LMFDB - Embedded newform 1920.2.bl.b.1249.7

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			1249.7
Character	$\chi$	$=$	1920.1249
Dual form			1920.2.bl.b.289.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

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
$5$	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	$-0.542681\pi$
$7$	−0.707398			−0.267371			−0.133686	+	0.991024i	$0.542681\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.79993	+	1.79993i	0.542699	+	0.542699i	0.924319	−	0.381621i	$-0.124634\pi$
$11$	1.79993	+	1.79993i	0.542699	+	0.542699i	−0.381621	+	0.924319i	$0.624634\pi$
$12$		0			0
$13$	−3.86348	−	3.86348i	−1.07154	−	1.07154i	−0.997236	−	0.0742996i	$-0.976328\pi$
$13$	−3.86348	−	3.86348i	−1.07154	−	1.07154i	−0.0742996	−	0.997236i	$-0.523672\pi$
$14$		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	−0.508233	−	0.861219i	$-0.669701\pi$
$19$	1.53863	−	1.53863i	0.352986	−	0.352986i	0.861219	+	0.508233i	$0.169701\pi$
$20$		0			0
$21$	0.500206	+	0.500206i	0.109154	+	0.109154i
$22$		0			0
$23$	−6.92280			−1.44350			−0.721752	−	0.692152i	$-0.756663\pi$
$23$	−6.92280			−1.44350			−0.721752	+	0.692152i	$0.756663\pi$
$24$		0			0
$25$	3.51775	−	3.55323i	0.703551	−	0.710645i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	4.89882	−	4.89882i	0.909688	−	0.909688i	−0.0865591	−	0.996247i	$-0.527587\pi$
$29$	4.89882	−	4.89882i	0.909688	−	0.909688i	0.996247	+	0.0865591i	$0.0275871\pi$
$30$		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
$35$	−1.45986	+	0.608988i	−0.246761	+	0.102938i
$36$		0			0
$37$	8.47863	−	8.47863i	1.39388	−	1.39388i	0.577459	−	0.816420i	$-0.304044\pi$
$37$	8.47863	−	8.47863i	1.39388	−	1.39388i	0.816420	−	0.577459i	$-0.195956\pi$
$38$		0			0
$39$			5.46378i			0.874905i
$40$		0			0
$41$		−	2.12118i		−	0.331272i	−0.986187	−	0.165636i	$-0.947032\pi$
$41$		−	2.12118i		−	0.331272i	0.986187	−	0.165636i	$-0.0529677\pi$
$42$		0			0
$43$	−0.684507	+	0.684507i	−0.104386	+	0.104386i	−0.757371	−	0.652985i	$-0.773517\pi$
$43$	−0.684507	+	0.684507i	−0.104386	+	0.104386i	0.652985	+	0.757371i	$0.273517\pi$
$44$		0			0
$45$	0.860885	+	2.06370i	0.128333	+	0.307639i
$46$		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	$-0.795612\pi$
$53$	−1.47026	+	1.47026i	−0.201956	+	0.201956i	0.598881	+	0.800838i	$0.295612\pi$
$54$		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	0.976875	−	0.213810i	$-0.0685874\pi$
$59$	5.86121	+	5.86121i	0.763065	+	0.763065i	−0.213810	+	0.976875i	$0.568587\pi$
$60$		0			0
$61$	−0.0537432	+	0.0537432i	−0.00688112	+	0.00688112i	−0.710539	−	0.703658i	$-0.751549\pi$
$61$	−0.0537432	+	0.0537432i	−0.00688112	+	0.00688112i	0.703658	+	0.710539i	$0.251549\pi$
$62$		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	$-0.487418\pi$
$67$	−7.85550	−	7.85550i	−0.959702	−	0.959702i	−0.999219	+	0.0395170i	$0.987418\pi$
$68$		0			0
$69$	4.89516	+	4.89516i	0.589308	+	0.589308i
$70$		0			0
$71$		−	2.08595i		−	0.247557i	−0.992310	−	0.123778i	$-0.960499\pi$
$71$		−	2.08595i		−	0.247557i	0.992310	−	0.123778i	$-0.0395012\pi$
$72$		0			0
$73$	9.69951			1.13524			0.567621	−	0.823290i	$-0.307864\pi$
$73$	9.69951			1.13524			0.567621	+	0.823290i	$0.307864\pi$
$74$		0			0
$75$	−4.99994	+	0.0250827i	−0.577343	+	0.00289630i
$76$		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	$-0.427061\pi$
$83$	−6.80291	−	6.80291i	−0.746716	−	0.746716i	−0.973861	+	0.227145i	$0.927061\pi$
$84$		0			0
$85$	0.210817	+	0.505369i	0.0228663	+	0.0548149i
$86$		0			0
$87$	−6.92797			−0.742757
$88$		0			0
$89$			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
$92$		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	−0.981415	−	0.191895i	$-0.938537\pi$
$101$	−11.7916	−	11.7916i	−1.17331	−	1.17331i	−0.191895	−	0.981415i	$-0.561463\pi$
$102$		0			0
$103$	−2.29240			−0.225877			−0.112938	−	0.993602i	$-0.536026\pi$
$103$	−2.29240			−0.225877			−0.112938	+	0.993602i	$0.536026\pi$
$104$		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	$-0.525301\pi$
$107$	9.49009	−	9.49009i	0.917442	−	0.917442i	0.996843	+	0.0794010i	$0.0253008\pi$
$108$		0			0
$109$	−11.9058	+	11.9058i	−1.14037	+	1.14037i	−0.151984	+	0.988383i	$0.548566\pi$
$109$	−11.9058	+	11.9058i	−1.14037	+	1.14037i	−0.988383	+	0.151984i	$0.951434\pi$
$110$		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
$115$	−14.2866	+	5.95974i	−1.33223	+	0.555748i
$116$		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
$125$	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	$0.668705\pi$
$128$		0			0
$129$	0.968040			0.0852311
$130$		0			0
$131$	−0.354049	+	0.354049i	−0.0309334	+	0.0309334i	−0.722404	−	0.691471i	$-0.756963\pi$
$131$	−0.354049	+	0.354049i	−0.0309334	+	0.0309334i	0.691471	+	0.722404i	$0.256963\pi$
$132$		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	$-0.600950\pi$
$137$	−7.30033			−0.623709			−0.311854	+	0.950130i	$0.600950\pi$
$138$		0			0
$139$	−8.85519	−	8.85519i	−0.751087	−	0.751087i	0.223595	−	0.974682i	$-0.428221\pi$
$139$	−8.85519	−	8.85519i	−0.751087	−	0.751087i	−0.974682	+	0.223595i	$0.928221\pi$
$140$		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	0.449673	−	0.893193i	$-0.351540\pi$
$149$	−5.41385	−	5.41385i	−0.443520	−	0.443520i	−0.893193	+	0.449673i	$0.851540\pi$
$150$		0			0
$151$		−	0.341548i		−	0.0277948i	−0.999903	−	0.0138974i	$-0.995576\pi$
$151$		−	0.341548i		−	0.0277948i	0.999903	−	0.0138974i	$-0.00442382\pi$
$152$		0			0
$153$	−0.244884			−0.0197977
$154$		0			0
$155$	−15.6993	+	6.54904i	−1.26100	+	0.526032i
$156$		0			0
$157$	2.86465	+	2.86465i	0.228624	+	0.228624i	0.812118	−	0.583494i	$-0.198315\pi$
$157$	2.86465	+	2.86465i	0.228624	+	0.228624i	−0.583494	+	0.812118i	$0.698315\pi$
$158$		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	$-0.356747\pi$
$163$	−5.94216	−	5.94216i	−0.465426	−	0.465426i	−0.900429	+	0.435003i	$0.856747\pi$
$164$		0			0
$165$	−2.19137	−	5.25312i	−0.170598	−	0.408955i
$166$		0			0
$167$	−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			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	$-0.133610\pi$
$173$	6.65096	+	6.65096i	0.505663	+	0.505663i	−0.407529	+	0.913192i	$0.633610\pi$
$174$		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	0.356052	−	0.934466i	$-0.384123\pi$
$179$	17.2660	−	17.2660i	1.29052	−	1.29052i	0.934466	−	0.356052i	$-0.115877\pi$
$180$		0			0
$181$	−5.12242	−	5.12242i	−0.380746	−	0.380746i	0.490625	−	0.871371i	$-0.336769\pi$
$181$	−5.12242	−	5.12242i	−0.380746	−	0.380746i	−0.871371	+	0.490625i	$0.836769\pi$
$182$		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
$195$	4.70369	+	11.2756i	0.336838	+	0.807465i
$196$		0			0
$197$	10.0764	−	10.0764i	0.717915	−	0.717915i	−0.250263	−	0.968178i	$-0.580517\pi$
$197$	10.0764	−	10.0764i	0.717915	−	0.717915i	0.968178	+	0.250263i	$0.0805171\pi$
$198$		0			0
$199$		−	5.74179i		−	0.407025i	−0.979072	−	0.203513i	$-0.934764\pi$
$199$		−	5.74179i		−	0.407025i	0.979072	−	0.203513i	$-0.0652358\pi$
$200$		0			0
$201$			11.1094i			0.783593i
$202$		0			0
$203$	−3.46541	+	3.46541i	−0.243224	+	0.243224i
$204$		0			0
$205$	−1.82609	−	4.37748i	−0.127540	−	0.305737i
$206$		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	−0.957730	−	0.287670i	$-0.907119\pi$
$211$	−9.73318	+	9.73318i	−0.670060	+	0.670060i	0.287670	+	0.957730i	$0.407119\pi$
$212$		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	$-0.169152\pi$
$227$	5.35387	+	5.35387i	0.355349	+	0.355349i	−0.506746	+	0.862095i	$0.669152\pi$
$228$		0			0
$229$	18.3018	+	18.3018i	1.20942	+	1.20942i	0.971215	+	0.238204i	$0.0765587\pi$
$229$	18.3018	+	18.3018i	1.20942	+	1.20942i	0.238204	+	0.971215i	$0.423441\pi$
$230$		0			0
$231$			1.80067i			0.118475i
$232$		0			0
$233$	−12.0546			−0.789721			−0.394861	−	0.918741i	$-0.629207\pi$
$233$	−12.0546			−0.789721			−0.394861	+	0.918741i	$0.629207\pi$
$234$		0			0
$235$	−3.85110	−	9.23182i	−0.251218	−	0.602217i
$236$		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
$245$	−13.4132	+	5.59540i	−0.856940	+	0.357477i
$246$		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	0.360252	−	0.932855i	$-0.382691\pi$
$251$	−9.07173	−	9.07173i	−0.572602	−	0.572602i	−0.932855	+	0.360252i	$0.882691\pi$
$252$		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	$-0.306179\pi$
$263$	18.5516			1.14394			0.571971	+	0.820274i	$0.306179\pi$
$264$		0			0
$265$	−1.76846	+	4.29992i	−0.108636	+	0.264142i
$266$		0			0
$267$	2.17423	−	2.17423i	0.133061	−	0.133061i
$268$		0			0
$269$	−14.3977	+	14.3977i	−0.877844	+	0.877844i	−0.993311	−	0.115467i	$-0.963163\pi$
$269$	−14.3977	+	14.3977i	−0.877844	+	0.877844i	0.115467	+	0.993311i	$0.463163\pi$
$270$		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
$275$	12.7272	−	0.0638476i	0.767482	−	0.00385016i
$276$		0			0
$277$	−3.52269	+	3.52269i	−0.211658	+	0.211658i	−0.804971	−	0.593314i	$-0.797819\pi$
$277$	−3.52269	+	3.52269i	−0.211658	+	0.211658i	0.593314	+	0.804971i	$0.297819\pi$
$278$		0			0
$279$		−	7.60734i		−	0.455439i
$280$		0			0
$281$		−	29.2076i		−	1.74238i	−0.490945	−	0.871191i	$-0.663348\pi$
$281$		−	29.2076i		−	1.74238i	0.490945	−	0.871191i	$-0.336652\pi$
$282$		0			0
$283$	−9.84279	+	9.84279i	−0.585093	+	0.585093i	−0.936298	−	0.351205i	$-0.885772\pi$
$283$	−9.84279	+	9.84279i	−0.585093	+	0.585093i	0.351205	+	0.936298i	$0.385772\pi$
$284$		0			0
$285$	−4.49052	+	1.87325i	−0.265996	+	0.110961i
$286$		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	$-0.912433\pi$
$293$	−11.8238	+	11.8238i	−0.690755	+	0.690755i	0.271643	+	0.962398i	$0.412433\pi$
$294$		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	$-0.0159269\pi$
$307$	16.6232	+	16.6232i	0.948733	+	0.948733i	−0.0500151	+	0.998748i	$0.515927\pi$
$308$		0			0
$309$	1.62097	+	1.62097i	0.0922139	+	0.0922139i
$310$		0			0
$311$			13.8069i			0.782920i	0.920195	+	0.391460i	$0.128030\pi$
$311$			13.8069i			0.782920i	−0.920195	+	0.391460i	$0.871970\pi$
$312$		0			0
$313$	−7.40380			−0.418488			−0.209244	−	0.977864i	$-0.567100\pi$
$313$	−7.40380			−0.418488			−0.209244	+	0.977864i	$0.567100\pi$
$314$		0			0
$315$	−0.608988	−	1.45986i	−0.0343126	−	0.0822538i
$316$		0			0
$317$	−1.80712	−	1.80712i	−0.101498	−	0.101498i	0.654534	−	0.756032i	$-0.272865\pi$
$317$	−1.80712	−	1.80712i	−0.101498	−	0.101498i	−0.756032	+	0.654534i	$0.772865\pi$
$318$		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
$325$	−27.3186	+	0.137046i	−1.51536	+	0.00760197i
$326$		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	0.528590	−	0.848877i	$-0.322721\pi$
$331$	−5.82711	−	5.82711i	−0.320287	−	0.320287i	−0.848877	+	0.528590i	$0.822721\pi$
$332$		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	$-0.517067\pi$
$347$	17.6028	−	17.6028i	0.944970	−	0.944970i	0.998563	+	0.0535933i	$0.0170675\pi$
$348$		0			0
$349$	5.07562	−	5.07562i	0.271692	−	0.271692i	−0.558089	−	0.829781i	$-0.688465\pi$
$349$	5.07562	−	5.07562i	0.271692	−	0.271692i	0.829781	+	0.558089i	$0.188465\pi$
$350$		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
$355$	−1.79576	−	4.30479i	−0.0953093	−	0.228474i
$356$		0			0
$357$	−0.122492	+	0.122492i	−0.00648299	+	0.00648299i
$358$		0			0
$359$		−	17.1694i		−	0.906169i	−0.891468	−	0.453084i	$-0.850324\pi$
$359$		−	17.1694i		−	0.906169i	0.891468	−	0.453084i	$-0.149676\pi$
$360$		0			0
$361$			14.2652i			0.750802i
$362$		0			0
$363$	−3.19649	+	3.19649i	−0.167772	+	0.167772i
$364$		0			0
$365$	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	$0.791792\pi$
$368$		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	$-0.763035\pi$
$373$	−1.11817	+	1.11817i	−0.0578964	+	0.0578964i	0.677566	+	0.735462i	$0.263035\pi$
$374$		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	0.986729	+	0.162375i	$0.0519153\pi$
$379$	22.3707	+	22.3707i	1.14910	+	1.14910i	0.162375	+	0.986729i	$0.448085\pi$
$380$		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	0.985946	+	0.167062i	$0.0534280\pi$
$389$	22.7409	+	22.7409i	1.15301	+	1.15301i	0.167062	+	0.985946i	$0.446572\pi$
$390$		0			0
$391$		−	1.69529i		−	0.0857342i
$392$		0			0
$393$	0.500701			0.0252570
$394$		0			0
$395$	15.1618	−	6.32484i	0.762874	−	0.318237i
$396$		0			0
$397$	21.6530	+	21.6530i	1.08673	+	1.08673i	0.995863	+	0.0908707i	$0.0289650\pi$
$397$	21.6530	+	21.6530i	1.08673	+	1.08673i	0.0908707	+	0.995863i	$0.471035\pi$
$398$		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
$405$	−2.06370	+	0.860885i	−0.102546	+	0.0427777i
$406$		0			0
$407$	30.5218			1.51291
$408$		0			0
$409$			17.9588i			0.888006i	0.896025	+	0.444003i	$0.146442\pi$
$409$			17.9588i			0.888006i	−0.896025	+	0.444003i	$0.853558\pi$
$410$		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	0.155476	−	0.987840i	$-0.450309\pi$
$419$	23.4031	−	23.4031i	1.14332	−	1.14332i	0.987840	−	0.155476i	$-0.0496913\pi$
$420$		0			0
$421$	27.0016	+	27.0016i	1.31598	+	1.31598i	0.916932	+	0.399043i	$0.130658\pi$
$421$	27.0016	+	27.0016i	1.31598	+	1.31598i	0.399043	+	0.916932i	$0.369342\pi$
$422$		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
$435$	−14.2973	+	5.96419i	−0.685503	+	0.285961i
$436$		0			0
$437$	−10.6516	+	10.6516i	−0.509537	+	0.509537i
$438$		0			0
$439$			10.4690i			0.499660i	0.968290	+	0.249830i	$0.0803748\pi$
$439$			10.4690i			0.499660i	−0.968290	+	0.249830i	$0.919625\pi$
$440$		0			0
$441$		−	6.49959i		−	0.309504i
$442$		0			0
$443$	−1.81582	+	1.81582i	−0.0862722	+	0.0862722i	−0.748926	−	0.662654i	$-0.769430\pi$
$443$	−1.81582	+	1.81582i	−0.0862722	+	0.0862722i	0.662654	+	0.748926i	$0.269430\pi$
$444$		0			0
$445$	2.64707	+	6.34554i	0.125483	+	0.300807i
$446$		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	$-0.407674\pi$
$457$	12.2280			0.572000			0.286000	+	0.958230i	$0.407674\pi$
$458$		0			0
$459$	0.173159	+	0.173159i	0.00808238	+	0.00808238i
$460$		0			0
$461$	−0.723447	+	0.723447i	−0.0336943	+	0.0336943i	−0.723753	−	0.690059i	$-0.757585\pi$
$461$	−0.723447	+	0.723447i	−0.0336943	+	0.0336943i	0.690059	+	0.723753i	$0.257585\pi$
$462$		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	$-0.393599\pi$
$467$	−13.3242	−	13.3242i	−0.616571	−	0.616571i	−0.944650	+	0.328079i	$0.893599\pi$
$468$		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
$475$	−0.0545788	−	10.8796i	−0.00250425	−	0.499191i
$476$		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
$485$	1.20457	+	2.88758i	0.0546967	+	0.131118i
$486$		0			0
$487$	−15.8116			−0.716491			−0.358246	−	0.933627i	$-0.616625\pi$
$487$	−15.8116			−0.716491			−0.358246	+	0.933627i	$0.616625\pi$
$488$		0			0
$489$			8.40349i			0.380019i
$490$		0			0
$491$	−15.6008	−	15.6008i	−0.704054	−	0.704054i	0.261224	−	0.965278i	$-0.415874\pi$
$491$	−15.6008	−	15.6008i	−0.704054	−	0.704054i	−0.965278	+	0.261224i	$0.915874\pi$
$492$		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	0.162159	−	0.986765i	$-0.448154\pi$
$499$	25.6650	−	25.6650i	1.14892	−	1.14892i	0.986765	−	0.162159i	$-0.0518459\pi$
$500$		0			0
$501$	10.2244	+	10.2244i	0.456792	+	0.456792i
$502$		0			0
$503$	−4.72004			−0.210456			−0.105228	−	0.994448i	$-0.533557\pi$
$503$	−4.72004			−0.210456			−0.105228	+	0.994448i	$0.533557\pi$
$504$		0			0
$505$	−34.4857	−	14.1832i	−1.53459	−	0.631144i
$506$		0			0
$507$	11.9168	−	11.9168i	0.529244	−	0.529244i
$508$		0			0
$509$	11.8862	−	11.8862i	0.526848	−	0.526848i	−0.392783	−	0.919631i	$-0.628488\pi$
$509$	11.8862	−	11.8862i	0.526848	−	0.526848i	0.919631	+	0.392783i	$0.128488\pi$
$510$		0			0
$511$	−6.86141			−0.303531
$512$		0			0
$513$		−	2.17595i		−	0.0960706i
$514$		0			0
$515$	−4.73084	+	1.97349i	−0.208466	+	0.0869625i
$516$		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	$0.0350365\pi$
$521$			5.01467i			0.219696i	−0.993948	+	0.109848i	$0.964964\pi$
$522$		0			0
$523$	18.9502	−	18.9502i	0.828635	−	0.828635i	−0.158693	−	0.987328i	$-0.550728\pi$
$523$	18.9502	−	18.9502i	0.828635	−	0.828635i	0.987328	+	0.158693i	$0.0507279\pi$
$524$		0			0
$525$	3.53694	−	0.0177435i	0.154365	−	0.000774388i
$526$		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	−0.0180153	−	0.999838i	$-0.505735\pi$
$541$	22.8366	−	22.8366i	0.981822	−	0.981822i	0.999838	+	0.0180153i	$0.00573475\pi$
$542$		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	$-0.250093\pi$
$547$	−0.00963023	−	0.00963023i	−0.000411759	−	0.000411759i	−0.707313	+	0.706901i	$0.750093\pi$
$548$		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
$555$	−24.7450	+	10.3225i	−1.05037	+	0.438167i
$556$		0			0
$557$	−25.6660	−	25.6660i	−1.08750	−	1.08750i	−0.995785	−	0.0917192i	$-0.970764\pi$
$557$	−25.6660	−	25.6660i	−1.08750	−	1.08750i	−0.0917192	−	0.995785i	$-0.529236\pi$
$558$		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	$-0.308836\pi$
$563$	−6.16719	−	6.16719i	−0.259916	−	0.259916i	−0.825020	+	0.565104i	$0.808836\pi$
$564$		0			0
$565$	−6.82515	−	16.3612i	−0.287136	−	0.688319i
$566$		0			0
$567$	0.707398			0.0297079
$568$		0			0
$569$			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	0.383301	−	0.923624i	$-0.374787\pi$
$571$	−12.9113	−	12.9113i	−0.540323	−	0.540323i	−0.923624	+	0.383301i	$0.874787\pi$
$572$		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	−0.159033	+	0.987273i	$0.550838\pi$
$587$	−27.7728	+	27.7728i	−1.14631	+	1.14631i	−0.987273	+	0.159033i	$0.949162\pi$
$588$		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
$595$	−0.149132	−	0.357497i	−0.00611380	−	0.0146559i
$596$		0			0
$597$	−4.06006	+	4.06006i	−0.166167	+	0.166167i
$598$		0			0
$599$			1.32051i			0.0539544i	0.999636	+	0.0269772i	$0.00858816\pi$
$599$			1.32051i			0.0539544i	−0.999636	+	0.0269772i	$0.991412\pi$
$600$		0			0
$601$		−	23.8236i		−	0.971787i	−0.874018	−	0.485893i	$-0.838494\pi$
$601$		−	23.8236i		−	0.971787i	0.874018	−	0.485893i	$-0.161506\pi$
$602$		0			0
$603$	7.85550	−	7.85550i	0.319901	−	0.319901i
$604$		0			0
$605$	−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	$0.992228\pi$
$608$		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	$-0.705828\pi$
$613$	4.84340	−	4.84340i	0.195623	−	0.195623i	0.798121	+	0.602498i	$0.205828\pi$
$614$		0			0
$615$	−1.80411	+	4.38659i	−0.0727486	+	0.176884i
$616$		0			0
$617$	26.9719			1.08585			0.542924	−	0.839782i	$-0.317317\pi$
$617$	26.9719			1.08585			0.542924	+	0.839782i	$0.317317\pi$
$618$		0			0
$619$	19.9202	+	19.9202i	0.800660	+	0.800660i	0.983199	−	0.182539i	$-0.0584316\pi$
$619$	19.9202	+	19.9202i	0.800660	+	0.800660i	−0.182539	+	0.983199i	$0.558432\pi$
$620$		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	$-0.918013\pi$
$631$		−	12.7975i		−	0.509462i	0.967012	−	0.254731i	$-0.0819870\pi$
$632$		0			0
$633$	13.7648			0.547101
$634$		0			0
$635$	16.7413	+	40.1321i	0.664360	+	1.59260i
$636$		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	$-0.0799311\pi$
$643$	18.2613	+	18.2613i	0.720157	+	0.720157i	−0.248480	+	0.968637i	$0.579931\pi$
$644$		0			0
$645$	1.99775	−	0.833371i	0.0786612	−	0.0328140i
$646$		0			0
$647$	−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
$650$		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	$-0.149850\pi$
$653$	11.1836	+	11.1836i	0.437648	+	0.437648i	−0.453572	+	0.891220i	$0.649850\pi$
$654$		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	−0.654507	−	0.756056i	$-0.727124\pi$
$659$	2.60687	−	2.60687i	0.101549	−	0.101549i	0.756056	+	0.654507i	$0.227124\pi$
$660$		0			0
$661$	−15.9084	−	15.9084i	−0.618766	−	0.618766i	0.326449	−	0.945215i	$-0.394148\pi$
$661$	−15.9084	−	15.9084i	−0.618766	−	0.618766i	−0.945215	+	0.326449i	$0.894148\pi$
$662$		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
$675$	−0.0250827	−	4.99994i	−0.000965434	−	0.192448i
$676$		0			0
$677$	−11.0637	+	11.0637i	−0.425211	+	0.425211i	−0.886993	−	0.461782i	$-0.847210\pi$
$677$	−11.0637	+	11.0637i	−0.425211	+	0.425211i	0.461782	+	0.886993i	$0.347210\pi$
$678$		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	$-0.593688\pi$
$683$	17.4289	−	17.4289i	0.666898	−	0.666898i	0.956997	+	0.290098i	$0.0936881\pi$
$684$		0			0
$685$	−15.0657	+	6.28474i	−0.575631	+	0.240128i
$686$		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	−0.00952887	−	0.999955i	$-0.503033\pi$
$691$	26.0352	−	26.0352i	0.990426	−	0.990426i	0.999955	+	0.00952887i	$0.00303318\pi$
$692$		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	−0.745305	−	0.666723i	$-0.767696\pi$
$701$	−2.08057	+	2.08057i	−0.0785822	+	0.0785822i	0.666723	+	0.745305i	$0.267696\pi$
$702$		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	0.765922	−	0.642933i	$-0.222283\pi$
$709$	3.27484	+	3.27484i	0.122989	+	0.122989i	−0.642933	+	0.765922i	$0.722283\pi$
$710$		0			0
$711$			7.34690i			0.275530i
$712$		0			0
$713$	52.6641			1.97229
$714$		0			0
$715$	−11.9732	−	28.7019i	−0.447771	−	1.07339i
$716$		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
$725$	−0.173772	−	34.6394i	−0.00645375	−	1.28648i
$726$		0			0
$727$	6.37077			0.236279			0.118139	−	0.992997i	$-0.462307\pi$
$727$	6.37077			0.236279			0.118139	+	0.992997i	$0.462307\pi$
$728$		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	$-0.308103\pi$
$733$	−6.95026	−	6.95026i	−0.256714	−	0.256714i	−0.823716	+	0.567002i	$0.808103\pi$
$734$		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	−0.706217	−	0.707995i	$-0.749600\pi$
$739$	0.0483355	−	0.0483355i	0.00177805	−	0.00177805i	0.707995	+	0.706217i	$0.249600\pi$
$740$		0			0
$741$	8.40674	+	8.40674i	0.308829	+	0.308829i
$742$		0			0
$743$	−0.148848			−0.00546069			−0.00273035	−	0.999996i	$-0.500869\pi$
$743$	−0.148848			−0.00546069			−0.00273035	+	0.999996i	$0.500869\pi$
$744$		0			0
$745$	−15.8333	−	6.51188i	−0.580087	−	0.238577i
$746$		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
$755$	−0.294034	−	0.704855i	−0.0107010	−	0.0256523i
$756$		0			0
$757$	−26.6876	+	26.6876i	−0.969977	+	0.969977i	−0.999562	−	0.0295851i	$-0.990581\pi$
$757$	−26.6876	+	26.6876i	−0.969977	+	0.969977i	0.0295851	+	0.999562i	$0.490581\pi$
$758$		0			0
$759$			17.6219i			0.639633i
$760$		0			0
$761$			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
$764$		0			0
$765$	−0.505369	+	0.210817i	−0.0182716	+	0.00762211i
$766$		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	$-0.504069\pi$
$773$	27.4452	−	27.4452i	0.987137	−	0.987137i	0.999918	+	0.0127818i	$0.00406868\pi$
$774$		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	$-0.171716\pi$
$787$	9.65912	+	9.65912i	0.344310	+	0.344310i	−0.513675	+	0.857985i	$0.671716\pi$
$788$		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
$795$	4.29099	−	1.79001i	0.152186	−	0.0634851i
$796$		0			0
$797$	−11.9978	−	11.9978i	−0.424984	−	0.424984i	0.461931	−	0.886916i	$-0.347157\pi$
$797$	−11.9978	−	11.9978i	−0.424984	−	0.424984i	−0.886916	+	0.461931i	$0.847157\pi$
$798$		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
$805$	10.1063	−	4.21590i	0.356201	−	0.148591i
$806$		0			0
$807$	20.3614			0.716756
$808$		0			0
$809$			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	0.940231	−	0.340538i	$-0.110609\pi$
$811$	17.0781	+	17.0781i	0.599693	+	0.599693i	−0.340538	+	0.940231i	$0.610609\pi$
$812$		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	0.212071	−	0.977254i	$-0.431979\pi$
$821$	−21.9249	−	21.9249i	−0.765183	−	0.765183i	−0.977254	+	0.212071i	$0.931979\pi$
$822$		0			0
$823$	4.38382			0.152810			0.0764052	−	0.997077i	$-0.475656\pi$
$823$	4.38382			0.152810			0.0764052	+	0.997077i	$0.475656\pi$
$824$		0			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	$-0.571877\pi$
$827$	21.5889	−	21.5889i	0.750718	−	0.750718i	0.974613	+	0.223895i	$0.0718772\pi$
$828$		0			0
$829$	−7.88066	+	7.88066i	−0.273707	+	0.273707i	−0.830590	−	0.556884i	$-0.811997\pi$
$829$	−7.88066	+	7.88066i	−0.273707	+	0.273707i	0.556884	+	0.830590i	$0.311997\pi$
$830$		0			0
$831$	4.98183			0.172818
$832$		0			0
$833$		−	1.59165i		−	0.0551473i
$834$		0			0
$835$	−29.8401	+	12.4480i	−1.03266	+	0.430779i
$836$		0			0
$837$	−5.37920	+	5.37920i	−0.185932	+	0.185932i
$838$		0			0
$839$		−	6.03706i		−	0.208423i	−0.994555	−	0.104211i	$-0.966768\pi$
$839$		−	6.03706i		−	0.208423i	0.994555	−	0.104211i	$-0.0332318\pi$
$840$		0			0
$841$		−	18.9968i		−	0.655063i
$842$		0			0
$843$	−20.6529	+	20.6529i	−0.711324	+	0.711324i
$844$		0			0
$845$	14.5084	+	34.7794i	0.499105	+	1.19645i
$846$		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	$-0.650770\pi$
$853$	12.6685	−	12.6685i	0.433763	−	0.433763i	0.889906	+	0.456144i	$0.150770\pi$
$854$		0			0
$855$	4.49986	+	1.85069i	0.153892	+	0.0632924i
$856$		0			0
$857$	4.79580			0.163821			0.0819106	−	0.996640i	$-0.473898\pi$
$857$	4.79580			0.163821			0.0819106	+	0.996640i	$0.473898\pi$
$858$		0			0
$859$	−34.0244	−	34.0244i	−1.16090	−	1.16090i	−0.984280	−	0.176616i	$-0.943485\pi$
$859$	−34.0244	−	34.0244i	−1.16090	−	1.16090i	−0.176616	−	0.984280i	$-0.556515\pi$
$860$		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
$875$	−2.97155	+	7.32948i	−0.100457	+	0.247782i
$876$		0			0
$877$	23.9525	+	23.9525i	0.808817	+	0.808817i	0.984455	−	0.175638i	$-0.0561987\pi$
$877$	23.9525	+	23.9525i	0.808817	+	0.808817i	−0.175638	+	0.984455i	$0.556199\pi$
$878$		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	$-0.433955\pi$
$883$	−22.9566	−	22.9566i	−0.772550	−	0.772550i	−0.978552	+	0.206001i	$0.933955\pi$
$884$		0			0
$885$	−7.13588	−	17.1061i	−0.239870	−	0.575014i
$886$		0			0
$887$	−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
$890$		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	$-0.915681\pi$
$907$	−21.1812	+	21.1812i	−0.703312	+	0.703312i	0.261808	+	0.965120i	$0.415681\pi$
$908$		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
$915$	0.156851	−	0.0654311i	0.00518532	−	0.00216308i
$916$		0			0
$917$	0.250454	−	0.250454i	0.00827070	−	0.00827070i
$918$		0			0
$919$		−	3.59430i		−	0.118565i	−0.998241	−	0.0592826i	$-0.981119\pi$
$919$		−	3.59430i		−	0.118565i	0.998241	−	0.0592826i	$-0.0188813\pi$
$920$		0			0
$921$		−	23.5087i		−	0.774638i
$922$		0			0
$923$	−8.05902	+	8.05902i	−0.265266	+	0.265266i
$924$		0			0
$925$	−0.300757	−	59.9522i	−0.00988882	−	1.97122i
$926$		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	$-0.268123\pi$
$937$	40.7563			1.33145			0.665725	+	0.746198i	$0.268123\pi$
$938$		0			0
$939$	5.23528	+	5.23528i	0.170847	+	0.170847i
$940$		0			0
$941$	−36.2143	+	36.2143i	−1.18055	+	1.18055i	−0.200950	+	0.979602i	$0.564403\pi$
$941$	−36.2143	+	36.2143i	−1.18055	+	1.18055i	−0.979602	+	0.200950i	$0.935597\pi$
$942$		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	−0.977926	−	0.208951i	$-0.932995\pi$
$947$	−36.5242	−	36.5242i	−1.18688	−	1.18688i	−0.208951	−	0.977926i	$-0.567005\pi$
$948$		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	$-0.583936\pi$
$953$	−16.0927			−0.521294			−0.260647	+	0.965434i	$0.583936\pi$
$954$		0			0
$955$	36.7421	−	15.3272i	1.18895	−	0.495975i
$956$		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
$965$	14.8264	+	35.5416i	0.477278	+	1.14413i
$966$		0			0
$967$	−21.3561			−0.686767			−0.343384	−	0.939195i	$-0.611573\pi$
$967$	−21.3561			−0.686767			−0.343384	+	0.939195i	$0.611573\pi$
$968$		0			0
$969$		−	0.532856i		−	0.0171178i
$970$		0			0
$971$	−20.0626	−	20.0626i	−0.643839	−	0.643839i	0.307658	−	0.951497i	$-0.400455\pi$
$971$	−20.0626	−	20.0626i	−0.643839	−	0.643839i	−0.951497	+	0.307658i	$0.900455\pi$
$972$		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	$-0.497827\pi$
$983$	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			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
$995$	−4.94303	−	11.8494i	−0.156704	−	0.375650i
$996$		0			0
$997$	20.1044	−	20.1044i	0.636713	−	0.636713i	−0.313030	−	0.949743i	$-0.601344\pi$
$997$	20.1044	−	20.1044i	0.636713	−	0.636713i	0.949743	+	0.313030i	$0.101344\pi$
$998$		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.1249.7		48
4.3	odd	2		1920.2.bl.a.1249.18		48
5.4	even	2	inner	1920.2.bl.b.1249.18		48
8.3	odd	2		240.2.bl.a.229.5	yes	48
8.5	even	2		960.2.bl.a.49.15		48
16.3	odd	4		1920.2.bl.a.289.7		48
16.5	even	4		960.2.bl.a.529.9		48
16.11	odd	4		240.2.bl.a.109.20	yes	48
16.13	even	4	inner	1920.2.bl.b.289.18		48
20.19	odd	2		1920.2.bl.a.1249.7		48
24.11	even	2		720.2.bm.h.469.20		48
40.19	odd	2		240.2.bl.a.229.20	yes	48
40.29	even	2		960.2.bl.a.49.9		48
48.11	even	4		720.2.bm.h.109.5		48
80.19	odd	4		1920.2.bl.a.289.18		48
80.29	even	4	inner	1920.2.bl.b.289.7		48
80.59	odd	4		240.2.bl.a.109.5	✓	48
80.69	even	4		960.2.bl.a.529.15		48
120.59	even	2		720.2.bm.h.469.5		48
240.59	even	4		720.2.bm.h.109.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.5	✓	48	80.59	odd	4
240.2.bl.a.109.20	yes	48	16.11	odd	4
240.2.bl.a.229.5	yes	48	8.3	odd	2
240.2.bl.a.229.20	yes	48	40.19	odd	2
720.2.bm.h.109.5		48	48.11	even	4
720.2.bm.h.109.20		48	240.59	even	4
720.2.bm.h.469.5		48	120.59	even	2
720.2.bm.h.469.20		48	24.11	even	2
960.2.bl.a.49.9		48	40.29	even	2
960.2.bl.a.49.15		48	8.5	even	2
960.2.bl.a.529.9		48	16.5	even	4
960.2.bl.a.529.15		48	80.69	even	4
1920.2.bl.a.289.7		48	16.3	odd	4
1920.2.bl.a.289.18		48	80.19	odd	4
1920.2.bl.a.1249.7		48	20.19	odd	2
1920.2.bl.a.1249.18		48	4.3	odd	2
1920.2.bl.b.289.7		48	80.29	even	4	inner
1920.2.bl.b.289.18		48	16.13	even	4	inner
1920.2.bl.b.1249.7		48	1.1	even	1	trivial
1920.2.bl.b.1249.18		48	5.4	even	2	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)

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

Introduction

L-functions

Modular forms

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Database

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