LMFDB - Embedded newform 640.2.x.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(81,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("640.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.x (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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	640.81
Dual form			640.2.x.a.561.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00190 - 0.829213i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-0.773883 + 0.773883i) q^{7} +(1.19868 + 1.19868i) q^{9} +O(q^{10})$	\(q+(-2.00190 - 0.829213i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-0.773883 + 0.773883i) q^{7} +(1.19868 + 1.19868i) q^{9} +(-2.18542 + 0.905229i) q^{11} +(-0.377090 + 0.910375i) q^{13} +2.16684i q^{15} +5.08117i q^{17} +(2.25559 - 5.44547i) q^{19} +(2.19095 - 0.907521i) q^{21} +(3.60888 + 3.60888i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(1.08197 + 2.61210i) q^{27} +(-3.45078 - 1.42936i) q^{29} +6.37732 q^{31} +5.12560 q^{33} +(1.01113 + 0.418823i) q^{35} +(3.41868 + 8.25342i) q^{37} +(1.50979 - 1.50979i) q^{39} +(2.02161 + 2.02161i) q^{41} +(-5.81731 + 2.40961i) q^{43} +(0.648719 - 1.56615i) q^{45} +8.71108i q^{47} +5.80221i q^{49} +(4.21337 - 10.1720i) q^{51} +(13.0470 - 5.40423i) q^{53} +(1.67264 + 1.67264i) q^{55} +(-9.03091 + 9.03091i) q^{57} +(4.44720 + 10.7365i) q^{59} +(-2.32909 - 0.964739i) q^{61} -1.85527 q^{63} +0.985383 q^{65} +(-7.34570 - 3.04269i) q^{67} +(-4.23207 - 10.2171i) q^{69} +(4.50934 - 4.50934i) q^{71} +(-7.98507 - 7.98507i) q^{73} +(2.00190 - 0.829213i) q^{75} +(0.990715 - 2.39180i) q^{77} +1.01222i q^{79} -11.2119i q^{81} +(-5.67612 + 13.7034i) q^{83} +(4.69439 - 1.94448i) q^{85} +(5.72285 + 5.72285i) q^{87} +(-4.67953 + 4.67953i) q^{89} +(-0.412701 - 0.996348i) q^{91} +(-12.7667 - 5.28816i) q^{93} -5.89414 q^{95} -13.0602 q^{97} +(-3.70468 - 1.53453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) $ 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	−2.00190	−	0.829213i	−1.15580	−	0.478746i	−0.279323	−	0.960197i	$-0.590110\pi$
$3$	−2.00190	−	0.829213i	−1.15580	−	0.478746i	−0.876473	+	0.481451i	$0.840110\pi$
$4$		0			0
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$6$		0			0
$7$	−0.773883	+	0.773883i	−0.292500	+	0.292500i	−0.838067	−	0.545567i	$-0.816314\pi$
$7$	−0.773883	+	0.773883i	−0.292500	+	0.292500i	0.545567	+	0.838067i	$0.316314\pi$
$8$		0			0
$9$	1.19868	+	1.19868i	0.399559	+	0.399559i
$10$		0			0
$11$	−2.18542	+	0.905229i	−0.658928	+	0.272937i	−0.686987	−	0.726669i	$-0.741067\pi$
$11$	−2.18542	+	0.905229i	−0.658928	+	0.272937i	0.0280596	+	0.999606i	$0.491067\pi$
$12$		0			0
$13$	−0.377090	+	0.910375i	−0.104586	+	0.252493i	−0.967506	−	0.252847i	$-0.918633\pi$
$13$	−0.377090	+	0.910375i	−0.104586	+	0.252493i	0.862920	+	0.505340i	$0.168633\pi$
$14$		0			0
$15$			2.16684i			0.559475i
$16$		0			0
$17$			5.08117i			1.23236i	0.787604	+	0.616182i	$0.211321\pi$
$17$			5.08117i			1.23236i	−0.787604	+	0.616182i	$0.788679\pi$
$18$		0			0
$19$	2.25559	−	5.44547i	0.517467	−	1.24928i	−0.421987	−	0.906602i	$-0.638667\pi$
$19$	2.25559	−	5.44547i	0.517467	−	1.24928i	0.939454	−	0.342675i	$-0.111333\pi$
$20$		0			0
$21$	2.19095	−	0.907521i	0.478104	−	0.198037i
$22$		0			0
$23$	3.60888	+	3.60888i	0.752503	+	0.752503i	0.974946	−	0.222443i	$-0.0714032\pi$
$23$	3.60888	+	3.60888i	0.752503	+	0.752503i	−0.222443	+	0.974946i	$0.571403\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	1.08197	+	2.61210i	0.208225	+	0.502700i
$28$		0			0
$29$	−3.45078	−	1.42936i	−0.640793	−	0.265425i	0.0385381	−	0.999257i	$-0.487730\pi$
$29$	−3.45078	−	1.42936i	−0.640793	−	0.265425i	−0.679331	+	0.733832i	$0.737730\pi$
$30$		0			0
$31$	6.37732			1.14540			0.572701	−	0.819765i	$-0.305896\pi$
$31$	6.37732			1.14540			0.572701	+	0.819765i	$0.305896\pi$
$32$		0			0
$33$	5.12560			0.892253
$34$		0			0
$35$	1.01113	+	0.418823i	0.170912	+	0.0707939i
$36$		0			0
$37$	3.41868	+	8.25342i	0.562028	+	1.35685i	0.908142	+	0.418662i	$0.137501\pi$
$37$	3.41868	+	8.25342i	0.562028	+	1.35685i	−0.346114	+	0.938192i	$0.612499\pi$
$38$		0			0
$39$	1.50979	−	1.50979i	0.241760	−	0.241760i
$40$		0			0
$41$	2.02161	+	2.02161i	0.315723	+	0.315723i	0.847122	−	0.531399i	$-0.178333\pi$
$41$	2.02161	+	2.02161i	0.315723	+	0.315723i	−0.531399	+	0.847122i	$0.678333\pi$
$42$		0			0
$43$	−5.81731	+	2.40961i	−0.887131	+	0.367462i	−0.779258	−	0.626703i	$-0.784404\pi$
$43$	−5.81731	+	2.40961i	−0.887131	+	0.367462i	−0.107873	+	0.994165i	$0.534404\pi$
$44$		0			0
$45$	0.648719	−	1.56615i	0.0967054	−	0.233467i
$46$		0			0
$47$			8.71108i			1.27064i	0.772248	+	0.635321i	$0.219132\pi$
$47$			8.71108i			1.27064i	−0.772248	+	0.635321i	$0.780868\pi$
$48$		0			0
$49$			5.80221i			0.828887i
$50$		0			0
$51$	4.21337	−	10.1720i	0.589990	−	1.42436i
$52$		0			0
$53$	13.0470	−	5.40423i	1.79214	−	0.742328i	0.802881	−	0.596139i	$-0.203299\pi$
$53$	13.0470	−	5.40423i	1.79214	−	0.742328i	0.989257	−	0.146188i	$-0.0467006\pi$
$54$		0			0
$55$	1.67264	+	1.67264i	0.225539	+	0.225539i
$56$		0			0
$57$	−9.03091	+	9.03091i	−1.19617	+	1.19617i
$58$		0			0
$59$	4.44720	+	10.7365i	0.578976	+	1.39777i	0.893733	+	0.448599i	$0.148077\pi$
$59$	4.44720	+	10.7365i	0.578976	+	1.39777i	−0.314757	+	0.949172i	$0.601923\pi$
$60$		0			0
$61$	−2.32909	−	0.964739i	−0.298209	−	0.123522i	0.228562	−	0.973529i	$-0.426598\pi$
$61$	−2.32909	−	0.964739i	−0.298209	−	0.123522i	−0.526771	+	0.850007i	$0.676598\pi$
$62$		0			0
$63$	−1.85527			−0.233742
$64$		0			0
$65$	0.985383			0.122222
$66$		0			0
$67$	−7.34570	−	3.04269i	−0.897419	−	0.371723i	−0.114192	−	0.993459i	$-0.536428\pi$
$67$	−7.34570	−	3.04269i	−0.897419	−	0.371723i	−0.783227	+	0.621735i	$0.786428\pi$
$68$		0			0
$69$	−4.23207	−	10.2171i	−0.509481	−	1.23000i
$70$		0			0
$71$	4.50934	−	4.50934i	0.535160	−	0.535160i	−0.386943	−	0.922103i	$-0.626469\pi$
$71$	4.50934	−	4.50934i	0.535160	−	0.535160i	0.922103	+	0.386943i	$0.126469\pi$
$72$		0			0
$73$	−7.98507	−	7.98507i	−0.934582	−	0.934582i	0.0634061	−	0.997988i	$-0.479804\pi$
$73$	−7.98507	−	7.98507i	−0.934582	−	0.934582i	−0.997988	+	0.0634061i	$0.979804\pi$
$74$		0			0
$75$	2.00190	−	0.829213i	0.231159	−	0.0957493i
$76$		0			0
$77$	0.990715	−	2.39180i	0.112902	−	0.272571i
$78$		0			0
$79$			1.01222i			0.113884i	0.998377	+	0.0569421i	$0.0181350\pi$
$79$			1.01222i			0.113884i	−0.998377	+	0.0569421i	$0.981865\pi$
$80$		0			0
$81$		−	11.2119i		−	1.24577i
$82$		0			0
$83$	−5.67612	+	13.7034i	−0.623035	+	1.50414i	0.225086	+	0.974339i	$0.427734\pi$
$83$	−5.67612	+	13.7034i	−0.623035	+	1.50414i	−0.848121	+	0.529802i	$0.822266\pi$
$84$		0			0
$85$	4.69439	−	1.94448i	0.509178	−	0.210908i
$86$		0			0
$87$	5.72285	+	5.72285i	0.613554	+	0.613554i
$88$		0			0
$89$	−4.67953	+	4.67953i	−0.496029	+	0.496029i	−0.910200	−	0.414170i	$-0.864072\pi$
$89$	−4.67953	+	4.67953i	−0.496029	+	0.496029i	0.414170	+	0.910200i	$0.364072\pi$
$90$		0			0
$91$	−0.412701	−	0.996348i	−0.0432628	−	0.104446i
$92$		0			0
$93$	−12.7667	−	5.28816i	−1.32385	−	0.548357i
$94$		0			0
$95$	−5.89414			−0.604726
$96$		0			0
$97$	−13.0602			−1.32606			−0.663030	−	0.748593i	$-0.730730\pi$
$97$	−13.0602			−1.32606			−0.663030	+	0.748593i	$0.730730\pi$
$98$		0			0
$99$	−3.70468	−	1.53453i	−0.372335	−	0.154226i
$100$		0			0
$101$	4.15287	+	10.0259i	0.413226	+	0.997616i	0.984266	+	0.176693i	$0.0565401\pi$
$101$	4.15287	+	10.0259i	0.413226	+	0.997616i	−0.571040	+	0.820922i	$0.693460\pi$
$102$		0			0
$103$	8.62040	−	8.62040i	0.849393	−	0.849393i	−0.140664	−	0.990057i	$-0.544924\pi$
$103$	8.62040	−	8.62040i	0.849393	−	0.849393i	0.990057	+	0.140664i	$0.0449238\pi$
$104$		0			0
$105$	−1.67688	−	1.67688i	−0.163647	−	0.163647i
$106$		0			0
$107$	−7.51166	+	3.11143i	−0.726180	+	0.300794i	−0.714981	−	0.699144i	$-0.753565\pi$
$107$	−7.51166	+	3.11143i	−0.726180	+	0.300794i	−0.0111988	+	0.999937i	$0.503565\pi$
$108$		0			0
$109$	3.82660	−	9.23823i	0.366522	−	0.884862i	−0.627793	−	0.778380i	$-0.716042\pi$
$109$	3.82660	−	9.23823i	0.366522	−	0.884862i	0.994315	−	0.106482i	$-0.0339585\pi$
$110$		0			0
$111$		−	19.3573i		−	1.83732i
$112$		0			0
$113$		−	10.6304i		−	1.00003i	−0.866018	−	0.500013i	$-0.833328\pi$
$113$		−	10.6304i		−	1.00003i	0.866018	−	0.500013i	$-0.166672\pi$
$114$		0			0
$115$	1.95311	−	4.71522i	0.182128	−	0.439697i
$116$		0			0
$117$	−1.54325	+	0.639237i	−0.142674	+	0.0590975i
$118$		0			0
$119$	−3.93223	−	3.93223i	−0.360467	−	0.360467i
$120$		0			0
$121$	−3.82157	+	3.82157i	−0.347416	+	0.347416i
$122$		0			0
$123$	−2.37071	−	5.72340i	−0.213760	−	0.516062i
$124$		0			0
$125$	0.923880	+	0.382683i	0.0826343	+	0.0342282i
$126$		0			0
$127$	−5.09641			−0.452233			−0.226117	−	0.974100i	$-0.572603\pi$
$127$	−5.09641			−0.452233			−0.226117	+	0.974100i	$0.572603\pi$
$128$		0			0
$129$	13.6437			1.20126
$130$		0			0
$131$	−10.2816	−	4.25878i	−0.898308	−	0.372091i	−0.114738	−	0.993396i	$-0.536603\pi$
$131$	−10.2816	−	4.25878i	−0.898308	−	0.372091i	−0.783569	+	0.621305i	$0.786603\pi$
$132$		0			0
$133$	2.46860	+	5.95972i	0.214055	+	0.516773i
$134$		0			0
$135$	1.99922	−	1.99922i	0.172065	−	0.172065i
$136$		0			0
$137$	1.18453	+	1.18453i	0.101201	+	0.101201i	0.755894	−	0.654694i	$-0.227202\pi$
$137$	1.18453	+	1.18453i	0.101201	+	0.101201i	−0.654694	+	0.755894i	$0.727202\pi$
$138$		0			0
$139$	−1.14518	+	0.474350i	−0.0971331	+	0.0402339i	−0.430721	−	0.902485i	$-0.641741\pi$
$139$	−1.14518	+	0.474350i	−0.0971331	+	0.0402339i	0.333588	+	0.942719i	$0.391741\pi$
$140$		0			0
$141$	7.22334	−	17.4387i	0.608315	−	1.46860i
$142$		0			0
$143$		−	2.33090i		−	0.194920i
$144$		0			0
$145$			3.73509i			0.310183i
$146$		0			0
$147$	4.81127	−	11.6154i	0.396827	−	0.958024i
$148$		0			0
$149$	−17.0014	+	7.04220i	−1.39281	+	0.576920i	−0.947874	−	0.318644i	$-0.896773\pi$
$149$	−17.0014	+	7.04220i	−1.39281	+	0.576920i	−0.444933	+	0.895564i	$0.646773\pi$
$150$		0			0
$151$	−2.53536	−	2.53536i	−0.206324	−	0.206324i	0.596379	−	0.802703i	$-0.296606\pi$
$151$	−2.53536	−	2.53536i	−0.206324	−	0.206324i	−0.802703	+	0.596379i	$0.796606\pi$
$152$		0			0
$153$	−6.09068	+	6.09068i	−0.492402	+	0.492402i
$154$		0			0
$155$	−2.44050	−	5.89188i	−0.196025	−	0.473247i
$156$		0			0
$157$	7.15979	+	2.96568i	0.571413	+	0.236687i	0.649632	−	0.760249i	$-0.274923\pi$
$157$	7.15979	+	2.96568i	0.571413	+	0.236687i	−0.0782183	+	0.996936i	$0.524923\pi$
$158$		0			0
$159$	−30.5999			−2.42673
$160$		0			0
$161$	−5.58570			−0.440215
$162$		0			0
$163$	9.31567	+	3.85868i	0.729659	+	0.302235i	0.716412	−	0.697677i	$-0.245783\pi$
$163$	9.31567	+	3.85868i	0.729659	+	0.302235i	0.0132474	+	0.999912i	$0.495783\pi$
$164$		0			0
$165$	−1.96148	−	4.73544i	−0.152701	−	0.368654i
$166$		0			0
$167$	−7.76143	+	7.76143i	−0.600598	+	0.600598i	−0.940471	−	0.339874i	$-0.889616\pi$
$167$	−7.76143	+	7.76143i	−0.600598	+	0.600598i	0.339874	+	0.940471i	$0.389616\pi$
$168$		0			0
$169$	8.50580	+	8.50580i	0.654292	+	0.654292i
$170$		0			0
$171$	9.23108	−	3.82364i	0.705919	−	0.292401i
$172$		0			0
$173$	−6.85261	+	16.5437i	−0.520994	+	1.25779i	0.416292	+	0.909231i	$0.363329\pi$
$173$	−6.85261	+	16.5437i	−0.520994	+	1.25779i	−0.937286	+	0.348561i	$0.886671\pi$
$174$		0			0
$175$		−	1.09444i		−	0.0827316i
$176$		0			0
$177$		−	25.1810i		−	1.89272i
$178$		0			0
$179$	−1.21669	+	2.93736i	−0.0909400	+	0.219549i	−0.962805	−	0.270198i	$-0.912911\pi$
$179$	−1.21669	+	2.93736i	−0.0909400	+	0.219549i	0.871865	+	0.489747i	$0.162911\pi$
$180$		0			0
$181$	−1.09049	+	0.451695i	−0.0810554	+	0.0335742i	−0.422843	−	0.906203i	$-0.638968\pi$
$181$	−1.09049	+	0.451695i	−0.0810554	+	0.0335742i	0.341787	+	0.939777i	$0.388968\pi$
$182$		0			0
$183$	3.86262	+	3.86262i	0.285533	+	0.285533i
$184$		0			0
$185$	6.31690	−	6.31690i	0.464428	−	0.464428i
$186$		0			0
$187$	−4.59962	−	11.1045i	−0.336357	−	0.812039i
$188$		0			0
$189$	−2.85878	−	1.18415i	−0.207946	−	0.0861340i
$190$		0			0
$191$	12.0847			0.874417			0.437209	−	0.899360i	$-0.355967\pi$
$191$	12.0847			0.874417			0.437209	+	0.899360i	$0.355967\pi$
$192$		0			0
$193$	20.7080			1.49060			0.745299	−	0.666731i	$-0.232307\pi$
$193$	20.7080			1.49060			0.745299	+	0.666731i	$0.232307\pi$
$194$		0			0
$195$	−1.97264	−	0.817092i	−0.141263	−	0.0585132i
$196$		0			0
$197$	2.13361	+	5.15100i	0.152014	+	0.366994i	0.981480	−	0.191563i	$-0.0613555\pi$
$197$	2.13361	+	5.15100i	0.152014	+	0.366994i	−0.829467	+	0.558556i	$0.811356\pi$
$198$		0			0
$199$	8.28622	−	8.28622i	0.587394	−	0.587394i	−0.349531	−	0.936925i	$-0.613659\pi$
$199$	8.28622	−	8.28622i	0.587394	−	0.587394i	0.936925	+	0.349531i	$0.113659\pi$
$200$		0			0
$201$	12.1823	+	12.1823i	0.859272	+	0.859272i
$202$		0			0
$203$	3.77665	−	1.56434i	0.265069	−	0.109795i
$204$		0			0
$205$	1.09409	−	2.64136i	0.0764144	−	0.184481i
$206$		0			0
$207$			8.65175i			0.601338i
$208$		0			0
$209$			13.9424i			0.964419i
$210$		0			0
$211$	2.82926	−	6.83044i	0.194774	−	0.470227i	−0.796075	−	0.605198i	$-0.793094\pi$
$211$	2.82926	−	6.83044i	0.194774	−	0.470227i	0.990850	+	0.134971i	$0.0430941\pi$
$212$		0			0
$213$	−12.7664	+	5.28803i	−0.874742	+	0.362330i
$214$		0			0
$215$	4.45237	+	4.45237i	0.303649	+	0.303649i
$216$		0			0
$217$	−4.93530	+	4.93530i	−0.335030	+	0.335030i
$218$		0			0
$219$	9.36396	+	22.6066i	0.632758	+	1.52761i
$220$		0			0
$221$	−4.62577	−	1.91606i	−0.311163	−	0.128888i
$222$		0			0
$223$	−12.0151			−0.804589			−0.402294	−	0.915510i	$-0.631787\pi$
$223$	−12.0151			−0.804589			−0.402294	+	0.915510i	$0.631787\pi$
$224$		0			0
$225$	−1.69519			−0.113012
$226$		0			0
$227$	4.88003	+	2.02137i	0.323899	+	0.134163i	0.538708	−	0.842493i	$-0.318913\pi$
$227$	4.88003	+	2.02137i	0.323899	+	0.134163i	−0.214809	+	0.976656i	$0.568913\pi$
$228$		0			0
$229$	5.82413	+	14.0607i	0.384869	+	0.929157i	0.991009	+	0.133798i	$0.0427175\pi$
$229$	5.82413	+	14.0607i	0.384869	+	0.929157i	−0.606139	+	0.795359i	$0.707283\pi$
$230$		0			0
$231$	−3.96662	+	3.96662i	−0.260984	+	0.260984i
$232$		0			0
$233$	4.39516	+	4.39516i	0.287936	+	0.287936i	0.836264	−	0.548327i	$-0.184735\pi$
$233$	4.39516	+	4.39516i	0.287936	+	0.287936i	−0.548327	+	0.836264i	$0.684735\pi$
$234$		0			0
$235$	8.04799	−	3.33359i	0.524993	−	0.217459i
$236$		0			0
$237$	0.839350	−	2.02637i	0.0545216	−	0.131627i
$238$		0			0
$239$			0.430119i			0.0278221i	0.999903	+	0.0139110i	$0.00442817\pi$
$239$			0.430119i			0.0278221i	−0.999903	+	0.0139110i	$0.995572\pi$
$240$		0			0
$241$		−	28.9486i		−	1.86475i	−0.361498	−	0.932373i	$-0.617734\pi$
$241$		−	28.9486i		−	1.86475i	0.361498	−	0.932373i	$-0.382266\pi$
$242$		0			0
$243$	−6.05115	+	14.6088i	−0.388181	+	0.937152i
$244$		0			0
$245$	5.36054	−	2.22041i	0.342472	−	0.141857i
$246$		0			0
$247$	4.10686	+	4.10686i	0.261313	+	0.261313i
$248$		0			0
$249$	22.7260	−	22.7260i	1.44020	−	1.44020i
$250$		0			0
$251$	7.50516	+	18.1191i	0.473722	+	1.14367i	0.962506	+	0.271261i	$0.0874405\pi$
$251$	7.50516	+	18.1191i	0.473722	+	1.14367i	−0.488784	+	0.872405i	$0.662559\pi$
$252$		0			0
$253$	−11.1538	−	4.62004i	−0.701230	−	0.290459i
$254$		0			0
$255$	−11.0101			−0.689477
$256$		0			0
$257$	−10.3593			−0.646196			−0.323098	−	0.946366i	$-0.604724\pi$
$257$	−10.3593			−0.646196			−0.323098	+	0.946366i	$0.604724\pi$
$258$		0			0
$259$	−9.03285	−	3.74153i	−0.561274	−	0.232487i
$260$		0			0
$261$	−2.42303	−	5.84970i	−0.149982	−	0.362088i
$262$		0			0
$263$	−5.80799	+	5.80799i	−0.358136	+	0.358136i	−0.863126	−	0.504989i	$-0.831496\pi$
$263$	−5.80799	+	5.80799i	−0.358136	+	0.358136i	0.504989	+	0.863126i	$0.331496\pi$
$264$		0			0
$265$	−9.98571	−	9.98571i	−0.613417	−	0.613417i
$266$		0			0
$267$	13.2483	−	5.48761i	0.810781	−	0.335836i
$268$		0			0
$269$	−11.0354	+	26.6419i	−0.672842	+	1.62439i	0.103916	+	0.994586i	$0.466863\pi$
$269$	−11.0354	+	26.6419i	−0.672842	+	1.62439i	−0.776758	+	0.629799i	$0.783137\pi$
$270$		0			0
$271$			20.8495i			1.26652i	0.773940	+	0.633260i	$0.218283\pi$
$271$			20.8495i			1.26652i	−0.773940	+	0.633260i	$0.781717\pi$
$272$		0			0
$273$			2.33680i			0.141430i
$274$		0			0
$275$	0.905229	−	2.18542i	0.0545874	−	0.131786i
$276$		0			0
$277$	9.69684	−	4.01656i	0.582627	−	0.241332i	−0.0718482	−	0.997416i	$-0.522890\pi$
$277$	9.69684	−	4.01656i	0.582627	−	0.241332i	0.654475	+	0.756084i	$0.272890\pi$
$278$		0			0
$279$	7.64435	+	7.64435i	0.457655	+	0.457655i
$280$		0			0
$281$	13.0890	−	13.0890i	0.780823	−	0.780823i	−0.199147	−	0.979970i	$-0.563817\pi$
$281$	13.0890	−	13.0890i	0.780823	−	0.780823i	0.979970	+	0.199147i	$0.0638170\pi$
$282$		0			0
$283$	−6.91016	−	16.6826i	−0.410766	−	0.991677i	−0.984933	−	0.172939i	$-0.944674\pi$
$283$	−6.91016	−	16.6826i	−0.410766	−	0.991677i	0.574166	−	0.818739i	$-0.305326\pi$
$284$		0			0
$285$	11.7995	+	4.88749i	0.698939	+	0.289510i
$286$		0			0
$287$	−3.12898			−0.184698
$288$		0			0
$289$	−8.81827			−0.518722
$290$		0			0
$291$	26.1451	+	10.8297i	1.53266	+	0.634847i
$292$		0			0
$293$	0.618642	+	1.49353i	0.0361414	+	0.0872532i	0.940920	−	0.338630i	$-0.109963\pi$
$293$	0.618642	+	1.49353i	0.0361414	+	0.0872532i	−0.904778	+	0.425883i	$0.859963\pi$
$294$		0			0
$295$	8.21735	−	8.21735i	0.478433	−	0.478433i
$296$		0			0
$297$	−4.72910	−	4.72910i	−0.274410	−	0.274410i
$298$		0			0
$299$	−4.64630	+	1.92456i	−0.268703	+	0.111300i
$300$		0			0
$301$	2.63716	−	6.36667i	0.152003	−	0.366969i
$302$		0			0
$303$		−	23.5145i		−	1.35087i
$304$		0			0
$305$			2.52098i			0.144351i
$306$		0			0
$307$	7.64887	−	18.4660i	0.436544	−	1.05391i	−0.540590	−	0.841286i	$-0.681799\pi$
$307$	7.64887	−	18.4660i	0.436544	−	1.05391i	0.977134	−	0.212624i	$-0.0682011\pi$
$308$		0			0
$309$	−24.4053	+	10.1090i	−1.38837	+	0.575081i
$310$		0			0
$311$	−11.6823	−	11.6823i	−0.662443	−	0.662443i	0.293513	−	0.955955i	$-0.405176\pi$
$311$	−11.6823	−	11.6823i	−0.662443	−	0.662443i	−0.955955	+	0.293513i	$0.905176\pi$
$312$		0			0
$313$	−13.7274	+	13.7274i	−0.775918	+	0.775918i	−0.979134	−	0.203216i	$-0.934861\pi$
$313$	−13.7274	+	13.7274i	−0.775918	+	0.775918i	0.203216	+	0.979134i	$0.434861\pi$
$314$		0			0
$315$	0.709982	+	1.71405i	0.0400030	+	0.0965757i
$316$		0			0
$317$	0.830334	+	0.343935i	0.0466362	+	0.0193173i	0.405880	−	0.913927i	$-0.366965\pi$
$317$	0.830334	+	0.343935i	0.0466362	+	0.0193173i	−0.359243	+	0.933244i	$0.616965\pi$
$318$		0			0
$319$	8.83528			0.494680
$320$		0			0
$321$	17.6176			0.983320
$322$		0			0
$323$	27.6694	+	11.4610i	1.53956	+	0.637708i
$324$		0			0
$325$	−0.377090	−	0.910375i	−0.0209172	−	0.0504985i
$326$		0			0
$327$	−15.3209	+	15.3209i	−0.847249	+	0.847249i
$328$		0			0
$329$	−6.74136	−	6.74136i	−0.371663	−	0.371663i
$330$		0			0
$331$	−15.0405	+	6.22999i	−0.826702	+	0.342431i	−0.755596	−	0.655038i	$-0.772653\pi$
$331$	−15.0405	+	6.22999i	−0.826702	+	0.342431i	−0.0711057	+	0.997469i	$0.522653\pi$
$332$		0			0
$333$	−5.79530	+	13.9911i	−0.317580	+	0.766707i
$334$		0			0
$335$			7.95092i			0.434405i
$336$		0			0
$337$			17.6558i			0.961771i	0.876783	+	0.480885i	$0.159685\pi$
$337$			17.6558i			0.961771i	−0.876783	+	0.480885i	$0.840315\pi$
$338$		0			0
$339$	−8.81489	+	21.2810i	−0.478759	+	1.15583i
$340$		0			0
$341$	−13.9371	+	5.77294i	−0.754736	+	0.312622i
$342$		0			0
$343$	−9.90742	−	9.90742i	−0.534950	−	0.534950i
$344$		0			0
$345$	−7.81985	+	7.81985i	−0.421006	+	0.421006i
$346$		0			0
$347$	3.72398	+	8.99048i	0.199914	+	0.482635i	0.991764	−	0.128081i	$-0.0408818\pi$
$347$	3.72398	+	8.99048i	0.199914	+	0.482635i	−0.791850	+	0.610716i	$0.790882\pi$
$348$		0			0
$349$	16.5460	+	6.85357i	0.885686	+	0.366863i	0.778699	−	0.627397i	$-0.215880\pi$
$349$	16.5460	+	6.85357i	0.885686	+	0.366863i	0.106987	+	0.994260i	$0.465880\pi$
$350$		0			0
$351$	−2.78599			−0.148705
$352$		0			0
$353$	−2.54858			−0.135647			−0.0678236	−	0.997697i	$-0.521606\pi$
$353$	−2.54858			−0.135647			−0.0678236	+	0.997697i	$0.521606\pi$
$354$		0			0
$355$	−5.89174	−	2.44044i	−0.312701	−	0.129525i
$356$		0			0
$357$	4.61126	+	11.1326i	0.244054	+	0.589199i
$358$		0			0
$359$	17.2372	−	17.2372i	0.909747	−	0.909747i	−0.0865043	−	0.996251i	$-0.527570\pi$
$359$	17.2372	−	17.2372i	0.909747	−	0.909747i	0.996251	+	0.0865043i	$0.0275696\pi$
$360$		0			0
$361$	−11.1305	−	11.1305i	−0.585813	−	0.585813i
$362$		0			0
$363$	10.8193	−	4.48150i	0.567865	−	0.235218i
$364$		0			0
$365$	−4.32149	+	10.4330i	−0.226197	+	0.546088i
$366$		0			0
$367$		−	4.85223i		−	0.253284i	−0.991948	−	0.126642i	$-0.959580\pi$
$367$		−	4.85223i		−	0.253284i	0.991948	−	0.126642i	$-0.0404200\pi$
$368$		0			0
$369$			4.84652i			0.252300i
$370$		0			0
$371$	−5.91458	+	14.2791i	−0.307070	+	0.741332i
$372$		0			0
$373$	29.9107	−	12.3894i	1.54872	−	0.641499i	0.565632	−	0.824658i	$-0.308632\pi$
$373$	29.9107	−	12.3894i	1.54872	−	0.641499i	0.983083	+	0.183159i	$0.0586323\pi$
$374$		0			0
$375$	−1.53219	−	1.53219i	−0.0791217	−	0.0791217i
$376$		0			0
$377$	2.60250	−	2.60250i	0.134036	−	0.134036i
$378$		0			0
$379$	10.7016	+	25.8359i	0.549704	+	1.32710i	0.917700	+	0.397275i	$0.130044\pi$
$379$	10.7016	+	25.8359i	0.549704	+	1.32710i	−0.367996	+	0.929827i	$0.619956\pi$
$380$		0			0
$381$	10.2025	+	4.22601i	0.522689	+	0.216505i
$382$		0			0
$383$	24.9606			1.27543			0.637713	−	0.770274i	$-0.279881\pi$
$383$	24.9606			1.27543			0.637713	+	0.770274i	$0.279881\pi$
$384$		0			0
$385$	−2.58886			−0.131941
$386$		0			0
$387$	−9.86141	−	4.08473i	−0.501284	−	0.207639i
$388$		0			0
$389$	−13.5182	−	32.6358i	−0.685400	−	1.65470i	−0.753850	−	0.657047i	$-0.771805\pi$
$389$	−13.5182	−	32.6358i	−0.685400	−	1.65470i	0.0684498	−	0.997655i	$-0.478195\pi$
$390$		0			0
$391$	−18.3373	+	18.3373i	−0.927357	+	0.927357i
$392$		0			0
$393$	17.0513	+	17.0513i	0.860123	+	0.860123i
$394$		0			0
$395$	0.935173	−	0.387362i	0.0470537	−	0.0194903i
$396$		0			0
$397$	1.89838	−	4.58310i	0.0952770	−	0.230019i	−0.869055	−	0.494716i	$-0.835272\pi$
$397$	1.89838	−	4.58310i	0.0952770	−	0.230019i	0.964332	+	0.264697i	$0.0852720\pi$
$398$		0			0
$399$		−	13.9777i		−	0.699762i
$400$		0			0
$401$			18.6119i			0.929432i	0.885460	+	0.464716i	$0.153843\pi$
$401$			18.6119i			0.929432i	−0.885460	+	0.464716i	$0.846157\pi$
$402$		0			0
$403$	−2.40482	+	5.80576i	−0.119793	+	0.289205i
$404$		0			0
$405$	−10.3584	+	4.29061i	−0.514715	+	0.213202i
$406$		0			0
$407$	−14.9425	−	14.9425i	−0.740671	−	0.740671i
$408$		0			0
$409$	20.1253	−	20.1253i	0.995131	−	0.995131i	−0.00485725	−	0.999988i	$-0.501546\pi$
$409$	20.1253	−	20.1253i	0.995131	−	0.995131i	0.999988	+	0.00485725i	$0.00154612\pi$
$410$		0			0
$411$	−1.38907	−	3.35352i	−0.0685180	−	0.165417i
$412$		0			0
$413$	−11.7504	−	4.86717i	−0.578199	−	0.239498i
$414$		0			0
$415$	14.8324			0.728095
$416$		0			0
$417$	2.68587			0.131528
$418$		0			0
$419$	9.22355	+	3.82052i	0.450600	+	0.186645i	0.596430	−	0.802665i	$-0.296585\pi$
$419$	9.22355	+	3.82052i	0.450600	+	0.186645i	−0.145830	+	0.989310i	$0.546585\pi$
$420$		0			0
$421$	2.52296	+	6.09096i	0.122962	+	0.296855i	0.973359	−	0.229285i	$-0.0736387\pi$
$421$	2.52296	+	6.09096i	0.122962	+	0.296855i	−0.850398	+	0.526140i	$0.823639\pi$
$422$		0			0
$423$	−10.4418	+	10.4418i	−0.507696	+	0.507696i
$424$		0			0
$425$	−3.59293	−	3.59293i	−0.174283	−	0.174283i
$426$		0			0
$427$	2.54904	−	1.05585i	0.123357	−	0.0510959i
$428$		0			0
$429$	−1.93281	+	4.66622i	−0.0933171	+	0.225287i
$430$		0			0
$431$		−	3.88483i		−	0.187126i	−0.995613	−	0.0935628i	$-0.970174\pi$
$431$		−	3.88483i		−	0.187126i	0.995613	−	0.0935628i	$-0.0298256\pi$
$432$		0			0
$433$			14.7888i			0.710704i	0.934733	+	0.355352i	$0.115639\pi$
$433$			14.7888i			0.710704i	−0.934733	+	0.355352i	$0.884361\pi$
$434$		0			0
$435$	3.09719	−	7.47727i	0.148499	−	0.358508i
$436$		0			0
$437$	27.7922	−	11.5119i	1.32948	−	0.550688i
$438$		0			0
$439$	1.12762	+	1.12762i	0.0538182	+	0.0538182i	0.733504	−	0.679685i	$-0.237884\pi$
$439$	1.12762	+	1.12762i	0.0538182	+	0.0538182i	−0.679685	+	0.733504i	$0.737884\pi$
$440$		0			0
$441$	−6.95498	+	6.95498i	−0.331189	+	0.331189i
$442$		0			0
$443$	−8.10399	−	19.5648i	−0.385032	−	0.929550i	−0.990976	−	0.134042i	$-0.957204\pi$
$443$	−8.10399	−	19.5648i	−0.385032	−	0.929550i	0.605944	−	0.795508i	$-0.292796\pi$
$444$		0			0
$445$	6.11410	+	2.53254i	0.289836	+	0.120054i
$446$		0			0
$447$	39.8745			1.88600
$448$		0			0
$449$	−11.3483			−0.535560			−0.267780	−	0.963480i	$-0.586290\pi$
$449$	−11.3483			−0.535560			−0.267780	+	0.963480i	$0.586290\pi$
$450$		0			0
$451$	−6.24808	−	2.58804i	−0.294211	−	0.121866i
$452$		0			0
$453$	2.97317	+	7.17787i	0.139692	+	0.337246i
$454$		0			0
$455$	−0.762572	+	0.762572i	−0.0357499	+	0.0357499i
$456$		0			0
$457$	−15.0165	−	15.0165i	−0.702443	−	0.702443i	0.262491	−	0.964934i	$-0.415456\pi$
$457$	−15.0165	−	15.0165i	−0.702443	−	0.702443i	−0.964934	+	0.262491i	$0.915456\pi$
$458$		0			0
$459$	−13.2725	+	5.49767i	−0.619509	+	0.256609i
$460$		0			0
$461$	−6.94676	+	16.7710i	−0.323543	+	0.781101i	0.675500	+	0.737360i	$0.263928\pi$
$461$	−6.94676	+	16.7710i	−0.323543	+	0.781101i	−0.999043	+	0.0437415i	$0.986072\pi$
$462$		0			0
$463$			5.12818i			0.238327i	0.992875	+	0.119163i	$0.0380212\pi$
$463$			5.12818i			0.238327i	−0.992875	+	0.119163i	$0.961979\pi$
$464$		0			0
$465$			13.8186i			0.640823i
$466$		0			0
$467$	−13.3497	+	32.2291i	−0.617752	+	1.49139i	0.236555	+	0.971618i	$0.423982\pi$
$467$	−13.3497	+	32.2291i	−0.617752	+	1.49139i	−0.854307	+	0.519768i	$0.826018\pi$
$468$		0			0
$469$	8.03940	−	3.33003i	0.371225	−	0.153766i
$470$		0			0
$471$	−11.8740	−	11.8740i	−0.547124	−	0.547124i
$472$		0			0
$473$	10.5320	−	10.5320i	0.484261	−	0.484261i
$474$		0			0
$475$	2.25559	+	5.44547i	0.103493	+	0.249855i
$476$		0			0
$477$	22.1170	+	9.16117i	1.01267	+	0.419461i
$478$		0			0
$479$	8.07095			0.368771			0.184386	−	0.982854i	$-0.440970\pi$
$479$	8.07095			0.368771			0.184386	+	0.982854i	$0.440970\pi$
$480$		0			0
$481$	−8.80286			−0.401376
$482$		0			0
$483$	11.1820	+	4.63173i	0.508798	+	0.210751i
$484$		0			0
$485$	4.99792	+	12.0660i	0.226944	+	0.547890i
$486$		0			0
$487$	−15.9947	+	15.9947i	−0.724791	+	0.724791i	−0.969577	−	0.244786i	$-0.921282\pi$
$487$	−15.9947	+	15.9947i	−0.724791	+	0.724791i	0.244786	+	0.969577i	$0.421282\pi$
$488$		0			0
$489$	−15.4493	−	15.4493i	−0.698643	−	0.698643i
$490$		0			0
$491$	1.24501	−	0.515699i	0.0561864	−	0.0232732i	−0.354413	−	0.935089i	$-0.615319\pi$
$491$	1.24501	−	0.515699i	0.0561864	−	0.0232732i	0.410600	+	0.911816i	$0.365319\pi$
$492$		0			0
$493$	7.26281	−	17.5340i	0.327100	−	0.789690i
$494$		0			0
$495$			4.00992i			0.180233i
$496$		0			0
$497$			6.97940i			0.313069i
$498$		0			0
$499$	13.1507	−	31.7486i	0.588706	−	1.42126i	−0.296035	−	0.955177i	$-0.595665\pi$
$499$	13.1507	−	31.7486i	0.588706	−	1.42126i	0.884741	−	0.466084i	$-0.154335\pi$
$500$		0			0
$501$	21.9735	−	9.10171i	0.981702	−	0.406634i
$502$		0			0
$503$	−27.6840	−	27.6840i	−1.23437	−	1.23437i	−0.962269	−	0.272099i	$-0.912282\pi$
$503$	−27.6840	−	27.6840i	−1.23437	−	1.23437i	−0.272099	−	0.962269i	$-0.587718\pi$
$504$		0			0
$505$	7.67350	−	7.67350i	0.341466	−	0.341466i
$506$		0			0
$507$	−9.97462	−	24.0809i	−0.442988	−	1.06947i
$508$		0			0
$509$	21.7005	+	8.98864i	0.961857	+	0.398414i	0.807675	−	0.589628i	$-0.200726\pi$
$509$	21.7005	+	8.98864i	0.961857	+	0.398414i	0.154183	+	0.988042i	$0.450726\pi$
$510$		0			0
$511$	12.3590			0.546731
$512$		0			0
$513$	16.6646			0.735761
$514$		0			0
$515$	−11.2631	−	4.66533i	−0.496311	−	0.205579i
$516$		0			0
$517$	−7.88552	−	19.0373i	−0.346805	−	0.837261i
$518$		0			0
$519$	27.4364	−	27.4364i	1.20433	−	1.20433i
$520$		0			0
$521$	17.6360	+	17.6360i	0.772648	+	0.772648i	0.978569	−	0.205921i	$-0.0660189\pi$
$521$	17.6360	+	17.6360i	0.772648	+	0.772648i	−0.205921	+	0.978569i	$0.566019\pi$
$522$		0			0
$523$	−10.9012	+	4.51543i	−0.476676	+	0.197446i	−0.608068	−	0.793885i	$-0.708055\pi$
$523$	−10.9012	+	4.51543i	−0.476676	+	0.197446i	0.131392	+	0.991330i	$0.458055\pi$
$524$		0			0
$525$	−0.907521	+	2.19095i	−0.0396074	+	0.0956208i
$526$		0			0
$527$			32.4043i			1.41155i
$528$		0			0
$529$			3.04797i			0.132520i
$530$		0			0
$531$	−7.53882	+	18.2003i	−0.327157	+	0.789827i
$532$		0			0
$533$	−2.60275	+	1.07810i	−0.112738	+	0.0466975i
$534$		0			0
$535$	5.74918	+	5.74918i	0.248559	+	0.248559i
$536$		0			0
$537$	4.87140	−	4.87140i	0.210216	−	0.210216i
$538$		0			0
$539$	−5.25233	−	12.6802i	−0.226234	−	0.546177i
$540$		0			0
$541$	−23.5308	−	9.74678i	−1.01167	−	0.419047i	−0.185606	−	0.982624i	$-0.559425\pi$
$541$	−23.5308	−	9.74678i	−1.01167	−	0.419047i	−0.826063	+	0.563577i	$0.809425\pi$
$542$		0			0
$543$	2.55760			0.109757
$544$		0			0
$545$	−9.99939			−0.428327
$546$		0			0
$547$	18.9717	+	7.85835i	0.811172	+	0.335999i	0.749422	−	0.662093i	$-0.230332\pi$
$547$	18.9717	+	7.85835i	0.811172	+	0.335999i	0.0617507	+	0.998092i	$0.480332\pi$
$548$		0			0
$549$	−1.63541	−	3.94823i	−0.0697977	−	0.168506i
$550$		0			0
$551$	−15.5671	+	15.5671i	−0.663179	+	0.663179i
$552$		0			0
$553$	−0.783344	−	0.783344i	−0.0333112	−	0.0333112i
$554$		0			0
$555$	−17.8838	+	7.40772i	−0.759126	+	0.314440i
$556$		0			0
$557$	−0.726149	+	1.75308i	−0.0307679	+	0.0742803i	−0.938517	−	0.345234i	$-0.887800\pi$
$557$	−0.726149	+	1.75308i	−0.0307679	+	0.0742803i	0.907749	+	0.419514i	$0.137800\pi$
$558$		0			0
$559$		−	6.20457i		−	0.262425i
$560$		0			0
$561$			26.0441i			1.09958i
$562$		0			0
$563$	10.6081	−	25.6103i	0.447079	−	1.07935i	−0.526332	−	0.850279i	$-0.676433\pi$
$563$	10.6081	−	25.6103i	0.447079	−	1.07935i	0.973411	−	0.229066i	$-0.0735671\pi$
$564$		0			0
$565$	−9.82124	+	4.06809i	−0.413183	+	0.171146i
$566$		0			0
$567$	8.67670	+	8.67670i	0.364387	+	0.364387i
$568$		0			0
$569$	21.3325	−	21.3325i	0.894306	−	0.894306i	−0.100619	−	0.994925i	$-0.532082\pi$
$569$	21.3325	−	21.3325i	0.894306	−	0.894306i	0.994925	+	0.100619i	$0.0320823\pi$
$570$		0			0
$571$	−17.4361	−	42.0944i	−0.729676	−	1.76159i	−0.643674	−	0.765300i	$-0.722591\pi$
$571$	−17.4361	−	42.0944i	−0.729676	−	1.76159i	−0.0860025	−	0.996295i	$-0.527409\pi$
$572$		0			0
$573$	−24.1923	−	10.0208i	−1.01065	−	0.418624i
$574$		0			0
$575$	−5.10372			−0.212840
$576$		0			0
$577$	−13.6278			−0.567331			−0.283665	−	0.958923i	$-0.591551\pi$
$577$	−13.6278			−0.567331			−0.283665	+	0.958923i	$0.591551\pi$
$578$		0			0
$579$	−41.4554	−	17.1714i	−1.72283	−	0.713618i
$580$		0			0
$581$	−6.21216	−	14.9975i	−0.257724	−	0.622200i
$582$		0			0
$583$	−23.6210	+	23.6210i	−0.978281	+	0.978281i
$584$		0			0
$585$	1.18116	+	1.18116i	0.0488348	+	0.0488348i
$586$		0			0
$587$	10.5227	−	4.35863i	0.434317	−	0.179900i	−0.154803	−	0.987945i	$-0.549474\pi$
$587$	10.5227	−	4.35863i	0.434317	−	0.179900i	0.589120	+	0.808045i	$0.299474\pi$
$588$		0			0
$589$	14.3846	−	34.7275i	0.592708	−	1.43092i
$590$		0			0
$591$		−	12.0810i		−	0.496946i
$592$		0			0
$593$		−	13.3023i		−	0.546260i	−0.961977	−	0.273130i	$-0.911941\pi$
$593$		−	13.3023i		−	0.546260i	0.961977	−	0.273130i	$-0.0880589\pi$
$594$		0			0
$595$	−2.12811	+	5.13771i	−0.0872439	+	0.210625i
$596$		0			0
$597$	−23.4592	+	9.71711i	−0.960121	+	0.397695i
$598$		0			0
$599$	−23.1591	−	23.1591i	−0.946255	−	0.946255i	0.0523731	−	0.998628i	$-0.483322\pi$
$599$	−23.1591	−	23.1591i	−0.946255	−	0.946255i	−0.998628	+	0.0523731i	$0.983322\pi$
$600$		0			0
$601$	−20.1473	+	20.1473i	−0.821825	+	0.821825i	−0.986370	−	0.164545i	$-0.947384\pi$
$601$	−20.1473	+	20.1473i	−0.821825	+	0.821825i	0.164545	+	0.986370i	$0.447384\pi$
$602$		0			0
$603$	−5.15792	−	12.4523i	−0.210047	−	0.507097i
$604$		0			0
$605$	4.99312	+	2.06822i	0.202999	+	0.0840851i
$606$		0			0
$607$	−10.5927			−0.429946			−0.214973	−	0.976620i	$-0.568966\pi$
$607$	−10.5927			−0.429946			−0.214973	+	0.976620i	$0.568966\pi$
$608$		0			0
$609$	−8.85764			−0.358930
$610$		0			0
$611$	−7.93035	−	3.28486i	−0.320828	−	0.132891i
$612$		0			0
$613$	−14.3556	−	34.6576i	−0.579819	−	1.39981i	−0.892975	−	0.450106i	$-0.851386\pi$
$613$	−14.3556	−	34.6576i	−0.579819	−	1.39981i	0.313156	−	0.949702i	$-0.398614\pi$
$614$		0			0
$615$	−4.38050	+	4.38050i	−0.176639	+	0.176639i
$616$		0			0
$617$	3.11039	+	3.11039i	0.125219	+	0.125219i	0.766939	−	0.641720i	$-0.221779\pi$
$617$	3.11039	+	3.11039i	0.125219	+	0.125219i	−0.641720	+	0.766939i	$0.721779\pi$
$618$		0			0
$619$	−1.68350	+	0.697328i	−0.0676656	+	0.0280280i	−0.416260	−	0.909246i	$-0.636659\pi$
$619$	−1.68350	+	0.697328i	−0.0676656	+	0.0280280i	0.348594	+	0.937274i	$0.386659\pi$
$620$		0			0
$621$	−5.52207	+	13.3315i	−0.221593	+	0.534973i
$622$		0			0
$623$		−	7.24282i		−	0.290178i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	11.5613	−	27.9113i	0.461712	−	1.11467i
$628$		0			0
$629$	−41.9370	+	17.3709i	−1.67214	+	0.692623i
$630$		0			0
$631$	28.7773	+	28.7773i	1.14561	+	1.14561i	0.987407	+	0.158201i	$0.0505694\pi$
$631$	28.7773	+	28.7773i	1.14561	+	1.14561i	0.158201	+	0.987407i	$0.449431\pi$
$632$		0			0
$633$	−11.3278	+	11.3278i	−0.450239	+	0.450239i
$634$		0			0
$635$	1.95031	+	4.70847i	0.0773958	+	0.186850i
$636$		0			0
$637$	−5.28219	−	2.18795i	−0.209288	−	0.0866899i
$638$		0			0
$639$	10.8105			0.427656
$640$		0			0
$641$	−14.8009			−0.584601			−0.292300	−	0.956327i	$-0.594421\pi$
$641$	−14.8009			−0.584601			−0.292300	+	0.956327i	$0.594421\pi$
$642$		0			0
$643$	−21.8812	−	9.06349i	−0.862911	−	0.357429i	−0.0930654	−	0.995660i	$-0.529667\pi$
$643$	−21.8812	−	9.06349i	−0.862911	−	0.357429i	−0.769845	+	0.638231i	$0.779667\pi$
$644$		0			0
$645$	−5.22123	−	12.6052i	−0.205586	−	0.496328i
$646$		0			0
$647$	12.6858	−	12.6858i	0.498730	−	0.498730i	−0.412312	−	0.911043i	$-0.635279\pi$
$647$	12.6858	−	12.6858i	0.498730	−	0.498730i	0.911043	+	0.412312i	$0.135279\pi$
$648$		0			0
$649$	−19.4380	−	19.4380i	−0.763006	−	0.763006i
$650$		0			0
$651$	13.9724	−	5.78755i	0.547621	−	0.226832i
$652$		0			0
$653$	6.30052	−	15.2108i	0.246559	−	0.595245i	−0.751349	−	0.659905i	$-0.770596\pi$
$653$	6.30052	−	15.2108i	0.246559	−	0.595245i	0.997907	+	0.0646603i	$0.0205964\pi$
$654$		0			0
$655$			11.1287i			0.434835i
$656$		0			0
$657$		−	19.1430i		−	0.746841i
$658$		0			0
$659$	0.638070	−	1.54044i	0.0248557	−	0.0600069i	−0.910964	−	0.412485i	$-0.864661\pi$
$659$	0.638070	−	1.54044i	0.0248557	−	0.0600069i	0.935820	+	0.352478i	$0.114661\pi$
$660$		0			0
$661$	−9.73039	+	4.03046i	−0.378468	+	0.156767i	−0.563804	−	0.825909i	$-0.690663\pi$
$661$	−9.73039	+	4.03046i	−0.378468	+	0.156767i	0.185336	+	0.982675i	$0.440663\pi$
$662$		0			0
$663$	7.67150	+	7.67150i	0.297936	+	0.297936i
$664$		0			0
$665$	4.56137	−	4.56137i	0.176882	−	0.176882i
$666$		0			0
$667$	−7.29504	−	17.6118i	−0.282465	−	0.681931i
$668$		0			0
$669$	24.0529	+	9.96305i	0.929940	+	0.385194i
$670$		0			0
$671$	5.96333			0.230212
$672$		0			0
$673$	−29.6782			−1.14401			−0.572005	−	0.820250i	$-0.693834\pi$
$673$	−29.6782			−1.14401			−0.572005	+	0.820250i	$0.693834\pi$
$674$		0			0
$675$	−2.61210	−	1.08197i	−0.100540	−	0.0416450i
$676$		0			0
$677$	−13.8988	−	33.5547i	−0.534175	−	1.28961i	−0.928735	−	0.370743i	$-0.879103\pi$
$677$	−13.8988	−	33.5547i	−0.534175	−	1.28961i	0.394560	−	0.918870i	$-0.370897\pi$
$678$		0			0
$679$	10.1071	−	10.1071i	0.387873	−	0.387873i
$680$		0			0
$681$	−8.09317	−	8.09317i	−0.310131	−	0.310131i
$682$		0			0
$683$	36.0699	−	14.9406i	1.38018	−	0.571688i	0.435648	−	0.900117i	$-0.356519\pi$
$683$	36.0699	−	14.9406i	1.38018	−	0.571688i	0.944529	+	0.328429i	$0.106519\pi$
$684$		0			0
$685$	0.641061	−	1.54766i	0.0244937	−	0.0591330i
$686$		0			0
$687$		−	32.9775i		−	1.25817i
$688$		0			0
$689$			13.9155i			0.530139i
$690$		0			0
$691$	−9.72379	+	23.4753i	−0.369910	+	0.893042i	0.623854	+	0.781541i	$0.285566\pi$
$691$	−9.72379	+	23.4753i	−0.369910	+	0.893042i	−0.993764	+	0.111501i	$0.964434\pi$
$692$		0			0
$693$	4.05454	−	1.67945i	0.154019	−	0.0637969i
$694$		0			0
$695$	0.876485	+	0.876485i	0.0332470	+	0.0332470i
$696$		0			0
$697$	−10.2721	+	10.2721i	−0.389085	+	0.389085i
$698$		0			0
$699$	−5.15413	−	12.4432i	−0.194947	−	0.470644i
$700$		0			0
$701$	−14.7952	−	6.12835i	−0.558805	−	0.231465i	0.0853611	−	0.996350i	$-0.472796\pi$
$701$	−14.7952	−	6.12835i	−0.558805	−	0.231465i	−0.644166	+	0.764885i	$0.722796\pi$
$702$		0			0
$703$	52.6549			1.98592
$704$		0			0
$705$	−18.8755			−0.710892
$706$		0			0
$707$	−10.9727	−	4.54505i	−0.412672	−	0.170934i
$708$		0			0
$709$	−12.9475	−	31.2580i	−0.486253	−	1.17392i	−0.956591	−	0.291433i	$-0.905868\pi$
$709$	−12.9475	−	31.2580i	−0.486253	−	1.17392i	0.470338	−	0.882486i	$-0.344132\pi$
$710$		0			0
$711$	−1.21333	+	1.21333i	−0.0455034	+	0.0455034i
$712$		0			0
$713$	23.0150	+	23.0150i	0.861917	+	0.861917i
$714$		0			0
$715$	−2.15347	+	0.891997i	−0.0805353	+	0.0333588i
$716$		0			0
$717$	0.356660	−	0.861054i	0.0133197	−	0.0321567i
$718$		0			0
$719$			39.0098i			1.45482i	0.686204	+	0.727409i	$0.259276\pi$
$719$			39.0098i			1.45482i	−0.686204	+	0.727409i	$0.740724\pi$
$720$		0			0
$721$			13.3424i			0.496896i
$722$		0			0
$723$	−24.0046	+	57.9522i	−0.892740	+	2.15527i
$724$		0			0
$725$	3.45078	−	1.42936i	0.128159	−	0.0530850i
$726$		0			0
$727$	21.4363	+	21.4363i	0.795028	+	0.795028i	0.982307	−	0.187279i	$-0.0599668\pi$
$727$	21.4363	+	21.4363i	0.795028	+	0.795028i	−0.187279	+	0.982307i	$0.559967\pi$
$728$		0			0
$729$	0.443507	−	0.443507i	0.0164262	−	0.0164262i
$730$		0			0
$731$	−12.2436	−	29.5587i	−0.452847	−	1.09327i
$732$		0			0
$733$	−4.52300	−	1.87349i	−0.167061	−	0.0691989i	0.297586	−	0.954695i	$-0.403819\pi$
$733$	−4.52300	−	1.87349i	−0.167061	−	0.0691989i	−0.464647	+	0.885496i	$0.653819\pi$
$734$		0			0
$735$	−12.5724			−0.463742
$736$		0			0
$737$	18.8077			0.692791
$738$		0			0
$739$	−0.195533	−	0.0809926i	−0.00719281	−	0.00297936i	0.379084	−	0.925362i	$-0.376239\pi$
$739$	−0.195533	−	0.0809926i	−0.00719281	−	0.00297936i	−0.386277	+	0.922383i	$0.626239\pi$
$740$		0			0
$741$	−4.81605	−	11.6270i	−0.176922	−	0.427128i
$742$		0			0
$743$	−12.1088	+	12.1088i	−0.444228	+	0.444228i	−0.893430	−	0.449202i	$-0.851708\pi$
$743$	−12.1088	+	12.1088i	−0.444228	+	0.444228i	0.449202	+	0.893430i	$0.351708\pi$
$744$		0			0
$745$	13.0123	+	13.0123i	0.476734	+	0.476734i
$746$		0			0
$747$	−23.2298	+	9.62208i	−0.849932	+	0.352054i
$748$		0			0
$749$	3.40527	−	8.22104i	0.124426	−	0.300390i
$750$		0			0
$751$			13.8495i			0.505375i	0.967548	+	0.252688i	$0.0813145\pi$
$751$			13.8495i			0.505375i	−0.967548	+	0.252688i	$0.918686\pi$
$752$		0			0
$753$		−	42.4959i		−	1.54864i
$754$		0			0
$755$	−1.37212	+	3.31260i	−0.0499367	+	0.120558i
$756$		0			0
$757$	19.9573	−	8.26660i	0.725362	−	0.300455i	0.0107173	−	0.999943i	$-0.496589\pi$
$757$	19.9573	−	8.26660i	0.725362	−	0.300455i	0.714644	+	0.699488i	$0.246589\pi$
$758$		0			0
$759$	18.4977	+	18.4977i	0.671423	+	0.671423i
$760$		0			0
$761$	4.54613	−	4.54613i	0.164797	−	0.164797i	−0.619891	−	0.784688i	$-0.712823\pi$
$761$	4.54613	−	4.54613i	0.164797	−	0.164797i	0.784688	+	0.619891i	$0.212823\pi$
$762$		0			0
$763$	4.18797	+	10.1107i	0.151615	+	0.366030i
$764$		0			0
$765$	7.95786	+	3.29625i	0.287717	+	0.119176i
$766$		0			0
$767$	−11.4512			−0.413480
$768$		0			0
$769$	25.0521			0.903403			0.451701	−	0.892169i	$-0.350817\pi$
$769$	25.0521			0.903403			0.451701	+	0.892169i	$0.350817\pi$
$770$		0			0
$771$	20.7383	+	8.59007i	0.746870	+	0.309364i
$772$		0			0
$773$	9.49451	+	22.9218i	0.341494	+	0.824439i	0.997565	+	0.0697400i	$0.0222170\pi$
$773$	9.49451	+	22.9218i	0.341494	+	0.824439i	−0.656071	+	0.754699i	$0.727783\pi$
$774$		0			0
$775$	−4.50945	+	4.50945i	−0.161984	+	0.161984i
$776$		0			0
$777$	14.9803	+	14.9803i	0.537415	+	0.537415i
$778$		0			0
$779$	15.5686	−	6.44871i	0.557801	−	0.231049i
$780$		0			0
$781$	−5.77280	+	13.9368i	−0.206567	+	0.498697i
$782$		0			0
$783$		−	10.5603i		−	0.377395i
$784$		0			0
$785$		−	7.74970i		−	0.276599i
$786$		0			0
$787$	1.57586	−	3.80445i	0.0561732	−	0.135614i	−0.893301	−	0.449458i	$-0.851617\pi$
$787$	1.57586	−	3.80445i	0.0561732	−	0.135614i	0.949474	+	0.313844i	$0.101617\pi$
$788$		0			0
$789$	16.4431	−	6.81094i	0.585389	−	0.242476i
$790$		0			0
$791$	8.22671	+	8.22671i	0.292508	+	0.292508i
$792$		0			0
$793$	1.75655	−	1.75655i	0.0623769	−	0.0623769i
$794$		0			0
$795$	11.7101	+	28.2706i	0.415314	+	1.00266i
$796$		0			0
$797$	6.91828	+	2.86565i	0.245058	+	0.101506i	0.501832	−	0.864965i	$-0.332660\pi$
$797$	6.91828	+	2.86565i	0.245058	+	0.101506i	−0.256774	+	0.966472i	$0.582660\pi$
$798$		0			0
$799$	−44.2625			−1.56589
$800$		0			0
$801$	−11.2185			−0.396386
$802$		0			0
$803$	24.6790	+	10.2224i	0.870903	+	0.360740i
$804$		0			0
$805$	2.13755	+	5.16051i	0.0753389	+	0.181884i
$806$		0			0
$807$	44.1836	−	44.1836i	1.55534	−	1.55534i
$808$		0			0
$809$	39.4681	+	39.4681i	1.38762	+	1.38762i	0.830285	+	0.557339i	$0.188178\pi$
$809$	39.4681	+	39.4681i	1.38762	+	1.38762i	0.557339	+	0.830285i	$0.311822\pi$
$810$		0			0
$811$	−12.1137	+	5.01767i	−0.425370	+	0.176194i	−0.585090	−	0.810968i	$-0.698941\pi$
$811$	−12.1137	+	5.01767i	−0.425370	+	0.176194i	0.159720	+	0.987162i	$0.448941\pi$
$812$		0			0
$813$	17.2887	−	41.7386i	0.606341	−	1.46384i
$814$		0			0
$815$		−	10.0832i		−	0.353199i
$816$		0			0
$817$			37.1131i			1.29842i
$818$		0			0
$819$	0.699604	−	1.68899i	0.0244462	−	0.0590182i
$820$		0			0
$821$	14.4623	−	5.99047i	0.504737	−	0.209069i	−0.115761	−	0.993277i	$-0.536931\pi$
$821$	14.4623	−	5.99047i	0.504737	−	0.209069i	0.620498	+	0.784208i	$0.286931\pi$
$822$		0			0
$823$	10.0570	+	10.0570i	0.350566	+	0.350566i	0.860320	−	0.509754i	$-0.170264\pi$
$823$	10.0570	+	10.0570i	0.350566	+	0.350566i	−0.509754	+	0.860320i	$0.670264\pi$
$824$		0			0
$825$	−3.62435	+	3.62435i	−0.126184	+	0.126184i
$826$		0			0
$827$	−13.2231	−	31.9233i	−0.459811	−	1.11008i	−0.968473	−	0.249117i	$-0.919860\pi$
$827$	−13.2231	−	31.9233i	−0.459811	−	1.11008i	0.508662	−	0.860966i	$-0.330140\pi$
$828$		0			0
$829$	50.9271	+	21.0947i	1.76877	+	0.732649i	0.995079	+	0.0990881i	$0.0315926\pi$
$829$	50.9271	+	21.0947i	1.76877	+	0.732649i	0.773693	+	0.633561i	$0.218407\pi$
$830$		0			0
$831$	−22.7427			−0.788934
$832$		0			0
$833$	−29.4820			−1.02149
$834$		0			0
$835$	10.1408	+	4.20046i	0.350937	+	0.145363i
$836$		0			0
$837$	6.90007	+	16.6582i	0.238501	+	0.575793i
$838$		0			0
$839$	−4.66760	+	4.66760i	−0.161144	+	0.161144i	−0.783073	−	0.621930i	$-0.786349\pi$
$839$	−4.66760	+	4.66760i	−0.161144	+	0.161144i	0.621930	+	0.783073i	$0.286349\pi$
$840$		0			0
$841$	−10.6413	−	10.6413i	−0.366942	−	0.366942i
$842$		0			0
$843$	−37.0563	+	15.3492i	−1.27629	+	0.528656i
$844$		0			0
$845$	4.60331	−	11.1134i	0.158359	−	0.382311i
$846$		0			0
$847$		−	5.91490i		−	0.203238i
$848$		0			0
$849$			39.1268i			1.34283i
$850$		0			0
$851$	−17.4480	+	42.1232i	−0.598109	+	1.44396i
$852$		0			0
$853$	−32.0306	+	13.2675i	−1.09671	+	0.454271i	−0.856341	−	0.516411i	$-0.827268\pi$
$853$	−32.0306	+	13.2675i	−1.09671	+	0.454271i	−0.240366	+	0.970682i	$0.577268\pi$
$854$		0			0
$855$	−7.06517	−	7.06517i	−0.241624	−	0.241624i
$856$		0			0
$857$	22.5460	−	22.5460i	0.770158	−	0.770158i	−0.207976	−	0.978134i	$-0.566688\pi$
$857$	22.5460	−	22.5460i	0.770158	−	0.770158i	0.978134	+	0.207976i	$0.0666875\pi$
$858$		0			0
$859$	3.41920	+	8.25468i	0.116662	+	0.281646i	0.971415	−	0.237389i	$-0.0762915\pi$
$859$	3.41920	+	8.25468i	0.116662	+	0.281646i	−0.854753	+	0.519035i	$0.826292\pi$
$860$		0			0
$861$	6.26390	+	2.59459i	0.213473	+	0.0884235i
$862$		0			0
$863$	18.9503			0.645076			0.322538	−	0.946557i	$-0.395464\pi$
$863$	18.9503			0.645076			0.322538	+	0.946557i	$0.395464\pi$
$864$		0			0
$865$	17.9067			0.608847
$866$		0			0
$867$	17.6533	+	7.31222i	0.599536	+	0.248336i
$868$		0			0
$869$	−0.916295	−	2.21213i	−0.0310832	−	0.0750414i
$870$		0			0
$871$	5.53997	−	5.53997i	0.187715	−	0.187715i
$872$		0			0
$873$	−15.6549	−	15.6549i	−0.529840	−	0.529840i
$874$		0			0
$875$	−1.01113	+	0.418823i	−0.0341823	+	0.0141588i
$876$		0			0
$877$	1.80064	−	4.34713i	0.0608033	−	0.146792i	−0.890558	−	0.454870i	$-0.849686\pi$
$877$	1.80064	−	4.34713i	0.0608033	−	0.146792i	0.951361	+	0.308078i	$0.0996857\pi$
$878$		0			0
$879$		−	3.50289i		−	0.118149i
$880$		0			0
$881$			10.2043i			0.343792i	0.985115	+	0.171896i	$0.0549893\pi$
$881$			10.2043i			0.343792i	−0.985115	+	0.171896i	$0.945011\pi$
$882$		0			0
$883$	9.46994	−	22.8625i	0.318689	−	0.769383i	−0.680635	−	0.732623i	$-0.738296\pi$
$883$	9.46994	−	22.8625i	0.318689	−	0.769383i	0.999324	−	0.0367606i	$-0.0117039\pi$
$884$		0			0
$885$	−23.2642	+	9.63635i	−0.782018	+	0.323923i
$886$		0			0
$887$	−20.9083	−	20.9083i	−0.702031	−	0.702031i	0.262816	−	0.964846i	$-0.415349\pi$
$887$	−20.9083	−	20.9083i	−0.702031	−	0.702031i	−0.964846	+	0.262816i	$0.915349\pi$
$888$		0			0
$889$	3.94403	−	3.94403i	0.132278	−	0.132278i
$890$		0			0
$891$	10.1493	+	24.5027i	0.340016	+	0.820870i
$892$		0			0
$893$	47.4359	+	19.6486i	1.58738	+	0.657516i
$894$		0			0
$895$	3.17938			0.106275
$896$		0			0
$897$	10.8973			0.363850
$898$		0			0
$899$	−22.0067	−	9.11548i	−0.733965	−	0.304018i
$900$		0			0
$901$	27.4598	+	66.2938i	0.914818	+	2.20857i
$902$		0			0
$903$	−10.5587	+	10.5587i	−0.351370	+	0.351370i
$904$		0			0
$905$	0.834624	+	0.834624i	0.0277438	+	0.0277438i
$906$		0			0
$907$	40.8389	−	16.9160i	1.35603	−	0.561688i	0.418069	−	0.908415i	$-0.362707\pi$
$907$	40.8389	−	16.9160i	1.35603	−	0.561688i	0.937966	+	0.346728i	$0.112707\pi$
$908$		0			0
$909$	−7.03988	+	16.9958i	−0.233498	+	0.563714i
$910$		0			0
$911$			3.45772i			0.114560i	0.998358	+	0.0572798i	$0.0182427\pi$
$911$			3.45772i			0.114560i	−0.998358	+	0.0572798i	$0.981757\pi$
$912$		0			0
$913$		−	35.0858i		−	1.16117i
$914$		0			0
$915$	2.09043	−	5.04675i	0.0691076	−	0.166840i
$916$		0			0
$917$	11.2526	−	4.66096i	0.371592	−	0.153919i
$918$		0			0
$919$	27.6535	+	27.6535i	0.912204	+	0.912204i	0.996445	−	0.0842410i	$-0.0268466\pi$
$919$	27.6535	+	27.6535i	0.912204	+	0.912204i	−0.0842410	+	0.996445i	$0.526847\pi$
$920$		0			0
$921$	−30.6245	+	30.6245i	−1.00911	+	1.00911i
$922$		0			0
$923$	2.40477	+	5.80562i	0.0791538	+	0.191094i
$924$		0			0
$925$	−8.25342	−	3.41868i	−0.271371	−	0.112406i
$926$		0			0
$927$	20.6661			0.678765
$928$		0			0
$929$	−30.3986			−0.997347			−0.498674	−	0.866790i	$-0.666179\pi$
$929$	−30.3986			−0.997347			−0.498674	+	0.866790i	$0.666179\pi$
$930$		0			0
$931$	31.5958	+	13.0874i	1.03551	+	0.428922i
$932$		0			0
$933$	13.6996	+	33.0739i	0.448506	+	1.08279i
$934$		0			0
$935$	−8.49899	+	8.49899i	−0.277947	+	0.277947i
$936$		0			0
$937$	1.71158	+	1.71158i	0.0559147	+	0.0559147i	0.734511	−	0.678597i	$-0.237411\pi$
$937$	1.71158	+	1.71158i	0.0559147	+	0.0559147i	−0.678597	+	0.734511i	$0.737411\pi$
$938$		0			0
$939$	38.8638	−	16.0979i	1.26827	−	0.525335i
$940$		0			0
$941$	−18.8076	+	45.4055i	−0.613109	+	1.48018i	0.246457	+	0.969154i	$0.420733\pi$
$941$	−18.8076	+	45.4055i	−0.613109	+	1.48018i	−0.859567	+	0.511023i	$0.829267\pi$
$942$		0			0
$943$			14.5915i			0.475164i
$944$		0			0
$945$			3.09432i			0.100658i
$946$		0			0
$947$	−18.3870	+	44.3902i	−0.597497	+	1.44249i	0.278626	+	0.960400i	$0.410121\pi$
$947$	−18.3870	+	44.3902i	−0.597497	+	1.44249i	−0.876123	+	0.482087i	$0.839879\pi$
$948$		0			0
$949$	10.2805	−	4.25832i	0.333719	−	0.138231i
$950$		0			0
$951$	−1.37705	−	1.37705i	−0.0446538	−	0.0446538i
$952$		0			0
$953$	−18.6549	+	18.6549i	−0.604291	+	0.604291i	−0.941448	−	0.337157i	$-0.890535\pi$
$953$	−18.6549	+	18.6549i	−0.604291	+	0.604291i	0.337157	+	0.941448i	$0.390535\pi$
$954$		0			0
$955$	−4.62461	−	11.1648i	−0.149649	−	0.361284i
$956$		0			0
$957$	−17.6873	−	7.32632i	−0.571750	−	0.236826i
$958$		0			0
$959$	−1.83337			−0.0592026
$960$		0			0
$961$	9.67026			0.311944
$962$		0			0
$963$	−12.7337	−	5.27446i	−0.410337	−	0.169967i
$964$		0			0
$965$	−7.92462	−	19.1317i	−0.255103	−	0.615872i
$966$		0			0
$967$	21.1415	−	21.1415i	0.679865	−	0.679865i	−0.280104	−	0.959970i	$-0.590369\pi$
$967$	21.1415	−	21.1415i	0.679865	−	0.679865i	0.959970	+	0.280104i	$0.0903690\pi$
$968$		0			0
$969$	−45.8876	−	45.8876i	−1.47412	−	1.47412i
$970$		0			0
$971$	−17.0008	+	7.04195i	−0.545581	+	0.225987i	−0.638412	−	0.769695i	$-0.720408\pi$
$971$	−17.0008	+	7.04195i	−0.545581	+	0.225987i	0.0928310	+	0.995682i	$0.470408\pi$
$972$		0			0
$973$	0.519146	−	1.25333i	0.0166431	−	0.0401799i
$974$		0			0
$975$			2.13517i			0.0683800i
$976$		0			0
$977$		−	13.8579i		−	0.443353i	−0.975120	−	0.221676i	$-0.928847\pi$
$977$		−	13.8579i		−	0.443353i	0.975120	−	0.221676i	$-0.0711529\pi$
$978$		0			0
$979$	5.99068	−	14.4628i	0.191463	−	0.462232i
$980$		0			0
$981$	15.6605	−	6.48680i	0.500002	−	0.207107i
$982$		0			0
$983$	−1.39968	−	1.39968i	−0.0446429	−	0.0446429i	0.684433	−	0.729076i	$-0.260050\pi$
$983$	−1.39968	−	1.39968i	−0.0446429	−	0.0446429i	−0.729076	+	0.684433i	$0.760050\pi$
$984$		0			0
$985$	3.94240	−	3.94240i	0.125615	−	0.125615i
$986$		0			0
$987$	7.90549	+	19.0855i	0.251634	+	0.607499i
$988$		0			0
$989$	−29.6899	−	12.2980i	−0.944084	−	0.391052i
$990$		0			0
$991$	−48.1231			−1.52868			−0.764341	−	0.644812i	$-0.776936\pi$
$991$	−48.1231			−1.52868			−0.764341	+	0.644812i	$0.776936\pi$
$992$		0			0
$993$	35.2756			1.11944
$994$		0			0
$995$	−10.8265	−	4.48447i	−0.343222	−	0.142167i
$996$		0			0
$997$	8.21937	+	19.8433i	0.260310	+	0.628444i	0.998958	−	0.0456479i	$-0.0145352\pi$
$997$	8.21937	+	19.8433i	0.260310	+	0.628444i	−0.738648	+	0.674092i	$0.764535\pi$
$998$		0			0
$999$	−17.8599	+	17.8599i	−0.565062	+	0.565062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.x.a.81.3		64
4.3	odd	2		160.2.x.a.61.10	yes	64
20.3	even	4		800.2.ba.e.349.1		64
20.7	even	4		800.2.ba.g.349.16		64
20.19	odd	2		800.2.y.c.701.7		64
32.11	odd	8		160.2.x.a.21.10	✓	64
32.21	even	8	inner	640.2.x.a.561.3		64
160.43	even	8		800.2.ba.g.149.16		64
160.107	even	8		800.2.ba.e.149.1		64
160.139	odd	8		800.2.y.c.501.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.x.a.21.10	✓	64	32.11	odd	8
160.2.x.a.61.10	yes	64	4.3	odd	2
640.2.x.a.81.3		64	1.1	even	1	trivial
640.2.x.a.561.3		64	32.21	even	8	inner
800.2.y.c.501.7		64	160.139	odd	8
800.2.y.c.701.7		64	20.19	odd	2
800.2.ba.e.149.1		64	160.107	even	8
800.2.ba.e.349.1		64	20.3	even	4
800.2.ba.g.149.16		64	160.43	even	8
800.2.ba.g.349.16		64	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00190 - 0.829213i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-0.773883 + 0.773883i) q^{7} +(1.19868 + 1.19868i) q^{9} +O(q^{10})\)	\(q+(-2.00190 - 0.829213i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-0.773883 + 0.773883i) q^{7} +(1.19868 + 1.19868i) q^{9} +(-2.18542 + 0.905229i) q^{11} +(-0.377090 + 0.910375i) q^{13} +2.16684i q^{15} +5.08117i q^{17} +(2.25559 - 5.44547i) q^{19} +(2.19095 - 0.907521i) q^{21} +(3.60888 + 3.60888i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(1.08197 + 2.61210i) q^{27} +(-3.45078 - 1.42936i) q^{29} +6.37732 q^{31} +5.12560 q^{33} +(1.01113 + 0.418823i) q^{35} +(3.41868 + 8.25342i) q^{37} +(1.50979 - 1.50979i) q^{39} +(2.02161 + 2.02161i) q^{41} +(-5.81731 + 2.40961i) q^{43} +(0.648719 - 1.56615i) q^{45} +8.71108i q^{47} +5.80221i q^{49} +(4.21337 - 10.1720i) q^{51} +(13.0470 - 5.40423i) q^{53} +(1.67264 + 1.67264i) q^{55} +(-9.03091 + 9.03091i) q^{57} +(4.44720 + 10.7365i) q^{59} +(-2.32909 - 0.964739i) q^{61} -1.85527 q^{63} +0.985383 q^{65} +(-7.34570 - 3.04269i) q^{67} +(-4.23207 - 10.2171i) q^{69} +(4.50934 - 4.50934i) q^{71} +(-7.98507 - 7.98507i) q^{73} +(2.00190 - 0.829213i) q^{75} +(0.990715 - 2.39180i) q^{77} +1.01222i q^{79} -11.2119i q^{81} +(-5.67612 + 13.7034i) q^{83} +(4.69439 - 1.94448i) q^{85} +(5.72285 + 5.72285i) q^{87} +(-4.67953 + 4.67953i) q^{89} +(-0.412701 - 0.996348i) q^{91} +(-12.7667 - 5.28816i) q^{93} -5.89414 q^{95} -13.0602 q^{97} +(-3.70468 - 1.53453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) \) 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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