LMFDB - Embedded newform 912.2.bh.f.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(239,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("912.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.2
Character	$\chi$	$=$	912.239
Dual form			912.2.bh.f.767.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.63249 - 0.578768i) q^{3} +(3.06808 + 1.77136i) q^{5} +0.587143i q^{7} +(2.33006 + 1.88967i) q^{9} +3.00869 q^{11} +(0.973896 + 1.68684i) q^{13} +(-3.98341 - 4.66744i) q^{15} +(-1.36968 - 0.790785i) q^{17} +(-4.34794 - 0.308898i) q^{19} +(0.339819 - 0.958506i) q^{21} +(1.35506 + 2.34703i) q^{23} +(3.77542 + 6.53922i) q^{25} +(-2.71012 - 4.43343i) q^{27} +(-4.59794 + 2.65462i) q^{29} +4.43343i q^{31} +(-4.91166 - 1.74133i) q^{33} +(-1.04004 + 1.80140i) q^{35} +6.60305 q^{37} +(-0.613589 - 3.31741i) q^{39} +(-7.82621 - 4.51846i) q^{41} +(5.77246 + 3.33273i) q^{43} +(3.80153 + 9.92502i) q^{45} +(3.48944 + 6.04389i) q^{47} +6.65526 q^{49} +(1.77831 + 2.08368i) q^{51} +(3.87735 - 2.23859i) q^{53} +(9.23091 + 5.32947i) q^{55} +(6.91919 + 3.02072i) q^{57} +(7.23960 - 12.5394i) q^{59} +(-0.0261043 - 0.0452140i) q^{61} +(-1.10950 + 1.36808i) q^{63} +6.90047i q^{65} +(0.662494 - 0.382491i) q^{67} +(-0.853736 - 4.61577i) q^{69} +(-5.86809 + 10.1638i) q^{71} +(-4.10305 + 7.10670i) q^{73} +(-2.37865 - 12.8603i) q^{75} +1.76653i q^{77} +(7.80639 + 4.50702i) q^{79} +(1.85832 + 8.80606i) q^{81} -13.6263 q^{83} +(-2.80153 - 4.85239i) q^{85} +(9.04251 - 1.67251i) q^{87} +(9.20425 - 5.31408i) q^{89} +(-0.990414 + 0.571816i) q^{91} +(2.56592 - 7.23753i) q^{93} +(-12.7927 - 8.64949i) q^{95} +(-5.27542 + 9.13730i) q^{97} +(7.01041 + 5.68542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) $ 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.63249	−	0.578768i	−0.942519	−	0.334152i
$3$	−1.63249	−	0.578768i	−0.942519	−	0.334152i
$4$		0			0
$5$	3.06808	+	1.77136i	1.37209	+	0.792176i	0.991191	−	0.132442i	$-0.0422817\pi$
$5$	3.06808	+	1.77136i	1.37209	+	0.792176i	0.380898	+	0.924617i	$0.375615\pi$
$6$		0			0
$7$			0.587143i			0.221919i	0.993825	+	0.110960i	$0.0353924\pi$
$7$			0.587143i			0.221919i	−0.993825	+	0.110960i	$0.964608\pi$
$8$		0			0
$9$	2.33006	+	1.88967i	0.776685	+	0.629889i
$10$		0			0
$11$	3.00869			0.907154			0.453577	−	0.891217i	$-0.350148\pi$
$11$	3.00869			0.907154			0.453577	+	0.891217i	$0.350148\pi$
$12$		0			0
$13$	0.973896	+	1.68684i	0.270110	+	0.467844i	0.968890	−	0.247493i	$-0.0796066\pi$
$13$	0.973896	+	1.68684i	0.270110	+	0.467844i	−0.698780	+	0.715337i	$0.746273\pi$
$14$		0			0
$15$	−3.98341	−	4.66744i	−1.02851	−	1.20513i
$16$		0			0
$17$	−1.36968	−	0.790785i	−0.332196	−	0.191794i	0.324620	−	0.945845i	$-0.394764\pi$
$17$	−1.36968	−	0.790785i	−0.332196	−	0.191794i	−0.656816	+	0.754051i	$0.728097\pi$
$18$		0			0
$19$	−4.34794	−	0.308898i	−0.997486	−	0.0708662i
$19$	−4.34794	−	0.308898i	−0.997486	−	0.0708662i
$20$		0			0
$21$	0.339819	−	0.958506i	0.0741547	−	0.209163i
$22$		0			0
$23$	1.35506	+	2.34703i	0.282549	+	0.489390i	0.972012	−	0.234932i	$-0.0754866\pi$
$23$	1.35506	+	2.34703i	0.282549	+	0.489390i	−0.689463	+	0.724321i	$0.742153\pi$
$24$		0			0
$25$	3.77542	+	6.53922i	0.755085	+	1.30784i
$26$		0			0
$27$	−2.71012	−	4.43343i	−0.521562	−	0.853213i
$28$		0			0
$29$	−4.59794	+	2.65462i	−0.853817	+	0.492951i	−0.861937	−	0.507016i	$-0.830749\pi$
$29$	−4.59794	+	2.65462i	−0.853817	+	0.492951i	0.00812014	+	0.999967i	$0.497415\pi$
$30$		0			0
$31$			4.43343i			0.796267i	0.917328	+	0.398133i	$0.130342\pi$
$31$			4.43343i			0.796267i	−0.917328	+	0.398133i	$0.869658\pi$
$32$		0			0
$33$	−4.91166	−	1.74133i	−0.855010	−	0.303127i
$34$		0			0
$35$	−1.04004	+	1.80140i	−0.175799	+	0.304493i
$36$		0			0
$37$	6.60305			1.08554			0.542768	−	0.839883i	$-0.317376\pi$
$37$	6.60305			1.08554			0.542768	+	0.839883i	$0.317376\pi$
$38$		0			0
$39$	−0.613589	−	3.31741i	−0.0982529	−	0.531210i
$40$		0			0
$41$	−7.82621	−	4.51846i	−1.22225	−	0.705665i	−0.256851	−	0.966451i	$-0.582685\pi$
$41$	−7.82621	−	4.51846i	−1.22225	−	0.705665i	−0.965397	+	0.260786i	$0.916018\pi$
$42$		0			0
$43$	5.77246	+	3.33273i	0.880292	+	0.508237i	0.870755	−	0.491718i	$-0.163631\pi$
$43$	5.77246	+	3.33273i	0.880292	+	0.508237i	0.00953750	+	0.999955i	$0.496964\pi$
$44$		0			0
$45$	3.80153	+	9.92502i	0.566698	+	1.47953i
$46$		0			0
$47$	3.48944	+	6.04389i	0.508987	+	0.881591i	0.999946	+	0.0104086i	$0.00331322\pi$
$47$	3.48944	+	6.04389i	0.508987	+	0.881591i	−0.490959	+	0.871183i	$0.663353\pi$
$48$		0			0
$49$	6.65526			0.950752
$50$		0			0
$51$	1.77831	+	2.08368i	0.249013	+	0.291773i
$52$		0			0
$53$	3.87735	−	2.23859i	0.532595	−	0.307494i	−0.209478	−	0.977813i	$-0.567176\pi$
$53$	3.87735	−	2.23859i	0.532595	−	0.307494i	0.742072	+	0.670320i	$0.233843\pi$
$54$		0			0
$55$	9.23091	+	5.32947i	1.24470	+	0.718625i
$56$		0			0
$57$	6.91919	+	3.02072i	0.916470	+	0.400104i
$58$		0			0
$59$	7.23960	−	12.5394i	0.942515	−	1.63248i	0.181864	−	0.983324i	$-0.441787\pi$
$59$	7.23960	−	12.5394i	0.942515	−	1.63248i	0.760651	−	0.649161i	$-0.224880\pi$
$60$		0			0
$61$	−0.0261043	−	0.0452140i	−0.00334232	−	0.00578907i	0.864349	−	0.502892i	$-0.167731\pi$
$61$	−0.0261043	−	0.0452140i	−0.00334232	−	0.00578907i	−0.867692	+	0.497103i	$0.834397\pi$
$62$		0			0
$63$	−1.10950	+	1.36808i	−0.139784	+	0.172361i
$64$		0			0
$65$			6.90047i			0.855898i
$66$		0			0
$67$	0.662494	−	0.382491i	0.0809366	−	0.0467288i	−0.458986	−	0.888444i	$-0.651787\pi$
$67$	0.662494	−	0.382491i	0.0809366	−	0.0467288i	0.539922	+	0.841715i	$0.318454\pi$
$68$		0			0
$69$	−0.853736	−	4.61577i	−0.102778	−	0.555674i
$70$		0			0
$71$	−5.86809	+	10.1638i	−0.696414	+	1.20623i	0.273287	+	0.961932i	$0.411889\pi$
$71$	−5.86809	+	10.1638i	−0.696414	+	1.20623i	−0.969702	+	0.244293i	$0.921444\pi$
$72$		0			0
$73$	−4.10305	+	7.10670i	−0.480226	+	0.831776i	−0.999743	−	0.0226842i	$-0.992779\pi$
$73$	−4.10305	+	7.10670i	−0.480226	+	0.831776i	0.519516	+	0.854460i	$0.326112\pi$
$74$		0			0
$75$	−2.37865	−	12.8603i	−0.274663	−	1.48498i
$76$		0			0
$77$			1.76653i			0.201315i
$78$		0			0
$79$	7.80639	+	4.50702i	0.878287	+	0.507079i	0.870093	−	0.492887i	$-0.164058\pi$
$79$	7.80639	+	4.50702i	0.878287	+	0.507079i	0.00819375	+	0.999966i	$0.497392\pi$
$80$		0			0
$81$	1.85832	+	8.80606i	0.206480	+	0.978451i
$82$		0			0
$83$	−13.6263			−1.49568			−0.747840	−	0.663879i	$-0.768909\pi$
$83$	−13.6263			−1.49568			−0.747840	+	0.663879i	$0.768909\pi$
$84$		0			0
$85$	−2.80153	−	4.85239i	−0.303868	−	0.526315i
$86$		0			0
$87$	9.04251	−	1.67251i	0.969459	−	0.179312i
$88$		0			0
$89$	9.20425	−	5.31408i	0.975648	−	0.563291i	0.0746949	−	0.997206i	$-0.476202\pi$
$89$	9.20425	−	5.31408i	0.975648	−	0.563291i	0.900954	+	0.433916i	$0.142868\pi$
$90$		0			0
$91$	−0.990414	+	0.571816i	−0.103824	+	0.0599426i
$92$		0			0
$93$	2.56592	−	7.23753i	0.266074	−	0.750497i
$94$		0			0
$95$	−12.7927	−	8.64949i	−1.31250	−	0.887419i
$96$		0			0
$97$	−5.27542	+	9.13730i	−0.535638	+	0.927752i	0.463494	+	0.886100i	$0.346596\pi$
$97$	−5.27542	+	9.13730i	−0.535638	+	0.927752i	−0.999132	+	0.0416523i	$0.986738\pi$
$98$		0			0
$99$	7.01041	+	5.68542i	0.704573	+	0.571406i
$100$		0			0
$101$	9.92484	−	5.73011i	0.987559	−	0.570167i	0.0830152	−	0.996548i	$-0.473545\pi$
$101$	9.92484	−	5.73011i	0.987559	−	0.570167i	0.904544	+	0.426381i	$0.140212\pi$
$102$		0			0
$103$			9.45399i			0.931530i	0.884909	+	0.465765i	$0.154221\pi$
$103$			9.45399i			0.931530i	−0.884909	+	0.465765i	$0.845779\pi$
$104$		0			0
$105$	2.74045	−	2.33883i	0.267441	−	0.228247i
$106$		0			0
$107$	6.01738			0.581722			0.290861	−	0.956765i	$-0.406058\pi$
$107$	6.01738			0.581722			0.290861	+	0.956765i	$0.406058\pi$
$108$		0			0
$109$	5.22321	−	9.04687i	0.500293	−	0.866533i	−0.499707	−	0.866195i	$-0.666559\pi$
$109$	5.22321	−	9.04687i	0.500293	−	0.866533i	1.00000		0.000338577i	$-0.000107772\pi$
$110$		0			0
$111$	−10.7794	−	3.82164i	−1.02314	−	0.362734i
$112$		0			0
$113$			6.25336i			0.588267i	0.955764	+	0.294133i	$0.0950310\pi$
$113$			6.25336i			0.588267i	−0.955764	+	0.294133i	$0.904969\pi$
$114$		0			0
$115$			9.60118i			0.895315i
$116$		0			0
$117$	−0.918328	+	5.77076i	−0.0848995	+	0.533507i
$118$		0			0
$119$	0.464304	−	0.804198i	0.0425627	−	0.0737207i
$120$		0			0
$121$	−1.94779			−0.177072
$122$		0			0
$123$	10.1611	+	11.9059i	0.916193	+	1.07352i
$124$		0			0
$125$			9.03693i			0.808287i
$126$		0			0
$127$	−3.96693	+	2.29031i	−0.352008	+	0.203232i	−0.665569	−	0.746336i	$-0.731811\pi$
$127$	−3.96693	+	2.29031i	−0.352008	+	0.203232i	0.313561	+	0.949568i	$0.398478\pi$
$128$		0			0
$129$	−7.49462	−	8.78157i	−0.659864	−	0.773174i
$130$		0			0
$131$	10.9569	−	18.9778i	0.957306	−	1.65810i	0.228304	−	0.973590i	$-0.426682\pi$
$131$	10.9569	−	18.9778i	0.957306	−	1.65810i	0.729002	−	0.684512i	$-0.239985\pi$
$132$		0			0
$133$	0.181368	−	2.55286i	0.0157266	−	0.221361i
$134$		0			0
$135$	−0.461679	−	18.4027i	−0.0397350	−	1.58385i
$136$		0			0
$137$	−3.95722	+	2.28470i	−0.338088	+	0.195195i	−0.659426	−	0.751769i	$-0.729201\pi$
$137$	−3.95722	+	2.28470i	−0.338088	+	0.195195i	0.321338	+	0.946965i	$0.395867\pi$
$138$		0			0
$139$	−4.70241	+	2.71494i	−0.398853	+	0.230278i	−0.685989	−	0.727612i	$-0.740630\pi$
$139$	−4.70241	+	2.71494i	−0.398853	+	0.230278i	0.287136	+	0.957890i	$0.407297\pi$
$140$		0			0
$141$	−2.19847	−	11.8862i	−0.185145	−	1.00100i
$142$		0			0
$143$	2.93015	+	5.07517i	0.245031	+	0.424407i
$144$		0			0
$145$	−18.8092			−1.56202
$146$		0			0
$147$	−10.8647	−	3.85185i	−0.896102	−	0.317695i
$148$		0			0
$149$	−13.0900	−	7.55749i	−1.07237	−	0.619134i	−0.143543	−	0.989644i	$-0.545850\pi$
$149$	−13.0900	−	7.55749i	−1.07237	−	0.619134i	−0.928828	+	0.370510i	$0.879183\pi$
$150$		0			0
$151$		−	16.9151i		−	1.37653i	−0.725459	−	0.688266i	$-0.758372\pi$
$151$		−	16.9151i		−	1.37653i	0.725459	−	0.688266i	$-0.241628\pi$
$152$		0			0
$153$	−1.69711	−	4.43081i	−0.137203	−	0.358210i
$154$		0			0
$155$	−7.85319	+	13.6021i	−0.630783	+	1.09255i
$156$		0			0
$157$	6.05085	−	10.4804i	0.482910	−	0.836425i	−0.516897	−	0.856047i	$-0.672913\pi$
$157$	6.05085	−	10.4804i	0.482910	−	0.836425i	0.999807	+	0.0196226i	$0.00624647\pi$
$158$		0			0
$159$	−7.62536	+	1.41039i	−0.604730	+	0.111851i
$160$		0			0
$161$	−1.37804	+	0.795613i	−0.108605	+	0.0627031i
$162$		0			0
$163$			23.0793i			1.80771i	0.427839	+	0.903855i	$0.359275\pi$
$163$			23.0793i			1.80771i	−0.427839	+	0.903855i	$0.640725\pi$
$164$		0			0
$165$	−11.9849	−	14.0429i	−0.933020	−	1.09324i
$166$		0			0
$167$	−11.0441	−	19.1289i	−0.854615	−	1.48024i	−0.877002	−	0.480487i	$-0.840460\pi$
$167$	−11.0441	−	19.1289i	−0.854615	−	1.48024i	0.0223875	−	0.999749i	$-0.492873\pi$
$168$		0			0
$169$	4.60305	−	7.97272i	0.354081	−	0.613286i
$170$		0			0
$171$	−9.54723	−	8.93591i	−0.730095	−	0.683346i
$172$		0			0
$173$	−11.7119	−	6.76188i	−0.890441	−	0.514096i	−0.0163541	−	0.999866i	$-0.505206\pi$
$173$	−11.7119	−	6.76188i	−0.890441	−	0.514096i	−0.874087	+	0.485770i	$0.838539\pi$
$174$		0			0
$175$	−3.83946	+	2.21671i	−0.290236	+	0.167568i
$176$		0			0
$177$	−19.0760	+	16.2803i	−1.43384	+	1.22370i
$178$		0			0
$179$	−15.7064			−1.17395			−0.586975	−	0.809605i	$-0.699681\pi$
$179$	−15.7064			−1.17395			−0.586975	+	0.809605i	$0.699681\pi$
$180$		0			0
$181$	−7.22321	−	12.5110i	−0.536897	−	0.929933i	−0.999069	−	0.0431429i	$-0.986263\pi$
$181$	−7.22321	−	12.5110i	−0.536897	−	0.929933i	0.462172	−	0.886790i	$-0.347070\pi$
$182$		0			0
$183$	0.0164467	+	0.0889199i	0.00121577	+	0.00657315i
$184$		0			0
$185$	20.2587	+	11.6964i	1.48945	+	0.859935i
$186$		0			0
$187$	−4.12094	−	2.37923i	−0.301353	−	0.173986i
$188$		0			0
$189$	2.60305	−	1.59123i	0.189344	−	0.115745i
$190$		0			0
$191$	12.8548			0.930138			0.465069	−	0.885274i	$-0.346029\pi$
$191$	12.8548			0.930138			0.465069	+	0.885274i	$0.346029\pi$
$192$		0			0
$193$	−9.57695	+	16.5878i	−0.689364	+	1.19401i	0.282680	+	0.959214i	$0.408777\pi$
$193$	−9.57695	+	16.5878i	−0.689364	+	1.19401i	−0.972044	+	0.234799i	$0.924557\pi$
$194$		0			0
$195$	3.99377	−	11.2650i	0.286000	−	0.806701i
$196$		0			0
$197$		−	18.3607i		−	1.30815i	−0.756432	−	0.654073i	$-0.773059\pi$
$197$		−	18.3607i		−	1.30815i	0.756432	−	0.654073i	$-0.226941\pi$
$198$		0			0
$199$	10.9104	−	6.29910i	0.773415	−	0.446531i	−0.0606764	−	0.998157i	$-0.519326\pi$
$199$	10.9104	−	6.29910i	0.773415	−	0.446531i	0.834092	+	0.551626i	$0.185992\pi$
$200$		0			0
$201$	−1.30289	+	0.240983i	−0.0918988	+	0.0169977i
$202$		0			0
$203$	−1.55864	−	2.69965i	−0.109395	−	0.189478i
$204$		0			0
$205$	−16.0076	−	27.7260i	−1.11802	−	1.93647i
$206$		0			0
$207$	−1.27774	+	8.02932i	−0.0888093	+	0.558076i
$208$		0			0
$209$	−13.0816	−	0.929379i	−0.904873	−	0.0642865i
$210$		0			0
$211$	1.95955	+	1.13135i	0.134901	+	0.0778851i	0.565932	−	0.824452i	$-0.308517\pi$
$211$	1.95955	+	1.13135i	0.134901	+	0.0778851i	−0.431031	+	0.902337i	$0.641850\pi$
$212$		0			0
$213$	15.4621	−	13.1961i	1.05945	−	0.904182i
$214$		0			0
$215$	11.8069	+	20.4502i	0.805226	+	1.39469i
$216$		0			0
$217$	−2.60305			−0.176707
$218$		0			0
$219$	10.8113	−	9.22691i	0.730562	−	0.623497i
$220$		0			0
$221$		−	3.08057i		−	0.207221i
$222$		0			0
$223$	−6.84252	−	3.95053i	−0.458209	−	0.264547i	0.253082	−	0.967445i	$-0.418556\pi$
$223$	−6.84252	−	3.95053i	−0.458209	−	0.264547i	−0.711291	+	0.702898i	$0.751889\pi$
$224$		0			0
$225$	−3.56001	+	22.3710i	−0.237334	+	1.49140i
$226$		0			0
$227$	1.70014			0.112842			0.0564210	−	0.998407i	$-0.482031\pi$
$227$	1.70014			0.112842			0.0564210	+	0.998407i	$0.482031\pi$
$228$		0			0
$229$	−18.9658			−1.25329			−0.626647	−	0.779303i	$-0.715573\pi$
$229$	−18.9658			−1.25329			−0.626647	+	0.779303i	$0.715573\pi$
$230$		0			0
$231$	1.02241	−	2.88385i	0.0672697	−	0.189743i
$232$		0			0
$233$	−20.0985	−	11.6039i	−1.31670	−	0.760197i	−0.333503	−	0.942749i	$-0.608231\pi$
$233$	−20.0985	−	11.6039i	−1.31670	−	0.760197i	−0.983196	+	0.182552i	$0.941564\pi$
$234$		0			0
$235$			24.7242i			1.61283i
$236$		0			0
$237$	−10.1353	−	11.8758i	−0.658361	−	0.771413i
$238$		0			0
$239$	19.2694			1.24643			0.623217	−	0.782049i	$-0.285825\pi$
$239$	19.2694			1.24643			0.623217	+	0.782049i	$0.285825\pi$
$240$		0			0
$241$	−2.05085	−	3.55217i	−0.132107	−	0.228815i	0.792382	−	0.610025i	$-0.208841\pi$
$241$	−2.05085	−	3.55217i	−0.132107	−	0.228815i	−0.924488	+	0.381210i	$0.875507\pi$
$242$		0			0
$243$	2.06297	−	15.4513i	0.132340	−	0.991204i
$244$		0			0
$245$	20.4189	+	11.7889i	1.30452	+	0.753163i
$246$		0			0
$247$	−3.71338	−	7.63510i	−0.236277	−	0.485810i
$248$		0			0
$249$	22.2448	+	7.88646i	1.40971	+	0.499784i
$250$		0			0
$251$	2.69367	+	4.66557i	0.170023	+	0.294488i	0.938428	−	0.345476i	$-0.112282\pi$
$251$	2.69367	+	4.66557i	0.170023	+	0.294488i	−0.768405	+	0.639964i	$0.778949\pi$
$252$		0			0
$253$	4.07695	+	7.06148i	0.256316	+	0.443952i
$254$		0			0
$255$	1.76506	+	9.54291i	0.110533	+	0.597600i
$256$		0			0
$257$	19.2094	−	11.0906i	1.19825	−	0.691810i	0.238085	−	0.971244i	$-0.423480\pi$
$257$	19.2094	−	11.0906i	1.19825	−	0.691810i	0.960165	+	0.279435i	$0.0901470\pi$
$258$		0			0
$259$			3.87694i			0.240901i
$260$		0			0
$261$	−15.7298	−	2.50316i	−0.973651	−	0.154942i
$262$		0			0
$263$	−1.89790	+	3.28726i	−0.117030	+	0.202701i	−0.918589	−	0.395214i	$-0.870671\pi$
$263$	−1.89790	+	3.28726i	−0.117030	+	0.202701i	0.801560	+	0.597915i	$0.204004\pi$
$264$		0			0
$265$	15.8614			0.974356
$266$		0			0
$267$	−18.1015	+	3.34806i	−1.10779	+	0.204898i
$268$		0			0
$269$	14.5144	+	8.37991i	0.884960	+	0.510932i	0.872291	−	0.488988i	$-0.162634\pi$
$269$	14.5144	+	8.37991i	0.884960	+	0.510932i	0.0126695	+	0.999920i	$0.495967\pi$
$270$		0			0
$271$	−4.98389	−	2.87745i	−0.302750	−	0.174793i	0.340928	−	0.940089i	$-0.389259\pi$
$271$	−4.98389	−	2.87745i	−0.302750	−	0.174793i	−0.643677	+	0.765297i	$0.722592\pi$
$272$		0			0
$273$	1.94779	−	0.360265i	0.117886	−	0.0218042i
$274$		0			0
$275$	11.3591	+	19.6745i	0.684978	+	1.18642i
$276$		0			0
$277$	5.05221			0.303558			0.151779	−	0.988414i	$-0.451500\pi$
$277$	5.05221			0.303558			0.151779	+	0.988414i	$0.451500\pi$
$278$		0			0
$279$	−8.37770	+	10.3301i	−0.501560	+	0.618449i
$280$		0			0
$281$	6.46489	−	3.73251i	0.385663	−	0.222663i	−0.294616	−	0.955616i	$-0.595192\pi$
$281$	6.46489	−	3.73251i	0.385663	−	0.222663i	0.680279	+	0.732953i	$0.261858\pi$
$282$		0			0
$283$	22.7368	+	13.1271i	1.35156	+	0.780324i	0.988468	−	0.151429i	$-0.0483876\pi$
$283$	22.7368	+	13.1271i	1.35156	+	0.780324i	0.363093	+	0.931753i	$0.381721\pi$
$284$		0			0
$285$	15.8779	+	21.5242i	0.940524	+	1.27498i
$286$		0			0
$287$	2.65298	−	4.59510i	0.156601	−	0.271240i
$288$		0			0
$289$	−7.24932	−	12.5562i	−0.426431	−	0.738599i
$290$		0			0
$291$	13.9005	−	11.8633i	0.814859	−	0.695440i
$292$		0			0
$293$			11.0077i			0.643078i	0.946896	+	0.321539i	$0.104200\pi$
$293$			11.0077i			0.643078i	−0.946896	+	0.321539i	$0.895800\pi$
$294$		0			0
$295$	44.4234	−	25.6478i	2.58643	−	1.49328i
$296$		0			0
$297$	−8.15390	−	13.3388i	−0.473137	−	0.773996i
$298$		0			0
$299$	−2.63937	+	4.57153i	−0.152639	+	0.264378i
$300$		0			0
$301$	−1.95679	+	3.38926i	−0.112788	+	0.195354i
$302$		0			0
$303$	−19.5186	+	3.61018i	−1.12132	+	0.207399i
$304$		0			0
$305$		−	0.184961i		−	0.0105908i
$306$		0			0
$307$	−0.126081	−	0.0727927i	−0.00719580	−	0.00415450i	0.496398	−	0.868095i	$-0.334656\pi$
$307$	−0.126081	−	0.0727927i	−0.00719580	−	0.00415450i	−0.503594	+	0.863941i	$0.667989\pi$
$308$		0			0
$309$	5.47167	−	15.4336i	0.311272	−	0.877985i
$310$		0			0
$311$	−19.8181			−1.12378			−0.561889	−	0.827212i	$-0.689925\pi$
$311$	−19.8181			−1.12378			−0.561889	+	0.827212i	$0.689925\pi$
$312$		0			0
$313$	6.27542	+	10.8694i	0.354708	+	0.614372i	0.987068	−	0.160303i	$-0.0512470\pi$
$313$	6.27542	+	10.8694i	0.354708	+	0.614372i	−0.632360	+	0.774675i	$0.717914\pi$
$314$		0			0
$315$	−5.82740	+	2.23204i	−0.328337	+	0.125761i
$316$		0			0
$317$	1.13799	−	0.657019i	0.0639159	−	0.0369018i	−0.467702	−	0.883886i	$-0.654918\pi$
$317$	1.13799	−	0.657019i	0.0639159	−	0.0369018i	0.531617	+	0.846985i	$0.321584\pi$
$318$		0			0
$319$	−13.8338	+	7.98694i	−0.774543	+	0.447183i
$320$		0			0
$321$	−9.82332	−	3.48266i	−0.548284	−	0.194383i
$322$		0			0
$323$	5.71101	+	3.86138i	0.317769	+	0.214853i
$324$		0			0
$325$	−7.35374	+	12.7370i	−0.407912	+	0.706524i
$326$		0			0
$327$	−13.7629	+	11.7459i	−0.761090	+	0.649550i
$328$		0			0
$329$	−3.54862	+	2.04880i	−0.195642	+	0.112954i
$330$		0			0
$331$		−	18.9386i		−	1.04096i	−0.853873	−	0.520481i	$-0.825753\pi$
$331$		−	18.9386i		−	1.04096i	0.853873	−	0.520481i	$-0.174247\pi$
$332$		0			0
$333$	15.3855	+	12.4776i	0.843119	+	0.683767i
$334$		0			0
$335$	2.71012			0.148070
$336$		0			0
$337$	−4.92169	+	8.52461i	−0.268101	+	0.464365i	−0.968372	−	0.249513i	$-0.919730\pi$
$337$	−4.92169	+	8.52461i	−0.268101	+	0.464365i	0.700270	+	0.713878i	$0.253063\pi$
$338$		0			0
$339$	3.61925	−	10.2086i	0.196570	−	0.554453i
$340$		0			0
$341$			13.3388i			0.722336i
$342$		0			0
$343$			8.01759i			0.432909i
$344$		0			0
$345$	5.55685	−	15.6738i	0.299171	−	0.843851i
$346$		0			0
$347$	9.31968	−	16.1422i	0.500307	−	0.866556i	−0.499693	−	0.866202i	$-0.666554\pi$
$347$	9.31968	−	16.1422i	0.500307	−	0.866556i	1.00000		0.000354038i	$-0.000112694\pi$
$348$		0			0
$349$	29.8586			1.59830			0.799148	−	0.601134i	$-0.205284\pi$
$349$	29.8586			1.59830			0.799148	+	0.601134i	$0.205284\pi$
$350$		0			0
$351$	4.83909	−	8.88922i	0.258292	−	0.474471i
$352$		0			0
$353$		−	3.99521i		−	0.212644i	−0.994332	−	0.106322i	$-0.966093\pi$
$353$		−	3.99521i		−	0.212644i	0.994332	−	0.106322i	$-0.0339074\pi$
$354$		0			0
$355$	−36.0076	+	20.7890i	−1.91108	+	1.10337i
$356$		0			0
$357$	−1.22342	+	1.04412i	−0.0647500	+	0.0552608i
$358$		0			0
$359$	−7.92393	+	13.7247i	−0.418209	+	0.724360i	−0.995759	−	0.0919956i	$-0.970675\pi$
$359$	−7.92393	+	13.7247i	−0.418209	+	0.724360i	0.577550	+	0.816355i	$0.304009\pi$
$360$		0			0
$361$	18.8092	+	2.68614i	0.989956	+	0.141376i
$362$		0			0
$363$	3.17975	+	1.12732i	0.166894	+	0.0591689i
$364$		0			0
$365$	−25.1770	+	14.5360i	−1.31783	+	0.760847i
$366$		0			0
$367$	32.8771	−	18.9816i	1.71617	−	0.990830i	0.790529	−	0.612425i	$-0.209806\pi$
$367$	32.8771	−	18.9816i	1.71617	−	0.990830i	0.925640	−	0.378406i	$-0.123528\pi$
$368$		0			0
$369$	−9.69711	−	25.3172i	−0.504811	−	1.31796i
$370$		0			0
$371$	1.31437	+	2.27656i	0.0682388	+	0.118193i
$372$		0			0
$373$	−8.73896			−0.452486			−0.226243	−	0.974071i	$-0.572644\pi$
$373$	−8.73896			−0.452486			−0.226243	+	0.974071i	$0.572644\pi$
$374$		0			0
$375$	5.23028	−	14.7527i	0.270091	−	0.761826i
$376$		0			0
$377$	−8.95583	−	5.17065i	−0.461249	−	0.266302i
$378$		0			0
$379$		−	10.6605i		−	0.547595i	−0.961787	−	0.273797i	$-0.911720\pi$
$379$		−	10.6605i		−	0.547595i	0.961787	−	0.273797i	$-0.0882798\pi$
$380$		0			0
$381$	7.80153	−	1.44298i	0.399684	−	0.0739259i
$382$		0			0
$383$	8.82248	−	15.2810i	0.450808	−	0.780822i	−0.547629	−	0.836722i	$-0.684469\pi$
$383$	8.82248	−	15.2810i	0.450808	−	0.780822i	0.998436	+	0.0558996i	$0.0178027\pi$
$384$		0			0
$385$	−3.12916	+	5.41986i	−0.159477	+	0.276222i
$386$		0			0
$387$	7.15240	+	18.6735i	0.363577	+	0.949226i
$388$		0			0
$389$	0.00836282	−	0.00482828i	0.000424012	−	0.000244803i	−0.499788	−	0.866148i	$-0.666589\pi$
$389$	0.00836282	−	0.00482828i	0.000424012	−	0.000244803i	0.500212	+	0.865903i	$0.333255\pi$
$390$		0			0
$391$		−	4.28624i		−	0.216764i
$392$		0			0
$393$	−28.8707	+	24.6397i	−1.45634	+	1.24291i
$394$		0			0
$395$	15.9671	+	27.6558i	0.803392	+	1.39152i
$396$		0			0
$397$	4.68137	−	8.10837i	0.234951	−	0.406947i	−0.724307	−	0.689477i	$-0.757840\pi$
$397$	4.68137	−	8.10837i	0.234951	−	0.406947i	0.959258	+	0.282530i	$0.0911737\pi$
$398$		0			0
$399$	−1.77360	+	4.06256i	−0.0887908	+	0.203382i
$400$		0			0
$401$	−26.6349	−	15.3777i	−1.33009	−	0.767925i	−0.344773	−	0.938686i	$-0.612044\pi$
$401$	−26.6349	−	15.3777i	−1.33009	−	0.767925i	−0.985312	+	0.170761i	$0.945377\pi$
$402$		0			0
$403$	−7.47847	+	4.31769i	−0.372529	+	0.215080i
$404$		0			0
$405$	−9.89721	+	30.3095i	−0.491796	+	1.50609i
$406$		0			0
$407$	19.8665			0.984748
$408$		0			0
$409$	−12.9829	−	22.4870i	−0.641963	−	1.11191i	−0.984994	−	0.172588i	$-0.944787\pi$
$409$	−12.9829	−	22.4870i	−0.641963	−	1.11191i	0.343031	−	0.939324i	$-0.388546\pi$
$410$		0			0
$411$	7.78244	−	1.43945i	0.383880	−	0.0710026i
$412$		0			0
$413$	7.36239	+	4.25068i	0.362280	+	0.209162i
$414$		0			0
$415$	−41.8066	−	24.1371i	−2.05221	−	1.18484i
$416$		0			0
$417$	9.24796	−	1.71051i	0.452874	−	0.0837639i
$418$		0			0
$419$	−16.7008			−0.815886			−0.407943	−	0.913007i	$-0.633754\pi$
$419$	−16.7008			−0.815886			−0.407943	+	0.913007i	$0.633754\pi$
$420$		0			0
$421$	−16.4293	+	28.4564i	−0.800716	+	1.38688i	0.118429	+	0.992963i	$0.462214\pi$
$421$	−16.4293	+	28.4564i	−0.800716	+	1.38688i	−0.919145	+	0.393919i	$0.871119\pi$
$422$		0			0
$423$	−3.29034	+	20.6765i	−0.159982	+	1.00532i
$424$		0			0
$425$		−	11.9422i		−	0.579281i
$426$		0			0
$427$	0.0265471	−	0.0153270i	0.00128470	−	0.000741725i
$428$		0			0
$429$	−1.84610	−	9.98104i	−0.0891305	−	0.481889i
$430$		0			0
$431$	−11.0984	−	19.2229i	−0.534589	−	0.925935i	−0.999183	−	0.0404114i	$-0.987133\pi$
$431$	−11.0984	−	19.2229i	−0.534589	−	0.925935i	0.464594	−	0.885524i	$-0.346200\pi$
$432$		0			0
$433$	11.5247	+	19.9614i	0.553844	+	0.959285i	0.997992	+	0.0633324i	$0.0201728\pi$
$433$	11.5247	+	19.9614i	0.553844	+	0.959285i	−0.444149	+	0.895953i	$0.646494\pi$
$434$		0			0
$435$	30.7058	+	10.8861i	1.47223	+	0.521950i
$436$		0			0
$437$	−5.16672	−	10.6233i	−0.247158	−	0.508182i
$438$		0			0
$439$	−17.3984	−	10.0450i	−0.830381	−	0.479421i	0.0236021	−	0.999721i	$-0.492487\pi$
$439$	−17.3984	−	10.0450i	−0.830381	−	0.479421i	−0.853983	+	0.520301i	$0.825820\pi$
$440$		0			0
$441$	15.5071	+	12.5762i	0.738435	+	0.598868i
$442$		0			0
$443$	−11.4212	−	19.7820i	−0.542636	−	0.939873i	−0.998752	−	0.0499526i	$-0.984093\pi$
$443$	−11.4212	−	19.7820i	−0.542636	−	0.939873i	0.456116	−	0.889921i	$-0.349240\pi$
$444$		0			0
$445$	37.6525			1.78490
$446$		0			0
$447$	16.9952	+	19.9136i	0.803846	+	0.941880i
$448$		0			0
$449$			20.1272i			0.949863i	0.880023	+	0.474931i	$0.157527\pi$
$449$			20.1272i			0.949863i	−0.880023	+	0.474931i	$0.842473\pi$
$450$		0			0
$451$	−23.5466	−	13.5946i	−1.10877	−	0.640147i
$452$		0			0
$453$	−9.78991	+	27.6137i	−0.459970	+	1.29741i
$454$		0			0
$455$	−4.05156			−0.189940
$456$		0			0
$457$	6.86137			0.320961			0.160481	−	0.987039i	$-0.448696\pi$
$457$	6.86137			0.320961			0.160481	+	0.987039i	$0.448696\pi$
$458$		0			0
$459$	0.206107	+	8.21549i	0.00962023	+	0.383466i
$460$		0			0
$461$	5.17552	+	2.98809i	0.241048	+	0.139169i	0.615658	−	0.788013i	$-0.288890\pi$
$461$	5.17552	+	2.98809i	0.241048	+	0.139169i	−0.374610	+	0.927182i	$0.622224\pi$
$462$		0			0
$463$			33.5374i			1.55862i	0.626641	+	0.779308i	$0.284429\pi$
$463$			33.5374i			1.55862i	−0.626641	+	0.779308i	$0.715571\pi$
$464$		0			0
$465$	20.6927	−	17.6602i	0.959602	−	0.818971i
$466$		0			0
$467$	−34.9273			−1.61624			−0.808121	−	0.589016i	$-0.799515\pi$
$467$	−34.9273			−1.61624			−0.808121	+	0.589016i	$0.799515\pi$
$468$		0			0
$469$	0.224577	+	0.388979i	0.0103700	+	0.0179614i
$470$		0			0
$471$	−15.9437	+	13.6071i	−0.734645	+	0.626981i
$472$		0			0
$473$	17.3675	+	10.0272i	0.798560	+	0.461049i
$474$		0			0
$475$	−14.3954	−	29.5984i	−0.660504	−	1.35807i
$476$		0			0
$477$	13.2646	+	2.11086i	0.607345	+	0.0966497i
$478$		0			0
$479$	−12.2169	−	21.1604i	−0.558206	−	0.966841i	−0.997646	−	0.0685694i	$-0.978157\pi$
$479$	−12.2169	−	21.1604i	−0.558206	−	0.966841i	0.439440	−	0.898272i	$-0.355177\pi$
$480$		0			0
$481$	6.43069	+	11.1383i	0.293214	+	0.507862i
$482$		0			0
$483$	2.71012	−	0.501265i	0.123315	−	0.0228083i
$484$		0			0
$485$	−32.3709	+	18.6893i	−1.46989	+	0.848639i
$486$		0			0
$487$		−	24.5464i		−	1.11230i	−0.831081	−	0.556151i	$-0.812278\pi$
$487$		−	24.5464i		−	1.11230i	0.831081	−	0.556151i	$-0.187722\pi$
$488$		0			0
$489$	13.3576	−	37.6768i	0.604049	−	1.70380i
$490$		0			0
$491$	9.64831	−	16.7114i	0.435422	−	0.754173i	−0.561908	−	0.827200i	$-0.689932\pi$
$491$	9.64831	−	16.7114i	0.435422	−	0.754173i	0.997330	+	0.0730266i	$0.0232658\pi$
$492$		0			0
$493$	8.39695			0.378179
$494$		0			0
$495$	11.4376	+	29.8613i	0.514082	+	1.34217i
$496$		0			0
$497$	−5.96762	−	3.44541i	−0.267684	−	0.154548i
$498$		0			0
$499$	−25.4251	−	14.6792i	−1.13819	−	0.657132i	−0.192205	−	0.981355i	$-0.561564\pi$
$499$	−25.4251	−	14.6792i	−1.13819	−	0.657132i	−0.945981	+	0.324223i	$0.894897\pi$
$500$		0			0
$501$	6.95815	+	37.6196i	0.310867	+	1.68072i
$502$		0			0
$503$	−20.6701	−	35.8017i	−0.921634	−	1.59632i	−0.796887	−	0.604129i	$-0.793521\pi$
$503$	−20.6701	−	35.8017i	−0.921634	−	1.59632i	−0.124747	−	0.992189i	$-0.539812\pi$
$504$		0			0
$505$	40.6003			1.80669
$506$		0			0
$507$	−12.1288	+	10.3513i	−0.538659	+	0.459718i
$508$		0			0
$509$	29.8001	−	17.2051i	1.32086	−	0.762601i	0.336998	−	0.941505i	$-0.390589\pi$
$509$	29.8001	−	17.2051i	1.32086	−	0.762601i	0.983867	+	0.178904i	$0.0572552\pi$
$510$		0			0
$511$	−4.17265	−	2.40908i	−0.184587	−	0.106571i
$512$		0			0
$513$	10.4139	+	20.1134i	0.459787	+	0.888029i
$514$		0			0
$515$	−16.7464	+	29.0056i	−0.737935	+	1.27814i
$516$		0			0
$517$	10.4986	+	18.1842i	0.461730	+	0.799739i
$518$		0			0
$519$	15.2060	+	17.8172i	0.667471	+	0.782088i
$520$		0			0
$521$			37.3690i			1.63717i	0.574388	+	0.818583i	$0.305240\pi$
$521$			37.3690i			1.63717i	−0.574388	+	0.818583i	$0.694760\pi$
$522$		0			0
$523$	24.2622	−	14.0078i	1.06091	−	0.612518i	0.135228	−	0.990815i	$-0.456823\pi$
$523$	24.2622	−	14.0078i	1.06091	−	0.612518i	0.925684	+	0.378296i	$0.123490\pi$
$524$		0			0
$525$	7.55085	−	1.39661i	0.329546	−	0.0609530i
$526$		0			0
$527$	3.50589	−	6.07237i	0.152719	−	0.264517i
$528$		0			0
$529$	7.82763	−	13.5579i	0.340332	−	0.589472i
$530$		0			0
$531$	40.5639	−	15.5370i	1.76032	−	0.674247i
$532$		0			0
$533$		−	17.6020i		−	0.762429i
$534$		0			0
$535$	18.4618	+	10.6589i	0.798174	+	0.460826i
$536$		0			0
$537$	25.6405	+	9.09034i	1.10647	+	0.392277i
$538$		0			0
$539$	20.0236			0.862478
$540$		0			0
$541$	13.9986	+	24.2464i	0.601848	+	1.04243i	0.992541	+	0.121911i	$0.0389022\pi$
$541$	13.9986	+	24.2464i	0.601848	+	1.04243i	−0.390693	+	0.920521i	$0.627764\pi$
$542$		0			0
$543$	4.55089	+	24.6046i	0.195297	+	1.05589i
$544$		0			0
$545$	32.0505	−	18.5044i	1.37289	−	0.792640i
$546$		0			0
$547$	10.5492	−	6.09061i	0.451053	−	0.260416i	−0.257222	−	0.966352i	$-0.582807\pi$
$547$	10.5492	−	6.09061i	0.451053	−	0.260416i	0.708275	+	0.705937i	$0.249474\pi$
$548$		0			0
$549$	0.0246149	−	0.154680i	0.00105054	−	0.00660157i
$550$		0			0
$551$	20.8116	−	10.1218i	0.886604	−	0.431205i
$552$		0			0
$553$	−2.64626	+	4.58346i	−0.112531	+	0.194909i
$554$		0			0
$555$	−26.3027	−	30.8193i	−1.11649	−	1.30821i
$556$		0			0
$557$	32.5394	−	18.7866i	1.37874	−	0.796016i	0.386732	−	0.922192i	$-0.373604\pi$
$557$	32.5394	−	18.7866i	1.37874	−	0.796016i	0.992008	+	0.126177i	$0.0402707\pi$
$558$		0			0
$559$			12.9829i			0.549120i
$560$		0			0
$561$	5.35038	+	6.26913i	0.225893	+	0.264683i
$562$		0			0
$563$	−1.85721			−0.0782723			−0.0391361	−	0.999234i	$-0.512461\pi$
$563$	−1.85721			−0.0782723			−0.0391361	+	0.999234i	$0.512461\pi$
$564$		0			0
$565$	−11.0770	+	19.1858i	−0.466011	+	0.807154i
$566$		0			0
$567$	−5.17041	+	1.09110i	−0.217137	+	0.0458219i
$568$		0			0
$569$			5.76174i			0.241545i	0.992680	+	0.120772i	$0.0385371\pi$
$569$			5.76174i			0.241545i	−0.992680	+	0.120772i	$0.961463\pi$
$570$		0			0
$571$			26.6635i			1.11583i	0.829898	+	0.557916i	$0.188399\pi$
$571$			26.6635i			1.11583i	−0.829898	+	0.557916i	$0.811601\pi$
$572$		0			0
$573$	−20.9853	−	7.43992i	−0.876673	−	0.310807i
$574$		0			0
$575$	−10.2318	+	17.7221i	−0.426697	+	0.739061i
$576$		0			0
$577$	−42.5661			−1.77205			−0.886025	−	0.463637i	$-0.846544\pi$
$577$	−42.5661			−1.77205			−0.886025	+	0.463637i	$0.846544\pi$
$578$		0			0
$579$	25.2348	−	21.5366i	1.04872	−	0.895029i
$580$		0			0
$581$		−	8.00058i		−	0.331920i
$582$		0			0
$583$	11.6657	−	6.73522i	0.483145	−	0.278944i
$584$		0			0
$585$	−13.0396	+	16.0785i	−0.539121	+	0.664764i
$586$		0			0
$587$	−5.76531	+	9.98581i	−0.237960	+	0.412159i	−0.960129	−	0.279558i	$-0.909812\pi$
$587$	−5.76531	+	9.98581i	−0.237960	+	0.412159i	0.722169	+	0.691717i	$0.243145\pi$
$588$		0			0
$589$	1.36948	−	19.2763i	0.0564284	−	0.794265i
$590$		0			0
$591$	−10.6266	+	29.9737i	−0.437119	+	1.23295i
$592$		0			0
$593$	−6.46489	+	3.73251i	−0.265481	+	0.153276i	−0.626832	−	0.779154i	$-0.715649\pi$
$593$	−6.46489	+	3.73251i	−0.265481	+	0.153276i	0.361351	+	0.932430i	$0.382316\pi$
$594$		0			0
$595$	2.84904	−	1.64490i	0.116799	−	0.0674342i
$596$		0			0
$597$	−21.4568	+	3.96866i	−0.878168	+	0.162426i
$598$		0			0
$599$	5.13528	+	8.89456i	0.209822	+	0.363422i	0.951658	−	0.307159i	$-0.0993783\pi$
$599$	5.13528	+	8.89456i	0.209822	+	0.363422i	−0.741837	+	0.670581i	$0.766045\pi$
$600$		0			0
$601$	2.03148			0.0828660			0.0414330	−	0.999141i	$-0.486808\pi$
$601$	2.03148			0.0828660			0.0414330	+	0.999141i	$0.486808\pi$
$602$		0			0
$603$	2.26643	+	0.360668i	0.0922962	+	0.0146875i
$604$		0			0
$605$	−5.97599	−	3.45024i	−0.242958	−	0.140272i
$606$		0			0
$607$		−	34.9125i		−	1.41706i	−0.705683	−	0.708528i	$-0.749360\pi$
$607$		−	34.9125i		−	1.41706i	0.705683	−	0.708528i	$-0.250640\pi$
$608$		0			0
$609$	0.982002	+	5.30925i	0.0397927	+	0.215142i
$610$		0			0
$611$	−6.79670	+	11.7722i	−0.274965	+	0.476253i
$612$		0			0
$613$	−13.0666	+	22.6320i	−0.527755	+	0.914098i	0.471722	+	0.881747i	$0.343633\pi$
$613$	−13.0666	+	22.6320i	−0.527755	+	0.914098i	−0.999477	+	0.0323504i	$0.989701\pi$
$614$		0			0
$615$	10.0854	+	54.5272i	0.406682	+	2.19875i
$616$		0			0
$617$	−28.0849	+	16.2148i	−1.13066	+	0.652785i	−0.944100	−	0.329659i	$-0.893066\pi$
$617$	−28.0849	+	16.2148i	−1.13066	+	0.652785i	−0.186557	+	0.982444i	$0.559733\pi$
$618$		0			0
$619$		−	1.17269i		−	0.0471342i	−0.999722	−	0.0235671i	$-0.992498\pi$
$619$		−	1.17269i		−	0.0471342i	0.999722	−	0.0235671i	$-0.00750234\pi$
$620$		0			0
$621$	6.73302	−	12.3683i	0.270187	−	0.496322i
$622$		0			0
$623$	3.12012	+	5.40421i	0.125005	+	0.216515i
$624$		0			0
$625$	2.86948	−	4.97008i	0.114779	−	0.198803i
$626$		0			0
$627$	20.8177	+	9.08841i	0.831379	+	0.362956i
$628$		0			0
$629$	−9.04407	−	5.22160i	−0.360611	−	0.208199i
$630$		0			0
$631$	−0.407561	+	0.235306i	−0.0162248	+	0.00936737i	−0.508090	−	0.861304i	$-0.669648\pi$
$631$	−0.407561	+	0.235306i	−0.0162248	+	0.00936737i	0.491866	+	0.870671i	$0.336315\pi$
$632$		0			0
$633$	−2.54416	−	2.98104i	−0.101121	−	0.118486i
$634$		0			0
$635$	−16.2278			−0.643981
$636$		0			0
$637$	6.48153	+	11.2263i	0.256808	+	0.444804i
$638$		0			0
$639$	−32.8792	+	12.5936i	−1.30068	+	0.498194i
$640$		0			0
$641$	4.76649	+	2.75193i	0.188265	+	0.108695i	0.591170	−	0.806547i	$-0.298666\pi$
$641$	4.76649	+	2.75193i	0.188265	+	0.108695i	−0.402905	+	0.915242i	$0.632000\pi$
$642$		0			0
$643$	−36.7179	−	21.1991i	−1.44801	−	0.836011i	−0.449650	−	0.893205i	$-0.648451\pi$
$643$	−36.7179	−	21.1991i	−1.44801	−	0.836011i	−0.998363	+	0.0571942i	$0.981785\pi$
$644$		0			0
$645$	−7.43879	−	40.2182i	−0.292902	−	1.58359i
$646$		0			0
$647$	−3.05150			−0.119967			−0.0599834	−	0.998199i	$-0.519105\pi$
$647$	−3.05150			−0.119967			−0.0599834	+	0.998199i	$0.519105\pi$
$648$		0			0
$649$	21.7817	−	37.7270i	0.855006	−	1.48091i
$650$		0			0
$651$	4.24946	+	1.50656i	0.166550	+	0.0590469i
$652$		0			0
$653$		−	2.22868i		−	0.0872150i	−0.999049	−	0.0436075i	$-0.986115\pi$
$653$		−	2.22868i		−	0.0872150i	0.999049	−	0.0436075i	$-0.0138851\pi$
$654$		0			0
$655$	67.2331	−	38.8171i	2.62702	−	1.51671i
$656$		0			0
$657$	−22.9896	+	8.80560i	−0.896911	+	0.343539i
$658$		0			0
$659$	4.16512	+	7.21420i	0.162250	+	0.281025i	0.935675	−	0.352862i	$-0.114792\pi$
$659$	4.16512	+	7.21420i	0.162250	+	0.281025i	−0.773425	+	0.633888i	$0.781458\pi$
$660$		0			0
$661$	−4.64490	−	8.04520i	−0.180666	−	0.312922i	0.761442	−	0.648233i	$-0.224492\pi$
$661$	−4.64490	−	8.04520i	−0.180666	−	0.312922i	−0.942107	+	0.335311i	$0.891159\pi$
$662$		0			0
$663$	−1.78293	+	5.02900i	−0.0692434	+	0.195310i
$664$		0			0
$665$	5.07849	−	7.51113i	0.196935	−	0.291269i
$666$		0			0
$667$	−12.4610	−	7.19434i	−0.482491	−	0.278566i
$668$		0			0
$669$	8.88391	+	10.4094i	0.343472	+	0.402452i
$670$		0			0
$671$	−0.0785398	−	0.136035i	−0.00303200	−	0.00525157i
$672$		0			0
$673$	6.44915			0.248597			0.124298	−	0.992245i	$-0.460332\pi$
$673$	6.44915			0.248597			0.124298	+	0.992245i	$0.460332\pi$
$674$		0			0
$675$	18.7593	−	34.4601i	0.722047	−	1.32637i
$676$		0			0
$677$			27.0475i			1.03952i	0.854312	+	0.519760i	$0.173979\pi$
$677$			27.0475i			1.03952i	−0.854312	+	0.519760i	$0.826021\pi$
$678$		0			0
$679$	−5.36490	−	3.09743i	−0.205886	−	0.118868i
$680$		0			0
$681$	−2.77546	−	0.983984i	−0.106356	−	0.0377063i
$682$		0			0
$683$	39.1960			1.49980			0.749898	−	0.661554i	$-0.230103\pi$
$683$	39.1960			1.49980			0.749898	+	0.661554i	$0.230103\pi$
$684$		0			0
$685$	−16.1881			−0.618516
$686$		0			0
$687$	30.9615	+	10.9768i	1.18125	+	0.418791i
$688$		0			0
$689$	7.55227	+	4.36030i	0.287718	+	0.166114i
$690$		0			0
$691$		−	3.16718i		−	0.120485i	−0.998184	−	0.0602426i	$-0.980813\pi$
$691$		−	3.16718i		−	0.120485i	0.998184	−	0.0602426i	$-0.0191874\pi$
$692$		0			0
$693$	−3.33815	+	4.11611i	−0.126806	+	0.156358i
$694$		0			0
$695$	−19.2365			−0.729682
$696$		0			0
$697$	7.14626	+	12.3777i	0.270684	+	0.468839i
$698$		0			0
$699$	26.0947	+	30.5756i	0.986993	+	1.15648i
$700$		0			0
$701$	−42.6077	−	24.5996i	−1.60927	−	0.929113i	−0.989533	−	0.144304i	$-0.953906\pi$
$701$	−42.6077	−	24.5996i	−1.60927	−	0.929113i	−0.619738	−	0.784809i	$-0.712761\pi$
$702$		0			0
$703$	−28.7097	−	2.03967i	−1.08281	−	0.0769277i
$704$		0			0
$705$	14.3096	−	40.3620i	0.538929	−	1.52012i
$706$		0			0
$707$	3.36439	+	5.82730i	0.126531	+	0.219158i
$708$		0			0
$709$	−22.0756	−	38.2360i	−0.829066	−	1.43598i	−0.898772	−	0.438417i	$-0.855539\pi$
$709$	−22.0756	−	38.2360i	−0.829066	−	1.43598i	0.0697056	−	0.997568i	$-0.477794\pi$
$710$		0			0
$711$	9.67255	+	25.2531i	0.362749	+	0.947064i
$712$		0			0
$713$	−10.4054	+	6.00755i	−0.389685	+	0.224985i
$714$		0			0
$715$			20.7614i			0.776432i
$716$		0			0
$717$	−31.4571	−	11.1525i	−1.17479	−	0.416498i
$718$		0			0
$719$	6.71816	−	11.6362i	0.250545	−	0.433957i	−0.713131	−	0.701031i	$-0.752724\pi$
$719$	6.71816	−	11.6362i	0.250545	−	0.433957i	0.963676	+	0.267074i	$0.0860568\pi$
$720$		0			0
$721$	−5.55085			−0.206724
$722$		0			0
$723$	1.29211	+	6.98585i	0.0480540	+	0.259807i
$724$		0			0
$725$	−34.7184	−	20.0447i	−1.28941	−	0.744440i
$726$		0			0
$727$	−3.33763	−	1.92698i	−0.123786	−	0.0714679i	0.436828	−	0.899545i	$-0.356102\pi$
$727$	−3.33763	−	1.92698i	−0.123786	−	0.0714679i	−0.560614	+	0.828077i	$0.689435\pi$
$728$		0			0
$729$	−12.3105	+	24.0302i	−0.455945	+	0.890008i
$730$		0			0
$731$	−5.27095	−	9.12955i	−0.194953	−	0.337669i
$732$		0			0
$733$	0.744408			0.0274953			0.0137477	−	0.999905i	$-0.495624\pi$
$733$	0.744408			0.0274953			0.0137477	+	0.999905i	$0.495624\pi$
$734$		0			0
$735$	−26.5107	−	31.0630i	−0.977861	−	1.14578i
$736$		0			0
$737$	1.99324	−	1.15080i	0.0734219	−	0.0423902i
$738$		0			0
$739$	31.9942	+	18.4719i	1.17693	+	0.679499i	0.955302	−	0.295633i	$-0.0955306\pi$
$739$	31.9942	+	18.4719i	1.17693	+	0.679499i	0.221625	+	0.975132i	$0.428864\pi$
$740$		0			0
$741$	1.64311	+	14.6134i	0.0603611	+	0.536837i
$742$		0			0
$743$	−17.8485	+	30.9146i	−0.654800	+	1.13415i	0.327144	+	0.944974i	$0.393914\pi$
$743$	−17.8485	+	30.9146i	−0.654800	+	1.13415i	−0.981944	+	0.189172i	$0.939420\pi$
$744$		0			0
$745$	−26.7741	−	46.3740i	−0.980926	−	1.69901i
$746$		0			0
$747$	−31.7500	−	25.7492i	−1.16167	−	0.942112i
$748$		0			0
$749$			3.53306i			0.129095i
$750$		0			0
$751$	20.3962	−	11.7758i	0.744268	−	0.429703i	−0.0793510	−	0.996847i	$-0.525285\pi$
$751$	20.3962	−	11.7758i	0.744268	−	0.429703i	0.823619	+	0.567143i	$0.191951\pi$
$752$		0			0
$753$	−1.69711	−	9.17552i	−0.0618461	−	0.334375i
$754$		0			0
$755$	29.9627	−	51.8969i	1.09045	−	1.88872i
$756$		0			0
$757$	7.73358	−	13.3949i	0.281082	−	0.486848i	−0.690570	−	0.723266i	$-0.742640\pi$
$757$	7.73358	−	13.3949i	0.281082	−	0.486848i	0.971651	+	0.236418i	$0.0759735\pi$
$758$		0			0
$759$	−2.56863	−	13.8874i	−0.0932352	−	0.504081i
$760$		0			0
$761$			27.4904i			0.996525i	0.867026	+	0.498262i	$0.166028\pi$
$761$			27.4904i			0.996525i	−0.867026	+	0.498262i	$0.833972\pi$
$762$		0			0
$763$	5.31181	+	3.06677i	0.192300	+	0.111025i
$764$		0			0
$765$	2.64168	−	16.6003i	0.0955102	−	0.600185i
$766$		0			0
$767$	28.2025			1.01833
$768$		0			0
$769$	−13.8942	−	24.0655i	−0.501038	−	0.867824i	−0.999999	−	0.00119943i	$-0.999618\pi$
$769$	−13.8942	−	24.0655i	−0.501038	−	0.867824i	0.498961	−	0.866624i	$-0.333715\pi$
$770$		0			0
$771$	−37.7780	+	6.98745i	−1.36054	+	0.251647i
$772$		0			0
$773$	1.03259	−	0.596168i	0.0371398	−	0.0214427i	−0.481315	−	0.876548i	$-0.659841\pi$
$773$	1.03259	−	0.596168i	0.0371398	−	0.0214427i	0.518455	+	0.855105i	$0.326507\pi$
$774$		0			0
$775$	−28.9912	+	16.7381i	−1.04139	+	0.601249i
$776$		0			0
$777$	2.24385	−	6.32907i	0.0804975	−	0.227054i
$778$		0			0
$779$	32.6321	+	22.0635i	1.16917	+	0.790507i
$780$		0			0
$781$	−17.6553	+	30.5798i	−0.631755	+	1.09423i
$782$		0			0
$783$	24.2300	+	13.1903i	0.865911	+	0.471383i
$784$		0			0
$785$	37.1290	−	21.4364i	1.32519	−	0.765099i
$786$		0			0
$787$			10.6896i			0.381043i	0.981683	+	0.190521i	$0.0610178\pi$
$787$			10.6896i			0.381043i	−0.981683	+	0.190521i	$0.938982\pi$
$788$		0			0
$789$	5.00087	−	4.26798i	0.178036	−	0.151944i
$790$		0			0
$791$	−3.67162			−0.130548
$792$		0			0
$793$	0.0508458	−	0.0880675i	0.00180559	−	0.00312737i
$794$		0			0
$795$	−25.8936	−	9.18005i	−0.918350	−	0.325583i
$796$		0			0
$797$			38.0258i			1.34694i	0.739214	+	0.673471i	$0.235197\pi$
$797$			38.0258i			1.34694i	−0.739214	+	0.673471i	$0.764803\pi$
$798$		0			0
$799$		−	11.0376i		−	0.390482i
$800$		0			0
$801$	31.4882	+	5.01087i	1.11258	+	0.177050i
$802$		0			0
$803$	−12.3448	+	21.3818i	−0.435639	+	0.754549i
$804$		0			0
$805$	−5.63726			−0.198687
$806$		0			0
$807$	−18.8447	−	22.0806i	−0.663363	−	0.777274i
$808$		0			0
$809$			8.46273i			0.297534i	0.988872	+	0.148767i	$0.0475304\pi$
$809$			8.46273i			0.297534i	−0.988872	+	0.148767i	$0.952470\pi$
$810$		0			0
$811$	−19.0726	+	11.0116i	−0.669730	+	0.386669i	−0.795974	−	0.605331i	$-0.793041\pi$
$811$	−19.0726	+	11.0116i	−0.669730	+	0.386669i	0.126245	+	0.991999i	$0.459708\pi$
$812$		0			0
$813$	6.47078	+	7.58192i	0.226940	+	0.265910i
$814$		0			0
$815$	−40.8817	+	70.8092i	−1.43202	+	2.48034i
$816$		0			0
$817$	−24.0688	−	16.2736i	−0.842062	−	0.569342i
$818$		0			0
$819$	−3.38826	−	0.539190i	−0.118395	−	0.0188408i
$820$		0			0
$821$	18.2947	−	10.5625i	0.638491	−	0.368633i	−0.145542	−	0.989352i	$-0.546493\pi$
$821$	18.2947	−	10.5625i	0.638491	−	0.368633i	0.784033	+	0.620719i	$0.213159\pi$
$822$		0			0
$823$	2.49596	−	1.44105i	0.0870038	−	0.0502317i	−0.455867	−	0.890048i	$-0.650671\pi$
$823$	2.49596	−	1.44105i	0.0870038	−	0.0502317i	0.542871	+	0.839816i	$0.317337\pi$
$824$		0			0
$825$	−7.15663	−	38.6927i	−0.249162	−	1.34711i
$826$		0			0
$827$	−5.56087	−	9.63171i	−0.193370	−	0.334927i	0.752995	−	0.658027i	$-0.228609\pi$
$827$	−5.56087	−	9.63171i	−0.193370	−	0.334927i	−0.946365	+	0.323099i	$0.895275\pi$
$828$		0			0
$829$	3.34201			0.116073			0.0580364	−	0.998314i	$-0.481516\pi$
$829$	3.34201			0.116073			0.0580364	+	0.998314i	$0.481516\pi$
$830$		0			0
$831$	−8.24769	−	2.92406i	−0.286109	−	0.101434i
$832$		0			0
$833$	−9.11558	−	5.26288i	−0.315836	−	0.182348i
$834$		0			0
$835$		−	78.2519i		−	2.70802i
$836$		0			0
$837$	19.6553	−	12.0151i	0.679385	−	0.415303i
$838$		0			0
$839$	19.4072	−	33.6142i	0.670011	−	1.16049i	−0.307890	−	0.951422i	$-0.599623\pi$
$839$	19.4072	−	33.6142i	0.670011	−	1.16049i	0.977901	−	0.209071i	$-0.0670438\pi$
$840$		0			0
$841$	−0.405945	+	0.703117i	−0.0139981	+	0.0242454i
$842$		0			0
$843$	−12.7141	+	2.35161i	−0.437898	+	0.0809939i
$844$		0			0
$845$	28.2451	−	16.3073i	0.971661	−	0.560989i
$846$		0			0
$847$		−	1.14363i		−	0.0392957i
$848$		0			0
$849$	−29.5200	−	34.5892i	−1.01313	−	1.18710i
$850$		0			0
$851$	8.94753	+	15.4976i	0.306717	+	0.531250i
$852$		0			0
$853$	−21.3092	+	36.9086i	−0.729612	+	1.26372i	0.227435	+	0.973793i	$0.426966\pi$
$853$	−21.3092	+	36.9086i	−0.729612	+	1.26372i	−0.957047	+	0.289932i	$0.906367\pi$
$854$		0			0
$855$	−13.4630	−	44.3277i	−0.460425	−	1.51597i
$856$		0			0
$857$	25.4087	+	14.6697i	0.867945	+	0.501108i	0.866665	−	0.498891i	$-0.166259\pi$
$857$	25.4087	+	14.6697i	0.867945	+	0.501108i	0.00128031	+	0.999999i	$0.499592\pi$
$858$		0			0
$859$	−32.5970	+	18.8199i	−1.11219	+	0.642126i	−0.939397	−	0.342832i	$-0.888614\pi$
$859$	−32.5970	+	18.8199i	−1.11219	+	0.642126i	−0.172797	+	0.984957i	$0.555281\pi$
$860$		0			0
$861$	−6.99047	+	5.96600i	−0.238235	+	0.203321i
$862$		0			0
$863$	45.3532			1.54384			0.771920	−	0.635719i	$-0.219296\pi$
$863$	45.3532			1.54384			0.771920	+	0.635719i	$0.219296\pi$
$864$		0			0
$865$	−23.9554	−	41.4920i	−0.814509	−	1.41077i
$866$		0			0
$867$	4.56733	+	24.6935i	0.155115	+	0.838637i
$868$		0			0
$869$	23.4870	+	13.5602i	0.796741	+	0.459999i
$870$		0			0
$871$	1.29040	+	0.745013i	0.0437236	+	0.0252438i
$872$		0			0
$873$	−29.5585	+	11.3216i	−1.00040	+	0.383179i
$874$		0			0
$875$	−5.30597			−0.179374
$876$		0			0
$877$	−3.65663	+	6.33346i	−0.123475	+	0.213866i	−0.921136	−	0.389241i	$-0.872737\pi$
$877$	−3.65663	+	6.33346i	−0.123475	+	0.213866i	0.797661	+	0.603107i	$0.206071\pi$
$878$		0			0
$879$	6.37092	−	17.9700i	0.214886	−	0.606114i
$880$		0			0
$881$		−	22.0985i		−	0.744519i	−0.928129	−	0.372259i	$-0.878583\pi$
$881$		−	22.0985i		−	0.744519i	0.928129	−	0.372259i	$-0.121417\pi$
$882$		0			0
$883$	−6.73633	+	3.88922i	−0.226696	+	0.130883i	−0.609047	−	0.793134i	$-0.708448\pi$
$883$	−6.73633	+	3.88922i	−0.226696	+	0.130883i	0.382351	+	0.924017i	$0.375114\pi$
$884$		0			0
$885$	−87.3649	+	16.1591i	−2.93674	+	0.543181i
$886$		0			0
$887$	14.0770	+	24.3821i	0.472659	+	0.818669i	0.999510	−	0.0312881i	$-0.00996095\pi$
$887$	14.0770	+	24.3821i	0.472659	+	0.818669i	−0.526852	+	0.849957i	$0.676628\pi$
$888$		0			0
$889$	−1.34474	−	2.32915i	−0.0451010	−	0.0781173i
$890$		0			0
$891$	5.59110	+	26.4947i	0.187309	+	0.887605i
$892$		0			0
$893$	−13.3049	−	27.3563i	−0.445232	−	0.915445i
$894$		0			0
$895$	−48.1885	−	27.8216i	−1.61076	−	0.929974i
$896$		0			0
$897$	6.95460	−	5.93539i	0.232207	−	0.198177i
$898$		0			0
$899$	−11.7691	−	20.3846i	−0.392521	−	0.679866i
$900$		0			0
$901$	−7.08097			−0.235901
$902$		0			0
$903$	5.15604	−	4.40041i	0.171582	−	0.146437i
$904$		0			0
$905$		−	51.1796i		−	1.70127i
$906$		0			0
$907$	−21.7729	−	12.5706i	−0.722957	−	0.417400i	0.0928829	−	0.995677i	$-0.470392\pi$
$907$	−21.7729	−	12.5706i	−0.722957	−	0.417400i	−0.815840	+	0.578277i	$0.803725\pi$
$908$		0			0
$909$	33.9534	+	5.40317i	1.12616	+	0.179212i
$910$		0			0
$911$	10.1948			0.337770			0.168885	−	0.985636i	$-0.445983\pi$
$911$	10.1948			0.337770			0.168885	+	0.985636i	$0.445983\pi$
$912$		0			0
$913$	−40.9973			−1.35681
$914$		0			0
$915$	−0.107049	+	0.301947i	−0.00353894	+	0.00998205i
$916$		0			0
$917$	11.1427	+	6.43324i	0.367965	+	0.212444i
$918$		0			0
$919$			59.7855i			1.97214i	0.166326	+	0.986071i	$0.446810\pi$
$919$			59.7855i			1.97214i	−0.166326	+	0.986071i	$0.553190\pi$
$920$		0			0
$921$	0.163696	+	0.191805i	0.00539395	+	0.00632019i
$922$		0			0
$923$	−22.8596			−0.752434
$924$		0			0
$925$	24.9293	+	43.1789i	0.819671	+	1.41971i
$926$		0			0
$927$	−17.8649	+	22.0283i	−0.586760	+	0.723505i
$928$		0			0
$929$	0.775378	+	0.447665i	0.0254393	+	0.0146874i	0.512666	−	0.858588i	$-0.328658\pi$
$929$	0.775378	+	0.447665i	0.0254393	+	0.0146874i	−0.487226	+	0.873276i	$0.661991\pi$
$930$		0			0
$931$	−28.9367	−	2.05580i	−0.948362	−	0.0673761i
$932$		0			0
$933$	32.3528	+	11.4701i	1.05918	+	0.375513i
$934$		0			0
$935$	−8.42892	−	14.5993i	−0.275655	−	0.477449i
$936$		0			0
$937$	−5.68137	−	9.84042i	−0.185602	−	0.321472i	0.758177	−	0.652049i	$-0.226090\pi$
$937$	−5.68137	−	9.84042i	−0.185602	−	0.321472i	−0.943779	+	0.330576i	$0.892757\pi$
$938$		0			0
$939$	−3.95374	−	21.3761i	−0.129026	−	0.697584i
$940$		0			0
$941$	26.8499	−	15.5018i	0.875282	−	0.505344i	0.00618199	−	0.999981i	$-0.498032\pi$
$941$	26.8499	−	15.5018i	0.875282	−	0.505344i	0.869100	+	0.494637i	$0.164699\pi$
$942$		0			0
$943$		−	24.4911i		−	0.797541i
$944$		0			0
$945$	10.8050	−	0.271072i	0.351487	−	0.00881796i
$946$		0			0
$947$	14.1070	−	24.4341i	0.458417	−	0.794002i	−0.540460	−	0.841370i	$-0.681750\pi$
$947$	14.1070	−	24.4341i	0.458417	−	0.794002i	0.998878	+	0.0473675i	$0.0150832\pi$
$948$		0			0
$949$	−15.9838			−0.518856
$950$		0			0
$951$	−2.23802	+	0.413946i	−0.0725728	+	0.0134231i
$952$		0			0
$953$	39.7253	+	22.9354i	1.28683	+	0.742952i	0.978088	−	0.208194i	$-0.0667586\pi$
$953$	39.7253	+	22.9354i	1.28683	+	0.742952i	0.308742	+	0.951146i	$0.400092\pi$
$954$		0			0
$955$	39.4395	+	22.7704i	1.27623	+	0.736833i
$956$		0			0
$957$	27.2061	−	5.03206i	0.879449	−	0.162663i
$958$		0			0
$959$	−1.34145	−	2.32345i	−0.0433176	−	0.0750283i
$960$		0			0
$961$	11.3447			0.365959
$962$		0			0
$963$	14.0208	+	11.3708i	0.451815	+	0.366420i
$964$		0			0
$965$	−58.7658	+	33.9284i	−1.89174	+	1.09219i
$966$		0			0
$967$	33.9471	+	19.5994i	1.09167	+	0.630274i	0.934019	−	0.357222i	$-0.116276\pi$
$967$	33.9471	+	19.5994i	1.09167	+	0.630274i	0.157646	+	0.987496i	$0.449609\pi$
$968$		0			0
$969$	−7.08834	−	9.60901i	−0.227710	−	0.308686i
$970$		0			0
$971$	9.99536	−	17.3125i	0.320766	−	0.555584i	−0.659880	−	0.751371i	$-0.729393\pi$
$971$	9.99536	−	17.3125i	0.320766	−	0.555584i	0.980646	+	0.195787i	$0.0627262\pi$
$972$		0			0
$973$	−1.59406	−	2.76098i	−0.0511031	−	0.0885131i
$974$		0			0
$975$	19.3767	−	16.5370i	0.620551	−	0.529608i
$976$		0			0
$977$		−	0.175304i		−	0.00560847i	−0.999996	−	0.00280424i	$-0.999107\pi$
$977$		−	0.175304i		−	0.00560847i	0.999996	−	0.00280424i	$-0.000892618\pi$
$978$		0			0
$979$	27.6927	−	15.9884i	0.885063	−	0.510992i
$980$		0			0
$981$	29.2660	−	11.2096i	0.934390	−	0.357894i
$982$		0			0
$983$	10.8454	−	18.7848i	0.345915	−	0.599143i	−0.639604	−	0.768704i	$-0.720902\pi$
$983$	10.8454	−	18.7848i	0.345915	−	0.599143i	0.985520	+	0.169561i	$0.0542351\pi$
$984$		0			0
$985$	32.5234	−	56.3321i	1.03628	−	1.79489i
$986$		0			0
$987$	6.97888	−	1.29082i	0.222140	−	0.0410872i
$988$		0			0
$989$			18.0642i			0.574408i
$990$		0			0
$991$	−0.783306	−	0.452242i	−0.0248825	−	0.0143659i	0.487507	−	0.873119i	$-0.337906\pi$
$991$	−0.783306	−	0.452242i	−0.0248825	−	0.0143659i	−0.512390	+	0.858753i	$0.671240\pi$
$992$		0			0
$993$	−10.9611	+	30.9172i	−0.347839	+	0.981127i
$994$		0			0
$995$	44.6319			1.41493
$996$		0			0
$997$	−12.1525	−	21.0488i	−0.384875	−	0.666623i	0.606877	−	0.794796i	$-0.292422\pi$
$997$	−12.1525	−	21.0488i	−0.384875	−	0.666623i	−0.991752	+	0.128173i	$0.959089\pi$
$998$		0			0
$999$	−17.8951	−	29.2742i	−0.566174	−	0.926193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bh.f.239.2	✓	24
3.2	odd	2	inner	912.2.bh.f.239.3	yes	24
4.3	odd	2	inner	912.2.bh.f.239.11	yes	24
12.11	even	2	inner	912.2.bh.f.239.10	yes	24
19.7	even	3	inner	912.2.bh.f.767.10	yes	24
57.26	odd	6	inner	912.2.bh.f.767.11	yes	24
76.7	odd	6	inner	912.2.bh.f.767.3	yes	24
228.83	even	6	inner	912.2.bh.f.767.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bh.f.239.2	✓	24	1.1	even	1	trivial
912.2.bh.f.239.3	yes	24	3.2	odd	2	inner
912.2.bh.f.239.10	yes	24	12.11	even	2	inner
912.2.bh.f.239.11	yes	24	4.3	odd	2	inner
912.2.bh.f.767.2	yes	24	228.83	even	6	inner
912.2.bh.f.767.3	yes	24	76.7	odd	6	inner
912.2.bh.f.767.10	yes	24	19.7	even	3	inner
912.2.bh.f.767.11	yes	24	57.26	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63249 - 0.578768i) q^{3} +(3.06808 + 1.77136i) q^{5} +0.587143i q^{7} +(2.33006 + 1.88967i) q^{9} +3.00869 q^{11} +(0.973896 + 1.68684i) q^{13} +(-3.98341 - 4.66744i) q^{15} +(-1.36968 - 0.790785i) q^{17} +(-4.34794 - 0.308898i) q^{19} +(0.339819 - 0.958506i) q^{21} +(1.35506 + 2.34703i) q^{23} +(3.77542 + 6.53922i) q^{25} +(-2.71012 - 4.43343i) q^{27} +(-4.59794 + 2.65462i) q^{29} +4.43343i q^{31} +(-4.91166 - 1.74133i) q^{33} +(-1.04004 + 1.80140i) q^{35} +6.60305 q^{37} +(-0.613589 - 3.31741i) q^{39} +(-7.82621 - 4.51846i) q^{41} +(5.77246 + 3.33273i) q^{43} +(3.80153 + 9.92502i) q^{45} +(3.48944 + 6.04389i) q^{47} +6.65526 q^{49} +(1.77831 + 2.08368i) q^{51} +(3.87735 - 2.23859i) q^{53} +(9.23091 + 5.32947i) q^{55} +(6.91919 + 3.02072i) q^{57} +(7.23960 - 12.5394i) q^{59} +(-0.0261043 - 0.0452140i) q^{61} +(-1.10950 + 1.36808i) q^{63} +6.90047i q^{65} +(0.662494 - 0.382491i) q^{67} +(-0.853736 - 4.61577i) q^{69} +(-5.86809 + 10.1638i) q^{71} +(-4.10305 + 7.10670i) q^{73} +(-2.37865 - 12.8603i) q^{75} +1.76653i q^{77} +(7.80639 + 4.50702i) q^{79} +(1.85832 + 8.80606i) q^{81} -13.6263 q^{83} +(-2.80153 - 4.85239i) q^{85} +(9.04251 - 1.67251i) q^{87} +(9.20425 - 5.31408i) q^{89} +(-0.990414 + 0.571816i) q^{91} +(2.56592 - 7.23753i) q^{93} +(-12.7927 - 8.64949i) q^{95} +(-5.27542 + 9.13730i) q^{97} +(7.01041 + 5.68542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) \) 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more