LMFDB - Embedded newform 920.2.bv.a.17.3

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			17.3
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.63218 + 1.43728i) q^{3} +(2.23215 - 0.132363i) q^{5} +(-0.0903793 - 0.120733i) q^{7} +(3.24067 - 5.04257i) q^{9} +(1.04216 - 0.475937i) q^{11} +(0.0996752 + 0.0746159i) q^{13} +(-5.68516 + 3.55662i) q^{15} +(-0.0921070 - 1.28782i) q^{17} +(-4.39077 - 5.06722i) q^{19} +(0.411420 + 0.187889i) q^{21} +(-3.02203 - 3.72389i) q^{23} +(4.96496 - 0.590908i) q^{25} +(-0.640585 + 8.95655i) q^{27} +(-3.89319 - 3.37347i) q^{29} +(3.39801 - 0.997747i) q^{31} +(-2.05909 + 2.75062i) q^{33} +(-0.217720 - 0.257530i) q^{35} +(-0.238669 + 0.0519194i) q^{37} +(-0.369607 - 0.0531414i) q^{39} +(7.98233 - 5.12993i) q^{41} +(1.35763 + 2.48631i) q^{43} +(6.56619 - 11.6847i) q^{45} +(5.94734 + 5.94734i) q^{47} +(1.96572 - 6.69463i) q^{49} +(2.09340 + 3.25740i) q^{51} +(-2.10456 + 1.57545i) q^{53} +(2.26325 - 1.20030i) q^{55} +(18.8403 + 7.02706i) q^{57} +(11.5159 - 1.65574i) q^{59} +(0.709519 + 2.41640i) q^{61} +(-0.901692 + 0.0644903i) q^{63} +(0.232366 + 0.153360i) q^{65} +(2.27000 + 6.08610i) q^{67} +(13.3068 + 5.45845i) q^{69} +(6.08654 - 13.3277i) q^{71} +(-1.57351 - 0.112540i) q^{73} +(-12.2194 + 8.69140i) q^{75} +(-0.151650 - 0.0828074i) q^{77} +(0.347237 + 2.41508i) q^{79} +(-3.71677 - 8.13858i) q^{81} +(-1.54768 - 7.11459i) q^{83} +(-0.376057 - 2.86242i) q^{85} +(15.0962 + 3.28397i) q^{87} +(-14.0710 - 4.13161i) q^{89} -0.0187778i q^{91} +(-7.51013 + 7.51013i) q^{93} +(-10.4716 - 10.7296i) q^{95} +(-0.905608 + 4.16301i) q^{97} +(0.977334 - 6.79751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.63218	+	1.43728i	−1.51969	+	0.829812i	−0.999703	−	0.0243631i	$-0.992244\pi$
$3$	−2.63218	+	1.43728i	−1.51969	+	0.829812i	−0.519985	+	0.854176i	$0.674062\pi$
$4$		0			0
$5$	2.23215	−	0.132363i	0.998246	−	0.0591946i
$5$	2.23215	−	0.132363i	0.998246	−	0.0591946i
$6$		0			0
$7$	−0.0903793	−	0.120733i	−0.0341602	−	0.0456326i	0.783136	−	0.621851i	$-0.213619\pi$
$7$	−0.0903793	−	0.120733i	−0.0341602	−	0.0456326i	−0.817296	+	0.576218i	$0.804528\pi$
$8$		0			0
$9$	3.24067	−	5.04257i	1.08022	−	1.68086i
$10$		0			0
$11$	1.04216	−	0.475937i	0.314222	−	0.143500i	−0.252061	−	0.967711i	$-0.581108\pi$
$11$	1.04216	−	0.475937i	0.314222	−	0.143500i	0.566283	+	0.824211i	$0.308381\pi$
$12$		0			0
$13$	0.0996752	+	0.0746159i	0.0276449	+	0.0206947i	0.613011	−	0.790075i	$-0.289958\pi$
$13$	0.0996752	+	0.0746159i	0.0276449	+	0.0206947i	−0.585366	+	0.810769i	$0.699049\pi$
$14$		0			0
$15$	−5.68516	+	3.55662i	−1.46790	+	0.918315i
$16$		0			0
$17$	−0.0921070	−	1.28782i	−0.0223392	−	0.312343i	−0.996320	−	0.0857122i	$-0.972683\pi$
$17$	−0.0921070	−	1.28782i	−0.0223392	−	0.312343i	0.973981	−	0.226631i	$-0.0727711\pi$
$18$		0			0
$19$	−4.39077	−	5.06722i	−1.00731	−	1.16250i	−0.986674	−	0.162713i	$-0.947976\pi$
$19$	−4.39077	−	5.06722i	−1.00731	−	1.16250i	−0.0206381	−	0.999787i	$-0.506570\pi$
$20$		0			0
$21$	0.411420	+	0.187889i	0.0897793	+	0.0410008i
$22$		0			0
$23$	−3.02203	−	3.72389i	−0.630136	−	0.776485i
$23$	−3.02203	−	3.72389i	−0.630136	−	0.776485i
$24$		0			0
$25$	4.96496	−	0.590908i	0.992992	−	0.118182i
$26$		0			0
$27$	−0.640585	+	8.95655i	−0.123281	+	1.72369i
$28$		0			0
$29$	−3.89319	−	3.37347i	−0.722947	−	0.626437i	0.213624	−	0.976916i	$-0.431473\pi$
$29$	−3.89319	−	3.37347i	−0.722947	−	0.626437i	−0.936571	+	0.350479i	$0.886019\pi$
$30$		0			0
$31$	3.39801	−	0.997747i	0.610301	−	0.179201i	0.0380457	−	0.999276i	$-0.487887\pi$
$31$	3.39801	−	0.997747i	0.610301	−	0.179201i	0.572255	+	0.820075i	$0.306069\pi$
$32$		0			0
$33$	−2.05909	+	2.75062i	−0.358441	+	0.478821i
$34$		0			0
$35$	−0.217720	−	0.257530i	−0.0368015	−	0.0435305i
$36$		0			0
$37$	−0.238669	+	0.0519194i	−0.0392370	+	0.00853549i	−0.232141	−	0.972682i	$-0.574573\pi$
$37$	−0.238669	+	0.0519194i	−0.0392370	+	0.00853549i	0.192904	+	0.981218i	$0.438209\pi$
$38$		0			0
$39$	−0.369607	−	0.0531414i	−0.0591844	−	0.00850944i
$40$		0			0
$41$	7.98233	−	5.12993i	1.24663	−	0.801161i	0.260234	−	0.965545i	$-0.416200\pi$
$41$	7.98233	−	5.12993i	1.24663	−	0.801161i	0.986396	+	0.164385i	$0.0525638\pi$
$42$		0			0
$43$	1.35763	+	2.48631i	0.207036	+	0.379158i	0.960478	−	0.278356i	$-0.0897896\pi$
$43$	1.35763	+	2.48631i	0.207036	+	0.379158i	−0.753442	+	0.657515i	$0.771608\pi$
$44$		0			0
$45$	6.56619	−	11.6847i	0.978830	−	1.74185i
$46$		0			0
$47$	5.94734	+	5.94734i	0.867509	+	0.867509i	0.992196	−	0.124688i	$-0.0397928\pi$
$47$	5.94734	+	5.94734i	0.867509	+	0.867509i	−0.124688	+	0.992196i	$0.539793\pi$
$48$		0			0
$49$	1.96572	−	6.69463i	0.280817	−	0.956375i
$50$		0			0
$51$	2.09340	+	3.25740i	0.293135	+	0.456127i
$52$		0			0
$53$	−2.10456	+	1.57545i	−0.289084	+	0.216405i	−0.733970	−	0.679182i	$-0.762335\pi$
$53$	−2.10456	+	1.57545i	−0.289084	+	0.216405i	0.444887	+	0.895587i	$0.353244\pi$
$54$		0			0
$55$	2.26325	−	1.20030i	0.305177	−	0.161849i
$56$		0			0
$57$	18.8403	+	7.02706i	2.49546	+	0.930757i
$58$		0			0
$59$	11.5159	−	1.65574i	1.49925	−	0.215559i	0.656687	−	0.754163i	$-0.271957\pi$
$59$	11.5159	−	1.65574i	1.49925	−	0.215559i	0.842559	+	0.538604i	$0.181048\pi$
$60$		0			0
$61$	0.709519	+	2.41640i	0.0908446	+	0.309388i	0.992363	−	0.123353i	$-0.0393647\pi$
$61$	0.709519	+	2.41640i	0.0908446	+	0.309388i	−0.901518	+	0.432741i	$0.857546\pi$
$62$		0			0
$63$	−0.901692	+	0.0644903i	−0.113603	+	0.00812501i
$64$		0			0
$65$	0.232366	+	0.153360i	0.0288215	+	0.0190220i
$66$		0			0
$67$	2.27000	+	6.08610i	0.277324	+	0.743536i	0.998699	+	0.0509906i	$0.0162379\pi$
$67$	2.27000	+	6.08610i	0.277324	+	0.743536i	−0.721375	+	0.692545i	$0.756489\pi$
$68$		0			0
$69$	13.3068	+	5.45845i	1.60195	+	0.657120i
$70$		0			0
$71$	6.08654	−	13.3277i	0.722339	−	1.58170i	−0.0882572	−	0.996098i	$-0.528130\pi$
$71$	6.08654	−	13.3277i	0.722339	−	1.58170i	0.810597	−	0.585605i	$-0.199143\pi$
$72$		0			0
$73$	−1.57351	−	0.112540i	−0.184165	−	0.0131718i	−0.0210481	−	0.999778i	$-0.506700\pi$
$73$	−1.57351	−	0.112540i	−0.184165	−	0.0131718i	−0.163117	+	0.986607i	$0.552155\pi$
$74$		0			0
$75$	−12.2194	+	8.69140i	−1.41097	+	1.00360i
$76$		0			0
$77$	−0.151650	−	0.0828074i	−0.0172822	−	0.00943678i
$78$		0			0
$79$	0.347237	+	2.41508i	0.0390672	+	0.271718i	0.999987	−	0.00510879i	$-0.00162619\pi$
$79$	0.347237	+	2.41508i	0.0390672	+	0.271718i	−0.960920	+	0.276827i	$0.910717\pi$
$80$		0			0
$81$	−3.71677	−	8.13858i	−0.412974	−	0.904287i
$82$		0			0
$83$	−1.54768	−	7.11459i	−0.169880	−	0.780927i	−0.980682	−	0.195607i	$-0.937332\pi$
$83$	−1.54768	−	7.11459i	−0.169880	−	0.780927i	0.810802	−	0.585321i	$-0.199031\pi$
$84$		0			0
$85$	−0.376057	−	2.86242i	−0.0407891	−	0.310473i
$86$		0			0
$87$	15.0962	+	3.28397i	1.61848	+	0.352079i
$88$		0			0
$89$	−14.0710	−	4.13161i	−1.49152	−	0.437950i	−0.568494	−	0.822687i	$-0.692474\pi$
$89$	−14.0710	−	4.13161i	−1.49152	−	0.437950i	−0.923026	+	0.384737i	$0.874292\pi$
$90$		0			0
$91$		−	0.0187778i		−	0.00196845i
$92$		0			0
$93$	−7.51013	+	7.51013i	−0.778764	+	0.778764i
$94$		0			0
$95$	−10.4716	−	10.7296i	−1.07436	−	1.10083i
$96$		0			0
$97$	−0.905608	+	4.16301i	−0.0919505	+	0.422690i	0.908042	+	0.418879i	$0.137577\pi$
$97$	−0.905608	+	4.16301i	−0.0919505	+	0.422690i	−0.999993	+	0.00381112i	$0.998787\pi$
$98$		0			0
$99$	0.977334	−	6.79751i	0.0982258	−	0.683175i
$100$		0			0
$101$	2.02414	+	1.30084i	0.201409	+	0.129438i	0.637458	−	0.770485i	$-0.279986\pi$
$101$	2.02414	+	1.30084i	0.201409	+	0.129438i	−0.436048	+	0.899923i	$0.643622\pi$
$102$		0			0
$103$	6.57163	−	17.6192i	0.647522	−	1.73607i	−0.0289233	−	0.999582i	$-0.509208\pi$
$103$	6.57163	−	17.6192i	0.647522	−	1.73607i	0.676446	−	0.736493i	$-0.263519\pi$
$104$		0			0
$105$	0.943220	+	0.364940i	0.0920489	+	0.0356145i
$106$		0			0
$107$	−5.54782	+	10.1601i	−0.536328	+	0.982211i	0.459253	+	0.888305i	$0.348117\pi$
$107$	−5.54782	+	10.1601i	−0.536328	+	0.982211i	−0.995581	+	0.0939056i	$0.970065\pi$
$108$		0			0
$109$	4.67274	−	5.39263i	0.447567	−	0.516520i	−0.486469	−	0.873698i	$-0.661716\pi$
$109$	4.67274	−	5.39263i	0.447567	−	0.516520i	0.934036	+	0.357178i	$0.116261\pi$
$110$		0			0
$111$	0.553598	−	0.479695i	0.0525452	−	0.0455306i
$112$		0			0
$113$	6.88605	−	2.56837i	0.647785	−	0.241611i	−0.00402677	−	0.999992i	$-0.501282\pi$
$113$	6.88605	−	2.56837i	0.647785	−	0.241611i	0.651812	+	0.758380i	$0.274009\pi$
$114$		0			0
$115$	−7.23851	−	7.91227i	−0.674995	−	0.737823i
$116$		0			0
$117$	0.699271	−	0.260814i	0.0646476	−	0.0241123i
$118$		0			0
$119$	−0.147158	+	0.127513i	−0.0134899	+	0.0116891i
$120$		0			0
$121$	−6.34389	+	7.32124i	−0.576718	+	0.665568i
$122$		0			0
$123$	−13.6378	+	24.9757i	−1.22968	+	2.25198i
$124$		0			0
$125$	11.0043	−	1.97617i	0.984255	−	0.176754i
$126$		0			0
$127$	7.29314	−	19.5537i	0.647162	−	1.73511i	−0.0302911	−	0.999541i	$-0.509643\pi$
$127$	7.29314	−	19.5537i	0.647162	−	1.73511i	0.677453	−	0.735566i	$-0.263084\pi$
$128$		0			0
$129$	−7.14702	−	4.59311i	−0.629260	−	0.404401i
$130$		0			0
$131$	−2.50084	+	17.3938i	−0.218500	+	1.51970i	0.525080	+	0.851053i	$0.324035\pi$
$131$	−2.50084	+	17.3938i	−0.218500	+	1.51970i	−0.743580	+	0.668647i	$0.766874\pi$
$132$		0			0
$133$	−0.214944	+	0.988080i	−0.0186380	+	0.0856774i
$134$		0			0
$135$	−0.244363	+	20.0771i	−0.0210314	+	1.72796i
$136$		0			0
$137$	−4.90279	+	4.90279i	−0.418874	+	0.418874i	−0.884815	−	0.465942i	$-0.845716\pi$
$137$	−4.90279	+	4.90279i	−0.418874	+	0.418874i	0.465942	+	0.884815i	$0.345716\pi$
$138$		0			0
$139$		−	6.15254i		−	0.521852i	−0.965359	−	0.260926i	$-0.915972\pi$
$139$		−	6.15254i		−	0.521852i	0.965359	−	0.260926i	$-0.0840278\pi$
$140$		0			0
$141$	−24.2024	−	7.10647i	−2.03821	−	0.598473i
$142$		0			0
$143$	0.139390	+	0.0303224i	0.0116564	+	0.00253568i
$144$		0			0
$145$	−9.13669	−	7.01476i	−0.758761	−	0.582544i
$146$		0			0
$147$	4.44791	+	20.4467i	0.366858	+	1.68642i
$148$		0			0
$149$	8.86059	+	19.4020i	0.725888	+	1.58947i	0.805465	+	0.592644i	$0.201916\pi$
$149$	8.86059	+	19.4020i	0.725888	+	1.58947i	−0.0795768	+	0.996829i	$0.525357\pi$
$150$		0			0
$151$	1.80557	+	12.5580i	0.146935	+	1.02196i	0.921199	+	0.389092i	$0.127211\pi$
$151$	1.80557	+	12.5580i	0.146935	+	1.02196i	−0.774264	+	0.632863i	$0.781880\pi$
$152$		0			0
$153$	−6.79243	−	3.70895i	−0.549136	−	0.299851i
$154$		0			0
$155$	7.45280	−	2.67689i	0.598623	−	0.215013i
$156$		0			0
$157$	−13.6466	−	0.976023i	−1.08912	−	0.0778951i	−0.484789	−	0.874631i	$-0.661104\pi$
$157$	−13.6466	−	0.976023i	−1.08912	−	0.0778951i	−0.604328	+	0.796736i	$0.706558\pi$
$158$		0			0
$159$	3.27521	−	7.17171i	0.259741	−	0.568754i
$160$		0			0
$161$	−0.176466	+	0.701419i	−0.0139075	+	0.0552796i
$162$		0			0
$163$	−1.75426	−	4.70336i	−0.137405	−	0.368396i	0.849963	−	0.526842i	$-0.176624\pi$
$163$	−1.75426	−	4.70336i	−0.137405	−	0.368396i	−0.987368	+	0.158446i	$0.949351\pi$
$164$		0			0
$165$	−4.23211	+	6.41233i	−0.329469	+	0.499199i
$166$		0			0
$167$	3.05478	−	0.218482i	0.236386	−	0.0169067i	0.0473564	−	0.998878i	$-0.484920\pi$
$167$	3.05478	−	0.218482i	0.236386	−	0.0169067i	0.189030	+	0.981971i	$0.439466\pi$
$168$		0			0
$169$	−3.65816	−	12.4585i	−0.281397	−	0.958349i
$170$		0			0
$171$	−39.7808	+	5.71962i	−3.04212	+	0.437390i
$172$		0			0
$173$	−4.12885	−	1.53998i	−0.313911	−	0.117083i	0.187571	−	0.982251i	$-0.439939\pi$
$173$	−4.12885	−	1.53998i	−0.313911	−	0.117083i	−0.501481	+	0.865169i	$0.667211\pi$
$174$		0			0
$175$	−0.520071	−	0.546027i	−0.0393137	−	0.0412757i
$176$		0			0
$177$	−27.9322	+	20.9098i	−2.09951	+	1.57168i
$178$		0			0
$179$	−5.21659	−	8.11717i	−0.389906	−	0.606706i	0.589703	−	0.807620i	$-0.299245\pi$
$179$	−5.21659	−	8.11717i	−0.389906	−	0.606706i	−0.979609	+	0.200915i	$0.935609\pi$
$180$		0			0
$181$	0.538147	−	1.83276i	0.0400002	−	0.136228i	−0.937072	−	0.349136i	$-0.886475\pi$
$181$	0.538147	−	1.83276i	0.0400002	−	0.136228i	0.977072	+	0.212908i	$0.0682934\pi$
$182$		0			0
$183$	−5.34061	−	5.34061i	−0.394790	−	0.394790i
$184$		0			0
$185$	−0.525873	+	0.147483i	−0.0386630	+	0.0108431i
$186$		0			0
$187$	−0.708913	−	1.29828i	−0.0518408	−	0.0949394i
$188$		0			0
$189$	1.13924	−	0.732147i	0.0828677	−	0.0532558i
$190$		0			0
$191$	−7.11046	−	1.02233i	−0.514495	−	0.0739732i	−0.119823	−	0.992795i	$-0.538233\pi$
$191$	−7.11046	−	1.02233i	−0.514495	−	0.0739732i	−0.394672	+	0.918822i	$0.629142\pi$
$192$		0			0
$193$	8.49373	−	1.84770i	0.611392	−	0.133000i	0.103801	−	0.994598i	$-0.466900\pi$
$193$	8.49373	−	1.84770i	0.611392	−	0.133000i	0.507591	+	0.861598i	$0.330536\pi$
$194$		0			0
$195$	−0.832050	−	0.0696971i	−0.0595844	−	0.00499112i
$196$		0			0
$197$	−11.3274	+	15.1316i	−0.807042	+	1.07808i	0.188341	+	0.982104i	$0.439689\pi$
$197$	−11.3274	+	15.1316i	−0.807042	+	1.07808i	−0.995383	+	0.0959785i	$0.969402\pi$
$198$		0			0
$199$	−10.1615	+	2.98369i	−0.720331	+	0.211508i	−0.621296	−	0.783576i	$-0.713394\pi$
$199$	−10.1615	+	2.98369i	−0.720331	+	0.211508i	−0.0990347	+	0.995084i	$0.531575\pi$
$200$		0			0
$201$	−14.7225	−	12.7571i	−1.03844	−	0.899815i
$202$		0			0
$203$	−0.0554238	+	0.774926i	−0.00388999	+	0.0543892i
$204$		0			0
$205$	17.1387	−	12.5073i	1.19702	−	0.873550i
$206$		0			0
$207$	−28.5714	+	3.17090i	−1.98585	+	0.220393i
$208$		0			0
$209$	−6.98755	−	3.19111i	−0.483339	−	0.220733i
$210$		0			0
$211$	0.326050	+	0.376282i	0.0224462	+	0.0259043i	0.766862	−	0.641812i	$-0.221817\pi$
$211$	0.326050	+	0.376282i	0.0224462	+	0.0259043i	−0.744415	+	0.667717i	$0.767272\pi$
$212$		0			0
$213$	3.13470	+	43.8288i	0.214786	+	3.00310i
$214$		0			0
$215$	3.35952	+	5.37010i	0.229117	+	0.366238i
$216$		0			0
$217$	−0.427570	−	0.320075i	−0.0290254	−	0.0217281i
$218$		0			0
$219$	4.30350	−	1.96534i	0.290804	−	0.132806i
$220$		0			0
$221$	0.0869114	−	0.135237i	0.00584629	−	0.00909701i
$222$		0			0
$223$	−4.67524	−	6.24539i	−0.313077	−	0.418222i	0.616209	−	0.787583i	$-0.288668\pi$
$223$	−4.67524	−	6.24539i	−0.313077	−	0.418222i	−0.929286	+	0.369360i	$0.879577\pi$
$224$		0			0
$225$	13.1101	−	26.9511i	0.874005	−	1.79674i
$226$		0			0
$227$	19.0221	−	10.3868i	1.26254	−	0.689399i	0.298310	−	0.954469i	$-0.403577\pi$
$227$	19.0221	−	10.3868i	1.26254	−	0.689399i	0.964229	+	0.265070i	$0.0853951\pi$
$228$		0			0
$229$	0.198868			0.0131415			0.00657077	−	0.999978i	$-0.497908\pi$
$229$	0.198868			0.0131415			0.00657077	+	0.999978i	$0.497908\pi$
$230$		0			0
$231$	0.518188			0.0340943
$232$		0			0
$233$	−17.9119	+	9.78065i	−1.17345	+	0.640752i	−0.943150	−	0.332368i	$-0.892152\pi$
$233$	−17.9119	+	9.78065i	−1.17345	+	0.640752i	−0.230300	+	0.973120i	$0.573971\pi$
$234$		0			0
$235$	14.0625	+	12.4881i	0.917339	+	0.814635i
$236$		0			0
$237$	−4.38513	−	5.85785i	−0.284845	−	0.380508i
$238$		0			0
$239$	−10.6023	+	16.4975i	−0.685807	+	1.06714i	0.307490	+	0.951551i	$0.400511\pi$
$239$	−10.6023	+	16.4975i	−0.685807	+	1.06714i	−0.993297	+	0.115586i	$0.963125\pi$
$240$		0			0
$241$	22.0112	−	10.0522i	1.41786	−	0.647517i	0.448644	−	0.893711i	$-0.351907\pi$
$241$	22.0112	−	10.0522i	1.41786	−	0.647517i	0.969221	+	0.246194i	$0.0791800\pi$
$242$		0			0
$243$	−0.0846179	−	0.0633441i	−0.00542824	−	0.00406353i
$244$		0			0
$245$	3.50165	−	15.2036i	0.223712	−	0.971321i
$246$		0			0
$247$	−0.0595557	−	0.832698i	−0.00378944	−	0.0529833i
$248$		0			0
$249$	14.2994	+	16.5024i	0.906188	+	1.04580i
$250$		0			0
$251$	5.08238	+	2.32105i	0.320797	+	0.146503i	0.569304	−	0.822127i	$-0.307213\pi$
$251$	5.08238	+	2.32105i	0.320797	+	0.146503i	−0.248507	+	0.968630i	$0.579940\pi$
$252$		0			0
$253$	−4.92176	−	2.44258i	−0.309429	−	0.153564i
$254$		0			0
$255$	5.10394	+	6.99390i	0.319621	+	0.437975i
$256$		0			0
$257$	1.40987	−	19.7126i	0.0879454	−	1.22964i	−0.741463	−	0.670994i	$-0.765868\pi$
$257$	1.40987	−	19.7126i	0.0879454	−	1.22964i	0.829408	−	0.558643i	$-0.188678\pi$
$258$		0			0
$259$	0.0278391	+	0.0241227i	0.00172984	+	0.00149891i
$260$		0			0
$261$	−29.6275	+	8.69942i	−1.83390	+	0.538480i
$262$		0			0
$263$	−13.5870	+	18.1501i	−0.837808	+	1.11918i	0.153569	+	0.988138i	$0.450923\pi$
$263$	−13.5870	+	18.1501i	−0.837808	+	1.11918i	−0.991377	+	0.131043i	$0.958168\pi$
$264$		0			0
$265$	−4.48916	+	3.79521i	−0.275767	+	0.233138i
$266$		0			0
$267$	42.9756	−	9.34876i	2.63006	−	0.572135i
$268$		0			0
$269$	10.1570	+	1.46036i	0.619284	+	0.0890395i	0.444814	−	0.895623i	$-0.353270\pi$
$269$	10.1570	+	1.46036i	0.619284	+	0.0890395i	0.174470	+	0.984663i	$0.444179\pi$
$270$		0			0
$271$	14.7762	−	9.49610i	0.897592	−	0.576847i	−0.00848347	−	0.999964i	$-0.502700\pi$
$271$	14.7762	−	9.49610i	0.897592	−	0.576847i	0.906075	+	0.423117i	$0.139064\pi$
$272$		0			0
$273$	0.0269889	+	0.0494264i	0.00163344	+	0.00299142i
$274$		0			0
$275$	4.89303	−	2.97883i	0.295061	−	0.179630i
$276$		0			0
$277$	−13.0317	−	13.0317i	−0.782997	−	0.782997i	0.197338	−	0.980335i	$-0.436770\pi$
$277$	−13.0317	−	13.0317i	−0.782997	−	0.782997i	−0.980335	+	0.197338i	$0.936770\pi$
$278$		0			0
$279$	5.98061	−	20.3681i	0.358050	−	1.21941i
$280$		0			0
$281$	7.37132	+	11.4700i	0.439736	+	0.684242i	0.988412	−	0.151792i	$-0.0485045\pi$
$281$	7.37132	+	11.4700i	0.439736	+	0.684242i	−0.548677	+	0.836035i	$0.684868\pi$
$282$		0			0
$283$	−3.01745	+	2.25884i	−0.179369	+	0.134274i	−0.685190	−	0.728365i	$-0.740281\pi$
$283$	−3.01745	+	2.25884i	−0.179369	+	0.134274i	0.505821	+	0.862639i	$0.331190\pi$
$284$		0			0
$285$	42.9844	+	13.1917i	2.54618	+	0.781407i
$286$		0			0
$287$	−1.34079	−	0.500088i	−0.0791442	−	0.0295192i
$288$		0			0
$289$	15.1770	−	2.18212i	0.892762	−	0.128360i
$290$		0			0
$291$	−3.59968	−	12.2594i	−0.211017	−	0.718658i
$292$		0			0
$293$	27.4273	−	1.96164i	1.60232	−	0.114600i	0.758663	−	0.651484i	$-0.225853\pi$
$293$	27.4273	−	1.96164i	1.60232	−	0.114600i	0.843656	+	0.536884i	$0.180399\pi$
$294$		0			0
$295$	25.4861	−	5.22014i	1.48386	−	0.303928i
$296$		0			0
$297$	3.59516	+	9.63900i	0.208613	+	0.559312i
$298$		0			0
$299$	−0.0233595	−	0.596671i	−0.00135091	−	0.0345064i
$300$		0			0
$301$	0.177477	−	0.388620i	0.0102296	−	0.0223997i
$302$		0			0
$303$	−7.19755	−	0.514779i	−0.413489	−	0.0295733i
$304$		0			0
$305$	1.90359	+	5.29984i	0.108999	+	0.303468i
$306$		0			0
$307$	−4.05021	−	2.21158i	−0.231157	−	0.126222i	0.359497	−	0.933146i	$-0.382948\pi$
$307$	−4.05021	−	2.21158i	−0.231157	−	0.126222i	−0.590654	+	0.806925i	$0.701130\pi$
$308$		0			0
$309$	8.02602	+	55.8222i	0.456584	+	3.17561i
$310$		0			0
$311$	−9.83161	−	21.5282i	−0.557500	−	1.22075i	−0.953191	−	0.302370i	$-0.902222\pi$
$311$	−9.83161	−	21.5282i	−0.557500	−	1.22075i	0.395691	−	0.918384i	$-0.370505\pi$
$312$		0			0
$313$	2.38342	+	10.9564i	0.134719	+	0.619294i	0.994147	+	0.108037i	$0.0344564\pi$
$313$	2.38342	+	10.9564i	0.134719	+	0.619294i	−0.859428	+	0.511257i	$0.829180\pi$
$314$		0			0
$315$	−2.00417	+	0.263303i	−0.112922	+	0.0148354i
$316$		0			0
$317$	−1.44321	−	0.313951i	−0.0810588	−	0.0176333i	0.171853	−	0.985123i	$-0.445025\pi$
$317$	−1.44321	−	0.313951i	−0.0810588	−	0.0176333i	−0.252912	+	0.967489i	$0.581388\pi$
$318$		0			0
$319$	−5.66287	−	1.66277i	−0.317060	−	0.0930972i
$320$		0			0
$321$		−	34.7168i		−	1.93771i
$322$		0			0
$323$	−6.12126	+	6.12126i	−0.340596	+	0.340596i
$324$		0			0
$325$	0.538975	+	0.311566i	0.0298969	+	0.0172826i
$326$		0			0
$327$	−4.54877	+	20.9104i	−0.251548	+	1.15635i
$328$		0			0
$329$	0.180521	−	1.25555i	0.00995246	−	0.0692209i
$330$		0			0
$331$	−27.6022	−	17.7389i	−1.51715	−	0.975016i	−0.992305	−	0.123821i	$-0.960485\pi$
$331$	−27.6022	−	17.7389i	−1.51715	−	0.975016i	−0.524850	−	0.851195i	$-0.675879\pi$
$332$		0			0
$333$	−0.511641	+	1.37176i	−0.0280377	+	0.0751721i
$334$		0			0
$335$	5.87255	+	13.2846i	0.320851	+	0.725816i
$336$		0			0
$337$	8.67959	−	15.8955i	0.472807	−	0.865882i	−0.527064	−	0.849826i	$-0.676707\pi$
$337$	8.67959	−	15.8955i	0.472807	−	0.865882i	0.999871	−	0.0160564i	$-0.00511113\pi$
$338$		0			0
$339$	−14.4339	+	16.6576i	−0.783939	+	0.904714i
$340$		0			0
$341$	3.06640	−	2.65705i	0.166055	−	0.143887i
$342$		0			0
$343$	−1.97505	+	0.736657i	−0.106643	+	0.0397757i
$344$		0			0
$345$	30.4252	+	10.4227i	1.63804	+	0.561141i
$346$		0			0
$347$	3.12330	−	1.16493i	0.167667	−	0.0625367i	−0.264229	−	0.964460i	$-0.585117\pi$
$347$	3.12330	−	1.16493i	0.167667	−	0.0625367i	0.431896	+	0.901923i	$0.357845\pi$
$348$		0			0
$349$	−9.05759	+	7.84845i	−0.484842	+	0.420118i	−0.862677	−	0.505755i	$-0.831214\pi$
$349$	−9.05759	+	7.84845i	−0.484842	+	0.420118i	0.377835	+	0.925873i	$0.376669\pi$
$350$		0			0
$351$	−0.732152	+	0.844948i	−0.0390794	+	0.0451000i
$352$		0			0
$353$	8.82715	−	16.1657i	0.469822	−	0.860414i	−0.530101	−	0.847935i	$-0.677846\pi$
$353$	8.82715	−	16.1657i	0.469822	−	0.860414i	0.999922	−	0.0124792i	$-0.00397237\pi$
$354$		0			0
$355$	11.8220	−	30.5549i	0.627445	−	1.62169i
$356$		0			0
$357$	0.204074	−	0.547143i	0.0108007	−	0.0289579i
$358$		0			0
$359$	22.4757	+	14.4443i	1.18622	+	0.762339i	0.976520	−	0.215426i	$-0.0691141\pi$
$359$	22.4757	+	14.4443i	1.18622	+	0.762339i	0.209702	+	0.977765i	$0.432750\pi$
$360$		0			0
$361$	−3.69386	+	25.6914i	−0.194414	+	1.35218i
$362$		0			0
$363$	6.17559	−	28.3887i	0.324135	−	1.49002i
$364$		0			0
$365$	−3.52720	−	0.0429303i	−0.184622	−	0.00224707i
$366$		0			0
$367$	2.24678	−	2.24678i	0.117281	−	0.117281i	−0.646031	−	0.763311i	$-0.723572\pi$
$367$	2.24678	−	2.24678i	0.117281	−	0.117281i	0.763311	+	0.646031i	$0.223572\pi$
$368$		0			0
$369$		−	56.8759i		−	2.96084i
$370$		0			0
$371$	0.380417	+	0.111701i	0.0197503	+	0.00579921i
$372$		0			0
$373$	−1.60817	−	0.349835i	−0.0832677	−	0.0181138i	0.170738	−	0.985316i	$-0.445385\pi$
$373$	−1.60817	−	0.349835i	−0.0832677	−	0.0181138i	−0.254006	+	0.967203i	$0.581748\pi$
$374$		0			0
$375$	−26.1250	+	21.0179i	−1.34909	+	1.08536i
$376$		0			0
$377$	−0.136340	−	0.626745i	−0.00702187	−	0.0322790i
$378$		0			0
$379$	−14.6635	−	32.1086i	−0.753213	−	1.64931i	−0.760505	−	0.649333i	$-0.775048\pi$
$379$	−14.6635	−	32.1086i	−0.753213	−	1.64931i	0.00729175	−	0.999973i	$-0.497679\pi$
$380$		0			0
$381$	8.90721	+	61.9510i	0.456330	+	3.17384i
$382$		0			0
$383$	1.97245	+	1.07704i	0.100788	+	0.0550342i	0.528852	−	0.848714i	$-0.322623\pi$
$383$	1.97245	+	1.07704i	0.100788	+	0.0550342i	−0.428065	+	0.903748i	$0.640804\pi$
$384$		0			0
$385$	−0.349467	−	0.164765i	−0.0178105	−	0.00839722i
$386$		0			0
$387$	16.9370	+	1.21136i	0.860956	+	0.0615768i
$388$		0			0
$389$	−12.7487	+	27.9157i	−0.646384	+	1.41538i	0.248300	+	0.968683i	$0.420128\pi$
$389$	−12.7487	+	27.9157i	−0.646384	+	1.41538i	−0.894684	+	0.446700i	$0.852599\pi$
$390$		0			0
$391$	−4.51736	+	4.23483i	−0.228453	+	0.214165i
$392$		0			0
$393$	−18.4170	−	49.3778i	−0.929014	−	2.49078i
$394$		0			0
$395$	1.09475	+	5.34486i	0.0550829	+	0.268929i
$396$		0			0
$397$	−26.5137	+	1.89629i	−1.33068	+	0.0951723i	−0.718490	−	0.695537i	$-0.755167\pi$
$397$	−26.5137	+	1.89629i	−1.33068	+	0.0951723i	−0.612192	+	0.790709i	$0.709712\pi$
$398$		0			0
$399$	−0.854375	−	2.90974i	−0.0427723	−	0.145669i
$400$		0			0
$401$	−33.0700	+	4.75474i	−1.65144	+	0.237441i	−0.904197	−	0.427116i	$-0.859530\pi$
$401$	−33.0700	+	4.75474i	−1.65144	+	0.237441i	−0.747238	+	0.664556i	$0.768621\pi$
$402$		0			0
$403$	0.413146	+	0.154095i	0.0205802	+	0.00767603i
$404$		0			0
$405$	−9.37362	−	17.6745i	−0.465779	−	0.878255i
$406$		0			0
$407$	−0.224021	+	0.167700i	−0.0111043	+	0.00831257i
$408$		0			0
$409$	9.22053	+	14.3474i	0.455926	+	0.709434i	0.990776	−	0.135513i	$-0.0432682\pi$
$409$	9.22053	+	14.3474i	0.455926	+	0.709434i	−0.534850	+	0.844947i	$0.679632\pi$
$410$		0			0
$411$	5.85834	−	19.9517i	0.288971	−	0.984144i
$412$		0			0
$413$	−1.24070	−	1.24070i	−0.0610510	−	0.0610510i
$414$		0			0
$415$	−4.39637	−	15.6759i	−0.215809	−	0.769502i
$416$		0			0
$417$	8.84290	+	16.1946i	0.433039	+	0.793051i
$418$		0			0
$419$	−30.7936	+	19.7898i	−1.50437	+	0.966797i	−0.510070	+	0.860133i	$0.670381\pi$
$419$	−30.7936	+	19.7898i	−1.50437	+	0.966797i	−0.994295	+	0.106664i	$0.965983\pi$
$420$		0			0
$421$	9.01171	+	1.29569i	0.439204	+	0.0631480i	0.358370	−	0.933580i	$-0.383333\pi$
$421$	9.01171	+	1.29569i	0.439204	+	0.0631480i	0.0808339	+	0.996728i	$0.474242\pi$
$422$		0			0
$423$	49.2632	−	10.7166i	2.39526	−	0.521057i
$424$		0			0
$425$	−1.21829	−	6.33957i	−0.0590959	−	0.307514i
$426$		0			0
$427$	0.227612	−	0.304054i	0.0110149	−	0.0147142i
$428$		0			0
$429$	−0.410480	+	0.120528i	−0.0198182	+	0.00581914i
$430$		0			0
$431$	28.3168	+	24.5367i	1.36397	+	1.18189i	0.964169	+	0.265288i	$0.0854672\pi$
$431$	28.3168	+	24.5367i	1.36397	+	1.18189i	0.399804	+	0.916601i	$0.369078\pi$
$432$		0			0
$433$	1.21819	−	17.0325i	0.0585424	−	0.818530i	−0.880351	−	0.474323i	$-0.842693\pi$
$433$	1.21819	−	17.0325i	0.0585424	−	0.818530i	0.938894	−	0.344208i	$-0.111852\pi$
$434$		0			0
$435$	34.1316	+	5.33213i	1.63648	+	0.255656i
$436$		0			0
$437$	−5.60075	+	31.6640i	−0.267920	+	1.51469i
$438$		0			0
$439$	−5.56836	−	2.54298i	−0.265763	−	0.121370i	0.278077	−	0.960559i	$-0.410303\pi$
$439$	−5.56836	−	2.54298i	−0.265763	−	0.121370i	−0.543840	+	0.839189i	$0.683030\pi$
$440$		0			0
$441$	−27.3879	−	31.6073i	−1.30419	−	1.50511i
$442$		0			0
$443$	1.17055	+	16.3664i	0.0556145	+	0.777593i	0.946365	+	0.323100i	$0.104725\pi$
$443$	1.17055	+	16.3664i	0.0556145	+	0.777593i	−0.890750	+	0.454493i	$0.849820\pi$
$444$		0			0
$445$	−31.9554	−	7.35988i	−1.51483	−	0.348892i
$446$		0			0
$447$	−51.2087	−	38.3343i	−2.42209	−	1.81315i
$448$		0			0
$449$	−29.5236	+	13.4830i	−1.39330	+	0.636301i	−0.963766	−	0.266748i	$-0.914051\pi$
$449$	−29.5236	+	13.4830i	−1.39330	+	0.636301i	−0.429538	+	0.903049i	$0.641323\pi$
$450$		0			0
$451$	5.87732	−	9.14528i	0.276752	−	0.430634i
$452$		0			0
$453$	−22.8019	−	30.4598i	−1.07133	−	1.43112i
$454$		0			0
$455$	−0.00248549	−	0.0419148i	−0.000116521	−	0.00196499i
$456$		0			0
$457$	17.7574	−	9.69626i	0.830655	−	0.453572i	−0.00686655	−	0.999976i	$-0.502186\pi$
$457$	17.7574	−	9.69626i	0.830655	−	0.453572i	0.837521	+	0.546405i	$0.184004\pi$
$458$		0			0
$459$	11.5935			0.541136
$460$		0			0
$461$	−20.7321			−0.965591			−0.482796	−	0.875733i	$-0.660379\pi$
$461$	−20.7321			−0.965591			−0.482796	+	0.875733i	$0.660379\pi$
$462$		0			0
$463$	−3.29721	+	1.80041i	−0.153234	+	0.0836723i	−0.554037	−	0.832492i	$-0.686913\pi$
$463$	−3.29721	+	1.80041i	−0.153234	+	0.0836723i	0.400802	+	0.916165i	$0.368731\pi$
$464$		0			0
$465$	−15.7697	+	17.7578i	−0.731300	+	0.823497i
$466$		0			0
$467$	4.06017	+	5.42375i	0.187882	+	0.250981i	0.884585	−	0.466378i	$-0.154441\pi$
$467$	4.06017	+	5.42375i	0.187882	+	0.250981i	−0.696703	+	0.717359i	$0.745351\pi$
$468$		0			0
$469$	0.529630	−	0.824120i	0.0244560	−	0.0380543i
$470$		0			0
$471$	37.3231	−	17.0449i	1.71976	−	0.785386i
$472$		0			0
$473$	2.59818	+	1.94498i	0.119465	+	0.0894301i
$474$		0			0
$475$	−24.7943	−	22.5640i	−1.13764	−	1.03531i
$476$		0			0
$477$	1.12417	+	15.7179i	0.0514721	+	0.719674i
$478$		0			0
$479$	11.4720	+	13.2394i	0.524169	+	0.604924i	0.954670	−	0.297667i	$-0.0962084\pi$
$479$	11.4720	+	13.2394i	0.524169	+	0.604924i	−0.430500	+	0.902590i	$0.641663\pi$
$480$		0			0
$481$	−0.0276634	−	0.0126335i	−0.00126134	−	0.000576037i
$482$		0			0
$483$	−0.543643	−	2.09989i	−0.0247366	−	0.0955483i
$484$		0			0
$485$	−1.47042	+	9.41232i	−0.0667684	+	0.427392i
$486$		0			0
$487$	1.32648	−	18.5466i	0.0601086	−	0.840429i	−0.874562	−	0.484914i	$-0.838851\pi$
$487$	1.32648	−	18.5466i	0.0601086	−	0.840429i	0.934671	−	0.355515i	$-0.115694\pi$
$488$		0			0
$489$	11.3776	+	9.85872i	0.514512	+	0.445827i
$490$		0			0
$491$	−16.4427	+	4.82800i	−0.742047	+	0.217885i	−0.630840	−	0.775913i	$-0.717290\pi$
$491$	−16.4427	+	4.82800i	−0.742047	+	0.217885i	−0.111206	+	0.993797i	$0.535471\pi$
$492$		0			0
$493$	−3.98584	+	5.32446i	−0.179513	+	0.239802i
$494$		0			0
$495$	1.28181	−	15.3024i	0.0576132	−	0.687792i
$496$		0			0
$497$	−2.15918	+	0.469701i	−0.0968525	+	0.0210690i
$498$		0			0
$499$	31.5006	+	4.52911i	1.41016	+	0.202751i	0.804964	−	0.593324i	$-0.202185\pi$
$499$	31.5006	+	4.52911i	1.41016	+	0.202751i	0.605199	+	0.796074i	$0.293094\pi$
$500$		0			0
$501$	−7.72670	+	4.96565i	−0.345203	+	0.221849i
$502$		0			0
$503$	17.0520	+	31.2284i	0.760310	+	1.39240i	0.914592	+	0.404377i	$0.132512\pi$
$503$	17.0520	+	31.2284i	0.760310	+	1.39240i	−0.154282	+	0.988027i	$0.549307\pi$
$504$		0			0
$505$	4.69036	+	2.63573i	0.208718	+	0.117289i
$506$		0			0
$507$	27.5353	+	27.5353i	1.22288	+	1.22288i
$508$		0			0
$509$	4.59053	−	15.6339i	0.203471	−	0.692960i	−0.793015	−	0.609203i	$-0.791490\pi$
$509$	4.59053	−	15.6339i	0.203471	−	0.692960i	0.996486	−	0.0837577i	$-0.0266922\pi$
$510$		0			0
$511$	0.128625	+	0.200145i	0.00569005	+	0.00885389i
$512$		0			0
$513$	48.1974	−	36.0802i	2.12797	−	1.59298i
$514$		0			0
$515$	12.3367	−	40.1986i	0.543621	−	1.77136i
$516$		0			0
$517$	9.02862	+	3.36750i	0.397078	+	0.148103i
$518$		0			0
$519$	13.0812	−	1.88080i	0.574203	−	0.0825579i
$520$		0			0
$521$	2.03226	+	6.92125i	0.0890350	+	0.303225i	0.991956	−	0.126580i	$-0.0404002\pi$
$521$	2.03226	+	6.92125i	0.0890350	+	0.303225i	−0.902921	+	0.429806i	$0.858582\pi$
$522$		0			0
$523$	−1.66013	+	0.118735i	−0.0725923	+	0.00519191i	−0.107588	−	0.994196i	$-0.534313\pi$
$523$	−1.66013	+	0.118735i	−0.0725923	+	0.00519191i	0.0349958	+	0.999387i	$0.488858\pi$
$524$		0			0
$525$	2.15371	+	0.689752i	0.0939957	+	0.0301032i
$526$		0			0
$527$	−1.59790	−	4.28414i	−0.0696057	−	0.186620i
$528$		0			0
$529$	−4.73473	+	22.5074i	−0.205858	+	0.978582i
$530$		0			0
$531$	28.9701	−	63.4356i	1.25719	−	2.75287i
$532$		0			0
$533$	1.17842	+	0.0842819i	0.0510428	+	0.00365066i
$534$		0			0
$535$	−11.0387	+	23.4131i	−0.477246	+	1.01224i
$536$		0			0
$537$	25.3976	+	13.8681i	1.09599	+	0.598454i
$538$		0			0
$539$	−1.13763	−	7.91241i	−0.0490013	−	0.340812i
$540$		0			0
$541$	13.3108	+	29.1466i	0.572277	+	1.25311i	0.945576	+	0.325401i	$0.105499\pi$
$541$	13.3108	+	29.1466i	0.572277	+	1.25311i	−0.373299	+	0.927711i	$0.621773\pi$
$542$		0			0
$543$	1.21769	+	5.59762i	0.0522560	+	0.240217i
$544$		0			0
$545$	9.71645	−	12.6556i	0.416207	−	0.542108i
$546$		0			0
$547$	12.1091	+	2.63418i	0.517749	+	0.112629i	0.463844	−	0.885917i	$-0.346470\pi$
$547$	12.1091	+	2.63418i	0.517749	+	0.112629i	0.0539046	+	0.998546i	$0.482833\pi$
$548$		0			0
$549$	14.4842	+	4.25294i	0.618170	+	0.181511i
$550$		0			0
$551$			34.5398i			1.47144i
$552$		0			0
$553$	0.260196	−	0.260196i	0.0110647	−	0.0110647i
$554$		0			0
$555$	1.17222	−	1.14403i	0.0497579	−	0.0485612i
$556$		0			0
$557$	5.27120	−	24.2313i	0.223348	−	1.02671i	−0.719759	−	0.694224i	$-0.755748\pi$
$557$	5.27120	−	24.2313i	0.223348	−	1.02671i	0.943107	−	0.332490i	$-0.107889\pi$
$558$		0			0
$559$	−0.0501964	+	0.349124i	−0.00212308	+	0.0147664i
$560$		0			0
$561$	3.73197	+	2.39839i	0.157564	+	0.101260i
$562$		0			0
$563$	−15.9173	+	42.6761i	−0.670836	+	1.79858i	−0.0724527	+	0.997372i	$0.523083\pi$
$563$	−15.9173	+	42.6761i	−0.670836	+	1.79858i	−0.598384	+	0.801210i	$0.704190\pi$
$564$		0			0
$565$	15.0307	−	6.64443i	0.632347	−	0.279533i
$566$		0			0
$567$	−0.646673	+	1.18429i	−0.0271577	+	0.0497357i
$568$		0			0
$569$	−14.9960	+	17.3063i	−0.628664	+	0.725517i	−0.977328	−	0.211731i	$-0.932090\pi$
$569$	−14.9960	+	17.3063i	−0.628664	+	0.725517i	0.348664	+	0.937248i	$0.386635\pi$
$570$		0			0
$571$	10.7569	−	9.32090i	0.450162	−	0.390068i	−0.400062	−	0.916488i	$-0.631012\pi$
$571$	10.7569	−	9.32090i	0.450162	−	0.390068i	0.850225	+	0.526420i	$0.176466\pi$
$572$		0			0
$573$	20.1854	−	7.52875i	0.843255	−	0.314518i
$574$		0			0
$575$	−17.2047	−	16.7032i	−0.717486	−	0.696573i
$576$		0			0
$577$	−44.1127	+	16.4532i	−1.83644	+	0.684955i	−0.848688	+	0.528893i	$0.822607\pi$
$577$	−44.1127	+	16.4532i	−1.83644	+	0.684955i	−0.987747	+	0.156062i	$0.950120\pi$
$578$		0			0
$579$	−19.7013	+	17.0713i	−0.818760	+	0.709460i
$580$		0			0
$581$	−0.719084	+	0.829867i	−0.0298326	+	0.0344287i
$582$		0			0
$583$	−1.44347	+	2.64351i	−0.0597822	+	0.109483i
$584$		0			0
$585$	1.52635	−	0.674734i	0.0631069	−	0.0278968i
$586$		0			0
$587$	10.3161	−	27.6585i	0.425790	−	1.14159i	−0.530118	−	0.847924i	$-0.677853\pi$
$587$	10.3161	−	27.6585i	0.425790	−	1.14159i	0.955909	−	0.293664i	$-0.0948748\pi$
$588$		0			0
$589$	−19.9757	−	12.8376i	−0.823084	−	0.528964i
$590$		0			0
$591$	8.06735	−	56.1096i	0.331846	−	2.30804i
$592$		0			0
$593$	9.67906	−	44.4939i	0.397471	−	1.82715i	−0.147963	−	0.988993i	$-0.547272\pi$
$593$	9.67906	−	44.4939i	0.397471	−	1.82715i	0.545434	−	0.838154i	$-0.316365\pi$
$594$		0			0
$595$	−0.311600	+	0.304106i	−0.0127743	+	0.0124671i
$596$		0			0
$597$	22.4585	−	22.4585i	0.919166	−	0.919166i
$598$		0			0
$599$			10.1749i			0.415736i	0.978157	+	0.207868i	$0.0666525\pi$
$599$			10.1749i			0.415736i	−0.978157	+	0.207868i	$0.933347\pi$
$600$		0			0
$601$	15.0790	+	4.42758i	0.615084	+	0.180605i	0.574410	−	0.818568i	$-0.305231\pi$
$601$	15.0790	+	4.42758i	0.615084	+	0.180605i	0.0406735	+	0.999172i	$0.487050\pi$
$602$		0			0
$603$	38.0459	+	8.27638i	1.54935	+	0.337040i
$604$		0			0
$605$	−13.1914	+	17.1818i	−0.536308	+	0.698539i
$606$		0			0
$607$	1.16567	+	5.35851i	0.0473132	+	0.217495i	0.994733	−	0.102497i	$-0.0326833\pi$
$607$	1.16567	+	5.35851i	0.0473132	+	0.217495i	−0.947420	+	0.319992i	$0.896320\pi$
$608$		0			0
$609$	−0.967899	−	2.11940i	−0.0392212	−	0.0858825i
$610$		0			0
$611$	0.149036	+	1.03657i	0.00602935	+	0.0419351i
$612$		0			0
$613$	−33.4241	−	18.2510i	−1.34999	−	0.737149i	−0.368674	−	0.929559i	$-0.620188\pi$
$613$	−33.4241	−	18.2510i	−1.34999	−	0.737149i	−0.981315	+	0.192410i	$0.938370\pi$
$614$		0			0
$615$	−27.1356	+	57.5546i	−1.09421	+	2.32083i
$616$		0			0
$617$	0.736836	+	0.0526995i	0.0296639	+	0.00212160i	0.0861632	−	0.996281i	$-0.472539\pi$
$617$	0.736836	+	0.0526995i	0.0296639	+	0.00212160i	−0.0564994	+	0.998403i	$0.517994\pi$
$618$		0			0
$619$	12.4387	−	27.2371i	0.499955	−	1.09475i	−0.476528	−	0.879159i	$-0.658105\pi$
$619$	12.4387	−	27.2371i	0.499955	−	1.09475i	0.976484	−	0.215591i	$-0.0691676\pi$
$620$		0			0
$621$	35.2891	−	24.6814i	1.41610	−	0.990432i
$622$		0			0
$623$	0.772904	+	2.07224i	0.0309658	+	0.0830224i
$624$		0			0
$625$	24.3017	−	5.86767i	0.972066	−	0.234707i
$626$		0			0
$627$	22.9790	−	1.64349i	0.917691	−	0.0656346i
$628$		0			0
$629$	0.0888461	+	0.302582i	0.00354253	+	0.0120647i
$630$		0			0
$631$	−32.4100	+	4.65985i	−1.29022	+	0.185506i	−0.753048	−	0.657966i	$-0.771417\pi$
$631$	−32.4100	+	4.65985i	−1.29022	+	0.185506i	−0.537174	+	0.843472i	$0.680508\pi$
$632$		0			0
$633$	−1.39904	−	0.521816i	−0.0556069	−	0.0207403i
$634$		0			0
$635$	13.6912	−	44.6120i	0.543318	−	1.77037i
$636$		0			0
$637$	0.695460	−	0.520614i	0.0275551	−	0.0206275i
$638$		0			0
$639$	−47.4813	−	73.8823i	−1.87833	−	2.92274i
$640$		0			0
$641$	0.456414	−	1.55440i	0.0180273	−	0.0613952i	−0.949988	−	0.312286i	$-0.898905\pi$
$641$	0.456414	−	1.55440i	0.0180273	−	0.0613952i	0.968015	+	0.250891i	$0.0807235\pi$
$642$		0			0
$643$	−24.8038	−	24.8038i	−0.978164	−	0.978164i	0.0216022	−	0.999767i	$-0.493123\pi$
$643$	−24.8038	−	24.8038i	−0.978164	−	0.978164i	−0.999767	+	0.0216022i	$0.993123\pi$
$644$		0			0
$645$	−16.5612	−	9.30650i	−0.652095	−	0.366443i
$646$		0			0
$647$	10.7153	+	19.6235i	0.421260	+	0.771480i	0.998999	−	0.0447416i	$-0.0142464\pi$
$647$	10.7153	+	19.6235i	0.421260	+	0.771480i	−0.577738	+	0.816222i	$0.696065\pi$
$648$		0			0
$649$	11.2134	−	7.20640i	0.440164	−	0.282876i
$650$		0			0
$651$	1.58548	+	0.227957i	0.0621398	+	0.00893435i
$652$		0			0
$653$	−42.5884	+	9.26453i	−1.66661	+	0.362549i	−0.944317	−	0.329037i	$-0.893276\pi$
$653$	−42.5884	+	9.26453i	−1.66661	+	0.362549i	−0.722294	+	0.691586i	$0.756912\pi$
$654$		0			0
$655$	−3.27996	+	39.1564i	−0.128159	+	1.52997i
$656$		0			0
$657$	−5.66671	+	7.56983i	−0.221079	+	0.295327i
$658$		0			0
$659$	−12.0003	+	3.52361i	−0.467466	+	0.137260i	−0.506978	−	0.861959i	$-0.669238\pi$
$659$	−12.0003	+	3.52361i	−0.467466	+	0.137260i	0.0395127	+	0.999219i	$0.487419\pi$
$660$		0			0
$661$	28.8180	+	24.9709i	1.12089	+	0.971256i	0.999771	−	0.0213823i	$-0.00680672\pi$
$661$	28.8180	+	24.9709i	1.12089	+	0.971256i	0.121118	+	0.992638i	$0.461352\pi$
$662$		0			0
$663$	−0.0343934	+	0.480883i	−0.00133573	+	0.0186759i
$664$		0			0
$665$	−0.349001	+	2.23399i	−0.0135337	+	0.0866305i
$666$		0			0
$667$	−0.797109	+	24.6925i	−0.0308642	+	0.956098i
$668$		0			0
$669$	21.2824	+	9.71936i	0.822826	+	0.375772i
$670$		0			0
$671$	1.88948	+	2.18058i	0.0729427	+	0.0841804i
$672$		0			0
$673$	2.50882	+	35.0779i	0.0967080	+	1.35215i	0.781723	+	0.623626i	$0.214341\pi$
$673$	2.50882	+	35.0779i	0.0967080	+	1.35215i	−0.685015	+	0.728529i	$0.740204\pi$
$674$		0			0
$675$	2.11202	+	44.8474i	0.0812916	+	1.72618i
$676$		0			0
$677$	32.3700	+	24.2319i	1.24408	+	0.931306i	0.999268	−	0.0382644i	$-0.0121829\pi$
$677$	32.3700	+	24.2319i	1.24408	+	0.931306i	0.244812	+	0.969571i	$0.421274\pi$
$678$		0			0
$679$	0.584459	−	0.266914i	0.0224295	−	0.0102432i
$680$		0			0
$681$	−35.1407	+	54.6800i	−1.34659	+	2.09534i
$682$		0			0
$683$	18.3908	+	24.5672i	0.703704	+	0.940039i	0.999886	−	0.0150926i	$-0.00480429\pi$
$683$	18.3908	+	24.5672i	0.703704	+	0.940039i	−0.296182	+	0.955132i	$0.595713\pi$
$684$		0			0
$685$	−10.2948	+	11.5927i	−0.393344	+	0.442934i
$686$		0			0
$687$	−0.523455	+	0.285828i	−0.0199710	+	0.0109050i
$688$		0			0
$689$	−0.327327			−0.0124702
$690$		0			0
$691$	35.6433			1.35594			0.677968	−	0.735091i	$-0.262861\pi$
$691$	35.6433			1.35594			0.677968	+	0.735091i	$0.262861\pi$
$692$		0			0
$693$	−0.909011	+	0.496358i	−0.0345305	+	0.0188551i
$694$		0			0
$695$	−0.814369	−	13.7334i	−0.0308908	−	0.520936i
$696$		0			0
$697$	−7.34168	−	9.80733i	−0.278086	−	0.371479i
$698$		0			0
$699$	33.0899	−	51.4888i	1.25157	−	1.94749i
$700$		0			0
$701$	35.9865	−	16.4345i	1.35919	−	0.620723i	0.403471	−	0.914993i	$-0.367804\pi$
$701$	35.9865	−	16.4345i	1.35919	−	0.620723i	0.955722	+	0.294270i	$0.0950765\pi$
$702$		0			0
$703$	1.31103	+	0.981424i	0.0494464	+	0.0370151i
$704$		0			0
$705$	−54.9640	−	12.6592i	−2.07006	−	0.476772i
$706$		0			0
$707$	−0.0258870	−	0.361948i	−0.000973582	−	0.0136125i
$708$		0			0
$709$	24.5088	+	28.2846i	0.920446	+	1.06225i	0.997869	+	0.0652530i	$0.0207854\pi$
$709$	24.5088	+	28.2846i	0.920446	+	1.06225i	−0.0774227	+	0.996998i	$0.524669\pi$
$710$		0			0
$711$	13.3035	+	6.07552i	0.498921	+	0.227850i
$712$		0			0
$713$	−13.9844	−	9.63861i	−0.523719	−	0.360969i
$714$		0			0
$715$	0.315152	+	0.0492339i	0.0117860	+	0.00184124i
$716$		0			0
$717$	4.19565	−	58.6629i	0.156690	−	2.19081i
$718$		0			0
$719$	5.50407	+	4.76930i	0.205267	+	0.177865i	0.751428	−	0.659816i	$-0.229366\pi$
$719$	5.50407	+	4.76930i	0.205267	+	0.177865i	−0.546160	+	0.837681i	$0.683911\pi$
$720$		0			0
$721$	−2.72115	+	0.799003i	−0.101341	+	0.0297564i
$722$		0			0
$723$	−43.4895	+	58.0952i	−1.61739	+	2.16058i
$724$		0			0
$725$	−21.3229	−	14.4486i	−0.791914	−	0.536608i
$726$		0			0
$727$	−19.0635	+	4.14700i	−0.707025	+	0.153804i	−0.551679	−	0.834056i	$-0.686013\pi$
$727$	−19.0635	+	4.14700i	−0.707025	+	0.153804i	−0.155345	+	0.987860i	$0.549649\pi$
$728$		0			0
$729$	26.8819	+	3.86504i	0.995626	+	0.143149i
$730$		0			0
$731$	3.07688	−	1.97739i	0.113802	−	0.0731364i
$732$		0			0
$733$	−6.60616	−	12.0983i	−0.244004	−	0.446860i	0.726761	−	0.686890i	$-0.241025\pi$
$733$	−6.60616	−	12.0983i	−0.244004	−	0.446860i	−0.970765	+	0.240030i	$0.922843\pi$
$734$		0			0
$735$	12.6348	+	45.0514i	0.466041	+	1.66174i
$736$		0			0
$737$	5.26230	+	5.26230i	0.193839	+	0.193839i
$738$		0			0
$739$	5.65340	−	19.2537i	0.207964	−	0.708259i	−0.787769	−	0.615971i	$-0.788764\pi$
$739$	5.65340	−	19.2537i	0.207964	−	0.708259i	0.995732	−	0.0922879i	$-0.0294180\pi$
$740$		0			0
$741$	1.35358	+	2.10621i	0.0497249	+	0.0773735i
$742$		0			0
$743$	0.135904	−	0.101736i	0.00498584	−	0.00373235i	−0.596782	−	0.802404i	$-0.703554\pi$
$743$	0.135904	−	0.101736i	0.00498584	−	0.00373235i	0.601768	+	0.798671i	$0.294463\pi$
$744$		0			0
$745$	22.3462	+	42.1353i	0.818703	+	1.54372i
$746$		0			0
$747$	−40.8914	−	15.2517i	−1.49614	−	0.558030i
$748$		0			0
$749$	1.72806	−	0.248457i	0.0631419	−	0.00907843i
$750$		0			0
$751$	6.09157	+	20.7460i	0.222285	+	0.757032i	0.992818	+	0.119633i	$0.0381716\pi$
$751$	6.09157	+	20.7460i	0.222285	+	0.757032i	−0.770534	+	0.637399i	$0.780010\pi$
$752$		0			0
$753$	−16.7137	+	1.19539i	−0.609082	+	0.0435624i
$754$		0			0
$755$	5.69251	+	27.7923i	0.207172	+	1.01147i
$756$		0			0
$757$	−9.83911	−	26.3797i	−0.357608	−	0.958785i	−0.983824	−	0.179136i	$-0.942670\pi$
$757$	−9.83911	−	26.3797i	−0.357608	−	0.958785i	0.626216	−	0.779650i	$-0.284603\pi$
$758$		0			0
$759$	16.4656	−	0.644623i	0.597664	−	0.0233983i
$760$		0			0
$761$	11.3379	−	24.8265i	0.410998	−	0.899960i	−0.585038	−	0.811006i	$-0.698920\pi$
$761$	11.3379	−	24.8265i	0.410998	−	0.899960i	0.996036	−	0.0889539i	$-0.0283524\pi$
$762$		0			0
$763$	−1.07338	−	0.0767699i	−0.0388591	−	0.00277926i
$764$		0			0
$765$	−15.6526	−	7.37985i	−0.565922	−	0.266819i
$766$		0			0
$767$	1.27140	+	0.694236i	0.0459075	+	0.0250674i
$768$		0			0
$769$	3.36066	+	23.3739i	0.121189	+	0.842885i	0.956213	+	0.292672i	$0.0945445\pi$
$769$	3.36066	+	23.3739i	0.121189	+	0.842885i	−0.835024	+	0.550213i	$0.814546\pi$
$770$		0			0
$771$	24.6214	+	53.9134i	0.886718	+	1.94164i
$772$		0			0
$773$	9.30821	+	42.7892i	0.334793	+	1.53902i	0.769618	+	0.638504i	$0.220447\pi$
$773$	9.30821	+	42.7892i	0.334793	+	1.53902i	−0.434825	+	0.900515i	$0.643190\pi$
$774$		0			0
$775$	16.2814	−	6.96169i	0.584846	−	0.250071i
$776$		0			0
$777$	−0.107949	−	0.0234828i	−0.00387263	−	0.000842440i
$778$		0			0
$779$	−61.0431	−	17.9239i	−2.18709	−	0.642189i
$780$		0			0
$781$		−	16.7863i		−	0.600662i
$782$		0			0
$783$	32.7085	−	32.7085i	1.16891	−	1.16891i
$784$		0			0
$785$	−30.5904	−	0.372322i	−1.09182	−	0.0132887i
$786$		0			0
$787$	8.66089	−	39.8135i	0.308728	−	1.41920i	−0.517414	−	0.855735i	$-0.673105\pi$
$787$	8.66089	−	39.8135i	0.308728	−	1.41920i	0.826142	−	0.563462i	$-0.190531\pi$
$788$		0			0
$789$	9.67662	−	67.3024i	0.344497	−	2.39603i
$790$		0			0
$791$	−0.932442	−	0.599244i	−0.0331538	−	0.0213067i
$792$		0			0
$793$	−0.109580	+	0.293797i	−0.00389132	+	0.0104330i
$794$		0			0
$795$	6.36148	−	16.4418i	0.225619	−	0.583132i
$796$		0			0
$797$	13.7661	−	25.2107i	0.487619	−	0.893008i	−0.511806	−	0.859101i	$-0.671023\pi$
$797$	13.7661	−	25.2107i	0.487619	−	0.893008i	0.999425	−	0.0339070i	$-0.0107950\pi$
$798$		0			0
$799$	7.11133	−	8.20691i	0.251581	−	0.290340i
$800$		0			0
$801$	−66.4333	+	57.5648i	−2.34730	+	2.03395i
$802$		0			0
$803$	−1.69340	+	0.631607i	−0.0597590	+	0.0222889i
$804$		0			0
$805$	−0.301057	+	1.58903i	−0.0106109	+	0.0560059i
$806$		0			0
$807$	−28.8340	+	10.7545i	−1.01500	+	0.378577i
$808$		0			0
$809$	8.98726	−	7.78750i	0.315975	−	0.273794i	−0.482404	−	0.875949i	$-0.660236\pi$
$809$	8.98726	−	7.78750i	0.315975	−	0.273794i	0.798379	+	0.602155i	$0.205691\pi$
$810$		0			0
$811$	−11.2694	+	13.0056i	−0.395722	+	0.456687i	−0.918289	−	0.395911i	$-0.870429\pi$
$811$	−11.2694	+	13.0056i	−0.395722	+	0.456687i	0.522567	+	0.852598i	$0.324974\pi$
$812$		0			0
$813$	−25.2451	+	46.2329i	−0.885384	+	1.62146i
$814$		0			0
$815$	−4.53833	−	10.2664i	−0.158971	−	0.359616i
$816$		0			0
$817$	6.63763	−	17.7962i	0.232221	−	0.622610i
$818$		0			0
$819$	−0.0946884	−	0.0608525i	−0.00330868	−	0.00212636i
$820$		0			0
$821$	5.99131	−	41.6705i	0.209098	−	1.45431i	−0.567011	−	0.823710i	$-0.691900\pi$
$821$	5.99131	−	41.6705i	0.209098	−	1.45431i	0.776109	−	0.630599i	$-0.217191\pi$
$822$		0			0
$823$	−5.06328	+	23.2755i	−0.176495	+	0.811334i	0.800713	+	0.599048i	$0.204454\pi$
$823$	−5.06328	+	23.2755i	−0.176495	+	0.811334i	−0.977208	+	0.212285i	$0.931909\pi$
$824$		0			0
$825$	−8.59792	+	14.8734i	−0.299341	+	0.517827i
$826$		0			0
$827$	−32.9666	+	32.9666i	−1.14636	+	1.14636i	−0.159099	+	0.987263i	$0.550859\pi$
$827$	−32.9666	+	32.9666i	−1.14636	+	1.14636i	−0.987263	+	0.159099i	$0.949141\pi$
$828$		0			0
$829$			1.95861i			0.0680254i	0.999421	+	0.0340127i	$0.0108287\pi$
$829$			1.95861i			0.0680254i	−0.999421	+	0.0340127i	$0.989171\pi$
$830$		0			0
$831$	53.0318	+	15.5715i	1.83965	+	0.540171i
$832$		0			0
$833$	−8.80255	−	1.91488i	−0.304990	−	0.0663466i
$834$		0			0
$835$	6.78980	−	0.892024i	0.234971	−	0.0308698i
$836$		0			0
$837$	6.75965	+	31.0736i	0.233648	+	1.07406i
$838$		0			0
$839$	11.4718	+	25.1198i	0.396052	+	0.867233i	0.997655	+	0.0684378i	$0.0218015\pi$
$839$	11.4718	+	25.1198i	0.396052	+	0.867233i	−0.601604	+	0.798795i	$0.705471\pi$
$840$		0			0
$841$	−0.350491	−	2.43772i	−0.0120859	−	0.0840593i
$842$		0			0
$843$	−35.8882	−	19.5964i	−1.23605	−	0.674936i
$844$		0			0
$845$	−9.81459	−	27.3251i	−0.337632	−	0.940011i
$846$		0			0
$847$	1.45727	+	0.104226i	0.0500724	+	0.00358125i
$848$		0			0
$849$	4.69590	−	10.2826i	0.161163	−	0.352897i
$850$		0			0
$851$	0.914607	+	0.731877i	0.0313523	+	0.0250884i
$852$		0			0
$853$	2.71350	+	7.27519i	0.0929086	+	0.249098i	0.975089	−	0.221814i	$-0.0711978\pi$
$853$	2.71350	+	7.27519i	0.0929086	+	0.249098i	−0.882180	+	0.470912i	$0.843925\pi$
$854$		0			0
$855$	−88.0396	+	18.0326i	−3.01089	+	0.616700i
$856$		0			0
$857$	−54.2841	+	3.88248i	−1.85431	+	0.132623i	−0.953462	−	0.301513i	$-0.902508\pi$
$857$	−54.2841	+	3.88248i	−1.85431	+	0.132623i	−0.900848	+	0.434136i	$0.857054\pi$
$858$		0			0
$859$	−11.7107	−	39.8829i	−0.399563	−	1.36079i	−0.876311	−	0.481746i	$-0.840003\pi$
$859$	−11.7107	−	39.8829i	−0.399563	−	1.36079i	0.476748	−	0.879040i	$-0.341815\pi$
$860$		0			0
$861$	4.24795	−	0.610763i	0.144770	−	0.0208148i
$862$		0			0
$863$	33.5744	+	12.5226i	1.14289	+	0.426275i	0.848387	−	0.529377i	$-0.177574\pi$
$863$	33.5744	+	12.5226i	1.14289	+	0.426275i	0.294500	+	0.955651i	$0.404847\pi$
$864$		0			0
$865$	−9.42003	−	2.89096i	−0.320291	−	0.0982955i
$866$		0			0
$867$	−36.8121	+	27.5572i	−1.25021	+	0.935892i
$868$		0			0
$869$	1.51130	+	2.35163i	0.0512675	+	0.0797737i
$870$		0			0
$871$	−0.227858	+	0.776012i	−0.00772066	+	0.0262941i
$872$		0			0
$873$	18.0575	+	18.0575i	0.611155	+	0.611155i
$874$		0			0
$875$	−1.23315	−	1.14997i	−0.0416881	−	0.0388762i
$876$		0			0
$877$	−7.60948	−	13.9357i	−0.256954	−	0.470576i	0.717076	−	0.696995i	$-0.245480\pi$
$877$	−7.60948	−	13.9357i	−0.256954	−	0.470576i	−0.974030	+	0.226419i	$0.927298\pi$
$878$		0			0
$879$	−69.3740	+	44.5840i	−2.33993	+	1.50378i
$880$		0			0
$881$	38.9474	+	5.59980i	1.31217	+	0.188662i	0.762647	−	0.646815i	$-0.223899\pi$
$881$	38.9474	+	5.59980i	1.31217	+	0.188662i	0.549526	+	0.835477i	$0.314808\pi$
$882$		0			0
$883$	−14.7260	+	3.20344i	−0.495569	+	0.107804i	−0.453402	−	0.891306i	$-0.649790\pi$
$883$	−14.7260	+	3.20344i	−0.495569	+	0.107804i	−0.0421671	+	0.999111i	$0.513426\pi$
$884$		0			0
$885$	−59.5811	+	50.3709i	−2.00280	+	1.69320i
$886$		0			0
$887$	−6.92191	+	9.24659i	−0.232415	+	0.310470i	−0.901554	−	0.432668i	$-0.857572\pi$
$887$	−6.92191	+	9.24659i	−0.232415	+	0.310470i	0.669138	+	0.743138i	$0.266663\pi$
$888$		0			0
$889$	−3.01991	+	0.886727i	−0.101285	+	0.0297399i
$890$		0			0
$891$	−7.74691	−	6.71273i	−0.259531	−	0.224885i
$892$		0			0
$893$	4.02307	−	56.2499i	0.134627	−	1.88233i
$894$		0			0
$895$	−12.7186	−	17.4282i	−0.425136	−	0.582562i
$896$		0			0
$897$	0.919068	+	1.53697i	0.0306868	+	0.0513179i
$898$		0			0
$899$	−16.5950	−	7.57867i	−0.553473	−	0.252763i
$900$		0			0
$901$	2.22275	+	2.56519i	0.0740506	+	0.0854590i
$902$		0			0
$903$	0.0914044	+	1.27800i	0.00304175	+	0.0425292i
$904$		0			0
$905$	0.958634	−	4.16222i	0.0318661	−	0.138357i
$906$		0			0
$907$	2.15455	+	1.61287i	0.0715406	+	0.0535546i	0.634449	−	0.772964i	$-0.281227\pi$
$907$	2.15455	+	1.61287i	0.0715406	+	0.0535546i	−0.562909	+	0.826519i	$0.690318\pi$
$908$		0			0
$909$	13.1191	−	5.99130i	0.435134	−	0.198719i
$910$		0			0
$911$	−22.6715	+	35.2776i	−0.751141	+	1.16880i	0.229562	+	0.973294i	$0.426270\pi$
$911$	−22.6715	+	35.2776i	−0.751141	+	1.16880i	−0.980703	+	0.195504i	$0.937366\pi$
$912$		0			0
$913$	−4.99903	−	6.67792i	−0.165444	−	0.221007i
$914$		0			0
$915$	−12.6279	−	11.2141i	−0.417467	−	0.370728i
$916$		0			0
$917$	2.32602	−	1.27010i	0.0768118	−	0.0419424i
$918$		0			0
$919$	−38.2781			−1.26268			−0.631339	−	0.775507i	$-0.717494\pi$
$919$	−38.2781			−1.26268			−0.631339	+	0.775507i	$0.717494\pi$
$920$		0			0
$921$	13.8395			0.456027
$922$		0			0
$923$	1.60113	−	0.874285i	0.0527020	−	0.0287774i
$924$		0			0
$925$	−1.15430	+	0.398809i	−0.0379533	+	0.0131128i
$926$		0			0
$927$	−67.5498	−	90.2360i	−2.21863	−	2.96374i
$928$		0			0
$929$	12.3302	−	19.1862i	0.404541	−	0.629478i	−0.577888	−	0.816116i	$-0.696123\pi$
$929$	12.3302	−	19.1862i	0.404541	−	0.629478i	0.982429	+	0.186638i	$0.0597593\pi$
$930$		0			0
$931$	−42.5542	+	19.4338i	−1.39466	+	0.636918i
$932$		0			0
$933$	56.8206	+	42.5353i	1.86022	+	1.39254i
$934$		0			0
$935$	−1.75424	−	2.80411i	−0.0573698	−	0.0917042i
$936$		0			0
$937$	−3.35152	−	46.8604i	−0.109489	−	1.53086i	−0.694296	−	0.719690i	$-0.744284\pi$
$937$	−3.35152	−	46.8604i	−0.109489	−	1.53086i	0.584806	−	0.811173i	$-0.301170\pi$
$938$		0			0
$939$	−22.0210	−	25.4136i	−0.718629	−	0.829342i
$940$		0			0
$941$	5.73984	+	2.62130i	0.187113	+	0.0854518i	0.506769	−	0.862082i	$-0.330840\pi$
$941$	5.73984	+	2.62130i	0.187113	+	0.0854518i	−0.319655	+	0.947534i	$0.603567\pi$
$942$		0			0
$943$	−43.2261	−	14.2225i	−1.40764	−	0.463150i
$944$		0			0
$945$	2.44605	−	1.78505i	0.0795699	−	0.0580678i
$946$		0			0
$947$	−1.23966	+	17.3327i	−0.0402836	+	0.563238i	0.936729	+	0.350056i	$0.113837\pi$
$947$	−1.23966	+	17.3327i	−0.0402836	+	0.563238i	−0.977012	+	0.213182i	$0.931617\pi$
$948$		0			0
$949$	−0.148443	−	0.128626i	−0.00481865	−	0.00417539i
$950$		0			0
$951$	4.25002	−	1.24792i	0.137816	−	0.0404665i
$952$		0			0
$953$	19.4995	−	26.0483i	0.631651	−	0.843787i	−0.364522	−	0.931195i	$-0.618768\pi$
$953$	19.4995	−	26.0483i	0.631651	−	0.843787i	0.996173	+	0.0874082i	$0.0278584\pi$
$954$		0			0
$955$	−16.0069	−	1.34083i	−0.517971	−	0.0433881i
$956$		0			0
$957$	17.2955	−	3.76242i	0.559085	−	0.121622i
$958$		0			0
$959$	1.03504	+	0.148816i	0.0334231	+	0.00480551i
$960$		0			0
$961$	−15.5279	+	9.97915i	−0.500899	+	0.321908i
$962$		0			0
$963$	33.2543	+	60.9007i	1.07160	+	1.96250i
$964$		0			0
$965$	18.7147	−	5.24859i	0.602447	−	0.168958i
$966$		0			0
$967$	36.6412	+	36.6412i	1.17830	+	1.17830i	0.980177	+	0.198124i	$0.0634849\pi$
$967$	36.6412	+	36.6412i	1.17830	+	1.17830i	0.198124	+	0.980177i	$0.436515\pi$
$968$		0			0
$969$	7.31429	−	24.9102i	0.234969	−	0.800231i
$970$		0			0
$971$	−11.0137	−	17.1377i	−0.353447	−	0.549974i	0.618317	−	0.785928i	$-0.287815\pi$
$971$	−11.0137	−	17.1377i	−0.353447	−	0.549974i	−0.971764	+	0.235955i	$0.924178\pi$
$972$		0			0
$973$	−0.742812	+	0.556062i	−0.0238135	+	0.0178265i
$974$		0			0
$975$	−1.86648	−	0.0454415i	−0.0597753	−	0.00145529i
$976$		0			0
$977$	−25.2326	−	9.41129i	−0.807264	−	0.301094i	−0.0882577	−	0.996098i	$-0.528130\pi$
$977$	−25.2326	−	9.41129i	−0.807264	−	0.301094i	−0.719006	+	0.695004i	$0.755403\pi$
$978$		0			0
$979$	−16.6306	+	2.39111i	−0.531515	+	0.0764203i
$980$		0			0
$981$	−12.0499	−	41.0383i	−0.384725	−	1.31025i
$982$		0			0
$983$	38.0665	−	2.72257i	1.21413	−	0.0868365i	0.550461	−	0.834861i	$-0.314452\pi$
$983$	38.0665	−	2.72257i	1.21413	−	0.0868365i	0.663671	+	0.748024i	$0.268997\pi$
$984$		0			0
$985$	−23.2815	+	35.2753i	−0.741810	+	1.12396i
$986$		0			0
$987$	1.32941	+	3.56430i	0.0423157	+	0.113453i
$988$		0			0
$989$	5.15595	−	12.5693i	0.163950	−	0.399681i
$990$		0			0
$991$	5.32760	−	11.6658i	0.169237	−	0.370577i	−0.805942	−	0.591994i	$-0.798341\pi$
$991$	5.32760	−	11.6658i	0.169237	−	0.370577i	0.975179	+	0.221417i	$0.0710682\pi$
$992$		0			0
$993$	98.1496	+	7.01979i	3.11468	+	0.222766i
$994$		0			0
$995$	−22.2871	+	8.00505i	−0.706548	+	0.253777i
$996$		0			0
$997$	27.7744	+	15.1660i	0.879624	+	0.480311i	0.854547	−	0.519374i	$-0.173835\pi$
$997$	27.7744	+	15.1660i	0.879624	+	0.480311i	0.0250775	+	0.999686i	$0.492017\pi$
$998$		0			0
$999$	−0.312130	−	2.17091i	−0.00987536	−	0.0686846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.3	✓	720
5.3	odd	4	inner	920.2.bv.a.753.3	yes	720
23.19	odd	22	inner	920.2.bv.a.617.3	yes	720
115.88	even	44	inner	920.2.bv.a.433.3	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.3	✓	720	1.1	even	1	trivial
920.2.bv.a.433.3	yes	720	115.88	even	44	inner
920.2.bv.a.617.3	yes	720	23.19	odd	22	inner
920.2.bv.a.753.3	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)

\(f(q)\)	\(=\)	\(q+(-2.63218 + 1.43728i) q^{3} +(2.23215 - 0.132363i) q^{5} +(-0.0903793 - 0.120733i) q^{7} +(3.24067 - 5.04257i) q^{9} +(1.04216 - 0.475937i) q^{11} +(0.0996752 + 0.0746159i) q^{13} +(-5.68516 + 3.55662i) q^{15} +(-0.0921070 - 1.28782i) q^{17} +(-4.39077 - 5.06722i) q^{19} +(0.411420 + 0.187889i) q^{21} +(-3.02203 - 3.72389i) q^{23} +(4.96496 - 0.590908i) q^{25} +(-0.640585 + 8.95655i) q^{27} +(-3.89319 - 3.37347i) q^{29} +(3.39801 - 0.997747i) q^{31} +(-2.05909 + 2.75062i) q^{33} +(-0.217720 - 0.257530i) q^{35} +(-0.238669 + 0.0519194i) q^{37} +(-0.369607 - 0.0531414i) q^{39} +(7.98233 - 5.12993i) q^{41} +(1.35763 + 2.48631i) q^{43} +(6.56619 - 11.6847i) q^{45} +(5.94734 + 5.94734i) q^{47} +(1.96572 - 6.69463i) q^{49} +(2.09340 + 3.25740i) q^{51} +(-2.10456 + 1.57545i) q^{53} +(2.26325 - 1.20030i) q^{55} +(18.8403 + 7.02706i) q^{57} +(11.5159 - 1.65574i) q^{59} +(0.709519 + 2.41640i) q^{61} +(-0.901692 + 0.0644903i) q^{63} +(0.232366 + 0.153360i) q^{65} +(2.27000 + 6.08610i) q^{67} +(13.3068 + 5.45845i) q^{69} +(6.08654 - 13.3277i) q^{71} +(-1.57351 - 0.112540i) q^{73} +(-12.2194 + 8.69140i) q^{75} +(-0.151650 - 0.0828074i) q^{77} +(0.347237 + 2.41508i) q^{79} +(-3.71677 - 8.13858i) q^{81} +(-1.54768 - 7.11459i) q^{83} +(-0.376057 - 2.86242i) q^{85} +(15.0962 + 3.28397i) q^{87} +(-14.0710 - 4.13161i) q^{89} -0.0187778i q^{91} +(-7.51013 + 7.51013i) q^{93} +(-10.4716 - 10.7296i) q^{95} +(-0.905608 + 4.16301i) q^{97} +(0.977334 - 6.79751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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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