			0.164897
$160$		0			0
$161$	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	$0.143253\pi$
$164$		0			0
$165$	−5.25312	+	2.19137i	−0.408955	+	0.170598i
$166$		0			0
$167$	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			0
$171$	1.53863	−	1.53863i	0.117662	−	0.117662i
$172$		0			0
$173$	−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
$176$		0			0
$177$		−	8.28901i		−	0.623040i
$178$		0			0
$179$	17.2660	+	17.2660i	1.29052	+	1.29052i	0.934466	+	0.356052i	$0.115877\pi$
$179$	17.2660	+	17.2660i	1.29052	+	1.29052i	0.356052	+	0.934466i	$0.384123\pi$
$180$		0			0
$181$	−5.12242	+	5.12242i	−0.380746	+	0.380746i	−0.871371	−	0.490625i	$-0.836769\pi$
$181$	−5.12242	+	5.12242i	−0.380746	+	0.380746i	0.490625	+	0.871371i	$0.336769\pi$
$182$		0			0
$183$	−0.0760044			−0.00561841
$184$		0			0
$185$	−10.1983	+	24.7965i	−0.749791	+	1.82308i
$186$		0			0
$187$	0.440774	+	0.440774i	0.0322326	+	0.0322326i
$188$		0			0
$189$	−0.500206	−	0.500206i	−0.0363846	−	0.0363846i
$190$		0			0
$191$	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	$0.787197\pi$
$194$		0			0
$195$	−11.2756	+	4.70369i	−0.807465	+	0.336838i
$196$		0			0
$197$	−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	$0.0652358\pi$
$199$			5.74179i			0.407025i	−0.979072	+	0.203513i	$0.934764\pi$
$200$		0			0
$201$		−	11.1094i		−	0.783593i
$202$		0			0
$203$	3.46541	+	3.46541i	0.243224	+	0.243224i
$204$		0			0
$205$	4.37748	−	1.82609i	0.305737	−	0.127540i
$206$		0			0
$207$		−	6.92280i		−	0.481168i
$208$		0			0
$209$	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	$0.907119\pi$
$212$		0			0
$213$	1.47499	+	1.47499i	0.101065	+	0.101065i
$214$		0			0
$215$	0.823339	−	2.00190i	0.0561512	−	0.136529i
$216$		0			0
$217$	−5.38141			−0.365314
$218$		0			0
$219$	−6.85859	+	6.85859i	−0.463460	+	0.463460i
$220$		0			0
$221$	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	$-0.265216\pi$
$224$		0			0
$225$	3.55323	+	3.51775i	0.236882	+	0.234517i
$226$		0			0
$227$	−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	$-0.423441\pi$
$229$	18.3018	−	18.3018i	1.20942	−	1.20942i	0.971215	−	0.238204i	$-0.0765587\pi$
$230$		0			0
$231$		−	1.80067i		−	0.118475i
$232$		0			0
$233$	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
$235$	−9.23182	+	3.85110i	−0.602217	+	0.251218i
$236$		0			0
$237$	5.19504	−	5.19504i	0.337454	−	0.337454i
$238$		0			0
$239$	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	$0.354402\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	5.59540	+	13.4132i	0.357477	+	0.856940i
$246$		0			0
$247$	11.8889			0.756474
$248$		0			0
$249$		−	9.62077i		−	0.609691i
$250$		0			0
$251$	−9.07173	+	9.07173i	−0.572602	+	0.572602i	−0.932855	−	0.360252i	$-0.882691\pi$
$251$	−9.07173	+	9.07173i	−0.572602	+	0.572602i	0.360252	+	0.932855i	$0.382691\pi$
$252$		0			0
$253$	12.4605	−	12.4605i	0.783388	−	0.783388i
$254$		0			0
$255$	0.208279	−	0.506420i	0.0130430	−	0.0317132i
$256$		0			0
$257$			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
$260$		0			0
$261$	4.89882	−	4.89882i	0.303229	−	0.303229i
$262$		0			0
$263$	−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
$266$		0			0
$267$	−2.17423	−	2.17423i	−0.133061	−	0.133061i
$268$		0			0
$269$	−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	$-0.699344\pi$
$271$	−19.2974			−1.17224			−0.586118	+	0.810226i	$0.699344\pi$
$272$		0			0
$273$		−	3.86507i		−	0.233924i
$274$		0			0
$275$	0.0638476	+	12.7272i	0.00385016	+	0.767482i
$276$		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	$0.702181\pi$
$278$		0			0
$279$			7.60734i			0.455439i
$280$		0			0
$281$			29.2076i			1.74238i	0.490945	+	0.871191i	$0.336652\pi$
$281$			29.2076i			1.74238i	−0.490945	+	0.871191i	$0.663348\pi$
$282$		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	$0.614228\pi$
$284$		0			0
$285$	−1.87325	−	4.49052i	−0.110961	−	0.265996i
$286$		0			0
$287$			1.50052i			0.0885726i
$288$		0			0
$289$	16.9400			0.996472
$290$		0			0
$291$	0.989400	+	0.989400i	0.0579997	+	0.0579997i
$292$		0			0
$293$	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
$296$		0			0
$297$	−2.54548			−0.147704
$298$		0			0
$299$	26.7461	−	26.7461i	1.54677	−	1.54677i
$300$		0			0
$301$	0.484219	+	0.484219i	0.0279099	+	0.0279099i
$302$		0			0
$303$			16.6759i			0.958004i
$304$		0			0
$305$	−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	$0.484073\pi$
$308$		0			0
$309$	1.62097	−	1.62097i	0.0922139	−	0.0922139i
$310$		0			0
$311$		−	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	$0.432900\pi$
$314$		0			0
$315$	−1.45986	+	0.608988i	−0.0822538	+	0.0343126i
$316$		0			0
$317$	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
$320$		0			0
$321$	−13.4210			−0.749088
$322$		0			0
$323$	−0.376786	+	0.376786i	−0.0209650	+	0.0209650i
$324$		0			0
$325$	0.137046	+	27.3186i	0.00760197	+	1.51536i
$326$		0			0
$327$	−16.8373			−0.931106
$328$		0			0
$329$		−	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	$0.322721\pi$
$332$		0			0
$333$	−8.47863	+	8.47863i	−0.464626	+	0.464626i
$334$		0			0
$335$	−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	$0.755178\pi$
$338$		0			0
$339$	−5.60598	−	5.60598i	−0.304475	−	0.304475i
$340$		0			0
$341$	−13.6927	+	13.6927i	−0.741499	+	0.741499i
$342$		0			0
$343$	−9.54958			−0.515629
$344$		0			0
$345$	−14.3163	−	5.88799i	−0.770766	−	0.316999i
$346$		0			0
$347$	−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	0.829781	−	0.558089i	$-0.188465\pi$
$349$	5.07562	+	5.07562i	0.271692	+	0.271692i	−0.558089	+	0.829781i	$0.688465\pi$
$350$		0			0
$351$	−5.46378			−0.291635
$352$		0			0
$353$			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
$355$	4.30479	−	1.79576i	0.228474	−	0.0953093i
$356$		0			0
$357$	0.122492	+	0.122492i	0.00648299	+	0.00648299i
$358$		0			0
$359$			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
$362$		0			0
$363$	3.19649	+	3.19649i	0.167772	+	0.167772i
$364$		0			0
$365$	8.35016	+	20.0169i	0.437068	+	1.04773i
$366$		0			0
$367$			23.3124i			1.21690i	0.793593	+	0.608450i	$0.208208\pi$
$367$			23.3124i			1.21690i	−0.793593	+	0.608450i	$0.791792\pi$
$368$		0			0
$369$	2.12118			0.110424
$370$		0			0
$371$	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			0
$375$	10.2968	−	4.35614i	0.531724	−	0.224950i
$376$		0			0
$377$	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	$-0.0519153\pi$
$380$		0			0
$381$	13.7509	+	13.7509i	0.704478	+	0.704478i
$382$		0			0
$383$			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
$386$		0			0
$387$	0.684507	−	0.684507i	0.0347955	−	0.0347955i
$388$		0			0
$389$	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
$392$		0			0
$393$	−0.500701			−0.0252570
$394$		0			0
$395$	−6.32484	−	15.1618i	−0.318237	−	0.762874i
$396$		0			0
$397$	−21.6530	+	21.6530i	−1.08673	+	1.08673i	−0.0908707	+	0.995863i	$0.528965\pi$
$397$	−21.6530	+	21.6530i	−1.08673	+	1.08673i	−0.995863	+	0.0908707i	$0.971035\pi$
$398$		0			0
$399$	1.53926			0.0770596
$400$		0			0
$401$	17.1600			0.856931			0.428466	−	0.903558i	$-0.359054\pi$
$401$	17.1600			0.856931			0.428466	+	0.903558i	$0.359054\pi$
$402$		0			0
$403$	−29.3908	+	29.3908i	−1.46406	+	1.46406i
$404$		0			0
$405$	0.860885	+	2.06370i	0.0427777	+	0.102546i
$406$		0			0
$407$	−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	$-0.146442\pi$
$410$		0			0
$411$	5.16211	−	5.16211i	0.254628	−	0.254628i
$412$		0			0
$413$	4.14621	−	4.14621i	0.204022	−	0.204022i
$414$		0			0
$415$	−19.8957	−	8.18267i	−0.976642	−	0.401671i
$416$		0			0
$417$			12.5231i			0.613260i
$418$		0			0
$419$	23.4031	+	23.4031i	1.14332	+	1.14332i	0.987840	+	0.155476i	$0.0496913\pi$
$419$	23.4031	+	23.4031i	1.14332	+	1.14332i	0.155476	+	0.987840i	$0.450309\pi$
$420$		0			0
$421$	27.0016	−	27.0016i	1.31598	−	1.31598i	0.399043	−	0.916932i	$-0.369342\pi$
$421$	27.0016	−	27.0016i	1.31598	−	1.31598i	0.916932	−	0.399043i	$-0.130658\pi$
$422$		0			0
$423$	−4.47342			−0.217505
$424$		0			0
$425$	−0.870129	−	0.861442i	−0.0422075	−	0.0417861i
$426$		0			0
$427$	−0.0380178	−	0.0380178i	−0.00183981	−	0.00183981i
$428$		0			0
$429$	−9.83441	−	9.83441i	−0.474810	−	0.474810i
$430$		0			0
$431$	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	$-0.0309920\pi$
$434$		0			0
$435$	−5.96419	−	14.2973i	−0.285961	−	0.685503i
$436$		0			0
$437$	10.6516	+	10.6516i	0.509537	+	0.509537i
$438$		0			0
$439$		−	10.4690i		−	0.499660i	−0.968290	−	0.249830i	$-0.919625\pi$
$439$		−	10.4690i		−	0.499660i	0.968290	−	0.249830i	$-0.0803748\pi$
$440$		0			0
$441$			6.49959i			0.309504i
$442$		0			0
$443$	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
$445$	−6.34554	+	2.64707i	−0.300807	+	0.125483i
$446$		0			0
$447$			7.65634i			0.362132i
$448$		0			0
$449$	−22.2064			−1.04799			−0.523993	−	0.851723i	$-0.675558\pi$
$449$	−22.2064			−1.04799			−0.523993	+	0.851723i	$0.675558\pi$
$450$		0			0
$451$	3.81797	+	3.81797i	0.179781	+	0.179781i
$452$		0			0
$453$	0.241511	+	0.241511i	0.0113472	+	0.0113472i
$454$		0			0
$455$	−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	$0.592326\pi$
$458$		0			0
$459$	0.173159	−	0.173159i	0.00808238	−	0.00808238i
$460$		0			0
$461$	−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	$0.959778\pi$
$464$		0			0
$465$	15.7320	+	6.47021i	0.729552	+	0.300049i
$466$		0			0
$467$	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
$470$		0			0
$471$			4.05122i			0.186671i
$472$		0			0
$473$	2.46413			0.113301
$474$		0			0
$475$	−10.8796	+	0.0545788i	−0.499191	+	0.00250425i
$476$		0			0
$477$	1.47026	−	1.47026i	0.0673188	−	0.0673188i
$478$		0			0
$479$	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
$482$		0			0
$483$	3.46282	−	3.46282i	0.157564	−	0.157564i
$484$		0			0
$485$	2.88758	−	1.20457i	0.131118	−	0.0546967i
$486$		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			0
$489$		−	8.40349i		−	0.380019i
$490$		0			0
$491$	−15.6008	+	15.6008i	−0.704054	+	0.704054i	−0.965278	−	0.261224i	$-0.915874\pi$
$491$	−15.6008	+	15.6008i	−0.704054	+	0.704054i	0.261224	+	0.965278i	$0.415874\pi$
$492$		0			0
$493$	−1.19964	+	1.19964i	−0.0540292	+	0.0540292i
$494$		0			0
$495$	−2.16499	+	5.26405i	−0.0973090	+	0.236601i
$496$		0			0
$497$			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	$0.448154\pi$
$500$		0			0
$501$	10.2244	−	10.2244i	0.456792	−	0.456792i
$502$		0			0
$503$	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
$506$		0			0
$507$	−11.9168	−	11.9168i	−0.529244	−	0.529244i
$508$		0			0
$509$	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
$512$		0			0
$513$		−	2.17595i		−	0.0960706i
$514$		0			0
$515$	−1.97349	−	4.73084i	−0.0869625	−	0.208466i
$516$		0			0
$517$	−8.05183	−	8.05183i	−0.354119	−	0.354119i
$518$		0			0
$519$			9.40587i			0.412872i
$520$		0			0
$521$		−	5.01467i		−	0.219696i	−0.993948	−	0.109848i	$-0.964964\pi$
$521$		−	5.01467i		−	0.219696i	0.993948	−	0.109848i	$-0.0350365\pi$
$522$		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			0
$525$	0.0177435	+	3.53694i	0.000774388	+	0.154365i
$526$		0			0
$527$		−	1.86292i		−	0.0811499i
$528$		0			0
$529$	24.9252			1.08370
$530$		0			0
$531$	−5.86121	−	5.86121i	−0.254355	−	0.254355i
$532$		0			0
$533$	8.19512	+	8.19512i	0.354970	+	0.354970i
$534$		0			0
$535$	−11.4149	+	27.7546i	−0.493508	+	1.19994i
$536$		0			0
$537$	24.4178			1.05370
$538$		0			0
$539$	−11.6988	+	11.6988i	−0.503903	+	0.503903i
$540$		0			0
$541$	22.8366	+	22.8366i	0.981822	+	0.981822i	0.999838	−	0.0180153i	$-0.00573475\pi$
$541$	22.8366	+	22.8366i	0.981822	+	0.981822i	−0.0180153	+	0.999838i	$0.505735\pi$
$542$		0			0
$543$			7.24419i			0.310878i
$544$		0			0
$545$	−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	$0.249907\pi$
$548$		0			0
$549$	−0.0537432	+	0.0537432i	−0.00229371	+	0.00229371i
$550$		0			0
$551$			15.0749i			0.642214i
$552$		0			0
$553$	5.19718			0.221006
$554$		0			0
$555$	10.3225	+	24.7450i	0.438167	+	1.05037i
$556$		0			0
$557$	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
$560$		0			0
$561$	0.623348			0.0263178
$562$		0			0
$563$	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
$565$	−16.3612	+	6.82515i	−0.688319	+	0.287136i
$566$		0			0
$567$	−0.707398			−0.0297079
$568$		0			0
$569$		−	4.05892i		−	0.170159i	−0.996374	−	0.0850794i	$-0.972886\pi$
$569$		−	4.05892i		−	0.170159i	0.996374	−	0.0850794i	$-0.0271144\pi$
$570$		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	$0.374787\pi$
$572$		0			0
$573$	12.5893	−	12.5893i	0.525925	−	0.525925i
$574$		0			0
$575$	−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	$-0.0695882\pi$
$578$		0			0
$579$	12.1780	+	12.1780i	0.506099	+	0.506099i
$580$		0			0
$581$	4.81236	−	4.81236i	0.199650	−	0.199650i
$582$		0			0
$583$	5.29274			0.219203
$584$		0			0
$585$	−4.64706	+	11.2991i	−0.192132	+	0.467160i
$586$		0			0
$587$	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
$590$		0			0
$591$	−14.2502			−0.586175
$592$		0			0
$593$			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
$595$	0.357497	−	0.149132i	0.0146559	−	0.00611380i
$596$		0			0
$597$	4.06006	+	4.06006i	0.166167	+	0.166167i
$598$		0			0
$599$		−	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			0
$603$	−7.85550	−	7.85550i	−0.319901	−	0.319901i
$604$		0			0
$605$	9.32902	−	3.89165i	0.379279	−	0.158218i
$606$		0			0
$607$			1.20300i			0.0488283i	0.999702	+	0.0244141i	$0.00777203\pi$
$607$			1.20300i			0.0488283i	−0.999702	+	0.0244141i	$0.992228\pi$
$608$		0			0
$609$	4.90083			0.198592
$610$		0			0
$611$	−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	$0.794172\pi$
$614$		0			0
$615$	1.80411	−	4.38659i	0.0727486	−	0.176884i
$616$		0			0
$617$	−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	$0.0584316\pi$
$620$		0			0
$621$	−4.89516	−	4.89516i	−0.196436	−	0.196436i
$622$		0			0
$623$		−	2.17513i		−	0.0871446i
$624$		0			0
$625$	−0.250824	−	24.9987i	−0.0100330	−	0.999950i
$626$		0			0
$627$	3.91656	−	3.91656i	0.156412	−	0.156412i
$628$		0			0
$629$	2.07628	−	2.07628i	0.0827868	−	0.0827868i
$630$		0			0
$631$			12.7975i			0.509462i	0.967012	+	0.254731i	$0.0819870\pi$
$631$			12.7975i			0.509462i	−0.967012	+	0.254731i	$0.918013\pi$
$632$		0			0
$633$	−13.7648			−0.547101
$634$		0			0
$635$	40.1321	−	16.7413i	1.59260	−	0.664360i
$636$		0			0
$637$	−25.1110	+	25.1110i	−0.994934	+	0.994934i
$638$		0			0
$639$	2.08595			0.0825190
$640$		0			0
$641$	10.9406			0.432129			0.216064	−	0.976379i	$-0.430678\pi$
$641$	10.9406			0.432129			0.216064	+	0.976379i	$0.430678\pi$
$642$		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	$0.420069\pi$
$644$		0			0
$645$	−0.833371	−	1.99775i	−0.0328140	−	0.0786612i
$646$		0			0
$647$	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
$650$		0			0
$651$	−3.80523	+	3.80523i	−0.149139	+	0.149139i
$652$		0			0
$653$	−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
$656$		0			0
$657$			9.69951i			0.378414i
$658$		0			0
$659$	2.60687	+	2.60687i	0.101549	+	0.101549i	0.756056	−	0.654507i	$-0.227124\pi$
$659$	2.60687	+	2.60687i	0.101549	+	0.101549i	−0.654507	+	0.756056i	$0.727124\pi$
$660$		0			0
$661$	−15.9084	+	15.9084i	−0.618766	+	0.618766i	−0.945215	−	0.326449i	$-0.894148\pi$
$661$	−15.9084	+	15.9084i	−0.618766	+	0.618766i	0.326449	+	0.945215i	$0.394148\pi$
$662$		0			0
$663$	1.33799			0.0519634
$664$		0			0
$665$	1.30918	−	3.18319i	0.0507677	−	0.123439i
$666$		0			0
$667$	33.9135	+	33.9135i	1.31314	+	1.31314i
$668$		0			0
$669$	−15.6297	−	15.6297i	−0.604278	−	0.604278i
$670$		0			0
$671$	−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	$-0.174997\pi$
$674$		0			0
$675$	4.99994	−	0.0250827i	0.192448	−	0.000965434i
$676$		0			0
$677$	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			0
$681$			7.57152i			0.290141i
$682$		0			0
$683$	−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
$685$	−6.28474	−	15.0657i	−0.240128	−	0.575631i
$686$		0			0
$687$		−	25.8827i		−	0.987487i
$688$		0			0
$689$	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	$0.503033\pi$
$692$		0			0
$693$	−1.27326	−	1.27326i	−0.0483673	−	0.0483673i
$694$		0			0
$695$	25.8978	+	10.6512i	0.982359	+	0.404023i
$696$		0			0
$697$	−0.519443			−0.0196753
$698$		0			0
$699$	8.52387	−	8.52387i	0.322402	−	0.322402i
$700$		0			0
$701$	−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
$704$		0			0
$705$	−3.80474	+	9.25102i	−0.143295	+	0.348414i
$706$		0			0
$707$	−8.34137	+	8.34137i	−0.313709	+	0.313709i
$708$		0			0
$709$	3.27484	−	3.27484i	0.122989	−	0.122989i	−0.642933	−	0.765922i	$-0.722283\pi$
$709$	3.27484	−	3.27484i	0.122989	−	0.122989i	0.765922	+	0.642933i	$0.222283\pi$
$710$		0			0
$711$		−	7.34690i		−	0.275530i
$712$		0			0
$713$	−52.6641			−1.97229
$714$		0			0
$715$	−28.7019	+	11.9732i	−1.07339	+	0.447771i
$716$		0			0
$717$	19.7419	−	19.7419i	0.737275	−	0.737275i
$718$		0			0
$719$	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
$722$		0			0
$723$	9.69568	−	9.69568i	0.360586	−	0.360586i
$724$		0			0
$725$	−34.6394	+	0.173772i	−1.28648	+	0.00645375i
$726$		0			0
$727$	−6.37077			−0.236279			−0.118139	−	0.992997i	$-0.537693\pi$
$727$	−6.37077			−0.236279			−0.118139	+	0.992997i	$0.537693\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−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	$0.191897\pi$
$734$		0			0
$735$	13.4411	+	5.52804i	0.495784	+	0.203905i
$736$		0			0
$737$		−	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	$0.749600\pi$
$740$		0			0
$741$	8.40674	−	8.40674i	0.308829	−	0.308829i
$742$		0			0
$743$	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
$746$		0			0
$747$	−6.80291	−	6.80291i	−0.248905	−	0.248905i
$748$		0			0
$749$	−6.71327	−	6.71327i	−0.245297	−	0.245297i
$750$		0			0
$751$	−1.69304			−0.0617798			−0.0308899	−	0.999523i	$-0.509834\pi$
$751$	−1.69304			−0.0617798			−0.0308899	+	0.999523i	$0.509834\pi$
$752$		0			0
$753$			12.8294i			0.467528i
$754$		0			0
$755$	0.704855	−	0.294034i	0.0256523	−	0.0107010i
$756$		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	$0.509419\pi$
$758$		0			0
$759$		−	17.6219i		−	0.639633i
$760$		0			0
$761$		−	17.1363i		−	0.621189i	−0.950542	−	0.310595i	$-0.899472\pi$
$761$		−	17.1363i		−	0.621189i	0.950542	−	0.310595i	$-0.100528\pi$
$762$		0			0
$763$	−8.42212	−	8.42212i	−0.304901	−	0.304901i
$764$		0			0
$765$	−0.210817	−	0.505369i	−0.00762211	−	0.0182716i
$766$		0			0
$767$		−	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	$0.652980\pi$
$770$		0			0
$771$	6.52954	+	6.52954i	0.235156	+	0.235156i
$772$		0			0
$773$	−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
$776$		0			0
$777$	−8.48212			−0.304294
$778$		0			0
$779$	−3.26371	+	3.26371i	−0.116934	+	0.116934i
$780$		0			0
$781$	3.75456	+	3.75456i	0.134349	+	0.134349i
$782$		0			0
$783$		−	6.92797i		−	0.247586i
$784$		0			0
$785$	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	$0.328284\pi$
$788$		0			0
$789$	−13.1180	+	13.1180i	−0.467012	+	0.467012i
$790$		0			0
$791$		−	5.60829i		−	0.199408i
$792$		0			0
$793$	−0.415271			−0.0147467
$794$		0			0
$795$	−1.79001	−	4.29099i	−0.0634851	−	0.152186i
$796$		0			0
$797$	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
$800$		0			0
$801$	−3.07483			−0.108644
$802$		0			0
$803$	−17.4584	+	17.4584i	−0.616094	+	0.616094i
$804$		0			0
$805$	−4.21590	−	10.1063i	−0.148591	−	0.356201i
$806$		0			0
$807$	−20.3614			−0.716756
$808$		0			0
$809$		−	36.2916i		−	1.27594i	−0.770060	−	0.637972i	$-0.779774\pi$
$809$		−	36.2916i		−	1.27594i	0.770060	−	0.637972i	$-0.220226\pi$
$810$		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	$0.110609\pi$
$812$		0			0
$813$	−13.6453	+	13.6453i	−0.478563	+	0.478563i
$814$		0			0
$815$	−17.3784	−	7.14735i	−0.608738	−	0.250361i
$816$		0			0
$817$			2.10641i			0.0736939i
$818$		0			0
$819$	−2.73301	−	2.73301i	−0.0954992	−	0.0954992i
$820$		0			0
$821$	−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			0
$825$	9.04467	+	8.95438i	0.314895	+	0.311751i
$826$		0			0
$827$	−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	0.556884	−	0.830590i	$-0.311997\pi$
$829$	−7.88066	−	7.88066i	−0.273707	−	0.273707i	−0.830590	+	0.556884i	$0.811997\pi$
$830$		0			0
$831$	4.98183			0.172818
$832$		0			0
$833$		−	1.59165i		−	0.0551473i
$834$		0			0
$835$	−12.4480	−	29.8401i	−0.430779	−	1.03266i
$836$		0			0
$837$	5.37920	+	5.37920i	0.185932	+	0.185932i
$838$		0			0
$839$			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
$842$		0			0
$843$	20.6529	+	20.6529i	0.711324	+	0.711324i
$844$		0			0
$845$	−34.7794	+	14.5084i	−1.19645	+	0.499105i
$846$		0			0
$847$			3.19781i			0.109878i
$848$		0			0
$849$	13.9198			0.477727
$850$		0			0
$851$	−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			0
$855$	−4.49986	−	1.85069i	−0.153892	−	0.0632924i
$856$		0			0
$857$	−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	$0.943485\pi$
$860$		0			0
$861$	1.06102	+	1.06102i	0.0361596	+	0.0361596i
$862$		0			0
$863$			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
$866$		0			0
$867$	11.9784	−	11.9784i	0.406808	−	0.406808i
$868$		0			0
$869$	13.2239	−	13.2239i	0.448590	−	0.448590i
$870$		0			0
$871$		−	60.6991i		−	2.05671i
$872$		0			0
$873$	1.39922			0.0473565
$874$		0			0
$875$	7.32948	+	2.97155i	0.247782	+	0.100457i
$876$		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	$0.443801\pi$
$878$		0			0
$879$	16.7214			0.563999
$880$		0			0
$881$	27.4850			0.925993			0.462997	−	0.886360i	$-0.346774\pi$
$881$	27.4850			0.925993			0.462997	+	0.886360i	$0.346774\pi$
$882$		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	$0.0660452\pi$
$884$		0			0
$885$	−17.1061	+	7.13588i	−0.575014	+	0.239870i
$886$		0			0
$887$	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
$890$		0			0
$891$	−1.79993	+	1.79993i	−0.0602998	+	0.0602998i
$892$		0			0
$893$	6.88294	−	6.88294i	0.230329	−	0.230329i
$894$		0			0
$895$	20.7678	−	50.4958i	0.694192	−	1.68789i
$896$		0			0
$897$		−	37.8247i		−	1.26293i
$898$		0			0
$899$	−37.2670	−	37.2670i	−1.24292	−	1.24292i
$900$		0			0
$901$	−0.360044	+	0.360044i	−0.0119948	+	0.0119948i
$902$		0			0
$903$	0.684789			0.0227883
$904$		0			0
$905$	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	$0.584319\pi$
$908$		0			0
$909$	11.7916	+	11.7916i	0.391104	+	0.391104i
$910$		0			0
$911$	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
$914$		0			0
$915$	0.0654311	+	0.156851i	0.00216308	+	0.00518532i
$916$		0			0
$917$	−0.250454	−	0.250454i	−0.00827070	−	0.00827070i
$918$		0			0
$919$			3.59430i			0.118565i	0.998241	+	0.0592826i	$0.0188813\pi$
$919$			3.59430i			0.118565i	−0.998241	+	0.0592826i	$0.981119\pi$
$920$		0			0
$921$			23.5087i			0.774638i
$922$		0			0
$923$	8.05902	+	8.05902i	0.265266	+	0.265266i
$924$		0			0
$925$	59.9522	−	0.300757i	1.97122	−	0.00988882i
$926$		0			0
$927$		−	2.29240i		−	0.0752923i
$928$		0			0
$929$	−35.8527			−1.17629			−0.588145	−	0.808756i	$-0.700142\pi$
$929$	−35.8527			−1.17629			−0.588145	+	0.808756i	$0.700142\pi$
$930$		0			0
$931$	−10.0005	−	10.0005i	−0.327752	−	0.327752i
$932$		0			0
$933$	−9.76298	−	9.76298i	−0.319626	−	0.319626i
$934$		0			0
$935$	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	$0.731877\pi$
$938$		0			0
$939$	5.23528	−	5.23528i	0.170847	−	0.170847i
$940$		0			0
$941$	−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
$944$		0			0
$945$	−0.601657	+	1.46290i	−0.0195719	+	0.0475880i
$946$		0			0
$947$	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
$950$		0			0
$951$		−	2.55566i		−	0.0828729i
$952$		0			0
$953$	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
$955$	−15.3272	−	36.7421i	−0.495975	−	1.18895i
$956$		0			0
$957$	12.4699	−	12.4699i	0.403093	−	0.403093i
$958$		0			0
$959$	5.16423			0.166762
$960$		0			0
$961$	26.8716			0.866826
$962$		0			0
$963$	−9.49009	+	9.49009i	−0.305814	+	0.305814i
$964$		0			0
$965$	35.5416	−	14.8264i	1.14413	−	0.477278i
$966$		0			0
$967$	21.3561			0.686767			0.343384	−	0.939195i	$-0.388427\pi$
$967$	21.3561			0.686767			0.343384	+	0.939195i	$0.388427\pi$
$968$		0			0
$969$			0.532856i			0.0171178i
$970$		0			0
$971$	−20.0626	+	20.0626i	−0.643839	+	0.643839i	−0.951497	−	0.307658i	$-0.900455\pi$
$971$	−20.0626	+	20.0626i	−0.643839	+	0.643839i	0.307658	+	0.951497i	$0.400455\pi$
$972$		0			0
$973$	−6.26414	+	6.26414i	−0.200819	+	0.200819i
$974$		0			0
$975$	19.4140	+	19.2202i	0.621747	+	0.615540i
$976$		0			0
$977$		−	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
$980$		0			0
$981$	−11.9058	+	11.9058i	−0.380122	+	0.380122i
$982$		0			0
$983$	−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			0
$987$	−2.23763	−	2.23763i	−0.0712245	−	0.0712245i
$988$		0			0
$989$	4.73871	+	4.73871i	0.150682	+	0.150682i
$990$		0			0
$991$	5.82267			0.184963			0.0924816	−	0.995714i	$-0.470520\pi$
$991$	5.82267			0.184963			0.0924816	+	0.995714i	$0.470520\pi$
$992$		0			0
$993$			8.24078i			0.261513i
$994$		0			0
$995$	11.8494	−	4.94303i	0.375650	−	0.156704i
$996$		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	$0.898656\pi$
$998$		0			0
$999$			11.9906i			0.379366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.b.289.18		48
4.3	odd	2		1920.2.bl.a.289.7		48
5.4	even	2	inner	1920.2.bl.b.289.7		48
8.3	odd	2		240.2.bl.a.109.20	yes	48
8.5	even	2		960.2.bl.a.529.9		48
16.3	odd	4		240.2.bl.a.229.5	yes	48
16.5	even	4	inner	1920.2.bl.b.1249.7		48
16.11	odd	4		1920.2.bl.a.1249.18		48
16.13	even	4		960.2.bl.a.49.15		48
20.19	odd	2		1920.2.bl.a.289.18		48
24.11	even	2		720.2.bm.h.109.5		48
40.19	odd	2		240.2.bl.a.109.5	✓	48
40.29	even	2		960.2.bl.a.529.15		48
48.35	even	4		720.2.bm.h.469.20		48
80.19	odd	4		240.2.bl.a.229.20	yes	48
80.29	even	4		960.2.bl.a.49.9		48
80.59	odd	4		1920.2.bl.a.1249.7		48
80.69	even	4	inner	1920.2.bl.b.1249.18		48
120.59	even	2		720.2.bm.h.109.20		48
240.179	even	4		720.2.bm.h.469.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.5	✓	48	40.19	odd	2
240.2.bl.a.109.20	yes	48	8.3	odd	2
240.2.bl.a.229.5	yes	48	16.3	odd	4
240.2.bl.a.229.20	yes	48	80.19	odd	4
720.2.bm.h.109.5		48	24.11	even	2
720.2.bm.h.109.20		48	120.59	even	2
720.2.bm.h.469.5		48	240.179	even	4
720.2.bm.h.469.20		48	48.35	even	4
960.2.bl.a.49.9		48	80.29	even	4
960.2.bl.a.49.15		48	16.13	even	4
960.2.bl.a.529.9		48	8.5	even	2
960.2.bl.a.529.15		48	40.29	even	2
1920.2.bl.a.289.7		48	4.3	odd	2
1920.2.bl.a.289.18		48	20.19	odd	2
1920.2.bl.a.1249.7		48	80.59	odd	4
1920.2.bl.a.1249.18		48	16.11	odd	4
1920.2.bl.b.289.7		48	5.4	even	2	inner
1920.2.bl.b.289.18		48	1.1	even	1	trivial
1920.2.bl.b.1249.7		48	16.5	even	4	inner
1920.2.bl.b.1249.18		48	80.69	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.860885 - 2.06370i) q^{5} +0.707398 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.860885 - 2.06370i) q^{5} +0.707398 q^{7} -1.00000i q^{9} +(1.79993 - 1.79993i) q^{11} +(3.86348 - 3.86348i) q^{13} +(-2.06800 - 0.850522i) q^{15} +0.244884i q^{17} +(1.53863 + 1.53863i) q^{19} +(0.500206 - 0.500206i) q^{21} +6.92280 q^{23} +(-3.51775 + 3.55323i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(4.89882 + 4.89882i) q^{29} -7.60734 q^{31} -2.54548i q^{33} +(-0.608988 - 1.45986i) q^{35} +(-8.47863 - 8.47863i) q^{37} -5.46378i q^{39} +2.12118i q^{41} +(0.684507 + 0.684507i) q^{43} +(-2.06370 + 0.860885i) q^{45} -4.47342i q^{47} -6.49959 q^{49} +(0.173159 + 0.173159i) q^{51} +(1.47026 + 1.47026i) q^{53} +(-5.26405 - 2.16499i) q^{55} +2.17595 q^{57} +(5.86121 - 5.86121i) q^{59} +(-0.0537432 - 0.0537432i) q^{61} -0.707398i q^{63} +(-11.2991 - 4.64706i) q^{65} +(7.85550 - 7.85550i) q^{67} +(4.89516 - 4.89516i) q^{69} +2.08595i q^{71} -9.69951 q^{73} +(0.0250827 + 4.99994i) q^{75} +(1.27326 - 1.27326i) q^{77} +7.34690 q^{79} -1.00000 q^{81} +(6.80291 - 6.80291i) q^{83} +(0.505369 - 0.210817i) q^{85} +6.92797 q^{87} -3.07483i q^{89} +(2.73301 - 2.73301i) q^{91} +(-5.37920 + 5.37920i) q^{93} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(-1.79993 - 1.79993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 8 q^{19} + 48 q^{31} + 24 q^{35} + 48 q^{49} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} - 16 q^{75} + 96 q^{79} - 48 q^{81} - 32 q^{91} + 48 q^{95}+O(q^{100}) \) 48 * q + 8 * q^19 + 48 * q^31 + 24 * q^35 + 48 * q^49 + 8 * q^51 - 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 - 16 * q^75 + 96 * q^79 - 48 * q^81 - 32 * q^91 + 48 * q^95

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