LMFDB - Embedded newform 720.2.u.a.179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.1
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(-1.81012 - 1.31281i) q^{5} +1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +O(q^{10})$	\(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(-1.81012 - 1.31281i) q^{5} +1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +(2.60775 + 1.78875i) q^{10} +(0.176123 - 0.176123i) q^{11} +(-1.72742 + 1.72742i) q^{13} +(-0.0522343 - 1.98904i) q^{14} +(3.97796 - 0.419308i) q^{16} +3.15721 q^{17} +(3.47385 - 3.47385i) q^{19} +(-3.75305 - 2.43199i) q^{20} +(-0.242451 + 0.255528i) q^{22} +1.97613 q^{23} +(1.55305 + 4.75269i) q^{25} +(2.37796 - 2.50623i) q^{26} +(0.147690 + 2.81002i) q^{28} +(2.62046 - 2.62046i) q^{29} -5.95492i q^{31} +(-5.60818 + 0.740472i) q^{32} +(-4.46342 + 0.117214i) q^{34} +(1.84706 - 2.54675i) q^{35} +(-5.72522 - 5.72522i) q^{37} +(-4.78211 + 5.04005i) q^{38} +(5.39608 + 3.29884i) q^{40} +0.159470 q^{41} +(6.63058 - 6.63058i) q^{43} +(0.333273 - 0.370248i) q^{44} +(-2.79371 + 0.0733658i) q^{46} +1.15223i q^{47} +5.02049 q^{49} +(-2.37204 - 6.66134i) q^{50} +(-3.26874 + 3.63141i) q^{52} +(5.35087 - 5.35087i) q^{53} +(-0.550020 + 0.0875872i) q^{55} +(-0.313118 - 3.96712i) q^{56} +(-3.60733 + 3.80190i) q^{58} +(-4.48547 + 4.48547i) q^{59} +(6.80718 + 6.80718i) q^{61} +(0.221082 + 8.41862i) q^{62} +(7.90094 - 1.25503i) q^{64} +(5.39461 - 0.859057i) q^{65} +(-9.97278 - 9.97278i) q^{67} +(6.30571 - 0.331417i) q^{68} +(-2.51669 + 3.66897i) q^{70} +0.0951463i q^{71} +7.99125 q^{73} +(8.30645 + 7.88134i) q^{74} +(6.57347 - 7.30278i) q^{76} +(0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(-7.75105 - 4.46332i) q^{80} +(-0.225446 + 0.00592045i) q^{82} +(12.2672 - 12.2672i) q^{83} +(-5.71492 - 4.14481i) q^{85} +(-9.12765 + 9.61998i) q^{86} +(-0.457410 + 0.535803i) q^{88} +10.9299 q^{89} +(-2.43039 - 2.43039i) q^{91} +(3.94682 - 0.207438i) q^{92} +(-0.0427774 - 1.62893i) q^{94} +(-10.8486 + 1.72757i) q^{95} -10.4415i q^{97} +(-7.09760 + 0.186390i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41373	+	0.0371259i	−0.999655	+	0.0262520i
$2$	−1.41373	+	0.0371259i	−0.999655	+	0.0262520i
$3$		0			0
$3$		0			0
$4$	1.99724	−	0.104972i	0.998622	−	0.0524859i
$5$	−1.81012	−	1.31281i	−0.809509	−	0.587107i
$5$	−1.81012	−	1.31281i	−0.809509	−	0.587107i
$6$		0			0
$7$			1.40695i			0.531777i	0.964004	+	0.265889i	$0.0856653\pi$
$7$			1.40695i			0.531777i	−0.964004	+	0.265889i	$0.914335\pi$
$8$	−2.81966	+	0.222551i	−0.996900	+	0.0786836i
$9$		0			0
$10$	2.60775	+	1.78875i	0.824643	+	0.565653i
$11$	0.176123	−	0.176123i	0.0531031	−	0.0531031i	−0.680057	−	0.733160i	$-0.738045\pi$
$11$	0.176123	−	0.176123i	0.0531031	−	0.0531031i	0.733160	+	0.680057i	$0.238045\pi$
$12$		0			0
$13$	−1.72742	+	1.72742i	−0.479100	+	0.479100i	−0.904844	−	0.425744i	$-0.860012\pi$
$13$	−1.72742	+	1.72742i	−0.479100	+	0.479100i	0.425744	+	0.904844i	$0.360012\pi$
$14$	−0.0522343	−	1.98904i	−0.0139602	−	0.531594i
$15$		0			0
$16$	3.97796	−	0.419308i	0.994490	−	0.104827i
$17$	3.15721			0.765735			0.382867	−	0.923803i	$-0.374937\pi$
$17$	3.15721			0.765735			0.382867	+	0.923803i	$0.374937\pi$
$18$		0			0
$19$	3.47385	−	3.47385i	0.796956	−	0.796956i	−0.185658	−	0.982614i	$-0.559442\pi$
$19$	3.47385	−	3.47385i	0.796956	−	0.796956i	0.982614	+	0.185658i	$0.0594417\pi$
$20$	−3.75305	−	2.43199i	−0.839208	−	0.543810i
$21$		0			0
$22$	−0.242451	+	0.255528i	−0.0516907	+	0.0544788i
$23$	1.97613			0.412052			0.206026	−	0.978546i	$-0.433947\pi$
$23$	1.97613			0.412052			0.206026	+	0.978546i	$0.433947\pi$
$24$		0			0
$25$	1.55305	+	4.75269i	0.310611	+	0.950537i
$26$	2.37796	−	2.50623i	0.466357	−	0.491512i
$27$		0			0
$28$	0.147690	+	2.81002i	0.0279108	+	0.531044i
$29$	2.62046	−	2.62046i	0.486607	−	0.486607i	−0.420627	−	0.907234i	$-0.638190\pi$
$29$	2.62046	−	2.62046i	0.486607	−	0.486607i	0.907234	+	0.420627i	$0.138190\pi$
$30$		0			0
$31$		−	5.95492i		−	1.06953i	−0.844999	−	0.534767i	$-0.820399\pi$
$31$		−	5.95492i		−	1.06953i	0.844999	−	0.534767i	$-0.179601\pi$
$32$	−5.60818	+	0.740472i	−0.991396	+	0.130898i
$33$		0			0
$34$	−4.46342	+	0.117214i	−0.765471	+	0.0201021i
$35$	1.84706	−	2.54675i	0.312210	−	0.430479i
$36$		0			0
$37$	−5.72522	−	5.72522i	−0.941221	−	0.941221i	0.0571453	−	0.998366i	$-0.481800\pi$
$37$	−5.72522	−	5.72522i	−0.941221	−	0.941221i	−0.998366	+	0.0571453i	$0.981800\pi$
$38$	−4.78211	+	5.04005i	−0.775760	+	0.817603i
$39$		0			0
$40$	5.39608	+	3.29884i	0.853195	+	0.521592i
$41$	0.159470			0.0249050			0.0124525	−	0.999922i	$-0.496036\pi$
$41$	0.159470			0.0249050			0.0124525	+	0.999922i	$0.496036\pi$
$42$		0			0
$43$	6.63058	−	6.63058i	1.01115	−	1.01115i	0.0112162	−	0.999937i	$-0.496430\pi$
$43$	6.63058	−	6.63058i	1.01115	−	1.01115i	0.999937	−	0.0112162i	$-0.00357031\pi$
$44$	0.333273	−	0.370248i	0.0502427	−	0.0558170i
$45$		0			0
$46$	−2.79371	+	0.0733658i	−0.411910	+	0.0108172i
$47$			1.15223i			0.168069i	0.996463	+	0.0840347i	$0.0267807\pi$
$47$			1.15223i			0.168069i	−0.996463	+	0.0840347i	$0.973219\pi$
$48$		0			0
$49$	5.02049			0.717213
$50$	−2.37204	−	6.66134i	−0.335457	−	0.942055i
$51$		0			0
$52$	−3.26874	+	3.63141i	−0.453293	+	0.503585i
$53$	5.35087	−	5.35087i	0.734999	−	0.734999i	−0.236606	−	0.971606i	$-0.576035\pi$
$53$	5.35087	−	5.35087i	0.734999	−	0.734999i	0.971606	+	0.236606i	$0.0760352\pi$
$54$		0			0
$55$	−0.550020	+	0.0875872i	−0.0741646	+	0.0118103i
$56$	−0.313118	−	3.96712i	−0.0418421	−	0.530128i
$57$		0			0
$58$	−3.60733	+	3.80190i	−0.473665	+	0.499214i
$59$	−4.48547	+	4.48547i	−0.583959	+	0.583959i	−0.935989	−	0.352030i	$-0.885492\pi$
$59$	−4.48547	+	4.48547i	−0.583959	+	0.583959i	0.352030	+	0.935989i	$0.385492\pi$
$60$		0			0
$61$	6.80718	+	6.80718i	0.871570	+	0.871570i	0.992643	−	0.121074i	$-0.0386338\pi$
$61$	6.80718	+	6.80718i	0.871570	+	0.871570i	−0.121074	+	0.992643i	$0.538634\pi$
$62$	0.221082	+	8.41862i	0.0280774	+	1.06917i
$63$		0			0
$64$	7.90094	−	1.25503i	0.987618	−	0.156879i
$65$	5.39461	−	0.859057i	0.669118	−	0.106553i
$66$		0			0
$67$	−9.97278	−	9.97278i	−1.21837	−	1.21837i	−0.968203	−	0.250166i	$-0.919515\pi$
$67$	−9.97278	−	9.97278i	−1.21837	−	1.21837i	−0.250166	−	0.968203i	$-0.580485\pi$
$68$	6.30571	−	0.331417i	0.764679	−	0.0401903i
$69$		0			0
$70$	−2.51669	+	3.66897i	−0.300802	+	0.438526i
$71$			0.0951463i			0.0112918i	0.999984	+	0.00564589i	$0.00179715\pi$
$71$			0.0951463i			0.0112918i	−0.999984	+	0.00564589i	$0.998203\pi$
$72$		0			0
$73$	7.99125			0.935305			0.467653	−	0.883912i	$-0.345100\pi$
$73$	7.99125			0.935305			0.467653	+	0.883912i	$0.345100\pi$
$74$	8.30645	+	7.88134i	0.965605	+	0.916187i
$75$		0			0
$76$	6.57347	−	7.30278i	0.754029	−	0.837687i
$77$	0.247796	+	0.247796i	0.0282390	+	0.0282390i
$78$		0			0
$79$		−	5.66620i		−	0.637497i	−0.947839	−	0.318748i	$-0.896737\pi$
$79$		−	5.66620i		−	0.637497i	0.947839	−	0.318748i	$-0.103263\pi$
$80$	−7.75105	−	4.46332i	−0.866594	−	0.499014i
$81$		0			0
$82$	−0.225446	+	0.00592045i	−0.0248964	+	0.000653804i
$83$	12.2672	−	12.2672i	1.34650	−	1.34650i	0.457068	−	0.889432i	$-0.348900\pi$
$83$	12.2672	−	12.2672i	1.34650	−	1.34650i	0.889432	−	0.457068i	$-0.151100\pi$
$84$		0			0
$85$	−5.71492	−	4.14481i	−0.619870	−	0.449568i
$86$	−9.12765	+	9.61998i	−0.984260	+	1.03735i
$87$		0			0
$88$	−0.457410	+	0.535803i	−0.0487601	+	0.0571168i
$89$	10.9299			1.15857			0.579284	−	0.815126i	$-0.303332\pi$
$89$	10.9299			1.15857			0.579284	+	0.815126i	$0.303332\pi$
$90$		0			0
$91$	−2.43039	−	2.43039i	−0.254774	−	0.254774i
$92$	3.94682	−	0.207438i	0.411484	−	0.0216269i
$93$		0			0
$94$	−0.0427774	−	1.62893i	−0.00441216	−	0.168011i
$95$	−10.8486	+	1.72757i	−1.11304	+	0.177245i
$96$		0			0
$97$		−	10.4415i		−	1.06017i	−0.847944	−	0.530086i	$-0.822160\pi$
$97$		−	10.4415i		−	1.06017i	0.847944	−	0.530086i	$-0.177840\pi$
$98$	−7.09760	+	0.186390i	−0.716966	+	0.0188283i
$99$		0			0
$100$	3.60072	+	9.32924i	0.360072	+	0.932924i
$101$	4.54532	+	4.54532i	0.452276	+	0.452276i	0.896109	−	0.443833i	$-0.146382\pi$
$101$	4.54532	+	4.54532i	0.452276	+	0.452276i	−0.443833	+	0.896109i	$0.646382\pi$
$102$		0			0
$103$			7.65680i			0.754447i	0.926122	+	0.377224i	$0.123121\pi$
$103$			7.65680i			0.754447i	−0.926122	+	0.377224i	$0.876879\pi$
$104$	4.48629	−	5.25517i	0.439917	−	0.515312i
$105$		0			0
$106$	−7.36601	+	7.76333i	−0.715451	+	0.754041i
$107$	4.25185	+	4.25185i	0.411042	+	0.411042i	0.882102	−	0.471059i	$-0.156128\pi$
$107$	4.25185	+	4.25185i	0.411042	+	0.411042i	−0.471059	+	0.882102i	$0.656128\pi$
$108$		0			0
$109$	0.180834	+	0.180834i	0.0173208	+	0.0173208i	0.715714	−	0.698393i	$-0.246101\pi$
$109$	0.180834	+	0.180834i	0.0173208	+	0.0173208i	−0.698393	+	0.715714i	$0.746101\pi$
$110$	0.774325	−	0.144244i	0.0738290	−	0.0137532i
$111$		0			0
$112$	0.589946	+	5.59679i	0.0557446	+	0.528847i
$113$	6.88868			0.648032			0.324016	−	0.946052i	$-0.394967\pi$
$113$	6.88868			0.648032			0.324016	+	0.946052i	$0.394967\pi$
$114$		0			0
$115$	−3.57703	−	2.59429i	−0.333560	−	0.241919i
$116$	4.95862	−	5.50877i	0.460396	−	0.511476i
$117$		0			0
$118$	6.17471	−	6.50776i	0.568428	−	0.599088i
$119$			4.44203i			0.407200i
$120$		0			0
$121$			10.9380i			0.994360i
$122$	−9.87621	−	9.37076i	−0.894150	−	0.848389i
$123$		0			0
$124$	−0.625098	−	11.8934i	−0.0561355	−	1.06806i
$125$	3.42817	−	10.6418i	0.306625	−	0.951831i
$126$		0			0
$127$	3.18115			0.282281			0.141141	−	0.989990i	$-0.454923\pi$
$127$	3.18115			0.282281			0.141141	+	0.989990i	$0.454923\pi$
$128$	−11.1232	+	2.06760i	−0.983159	+	0.182752i
$129$		0			0
$130$	−7.59460	+	1.41475i	−0.666091	+	0.124082i
$131$	−8.49459	−	8.49459i	−0.742175	−	0.742175i	0.230821	−	0.972996i	$-0.425859\pi$
$131$	−8.49459	−	8.49459i	−0.742175	−	0.742175i	−0.972996	+	0.230821i	$0.925859\pi$
$132$		0			0
$133$	4.88754	+	4.88754i	0.423803	+	0.423803i
$134$	14.4690	+	13.7285i	1.24993	+	1.18596i
$135$		0			0
$136$	−8.90224	+	0.702639i	−0.763361	+	0.0602508i
$137$			15.1013i			1.29019i	0.764102	+	0.645096i	$0.223182\pi$
$137$			15.1013i			1.29019i	−0.764102	+	0.645096i	$0.776818\pi$
$138$		0			0
$139$	−11.6635	−	11.6635i	−0.989286	−	0.989286i	0.0106573	−	0.999943i	$-0.496608\pi$
$139$	−11.6635	−	11.6635i	−0.989286	−	0.989286i	−0.999943	+	0.0106573i	$0.996608\pi$
$140$	3.42169	−	5.28036i	0.289186	−	0.446272i
$141$		0			0
$142$	−0.00353239	−	0.134511i	−0.000296432	−	0.0112879i
$143$			0.608476i			0.0508833i
$144$		0			0
$145$	−8.18351	+	1.30317i	−0.679604	+	0.108223i
$146$	−11.2974	+	0.296682i	−0.934983	+	0.0245536i
$147$		0			0
$148$	−12.0356	−	10.8337i	−0.989324	−	0.890522i
$149$	11.1281	+	11.1281i	0.911646	+	0.911646i	0.996402	−	0.0847561i	$-0.0270111\pi$
$149$	11.1281	+	11.1281i	0.911646	+	0.911646i	−0.0847561	+	0.996402i	$0.527011\pi$
$150$		0			0
$151$	−21.8766			−1.78030			−0.890148	−	0.455672i	$-0.849399\pi$
$151$	−21.8766			−1.78030			−0.890148	+	0.455672i	$0.849399\pi$
$152$	−9.02197	+	10.5682i	−0.731778	+	0.857193i
$153$		0			0
$154$	−0.359516	−	0.341116i	−0.0289706	−	0.0274879i
$155$	−7.81768	+	10.7791i	−0.627931	+	0.865798i
$156$		0			0
$157$	−15.3928	+	15.3928i	−1.22848	+	1.22848i	−0.263935	+	0.964541i	$0.585020\pi$
$157$	−15.3928	+	15.3928i	−1.22848	+	1.22848i	−0.964541	+	0.263935i	$0.914980\pi$
$158$	0.210363	+	8.01045i	0.0167356	+	0.637277i
$159$		0			0
$160$	11.1236	+	6.02214i	0.879395	+	0.476092i
$161$			2.78032i			0.219120i
$162$		0			0
$163$	4.90113	+	4.90113i	0.383886	+	0.383886i	0.872500	−	0.488614i	$-0.162497\pi$
$163$	4.90113	+	4.90113i	0.383886	+	0.383886i	−0.488614	+	0.872500i	$0.662497\pi$
$164$	0.318499	−	0.0167398i	0.0248706	−	0.00130716i
$165$		0			0
$166$	−16.8870	+	17.7979i	−1.31069	+	1.38138i
$167$	−17.4380			−1.34939			−0.674695	−	0.738097i	$-0.735725\pi$
$167$	−17.4380			−1.34939			−0.674695	+	0.738097i	$0.735725\pi$
$168$		0			0
$169$			7.03205i			0.540927i
$170$	8.23320	+	5.64746i	0.631458	+	0.433141i
$171$		0			0
$172$	12.5469	−	13.9389i	0.956688	−	1.06283i
$173$	−17.4288	−	17.4288i	−1.32509	−	1.32509i	−0.909598	−	0.415490i	$-0.863610\pi$
$173$	−17.4288	−	17.4288i	−1.32509	−	1.32509i	−0.415490	−	0.909598i	$-0.636390\pi$
$174$		0			0
$175$	−6.68679	+	2.18507i	−0.505474	+	0.165176i
$176$	0.626761	−	0.774460i	0.0472439	−	0.0583771i
$177$		0			0
$178$	−15.4519	+	0.405783i	−1.15817	+	0.0304147i
$179$	12.4635	+	12.4635i	0.931565	+	0.931565i	0.997804	−	0.0662383i	$-0.0210998\pi$
$179$	12.4635	+	12.4635i	0.931565	+	0.931565i	−0.0662383	+	0.997804i	$0.521100\pi$
$180$		0			0
$181$	−7.07994	+	7.07994i	−0.526248	+	0.526248i	−0.919451	−	0.393203i	$-0.871367\pi$
$181$	−7.07994	+	7.07994i	−0.526248	+	0.526248i	0.393203	+	0.919451i	$0.371367\pi$
$182$	3.52614	+	3.34568i	0.261375	+	0.247998i
$183$		0			0
$184$	−5.57202	+	0.439790i	−0.410775	+	0.0324218i
$185$	2.84719	+	17.8795i	0.209330	+	1.31452i
$186$		0			0
$187$	0.556057	−	0.556057i	0.0406629	−	0.0406629i
$188$	0.120951	+	2.30128i	0.00882127	+	0.167838i
$189$		0			0
$190$	15.2728	−	2.84508i	1.10801	−	0.206403i
$191$	−12.6011			−0.911781			−0.455891	−	0.890036i	$-0.650679\pi$
$191$	−12.6011			−0.911781			−0.455891	+	0.890036i	$0.650679\pi$
$192$		0			0
$193$			5.15723i			0.371226i	0.982623	+	0.185613i	$0.0594270\pi$
$193$			5.15723i			0.371226i	−0.982623	+	0.185613i	$0.940573\pi$
$194$	0.387649	+	14.7614i	0.0278316	+	1.05981i
$195$		0			0
$196$	10.0271	−	0.527010i	0.716225	−	0.0376436i
$197$	3.59790	−	3.59790i	0.256340	−	0.256340i	−0.567224	−	0.823564i	$-0.691983\pi$
$197$	3.59790	−	3.59790i	0.256340	−	0.256340i	0.823564	+	0.567224i	$0.191983\pi$
$198$		0			0
$199$	7.58554			0.537725			0.268862	−	0.963179i	$-0.413352\pi$
$199$	7.58554			0.537725			0.268862	+	0.963179i	$0.413352\pi$
$200$	−5.43680	−	13.0553i	−0.384439	−	0.923150i
$201$		0			0
$202$	−6.59458	−	6.25708i	−0.463993	−	0.440247i
$203$	3.68686	+	3.68686i	0.258767	+	0.258767i
$204$		0			0
$205$	−0.288659	−	0.209353i	−0.0201608	−	0.0146219i
$206$	−0.284266	−	10.8246i	−0.0198057	−	0.754187i
$207$		0			0
$208$	−6.14728	+	7.59593i	−0.426237	+	0.526683i
$209$		−	1.22365i		−	0.0846417i
$210$		0			0
$211$	0.605008	−	0.605008i	0.0416505	−	0.0416505i	−0.685975	−	0.727625i	$-0.740624\pi$
$211$	0.605008	−	0.605008i	0.0416505	−	0.0416505i	0.727625	+	0.685975i	$0.240624\pi$
$212$	10.1253	−	11.2487i	0.695409	−	0.772563i
$213$		0			0
$214$	−6.16881	−	5.85310i	−0.421691	−	0.400110i
$215$	−20.7068	+	3.29743i	−1.41219	+	0.224883i
$216$		0			0
$217$	8.37827			0.568754
$218$	−0.262363	−	0.248936i	−0.0177695	−	0.0168601i
$219$		0			0
$220$	−1.08933	+	0.232669i	−0.0734425	+	0.0156866i
$221$	−5.45382	+	5.45382i	−0.366863	+	0.366863i
$222$		0			0
$223$	25.2652			1.69188			0.845940	−	0.533278i	$-0.179040\pi$
$223$	25.2652			1.69188			0.845940	+	0.533278i	$0.179040\pi$
$224$	−1.04181	−	7.89043i	−0.0696087	−	0.527202i
$225$		0			0
$226$	−9.73870	+	0.255748i	−0.647809	+	0.0170121i
$227$	6.61823	−	6.61823i	0.439267	−	0.439267i	−0.452498	−	0.891765i	$-0.649467\pi$
$227$	6.61823	−	6.61823i	0.439267	−	0.439267i	0.891765	+	0.452498i	$0.149467\pi$
$228$		0			0
$229$	−0.0446899	+	0.0446899i	−0.00295319	+	0.00295319i	−0.708582	−	0.705629i	$-0.750665\pi$
$229$	−0.0446899	+	0.0446899i	−0.00295319	+	0.00295319i	0.705629	+	0.708582i	$0.250665\pi$
$230$	5.15326	+	3.53482i	0.339796	+	0.233079i
$231$		0			0
$232$	−6.80562	+	7.97199i	−0.446811	+	0.523387i
$233$			13.5011i			0.884488i	0.896895	+	0.442244i	$0.145817\pi$
$233$			13.5011i			0.884488i	−0.896895	+	0.442244i	$0.854183\pi$
$234$		0			0
$235$	1.51265	−	2.08566i	0.0986747	−	0.136054i
$236$	−8.48774	+	9.42943i	−0.552505	+	0.613804i
$237$		0			0
$238$	−0.164914	−	6.27982i	−0.0106898	−	0.407060i
$239$	5.58106			0.361009			0.180504	−	0.983574i	$-0.442227\pi$
$239$	5.58106			0.361009			0.180504	+	0.983574i	$0.442227\pi$
$240$		0			0
$241$	15.7677			1.01569			0.507845	−	0.861449i	$-0.330442\pi$
$241$	15.7677			1.01569			0.507845	+	0.861449i	$0.330442\pi$
$242$	−0.406082	−	15.4633i	−0.0261039	−	0.994017i
$243$		0			0
$244$	14.3101	+	12.8810i	0.916113	+	0.824623i
$245$	−9.08768	−	6.59096i	−0.580591	−	0.421081i
$246$		0			0
$247$			12.0016i			0.763643i
$248$	1.32527	+	16.7908i	0.0841548	+	1.06622i
$249$		0			0
$250$	−4.45140	+	15.1718i	−0.281532	+	0.959552i
$251$	10.5401	−	10.5401i	0.665287	−	0.665287i	−0.291334	−	0.956621i	$-0.594099\pi$
$251$	10.5401	−	10.5401i	0.665287	−	0.665287i	0.956621	+	0.291334i	$0.0940992\pi$
$252$		0			0
$253$	0.348043	−	0.348043i	0.0218812	−	0.0218812i
$254$	−4.49727	+	0.118103i	−0.282184	+	0.00741044i
$255$		0			0
$256$	15.6484	−	3.33598i	0.978023	−	0.208499i
$257$	−20.0698			−1.25192			−0.625959	−	0.779856i	$-0.715292\pi$
$257$	−20.0698			−1.25192			−0.625959	+	0.779856i	$0.715292\pi$
$258$		0			0
$259$	8.05510	−	8.05510i	0.500520	−	0.500520i
$260$	10.6842	−	2.28203i	0.662604	−	0.141525i
$261$		0			0
$262$	12.3244	+	11.6937i	0.761403	+	0.722436i
$263$	−28.6944			−1.76937			−0.884687	−	0.466185i	$-0.845628\pi$
$263$	−28.6944			−1.76937			−0.884687	+	0.466185i	$0.845628\pi$
$264$		0			0
$265$	−16.7104	+	2.66103i	−1.02651	+	0.163466i
$266$	−7.09109	−	6.72818i	−0.434783	−	0.412531i
$267$		0			0
$268$	−20.9649	−	18.8712i	−1.28064	−	1.15274i
$269$	13.7007	−	13.7007i	0.835349	−	0.835349i	−0.152894	−	0.988243i	$-0.548859\pi$
$269$	13.7007	−	13.7007i	0.835349	−	0.835349i	0.988243	+	0.152894i	$0.0488592\pi$
$270$		0			0
$271$		−	6.47842i		−	0.393536i	−0.980450	−	0.196768i	$-0.936955\pi$
$271$		−	6.47842i		−	0.393536i	0.980450	−	0.196768i	$-0.0630445\pi$
$272$	12.5592	−	1.32384i	0.761516	−	0.0802697i
$273$		0			0
$274$	−0.560650	−	21.3491i	−0.0338701	−	1.28975i
$275$	1.11059	+	0.563529i	0.0669708	+	0.0339821i
$276$		0			0
$277$	10.7023	+	10.7023i	0.643041	+	0.643041i	0.951302	−	0.308261i	$-0.0997469\pi$
$277$	10.7023	+	10.7023i	0.643041	+	0.643041i	−0.308261	+	0.951302i	$0.599747\pi$
$278$	16.9220	+	16.0560i	1.01492	+	0.962974i
$279$		0			0
$280$	−4.64130	+	7.59202i	−0.277370	+	0.453710i
$281$	−23.3237			−1.39138			−0.695688	−	0.718344i	$-0.744900\pi$
$281$	−23.3237			−1.39138			−0.695688	+	0.718344i	$0.744900\pi$
$282$		0			0
$283$	−7.39967	+	7.39967i	−0.439865	+	0.439865i	−0.891966	−	0.452102i	$-0.850674\pi$
$283$	−7.39967	+	7.39967i	−0.439865	+	0.439865i	0.452102	+	0.891966i	$0.350674\pi$
$284$	0.00998767	+	0.190030i	0.000592659	+	0.0112762i
$285$		0			0
$286$	−0.0225902	−	0.860219i	−0.00133579	−	0.0508658i
$287$			0.224366i			0.0132439i
$288$		0			0
$289$	−7.03205			−0.413650
$290$	11.5209	−	2.14615i	0.676528	−	0.126026i
$291$		0			0
$292$	15.9605	−	0.838855i	0.934016	−	0.0490903i
$293$	5.94867	−	5.94867i	0.347525	−	0.347525i	−0.511662	−	0.859187i	$-0.670970\pi$
$293$	5.94867	−	5.94867i	0.347525	−	0.347525i	0.859187	+	0.511662i	$0.170970\pi$
$294$		0			0
$295$	14.0078	−	2.23066i	0.815567	−	0.129874i
$296$	17.4173	+	14.8690i	1.01236	+	0.864244i
$297$		0			0
$298$	−16.1452	−	15.3189i	−0.935264	−	0.887399i
$299$	−3.41361	+	3.41361i	−0.197414	+	0.197414i
$300$		0			0
$301$	9.32889	+	9.32889i	0.537708	+	0.537708i
$302$	30.9276	−	0.812190i	1.77968	−	0.0467363i
$303$		0			0
$304$	12.3622	−	15.2755i	0.709023	−	0.876108i
$305$	−3.38526	−	21.2583i	−0.193839	−	1.21725i
$306$		0			0
$307$	−12.0570	−	12.0570i	−0.688130	−	0.688130i	0.273689	−	0.961818i	$-0.411756\pi$
$307$	−12.0570	−	12.0570i	−0.688130	−	0.688130i	−0.961818	+	0.273689i	$0.911756\pi$
$308$	0.520921	+	0.468898i	0.0296822	+	0.0267179i
$309$		0			0
$310$	10.6519	−	15.5289i	0.604986	−	0.881984i
$311$		−	31.3243i		−	1.77624i	−0.459615	−	0.888118i	$-0.652012\pi$
$311$		−	31.3243i		−	1.77624i	0.459615	−	0.888118i	$-0.347988\pi$
$312$		0			0
$313$	24.0690			1.36046			0.680230	−	0.732999i	$-0.261880\pi$
$313$	24.0690			1.36046			0.680230	+	0.732999i	$0.261880\pi$
$314$	21.1897	−	22.3326i	1.19580	−	1.26030i
$315$		0			0
$316$	−0.594790	−	11.3168i	−0.0334596	−	0.636618i
$317$	−10.2657	−	10.2657i	−0.576579	−	0.576579i	0.357380	−	0.933959i	$-0.383670\pi$
$317$	−10.2657	−	10.2657i	−0.576579	−	0.576579i	−0.933959	+	0.357380i	$0.883670\pi$
$318$		0			0
$319$		−	0.923046i		−	0.0516807i
$320$	−15.9493	−	8.10069i	−0.891591	−	0.452842i
$321$		0			0
$322$	−0.103222	−	3.93061i	−0.00575233	−	0.219044i
$323$	10.9677	−	10.9677i	0.610257	−	0.610257i
$324$		0			0
$325$	−10.8927	−	5.52710i	−0.604216	−	0.306589i
$326$	−7.11082	−	6.74690i	−0.393832	−	0.373676i
$327$		0			0
$328$	−0.449649	+	0.0354901i	−0.0248277	+	0.00195961i
$329$	−1.62112			−0.0893755
$330$		0			0
$331$	−12.7608	−	12.7608i	−0.701395	−	0.701395i	0.263315	−	0.964710i	$-0.415184\pi$
$331$	−12.7608	−	12.7608i	−0.701395	−	0.701395i	−0.964710	+	0.263315i	$0.915184\pi$
$332$	23.2129	−	25.7883i	1.27397	−	1.41532i
$333$		0			0
$334$	24.6525	−	0.647400i	1.34892	−	0.0354242i
$335$	4.95953	+	31.1443i	0.270968	+	1.70159i
$336$		0			0
$337$		−	17.3967i		−	0.947660i	−0.880616	−	0.473830i	$-0.842871\pi$
$337$		−	17.3967i		−	0.947660i	0.880616	−	0.473830i	$-0.157129\pi$
$338$	−0.261071	−	9.94139i	−0.0142004	−	0.540741i
$339$		0			0
$340$	−11.8492	−	7.67830i	−0.642611	−	0.416414i
$341$	−1.04880	−	1.04880i	−0.0567956	−	0.0567956i
$342$		0			0
$343$			16.9122i			0.913175i
$344$	−17.2203	+	20.1716i	−0.928457	+	1.08758i
$345$		0			0
$346$	25.2866	+	23.9925i	1.35942	+	1.28984i
$347$	9.64234	+	9.64234i	0.517628	+	0.517628i	0.916853	−	0.399225i	$-0.130721\pi$
$347$	9.64234	+	9.64234i	0.517628	+	0.517628i	−0.399225	+	0.916853i	$0.630721\pi$
$348$		0			0
$349$	−3.66120	−	3.66120i	−0.195980	−	0.195980i	0.602294	−	0.798274i	$-0.294253\pi$
$349$	−3.66120	−	3.66120i	−0.195980	−	0.195980i	−0.798274	+	0.602294i	$0.794253\pi$
$350$	9.37217	−	3.33734i	0.500964	−	0.178388i
$351$		0			0
$352$	−0.857315	+	1.11814i	−0.0456951	+	0.0595973i
$353$	18.9960			1.01106			0.505528	−	0.862810i	$-0.331298\pi$
$353$	18.9960			1.01106			0.505528	+	0.862810i	$0.331298\pi$
$354$		0			0
$355$	0.124909	−	0.172226i	0.00662949	−	0.00914081i
$356$	21.8297	−	1.14733i	1.15697	−	0.0608084i
$357$		0			0
$358$	−18.0827	−	17.1573i	−0.955700	−	0.906789i
$359$			8.71770i			0.460103i	0.973178	+	0.230051i	$0.0738894\pi$
$359$			8.71770i			0.460103i	−0.973178	+	0.230051i	$0.926111\pi$
$360$		0			0
$361$		−	5.13530i		−	0.270279i
$362$	9.74625	−	10.2719i	0.512252	−	0.539882i
$363$		0			0
$364$	−5.10921	−	4.59896i	−0.267795	−	0.241051i
$365$	−14.4651	−	10.4910i	−0.757138	−	0.549124i
$366$		0			0
$367$	28.0501			1.46420			0.732101	−	0.681196i	$-0.238540\pi$
$367$	28.0501			1.46420			0.732101	+	0.681196i	$0.238540\pi$
$368$	7.86098	−	0.828609i	0.409782	−	0.0431942i
$369$		0			0
$370$	−4.68894	−	25.1710i	−0.243766	−	1.30858i
$371$	7.52841	+	7.52841i	0.390856	+	0.390856i
$372$		0			0
$373$	4.90740	+	4.90740i	0.254096	+	0.254096i	0.822647	−	0.568552i	$-0.192496\pi$
$373$	4.90740	+	4.90740i	0.254096	+	0.254096i	−0.568552	+	0.822647i	$0.692496\pi$
$374$	−0.765468	+	0.806756i	−0.0395814	+	0.0417163i
$375$		0			0
$376$	−0.256429	−	3.24888i	−0.0132243	−	0.167548i
$377$			9.05326i			0.466267i
$378$		0			0
$379$	26.0620	+	26.0620i	1.33872	+	1.33872i	0.897305	+	0.441412i	$0.145522\pi$
$379$	26.0620	+	26.0620i	1.33872	+	1.33872i	0.441412	+	0.897305i	$0.354478\pi$
$380$	−21.4859	+	4.58917i	−1.10221	+	0.235420i
$381$		0			0
$382$	17.8145	−	0.467826i	0.911467	−	0.0239361i
$383$		−	6.91314i		−	0.353245i	−0.984279	−	0.176623i	$-0.943483\pi$
$383$		−	6.91314i		−	0.353245i	0.984279	−	0.176623i	$-0.0565172\pi$
$384$		0			0
$385$	−0.123231	−	0.773850i	−0.00628042	−	0.0394391i
$386$	−0.191467	−	7.29091i	−0.00974541	−	0.371098i
$387$		0			0
$388$	−1.09606	−	20.8542i	−0.0556440	−	1.05871i
$389$	−14.5222	−	14.5222i	−0.736302	−	0.736302i	0.235558	−	0.971860i	$-0.424308\pi$
$389$	−14.5222	−	14.5222i	−0.736302	−	0.736302i	−0.971860	+	0.235558i	$0.924308\pi$
$390$		0			0
$391$	6.23906			0.315523
$392$	−14.1561	+	1.11731i	−0.714989	+	0.0564329i
$393$		0			0
$394$	−4.95287	+	5.22002i	−0.249522	+	0.262981i
$395$	−7.43864	+	10.2565i	−0.374279	+	0.516060i
$396$		0			0
$397$	−18.3367	+	18.3367i	−0.920291	+	0.920291i	−0.997050	−	0.0767588i	$-0.975543\pi$
$397$	−18.3367	+	18.3367i	−0.920291	+	0.920291i	0.0767588	+	0.997050i	$0.475543\pi$
$398$	−10.7239	+	0.281620i	−0.537540	+	0.0141163i
$399$		0			0
$400$	8.17083	+	18.2548i	0.408541	+	0.912740i
$401$			33.5380i			1.67481i	0.546585	+	0.837404i	$0.315927\pi$
$401$			33.5380i			1.67481i	−0.546585	+	0.837404i	$0.684073\pi$
$402$		0			0
$403$	10.2866	+	10.2866i	0.512414	+	0.512414i
$404$	9.55523	+	8.60097i	0.475391	+	0.427914i
$405$		0			0
$406$	−5.34908	−	5.07533i	−0.265471	−	0.251884i
$407$	−2.01669			−0.0999634
$408$		0			0
$409$		−	18.0044i		−	0.890260i	−0.895466	−	0.445130i	$-0.853158\pi$
$409$		−	18.0044i		−	0.890260i	0.895466	−	0.445130i	$-0.146842\pi$
$410$	0.415857	+	0.285252i	0.0205377	+	0.0140876i
$411$		0			0
$412$	0.803748	+	15.2925i	0.0395978	+	0.753407i
$413$	−6.31084	−	6.31084i	−0.310536	−	0.310536i
$414$		0			0
$415$	−38.3096	+	6.10056i	−1.88054	+	0.299465i
$416$	8.40857	−	10.9668i	0.412264	−	0.537691i
$417$		0			0
$418$	0.0454291	+	1.72991i	0.00222201	+	0.0846125i
$419$	−16.7671	−	16.7671i	−0.819126	−	0.819126i	0.166856	−	0.985981i	$-0.446639\pi$
$419$	−16.7671	−	16.7671i	−0.819126	−	0.819126i	−0.985981	+	0.166856i	$0.946639\pi$
$420$		0			0
$421$	9.17528	−	9.17528i	0.447176	−	0.447176i	−0.447239	−	0.894415i	$-0.647593\pi$
$421$	9.17528	−	9.17528i	0.447176	−	0.447176i	0.894415	+	0.447239i	$0.147593\pi$
$422$	−0.832854	+	0.877777i	−0.0405427	+	0.0427295i
$423$		0			0
$424$	−13.8968	+	16.2785i	−0.674888	+	0.790553i
$425$	4.90331	+	15.0052i	0.237846	+	0.727859i
$426$		0			0
$427$	−9.57736	+	9.57736i	−0.463481	+	0.463481i
$428$	8.93831	+	8.04566i	0.432049	+	0.388902i
$429$		0			0
$430$	29.1514	−	5.43042i	1.40580	−	0.261878i
$431$	36.6726			1.76646			0.883228	−	0.468943i	$-0.155365\pi$
$431$	36.6726			1.76646			0.883228	+	0.468943i	$0.155365\pi$
$432$		0			0
$433$			28.1455i			1.35259i	0.736633	+	0.676293i	$0.236414\pi$
$433$			28.1455i			1.35259i	−0.736633	+	0.676293i	$0.763586\pi$
$434$	−11.8446	+	0.311051i	−0.568558	+	0.0149309i
$435$		0			0
$436$	0.380152	+	0.342187i	0.0182060	+	0.0163878i
$437$	6.86480	−	6.86480i	0.328388	−	0.328388i
$438$		0			0
$439$	−3.32665			−0.158772			−0.0793862	−	0.996844i	$-0.525296\pi$
$439$	−3.32665			−0.158772			−0.0793862	+	0.996844i	$0.525296\pi$
$440$	1.53137	−	0.369373i	0.0730054	−	0.0176092i
$441$		0			0
$442$	7.50772	−	7.91268i	0.357106	−	0.376368i
$443$	−6.03644	−	6.03644i	−0.286800	−	0.286800i	0.549013	−	0.835814i	$-0.315004\pi$
$443$	−6.03644	−	6.03644i	−0.286800	−	0.286800i	−0.835814	+	0.549013i	$0.815004\pi$
$444$		0			0
$445$	−19.7844	−	14.3489i	−0.937871	−	0.680203i
$446$	−35.7180	+	0.937992i	−1.69130	+	0.0444152i
$447$		0			0
$448$	1.76577	+	11.1162i	0.0834248	+	0.525193i
$449$		−	14.2691i		−	0.673402i	−0.941612	−	0.336701i	$-0.890689\pi$
$449$		−	14.2691i		−	0.673402i	0.941612	−	0.336701i	$-0.109311\pi$
$450$		0			0
$451$	0.0280862	−	0.0280862i	0.00132253	−	0.00132253i
$452$	13.7584	−	0.723116i	0.647139	−	0.0340125i
$453$		0			0
$454$	−9.11065	+	9.60207i	−0.427584	+	0.450647i
$455$	1.20865	+	7.58994i	0.0566624	+	0.355822i
$456$		0			0
$457$	25.0611			1.17231			0.586154	−	0.810200i	$-0.300641\pi$
$457$	25.0611			1.17231			0.586154	+	0.810200i	$0.300641\pi$
$458$	0.0615201	−	0.0648384i	0.00287464	−	0.00302970i
$459$		0			0
$460$	−7.41654	−	4.80594i	−0.345798	−	0.224078i
$461$	−11.6030	+	11.6030i	−0.540407	+	0.540407i	−0.923648	−	0.383241i	$-0.874808\pi$
$461$	−11.6030	+	11.6030i	−0.540407	+	0.540407i	0.383241	+	0.923648i	$0.374808\pi$
$462$		0			0
$463$	−8.74913			−0.406607			−0.203303	−	0.979116i	$-0.565168\pi$
$463$	−8.74913			−0.406607			−0.203303	+	0.979116i	$0.565168\pi$
$464$	9.32531	−	11.5229i	0.432917	−	0.534936i
$465$		0			0
$466$	−0.501241	−	19.0869i	−0.0232196	−	0.884183i
$467$	−19.3047	+	19.3047i	−0.893316	+	0.893316i	−0.994834	−	0.101518i	$-0.967630\pi$
$467$	−19.3047	+	19.3047i	−0.893316	+	0.893316i	0.101518	+	0.994834i	$0.467630\pi$
$468$		0			0
$469$	14.0312	−	14.0312i	0.647901	−	0.647901i
$470$	−2.06105	+	3.00472i	−0.0950690	+	0.138597i
$471$		0			0
$472$	11.6493	−	13.6458i	0.536201	−	0.628097i
$473$		−	2.33559i		−	0.107391i
$474$		0			0
$475$	21.9052	+	11.1150i	1.00508	+	0.509993i
$476$	0.466288	+	8.87182i	0.0213723	+	0.406639i
$477$		0			0
$478$	−7.89009	+	0.207202i	−0.360884	+	0.00947719i
$479$	−19.9695			−0.912431			−0.456215	−	0.889869i	$-0.650795\pi$
$479$	−19.9695			−0.912431			−0.456215	+	0.889869i	$0.650795\pi$
$480$		0			0
$481$	19.7797			0.901877
$482$	−22.2913	+	0.585392i	−1.01534	+	0.0266639i
$483$		0			0
$484$	1.14818	+	21.8458i	0.0521899	+	0.992990i
$485$	−13.7077	+	18.9003i	−0.622434	+	0.858219i
$486$		0			0
$487$			34.8592i			1.57962i	0.613351	+	0.789811i	$0.289821\pi$
$487$			34.8592i			1.57962i	−0.613351	+	0.789811i	$0.710179\pi$
$488$	−20.7089	−	17.6790i	−0.937446	−	0.800289i
$489$		0			0
$490$	13.0922	+	8.98042i	0.591445	+	0.405694i
$491$	21.4659	−	21.4659i	0.968743	−	0.968743i	−0.0307829	−	0.999526i	$-0.509800\pi$
$491$	21.4659	−	21.4659i	0.968743	−	0.968743i	0.999526	+	0.0307829i	$0.00980006\pi$
$492$		0			0
$493$	8.27333	−	8.27333i	0.372612	−	0.372612i
$494$	−0.445570	−	16.9670i	−0.0200471	−	0.763380i
$495$		0			0
$496$	−2.49695	−	23.6884i	−0.112116	−	1.06364i
$497$	−0.133866			−0.00600471
$498$		0			0
$499$	−18.0781	+	18.0781i	−0.809287	+	0.809287i	−0.984526	−	0.175239i	$-0.943930\pi$
$499$	−18.0781	+	18.0781i	−0.809287	+	0.809287i	0.175239	+	0.984526i	$0.443930\pi$
$500$	5.72980	−	21.6141i	0.256244	−	0.966612i
$501$		0			0
$502$	−14.5095	+	15.2922i	−0.647593	+	0.682523i
$503$	−3.90394			−0.174068			−0.0870341	−	0.996205i	$-0.527739\pi$
$503$	−3.90394			−0.174068			−0.0870341	+	0.996205i	$0.527739\pi$
$504$		0			0
$505$	−2.26042	−	14.1947i	−0.100587	−	0.631656i
$506$	−0.479115	+	0.504958i	−0.0212993	+	0.0224481i
$507$		0			0
$508$	6.35353	−	0.333931i	0.281892	−	0.0148158i
$509$	−11.0778	+	11.0778i	−0.491014	+	0.491014i	−0.908626	−	0.417612i	$-0.862867\pi$
$509$	−11.0778	+	11.0778i	−0.491014	+	0.491014i	0.417612	+	0.908626i	$0.362867\pi$
$510$		0			0
$511$			11.2433i			0.497374i
$512$	−21.9986	+	5.29713i	−0.972212	+	0.234102i
$513$		0			0
$514$	28.3731	−	0.745108i	1.25149	−	0.0328653i
$515$	10.0519	−	13.8597i	0.442941	−	0.610732i
$516$		0			0
$517$	0.202933	+	0.202933i	0.00892500	+	0.00892500i
$518$	−11.0887	+	11.6868i	−0.487207	+	0.513487i
$519$		0			0
$520$	−15.0198	+	3.62282i	−0.658660	+	0.158871i
$521$	−2.61052			−0.114369			−0.0571844	−	0.998364i	$-0.518212\pi$
$521$	−2.61052			−0.114369			−0.0571844	+	0.998364i	$0.518212\pi$
$522$		0			0
$523$	21.2735	−	21.2735i	0.930226	−	0.930226i	−0.0674935	−	0.997720i	$-0.521500\pi$
$523$	21.2735	−	21.2735i	0.930226	−	0.930226i	0.997720	+	0.0674935i	$0.0215002\pi$
$524$	−17.8574	−	16.0741i	−0.780106	−	0.702199i
$525$		0			0
$526$	40.5661	−	1.06531i	1.76876	−	0.0464496i
$527$		−	18.8009i		−	0.818980i
$528$		0			0
$529$	−19.0949			−0.830213
$530$	23.5251	−	4.38235i	1.02187	−	0.190357i
$531$		0			0
$532$	10.2747	+	9.24855i	0.445463	+	0.400975i
$533$	−0.275471	+	0.275471i	−0.0119320	+	0.0119320i
$534$		0			0
$535$	−2.11448	−	13.2782i	−0.0914168	−	0.574068i
$536$	30.3393	+	25.9004i	1.31046	+	1.11873i
$537$		0			0
$538$	−18.8604	+	19.8777i	−0.813132	+	0.856991i
$539$	0.884224	−	0.884224i	0.0380862	−	0.0380862i
$540$		0			0
$541$	−8.92150	−	8.92150i	−0.383565	−	0.383565i	0.488820	−	0.872385i	$-0.337428\pi$
$541$	−8.92150	−	8.92150i	−0.383565	−	0.383565i	−0.872385	+	0.488820i	$0.837428\pi$
$542$	0.240517	+	9.15871i	0.0103311	+	0.393400i
$543$		0			0
$544$	−17.7062	+	2.33782i	−0.759146	+	0.100233i
$545$	−0.0899300	−	0.564732i	−0.00385218	−	0.0241905i
$546$		0			0
$547$	−24.0470	−	24.0470i	−1.02818	−	1.02818i	−0.999591	−	0.0285840i	$-0.990900\pi$
$547$	−24.0470	−	24.0470i	−1.02818	−	1.02818i	−0.0285840	−	0.999591i	$-0.509100\pi$
$548$	1.58521	+	30.1610i	0.0677168	+	1.28841i
$549$		0			0
$550$	−1.59099	−	0.755444i	−0.0678399	−	0.0322122i
$551$		−	18.2062i		−	0.775609i
$552$		0			0
$553$	7.97205			0.339006
$554$	−15.5275	−	14.7328i	−0.659701	−	0.625939i
$555$		0			0
$556$	−24.5192	−	22.0705i	−1.03985	−	0.935999i
$557$	17.5090	+	17.5090i	0.741879	+	0.741879i	0.972939	−	0.231060i	$-0.0742195\pi$
$557$	17.5090	+	17.5090i	0.741879	+	0.741879i	−0.231060	+	0.972939i	$0.574220\pi$
$558$		0			0
$559$			22.9076i			0.968886i
$560$	6.27966	−	10.9053i	0.265364	−	0.460835i
$561$		0			0
$562$	32.9733	−	0.865914i	1.39090	−	0.0365264i
$563$	11.2032	−	11.2032i	0.472157	−	0.472157i	−0.430455	−	0.902612i	$-0.641647\pi$
$563$	11.2032	−	11.2032i	0.472157	−	0.472157i	0.902612	+	0.430455i	$0.141647\pi$
$564$		0			0
$565$	−12.4693	−	9.04353i	−0.524588	−	0.380464i
$566$	10.1864	−	10.7358i	0.428166	−	0.451260i
$567$		0			0
$568$	−0.0211749	−	0.268280i	−0.000888478	−	0.0112568i
$569$	−4.83805			−0.202821			−0.101411	−	0.994845i	$-0.532336\pi$
$569$	−4.83805			−0.202821			−0.101411	+	0.994845i	$0.532336\pi$
$570$		0			0
$571$	9.64695	+	9.64695i	0.403712	+	0.403712i	0.879539	−	0.475827i	$-0.157851\pi$
$571$	9.64695	+	9.64695i	0.403712	+	0.403712i	−0.475827	+	0.879539i	$0.657851\pi$
$572$	0.0638728	+	1.21528i	0.00267066	+	0.0508132i
$573$		0			0
$574$	−0.00832978	−	0.317192i	−0.000347678	−	0.0132393i
$575$	3.06904	+	9.39194i	0.127988	+	0.391671i
$576$		0			0
$577$		−	18.0261i		−	0.750438i	−0.926936	−	0.375219i	$-0.877568\pi$
$577$		−	18.0261i		−	0.750438i	0.926936	−	0.375219i	$-0.122432\pi$
$578$	9.94139	−	0.261071i	0.413508	−	0.0108591i
$579$		0			0
$580$	−16.2077	+	3.46179i	−0.672987	+	0.143743i
$581$	17.2593	+	17.2593i	0.716038	+	0.716038i
$582$		0			0
$583$		−	1.88482i		−	0.0780614i
$584$	−22.5326	+	1.77846i	−0.932405	+	0.0735932i
$585$		0			0
$586$	−8.18894	+	8.63064i	−0.338282	+	0.356528i
$587$	−5.25140	−	5.25140i	−0.216749	−	0.216749i	0.590378	−	0.807127i	$-0.298979\pi$
$587$	−5.25140	−	5.25140i	−0.216749	−	0.216749i	−0.807127	+	0.590378i	$0.798979\pi$
$588$		0			0
$589$	−20.6865	−	20.6865i	−0.852373	−	0.852373i
$590$	−19.7204	+	3.67359i	−0.811876	+	0.151239i
$591$		0			0
$592$	−25.1753	−	20.3741i	−1.03470	−	0.837369i
$593$	−0.0811054			−0.00333060			−0.00166530	−	0.999999i	$-0.500530\pi$
$593$	−0.0811054			−0.00333060			−0.00166530	+	0.999999i	$0.500530\pi$
$594$		0			0
$595$	5.83155	−	8.04060i	0.239070	−	0.329632i
$596$	23.3936	+	21.0573i	0.958238	+	0.862541i
$597$		0			0
$598$	4.69918	−	4.95264i	0.192164	−	0.202529i
$599$		−	8.29253i		−	0.338824i	−0.985545	−	0.169412i	$-0.945813\pi$
$599$		−	8.29253i		−	0.338824i	0.985545	−	0.169412i	$-0.0541868\pi$
$600$		0			0
$601$		−	5.82196i		−	0.237483i	−0.992925	−	0.118741i	$-0.962114\pi$
$601$		−	5.82196i		−	0.237483i	0.992925	−	0.118741i	$-0.0378859\pi$
$602$	−13.5348	−	12.8422i	−0.551639	−	0.523407i
$603$		0			0
$604$	−43.6930	+	2.29643i	−1.77784	+	0.0934404i
$605$	14.3595	−	19.7990i	0.583796	−	0.804944i
$606$		0			0
$607$	22.0548			0.895178			0.447589	−	0.894239i	$-0.352283\pi$
$607$	22.0548			0.895178			0.447589	+	0.894239i	$0.352283\pi$
$608$	−16.9097	+	22.0543i	−0.685779	+	0.894419i
$609$		0			0
$610$	5.57506	+	29.9278i	0.225728	+	1.21174i
$611$	−1.99038	−	1.99038i	−0.0805220	−	0.0805220i
$612$		0			0
$613$	−14.9250	−	14.9250i	−0.602816	−	0.602816i	0.338243	−	0.941059i	$-0.390168\pi$
$613$	−14.9250	−	14.9250i	−0.602816	−	0.602816i	−0.941059	+	0.338243i	$0.890168\pi$
$614$	17.4929	+	16.5977i	0.705957	+	0.669828i
$615$		0			0
$616$	−0.753848	−	0.643553i	−0.0303734	−	0.0259295i
$617$		−	31.5403i		−	1.26976i	−0.772609	−	0.634882i	$-0.781049\pi$
$617$		−	31.5403i		−	1.26976i	0.772609	−	0.634882i	$-0.218951\pi$
$618$		0			0
$619$	6.89013	+	6.89013i	0.276938	+	0.276938i	0.831885	−	0.554947i	$-0.187262\pi$
$619$	6.89013	+	6.89013i	0.276938	+	0.276938i	−0.554947	+	0.831885i	$0.687262\pi$
$620$	−14.4823	+	22.3491i	−0.581624	+	0.897563i
$621$		0			0
$622$	1.16294	+	44.2840i	0.0466297	+	1.77562i
$623$			15.3778i			0.616100i
$624$		0			0
$625$	−20.1760	+	14.7624i	−0.807042	+	0.590494i
$626$	−34.0270	+	0.893583i	−1.35999	+	0.0357148i
$627$		0			0
$628$	−29.1273	+	32.3589i	−1.16230	+	1.29126i
$629$	−18.0757	−	18.0757i	−0.720725	−	0.720725i
$630$		0			0
$631$	−32.9043			−1.30990			−0.654950	−	0.755672i	$-0.727310\pi$
$631$	−32.9043			−1.30990			−0.654950	+	0.755672i	$0.727310\pi$
$632$	1.26102	+	15.9767i	0.0501605	+	0.635520i
$633$		0			0
$634$	14.8940	+	14.1318i	0.591517	+	0.561244i
$635$	−5.75825	−	4.17625i	−0.228509	−	0.165729i
$636$		0			0
$637$	−8.67249	+	8.67249i	−0.343617	+	0.343617i
$638$	0.0342689	+	1.30493i	0.00135672	+	0.0516629i
$639$		0			0
$640$	22.8486	+	10.8600i	0.903171	+	0.429280i
$641$			28.3921i			1.12142i	0.828013	+	0.560710i	$0.189472\pi$
$641$			28.3921i			1.12142i	−0.828013	+	0.560710i	$0.810528\pi$
$642$		0			0
$643$	2.71547	+	2.71547i	0.107088	+	0.107088i	0.758621	−	0.651533i	$-0.225874\pi$
$643$	2.71547	+	2.71547i	0.107088	+	0.107088i	−0.651533	+	0.758621i	$0.725874\pi$
$644$	0.291855	+	5.55298i	0.0115007	+	0.218818i
$645$		0			0
$646$	−15.0981	+	15.9125i	−0.594027	+	0.626067i
$647$	33.2882			1.30869			0.654346	−	0.756195i	$-0.272944\pi$
$647$	33.2882			1.30869			0.654346	+	0.756195i	$0.272944\pi$
$648$		0			0
$649$			1.57999i			0.0620200i
$650$	15.6044	+	7.40941i	0.612056	+	0.290621i
$651$		0			0
$652$	10.3032	+	9.27427i	0.403506	+	0.363208i
$653$	4.82719	+	4.82719i	0.188902	+	0.188902i	0.795221	−	0.606319i	$-0.207355\pi$
$653$	4.82719	+	4.82719i	0.188902	+	0.188902i	−0.606319	+	0.795221i	$0.707355\pi$
$654$		0			0
$655$	4.22442	+	26.5280i	0.165062	+	1.03653i
$656$	0.634364	−	0.0668669i	0.0247677	−	0.00261071i
$657$		0			0
$658$	2.29183	−	0.0601857i	0.0893447	−	0.00234628i
$659$	22.5484	+	22.5484i	0.878359	+	0.878359i	0.993365	−	0.115005i	$-0.0366885\pi$
$659$	22.5484	+	22.5484i	0.878359	+	0.878359i	−0.115005	+	0.993365i	$0.536689\pi$
$660$		0			0
$661$	17.3551	−	17.3551i	0.675035	−	0.675035i	−0.283838	−	0.958872i	$-0.591608\pi$
$661$	17.3551	−	17.3551i	0.675035	−	0.675035i	0.958872	+	0.283838i	$0.0916077\pi$
$662$	18.5140	+	17.5665i	0.719567	+	0.682741i
$663$		0			0
$664$	−31.8592	+	37.3194i	−1.23638	+	1.44827i
$665$	−2.43061	−	15.2634i	−0.0942548	−	0.591890i
$666$		0			0
$667$	5.17838	−	5.17838i	0.200508	−	0.200508i
$668$	−34.8278	+	1.83049i	−1.34753	+	0.0708239i
$669$		0			0
$670$	−8.16768	−	43.8453i	−0.315545	−	1.69389i
$671$	2.39780			0.0925661
$672$		0			0
$673$		−	20.2889i		−	0.782080i	−0.920374	−	0.391040i	$-0.872115\pi$
$673$		−	20.2889i		−	0.782080i	0.920374	−	0.391040i	$-0.127885\pi$
$674$	0.645869	+	24.5942i	0.0248780	+	0.947334i
$675$		0			0
$676$	0.738167	+	14.0447i	0.0283910	+	0.540181i
$677$	−0.349388	+	0.349388i	−0.0134281	+	0.0134281i	−0.713789	−	0.700361i	$-0.753022\pi$
$677$	−0.349388	+	0.349388i	−0.0134281	+	0.0134281i	0.700361	+	0.713789i	$0.253022\pi$
$678$		0			0
$679$	14.6906			0.563775
$680$	17.0365	+	10.4151i	0.653321	+	0.399401i
$681$		0			0
$682$	1.52165	+	1.44378i	0.0582670	+	0.0552850i
$683$	−4.40464	−	4.40464i	−0.168539	−	0.168539i	0.617798	−	0.786337i	$-0.288025\pi$
$683$	−4.40464	−	4.40464i	−0.168539	−	0.168539i	−0.786337	+	0.617798i	$0.788025\pi$
$684$		0			0
$685$	19.8252	−	27.3351i	0.757480	−	1.04442i
$686$	−0.627882	−	23.9093i	−0.0239726	−	0.912860i
$687$		0			0
$688$	23.5959	−	29.1564i	0.899586	−	1.11158i
$689$			18.4864i			0.704276i
$690$		0			0
$691$	−22.7615	+	22.7615i	−0.865890	+	0.865890i	−0.992014	−	0.126125i	$-0.959746\pi$
$691$	−22.7615	+	22.7615i	−0.865890	+	0.865890i	0.126125	+	0.992014i	$0.459746\pi$
$692$	−36.6391	−	32.9800i	−1.39281	−	1.25371i
$693$		0			0
$694$	−13.9896	−	13.2736i	−0.531038	−	0.503861i
$695$	5.80034	+	36.4243i	0.220020	+	1.38165i
$696$		0			0
$697$	0.503478			0.0190706
$698$	5.31186	+	5.04001i	0.201057	+	0.190767i
$699$		0			0
$700$	−13.1258	+	5.06604i	−0.496108	+	0.191478i
$701$	−34.9589	+	34.9589i	−1.32038	+	1.32038i	−0.406913	+	0.913467i	$0.633395\pi$
$701$	−34.9589	+	34.9589i	−1.32038	+	1.32038i	−0.913467	+	0.406913i	$0.866605\pi$
$702$		0			0
$703$	−39.7771			−1.50022
$704$	1.17050	−	1.61258i	0.0441148	−	0.0607763i
$705$		0			0
$706$	−26.8552	+	0.705245i	−1.01071	+	0.0265422i
$707$	−6.39503	+	6.39503i	−0.240510	+	0.240510i
$708$		0			0
$709$	−20.7652	+	20.7652i	−0.779854	+	0.779854i	−0.979806	−	0.199952i	$-0.935922\pi$
$709$	−20.7652	+	20.7652i	−0.779854	+	0.779854i	0.199952	+	0.979806i	$0.435922\pi$
$710$	−0.170193	+	0.248118i	−0.00638724	+	0.00931169i
$711$		0			0
$712$	−30.8186	+	2.43246i	−1.15498	+	0.0911602i
$713$		−	11.7677i		−	0.440704i
$714$		0			0
$715$	0.798814	−	1.10141i	0.0298740	−	0.0411905i
$716$	26.2010	+	23.5843i	0.979175	+	0.881387i
$717$		0			0
$718$	−0.323653	−	12.3244i	−0.0120786	−	0.459944i
$719$	9.48453			0.353713			0.176857	−	0.984237i	$-0.443407\pi$
$719$	9.48453			0.353713			0.176857	+	0.984237i	$0.443407\pi$
$720$		0			0
$721$	−10.7727			−0.401198
$722$	0.190653	+	7.25991i	0.00709536	+	0.270186i
$723$		0			0
$724$	−13.3972	+	14.8836i	−0.497902	+	0.553143i
$725$	16.5239	+	8.38451i	0.613684	+	0.311393i
$726$		0			0
$727$		−	29.4631i		−	1.09272i	−0.837549	−	0.546362i	$-0.816012\pi$
$727$		−	29.4631i		−	1.09272i	0.837549	−	0.546362i	$-0.183988\pi$
$728$	7.39376	+	6.31199i	0.274031	+	0.233938i
$729$		0			0
$730$	20.8392	+	14.2944i	0.771293	+	0.529059i
$731$	20.9341	−	20.9341i	0.774275	−	0.774275i
$732$		0			0
$733$	13.5703	−	13.5703i	0.501231	−	0.501231i	−0.410590	−	0.911820i	$-0.634677\pi$
$733$	13.5703	−	13.5703i	0.501231	−	0.501231i	0.911820	+	0.410590i	$0.134677\pi$
$734$	−39.6551	+	1.04138i	−1.46370	+	0.0384382i
$735$		0			0
$736$	−11.0825	+	1.46327i	−0.408507	+	0.0539369i
$737$	−3.51287			−0.129398
$738$		0			0
$739$	−1.19592	+	1.19592i	−0.0439927	+	0.0439927i	−0.728761	−	0.684768i	$-0.759903\pi$
$739$	−1.19592	+	1.19592i	−0.0439927	+	0.0439927i	0.684768	+	0.728761i	$0.259903\pi$
$740$	7.56337	+	35.4108i	0.278035	+	1.30173i
$741$		0			0
$742$	−10.9226	−	10.3636i	−0.400982	−	0.380460i
$743$	48.8695			1.79285			0.896424	−	0.443197i	$-0.146156\pi$
$743$	48.8695			1.79285			0.896424	+	0.443197i	$0.146156\pi$
$744$		0			0
$745$	−5.53406	−	34.7521i	−0.202752	−	1.27322i
$746$	−7.11991	−	6.75553i	−0.260679	−	0.247338i
$747$		0			0
$748$	1.05221	−	1.16895i	0.0384726	−	0.0427411i
$749$	−5.98214	+	5.98214i	−0.218583	+	0.218583i
$750$		0			0
$751$			17.8326i			0.650721i	0.945590	+	0.325360i	$0.105486\pi$
$751$			17.8326i			0.650721i	−0.945590	+	0.325360i	$0.894514\pi$
$752$	0.483138	+	4.58351i	0.0176182	+	0.167143i
$753$		0			0
$754$	−0.336111	−	12.7988i	−0.0122404	−	0.466106i
$755$	39.5993	+	28.7199i	1.44117	+	1.04522i
$756$		0			0
$757$	−19.7676	−	19.7676i	−0.718467	−	0.718467i	0.249824	−	0.968291i	$-0.419627\pi$
$757$	−19.7676	−	19.7676i	−0.718467	−	0.718467i	−0.968291	+	0.249824i	$0.919627\pi$
$758$	−37.8121	−	35.8770i	−1.37340	−	1.30311i
$759$		0			0
$760$	30.2049	−	7.28552i	1.09565	−	0.264274i
$761$	−3.72357			−0.134979			−0.0674896	−	0.997720i	$-0.521499\pi$
$761$	−3.72357			−0.134979			−0.0674896	+	0.997720i	$0.521499\pi$
$762$		0			0
$763$	−0.254425	+	0.254425i	−0.00921079	+	0.00921079i
$764$	−25.1674	+	1.32276i	−0.910524	+	0.0478556i
$765$		0			0
$766$	0.256657	+	9.77329i	0.00927339	+	0.353123i
$767$		−	15.4966i		−	0.559549i
$768$		0			0
$769$	−17.9937			−0.648868			−0.324434	−	0.945908i	$-0.605174\pi$
$769$	−17.9937			−0.648868			−0.324434	+	0.945908i	$0.605174\pi$
$770$	0.202944	+	1.08944i	0.00731361	+	0.0392606i
$771$		0			0
$772$	0.541363	+	10.3002i	0.0194841	+	0.370714i
$773$	14.5506	−	14.5506i	0.523350	−	0.523350i	−0.395232	−	0.918582i	$-0.629336\pi$
$773$	14.5506	−	14.5506i	0.523350	−	0.523350i	0.918582	+	0.395232i	$0.129336\pi$
$774$		0			0
$775$	28.3019	−	9.24831i	1.01663	−	0.332209i
$776$	2.32376	+	29.4414i	0.0834181	+	1.05688i
$777$		0			0
$778$	21.0695	+	19.9912i	0.755378	+	0.716719i
$779$	0.553973	−	0.553973i	0.0198482	−	0.0198482i
$780$		0			0
$781$	0.0167574	+	0.0167574i	0.000599629	+	0.000599629i
$782$	−8.82032	+	0.231631i	−0.315414	+	0.00828310i
$783$		0			0
$784$	19.9713	−	2.10513i	0.713262	−	0.0751833i
$785$	48.0705	−	7.65492i	1.71571	−	0.273216i
$786$		0			0
$787$	−27.4478	−	27.4478i	−0.978410	−	0.978410i	0.0213618	−	0.999772i	$-0.493200\pi$
$787$	−27.4478	−	27.4478i	−0.978410	−	0.978410i	−0.999772	+	0.0213618i	$0.993200\pi$
$788$	6.80820	−	7.56356i	0.242532	−	0.269441i
$789$		0			0
$790$	10.1354	−	14.7760i	0.360602	−	0.525707i
$791$			9.69203i			0.344609i
$792$		0			0
$793$	−23.5177			−0.835137
$794$	25.2423	−	26.6038i	0.895814	−	0.944133i
$795$		0			0
$796$	15.1502	−	0.796268i	0.536984	−	0.0282230i
$797$	33.5148	+	33.5148i	1.18715	+	1.18715i	0.977851	+	0.209303i	$0.0671197\pi$
$797$	33.5148	+	33.5148i	1.18715	+	1.18715i	0.209303	+	0.977851i	$0.432880\pi$
$798$		0			0
$799$			3.63781i			0.128697i
$800$	−12.2290	−	25.5039i	−0.432362	−	0.901700i
$801$		0			0
$802$	−1.24513	−	47.4135i	−0.0439670	−	1.67423i
$803$	1.40744	−	1.40744i	0.0496676	−	0.0496676i
$804$		0			0
$805$	3.65004	−	5.03271i	0.128647	−	0.177380i
$806$	−14.9244	−	14.1606i	−0.525689	−	0.498785i
$807$		0			0
$808$	−13.8278	−	11.8047i	−0.486460	−	0.415287i
$809$	−44.1238			−1.55131			−0.775654	−	0.631158i	$-0.782580\pi$
$809$	−44.1238			−1.55131			−0.775654	+	0.631158i	$0.782580\pi$
$810$		0			0
$811$	−27.5547	−	27.5547i	−0.967578	−	0.967578i	0.0319126	−	0.999491i	$-0.489840\pi$
$811$	−27.5547	−	27.5547i	−0.967578	−	0.967578i	−0.999491	+	0.0319126i	$0.989840\pi$
$812$	7.75056	+	6.97653i	0.271991	+	0.244828i
$813$		0			0
$814$	2.85104	−	0.0748713i	0.0999290	−	0.00262424i
$815$	−2.43737	−	15.3059i	−0.0853772	−	0.536142i
$816$		0			0
$817$		−	46.0673i		−	1.61169i
$818$	0.668429	+	25.4533i	0.0233711	+	0.889953i
$819$		0			0
$820$	−0.598498	−	0.387829i	−0.0209004	−	0.0135436i
$821$	−8.29165	−	8.29165i	−0.289381	−	0.289381i	0.547455	−	0.836835i	$-0.315597\pi$
$821$	−8.29165	−	8.29165i	−0.289381	−	0.289381i	−0.836835	+	0.547455i	$0.815597\pi$
$822$		0			0
$823$		−	16.2616i		−	0.566845i	−0.958995	−	0.283422i	$-0.908530\pi$
$823$		−	16.2616i		−	0.566845i	0.958995	−	0.283422i	$-0.0914698\pi$
$824$	−1.70403	−	21.5896i	−0.0593626	−	0.752108i
$825$		0			0
$826$	9.15609	+	8.68750i	0.318581	+	0.302277i
$827$	18.8727	+	18.8727i	0.656266	+	0.656266i	0.954495	−	0.298228i	$-0.0963956\pi$
$827$	18.8727	+	18.8727i	0.656266	+	0.656266i	−0.298228	+	0.954495i	$0.596396\pi$
$828$		0			0
$829$	7.56155	+	7.56155i	0.262624	+	0.262624i	0.826119	−	0.563495i	$-0.190544\pi$
$829$	7.56155	+	7.56155i	0.262624	+	0.262624i	−0.563495	+	0.826119i	$0.690544\pi$
$830$	53.9328	−	10.0468i	1.87203	−	0.348729i
$831$		0			0
$832$	−11.4803	+	15.8162i	−0.398007	+	0.548328i
$833$	15.8507			0.549195
$834$		0			0
$835$	31.5648	+	22.8927i	1.09234	+	0.792236i
$836$	−0.128449	−	2.44393i	−0.00444249	−	0.0845250i
$837$		0			0
$838$	24.3266	+	23.0816i	0.840347	+	0.797340i
$839$		−	1.30357i		−	0.0450042i	−0.999747	−	0.0225021i	$-0.992837\pi$
$839$		−	1.30357i		−	0.0450042i	0.999747	−	0.0225021i	$-0.00716324\pi$
$840$		0			0
$841$			15.2664i			0.526427i
$842$	−12.6307	+	13.3120i	−0.435283	+	0.458761i
$843$		0			0
$844$	1.14484	−	1.27186i	0.0394070	−	0.0437791i
$845$	9.23175	−	12.7288i	0.317582	−	0.437885i
$846$		0			0
$847$	−15.3892			−0.528778
$848$	19.0419	−	23.5292i	0.653902	−	0.807997i
$849$		0			0
$850$	−7.48902	−	21.0312i	−0.256871	−	0.721365i
$851$	−11.3138	−	11.3138i	−0.387832	−	0.387832i
$852$		0			0
$853$	20.3937	+	20.3937i	0.698268	+	0.698268i	0.964037	−	0.265769i	$-0.0856258\pi$
$853$	20.3937	+	20.3937i	0.698268	+	0.698268i	−0.265769	+	0.964037i	$0.585626\pi$
$854$	13.1842	−	13.8953i	0.451154	−	0.475488i
$855$		0			0
$856$	−12.9350	−	11.0425i	−0.442110	−	0.377426i
$857$		−	17.9066i		−	0.611678i	−0.952083	−	0.305839i	$-0.901063\pi$
$857$		−	17.9066i		−	0.611678i	0.952083	−	0.305839i	$-0.0989369\pi$
$858$		0			0
$859$	17.0524	+	17.0524i	0.581821	+	0.581821i	0.935403	−	0.353582i	$-0.115037\pi$
$859$	17.0524	+	17.0524i	0.581821	+	0.581821i	−0.353582	+	0.935403i	$0.615037\pi$
$860$	−41.0104	+	8.75940i	−1.39844	+	0.298693i
$861$		0			0
$862$	−51.8450	+	1.36150i	−1.76585	+	0.0463730i
$863$		−	1.33105i		−	0.0453095i	−0.999743	−	0.0226548i	$-0.992788\pi$
$863$		−	1.33105i		−	0.0453095i	0.999743	−	0.0226548i	$-0.00721185\pi$
$864$		0			0
$865$	8.66746	+	54.4289i	0.294703	+	1.85064i
$866$	−1.04493	−	39.7900i	−0.0355080	−	1.35212i
$867$		0			0
$868$	16.7334	−	0.879482i	0.567970	−	0.0298516i
$869$	−0.997947	−	0.997947i	−0.0338530	−	0.0338530i
$870$		0			0
$871$	34.4543			1.16744
$872$	−0.550135	−	0.469645i	−0.0186299	−	0.0159042i
$873$		0			0
$874$	−9.45008	+	9.95980i	−0.319654	+	0.336895i
$875$	14.9725	+	4.82326i	0.506162	+	0.163056i
$876$		0			0
$877$	−19.7763	+	19.7763i	−0.667799	+	0.667799i	−0.957206	−	0.289407i	$-0.906542\pi$
$877$	−19.7763	+	19.7763i	−0.667799	+	0.667799i	0.289407	+	0.957206i	$0.406542\pi$
$878$	4.70297	−	0.123505i	0.158718	−	0.00416809i
$879$		0			0
$880$	−2.15123	+	0.579046i	−0.0725180	+	0.0195196i
$881$		−	16.6926i		−	0.562389i	−0.959651	−	0.281194i	$-0.909269\pi$
$881$		−	16.6926i		−	0.562389i	0.959651	−	0.281194i	$-0.0907305\pi$
$882$		0			0
$883$	17.2285	+	17.2285i	0.579785	+	0.579785i	0.934844	−	0.355059i	$-0.115539\pi$
$883$	17.2285	+	17.2285i	0.579785	+	0.579785i	−0.355059	+	0.934844i	$0.615539\pi$
$884$	−10.3201	+	11.4651i	−0.347103	+	0.385613i
$885$		0			0
$886$	8.75799	+	8.30977i	0.294230	+	0.279172i
$887$	18.0017			0.604436			0.302218	−	0.953239i	$-0.402273\pi$
$887$	18.0017			0.604436			0.302218	+	0.953239i	$0.402273\pi$
$888$		0			0
$889$			4.47572i			0.150111i
$890$	28.5025	+	19.5509i	0.955405	+	0.655348i
$891$		0			0
$892$	50.4607	−	2.65213i	1.68955	−	0.0887998i
$893$	4.00266	+	4.00266i	0.133944	+	0.133944i
$894$		0			0
$895$	−6.19818	−	38.9226i	−0.207182	−	1.30104i
$896$	−2.90902	−	15.6498i	−0.0971834	−	0.522821i
$897$		0			0
$898$	0.529755	+	20.1727i	0.0176781	+	0.673170i
$899$	−15.6046	−	15.6046i	−0.520443	−	0.520443i
$900$		0			0
$901$	16.8938	−	16.8938i	0.562814	−	0.562814i
$902$	−0.0386635	+	0.0407490i	−0.00128735	+	0.00135679i
$903$		0			0
$904$	−19.4237	+	1.53308i	−0.646023	+	0.0509895i
$905$	22.1102	−	3.52090i	0.734967	−	0.117039i
$906$		0			0
$907$	−25.3515	+	25.3515i	−0.841784	+	0.841784i	−0.989091	−	0.147307i	$-0.952940\pi$
$907$	−25.3515	+	25.3515i	−0.841784	+	0.841784i	0.147307	+	0.989091i	$0.452940\pi$
$908$	12.5235	−	13.9129i	0.415606	−	0.461717i
$909$		0			0
$910$	−1.99048	−	10.6852i	−0.0659839	−	0.354212i
$911$	54.8371			1.81683			0.908417	−	0.418066i	$-0.137292\pi$
$911$	54.8371			1.81683			0.908417	+	0.418066i	$0.137292\pi$
$912$		0			0
$913$		−	4.32107i		−	0.143007i
$914$	−35.4295	+	0.930415i	−1.17190	+	0.0307754i
$915$		0			0
$916$	−0.0845653	+	0.0939477i	−0.00279412	+	0.00310412i
$917$	11.9515	−	11.9515i	0.394672	−	0.394672i
$918$		0			0
$919$	−26.4141			−0.871321			−0.435661	−	0.900111i	$-0.643485\pi$
$919$	−26.4141			−0.871321			−0.435661	+	0.900111i	$0.643485\pi$
$920$	10.6634	+	6.51894i	0.351561	+	0.214923i
$921$		0			0
$922$	15.9727	−	16.8343i	0.526034	−	0.554408i
$923$	−0.164357	−	0.164357i	−0.00540989	−	0.00540989i
$924$		0			0
$925$	18.3186	−	36.1018i	0.602312	−	1.18702i
$926$	12.3689	−	0.324819i	0.406466	−	0.0106742i
$927$		0			0
$928$	−12.7556	+	16.6364i	−0.418724	+	0.546116i
$929$		−	43.1302i		−	1.41506i	−0.706685	−	0.707528i	$-0.749810\pi$
$929$		−	43.1302i		−	1.41506i	0.706685	−	0.707528i	$-0.250190\pi$
$930$		0			0
$931$	17.4404	−	17.4404i	0.571588	−	0.571588i
$932$	1.41724	+	26.9650i	0.0464231	+	0.883269i
$933$		0			0
$934$	26.5749	−	28.0083i	0.869557	−	0.916460i
$935$	−1.73653	+	0.276531i	−0.0567904	+	0.00904352i
$936$		0			0
$937$	−17.0711			−0.557689			−0.278845	−	0.960336i	$-0.589951\pi$
$937$	−17.0711			−0.557689			−0.278845	+	0.960336i	$0.589951\pi$
$938$	−19.3154	+	20.3572i	−0.630669	+	0.664686i
$939$		0			0
$940$	2.80220	−	4.32437i	0.0913978	−	0.141045i
$941$	−27.6649	+	27.6649i	−0.901850	+	0.901850i	−0.995596	−	0.0937464i	$-0.970116\pi$
$941$	−27.6649	+	27.6649i	−0.901850	+	0.901850i	0.0937464	+	0.995596i	$0.470116\pi$
$942$		0			0
$943$	0.315133			0.0102621
$944$	−15.9623	+	19.7238i	−0.519527	+	0.641956i
$945$		0			0
$946$	0.0867110	+	3.30189i	0.00281922	+	0.107354i
$947$	−38.6985	+	38.6985i	−1.25753	+	1.25753i	−0.305265	+	0.952267i	$0.598745\pi$
$947$	−38.6985	+	38.6985i	−1.25753	+	1.25753i	−0.952267	+	0.305265i	$0.901255\pi$
$948$		0			0
$949$	−13.8042	+	13.8042i	−0.448104	+	0.448104i
$950$	−31.3806	−	14.9004i	−1.01812	−	0.483432i
$951$		0			0
$952$	−0.988577	−	12.5250i	−0.0320400	−	0.405938i
$953$		−	21.7149i		−	0.703413i	−0.936110	−	0.351707i	$-0.885601\pi$
$953$		−	21.7149i		−	0.703413i	0.936110	−	0.351707i	$-0.114399\pi$
$954$		0			0
$955$	22.8094	+	16.5428i	0.738095	+	0.535313i
$956$	11.1467	−	0.585853i	0.360511	−	0.0189478i
$957$		0			0
$958$	28.2314	−	0.741387i	0.912116	−	0.0239531i
$959$	−21.2468			−0.686094
$960$		0			0
$961$	−4.46104			−0.143905
$962$	−27.9631	+	0.734340i	−0.901566	+	0.0236761i
$963$		0			0
$964$	31.4920	−	1.65517i	1.01429	−	0.0533093i
$965$	6.77047	−	9.33520i	0.217949	−	0.300511i
$966$		0			0
$967$		−	7.39782i		−	0.237898i	−0.992900	−	0.118949i	$-0.962048\pi$
$967$		−	7.39782i		−	0.237898i	0.992900	−	0.118949i	$-0.0379525\pi$
$968$	−2.43425	−	30.8413i	−0.0782398	−	0.991277i
$969$		0			0
$970$	18.6772	−	27.2288i	0.599690	−	0.874263i
$971$	−14.0731	+	14.0731i	−0.451626	+	0.451626i	−0.895894	−	0.444268i	$-0.853464\pi$
$971$	−14.0731	+	14.0731i	−0.451626	+	0.451626i	0.444268	+	0.895894i	$0.353464\pi$
$972$		0			0
$973$	16.4100	−	16.4100i	0.526080	−	0.526080i
$974$	−1.29418	−	49.2814i	−0.0414682	−	1.57908i
$975$		0			0
$976$	29.9330	+	24.2244i	0.958132	+	0.775404i
$977$	−60.5514			−1.93721			−0.968605	−	0.248603i	$-0.920029\pi$
$977$	−60.5514			−1.93721			−0.968605	+	0.248603i	$0.920029\pi$
$978$		0			0
$979$	1.92501	−	1.92501i	0.0615235	−	0.0615235i
$980$	−18.8422	−	12.2098i	−0.601891	−	0.390028i
$981$		0			0
$982$	−29.5500	+	31.1439i	−0.942978	+	0.993841i
$983$	6.63756			0.211705			0.105853	−	0.994382i	$-0.466243\pi$
$983$	6.63756			0.211705			0.105853	+	0.994382i	$0.466243\pi$
$984$		0			0
$985$	−11.2360	+	1.78926i	−0.358008	+	0.0570106i
$986$	−11.3891	+	12.0034i	−0.362702	+	0.382265i
$987$		0			0
$988$	1.25983	+	23.9701i	0.0400805	+	0.762591i
$989$	13.1029	−	13.1029i	0.416648	−	0.416648i
$990$		0			0
$991$		−	48.7239i		−	1.54777i	−0.633328	−	0.773883i	$-0.718312\pi$
$991$		−	48.7239i		−	1.54777i	0.633328	−	0.773883i	$-0.281688\pi$
$992$	4.40945	+	33.3963i	0.140000	+	1.06033i
$993$		0			0
$994$	0.189250	−	0.00496990i	0.00600264	−	0.000157636i
$995$	−13.7307	−	9.95839i	−0.435293	−	0.315702i
$996$		0			0
$997$	40.6755	+	40.6755i	1.28821	+	1.28821i	0.935876	+	0.352330i	$0.114611\pi$
$997$	40.6755	+	40.6755i	1.28821	+	1.28821i	0.352330	+	0.935876i	$0.385389\pi$
$998$	24.8863	−	26.2287i	0.787763	−	0.830254i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.1	✓	96
3.2	odd	2	inner	720.2.u.a.179.48	yes	96
4.3	odd	2		2880.2.u.a.2159.9		96
5.4	even	2	inner	720.2.u.a.179.47	yes	96
12.11	even	2		2880.2.u.a.2159.40		96
15.14	odd	2	inner	720.2.u.a.179.2	yes	96
16.5	even	4		2880.2.u.a.719.33		96
16.11	odd	4	inner	720.2.u.a.539.2	yes	96
20.19	odd	2		2880.2.u.a.2159.16		96
48.5	odd	4		2880.2.u.a.719.16		96
48.11	even	4	inner	720.2.u.a.539.47	yes	96
60.59	even	2		2880.2.u.a.2159.33		96
80.59	odd	4	inner	720.2.u.a.539.48	yes	96
80.69	even	4		2880.2.u.a.719.40		96
240.59	even	4	inner	720.2.u.a.539.1	yes	96
240.149	odd	4		2880.2.u.a.719.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.1	✓	96	1.1	even	1	trivial
720.2.u.a.179.2	yes	96	15.14	odd	2	inner
720.2.u.a.179.47	yes	96	5.4	even	2	inner
720.2.u.a.179.48	yes	96	3.2	odd	2	inner
720.2.u.a.539.1	yes	96	240.59	even	4	inner
720.2.u.a.539.2	yes	96	16.11	odd	4	inner
720.2.u.a.539.47	yes	96	48.11	even	4	inner
720.2.u.a.539.48	yes	96	80.59	odd	4	inner
2880.2.u.a.719.9		96	240.149	odd	4
2880.2.u.a.719.16		96	48.5	odd	4
2880.2.u.a.719.33		96	16.5	even	4
2880.2.u.a.719.40		96	80.69	even	4
2880.2.u.a.2159.9		96	4.3	odd	2
2880.2.u.a.2159.16		96	20.19	odd	2
2880.2.u.a.2159.33		96	60.59	even	2
2880.2.u.a.2159.40		96	12.11	even	2

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.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(-1.81012 - 1.31281i) q^{5} +1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +O(q^{10})\)	\(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(-1.81012 - 1.31281i) q^{5} +1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +(2.60775 + 1.78875i) q^{10} +(0.176123 - 0.176123i) q^{11} +(-1.72742 + 1.72742i) q^{13} +(-0.0522343 - 1.98904i) q^{14} +(3.97796 - 0.419308i) q^{16} +3.15721 q^{17} +(3.47385 - 3.47385i) q^{19} +(-3.75305 - 2.43199i) q^{20} +(-0.242451 + 0.255528i) q^{22} +1.97613 q^{23} +(1.55305 + 4.75269i) q^{25} +(2.37796 - 2.50623i) q^{26} +(0.147690 + 2.81002i) q^{28} +(2.62046 - 2.62046i) q^{29} -5.95492i q^{31} +(-5.60818 + 0.740472i) q^{32} +(-4.46342 + 0.117214i) q^{34} +(1.84706 - 2.54675i) q^{35} +(-5.72522 - 5.72522i) q^{37} +(-4.78211 + 5.04005i) q^{38} +(5.39608 + 3.29884i) q^{40} +0.159470 q^{41} +(6.63058 - 6.63058i) q^{43} +(0.333273 - 0.370248i) q^{44} +(-2.79371 + 0.0733658i) q^{46} +1.15223i q^{47} +5.02049 q^{49} +(-2.37204 - 6.66134i) q^{50} +(-3.26874 + 3.63141i) q^{52} +(5.35087 - 5.35087i) q^{53} +(-0.550020 + 0.0875872i) q^{55} +(-0.313118 - 3.96712i) q^{56} +(-3.60733 + 3.80190i) q^{58} +(-4.48547 + 4.48547i) q^{59} +(6.80718 + 6.80718i) q^{61} +(0.221082 + 8.41862i) q^{62} +(7.90094 - 1.25503i) q^{64} +(5.39461 - 0.859057i) q^{65} +(-9.97278 - 9.97278i) q^{67} +(6.30571 - 0.331417i) q^{68} +(-2.51669 + 3.66897i) q^{70} +0.0951463i q^{71} +7.99125 q^{73} +(8.30645 + 7.88134i) q^{74} +(6.57347 - 7.30278i) q^{76} +(0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(-7.75105 - 4.46332i) q^{80} +(-0.225446 + 0.00592045i) q^{82} +(12.2672 - 12.2672i) q^{83} +(-5.71492 - 4.14481i) q^{85} +(-9.12765 + 9.61998i) q^{86} +(-0.457410 + 0.535803i) q^{88} +10.9299 q^{89} +(-2.43039 - 2.43039i) q^{91} +(3.94682 - 0.207438i) q^{92} +(-0.0427774 - 1.62893i) q^{94} +(-10.8486 + 1.72757i) q^{95} -10.4415i q^{97} +(-7.09760 + 0.186390i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more