LMFDB - Embedded newform 720.2.u.a.539.1

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			539.1
Character	$\chi$	$=$	720.539
Dual form			720.2.u.a.179.1

$q$-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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

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	$-0.914335\pi$
$7$		−	1.40695i		−	0.531777i	0.964004	−	0.265889i	$-0.0856653\pi$
$8$	−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	0.733160	−	0.680057i	$-0.238045\pi$
$11$	0.176123	+	0.176123i	0.0531031	+	0.0531031i	−0.680057	+	0.733160i	$0.738045\pi$
$12$		0			0
$13$	−1.72742	−	1.72742i	−0.479100	−	0.479100i	0.425744	−	0.904844i	$-0.360012\pi$
$13$	−1.72742	−	1.72742i	−0.479100	−	0.479100i	−0.904844	+	0.425744i	$0.860012\pi$
$14$	−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	0.982614	−	0.185658i	$-0.0594417\pi$
$19$	3.47385	+	3.47385i	0.796956	+	0.796956i	−0.185658	+	0.982614i	$0.559442\pi$
$20$	−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	0.907234	−	0.420627i	$-0.138190\pi$
$29$	2.62046	+	2.62046i	0.486607	+	0.486607i	−0.420627	+	0.907234i	$0.638190\pi$
$30$		0			0
$31$			5.95492i			1.06953i	0.844999	+	0.534767i	$0.179601\pi$
$31$			5.95492i			1.06953i	−0.844999	+	0.534767i	$0.820399\pi$
$32$	−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	−0.998366	−	0.0571453i	$-0.981800\pi$
$37$	−5.72522	+	5.72522i	−0.941221	+	0.941221i	0.0571453	+	0.998366i	$0.481800\pi$
$38$	−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	0.999937	+	0.0112162i	$0.00357031\pi$
$43$	6.63058	+	6.63058i	1.01115	+	1.01115i	0.0112162	+	0.999937i	$0.496430\pi$
$44$	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	$-0.973219\pi$
$47$		−	1.15223i		−	0.168069i	0.996463	−	0.0840347i	$-0.0267807\pi$
$48$		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	0.971606	−	0.236606i	$-0.0760352\pi$
$53$	5.35087	+	5.35087i	0.734999	+	0.734999i	−0.236606	+	0.971606i	$0.576035\pi$
$54$		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	0.352030	−	0.935989i	$-0.385492\pi$
$59$	−4.48547	−	4.48547i	−0.583959	−	0.583959i	−0.935989	+	0.352030i	$0.885492\pi$
$60$		0			0
$61$	6.80718	−	6.80718i	0.871570	−	0.871570i	−0.121074	−	0.992643i	$-0.538634\pi$
$61$	6.80718	−	6.80718i	0.871570	−	0.871570i	0.992643	+	0.121074i	$0.0386338\pi$
$62$	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	−0.250166	+	0.968203i	$0.580485\pi$
$67$	−9.97278	+	9.97278i	−1.21837	+	1.21837i	−0.968203	+	0.250166i	$0.919515\pi$
$68$	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	$-0.998203\pi$
$71$		−	0.0951463i		−	0.0112918i	0.999984	−	0.00564589i	$-0.00179715\pi$
$72$		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	$0.103263\pi$
$79$			5.66620i			0.637497i	−0.947839	+	0.318748i	$0.896737\pi$
$80$	−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	0.889432	+	0.457068i	$0.151100\pi$
$83$	12.2672	+	12.2672i	1.34650	+	1.34650i	0.457068	+	0.889432i	$0.348900\pi$
$84$		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	$0.177840\pi$
$97$			10.4415i			1.06017i	−0.847944	+	0.530086i	$0.822160\pi$
$98$	−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	−0.443833	−	0.896109i	$-0.646382\pi$
$101$	4.54532	−	4.54532i	0.452276	−	0.452276i	0.896109	+	0.443833i	$0.146382\pi$
$102$		0			0
$103$		−	7.65680i		−	0.754447i	−0.926122	−	0.377224i	$-0.876879\pi$
$103$		−	7.65680i		−	0.754447i	0.926122	−	0.377224i	$-0.123121\pi$
$104$	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	−0.471059	−	0.882102i	$-0.656128\pi$
$107$	4.25185	−	4.25185i	0.411042	−	0.411042i	0.882102	+	0.471059i	$0.156128\pi$
$108$		0			0
$109$	0.180834	−	0.180834i	0.0173208	−	0.0173208i	−0.698393	−	0.715714i	$-0.746101\pi$
$109$	0.180834	−	0.180834i	0.0173208	−	0.0173208i	0.715714	+	0.698393i	$0.246101\pi$
$110$	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	−0.972996	−	0.230821i	$-0.925859\pi$
$131$	−8.49459	+	8.49459i	−0.742175	+	0.742175i	0.230821	+	0.972996i	$0.425859\pi$
$132$		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	$-0.776818\pi$
$137$		−	15.1013i		−	1.29019i	0.764102	−	0.645096i	$-0.223182\pi$
$138$		0			0
$139$	−11.6635	+	11.6635i	−0.989286	+	0.989286i	−0.999943	−	0.0106573i	$-0.996608\pi$
$139$	−11.6635	+	11.6635i	−0.989286	+	0.989286i	0.0106573	+	0.999943i	$0.496608\pi$
$140$	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	−0.0847561	−	0.996402i	$-0.527011\pi$
$149$	11.1281	−	11.1281i	0.911646	−	0.911646i	0.996402	+	0.0847561i	$0.0270111\pi$
$150$		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	−0.964541	−	0.263935i	$-0.914980\pi$
$157$	−15.3928	−	15.3928i	−1.22848	−	1.22848i	−0.263935	−	0.964541i	$-0.585020\pi$
$158$	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	−0.488614	−	0.872500i	$-0.662497\pi$
$163$	4.90113	−	4.90113i	0.383886	−	0.383886i	0.872500	+	0.488614i	$0.162497\pi$
$164$	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	−0.415490	+	0.909598i	$0.636390\pi$
$173$	−17.4288	+	17.4288i	−1.32509	+	1.32509i	−0.909598	+	0.415490i	$0.863610\pi$
$174$		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	−0.0662383	−	0.997804i	$-0.521100\pi$
$179$	12.4635	−	12.4635i	0.931565	−	0.931565i	0.997804	+	0.0662383i	$0.0210998\pi$
$180$		0			0
$181$	−7.07994	−	7.07994i	−0.526248	−	0.526248i	0.393203	−	0.919451i	$-0.371367\pi$
$181$	−7.07994	−	7.07994i	−0.526248	−	0.526248i	−0.919451	+	0.393203i	$0.871367\pi$
$182$	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	$-0.940573\pi$
$193$		−	5.15723i		−	0.371226i	0.982623	−	0.185613i	$-0.0594270\pi$
$194$	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	0.823564	−	0.567224i	$-0.191983\pi$
$197$	3.59790	+	3.59790i	0.256340	+	0.256340i	−0.567224	+	0.823564i	$0.691983\pi$
$198$		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	0.727625	−	0.685975i	$-0.240624\pi$
$211$	0.605008	+	0.605008i	0.0416505	+	0.0416505i	−0.685975	+	0.727625i	$0.740624\pi$
$212$	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	0.891765	−	0.452498i	$-0.149467\pi$
$227$	6.61823	+	6.61823i	0.439267	+	0.439267i	−0.452498	+	0.891765i	$0.649467\pi$
$228$		0			0
$229$	−0.0446899	−	0.0446899i	−0.00295319	−	0.00295319i	0.705629	−	0.708582i	$-0.250665\pi$
$229$	−0.0446899	−	0.0446899i	−0.00295319	−	0.00295319i	−0.708582	+	0.705629i	$0.750665\pi$
$230$	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	$-0.854183\pi$
$233$		−	13.5011i		−	0.884488i	0.896895	−	0.442244i	$-0.145817\pi$
$234$		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	0.956621	−	0.291334i	$-0.0940992\pi$
$251$	10.5401	+	10.5401i	0.665287	+	0.665287i	−0.291334	+	0.956621i	$0.594099\pi$
$252$		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	0.988243	−	0.152894i	$-0.0488592\pi$
$269$	13.7007	+	13.7007i	0.835349	+	0.835349i	−0.152894	+	0.988243i	$0.548859\pi$
$270$		0			0
$271$			6.47842i			0.393536i	0.980450	+	0.196768i	$0.0630445\pi$
$271$			6.47842i			0.393536i	−0.980450	+	0.196768i	$0.936955\pi$
$272$	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	−0.308261	−	0.951302i	$-0.599747\pi$
$277$	10.7023	−	10.7023i	0.643041	−	0.643041i	0.951302	+	0.308261i	$0.0997469\pi$
$278$	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	0.452102	−	0.891966i	$-0.350674\pi$
$283$	−7.39967	−	7.39967i	−0.439865	−	0.439865i	−0.891966	+	0.452102i	$0.850674\pi$
$284$	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	0.859187	−	0.511662i	$-0.170970\pi$
$293$	5.94867	+	5.94867i	0.347525	+	0.347525i	−0.511662	+	0.859187i	$0.670970\pi$
$294$		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	−0.961818	−	0.273689i	$-0.911756\pi$
$307$	−12.0570	+	12.0570i	−0.688130	+	0.688130i	0.273689	+	0.961818i	$0.411756\pi$
$308$	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	$0.347988\pi$
$311$			31.3243i			1.77624i	−0.459615	+	0.888118i	$0.652012\pi$
$312$		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	−0.933959	−	0.357380i	$-0.883670\pi$
$317$	−10.2657	+	10.2657i	−0.576579	+	0.576579i	0.357380	+	0.933959i	$0.383670\pi$
$318$		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	−0.964710	−	0.263315i	$-0.915184\pi$
$331$	−12.7608	+	12.7608i	−0.701395	+	0.701395i	0.263315	+	0.964710i	$0.415184\pi$
$332$	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	$0.157129\pi$
$337$			17.3967i			0.947660i	−0.880616	+	0.473830i	$0.842871\pi$
$338$	−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	−0.399225	−	0.916853i	$-0.630721\pi$
$347$	9.64234	−	9.64234i	0.517628	−	0.517628i	0.916853	+	0.399225i	$0.130721\pi$
$348$		0			0
$349$	−3.66120	+	3.66120i	−0.195980	+	0.195980i	−0.798274	−	0.602294i	$-0.794253\pi$
$349$	−3.66120	+	3.66120i	−0.195980	+	0.195980i	0.602294	+	0.798274i	$0.294253\pi$
$350$	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	$-0.926111\pi$
$359$		−	8.71770i		−	0.460103i	0.973178	−	0.230051i	$-0.0738894\pi$
$360$		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	−0.568552	−	0.822647i	$-0.692496\pi$
$373$	4.90740	−	4.90740i	0.254096	−	0.254096i	0.822647	+	0.568552i	$0.192496\pi$
$374$	−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	0.441412	−	0.897305i	$-0.354478\pi$
$379$	26.0620	−	26.0620i	1.33872	−	1.33872i	0.897305	−	0.441412i	$-0.145522\pi$
$380$	−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	$0.0565172\pi$
$383$			6.91314i			0.353245i	−0.984279	+	0.176623i	$0.943483\pi$
$384$		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	−0.971860	−	0.235558i	$-0.924308\pi$
$389$	−14.5222	+	14.5222i	−0.736302	+	0.736302i	0.235558	+	0.971860i	$0.424308\pi$
$390$		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	0.0767588	−	0.997050i	$-0.475543\pi$
$397$	−18.3367	−	18.3367i	−0.920291	−	0.920291i	−0.997050	+	0.0767588i	$0.975543\pi$
$398$	−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	$-0.684073\pi$
$401$		−	33.5380i		−	1.67481i	0.546585	−	0.837404i	$-0.315927\pi$
$402$		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	$0.146842\pi$
$409$			18.0044i			0.890260i	−0.895466	+	0.445130i	$0.853158\pi$
$410$	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	−0.985981	−	0.166856i	$-0.946639\pi$
$419$	−16.7671	+	16.7671i	−0.819126	+	0.819126i	0.166856	+	0.985981i	$0.446639\pi$
$420$		0			0
$421$	9.17528	+	9.17528i	0.447176	+	0.447176i	0.894415	−	0.447239i	$-0.147593\pi$
$421$	9.17528	+	9.17528i	0.447176	+	0.447176i	−0.447239	+	0.894415i	$0.647593\pi$
$422$	−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	$-0.763586\pi$
$433$		−	28.1455i		−	1.35259i	0.736633	−	0.676293i	$-0.236414\pi$
$434$	−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	−0.835814	−	0.549013i	$-0.815004\pi$
$443$	−6.03644	+	6.03644i	−0.286800	+	0.286800i	0.549013	+	0.835814i	$0.315004\pi$
$444$		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	$0.109311\pi$
$449$			14.2691i			0.673402i	−0.941612	+	0.336701i	$0.890689\pi$
$450$		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	0.383241	−	0.923648i	$-0.374808\pi$
$461$	−11.6030	−	11.6030i	−0.540407	−	0.540407i	−0.923648	+	0.383241i	$0.874808\pi$
$462$		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	0.101518	−	0.994834i	$-0.467630\pi$
$467$	−19.3047	−	19.3047i	−0.893316	−	0.893316i	−0.994834	+	0.101518i	$0.967630\pi$
$468$		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	$-0.710179\pi$
$487$		−	34.8592i		−	1.57962i	0.613351	−	0.789811i	$-0.289821\pi$
$488$	−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	0.999526	−	0.0307829i	$-0.00980006\pi$
$491$	21.4659	+	21.4659i	0.968743	+	0.968743i	−0.0307829	+	0.999526i	$0.509800\pi$
$492$		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	0.175239	−	0.984526i	$-0.443930\pi$
$499$	−18.0781	−	18.0781i	−0.809287	−	0.809287i	−0.984526	+	0.175239i	$0.943930\pi$
$500$	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	0.417612	−	0.908626i	$-0.362867\pi$
$509$	−11.0778	−	11.0778i	−0.491014	−	0.491014i	−0.908626	+	0.417612i	$0.862867\pi$
$510$		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	0.997720	−	0.0674935i	$-0.0215002\pi$
$523$	21.2735	+	21.2735i	0.930226	+	0.930226i	−0.0674935	+	0.997720i	$0.521500\pi$
$524$	−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	−0.872385	−	0.488820i	$-0.837428\pi$
$541$	−8.92150	+	8.92150i	−0.383565	+	0.383565i	0.488820	+	0.872385i	$0.337428\pi$
$542$	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	−0.0285840	+	0.999591i	$0.509100\pi$
$547$	−24.0470	+	24.0470i	−1.02818	+	1.02818i	−0.999591	+	0.0285840i	$0.990900\pi$
$548$	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	−0.231060	−	0.972939i	$-0.574220\pi$
$557$	17.5090	−	17.5090i	0.741879	−	0.741879i	0.972939	+	0.231060i	$0.0742195\pi$
$558$		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	0.902612	−	0.430455i	$-0.141647\pi$
$563$	11.2032	+	11.2032i	0.472157	+	0.472157i	−0.430455	+	0.902612i	$0.641647\pi$
$564$		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	−0.475827	−	0.879539i	$-0.657851\pi$
$571$	9.64695	−	9.64695i	0.403712	−	0.403712i	0.879539	+	0.475827i	$0.157851\pi$
$572$	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	$0.122432\pi$
$577$			18.0261i			0.750438i	−0.926936	+	0.375219i	$0.877568\pi$
$578$	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	−0.807127	−	0.590378i	$-0.798979\pi$
$587$	−5.25140	+	5.25140i	−0.216749	+	0.216749i	0.590378	+	0.807127i	$0.298979\pi$
$588$		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	$0.0541868\pi$
$599$			8.29253i			0.338824i	−0.985545	+	0.169412i	$0.945813\pi$
$600$		0			0
$601$			5.82196i			0.237483i	0.992925	+	0.118741i	$0.0378859\pi$
$601$			5.82196i			0.237483i	−0.992925	+	0.118741i	$0.962114\pi$
$602$	−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	−0.941059	−	0.338243i	$-0.890168\pi$
$613$	−14.9250	+	14.9250i	−0.602816	+	0.602816i	0.338243	+	0.941059i	$0.390168\pi$
$614$	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	$0.218951\pi$
$617$			31.5403i			1.26976i	−0.772609	+	0.634882i	$0.781049\pi$
$618$		0			0
$619$	6.89013	−	6.89013i	0.276938	−	0.276938i	−0.554947	−	0.831885i	$-0.687262\pi$
$619$	6.89013	−	6.89013i	0.276938	−	0.276938i	0.831885	+	0.554947i	$0.187262\pi$
$620$	−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	$-0.810528\pi$
$641$		−	28.3921i		−	1.12142i	0.828013	−	0.560710i	$-0.189472\pi$
$642$		0			0
$643$	2.71547	−	2.71547i	0.107088	−	0.107088i	−0.651533	−	0.758621i	$-0.725874\pi$
$643$	2.71547	−	2.71547i	0.107088	−	0.107088i	0.758621	+	0.651533i	$0.225874\pi$
$644$	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	−0.606319	−	0.795221i	$-0.707355\pi$
$653$	4.82719	−	4.82719i	0.188902	−	0.188902i	0.795221	+	0.606319i	$0.207355\pi$
$654$		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	−0.115005	−	0.993365i	$-0.536689\pi$
$659$	22.5484	−	22.5484i	0.878359	−	0.878359i	0.993365	+	0.115005i	$0.0366885\pi$
$660$		0			0
$661$	17.3551	+	17.3551i	0.675035	+	0.675035i	0.958872	−	0.283838i	$-0.0916077\pi$
$661$	17.3551	+	17.3551i	0.675035	+	0.675035i	−0.283838	+	0.958872i	$0.591608\pi$
$662$	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	$0.127885\pi$
$673$			20.2889i			0.782080i	−0.920374	+	0.391040i	$0.872115\pi$
$674$	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	0.700361	−	0.713789i	$-0.253022\pi$
$677$	−0.349388	−	0.349388i	−0.0134281	−	0.0134281i	−0.713789	+	0.700361i	$0.753022\pi$
$678$		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	−0.786337	−	0.617798i	$-0.788025\pi$
$683$	−4.40464	+	4.40464i	−0.168539	+	0.168539i	0.617798	+	0.786337i	$0.288025\pi$
$684$		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	0.126125	−	0.992014i	$-0.459746\pi$
$691$	−22.7615	−	22.7615i	−0.865890	−	0.865890i	−0.992014	+	0.126125i	$0.959746\pi$
$692$	−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	−0.913467	−	0.406913i	$-0.866605\pi$
$701$	−34.9589	−	34.9589i	−1.32038	−	1.32038i	−0.406913	−	0.913467i	$-0.633395\pi$
$702$		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	0.199952	−	0.979806i	$-0.435922\pi$
$709$	−20.7652	−	20.7652i	−0.779854	−	0.779854i	−0.979806	+	0.199952i	$0.935922\pi$
$710$	−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	$0.183988\pi$
$727$			29.4631i			1.09272i	−0.837549	+	0.546362i	$0.816012\pi$
$728$	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	0.911820	−	0.410590i	$-0.134677\pi$
$733$	13.5703	+	13.5703i	0.501231	+	0.501231i	−0.410590	+	0.911820i	$0.634677\pi$
$734$	−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	0.684768	−	0.728761i	$-0.259903\pi$
$739$	−1.19592	−	1.19592i	−0.0439927	−	0.0439927i	−0.728761	+	0.684768i	$0.759903\pi$
$740$	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	$-0.894514\pi$
$751$		−	17.8326i		−	0.650721i	0.945590	−	0.325360i	$-0.105486\pi$
$752$	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	−0.968291	−	0.249824i	$-0.919627\pi$
$757$	−19.7676	+	19.7676i	−0.718467	+	0.718467i	0.249824	+	0.968291i	$0.419627\pi$
$758$	−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	0.918582	−	0.395232i	$-0.129336\pi$
$773$	14.5506	+	14.5506i	0.523350	+	0.523350i	−0.395232	+	0.918582i	$0.629336\pi$
$774$		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	−0.999772	−	0.0213618i	$-0.993200\pi$
$787$	−27.4478	+	27.4478i	−0.978410	+	0.978410i	0.0213618	+	0.999772i	$0.493200\pi$
$788$	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	0.209303	−	0.977851i	$-0.432880\pi$
$797$	33.5148	−	33.5148i	1.18715	−	1.18715i	0.977851	−	0.209303i	$-0.0671197\pi$
$798$		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	−0.999491	−	0.0319126i	$-0.989840\pi$
$811$	−27.5547	+	27.5547i	−0.967578	+	0.967578i	0.0319126	+	0.999491i	$0.489840\pi$
$812$	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	−0.836835	−	0.547455i	$-0.815597\pi$
$821$	−8.29165	+	8.29165i	−0.289381	+	0.289381i	0.547455	+	0.836835i	$0.315597\pi$
$822$		0			0
$823$			16.2616i			0.566845i	0.958995	+	0.283422i	$0.0914698\pi$
$823$			16.2616i			0.566845i	−0.958995	+	0.283422i	$0.908530\pi$
$824$	−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	−0.298228	−	0.954495i	$-0.596396\pi$
$827$	18.8727	−	18.8727i	0.656266	−	0.656266i	0.954495	+	0.298228i	$0.0963956\pi$
$828$		0			0
$829$	7.56155	−	7.56155i	0.262624	−	0.262624i	−0.563495	−	0.826119i	$-0.690544\pi$
$829$	7.56155	−	7.56155i	0.262624	−	0.262624i	0.826119	+	0.563495i	$0.190544\pi$
$830$	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	$0.00716324\pi$
$839$			1.30357i			0.0450042i	−0.999747	+	0.0225021i	$0.992837\pi$
$840$		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	−0.265769	−	0.964037i	$-0.585626\pi$
$853$	20.3937	−	20.3937i	0.698268	−	0.698268i	0.964037	+	0.265769i	$0.0856258\pi$
$854$	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	$0.0989369\pi$
$857$			17.9066i			0.611678i	−0.952083	+	0.305839i	$0.901063\pi$
$858$		0			0
$859$	17.0524	−	17.0524i	0.581821	−	0.581821i	−0.353582	−	0.935403i	$-0.615037\pi$
$859$	17.0524	−	17.0524i	0.581821	−	0.581821i	0.935403	+	0.353582i	$0.115037\pi$
$860$	−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	$0.00721185\pi$
$863$			1.33105i			0.0453095i	−0.999743	+	0.0226548i	$0.992788\pi$
$864$		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	0.289407	−	0.957206i	$-0.406542\pi$
$877$	−19.7763	−	19.7763i	−0.667799	−	0.667799i	−0.957206	+	0.289407i	$0.906542\pi$
$878$	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	$0.0907305\pi$
$881$			16.6926i			0.562389i	−0.959651	+	0.281194i	$0.909269\pi$
$882$		0			0
$883$	17.2285	−	17.2285i	0.579785	−	0.579785i	−0.355059	−	0.934844i	$-0.615539\pi$
$883$	17.2285	−	17.2285i	0.579785	−	0.579785i	0.934844	+	0.355059i	$0.115539\pi$
$884$	−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	0.147307	−	0.989091i	$-0.452940\pi$
$907$	−25.3515	−	25.3515i	−0.841784	−	0.841784i	−0.989091	+	0.147307i	$0.952940\pi$
$908$	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	$0.250190\pi$
$929$			43.1302i			1.41506i	−0.706685	+	0.707528i	$0.749810\pi$
$930$		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	0.0937464	−	0.995596i	$-0.470116\pi$
$941$	−27.6649	−	27.6649i	−0.901850	−	0.901850i	−0.995596	+	0.0937464i	$0.970116\pi$
$942$		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	−0.952267	−	0.305265i	$-0.901255\pi$
$947$	−38.6985	−	38.6985i	−1.25753	−	1.25753i	−0.305265	−	0.952267i	$-0.598745\pi$
$948$		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	$0.114399\pi$
$953$			21.7149i			0.703413i	−0.936110	+	0.351707i	$0.885601\pi$
$954$		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	$0.0379525\pi$
$967$			7.39782i			0.237898i	−0.992900	+	0.118949i	$0.962048\pi$
$968$	−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	0.444268	−	0.895894i	$-0.353464\pi$
$971$	−14.0731	−	14.0731i	−0.451626	−	0.451626i	−0.895894	+	0.444268i	$0.853464\pi$
$972$		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	$0.281688\pi$
$991$			48.7239i			1.54777i	−0.633328	+	0.773883i	$0.718312\pi$
$992$	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	0.352330	−	0.935876i	$-0.385389\pi$
$997$	40.6755	−	40.6755i	1.28821	−	1.28821i	0.935876	−	0.352330i	$-0.114611\pi$
$998$	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.539.1	yes	96
3.2	odd	2	inner	720.2.u.a.539.48	yes	96
4.3	odd	2		2880.2.u.a.719.9		96
5.4	even	2	inner	720.2.u.a.539.47	yes	96
12.11	even	2		2880.2.u.a.719.40		96
15.14	odd	2	inner	720.2.u.a.539.2	yes	96
16.3	odd	4	inner	720.2.u.a.179.2	yes	96
16.13	even	4		2880.2.u.a.2159.33		96
20.19	odd	2		2880.2.u.a.719.16		96
48.29	odd	4		2880.2.u.a.2159.16		96
48.35	even	4	inner	720.2.u.a.179.47	yes	96
60.59	even	2		2880.2.u.a.719.33		96
80.19	odd	4	inner	720.2.u.a.179.48	yes	96
80.29	even	4		2880.2.u.a.2159.40		96
240.29	odd	4		2880.2.u.a.2159.9		96
240.179	even	4	inner	720.2.u.a.179.1	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.1	✓	96	240.179	even	4	inner
720.2.u.a.179.2	yes	96	16.3	odd	4	inner
720.2.u.a.179.47	yes	96	48.35	even	4	inner
720.2.u.a.179.48	yes	96	80.19	odd	4	inner
720.2.u.a.539.1	yes	96	1.1	even	1	trivial
720.2.u.a.539.2	yes	96	15.14	odd	2	inner
720.2.u.a.539.47	yes	96	5.4	even	2	inner
720.2.u.a.539.48	yes	96	3.2	odd	2	inner
2880.2.u.a.719.9		96	4.3	odd	2
2880.2.u.a.719.16		96	20.19	odd	2
2880.2.u.a.719.33		96	60.59	even	2
2880.2.u.a.719.40		96	12.11	even	2
2880.2.u.a.2159.9		96	240.29	odd	4
2880.2.u.a.2159.16		96	48.29	odd	4
2880.2.u.a.2159.33		96	16.13	even	4
2880.2.u.a.2159.40		96	80.29	even	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.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

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