LMFDB - Embedded newform 288.2.s.a.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(95,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("288.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.s (of order $6$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.4
Character	$\chi$	$=$	288.191
Dual form			288.2.s.a.95.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05094 - 1.37678i) q^{3} +(-3.01113 + 1.73848i) q^{5} +(3.12309 + 1.80312i) q^{7} +(-0.791040 + 2.89383i) q^{9} +O(q^{10})$	\(q+(-1.05094 - 1.37678i) q^{3} +(-3.01113 + 1.73848i) q^{5} +(3.12309 + 1.80312i) q^{7} +(-0.791040 + 2.89383i) q^{9} +(1.32430 - 2.29375i) q^{11} +(2.36304 + 4.09290i) q^{13} +(5.55802 + 2.31862i) q^{15} +1.79223i q^{17} +4.55459i q^{19} +(-0.799695 - 6.19478i) q^{21} +(-0.377525 - 0.653893i) q^{23} +(3.54460 - 6.13942i) q^{25} +(4.81550 - 1.95216i) q^{27} +(7.19382 + 4.15336i) q^{29} +(-1.94259 + 1.12156i) q^{31} +(-4.54974 + 0.587334i) q^{33} -12.5387 q^{35} -3.98496 q^{37} +(3.15160 - 7.55478i) q^{39} +(-5.57798 + 3.22045i) q^{41} +(-7.60601 - 4.39133i) q^{43} +(-2.64893 - 10.0889i) q^{45} +(-1.37819 + 2.38710i) q^{47} +(3.00247 + 5.20044i) q^{49} +(2.46751 - 1.88353i) q^{51} +4.41211i q^{53} +9.20903i q^{55} +(6.27067 - 4.78662i) q^{57} +(-1.36081 - 2.35700i) q^{59} +(1.19156 - 2.06384i) q^{61} +(-7.68841 + 7.61136i) q^{63} +(-14.2308 - 8.21616i) q^{65} +(8.78651 - 5.07289i) q^{67} +(-0.503509 + 1.20697i) q^{69} -0.0730340 q^{71} +13.3207 q^{73} +(-12.1778 + 1.57205i) q^{75} +(8.27180 - 4.77573i) q^{77} +(-4.51115 - 2.60452i) q^{79} +(-7.74851 - 4.57827i) q^{81} +(-0.244846 + 0.424085i) q^{83} +(-3.11576 - 5.39665i) q^{85} +(-1.84204 - 14.2692i) q^{87} -4.41211i q^{89} +17.0433i q^{91} +(3.58569 + 1.49583i) q^{93} +(-7.91805 - 13.7145i) q^{95} +(7.21855 - 12.5029i) q^{97} +(5.59015 + 5.64674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.05094	−	1.37678i	−0.606762	−	0.794884i
$3$	−1.05094	−	1.37678i	−0.606762	−	0.794884i
$4$		0			0
$5$	−3.01113	+	1.73848i	−1.34662	+	0.777470i	−0.987769	−	0.155925i	$-0.950164\pi$
$5$	−3.01113	+	1.73848i	−1.34662	+	0.777470i	−0.358849	+	0.933396i	$0.616831\pi$
$6$		0			0
$7$	3.12309	+	1.80312i	1.18042	+	0.681515i	0.956111	−	0.293004i	$-0.0946548\pi$
$7$	3.12309	+	1.80312i	1.18042	+	0.681515i	0.224307	+	0.974519i	$0.427988\pi$
$8$		0			0
$9$	−0.791040	+	2.89383i	−0.263680	+	0.964610i
$10$		0			0
$11$	1.32430	−	2.29375i	0.399290	−	0.691591i	−0.594348	−	0.804208i	$-0.702590\pi$
$11$	1.32430	−	2.29375i	0.399290	−	0.691591i	0.993639	+	0.112617i	$0.0359232\pi$
$12$		0			0
$13$	2.36304	+	4.09290i	0.655388	+	1.13517i	0.981796	+	0.189937i	$0.0608283\pi$
$13$	2.36304	+	4.09290i	0.655388	+	1.13517i	−0.326408	+	0.945229i	$0.605838\pi$
$14$		0			0
$15$	5.55802	+	2.31862i	1.43507	+	0.598665i
$16$		0			0
$17$			1.79223i			0.434681i	0.976096	+	0.217340i	$0.0697381\pi$
$17$			1.79223i			0.434681i	−0.976096	+	0.217340i	$0.930262\pi$
$18$		0			0
$19$			4.55459i			1.04490i	0.852671	+	0.522448i	$0.174981\pi$
$19$			4.55459i			1.04490i	−0.852671	+	0.522448i	$0.825019\pi$
$20$		0			0
$21$	−0.799695	−	6.19478i	−0.174508	−	1.35181i
$22$		0			0
$23$	−0.377525	−	0.653893i	−0.0787195	−	0.136346i	0.823978	−	0.566621i	$-0.191750\pi$
$23$	−0.377525	−	0.653893i	−0.0787195	−	0.136346i	−0.902698	+	0.430275i	$0.858416\pi$
$24$		0			0
$25$	3.54460	−	6.13942i	0.708920	−	1.22788i
$26$		0			0
$27$	4.81550	−	1.95216i	0.926744	−	0.375694i
$28$		0			0
$29$	7.19382	+	4.15336i	1.33586	+	0.771259i	0.986191	−	0.165614i	$-0.0529607\pi$
$29$	7.19382	+	4.15336i	1.33586	+	0.771259i	0.349669	+	0.936873i	$0.386294\pi$
$30$		0			0
$31$	−1.94259	+	1.12156i	−0.348900	+	0.201437i	−0.664201	−	0.747554i	$-0.731228\pi$
$31$	−1.94259	+	1.12156i	−0.348900	+	0.201437i	0.315301	+	0.948992i	$0.397895\pi$
$32$		0			0
$33$	−4.54974	+	0.587334i	−0.792009	+	0.102242i
$34$		0			0
$35$	−12.5387			−2.11943
$36$		0			0
$37$	−3.98496			−0.655123			−0.327561	−	0.944830i	$-0.606227\pi$
$37$	−3.98496			−0.655123			−0.327561	+	0.944830i	$0.606227\pi$
$38$		0			0
$39$	3.15160	−	7.55478i	0.504660	−	1.20973i
$40$		0			0
$41$	−5.57798	+	3.22045i	−0.871134	+	0.502949i	−0.867725	−	0.497045i	$-0.834418\pi$
$41$	−5.57798	+	3.22045i	−0.871134	+	0.502949i	−0.00340902	+	0.999994i	$0.501085\pi$
$42$		0			0
$43$	−7.60601	−	4.39133i	−1.15991	−	0.669672i	−0.208624	−	0.977996i	$-0.566899\pi$
$43$	−7.60601	−	4.39133i	−1.15991	−	0.669672i	−0.951281	+	0.308324i	$0.900232\pi$
$44$		0			0
$45$	−2.64893	−	10.0889i	−0.394879	−	1.50396i
$46$		0			0
$47$	−1.37819	+	2.38710i	−0.201030	+	0.348194i	−0.948861	−	0.315696i	$-0.897762\pi$
$47$	−1.37819	+	2.38710i	−0.201030	+	0.348194i	0.747831	+	0.663890i	$0.231096\pi$
$48$		0			0
$49$	3.00247	+	5.20044i	0.428925	+	0.742920i
$50$		0			0
$51$	2.46751	−	1.88353i	0.345521	−	0.263748i
$52$		0			0
$53$			4.41211i			0.606050i	0.952983	+	0.303025i	$0.0979966\pi$
$53$			4.41211i			0.606050i	−0.952983	+	0.303025i	$0.902003\pi$
$54$		0			0
$55$			9.20903i			1.24175i
$56$		0			0
$57$	6.27067	−	4.78662i	0.830571	−	0.634003i
$58$		0			0
$59$	−1.36081	−	2.35700i	−0.177163	−	0.306855i	0.763745	−	0.645518i	$-0.223359\pi$
$59$	−1.36081	−	2.35700i	−0.177163	−	0.306855i	−0.940908	+	0.338663i	$0.890025\pi$
$60$		0			0
$61$	1.19156	−	2.06384i	0.152563	−	0.264248i	−0.779606	−	0.626271i	$-0.784580\pi$
$61$	1.19156	−	2.06384i	0.152563	−	0.264248i	0.932169	+	0.362023i	$0.117914\pi$
$62$		0			0
$63$	−7.68841	+	7.61136i	−0.968649	+	0.958942i
$64$		0			0
$65$	−14.2308	−	8.21616i	−1.76511	−	1.01909i
$66$		0			0
$67$	8.78651	−	5.07289i	1.07344	−	0.619753i	0.144323	−	0.989531i	$-0.453900\pi$
$67$	8.78651	−	5.07289i	1.07344	−	0.619753i	0.929120	+	0.369778i	$0.120566\pi$
$68$		0			0
$69$	−0.503509	+	1.20697i	−0.0606153	+	0.145302i
$70$		0			0
$71$	−0.0730340			−0.00866754			−0.00433377	−	0.999991i	$-0.501379\pi$
$71$	−0.0730340			−0.00866754			−0.00433377	+	0.999991i	$0.501379\pi$
$72$		0			0
$73$	13.3207			1.55907			0.779536	−	0.626358i	$-0.215455\pi$
$73$	13.3207			1.55907			0.779536	+	0.626358i	$0.215455\pi$
$74$		0			0
$75$	−12.1778	+	1.57205i	−1.40617	+	0.181525i
$76$		0			0
$77$	8.27180	−	4.77573i	0.942659	−	0.544245i
$78$		0			0
$79$	−4.51115	−	2.60452i	−0.507544	−	0.293031i	0.224279	−	0.974525i	$-0.427997\pi$
$79$	−4.51115	−	2.60452i	−0.507544	−	0.293031i	−0.731824	+	0.681494i	$0.761331\pi$
$80$		0			0
$81$	−7.74851	−	4.57827i	−0.860946	−	0.508697i
$82$		0			0
$83$	−0.244846	+	0.424085i	−0.0268753	+	0.0465494i	−0.879150	−	0.476545i	$-0.841889\pi$
$83$	−0.244846	+	0.424085i	−0.0268753	+	0.0465494i	0.852275	+	0.523094i	$0.175222\pi$
$84$		0			0
$85$	−3.11576	−	5.39665i	−0.337951	−	0.585349i
$86$		0			0
$87$	−1.84204	−	14.2692i	−0.197488	−	1.52982i
$88$		0			0
$89$		−	4.41211i		−	0.467683i	−0.972275	−	0.233841i	$-0.924870\pi$
$89$		−	4.41211i		−	0.467683i	0.972275	−	0.233841i	$-0.0751297\pi$
$90$		0			0
$91$			17.0433i			1.78663i
$92$		0			0
$93$	3.58569	+	1.49583i	0.371818	+	0.155110i
$94$		0			0
$95$	−7.91805	−	13.7145i	−0.812375	−	1.40708i
$96$		0			0
$97$	7.21855	−	12.5029i	0.732933	−	1.26948i	−0.222692	−	0.974889i	$-0.571484\pi$
$97$	7.21855	−	12.5029i	0.732933	−	1.26948i	0.955624	−	0.294588i	$-0.0951823\pi$
$98$		0			0
$99$	5.59015	+	5.64674i	0.561831	+	0.567518i
$100$		0			0
$101$	1.88785	+	1.08995i	0.187848	+	0.108454i	0.590975	−	0.806690i	$-0.298743\pi$
$101$	1.88785	+	1.08995i	0.187848	+	0.108454i	−0.403127	+	0.915144i	$0.632077\pi$
$102$		0			0
$103$	3.33065	−	1.92295i	0.328179	−	0.189474i	−0.326853	−	0.945075i	$-0.605988\pi$
$103$	3.33065	−	1.92295i	0.328179	−	0.189474i	0.655032	+	0.755601i	$0.272655\pi$
$104$		0			0
$105$	13.1775	+	17.2630i	1.28599	+	1.68470i
$106$		0			0
$107$	19.4071			1.87615			0.938077	−	0.346426i	$-0.112605\pi$
$107$	19.4071			1.87615			0.938077	+	0.346426i	$0.112605\pi$
$108$		0			0
$109$	−13.0941			−1.25419			−0.627096	−	0.778942i	$-0.715757\pi$
$109$	−13.0941			−1.25419			−0.627096	+	0.778942i	$0.715757\pi$
$110$		0			0
$111$	4.18796	+	5.48640i	0.397503	+	0.520746i
$112$		0			0
$113$	−1.23482	+	0.712921i	−0.116162	+	0.0670660i	−0.556955	−	0.830543i	$-0.688030\pi$
$113$	−1.23482	+	0.712921i	−0.116162	+	0.0670660i	0.440793	+	0.897609i	$0.354697\pi$
$114$		0			0
$115$	2.27355	+	1.31264i	0.212010	+	0.122404i
$116$		0			0
$117$	−13.7134	+	3.60058i	−1.26781	+	0.332873i
$118$		0			0
$119$	−3.23161	+	5.59731i	−0.296241	+	0.513105i
$120$		0			0
$121$	1.99248	+	3.45107i	0.181134	+	0.313734i
$122$		0			0
$123$	10.2960	+	4.29514i	0.928357	+	0.387280i
$124$		0			0
$125$			7.26404i			0.649715i
$126$		0			0
$127$		−	13.5554i		−	1.20285i	−0.798929	−	0.601425i	$-0.794600\pi$
$127$		−	13.5554i		−	1.20285i	0.798929	−	0.601425i	$-0.205400\pi$
$128$		0			0
$129$	1.94758	+	15.0868i	0.171475	+	1.32832i
$130$		0			0
$131$	7.88176	+	13.6516i	0.688632	+	1.19275i	0.972280	+	0.233818i	$0.0751219\pi$
$131$	7.88176	+	13.6516i	0.688632	+	1.19275i	−0.283648	+	0.958928i	$0.591545\pi$
$132$		0			0
$133$	−8.21247	+	14.2244i	−0.712112	+	1.23341i
$134$		0			0
$135$	−11.1063	+	14.2498i	−0.955879	+	1.22643i
$136$		0			0
$137$	6.70126	+	3.86897i	0.572527	+	0.330549i	0.758158	−	0.652071i	$-0.226100\pi$
$137$	6.70126	+	3.86897i	0.572527	+	0.330549i	−0.185631	+	0.982620i	$0.559433\pi$
$138$		0			0
$139$	0.490339	−	0.283097i	0.0415900	−	0.0240120i	−0.479061	−	0.877782i	$-0.659023\pi$
$139$	0.490339	−	0.283097i	0.0415900	−	0.0240120i	0.520651	+	0.853770i	$0.325689\pi$
$140$		0			0
$141$	4.73491	−	0.611237i	0.398751	−	0.0514755i
$142$		0			0
$143$	12.5174			1.04676
$144$		0			0
$145$	−28.8820			−2.39852
$146$		0			0
$147$	4.00443	−	9.59910i	0.330280	−	0.791721i
$148$		0			0
$149$	8.19013	−	4.72857i	0.670961	−	0.387380i	−0.125479	−	0.992096i	$-0.540047\pi$
$149$	8.19013	−	4.72857i	0.670961	−	0.387380i	0.796441	+	0.604716i	$0.206714\pi$
$150$		0			0
$151$	−16.5260	−	9.54127i	−1.34486	−	0.776458i	−0.357347	−	0.933972i	$-0.616319\pi$
$151$	−16.5260	−	9.54127i	−1.34486	−	0.776458i	−0.987517	+	0.157514i	$0.949652\pi$
$152$		0			0
$153$	−5.18642	−	1.41773i	−0.419297	−	0.114617i
$154$		0			0
$155$	3.89960	−	6.75430i	0.313223	−	0.542519i
$156$		0			0
$157$	10.5680	+	18.3043i	0.843417	+	1.46084i	0.886989	+	0.461791i	$0.152793\pi$
$157$	10.5680	+	18.3043i	0.843417	+	1.46084i	−0.0435713	+	0.999050i	$0.513874\pi$
$158$		0			0
$159$	6.07450	−	4.63688i	0.481739	−	0.367728i
$160$		0			0
$161$		−	2.72289i		−	0.214594i
$162$		0			0
$163$		−	22.6646i		−	1.77523i	−0.460586	−	0.887615i	$-0.652361\pi$
$163$		−	22.6646i		−	1.77523i	0.460586	−	0.887615i	$-0.347639\pi$
$164$		0			0
$165$	12.6788	−	9.67816i	0.987043	−	0.753444i
$166$		0			0
$167$	2.92712	+	5.06992i	0.226507	+	0.392322i	0.956771	−	0.290844i	$-0.0939359\pi$
$167$	2.92712	+	5.06992i	0.226507	+	0.392322i	−0.730263	+	0.683166i	$0.760603\pi$
$168$		0			0
$169$	−4.66788	+	8.08500i	−0.359067	+	0.621923i
$170$		0			0
$171$	−13.1802	−	3.60287i	−1.00792	−	0.275518i
$172$		0			0
$173$	−5.11907	−	2.95549i	−0.389195	−	0.224702i	0.292616	−	0.956230i	$-0.405474\pi$
$173$	−5.11907	−	2.95549i	−0.389195	−	0.224702i	−0.681811	+	0.731528i	$0.738808\pi$
$174$		0			0
$175$	22.1402	−	12.7827i	1.67364	−	0.966279i
$176$		0			0
$177$	−1.81493	+	4.35061i	−0.136418	+	0.327012i
$178$		0			0
$179$	−12.8823			−0.962871			−0.481436	−	0.876481i	$-0.659884\pi$
$179$	−12.8823			−0.962871			−0.481436	+	0.876481i	$0.659884\pi$
$180$		0			0
$181$	−10.1934			−0.757672			−0.378836	−	0.925464i	$-0.623676\pi$
$181$	−10.1934			−0.757672			−0.378836	+	0.925464i	$0.623676\pi$
$182$		0			0
$183$	−4.09371	+	0.528464i	−0.302616	+	0.0390652i
$184$		0			0
$185$	11.9992	−	6.92775i	0.882200	−	0.509338i
$186$		0			0
$187$	4.11093	+	2.37345i	0.300621	+	0.173564i
$188$		0			0
$189$	18.5592	+	2.58614i	1.34999	+	0.188114i
$190$		0			0
$191$	−11.2960	+	19.5653i	−0.817353	+	1.41570i	0.0902735	+	0.995917i	$0.471226\pi$
$191$	−11.2960	+	19.5653i	−0.817353	+	1.41570i	−0.907626	+	0.419779i	$0.862107\pi$
$192$		0			0
$193$	−1.12935	−	1.95610i	−0.0812926	−	0.140803i	0.822513	−	0.568747i	$-0.192571\pi$
$193$	−1.12935	−	1.95610i	−0.0812926	−	0.140803i	−0.903805	+	0.427944i	$0.859238\pi$
$194$		0			0
$195$	3.64392	+	28.2274i	0.260947	+	2.02141i
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$			13.8193i			0.979621i	0.871829	+	0.489811i	$0.162934\pi$
$199$			13.8193i			0.979621i	−0.871829	+	0.489811i	$0.837066\pi$
$200$		0			0
$201$	−16.2184	−	6.76576i	−1.14396	−	0.477220i
$202$		0			0
$203$	14.9780	+	25.9426i	1.05125	+	1.82082i
$204$		0			0
$205$	11.1973	−	19.3944i	0.782056	−	1.35456i
$206$		0			0
$207$	2.19089	−	0.575239i	0.152278	−	0.0399818i
$208$		0			0
$209$	10.4471	+	6.03163i	0.722641	+	0.417217i
$210$		0			0
$211$	5.52413	−	3.18936i	0.380297	−	0.219565i	−0.297651	−	0.954675i	$-0.596203\pi$
$211$	5.52413	−	3.18936i	0.380297	−	0.219565i	0.677947	+	0.735110i	$0.262870\pi$
$212$		0			0
$213$	0.0767545	+	0.100552i	0.00525913	+	0.00688968i
$214$		0			0
$215$	30.5369			2.08260
$216$		0			0
$217$	−8.08920			−0.549130
$218$		0			0
$219$	−13.9993	−	18.3397i	−0.945985	−	1.23928i
$220$		0			0
$221$	−7.33543	+	4.23511i	−0.493435	+	0.284885i
$222$		0			0
$223$	−2.25361	−	1.30112i	−0.150913	−	0.0871296i	0.422642	−	0.906297i	$-0.361103\pi$
$223$	−2.25361	−	1.30112i	−0.150913	−	0.0871296i	−0.573555	+	0.819167i	$0.694436\pi$
$224$		0			0
$225$	14.9625	+	15.1140i	0.997502	+	1.00760i
$226$		0			0
$227$	10.7192	−	18.5663i	0.711461	−	1.23229i	−0.252848	−	0.967506i	$-0.581367\pi$
$227$	10.7192	−	18.5663i	0.711461	−	1.23229i	0.964309	−	0.264780i	$-0.0852993\pi$
$228$		0			0
$229$	−0.370558	−	0.641825i	−0.0244872	−	0.0424130i	0.853522	−	0.521057i	$-0.174462\pi$
$229$	−0.370558	−	0.641825i	−0.0244872	−	0.0424130i	−0.878009	+	0.478644i	$0.841129\pi$
$230$		0			0
$231$	−15.2683	−	6.36943i	−1.00458	−	0.419078i
$232$		0			0
$233$		−	20.3832i		−	1.33535i	−0.744454	−	0.667673i	$-0.767290\pi$
$233$		−	20.3832i		−	1.33535i	0.744454	−	0.667673i	$-0.232710\pi$
$234$		0			0
$235$		−	9.58381i		−	0.625179i
$236$		0			0
$237$	1.15512	+	8.94806i	0.0750331	+	0.581239i
$238$		0			0
$239$	−4.78964	−	8.29589i	−0.309816	−	0.536617i	0.668506	−	0.743707i	$-0.266934\pi$
$239$	−4.78964	−	8.29589i	−0.309816	−	0.536617i	−0.978322	+	0.207090i	$0.933601\pi$
$240$		0			0
$241$	3.17787	−	5.50424i	0.204705	−	0.354559i	−0.745334	−	0.666691i	$-0.767710\pi$
$241$	3.17787	−	5.50424i	0.204705	−	0.354559i	0.950039	+	0.312132i	$0.101043\pi$
$242$		0			0
$243$	1.83997	+	15.4795i	0.118034	+	0.993010i
$244$		0			0
$245$	−18.0817	−	10.4395i	−1.15520	−	0.666953i
$246$		0			0
$247$	−18.6415	+	10.7627i	−1.18613	+	0.684812i
$248$		0			0
$249$	0.841191	−	0.108591i	0.0533083	−	0.00688166i
$250$		0			0
$251$	−27.0938			−1.71014			−0.855072	−	0.518509i	$-0.826487\pi$
$251$	−27.0938			−1.71014			−0.855072	+	0.518509i	$0.826487\pi$
$252$		0			0
$253$	−1.99982			−0.125728
$254$		0			0
$255$	−4.15551	+	9.96127i	−0.260228	+	0.623799i
$256$		0			0
$257$	−3.31700	+	1.91507i	−0.206909	+	0.119459i	−0.599874	−	0.800095i	$-0.704783\pi$
$257$	−3.31700	+	1.91507i	−0.206909	+	0.119459i	0.392965	+	0.919553i	$0.371449\pi$
$258$		0			0
$259$	−12.4454	−	7.18535i	−0.773319	−	0.446476i
$260$		0			0
$261$	−17.7097	+	17.5322i	−1.09620	+	1.08522i
$262$		0			0
$263$	16.0988	−	27.8840i	0.992697	−	1.71940i	0.391878	−	0.920017i	$-0.371826\pi$
$263$	16.0988	−	27.8840i	0.992697	−	1.71940i	0.600819	−	0.799385i	$-0.294841\pi$
$264$		0			0
$265$	−7.67035	−	13.2854i	−0.471186	−	0.816118i
$266$		0			0
$267$	−6.07450	+	4.63688i	−0.371754	+	0.283772i
$268$		0			0
$269$		−	27.2601i		−	1.66208i	−0.556214	−	0.831039i	$-0.687747\pi$
$269$		−	27.2601i		−	1.66208i	0.556214	−	0.831039i	$-0.312253\pi$
$270$		0			0
$271$			8.48623i			0.515501i	0.966211	+	0.257751i	$0.0829813\pi$
$271$			8.48623i			0.515501i	−0.966211	+	0.257751i	$0.917019\pi$
$272$		0			0
$273$	23.4649	−	17.9116i	1.42016	−	1.08406i
$274$		0			0
$275$	−9.38820	−	16.2608i	−0.566130	−	0.980565i
$276$		0			0
$277$	3.90516	−	6.76394i	0.234638	−	0.406405i	−0.724529	−	0.689244i	$-0.757943\pi$
$277$	3.90516	−	6.76394i	0.234638	−	0.406405i	0.959168	+	0.282839i	$0.0912761\pi$
$278$		0			0
$279$	−1.70892	−	6.50873i	−0.102311	−	0.389667i
$280$		0			0
$281$	6.05260	+	3.49447i	0.361068	+	0.208462i	0.669549	−	0.742768i	$-0.266487\pi$
$281$	6.05260	+	3.49447i	0.361068	+	0.208462i	−0.308481	+	0.951230i	$0.599821\pi$
$282$		0			0
$283$	−24.3037	+	14.0318i	−1.44471	+	0.834101i	−0.998159	−	0.0606590i	$-0.980680\pi$
$283$	−24.3037	+	14.0318i	−1.44471	+	0.834101i	−0.446547	+	0.894760i	$0.647346\pi$
$284$		0			0
$285$	−10.5604	+	25.3145i	−0.625543	+	1.49950i
$286$		0			0
$287$	−23.2274			−1.37107
$288$		0			0
$289$	13.7879			0.811053
$290$		0			0
$291$	−24.8000	+	3.20147i	−1.45380	+	0.187674i
$292$		0			0
$293$	7.54841	−	4.35808i	0.440983	−	0.254602i	−0.263031	−	0.964787i	$-0.584722\pi$
$293$	7.54841	−	4.35808i	0.440983	−	0.254602i	0.704015	+	0.710186i	$0.251389\pi$
$294$		0			0
$295$	8.19517	+	4.73148i	0.477141	+	0.275478i
$296$		0			0
$297$	1.89939	−	13.6308i	0.110214	−	0.790939i
$298$		0			0
$299$	1.78421	−	3.09035i	0.103184	−	0.178719i
$300$		0			0
$301$	−15.8362	−	27.4291i	−0.912782	−	1.58099i
$302$		0			0
$303$	−0.483400	−	3.74463i	−0.0277706	−	0.215123i
$304$		0			0
$305$			8.28599i			0.474454i
$306$		0			0
$307$		−	9.62380i		−	0.549259i	−0.961550	−	0.274630i	$-0.911445\pi$
$307$		−	9.62380i		−	0.549259i	0.961550	−	0.274630i	$-0.0885552\pi$
$308$		0			0
$309$	−6.14780	−	2.56466i	−0.349736	−	0.145898i
$310$		0			0
$311$	8.31685	+	14.4052i	0.471606	+	0.816845i	0.999472	−	0.0324824i	$-0.0103413\pi$
$311$	8.31685	+	14.4052i	0.471606	+	0.816845i	−0.527867	+	0.849327i	$0.677008\pi$
$312$		0			0
$313$	−12.3153	+	21.3307i	−0.696100	+	1.20568i	0.273708	+	0.961813i	$0.411750\pi$
$313$	−12.3153	+	21.3307i	−0.696100	+	1.20568i	−0.969808	+	0.243868i	$0.921584\pi$
$314$		0			0
$315$	9.91863	−	36.2849i	0.558852	−	2.04442i
$316$		0			0
$317$	20.8576	+	12.0421i	1.17148	+	0.676354i	0.954028	−	0.299717i	$-0.0968922\pi$
$317$	20.8576	+	12.0421i	1.17148	+	0.676354i	0.217452	+	0.976071i	$0.430226\pi$
$318$		0			0
$319$	19.0535	−	11.0005i	1.06679	−	0.615913i
$320$		0			0
$321$	−20.3957	−	26.7193i	−1.13838	−	1.49132i
$322$		0			0
$323$	−8.16290			−0.454196
$324$		0			0
$325$	33.5041			1.85847
$326$		0			0
$327$	13.7612	+	18.0277i	0.760996	+	0.996936i
$328$		0			0
$329$	−8.60844	+	4.97009i	−0.474599	+	0.274010i
$330$		0			0
$331$	11.1084	+	6.41343i	0.610573	+	0.352514i	0.773189	−	0.634175i	$-0.218660\pi$
$331$	11.1084	+	6.41343i	0.610573	+	0.352514i	−0.162617	+	0.986689i	$0.551993\pi$
$332$		0			0
$333$	3.15226	−	11.5318i	0.172743	−	0.631938i
$334$		0			0
$335$	−17.6382	+	30.5503i	−0.963678	+	1.66914i
$336$		0			0
$337$	10.0754	+	17.4511i	0.548843	+	0.950624i	0.998354	+	0.0573495i	$0.0182649\pi$
$337$	10.0754	+	17.4511i	0.548843	+	0.950624i	−0.449511	+	0.893275i	$0.648402\pi$
$338$		0			0
$339$	2.27925	+	0.950829i	0.123792	+	0.0516419i
$340$		0			0
$341$			5.94109i			0.321728i
$342$		0			0
$343$		−	3.58839i		−	0.193755i
$344$		0			0
$345$	−0.582163	−	4.50969i	−0.0313426	−	0.242793i
$346$		0			0
$347$	−3.50392	−	6.06897i	−0.188100	−	0.325800i	0.756516	−	0.653975i	$-0.226900\pi$
$347$	−3.50392	−	6.06897i	−0.188100	−	0.325800i	−0.944617	+	0.328175i	$0.893566\pi$
$348$		0			0
$349$	−2.47879	+	4.29339i	−0.132687	+	0.229820i	−0.924711	−	0.380669i	$-0.875694\pi$
$349$	−2.47879	+	4.29339i	−0.132687	+	0.229820i	0.792025	+	0.610489i	$0.209027\pi$
$350$		0			0
$351$	19.3692	+	15.0963i	1.03385	+	0.805783i
$352$		0			0
$353$	−3.05985	−	1.76661i	−0.162859	−	0.0940270i	0.416355	−	0.909202i	$-0.363307\pi$
$353$	−3.05985	−	1.76661i	−0.162859	−	0.0940270i	−0.579215	+	0.815175i	$0.696641\pi$
$354$		0			0
$355$	0.219915	−	0.126968i	0.0116719	−	0.00673875i
$356$		0			0
$357$	11.1025	−	1.43324i	0.587607	−	0.0758551i
$358$		0			0
$359$	15.2054			0.802511			0.401255	−	0.915966i	$-0.368574\pi$
$359$	15.2054			0.802511			0.401255	+	0.915966i	$0.368574\pi$
$360$		0			0
$361$	−1.74433			−0.0918070
$362$		0			0
$363$	2.65739	−	6.37008i	0.139477	−	0.334343i
$364$		0			0
$365$	−40.1104	+	23.1577i	−2.09947	+	1.21213i
$366$		0			0
$367$	3.23512	+	1.86780i	0.168872	+	0.0974983i	0.582054	−	0.813150i	$-0.302249\pi$
$367$	3.23512	+	1.86780i	0.168872	+	0.0974983i	−0.413182	+	0.910649i	$0.635583\pi$
$368$		0			0
$369$	−4.90702	−	18.6892i	−0.255449	−	0.972922i
$370$		0			0
$371$	−7.95556	+	13.7794i	−0.413032	+	0.715393i
$372$		0			0
$373$	0.760243	+	1.31678i	0.0393639	+	0.0681802i	0.885036	−	0.465522i	$-0.154134\pi$
$373$	0.760243	+	1.31678i	0.0393639	+	0.0681802i	−0.845672	+	0.533703i	$0.820800\pi$
$374$		0			0
$375$	10.0010	−	7.63408i	0.516448	−	0.394222i
$376$		0			0
$377$			39.2581i			2.02190i
$378$		0			0
$379$			23.7948i			1.22226i	0.791531	+	0.611129i	$0.209284\pi$
$379$			23.7948i			1.22226i	−0.791531	+	0.611129i	$0.790716\pi$
$380$		0			0
$381$	−18.6628	+	14.2460i	−0.956126	+	0.729843i
$382$		0			0
$383$	−1.48499	−	2.57208i	−0.0758796	−	0.131427i	0.825589	−	0.564272i	$-0.190843\pi$
$383$	−1.48499	−	2.57208i	−0.0758796	−	0.131427i	−0.901468	+	0.432845i	$0.857510\pi$
$384$		0			0
$385$	−16.6050	+	28.7607i	−0.846268	+	1.46578i
$386$		0			0
$387$	18.7244	−	18.5368i	0.951816	−	0.942278i
$388$		0			0
$389$	−3.55562	−	2.05284i	−0.180277	−	0.104083i	0.407146	−	0.913363i	$-0.366524\pi$
$389$	−3.55562	−	2.05284i	−0.180277	−	0.104083i	−0.587423	+	0.809280i	$0.699857\pi$
$390$		0			0
$391$	1.17193	−	0.676614i	0.0592670	−	0.0342178i
$392$		0			0
$393$	10.5120	−	25.1985i	0.530259	−	1.27110i
$394$		0			0
$395$	18.1116			0.911291
$396$		0			0
$397$	16.4643			0.826319			0.413160	−	0.910659i	$-0.364425\pi$
$397$	16.4643			0.826319			0.413160	+	0.910659i	$0.364425\pi$
$398$		0			0
$399$	28.2147	−	3.64229i	1.41250	−	0.182342i
$400$		0			0
$401$	26.8460	−	15.4996i	1.34063	−	0.774012i	0.353728	−	0.935348i	$-0.384914\pi$
$401$	26.8460	−	15.4996i	1.34063	−	0.774012i	0.986899	+	0.161337i	$0.0515805\pi$
$402$		0			0
$403$	−9.18083	−	5.30056i	−0.457330	−	0.264039i
$404$		0			0
$405$	31.2910	+	0.315173i	1.55486	+	0.0156611i
$406$		0			0
$407$	−5.27726	+	9.14049i	−0.261584	+	0.453077i
$408$		0			0
$409$	2.24112	+	3.88173i	0.110816	+	0.191939i	0.916100	−	0.400951i	$-0.131320\pi$
$409$	2.24112	+	3.88173i	0.110816	+	0.191939i	−0.805283	+	0.592890i	$0.797987\pi$
$410$		0			0
$411$	−1.71591	−	13.2922i	−0.0846398	−	0.655657i
$412$		0			0
$413$		−	9.81483i		−	0.482956i
$414$		0			0
$415$		−	1.70263i		−	0.0835791i
$416$		0			0
$417$	−0.905080	−	0.377569i	−0.0443220	−	0.0184897i
$418$		0			0
$419$	6.48571	+	11.2336i	0.316848	+	0.548796i	0.979829	−	0.199840i	$-0.0640423\pi$
$419$	6.48571	+	11.2336i	0.316848	+	0.548796i	−0.662981	+	0.748636i	$0.730709\pi$
$420$		0			0
$421$	9.21256	−	15.9566i	0.448993	−	0.777679i	−0.549328	−	0.835607i	$-0.685116\pi$
$421$	9.21256	−	15.9566i	0.448993	−	0.777679i	0.998321	+	0.0579284i	$0.0184495\pi$
$422$		0			0
$423$	−5.81765	−	5.87654i	−0.282864	−	0.285727i
$424$		0			0
$425$	11.0033	+	6.35275i	0.533738	+	0.308154i
$426$		0			0
$427$	7.44270	−	4.29704i	0.360177	−	0.207949i
$428$		0			0
$429$	−13.1551	−	17.2337i	−0.635135	−	0.832053i
$430$		0			0
$431$	−22.3743			−1.07773			−0.538867	−	0.842391i	$-0.681148\pi$
$431$	−22.3743			−1.07773			−0.538867	+	0.842391i	$0.681148\pi$
$432$		0			0
$433$	0.857684			0.0412177			0.0206088	−	0.999788i	$-0.493440\pi$
$433$	0.857684			0.0412177			0.0206088	+	0.999788i	$0.493440\pi$
$434$		0			0
$435$	30.3534	+	39.7642i	1.45533	+	1.90655i
$436$		0			0
$437$	2.97822	−	1.71947i	0.142467	−	0.0822536i
$438$		0			0
$439$	10.3089	+	5.95187i	0.492019	+	0.284067i	0.725412	−	0.688315i	$-0.241649\pi$
$439$	10.3089	+	5.95187i	0.492019	+	0.284067i	−0.233393	+	0.972383i	$0.574983\pi$
$440$		0			0
$441$	−17.4243	+	4.57490i	−0.829727	+	0.217852i
$442$		0			0
$443$	8.99773	−	15.5845i	0.427495	−	0.740443i	−0.569155	−	0.822230i	$-0.692730\pi$
$443$	8.99773	−	15.5845i	0.427495	−	0.740443i	0.996650	+	0.0817875i	$0.0260629\pi$
$444$		0			0
$445$	7.67035	+	13.2854i	0.363610	+	0.629790i
$446$		0			0
$447$	−15.1176	−	6.30654i	−0.715036	−	0.298289i
$448$		0			0
$449$			37.0489i			1.74845i	0.485524	+	0.874223i	$0.338629\pi$
$449$			37.0489i			1.74845i	−0.485524	+	0.874223i	$0.661371\pi$
$450$		0			0
$451$			17.0593i			0.803291i
$452$		0			0
$453$	4.23162	+	32.7799i	0.198819	+	1.54014i
$454$		0			0
$455$	−29.6294	−	51.3197i	−1.38905	−	2.40590i
$456$		0			0
$457$	4.16540	−	7.21469i	0.194849	−	0.337489i	−0.752002	−	0.659161i	$-0.770912\pi$
$457$	4.16540	−	7.21469i	0.194849	−	0.337489i	0.946851	+	0.321672i	$0.104245\pi$
$458$		0			0
$459$	3.49873	+	8.63051i	0.163307	+	0.402838i
$460$		0			0
$461$	−20.2118	−	11.6693i	−0.941356	−	0.543492i	−0.0509708	−	0.998700i	$-0.516232\pi$
$461$	−20.2118	−	11.6693i	−0.941356	−	0.543492i	−0.890385	+	0.455208i	$0.849565\pi$
$462$		0			0
$463$	−29.9990	+	17.3199i	−1.39417	+	0.804926i	−0.993774	−	0.111415i	$-0.964462\pi$
$463$	−29.9990	+	17.3199i	−1.39417	+	0.804926i	−0.400399	+	0.916341i	$0.631128\pi$
$464$		0			0
$465$	−13.3974	+	1.72950i	−0.621291	+	0.0802035i
$466$		0			0
$467$	−17.1281			−0.792595			−0.396298	−	0.918122i	$-0.629705\pi$
$467$	−17.1281			−0.792595			−0.396298	+	0.918122i	$0.629705\pi$
$468$		0			0
$469$	36.5881			1.68948
$470$		0			0
$471$	14.0946	−	33.7865i	0.649446	−	1.55680i
$472$		0			0
$473$	−20.1452	+	11.6308i	−0.926278	+	0.534787i
$474$		0			0
$475$	27.9626	+	16.1442i	1.28301	+	0.740747i
$476$		0			0
$477$	−12.7679	−	3.49016i	−0.584602	−	0.159803i
$478$		0			0
$479$	18.1500	−	31.4366i	0.829293	−	1.43638i	−0.0693014	−	0.997596i	$-0.522077\pi$
$479$	18.1500	−	31.4366i	0.829293	−	1.43638i	0.898594	−	0.438781i	$-0.144590\pi$
$480$		0			0
$481$	−9.41659	−	16.3100i	−0.429360	−	0.743673i
$482$		0			0
$483$	−3.74882	+	2.86160i	−0.170577	+	0.130207i
$484$		0			0
$485$			50.1971i			2.27933i
$486$		0			0
$487$		−	1.00757i		−	0.0456575i	−0.999739	−	0.0228287i	$-0.992733\pi$
$487$		−	1.00757i		−	0.0456575i	0.999739	−	0.0228287i	$-0.00726724\pi$
$488$		0			0
$489$	−31.2042	+	23.8192i	−1.41110	+	1.07714i
$490$		0			0
$491$	−5.20416	−	9.01387i	−0.234860	−	0.406790i	0.724372	−	0.689410i	$-0.242130\pi$
$491$	−5.20416	−	9.01387i	−0.234860	−	0.406790i	−0.959232	+	0.282620i	$0.908797\pi$
$492$		0			0
$493$	−7.44379	+	12.8930i	−0.335251	+	0.580672i
$494$		0			0
$495$	−26.6494	−	7.28472i	−1.19780	−	0.327424i
$496$		0			0
$497$	−0.228092	−	0.131689i	−0.0102313	−	0.00590705i
$498$		0			0
$499$	3.25233	−	1.87773i	0.145594	−	0.0840590i	−0.425433	−	0.904990i	$-0.639878\pi$
$499$	3.25233	−	1.87773i	0.145594	−	0.0840590i	0.571028	+	0.820931i	$0.306545\pi$
$500$		0			0
$501$	3.90393	−	9.35819i	0.174415	−	0.418093i
$502$		0			0
$503$	20.5980			0.918417			0.459209	−	0.888328i	$-0.348133\pi$
$503$	20.5980			0.918417			0.459209	+	0.888328i	$0.348133\pi$
$504$		0			0
$505$	−7.57942			−0.337280
$506$		0			0
$507$	16.0369	−	2.07023i	0.712225	−	0.0919423i
$508$		0			0
$509$	−10.7984	+	6.23445i	−0.478630	+	0.276337i	−0.719845	−	0.694135i	$-0.755787\pi$
$509$	−10.7984	+	6.23445i	−0.478630	+	0.276337i	0.241216	+	0.970472i	$0.422454\pi$
$510$		0			0
$511$	41.6018	+	24.0188i	1.84036	+	1.06253i
$512$		0			0
$513$	8.89130	+	21.9327i	0.392561	+	0.968351i
$514$		0			0
$515$	−6.68602	+	11.5805i	−0.294621	+	0.510299i
$516$		0			0
$517$	3.65027	+	6.32245i	0.160539	+	0.278061i
$518$		0			0
$519$	1.31078	+	10.1539i	0.0575369	+	0.445706i
$520$		0			0
$521$		−	15.9193i		−	0.697438i	−0.937227	−	0.348719i	$-0.886617\pi$
$521$		−	15.9193i		−	0.697438i	0.937227	−	0.348719i	$-0.113383\pi$
$522$		0			0
$523$			3.71297i			0.162357i	0.996700	+	0.0811784i	$0.0258683\pi$
$523$			3.71297i			0.162357i	−0.996700	+	0.0811784i	$0.974132\pi$
$524$		0			0
$525$	−40.8670	−	17.0483i	−1.78358	−	0.744051i
$526$		0			0
$527$	−2.01009	−	3.48158i	−0.0875610	−	0.151660i
$528$		0			0
$529$	11.2149	−	19.4249i	0.487606	−	0.844559i
$530$		0			0
$531$	7.89721	−	2.07348i	0.342710	−	0.0899815i
$532$		0			0
$533$	−26.3619	−	15.2201i	−1.14186	−	0.659254i
$534$		0			0
$535$	−58.4373	+	33.7388i	−2.52646	+	1.45865i
$536$		0			0
$537$	13.5386	+	17.7361i	0.584234	+	0.765371i
$538$		0			0
$539$	15.9047			0.685062
$540$		0			0
$541$	19.1191			0.821994			0.410997	−	0.911637i	$-0.365181\pi$
$541$	19.1191			0.821994			0.410997	+	0.911637i	$0.365181\pi$
$542$		0			0
$543$	10.7127	+	14.0341i	0.459727	+	0.602261i
$544$		0			0
$545$	39.4282	−	22.7639i	1.68892	−	0.975097i
$546$		0			0
$547$	22.8869	+	13.2137i	0.978571	+	0.564978i	0.901839	−	0.432073i	$-0.142218\pi$
$547$	22.8869	+	13.2137i	0.978571	+	0.564978i	0.0767328	+	0.997052i	$0.475551\pi$
$548$		0			0
$549$	5.02983	+	5.08075i	0.214668	+	0.216841i
$550$		0			0
$551$	−18.9169	+	32.7650i	−0.805885	+	1.39583i
$552$		0			0
$553$	−9.39250	−	16.2683i	−0.399410	−	0.691798i
$554$		0			0
$555$	−22.1485	−	9.23960i	−0.940150	−	0.392199i
$556$		0			0
$557$		−	24.9370i		−	1.05662i	−0.849053	−	0.528308i	$-0.822827\pi$
$557$		−	24.9370i		−	1.05662i	0.849053	−	0.528308i	$-0.177173\pi$
$558$		0			0
$559$		−	41.5075i		−	1.75558i
$560$		0			0
$561$	−1.05264	−	8.15421i	−0.0444425	−	0.344271i
$562$		0			0
$563$	−15.2599	−	26.4309i	−0.643127	−	1.11393i	−0.984731	−	0.174084i	$-0.944304\pi$
$563$	−15.2599	−	26.4309i	−0.643127	−	1.11393i	0.341604	−	0.939844i	$-0.389030\pi$
$564$		0			0
$565$	2.47879	−	4.29339i	0.104284	−	0.180624i
$566$		0			0
$567$	−15.9441	−	28.2699i	−0.669591	−	1.18722i
$568$		0			0
$569$	−8.93936	−	5.16114i	−0.374758	−	0.216366i	0.300777	−	0.953694i	$-0.402754\pi$
$569$	−8.93936	−	5.16114i	−0.374758	−	0.216366i	−0.675535	+	0.737328i	$0.736087\pi$
$570$		0			0
$571$	−7.55903	+	4.36421i	−0.316335	+	0.182636i	−0.649758	−	0.760141i	$-0.725130\pi$
$571$	−7.55903	+	4.36421i	−0.316335	+	0.182636i	0.333423	+	0.942777i	$0.391796\pi$
$572$		0			0
$573$	38.8086	−	5.00987i	1.62125	−	0.209290i
$574$		0			0
$575$	−5.35270			−0.223223
$576$		0			0
$577$	34.4398			1.43375			0.716874	−	0.697203i	$-0.245572\pi$
$577$	34.4398			1.43375			0.716874	+	0.697203i	$0.245572\pi$
$578$		0			0
$579$	−1.50623	+	3.61061i	−0.0625967	+	0.150052i
$580$		0			0
$581$	−1.52935	+	0.882972i	−0.0634483	+	0.0366319i
$582$		0			0
$583$	10.1203	+	5.84294i	0.419139	+	0.241990i
$584$		0			0
$585$	35.0333	−	34.6822i	1.44845	−	1.43393i
$586$		0			0
$587$	2.31697	−	4.01312i	0.0956318	−	0.165639i	−0.814240	−	0.580528i	$-0.802846\pi$
$587$	2.31697	−	4.01312i	0.0956318	−	0.165639i	0.909872	+	0.414889i	$0.136180\pi$
$588$		0			0
$589$	−5.10823	−	8.84772i	−0.210481	−	0.364564i
$590$		0			0
$591$	−7.78824	+	5.94503i	−0.320365	+	0.244546i
$592$		0			0
$593$		−	1.49543i		−	0.0614098i	−0.999528	−	0.0307049i	$-0.990225\pi$
$593$		−	1.49543i		−	0.0614098i	0.999528	−	0.0307049i	$-0.00977521\pi$
$594$		0			0
$595$		−	22.4723i		−	0.921275i
$596$		0			0
$597$	19.0261	−	14.5232i	0.778685	−	0.594397i
$598$		0			0
$599$	15.8095	+	27.3828i	0.645957	+	1.11883i	0.984080	+	0.177728i	$0.0568748\pi$
$599$	15.8095	+	27.3828i	0.645957	+	1.11883i	−0.338123	+	0.941102i	$0.609792\pi$
$600$		0			0
$601$	7.08294	−	12.2680i	0.288919	−	0.500423i	−0.684633	−	0.728888i	$-0.740037\pi$
$601$	7.08294	−	12.2680i	0.288919	−	0.500423i	0.973552	+	0.228465i	$0.0733707\pi$
$602$		0			0
$603$	7.72961	+	29.4395i	0.314774	+	1.19887i
$604$		0			0
$605$	−11.9992	−	6.92775i	−0.487837	−	0.281653i
$606$		0			0
$607$	−7.26079	+	4.19202i	−0.294706	+	0.170149i	−0.640062	−	0.768323i	$-0.721092\pi$
$607$	−7.26079	+	4.19202i	−0.294706	+	0.170149i	0.345356	+	0.938472i	$0.387758\pi$
$608$		0			0
$609$	19.9763	−	47.8856i	0.809479	−	1.94042i
$610$		0			0
$611$	−13.0269			−0.527011
$612$		0			0
$613$	−20.9574			−0.846462			−0.423231	−	0.906022i	$-0.639104\pi$
$613$	−20.9574			−0.846462			−0.423231	+	0.906022i	$0.639104\pi$
$614$		0			0
$615$	−38.4695	+	4.96609i	−1.55124	+	0.200252i
$616$		0			0
$617$	−25.5516	+	14.7522i	−1.02867	+	0.593903i	−0.916603	−	0.399798i	$-0.869080\pi$
$617$	−25.5516	+	14.7522i	−1.02867	+	0.593903i	−0.112066	+	0.993701i	$0.535747\pi$
$618$		0			0
$619$	−32.7743	−	18.9222i	−1.31731	−	0.760549i	−0.334015	−	0.942568i	$-0.608404\pi$
$619$	−32.7743	−	18.9222i	−1.31731	−	0.760549i	−0.983295	+	0.182019i	$0.941737\pi$
$620$		0			0
$621$	−3.09448	−	2.41183i	−0.124177	−	0.0967835i
$622$		0			0
$623$	7.95556	−	13.7794i	0.318733	−	0.552061i
$624$		0			0
$625$	5.09464	+	8.82417i	0.203786	+	0.352967i
$626$		0			0
$627$	−2.67507	−	20.7222i	−0.106832	−	0.827567i
$628$		0			0
$629$		−	7.14197i		−	0.284769i
$630$		0			0
$631$		−	15.9867i		−	0.636420i	−0.948020	−	0.318210i	$-0.896918\pi$
$631$		−	15.9867i		−	0.636420i	0.948020	−	0.318210i	$-0.103082\pi$
$632$		0			0
$633$	−10.1966	−	4.25368i	−0.405278	−	0.169068i
$634$		0			0
$635$	23.5658	+	40.8171i	0.935180	+	1.61978i
$636$		0			0
$637$	−14.1899	+	24.5776i	−0.562225	+	0.973802i
$638$		0			0
$639$	0.0577728	−	0.211348i	0.00228546	−	0.00836079i
$640$		0			0
$641$	28.3907	+	16.3914i	1.12136	+	0.647420i	0.941749	−	0.336317i	$-0.109181\pi$
$641$	28.3907	+	16.3914i	1.12136	+	0.647420i	0.179616	+	0.983737i	$0.442515\pi$
$642$		0			0
$643$	4.53896	−	2.62057i	0.178999	−	0.103345i	−0.407823	−	0.913061i	$-0.633712\pi$
$643$	4.53896	−	2.62057i	0.178999	−	0.103345i	0.586822	+	0.809716i	$0.300379\pi$
$644$		0			0
$645$	−32.0925	−	42.0426i	−1.26364	−	1.65542i
$646$		0			0
$647$	−30.4906			−1.19871			−0.599354	−	0.800484i	$-0.704576\pi$
$647$	−30.4906			−1.19871			−0.599354	+	0.800484i	$0.704576\pi$
$648$		0			0
$649$	−7.20848			−0.282958
$650$		0			0
$651$	8.50128	+	11.1370i	0.333191	+	0.436495i
$652$		0			0
$653$	21.9758	−	12.6877i	0.859980	−	0.496510i	−0.00402567	−	0.999992i	$-0.501281\pi$
$653$	21.9758	−	12.6877i	0.859980	−	0.496510i	0.864006	+	0.503482i	$0.167948\pi$
$654$		0			0
$655$	−47.4660	−	27.4045i	−1.85465	−	1.07078i
$656$		0			0
$657$	−10.5372	+	38.5479i	−0.411096	+	1.50390i
$658$		0			0
$659$	−16.6127	+	28.7740i	−0.647137	+	1.12087i	0.336666	+	0.941624i	$0.390701\pi$
$659$	−16.6127	+	28.7740i	−0.647137	+	1.12087i	−0.983803	+	0.179250i	$0.942633\pi$
$660$		0			0
$661$	−15.9993	−	27.7116i	−0.622301	−	1.07786i	−0.989056	−	0.147539i	$-0.952865\pi$
$661$	−15.9993	−	27.7116i	−0.622301	−	1.07786i	0.366755	−	0.930317i	$-0.380469\pi$
$662$		0			0
$663$	13.5399	+	5.64841i	0.525847	+	0.219366i
$664$		0			0
$665$		−	57.1088i		−	2.21458i
$666$		0			0
$667$		−	6.27199i		−	0.242852i
$668$		0			0
$669$	0.577056	+	4.47013i	0.0223103	+	0.172825i
$670$		0			0
$671$	−3.15595	−	5.46627i	−0.121834	−	0.211023i
$672$		0			0
$673$	−25.1871	+	43.6253i	−0.970891	+	1.68163i	−0.278013	+	0.960577i	$0.589676\pi$
$673$	−25.1871	+	43.6253i	−0.970891	+	1.68163i	−0.692878	+	0.721055i	$0.743658\pi$
$674$		0			0
$675$	5.08388	−	36.4840i	0.195679	−	1.40427i
$676$		0			0
$677$	29.1301	+	16.8183i	1.11956	+	0.646379i	0.941289	−	0.337603i	$-0.109616\pi$
$677$	29.1301	+	16.8183i	1.11956	+	0.646379i	0.178272	+	0.983981i	$0.442949\pi$
$678$		0			0
$679$	45.0884	−	26.0318i	1.73033	−	0.999009i
$680$		0			0
$681$	−36.8269	+	4.75405i	−1.41121	+	0.182176i
$682$		0			0
$683$	−12.2382			−0.468280			−0.234140	−	0.972203i	$-0.575227\pi$
$683$	−12.2382			−0.468280			−0.234140	+	0.972203i	$0.575227\pi$
$684$		0			0
$685$	−26.9045			−1.02797
$686$		0			0
$687$	−0.494216	+	1.18470i	−0.0188555	+	0.0451990i
$688$		0			0
$689$	−18.0583	+	10.4260i	−0.687967	+	0.397198i
$690$		0			0
$691$	29.2860	+	16.9083i	1.11409	+	0.643222i	0.939886	−	0.341487i	$-0.110931\pi$
$691$	29.2860	+	16.9083i	1.11409	+	0.643222i	0.174207	+	0.984709i	$0.444264\pi$
$692$		0			0
$693$	7.27682	+	27.7150i	0.276423	+	1.05281i
$694$		0			0
$695$	−0.984316	+	1.70488i	−0.0373372	+	0.0646700i
$696$		0			0
$697$	−5.77180	−	9.99704i	−0.218622	−	0.378665i
$698$		0			0
$699$	−28.0631	+	21.4216i	−1.06145	+	0.810238i
$700$		0			0
$701$			40.9032i			1.54489i	0.635079	+	0.772447i	$0.280967\pi$
$701$			40.9032i			1.54489i	−0.635079	+	0.772447i	$0.719033\pi$
$702$		0			0
$703$		−	18.1499i		−	0.684535i
$704$		0			0
$705$	−13.1948	+	10.0720i	−0.496945	+	0.379335i
$706$		0			0
$707$	3.93062	+	6.80804i	0.147826	+	0.256043i
$708$		0			0
$709$	0.286310	−	0.495903i	0.0107526	−	0.0186240i	−0.860599	−	0.509283i	$-0.829911\pi$
$709$	0.286310	−	0.495903i	0.0107526	−	0.0186240i	0.871352	+	0.490659i	$0.163244\pi$
$710$		0			0
$711$	11.1055	−	10.9942i	0.416490	−	0.412316i
$712$		0			0
$713$	1.46676	+	0.846832i	0.0549304	+	0.0317141i
$714$		0			0
$715$	−37.6916	+	21.7613i	−1.40959	+	0.813825i
$716$		0			0
$717$	−6.38798	+	15.3128i	−0.238564	+	0.571866i
$718$		0			0
$719$	−0.517752			−0.0193089			−0.00965445	−	0.999953i	$-0.503073\pi$
$719$	−0.517752			−0.0193089			−0.00965445	+	0.999953i	$0.503073\pi$
$720$		0			0
$721$	13.8692			0.516518
$722$		0			0
$723$	−10.9179	+	1.40941i	−0.406040	+	0.0524164i
$724$		0			0
$725$	50.9984	−	29.4440i	1.89403	−	1.09352i
$726$		0			0
$727$	7.28291	+	4.20479i	0.270108	+	0.155947i	0.628937	−	0.777456i	$-0.283490\pi$
$727$	7.28291	+	4.20479i	0.270108	+	0.155947i	−0.358829	+	0.933403i	$0.616824\pi$
$728$		0			0
$729$	19.3781	−	18.8013i	0.717709	−	0.696344i
$730$		0			0
$731$	7.87029	−	13.6318i	0.291093	−	0.504188i
$732$		0			0
$733$	−6.55945	−	11.3613i	−0.242279	−	0.419639i	0.719084	−	0.694923i	$-0.244562\pi$
$733$	−6.55945	−	11.3613i	−0.242279	−	0.419639i	−0.961363	+	0.275284i	$0.911228\pi$
$734$		0			0
$735$	4.62997	+	35.8657i	0.170779	+	1.32293i
$736$		0			0
$737$		−	26.8721i		−	0.989845i
$738$		0			0
$739$		−	9.78098i		−	0.359799i	−0.983685	−	0.179900i	$-0.942423\pi$
$739$		−	9.78098i		−	0.359799i	0.983685	−	0.179900i	$-0.0575773\pi$
$740$		0			0
$741$	34.4090	+	14.3543i	1.26404	+	0.527317i
$742$		0			0
$743$	−0.703207	−	1.21799i	−0.0257982	−	0.0446838i	0.852838	−	0.522175i	$-0.174879\pi$
$743$	−0.703207	−	1.21799i	−0.0257982	−	0.0446838i	−0.878636	+	0.477492i	$0.841546\pi$
$744$		0			0
$745$	−16.4410	+	28.4767i	−0.602352	+	1.04330i
$746$		0			0
$747$	−1.03355	−	1.04401i	−0.0378156	−	0.0381984i
$748$		0			0
$749$	60.6102	+	34.9933i	2.21465	+	1.27863i
$750$		0			0
$751$	−6.49013	+	3.74708i	−0.236828	+	0.136733i	−0.613718	−	0.789525i	$-0.710327\pi$
$751$	−6.49013	+	3.74708i	−0.236828	+	0.136733i	0.376890	+	0.926258i	$0.376993\pi$
$752$		0			0
$753$	28.4740	+	37.3022i	1.03765	+	1.35937i
$754$		0			0
$755$	66.3491			2.41469
$756$		0			0
$757$	−36.6513			−1.33211			−0.666057	−	0.745901i	$-0.732019\pi$
$757$	−36.6513			−1.33211			−0.666057	+	0.745901i	$0.732019\pi$
$758$		0			0
$759$	2.10170	+	2.75331i	0.0762868	+	0.0999389i
$760$		0			0
$761$	−30.5513	+	17.6388i	−1.10749	+	0.639407i	−0.938177	−	0.346156i	$-0.887487\pi$
$761$	−30.5513	+	17.6388i	−1.10749	+	0.639407i	−0.169308	+	0.985563i	$0.554153\pi$
$762$		0			0
$763$	−40.8942	−	23.6103i	−1.48047	−	0.854750i
$764$		0			0
$765$	18.0817	−	4.74750i	0.653744	−	0.171646i
$766$		0			0
$767$	6.43130	−	11.1393i	0.232221	−	0.402218i
$768$		0			0
$769$	−19.4694	−	33.7219i	−0.702083	−	1.21604i	−0.967734	−	0.251975i	$-0.918920\pi$
$769$	−19.4694	−	33.7219i	−0.702083	−	1.21604i	0.265650	−	0.964069i	$-0.414413\pi$
$770$		0			0
$771$	6.12260	+	2.55414i	0.220500	+	0.0919853i
$772$		0			0
$773$		−	47.4524i		−	1.70674i	−0.521303	−	0.853372i	$-0.674554\pi$
$773$		−	47.4524i		−	1.70674i	0.521303	−	0.853372i	$-0.325446\pi$
$774$		0			0
$775$			15.9019i			0.571212i
$776$		0			0
$777$	3.18675	+	24.6859i	0.114324	+	0.885603i
$778$		0			0
$779$	−14.6678	−	25.4054i	−0.525530	−	0.910244i
$780$		0			0
$781$	−0.0967186	+	0.167522i	−0.00346086	+	0.00599439i
$782$		0			0
$783$	42.7499	+	5.95699i	1.52776	+	0.212886i
$784$		0			0
$785$	−63.6432	−	36.7444i	−2.27152	−	1.31146i
$786$		0			0
$787$	19.0786	−	11.0150i	0.680078	−	0.392643i	−0.119806	−	0.992797i	$-0.538227\pi$
$787$	19.0786	−	11.0150i	0.680078	−	0.392643i	0.799884	+	0.600154i	$0.204894\pi$
$788$		0			0
$789$	−55.3091	+	7.13994i	−1.96906	+	0.254189i
$790$		0			0
$791$	−5.14192			−0.182826
$792$		0			0
$793$	11.2628			0.399953
$794$		0			0
$795$	−10.2300	+	24.5226i	−0.362821	+	0.869727i
$796$		0			0
$797$	7.74174	−	4.46970i	0.274227	−	0.158325i	−0.356580	−	0.934265i	$-0.616057\pi$
$797$	7.74174	−	4.46970i	0.274227	−	0.158325i	0.630807	+	0.775940i	$0.282724\pi$
$798$		0			0
$799$	−4.27824	−	2.47004i	−0.151353	−	0.0873838i
$800$		0			0
$801$	12.7679	+	3.49016i	0.451132	+	0.123319i
$802$		0			0
$803$	17.6406	−	30.5544i	0.622522	−	1.07824i
$804$		0			0
$805$	4.73368	+	8.19898i	0.166840	+	0.288976i
$806$		0			0
$807$	−37.5311	+	28.6488i	−1.32116	+	1.00849i
$808$		0			0
$809$			8.93421i			0.314110i	0.987590	+	0.157055i	$0.0502000\pi$
$809$			8.93421i			0.314110i	−0.987590	+	0.157055i	$0.949800\pi$
$810$		0			0
$811$		−	22.1717i		−	0.778552i	−0.921121	−	0.389276i	$-0.872725\pi$
$811$		−	22.1717i		−	0.778552i	0.921121	−	0.389276i	$-0.127275\pi$
$812$		0			0
$813$	11.6837	−	8.91853i	0.409764	−	0.312787i
$814$		0			0
$815$	39.4019	+	68.2461i	1.38019	+	2.39056i
$816$		0			0
$817$	20.0007	−	34.6423i	0.699737	−	1.21198i
$818$		0			0
$819$	−49.3205	−	13.4820i	−1.72340	−	0.471098i
$820$		0			0
$821$	1.83428	+	1.05902i	0.0640167	+	0.0369601i	0.531667	−	0.846954i	$-0.321566\pi$
$821$	1.83428	+	1.05902i	0.0640167	+	0.0369601i	−0.467650	+	0.883914i	$0.654899\pi$
$822$		0			0
$823$	20.3807	−	11.7668i	0.710428	−	0.410166i	−0.100792	−	0.994908i	$-0.532138\pi$
$823$	20.3807	−	11.7668i	0.710428	−	0.410166i	0.811219	+	0.584742i	$0.198804\pi$
$824$		0			0
$825$	−12.5211	+	30.0147i	−0.435929	+	1.04498i
$826$		0			0
$827$	15.3293			0.533051			0.266526	−	0.963828i	$-0.414124\pi$
$827$	15.3293			0.533051			0.266526	+	0.963828i	$0.414124\pi$
$828$		0			0
$829$	−6.88566			−0.239149			−0.119574	−	0.992825i	$-0.538153\pi$
$829$	−6.88566			−0.239149			−0.119574	+	0.992825i	$0.538153\pi$
$830$		0			0
$831$	−13.4165	+	1.73196i	−0.465415	+	0.0600812i
$832$		0			0
$833$	−9.32040	+	5.38114i	−0.322933	+	0.186445i
$834$		0			0
$835$	−17.6279	−	10.1775i	−0.610038	−	0.352205i
$836$		0			0
$837$	−7.16510	+	9.19311i	−0.247662	+	0.317760i
$838$		0			0
$839$	17.1856	−	29.7663i	0.593312	−	1.02765i	−0.400470	−	0.916310i	$-0.631153\pi$
$839$	17.1856	−	29.7663i	0.593312	−	1.02765i	0.993783	−	0.111337i	$-0.0355134\pi$
$840$		0			0
$841$	20.0007	+	34.6423i	0.689681	+	1.19456i
$842$		0			0
$843$	−1.54982	−	12.0056i	−0.0533786	−	0.413494i
$844$		0			0
$845$		−	32.4600i		−	1.11666i
$846$		0			0
$847$			14.3707i			0.493783i
$848$		0			0
$849$	44.8604	+	18.7143i	1.53961	+	0.642272i
$850$		0			0
$851$	1.50442	+	2.60574i	0.0515709	+	0.0893234i
$852$		0			0
$853$	−28.4800	+	49.3288i	−0.975136	+	1.68898i	−0.295650	+	0.955296i	$0.595536\pi$
$853$	−28.4800	+	49.3288i	−0.975136	+	1.68898i	−0.679486	+	0.733688i	$0.737797\pi$
$854$		0			0
$855$	45.9509	−	12.0648i	1.57149	−	0.412608i
$856$		0			0
$857$	12.9801	+	7.49405i	0.443391	+	0.255992i	0.705035	−	0.709172i	$-0.250931\pi$
$857$	12.9801	+	7.49405i	0.443391	+	0.255992i	−0.261644	+	0.965164i	$0.584265\pi$
$858$		0			0
$859$	37.3920	−	21.5883i	1.27580	−	0.736583i	0.299725	−	0.954025i	$-0.403105\pi$
$859$	37.3920	−	21.5883i	1.27580	−	0.736583i	0.976073	+	0.217443i	$0.0697716\pi$
$860$		0			0
$861$	24.4107	+	31.9790i	0.831913	+	1.08984i
$862$		0			0
$863$	48.9439			1.66607			0.833035	−	0.553220i	$-0.186601\pi$
$863$	48.9439			1.66607			0.833035	+	0.553220i	$0.186601\pi$
$864$		0			0
$865$	20.5522			0.698797
$866$		0			0
$867$	−14.4903	−	18.9829i	−0.492116	−	0.644693i
$868$		0			0
$869$	−11.9482	+	6.89830i	−0.405315	+	0.234009i
$870$		0			0
$871$	41.5257	+	23.9749i	1.40704	+	0.812357i
$872$		0			0
$873$	30.4711	+	30.7796i	1.03129	+	1.04173i
$874$		0			0
$875$	−13.0979	+	22.6863i	−0.442791	+	0.766936i
$876$		0			0
$877$	−14.4280	−	24.9901i	−0.487200	−	0.843854i	0.512692	−	0.858573i	$-0.328648\pi$
$877$	−14.4280	−	24.9901i	−0.487200	−	0.843854i	−0.999892	+	0.0147181i	$0.995315\pi$
$878$		0			0
$879$	−13.9331	−	5.81241i	−0.469950	−	0.196048i
$880$		0			0
$881$			10.9613i			0.369294i	0.982805	+	0.184647i	$0.0591143\pi$
$881$			10.9613i			0.369294i	−0.982805	+	0.184647i	$0.940886\pi$
$882$		0			0
$883$			23.8707i			0.803313i	0.915790	+	0.401657i	$0.131565\pi$
$883$			23.8707i			0.803313i	−0.915790	+	0.401657i	$0.868435\pi$
$884$		0			0
$885$	−2.09844	−	16.2555i	−0.0705384	−	0.546421i
$886$		0			0
$887$	27.2765	+	47.2442i	0.915854	+	1.58631i	0.805647	+	0.592397i	$0.201818\pi$
$887$	27.2765	+	47.2442i	0.915854	+	1.58631i	0.110207	+	0.993909i	$0.464849\pi$
$888$		0			0
$889$	24.4420	−	42.3349i	0.819760	−	1.41987i
$890$		0			0
$891$	−20.7627	+	11.7101i	−0.695578	+	0.392305i
$892$		0			0
$893$	−10.8723	−	6.27711i	−0.363826	−	0.210055i
$894$		0			0
$895$	38.7904	−	22.3956i	1.29662	−	0.748604i
$896$		0			0
$897$	−6.12983	+	0.791310i	−0.204669	+	0.0264211i
$898$		0			0
$899$	−18.6329			−0.621442
$900$		0			0
$901$	−7.90754			−0.263438
$902$		0			0
$903$	−21.1209	+	50.6293i	−0.702858	+	1.68484i
$904$		0			0
$905$	30.6938	−	17.7210i	1.02029	−	0.589068i
$906$		0			0
$907$	44.9556	+	25.9552i	1.49273	+	0.861827i	0.999965	−	0.00833717i	$-0.00265384\pi$
$907$	44.9556	+	25.9552i	1.49273	+	0.861827i	0.492762	+	0.870164i	$0.335987\pi$
$908$		0			0
$909$	−4.64750	+	4.60092i	−0.154148	+	0.152603i
$910$		0			0
$911$	27.0141	−	46.7897i	0.895016	−	1.55021i	0.0612304	−	0.998124i	$-0.480498\pi$
$911$	27.0141	−	46.7897i	0.895016	−	1.55021i	0.833785	−	0.552089i	$-0.186169\pi$
$912$		0			0
$913$	0.648497	+	1.12323i	0.0214621	+	0.0371735i
$914$		0			0
$915$	11.4080	−	8.70809i	0.377136	−	0.287881i
$916$		0			0
$917$			56.8470i			1.87725i
$918$		0			0
$919$			26.0348i			0.858808i	0.903113	+	0.429404i	$0.141276\pi$
$919$			26.0348i			0.858808i	−0.903113	+	0.429404i	$0.858724\pi$
$920$		0			0
$921$	−13.2498	+	10.1141i	−0.436597	+	0.333270i
$922$		0			0
$923$	−0.172582	−	0.298921i	−0.00568060	−	0.00983909i
$924$		0			0
$925$	−14.1251	+	24.4653i	−0.464429	+	0.804415i
$926$		0			0
$927$	2.93002	+	11.1595i	0.0962345	+	0.366525i
$928$		0			0
$929$	−33.1077	−	19.1148i	−1.08623	−	0.627135i	−0.153659	−	0.988124i	$-0.549106\pi$
$929$	−33.1077	−	19.1148i	−1.08623	−	0.627135i	−0.932570	+	0.360989i	$0.882439\pi$
$930$		0			0
$931$	−23.6859	+	13.6751i	−0.776274	+	0.448182i
$932$		0			0
$933$	11.0923	−	26.5895i	0.363144	−	0.870502i
$934$		0			0
$935$	−16.5047			−0.539763
$936$		0			0
$937$	−19.6872			−0.643154			−0.321577	−	0.946883i	$-0.604213\pi$
$937$	−19.6872			−0.643154			−0.321577	+	0.946883i	$0.604213\pi$
$938$		0			0
$939$	42.3103	−	5.46190i	1.38074	−	0.178242i
$940$		0			0
$941$	−26.5374	+	15.3214i	−0.865094	+	0.499462i	−0.865715	−	0.500537i	$-0.833136\pi$
$941$	−26.5374	+	15.3214i	−0.865094	+	0.499462i	0.000620548		1.00000i	$0.499802\pi$
$942$		0			0
$943$	4.21166	+	2.43160i	0.137150	+	0.0791838i
$944$		0			0
$945$	−60.3802	+	24.4776i	−1.96417	+	0.796256i
$946$		0			0
$947$	−16.8490	+	29.1833i	−0.547519	+	0.948331i	0.450925	+	0.892562i	$0.351094\pi$
$947$	−16.8490	+	29.1833i	−0.547519	+	0.948331i	−0.998444	+	0.0557689i	$0.982239\pi$
$948$		0			0
$949$	31.4773	+	54.5203i	1.02180	+	1.76980i
$950$		0			0
$951$	−5.34077	−	41.3719i	−0.173186	−	1.34158i
$952$		0			0
$953$		−	58.8965i		−	1.90784i	−0.300054	−	0.953922i	$-0.597005\pi$
$953$		−	58.8965i		−	1.90784i	0.300054	−	0.953922i	$-0.402995\pi$
$954$		0			0
$955$		−	78.5516i		−	2.54187i
$956$		0			0
$957$	−35.1695	−	14.6715i	−1.13687	−	0.474263i
$958$		0			0
$959$	13.9524	+	24.1663i	0.450548	+	0.780371i
$960$		0			0
$961$	−12.9842	+	22.4893i	−0.418846	+	0.725462i
$962$		0			0
$963$	−15.3518	+	56.1608i	−0.494705	+	1.80976i
$964$		0			0
$965$	6.80126	+	3.92671i	0.218940	+	0.126405i
$966$		0			0
$967$	−0.153116	+	0.0884018i	−0.00492389	+	0.00284281i	−0.502460	−	0.864600i	$-0.667572\pi$
$967$	−0.153116	+	0.0884018i	−0.00492389	+	0.00284281i	0.497536	+	0.867443i	$0.334238\pi$
$968$		0			0
$969$	8.57874	+	11.2385i	0.275589	+	0.361033i
$970$		0			0
$971$	−8.94370			−0.287017			−0.143509	−	0.989649i	$-0.545838\pi$
$971$	−8.94370			−0.287017			−0.143509	+	0.989649i	$0.545838\pi$
$972$		0			0
$973$	2.04183			0.0654581
$974$		0			0
$975$	−35.2108	−	46.1277i	−1.12765	−	1.47727i
$976$		0			0
$977$	1.61238	−	0.930909i	0.0515847	−	0.0297824i	−0.473986	−	0.880532i	$-0.657185\pi$
$977$	1.61238	−	0.930909i	0.0515847	−	0.0297824i	0.525571	+	0.850750i	$0.323852\pi$
$978$		0			0
$979$	−10.1203	−	5.84294i	−0.323445	−	0.186741i
$980$		0			0
$981$	10.3580	−	37.8922i	0.330705	−	1.20981i
$982$		0			0
$983$	−8.41816	+	14.5807i	−0.268498	+	0.465052i	−0.968474	−	0.249114i	$-0.919861\pi$
$983$	−8.41816	+	14.5807i	−0.268498	+	0.465052i	0.699976	+	0.714166i	$0.253194\pi$
$984$		0			0
$985$	9.83431	+	17.0335i	0.313347	+	0.542733i
$986$		0			0
$987$	15.8897	+	6.62865i	0.505774	+	0.210992i
$988$		0			0
$989$			6.63136i			0.210865i
$990$		0			0
$991$			15.9182i			0.505658i	0.967511	+	0.252829i	$0.0813609\pi$
$991$			15.9182i			0.505658i	−0.967511	+	0.252829i	$0.918639\pi$
$992$		0			0
$993$	−2.84440	−	22.0340i	−0.0902643	−	0.699226i
$994$		0			0
$995$	−24.0245	−	41.6116i	−0.761626	−	1.31918i
$996$		0			0
$997$	−3.40192	+	5.89230i	−0.107740	+	0.186611i	−0.914854	−	0.403784i	$-0.867695\pi$
$997$	−3.40192	+	5.89230i	−0.107740	+	0.186611i	0.807114	+	0.590395i	$0.201028\pi$
$998$		0			0
$999$	−19.1896	+	7.77928i	−0.607131	+	0.246125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.s.a.191.4	yes	24
3.2	odd	2		864.2.s.a.575.12		24
4.3	odd	2	inner	288.2.s.a.191.9	yes	24
8.3	odd	2		576.2.s.g.191.4		24
8.5	even	2		576.2.s.g.191.9		24
9.2	odd	6		2592.2.c.c.2591.21		24
9.4	even	3		864.2.s.a.287.11		24
9.5	odd	6	inner	288.2.s.a.95.9	yes	24
9.7	even	3		2592.2.c.c.2591.3		24
12.11	even	2		864.2.s.a.575.11		24
24.5	odd	2		1728.2.s.g.575.2		24
24.11	even	2		1728.2.s.g.575.1		24
36.7	odd	6		2592.2.c.c.2591.4		24
36.11	even	6		2592.2.c.c.2591.22		24
36.23	even	6	inner	288.2.s.a.95.4	✓	24
36.31	odd	6		864.2.s.a.287.12		24
72.5	odd	6		576.2.s.g.383.4		24
72.11	even	6		5184.2.c.m.5183.4		24
72.13	even	6		1728.2.s.g.1151.1		24
72.29	odd	6		5184.2.c.m.5183.3		24
72.43	odd	6		5184.2.c.m.5183.22		24
72.59	even	6		576.2.s.g.383.9		24
72.61	even	6		5184.2.c.m.5183.21		24
72.67	odd	6		1728.2.s.g.1151.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.4	✓	24	36.23	even	6	inner
288.2.s.a.95.9	yes	24	9.5	odd	6	inner
288.2.s.a.191.4	yes	24	1.1	even	1	trivial
288.2.s.a.191.9	yes	24	4.3	odd	2	inner
576.2.s.g.191.4		24	8.3	odd	2
576.2.s.g.191.9		24	8.5	even	2
576.2.s.g.383.4		24	72.5	odd	6
576.2.s.g.383.9		24	72.59	even	6
864.2.s.a.287.11		24	9.4	even	3
864.2.s.a.287.12		24	36.31	odd	6
864.2.s.a.575.11		24	12.11	even	2
864.2.s.a.575.12		24	3.2	odd	2
1728.2.s.g.575.1		24	24.11	even	2
1728.2.s.g.575.2		24	24.5	odd	2
1728.2.s.g.1151.1		24	72.13	even	6
1728.2.s.g.1151.2		24	72.67	odd	6
2592.2.c.c.2591.3		24	9.7	even	3
2592.2.c.c.2591.4		24	36.7	odd	6
2592.2.c.c.2591.21		24	9.2	odd	6
2592.2.c.c.2591.22		24	36.11	even	6
5184.2.c.m.5183.3		24	72.29	odd	6
5184.2.c.m.5183.4		24	72.11	even	6
5184.2.c.m.5183.21		24	72.61	even	6
5184.2.c.m.5183.22		24	72.43	odd	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05094 - 1.37678i) q^{3} +(-3.01113 + 1.73848i) q^{5} +(3.12309 + 1.80312i) q^{7} +(-0.791040 + 2.89383i) q^{9} +O(q^{10})\)	\(q+(-1.05094 - 1.37678i) q^{3} +(-3.01113 + 1.73848i) q^{5} +(3.12309 + 1.80312i) q^{7} +(-0.791040 + 2.89383i) q^{9} +(1.32430 - 2.29375i) q^{11} +(2.36304 + 4.09290i) q^{13} +(5.55802 + 2.31862i) q^{15} +1.79223i q^{17} +4.55459i q^{19} +(-0.799695 - 6.19478i) q^{21} +(-0.377525 - 0.653893i) q^{23} +(3.54460 - 6.13942i) q^{25} +(4.81550 - 1.95216i) q^{27} +(7.19382 + 4.15336i) q^{29} +(-1.94259 + 1.12156i) q^{31} +(-4.54974 + 0.587334i) q^{33} -12.5387 q^{35} -3.98496 q^{37} +(3.15160 - 7.55478i) q^{39} +(-5.57798 + 3.22045i) q^{41} +(-7.60601 - 4.39133i) q^{43} +(-2.64893 - 10.0889i) q^{45} +(-1.37819 + 2.38710i) q^{47} +(3.00247 + 5.20044i) q^{49} +(2.46751 - 1.88353i) q^{51} +4.41211i q^{53} +9.20903i q^{55} +(6.27067 - 4.78662i) q^{57} +(-1.36081 - 2.35700i) q^{59} +(1.19156 - 2.06384i) q^{61} +(-7.68841 + 7.61136i) q^{63} +(-14.2308 - 8.21616i) q^{65} +(8.78651 - 5.07289i) q^{67} +(-0.503509 + 1.20697i) q^{69} -0.0730340 q^{71} +13.3207 q^{73} +(-12.1778 + 1.57205i) q^{75} +(8.27180 - 4.77573i) q^{77} +(-4.51115 - 2.60452i) q^{79} +(-7.74851 - 4.57827i) q^{81} +(-0.244846 + 0.424085i) q^{83} +(-3.11576 - 5.39665i) q^{85} +(-1.84204 - 14.2692i) q^{87} -4.41211i q^{89} +17.0433i q^{91} +(3.58569 + 1.49583i) q^{93} +(-7.91805 - 13.7145i) q^{95} +(7.21855 - 12.5029i) q^{97} +(5.59015 + 5.64674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more