LMFDB - Embedded newform 720.2.cu.a.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	720.257
Dual form			720.2.cu.a.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.599900 + 1.62484i) q^{3} +(0.792893 + 2.09077i) q^{5} +(-1.18034 + 4.40508i) q^{7} +(-2.28024 - 1.94949i) q^{9} +(0.550510 - 0.317837i) q^{11} +(0.896575 + 3.34607i) q^{13} +(-3.87283 + 0.0340742i) q^{15} +(-0.317837 + 0.317837i) q^{17} -6.44949i q^{19} +(-6.44949 - 4.56048i) q^{21} +(0.965926 - 0.258819i) q^{23} +(-3.74264 + 3.31552i) q^{25} +(4.53553 - 2.53553i) q^{27} +(0.158919 + 0.275255i) q^{29} +(0.224745 - 0.389270i) q^{31} +(0.186185 + 1.08516i) q^{33} +(-10.1459 + 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-5.97469 - 0.550510i) q^{39} +(6.39898 + 3.69445i) q^{41} +(-3.34607 - 0.896575i) q^{43} +(2.26795 - 6.31319i) q^{45} +(8.69333 + 2.32937i) q^{47} +(-11.9494 - 6.89898i) q^{49} +(-0.325765 - 0.707107i) q^{51} +(-3.78194 - 3.78194i) q^{53} +(1.10102 + 0.898979i) q^{55} +(10.4794 + 3.86905i) q^{57} +(-4.48905 + 7.77526i) q^{59} +(0.275255 + 0.476756i) q^{61} +(11.2791 - 7.74358i) q^{63} +(-6.28497 + 4.52761i) q^{65} +(-6.38512 + 1.71089i) q^{67} +(-0.158919 + 1.72474i) q^{69} +6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +(-3.14198 - 8.07019i) q^{75} +(0.750311 + 2.80020i) q^{77} +(-2.12132 + 1.22474i) q^{79} +(1.39898 + 8.89060i) q^{81} +(-1.41043 + 5.26380i) q^{83} +(-0.916536 - 0.412514i) q^{85} +(-0.542582 + 0.0930924i) q^{87} +8.02458 q^{89} -15.7980 q^{91} +(0.497678 + 0.598698i) q^{93} +(13.4844 - 5.11376i) q^{95} +(0.695075 - 2.59405i) q^{97} +(-1.87492 - 0.348469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 12 q^{5} + 8 q^{7} + 24 q^{11} - 16 q^{15} - 32 q^{21} + 4 q^{25} + 8 q^{27} - 8 q^{31} + 16 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} - 32 q^{51} + 48 q^{55} + 28 q^{57} + 12 q^{61} + 32 q^{63}+ \cdots + 12 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^5 + 8 * q^7 + 24 * q^11 - 16 * q^15 - 32 * q^21 + 4 * q^25 + 8 * q^27 - 8 * q^31 + 16 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 - 32 * q^51 + 48 * q^55 + 28 * q^57 + 12 * q^61 + 32 * q^63 - 24 * q^65 - 4 * q^67 - 16 * q^73 - 8 * q^75 + 24 * q^77 - 28 * q^81 - 12 * q^83 - 20 * q^85 + 8 * q^87 - 48 * q^91 - 20 * q^93 + 24 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.599900	+	1.62484i	−0.346353	+	0.938104i
$3$	−0.599900	+	1.62484i	−0.346353	+	0.938104i
$4$		0			0
$5$	0.792893	+	2.09077i	0.354593	+	0.935021i
$5$	0.792893	+	2.09077i	0.354593	+	0.935021i
$6$		0			0
$7$	−1.18034	+	4.40508i	−0.446126	+	1.66497i	0.266820	+	0.963746i	$0.414027\pi$
$7$	−1.18034	+	4.40508i	−0.446126	+	1.66497i	−0.712946	+	0.701219i	$0.752640\pi$
$8$		0			0
$9$	−2.28024	−	1.94949i	−0.760080	−	0.649830i
$10$		0			0
$11$	0.550510	−	0.317837i	0.165985	−	0.0958315i	−0.414706	−	0.909955i	$-0.636116\pi$
$11$	0.550510	−	0.317837i	0.165985	−	0.0958315i	0.580691	+	0.814124i	$0.302782\pi$
$12$		0			0
$13$	0.896575	+	3.34607i	0.248665	+	0.928032i	0.971506	+	0.237016i	$0.0761695\pi$
$13$	0.896575	+	3.34607i	0.248665	+	0.928032i	−0.722840	+	0.691015i	$0.757164\pi$
$14$		0			0
$15$	−3.87283	+	0.0340742i	−0.999961	+	0.00879791i
$16$		0			0
$17$	−0.317837	+	0.317837i	−0.0770869	+	0.0770869i	−0.744599	−	0.667512i	$-0.767359\pi$
$17$	−0.317837	+	0.317837i	−0.0770869	+	0.0770869i	0.667512	+	0.744599i	$0.267359\pi$
$18$		0			0
$19$		−	6.44949i		−	1.47961i	−0.672819	−	0.739807i	$-0.734917\pi$
$19$		−	6.44949i		−	1.47961i	0.672819	−	0.739807i	$-0.265083\pi$
$20$		0			0
$21$	−6.44949	−	4.56048i	−1.40739	−	0.995178i
$22$		0			0
$23$	0.965926	−	0.258819i	0.201409	−	0.0539675i	−0.156704	−	0.987646i	$-0.550087\pi$
$23$	0.965926	−	0.258819i	0.201409	−	0.0539675i	0.358113	+	0.933678i	$0.383420\pi$
$24$		0			0
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$		0			0
$27$	4.53553	−	2.53553i	0.872864	−	0.487964i
$28$		0			0
$29$	0.158919	+	0.275255i	0.0295104	+	0.0511136i	0.880403	−	0.474225i	$-0.157272\pi$
$29$	0.158919	+	0.275255i	0.0295104	+	0.0511136i	−0.850893	+	0.525339i	$0.823939\pi$
$30$		0			0
$31$	0.224745	−	0.389270i	0.0403654	−	0.0699149i	−0.845137	−	0.534550i	$-0.820481\pi$
$31$	0.224745	−	0.389270i	0.0403654	−	0.0699149i	0.885502	+	0.464635i	$0.153814\pi$
$32$		0			0
$33$	0.186185	+	1.08516i	0.0324106	+	0.188903i
$34$		0			0
$35$	−10.1459	+	1.02494i	−1.71497	+	0.173247i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$	−5.97469	−	0.550510i	−0.956716	−	0.0881522i
$40$		0			0
$41$	6.39898	+	3.69445i	0.999353	+	0.576977i	0.908057	−	0.418847i	$-0.137566\pi$
$41$	6.39898	+	3.69445i	0.999353	+	0.576977i	0.0912960	+	0.995824i	$0.470899\pi$
$42$		0			0
$43$	−3.34607	−	0.896575i	−0.510270	−	0.136726i	−0.00550783	−	0.999985i	$-0.501753\pi$
$43$	−3.34607	−	0.896575i	−0.510270	−	0.136726i	−0.504762	+	0.863258i	$0.668420\pi$
$44$		0			0
$45$	2.26795	−	6.31319i	0.338086	−	0.941115i
$46$		0			0
$47$	8.69333	+	2.32937i	1.26805	+	0.339774i	0.829285	−	0.558827i	$-0.188748\pi$
$47$	8.69333	+	2.32937i	1.26805	+	0.339774i	0.438768	+	0.898600i	$0.355415\pi$
$48$		0			0
$49$	−11.9494	−	6.89898i	−1.70705	−	0.985568i
$50$		0			0
$51$	−0.325765	−	0.707107i	−0.0456163	−	0.0990148i
$52$		0			0
$53$	−3.78194	−	3.78194i	−0.519489	−	0.519489i	0.397928	−	0.917417i	$-0.369730\pi$
$53$	−3.78194	−	3.78194i	−0.519489	−	0.519489i	−0.917417	+	0.397928i	$0.869730\pi$
$54$		0			0
$55$	1.10102	+	0.898979i	0.148462	+	0.121218i
$56$		0			0
$57$	10.4794	+	3.86905i	1.38803	+	0.512468i
$58$		0			0
$59$	−4.48905	+	7.77526i	−0.584424	+	1.01225i	0.410523	+	0.911850i	$0.365346\pi$
$59$	−4.48905	+	7.77526i	−0.584424	+	1.01225i	−0.994947	+	0.100402i	$0.967987\pi$
$60$		0			0
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	0.883109	−	0.469168i	$-0.155446\pi$
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	−0.847866	+	0.530211i	$0.822113\pi$
$62$		0			0
$63$	11.2791	−	7.74358i	1.42104	−	0.975600i
$64$		0			0
$65$	−6.28497	+	4.52761i	−0.779554	+	0.561580i
$66$		0			0
$67$	−6.38512	+	1.71089i	−0.780067	+	0.209018i	−0.626814	−	0.779169i	$-0.715642\pi$
$67$	−6.38512	+	1.71089i	−0.780067	+	0.209018i	−0.153253	+	0.988187i	$0.548975\pi$
$68$		0			0
$69$	−0.158919	+	1.72474i	−0.0191316	+	0.207635i
$70$		0			0
$71$			6.29253i			0.746786i	0.927673	+	0.373393i	$0.121806\pi$
$71$			6.29253i			0.746786i	−0.927673	+	0.373393i	$0.878194\pi$
$72$		0			0
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	−0.984249	−	0.176785i	$-0.943430\pi$
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	0.176785	+	0.984249i	$0.443430\pi$
$74$		0			0
$75$	−3.14198	−	8.07019i	−0.362805	−	0.931865i
$76$		0			0
$77$	0.750311	+	2.80020i	0.0855059	+	0.319112i
$78$		0			0
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	−0.614564	−	0.788867i	$-0.710668\pi$
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	0.375897	+	0.926662i	$0.377335\pi$
$80$		0			0
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$		0			0
$83$	−1.41043	+	5.26380i	−0.154815	+	0.577777i	0.844306	+	0.535861i	$0.180013\pi$
$83$	−1.41043	+	5.26380i	−0.154815	+	0.577777i	−0.999121	+	0.0419163i	$0.986654\pi$
$84$		0			0
$85$	−0.916536	−	0.412514i	−0.0994123	−	0.0447434i
$86$		0			0
$87$	−0.542582	+	0.0930924i	−0.0581709	+	0.00998055i
$88$		0			0
$89$	8.02458			0.850604			0.425302	−	0.905052i	$-0.360168\pi$
$89$	8.02458			0.850604			0.425302	+	0.905052i	$0.360168\pi$
$90$		0			0
$91$	−15.7980			−1.65608
$92$		0			0
$93$	0.497678	+	0.598698i	0.0516068	+	0.0620821i
$94$		0			0
$95$	13.4844	−	5.11376i	1.38347	−	0.524660i
$96$		0			0
$97$	0.695075	−	2.59405i	0.0705741	−	0.263386i	−0.921619	−	0.388095i	$-0.873133\pi$
$97$	0.695075	−	2.59405i	0.0705741	−	0.263386i	0.992193	+	0.124709i	$0.0397998\pi$
$98$		0			0
$99$	−1.87492	−	0.348469i	−0.188436	−	0.0350225i
$100$		0			0
$101$	10.8990	−	6.29253i	1.08449	−	0.626130i	0.152385	−	0.988321i	$-0.451305\pi$
$101$	10.8990	−	6.29253i	1.08449	−	0.626130i	0.932104	+	0.362191i	$0.117971\pi$
$102$		0			0
$103$	2.52520	+	9.42418i	0.248816	+	0.928592i	0.971427	+	0.237338i	$0.0762749\pi$
$103$	2.52520	+	9.42418i	0.248816	+	0.928592i	−0.722612	+	0.691254i	$0.757058\pi$
$104$		0			0
$105$	4.42116	−	17.1004i	0.431461	−	1.66883i
$106$		0			0
$107$	13.6100	−	13.6100i	1.31573	−	1.31573i	0.398606	−	0.917122i	$-0.369494\pi$
$107$	13.6100	−	13.6100i	1.31573	−	1.31573i	0.917122	−	0.398606i	$-0.130506\pi$
$108$		0			0
$109$		−	5.65153i		−	0.541318i	−0.962675	−	0.270659i	$-0.912758\pi$
$109$		−	5.65153i		−	0.541318i	0.962675	−	0.270659i	$-0.0872417\pi$
$110$		0			0
$111$	6.67423	−	3.07483i	0.633490	−	0.291850i
$112$		0			0
$113$	−5.60040	+	1.50062i	−0.526841	+	0.141167i	−0.512429	−	0.858729i	$-0.671254\pi$
$113$	−5.60040	+	1.50062i	−0.526841	+	0.141167i	−0.0144120	+	0.999896i	$0.504588\pi$
$114$		0			0
$115$	1.30701	+	1.81431i	0.121879	+	0.169186i
$116$		0			0
$117$	4.47871	−	9.37769i	0.414057	−	0.866968i
$118$		0			0
$119$	−1.02494	−	1.77526i	−0.0939565	−	0.162737i
$120$		0			0
$121$	−5.29796	+	9.17633i	−0.481633	+	0.834212i
$122$		0			0
$123$	−9.84166	+	8.18104i	−0.887393	+	0.737660i
$124$		0			0
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$		0			0
$127$	−1.87628	−	1.87628i	−0.166493	−	0.166493i	0.618943	−	0.785436i	$-0.287561\pi$
$127$	−1.87628	−	1.87628i	−0.166493	−	0.166493i	−0.785436	+	0.618943i	$0.787561\pi$
$128$		0			0
$129$	3.46410	−	4.89898i	0.304997	−	0.431331i
$130$		0			0
$131$	3.12372	+	1.80348i	0.272921	+	0.157571i	0.630214	−	0.776421i	$-0.282967\pi$
$131$	3.12372	+	1.80348i	0.272921	+	0.157571i	−0.357293	+	0.933992i	$0.616300\pi$
$132$		0			0
$133$	28.4105	+	7.61258i	2.46351	+	0.660095i
$134$		0			0
$135$	8.89741	+	7.47235i	0.765767	+	0.643118i
$136$		0			0
$137$	21.0552	+	5.64173i	1.79887	+	0.482005i	0.993801	−	0.111178i	$-0.0354623\pi$
$137$	21.0552	+	5.64173i	1.79887	+	0.482005i	0.805068	+	0.593183i	$0.202129\pi$
$138$		0			0
$139$	2.68556	+	1.55051i	0.227786	+	0.131513i	0.609550	−	0.792747i	$-0.291350\pi$
$139$	2.68556	+	1.55051i	0.227786	+	0.131513i	−0.381764	+	0.924260i	$0.624683\pi$
$140$		0			0
$141$	−9.00000	+	12.7279i	−0.757937	+	1.07188i
$142$		0			0
$143$	1.55708	+	1.55708i	0.130209	+	0.130209i
$144$		0			0
$145$	−0.449490	+	0.550510i	−0.0373281	+	0.0457174i
$146$		0			0
$147$	18.3782	−	15.2772i	1.51581	−	1.26004i
$148$		0			0
$149$	−2.20881	+	3.82577i	−0.180952	+	0.313419i	−0.942205	−	0.335036i	$-0.891251\pi$
$149$	−2.20881	+	3.82577i	−0.180952	+	0.313419i	0.761253	+	0.648455i	$0.224585\pi$
$150$		0			0
$151$	8.79796	+	15.2385i	0.715968	+	1.24009i	0.962585	+	0.270980i	$0.0873476\pi$
$151$	8.79796	+	15.2385i	0.715968	+	1.24009i	−0.246617	+	0.969113i	$0.579319\pi$
$152$		0			0
$153$	1.34437	−	0.105124i	0.108685	−	0.00849881i
$154$		0			0
$155$	0.992072	+	0.161241i	0.0796851	+	0.0129512i
$156$		0			0
$157$	14.1363	−	3.78780i	1.12820	−	0.302300i	0.354001	−	0.935245i	$-0.384821\pi$
$157$	14.1363	−	3.78780i	1.12820	−	0.302300i	0.774196	+	0.632945i	$0.218154\pi$
$158$		0			0
$159$	8.41385	−	3.87628i	0.667262	−	0.307409i
$160$		0			0
$161$			4.56048i			0.359416i
$162$		0			0
$163$	−4.44949	+	4.44949i	−0.348511	+	0.348511i	−0.859555	−	0.511044i	$-0.829259\pi$
$163$	−4.44949	+	4.44949i	−0.348511	+	0.348511i	0.511044	+	0.859555i	$0.329259\pi$
$164$		0			0
$165$	−2.12120	+	1.24969i	−0.165136	+	0.0972881i
$166$		0			0
$167$	2.27708	+	8.49818i	0.176206	+	0.657609i	0.996343	+	0.0854420i	$0.0272302\pi$
$167$	2.27708	+	8.49818i	0.176206	+	0.657609i	−0.820137	+	0.572167i	$0.806103\pi$
$168$		0			0
$169$	0.866025	−	0.500000i	0.0666173	−	0.0384615i
$170$		0			0
$171$	−12.5732	+	14.7064i	−0.961498	+	1.12462i
$172$		0			0
$173$	−3.33850	+	12.4595i	−0.253822	+	0.947275i	0.714921	+	0.699206i	$0.246463\pi$
$173$	−3.33850	+	12.4595i	−0.253822	+	0.947275i	−0.968742	+	0.248069i	$0.920204\pi$
$174$		0			0
$175$	−10.1875	−	20.4001i	−0.770105	−	1.54210i
$176$		0			0
$177$	−9.94060	−	11.9584i	−0.747181	−	0.898847i
$178$		0			0
$179$	10.6780			0.798114			0.399057	−	0.916926i	$-0.369338\pi$
$179$	10.6780			0.798114			0.399057	+	0.916926i	$0.369338\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$		0			0
$183$	−0.939780	+	0.161241i	−0.0694705	+	0.0119193i
$184$		0			0
$185$	3.89363	−	8.65099i	0.286265	−	0.636033i
$186$		0			0
$187$	−0.0739521	+	0.275993i	−0.00540792	+	0.0201826i
$188$		0			0
$189$	5.81577	+	22.9722i	0.423035	+	1.67098i
$190$		0			0
$191$	15.1237	−	8.73169i	1.09431	−	0.631803i	0.159593	−	0.987183i	$-0.448982\pi$
$191$	15.1237	−	8.73169i	1.09431	−	0.631803i	0.934722	+	0.355380i	$0.115649\pi$
$192$		0			0
$193$	−4.48288	−	16.7303i	−0.322685	−	1.20428i	−0.916619	−	0.399762i	$-0.869093\pi$
$193$	−4.48288	−	16.7303i	−0.322685	−	1.20428i	0.593934	−	0.804513i	$-0.297574\pi$
$194$		0			0
$195$	−3.58630	−	12.9282i	−0.256820	−	0.925808i
$196$		0			0
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	−0.909443	−	0.415829i	$-0.863492\pi$
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	0.415829	+	0.909443i	$0.363492\pi$
$198$		0			0
$199$		−	8.44949i		−	0.598968i	−0.954101	−	0.299484i	$-0.903185\pi$
$199$		−	8.44949i		−	0.598968i	0.954101	−	0.299484i	$-0.0968146\pi$
$200$		0			0
$201$	1.05051	−	11.4012i	0.0740973	−	0.804178i
$202$		0			0
$203$	−1.40010	+	0.375156i	−0.0982677	+	0.0263308i
$204$		0			0
$205$	−2.65054	+	16.3081i	−0.185122	+	1.13901i
$206$		0			0
$207$	−2.70711	−	1.29289i	−0.188157	−	0.0898623i
$208$		0			0
$209$	−2.04989	−	3.55051i	−0.141794	−	0.245594i
$210$		0			0
$211$	4.55051	−	7.88171i	0.313270	−	0.542600i	−0.665798	−	0.746132i	$-0.731909\pi$
$211$	4.55051	−	7.88171i	0.313270	−	0.542600i	0.979068	+	0.203532i	$0.0652422\pi$
$212$		0			0
$213$	−10.2244	−	3.77489i	−0.700563	−	0.258651i
$214$		0			0
$215$	−0.778539	−	7.70674i	−0.0530959	−	0.525595i
$216$		0			0
$217$	1.44949	+	1.44949i	0.0983978	+	0.0983978i
$218$		0			0
$219$	−7.07107	−	15.3485i	−0.477818	−	1.03715i
$220$		0			0
$221$	−1.34847	−	0.778539i	−0.0907079	−	0.0523702i
$222$		0			0
$223$	24.7575	+	6.63374i	1.65788	+	0.444228i	0.961804	−	0.273738i	$-0.0882600\pi$
$223$	24.7575	+	6.63374i	1.65788	+	0.444228i	0.696078	+	0.717966i	$0.254927\pi$
$224$		0			0
$225$	14.9977	−	0.263927i	0.999845	−	0.0175951i
$226$		0			0
$227$	−24.0506	−	6.44433i	−1.59629	−	0.427725i	−0.652372	−	0.757899i	$-0.726226\pi$
$227$	−24.0506	−	6.44433i	−1.59629	−	0.427725i	−0.943920	+	0.330174i	$0.892893\pi$
$228$		0			0
$229$	1.43027	+	0.825765i	0.0945147	+	0.0545681i	0.546512	−	0.837451i	$-0.315955\pi$
$229$	1.43027	+	0.825765i	0.0945147	+	0.0545681i	−0.451998	+	0.892019i	$0.649288\pi$
$230$		0			0
$231$	−5.00000	−	0.460702i	−0.328976	−	0.0303120i
$232$		0			0
$233$	14.4600	+	14.4600i	0.947304	+	0.947304i	0.998679	−	0.0513751i	$-0.0163604\pi$
$233$	14.4600	+	14.4600i	0.947304	+	0.947304i	−0.0513751	+	0.998679i	$0.516360\pi$
$234$		0			0
$235$	2.02270	+	20.0227i	0.131947	+	1.30614i
$236$		0			0
$237$	−0.717439	−	4.18154i	−0.0466027	−	0.271620i
$238$		0			0
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	0.449485	+	0.893288i	$0.351607\pi$
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	−0.998353	+	0.0573782i	$0.981726\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$		0			0
$243$	−15.2851	−	3.06035i	−0.980540	−	0.196322i
$244$		0			0
$245$	4.94960	−	30.4536i	0.316218	−	1.94561i
$246$		0			0
$247$	21.5804	−	5.78245i	1.37313	−	0.367929i
$248$		0			0
$249$	−7.70674	−	5.44949i	−0.488395	−	0.345347i
$250$		0			0
$251$			2.68556i			0.169511i	0.996402	+	0.0847556i	$0.0270110\pi$
$251$			2.68556i			0.169511i	−0.996402	+	0.0847556i	$0.972989\pi$
$252$		0			0
$253$	0.449490	−	0.449490i	0.0282592	−	0.0282592i
$254$		0			0
$255$	1.22010	−	1.24176i	0.0764057	−	0.0777621i
$256$		0			0
$257$	−4.67050	−	17.4305i	−0.291337	−	1.08729i	−0.944083	−	0.329709i	$-0.893049\pi$
$257$	−4.67050	−	17.4305i	−0.291337	−	1.08729i	0.652745	−	0.757578i	$-0.273617\pi$
$258$		0			0
$259$	16.7563	−	9.67423i	1.04118	−	0.601128i
$260$		0			0
$261$	0.174235	−	0.937458i	0.0107849	−	0.0580272i
$262$		0			0
$263$	−4.32149	+	16.1280i	−0.266474	+	0.994495i	0.694868	+	0.719138i	$0.255463\pi$
$263$	−4.32149	+	16.1280i	−0.266474	+	0.994495i	−0.961342	+	0.275358i	$0.911204\pi$
$264$		0			0
$265$	4.90849	−	10.9058i	0.301526	−	0.669940i
$266$		0			0
$267$	−4.81395	+	13.0387i	−0.294609	+	0.797955i
$268$		0			0
$269$	15.0956			0.920398			0.460199	−	0.887816i	$-0.347778\pi$
$269$	15.0956			0.920398			0.460199	+	0.887816i	$0.347778\pi$
$270$		0			0
$271$	−28.0454			−1.70364			−0.851819	−	0.523837i	$-0.824500\pi$
$271$	−28.0454			−1.70364			−0.851819	+	0.523837i	$0.824500\pi$
$272$		0			0
$273$	9.47720	−	25.6692i	0.573586	−	1.55357i
$274$		0			0
$275$	−1.00657	+	3.01478i	−0.0606983	+	0.181798i
$276$		0			0
$277$	−7.28353	+	27.1825i	−0.437625	+	1.63324i	0.297080	+	0.954852i	$0.403987\pi$
$277$	−7.28353	+	27.1825i	−0.437625	+	1.63324i	−0.734705	+	0.678386i	$0.762680\pi$
$278$		0			0
$279$	−1.27135	+	0.449490i	−0.0761137	+	0.0269102i
$280$		0			0
$281$	−14.8485	+	8.57277i	−0.885785	+	0.511408i	−0.872562	−	0.488504i	$-0.837543\pi$
$281$	−14.8485	+	8.57277i	−0.885785	+	0.511408i	−0.0132238	+	0.999913i	$0.504209\pi$
$282$		0			0
$283$	−6.26772	−	23.3914i	−0.372577	−	1.39048i	−0.856853	−	0.515561i	$-0.827583\pi$
$283$	−6.26772	−	23.3914i	−0.372577	−	1.39048i	0.484275	−	0.874916i	$-0.339083\pi$
$284$		0			0
$285$	0.219761	+	24.9778i	0.0130175	+	1.47956i
$286$		0			0
$287$	−23.8273	+	23.8273i	−1.40648	+	1.40648i
$288$		0			0
$289$			16.7980i			0.988115i
$290$		0			0
$291$	3.79796	+	2.68556i	0.222640	+	0.157430i
$292$		0			0
$293$	21.2942	−	5.70577i	1.24402	−	0.333335i	0.423998	−	0.905663i	$-0.360626\pi$
$293$	21.2942	−	5.70577i	1.24402	−	0.333335i	0.820024	+	0.572329i	$0.193960\pi$
$294$		0			0
$295$	−19.8156	−	3.22062i	−1.15371	−	0.187512i
$296$		0			0
$297$	1.69097	−	2.83740i	0.0981201	−	0.164643i
$298$		0			0
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$		0			0
$301$	7.89898	−	13.6814i	0.455290	−	0.788585i
$302$		0			0
$303$	3.68608	+	21.4840i	0.211760	+	1.23423i
$304$		0			0
$305$	−0.778539	+	0.953512i	−0.0445790	+	0.0545979i
$306$		0			0
$307$	6.67423	+	6.67423i	0.380919	+	0.380919i	0.871433	−	0.490514i	$-0.163191\pi$
$307$	6.67423	+	6.67423i	0.380919	+	0.380919i	−0.490514	+	0.871433i	$0.663191\pi$
$308$		0			0
$309$	−16.8277	−	1.55051i	−0.957294	−	0.0882054i
$310$		0			0
$311$	−23.8207	−	13.7529i	−1.35075	−	0.779853i	−0.362392	−	0.932026i	$-0.618040\pi$
$311$	−23.8207	−	13.7529i	−1.35075	−	0.779853i	−0.988354	+	0.152172i	$0.951373\pi$
$312$		0			0
$313$	−11.5422	−	3.09273i	−0.652405	−	0.174811i	−0.0825888	−	0.996584i	$-0.526319\pi$
$313$	−11.5422	−	3.09273i	−0.652405	−	0.174811i	−0.569816	+	0.821772i	$0.692985\pi$
$314$		0			0
$315$	25.1332	+	17.4422i	1.41610	+	0.982757i
$316$		0			0
$317$	−10.5276	−	2.82086i	−0.591289	−	0.158435i	−0.0492469	−	0.998787i	$-0.515682\pi$
$317$	−10.5276	−	2.82086i	−0.591289	−	0.158435i	−0.542042	+	0.840351i	$0.682349\pi$
$318$		0			0
$319$	0.174973	+	0.101021i	0.00979659	+	0.00565606i
$320$		0			0
$321$	13.9495	+	30.2788i	0.778585	+	1.69000i
$322$		0			0
$323$	2.04989	+	2.04989i	0.114059	+	0.114059i
$324$		0			0
$325$	−14.4495	−	9.55051i	−0.801513	−	0.529767i
$326$		0			0
$327$	9.18286	+	3.39036i	0.507813	+	0.187487i
$328$		0			0
$329$	−20.5222	+	35.5454i	−1.13142	+	1.95968i
$330$		0			0
$331$	0.224745	+	0.389270i	0.0123531	+	0.0213962i	0.872136	−	0.489264i	$-0.162734\pi$
$331$	0.224745	+	0.389270i	0.0123531	+	0.0213962i	−0.859783	+	0.510660i	$0.829401\pi$
$332$		0			0
$333$	0.992248	+	12.6892i	0.0543748	+	0.695363i
$334$		0			0
$335$	−8.63980	−	11.9933i	−0.472042	−	0.655263i
$336$		0			0
$337$	3.00804	−	0.806003i	0.163859	−	0.0439058i	−0.175957	−	0.984398i	$-0.556302\pi$
$337$	3.00804	−	0.806003i	0.163859	−	0.0439058i	0.339816	+	0.940492i	$0.389635\pi$
$338$		0			0
$339$	0.921404	−	10.0000i	0.0500438	−	0.543125i
$340$		0			0
$341$		−	0.285729i		−	0.0154731i
$342$		0			0
$343$	21.9217	−	21.9217i	1.18366	−	1.18366i
$344$		0			0
$345$	−3.73205	+	1.03528i	−0.200927	+	0.0557374i
$346$		0			0
$347$	−6.15937	−	22.9871i	−0.330652	−	1.23401i	−0.908507	−	0.417870i	$-0.862777\pi$
$347$	−6.15937	−	22.9871i	−0.330652	−	1.23401i	0.577855	−	0.816140i	$-0.303890\pi$
$348$		0			0
$349$	25.1541	−	14.5227i	1.34647	−	0.777383i	0.358719	−	0.933446i	$-0.383214\pi$
$349$	25.1541	−	14.5227i	1.34647	−	0.777383i	0.987747	+	0.156063i	$0.0498803\pi$
$350$		0			0
$351$	12.5505	+	12.9029i	0.669897	+	0.688706i
$352$		0			0
$353$	−8.87564	+	33.1244i	−0.472403	+	1.76303i	0.158694	+	0.987328i	$0.449272\pi$
$353$	−8.87564	+	33.1244i	−0.472403	+	1.76303i	−0.631097	+	0.775704i	$0.717395\pi$
$354$		0			0
$355$	−13.1562	+	4.98930i	−0.698260	+	0.264805i
$356$		0			0
$357$	3.49938	−	0.600398i	0.185207	−	0.0317764i
$358$		0			0
$359$	3.32124			0.175288			0.0876441	−	0.996152i	$-0.472066\pi$
$359$	3.32124			0.175288			0.0876441	+	0.996152i	$0.472066\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$		0			0
$363$	−11.7319	−	14.1132i	−0.615763	−	0.740753i
$364$		0			0
$365$	−19.8943	−	8.95403i	−1.04132	−	0.468675i
$366$		0			0
$367$	1.06110	−	3.96008i	0.0553890	−	0.206714i	−0.932686	−	0.360690i	$-0.882541\pi$
$367$	1.06110	−	3.96008i	0.0553890	−	0.206714i	0.988075	+	0.153976i	$0.0492078\pi$
$368$		0			0
$369$	−7.38891	−	20.8990i	−0.384651	−	1.08796i
$370$		0			0
$371$	21.1237	−	12.1958i	1.09669	−	0.633174i
$372$		0			0
$373$	−0.127549	−	0.476018i	−0.00660422	−	0.0246473i	0.962545	−	0.271122i	$-0.0873946\pi$
$373$	−0.127549	−	0.476018i	−0.00660422	−	0.0246473i	−0.969149	+	0.246474i	$0.920728\pi$
$374$		0			0
$375$	14.3817	−	12.9680i	0.742665	−	0.669663i
$376$		0			0
$377$	−0.778539	+	0.778539i	−0.0400968	+	0.0400968i
$378$		0			0
$379$			21.3485i			1.09660i	0.836283	+	0.548299i	$0.184724\pi$
$379$			21.3485i			1.09660i	−0.836283	+	0.548299i	$0.815276\pi$
$380$		0			0
$381$	4.17423	−	1.92308i	0.213853	−	0.0985222i
$382$		0			0
$383$	7.92256	−	2.12284i	0.404824	−	0.108472i	−0.0506606	−	0.998716i	$-0.516133\pi$
$383$	7.92256	−	2.12284i	0.404824	−	0.108472i	0.455485	+	0.890244i	$0.349466\pi$
$384$		0			0
$385$	−5.25966	+	3.78899i	−0.268057	+	0.193105i
$386$		0			0
$387$	5.88196	+	8.56753i	0.298997	+	0.435512i
$388$		0			0
$389$	−18.4008	−	31.8712i	−0.932959	−	1.61593i	−0.778233	−	0.627975i	$-0.783884\pi$
$389$	−18.4008	−	31.8712i	−0.932959	−	1.61593i	−0.154726	−	0.987957i	$-0.549449\pi$
$390$		0			0
$391$	−0.224745	+	0.389270i	−0.0113658	+	0.0196862i
$392$		0			0
$393$	−4.80430	+	3.99366i	−0.242345	+	0.201453i
$394$		0			0
$395$	−4.24264	−	3.46410i	−0.213470	−	0.174298i
$396$		0			0
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	0.920428	−	0.390913i	$-0.127841\pi$
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	−0.390913	+	0.920428i	$0.627841\pi$
$398$		0			0
$399$	−29.4128	+	41.5959i	−1.47248	+	2.08240i
$400$		0			0
$401$	7.65153	+	4.41761i	0.382099	+	0.220605i	0.678731	−	0.734387i	$-0.262530\pi$
$401$	7.65153	+	4.41761i	0.382099	+	0.220605i	−0.296632	+	0.954992i	$0.595863\pi$
$402$		0			0
$403$	1.50402	+	0.403001i	0.0749207	+	0.0200749i
$404$		0			0
$405$	−17.4790	+	9.97425i	−0.868537	+	0.495624i
$406$		0			0
$407$	−2.60504	−	0.698019i	−0.129127	−	0.0345995i
$408$		0			0
$409$	25.0273	+	14.4495i	1.23752	+	0.714481i	0.968586	−	0.248678i	$-0.0799961\pi$
$409$	25.0273	+	14.4495i	1.23752	+	0.714481i	0.268932	+	0.963159i	$0.413329\pi$
$410$		0			0
$411$	−21.7980	+	30.8270i	−1.07521	+	1.52058i
$412$		0			0
$413$	−28.9521	−	28.9521i	−1.42464	−	1.42464i
$414$		0			0
$415$	−12.1237	+	1.22474i	−0.595130	+	0.0601204i
$416$		0			0
$417$	−4.13041	+	3.43347i	−0.202267	+	0.168138i
$418$		0			0
$419$	2.51059	−	4.34847i	0.122650	−	0.212437i	−0.798162	−	0.602443i	$-0.794194\pi$
$419$	2.51059	−	4.34847i	0.122650	−	0.212437i	0.920812	+	0.390007i	$0.127527\pi$
$420$		0			0
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	0.921461	−	0.388471i	$-0.126997\pi$
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	−0.797157	+	0.603773i	$0.793663\pi$
$422$		0			0
$423$	−15.2818	−	22.2591i	−0.743026	−	1.08227i
$424$		0			0
$425$	0.135756	−	2.24334i	0.00658515	−	0.108818i
$426$		0			0
$427$	−2.42504	+	0.649788i	−0.117356	+	0.0314455i
$428$		0			0
$429$	−3.46410	+	1.59592i	−0.167248	+	0.0770516i
$430$		0			0
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$		0			0
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	−0.305766	−	0.952107i	$-0.598912\pi$
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	0.952107	+	0.305766i	$0.0989124\pi$
$434$		0			0
$435$	−0.624844	−	1.06060i	−0.0299590	−	0.0508520i
$436$		0			0
$437$	−1.66925	−	6.22973i	−0.0798511	−	0.298008i
$438$		0			0
$439$	−25.8058	+	14.8990i	−1.23164	+	0.711089i	−0.967372	−	0.253359i	$-0.918465\pi$
$439$	−25.8058	+	14.8990i	−1.23164	+	0.711089i	−0.264271	+	0.964449i	$0.585131\pi$
$440$		0			0
$441$	13.7980	+	39.0265i	0.657046	+	1.85841i
$442$		0			0
$443$	1.41043	−	5.26380i	0.0670116	−	0.250091i	−0.924292	−	0.381687i	$-0.875343\pi$
$443$	1.41043	−	5.26380i	0.0670116	−	0.250091i	0.991303	+	0.131596i	$0.0420101\pi$
$444$		0			0
$445$	6.36263	+	16.7776i	0.301618	+	0.795332i
$446$		0			0
$447$	−4.89121	−	5.88405i	−0.231346	−	0.278306i
$448$		0			0
$449$	−0.921404			−0.0434837			−0.0217419	−	0.999764i	$-0.506921\pi$
$449$	−0.921404			−0.0434837			−0.0217419	+	0.999764i	$0.506921\pi$
$450$		0			0
$451$	4.69694			0.221170
$452$		0			0
$453$	−30.0381	+	5.15373i	−1.41131	+	0.242143i
$454$		0			0
$455$	−12.5261	−	33.0299i	−0.587232	−	1.54847i
$456$		0			0
$457$	−3.78780	+	14.1363i	−0.177186	+	0.661267i	0.818983	+	0.573818i	$0.194538\pi$
$457$	−3.78780	+	14.1363i	−0.177186	+	0.661267i	−0.996169	+	0.0874492i	$0.972128\pi$
$458$		0			0
$459$	−0.635674	+	2.24745i	−0.0296707	+	0.104902i
$460$		0			0
$461$	28.6237	−	16.5259i	1.33314	−	0.769689i	0.347360	−	0.937732i	$-0.387078\pi$
$461$	28.6237	−	16.5259i	1.33314	−	0.769689i	0.985780	+	0.168043i	$0.0537448\pi$
$462$		0			0
$463$	3.16668	+	11.8182i	0.147168	+	0.549239i	0.999649	+	0.0264810i	$0.00843014\pi$
$463$	3.16668	+	11.8182i	0.147168	+	0.549239i	−0.852481	+	0.522758i	$0.824903\pi$
$464$		0			0
$465$	−0.857135	+	1.51523i	−0.0397487	+	0.0702673i
$466$		0			0
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	−0.638630	−	0.769514i	$-0.720499\pi$
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	0.769514	+	0.638630i	$0.220499\pi$
$468$		0			0
$469$		−	30.1464i		−	1.39203i
$470$		0			0
$471$	−2.32577	+	25.2415i	−0.107166	+	1.16307i
$472$		0			0
$473$	−2.12701	+	0.569930i	−0.0977999	+	0.0262054i
$474$		0			0
$475$	21.3834	+	24.1381i	0.981137	+	1.10753i
$476$		0			0
$477$	1.25087	+	15.9966i	0.0572736	+	0.732433i
$478$		0			0
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	0.773879	−	0.633333i	$-0.218314\pi$
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	−0.935422	+	0.353533i	$0.884980\pi$
$480$		0			0
$481$	7.34847	−	12.7279i	0.335061	−	0.580343i
$482$		0			0
$483$	−7.41007	−	2.73583i	−0.337170	−	0.124485i
$484$		0			0
$485$	5.97469	−	0.603566i	0.271297	−	0.0274065i
$486$		0			0
$487$	12.0000	+	12.0000i	0.543772	+	0.543772i	0.924632	−	0.380861i	$-0.124372\pi$
$487$	12.0000	+	12.0000i	0.543772	+	0.543772i	−0.380861	+	0.924632i	$0.624372\pi$
$488$		0			0
$489$	−4.56048	−	9.89898i	−0.206232	−	0.447647i
$490$		0			0
$491$	24.2474	+	13.9993i	1.09427	+	0.631778i	0.934711	−	0.355410i	$-0.115659\pi$
$491$	24.2474	+	13.9993i	1.09427	+	0.631778i	0.159561	+	0.987188i	$0.448992\pi$
$492$		0			0
$493$	−0.137997	−	0.0369761i	−0.00621505	−	0.00166532i
$494$		0			0
$495$	−0.758039	−	4.19632i	−0.0340713	−	0.188610i
$496$		0			0
$497$	−27.7191	−	7.42731i	−1.24337	−	0.333161i
$498$		0			0
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	0.517325	−	0.855789i	$-0.326928\pi$
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	−0.482473	+	0.875911i	$0.660261\pi$
$500$		0			0
$501$	−15.1742	−	1.39816i	−0.677935	−	0.0624652i
$502$		0			0
$503$	4.02834	+	4.02834i	0.179615	+	0.179615i	0.791188	−	0.611573i	$-0.209463\pi$
$503$	4.02834	+	4.02834i	0.179615	+	0.179615i	−0.611573	+	0.791188i	$0.709463\pi$
$504$		0			0
$505$	21.7980	+	17.7980i	0.969996	+	0.791999i
$506$		0			0
$507$	0.292893	+	1.70711i	0.0130078	+	0.0758153i
$508$		0			0
$509$	4.22659	−	7.32066i	0.187340	−	0.324483i	−0.757022	−	0.653389i	$-0.773347\pi$
$509$	4.22659	−	7.32066i	0.187340	−	0.324483i	0.944363	+	0.328906i	$0.106680\pi$
$510$		0			0
$511$	−22.2474	−	38.5337i	−0.984169	−	1.70463i
$512$		0			0
$513$	−16.3529	−	29.2519i	−0.721998	−	1.29150i
$514$		0			0
$515$	−17.7016	+	12.7520i	−0.780025	+	0.561920i
$516$		0			0
$517$	5.52613	−	1.48072i	0.243039	−	0.0651221i
$518$		0			0
$519$	−18.2419	−	12.8990i	−0.800731	−	0.566202i
$520$		0			0
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$		0			0
$523$	−4.22474	+	4.22474i	−0.184735	+	0.184735i	−0.793416	−	0.608680i	$-0.791699\pi$
$523$	−4.22474	+	4.22474i	−0.184735	+	0.184735i	0.608680	+	0.793416i	$0.291699\pi$
$524$		0			0
$525$	39.2585	−	4.31515i	1.71338	−	0.188329i
$526$		0			0
$527$	0.0522921	+	0.195157i	0.00227788	+	0.00850116i
$528$		0			0
$529$	−19.0526	+	11.0000i	−0.828372	+	0.478261i
$530$		0			0
$531$	25.3939	−	8.97809i	1.10200	−	0.389616i
$532$		0			0
$533$	−6.62471	+	24.7238i	−0.286948	+	1.07090i
$534$		0			0
$535$	39.2467	+	17.6641i	1.69678	+	0.763686i
$536$		0			0
$537$	−6.40576	+	17.3501i	−0.276429	+	0.748714i
$538$		0			0
$539$	−8.77101			−0.377794
$540$		0			0
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$		0			0
$543$	9.26816	−	25.1030i	0.397735	−	1.07727i
$544$		0			0
$545$	11.8161	−	4.48106i	0.506144	−	0.191948i
$546$		0			0
$547$	1.05279	−	3.92907i	0.0450140	−	0.167995i	−0.939760	−	0.341836i	$-0.888951\pi$
$547$	1.05279	−	3.92907i	0.0450140	−	0.167995i	0.984774	+	0.173841i	$0.0556180\pi$
$548$		0			0
$549$	0.301783	−	1.62372i	0.0128798	−	0.0692989i
$550$		0			0
$551$	1.77526	−	1.02494i	0.0756284	−	0.0436641i
$552$		0			0
$553$	−2.89123	−	10.7902i	−0.122947	−	0.458846i
$554$		0			0
$555$	11.7207	+	11.5163i	0.497517	+	0.488839i
$556$		0			0
$557$	7.88171	−	7.88171i	0.333959	−	0.333959i	−0.520129	−	0.854088i	$-0.674116\pi$
$557$	7.88171	−	7.88171i	0.333959	−	0.333959i	0.854088	+	0.520129i	$0.174116\pi$
$558$		0			0
$559$		−	12.0000i		−	0.507546i
$560$		0			0
$561$	−0.404082	−	0.285729i	−0.0170604	−	0.0120635i
$562$		0			0
$563$	−18.9819	+	5.08619i	−0.799993	+	0.214357i	−0.635581	−	0.772034i	$-0.719239\pi$
$563$	−18.9819	+	5.08619i	−0.799993	+	0.214357i	−0.164412	+	0.986392i	$0.552573\pi$
$564$		0			0
$565$	−7.57797	−	10.5193i	−0.318808	−	0.442551i
$566$		0			0
$567$	−40.8151	−	4.33130i	−1.71407	−	0.181898i
$568$		0			0
$569$	9.58166	+	16.5959i	0.401684	+	0.695737i	0.993929	−	0.110021i	$-0.0350917\pi$
$569$	9.58166	+	16.5959i	0.401684	+	0.695737i	−0.592245	+	0.805758i	$0.701758\pi$
$570$		0			0
$571$	18.4495	−	31.9555i	0.772087	−	1.33729i	−0.164330	−	0.986405i	$-0.552546\pi$
$571$	18.4495	−	31.9555i	0.772087	−	1.33729i	0.936417	−	0.350889i	$-0.114120\pi$
$572$		0			0
$573$	5.11490	+	29.8118i	0.213678	+	1.24541i
$574$		0			0
$575$	−2.75699	+	4.17121i	−0.114975	+	0.173951i
$576$		0			0
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$		0			0
$579$	29.8735	+	2.75255i	1.24150	+	0.114392i
$580$		0			0
$581$	−21.5227	−	12.4261i	−0.892912	−	0.515523i
$582$		0			0
$583$	−3.28404	−	0.879955i	−0.136011	−	0.0364440i
$584$		0			0
$585$	23.1577	+	1.92845i	0.957455	+	0.0797317i
$586$		0			0
$587$	−12.6009	−	3.37640i	−0.520095	−	0.139359i	−0.0107843	−	0.999942i	$-0.503433\pi$
$587$	−12.6009	−	3.37640i	−0.520095	−	0.139359i	−0.509310	+	0.860583i	$0.670099\pi$
$588$		0			0
$589$	−2.51059	−	1.44949i	−0.103447	−	0.0597252i
$590$		0			0
$591$	−7.10102	−	15.4135i	−0.292097	−	0.634026i
$592$		0			0
$593$	7.24604	+	7.24604i	0.297559	+	0.297559i	0.840057	−	0.542498i	$-0.182521\pi$
$593$	7.24604	+	7.24604i	0.297559	+	0.297559i	−0.542498	+	0.840057i	$0.682521\pi$
$594$		0			0
$595$	2.89898	−	3.55051i	0.118847	−	0.145557i
$596$		0			0
$597$	13.7291	+	5.06885i	0.561895	+	0.207454i
$598$		0			0
$599$	9.97093	−	17.2702i	0.407401	−	0.705639i	−0.587197	−	0.809444i	$-0.699768\pi$
$599$	9.97093	−	17.2702i	0.407401	−	0.705639i	0.994598	+	0.103805i	$0.0331018\pi$
$600$		0			0
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	0.806866	−	0.590735i	$-0.201162\pi$
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	−0.915024	+	0.403399i	$0.867829\pi$
$602$		0			0
$603$	17.8950	+	8.54650i	0.728739	+	0.348040i
$604$		0			0
$605$	−23.3863	−	3.80096i	−0.950789	−	0.154531i
$606$		0			0
$607$	11.3732	−	3.04744i	0.461624	−	0.123692i	−0.0205092	−	0.999790i	$-0.506529\pi$
$607$	11.3732	−	3.04744i	0.461624	−	0.123692i	0.482133	+	0.876098i	$0.339862\pi$
$608$		0			0
$609$	0.230351	−	2.50000i	0.00933429	−	0.101305i
$610$		0			0
$611$			31.1769i			1.26128i
$612$		0			0
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	−0.556369	−	0.830936i	$-0.687806\pi$
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	0.830936	+	0.556369i	$0.187806\pi$
$614$		0			0
$615$	−24.9081	−	14.0900i	−1.00439	−	0.568162i
$616$		0			0
$617$	−4.37378	−	16.3232i	−0.176082	−	0.657146i	−0.996365	−	0.0851882i	$-0.972851\pi$
$617$	−4.37378	−	16.3232i	−0.176082	−	0.657146i	0.820283	−	0.571958i	$-0.193816\pi$
$618$		0			0
$619$	42.2121	−	24.3712i	1.69665	−	0.979560i	0.747748	−	0.663982i	$-0.231135\pi$
$619$	42.2121	−	24.3712i	1.69665	−	0.979560i	0.948900	−	0.315578i	$-0.102198\pi$
$620$		0			0
$621$	3.72474	−	3.62302i	0.149469	−	0.145387i
$622$		0			0
$623$	−9.47172	+	35.3489i	−0.379476	+	1.41623i
$624$		0			0
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$		0			0
$627$	6.99876	−	1.20080i	0.279503	−	0.0479552i
$628$		0			0
$629$	1.90702			0.0760380
$630$		0			0
$631$	3.10102			0.123450			0.0617248	−	0.998093i	$-0.480340\pi$
$631$	3.10102			0.123450			0.0617248	+	0.998093i	$0.480340\pi$
$632$		0			0
$633$	10.0767	+	12.1221i	0.400513	+	0.481811i
$634$		0			0
$635$	2.43518	−	5.41055i	0.0966370	−	0.214711i
$636$		0			0
$637$	12.3709	−	46.1689i	0.490153	−	1.82928i
$638$		0			0
$639$	12.2672	−	14.3485i	0.485284	−	0.567617i
$640$		0			0
$641$	16.7474	−	9.66914i	0.661484	−	0.381908i	−0.131358	−	0.991335i	$-0.541934\pi$
$641$	16.7474	−	9.66914i	0.661484	−	0.381908i	0.792842	+	0.609427i	$0.208600\pi$
$642$		0			0
$643$	−1.63694	−	6.10913i	−0.0645545	−	0.240921i	0.926108	−	0.377259i	$-0.123133\pi$
$643$	−1.63694	−	6.10913i	−0.0645545	−	0.240921i	−0.990662	+	0.136338i	$0.956467\pi$
$644$		0			0
$645$	12.9893	+	3.35827i	0.511453	+	0.132232i
$646$		0			0
$647$	23.5416	−	23.5416i	0.925516	−	0.925516i	−0.0718961	−	0.997412i	$-0.522905\pi$
$647$	23.5416	−	23.5416i	0.925516	−	0.925516i	0.997412	+	0.0718961i	$0.0229050\pi$
$648$		0			0
$649$			5.70714i			0.224025i
$650$		0			0
$651$	−3.22474	+	1.48565i	−0.126388	+	0.0582271i
$652$		0			0
$653$	25.5482	−	6.84563i	0.999780	−	0.267890i	0.278427	−	0.960457i	$-0.410187\pi$
$653$	25.5482	−	6.84563i	0.999780	−	0.267890i	0.721353	+	0.692567i	$0.243520\pi$
$654$		0			0
$655$	−1.29389	+	7.96096i	−0.0505564	+	0.311060i
$656$		0			0
$657$	29.1808	−	2.28183i	1.13845	−	0.0890227i
$658$		0			0
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	0.954917	−	0.296872i	$-0.0959435\pi$
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	−0.734557	+	0.678546i	$0.762610\pi$
$660$		0			0
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	−0.853076	−	0.521786i	$-0.825266\pi$
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	0.878418	+	0.477893i	$0.158599\pi$
$662$		0			0
$663$	2.07395	−	1.72401i	0.0805456	−	0.0669549i
$664$		0			0
$665$	6.61037	+	65.4359i	0.256339	+	2.53749i
$666$		0			0
$667$	0.224745	+	0.224745i	0.00870216	+	0.00870216i
$668$		0			0
$669$	−25.6308	+	36.2474i	−0.990945	+	1.40141i
$670$		0			0
$671$	0.303062	+	0.174973i	0.0116996	+	0.00675474i
$672$		0			0
$673$	22.4704	+	6.02093i	0.866171	+	0.232090i	0.664431	−	0.747349i	$-0.268674\pi$
$673$	22.4704	+	6.02093i	0.866171	+	0.232090i	0.201740	+	0.979439i	$0.435340\pi$
$674$		0			0
$675$	−8.56827	+	24.5272i	−0.329793	+	0.944053i
$676$		0			0
$677$	−44.0423	−	11.8011i	−1.69268	−	0.453553i	−0.721602	−	0.692308i	$-0.756594\pi$
$677$	−44.0423	−	11.8011i	−1.69268	−	0.453553i	−0.971080	+	0.238755i	$0.923261\pi$
$678$		0			0
$679$	10.6066	+	6.12372i	0.407044	+	0.235007i
$680$		0			0
$681$	24.8990	−	35.2125i	0.954131	−	1.34934i
$682$		0			0
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	0.390431	−	0.920632i	$-0.372326\pi$
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	−0.920632	+	0.390431i	$0.872326\pi$
$684$		0			0
$685$	4.89898	+	48.4949i	0.187180	+	1.85289i
$686$		0			0
$687$	−2.19976	+	1.82859i	−0.0839260	+	0.0697649i
$688$		0			0
$689$	9.26382	−	16.0454i	0.352923	−	0.611281i
$690$		0			0
$691$	−10.4722	−	18.1384i	−0.398381	−	0.690016i	0.595145	−	0.803618i	$-0.297094\pi$
$691$	−10.4722	−	18.1384i	−0.398381	−	0.690016i	−0.993526	+	0.113602i	$0.963761\pi$
$692$		0			0
$693$	3.74807	−	7.84785i	0.142377	−	0.298115i
$694$		0			0
$695$	−1.11240	+	6.84428i	−0.0421956	+	0.259618i
$696$		0			0
$697$	−3.20807	+	0.859599i	−0.121514	+	0.0325596i
$698$		0			0
$699$	−32.1698	+	14.8207i	−1.21677	+	0.560569i
$700$		0			0
$701$			21.1024i			0.797028i	0.917162	+	0.398514i	$0.130474\pi$
$701$			21.1024i			0.797028i	−0.917162	+	0.398514i	$0.869526\pi$
$702$		0			0
$703$	−19.3485	+	19.3485i	−0.729741	+	0.729741i
$704$		0			0
$705$	−33.7472	−	8.72505i	−1.27099	−	0.328604i
$706$		0			0
$707$	14.8546	+	55.4382i	0.558666	+	2.08497i
$708$		0			0
$709$	25.6790	−	14.8258i	0.964394	−	0.556793i	0.0668716	−	0.997762i	$-0.478698\pi$
$709$	25.6790	−	14.8258i	0.964394	−	0.556793i	0.897523	+	0.440968i	$0.145365\pi$
$710$		0			0
$711$	7.22474	+	1.34278i	0.270949	+	0.0503582i
$712$		0			0
$713$	0.116337	−	0.434174i	0.00435684	−	0.0162599i
$714$		0			0
$715$	−2.02090	+	4.49009i	−0.0755772	+	0.167920i
$716$		0			0
$717$	−18.7899	−	22.6040i	−0.701722	−	0.844160i
$718$		0			0
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$		0			0
$723$	32.4350	−	5.56497i	1.20627	−	0.206964i
$724$		0			0
$725$	−1.50739	−	0.503284i	−0.0559830	−	0.0186915i
$726$		0			0
$727$	−12.5068	+	46.6759i	−0.463850	+	1.73111i	0.196822	+	0.980439i	$0.436938\pi$
$727$	−12.5068	+	46.6759i	−0.463850	+	1.73111i	−0.660673	+	0.750674i	$0.729729\pi$
$728$		0			0
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$		0			0
$731$	1.34847	−	0.778539i	0.0498749	−	0.0287953i
$732$		0			0
$733$	8.83821	+	32.9846i	0.326447	+	1.21832i	0.912850	+	0.408296i	$0.133877\pi$
$733$	8.83821	+	32.9846i	0.326447	+	1.21832i	−0.586403	+	0.810019i	$0.699457\pi$
$734$		0			0
$735$	46.5130	+	26.3114i	1.71566	+	0.970512i
$736$		0			0
$737$	−2.97129	+	2.97129i	−0.109449	+	0.109449i
$738$		0			0
$739$		−	28.9444i		−	1.06474i	−0.846513	−	0.532368i	$-0.821302\pi$
$739$		−	28.9444i		−	1.06474i	0.846513	−	0.532368i	$-0.178698\pi$
$740$		0			0
$741$	−3.55051	+	38.5337i	−0.130431	+	1.41557i
$742$		0			0
$743$	9.56168	−	2.56204i	0.350784	−	0.0939923i	−0.0791245	−	0.996865i	$-0.525212\pi$
$743$	9.56168	−	2.56204i	0.350784	−	0.0939923i	0.429909	+	0.902872i	$0.358546\pi$
$744$		0			0
$745$	−9.75014	−	1.58468i	−0.357218	−	0.0580583i
$746$		0			0
$747$	13.4779	−	9.25311i	0.493129	−	0.338553i
$748$		0			0
$749$	43.8888	+	76.0176i	1.60366	+	2.77762i
$750$		0			0
$751$	10.3485	−	17.9241i	0.377621	−	0.654059i	−0.613095	−	0.790010i	$-0.710076\pi$
$751$	10.3485	−	17.9241i	0.377621	−	0.654059i	0.990716	+	0.135951i	$0.0434089\pi$
$752$		0			0
$753$	−4.36362	−	1.61107i	−0.159019	−	0.0587107i
$754$		0			0
$755$	−24.8844	+	30.4770i	−0.905636	+	1.10917i
$756$		0			0
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	0.983292	−	0.182038i	$-0.0582693\pi$
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	−0.182038	+	0.983292i	$0.558269\pi$
$758$		0			0
$759$	0.460702	+	1.00000i	0.0167224	+	0.0362977i
$760$		0			0
$761$	−5.60102	−	3.23375i	−0.203037	−	0.117223i	0.395034	−	0.918666i	$-0.370733\pi$
$761$	−5.60102	−	3.23375i	−0.203037	−	0.117223i	−0.598071	+	0.801443i	$0.704066\pi$
$762$		0			0
$763$	24.8955	+	6.67072i	0.901276	+	0.241496i
$764$		0			0
$765$	1.28573	+	2.72741i	0.0464856	+	0.0986096i
$766$		0			0
$767$	−30.0413	−	8.04954i	−1.08473	−	0.290652i
$768$		0			0
$769$	8.39780	+	4.84847i	0.302832	+	0.174840i	0.643715	−	0.765266i	$-0.277392\pi$
$769$	8.39780	+	4.84847i	0.302832	+	0.174840i	−0.340882	+	0.940106i	$0.610726\pi$
$770$		0			0
$771$	31.1237	+	2.86775i	1.12089	+	0.103280i
$772$		0			0
$773$	−30.8270	−	30.8270i	−1.10877	−	1.10877i	−0.993313	−	0.115456i	$-0.963167\pi$
$773$	−30.8270	−	30.8270i	−1.10877	−	1.10877i	−0.115456	−	0.993313i	$-0.536833\pi$
$774$		0			0
$775$	0.449490	+	2.20204i	0.0161461	+	0.0790996i
$776$		0			0
$777$	5.66704	+	33.0299i	0.203304	+	1.18494i
$778$		0			0
$779$	23.8273	−	41.2702i	0.853703	−	1.47866i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$		0			0
$783$	1.41870	+	0.845485i	0.0507002	+	0.0302152i
$784$		0			0
$785$	19.1280	+	26.5524i	0.682707	+	0.947695i
$786$		0			0
$787$	−9.42418	+	2.52520i	−0.335936	+	0.0900137i	−0.422844	−	0.906203i	$-0.638968\pi$
$787$	−9.42418	+	2.52520i	−0.335936	+	0.0900137i	0.0869079	+	0.996216i	$0.472301\pi$
$788$		0			0
$789$	−23.6130	−	16.6969i	−0.840646	−	0.594427i
$790$		0			0
$791$		−	26.4415i		−	0.940150i
$792$		0			0
$793$	−1.34847	+	1.34847i	−0.0478855	+	0.0478855i
$794$		0			0
$795$	14.7757	+	14.5180i	0.524040	+	0.514899i
$796$		0			0
$797$	10.3005	+	38.4419i	0.364861	+	1.36168i	0.867609	+	0.497248i	$0.165656\pi$
$797$	10.3005	+	38.4419i	0.364861	+	1.36168i	−0.502747	+	0.864433i	$0.667677\pi$
$798$		0			0
$799$	−3.50343	+	2.02270i	−0.123942	+	0.0715581i
$800$		0			0
$801$	−18.2980	−	15.6438i	−0.646527	−	0.552748i
$802$		0			0
$803$	−1.60521	+	5.99071i	−0.0566465	+	0.211408i
$804$		0			0
$805$	−9.53491	+	3.61597i	−0.336061	+	0.127446i
$806$		0			0
$807$	−9.05589	+	24.5281i	−0.318782	+	0.863429i
$808$		0			0
$809$	19.4490			0.683792			0.341896	−	0.939738i	$-0.388931\pi$
$809$	19.4490			0.683792			0.341896	+	0.939738i	$0.388931\pi$
$810$		0			0
$811$	39.6413			1.39200			0.695998	−	0.718044i	$-0.254962\pi$
$811$	39.6413			1.39200			0.695998	+	0.718044i	$0.254962\pi$
$812$		0			0
$813$	16.8245	−	45.5694i	0.590059	−	1.59819i
$814$		0			0
$815$	−12.8308	−	5.77489i	−0.449444	−	0.202286i
$816$		0			0
$817$	−5.78245	+	21.5804i	−0.202302	+	0.755003i
$818$		0			0
$819$	36.0231	+	30.7980i	1.25875	+	1.07617i
$820$		0			0
$821$	19.3207	−	11.1548i	0.674296	−	0.389305i	−0.123407	−	0.992356i	$-0.539382\pi$
$821$	19.3207	−	11.1548i	0.674296	−	0.389305i	0.797702	+	0.603051i	$0.206049\pi$
$822$		0			0
$823$	−0.867910	−	3.23908i	−0.0302534	−	0.112907i	0.949148	−	0.314830i	$-0.101948\pi$
$823$	−0.867910	−	3.23908i	−0.0302534	−	0.112907i	−0.979401	+	0.201923i	$0.935281\pi$
$824$		0			0
$825$	−4.29470	−	3.44408i	−0.149522	−	0.119908i
$826$		0			0
$827$	31.5662	−	31.5662i	1.09766	−	1.09766i	0.102980	−	0.994683i	$-0.467162\pi$
$827$	31.5662	−	31.5662i	1.09766	−	1.09766i	0.994683	−	0.102980i	$-0.0328379\pi$
$828$		0			0
$829$		−	10.5505i		−	0.366434i	−0.983072	−	0.183217i	$-0.941349\pi$
$829$		−	10.5505i		−	0.366434i	0.983072	−	0.183217i	$-0.0586512\pi$
$830$		0			0
$831$	−39.7980	−	28.1414i	−1.38058	−	0.976215i
$832$		0			0
$833$	5.99071	−	1.60521i	0.207566	−	0.0556171i
$834$		0			0
$835$	−15.9623	+	11.4990i	−0.552397	+	0.397939i
$836$		0			0
$837$	0.0323319	−	2.33539i	0.00111755	−	0.0807230i
$838$		0			0
$839$	0.246405	+	0.426786i	0.00850684	+	0.0147343i	0.870247	−	0.492615i	$-0.163959\pi$
$839$	0.246405	+	0.426786i	0.00850684	+	0.0147343i	−0.861741	+	0.507349i	$0.830625\pi$
$840$		0			0
$841$	14.4495	−	25.0273i	0.498258	−	0.863009i
$842$		0			0
$843$	−5.02181	−	29.2693i	−0.172960	−	1.00809i
$844$		0			0
$845$	1.73205	+	1.41421i	0.0595844	+	0.0486504i
$846$		0			0
$847$	−34.1691	−	34.1691i	−1.17407	−	1.17407i
$848$		0			0
$849$	41.7675	+	3.84847i	1.43346	+	0.132079i
$850$		0			0
$851$	−3.67423	−	2.12132i	−0.125951	−	0.0727179i
$852$		0			0
$853$	2.39403	+	0.641478i	0.0819700	+	0.0219638i	0.299571	−	0.954074i	$-0.403156\pi$
$853$	2.39403	+	0.641478i	0.0819700	+	0.0219638i	−0.217601	+	0.976038i	$0.569823\pi$
$854$		0			0
$855$	−40.7169	−	14.6271i	−1.39249	−	0.500237i
$856$		0			0
$857$	15.2597	+	4.08881i	0.521260	+	0.139671i	0.509849	−	0.860264i	$-0.329701\pi$
$857$	15.2597	+	4.08881i	0.521260	+	0.139671i	0.0114106	+	0.999935i	$0.496368\pi$
$858$		0			0
$859$	−40.2658	−	23.2474i	−1.37385	−	0.793193i	−0.382440	−	0.923980i	$-0.624916\pi$
$859$	−40.2658	−	23.2474i	−1.37385	−	0.793193i	−0.991410	+	0.130788i	$0.958249\pi$
$860$		0			0
$861$	−24.4217	−	53.0097i	−0.832289	−	1.80657i
$862$		0			0
$863$	−20.7132	−	20.7132i	−0.705085	−	0.705085i	0.260413	−	0.965497i	$-0.416141\pi$
$863$	−20.7132	−	20.7132i	−0.705085	−	0.705085i	−0.965497	+	0.260413i	$0.916141\pi$
$864$		0			0
$865$	−28.6969	+	2.89898i	−0.975725	+	0.0985683i
$866$		0			0
$867$	−27.2941	−	10.0771i	−0.926955	−	0.342236i
$868$		0			0
$869$	−0.778539	+	1.34847i	−0.0264101	+	0.0457437i
$870$		0			0
$871$	−11.4495	−	19.8311i	−0.387951	−	0.671951i
$872$		0			0
$873$	−6.64202	+	4.56002i	−0.224798	+	0.154333i
$874$		0			0
$875$	34.5742	−	37.4749i	1.16882	−	1.26688i
$876$		0			0
$877$	−41.3188	+	11.0713i	−1.39524	+	0.373852i	−0.876632	−	0.481162i	$-0.840215\pi$
$877$	−41.3188	+	11.0713i	−1.39524	+	0.373852i	−0.518604	+	0.855014i	$0.673548\pi$
$878$		0			0
$879$	−3.50343	+	38.0227i	−0.118168	+	1.28247i
$880$		0			0
$881$		−	54.8365i		−	1.84749i	−0.383010	−	0.923744i	$-0.625113\pi$
$881$		−	54.8365i		−	1.84749i	0.383010	−	0.923744i	$-0.374887\pi$
$882$		0			0
$883$	−6.27015	+	6.27015i	−0.211007	+	0.211007i	−0.804695	−	0.593688i	$-0.797671\pi$
$883$	−6.27015	+	6.27015i	−0.211007	+	0.211007i	0.593688	+	0.804695i	$0.297671\pi$
$884$		0			0
$885$	17.1204	−	30.2652i	0.575496	−	1.01735i
$886$		0			0
$887$	2.12284	+	7.92256i	0.0712781	+	0.266014i	0.992364	−	0.123347i	$-0.0393627\pi$
$887$	2.12284	+	7.92256i	0.0712781	+	0.266014i	−0.921085	+	0.389360i	$0.872696\pi$
$888$		0			0
$889$	10.4798	−	6.05051i	0.351481	−	0.202928i
$890$		0			0
$891$	3.59592	+	4.44972i	0.120468	+	0.149071i
$892$		0			0
$893$	15.0233	−	56.0676i	0.502734	−	1.87623i
$894$		0			0
$895$	8.46654	+	22.3253i	0.283005	+	0.746253i
$896$		0			0
$897$	−5.91359	+	1.01461i	−0.197449	+	0.0338769i
$898$		0			0
$899$	0.142865			0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$		0			0
$903$	17.4916	+	21.0421i	0.582084	+	0.700238i
$904$		0			0
$905$	−12.2498	−	32.3013i	−0.407197	−	1.07373i
$906$		0			0
$907$	0.978838	−	3.65307i	0.0325018	−	0.121298i	−0.947769	−	0.318957i	$-0.896667\pi$
$907$	0.978838	−	3.65307i	0.0325018	−	0.121298i	0.980271	+	0.197659i	$0.0633339\pi$
$908$		0			0
$909$	−37.1195	−	6.89898i	−1.23118	−	0.228825i
$910$		0			0
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	−0.395114	−	0.918632i	$-0.629295\pi$
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	0.598002	+	0.801495i	$0.295962\pi$
$912$		0			0
$913$	0.896575	+	3.34607i	0.0296723	+	0.110739i
$914$		0			0
$915$	−1.08226	−	1.83702i	−0.0357785	−	0.0607299i
$916$		0			0
$917$	−11.6315	+	11.6315i	−0.384107	+	0.384107i
$918$		0			0
$919$		−	12.6515i		−	0.417335i	−0.977987	−	0.208668i	$-0.933087\pi$
$919$		−	12.6515i		−	0.417335i	0.977987	−	0.208668i	$-0.0669127\pi$
$920$		0			0
$921$	−14.8485	+	6.84072i	−0.489274	+	0.225409i
$922$		0			0
$923$	−21.0552	+	5.64173i	−0.693041	+	0.185700i
$924$		0			0
$925$	21.1745	+	1.28138i	0.696212	+	0.0421314i
$926$		0			0
$927$	12.6143	−	26.4122i	0.414307	−	0.867492i
$928$		0			0
$929$	−21.1024	−	36.5505i	−0.692349	−	1.19918i	−0.971066	−	0.238810i	$-0.923243\pi$
$929$	−21.1024	−	36.5505i	−0.692349	−	1.19918i	0.278717	−	0.960373i	$-0.410091\pi$
$930$		0			0
$931$	−44.4949	+	77.0674i	−1.45826	+	2.52578i
$932$		0			0
$933$	36.6363	−	30.4545i	1.19942	−	0.997036i
$934$		0			0
$935$	−0.635674	+	0.0642162i	−0.0207888	+	0.00210009i
$936$		0			0
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	0.654637	−	0.755943i	$-0.272821\pi$
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	−0.755943	+	0.654637i	$0.772821\pi$
$938$		0			0
$939$	11.9494	−	16.8990i	0.389953	−	0.551477i
$940$		0			0
$941$	27.5227	+	15.8902i	0.897215	+	0.518007i	0.876295	−	0.481774i	$-0.160007\pi$
$941$	27.5227	+	15.8902i	0.897215	+	0.518007i	0.0209191	+	0.999781i	$0.493341\pi$
$942$		0			0
$943$	7.13713	+	1.91239i	0.232417	+	0.0622760i
$944$		0			0
$945$	−43.4183	+	30.3739i	−1.41240	+	0.988064i
$946$		0			0
$947$	−2.94164	−	0.788210i	−0.0955904	−	0.0256134i	0.210707	−	0.977549i	$-0.432423\pi$
$947$	−2.94164	−	0.788210i	−0.0955904	−	0.0256134i	−0.306297	+	0.951936i	$0.599090\pi$
$948$		0			0
$949$	−29.2699	−	16.8990i	−0.950141	−	0.548564i
$950$		0			0
$951$	10.8990	−	15.4135i	0.353424	−	0.499816i
$952$		0			0
$953$	5.79972	+	5.79972i	0.187871	+	0.187871i	0.794775	−	0.606904i	$-0.207589\pi$
$953$	5.79972	+	5.79972i	0.187871	+	0.187871i	−0.606904	+	0.794775i	$0.707589\pi$
$954$		0			0
$955$	30.2474	+	24.6969i	0.978784	+	0.799174i
$956$		0			0
$957$	−0.269109	+	0.223701i	−0.00869905	+	0.00723123i
$958$		0			0
$959$	−49.7046	+	86.0908i	−1.60504	+	2.78002i
$960$		0			0
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$		0			0
$963$	−57.5666	+	4.50150i	−1.85506	+	0.145059i
$964$		0			0
$965$	31.4248	−	22.6380i	1.01160	−	0.728744i
$966$		0			0
$967$	−38.6937	+	10.3679i	−1.24431	+	0.333411i	−0.820134	−	0.572171i	$-0.806101\pi$
$967$	−38.6937	+	10.3679i	−1.24431	+	0.333411i	−0.424172	+	0.905582i	$0.639435\pi$
$968$		0			0
$969$	−4.56048	+	2.10102i	−0.146504	+	0.0674945i
$970$		0			0
$971$		−	21.4989i		−	0.689934i	−0.938615	−	0.344967i	$-0.887890\pi$
$971$		−	21.4989i		−	0.689934i	0.938615	−	0.344967i	$-0.112110\pi$
$972$		0			0
$973$	−10.0000	+	10.0000i	−0.320585	+	0.320585i
$974$		0			0
$975$	24.1863	−	17.7488i	0.774583	−	0.568417i
$976$		0			0
$977$	1.68100	+	6.27359i	0.0537801	+	0.200710i	0.987589	−	0.157063i	$-0.0502027\pi$
$977$	1.68100	+	6.27359i	0.0537801	+	0.200710i	−0.933808	+	0.357773i	$0.883536\pi$
$978$		0			0
$979$	4.41761	−	2.55051i	0.141188	−	0.0815147i
$980$		0			0
$981$	−11.0176	+	12.8868i	−0.351765	+	0.411445i
$982$		0			0
$983$	7.04041	−	26.2752i	0.224554	−	0.838047i	−0.758029	−	0.652221i	$-0.773837\pi$
$983$	7.04041	−	26.2752i	0.224554	−	0.838047i	0.982583	−	0.185826i	$-0.0594961\pi$
$984$		0			0
$985$	−19.9786	−	8.99196i	−0.636571	−	0.286508i
$986$		0			0
$987$	−45.4445	−	54.6690i	−1.44651	−	1.74013i
$988$		0			0
$989$	−3.46410			−0.110152
$990$		0			0
$991$	−16.7423			−0.531838			−0.265919	−	0.963995i	$-0.585675\pi$
$991$	−16.7423			−0.531838			−0.265919	+	0.963995i	$0.585675\pi$
$992$		0			0
$993$	−0.767327	+	0.131652i	−0.0243504	+	0.00417787i
$994$		0			0
$995$	17.6659	−	6.69954i	0.560048	−	0.212390i
$996$		0			0
$997$	−1.73955	+	6.49211i	−0.0550922	+	0.205607i	−0.987986	−	0.154545i	$-0.950609\pi$
$997$	−1.73955	+	6.49211i	−0.0550922	+	0.205607i	0.932893	+	0.360153i	$0.117275\pi$
$998$		0			0
$999$	−21.2132	−	6.00000i	−0.671156	−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.a.257.1		8
4.3	odd	2		90.2.l.a.77.1	yes	8
5.3	odd	4	inner	720.2.cu.a.113.1		8
9.2	odd	6	inner	720.2.cu.a.497.1		8
12.11	even	2		270.2.m.a.17.2		8
20.3	even	4		90.2.l.a.23.1	✓	8
20.7	even	4		450.2.p.a.293.2		8
20.19	odd	2		450.2.p.a.257.2		8
36.7	odd	6		270.2.m.a.197.2		8
36.11	even	6		90.2.l.a.47.1	yes	8
36.23	even	6		810.2.f.b.647.2		8
36.31	odd	6		810.2.f.b.647.3		8
45.38	even	12	inner	720.2.cu.a.353.1		8
60.23	odd	4		270.2.m.a.233.2		8
60.47	odd	4		1350.2.q.g.1043.1		8
60.59	even	2		1350.2.q.g.557.1		8
180.7	even	12		1350.2.q.g.143.1		8
180.23	odd	12		810.2.f.b.323.4		8
180.43	even	12		270.2.m.a.143.2		8
180.47	odd	12		450.2.p.a.443.2		8
180.79	odd	6		1350.2.q.g.1007.1		8
180.83	odd	12		90.2.l.a.83.1	yes	8
180.103	even	12		810.2.f.b.323.1		8
180.119	even	6		450.2.p.a.407.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	20.3	even	4
90.2.l.a.47.1	yes	8	36.11	even	6
90.2.l.a.77.1	yes	8	4.3	odd	2
90.2.l.a.83.1	yes	8	180.83	odd	12
270.2.m.a.17.2		8	12.11	even	2
270.2.m.a.143.2		8	180.43	even	12
270.2.m.a.197.2		8	36.7	odd	6
270.2.m.a.233.2		8	60.23	odd	4
450.2.p.a.257.2		8	20.19	odd	2
450.2.p.a.293.2		8	20.7	even	4
450.2.p.a.407.2		8	180.119	even	6
450.2.p.a.443.2		8	180.47	odd	12
720.2.cu.a.113.1		8	5.3	odd	4	inner
720.2.cu.a.257.1		8	1.1	even	1	trivial
720.2.cu.a.353.1		8	45.38	even	12	inner
720.2.cu.a.497.1		8	9.2	odd	6	inner
810.2.f.b.323.1		8	180.103	even	12
810.2.f.b.323.4		8	180.23	odd	12
810.2.f.b.647.2		8	36.23	even	6
810.2.f.b.647.3		8	36.31	odd	6
1350.2.q.g.143.1		8	180.7	even	12
1350.2.q.g.557.1		8	60.59	even	2
1350.2.q.g.1007.1		8	180.79	odd	6
1350.2.q.g.1043.1		8	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.599900 + 1.62484i) q^{3} +(0.792893 + 2.09077i) q^{5} +(-1.18034 + 4.40508i) q^{7} +(-2.28024 - 1.94949i) q^{9} +(0.550510 - 0.317837i) q^{11} +(0.896575 + 3.34607i) q^{13} +(-3.87283 + 0.0340742i) q^{15} +(-0.317837 + 0.317837i) q^{17} -6.44949i q^{19} +(-6.44949 - 4.56048i) q^{21} +(0.965926 - 0.258819i) q^{23} +(-3.74264 + 3.31552i) q^{25} +(4.53553 - 2.53553i) q^{27} +(0.158919 + 0.275255i) q^{29} +(0.224745 - 0.389270i) q^{31} +(0.186185 + 1.08516i) q^{33} +(-10.1459 + 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-5.97469 - 0.550510i) q^{39} +(6.39898 + 3.69445i) q^{41} +(-3.34607 - 0.896575i) q^{43} +(2.26795 - 6.31319i) q^{45} +(8.69333 + 2.32937i) q^{47} +(-11.9494 - 6.89898i) q^{49} +(-0.325765 - 0.707107i) q^{51} +(-3.78194 - 3.78194i) q^{53} +(1.10102 + 0.898979i) q^{55} +(10.4794 + 3.86905i) q^{57} +(-4.48905 + 7.77526i) q^{59} +(0.275255 + 0.476756i) q^{61} +(11.2791 - 7.74358i) q^{63} +(-6.28497 + 4.52761i) q^{65} +(-6.38512 + 1.71089i) q^{67} +(-0.158919 + 1.72474i) q^{69} +6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +(-3.14198 - 8.07019i) q^{75} +(0.750311 + 2.80020i) q^{77} +(-2.12132 + 1.22474i) q^{79} +(1.39898 + 8.89060i) q^{81} +(-1.41043 + 5.26380i) q^{83} +(-0.916536 - 0.412514i) q^{85} +(-0.542582 + 0.0930924i) q^{87} +8.02458 q^{89} -15.7980 q^{91} +(0.497678 + 0.598698i) q^{93} +(13.4844 - 5.11376i) q^{95} +(0.695075 - 2.59405i) q^{97} +(-1.87492 - 0.348469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 12 q^{5} + 8 q^{7} + 24 q^{11} - 16 q^{15} - 32 q^{21} + 4 q^{25} + 8 q^{27} - 8 q^{31} + 16 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} - 32 q^{51} + 48 q^{55} + 28 q^{57} + 12 q^{61} + 32 q^{63}+ \cdots + 12 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^5 + 8 * q^7 + 24 * q^11 - 16 * q^15 - 32 * q^21 + 4 * q^25 + 8 * q^27 - 8 * q^31 + 16 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 - 32 * q^51 + 48 * q^55 + 28 * q^57 + 12 * q^61 + 32 * q^63 - 24 * q^65 - 4 * q^67 - 16 * q^73 - 8 * q^75 + 24 * q^77 - 28 * q^81 - 12 * q^83 - 20 * q^85 + 8 * q^87 - 48 * q^91 - 20 * q^93 + 24 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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