LMFDB - Embedded newform 768.2.n.b.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, degree $4$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			289.2
Character	$\chi$	$=$	768.289
Dual form			768.2.n.b.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 + 0.923880i) q^{3} +(-1.60930 + 0.666593i) q^{5} +(0.589445 - 0.589445i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 + 0.923880i) q^{3} +(-1.60930 + 0.666593i) q^{5} +(0.589445 - 0.589445i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-0.657053 - 1.58627i) q^{11} +(-3.87213 - 1.60389i) q^{13} -1.74189i q^{15} -7.96502i q^{17} +(3.97306 + 1.64569i) q^{19} +(0.319006 + 0.770147i) q^{21} +(0.452012 + 0.452012i) q^{23} +(-1.39004 + 1.39004i) q^{25} +(0.923880 - 0.382683i) q^{27} +(1.69130 - 4.08316i) q^{29} +9.32808 q^{31} +1.71696 q^{33} +(-0.555673 + 1.34151i) q^{35} +(-0.810329 + 0.335649i) q^{37} +(2.96360 - 2.96360i) q^{39} +(-6.65023 - 6.65023i) q^{41} +(-2.22413 - 5.36952i) q^{43} +(1.60930 + 0.666593i) q^{45} -8.50500i q^{47} +6.30511i q^{49} +(7.35872 + 3.04808i) q^{51} +(-1.10759 - 2.67397i) q^{53} +(2.11479 + 2.11479i) q^{55} +(-3.04084 + 3.04084i) q^{57} +(-1.92200 + 0.796118i) q^{59} +(4.70435 - 11.3573i) q^{61} -0.833602 q^{63} +7.30055 q^{65} +(4.54765 - 10.9790i) q^{67} +(-0.590582 + 0.244627i) q^{69} +(-9.09946 + 9.09946i) q^{71} +(1.65052 + 1.65052i) q^{73} +(-0.752286 - 1.81618i) q^{75} +(-1.32231 - 0.547721i) q^{77} -0.580469i q^{79} +1.00000i q^{81} +(3.33576 + 1.38172i) q^{83} +(5.30942 + 12.8181i) q^{85} +(3.12512 + 3.12512i) q^{87} +(-4.91488 + 4.91488i) q^{89} +(-3.22782 + 1.33701i) q^{91} +(-3.56970 + 8.61802i) q^{93} -7.49083 q^{95} -3.30926 q^{97} +(-0.657053 + 1.58627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{8}\right)$

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
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		0			0
$5$	−1.60930	+	0.666593i	−0.719700	+	0.298109i	−0.712312	−	0.701863i	$-0.752352\pi$
$5$	−1.60930	+	0.666593i	−0.719700	+	0.298109i	−0.00738796	+	0.999973i	$0.502352\pi$
$6$		0			0
$7$	0.589445	−	0.589445i	0.222789	−	0.222789i	−0.586883	−	0.809672i	$-0.699645\pi$
$7$	0.589445	−	0.589445i	0.222789	−	0.222789i	0.809672	+	0.586883i	$0.199645\pi$
$8$		0			0
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$		0			0
$11$	−0.657053	−	1.58627i	−0.198109	−	0.478277i	0.793339	−	0.608780i	$-0.208341\pi$
$11$	−0.657053	−	1.58627i	−0.198109	−	0.478277i	−0.991448	+	0.130503i	$0.958341\pi$
$12$		0			0
$13$	−3.87213	−	1.60389i	−1.07394	−	0.444839i	−0.225558	−	0.974230i	$-0.572421\pi$
$13$	−3.87213	−	1.60389i	−1.07394	−	0.444839i	−0.848378	+	0.529391i	$0.822421\pi$
$14$		0			0
$15$		−	1.74189i		−	0.449754i
$16$		0			0
$17$		−	7.96502i		−	1.93180i	−0.258913	−	0.965901i	$-0.583364\pi$
$17$		−	7.96502i		−	1.93180i	0.258913	−	0.965901i	$-0.416636\pi$
$18$		0			0
$19$	3.97306	+	1.64569i	0.911481	+	0.377548i	0.788624	−	0.614876i	$-0.210794\pi$
$19$	3.97306	+	1.64569i	0.911481	+	0.377548i	0.122858	+	0.992424i	$0.460794\pi$
$20$		0			0
$21$	0.319006	+	0.770147i	0.0696127	+	0.168060i
$22$		0			0
$23$	0.452012	+	0.452012i	0.0942511	+	0.0942511i	0.752660	−	0.658409i	$-0.228770\pi$
$23$	0.452012	+	0.452012i	0.0942511	+	0.0942511i	−0.658409	+	0.752660i	$0.728770\pi$
$24$		0			0
$25$	−1.39004	+	1.39004i	−0.278009	+	0.278009i
$26$		0			0
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$		0			0
$29$	1.69130	−	4.08316i	0.314067	−	0.758224i	−0.685479	−	0.728092i	$-0.740407\pi$
$29$	1.69130	−	4.08316i	0.314067	−	0.758224i	0.999546	−	0.0301318i	$-0.00959270\pi$
$30$		0			0
$31$	9.32808			1.67537			0.837686	−	0.546152i	$-0.183908\pi$
$31$	9.32808			1.67537			0.837686	+	0.546152i	$0.183908\pi$
$32$		0			0
$33$	1.71696			0.298885
$34$		0			0
$35$	−0.555673	+	1.34151i	−0.0939258	+	0.226757i
$36$		0			0
$37$	−0.810329	+	0.335649i	−0.133217	+	0.0551804i	−0.448296	−	0.893885i	$-0.647969\pi$
$37$	−0.810329	+	0.335649i	−0.133217	+	0.0551804i	0.315079	+	0.949065i	$0.397969\pi$
$38$		0			0
$39$	2.96360	−	2.96360i	0.474556	−	0.474556i
$40$		0			0
$41$	−6.65023	−	6.65023i	−1.03859	−	1.03859i	−0.999225	−	0.0393665i	$-0.987466\pi$
$41$	−6.65023	−	6.65023i	−1.03859	−	1.03859i	−0.0393665	−	0.999225i	$-0.512534\pi$
$42$		0			0
$43$	−2.22413	−	5.36952i	−0.339176	−	0.818844i	−0.997795	−	0.0663675i	$-0.978859\pi$
$43$	−2.22413	−	5.36952i	−0.339176	−	0.818844i	0.658619	−	0.752477i	$-0.271141\pi$
$44$		0			0
$45$	1.60930	+	0.666593i	0.239900	+	0.0993698i
$46$		0			0
$47$		−	8.50500i		−	1.24058i	−0.784372	−	0.620291i	$-0.787015\pi$
$47$		−	8.50500i		−	1.24058i	0.784372	−	0.620291i	$-0.212985\pi$
$48$		0			0
$49$			6.30511i			0.900730i
$50$		0			0
$51$	7.35872	+	3.04808i	1.03043	+	0.426817i
$52$		0			0
$53$	−1.10759	−	2.67397i	−0.152140	−	0.367298i	0.829373	−	0.558696i	$-0.188698\pi$
$53$	−1.10759	−	2.67397i	−0.152140	−	0.367298i	−0.981513	+	0.191398i	$0.938698\pi$
$54$		0			0
$55$	2.11479	+	2.11479i	0.285158	+	0.285158i
$56$		0			0
$57$	−3.04084	+	3.04084i	−0.402770	+	0.402770i
$58$		0			0
$59$	−1.92200	+	0.796118i	−0.250223	+	0.103646i	−0.504270	−	0.863546i	$-0.668238\pi$
$59$	−1.92200	+	0.796118i	−0.250223	+	0.103646i	0.254047	+	0.967192i	$0.418238\pi$
$60$		0			0
$61$	4.70435	−	11.3573i	0.602331	−	1.45416i	−0.268845	−	0.963183i	$-0.586642\pi$
$61$	4.70435	−	11.3573i	0.602331	−	1.45416i	0.871176	−	0.490972i	$-0.163358\pi$
$62$		0			0
$63$	−0.833602			−0.105024
$64$		0			0
$65$	7.30055			0.905522
$66$		0			0
$67$	4.54765	−	10.9790i	0.555583	−	1.34130i	−0.357648	−	0.933856i	$-0.616421\pi$
$67$	4.54765	−	10.9790i	0.555583	−	1.34130i	0.913232	−	0.407441i	$-0.133579\pi$
$68$		0			0
$69$	−0.590582	+	0.244627i	−0.0710978	+	0.0294497i
$70$		0			0
$71$	−9.09946	+	9.09946i	−1.07991	+	1.07991i	−0.0833896	+	0.996517i	$0.526575\pi$
$71$	−9.09946	+	9.09946i	−1.07991	+	1.07991i	−0.996517	+	0.0833896i	$0.973425\pi$
$72$		0			0
$73$	1.65052	+	1.65052i	0.193179	+	0.193179i	0.797068	−	0.603889i	$-0.206383\pi$
$73$	1.65052	+	1.65052i	0.193179	+	0.193179i	−0.603889	+	0.797068i	$0.706383\pi$
$74$		0			0
$75$	−0.752286	−	1.81618i	−0.0868665	−	0.209714i
$76$		0			0
$77$	−1.32231	−	0.547721i	−0.150692	−	0.0624186i
$78$		0			0
$79$		−	0.580469i		−	0.0653079i	−0.999467	−	0.0326540i	$-0.989604\pi$
$79$		−	0.580469i		−	0.0653079i	0.999467	−	0.0326540i	$-0.0103959\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	3.33576	+	1.38172i	0.366147	+	0.151663i	0.558168	−	0.829728i	$-0.311504\pi$
$83$	3.33576	+	1.38172i	0.366147	+	0.151663i	−0.192021	+	0.981391i	$0.561504\pi$
$84$		0			0
$85$	5.30942	+	12.8181i	0.575888	+	1.39032i
$86$		0			0
$87$	3.12512	+	3.12512i	0.335048	+	0.335048i
$88$		0			0
$89$	−4.91488	+	4.91488i	−0.520976	+	0.520976i	−0.917866	−	0.396890i	$-0.870089\pi$
$89$	−4.91488	+	4.91488i	−0.520976	+	0.520976i	0.396890	+	0.917866i	$0.370089\pi$
$90$		0			0
$91$	−3.22782	+	1.33701i	−0.338367	+	0.140156i
$92$		0			0
$93$	−3.56970	+	8.61802i	−0.370161	+	0.893647i
$94$		0			0
$95$	−7.49083			−0.768543
$96$		0			0
$97$	−3.30926			−0.336005			−0.168002	−	0.985787i	$-0.553732\pi$
$97$	−3.30926			−0.336005			−0.168002	+	0.985787i	$0.553732\pi$
$98$		0			0
$99$	−0.657053	+	1.58627i	−0.0660363	+	0.159426i
$100$		0			0
$101$	2.59134	−	1.07337i	0.257848	−	0.106804i	−0.250015	−	0.968242i	$-0.580436\pi$
$101$	2.59134	−	1.07337i	0.257848	−	0.106804i	0.507863	+	0.861438i	$0.330436\pi$
$102$		0			0
$103$	−12.7576	+	12.7576i	−1.25705	+	1.25705i	−0.304550	+	0.952496i	$0.598506\pi$
$103$	−12.7576	+	12.7576i	−1.25705	+	1.25705i	−0.952496	+	0.304550i	$0.901494\pi$
$104$		0			0
$105$	−1.02675	−	1.02675i	−0.100200	−	0.100200i
$106$		0			0
$107$	−3.17275	−	7.65969i	−0.306721	−	0.740490i	−0.999807	−	0.0196351i	$-0.993750\pi$
$107$	−3.17275	−	7.65969i	−0.306721	−	0.740490i	0.693086	−	0.720855i	$-0.256250\pi$
$108$		0			0
$109$	−10.8733	−	4.50386i	−1.04147	−	0.431391i	−0.204631	−	0.978839i	$-0.565599\pi$
$109$	−10.8733	−	4.50386i	−1.04147	−	0.431391i	−0.836840	+	0.547448i	$0.815599\pi$
$110$		0			0
$111$		−	0.877093i		−	0.0832500i
$112$		0			0
$113$			1.05718i			0.0994515i	0.998763	+	0.0497257i	$0.0158347\pi$
$113$			1.05718i			0.0994515i	−0.998763	+	0.0497257i	$0.984165\pi$
$114$		0			0
$115$	−1.02873	−	0.426114i	−0.0959296	−	0.0397353i
$116$		0			0
$117$	1.60389	+	3.87213i	0.148280	+	0.357979i
$118$		0			0
$119$	−4.69494	−	4.69494i	−0.430385	−	0.430385i
$120$		0			0
$121$	5.69365	−	5.69365i	0.517605	−	0.517605i
$122$		0			0
$123$	8.68894	−	3.59908i	0.783456	−	0.324518i
$124$		0			0
$125$	4.64336	−	11.2101i	0.415315	−	1.00266i
$126$		0			0
$127$	7.93736			0.704327			0.352163	−	0.935939i	$-0.385446\pi$
$127$	7.93736			0.704327			0.352163	+	0.935939i	$0.385446\pi$
$128$		0			0
$129$	5.81193			0.511712
$130$		0			0
$131$	−7.20756	+	17.4006i	−0.629727	+	1.52030i	0.210234	+	0.977651i	$0.432577\pi$
$131$	−7.20756	+	17.4006i	−0.629727	+	1.52030i	−0.839962	+	0.542645i	$0.817423\pi$
$132$		0			0
$133$	3.31195	−	1.37185i	0.287182	−	0.118955i
$134$		0			0
$135$	−1.23170	+	1.23170i	−0.106008	+	0.106008i
$136$		0			0
$137$	0.305733	+	0.305733i	0.0261205	+	0.0261205i	0.720046	−	0.693926i	$-0.244120\pi$
$137$	0.305733	+	0.305733i	0.0261205	+	0.0261205i	−0.693926	+	0.720046i	$0.744120\pi$
$138$		0			0
$139$	6.72200	+	16.2283i	0.570153	+	1.37647i	0.901425	+	0.432935i	$0.142522\pi$
$139$	6.72200	+	16.2283i	0.570153	+	1.37647i	−0.331273	+	0.943535i	$0.607478\pi$
$140$		0			0
$141$	7.85759	+	3.25472i	0.661729	+	0.274097i
$142$		0			0
$143$			7.19608i			0.601766i
$144$		0			0
$145$			7.69843i			0.639320i
$146$		0			0
$147$	−5.82516	−	2.41286i	−0.480451	−	0.199009i
$148$		0			0
$149$	−2.14465	−	5.17765i	−0.175697	−	0.424170i	0.811359	−	0.584549i	$-0.198728\pi$
$149$	−2.14465	−	5.17765i	−0.175697	−	0.424170i	−0.987056	+	0.160379i	$0.948728\pi$
$150$		0			0
$151$	−10.2384	−	10.2384i	−0.833193	−	0.833193i	0.154759	−	0.987952i	$-0.450540\pi$
$151$	−10.2384	−	10.2384i	−0.833193	−	0.833193i	−0.987952	+	0.154759i	$0.950540\pi$
$152$		0			0
$153$	−5.63212	+	5.63212i	−0.455330	+	0.455330i
$154$		0			0
$155$	−15.0116	+	6.21803i	−1.20576	+	0.499444i
$156$		0			0
$157$	−4.64097	+	11.2043i	−0.370389	+	0.894199i	0.623295	+	0.781987i	$0.285794\pi$
$157$	−4.64097	+	11.2043i	−0.370389	+	0.894199i	−0.993684	+	0.112212i	$0.964206\pi$
$158$		0			0
$159$	2.89428			0.229532
$160$		0			0
$161$	0.532873			0.0419963
$162$		0			0
$163$	0.981891	−	2.37049i	0.0769076	−	0.185671i	−0.880750	−	0.473582i	$-0.842961\pi$
$163$	0.981891	−	2.37049i	0.0769076	−	0.185671i	0.957657	+	0.287911i	$0.0929607\pi$
$164$		0			0
$165$	−2.76310	+	1.14451i	−0.215107	+	0.0891004i
$166$		0			0
$167$	6.83087	−	6.83087i	0.528588	−	0.528588i	−0.391563	−	0.920151i	$-0.628066\pi$
$167$	6.83087	−	6.83087i	0.528588	−	0.528588i	0.920151	+	0.391563i	$0.128066\pi$
$168$		0			0
$169$	3.22856	+	3.22856i	0.248351	+	0.248351i
$170$		0			0
$171$	−1.64569	−	3.97306i	−0.125849	−	0.303827i
$172$		0			0
$173$	−2.76667	−	1.14599i	−0.210346	−	0.0871282i	0.275023	−	0.961438i	$-0.411315\pi$
$173$	−2.76667	−	1.14599i	−0.210346	−	0.0871282i	−0.485369	+	0.874310i	$0.661315\pi$
$174$		0			0
$175$			1.63871i			0.123875i
$176$		0			0
$177$		−	2.08036i		−	0.156369i
$178$		0			0
$179$	−13.3854	−	5.54441i	−1.00047	−	0.414409i	−0.178501	−	0.983940i	$-0.557125\pi$
$179$	−13.3854	−	5.54441i	−1.00047	−	0.414409i	−0.821970	+	0.569531i	$0.807125\pi$
$180$		0			0
$181$	9.03488	+	21.8121i	0.671557	+	1.62128i	0.778965	+	0.627068i	$0.215745\pi$
$181$	9.03488	+	21.8121i	0.671557	+	1.62128i	−0.107407	+	0.994215i	$0.534255\pi$
$182$		0			0
$183$	8.69251	+	8.69251i	0.642569	+	0.642569i
$184$		0			0
$185$	1.08032	−	1.08032i	0.0794266	−	0.0794266i
$186$		0			0
$187$	−12.6346	+	5.23344i	−0.923937	+	0.382707i
$188$		0			0
$189$	0.319006	−	0.770147i	0.0232042	−	0.0560200i
$190$		0			0
$191$	−15.9720			−1.15570			−0.577848	−	0.816144i	$-0.696107\pi$
$191$	−15.9720			−1.15570			−0.577848	+	0.816144i	$0.696107\pi$
$192$		0			0
$193$	0.411129			0.0295937			0.0147968	−	0.999891i	$-0.495290\pi$
$193$	0.411129			0.0295937			0.0147968	+	0.999891i	$0.495290\pi$
$194$		0			0
$195$	−2.79380	+	6.74483i	−0.200068	+	0.483007i
$196$		0			0
$197$	4.09727	−	1.69715i	0.291919	−	0.120917i	−0.231918	−	0.972735i	$-0.574500\pi$
$197$	4.09727	−	1.69715i	0.291919	−	0.120917i	0.523837	+	0.851819i	$0.324500\pi$
$198$		0			0
$199$	8.65705	−	8.65705i	0.613682	−	0.613682i	−0.330221	−	0.943904i	$-0.607123\pi$
$199$	8.65705	−	8.65705i	0.613682	−	0.613682i	0.943904	+	0.330221i	$0.107123\pi$
$200$		0			0
$201$	8.40296	+	8.40296i	0.592699	+	0.592699i
$202$		0			0
$203$	−1.40987	−	3.40373i	−0.0989535	−	0.238895i
$204$		0			0
$205$	15.1352	+	6.26920i	1.05709	+	0.437860i
$206$		0			0
$207$		−	0.639242i		−	0.0444304i
$208$		0			0
$209$		−	7.38363i		−	0.510737i
$210$		0			0
$211$	−4.51505	−	1.87019i	−0.310829	−	0.128749i	0.221816	−	0.975089i	$-0.428802\pi$
$211$	−4.51505	−	1.87019i	−0.310829	−	0.128749i	−0.532644	+	0.846339i	$0.678802\pi$
$212$		0			0
$213$	−4.92459	−	11.8890i	−0.337427	−	0.814622i
$214$		0			0
$215$	7.15857	+	7.15857i	0.488210	+	0.488210i
$216$		0			0
$217$	5.49839	−	5.49839i	0.373255	−	0.373255i
$218$		0			0
$219$	−2.15651	+	0.893256i	−0.145723	+	0.0603606i
$220$		0			0
$221$	−12.7750	+	30.8416i	−0.859341	+	2.07463i
$222$		0			0
$223$	8.07183			0.540530			0.270265	−	0.962786i	$-0.412889\pi$
$223$	8.07183			0.540530			0.270265	+	0.962786i	$0.412889\pi$
$224$		0			0
$225$	1.96582			0.131054
$226$		0			0
$227$	−0.993337	+	2.39813i	−0.0659301	+	0.159169i	−0.953410	−	0.301676i	$-0.902454\pi$
$227$	−0.993337	+	2.39813i	−0.0659301	+	0.159169i	0.887480	+	0.460846i	$0.152454\pi$
$228$		0			0
$229$	−9.46203	+	3.91930i	−0.625269	+	0.258995i	−0.672741	−	0.739878i	$-0.734883\pi$
$229$	−9.46203	+	3.91930i	−0.625269	+	0.258995i	0.0474727	+	0.998873i	$0.484883\pi$
$230$		0			0
$231$	1.01206	−	1.01206i	0.0665884	−	0.0665884i
$232$		0			0
$233$	5.94847	+	5.94847i	0.389698	+	0.389698i	0.874580	−	0.484882i	$-0.161137\pi$
$233$	5.94847	+	5.94847i	0.389698	+	0.389698i	−0.484882	+	0.874580i	$0.661137\pi$
$234$		0			0
$235$	5.66937	+	13.6871i	0.369829	+	0.892846i
$236$		0			0
$237$	0.536284	+	0.222136i	0.0348354	+	0.0144293i
$238$		0			0
$239$			2.07158i			0.134000i	0.997753	+	0.0669998i	$0.0213427\pi$
$239$			2.07158i			0.134000i	−0.997753	+	0.0669998i	$0.978657\pi$
$240$		0			0
$241$			5.10031i			0.328540i	0.986415	+	0.164270i	$0.0525268\pi$
$241$			5.10031i			0.328540i	−0.986415	+	0.164270i	$0.947473\pi$
$242$		0			0
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$		0			0
$245$	−4.20294	−	10.1468i	−0.268516	−	0.648255i
$246$		0			0
$247$	−12.7447	−	12.7447i	−0.810925	−	0.810925i
$248$		0			0
$249$	−2.55308	+	2.55308i	−0.161795	+	0.161795i
$250$		0			0
$251$	15.6741	−	6.49243i	0.989341	−	0.409798i	0.171463	−	0.985191i	$-0.445151\pi$
$251$	15.6741	−	6.49243i	0.989341	−	0.409798i	0.817878	+	0.575392i	$0.195151\pi$
$252$		0			0
$253$	0.420016	−	1.01401i	0.0264062	−	0.0637501i
$254$		0			0
$255$	−13.8742			−0.868836
$256$		0			0
$257$	12.7920			0.797942			0.398971	−	0.916964i	$-0.369367\pi$
$257$	12.7920			0.797942			0.398971	+	0.916964i	$0.369367\pi$
$258$		0			0
$259$	−0.279798	+	0.675491i	−0.0173858	+	0.0419730i
$260$		0			0
$261$	−4.08316	+	1.69130i	−0.252741	+	0.104689i
$262$		0			0
$263$	5.06752	−	5.06752i	0.312477	−	0.312477i	−0.533392	−	0.845868i	$-0.679083\pi$
$263$	5.06752	−	5.06752i	0.312477	−	0.312477i	0.845868	+	0.533392i	$0.179083\pi$
$264$		0			0
$265$	3.56490	+	3.56490i	0.218990	+	0.218990i
$266$		0			0
$267$	−2.65991	−	6.42160i	−0.162784	−	0.392995i
$268$		0			0
$269$	16.4527	+	6.81494i	1.00314	+	0.415514i	0.822948	−	0.568117i	$-0.192328\pi$
$269$	16.4527	+	6.81494i	1.00314	+	0.415514i	0.180192	+	0.983631i	$0.442328\pi$
$270$		0			0
$271$			6.40145i			0.388860i	0.980916	+	0.194430i	$0.0622857\pi$
$271$			6.40145i			0.388860i	−0.980916	+	0.194430i	$0.937714\pi$
$272$		0			0
$273$		−	3.49376i		−	0.211452i
$274$		0			0
$275$	3.11831	+	1.29165i	0.188041	+	0.0778892i
$276$		0			0
$277$	−2.00777	−	4.84718i	−0.120635	−	0.291239i	0.852014	−	0.523519i	$-0.175381\pi$
$277$	−2.00777	−	4.84718i	−0.120635	−	0.291239i	−0.972649	+	0.232281i	$0.925381\pi$
$278$		0			0
$279$	−6.59595	−	6.59595i	−0.394889	−	0.394889i
$280$		0			0
$281$	9.02739	−	9.02739i	0.538529	−	0.538529i	−0.384568	−	0.923097i	$-0.625649\pi$
$281$	9.02739	−	9.02739i	0.538529	−	0.538529i	0.923097	+	0.384568i	$0.125649\pi$
$282$		0			0
$283$	7.91426	−	3.27819i	0.470454	−	0.194868i	−0.134845	−	0.990867i	$-0.543054\pi$
$283$	7.91426	−	3.27819i	0.470454	−	0.194868i	0.605299	+	0.795998i	$0.293054\pi$
$284$		0			0
$285$	2.86662	−	6.92063i	0.169804	−	0.409943i
$286$		0			0
$287$	−7.83989			−0.462774
$288$		0			0
$289$	−46.4416			−2.73186
$290$		0			0
$291$	1.26640	−	3.05736i	0.0742377	−	0.179226i
$292$		0			0
$293$	1.10609	−	0.458156i	0.0646183	−	0.0267658i	−0.350140	−	0.936697i	$-0.613866\pi$
$293$	1.10609	−	0.458156i	0.0646183	−	0.0267658i	0.414758	+	0.909932i	$0.363866\pi$
$294$		0			0
$295$	2.56238	−	2.56238i	0.149188	−	0.149188i
$296$		0			0
$297$	−1.21408	−	1.21408i	−0.0704478	−	0.0704478i
$298$		0			0
$299$	−1.02527	−	2.47523i	−0.0592931	−	0.143146i
$300$		0			0
$301$	−4.47604	−	1.85404i	−0.257995	−	0.106865i
$302$		0			0
$303$			2.80485i			0.161134i
$304$		0			0
$305$			21.4132i			1.22612i
$306$		0			0
$307$	10.0335	+	4.15602i	0.572643	+	0.237197i	0.650164	−	0.759794i	$-0.274700\pi$
$307$	10.0335	+	4.15602i	0.572643	+	0.237197i	−0.0775205	+	0.996991i	$0.524700\pi$
$308$		0			0
$309$	−6.90438	−	16.6686i	−0.392776	−	0.948246i
$310$		0			0
$311$	11.1912	+	11.1912i	0.634595	+	0.634595i	0.949217	−	0.314622i	$-0.101878\pi$
$311$	11.1912	+	11.1912i	0.634595	+	0.634595i	−0.314622	+	0.949217i	$0.601878\pi$
$312$		0			0
$313$	15.1491	−	15.1491i	0.856279	−	0.856279i	−0.134619	−	0.990897i	$-0.542981\pi$
$313$	15.1491	−	15.1491i	0.856279	−	0.856279i	0.990897	+	0.134619i	$0.0429809\pi$
$314$		0			0
$315$	1.34151	−	0.555673i	0.0755857	−	0.0313086i
$316$		0			0
$317$	2.50910	−	6.05751i	0.140925	−	0.340223i	−0.837621	−	0.546252i	$-0.816054\pi$
$317$	2.50910	−	6.05751i	0.140925	−	0.340223i	0.978546	+	0.206029i	$0.0660540\pi$
$318$		0			0
$319$	−7.58826			−0.424861
$320$		0			0
$321$	8.29078			0.462746
$322$		0			0
$323$	13.1080	−	31.6455i	0.729348	−	1.76080i
$324$		0			0
$325$	7.61191	−	3.15295i	0.422233	−	0.174894i
$326$		0			0
$327$	8.32204	−	8.32204i	0.460210	−	0.460210i
$328$		0			0
$329$	−5.01323	−	5.01323i	−0.276388	−	0.276388i
$330$		0			0
$331$	7.52873	+	18.1760i	0.413817	+	0.999042i	0.984103	+	0.177596i	$0.0568321\pi$
$331$	7.52873	+	18.1760i	0.413817	+	0.999042i	−0.570287	+	0.821446i	$0.693168\pi$
$332$		0			0
$333$	0.810329	+	0.335649i	0.0444057	+	0.0183935i
$334$		0			0
$335$			20.6999i			1.13096i
$336$		0			0
$337$		−	29.9155i		−	1.62960i	−0.579741	−	0.814801i	$-0.696846\pi$
$337$		−	29.9155i		−	1.62960i	0.579741	−	0.814801i	$-0.303154\pi$
$338$		0			0
$339$	−0.976711	−	0.404567i	−0.0530476	−	0.0219731i
$340$		0			0
$341$	−6.12904	−	14.7968i	−0.331906	−	0.801293i
$342$		0			0
$343$	7.84263	+	7.84263i	0.423462	+	0.423462i
$344$		0			0
$345$	0.787356	−	0.787356i	0.0423898	−	0.0423898i
$346$		0			0
$347$	18.9783	−	7.86106i	1.01881	−	0.422004i	0.190147	−	0.981756i	$-0.439103\pi$
$347$	18.9783	−	7.86106i	1.01881	−	0.422004i	0.828660	+	0.559752i	$0.189103\pi$
$348$		0			0
$349$	2.93498	−	7.08568i	0.157106	−	0.379288i	−0.825653	−	0.564178i	$-0.809193\pi$
$349$	2.93498	−	7.08568i	0.157106	−	0.379288i	0.982759	+	0.184891i	$0.0591931\pi$
$350$		0			0
$351$	−4.19117			−0.223708
$352$		0			0
$353$	−28.6693			−1.52591			−0.762956	−	0.646450i	$-0.776253\pi$
$353$	−28.6693			−1.52591			−0.762956	+	0.646450i	$0.776253\pi$
$354$		0			0
$355$	8.57810	−	20.7094i	0.455278	−	1.09914i
$356$		0			0
$357$	6.13424	−	2.54089i	0.324658	−	0.134478i
$358$		0			0
$359$	13.9965	−	13.9965i	0.738709	−	0.738709i	−0.233619	−	0.972328i	$-0.575057\pi$
$359$	13.9965	−	13.9965i	0.738709	−	0.738709i	0.972328	+	0.233619i	$0.0750569\pi$
$360$		0			0
$361$	−0.358168	−	0.358168i	−0.0188510	−	0.0188510i
$362$		0			0
$363$	3.08138	+	7.43911i	0.161731	+	0.390452i
$364$		0			0
$365$	−3.75641	−	1.55595i	−0.196619	−	0.0814424i
$366$		0			0
$367$		−	11.6706i		−	0.609203i	−0.952480	−	0.304601i	$-0.901477\pi$
$367$		−	11.6706i		−	0.609203i	0.952480	−	0.304601i	$-0.0985232\pi$
$368$		0			0
$369$			9.40484i			0.489597i
$370$		0			0
$371$	−2.22902	−	0.923292i	−0.115725	−	0.0479350i
$372$		0			0
$373$	−10.5778	−	25.5370i	−0.547697	−	1.32226i	−0.919187	−	0.393820i	$-0.871153\pi$
$373$	−10.5778	−	25.5370i	−0.547697	−	1.32226i	0.371491	−	0.928437i	$-0.378847\pi$
$374$		0			0
$375$	8.57982	+	8.57982i	0.443060	+	0.443060i
$376$		0			0
$377$	−13.0979	+	13.0979i	−0.674575	+	0.674575i
$378$		0			0
$379$	11.2755	−	4.67048i	0.579185	−	0.239906i	−0.0738049	−	0.997273i	$-0.523514\pi$
$379$	11.2755	−	4.67048i	0.579185	−	0.239906i	0.652990	+	0.757366i	$0.273514\pi$
$380$		0			0
$381$	−3.03750	+	7.33317i	−0.155616	+	0.375689i
$382$		0			0
$383$	14.2648			0.728897			0.364448	−	0.931224i	$-0.381258\pi$
$383$	14.2648			0.728897			0.364448	+	0.931224i	$0.381258\pi$
$384$		0			0
$385$	2.49310			0.127060
$386$		0			0
$387$	−2.22413	+	5.36952i	−0.113059	+	0.272948i
$388$		0			0
$389$	−16.9675	+	7.02815i	−0.860284	+	0.356341i	−0.768819	−	0.639467i	$-0.779155\pi$
$389$	−16.9675	+	7.02815i	−0.860284	+	0.356341i	−0.0914656	+	0.995808i	$0.529155\pi$
$390$		0			0
$391$	3.60029	−	3.60029i	0.182074	−	0.182074i
$392$		0			0
$393$	−13.3178	−	13.3178i	−0.671796	−	0.671796i
$394$		0			0
$395$	0.386937	+	0.934148i	0.0194689	+	0.0470021i
$396$		0			0
$397$	−12.7413	−	5.27761i	−0.639466	−	0.264875i	0.0393030	−	0.999227i	$-0.487486\pi$
$397$	−12.7413	−	5.27761i	−0.639466	−	0.264875i	−0.678769	+	0.734352i	$0.737486\pi$
$398$		0			0
$399$			3.58482i			0.179466i
$400$		0			0
$401$		−	20.6525i		−	1.03134i	−0.856788	−	0.515669i	$-0.827543\pi$
$401$		−	20.6525i		−	1.03134i	0.856788	−	0.515669i	$-0.172457\pi$
$402$		0			0
$403$	−36.1196	−	14.9612i	−1.79924	−	0.745271i
$404$		0			0
$405$	−0.666593	−	1.60930i	−0.0331233	−	0.0799666i
$406$		0			0
$407$	1.06486	+	1.06486i	0.0527831	+	0.0527831i
$408$		0			0
$409$	6.38072	−	6.38072i	0.315506	−	0.315506i	−0.531532	−	0.847038i	$-0.678383\pi$
$409$	6.38072	−	6.38072i	0.315506	−	0.315506i	0.847038	+	0.531532i	$0.178383\pi$
$410$		0			0
$411$	−0.399459	+	0.165462i	−0.0197039	+	0.00816161i
$412$		0			0
$413$	−0.663645	+	1.60218i	−0.0326558	+	0.0788382i
$414$		0			0
$415$	−6.28927			−0.308728
$416$		0			0
$417$	−17.5654			−0.860183
$418$		0			0
$419$	−8.46204	+	20.4292i	−0.413398	+	0.998030i	0.570821	+	0.821075i	$0.306625\pi$
$419$	−8.46204	+	20.4292i	−0.413398	+	0.998030i	−0.984219	+	0.176956i	$0.943375\pi$
$420$		0			0
$421$	28.2742	−	11.7116i	1.37800	−	0.570786i	0.434054	−	0.900887i	$-0.357083\pi$
$421$	28.2742	−	11.7116i	1.37800	−	0.570786i	0.943946	+	0.330100i	$0.107083\pi$
$422$		0			0
$423$	−6.01394	+	6.01394i	−0.292408	+	0.292408i
$424$		0			0
$425$	11.0717	+	11.0717i	0.537057	+	0.537057i
$426$		0			0
$427$	−3.92156	−	9.46748i	−0.189777	−	0.458163i
$428$		0			0
$429$	−6.64831	−	2.75382i	−0.320983	−	0.132956i
$430$		0			0
$431$			8.30038i			0.399815i	0.979815	+	0.199908i	$0.0640642\pi$
$431$			8.30038i			0.399815i	−0.979815	+	0.199908i	$0.935936\pi$
$432$		0			0
$433$			29.4261i			1.41413i	0.707150	+	0.707063i	$0.249980\pi$
$433$			29.4261i			1.41413i	−0.707150	+	0.707063i	$0.750020\pi$
$434$		0			0
$435$	−7.11242	−	2.94606i	−0.341014	−	0.141253i
$436$		0			0
$437$	1.05200	+	2.53974i	0.0503238	+	0.121492i
$438$		0			0
$439$	−20.3138	−	20.3138i	−0.969524	−	0.969524i	0.0300252	−	0.999549i	$-0.490441\pi$
$439$	−20.3138	−	20.3138i	−0.969524	−	0.969524i	−0.999549	+	0.0300252i	$0.990441\pi$
$440$		0			0
$441$	4.45838	−	4.45838i	0.212304	−	0.212304i
$442$		0			0
$443$	18.1169	−	7.50428i	0.860762	−	0.356539i	0.0917565	−	0.995781i	$-0.470752\pi$
$443$	18.1169	−	7.50428i	0.860762	−	0.356539i	0.769005	+	0.639242i	$0.220752\pi$
$444$		0			0
$445$	4.63328	−	11.1857i	0.219638	−	0.530254i
$446$		0			0
$447$	5.60425			0.265072
$448$		0			0
$449$	−8.20853			−0.387384			−0.193692	−	0.981062i	$-0.562046\pi$
$449$	−8.20853			−0.387384			−0.193692	+	0.981062i	$0.562046\pi$
$450$		0			0
$451$	−6.17948	+	14.9186i	−0.290981	+	0.702489i
$452$		0			0
$453$	13.3772	−	5.54101i	0.628514	−	0.260339i
$454$		0			0
$455$	4.30328	−	4.30328i	0.201741	−	0.201741i
$456$		0			0
$457$	−12.2056	−	12.2056i	−0.570953	−	0.570953i	0.361442	−	0.932395i	$-0.382285\pi$
$457$	−12.2056	−	12.2056i	−0.570953	−	0.570953i	−0.932395	+	0.361442i	$0.882285\pi$
$458$		0			0
$459$	−3.04808	−	7.35872i	−0.142272	−	0.343476i
$460$		0			0
$461$	28.6007	+	11.8468i	1.33207	+	0.551761i	0.931245	−	0.364394i	$-0.118724\pi$
$461$	28.6007	+	11.8468i	1.33207	+	0.551761i	0.400824	+	0.916155i	$0.368724\pi$
$462$		0			0
$463$			22.9354i			1.06590i	0.846148	+	0.532948i	$0.178916\pi$
$463$			22.9354i			1.06590i	−0.846148	+	0.532948i	$0.821084\pi$
$464$		0			0
$465$		−	16.2485i		−	0.753506i
$466$		0			0
$467$	20.6535	+	8.55495i	0.955729	+	0.395876i	0.805381	−	0.592757i	$-0.201961\pi$
$467$	20.6535	+	8.55495i	0.955729	+	0.395876i	0.150348	+	0.988633i	$0.451961\pi$
$468$		0			0
$469$	−3.79093	−	9.15210i	−0.175049	−	0.422605i
$470$		0			0
$471$	−8.57539	−	8.57539i	−0.395133	−	0.395133i
$472$		0			0
$473$	−7.05612	+	7.05612i	−0.324441	+	0.324441i
$474$		0			0
$475$	−7.81030	+	3.23513i	−0.358361	+	0.148438i
$476$		0			0
$477$	−1.10759	+	2.67397i	−0.0507133	+	0.122433i
$478$		0			0
$479$	41.8313			1.91132			0.955661	−	0.294468i	$-0.0951424\pi$
$479$	41.8313			1.91132			0.955661	+	0.294468i	$0.0951424\pi$
$480$		0			0
$481$	3.67604			0.167613
$482$		0			0
$483$	−0.203922	+	0.492310i	−0.00927876	+	0.0224009i
$484$		0			0
$485$	5.32559	−	2.20593i	0.241822	−	0.100166i
$486$		0			0
$487$	−4.02796	+	4.02796i	−0.182524	+	0.182524i	−0.792455	−	0.609931i	$-0.791197\pi$
$487$	−4.02796	+	4.02796i	−0.182524	+	0.182524i	0.609931	+	0.792455i	$0.291197\pi$
$488$		0			0
$489$	1.81430	+	1.81430i	0.0820454	+	0.0820454i
$490$		0			0
$491$	15.7614	+	38.0514i	0.711301	+	1.71723i	0.696724	+	0.717340i	$0.254640\pi$
$491$	15.7614	+	38.0514i	0.711301	+	1.71723i	0.0145778	+	0.999894i	$0.495360\pi$
$492$		0			0
$493$	−32.5225	−	13.4712i	−1.46474	−	0.606714i
$494$		0			0
$495$		−	2.99076i		−	0.134425i
$496$		0			0
$497$			10.7273i			0.481184i
$498$		0			0
$499$	7.53276	+	3.12017i	0.337213	+	0.139678i	0.544863	−	0.838525i	$-0.316582\pi$
$499$	7.53276	+	3.12017i	0.337213	+	0.139678i	−0.207650	+	0.978203i	$0.566582\pi$
$500$		0			0
$501$	3.69684	+	8.92496i	0.165163	+	0.398738i
$502$		0			0
$503$	−10.0612	−	10.0612i	−0.448607	−	0.448607i	0.446284	−	0.894891i	$-0.352747\pi$
$503$	−10.0612	−	10.0612i	−0.448607	−	0.448607i	−0.894891	+	0.446284i	$0.852747\pi$
$504$		0			0
$505$	−3.45474	+	3.45474i	−0.153734	+	0.153734i
$506$		0			0
$507$	−4.21832	+	1.74728i	−0.187342	+	0.0775996i
$508$		0			0
$509$	−5.89292	+	14.2268i	−0.261199	+	0.630590i	−0.999013	−	0.0444138i	$-0.985858\pi$
$509$	−5.89292	+	14.2268i	−0.261199	+	0.630590i	0.737814	+	0.675004i	$0.235858\pi$
$510$		0			0
$511$	1.94578			0.0860765
$512$		0			0
$513$	4.30040			0.189867
$514$		0			0
$515$	12.0267	−	29.0350i	0.529958	−	1.27943i
$516$		0			0
$517$	−13.4912	+	5.58824i	−0.593342	+	0.245770i
$518$		0			0
$519$	2.11752	−	2.11752i	0.0929487	−	0.0929487i
$520$		0			0
$521$	11.9481	+	11.9481i	0.523456	+	0.523456i	0.918613	−	0.395158i	$-0.129310\pi$
$521$	11.9481	+	11.9481i	0.523456	+	0.523456i	−0.395158	+	0.918613i	$0.629310\pi$
$522$		0			0
$523$	−6.15336	−	14.8555i	−0.269068	−	0.649587i	0.730372	−	0.683049i	$-0.239347\pi$
$523$	−6.15336	−	14.8555i	−0.269068	−	0.649587i	−0.999440	+	0.0334625i	$0.989347\pi$
$524$		0			0
$525$	−1.51397	−	0.627107i	−0.0660750	−	0.0273692i
$526$		0			0
$527$		−	74.2983i		−	3.23649i
$528$		0			0
$529$		−	22.5914i		−	0.982233i
$530$		0			0
$531$	1.92200	+	0.796118i	0.0834076	+	0.0345486i
$532$		0			0
$533$	15.0843	+	36.4168i	0.653375	+	1.57739i
$534$		0			0
$535$	10.2118	+	10.2118i	0.441494	+	0.441494i
$536$		0			0
$537$	10.2447	−	10.2447i	0.442093	−	0.442093i
$538$		0			0
$539$	10.0016	−	4.14279i	0.430799	−	0.178443i
$540$		0			0
$541$	−8.64537	+	20.8718i	−0.371693	+	0.897347i	0.621770	+	0.783200i	$0.286414\pi$
$541$	−8.64537	+	20.8718i	−0.371693	+	0.897347i	−0.993464	+	0.114148i	$0.963586\pi$
$542$		0			0
$543$	−23.6093			−1.01317
$544$		0			0
$545$	20.5006			0.878148
$546$		0			0
$547$	10.1653	−	24.5412i	0.434637	−	1.04931i	−0.543137	−	0.839644i	$-0.682764\pi$
$547$	10.1653	−	24.5412i	0.434637	−	1.04931i	0.977774	−	0.209662i	$-0.0672363\pi$
$548$		0			0
$549$	−11.3573	+	4.70435i	−0.484718	+	0.200777i
$550$		0			0
$551$	13.4393	−	13.4393i	0.572532	−	0.572532i
$552$		0			0
$553$	−0.342155	−	0.342155i	−0.0145499	−	0.0145499i
$554$		0			0
$555$	0.584664	+	1.41150i	0.0248176	+	0.0599150i
$556$		0			0
$557$	−40.0425	−	16.5861i	−1.69666	−	0.702778i	−0.696761	−	0.717303i	$-0.745376\pi$
$557$	−40.0425	−	16.5861i	−1.69666	−	0.702778i	−0.999894	+	0.0145256i	$0.995376\pi$
$558$		0			0
$559$			24.3588i			1.03027i
$560$		0			0
$561$		−	13.6756i		−	0.577386i
$562$		0			0
$563$	−18.6724	−	7.73435i	−0.786947	−	0.325964i	−0.0472316	−	0.998884i	$-0.515040\pi$
$563$	−18.6724	−	7.73435i	−0.786947	−	0.325964i	−0.739715	+	0.672920i	$0.765040\pi$
$564$		0			0
$565$	−0.704711	−	1.70132i	−0.0296474	−	0.0715752i
$566$		0			0
$567$	0.589445	+	0.589445i	0.0247544	+	0.0247544i
$568$		0			0
$569$	8.77986	−	8.77986i	0.368071	−	0.368071i	−0.498702	−	0.866773i	$-0.666190\pi$
$569$	8.77986	−	8.77986i	0.368071	−	0.368071i	0.866773	+	0.498702i	$0.166190\pi$
$570$		0			0
$571$	−23.2136	+	9.61539i	−0.971459	+	0.402392i	−0.811255	−	0.584692i	$-0.801215\pi$
$571$	−23.2136	+	9.61539i	−0.971459	+	0.402392i	−0.160204	+	0.987084i	$0.551215\pi$
$572$		0			0
$573$	6.11224	−	14.7562i	0.255342	−	0.616451i
$574$		0			0
$575$	−1.25663			−0.0524052
$576$		0			0
$577$	32.9671			1.37244			0.686220	−	0.727394i	$-0.259269\pi$
$577$	32.9671			1.37244			0.686220	+	0.727394i	$0.259269\pi$
$578$		0			0
$579$	−0.157332	+	0.379833i	−0.00653850	+	0.0157853i
$580$		0			0
$581$	2.78069	−	1.15180i	0.115363	−	0.0477848i
$582$		0			0
$583$	−3.51388	+	3.51388i	−0.145530	+	0.145530i
$584$		0			0
$585$	−5.16227	−	5.16227i	−0.213434	−	0.213434i
$586$		0			0
$587$	6.05934	+	14.6285i	0.250096	+	0.603785i	0.998211	−	0.0597837i	$-0.0190411\pi$
$587$	6.05934	+	14.6285i	0.250096	+	0.603785i	−0.748115	+	0.663569i	$0.769041\pi$
$588$		0			0
$589$	37.0610	+	15.3512i	1.52707	+	0.632533i
$590$		0			0
$591$			4.43486i			0.182426i
$592$		0			0
$593$			21.5942i			0.886767i	0.896332	+	0.443384i	$0.146222\pi$
$593$			21.5942i			0.886767i	−0.896332	+	0.443384i	$0.853778\pi$
$594$		0			0
$595$	10.6852	+	4.42595i	0.438050	+	0.181446i
$596$		0			0
$597$	4.68516	+	11.3110i	0.191751	+	0.462928i
$598$		0			0
$599$	16.6522	+	16.6522i	0.680392	+	0.680392i	0.960089	−	0.279696i	$-0.0902338\pi$
$599$	16.6522	+	16.6522i	0.680392	+	0.680392i	−0.279696	+	0.960089i	$0.590234\pi$
$600$		0			0
$601$	17.8090	−	17.8090i	0.726445	−	0.726445i	−0.243465	−	0.969910i	$-0.578284\pi$
$601$	17.8090	−	17.8090i	0.726445	−	0.726445i	0.969910	+	0.243465i	$0.0782840\pi$
$602$		0			0
$603$	−10.9790	+	4.54765i	−0.447099	+	0.185194i
$604$		0			0
$605$	−5.36743	+	12.9581i	−0.218217	+	0.526823i
$606$		0			0
$607$	2.08575			0.0846579			0.0423289	−	0.999104i	$-0.486522\pi$
$607$	2.08575			0.0846579			0.0423289	+	0.999104i	$0.486522\pi$
$608$		0			0
$609$	3.68417			0.149290
$610$		0			0
$611$	−13.6411	+	32.9325i	−0.551859	+	1.33231i
$612$		0			0
$613$	−23.3947	+	9.69039i	−0.944902	+	0.391391i	−0.801312	−	0.598246i	$-0.795865\pi$
$613$	−23.3947	+	9.69039i	−0.944902	+	0.391391i	−0.143590	+	0.989637i	$0.545865\pi$
$614$		0			0
$615$	−11.5840	+	11.5840i	−0.467111	+	0.467111i
$616$		0			0
$617$	−3.94760	−	3.94760i	−0.158924	−	0.158924i	0.623166	−	0.782090i	$-0.285846\pi$
$617$	−3.94760	−	3.94760i	−0.158924	−	0.158924i	−0.782090	+	0.623166i	$0.785846\pi$
$618$		0			0
$619$	−13.7586	−	33.2161i	−0.553004	−	1.33507i	−0.915212	−	0.402972i	$-0.867977\pi$
$619$	−13.7586	−	33.2161i	−0.553004	−	1.33507i	0.362208	−	0.932097i	$-0.382023\pi$
$620$		0			0
$621$	0.590582	+	0.244627i	0.0236993	+	0.00981655i
$622$		0			0
$623$			5.79410i			0.232136i
$624$		0			0
$625$			11.3065i			0.452259i
$626$		0			0
$627$	6.82159	+	2.82559i	0.272428	+	0.112843i
$628$		0			0
$629$	2.67345	+	6.45428i	0.106598	+	0.257349i
$630$		0			0
$631$	28.2524	+	28.2524i	1.12471	+	1.12471i	0.991024	+	0.133687i	$0.0426817\pi$
$631$	28.2524	+	28.2524i	1.12471	+	1.12471i	0.133687	+	0.991024i	$0.457318\pi$
$632$		0			0
$633$	3.45567	−	3.45567i	0.137350	−	0.137350i
$634$		0			0
$635$	−12.7736	+	5.29099i	−0.506904	+	0.209966i
$636$		0			0
$637$	10.1127	−	24.4142i	0.400680	−	0.967326i
$638$		0			0
$639$	12.8686			0.509073
$640$		0			0
$641$	9.34587			0.369140			0.184570	−	0.982819i	$-0.440911\pi$
$641$	9.34587			0.369140			0.184570	+	0.982819i	$0.440911\pi$
$642$		0			0
$643$	−14.3013	+	34.5265i	−0.563989	+	1.36159i	0.342562	+	0.939495i	$0.388705\pi$
$643$	−14.3013	+	34.5265i	−0.563989	+	1.36159i	−0.906551	+	0.422096i	$0.861295\pi$
$644$		0			0
$645$	−9.35312	+	3.87419i	−0.368279	+	0.152546i
$646$		0			0
$647$	−29.8159	+	29.8159i	−1.17218	+	1.17218i	−0.190496	+	0.981688i	$0.561010\pi$
$647$	−29.8159	+	29.8159i	−1.17218	+	1.17218i	−0.981688	+	0.190496i	$0.938990\pi$
$648$		0			0
$649$	2.52571	+	2.52571i	0.0991428	+	0.0991428i
$650$		0			0
$651$	2.97571	+	7.18400i	0.116627	+	0.281563i
$652$		0			0
$653$	30.3070	+	12.5536i	1.18600	+	0.491259i	0.886452	−	0.462821i	$-0.153163\pi$
$653$	30.3070	+	12.5536i	1.18600	+	0.491259i	0.299552	+	0.954080i	$0.403163\pi$
$654$		0			0
$655$		−	32.8072i		−	1.28188i
$656$		0			0
$657$		−	2.33419i		−	0.0910654i
$658$		0			0
$659$	23.8281	+	9.86994i	0.928212	+	0.384478i	0.795000	−	0.606609i	$-0.207471\pi$
$659$	23.8281	+	9.86994i	0.928212	+	0.384478i	0.133212	+	0.991088i	$0.457471\pi$
$660$		0			0
$661$	1.40604	+	3.39448i	0.0546886	+	0.132030i	0.948862	−	0.315690i	$-0.102236\pi$
$661$	1.40604	+	3.39448i	0.0546886	+	0.132030i	−0.894174	+	0.447720i	$0.852236\pi$
$662$		0			0
$663$	−23.6052	−	23.6052i	−0.916748	−	0.916748i
$664$		0			0
$665$	−4.41544	+	4.41544i	−0.171223	+	0.171223i
$666$		0			0
$667$	2.61013	−	1.08115i	0.101065	−	0.0418623i
$668$		0			0
$669$	−3.08896	+	7.45740i	−0.119426	+	0.288320i
$670$		0			0
$671$	−21.1067			−0.814817
$672$		0			0
$673$	19.4796			0.750885			0.375442	−	0.926846i	$-0.377491\pi$
$673$	19.4796			0.750885			0.375442	+	0.926846i	$0.377491\pi$
$674$		0			0
$675$	−0.752286	+	1.81618i	−0.0289555	+	0.0699047i
$676$		0			0
$677$	−19.1189	+	7.91933i	−0.734801	+	0.304364i	−0.718523	−	0.695503i	$-0.755182\pi$
$677$	−19.1189	+	7.91933i	−0.734801	+	0.304364i	−0.0162777	+	0.999868i	$0.505182\pi$
$678$		0			0
$679$	−1.95063	+	1.95063i	−0.0748583	+	0.0748583i
$680$		0			0
$681$	−1.83545	−	1.83545i	−0.0703345	−	0.0703345i
$682$		0			0
$683$	−8.46056	−	20.4256i	−0.323734	−	0.781564i	−0.999031	−	0.0440175i	$-0.985984\pi$
$683$	−8.46056	−	20.4256i	−0.323734	−	0.781564i	0.675296	−	0.737547i	$-0.264016\pi$
$684$		0			0
$685$	−0.695815	−	0.288216i	−0.0265857	−	0.0110122i
$686$		0			0
$687$		−	10.2416i		−	0.390743i
$688$		0			0
$689$			12.1304i			0.462132i
$690$		0			0
$691$	−14.6182	−	6.05507i	−0.556104	−	0.230346i	0.0868889	−	0.996218i	$-0.472307\pi$
$691$	−14.6182	−	6.05507i	−0.556104	−	0.230346i	−0.642993	+	0.765872i	$0.722307\pi$
$692$		0			0
$693$	0.547721	+	1.32231i	0.0208062	+	0.0502306i
$694$		0			0
$695$	−21.6354	−	21.6354i	−0.820677	−	0.820677i
$696$		0			0
$697$	−52.9692	+	52.9692i	−2.00635	+	2.00635i
$698$		0			0
$699$	−7.77206	+	3.21929i	−0.293966	+	0.121765i
$700$		0			0
$701$	9.53654	−	23.0232i	0.360190	−	0.869576i	−0.635082	−	0.772445i	$-0.719034\pi$
$701$	9.53654	−	23.0232i	0.360190	−	0.869576i	0.995272	−	0.0971307i	$-0.0309665\pi$
$702$		0			0
$703$	−3.77186			−0.142258
$704$		0			0
$705$	−14.8148			−0.557957
$706$		0			0
$707$	0.894763	−	2.16015i	0.0336510	−	0.0812407i
$708$		0			0
$709$	4.53151	−	1.87701i	0.170184	−	0.0704927i	−0.295965	−	0.955199i	$-0.595641\pi$
$709$	4.53151	−	1.87701i	0.170184	−	0.0704927i	0.466149	+	0.884706i	$0.345641\pi$
$710$		0			0
$711$	−0.410454	+	0.410454i	−0.0153932	+	0.0153932i
$712$		0			0
$713$	4.21641	+	4.21641i	0.157906	+	0.157906i
$714$		0			0
$715$	−4.79685	−	11.5806i	−0.179392	−	0.433091i
$716$		0			0
$717$	−1.91389	−	0.792761i	−0.0714757	−	0.0296062i
$718$		0			0
$719$			39.7315i			1.48173i	0.671652	+	0.740867i	$0.265585\pi$
$719$			39.7315i			1.48173i	−0.671652	+	0.740867i	$0.734415\pi$
$720$		0			0
$721$			15.0398i			0.560113i
$722$		0			0
$723$	−4.71207	−	1.95180i	−0.175244	−	0.0725883i
$724$		0			0
$725$	3.32479	+	8.02675i	0.123480	+	0.298106i
$726$		0			0
$727$	6.99691	+	6.99691i	0.259501	+	0.259501i	0.824851	−	0.565350i	$-0.191259\pi$
$727$	6.99691	+	6.99691i	0.259501	+	0.259501i	−0.565350	+	0.824851i	$0.691259\pi$
$728$		0			0
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$		0			0
$731$	−42.7683	+	17.7152i	−1.58184	+	0.655221i
$732$		0			0
$733$	−1.40532	+	3.39275i	−0.0519068	+	0.125314i	−0.947706	−	0.319145i	$-0.896604\pi$
$733$	−1.40532	+	3.39275i	−0.0519068	+	0.125314i	0.895799	+	0.444459i	$0.146604\pi$
$734$		0			0
$735$	10.9828			0.405107
$736$		0			0
$737$	−20.4037			−0.751578
$738$		0			0
$739$	−8.11566	+	19.5929i	−0.298539	+	0.720738i	0.701429	+	0.712740i	$0.252546\pi$
$739$	−8.11566	+	19.5929i	−0.298539	+	0.720738i	−0.999968	+	0.00799797i	$0.997454\pi$
$740$		0			0
$741$	16.6517	−	6.89737i	0.611717	−	0.253381i
$742$		0			0
$743$	−5.67248	+	5.67248i	−0.208103	+	0.208103i	−0.803461	−	0.595358i	$-0.797010\pi$
$743$	−5.67248	+	5.67248i	−0.208103	+	0.208103i	0.595358	+	0.803461i	$0.297010\pi$
$744$		0			0
$745$	6.90277	+	6.90277i	0.252898	+	0.252898i
$746$		0			0
$747$	−1.38172	−	3.33576i	−0.0505544	−	0.122049i
$748$		0			0
$749$	−6.38513	−	2.64481i	−0.233307	−	0.0966391i
$750$		0			0
$751$		−	14.2209i		−	0.518930i	−0.965753	−	0.259465i	$-0.916454\pi$
$751$		−	14.2209i		−	0.518930i	0.965753	−	0.259465i	$-0.0835462\pi$
$752$		0			0
$753$			16.9655i			0.618258i
$754$		0			0
$755$	23.3016	+	9.65183i	0.848031	+	0.351266i
$756$		0			0
$757$	6.45206	+	15.5767i	0.234504	+	0.566143i	0.996697	−	0.0812065i	$-0.0258773\pi$
$757$	6.45206	+	15.5767i	0.234504	+	0.566143i	−0.762193	+	0.647350i	$0.775877\pi$
$758$		0			0
$759$	0.776088	+	0.776088i	0.0281702	+	0.0281702i
$760$		0			0
$761$	−8.62429	+	8.62429i	−0.312630	+	0.312630i	−0.845928	−	0.533298i	$-0.820953\pi$
$761$	−8.62429	+	8.62429i	−0.312630	+	0.312630i	0.533298	+	0.845928i	$0.320953\pi$
$762$		0			0
$763$	−9.06398	+	3.75442i	−0.328138	+	0.135919i
$764$		0			0
$765$	5.30942	−	12.8181i	0.191963	−	0.463439i
$766$		0			0
$767$	8.71912			0.314829
$768$		0			0
$769$	13.1949			0.475821			0.237911	−	0.971287i	$-0.423537\pi$
$769$	13.1949			0.475821			0.237911	+	0.971287i	$0.423537\pi$
$770$		0			0
$771$	−4.89528	+	11.8183i	−0.176299	+	0.425624i
$772$		0			0
$773$	23.3275	−	9.66257i	0.839032	−	0.347538i	0.0785601	−	0.996909i	$-0.474968\pi$
$773$	23.3275	−	9.66257i	0.839032	−	0.347538i	0.760472	+	0.649371i	$0.224968\pi$
$774$		0			0
$775$	−12.9664	+	12.9664i	−0.465768	+	0.465768i
$776$		0			0
$777$	−0.516999	−	0.516999i	−0.0185472	−	0.0185472i
$778$		0			0
$779$	−15.4775	−	37.3660i	−0.554539	−	1.33877i
$780$		0			0
$781$	20.4130	+	8.45534i	0.730434	+	0.302556i
$782$		0			0
$783$		−	4.41958i		−	0.157943i
$784$		0			0
$785$		−	21.1247i		−	0.753971i
$786$		0			0
$787$	12.3210	+	5.10352i	0.439196	+	0.181921i	0.591314	−	0.806442i	$-0.298609\pi$
$787$	12.3210	+	5.10352i	0.439196	+	0.181921i	−0.152118	+	0.988362i	$0.548609\pi$
$788$		0			0
$789$	2.74252	+	6.62104i	0.0976364	+	0.235715i
$790$		0			0
$791$	0.623152	+	0.623152i	0.0221567	+	0.0221567i
$792$		0			0
$793$	−36.4318	+	36.4318i	−1.29373	+	1.29373i
$794$		0			0
$795$	−4.65776	+	1.92931i	−0.165194	+	0.0684255i
$796$		0			0
$797$	0.0303911	−	0.0733705i	0.00107651	−	0.00259892i	−0.923340	−	0.383983i	$-0.874552\pi$
$797$	0.0303911	−	0.0733705i	0.00107651	−	0.00259892i	0.924417	+	0.381384i	$0.124552\pi$
$798$		0			0
$799$	−67.7425			−2.39656
$800$		0			0
$801$	6.95069			0.245590
$802$		0			0
$803$	1.53369	−	3.70265i	0.0541226	−	0.130664i
$804$		0			0
$805$	−0.857551	+	0.355209i	−0.0302247	+	0.0125195i
$806$		0			0
$807$	−12.5924	+	12.5924i	−0.443272	+	0.443272i
$808$		0			0
$809$	−6.49942	−	6.49942i	−0.228507	−	0.228507i	0.583562	−	0.812069i	$-0.301659\pi$
$809$	−6.49942	−	6.49942i	−0.228507	−	0.228507i	−0.812069	+	0.583562i	$0.801659\pi$
$810$		0			0
$811$	6.45066	+	15.5733i	0.226513	+	0.546852i	0.995748	−	0.0921142i	$-0.0293625\pi$
$811$	6.45066	+	15.5733i	0.226513	+	0.546852i	−0.769235	+	0.638966i	$0.779362\pi$
$812$		0			0
$813$	−5.91417	−	2.44973i	−0.207419	−	0.0859157i
$814$		0			0
$815$			4.46935i			0.156555i
$816$		0			0
$817$		−	24.9936i		−	0.874417i
$818$		0			0
$819$	3.22782	+	1.33701i	0.112789	+	0.0467187i
$820$		0			0
$821$	20.6508	+	49.8554i	0.720717	+	1.73996i	0.671300	+	0.741185i	$0.265736\pi$
$821$	20.6508	+	49.8554i	0.720717	+	1.73996i	0.0494163	+	0.998778i	$0.484264\pi$
$822$		0			0
$823$	22.2511	+	22.2511i	0.775623	+	0.775623i	0.979083	−	0.203460i	$-0.0652187\pi$
$823$	22.2511	+	22.2511i	0.775623	+	0.775623i	−0.203460	+	0.979083i	$0.565219\pi$
$824$		0			0
$825$	−2.38665	+	2.38665i	−0.0830925	+	0.0830925i
$826$		0			0
$827$	−34.4764	+	14.2806i	−1.19886	+	0.496584i	−0.890631	−	0.454728i	$-0.849737\pi$
$827$	−34.4764	+	14.2806i	−1.19886	+	0.496584i	−0.308230	+	0.951312i	$0.599737\pi$
$828$		0			0
$829$	0.158799	−	0.383374i	0.00551531	−	0.0133151i	−0.921098	−	0.389331i	$-0.872706\pi$
$829$	0.158799	−	0.383374i	0.00551531	−	0.0133151i	0.926613	+	0.376016i	$0.122706\pi$
$830$		0			0
$831$	5.24655			0.182001
$832$		0			0
$833$	50.2203			1.74003
$834$		0			0
$835$	−6.43949	+	15.5463i	−0.222848	+	0.538002i
$836$		0			0
$837$	8.61802	−	3.56970i	0.297882	−	0.123387i
$838$		0			0
$839$	−19.2723	+	19.2723i	−0.665353	+	0.665353i	−0.956637	−	0.291284i	$-0.905918\pi$
$839$	−19.2723	+	19.2723i	−0.665353	+	0.665353i	0.291284	+	0.956637i	$0.405918\pi$
$840$		0			0
$841$	6.69439	+	6.69439i	0.230841	+	0.230841i
$842$		0			0
$843$	4.88559	+	11.7949i	0.168269	+	0.406237i
$844$		0			0
$845$	−7.34785	−	3.04358i	−0.252774	−	0.104702i
$846$		0			0
$847$		−	6.71219i		−	0.230634i
$848$		0			0
$849$			8.56633i			0.293996i
$850$		0			0
$851$	−0.517996	−	0.214561i	−0.0177567	−	0.00735505i
$852$		0			0
$853$	−11.9556	−	28.8634i	−0.409352	−	0.988263i	−0.985309	−	0.170783i	$-0.945370\pi$
$853$	−11.9556	−	28.8634i	−0.409352	−	0.988263i	0.575957	−	0.817480i	$-0.304630\pi$
$854$		0			0
$855$	5.29682	+	5.29682i	0.181147	+	0.181147i
$856$		0			0
$857$	−7.59541	+	7.59541i	−0.259454	+	0.259454i	−0.824832	−	0.565378i	$-0.808730\pi$
$857$	−7.59541	+	7.59541i	−0.259454	+	0.259454i	0.565378	+	0.824832i	$0.308730\pi$
$858$		0			0
$859$	31.8605	−	13.1970i	1.08707	−	0.450277i	0.234083	−	0.972217i	$-0.424791\pi$
$859$	31.8605	−	13.1970i	1.08707	−	0.450277i	0.852983	+	0.521939i	$0.174791\pi$
$860$		0			0
$861$	3.00020	−	7.24312i	0.102246	−	0.246845i
$862$		0			0
$863$	10.7216			0.364968			0.182484	−	0.983209i	$-0.441586\pi$
$863$	10.7216			0.364968			0.182484	+	0.983209i	$0.441586\pi$
$864$		0			0
$865$	5.21630			0.177360
$866$		0			0
$867$	17.7724	−	42.9064i	0.603583	−	1.45718i
$868$		0			0
$869$	−0.920779	+	0.381399i	−0.0312353	+	0.0129381i
$870$		0			0
$871$	−35.2182	+	35.2182i	−1.19332	+	1.19332i
$872$		0			0
$873$	2.34000	+	2.34000i	0.0791971	+	0.0791971i
$874$		0			0
$875$	−3.87071	−	9.34473i	−0.130854	−	0.315910i
$876$		0			0
$877$	−8.29027	−	3.43394i	−0.279943	−	0.115956i	0.238295	−	0.971193i	$-0.423412\pi$
$877$	−8.29027	−	3.43394i	−0.279943	−	0.115956i	−0.518237	+	0.855237i	$0.673412\pi$
$878$		0			0
$879$			1.19722i			0.0403812i
$880$		0			0
$881$			13.4623i			0.453557i	0.973946	+	0.226779i	$0.0728194\pi$
$881$			13.4623i			0.453557i	−0.973946	+	0.226779i	$0.927181\pi$
$882$		0			0
$883$	28.1854	+	11.6748i	0.948513	+	0.392887i	0.802672	−	0.596421i	$-0.203411\pi$
$883$	28.1854	+	11.6748i	0.948513	+	0.392887i	0.145841	+	0.989308i	$0.453411\pi$
$884$		0			0
$885$	1.38675	+	3.34791i	0.0466151	+	0.112539i
$886$		0			0
$887$	−12.7798	−	12.7798i	−0.429102	−	0.429102i	0.459220	−	0.888322i	$-0.348129\pi$
$887$	−12.7798	−	12.7798i	−0.429102	−	0.429102i	−0.888322	+	0.459220i	$0.848129\pi$
$888$		0			0
$889$	4.67864	−	4.67864i	0.156917	−	0.156917i
$890$		0			0
$891$	1.58627	−	0.657053i	0.0531419	−	0.0220121i
$892$		0			0
$893$	13.9966	−	33.7908i	0.468379	−	1.13077i
$894$		0			0
$895$	25.2369			0.843578
$896$		0			0
$897$	2.67917			0.0894548
$898$		0			0
$899$	15.7766	−	38.0880i	0.526179	−	1.27031i
$900$		0			0
$901$	−21.2982	+	8.82201i	−0.709547	+	0.293904i
$902$		0			0
$903$	3.42581	−	3.42581i	0.114004	−	0.114004i
$904$		0			0
$905$	−29.0796	−	29.0796i	−0.966639	−	0.966639i
$906$		0			0
$907$	−20.4543	−	49.3811i	−0.679175	−	1.63967i	−0.765524	−	0.643408i	$-0.777520\pi$
$907$	−20.4543	−	49.3811i	−0.679175	−	1.63967i	0.0863491	−	0.996265i	$-0.472480\pi$
$908$		0			0
$909$	−2.59134	−	1.07337i	−0.0859494	−	0.0356014i
$910$		0			0
$911$			19.5928i			0.649138i	0.945862	+	0.324569i	$0.105219\pi$
$911$			19.5928i			0.649138i	−0.945862	+	0.324569i	$0.894781\pi$
$912$		0			0
$913$		−	6.19927i		−	0.205166i
$914$		0			0
$915$	−19.7832	−	8.19447i	−0.654012	−	0.270901i
$916$		0			0
$917$	6.00823	+	14.5052i	0.198409	+	0.479003i
$918$		0			0
$919$	−33.9389	−	33.9389i	−1.11954	−	1.11954i	−0.991809	−	0.127732i	$-0.959230\pi$
$919$	−33.9389	−	33.9389i	−1.11954	−	1.11954i	−0.127732	−	0.991809i	$-0.540770\pi$
$920$		0			0
$921$	−7.67932	+	7.67932i	−0.253042	+	0.253042i
$922$		0			0
$923$	49.8288	−	20.6398i	1.64014	−	0.679366i
$924$		0			0
$925$	0.659825	−	1.59296i	0.0216949	−	0.0523761i
$926$		0			0
$927$	18.0420			0.592577
$928$		0			0
$929$	−42.5730			−1.39678			−0.698388	−	0.715720i	$-0.746099\pi$
$929$	−42.5730			−1.39678			−0.698388	+	0.715720i	$0.746099\pi$
$930$		0			0
$931$	−10.3763	+	25.0505i	−0.340069	+	0.820998i
$932$		0			0
$933$	−14.6220	+	6.05664i	−0.478704	+	0.198286i
$934$		0			0
$935$	16.8443	−	16.8443i	0.550868	−	0.550868i
$936$		0			0
$937$	−13.0124	−	13.0124i	−0.425098	−	0.425098i	0.461857	−	0.886954i	$-0.347183\pi$
$937$	−13.0124	−	13.0124i	−0.425098	−	0.425098i	−0.886954	+	0.461857i	$0.847183\pi$
$938$		0			0
$939$	8.19864	+	19.7933i	0.267553	+	0.645929i
$940$		0			0
$941$	−12.9144	−	5.34932i	−0.420998	−	0.174383i	0.162119	−	0.986771i	$-0.448167\pi$
$941$	−12.9144	−	5.34932i	−0.420998	−	0.174383i	−0.583117	+	0.812388i	$0.698167\pi$
$942$		0			0
$943$		−	6.01197i		−	0.195777i
$944$		0			0
$945$			1.45204i			0.0472350i
$946$		0			0
$947$	1.72532	+	0.714653i	0.0560655	+	0.0232231i	0.410540	−	0.911843i	$-0.365340\pi$
$947$	1.72532	+	0.714653i	0.0560655	+	0.0232231i	−0.354474	+	0.935066i	$0.615340\pi$
$948$		0			0
$949$	−3.74378	−	9.03829i	−0.121528	−	0.293395i
$950$		0			0
$951$	4.63622	+	4.63622i	0.150340	+	0.150340i
$952$		0			0
$953$	19.2732	−	19.2732i	0.624321	−	0.624321i	−0.322312	−	0.946633i	$-0.604460\pi$
$953$	19.2732	−	19.2732i	0.624321	−	0.624321i	0.946633	+	0.322312i	$0.104460\pi$
$954$		0			0
$955$	25.7038	−	10.6468i	0.831754	−	0.344524i
$956$		0			0
$957$	2.90390	−	7.01063i	0.0938698	−	0.226622i
$958$		0			0
$959$	0.360426			0.0116388
$960$		0			0
$961$	56.0131			1.80687
$962$		0			0
$963$	−3.17275	+	7.65969i	−0.102240	+	0.246830i
$964$		0			0
$965$	−0.661628	+	0.274055i	−0.0212986	+	0.00882215i
$966$		0			0
$967$	39.5173	−	39.5173i	1.27079	−	1.27079i	0.325118	−	0.945674i	$-0.394596\pi$
$967$	39.5173	−	39.5173i	1.27079	−	1.27079i	0.945674	−	0.325118i	$-0.105404\pi$
$968$		0			0
$969$	24.2204	+	24.2204i	0.778071	+	0.778071i
$970$		0			0
$971$	−1.47350	−	3.55734i	−0.0472868	−	0.114161i	0.898471	−	0.439033i	$-0.144679\pi$
$971$	−1.47350	−	3.55734i	−0.0472868	−	0.114161i	−0.945758	+	0.324872i	$0.894679\pi$
$972$		0			0
$973$	13.5280	+	5.60347i	0.433687	+	0.179639i
$974$		0			0
$975$			8.23907i			0.263861i
$976$		0			0
$977$		−	11.1620i		−	0.357103i	−0.983931	−	0.178551i	$-0.942859\pi$
$977$		−	11.1620i		−	0.357103i	0.983931	−	0.178551i	$-0.0571410\pi$
$978$		0			0
$979$	11.0256	+	4.56697i	0.352381	+	0.145961i
$980$		0			0
$981$	4.50386	+	10.8733i	0.143797	+	0.347157i
$982$		0			0
$983$	14.2055	+	14.2055i	0.453085	+	0.453085i	0.896377	−	0.443292i	$-0.146190\pi$
$983$	14.2055	+	14.2055i	0.453085	+	0.453085i	−0.443292	+	0.896377i	$0.646190\pi$
$984$		0			0
$985$	−5.46242	+	5.46242i	−0.174047	+	0.174047i
$986$		0			0
$987$	6.55010	−	2.71314i	0.208492	−	0.0863602i
$988$		0			0
$989$	1.42176	−	3.43242i	0.0452092	−	0.109145i
$990$		0			0
$991$	31.5264			1.00147			0.500734	−	0.865601i	$-0.333063\pi$
$991$	31.5264			1.00147			0.500734	+	0.865601i	$0.333063\pi$
$992$		0			0
$993$	−19.6735			−0.624321
$994$		0			0
$995$	−8.16104	+	19.7025i	−0.258722	+	0.624611i
$996$		0			0
$997$	25.5314	−	10.5755i	0.808588	−	0.334928i	0.0601976	−	0.998186i	$-0.480827\pi$
$997$	25.5314	−	10.5755i	0.808588	−	0.334928i	0.748391	+	0.663258i	$0.230827\pi$
$998$		0			0
$999$	−0.620199	+	0.620199i	−0.0196222	+	0.0196222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.289.2		32
4.3	odd	2		768.2.n.a.289.6		32
8.3	odd	2		96.2.n.a.13.5	✓	32
8.5	even	2		384.2.n.a.145.7		32
24.5	odd	2		1152.2.v.c.145.3		32
24.11	even	2		288.2.v.d.109.4		32
32.5	even	8	inner	768.2.n.b.481.2		32
32.11	odd	8		96.2.n.a.37.5	yes	32
32.21	even	8		384.2.n.a.241.7		32
32.27	odd	8		768.2.n.a.481.6		32
96.11	even	8		288.2.v.d.37.4		32
96.53	odd	8		1152.2.v.c.1009.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.5	✓	32	8.3	odd	2
96.2.n.a.37.5	yes	32	32.11	odd	8
288.2.v.d.37.4		32	96.11	even	8
288.2.v.d.109.4		32	24.11	even	2
384.2.n.a.145.7		32	8.5	even	2
384.2.n.a.241.7		32	32.21	even	8
768.2.n.a.289.6		32	4.3	odd	2
768.2.n.a.481.6		32	32.27	odd	8
768.2.n.b.289.2		32	1.1	even	1	trivial
768.2.n.b.481.2		32	32.5	even	8	inner
1152.2.v.c.145.3		32	24.5	odd	2
1152.2.v.c.1009.3		32	96.53	odd	8

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{3} +(-1.60930 + 0.666593i) q^{5} +(0.589445 - 0.589445i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 + 0.923880i) q^{3} +(-1.60930 + 0.666593i) q^{5} +(0.589445 - 0.589445i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-0.657053 - 1.58627i) q^{11} +(-3.87213 - 1.60389i) q^{13} -1.74189i q^{15} -7.96502i q^{17} +(3.97306 + 1.64569i) q^{19} +(0.319006 + 0.770147i) q^{21} +(0.452012 + 0.452012i) q^{23} +(-1.39004 + 1.39004i) q^{25} +(0.923880 - 0.382683i) q^{27} +(1.69130 - 4.08316i) q^{29} +9.32808 q^{31} +1.71696 q^{33} +(-0.555673 + 1.34151i) q^{35} +(-0.810329 + 0.335649i) q^{37} +(2.96360 - 2.96360i) q^{39} +(-6.65023 - 6.65023i) q^{41} +(-2.22413 - 5.36952i) q^{43} +(1.60930 + 0.666593i) q^{45} -8.50500i q^{47} +6.30511i q^{49} +(7.35872 + 3.04808i) q^{51} +(-1.10759 - 2.67397i) q^{53} +(2.11479 + 2.11479i) q^{55} +(-3.04084 + 3.04084i) q^{57} +(-1.92200 + 0.796118i) q^{59} +(4.70435 - 11.3573i) q^{61} -0.833602 q^{63} +7.30055 q^{65} +(4.54765 - 10.9790i) q^{67} +(-0.590582 + 0.244627i) q^{69} +(-9.09946 + 9.09946i) q^{71} +(1.65052 + 1.65052i) q^{73} +(-0.752286 - 1.81618i) q^{75} +(-1.32231 - 0.547721i) q^{77} -0.580469i q^{79} +1.00000i q^{81} +(3.33576 + 1.38172i) q^{83} +(5.30942 + 12.8181i) q^{85} +(3.12512 + 3.12512i) q^{87} +(-4.91488 + 4.91488i) q^{89} +(-3.22782 + 1.33701i) q^{91} +(-3.56970 + 8.61802i) q^{93} -7.49083 q^{95} -3.30926 q^{97} +(-0.657053 + 1.58627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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