LMFDB - Embedded newform 920.2.bv.a.617.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [920,2,Mod(17,920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			617.2
Character	$\chi$	$=$	920.617
Dual form			920.2.bv.a.753.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.54911 + 2.83699i) q^{3} +(-2.23313 + 0.114500i) q^{5} +(-3.34466 - 2.50378i) q^{7} +(-4.02684 - 6.26588i) q^{9} +(-2.09151 - 0.955162i) q^{11} +(2.95328 + 3.94512i) q^{13} +(3.13454 - 6.51275i) q^{15} +(4.28157 + 0.306224i) q^{17} +(-3.62640 + 4.18509i) q^{19} +(12.2844 - 5.61012i) q^{21} +(3.03456 - 3.71368i) q^{23} +(4.97378 - 0.511389i) q^{25} +(14.3418 - 1.02575i) q^{27} +(-4.00107 + 3.46695i) q^{29} +(-7.20387 - 2.11525i) q^{31} +(5.94977 - 4.45395i) q^{33} +(7.75575 + 5.20831i) q^{35} +(1.29686 - 5.96155i) q^{37} +(-15.7673 + 2.26699i) q^{39} +(2.67857 + 1.72141i) q^{41} +(0.928072 + 0.506766i) q^{43} +(9.70992 + 13.5315i) q^{45} +(1.89883 + 1.89883i) q^{47} +(2.94569 + 10.0321i) q^{49} +(-7.50139 + 11.6724i) q^{51} +(-2.79232 + 3.73011i) q^{53} +(4.77999 + 1.89353i) q^{55} +(-6.25535 - 16.7712i) q^{57} +(8.23557 + 1.18410i) q^{59} +(3.86637 - 13.1677i) q^{61} +(-2.21999 + 31.0395i) q^{63} +(-7.04680 - 8.47184i) q^{65} +(2.31104 + 0.861972i) q^{67} +(5.83481 + 14.3619i) q^{69} +(0.667794 + 1.46227i) q^{71} +(-0.504447 - 7.05309i) q^{73} +(-6.25414 + 14.9028i) q^{75} +(4.60388 + 8.43137i) q^{77} +(1.31624 - 9.15465i) q^{79} +(-10.0247 + 21.9511i) q^{81} +(-4.48476 - 0.975600i) q^{83} +(-9.59638 - 0.193598i) q^{85} +(-3.63758 - 16.7217i) q^{87} +(5.18455 - 1.52232i) q^{89} -20.5895i q^{91} +(17.1606 - 17.1606i) q^{93} +(7.61905 - 9.76109i) q^{95} +(11.5013 - 2.50196i) q^{97} +(2.43725 + 16.9514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.54911	+	2.83699i	−0.894381	+	1.63794i	−0.131579	+	0.991306i	$0.542005\pi$
$3$	−1.54911	+	2.83699i	−0.894381	+	1.63794i	−0.762803	+	0.646631i	$0.776177\pi$
$4$		0			0
$5$	−2.23313	+	0.114500i	−0.998688	+	0.0512061i
$5$	−2.23313	+	0.114500i	−0.998688	+	0.0512061i
$6$		0			0
$7$	−3.34466	−	2.50378i	−1.26416	−	0.946339i	−0.264325	−	0.964434i	$-0.585149\pi$
$7$	−3.34466	−	2.50378i	−1.26416	−	0.946339i	−0.999836	+	0.0180943i	$0.994240\pi$
$8$		0			0
$9$	−4.02684	−	6.26588i	−1.34228	−	2.08863i
$10$		0			0
$11$	−2.09151	−	0.955162i	−0.630615	−	0.287992i	0.0743525	−	0.997232i	$-0.476311\pi$
$11$	−2.09151	−	0.955162i	−0.630615	−	0.287992i	−0.704967	+	0.709240i	$0.749038\pi$
$12$		0			0
$13$	2.95328	+	3.94512i	0.819093	+	1.09418i	0.993977	+	0.109591i	$0.0349542\pi$
$13$	2.95328	+	3.94512i	0.819093	+	1.09418i	−0.174883	+	0.984589i	$0.555955\pi$
$14$		0			0
$15$	3.13454	−	6.51275i	0.809336	−	1.68159i
$16$		0			0
$17$	4.28157	+	0.306224i	1.03843	+	0.0742702i	0.580128	−	0.814525i	$-0.303002\pi$
$17$	4.28157	+	0.306224i	1.03843	+	0.0742702i	0.458305	+	0.888795i	$0.348457\pi$
$18$		0			0
$19$	−3.62640	+	4.18509i	−0.831953	+	0.960125i	−0.999669	−	0.0257099i	$-0.991815\pi$
$19$	−3.62640	+	4.18509i	−0.831953	+	0.960125i	0.167716	+	0.985835i	$0.446361\pi$
$20$		0			0
$21$	12.2844	−	5.61012i	2.68069	−	1.22423i
$22$		0			0
$23$	3.03456	−	3.71368i	0.632749	−	0.774357i
$23$	3.03456	−	3.71368i	0.632749	−	0.774357i
$24$		0			0
$25$	4.97378	−	0.511389i	0.994756	−	0.102278i
$26$		0			0
$27$	14.3418	−	1.02575i	2.76009	−	0.197406i
$28$		0			0
$29$	−4.00107	+	3.46695i	−0.742980	+	0.643796i	−0.941774	−	0.336246i	$-0.890843\pi$
$29$	−4.00107	+	3.46695i	−0.742980	+	0.643796i	0.198795	+	0.980041i	$0.436297\pi$
$30$		0			0
$31$	−7.20387	−	2.11525i	−1.29385	−	0.379910i	−0.438864	−	0.898554i	$-0.644619\pi$
$31$	−7.20387	−	2.11525i	−1.29385	−	0.379910i	−0.854990	+	0.518644i	$0.826437\pi$
$32$		0			0
$33$	5.94977	−	4.45395i	1.03572	−	0.775332i
$34$		0			0
$35$	7.75575	+	5.20831i	1.31096	+	0.880365i
$36$		0			0
$37$	1.29686	−	5.96155i	0.213202	−	0.980073i	−0.738787	−	0.673939i	$-0.764601\pi$
$37$	1.29686	−	5.96155i	0.213202	−	0.980073i	0.951989	−	0.306133i	$-0.0990354\pi$
$38$		0			0
$39$	−15.7673	+	2.26699i	−2.52478	+	0.363009i
$40$		0			0
$41$	2.67857	+	1.72141i	0.418322	+	0.268839i	0.732825	−	0.680417i	$-0.238201\pi$
$41$	2.67857	+	1.72141i	0.418322	+	0.268839i	−0.314503	+	0.949256i	$0.601838\pi$
$42$		0			0
$43$	0.928072	+	0.506766i	0.141530	+	0.0772811i	0.548454	−	0.836181i	$-0.315217\pi$
$43$	0.928072	+	0.506766i	0.141530	+	0.0772811i	−0.406924	+	0.913462i	$0.633399\pi$
$44$		0			0
$45$	9.70992	+	13.5315i	1.44747	+	2.01715i
$46$		0			0
$47$	1.89883	+	1.89883i	0.276973	+	0.276973i	0.831899	−	0.554926i	$-0.187254\pi$
$47$	1.89883	+	1.89883i	0.276973	+	0.276973i	−0.554926	+	0.831899i	$0.687254\pi$
$48$		0			0
$49$	2.94569	+	10.0321i	0.420813	+	1.43316i
$50$		0			0
$51$	−7.50139	+	11.6724i	−1.05041	+	1.63446i
$52$		0			0
$53$	−2.79232	+	3.73011i	−0.383555	+	0.512369i	−0.950220	−	0.311579i	$-0.899142\pi$
$53$	−2.79232	+	3.73011i	−0.383555	+	0.512369i	0.566665	+	0.823948i	$0.308233\pi$
$54$		0			0
$55$	4.77999	+	1.89353i	0.644534	+	0.255323i
$56$		0			0
$57$	−6.25535	−	16.7712i	−0.828542	−	2.22141i
$58$		0			0
$59$	8.23557	+	1.18410i	1.07218	+	0.154156i	0.655725	−	0.755000i	$-0.272363\pi$
$59$	8.23557	+	1.18410i	1.07218	+	0.154156i	0.416455	+	0.909156i	$0.363272\pi$
$60$		0			0
$61$	3.86637	−	13.1677i	0.495038	−	1.68595i	−0.210764	−	0.977537i	$-0.567595\pi$
$61$	3.86637	−	13.1677i	0.495038	−	1.68595i	0.705802	−	0.708409i	$-0.250587\pi$
$62$		0			0
$63$	−2.21999	+	31.0395i	−0.279693	+	3.91061i
$64$		0			0
$65$	−7.04680	−	8.47184i	−0.874047	−	1.05080i
$66$		0			0
$67$	2.31104	+	0.861972i	0.282338	+	0.105307i	0.486644	−	0.873601i	$-0.338221\pi$
$67$	2.31104	+	0.861972i	0.282338	+	0.105307i	−0.204306	+	0.978907i	$0.565494\pi$
$68$		0			0
$69$	5.83481	+	14.3619i	0.702429	+	1.72897i
$70$		0			0
$71$	0.667794	+	1.46227i	0.0792526	+	0.173539i	0.945110	−	0.326751i	$-0.105954\pi$
$71$	0.667794	+	1.46227i	0.0792526	+	0.173539i	−0.865858	+	0.500290i	$0.833227\pi$
$72$		0			0
$73$	−0.504447	−	7.05309i	−0.0590410	−	0.825502i	−0.937566	−	0.347806i	$-0.886927\pi$
$73$	−0.504447	−	7.05309i	−0.0590410	−	0.825502i	0.878525	−	0.477696i	$-0.158528\pi$
$74$		0			0
$75$	−6.25414	+	14.9028i	−0.722166	+	1.72082i
$76$		0			0
$77$	4.60388	+	8.43137i	0.524660	+	0.960844i
$78$		0			0
$79$	1.31624	−	9.15465i	0.148089	−	1.02998i	−0.771256	−	0.636525i	$-0.780371\pi$
$79$	1.31624	−	9.15465i	0.148089	−	1.02998i	0.919344	−	0.393454i	$-0.128720\pi$
$80$		0			0
$81$	−10.0247	+	21.9511i	−1.11386	+	2.43902i
$82$		0			0
$83$	−4.48476	−	0.975600i	−0.492266	−	0.107086i	−0.0404218	−	0.999183i	$-0.512870\pi$
$83$	−4.48476	−	0.975600i	−0.492266	−	0.107086i	−0.451844	+	0.892097i	$0.649234\pi$
$84$		0			0
$85$	−9.59638	−	0.193598i	−1.04087	−	0.0209986i
$86$		0			0
$87$	−3.63758	−	16.7217i	−0.389989	−	1.79275i
$88$		0			0
$89$	5.18455	−	1.52232i	0.549561	−	0.161366i	0.00484811	−	0.999988i	$-0.498457\pi$
$89$	5.18455	−	1.52232i	0.549561	−	0.161366i	0.544713	+	0.838623i	$0.316639\pi$
$90$		0			0
$91$		−	20.5895i		−	2.15836i
$92$		0			0
$93$	17.1606	−	17.1606i	1.77947	−	1.77947i
$94$		0			0
$95$	7.61905	−	9.76109i	0.781698	−	1.00147i
$96$		0			0
$97$	11.5013	−	2.50196i	1.16778	−	0.254036i	0.413450	−	0.910527i	$-0.364324\pi$
$97$	11.5013	−	2.50196i	1.16778	−	0.254036i	0.754334	+	0.656491i	$0.227960\pi$
$98$		0			0
$99$	2.43725	+	16.9514i	0.244953	+	1.70368i
$100$		0			0
$101$	5.13105	−	3.29752i	0.510558	−	0.328116i	−0.259869	−	0.965644i	$-0.583679\pi$
$101$	5.13105	−	3.29752i	0.510558	−	0.328116i	0.770427	+	0.637528i	$0.220043\pi$
$102$		0			0
$103$	14.4838	−	5.40218i	1.42713	−	0.532293i	0.487091	−	0.873351i	$-0.338058\pi$
$103$	14.4838	−	5.40218i	1.42713	−	0.532293i	0.940042	+	0.341058i	$0.110785\pi$
$104$		0			0
$105$	−26.7905	+	13.9347i	−2.61448	+	1.35989i
$106$		0			0
$107$	5.00008	−	2.73025i	0.483376	−	0.263943i	−0.219032	−	0.975718i	$-0.570290\pi$
$107$	5.00008	−	2.73025i	0.483376	−	0.263943i	0.702408	+	0.711774i	$0.252108\pi$
$108$		0			0
$109$	−8.99848	−	10.3848i	−0.861898	−	0.994683i	−0.999991	−	0.00426394i	$-0.998643\pi$
$109$	−8.99848	−	10.3848i	−0.861898	−	0.994683i	0.138093	−	0.990419i	$-0.455903\pi$
$110$		0			0
$111$	14.9039	+	12.9143i	1.41461	+	1.22577i
$112$		0			0
$113$	−5.30620	+	14.2265i	−0.499165	+	1.33831i	0.406240	+	0.913766i	$0.366840\pi$
$113$	−5.30620	+	14.2265i	−0.499165	+	1.33831i	−0.905406	+	0.424548i	$0.860433\pi$
$114$		0			0
$115$	−6.35136	+	8.64062i	−0.592267	+	0.805742i
$116$		0			0
$117$	12.8273	−	34.3913i	1.18588	−	3.17948i
$118$		0			0
$119$	−13.5537	−	11.7443i	−1.24246	−	1.07660i
$120$		0			0
$121$	−3.74138	−	4.31778i	−0.340125	−	0.392526i
$122$		0			0
$123$	−9.03303	+	4.93241i	−0.814481	+	0.444740i
$124$		0			0
$125$	−11.0486	+	1.71150i	−0.988214	+	0.153081i
$126$		0			0
$127$	14.1918	−	5.29327i	1.25932	−	0.469702i	0.370873	−	0.928684i	$-0.379059\pi$
$127$	14.1918	−	5.29327i	1.25932	−	0.469702i	0.888446	+	0.458982i	$0.151786\pi$
$128$		0			0
$129$	−2.87538	+	1.84789i	−0.253163	+	0.162698i
$130$		0			0
$131$	−0.00349255	−	0.0242912i	−0.000305145	−	0.00212233i	0.989668	−	0.143376i	$-0.0457958\pi$
$131$	−0.00349255	−	0.0242912i	−0.000305145	−	0.00212233i	−0.989973	+	0.141254i	$0.954887\pi$
$132$		0			0
$133$	22.6076	−	4.91798i	1.96033	−	0.426443i
$134$		0			0
$135$	−31.9098	+	3.93278i	−2.74636	+	0.338480i
$136$		0			0
$137$	−0.503236	+	0.503236i	−0.0429944	+	0.0429944i	−0.728277	−	0.685283i	$-0.759679\pi$
$137$	−0.503236	+	0.503236i	−0.0429944	+	0.0429944i	0.685283	+	0.728277i	$0.259679\pi$
$138$		0			0
$139$			6.91548i			0.586564i	0.956026	+	0.293282i	$0.0947474\pi$
$139$			6.91548i			0.586564i	−0.956026	+	0.293282i	$0.905253\pi$
$140$		0			0
$141$	−8.32847	+	2.44546i	−0.701384	+	0.205945i
$142$		0			0
$143$	−2.40860	−	11.0721i	−0.201417	−	0.925899i
$144$		0			0
$145$	8.53796	−	8.20028i	0.709039	−	0.680996i
$146$		0			0
$147$	−33.0242	−	7.18398i	−2.72379	−	0.592524i
$148$		0			0
$149$	3.47939	−	7.61881i	0.285043	−	0.624157i	−0.711901	−	0.702280i	$-0.752165\pi$
$149$	3.47939	−	7.61881i	0.285043	−	0.624157i	0.996944	+	0.0781229i	$0.0248927\pi$
$150$		0			0
$151$	−0.590028	+	4.10373i	−0.0480158	+	0.333957i	0.951628	+	0.307254i	$0.0994100\pi$
$151$	−0.590028	+	4.10373i	−0.0480158	+	0.333957i	−0.999643	+	0.0267033i	$0.991499\pi$
$152$		0			0
$153$	−15.3224	−	28.0609i	−1.23874	−	2.26859i
$154$		0			0
$155$	16.3294	+	3.89879i	1.31161	+	0.313158i
$156$		0			0
$157$	0.517217	+	7.23164i	0.0412784	+	0.577148i	0.975435	+	0.220286i	$0.0706989\pi$
$157$	0.517217	+	7.23164i	0.0412784	+	0.577148i	−0.934157	+	0.356862i	$0.883847\pi$
$158$		0			0
$159$	−6.25665	−	13.7002i	−0.496185	−	1.08649i
$160$		0			0
$161$	−19.4478	+	4.82314i	−1.53270	+	0.380116i
$162$		0			0
$163$	−12.0433	−	4.49192i	−0.943304	−	0.351834i	−0.169694	−	0.985497i	$-0.554278\pi$
$163$	−12.0433	−	4.49192i	−0.943304	−	0.351834i	−0.773610	+	0.633663i	$0.781551\pi$
$164$		0			0
$165$	−12.7767	+	10.6275i	−0.994662	+	0.827351i
$166$		0			0
$167$	−1.12674	+	15.7539i	−0.0871900	+	1.21907i	0.745946	+	0.666007i	$0.231998\pi$
$167$	−1.12674	+	15.7539i	−0.0871900	+	1.21907i	−0.833136	+	0.553068i	$0.813457\pi$
$168$		0			0
$169$	−3.17960	+	10.8287i	−0.244585	+	0.832979i
$170$		0			0
$171$	40.8262	+	5.86992i	3.12206	+	0.448884i
$172$		0			0
$173$	1.57308	+	4.21759i	0.119599	+	0.320657i	0.982930	−	0.183981i	$-0.0588985\pi$
$173$	1.57308	+	4.21759i	0.119599	+	0.320657i	−0.863331	+	0.504639i	$0.831626\pi$
$174$		0			0
$175$	−17.9160	−	10.7428i	−1.35432	−	0.812081i
$176$		0			0
$177$	−16.1171	+	21.5299i	−1.21144	+	1.61829i
$178$		0			0
$179$	5.09858	−	7.93355i	0.381086	−	0.592981i	−0.596731	−	0.802441i	$-0.703534\pi$
$179$	5.09858	−	7.93355i	0.381086	−	0.592981i	0.977817	+	0.209460i	$0.0671706\pi$
$180$		0			0
$181$	−5.76781	−	19.6434i	−0.428718	−	1.46008i	−0.836990	−	0.547219i	$-0.815687\pi$
$181$	−5.76781	−	19.6434i	−0.428718	−	1.46008i	0.408272	−	0.912861i	$-0.366132\pi$
$182$		0			0
$183$	31.3671	+	31.3671i	2.31872	+	2.31872i
$184$		0			0
$185$	−2.21345	+	13.4614i	−0.162736	+	0.989704i
$186$		0			0
$187$	−8.66246	−	4.73006i	−0.633462	−	0.345896i
$188$		0			0
$189$	−50.5368	−	32.4780i	−3.67601	−	2.36243i
$190$		0			0
$191$	4.56066	−	0.655723i	0.329997	−	0.0474465i	0.0246751	−	0.999696i	$-0.492145\pi$
$191$	4.56066	−	0.655723i	0.329997	−	0.0474465i	0.305322	+	0.952249i	$0.401236\pi$
$192$		0			0
$193$	0.615808	−	2.83082i	0.0443268	−	0.203767i	−0.949657	−	0.313290i	$-0.898569\pi$
$193$	0.615808	−	2.83082i	0.0443268	−	0.203767i	0.993984	+	0.109523i	$0.0349324\pi$
$194$		0			0
$195$	34.9508	−	6.86785i	2.50288	−	0.491817i
$196$		0			0
$197$	11.6904	−	8.75134i	0.832908	−	0.623507i	−0.0953500	−	0.995444i	$-0.530397\pi$
$197$	11.6904	−	8.75134i	0.832908	−	0.623507i	0.928258	+	0.371937i	$0.121306\pi$
$198$		0			0
$199$	2.62762	+	0.771540i	0.186267	+	0.0546930i	0.373536	−	0.927616i	$-0.378145\pi$
$199$	2.62762	+	0.771540i	0.186267	+	0.0546930i	−0.187269	+	0.982309i	$0.559963\pi$
$200$		0			0
$201$	−6.02546	+	5.22109i	−0.425003	+	0.368267i
$202$		0			0
$203$	22.0627	−	1.57795i	1.54850	−	0.110751i
$204$		0			0
$205$	−6.17870	−	3.53744i	−0.431539	−	0.247066i
$206$		0			0
$207$	−35.4892	−	4.05978i	−2.46667	−	0.282174i
$208$		0			0
$209$	11.5821	−	5.28937i	0.801151	−	0.365873i
$210$		0			0
$211$	7.34378	−	8.47517i	0.505567	−	0.583455i	−0.444391	−	0.895833i	$-0.646580\pi$
$211$	7.34378	−	8.47517i	0.505567	−	0.583455i	0.949958	+	0.312378i	$0.101125\pi$
$212$		0			0
$213$	−5.18292	−	0.370690i	−0.355128	−	0.0253992i
$214$		0			0
$215$	−2.13054	−	1.02541i	−0.145301	−	0.0699325i
$216$		0			0
$217$	18.7984	+	25.1117i	1.27612	+	1.70469i
$218$		0			0
$219$	20.7910	+	9.49493i	1.40492	+	0.641608i
$220$		0			0
$221$	11.4366	+	17.7957i	0.769309	+	1.19707i
$222$		0			0
$223$	−11.5674	−	8.65924i	−0.774610	−	0.579866i	0.137169	−	0.990548i	$-0.456200\pi$
$223$	−11.5674	−	8.65924i	−0.774610	−	0.579866i	−0.911779	+	0.410682i	$0.865291\pi$
$224$		0			0
$225$	−23.2329	−	29.1058i	−1.54886	−	1.94039i
$226$		0			0
$227$	2.69021	−	4.92676i	0.178556	−	0.327000i	−0.773038	−	0.634360i	$-0.781264\pi$
$227$	2.69021	−	4.92676i	0.178556	−	0.327000i	0.951593	+	0.307360i	$0.0994455\pi$
$228$		0			0
$229$	−19.0327			−1.25771			−0.628857	−	0.777521i	$-0.716477\pi$
$229$	−19.0327			−1.25771			−0.628857	+	0.777521i	$0.716477\pi$
$230$		0			0
$231$	−31.0516			−2.04305
$232$		0			0
$233$	−6.92611	+	12.6842i	−0.453744	+	0.830971i	−0.999978	−	0.00666235i	$-0.997879\pi$
$233$	−6.92611	+	12.6842i	−0.453744	+	0.830971i	0.546234	+	0.837633i	$0.316061\pi$
$234$		0			0
$235$	−4.45776	−	4.02293i	−0.290792	−	0.262427i
$236$		0			0
$237$	23.9327	+	17.9158i	1.55459	+	1.16375i
$238$		0			0
$239$	−6.95690	−	10.8251i	−0.450004	−	0.700221i	0.539936	−	0.841706i	$-0.318448\pi$
$239$	−6.95690	−	10.8251i	−0.450004	−	0.700221i	−0.989940	+	0.141486i	$0.954812\pi$
$240$		0			0
$241$	−2.91855	−	1.33286i	−0.188000	−	0.0858568i	0.319191	−	0.947690i	$-0.396589\pi$
$241$	−2.91855	−	1.33286i	−0.188000	−	0.0858568i	−0.507191	+	0.861834i	$0.669316\pi$
$242$		0			0
$243$	−20.8956	−	27.9132i	−1.34045	−	1.79063i
$244$		0			0
$245$	−7.72681	−	22.0658i	−0.493648	−	1.40973i
$246$		0			0
$247$	−27.2205	−	1.94685i	−1.73200	−	0.123875i
$248$		0			0
$249$	9.71517	−	11.2119i	0.615674	−	0.710526i
$250$		0			0
$251$	2.58110	−	1.17875i	0.162918	−	0.0744021i	−0.332287	−	0.943178i	$-0.607820\pi$
$251$	2.58110	−	1.17875i	0.162918	−	0.0744021i	0.495205	+	0.868776i	$0.335093\pi$
$252$		0			0
$253$	−9.89398	+	4.86872i	−0.622029	+	0.306094i
$254$		0			0
$255$	15.4151	−	26.9249i	0.965333	−	1.68611i
$256$		0			0
$257$	−10.4576	+	0.747940i	−0.652325	+	0.0466552i	−0.393580	−	0.919290i	$-0.628764\pi$
$257$	−10.4576	+	0.747940i	−0.652325	+	0.0466552i	−0.258745	+	0.965946i	$0.583309\pi$
$258$		0			0
$259$	−19.2639	+	16.6923i	−1.19700	+	1.03721i
$260$		0			0
$261$	37.8351	+	11.1094i	2.34194	+	0.687654i
$262$		0			0
$263$	−5.61971	+	4.20686i	−0.346526	+	0.259406i	−0.758336	−	0.651864i	$-0.773987\pi$
$263$	−5.61971	+	4.20686i	−0.346526	+	0.259406i	0.411810	+	0.911270i	$0.364897\pi$
$264$		0			0
$265$	5.80853	−	8.64955i	0.356815	−	0.531338i
$266$		0			0
$267$	−3.71265	+	17.0668i	−0.227210	+	1.04447i
$268$		0			0
$269$	28.2928	−	4.06789i	1.72504	−	0.248024i	0.792703	−	0.609608i	$-0.208673\pi$
$269$	28.2928	−	4.06789i	1.72504	−	0.248024i	0.932339	+	0.361584i	$0.117764\pi$
$270$		0			0
$271$	−17.5599	−	11.2851i	−1.06669	−	0.685518i	−0.115242	−	0.993337i	$-0.536764\pi$
$271$	−17.5599	−	11.2851i	−1.06669	−	0.685518i	−0.951445	+	0.307819i	$0.900401\pi$
$272$		0			0
$273$	58.4121	+	31.8954i	3.53526	+	1.93040i
$274$		0			0
$275$	−10.8912	−	3.68119i	−0.656763	−	0.221984i
$276$		0			0
$277$	3.14698	+	3.14698i	0.189084	+	0.189084i	0.795300	−	0.606216i	$-0.207313\pi$
$277$	3.14698	+	3.14698i	0.189084	+	0.189084i	−0.606216	+	0.795300i	$0.707313\pi$
$278$		0			0
$279$	15.7549	+	53.6564i	0.943223	+	3.21232i
$280$		0			0
$281$	−11.4871	+	17.8743i	−0.685265	+	1.06629i	0.308108	+	0.951351i	$0.400304\pi$
$281$	−11.4871	+	17.8743i	−0.685265	+	1.06629i	−0.993372	+	0.114941i	$0.963332\pi$
$282$		0			0
$283$	−6.04173	+	8.07081i	−0.359144	+	0.479760i	−0.943328	−	0.331861i	$-0.892324\pi$
$283$	−6.04173	+	8.07081i	−0.359144	+	0.479760i	0.584185	+	0.811621i	$0.301414\pi$
$284$		0			0
$285$	15.8894	+	36.7362i	0.941204	+	2.17607i
$286$		0			0
$287$	−4.64885	−	12.4641i	−0.274413	−	0.735730i
$288$		0			0
$289$	1.41110	+	0.202885i	0.0830058	+	0.0119344i
$290$		0			0
$291$	−10.7188	+	36.5050i	−0.628349	+	2.13996i
$292$		0			0
$293$	0.522794	−	7.30962i	0.0305420	−	0.427033i	−0.959060	−	0.283202i	$-0.908603\pi$
$293$	0.522794	−	7.30962i	0.0305420	−	0.427033i	0.989602	−	0.143831i	$-0.0459421\pi$
$294$		0			0
$295$	−18.5267	−	1.70127i	−1.07867	−	0.0990518i
$296$		0			0
$297$	−30.9759	−	11.5534i	−1.79740	−	0.670397i
$298$		0			0
$299$	23.6129	+	1.00415i	1.36557	+	0.0580715i
$300$		0			0
$301$	−1.83525	−	4.01865i	−0.105782	−	0.231631i
$302$		0			0
$303$	1.40647	+	19.6650i	0.0807994	+	1.12972i
$304$		0			0
$305$	−7.12643	+	29.8479i	−0.408058	+	1.70908i
$306$		0			0
$307$	−11.7449	−	21.5092i	−0.670317	−	1.22759i	−0.962513	−	0.271236i	$-0.912568\pi$
$307$	−11.7449	−	21.5092i	−0.670317	−	1.22759i	0.292196	−	0.956358i	$-0.405614\pi$
$308$		0			0
$309$	−7.11114	+	49.4590i	−0.404538	+	2.81363i
$310$		0			0
$311$	−3.86753	+	8.46870i	−0.219307	+	0.480216i	−0.987024	−	0.160574i	$-0.948666\pi$
$311$	−3.86753	+	8.46870i	−0.219307	+	0.480216i	0.767717	+	0.640790i	$0.221393\pi$
$312$		0			0
$313$	13.2222	+	2.87631i	0.747363	+	0.162579i	0.570089	−	0.821583i	$-0.306909\pi$
$313$	13.2222	+	2.87631i	0.747363	+	0.162579i	0.177274	+	0.984162i	$0.443272\pi$
$314$		0			0
$315$	1.40350	−	69.5696i	0.0790783	−	3.91980i
$316$		0			0
$317$	−2.87438	−	13.2133i	−0.161441	−	0.742133i	−0.984671	−	0.174424i	$-0.944194\pi$
$317$	−2.87438	−	13.2133i	−0.161441	−	0.742133i	0.823230	−	0.567709i	$-0.192170\pi$
$318$		0			0
$319$	11.6798	−	3.42949i	0.653942	−	0.192015i
$320$		0			0
$321$			18.4147i			1.02781i
$322$		0			0
$323$	−16.8083	+	16.8083i	−0.935237	+	0.935237i
$324$		0			0
$325$	16.7065	+	18.1119i	0.926708	+	1.00467i
$326$		0			0
$327$	43.4012	−	9.44136i	2.40009	−	0.522108i
$328$		0			0
$329$	−1.59669	−	11.1052i	−0.0880281	−	0.612249i
$330$		0			0
$331$	−23.5800	+	15.1540i	−1.29608	+	0.832938i	−0.992779	−	0.119959i	$-0.961724\pi$
$331$	−23.5800	+	15.1540i	−1.29608	+	0.832938i	−0.303297	+	0.952896i	$0.598087\pi$
$332$		0			0
$333$	−42.5766	+	15.8802i	−2.33318	+	0.870232i
$334$		0			0
$335$	−5.25955	−	1.66028i	−0.287360	−	0.0907110i
$336$		0			0
$337$	17.2431	−	9.41546i	0.939293	−	0.512893i	0.0647826	−	0.997899i	$-0.479365\pi$
$337$	17.2431	−	9.41546i	0.939293	−	0.512893i	0.874511	+	0.485007i	$0.161183\pi$
$338$		0			0
$339$	−32.1405	−	37.0921i	−1.74563	−	2.01456i
$340$		0			0
$341$	13.0466	+	11.3049i	0.706512	+	0.612196i
$342$		0			0
$343$	5.04543	−	13.5273i	0.272428	−	0.730407i
$344$		0			0
$345$	−14.6744	−	31.4040i	−0.790041	−	1.69074i
$346$		0			0
$347$	−7.30108	+	19.5750i	−0.391943	+	1.05084i	0.579792	+	0.814764i	$0.303134\pi$
$347$	−7.30108	+	19.5750i	−0.391943	+	1.05084i	−0.971735	+	0.236075i	$0.924139\pi$
$348$		0			0
$349$	12.6493	+	10.9607i	0.677100	+	0.586711i	0.924029	−	0.382323i	$-0.124876\pi$
$349$	12.6493	+	10.9607i	0.677100	+	0.586711i	−0.246928	+	0.969034i	$0.579421\pi$
$350$		0			0
$351$	46.4022	+	53.5510i	2.47677	+	2.85834i
$352$		0			0
$353$	11.8496	−	6.47038i	0.630691	−	0.344383i	−0.131901	−	0.991263i	$-0.542108\pi$
$353$	11.8496	−	6.47038i	0.630691	−	0.344383i	0.762592	+	0.646880i	$0.223926\pi$
$354$		0			0
$355$	−1.65870	−	3.18897i	−0.0880349	−	0.169253i
$356$		0			0
$357$	54.3147	−	20.2583i	2.87464	−	1.07218i
$358$		0			0
$359$	19.7419	−	12.6873i	1.04194	−	0.669611i	0.0964707	−	0.995336i	$-0.469245\pi$
$359$	19.7419	−	12.6873i	1.04194	−	0.669611i	0.945465	+	0.325725i	$0.105608\pi$
$360$		0			0
$361$	−1.66021	−	11.5470i	−0.0873795	−	0.607738i
$362$		0			0
$363$	18.0453	−	3.92552i	0.947134	−	0.206036i
$364$		0			0
$365$	1.93408	+	15.6927i	0.101234	+	0.821395i
$366$		0			0
$367$	6.54247	−	6.54247i	0.341514	−	0.341514i	−0.515422	−	0.856936i	$-0.672365\pi$
$367$	6.54247	−	6.54247i	0.341514	−	0.341514i	0.856936	+	0.515422i	$0.172365\pi$
$368$		0			0
$369$		−	23.7154i		−	1.23458i
$370$		0			0
$371$	18.6787	−	5.48457i	0.969751	−	0.284745i
$372$		0			0
$373$	−1.14513	−	5.26408i	−0.0592926	−	0.272564i	0.937950	−	0.346770i	$-0.112721\pi$
$373$	−1.14513	−	5.26408i	−0.0592926	−	0.272564i	−0.997243	+	0.0742059i	$0.976358\pi$
$374$		0			0
$375$	12.2600	−	33.9960i	0.633102	−	1.75554i
$376$		0			0
$377$	−25.4938	−	5.54584i	−1.31300	−	0.285625i
$378$		0			0
$379$	12.7747	−	27.9727i	0.656193	−	1.43686i	−0.229834	−	0.973230i	$-0.573818\pi$
$379$	12.7747	−	27.9727i	0.656193	−	1.43686i	0.886027	−	0.463633i	$-0.153454\pi$
$380$		0			0
$381$	−6.96776	+	48.4619i	−0.356969	+	2.48278i
$382$		0			0
$383$	−0.693322	−	1.26972i	−0.0354271	−	0.0648799i	0.859366	−	0.511361i	$-0.170859\pi$
$383$	−0.693322	−	1.26972i	−0.0354271	−	0.0648799i	−0.894793	+	0.446482i	$0.852677\pi$
$384$		0			0
$385$	−11.2465	−	18.3012i	−0.573173	−	0.932717i
$386$		0			0
$387$	−0.561862	−	7.85586i	−0.0285610	−	0.399336i
$388$		0			0
$389$	−14.7804	−	32.3645i	−0.749394	−	1.64094i	−0.767452	−	0.641107i	$-0.778476\pi$
$389$	−14.7804	−	32.3645i	−0.749394	−	1.64094i	0.0180581	−	0.999837i	$-0.494252\pi$
$390$		0			0
$391$	14.1299	−	14.9711i	0.714579	−	0.757123i
$392$		0			0
$393$	0.0743242	+	0.0277215i	0.00374916	+	0.00139836i
$394$		0			0
$395$	−1.89113	+	20.5943i	−0.0951531	+	1.03621i
$396$		0			0
$397$	0.798620	−	11.1662i	0.0400816	−	0.560414i	−0.937244	−	0.348673i	$-0.886632\pi$
$397$	0.798620	−	11.1662i	0.0400816	−	0.560414i	0.977326	−	0.211741i	$-0.0679132\pi$
$398$		0			0
$399$	−21.0695	+	71.7561i	−1.05479	+	3.59230i
$400$		0			0
$401$	2.59697	+	0.373389i	0.129687	+	0.0186461i	0.206852	−	0.978372i	$-0.433678\pi$
$401$	2.59697	+	0.373389i	0.129687	+	0.0186461i	−0.0771658	+	0.997018i	$0.524587\pi$
$402$		0			0
$403$	−12.9302	−	34.6671i	−0.644097	−	1.72689i
$404$		0			0
$405$	19.8732	−	50.1677i	0.987507	−	2.49285i
$406$		0			0
$407$	−8.40663	+	11.2299i	−0.416701	+	0.556648i
$408$		0			0
$409$	−20.8619	+	32.4618i	−1.03156	+	1.60513i	−0.263600	+	0.964632i	$0.584910\pi$
$409$	−20.8619	+	32.4618i	−1.03156	+	1.60513i	−0.767957	+	0.640502i	$0.778726\pi$
$410$		0			0
$411$	−0.648106	−	2.20725i	−0.0319687	−	0.108875i
$412$		0			0
$413$	−24.5804	−	24.5804i	−1.20952	−	1.20952i
$414$		0			0
$415$	10.1268	+	1.66514i	0.497104	+	0.0817385i
$416$		0			0
$417$	−19.6192	−	10.7129i	−0.960755	−	0.524612i
$418$		0			0
$419$	−2.57092	−	1.65223i	−0.125598	−	0.0807167i	0.476334	−	0.879265i	$-0.341965\pi$
$419$	−2.57092	−	1.65223i	−0.125598	−	0.0807167i	−0.601931	+	0.798548i	$0.705602\pi$
$420$		0			0
$421$	−3.89707	+	0.560315i	−0.189932	+	0.0273081i	−0.236624	−	0.971601i	$-0.576041\pi$
$421$	−3.89707	+	0.560315i	−0.189932	+	0.0273081i	0.0466924	+	0.998909i	$0.485132\pi$
$422$		0			0
$423$	4.25157	−	19.5441i	0.206718	−	0.950268i
$424$		0			0
$425$	21.4522	−	0.666459i	1.04058	−	0.0323280i
$426$		0			0
$427$	−45.9006	+	34.3608i	−2.22129	+	1.66283i
$428$		0			0
$429$	35.1427	+	10.3188i	1.69671	+	0.498198i
$430$		0			0
$431$	1.14882	−	0.995462i	0.0553369	−	0.0479497i	−0.626753	−	0.779218i	$-0.715617\pi$
$431$	1.14882	−	0.995462i	0.0553369	−	0.0479497i	0.682090	+	0.731268i	$0.261071\pi$
$432$		0			0
$433$	−15.9372	+	1.13985i	−0.765893	+	0.0547777i	−0.448818	−	0.893623i	$-0.648155\pi$
$433$	−15.9372	+	1.13985i	−0.765893	+	0.0547777i	−0.317074	+	0.948401i	$0.602700\pi$
$434$		0			0
$435$	10.0378	+	36.9253i	0.481278	+	1.77043i
$436$		0			0
$437$	4.53758	+	26.1672i	0.217062	+	1.25175i
$438$		0			0
$439$	13.7224	−	6.26682i	0.654935	−	0.299099i	−0.0600948	−	0.998193i	$-0.519140\pi$
$439$	13.7224	−	6.26682i	0.654935	−	0.299099i	0.715030	+	0.699094i	$0.246413\pi$
$440$		0			0
$441$	50.9982	−	58.8550i	2.42848	−	2.80262i
$442$		0			0
$443$	−9.86767	−	0.705750i	−0.468827	−	0.0335312i	−0.165073	−	0.986281i	$-0.552786\pi$
$443$	−9.86767	−	0.705750i	−0.468827	−	0.0335312i	−0.303755	+	0.952750i	$0.598240\pi$
$444$		0			0
$445$	−11.4035	+	3.99318i	−0.540577	+	0.189295i
$446$		0			0
$447$	16.2245	+	21.6734i	0.767393	+	1.02512i
$448$		0			0
$449$	18.7693	+	8.57166i	0.885779	+	0.404522i	0.805740	−	0.592270i	$-0.201768\pi$
$449$	18.7693	+	8.57166i	0.885779	+	0.404522i	0.0800395	+	0.996792i	$0.474495\pi$
$450$		0			0
$451$	−3.95803	−	6.15881i	−0.186376	−	0.290007i
$452$		0			0
$453$	−10.7282	−	8.03105i	−0.504056	−	0.377332i
$454$		0			0
$455$	2.35750	+	45.9790i	0.110521	+	2.15553i
$456$		0			0
$457$	4.75963	−	8.71660i	0.222646	−	0.407745i	−0.742349	−	0.670013i	$-0.766288\pi$
$457$	4.75963	−	8.71660i	0.222646	−	0.407745i	0.964995	+	0.262268i	$0.0844703\pi$
$458$		0			0
$459$	61.7197			2.88083
$460$		0			0
$461$	−14.3758			−0.669549			−0.334775	−	0.942298i	$-0.608660\pi$
$461$	−14.3758			−0.669549			−0.334775	+	0.942298i	$0.608660\pi$
$462$		0			0
$463$	17.9326	−	32.8411i	0.833399	−	1.52626i	−0.0168394	−	0.999858i	$-0.505360\pi$
$463$	17.9326	−	32.8411i	0.833399	−	1.52626i	0.850238	−	0.526398i	$-0.176458\pi$
$464$		0			0
$465$	−36.3569	+	40.2867i	−1.68601	+	1.86825i
$466$		0			0
$467$	23.1387	+	17.3214i	1.07073	+	0.801538i	0.980918	−	0.194421i	$-0.0622828\pi$
$467$	23.1387	+	17.3214i	1.07073	+	0.801538i	0.0898110	+	0.995959i	$0.471374\pi$
$468$		0			0
$469$	−5.57143	−	8.66932i	−0.257265	−	0.400312i
$470$		0			0
$471$	−21.3173	−	9.73530i	−0.982250	−	0.448579i
$472$		0			0
$473$	−1.45703	−	1.94637i	−0.0669944	−	0.0894940i
$474$		0			0
$475$	−15.8967	+	22.6702i	−0.729391	+	1.04018i
$476$		0			0
$477$	34.6166	+	2.47583i	1.58499	+	0.113360i
$478$		0			0
$479$	22.9239	−	26.4556i	1.04742	−	1.20879i	0.0699870	−	0.997548i	$-0.477704\pi$
$479$	22.9239	−	26.4556i	1.04742	−	1.20879i	0.977434	−	0.211241i	$-0.0677503\pi$
$480$		0			0
$481$	27.3490	−	12.4899i	1.24701	−	0.569490i
$482$		0			0
$483$	16.4437	−	62.6448i	0.748213	−	2.85044i
$484$		0			0
$485$	−25.3976	+	6.90413i	−1.15324	+	0.313500i
$486$		0			0
$487$	33.9184	−	2.42589i	1.53699	−	0.109928i	0.723017	−	0.690830i	$-0.242755\pi$
$487$	33.9184	−	2.42589i	1.53699	−	0.109928i	0.813973	+	0.580903i	$0.197300\pi$
$488$		0			0
$489$	31.4000	−	27.2082i	1.41996	−	1.23040i
$490$		0			0
$491$	0.209759	+	0.0615907i	0.00946627	+	0.00277955i	0.286462	−	0.958092i	$-0.407521\pi$
$491$	0.209759	+	0.0615907i	0.00946627	+	0.00277955i	−0.276996	+	0.960871i	$0.589339\pi$
$492$		0			0
$493$	−18.1925	+	13.6187i	−0.819350	+	0.613357i
$494$		0			0
$495$	−7.38365	−	37.5758i	−0.331871	−	1.68891i
$496$		0			0
$497$	1.42765	−	6.56278i	0.0640387	−	0.294381i
$498$		0			0
$499$	34.2383	−	4.92272i	1.53271	−	0.220371i	0.676287	−	0.736638i	$-0.263588\pi$
$499$	34.2383	−	4.92272i	1.53271	−	0.220371i	0.856428	+	0.516267i	$0.172679\pi$
$500$		0			0
$501$	−42.9483	−	27.6012i	−1.91879	−	1.23313i
$502$		0			0
$503$	5.51113	+	3.00930i	0.245729	+	0.134178i	0.597394	−	0.801948i	$-0.296203\pi$
$503$	5.51113	+	3.00930i	0.245729	+	0.134178i	−0.351665	+	0.936126i	$0.614384\pi$
$504$		0			0
$505$	−11.0807	+	7.95132i	−0.493087	+	0.353829i
$506$		0			0
$507$	−25.7954	−	25.7954i	−1.14562	−	1.14562i
$508$		0			0
$509$	11.0233	+	37.5420i	0.488600	+	1.66402i	0.722198	+	0.691687i	$0.243132\pi$
$509$	11.0233	+	37.5420i	0.488600	+	1.66402i	−0.233597	+	0.972333i	$0.575050\pi$
$510$		0			0
$511$	−15.9722	+	24.8532i	−0.706567	+	1.09944i
$512$		0			0
$513$	−47.7164	+	63.7417i	−2.10673	+	2.81426i
$514$		0			0
$515$	−31.7258	+	13.7222i	−1.39800	+	0.604673i
$516$		0			0
$517$	−2.15774	−	5.78512i	−0.0948972	−	0.254429i
$518$		0			0
$519$	−14.4021	−	2.07072i	−0.632184	−	0.0908943i
$520$		0			0
$521$	5.72139	−	19.4853i	0.250659	−	0.853666i	−0.733996	−	0.679154i	$-0.762347\pi$
$521$	5.72139	−	19.4853i	0.250659	−	0.853666i	0.984655	−	0.174512i	$-0.0558348\pi$
$522$		0			0
$523$	−0.313672	+	4.38571i	−0.0137159	+	0.191774i	0.985975	+	0.166896i	$0.0533743\pi$
$523$	−0.313672	+	4.38571i	−0.0137159	+	0.191774i	−0.999690	+	0.0248781i	$0.992080\pi$
$524$		0			0
$525$	58.2312	−	34.1856i	2.54142	−	1.49198i
$526$		0			0
$527$	−30.1961	−	11.2626i	−1.31536	−	0.490606i
$528$		0			0
$529$	−4.58291	−	22.5388i	−0.199257	−	0.979947i
$530$		0			0
$531$	−25.7439	−	56.3713i	−1.11719	−	2.44631i
$532$		0			0
$533$	1.11939	+	15.6511i	0.0484861	+	0.677924i
$534$		0			0
$535$	−10.8532	+	6.66953i	−0.469227	+	0.288349i
$536$		0			0
$537$	14.6091	+	26.7546i	0.630430	+	1.15455i
$538$		0			0
$539$	3.42133	−	23.7959i	0.147367	−	1.02496i
$540$		0			0
$541$	−10.5234	+	23.0431i	−0.452437	+	0.990699i	0.536710	+	0.843767i	$0.319667\pi$
$541$	−10.5234	+	23.0431i	−0.452437	+	0.990699i	−0.989147	+	0.146932i	$0.953060\pi$
$542$		0			0
$543$	64.6630	+	14.0666i	2.77496	+	0.603655i
$544$		0			0
$545$	21.2839	+	22.1603i	0.911701	+	0.949244i
$546$		0			0
$547$	−4.11046	−	18.8955i	−0.175751	−	0.807912i	−0.977614	−	0.210405i	$-0.932522\pi$
$547$	−4.11046	−	18.8955i	−0.175751	−	0.807912i	0.801864	−	0.597507i	$-0.203842\pi$
$548$		0			0
$549$	−98.0763	+	28.7978i	−4.18579	+	1.22906i
$550$		0			0
$551$		−	29.3174i		−	1.24896i
$552$		0			0
$553$	−27.3236	+	27.3236i	−1.16192	+	1.16192i
$554$		0			0
$555$	−34.7611	−	27.1328i	−1.47552	−	1.15172i
$556$		0			0
$557$	−9.37056	+	2.03844i	−0.397043	+	0.0863715i	−0.406654	−	0.913582i	$-0.633305\pi$
$557$	−9.37056	+	2.03844i	−0.397043	+	0.0863715i	0.00961040	+	0.999954i	$0.496941\pi$
$558$		0			0
$559$	0.741606	+	5.15798i	0.0313666	+	0.218159i
$560$		0			0
$561$	26.8383	−	17.2479i	1.13311	−	0.728207i
$562$		0			0
$563$	20.6166	−	7.68958i	0.868884	−	0.324077i	0.124815	−	0.992180i	$-0.460166\pi$
$563$	20.6166	−	7.68958i	0.868884	−	0.324077i	0.744069	+	0.668103i	$0.232893\pi$
$564$		0			0
$565$	10.2205	−	32.3772i	0.429981	−	1.36212i
$566$		0			0
$567$	88.4901	−	48.3193i	3.71624	−	2.02922i
$568$		0			0
$569$	−25.7436	−	29.7097i	−1.07923	−	1.24549i	−0.967799	−	0.251722i	$-0.919003\pi$
$569$	−25.7436	−	29.7097i	−1.07923	−	1.24549i	−0.111428	−	0.993773i	$-0.535542\pi$
$570$		0			0
$571$	14.2793	+	12.3731i	0.597570	+	0.517798i	0.900295	−	0.435280i	$-0.143351\pi$
$571$	14.2793	+	12.3731i	0.597570	+	0.517798i	−0.302725	+	0.953078i	$0.597896\pi$
$572$		0			0
$573$	−5.20469	+	13.9543i	−0.217429	+	0.582950i
$574$		0			0
$575$	13.1941	−	20.0229i	0.550231	−	0.835012i
$576$		0			0
$577$	−0.774082	+	2.07540i	−0.0322255	+	0.0863998i	−0.952066	−	0.305893i	$-0.901045\pi$
$577$	−0.774082	+	2.07540i	−0.0322255	+	0.0863998i	0.919841	+	0.392292i	$0.128318\pi$
$578$		0			0
$579$	7.07706	+	6.13231i	0.294113	+	0.254850i
$580$		0			0
$581$	12.5573	+	14.4919i	0.520964	+	0.601225i
$582$		0			0
$583$	9.40303	−	5.13444i	0.389434	−	0.212647i
$584$		0			0
$585$	−24.7072	+	78.2691i	−1.02152	+	3.23603i
$586$		0			0
$587$	0.128928	−	0.0480875i	0.00532141	−	0.00198478i	−0.346802	−	0.937938i	$-0.612732\pi$
$587$	0.128928	−	0.0480875i	0.00532141	−	0.00198478i	0.352123	+	0.935954i	$0.385460\pi$
$588$		0			0
$589$	34.9766	−	22.4781i	1.44119	−	0.926195i
$590$		0			0
$591$	6.71767	+	46.7224i	0.276328	+	1.92190i
$592$		0			0
$593$	38.2479	−	8.32032i	1.57065	−	0.341675i	0.658841	−	0.752282i	$-0.271047\pi$
$593$	38.2479	−	8.32032i	1.57065	−	0.341675i	0.911812	+	0.410607i	$0.134683\pi$
$594$		0			0
$595$	31.6119	+	24.6747i	1.29596	+	1.01157i
$596$		0			0
$597$	−6.25934	+	6.25934i	−0.256178	+	0.256178i
$598$		0			0
$599$			39.1031i			1.59771i	0.601524	+	0.798855i	$0.294561\pi$
$599$			39.1031i			1.59771i	−0.601524	+	0.798855i	$0.705439\pi$
$600$		0			0
$601$	−25.6764	+	7.53926i	−1.04736	+	0.307533i	−0.759751	−	0.650215i	$-0.774679\pi$
$601$	−25.6764	+	7.53926i	−1.04736	+	0.307533i	−0.287610	+	0.957748i	$0.592861\pi$
$602$		0			0
$603$	−3.90515	−	17.9517i	−0.159030	−	0.731049i
$604$		0			0
$605$	8.84939	+	9.21380i	0.359779	+	0.374594i
$606$		0			0
$607$	38.1582	+	8.30081i	1.54879	+	0.336919i	0.904032	−	0.427464i	$-0.140593\pi$
$607$	38.1582	+	8.30081i	1.54879	+	0.336919i	0.644761	+	0.764384i	$0.276957\pi$
$608$		0			0
$609$	−29.7009	+	65.0360i	−1.20354	+	2.63539i
$610$		0			0
$611$	−1.88334	+	13.0989i	−0.0761917	+	0.529925i
$612$		0			0
$613$	10.2815	+	18.8292i	0.415266	+	0.760503i	0.998664	−	0.0516836i	$-0.0164587\pi$
$613$	10.2815	+	18.8292i	0.415266	+	0.760503i	−0.583397	+	0.812187i	$0.698277\pi$
$614$		0			0
$615$	19.6072	−	12.0490i	0.790639	−	0.485863i
$616$		0			0
$617$	−0.324597	−	4.53845i	−0.0130678	−	0.182711i	−0.999794	−	0.0203163i	$-0.993533\pi$
$617$	−0.324597	−	4.53845i	−0.0130678	−	0.182711i	0.986726	−	0.162395i	$-0.0519219\pi$
$618$		0			0
$619$	10.0698	+	22.0498i	0.404740	+	0.886256i	0.996768	+	0.0803389i	$0.0256003\pi$
$619$	10.0698	+	22.0498i	0.404740	+	0.886256i	−0.592028	+	0.805917i	$0.701672\pi$
$620$		0			0
$621$	39.7119	−	56.3738i	1.59358	−	2.26220i
$622$		0			0
$623$	−21.1521	−	7.88932i	−0.847441	−	0.316079i
$624$		0			0
$625$	24.4770	−	5.08708i	0.979078	−	0.203483i
$626$		0			0
$627$	−2.93611	+	41.0521i	−0.117257	+	1.63946i
$628$		0			0
$629$	7.37815	−	25.1277i	0.294186	−	1.00191i
$630$		0			0
$631$	22.1266	+	3.18133i	0.880847	+	0.126647i	0.567874	−	0.823115i	$-0.307766\pi$
$631$	22.1266	+	3.18133i	0.880847	+	0.126647i	0.312973	+	0.949762i	$0.398675\pi$
$632$		0			0
$633$	12.6676	+	33.9632i	0.503493	+	1.34992i
$634$		0			0
$635$	−31.0861	+	13.4455i	−1.23361	+	0.533570i
$636$		0			0
$637$	−30.8784	+	41.2488i	−1.22345	+	1.63434i
$638$		0			0
$639$	6.47328	−	10.0726i	0.256079	−	0.398467i
$640$		0			0
$641$	−8.14988	−	27.7559i	−0.321901	−	1.09629i	−0.948454	−	0.316915i	$-0.897353\pi$
$641$	−8.14988	−	27.7559i	−0.321901	−	1.09629i	0.626553	−	0.779379i	$-0.284465\pi$
$642$		0			0
$643$	−18.1303	−	18.1303i	−0.714991	−	0.714991i	0.252584	−	0.967575i	$-0.418720\pi$
$643$	−18.1303	−	18.1303i	−0.714991	−	0.714991i	−0.967575	+	0.252584i	$0.918720\pi$
$644$		0			0
$645$	6.20952	−	4.45583i	0.244500	−	0.175448i
$646$		0			0
$647$	−9.88940	−	5.40002i	−0.388792	−	0.212297i	0.272950	−	0.962028i	$-0.412001\pi$
$647$	−9.88940	−	5.40002i	−0.388792	−	0.212297i	−0.661742	+	0.749732i	$0.730183\pi$
$648$		0			0
$649$	−16.0938	−	10.3429i	−0.631737	−	0.405993i
$650$		0			0
$651$	−100.362	+	14.4299i	−3.93351	+	0.565554i
$652$		0			0
$653$	−7.86005	+	36.1320i	−0.307587	+	1.41396i	0.520742	+	0.853714i	$0.325655\pi$
$653$	−7.86005	+	36.1320i	−0.307587	+	1.41396i	−0.828329	+	0.560242i	$0.810708\pi$
$654$		0			0
$655$	0.0105807	+	0.0538456i	0.000413421	+	0.00210392i
$656$		0			0
$657$	−42.1625	+	31.5624i	−1.64492	+	1.23137i
$658$		0			0
$659$	34.0520	+	9.99856i	1.32648	+	0.389489i	0.866826	−	0.498611i	$-0.166156\pi$
$659$	34.0520	+	9.99856i	1.32648	+	0.389489i	0.459651	+	0.888100i	$0.347975\pi$
$660$		0			0
$661$	2.19716	−	1.90385i	0.0854598	−	0.0740513i	−0.611083	−	0.791566i	$-0.709266\pi$
$661$	2.19716	−	1.90385i	0.0854598	−	0.0740513i	0.696543	+	0.717515i	$0.254721\pi$
$662$		0			0
$663$	−68.2028	+	4.87796i	−2.64878	+	0.189444i
$664$		0			0
$665$	−49.9227	+	13.5711i	−1.93592	+	0.526265i
$666$		0			0
$667$	0.733665	+	25.3794i	0.0284076	+	0.982693i
$668$		0			0
$669$	42.4854	−	19.4024i	1.64258	−	0.750141i
$670$		0			0
$671$	−20.6638	+	23.8473i	−0.797718	+	0.920615i
$672$		0			0
$673$	17.2311	+	1.23239i	0.664210	+	0.0475052i	0.399374	−	0.916788i	$-0.369228\pi$
$673$	17.2311	+	1.23239i	0.664210	+	0.0475052i	0.264836	+	0.964293i	$0.414682\pi$
$674$		0			0
$675$	70.8086	−	12.4361i	2.72543	−	0.478666i
$676$		0			0
$677$	−22.4257	−	29.9572i	−0.861890	−	1.15135i	−0.987240	−	0.159238i	$-0.949096\pi$
$677$	−22.4257	−	29.9572i	−0.861890	−	1.15135i	0.125350	−	0.992113i	$-0.459994\pi$
$678$		0			0
$679$	−44.7324	−	20.4286i	−1.71667	−	0.783978i
$680$		0			0
$681$	9.80972	+	15.2642i	0.375909	+	0.584926i
$682$		0			0
$683$	25.1699	+	18.8420i	0.963100	+	0.720968i	0.960283	−	0.279028i	$-0.0900124\pi$
$683$	25.1699	+	18.8420i	0.963100	+	0.720968i	0.00281712	+	0.999996i	$0.499103\pi$
$684$		0			0
$685$	1.06617	−	1.18141i	0.0407364	−	0.0451395i
$686$		0			0
$687$	29.4838	−	53.9955i	1.12488	−	2.06006i
$688$		0			0
$689$	−22.9623			−0.874792
$690$		0			0
$691$	28.8391			1.09709			0.548546	−	0.836120i	$-0.315182\pi$
$691$	28.8391			1.09709			0.548546	+	0.836120i	$0.315182\pi$
$692$		0			0
$693$	34.2909	−	62.7991i	1.30260	−	2.38554i
$694$		0			0
$695$	−0.791825	−	15.4432i	−0.0300357	−	0.585794i
$696$		0			0
$697$	10.9413	+	8.19058i	0.414432	+	0.310240i
$698$		0			0
$699$	−25.2557	−	39.2986i	−0.955257	−	1.48641i
$700$		0			0
$701$	8.28667	+	3.78439i	0.312983	+	0.142935i	0.565713	−	0.824602i	$-0.308601\pi$
$701$	8.28667	+	3.78439i	0.312983	+	0.142935i	−0.252730	+	0.967537i	$0.581328\pi$
$702$		0			0
$703$	20.2467	+	27.0464i	0.763619	+	1.02008i
$704$		0			0
$705$	18.3186	−	6.41465i	0.689918	−	0.241590i
$706$		0			0
$707$	−25.4179	−	1.81792i	−0.955937	−	0.0683699i
$708$		0			0
$709$	−14.7992	+	17.0792i	−0.555795	+	0.641422i	−0.962223	−	0.272261i	$-0.912229\pi$
$709$	−14.7992	+	17.0792i	−0.555795	+	0.641422i	0.406428	+	0.913683i	$0.366774\pi$
$710$		0			0
$711$	−62.6623	+	28.6169i	−2.35002	+	1.07322i
$712$		0			0
$713$	−29.7159	+	20.3341i	−1.11287	+	0.761517i
$714$		0			0
$715$	6.64648	+	24.4498i	0.248564	+	0.914370i
$716$		0			0
$717$	41.4879	−	2.96727i	1.54939	−	0.110815i
$718$		0			0
$719$	−31.2180	+	27.0506i	−1.16424	+	1.00882i	−0.164487	+	0.986379i	$0.552597\pi$
$719$	−31.2180	+	27.0506i	−1.16424	+	1.00882i	−0.999748	+	0.0224362i	$0.992858\pi$
$720$		0			0
$721$	−61.9693	−	18.1958i	−2.30786	−	0.677648i
$722$		0			0
$723$	8.30246	−	6.21514i	0.308772	−	0.231144i
$724$		0			0
$725$	−18.1275	+	19.2899i	−0.673237	+	0.716410i
$726$		0			0
$727$	−1.91054	+	8.78260i	−0.0708579	+	0.325728i	−0.998908	−	0.0467277i	$-0.985121\pi$
$727$	−1.91054	+	8.78260i	−0.0708579	+	0.325728i	0.928050	+	0.372456i	$0.121484\pi$
$728$		0			0
$729$	39.9004	−	5.73681i	1.47779	−	0.212474i
$730$		0			0
$731$	3.81842	+	2.45395i	0.141229	+	0.0907627i
$732$		0			0
$733$	24.9032	+	13.5982i	0.919820	+	0.502260i	0.868093	−	0.496401i	$-0.165346\pi$
$733$	24.9032	+	13.5982i	0.919820	+	0.502260i	0.0517271	+	0.998661i	$0.483527\pi$
$734$		0			0
$735$	74.5701	+	12.2615i	2.75056	+	0.452272i
$736$		0			0
$737$	−4.01024	−	4.01024i	−0.147719	−	0.147719i
$738$		0			0
$739$	14.1334	+	48.1338i	0.519904	+	1.77063i	0.629876	+	0.776696i	$0.283106\pi$
$739$	14.1334	+	48.1338i	0.519904	+	1.77063i	−0.109972	+	0.993935i	$0.535076\pi$
$740$		0			0
$741$	47.6908	−	74.2084i	1.75197	−	2.72611i
$742$		0			0
$743$	8.32714	−	11.1238i	0.305493	−	0.408091i	−0.621354	−	0.783530i	$-0.713417\pi$
$743$	8.32714	−	11.1238i	0.305493	−	0.408091i	0.926847	+	0.375439i	$0.122508\pi$
$744$		0			0
$745$	−6.89760	+	17.4122i	−0.252708	+	0.637934i
$746$		0			0
$747$	11.9464	+	32.0296i	0.437096	+	1.17190i
$748$		0			0
$749$	−23.5595	−	3.38735i	−0.860845	−	0.123771i
$750$		0			0
$751$	6.66147	−	22.6869i	0.243080	−	0.827856i	−0.744076	−	0.668096i	$-0.767110\pi$
$751$	6.66147	−	22.6869i	0.243080	−	0.827856i	0.987156	−	0.159760i	$-0.0510721\pi$
$752$		0			0
$753$	−0.654320	+	9.14859i	−0.0238447	+	0.333393i
$754$		0			0
$755$	0.847732	−	9.23175i	0.0308521	−	0.335978i
$756$		0			0
$757$	3.83338	+	1.42978i	0.139327	+	0.0519661i	0.418160	−	0.908373i	$-0.362675\pi$
$757$	3.83338	+	1.42978i	0.139327	+	0.0519661i	−0.278834	+	0.960339i	$0.589948\pi$
$758$		0			0
$759$	1.51439	−	35.6113i	0.0549689	−	1.29261i
$760$		0			0
$761$	−15.7521	−	34.4922i	−0.571012	−	1.25034i	−0.946257	−	0.323417i	$-0.895168\pi$
$761$	−15.7521	−	34.4922i	−0.571012	−	1.25034i	0.375244	−	0.926926i	$-0.377559\pi$
$762$		0			0
$763$	4.09559	+	57.2638i	0.148270	+	2.07309i
$764$		0			0
$765$	37.4300	+	60.9094i	1.35329	+	2.20218i
$766$		0			0
$767$	19.6506	+	35.9873i	0.709541	+	1.29943i
$768$		0			0
$769$	0.722968	−	5.02835i	0.0260709	−	0.181327i	−0.972625	−	0.232380i	$-0.925349\pi$
$769$	0.722968	−	5.02835i	0.0260709	−	0.181327i	0.998696	+	0.0510530i	$0.0162578\pi$
$770$		0			0
$771$	14.0781	−	30.8267i	0.507009	−	1.11020i
$772$		0			0
$773$	10.7096	+	2.32974i	0.385199	+	0.0837950i	0.400995	−	0.916080i	$-0.368664\pi$
$773$	10.7096	+	2.32974i	0.385199	+	0.0837950i	−0.0157957	+	0.999875i	$0.505028\pi$
$774$		0			0
$775$	−36.9122	−	6.83679i	−1.32593	−	0.245585i
$776$		0			0
$777$	−17.5138	−	80.5099i	−0.628306	−	2.88828i
$778$		0			0
$779$	−16.9178	+	4.96752i	−0.606144	+	0.177980i
$780$		0			0
$781$		−	3.69620i		−	0.132260i
$782$		0			0
$783$	−53.8265	+	53.8265i	−1.92360	+	1.92360i
$784$		0			0
$785$	−1.98304	−	16.0900i	−0.0707778	−	0.574277i
$786$		0			0
$787$	−24.7543	+	5.38497i	−0.882396	+	0.191953i	−0.630862	−	0.775895i	$-0.717299\pi$
$787$	−24.7543	+	5.38497i	−0.882396	+	0.191953i	−0.251534	+	0.967848i	$0.580935\pi$
$788$		0			0
$789$	−3.22925	−	22.4600i	−0.114964	−	0.799596i
$790$		0			0
$791$	53.3673	−	34.2971i	1.89752	−	1.21946i
$792$		0			0
$793$	63.3665	−	23.6345i	2.25021	−	0.839286i
$794$		0			0
$795$	15.5406	+	29.8779i	0.551169	+	1.05966i
$796$		0			0
$797$	−18.2752	+	9.97904i	−0.647342	+	0.353476i	−0.769141	−	0.639079i	$-0.779316\pi$
$797$	−18.2752	+	9.97904i	−0.647342	+	0.353476i	0.121799	+	0.992555i	$0.461134\pi$
$798$		0			0
$799$	7.54851	+	8.71145i	0.267047	+	0.308189i
$800$		0			0
$801$	−30.4160	−	26.3556i	−1.07470	−	0.931230i
$802$		0			0
$803$	−5.68178	+	15.2334i	−0.200506	+	0.537577i
$804$		0			0
$805$	42.8773	−	12.9975i	1.51123	−	0.458101i
$806$		0			0
$807$	−32.2882	+	86.5680i	−1.13660	+	3.04734i
$808$		0			0
$809$	−4.58736	−	3.97497i	−0.161283	−	0.139753i	0.570480	−	0.821311i	$-0.306757\pi$
$809$	−4.58736	−	3.97497i	−0.161283	−	0.139753i	−0.731764	+	0.681559i	$0.761302\pi$
$810$		0			0
$811$	−33.2168	−	38.3343i	−1.16640	−	1.34610i	−0.926948	−	0.375190i	$-0.877577\pi$
$811$	−33.2168	−	38.3343i	−1.16640	−	1.34610i	−0.239453	−	0.970908i	$-0.576968\pi$
$812$		0			0
$813$	59.2179	−	32.3354i	2.07686	−	1.13405i
$814$		0			0
$815$	27.4086	+	8.65210i	0.960083	+	0.303070i
$816$		0			0
$817$	−5.48642	+	2.04633i	−0.191946	+	0.0715920i
$818$		0			0
$819$	−129.011	+	82.9104i	−4.50801	+	2.89712i
$820$		0			0
$821$	1.76169	+	12.2528i	0.0614835	+	0.427627i	0.997194	+	0.0748585i	$0.0238505\pi$
$821$	1.76169	+	12.2528i	0.0614835	+	0.427627i	−0.935711	+	0.352768i	$0.885240\pi$
$822$		0			0
$823$	−13.4731	+	2.93089i	−0.469642	+	0.102164i	−0.441157	−	0.897430i	$-0.645432\pi$
$823$	−13.4731	+	2.93089i	−0.469642	+	0.102164i	−0.0284846	+	0.999594i	$0.509068\pi$
$824$		0			0
$825$	27.3152	−	25.1956i	0.950992	−	0.877198i
$826$		0			0
$827$	−7.11232	+	7.11232i	−0.247320	+	0.247320i	−0.819870	−	0.572550i	$-0.805954\pi$
$827$	−7.11232	+	7.11232i	−0.247320	+	0.247320i	0.572550	+	0.819870i	$0.305954\pi$
$828$		0			0
$829$		−	42.7316i		−	1.48413i	−0.670329	−	0.742064i	$-0.733847\pi$
$829$		−	42.7316i		−	1.48413i	0.670329	−	0.742064i	$-0.266153\pi$
$830$		0			0
$831$	−13.8030	+	4.05292i	−0.478820	+	0.140594i
$832$		0			0
$833$	9.54012	+	43.8552i	0.330545	+	1.51949i
$834$		0			0
$835$	0.712338	−	35.3096i	0.0246515	−	1.22194i
$836$		0			0
$837$	−105.487	−	22.9472i	−3.64615	−	0.793171i
$838$		0			0
$839$	−14.6209	+	32.0152i	−0.504769	+	1.10529i	0.470121	+	0.882602i	$0.344210\pi$
$839$	−14.6209	+	32.0152i	−0.504769	+	1.10529i	−0.974890	+	0.222687i	$0.928517\pi$
$840$		0			0
$841$	−0.138294	+	0.961854i	−0.00476875	+	0.0331674i
$842$		0			0
$843$	−32.9144	−	60.2782i	−1.13363	−	2.07609i
$844$		0			0
$845$	5.86058	−	24.5461i	0.201610	−	0.844410i
$846$		0			0
$847$	1.70286	+	23.8091i	0.0585109	+	0.818090i
$848$		0			0
$849$	−13.5375	−	29.6429i	−0.464605	−	1.01734i
$850$		0			0
$851$	−18.2039	−	22.9068i	−0.624023	−	0.785234i
$852$		0			0
$853$	−45.7228	−	17.0537i	−1.56552	−	0.583909i	−0.590698	−	0.806893i	$-0.701147\pi$
$853$	−45.7228	−	17.0537i	−1.56552	−	0.583909i	−0.974822	+	0.222985i	$0.928420\pi$
$854$		0			0
$855$	−91.8425	−	8.43371i	−3.14095	−	0.288427i
$856$		0			0
$857$	1.83633	−	25.6752i	0.0627278	−	0.877049i	−0.864519	−	0.502600i	$-0.832377\pi$
$857$	1.83633	−	25.6752i	0.0627278	−	0.877049i	0.927247	−	0.374450i	$-0.122168\pi$
$858$		0			0
$859$	13.3715	−	45.5390i	0.456228	−	1.55377i	−0.334980	−	0.942225i	$-0.608730\pi$
$859$	13.3715	−	45.5390i	0.456228	−	1.55377i	0.791209	−	0.611546i	$-0.209452\pi$
$860$		0			0
$861$	42.5620	+	6.11950i	1.45051	+	0.208552i
$862$		0			0
$863$	0.0330663	+	0.0886542i	0.00112559	+	0.00301782i	0.937511	−	0.347955i	$-0.113124\pi$
$863$	0.0330663	+	0.0886542i	0.00112559	+	0.00301782i	−0.936386	+	0.350973i	$0.885851\pi$
$864$		0			0
$865$	−3.99581	−	9.23833i	−0.135862	−	0.314113i
$866$		0			0
$867$	−2.76154	+	3.68898i	−0.0937867	+	0.125284i
$868$		0			0
$869$	−11.4971	+	17.8898i	−0.390013	+	0.606871i
$870$		0			0
$871$	3.42456	+	11.6630i	0.116037	+	0.395185i
$872$		0			0
$873$	−61.9910	−	61.9910i	−2.09808	−	2.09808i
$874$		0			0
$875$	41.2389	+	21.9388i	1.39413	+	0.741666i
$876$		0			0
$877$	−24.2848	−	13.2605i	−0.820041	−	0.447776i	0.0137174	−	0.999906i	$-0.495633\pi$
$877$	−24.2848	−	13.2605i	−0.820041	−	0.447776i	−0.833758	+	0.552130i	$0.813815\pi$
$878$		0			0
$879$	19.9275	+	12.8066i	0.672136	+	0.431956i
$880$		0			0
$881$	17.6335	−	2.53531i	0.594088	−	0.0854169i	0.161288	−	0.986907i	$-0.448435\pi$
$881$	17.6335	−	2.53531i	0.594088	−	0.0854169i	0.432799	+	0.901490i	$0.357526\pi$
$882$		0			0
$883$	4.86128	−	22.3469i	0.163595	−	0.752034i	−0.820104	−	0.572214i	$-0.806085\pi$
$883$	4.86128	−	22.3469i	0.163595	−	0.752034i	0.983699	−	0.179820i	$-0.0575516\pi$
$884$		0			0
$885$	33.5265	−	49.9247i	1.12698	−	1.67820i
$886$		0			0
$887$	40.1788	−	30.0775i	1.34907	−	1.00990i	0.351803	−	0.936074i	$-0.385569\pi$
$887$	40.1788	−	30.0775i	1.34907	−	1.00990i	0.997271	−	0.0738299i	$-0.0235222\pi$
$888$		0			0
$889$	−60.7199	−	17.8290i	−2.03648	−	0.597964i
$890$		0			0
$891$	41.9338	−	36.3358i	1.40483	−	1.21730i
$892$		0			0
$893$	−14.8327	+	1.06086i	−0.496357	+	0.0355002i
$894$		0			0
$895$	−10.4774	+	18.3005i	−0.350222	+	0.611717i
$896$		0			0
$897$	−39.4278	+	65.4339i	−1.31645	+	2.18477i
$898$		0			0
$899$	36.1566	−	16.5122i	1.20589	−	0.550712i
$900$		0			0
$901$	−13.0978	+	15.1156i	−0.436350	+	0.503575i
$902$		0			0
$903$	14.2439	+	1.01874i	0.474006	+	0.0339016i
$904$		0			0
$905$	15.1295	+	43.2058i	0.502921	+	1.43621i
$906$		0			0
$907$	−9.35076	−	12.4912i	−0.310487	−	0.414762i	0.617970	−	0.786202i	$-0.287955\pi$
$907$	−9.35076	−	12.4912i	−0.310487	−	0.414762i	−0.928457	+	0.371439i	$0.878864\pi$
$908$		0			0
$909$	−41.3238	−	18.8719i	−1.37062	−	0.625943i
$910$		0			0
$911$	−11.0404	−	17.1791i	−0.365783	−	0.569170i	0.608764	−	0.793351i	$-0.291666\pi$
$911$	−11.0404	−	17.1791i	−0.365783	−	0.569170i	−0.974547	+	0.224181i	$0.928029\pi$
$912$		0			0
$913$	8.44807	+	6.32415i	0.279590	+	0.209299i
$914$		0			0
$915$	−73.6384	−	66.4553i	−2.43441	−	2.19695i
$916$		0			0
$917$	−0.0491384	+	0.0899903i	−0.00162269	+	0.00297174i
$918$		0			0
$919$	−22.4132			−0.739343			−0.369671	−	0.929163i	$-0.620530\pi$
$919$	−22.4132			−0.739343			−0.369671	+	0.929163i	$0.620530\pi$
$920$		0			0
$921$	79.2155			2.61024
$922$		0			0
$923$	−3.79663	+	6.95301i	−0.124968	+	0.228861i
$924$		0			0
$925$	3.40160	−	30.3146i	0.111844	−	0.996739i
$926$		0			0
$927$	−92.1734	−	69.0002i	−3.02737	−	2.26626i
$928$		0			0
$929$	11.0398	+	17.1783i	0.362204	+	0.563600i	0.973753	−	0.227606i	$-0.0730898\pi$
$929$	11.0398	+	17.1783i	0.362204	+	0.563600i	−0.611549	+	0.791206i	$0.709453\pi$
$930$		0			0
$931$	−52.6675	−	24.0525i	−1.72611	−	0.788287i
$932$		0			0
$933$	−18.0344	−	24.0911i	−0.590419	−	0.788708i
$934$		0			0
$935$	19.8860	+	9.57101i	0.650343	+	0.313005i
$936$		0			0
$937$	16.1300	+	1.15364i	0.526946	+	0.0376879i	0.332278	−	0.943181i	$-0.392183\pi$
$937$	16.1300	+	1.15364i	0.526946	+	0.0376879i	0.194667	+	0.980869i	$0.437637\pi$
$938$		0			0
$939$	−28.6428	+	33.0555i	−0.934721	+	1.07873i
$940$		0			0
$941$	−51.1471	+	23.3581i	−1.66735	+	0.761452i	−0.667488	+	0.744620i	$0.732631\pi$
$941$	−51.1471	+	23.3581i	−1.66735	+	0.761452i	−0.999858	+	0.0168314i	$0.994642\pi$
$942$		0			0
$943$	14.5210	−	4.72363i	0.472870	−	0.153823i
$944$		0			0
$945$	116.574	+	66.7413i	3.79216	+	2.17110i
$946$		0			0
$947$	13.4467	−	0.961725i	0.436958	−	0.0312519i	0.148872	−	0.988856i	$-0.452436\pi$
$947$	13.4467	−	0.961725i	0.436958	−	0.0312519i	0.288086	+	0.957605i	$0.406981\pi$
$948$		0			0
$949$	26.3355	−	22.8199i	0.854888	−	0.740764i
$950$		0			0
$951$	41.9387	+	12.3143i	1.35996	+	0.399319i
$952$		0			0
$953$	41.1618	−	30.8133i	1.33336	−	0.998142i	0.334925	−	0.942245i	$-0.391289\pi$
$953$	41.1618	−	30.8133i	1.33336	−	0.998142i	0.998437	−	0.0558973i	$-0.0178019\pi$
$954$		0			0
$955$	−10.1095	+	1.98651i	−0.327135	+	0.0642821i
$956$		0			0
$957$	−8.36387	+	38.4481i	−0.270365	+	1.24285i
$958$		0			0
$959$	2.94314	−	0.423160i	0.0950391	−	0.0136646i
$960$		0			0
$961$	21.3427	+	13.7161i	0.688473	+	0.442455i
$962$		0			0
$963$	−37.2419	−	20.3356i	−1.20011	−	0.655307i
$964$		0			0
$965$	−1.05105	+	6.39212i	−0.0338345	+	0.205770i
$966$		0			0
$967$	−28.5701	−	28.5701i	−0.918753	−	0.918753i	0.0781856	−	0.996939i	$-0.475087\pi$
$967$	−28.5701	−	28.5701i	−0.918753	−	0.918753i	−0.996939	+	0.0781856i	$0.975087\pi$
$968$		0			0
$969$	−21.6470	−	73.7228i	−0.695401	−	2.36832i
$970$		0			0
$971$	15.9668	−	24.8448i	0.512399	−	0.797308i	−0.484599	−	0.874736i	$-0.661034\pi$
$971$	15.9668	−	24.8448i	0.512399	−	0.797308i	0.996998	+	0.0774281i	$0.0246708\pi$
$972$		0			0
$973$	17.3148	−	23.1299i	0.555088	−	0.741511i
$974$		0			0
$975$	−77.2635	+	19.3387i	−2.47441	+	0.619334i
$976$		0			0
$977$	20.9997	+	56.3025i	0.671841	+	1.80128i	0.594233	+	0.804293i	$0.297456\pi$
$977$	20.9997	+	56.3025i	0.671841	+	1.80128i	0.0776081	+	0.996984i	$0.475272\pi$
$978$		0			0
$979$	−12.2976	−	1.76813i	−0.393033	−	0.0565097i
$980$		0			0
$981$	−28.8345	+	98.2013i	−0.920615	+	3.13533i
$982$		0			0
$983$	−0.616629	+	8.62160i	−0.0196674	+	0.274986i	0.978097	+	0.208151i	$0.0667446\pi$
$983$	−0.616629	+	8.62160i	−0.0196674	+	0.274986i	−0.997764	+	0.0668350i	$0.978710\pi$
$984$		0			0
$985$	−25.1043	+	20.8815i	−0.799888	+	0.665339i
$986$		0			0
$987$	33.9788	+	12.6734i	1.08156	+	0.403400i
$988$		0			0
$989$	4.69826	−	1.90876i	0.149396	−	0.0606950i
$990$		0			0
$991$	−18.4846	−	40.4757i	−0.587184	−	1.28575i	−0.937129	−	0.348983i	$-0.886527\pi$
$991$	−18.4846	−	40.4757i	−0.587184	−	1.28575i	0.349945	−	0.936770i	$-0.386200\pi$
$992$		0			0
$993$	−6.46350	−	90.3716i	−0.205113	−	2.86785i
$994$		0			0
$995$	−5.95618	−	1.42209i	−0.188824	−	0.0450832i
$996$		0			0
$997$	22.2631	+	40.7718i	0.705080	+	1.29126i	0.947085	+	0.320982i	$0.104013\pi$
$997$	22.2631	+	40.7718i	0.705080	+	1.29126i	−0.242006	+	0.970275i	$0.577805\pi$
$998$		0			0
$999$	12.4843	−	86.8299i	0.394984	−	2.74718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.617.2	yes	720
5.3	odd	4	inner	920.2.bv.a.433.2	yes	720
23.17	odd	22	inner	920.2.bv.a.17.2	✓	720
115.63	even	44	inner	920.2.bv.a.753.2	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.2	✓	720	23.17	odd	22	inner
920.2.bv.a.433.2	yes	720	5.3	odd	4	inner
920.2.bv.a.617.2	yes	720	1.1	even	1	trivial
920.2.bv.a.753.2	yes	720	115.63	even	44	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.54911 + 2.83699i) q^{3} +(-2.23313 + 0.114500i) q^{5} +(-3.34466 - 2.50378i) q^{7} +(-4.02684 - 6.26588i) q^{9} +(-2.09151 - 0.955162i) q^{11} +(2.95328 + 3.94512i) q^{13} +(3.13454 - 6.51275i) q^{15} +(4.28157 + 0.306224i) q^{17} +(-3.62640 + 4.18509i) q^{19} +(12.2844 - 5.61012i) q^{21} +(3.03456 - 3.71368i) q^{23} +(4.97378 - 0.511389i) q^{25} +(14.3418 - 1.02575i) q^{27} +(-4.00107 + 3.46695i) q^{29} +(-7.20387 - 2.11525i) q^{31} +(5.94977 - 4.45395i) q^{33} +(7.75575 + 5.20831i) q^{35} +(1.29686 - 5.96155i) q^{37} +(-15.7673 + 2.26699i) q^{39} +(2.67857 + 1.72141i) q^{41} +(0.928072 + 0.506766i) q^{43} +(9.70992 + 13.5315i) q^{45} +(1.89883 + 1.89883i) q^{47} +(2.94569 + 10.0321i) q^{49} +(-7.50139 + 11.6724i) q^{51} +(-2.79232 + 3.73011i) q^{53} +(4.77999 + 1.89353i) q^{55} +(-6.25535 - 16.7712i) q^{57} +(8.23557 + 1.18410i) q^{59} +(3.86637 - 13.1677i) q^{61} +(-2.21999 + 31.0395i) q^{63} +(-7.04680 - 8.47184i) q^{65} +(2.31104 + 0.861972i) q^{67} +(5.83481 + 14.3619i) q^{69} +(0.667794 + 1.46227i) q^{71} +(-0.504447 - 7.05309i) q^{73} +(-6.25414 + 14.9028i) q^{75} +(4.60388 + 8.43137i) q^{77} +(1.31624 - 9.15465i) q^{79} +(-10.0247 + 21.9511i) q^{81} +(-4.48476 - 0.975600i) q^{83} +(-9.59638 - 0.193598i) q^{85} +(-3.63758 - 16.7217i) q^{87} +(5.18455 - 1.52232i) q^{89} -20.5895i q^{91} +(17.1606 - 17.1606i) q^{93} +(7.61905 - 9.76109i) q^{95} +(11.5013 - 2.50196i) q^{97} +(2.43725 + 16.9514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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

Related objects

Downloads

Learn more