LMFDB - Embedded newform 920.2.bv.a.17.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.19
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00457693 + 0.00249919i) q^{3} +(2.23374 - 0.101999i) q^{5} +(-1.95297 - 2.60886i) q^{7} +(-1.62191 + 2.52374i) q^{9} +(-3.17383 + 1.44944i) q^{11} +(-3.97765 - 2.97763i) q^{13} +(-0.00996875 + 0.00604939i) q^{15} +(-0.510554 - 7.13848i) q^{17} +(-3.33403 - 3.84767i) q^{19} +(0.0154587 + 0.00705973i) q^{21} +(-4.53722 + 1.55359i) q^{23} +(4.97919 - 0.455680i) q^{25} +(0.00223211 - 0.0312090i) q^{27} +(3.11015 + 2.69496i) q^{29} +(-1.88961 + 0.554841i) q^{31} +(0.0109039 - 0.0145660i) q^{33} +(-4.62853 - 5.62832i) q^{35} +(8.36550 - 1.81980i) q^{37} +(0.0256471 + 0.00368749i) q^{39} +(-4.08835 + 2.62742i) q^{41} +(-1.96262 - 3.59428i) q^{43} +(-3.36550 + 5.80281i) q^{45} +(3.58642 + 3.58642i) q^{47} +(-1.01995 + 3.47362i) q^{49} +(0.0201772 + 0.0313963i) q^{51} +(-8.90212 + 6.66404i) q^{53} +(-6.94166 + 3.56140i) q^{55} +(0.0248757 + 0.00927815i) q^{57} +(5.46562 - 0.785838i) q^{59} +(-0.654342 - 2.22848i) q^{61} +(9.75163 - 0.697450i) q^{63} +(-9.18875 - 6.24553i) q^{65} +(-5.28978 - 14.1825i) q^{67} +(0.0168838 - 0.0184500i) q^{69} +(0.281573 - 0.616558i) q^{71} +(13.0564 + 0.933811i) q^{73} +(-0.0216506 + 0.0145296i) q^{75} +(9.97978 + 5.44937i) q^{77} +(-2.15063 - 14.9580i) q^{79} +(-3.73863 - 8.18647i) q^{81} +(0.700230 + 3.21891i) q^{83} +(-1.86856 - 15.8934i) q^{85} +(-0.0209701 - 0.00456177i) q^{87} +(-7.31005 - 2.14642i) q^{89} +16.1924i q^{91} +(0.00726197 - 0.00726197i) q^{93} +(-7.83981 - 8.25463i) q^{95} +(-1.63190 + 7.50171i) q^{97} +(1.48965 - 10.3608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.00457693	+	0.00249919i	−0.00264249	+	0.00144291i	−0.480570	−	0.876957i	$-0.659570\pi$
$3$	−0.00457693	+	0.00249919i	−0.00264249	+	0.00144291i	0.477927	+	0.878399i	$0.341388\pi$
$4$		0			0
$5$	2.23374	−	0.101999i	0.998959	−	0.0456155i
$5$	2.23374	−	0.101999i	0.998959	−	0.0456155i
$6$		0			0
$7$	−1.95297	−	2.60886i	−0.738154	−	0.986058i	−0.999782	−	0.0208893i	$-0.993350\pi$
$7$	−1.95297	−	2.60886i	−0.738154	−	0.986058i	0.261628	−	0.965169i	$-0.415741\pi$
$8$		0			0
$9$	−1.62191	+	2.52374i	−0.540636	+	0.841246i
$10$		0			0
$11$	−3.17383	+	1.44944i	−0.956945	+	0.437022i	−0.831775	−	0.555113i	$-0.812675\pi$
$11$	−3.17383	+	1.44944i	−0.956945	+	0.437022i	−0.125170	+	0.992135i	$0.539948\pi$
$12$		0			0
$13$	−3.97765	−	2.97763i	−1.10320	−	0.825846i	−0.117287	−	0.993098i	$-0.537420\pi$
$13$	−3.97765	−	2.97763i	−1.10320	−	0.825846i	−0.985914	+	0.167252i	$0.946511\pi$
$14$		0			0
$15$	−0.00996875	+	0.00604939i	−0.00257392	+	0.00156195i
$16$		0			0
$17$	−0.510554	−	7.13848i	−0.123828	−	1.73133i	−0.557424	−	0.830228i	$-0.688210\pi$
$17$	−0.510554	−	7.13848i	−0.123828	−	1.73133i	0.433597	−	0.901107i	$-0.357244\pi$
$18$		0			0
$19$	−3.33403	−	3.84767i	−0.764878	−	0.882717i	0.231043	−	0.972944i	$-0.425786\pi$
$19$	−3.33403	−	3.84767i	−0.764878	−	0.882717i	−0.995921	+	0.0902268i	$0.971241\pi$
$20$		0			0
$21$	0.0154587	+	0.00705973i	0.00337336	+	0.00154056i
$22$		0			0
$23$	−4.53722	+	1.55359i	−0.946076	+	0.323946i
$23$	−4.53722	+	1.55359i	−0.946076	+	0.323946i
$24$		0			0
$25$	4.97919	−	0.455680i	0.995838	−	0.0911360i
$26$		0			0
$27$	0.00223211	−	0.0312090i	0.000429570	−	0.00600617i
$28$		0			0
$29$	3.11015	+	2.69496i	0.577540	+	0.500441i	0.893941	−	0.448184i	$-0.147929\pi$
$29$	3.11015	+	2.69496i	0.577540	+	0.500441i	−0.316401	+	0.948625i	$0.602475\pi$
$30$		0			0
$31$	−1.88961	+	0.554841i	−0.339385	+	0.0996524i	−0.446984	−	0.894542i	$-0.647502\pi$
$31$	−1.88961	+	0.554841i	−0.339385	+	0.0996524i	0.107599	+	0.994194i	$0.465684\pi$
$32$		0			0
$33$	0.0109039	−	0.0145660i	0.00189813	−	0.00253561i
$34$		0			0
$35$	−4.62853	−	5.62832i	−0.782365	−	0.951360i
$36$		0			0
$37$	8.36550	−	1.81980i	1.37528	−	0.299174i	0.536618	−	0.843825i	$-0.319702\pi$
$37$	8.36550	−	1.81980i	1.37528	−	0.299174i	0.838662	+	0.544651i	$0.183338\pi$
$38$		0			0
$39$	0.0256471	+	0.00368749i	0.00410682	+	0.000590471i
$40$		0			0
$41$	−4.08835	+	2.62742i	−0.638493	+	0.410335i	−0.819445	−	0.573157i	$-0.805718\pi$
$41$	−4.08835	+	2.62742i	−0.638493	+	0.410335i	0.180952	+	0.983492i	$0.442082\pi$
$42$		0			0
$43$	−1.96262	−	3.59428i	−0.299297	−	0.548122i	0.684144	−	0.729347i	$-0.260176\pi$
$43$	−1.96262	−	3.59428i	−0.299297	−	0.548122i	−0.983442	+	0.181224i	$0.941994\pi$
$44$		0			0
$45$	−3.36550	+	5.80281i	−0.501699	+	0.865032i
$46$		0			0
$47$	3.58642	+	3.58642i	0.523133	+	0.523133i	0.918516	−	0.395384i	$-0.129388\pi$
$47$	3.58642	+	3.58642i	0.523133	+	0.523133i	−0.395384	+	0.918516i	$0.629388\pi$
$48$		0			0
$49$	−1.01995	+	3.47362i	−0.145707	+	0.496232i
$50$		0			0
$51$	0.0201772	+	0.0313963i	0.00282537	+	0.00439636i
$52$		0			0
$53$	−8.90212	+	6.66404i	−1.22280	+	0.915376i	−0.998253	−	0.0590869i	$-0.981181\pi$
$53$	−8.90212	+	6.66404i	−1.22280	+	0.915376i	−0.224547	+	0.974463i	$0.572090\pi$
$54$		0			0
$55$	−6.94166	+	3.56140i	−0.936014	+	0.480219i
$56$		0			0
$57$	0.0248757	+	0.00927815i	0.00329486	+	0.00122892i
$58$		0			0
$59$	5.46562	−	0.785838i	0.711564	−	0.102307i	0.222978	−	0.974823i	$-0.428422\pi$
$59$	5.46562	−	0.785838i	0.711564	−	0.102307i	0.488585	+	0.872516i	$0.337513\pi$
$60$		0			0
$61$	−0.654342	−	2.22848i	−0.0837799	−	0.285328i	0.906938	−	0.421265i	$-0.138414\pi$
$61$	−0.654342	−	2.22848i	−0.0837799	−	0.285328i	−0.990717	+	0.135937i	$0.956596\pi$
$62$		0			0
$63$	9.75163	−	0.697450i	1.22859	−	0.0878705i
$64$		0			0
$65$	−9.18875	−	6.24553i	−1.13972	−	0.774663i
$66$		0			0
$67$	−5.28978	−	14.1825i	−0.646250	−	1.73266i	−0.679978	−	0.733232i	$-0.738011\pi$
$67$	−5.28978	−	14.1825i	−0.646250	−	1.73266i	0.0337285	−	0.999431i	$-0.489262\pi$
$68$		0			0
$69$	0.0168838	−	0.0184500i	0.00203257	−	0.00222112i
$70$		0			0
$71$	0.281573	−	0.616558i	0.0334165	−	0.0731720i	−0.892188	−	0.451665i	$-0.850830\pi$
$71$	0.281573	−	0.616558i	0.0334165	−	0.0731720i	0.925604	+	0.378493i	$0.123558\pi$
$72$		0			0
$73$	13.0564	+	0.933811i	1.52813	+	0.109294i	0.809925	−	0.586534i	$-0.199508\pi$
$73$	13.0564	+	0.933811i	1.52813	+	0.109294i	0.718209	+	0.695828i	$0.244962\pi$
$74$		0			0
$75$	−0.0216506	+	0.0145296i	−0.00249999	+	0.00167773i
$76$		0			0
$77$	9.97978	+	5.44937i	1.13730	+	0.621014i
$78$		0			0
$79$	−2.15063	−	14.9580i	−0.241965	−	1.68290i	−0.642237	−	0.766506i	$-0.721993\pi$
$79$	−2.15063	−	14.9580i	−0.241965	−	1.68290i	0.400272	−	0.916396i	$-0.368916\pi$
$80$		0			0
$81$	−3.73863	−	8.18647i	−0.415404	−	0.909607i
$82$		0			0
$83$	0.700230	+	3.21891i	0.0768603	+	0.353321i	0.999475	−	0.0324021i	$-0.0103157\pi$
$83$	0.700230	+	3.21891i	0.0768603	+	0.353321i	−0.922615	+	0.385723i	$0.873952\pi$
$84$		0			0
$85$	−1.86856	−	15.8934i	−0.202674	−	1.72388i
$86$		0			0
$87$	−0.0209701	−	0.00456177i	−0.00224823	−	0.000489073i
$88$		0			0
$89$	−7.31005	−	2.14642i	−0.774863	−	0.227520i	−0.129688	−	0.991555i	$-0.541398\pi$
$89$	−7.31005	−	2.14642i	−0.774863	−	0.227520i	−0.645175	+	0.764034i	$0.723216\pi$
$90$		0			0
$91$			16.1924i			1.69742i
$92$		0			0
$93$	0.00726197	−	0.00726197i	0.000753032	−	0.000753032i
$94$		0			0
$95$	−7.83981	−	8.25463i	−0.804348	−	0.846908i
$96$		0			0
$97$	−1.63190	+	7.50171i	−0.165694	+	0.761683i	0.817028	+	0.576597i	$0.195620\pi$
$97$	−1.63190	+	7.50171i	−0.165694	+	0.761683i	−0.982722	+	0.185086i	$0.940744\pi$
$98$		0			0
$99$	1.48965	−	10.3608i	0.149716	−	1.04130i
$100$		0			0
$101$	0.463739	+	0.298027i	0.0461437	+	0.0296548i	0.563509	−	0.826110i	$-0.309451\pi$
$101$	0.463739	+	0.298027i	0.0461437	+	0.0296548i	−0.517366	+	0.855764i	$0.673087\pi$
$102$		0			0
$103$	−4.65725	+	12.4866i	−0.458893	+	1.23034i	0.477265	+	0.878759i	$0.341628\pi$
$103$	−4.65725	+	12.4866i	−0.458893	+	1.23034i	−0.936158	+	0.351580i	$0.885645\pi$
$104$		0			0
$105$	0.0352507	+	0.0141928i	0.00344012	+	0.00138508i
$106$		0			0
$107$	4.45975	−	8.16742i	0.431140	−	0.789574i	−0.568307	−	0.822817i	$-0.692401\pi$
$107$	4.45975	−	8.16742i	0.431140	−	0.789574i	0.999447	+	0.0332421i	$0.0105833\pi$
$108$		0			0
$109$	−4.52259	+	5.21934i	−0.433185	+	0.499922i	−0.929808	−	0.368044i	$-0.880028\pi$
$109$	−4.52259	+	5.21934i	−0.433185	+	0.499922i	0.496623	+	0.867966i	$0.334573\pi$
$110$		0			0
$111$	−0.0337403	+	0.0292361i	−0.00320248	+	0.00277497i
$112$		0			0
$113$	7.10932	−	2.65164i	0.668789	−	0.249445i	0.00794455	−	0.999968i	$-0.497471\pi$
$113$	7.10932	−	2.65164i	0.668789	−	0.249445i	0.660844	+	0.750523i	$0.270198\pi$
$114$		0			0
$115$	−9.97650	+	3.93311i	−0.930314	+	0.366764i
$116$		0			0
$117$	13.9661	−	5.20910i	1.29117	−	0.481581i
$118$		0			0
$119$	−17.6262	+	15.2732i	−1.61579	+	1.40009i
$120$		0			0
$121$	0.768835	−	0.887283i	0.0698941	−	0.0806621i
$122$		0			0
$123$	0.0121457	−	0.0222431i	0.00109514	−	0.00200559i
$124$		0			0
$125$	11.0757	−	1.52575i	0.990645	−	0.136467i
$126$		0			0
$127$	−2.14639	+	5.75469i	−0.190461	+	0.510646i	−0.996721	−	0.0809154i	$-0.974216\pi$
$127$	−2.14639	+	5.75469i	−0.190461	+	0.510646i	0.806260	+	0.591562i	$0.201488\pi$
$128$		0			0
$129$	0.0179656	+	0.0115458i	0.00158178	+	0.00101655i
$130$		0			0
$131$	−1.78785	+	12.4348i	−0.156205	+	1.08643i	0.749341	+	0.662184i	$0.230370\pi$
$131$	−1.78785	+	12.4348i	−0.156205	+	1.08643i	−0.905547	+	0.424247i	$0.860539\pi$
$132$		0			0
$133$	−3.52680	+	16.2124i	−0.305812	+	1.40580i
$134$		0			0
$135$	0.00180266	−	0.0699404i	0.000155148	−	0.00601951i
$136$		0			0
$137$	4.30968	−	4.30968i	0.368201	−	0.368201i	−0.498620	−	0.866821i	$-0.666160\pi$
$137$	4.30968	−	4.30968i	0.368201	−	0.368201i	0.866821	+	0.498620i	$0.166160\pi$
$138$		0			0
$139$			6.36126i			0.539555i	0.962923	+	0.269777i	$0.0869501\pi$
$139$			6.36126i			0.539555i	−0.962923	+	0.269777i	$0.913050\pi$
$140$		0			0
$141$	−0.0253779	−	0.00745162i	−0.00213721	−	0.000627540i
$142$		0			0
$143$	16.9403	+	3.68513i	1.41662	+	0.308166i
$144$		0			0
$145$	7.22214	+	5.70260i	0.599766	+	0.473575i
$146$		0			0
$147$	−0.00401302	−	0.0184476i	−0.000330989	−	0.00152153i
$148$		0			0
$149$	−3.08848	−	6.76282i	−0.253018	−	0.554032i	0.739916	−	0.672699i	$-0.234865\pi$
$149$	−3.08848	−	6.76282i	−0.253018	−	0.554032i	−0.992934	+	0.118667i	$0.962138\pi$
$150$		0			0
$151$	−1.55858	−	10.8401i	−0.126835	−	0.882158i	−0.949530	−	0.313675i	$-0.898440\pi$
$151$	−1.55858	−	10.8401i	−0.126835	−	0.882158i	0.822695	−	0.568483i	$-0.192469\pi$
$152$		0			0
$153$	18.8437	+	10.2894i	1.52342	+	0.831852i
$154$		0			0
$155$	−4.16431	+	1.43211i	−0.334486	+	0.115030i
$156$		0			0
$157$	−14.7331	−	1.05373i	−1.17583	−	0.0840971i	−0.530285	−	0.847819i	$-0.677915\pi$
$157$	−14.7331	−	1.05373i	−1.17583	−	0.0840971i	−0.645545	+	0.763722i	$0.723370\pi$
$158$		0			0
$159$	0.0240896	−	0.0527489i	0.00191043	−	0.00418326i
$160$		0			0
$161$	12.9142	+	8.80287i	1.01778	+	0.693764i
$162$		0			0
$163$	−2.62119	−	7.02768i	−0.205307	−	0.550450i	0.792961	−	0.609272i	$-0.208538\pi$
$163$	−2.62119	−	7.02768i	−0.205307	−	0.550450i	−0.998268	+	0.0588219i	$0.981266\pi$
$164$		0			0
$165$	0.0228709	−	0.0336488i	0.00178049	−	0.00261955i
$166$		0			0
$167$	−3.49967	+	0.250301i	−0.270812	+	0.0193689i	−0.206085	−	0.978534i	$-0.566072\pi$
$167$	−3.49967	+	0.250301i	−0.270812	+	0.0193689i	−0.0647274	+	0.997903i	$0.520618\pi$
$168$		0			0
$169$	3.29288	+	11.2145i	0.253298	+	0.862655i
$170$		0			0
$171$	15.1180	−	2.17364i	1.15610	−	0.166222i
$172$		0			0
$173$	−6.49042	−	2.42080i	−0.493458	−	0.184050i	0.0904011	−	0.995905i	$-0.471185\pi$
$173$	−6.49042	−	2.42080i	−0.493458	−	0.184050i	−0.583859	+	0.811855i	$0.698458\pi$
$174$		0			0
$175$	−10.9130	−	12.1001i	−0.824947	−	0.914682i
$176$		0			0
$177$	−0.0230518	+	0.0172564i	−0.00173268	+	0.00129707i
$178$		0			0
$179$	5.76400	+	8.96896i	0.430821	+	0.670371i	0.987005	−	0.160688i	$-0.0513713\pi$
$179$	5.76400	+	8.96896i	0.430821	+	0.670371i	−0.556184	+	0.831059i	$0.687735\pi$
$180$		0			0
$181$	−0.570659	+	1.94349i	−0.0424168	+	0.144458i	−0.977979	−	0.208704i	$-0.933075\pi$
$181$	−0.570659	+	1.94349i	−0.0424168	+	0.144458i	0.935562	+	0.353162i	$0.114894\pi$
$182$		0			0
$183$	0.00856428	+	0.00856428i	0.000633090	+	0.000633090i
$184$		0			0
$185$	18.5007	−	4.91825i	1.36020	−	0.361597i
$186$		0			0
$187$	11.9672	+	21.9163i	0.875127	+	1.60268i
$188$		0			0
$189$	−0.0857792	+	0.0551270i	−0.00623952	+	0.00400990i
$190$		0			0
$191$	7.76679	+	1.11670i	0.561985	+	0.0808013i	0.417453	−	0.908699i	$-0.362923\pi$
$191$	7.76679	+	1.11670i	0.561985	+	0.0808013i	0.144533	+	0.989500i	$0.453832\pi$
$192$		0			0
$193$	2.54207	−	0.552994i	0.182982	−	0.0398054i	−0.120140	−	0.992757i	$-0.538334\pi$
$193$	2.54207	−	0.552994i	0.182982	−	0.0398054i	0.303123	+	0.952952i	$0.401971\pi$
$194$		0			0
$195$	0.0576650	+	0.00562092i	0.00412948	+	0.000402522i
$196$		0			0
$197$	3.61834	−	4.83354i	0.257796	−	0.344375i	−0.652906	−	0.757439i	$-0.726450\pi$
$197$	3.61834	−	4.83354i	0.257796	−	0.344375i	0.910702	+	0.413064i	$0.135541\pi$
$198$		0			0
$199$	13.9382	−	4.09262i	0.988052	−	0.290118i	0.252508	−	0.967595i	$-0.418745\pi$
$199$	13.9382	−	4.09262i	0.988052	−	0.290118i	0.735544	+	0.677477i	$0.236926\pi$
$200$		0			0
$201$	0.0596556	+	0.0516919i	0.00420778	+	0.00364607i
$202$		0			0
$203$	0.956751	−	13.3771i	0.0671508	−	0.938890i
$204$		0			0
$205$	−8.86432	+	6.28599i	−0.619111	+	0.439033i
$206$		0			0
$207$	3.43810	−	13.9705i	0.238964	−	0.971019i
$208$		0			0
$209$	16.1586	+	7.37938i	1.11771	+	0.510442i
$210$		0			0
$211$	13.9755	+	16.1286i	0.962116	+	1.11034i	0.993838	+	0.110844i	$0.0353554\pi$
$211$	13.9755	+	16.1286i	0.962116	+	1.11034i	−0.0317222	+	0.999497i	$0.510099\pi$
$212$		0			0
$213$	0.000252159		0.00352565i	1.72777e−5		0.000241573i
$214$		0			0
$215$	−4.75061	−	7.82850i	−0.323989	−	0.533899i
$216$		0			0
$217$	5.13787	+	3.84616i	0.348781	+	0.261094i
$218$		0			0
$219$	−0.0620919	+	0.0283564i	−0.00419578	+	0.00191615i
$220$		0			0
$221$	−19.2249	+	29.9146i	−1.29321	+	2.01227i
$222$		0			0
$223$	5.41562	+	7.23441i	0.362656	+	0.484452i	0.944344	−	0.328960i	$-0.106698\pi$
$223$	5.41562	+	7.23441i	0.362656	+	0.484452i	−0.581687	+	0.813412i	$0.697607\pi$
$224$		0			0
$225$	−6.92577	+	13.3052i	−0.461718	+	0.887016i
$226$		0			0
$227$	7.18827	−	3.92509i	0.477102	−	0.260517i	−0.222656	−	0.974897i	$-0.571473\pi$
$227$	7.18827	−	3.92509i	0.477102	−	0.260517i	0.699758	+	0.714380i	$0.253291\pi$
$228$		0			0
$229$	−19.3373			−1.27784			−0.638921	−	0.769272i	$-0.720619\pi$
$229$	−19.3373			−1.27784			−0.638921	+	0.769272i	$0.720619\pi$
$230$		0			0
$231$	−0.0592957			−0.00390137
$232$		0			0
$233$	24.5022	−	13.3792i	1.60519	−	0.876501i	0.608646	−	0.793442i	$-0.291713\pi$
$233$	24.5022	−	13.3792i	1.60519	−	0.876501i	0.996545	−	0.0830589i	$-0.0264690\pi$
$234$		0			0
$235$	8.37693	+	7.64531i	0.546451	+	0.498725i
$236$		0			0
$237$	0.0472261	+	0.0630867i	0.00306766	+	0.00409792i
$238$		0			0
$239$	8.95374	−	13.9323i	0.579169	−	0.901205i	−0.420813	−	0.907147i	$-0.638255\pi$
$239$	8.95374	−	13.9323i	0.579169	−	0.901205i	0.999982	+	0.00594241i	$0.00189154\pi$
$240$		0			0
$241$	18.5388	−	8.46640i	1.19419	−	0.545369i	0.283706	−	0.958911i	$-0.408436\pi$
$241$	18.5388	−	8.46640i	1.19419	−	0.545369i	0.910485	+	0.413543i	$0.135709\pi$
$242$		0			0
$243$	0.112715	+	0.0843772i	0.00723065	+	0.00541280i
$244$		0			0
$245$	−1.92399	+	7.86321i	−0.122919	+	0.502362i
$246$		0			0
$247$	1.80464	+	25.2322i	0.114827	+	1.60549i
$248$		0			0
$249$	−0.0112496	−	0.0129827i	−0.000712912	−	0.000822745i
$250$		0			0
$251$	−23.3404	−	10.6592i	−1.47323	−	0.672804i	−0.492889	−	0.870092i	$-0.664059\pi$
$251$	−23.3404	−	10.6592i	−1.47323	−	0.672804i	−0.980346	+	0.197288i	$0.936787\pi$
$252$		0			0
$253$	12.1485	−	11.5072i	0.763771	−	0.723454i
$254$		0			0
$255$	0.0482730	+	0.0680731i	0.00302297	+	0.00426291i
$256$		0			0
$257$	2.16802	−	30.3129i	0.135237	−	1.89087i	−0.250291	−	0.968171i	$-0.580526\pi$
$257$	2.16802	−	30.3129i	0.135237	−	1.89087i	0.385528	−	0.922696i	$-0.374019\pi$
$258$		0			0
$259$	−21.0852	−	18.2704i	−1.31017	−	1.13527i
$260$		0			0
$261$	−11.8457	+	3.47822i	−0.733233	+	0.215297i
$262$		0			0
$263$	3.08575	−	4.12208i	0.190275	−	0.254178i	−0.695251	−	0.718767i	$-0.744707\pi$
$263$	3.08575	−	4.12208i	0.190275	−	0.254178i	0.885527	+	0.464589i	$0.153798\pi$
$264$		0			0
$265$	−19.2053	+	15.7937i	−1.17977	+	0.970202i
$266$		0			0
$267$	0.0388219	−	0.00844518i	0.00237586	−	0.000516837i
$268$		0			0
$269$	8.87365	+	1.27584i	0.541036	+	0.0777892i	0.407415	−	0.913243i	$-0.366430\pi$
$269$	8.87365	+	1.27584i	0.541036	+	0.0777892i	0.133621	+	0.991032i	$0.457339\pi$
$270$		0			0
$271$	3.30260	−	2.12245i	0.200618	−	0.128930i	−0.436475	−	0.899717i	$-0.643773\pi$
$271$	3.30260	−	2.12245i	0.200618	−	0.128930i	0.637093	+	0.770787i	$0.280137\pi$
$272$		0			0
$273$	−0.0404678	−	0.0741113i	−0.00244922	−	0.00448542i
$274$		0			0
$275$	−15.1426	+	8.66328i	−0.913134	+	0.522415i
$276$		0			0
$277$	−16.9381	−	16.9381i	−1.01771	−	1.01771i	−0.999840	−	0.0178706i	$-0.994311\pi$
$277$	−16.9381	−	16.9381i	−1.01771	−	1.01771i	−0.0178706	−	0.999840i	$-0.505689\pi$
$278$		0			0
$279$	1.66451	−	5.66879i	0.0996515	−	0.339382i
$280$		0			0
$281$	0.318673	+	0.495865i	0.0190104	+	0.0295808i	0.850629	−	0.525767i	$-0.176222\pi$
$281$	0.318673	+	0.495865i	0.0190104	+	0.0295808i	−0.831618	+	0.555348i	$0.812585\pi$
$282$		0			0
$283$	−23.3392	+	17.4715i	−1.38737	+	1.03857i	−0.394562	+	0.918869i	$0.629104\pi$
$283$	−23.3392	+	17.4715i	−1.38737	+	1.03857i	−0.992810	+	0.119704i	$0.961805\pi$
$284$		0			0
$285$	0.0565122	+	0.0181877i	0.00334749	+	0.00107734i
$286$		0			0
$287$	14.8390	+	5.53467i	0.875920	+	0.326701i
$288$		0			0
$289$	−33.8702	+	4.86980i	−1.99237	+	0.286459i
$290$		0			0
$291$	−0.0112791	−	0.0384132i	−0.000661194	−	0.00225182i
$292$		0			0
$293$	−11.3188	+	0.809535i	−0.661250	+	0.0472935i	−0.397931	−	0.917415i	$-0.630272\pi$
$293$	−11.3188	+	0.809535i	−0.661250	+	0.0472935i	−0.263319	+	0.964709i	$0.584817\pi$
$294$		0			0
$295$	12.1286	−	2.31285i	0.706156	−	0.134659i
$296$		0			0
$297$	0.0381512	+	0.102287i	0.00221375	+	0.00593531i
$298$		0			0
$299$	22.6735	+	7.33053i	1.31124	+	0.423935i
$300$		0			0
$301$	−5.54403	+	12.1397i	−0.319553	+	0.699723i
$302$		0			0
$303$	−0.00286732		0.000205075i	−0.000164723		1.17813e-5i
$304$		0			0
$305$	−1.68893	−	4.91111i	−0.0967080	−	0.281209i
$306$		0			0
$307$	21.7808	+	11.8932i	1.24310	+	0.678783i	0.959917	−	0.280284i	$-0.0904287\pi$
$307$	21.7808	+	11.8932i	1.24310	+	0.678783i	0.283180	+	0.959067i	$0.408610\pi$
$308$		0			0
$309$	−0.00989044	−	0.0687895i	−0.000562648	−	0.00391330i
$310$		0			0
$311$	12.1758	+	26.6613i	0.690428	+	1.51183i	0.851204	+	0.524835i	$0.175873\pi$
$311$	12.1758	+	26.6613i	0.690428	+	1.51183i	−0.160776	+	0.986991i	$0.551400\pi$
$312$		0			0
$313$	−1.64340	−	7.55459i	−0.0928905	−	0.427011i	−0.999982	−	0.00607632i	$-0.998066\pi$
$313$	−1.64340	−	7.55459i	−0.0928905	−	0.427011i	0.907091	−	0.420935i	$-0.138298\pi$
$314$		0			0
$315$	21.7115	−	2.55258i	1.22330	−	0.143822i
$316$		0			0
$317$	−10.8671	−	2.36399i	−0.610356	−	0.132775i	−0.103246	−	0.994656i	$-0.532923\pi$
$317$	−10.8671	−	2.36399i	−0.610356	−	0.132775i	−0.507111	+	0.861881i	$0.669286\pi$
$318$		0			0
$319$	−13.7772	−	4.04536i	−0.771377	−	0.226497i
$320$		0			0
$321$			0.0485275i			0.00270854i
$322$		0			0
$323$	−25.7643	+	25.7643i	−1.43357	+	1.43357i
$324$		0			0
$325$	−21.1623	−	13.0137i	−1.17387	−	0.721868i
$326$		0			0
$327$	0.00765541	−	0.0351914i	0.000423345	−	0.00194609i
$328$		0			0
$329$	2.35231	−	16.3606i	0.129687	−	0.901991i
$330$		0			0
$331$	−12.1731	−	7.82319i	−0.669095	−	0.430001i	0.161504	−	0.986872i	$-0.448365\pi$
$331$	−12.1731	−	7.82319i	−0.669095	−	0.430001i	−0.830599	+	0.556871i	$0.812002\pi$
$332$		0			0
$333$	−8.97537	+	24.0639i	−0.491847	+	1.31869i
$334$		0			0
$335$	−13.2626	−	31.1404i	−0.724614	−	1.70138i
$336$		0			0
$337$	6.52657	−	11.9525i	0.355525	−	0.651095i	−0.637308	−	0.770610i	$-0.719952\pi$
$337$	6.52657	−	11.9525i	0.355525	−	0.651095i	0.992832	+	0.119514i	$0.0381337\pi$
$338$		0			0
$339$	−0.0259119	+	0.0299039i	−0.00140734	+	0.00162416i
$340$		0			0
$341$	5.19310	−	4.49985i	0.281222	−	0.243680i
$342$		0			0
$343$	−10.3197	+	3.84904i	−0.557210	+	0.207829i
$344$		0			0
$345$	0.0358321	−	0.0429347i	0.00192914	−	0.00231153i
$346$		0			0
$347$	7.91860	−	2.95349i	0.425093	−	0.158551i	−0.127807	−	0.991799i	$-0.540794\pi$
$347$	7.91860	−	2.95349i	0.425093	−	0.158551i	0.552900	+	0.833248i	$0.313521\pi$
$348$		0			0
$349$	−15.9406	+	13.8126i	−0.853281	+	0.739372i	−0.967172	−	0.254121i	$-0.918214\pi$
$349$	−15.9406	+	13.8126i	−0.853281	+	0.739372i	0.113891	+	0.993493i	$0.463668\pi$
$350$		0			0
$351$	−0.101807	+	0.117492i	−0.00543407	+	0.00627126i
$352$		0			0
$353$	16.6700	−	30.5289i	0.887256	−	1.62489i	0.111581	−	0.993755i	$-0.464409\pi$
$353$	16.6700	−	30.5289i	0.887256	−	1.62489i	0.775675	−	0.631133i	$-0.217410\pi$
$354$		0			0
$355$	0.566072	−	1.40595i	0.0300440	−	0.0746201i
$356$		0			0
$357$	0.0425033	−	0.113956i	0.00224951	−	0.00603117i
$358$		0			0
$359$	18.4493	+	11.8567i	0.973718	+	0.625771i	0.927762	−	0.373173i	$-0.121730\pi$
$359$	18.4493	+	11.8567i	0.973718	+	0.625771i	0.0459562	+	0.998943i	$0.485367\pi$
$360$		0			0
$361$	−0.984865	+	6.84989i	−0.0518350	+	0.360520i
$362$		0			0
$363$	−0.00130141	+	0.00598250i	−6.83065e−5	+	0.000314000i
$364$		0			0
$365$	29.2598	+	0.754148i	1.53153	+	0.0394739i
$366$		0			0
$367$	24.0326	−	24.0326i	1.25449	−	1.25449i	0.300809	−	0.953684i	$-0.402743\pi$
$367$	24.0326	−	24.0326i	1.25449	−	1.25449i	0.953684	−	0.300809i	$-0.0972567\pi$
$368$		0			0
$369$		−	14.5794i		−	0.758972i
$370$		0			0
$371$	34.7712	+	10.2097i	1.80523	+	0.530063i
$372$		0			0
$373$	−11.5647	−	2.51574i	−0.598797	−	0.130260i	−0.0970571	−	0.995279i	$-0.530943\pi$
$373$	−11.5647	−	2.51574i	−0.598797	−	0.130260i	−0.501740	+	0.865018i	$0.667307\pi$
$374$		0			0
$375$	−0.0468797	+	0.0346636i	−0.00242086	+	0.00179002i
$376$		0			0
$377$	−4.34648	−	19.9805i	−0.223855	−	1.02905i
$378$		0			0
$379$	−12.7291	−	27.8728i	−0.653850	−	1.43173i	−0.888144	−	0.459566i	$-0.848005\pi$
$379$	−12.7291	−	27.8728i	−0.653850	−	1.43173i	0.234294	−	0.972166i	$-0.424722\pi$
$380$		0			0
$381$	−0.00455821	−	0.0317030i	−0.000233524	−	0.00162420i
$382$		0			0
$383$	28.2703	+	15.4367i	1.44454	+	0.788780i	0.994551	−	0.104253i	$-0.0332450\pi$
$383$	28.2703	+	15.4367i	1.44454	+	0.788780i	0.449992	+	0.893033i	$0.351427\pi$
$384$		0			0
$385$	22.8481	+	11.1546i	1.16445	+	0.568489i
$386$		0			0
$387$	12.2542	+	0.876438i	0.622917	+	0.0445519i
$388$		0			0
$389$	−11.2025	+	24.5299i	−0.567987	+	1.24372i	0.379875	+	0.925038i	$0.375967\pi$
$389$	−11.2025	+	24.5299i	−0.567987	+	1.24372i	−0.947862	+	0.318680i	$0.896760\pi$
$390$		0			0
$391$	13.4068	+	31.5956i	0.678009	+	1.59786i
$392$		0			0
$393$	−0.0228940	−	0.0613812i	−0.00115485	−	0.00309627i
$394$		0			0
$395$	−6.32965	−	33.1929i	−0.318479	−	1.67011i
$396$		0			0
$397$	−0.732675	+	0.0524020i	−0.0367719	+	0.00262998i	−0.0897130	−	0.995968i	$-0.528595\pi$
$397$	−0.732675	+	0.0524020i	−0.0367719	+	0.00262998i	0.0529411	+	0.998598i	$0.483140\pi$
$398$		0			0
$399$	−0.0243761	−	0.0830172i	−0.00122033	−	0.00415606i
$400$		0			0
$401$	−5.14335	+	0.739503i	−0.256847	+	0.0369290i	−0.269535	−	0.962990i	$-0.586870\pi$
$401$	−5.14335	+	0.739503i	−0.256847	+	0.0369290i	0.0126885	+	0.999919i	$0.495961\pi$
$402$		0			0
$403$	9.16833	+	3.41961i	0.456707	+	0.170343i
$404$		0			0
$405$	−9.18615	−	17.9051i	−0.456463	−	0.889712i
$406$		0			0
$407$	−23.9130	+	17.9010i	−1.18532	+	0.887321i
$408$		0			0
$409$	−5.64916	−	8.79026i	−0.279333	−	0.434651i	0.673031	−	0.739614i	$-0.264992\pi$
$409$	−5.64916	−	8.79026i	−0.279333	−	0.434651i	−0.952364	+	0.304964i	$0.901356\pi$
$410$		0			0
$411$	−0.00895438	+	0.0304958i	−0.000441687	+	0.00150425i
$412$		0			0
$413$	−12.7244	−	12.7244i	−0.626124	−	0.626124i
$414$		0			0
$415$	1.89246	+	7.11878i	0.0928972	+	0.349447i
$416$		0			0
$417$	−0.0158980	−	0.0291150i	−0.000778528	−	0.00142577i
$418$		0			0
$419$	6.65350	−	4.27595i	0.325045	−	0.208894i	−0.367933	−	0.929852i	$-0.619935\pi$
$419$	6.65350	−	4.27595i	0.325045	−	0.208894i	0.692978	+	0.720959i	$0.256298\pi$
$420$		0			0
$421$	−18.4219	−	2.64867i	−0.897830	−	0.129088i	−0.322078	−	0.946713i	$-0.604381\pi$
$421$	−18.4219	−	2.64867i	−0.897830	−	0.129088i	−0.575752	+	0.817625i	$0.695291\pi$
$422$		0			0
$423$	−14.8680	+	3.23434i	−0.722907	+	0.157259i
$424$		0			0
$425$	−5.79501	−	35.3112i	−0.281099	−	1.71284i
$426$		0			0
$427$	−4.53590	+	6.05925i	−0.219508	+	0.293228i
$428$		0			0
$429$	−0.0867441	+	0.0254704i	−0.00418805	+	0.00122972i
$430$		0			0
$431$	−9.13587	−	7.91628i	−0.440060	−	0.381314i	0.406462	−	0.913667i	$-0.366762\pi$
$431$	−9.13587	−	7.91628i	−0.440060	−	0.381314i	−0.846522	+	0.532354i	$0.821308\pi$
$432$		0			0
$433$	−2.38981	+	33.4140i	−0.114847	+	1.60577i	0.534424	+	0.845216i	$0.320528\pi$
$433$	−2.38981	+	33.4140i	−0.114847	+	1.60577i	−0.649271	+	0.760557i	$0.724926\pi$
$434$		0			0
$435$	−0.0473071	−	0.00805088i	−0.00226820	−	0.000386010i
$436$		0			0
$437$	21.1049	+	12.2780i	1.00959	+	0.587338i
$438$		0			0
$439$	−23.7974	−	10.8679i	−1.13579	−	0.518696i	−0.243380	−	0.969931i	$-0.578256\pi$
$439$	−23.7974	−	10.8679i	−1.13579	−	0.518696i	−0.892405	+	0.451235i	$0.850984\pi$
$440$		0			0
$441$	−7.11226	−	8.20798i	−0.338679	−	0.390856i
$442$		0			0
$443$	−1.18754	−	16.6040i	−0.0564217	−	0.788879i	−0.944359	−	0.328915i	$-0.893317\pi$
$443$	−1.18754	−	16.6040i	−0.0564217	−	0.788879i	0.887938	−	0.459964i	$-0.152138\pi$
$444$		0			0
$445$	−16.5477	−	4.04893i	−0.784435	−	0.191938i
$446$		0			0
$447$	0.0310373	+	0.0232342i	0.00146801	+	0.00109894i
$448$		0			0
$449$	11.8957	−	5.43259i	0.561394	−	0.256380i	−0.114445	−	0.993430i	$-0.536509\pi$
$449$	11.8957	−	5.43259i	0.561394	−	0.256380i	0.675838	+	0.737050i	$0.263782\pi$
$450$		0			0
$451$	9.16743	−	14.2648i	0.431677	−	0.671703i
$452$		0			0
$453$	0.0342251	+	0.0457193i	0.00160803	+	0.00214808i
$454$		0			0
$455$	1.65161	+	36.1696i	0.0774287	+	1.69565i
$456$		0			0
$457$	4.27974	−	2.33692i	0.200198	−	0.109316i	−0.376023	−	0.926610i	$-0.622709\pi$
$457$	4.27974	−	2.33692i	0.200198	−	0.109316i	0.576221	+	0.817294i	$0.304527\pi$
$458$		0			0
$459$	−0.223924			−0.0104519
$460$		0			0
$461$	−14.0026			−0.652167			−0.326084	−	0.945341i	$-0.605729\pi$
$461$	−14.0026			−0.652167			−0.326084	+	0.945341i	$0.605729\pi$
$462$		0			0
$463$	−18.2619	+	9.97177i	−0.848704	+	0.463427i	−0.843862	−	0.536561i	$-0.819723\pi$
$463$	−18.2619	+	9.97177i	−0.848704	+	0.463427i	−0.00484216	+	0.999988i	$0.501541\pi$
$464$		0			0
$465$	0.0154806	−	0.0169621i	0.000717898	−	0.000786598i
$466$		0			0
$467$	−1.82724	−	2.44090i	−0.0845544	−	0.112952i	0.756269	−	0.654260i	$-0.227020\pi$
$467$	−1.82724	−	2.44090i	−0.0845544	−	0.112952i	−0.840824	+	0.541309i	$0.817929\pi$
$468$		0			0
$469$	−26.6693	+	41.4983i	−1.23147	+	1.91621i
$470$		0			0
$471$	0.0700659	−	0.0319980i	0.00322846	−	0.00147439i
$472$		0			0
$473$	11.4387	+	8.56291i	0.525953	+	0.393723i
$474$		0			0
$475$	−18.3541	−	17.6391i	−0.842143	−	0.809335i
$476$		0			0
$477$	−2.37988	−	33.2751i	−0.108967	−	1.52356i
$478$		0			0
$479$	16.6392	+	19.2027i	0.760266	+	0.877394i	0.995521	−	0.0945399i	$-0.0301380\pi$
$479$	16.6392	+	19.2027i	0.760266	+	0.877394i	−0.235255	+	0.971934i	$0.575593\pi$
$480$		0			0
$481$	−38.6937	−	17.6708i	−1.76428	−	0.805721i
$482$		0			0
$483$	−0.0811072	−	0.00801514i	−0.00369051	−	0.000364702i
$484$		0			0
$485$	−2.88006	+	16.9233i	−0.130777	+	0.768448i
$486$		0			0
$487$	1.23170	−	17.2215i	0.0558138	−	0.780379i	−0.890060	−	0.455844i	$-0.849338\pi$
$487$	1.23170	−	17.2215i	0.0558138	−	0.780379i	0.945874	−	0.324535i	$-0.105208\pi$
$488$		0			0
$489$	0.0295605	+	0.0256143i	0.00133677	+	0.00115832i
$490$		0			0
$491$	−24.7694	+	7.27295i	−1.11783	+	0.328224i	−0.787912	−	0.615787i	$-0.788838\pi$
$491$	−24.7694	+	7.27295i	−1.11783	+	0.328224i	−0.329914	+	0.944011i	$0.607020\pi$
$492$		0			0
$493$	17.6500	−	23.5776i	0.794916	−	1.06188i
$494$		0			0
$495$	2.27071	−	23.2952i	0.102061	−	1.04704i
$496$		0			0
$497$	−2.15842	+	0.469536i	−0.0968184	+	0.0210616i
$498$		0			0
$499$	28.1857	+	4.05249i	1.26177	+	0.181414i	0.740544	−	0.672008i	$-0.234568\pi$
$499$	28.1857	+	4.05249i	1.26177	+	0.181414i	0.521221	+	0.853422i	$0.325477\pi$
$500$		0			0
$501$	0.0153922	−	0.00989195i	0.000687671	−	0.000441940i
$502$		0			0
$503$	−19.7610	−	36.1896i	−0.881101	−	1.61362i	−0.786066	−	0.618142i	$-0.787886\pi$
$503$	−19.7610	−	36.1896i	−0.881101	−	1.61362i	−0.0950350	−	0.995474i	$-0.530296\pi$
$504$		0			0
$505$	1.06627	+	0.618413i	0.0474484	+	0.0275190i
$506$		0			0
$507$	−0.0430985	−	0.0430985i	−0.00191407	−	0.00191407i
$508$		0			0
$509$	−8.16519	+	27.8081i	−0.361916	+	1.23257i	0.554446	+	0.832220i	$0.312930\pi$
$509$	−8.16519	+	27.8081i	−0.361916	+	1.23257i	−0.916362	+	0.400352i	$0.868888\pi$
$510$		0			0
$511$	−23.0625	−	35.8860i	−1.02023	−	1.58750i
$512$		0			0
$513$	−0.127524	+	0.0954632i	−0.00563032	+	0.00421480i
$514$		0			0
$515$	−9.12947	+	28.3668i	−0.402293	+	1.24999i
$516$		0			0
$517$	−16.5810	−	6.18437i	−0.729229	−	0.271988i
$518$		0			0
$519$	0.0357562	−	0.00514097i	0.00156952	−	0.000225664i
$520$		0			0
$521$	3.71877	+	12.6650i	0.162922	+	0.554863i	0.999970	+	0.00773290i	$0.00246148\pi$
$521$	3.71877	+	12.6650i	0.162922	+	0.554863i	−0.837048	+	0.547130i	$0.815720\pi$
$522$		0			0
$523$	−20.0558	+	1.43442i	−0.876979	+	0.0627228i	−0.502566	−	0.864539i	$-0.667610\pi$
$523$	−20.0558	+	1.43442i	−0.876979	+	0.0627228i	−0.374413	+	0.927262i	$0.622156\pi$
$524$		0			0
$525$	0.0801886	+	0.0281076i	0.00349972	+	0.00122671i
$526$		0			0
$527$	4.92547	+	13.2057i	0.214557	+	0.575249i
$528$		0			0
$529$	18.1727	−	14.0980i	0.790118	−	0.612955i
$530$		0			0
$531$	−6.88149	+	15.0684i	−0.298631	+	0.653911i
$532$		0			0
$533$	24.0855	+	1.72263i	1.04326	+	0.0746154i
$534$		0			0
$535$	9.12885	−	18.6988i	0.394675	−	0.808419i
$536$		0			0
$537$	−0.0487965	−	0.0266449i	−0.00210573	−	0.00114981i
$538$		0			0
$539$	−1.79766	−	12.5030i	−0.0774309	−	0.538544i
$540$		0			0
$541$	−16.9944	−	37.2126i	−0.730647	−	1.59989i	−0.798355	−	0.602188i	$-0.794296\pi$
$541$	−16.9944	−	37.2126i	−0.730647	−	1.59989i	0.0677080	−	0.997705i	$-0.478431\pi$
$542$		0			0
$543$	−0.00224528	−	0.0103214i	−9.63542e−5	−	0.000442933i
$544$		0			0
$545$	−9.56991	+	12.1200i	−0.409930	+	0.519162i
$546$		0			0
$547$	−22.0155	−	4.78918i	−0.941314	−	0.204770i	−0.284374	−	0.958713i	$-0.591786\pi$
$547$	−22.0155	−	4.78918i	−0.941314	−	0.204770i	−0.656940	+	0.753943i	$0.728149\pi$
$548$		0			0
$549$	6.68539	+	1.96301i	0.285325	+	0.0837791i
$550$		0			0
$551$		−	20.9519i		−	0.892581i
$552$		0			0
$553$	−34.8232	+	34.8232i	−1.48083	+	1.48083i
$554$		0			0
$555$	−0.0723849	+	0.0687473i	−0.00307257	+	0.00291816i
$556$		0			0
$557$	1.57739	−	7.25113i	0.0668360	−	0.307240i	−0.931578	−	0.363542i	$-0.881567\pi$
$557$	1.57739	−	7.25113i	0.0668360	−	0.307240i	0.998414	+	0.0563018i	$0.0179309\pi$
$558$		0			0
$559$	−2.89580	+	20.1407i	−0.122479	+	0.851863i
$560$		0			0
$561$	−0.109546	−	0.0704009i	−0.00462503	−	0.00297233i
$562$		0			0
$563$	14.4590	−	38.7661i	0.609375	−	1.63380i	−0.154171	−	0.988044i	$-0.549271\pi$
$563$	14.4590	−	38.7661i	0.609375	−	1.63380i	0.763546	−	0.645753i	$-0.223457\pi$
$564$		0			0
$565$	15.6099	−	6.64822i	0.656714	−	0.279693i
$566$		0			0
$567$	−14.0559	+	25.7415i	−0.590294	+	1.08104i
$568$		0			0
$569$	7.49448	−	8.64909i	0.314185	−	0.362589i	−0.576590	−	0.817034i	$-0.695617\pi$
$569$	7.49448	−	8.64909i	0.314185	−	0.362589i	0.890775	+	0.454445i	$0.150162\pi$
$570$		0			0
$571$	35.6147	−	30.8603i	1.49043	−	1.29146i	0.636248	−	0.771485i	$-0.280486\pi$
$571$	35.6147	−	30.8603i	1.49043	−	1.29146i	0.854180	−	0.519978i	$-0.174060\pi$
$572$		0			0
$573$	−0.0383389	+	0.0142997i	−0.00160163	+	0.000597377i
$574$		0			0
$575$	−21.8837	+	9.80314i	−0.912615	+	0.408819i
$576$		0			0
$577$	−40.4945	+	15.1037i	−1.68581	+	0.628774i	−0.995502	−	0.0947424i	$-0.969797\pi$
$577$	−40.4945	+	15.1037i	−1.68581	+	0.628774i	−0.690307	+	0.723517i	$0.742525\pi$
$578$		0			0
$579$	−0.0102528	+	0.00888414i	−0.000426094	+	0.000369212i
$580$		0			0
$581$	7.03016	−	8.11324i	0.291660	−	0.336594i
$582$		0			0
$583$	18.5947	−	34.0536i	0.770112	−	1.41035i
$584$		0			0
$585$	30.6654	−	13.0603i	1.26786	−	0.539977i
$586$		0			0
$587$	1.95543	−	5.24270i	0.0807090	−	0.216389i	−0.890327	−	0.455321i	$-0.849524\pi$
$587$	1.95543	−	5.24270i	0.0807090	−	0.216389i	0.971036	+	0.238932i	$0.0767972\pi$
$588$		0			0
$589$	8.43487	+	5.42076i	0.347553	+	0.223359i
$590$		0			0
$591$	−0.00448095	+	0.0311657i	−0.000184322	+	0.00128198i
$592$		0			0
$593$	−3.93769	+	18.1013i	−0.161701	+	0.743330i	0.822853	+	0.568254i	$0.192381\pi$
$593$	−3.93769	+	18.1013i	−0.161701	+	0.743330i	−0.984555	+	0.175076i	$0.943983\pi$
$594$		0			0
$595$	−37.8145	+	35.9142i	−1.55025	+	1.47234i
$596$		0			0
$597$	−0.0535658	+	0.0535658i	−0.00219230	+	0.00219230i
$598$		0			0
$599$		−	6.01335i		−	0.245699i	−0.992425	−	0.122849i	$-0.960797\pi$
$599$		−	6.01335i		−	0.245699i	0.992425	−	0.122849i	$-0.0392032\pi$
$600$		0			0
$601$	−26.4913	−	7.77856i	−1.08060	−	0.317294i	−0.307484	−	0.951553i	$-0.599487\pi$
$601$	−26.4913	−	7.77856i	−1.08060	−	0.317294i	−0.773120	+	0.634259i	$0.781305\pi$
$602$		0			0
$603$	44.3723	+	9.65261i	1.80698	+	0.393085i
$604$		0			0
$605$	1.62688	−	2.06038i	0.0661419	−	0.0837664i
$606$		0			0
$607$	1.54187	+	7.08787i	0.0625827	+	0.287688i	0.997793	−	0.0664056i	$-0.0211531\pi$
$607$	1.54187	+	7.08787i	0.0625827	+	0.287688i	−0.935210	+	0.354093i	$0.884789\pi$
$608$		0			0
$609$	0.0290530	+	0.0636172i	0.00117729	+	0.00257790i
$610$		0			0
$611$	−3.58648	−	24.9445i	−0.145093	−	1.00915i
$612$		0			0
$613$	21.8946	+	11.9554i	0.884314	+	0.482872i	0.856148	−	0.516731i	$-0.172851\pi$
$613$	21.8946	+	11.9554i	0.884314	+	0.482872i	0.0281666	+	0.999603i	$0.491033\pi$
$614$		0			0
$615$	0.0248615	−	0.0509242i	0.00100251	−	0.00205346i
$616$		0			0
$617$	−28.9640	−	2.07155i	−1.16605	−	0.0833973i	−0.525140	−	0.851016i	$-0.675987\pi$
$617$	−28.9640	−	2.07155i	−1.16605	−	0.0833973i	−0.640907	+	0.767619i	$0.721442\pi$
$618$		0			0
$619$	−3.14260	+	6.88134i	−0.126312	+	0.276584i	−0.962214	−	0.272294i	$-0.912218\pi$
$619$	−3.14260	+	6.88134i	−0.126312	+	0.276584i	0.835902	+	0.548878i	$0.184945\pi$
$620$		0			0
$621$	0.0383584	+	0.145070i	0.00153927	+	0.00582145i
$622$		0			0
$623$	8.67658	+	23.2628i	0.347620	+	0.932005i
$624$		0			0
$625$	24.5847	−	4.53784i	0.983388	−	0.181514i
$626$		0			0
$627$	−0.0923992	+	0.00660852i	−0.00369007	+	0.000263919i
$628$		0			0
$629$	−17.2617	−	58.7878i	−0.688268	−	2.34402i
$630$		0			0
$631$	−11.5627	+	1.66247i	−0.460304	+	0.0661817i	−0.368566	−	0.929602i	$-0.620151\pi$
$631$	−11.5627	+	1.66247i	−0.460304	+	0.0661817i	−0.0917376	+	0.995783i	$0.529242\pi$
$632$		0			0
$633$	−0.104274	−	0.0388920i	−0.00414450	−	0.00154582i
$634$		0			0
$635$	−4.20750	+	13.0734i	−0.166970	+	0.518803i
$636$		0			0
$637$	14.4002	−	10.7798i	0.570555	−	0.427112i
$638$		0			0
$639$	1.09935	+	1.71062i	0.0434895	+	0.0676709i
$640$		0			0
$641$	13.1885	−	44.9159i	0.520914	−	1.77407i	−0.105323	−	0.994438i	$-0.533588\pi$
$641$	13.1885	−	44.9159i	0.520914	−	1.77407i	0.626237	−	0.779633i	$-0.284594\pi$
$642$		0			0
$643$	25.3125	+	25.3125i	0.998227	+	0.998227i	0.999998	−	0.00177129i	$-0.000563818\pi$
$643$	25.3125	+	25.3125i	0.998227	+	0.998227i	−0.00177129	+	0.999998i	$0.500564\pi$
$644$		0			0
$645$	0.0413081	+	0.0239578i	0.00162650	+	0.000943337i
$646$		0			0
$647$	3.74819	+	6.86430i	0.147357	+	0.269864i	0.940923	−	0.338620i	$-0.109960\pi$
$647$	3.74819	+	6.86430i	0.147357	+	0.269864i	−0.793567	+	0.608483i	$0.791778\pi$
$648$		0			0
$649$	−16.2079	+	10.4162i	−0.636216	+	0.408871i
$650$		0			0
$651$	−0.0331279	−	0.00476308i	−0.00129839	−	0.000186680i
$652$		0			0
$653$	−19.3770	+	4.21521i	−0.758282	+	0.164954i	−0.575053	−	0.818116i	$-0.695019\pi$
$653$	−19.3770	+	4.21521i	−0.758282	+	0.164954i	−0.183229	+	0.983070i	$0.558655\pi$
$654$		0			0
$655$	−2.72525	+	27.9584i	−0.106484	+	1.09243i
$656$		0			0
$657$	−23.5329	+	31.4363i	−0.918107	+	1.22645i
$658$		0			0
$659$	25.1027	−	7.37081i	0.977861	−	0.287126i	0.246520	−	0.969138i	$-0.420713\pi$
$659$	25.1027	−	7.37081i	0.977861	−	0.287126i	0.731341	+	0.682012i	$0.238895\pi$
$660$		0			0
$661$	19.5849	+	16.9704i	0.761763	+	0.660072i	0.946495	−	0.322717i	$-0.104596\pi$
$661$	19.5849	+	16.9704i	0.761763	+	0.660072i	−0.184732	+	0.982789i	$0.559142\pi$
$662$		0			0
$663$	0.0132289	−	0.184964i	0.000513766	−	0.00718339i
$664$		0			0
$665$	−6.22429	+	36.5741i	−0.241368	+	1.41828i
$666$		0			0
$667$	−18.2983	−	7.39572i	−0.708512	−	0.286363i
$668$		0			0
$669$	−0.0428671	−	0.0195767i	−0.00165734	−	0.000756880i
$670$		0			0
$671$	5.30681	+	6.12439i	0.204867	+	0.236429i
$672$		0			0
$673$	−1.47308	−	20.5963i	−0.0567830	−	0.793930i	−0.943449	−	0.331519i	$-0.892439\pi$
$673$	−1.47308	−	20.5963i	−0.0567830	−	0.793930i	0.886666	−	0.462411i	$-0.153016\pi$
$674$		0			0
$675$	−0.00310721	−	0.156413i	−0.000119596	−	0.00602033i
$676$		0			0
$677$	−13.0015	−	9.73279i	−0.499688	−	0.374061i	0.319501	−	0.947586i	$-0.396485\pi$
$677$	−13.0015	−	9.73279i	−0.499688	−	0.374061i	−0.819188	+	0.573525i	$0.805576\pi$
$678$		0			0
$679$	22.7580	−	10.3932i	0.873371	−	0.398855i
$680$		0			0
$681$	−0.0230906	+	0.0359297i	−0.000884835	+	0.00137683i
$682$		0			0
$683$	−7.86503	−	10.5065i	−0.300947	−	0.402018i	0.624421	−	0.781088i	$-0.285335\pi$
$683$	−7.86503	−	10.5065i	−0.300947	−	0.402018i	−0.925368	+	0.379070i	$0.876244\pi$
$684$		0			0
$685$	9.18713	−	10.0663i	0.351022	−	0.384613i
$686$		0			0
$687$	0.0885052	−	0.0483275i	0.00337669	−	0.00184381i
$688$		0			0
$689$	55.2525			2.10495
$690$		0			0
$691$	11.7226			0.445948			0.222974	−	0.974824i	$-0.428424\pi$
$691$	11.7226			0.445948			0.222974	+	0.974824i	$0.428424\pi$
$692$		0			0
$693$	−29.9391	+	16.3480i	−1.13729	+	0.621008i
$694$		0			0
$695$	0.648844	+	14.2094i	0.0246121	+	0.538993i
$696$		0			0
$697$	20.8431	+	27.8432i	0.789490	+	1.05463i
$698$		0			0
$699$	−0.0787075	+	0.122471i	−0.00297699	+	0.00463229i
$700$		0			0
$701$	27.1940	−	12.4191i	1.02710	−	0.469063i	0.170675	−	0.985327i	$-0.445405\pi$
$701$	27.1940	−	12.4191i	1.02710	−	0.469063i	0.856429	+	0.516264i	$0.172678\pi$
$702$		0			0
$703$	−34.8928	−	26.1204i	−1.31601	−	0.985151i
$704$		0			0
$705$	−0.0574477	−	0.0140565i	−0.00216361	−	0.000529397i
$706$		0			0
$707$	−0.128157	−	1.79187i	−0.00481984	−	0.0673902i
$708$		0			0
$709$	6.31151	+	7.28387i	0.237034	+	0.273552i	0.861787	−	0.507271i	$-0.169346\pi$
$709$	6.31151	+	7.28387i	0.237034	+	0.273552i	−0.624753	+	0.780823i	$0.714800\pi$
$710$		0			0
$711$	41.2381	+	18.8328i	1.54655	+	0.706286i
$712$		0			0
$713$	7.71160	−	5.45312i	0.288802	−	0.204221i
$714$		0			0
$715$	38.2160	+	6.50372i	1.42920	+	0.243225i
$716$		0			0
$717$	−0.00616115	+	0.0861442i	−0.000230092	+	0.00321711i
$718$		0			0
$719$	−5.18066	−	4.48906i	−0.193206	−	0.167414i	0.552886	−	0.833257i	$-0.313527\pi$
$719$	−5.18066	−	4.48906i	−0.193206	−	0.167414i	−0.746092	+	0.665843i	$0.768072\pi$
$720$		0			0
$721$	41.6713	−	12.2358i	1.55192	−	0.455685i
$722$		0			0
$723$	−0.0636917	+	0.0850821i	−0.00236872	+	0.00316424i
$724$		0			0
$725$	16.7141	+	12.0015i	0.620745	+	0.445724i
$726$		0			0
$727$	32.2537	−	7.01636i	1.19622	−	0.260222i	0.430019	−	0.902820i	$-0.358507\pi$
$727$	32.2537	−	7.01636i	1.19622	−	0.260222i	0.766204	+	0.642597i	$0.222143\pi$
$728$		0			0
$729$	26.7237	+	3.84229i	0.989768	+	0.142307i
$730$		0			0
$731$	−24.6556	+	15.8452i	−0.911922	+	0.586057i
$732$		0			0
$733$	−17.6296	−	32.2863i	−0.651166	−	1.19252i	−0.969628	−	0.244585i	$-0.921348\pi$
$733$	−17.6296	−	32.2863i	−0.651166	−	1.19252i	0.318462	−	0.947936i	$-0.396834\pi$
$734$		0			0
$735$	−0.0108457	−	0.0407978i	−0.000400049	−	0.00150485i
$736$		0			0
$737$	37.3454	+	37.3454i	1.37564	+	1.37564i
$738$		0			0
$739$	−6.21519	+	21.1670i	−0.228629	+	0.778640i	0.762644	+	0.646818i	$0.223901\pi$
$739$	−6.21519	+	21.1670i	−0.228629	+	0.778640i	−0.991273	+	0.131822i	$0.957917\pi$
$740$		0			0
$741$	−0.0713198	−	0.110976i	−0.00262000	−	0.00407680i
$742$		0			0
$743$	−38.2949	+	28.6672i	−1.40490	+	1.05170i	−0.415022	+	0.909811i	$0.636226\pi$
$743$	−38.2949	+	28.6672i	−1.40490	+	1.05170i	−0.989883	+	0.141887i	$0.954683\pi$
$744$		0			0
$745$	−7.58865	−	14.7914i	−0.278027	−	0.541913i
$746$		0			0
$747$	−9.25938	−	3.45357i	−0.338783	−	0.126360i
$748$		0			0
$749$	−30.0175	+	4.31586i	−1.09681	+	0.157698i
$750$		0			0
$751$	9.74816	+	33.1992i	0.355715	+	1.21146i	0.921982	+	0.387233i	$0.126569\pi$
$751$	9.74816	+	33.1992i	0.355715	+	1.21146i	−0.566267	+	0.824222i	$0.691613\pi$
$752$		0			0
$753$	0.133467	−	0.00954574i	0.00486380	−	0.000347866i
$754$		0			0
$755$	−4.58714	−	24.0551i	−0.166943	−	0.875454i
$756$		0			0
$757$	5.57466	+	14.9462i	0.202614	+	0.543230i	0.998023	−	0.0628427i	$-0.0200166\pi$
$757$	5.57466	+	14.9462i	0.202614	+	0.543230i	−0.795409	+	0.606073i	$0.792744\pi$
$758$		0			0
$759$	−0.0268441	+	0.0830293i	−0.000974378	+	0.00301377i
$760$		0			0
$761$	−13.4569	+	29.4665i	−0.487813	+	1.06816i	0.492428	+	0.870353i	$0.336109\pi$
$761$	−13.4569	+	29.4665i	−0.487813	+	1.06816i	−0.980241	+	0.197808i	$0.936618\pi$
$762$		0			0
$763$	22.4490	+	1.60559i	0.812710	+	0.0581262i
$764$		0			0
$765$	43.1415	+	21.0619i	1.55978	+	0.761495i
$766$		0			0
$767$	−24.0803	−	13.1488i	−0.869488	−	0.474776i
$768$		0			0
$769$	0.573884	+	3.99145i	0.0206948	+	0.143935i	0.997549	−	0.0699705i	$-0.0222905\pi$
$769$	0.573884	+	3.99145i	0.0206948	+	0.143935i	−0.976854	+	0.213906i	$0.931381\pi$
$770$		0			0
$771$	0.0658349	+	0.144158i	0.00237098	+	0.00519173i
$772$		0			0
$773$	−9.56987	−	43.9920i	−0.344204	−	1.58228i	−0.745611	−	0.666382i	$-0.767842\pi$
$773$	−9.56987	−	43.9920i	−0.344204	−	1.58228i	0.401407	−	0.915900i	$-0.368521\pi$
$774$		0			0
$775$	−9.15592	+	3.62372i	−0.328890	+	0.130168i
$776$		0			0
$777$	0.142167	+	0.0309265i	0.00510021	+	0.00110948i
$778$		0			0
$779$	23.7401	+	6.97074i	0.850579	+	0.249753i
$780$		0			0
$781$			2.36497i			0.0846253i
$782$		0			0
$783$	0.0910491	−	0.0910491i	0.00325383	−	0.00325383i
$784$		0			0
$785$	−33.0174	−	0.850998i	−1.17844	−	0.0303734i
$786$		0			0
$787$	−8.14000	+	37.4190i	−0.290160	+	1.33384i	0.569085	+	0.822279i	$0.307297\pi$
$787$	−8.14000	+	37.4190i	−0.290160	+	1.33384i	−0.859245	+	0.511564i	$0.829066\pi$
$788$		0			0
$789$	−0.00382139	+	0.0265783i	−0.000136045	+	0.000946214i
$790$		0			0
$791$	−20.8021	−	13.3687i	−0.739636	−	0.475336i
$792$		0			0
$793$	−4.03286	+	10.8125i	−0.143211	+	0.383963i
$794$		0			0
$795$	0.0484296	−	0.120285i	0.00171762	−	0.00426605i
$796$		0			0
$797$	−18.2619	+	33.4442i	−0.646870	+	1.18465i	0.324230	+	0.945978i	$0.394895\pi$
$797$	−18.2619	+	33.4442i	−0.646870	+	1.18465i	−0.971099	+	0.238675i	$0.923287\pi$
$798$		0			0
$799$	23.7705	−	27.4326i	0.840939	−	0.970496i
$800$		0			0
$801$	17.2732	−	14.9673i	0.610320	−	0.528845i
$802$		0			0
$803$	−42.7922	+	15.9607i	−1.51010	+	0.563239i
$804$		0			0
$805$	29.7448	+	18.3461i	1.04837	+	0.646615i
$806$		0			0
$807$	−0.0438026	+	0.0163375i	−0.00154193	+	0.000575108i
$808$		0			0
$809$	−11.9799	+	10.3806i	−0.421191	+	0.364964i	−0.839517	−	0.543333i	$-0.817162\pi$
$809$	−11.9799	+	10.3806i	−0.421191	+	0.364964i	0.418327	+	0.908297i	$0.362617\pi$
$810$		0			0
$811$	33.5042	−	38.6660i	1.17649	−	1.35775i	0.256148	−	0.966637i	$-0.417546\pi$
$811$	33.5042	−	38.6660i	1.17649	−	1.35775i	0.920345	−	0.391108i	$-0.127908\pi$
$812$		0			0
$813$	−0.00981134	+	0.0179681i	−0.000344099	+	0.000630169i
$814$		0			0
$815$	−6.57187	−	15.4307i	−0.230203	−	0.540512i
$816$		0			0
$817$	−7.28616	+	19.5350i	−0.254911	+	0.683442i
$818$		0			0
$819$	−40.8653	−	26.2625i	−1.42795	−	0.917687i
$820$		0			0
$821$	−3.37929	+	23.5035i	−0.117938	+	0.820276i	0.841882	+	0.539661i	$0.181448\pi$
$821$	−3.37929	+	23.5035i	−0.117938	+	0.820276i	−0.959820	+	0.280615i	$0.909462\pi$
$822$		0			0
$823$	4.85134	−	22.3012i	0.169107	−	0.777372i	−0.811962	−	0.583711i	$-0.801600\pi$
$823$	4.85134	−	22.3012i	0.169107	−	0.777372i	0.981068	−	0.193661i	$-0.0620362\pi$
$824$		0			0
$825$	0.0476554	−	0.0774955i	0.00165915	−	0.00269805i
$826$		0			0
$827$	−4.85964	+	4.85964i	−0.168986	+	0.168986i	−0.786534	−	0.617548i	$-0.788126\pi$
$827$	−4.85964	+	4.85964i	−0.168986	+	0.168986i	0.617548	+	0.786534i	$0.288126\pi$
$828$		0			0
$829$			5.96058i			0.207019i	0.994628	+	0.103510i	$0.0330073\pi$
$829$			5.96058i			0.207019i	−0.994628	+	0.103510i	$0.966993\pi$
$830$		0			0
$831$	0.119856	+	0.0351929i	0.00415775	+	0.00122083i
$832$		0			0
$833$	25.3171	+	5.50740i	0.877186	+	0.190820i
$834$		0			0
$835$	−7.79182	+	0.916072i	−0.269647	+	0.0317020i
$836$		0			0
$837$	0.0130982	+	0.0602114i	0.000452740	+	0.00208121i
$838$		0			0
$839$	−12.8371	−	28.1094i	−0.443187	−	0.970443i	−0.991002	−	0.133844i	$-0.957268\pi$
$839$	−12.8371	−	28.1094i	−0.443187	−	0.970443i	0.547816	−	0.836599i	$-0.315459\pi$
$840$		0			0
$841$	−1.71691	−	11.9414i	−0.0592039	−	0.411772i
$842$		0			0
$843$	−0.00269780	−	0.00147311i	−9.29173e−5	−	5.07367e-5i
$844$		0			0
$845$	8.49931	+	24.7145i	0.292385	+	0.850203i
$846$		0			0
$847$	−3.81632	−	0.272948i	−0.131130	−	0.00937861i
$848$		0			0
$849$	0.0631572	−	0.138295i	0.00216755	−	0.00474627i
$850$		0			0
$851$	−35.1289	+	21.2534i	−1.20420	+	0.728558i
$852$		0			0
$853$	4.30136	+	11.5324i	0.147276	+	0.394862i	0.989550	−	0.144187i	$-0.0460567\pi$
$853$	4.30136	+	11.5324i	0.147276	+	0.394862i	−0.842275	+	0.539049i	$0.818784\pi$
$854$		0			0
$855$	33.5480	−	6.39738i	1.14732	−	0.218786i
$856$		0			0
$857$	9.58960	−	0.685862i	0.327575	−	0.0234286i	0.0934165	−	0.995627i	$-0.470221\pi$
$857$	9.58960	−	0.685862i	0.327575	−	0.0234286i	0.234158	+	0.972199i	$0.424767\pi$
$858$		0			0
$859$	1.89517	+	6.45436i	0.0646624	+	0.220220i	0.985485	−	0.169761i	$-0.0542997\pi$
$859$	1.89517	+	6.45436i	0.0646624	+	0.220220i	−0.920823	+	0.389981i	$0.872481\pi$
$860$		0			0
$861$	−0.0817493	+	0.0117538i	−0.00278601	+	0.000400568i
$862$		0			0
$863$	11.0950	+	4.13821i	0.377678	+	0.140866i	0.531132	−	0.847289i	$-0.321767\pi$
$863$	11.0950	+	4.13821i	0.377678	+	0.140866i	−0.153454	+	0.988156i	$0.549040\pi$
$864$		0			0
$865$	−14.7448	−	4.74543i	−0.501340	−	0.161349i
$866$		0			0
$867$	0.142851	−	0.106937i	0.00485147	−	0.00363177i
$868$		0			0
$869$	28.5064	+	44.3568i	0.967013	+	1.50470i
$870$		0			0
$871$	−21.1892	+	72.1638i	−0.717969	+	2.44518i
$872$		0			0
$873$	−16.2856	−	16.2856i	−0.551183	−	0.551183i
$874$		0			0
$875$	−25.6111	−	25.9154i	−0.865812	−	0.876100i
$876$		0			0
$877$	−10.4941	−	19.2184i	−0.354359	−	0.648960i	0.638316	−	0.769774i	$-0.279631\pi$
$877$	−10.4941	−	19.2184i	−0.354359	−	0.648960i	−0.992675	+	0.120814i	$0.961449\pi$
$878$		0			0
$879$	0.0497820	−	0.0319930i	0.00167911	−	0.00107910i
$880$		0			0
$881$	12.8485	+	1.84733i	0.432876	+	0.0622382i	0.355309	−	0.934749i	$-0.384376\pi$
$881$	12.8485	+	1.84733i	0.432876	+	0.0622382i	0.0775671	+	0.996987i	$0.475285\pi$
$882$		0			0
$883$	3.70109	−	0.805123i	0.124552	−	0.0270946i	−0.149857	−	0.988708i	$-0.547881\pi$
$883$	3.70109	−	0.805123i	0.124552	−	0.0270946i	0.274409	+	0.961613i	$0.411518\pi$
$884$		0			0
$885$	−0.0497316	+	0.0408975i	−0.00167171	+	0.00137475i
$886$		0			0
$887$	−17.7091	+	23.6566i	−0.594614	+	0.794311i	−0.992385	−	0.123174i	$-0.960693\pi$
$887$	−17.7091	+	23.6566i	−0.594614	+	0.794311i	0.397771	+	0.917485i	$0.369784\pi$
$888$		0			0
$889$	19.2050	−	5.63911i	0.644116	−	0.189130i
$890$		0			0
$891$	23.7315	+	20.5635i	0.795037	+	0.688903i
$892$		0			0
$893$	1.84215	−	25.7566i	0.0616451	−	0.861911i
$894$		0			0
$895$	13.7901	+	19.4464i	0.460952	+	0.650021i
$896$		0			0
$897$	−0.122095	+	0.0231141i	−0.00407664	+	0.000771756i
$898$		0			0
$899$	−7.37225	−	3.36679i	−0.245878	−	0.112289i
$900$		0			0
$901$	52.1161	+	60.1452i	1.73624	+	2.00373i
$902$		0			0
$903$	−0.00496490	−	0.0694183i	−0.000165221	−	0.00231010i
$904$		0			0
$905$	−1.07647	+	4.39945i	−0.0357831	+	0.146243i
$906$		0			0
$907$	−15.6926	−	11.7474i	−0.521065	−	0.390065i	0.306121	−	0.951993i	$-0.400969\pi$
$907$	−15.6926	−	11.7474i	−0.521065	−	0.390065i	−0.827186	+	0.561928i	$0.810060\pi$
$908$		0			0
$909$	−1.50428	+	0.686983i	−0.0498939	+	0.0227858i
$910$		0			0
$911$	23.7435	−	36.9456i	0.786657	−	1.22406i	−0.183842	−	0.982956i	$-0.558853\pi$
$911$	23.7435	−	36.9456i	0.786657	−	1.22406i	0.970499	−	0.241106i	$-0.0775101\pi$
$912$		0			0
$913$	−6.88801	−	9.20131i	−0.227960	−	0.304519i
$914$		0			0
$915$	0.0200039	+	0.0182568i	0.000661309	+	0.000603552i
$916$		0			0
$917$	35.9322	−	19.6205i	1.18659	−	0.647926i
$918$		0			0
$919$	−17.8568			−0.589040			−0.294520	−	0.955645i	$-0.595160\pi$
$919$	−17.8568			−0.589040			−0.294520	+	0.955645i	$0.595160\pi$
$920$		0			0
$921$	−0.129413			−0.00426429
$922$		0			0
$923$	−2.95588	+	1.61403i	−0.0972940	+	0.0531265i
$924$		0			0
$925$	40.8242	−	12.8731i	1.34229	−	0.423266i
$926$		0			0
$927$	−23.9592	−	32.0058i	−0.786924	−	1.05121i
$928$		0			0
$929$	4.01575	−	6.24862i	0.131752	−	0.205011i	−0.769109	−	0.639118i	$-0.779300\pi$
$929$	4.01575	−	6.24862i	0.131752	−	0.205011i	0.900861	+	0.434107i	$0.142936\pi$
$930$		0			0
$931$	16.7659	−	7.65673i	0.549480	−	0.250939i
$932$		0			0
$933$	−0.122360	−	0.0915973i	−0.00400588	−	0.00299876i
$934$		0			0
$935$	28.9670	+	47.7346i	0.947323	+	1.56109i
$936$		0			0
$937$	−1.40384	−	19.6283i	−0.0458616	−	0.641229i	−0.967450	−	0.253061i	$-0.918563\pi$
$937$	−1.40384	−	19.6283i	−0.0458616	−	0.641229i	0.921589	−	0.388168i	$-0.126892\pi$
$938$		0			0
$939$	0.0264021	+	0.0304696i	0.000861600	+	0.000994339i
$940$		0			0
$941$	−0.804773	−	0.367527i	−0.0262348	−	0.0119811i	0.402254	−	0.915528i	$-0.368227\pi$
$941$	−0.804773	−	0.367527i	−0.0262348	−	0.0119811i	−0.428489	+	0.903547i	$0.640954\pi$
$942$		0			0
$943$	14.4678	−	18.2728i	0.471137	−	0.595045i
$944$		0			0
$945$	−0.185986	+	0.131889i	−0.00605011	+	0.00429034i
$946$		0			0
$947$	−1.80485	+	25.2351i	−0.0586497	+	0.820030i	0.879960	+	0.475048i	$0.157569\pi$
$947$	−1.80485	+	25.2351i	−0.0586497	+	0.820030i	−0.938609	+	0.344982i	$0.887885\pi$
$948$		0			0
$949$	−49.1531	−	42.5914i	−1.59558	−	1.38258i
$950$		0			0
$951$	0.0556459	−	0.0163391i	0.00180444	−	0.000529832i
$952$		0			0
$953$	25.8573	−	34.5413i	0.837601	−	1.11890i	−0.153807	−	0.988101i	$-0.549154\pi$
$953$	25.8573	−	34.5413i	0.837601	−	1.11890i	0.991408	−	0.130803i	$-0.0417556\pi$
$954$		0			0
$955$	17.4629	+	1.70220i	0.565086	+	0.0550819i
$956$		0			0
$957$	0.0731676	−	0.0159166i	0.00236517	−	0.000514511i
$958$		0			0
$959$	−19.6601	−	2.82669i	−0.634856	−	0.0912786i
$960$		0			0
$961$	−22.8161	+	14.6630i	−0.736002	+	0.473000i
$962$		0			0
$963$	13.3791	+	24.5020i	0.431136	+	0.789567i
$964$		0			0
$965$	5.62193	−	1.49453i	0.180976	−	0.0481108i
$966$		0			0
$967$	−15.2916	−	15.2916i	−0.491746	−	0.491746i	0.417110	−	0.908856i	$-0.363043\pi$
$967$	−15.2916	−	15.2916i	−0.491746	−	0.491746i	−0.908856	+	0.417110i	$0.863043\pi$
$968$		0			0
$969$	0.0535314	−	0.182311i	0.00171968	−	0.00585669i
$970$		0			0
$971$	−6.59675	−	10.2647i	−0.211700	−	0.329411i	0.719123	−	0.694883i	$-0.244544\pi$
$971$	−6.59675	−	10.2647i	−0.211700	−	0.329411i	−0.930822	+	0.365472i	$0.880908\pi$
$972$		0			0
$973$	16.5957	−	12.4234i	0.532032	−	0.398274i
$974$		0			0
$975$	0.129382	+	0.00667387i	0.00414354	+	0.000213735i
$976$		0			0
$977$	33.1439	+	12.3620i	1.06037	+	0.395496i	0.818317	−	0.574768i	$-0.194908\pi$
$977$	33.1439	+	12.3620i	1.06037	+	0.395496i	0.242050	+	0.970264i	$0.422180\pi$
$978$		0			0
$979$	26.3119	−	3.78308i	0.840933	−	0.120908i
$980$		0			0
$981$	−5.83703	−	19.8791i	−0.186362	−	0.634691i
$982$		0			0
$983$	−0.161482	+	0.0115495i	−0.00515049	+	0.000368370i	−0.0739142	−	0.997265i	$-0.523549\pi$
$983$	−0.161482	+	0.0115495i	−0.00515049	+	0.000368370i	0.0687637	+	0.997633i	$0.478095\pi$
$984$		0			0
$985$	7.58941	−	11.1659i	0.241819	−	0.355776i
$986$		0			0
$987$	0.0301220	+	0.0807603i	0.000958795	+	0.00257063i
$988$		0			0
$989$	14.4889	+	13.2589i	0.460720	+	0.421609i
$990$		0			0
$991$	9.11550	−	19.9602i	0.289563	−	0.634055i	−0.707817	−	0.706396i	$-0.750320\pi$
$991$	9.11550	−	19.9602i	0.289563	−	0.634055i	0.997380	+	0.0723409i	$0.0230470\pi$
$992$		0			0
$993$	0.0752671	+	0.00538321i	0.00238853	+	0.000170831i
$994$		0			0
$995$	30.7169	−	10.5635i	0.973790	−	0.334887i
$996$		0			0
$997$	15.4761	+	8.45057i	0.490132	+	0.267632i	0.705254	−	0.708955i	$-0.250833\pi$
$997$	15.4761	+	8.45057i	0.490132	+	0.267632i	−0.215122	+	0.976587i	$0.569015\pi$
$998$		0			0
$999$	−0.0381215	−	0.265141i	−0.00120611	−	0.00838869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.19	✓	720
5.3	odd	4	inner	920.2.bv.a.753.19	yes	720
23.19	odd	22	inner	920.2.bv.a.617.19	yes	720
115.88	even	44	inner	920.2.bv.a.433.19	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.19	✓	720	1.1	even	1	trivial
920.2.bv.a.433.19	yes	720	115.88	even	44	inner
920.2.bv.a.617.19	yes	720	23.19	odd	22	inner
920.2.bv.a.753.19	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00457693 + 0.00249919i) q^{3} +(2.23374 - 0.101999i) q^{5} +(-1.95297 - 2.60886i) q^{7} +(-1.62191 + 2.52374i) q^{9} +(-3.17383 + 1.44944i) q^{11} +(-3.97765 - 2.97763i) q^{13} +(-0.00996875 + 0.00604939i) q^{15} +(-0.510554 - 7.13848i) q^{17} +(-3.33403 - 3.84767i) q^{19} +(0.0154587 + 0.00705973i) q^{21} +(-4.53722 + 1.55359i) q^{23} +(4.97919 - 0.455680i) q^{25} +(0.00223211 - 0.0312090i) q^{27} +(3.11015 + 2.69496i) q^{29} +(-1.88961 + 0.554841i) q^{31} +(0.0109039 - 0.0145660i) q^{33} +(-4.62853 - 5.62832i) q^{35} +(8.36550 - 1.81980i) q^{37} +(0.0256471 + 0.00368749i) q^{39} +(-4.08835 + 2.62742i) q^{41} +(-1.96262 - 3.59428i) q^{43} +(-3.36550 + 5.80281i) q^{45} +(3.58642 + 3.58642i) q^{47} +(-1.01995 + 3.47362i) q^{49} +(0.0201772 + 0.0313963i) q^{51} +(-8.90212 + 6.66404i) q^{53} +(-6.94166 + 3.56140i) q^{55} +(0.0248757 + 0.00927815i) q^{57} +(5.46562 - 0.785838i) q^{59} +(-0.654342 - 2.22848i) q^{61} +(9.75163 - 0.697450i) q^{63} +(-9.18875 - 6.24553i) q^{65} +(-5.28978 - 14.1825i) q^{67} +(0.0168838 - 0.0184500i) q^{69} +(0.281573 - 0.616558i) q^{71} +(13.0564 + 0.933811i) q^{73} +(-0.0216506 + 0.0145296i) q^{75} +(9.97978 + 5.44937i) q^{77} +(-2.15063 - 14.9580i) q^{79} +(-3.73863 - 8.18647i) q^{81} +(0.700230 + 3.21891i) q^{83} +(-1.86856 - 15.8934i) q^{85} +(-0.0209701 - 0.00456177i) q^{87} +(-7.31005 - 2.14642i) q^{89} +16.1924i q^{91} +(0.00726197 - 0.00726197i) q^{93} +(-7.83981 - 8.25463i) q^{95} +(-1.63190 + 7.50171i) q^{97} +(1.48965 - 10.3608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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