LMFDB - Embedded newform 576.2.y.a.335.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.8
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03912 - 1.38573i) q^{3} +(1.15827 + 0.310357i) q^{5} +(-0.356047 + 0.616691i) q^{7} +(-0.840471 + 2.87986i) q^{9} +O(q^{10})$	\(q+(-1.03912 - 1.38573i) q^{3} +(1.15827 + 0.310357i) q^{5} +(-0.356047 + 0.616691i) q^{7} +(-0.840471 + 2.87986i) q^{9} +(2.28146 - 0.611314i) q^{11} +(4.90394 + 1.31401i) q^{13} +(-0.773508 - 1.92754i) q^{15} -0.863180i q^{17} +(0.539682 + 0.539682i) q^{19} +(1.22454 - 0.147431i) q^{21} +(0.689728 - 0.398215i) q^{23} +(-3.08486 - 1.78104i) q^{25} +(4.86405 - 1.82785i) q^{27} +(8.31534 - 2.22809i) q^{29} +(4.18508 - 2.41626i) q^{31} +(-3.21781 - 2.52625i) q^{33} +(-0.603793 + 0.603793i) q^{35} +(-6.95600 - 6.95600i) q^{37} +(-3.27492 - 8.16093i) q^{39} +(-3.17027 - 5.49108i) q^{41} +(3.22509 + 12.0362i) q^{43} +(-1.86728 + 3.07481i) q^{45} +(-1.31575 + 2.27895i) q^{47} +(3.24646 + 5.62304i) q^{49} +(-1.19613 + 0.896946i) q^{51} +(8.87081 - 8.87081i) q^{53} +2.83227 q^{55} +(0.187058 - 1.30864i) q^{57} +(3.40363 - 12.7025i) q^{59} +(-0.146922 - 0.548319i) q^{61} +(-1.47674 - 1.54368i) q^{63} +(5.27228 + 3.04395i) q^{65} +(-1.84784 + 6.89625i) q^{67} +(-1.26852 - 0.541982i) q^{69} -3.03550i q^{71} +11.6817i q^{73} +(0.737491 + 6.12548i) q^{75} +(-0.435313 + 1.62461i) q^{77} +(0.841919 + 0.486082i) q^{79} +(-7.58722 - 4.84088i) q^{81} +(2.99289 + 11.1696i) q^{83} +(0.267894 - 0.999796i) q^{85} +(-11.7281 - 9.20754i) q^{87} -4.35531 q^{89} +(-2.55637 + 2.55637i) q^{91} +(-7.69706 - 3.28860i) q^{93} +(0.457603 + 0.792591i) q^{95} +(-2.89654 + 5.01695i) q^{97} +(-0.156998 + 7.08407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.03912	−	1.38573i	−0.599935	−	0.800049i
$3$	−1.03912	−	1.38573i	−0.599935	−	0.800049i
$4$		0			0
$5$	1.15827	+	0.310357i	0.517994	+	0.138796i	0.508339	−	0.861157i	$-0.330260\pi$
$5$	1.15827	+	0.310357i	0.517994	+	0.138796i	0.00965542	+	0.999953i	$0.496927\pi$
$6$		0			0
$7$	−0.356047	+	0.616691i	−0.134573	+	0.233087i	−0.925434	−	0.378908i	$-0.876300\pi$
$7$	−0.356047	+	0.616691i	−0.134573	+	0.233087i	0.790861	+	0.611996i	$0.209633\pi$
$8$		0			0
$9$	−0.840471	+	2.87986i	−0.280157	+	0.959954i
$10$		0			0
$11$	2.28146	−	0.611314i	0.687885	−	0.184318i	0.102087	−	0.994775i	$-0.467448\pi$
$11$	2.28146	−	0.611314i	0.687885	−	0.184318i	0.585798	+	0.810457i	$0.300781\pi$
$12$		0			0
$13$	4.90394	+	1.31401i	1.36011	+	0.364440i	0.863857	−	0.503738i	$-0.168042\pi$
$13$	4.90394	+	1.31401i	1.36011	+	0.364440i	0.496253	+	0.868178i	$0.334709\pi$
$14$		0			0
$15$	−0.773508	−	1.92754i	−0.199719	−	0.497689i
$16$		0			0
$17$		−	0.863180i		−	0.209352i	−0.994506	−	0.104676i	$-0.966619\pi$
$17$		−	0.863180i		−	0.209352i	0.994506	−	0.104676i	$-0.0333806\pi$
$18$		0			0
$19$	0.539682	+	0.539682i	0.123811	+	0.123811i	0.766297	−	0.642486i	$-0.222097\pi$
$19$	0.539682	+	0.539682i	0.123811	+	0.123811i	−0.642486	+	0.766297i	$0.722097\pi$
$20$		0			0
$21$	1.22454	−	0.147431i	0.267216	−	0.0321721i
$22$		0			0
$23$	0.689728	−	0.398215i	0.143818	−	0.0830335i	−0.426364	−	0.904552i	$-0.640206\pi$
$23$	0.689728	−	0.398215i	0.143818	−	0.0830335i	0.570182	+	0.821518i	$0.306872\pi$
$24$		0			0
$25$	−3.08486	−	1.78104i	−0.616972	−	0.356209i
$26$		0			0
$27$	4.86405	−	1.82785i	0.936086	−	0.351770i
$28$		0			0
$29$	8.31534	−	2.22809i	1.54412	−	0.413746i	0.616526	−	0.787335i	$-0.288540\pi$
$29$	8.31534	−	2.22809i	1.54412	−	0.413746i	0.927594	+	0.373589i	$0.121873\pi$
$30$		0			0
$31$	4.18508	−	2.41626i	0.751663	−	0.433973i	−0.0746314	−	0.997211i	$-0.523778\pi$
$31$	4.18508	−	2.41626i	0.751663	−	0.433973i	0.826295	+	0.563238i	$0.190445\pi$
$32$		0			0
$33$	−3.21781	−	2.52625i	−0.560150	−	0.439763i
$34$		0			0
$35$	−0.603793	+	0.603793i	−0.102060	+	0.102060i
$36$		0			0
$37$	−6.95600	−	6.95600i	−1.14356	−	1.14356i	−0.987794	−	0.155765i	$-0.950216\pi$
$37$	−6.95600	−	6.95600i	−1.14356	−	1.14356i	−0.155765	−	0.987794i	$-0.549784\pi$
$38$		0			0
$39$	−3.27492	−	8.16093i	−0.524407	−	1.30679i
$40$		0			0
$41$	−3.17027	−	5.49108i	−0.495114	−	0.857562i	0.504870	−	0.863195i	$-0.331540\pi$
$41$	−3.17027	−	5.49108i	−0.495114	−	0.857562i	−0.999984	+	0.00563304i	$0.998207\pi$
$42$		0			0
$43$	3.22509	+	12.0362i	0.491822	+	1.83550i	0.547150	+	0.837035i	$0.315713\pi$
$43$	3.22509	+	12.0362i	0.491822	+	1.83550i	−0.0553283	+	0.998468i	$0.517621\pi$
$44$		0			0
$45$	−1.86728	+	3.07481i	−0.278358	+	0.458366i
$46$		0			0
$47$	−1.31575	+	2.27895i	−0.191923	+	0.332420i	−0.945887	−	0.324495i	$-0.894806\pi$
$47$	−1.31575	+	2.27895i	−0.191923	+	0.332420i	0.753965	+	0.656915i	$0.228139\pi$
$48$		0			0
$49$	3.24646	+	5.62304i	0.463780	+	0.803291i
$50$		0			0
$51$	−1.19613	+	0.896946i	−0.167492	+	0.125597i
$52$		0			0
$53$	8.87081	−	8.87081i	1.21850	−	1.21850i	0.250342	−	0.968157i	$-0.419457\pi$
$53$	8.87081	−	8.87081i	1.21850	−	1.21850i	0.968157	−	0.250342i	$-0.0805431\pi$
$54$		0			0
$55$	2.83227			0.381903
$56$		0			0
$57$	0.187058	−	1.30864i	0.0247765	−	0.173334i
$58$		0			0
$59$	3.40363	−	12.7025i	0.443115	−	1.65373i	−0.277749	−	0.960654i	$-0.589588\pi$
$59$	3.40363	−	12.7025i	0.443115	−	1.65373i	0.720865	−	0.693076i	$-0.243745\pi$
$60$		0			0
$61$	−0.146922	−	0.548319i	−0.0188114	−	0.0702051i	0.955882	−	0.293751i	$-0.0949035\pi$
$61$	−0.146922	−	0.548319i	−0.0188114	−	0.0702051i	−0.974693	+	0.223546i	$0.928237\pi$
$62$		0			0
$63$	−1.47674	−	1.54368i	−0.186052	−	0.194485i
$64$		0			0
$65$	5.27228	+	3.04395i	0.653946	+	0.377556i
$66$		0			0
$67$	−1.84784	+	6.89625i	−0.225750	+	0.842511i	0.756352	+	0.654164i	$0.226980\pi$
$67$	−1.84784	+	6.89625i	−0.225750	+	0.842511i	−0.982103	+	0.188347i	$0.939687\pi$
$68$		0			0
$69$	−1.26852	−	0.541982i	−0.152712	−	0.0652470i
$70$		0			0
$71$		−	3.03550i		−	0.360248i	−0.983644	−	0.180124i	$-0.942350\pi$
$71$		−	3.03550i		−	0.360248i	0.983644	−	0.180124i	$-0.0576499\pi$
$72$		0			0
$73$			11.6817i			1.36724i	0.729839	+	0.683619i	$0.239595\pi$
$73$			11.6817i			1.36724i	−0.729839	+	0.683619i	$0.760405\pi$
$74$		0			0
$75$	0.737491	+	6.12548i	0.0851581	+	0.707310i
$76$		0			0
$77$	−0.435313	+	1.62461i	−0.0496085	+	0.185142i
$78$		0			0
$79$	0.841919	+	0.486082i	0.0947233	+	0.0546885i	0.546613	−	0.837385i	$-0.315917\pi$
$79$	0.841919	+	0.486082i	0.0947233	+	0.0546885i	−0.451890	+	0.892074i	$0.649250\pi$
$80$		0			0
$81$	−7.58722	−	4.84088i	−0.843024	−	0.537876i
$82$		0			0
$83$	2.99289	+	11.1696i	0.328512	+	1.22602i	0.910734	+	0.412994i	$0.135517\pi$
$83$	2.99289	+	11.1696i	0.328512	+	1.22602i	−0.582221	+	0.813030i	$0.697816\pi$
$84$		0			0
$85$	0.267894	−	0.999796i	0.0290572	−	0.108443i
$86$		0			0
$87$	−11.7281	−	9.20754i	−1.25739	−	0.987152i
$88$		0			0
$89$	−4.35531			−0.461662			−0.230831	−	0.972994i	$-0.574144\pi$
$89$	−4.35531			−0.461662			−0.230831	+	0.972994i	$0.574144\pi$
$90$		0			0
$91$	−2.55637	+	2.55637i	−0.267981	+	0.267981i
$92$		0			0
$93$	−7.69706	−	3.28860i	−0.798148	−	0.341012i
$94$		0			0
$95$	0.457603	+	0.792591i	0.0469490	+	0.0813181i
$96$		0			0
$97$	−2.89654	+	5.01695i	−0.294099	+	0.509395i	−0.974775	−	0.223190i	$-0.928353\pi$
$97$	−2.89654	+	5.01695i	−0.294099	+	0.509395i	0.680676	+	0.732585i	$0.261686\pi$
$98$		0			0
$99$	−0.156998	+	7.08407i	−0.0157789	+	0.711976i
$100$		0			0
$101$	2.41480	+	9.01216i	0.240282	+	0.896744i	0.975696	+	0.219127i	$0.0703207\pi$
$101$	2.41480	+	9.01216i	0.240282	+	0.896744i	−0.735415	+	0.677617i	$0.763013\pi$
$102$		0			0
$103$	2.02100	+	3.50047i	0.199135	+	0.344911i	0.948248	−	0.317530i	$-0.102854\pi$
$103$	2.02100	+	3.50047i	0.199135	+	0.344911i	−0.749113	+	0.662442i	$0.769520\pi$
$104$		0			0
$105$	1.46410	+	0.209280i	0.142882	+	0.0204236i
$106$		0			0
$107$	−7.91703	−	7.91703i	−0.765368	−	0.765368i	0.211919	−	0.977287i	$-0.432029\pi$
$107$	−7.91703	−	7.91703i	−0.765368	−	0.765368i	−0.977287	+	0.211919i	$0.932029\pi$
$108$		0			0
$109$	−8.25467	+	8.25467i	−0.790654	+	0.790654i	−0.981600	−	0.190946i	$-0.938844\pi$
$109$	−8.25467	+	8.25467i	−0.790654	+	0.790654i	0.190946	+	0.981600i	$0.438844\pi$
$110$		0			0
$111$	−2.41101	+	16.8672i	−0.228843	+	1.60096i
$112$		0			0
$113$	−6.70455	+	3.87087i	−0.630711	+	0.364141i	−0.781027	−	0.624497i	$-0.785304\pi$
$113$	−6.70455	+	3.87087i	−0.630711	+	0.364141i	0.150316	+	0.988638i	$0.451971\pi$
$114$		0			0
$115$	0.922480	−	0.247178i	0.0860217	−	0.0230494i
$116$		0			0
$117$	−7.90579	+	13.0183i	−0.730890	+	1.20354i
$118$		0			0
$119$	0.532316	+	0.307333i	0.0487973	+	0.0281731i
$120$		0			0
$121$	−4.69494	+	2.71063i	−0.426813	+	0.246421i
$122$		0			0
$123$	−4.31484	+	10.0990i	−0.389056	+	0.910596i
$124$		0			0
$125$	−7.25990	−	7.25990i	−0.649345	−	0.649345i
$126$		0			0
$127$		−	7.21656i		−	0.640366i	−0.947356	−	0.320183i	$-0.896256\pi$
$127$		−	7.21656i		−	0.640366i	0.947356	−	0.320183i	$-0.103744\pi$
$128$		0			0
$129$	13.3276	−	16.9761i	1.17343	−	1.49466i
$130$		0			0
$131$	−5.83309	−	1.56297i	−0.509640	−	0.136558i	−0.00516943	−	0.999987i	$-0.501645\pi$
$131$	−5.83309	−	1.56297i	−0.509640	−	0.136558i	−0.504470	+	0.863429i	$0.668312\pi$
$132$		0			0
$133$	−0.524969	+	0.140665i	−0.0455206	+	0.0121972i
$134$		0			0
$135$	6.20117	−	0.607551i	0.533711	−	0.0522897i
$136$		0			0
$137$	−2.72483	+	4.71954i	−0.232798	+	0.403217i	−0.958630	−	0.284654i	$-0.908121\pi$
$137$	−2.72483	+	4.71954i	−0.232798	+	0.403217i	0.725833	+	0.687871i	$0.241455\pi$
$138$		0			0
$139$	−14.3793	−	3.85291i	−1.21963	−	0.326800i	−0.409098	−	0.912490i	$-0.634157\pi$
$139$	−14.3793	−	3.85291i	−1.21963	−	0.326800i	−0.810534	+	0.585691i	$0.800823\pi$
$140$		0			0
$141$	4.52523	−	0.544825i	0.381093	−	0.0458825i
$142$		0			0
$143$	11.9914			1.00277
$144$		0			0
$145$	10.3229			0.857271
$146$		0			0
$147$	4.41853	−	10.3417i	0.364434	−	0.852969i
$148$		0			0
$149$	11.1485	+	2.98723i	0.913321	+	0.244724i	0.684728	−	0.728798i	$-0.259921\pi$
$149$	11.1485	+	2.98723i	0.913321	+	0.244724i	0.228593	+	0.973522i	$0.426588\pi$
$150$		0			0
$151$	−4.79677	+	8.30825i	−0.390355	+	0.676116i	−0.992496	−	0.122274i	$-0.960981\pi$
$151$	−4.79677	+	8.30825i	−0.390355	+	0.676116i	0.602141	+	0.798390i	$0.294315\pi$
$152$		0			0
$153$	2.48584	+	0.725479i	0.200968	+	0.0586515i
$154$		0			0
$155$	5.59736	−	1.49981i	0.449591	−	0.120467i
$156$		0			0
$157$	10.5494	+	2.82669i	0.841931	+	0.225595i	0.653912	−	0.756571i	$-0.273127\pi$
$157$	10.5494	+	2.82669i	0.841931	+	0.225595i	0.188019	+	0.982165i	$0.439793\pi$
$158$		0			0
$159$	−21.5103	−	3.07470i	−1.70588	−	0.243840i
$160$		0			0
$161$			0.567132i			0.0446963i
$162$		0			0
$163$	−10.4644	−	10.4644i	−0.819633	−	0.819633i	0.166422	−	0.986055i	$-0.446779\pi$
$163$	−10.4644	−	10.4644i	−0.819633	−	0.819633i	−0.986055	+	0.166422i	$0.946779\pi$
$164$		0			0
$165$	−2.94306	−	3.92475i	−0.229117	−	0.305541i
$166$		0			0
$167$	−11.5061	+	6.64303i	−0.890367	+	0.514053i	−0.874062	−	0.485814i	$-0.838523\pi$
$167$	−11.5061	+	6.64303i	−0.890367	+	0.514053i	−0.0163043	+	0.999867i	$0.505190\pi$
$168$		0			0
$169$	11.0637	+	6.38764i	0.851056	+	0.491357i
$170$		0			0
$171$	−2.00780	+	1.10062i	−0.153540	+	0.0841667i
$172$		0			0
$173$	−7.28191	+	1.95118i	−0.553633	+	0.148346i	−0.524780	−	0.851238i	$-0.675852\pi$
$173$	−7.28191	+	1.95118i	−0.553633	+	0.148346i	−0.0288536	+	0.999584i	$0.509186\pi$
$174$		0			0
$175$	2.19671	−	1.26827i	0.166056	−	0.0958723i
$176$		0			0
$177$	−21.1390	+	8.48292i	−1.58890	+	0.637615i
$178$		0			0
$179$	15.1045	−	15.1045i	1.12896	−	1.12896i	0.138617	−	0.990346i	$-0.455734\pi$
$179$	15.1045	−	15.1045i	1.12896	−	1.12896i	0.990346	−	0.138617i	$-0.0442657\pi$
$180$		0			0
$181$	−3.08895	−	3.08895i	−0.229600	−	0.229600i	0.582926	−	0.812525i	$-0.301908\pi$
$181$	−3.08895	−	3.08895i	−0.229600	−	0.229600i	−0.812525	+	0.582926i	$0.801908\pi$
$182$		0			0
$183$	−0.607151	+	0.773361i	−0.0448819	+	0.0571685i
$184$		0			0
$185$	−5.89808	−	10.2158i	−0.433635	−	0.751078i
$186$		0			0
$187$	−0.527675	−	1.96931i	−0.0385874	−	0.144010i
$188$		0			0
$189$	−0.604609	+	3.65042i	−0.0439788	+	0.265529i
$190$		0			0
$191$	2.50481	−	4.33846i	0.181242	−	0.313920i	−0.761062	−	0.648679i	$-0.775322\pi$
$191$	2.50481	−	4.33846i	0.181242	−	0.313920i	0.942304	+	0.334759i	$0.108655\pi$
$192$		0			0
$193$	−2.87512	−	4.97985i	−0.206956	−	0.358457i	0.743799	−	0.668404i	$-0.233022\pi$
$193$	−2.87512	−	4.97985i	−0.206956	−	0.358457i	−0.950754	+	0.309946i	$0.899689\pi$
$194$		0			0
$195$	−1.26043	−	10.4690i	−0.0902615	−	0.749697i
$196$		0			0
$197$	0.515447	−	0.515447i	0.0367240	−	0.0367240i	−0.688506	−	0.725230i	$-0.741733\pi$
$197$	0.515447	−	0.515447i	0.0367240	−	0.0367240i	0.725230	+	0.688506i	$0.241733\pi$
$198$		0			0
$199$	21.6583			1.53532			0.767659	−	0.640858i	$-0.221421\pi$
$199$	21.6583			1.53532			0.767659	+	0.640858i	$0.221421\pi$
$200$		0			0
$201$	11.4764	−	4.60541i	0.809486	−	0.324840i
$202$		0			0
$203$	−1.58661	+	5.92130i	−0.111358	+	0.415594i
$204$		0			0
$205$	−1.96784	−	7.34407i	−0.137440	−	0.512932i
$206$		0			0
$207$	0.567107	+	2.32101i	0.0394166	+	0.161321i
$208$		0			0
$209$	1.56118	+	0.901345i	0.107989	+	0.0623473i
$210$		0			0
$211$	0.602272	−	2.24771i	0.0414621	−	0.154739i	−0.942091	−	0.335357i	$-0.891143\pi$
$211$	0.602272	−	2.24771i	0.0414621	−	0.154739i	0.983553	+	0.180618i	$0.0578098\pi$
$212$		0			0
$213$	−4.20637	+	3.15424i	−0.288216	+	0.216125i
$214$		0			0
$215$			14.9421i			1.01904i
$216$		0			0
$217$			3.44121i			0.233604i
$218$		0			0
$219$	16.1876	−	12.1386i	1.09386	−	0.820253i
$220$		0			0
$221$	1.13423	−	4.23299i	0.0762963	−	0.284742i
$222$		0			0
$223$	−16.3604	−	9.44569i	−1.09557	−	0.632530i	−0.160520	−	0.987033i	$-0.551317\pi$
$223$	−16.3604	−	9.44569i	−1.09557	−	0.632530i	−0.935055	+	0.354502i	$0.884650\pi$
$224$		0			0
$225$	7.72190	−	7.38706i	0.514793	−	0.492470i
$226$		0			0
$227$	−2.11189	−	7.88169i	−0.140171	−	0.523126i	−0.999923	−	0.0124139i	$-0.996048\pi$
$227$	−2.11189	−	7.88169i	−0.140171	−	0.523126i	0.859752	−	0.510712i	$-0.170618\pi$
$228$		0			0
$229$	1.95948	−	7.31287i	0.129486	−	0.483248i	−0.870474	−	0.492215i	$-0.836187\pi$
$229$	1.95948	−	7.31287i	0.129486	−	0.483248i	0.999960	+	0.00896646i	$0.00285415\pi$
$230$		0			0
$231$	2.70361	−	1.08494i	0.177884	−	0.0713836i
$232$		0			0
$233$	−6.77947			−0.444138			−0.222069	−	0.975031i	$-0.571281\pi$
$233$	−6.77947			−0.444138			−0.222069	+	0.975031i	$0.571281\pi$
$234$		0			0
$235$	−2.23129	+	2.23129i	−0.145553	+	0.145553i
$236$		0			0
$237$	−0.201276	−	1.67177i	−0.0130743	−	0.108593i
$238$		0			0
$239$	9.48431	+	16.4273i	0.613489	+	1.06259i	0.990648	+	0.136445i	$0.0435677\pi$
$239$	9.48431	+	16.4273i	0.613489	+	1.06259i	−0.377159	+	0.926149i	$0.623099\pi$
$240$		0			0
$241$	0.0512556	−	0.0887774i	0.00330167	−	0.00571865i	−0.864370	−	0.502857i	$-0.832282\pi$
$241$	0.0512556	−	0.0887774i	0.00330167	−	0.00571865i	0.867672	+	0.497138i	$0.165616\pi$
$242$		0			0
$243$	1.17587	+	15.5440i	0.0754319	+	0.997151i
$244$		0			0
$245$	2.01513	+	7.52056i	0.128742	+	0.480471i
$246$		0			0
$247$	1.93742	+	3.35571i	0.123275	+	0.213519i
$248$		0			0
$249$	12.3681	−	15.7539i	0.783794	−	0.998360i
$250$		0			0
$251$	−6.59142	−	6.59142i	−0.416047	−	0.416047i	0.467792	−	0.883839i	$-0.345050\pi$
$251$	−6.59142	−	6.59142i	−0.416047	−	0.416047i	−0.883839	+	0.467792i	$0.845050\pi$
$252$		0			0
$253$	1.33015	−	1.33015i	0.0836258	−	0.0836258i
$254$		0			0
$255$	−1.66382	+	0.667677i	−0.104192	+	0.0418115i
$256$		0			0
$257$	−14.3072	+	8.26024i	−0.892456	+	0.515260i	−0.874745	−	0.484583i	$-0.838971\pi$
$257$	−14.3072	+	8.26024i	−0.892456	+	0.515260i	−0.0177109	+	0.999843i	$0.505638\pi$
$258$		0			0
$259$	6.76637	−	1.81304i	0.420442	−	0.112657i
$260$		0			0
$261$	−0.572217	+	25.8197i	−0.0354194	+	1.59820i
$262$		0			0
$263$	22.2913	+	12.8699i	1.37454	+	0.793593i	0.991496	−	0.130136i	$-0.0415415\pi$
$263$	22.2913	+	12.8699i	1.37454	+	0.793593i	0.383047	+	0.923729i	$0.374875\pi$
$264$		0			0
$265$	13.0279	−	7.52167i	0.800298	−	0.462052i
$266$		0			0
$267$	4.52567	+	6.03526i	0.276967	+	0.369352i
$268$		0			0
$269$	4.62506	+	4.62506i	0.281995	+	0.281995i	0.833904	−	0.551909i	$-0.186101\pi$
$269$	4.62506	+	4.62506i	0.281995	+	0.281995i	−0.551909	+	0.833904i	$0.686101\pi$
$270$		0			0
$271$			6.13012i			0.372378i	0.982514	+	0.186189i	$0.0596137\pi$
$271$			6.13012i			0.372378i	−0.982514	+	0.186189i	$0.940386\pi$
$272$		0			0
$273$	6.19880	+	0.886060i	0.375168	+	0.0536268i
$274$		0			0
$275$	−8.12675	−	2.17756i	−0.490062	−	0.131312i
$276$		0			0
$277$	0.690716	−	0.185077i	0.0415011	−	0.0111202i	−0.238009	−	0.971263i	$-0.576495\pi$
$277$	0.690716	−	0.185077i	0.0415011	−	0.0111202i	0.279510	+	0.960143i	$0.409828\pi$
$278$		0			0
$279$	3.44105	+	14.0833i	0.206010	+	0.843143i
$280$		0			0
$281$	5.17559	−	8.96438i	0.308750	−	0.534770i	−0.669339	−	0.742957i	$-0.733423\pi$
$281$	5.17559	−	8.96438i	0.308750	−	0.534770i	0.978089	+	0.208187i	$0.0667561\pi$
$282$		0			0
$283$	−25.3663	−	6.79689i	−1.50787	−	0.404033i	−0.592144	−	0.805832i	$-0.701718\pi$
$283$	−25.3663	−	6.79689i	−1.50787	−	0.404033i	−0.915728	+	0.401799i	$0.868385\pi$
$284$		0			0
$285$	0.622811	−	1.45771i	0.0368921	−	0.0863471i
$286$		0			0
$287$	4.51507			0.266516
$288$		0			0
$289$	16.2549			0.956172
$290$		0			0
$291$	9.96197	−	1.19939i	0.583981	−	0.0703097i
$292$		0			0
$293$	−19.4618	−	5.21478i	−1.13697	−	0.304651i	−0.359239	−	0.933246i	$-0.616964\pi$
$293$	−19.4618	−	5.21478i	−1.13697	−	0.304651i	−0.777733	+	0.628595i	$0.783630\pi$
$294$		0			0
$295$	7.88465	−	13.6566i	0.459062	−	0.795119i
$296$		0			0
$297$	9.97972	−	7.14362i	0.579082	−	0.414515i
$298$		0			0
$299$	3.90564	−	1.04651i	0.225869	−	0.0605215i
$300$		0			0
$301$	−8.57090	−	2.29657i	−0.494018	−	0.132372i
$302$		0			0
$303$	9.97913	−	12.7109i	0.573286	−	0.730225i
$304$		0			0
$305$		−	0.680700i		−	0.0389768i
$306$		0			0
$307$	5.92691	+	5.92691i	0.338267	+	0.338267i	0.855715	−	0.517448i	$-0.173118\pi$
$307$	5.92691	+	5.92691i	0.338267	+	0.338267i	−0.517448	+	0.855715i	$0.673118\pi$
$308$		0			0
$309$	2.75064	−	6.43794i	0.156478	−	0.366242i
$310$		0			0
$311$	−22.5904	+	13.0426i	−1.28098	+	0.739576i	−0.977028	−	0.213110i	$-0.931641\pi$
$311$	−22.5904	+	13.0426i	−1.28098	+	0.739576i	−0.303956	+	0.952686i	$0.598308\pi$
$312$		0			0
$313$	−0.538716	−	0.311028i	−0.0304500	−	0.0175803i	0.484698	−	0.874682i	$-0.338930\pi$
$313$	−0.538716	−	0.311028i	−0.0304500	−	0.0175803i	−0.515148	+	0.857101i	$0.672263\pi$
$314$		0			0
$315$	−1.23137	−	2.24631i	−0.0693798	−	0.126565i
$316$		0			0
$317$	−13.7037	+	3.67189i	−0.769675	+	0.206234i	−0.622228	−	0.782836i	$-0.713772\pi$
$317$	−13.7037	+	3.67189i	−0.769675	+	0.206234i	−0.147447	+	0.989070i	$0.547106\pi$
$318$		0			0
$319$	17.6090	−	10.1666i	0.985916	−	0.569219i
$320$		0			0
$321$	−2.74411	+	19.1976i	−0.153161	+	1.07150i
$322$		0			0
$323$	0.465843	−	0.465843i	0.0259202	−	0.0259202i
$324$		0			0
$325$	−12.7877	−	12.7877i	−0.709333	−	0.709333i
$326$		0			0
$327$	20.0163	+	2.86114i	1.10690	+	0.158221i
$328$		0			0
$329$	−0.936941	−	1.62283i	−0.0516552	−	0.0894694i
$330$		0			0
$331$	2.77508	+	10.3567i	0.152532	+	0.569257i	0.999304	+	0.0373014i	$0.0118762\pi$
$331$	2.77508	+	10.3567i	0.152532	+	0.569257i	−0.846772	+	0.531956i	$0.821457\pi$
$332$		0			0
$333$	25.8786	−	14.1860i	1.41814	−	0.777388i
$334$		0			0
$335$	−4.28061	+	7.41423i	−0.233874	+	0.405082i
$336$		0			0
$337$	−5.91237	−	10.2405i	−0.322067	−	0.557837i	0.658847	−	0.752277i	$-0.271044\pi$
$337$	−5.91237	−	10.2405i	−0.322067	−	0.557837i	−0.980914	+	0.194440i	$0.937711\pi$
$338$		0			0
$339$	12.3308	+	5.26838i	0.669716	+	0.286139i
$340$		0			0
$341$	8.07099	−	8.07099i	0.437069	−	0.437069i
$342$		0			0
$343$	−9.60823			−0.518795
$344$		0			0
$345$	−1.30108	−	1.02146i	−0.0700481	−	0.0549934i
$346$		0			0
$347$	0.0889961	−	0.332138i	0.00477756	−	0.0178301i	−0.963496	−	0.267723i	$-0.913729\pi$
$347$	0.0889961	−	0.332138i	0.00477756	−	0.0178301i	0.968273	+	0.249893i	$0.0803954\pi$
$348$		0			0
$349$	−6.40780	−	23.9142i	−0.343001	−	1.28010i	−0.894930	−	0.446207i	$-0.852774\pi$
$349$	−6.40780	−	23.9142i	−0.343001	−	1.28010i	0.551928	−	0.833892i	$-0.313892\pi$
$350$		0			0
$351$	26.2548	−	2.57228i	1.40138	−	0.137298i
$352$		0			0
$353$	−5.76381	−	3.32774i	−0.306776	−	0.177117i	0.338707	−	0.940892i	$-0.390011\pi$
$353$	−5.76381	−	3.32774i	−0.306776	−	0.177117i	−0.645483	+	0.763775i	$0.723344\pi$
$354$		0			0
$355$	0.942090	−	3.51593i	0.0500010	−	0.186606i
$356$		0			0
$357$	−0.127260	−	1.05700i	−0.00673530	−	0.0559423i
$358$		0			0
$359$		−	25.7733i		−	1.36026i	−0.733091	−	0.680130i	$-0.761923\pi$
$359$		−	25.7733i		−	1.36026i	0.733091	−	0.680130i	$-0.238077\pi$
$360$		0			0
$361$		−	18.4175i		−	0.969341i
$362$		0			0
$363$	8.63478	+	3.68924i	0.453208	+	0.193635i
$364$		0			0
$365$	−3.62550	+	13.5305i	−0.189767	+	0.708221i
$366$		0			0
$367$	−10.6689	−	6.15969i	−0.556912	−	0.321533i	0.194993	−	0.980805i	$-0.437532\pi$
$367$	−10.6689	−	6.15969i	−0.556912	−	0.321533i	−0.751905	+	0.659271i	$0.770865\pi$
$368$		0			0
$369$	18.4781	−	4.51486i	0.961930	−	0.235034i
$370$		0			0
$371$	2.31213	+	8.62898i	0.120040	+	0.447994i
$372$		0			0
$373$	−7.18223	+	26.8045i	−0.371882	+	1.38788i	0.485966	+	0.873978i	$0.338468\pi$
$373$	−7.18223	+	26.8045i	−0.371882	+	1.38788i	−0.857848	+	0.513904i	$0.828199\pi$
$374$		0			0
$375$	−2.51634	+	17.6041i	−0.129943	+	0.909073i
$376$		0			0
$377$	43.7057			2.25096
$378$		0			0
$379$	20.2758	−	20.2758i	1.04150	−	1.04150i	0.0423953	−	0.999101i	$-0.486501\pi$
$379$	20.2758	−	20.2758i	1.04150	−	1.04150i	0.999101	−	0.0423953i	$-0.0134989\pi$
$380$		0			0
$381$	−10.0002	+	7.49885i	−0.512324	+	0.384178i
$382$		0			0
$383$	−12.9618	−	22.4505i	−0.662317	−	1.14717i	−0.980005	−	0.198971i	$-0.936240\pi$
$383$	−12.9618	−	22.4505i	−0.662317	−	1.14717i	0.317689	−	0.948195i	$-0.397093\pi$
$384$		0			0
$385$	−1.00842	+	1.74663i	−0.0513938	+	0.0890167i
$386$		0			0
$387$	−37.3732	−	0.828267i	−1.89979	−	0.0421032i
$388$		0			0
$389$	1.85064	+	6.90667i	0.0938310	+	0.350182i	0.996840	−	0.0794404i	$-0.0253134\pi$
$389$	1.85064	+	6.90667i	0.0938310	+	0.350182i	−0.903009	+	0.429622i	$0.858647\pi$
$390$		0			0
$391$	−0.343731	−	0.595360i	−0.0173832	−	0.0301086i
$392$		0			0
$393$	3.89541	+	9.70718i	0.196498	+	0.489662i
$394$		0			0
$395$	0.824310	+	0.824310i	0.0414756	+	0.0414756i
$396$		0			0
$397$	−14.8178	+	14.8178i	−0.743683	+	0.743683i	−0.973285	−	0.229602i	$-0.926258\pi$
$397$	−14.8178	+	14.8178i	−0.743683	+	0.743683i	0.229602	+	0.973285i	$0.426258\pi$
$398$		0			0
$399$	0.740427	+	0.581296i	0.0370677	+	0.0291012i
$400$		0			0
$401$	−4.39082	+	2.53504i	−0.219267	+	0.126594i	−0.605611	−	0.795761i	$-0.707071\pi$
$401$	−4.39082	+	2.53504i	−0.219267	+	0.126594i	0.386344	+	0.922355i	$0.373738\pi$
$402$		0			0
$403$	23.6984	−	6.34997i	1.18050	−	0.316314i
$404$		0			0
$405$	−7.28564	−	7.96180i	−0.362026	−	0.395625i
$406$		0			0
$407$	−20.1221	−	11.6175i	−0.997416	−	0.575858i
$408$		0			0
$409$	−20.8923	+	12.0622i	−1.03306	+	0.596436i	−0.917859	−	0.396906i	$-0.870084\pi$
$409$	−20.8923	+	12.0622i	−1.03306	+	0.596436i	−0.115199	+	0.993342i	$0.536750\pi$
$410$		0			0
$411$	9.37140	−	1.12829i	0.462257	−	0.0556545i
$412$		0			0
$413$	6.62169	+	6.62169i	0.325832	+	0.325832i
$414$		0			0
$415$			13.8663i			0.680670i
$416$		0			0
$417$	9.60265	+	23.9293i	0.470244	+	1.17182i
$418$		0			0
$419$	−19.2387	−	5.15499i	−0.939871	−	0.251838i	−0.243812	−	0.969822i	$-0.578398\pi$
$419$	−19.2387	−	5.15499i	−0.939871	−	0.251838i	−0.696059	+	0.717985i	$0.745065\pi$
$420$		0			0
$421$	31.5799	−	8.46180i	1.53911	−	0.412403i	0.613131	−	0.789981i	$-0.289910\pi$
$421$	31.5799	−	8.46180i	1.53911	−	0.412403i	0.925978	+	0.377578i	$0.123243\pi$
$422$		0			0
$423$	−5.45722	−	5.70459i	−0.265339	−	0.277367i
$424$		0			0
$425$	−1.53736	+	2.66279i	−0.0745731	+	0.129164i
$426$		0			0
$427$	0.390455	+	0.104622i	0.0188954	+	0.00506302i
$428$		0			0
$429$	−12.4605	−	16.6168i	−0.601597	−	0.802267i
$430$		0			0
$431$	−11.5413			−0.555923			−0.277962	−	0.960592i	$-0.589659\pi$
$431$	−11.5413			−0.555923			−0.277962	+	0.960592i	$0.589659\pi$
$432$		0			0
$433$	24.2215			1.16401			0.582006	−	0.813184i	$-0.302268\pi$
$433$	24.2215			1.16401			0.582006	+	0.813184i	$0.302268\pi$
$434$		0			0
$435$	−10.7267	−	14.3047i	−0.514307	−	0.685859i
$436$		0			0
$437$	0.587143	+	0.157324i	0.0280868	+	0.00752585i
$438$		0			0
$439$	4.47756	−	7.75537i	0.213702	−	0.370143i	−0.739168	−	0.673521i	$-0.764781\pi$
$439$	4.47756	−	7.75537i	0.213702	−	0.370143i	0.952870	+	0.303378i	$0.0981144\pi$
$440$		0			0
$441$	−18.9221	+	4.62336i	−0.901054	+	0.220160i
$442$		0			0
$443$	−19.7541	+	5.29309i	−0.938545	+	0.251482i	−0.695495	−	0.718531i	$-0.744815\pi$
$443$	−19.7541	+	5.29309i	−0.938545	+	0.251482i	−0.243051	+	0.970014i	$0.578148\pi$
$444$		0			0
$445$	−5.04462	−	1.35170i	−0.239138	−	0.0640768i
$446$		0			0
$447$	−7.44512	−	18.5529i	−0.352142	−	0.877520i
$448$		0			0
$449$			2.34595i			0.110712i	0.998467	+	0.0553561i	$0.0176294\pi$
$449$			2.34595i			0.110712i	−0.998467	+	0.0553561i	$0.982371\pi$
$450$		0			0
$451$	−10.5896	−	10.5896i	−0.498646	−	0.498646i
$452$		0			0
$453$	16.4974	−	1.98624i	0.775113	−	0.0933215i
$454$		0			0
$455$	−3.75436	+	2.16758i	−0.176007	+	0.101618i
$456$		0			0
$457$	−24.1000	−	13.9141i	−1.12735	−	0.650876i	−0.184084	−	0.982911i	$-0.558932\pi$
$457$	−24.1000	−	13.9141i	−1.12735	−	0.650876i	−0.943267	+	0.332034i	$0.892265\pi$
$458$		0			0
$459$	−1.57777	−	4.19855i	−0.0736438	−	0.195972i
$460$		0			0
$461$	19.2263	−	5.15168i	0.895459	−	0.239937i	0.218394	−	0.975861i	$-0.429918\pi$
$461$	19.2263	−	5.15168i	0.895459	−	0.239937i	0.677065	+	0.735923i	$0.263252\pi$
$462$		0			0
$463$	21.3818	−	12.3448i	0.993699	−	0.573712i	0.0873209	−	0.996180i	$-0.472169\pi$
$463$	21.3818	−	12.3448i	0.993699	−	0.573712i	0.906378	+	0.422468i	$0.138836\pi$
$464$		0			0
$465$	−7.89463	−	6.19793i	−0.366105	−	0.287422i
$466$		0			0
$467$	−14.0708	+	14.0708i	−0.651120	+	0.651120i	−0.953263	−	0.302143i	$-0.902298\pi$
$467$	−14.0708	+	14.0708i	−0.651120	+	0.651120i	0.302143	+	0.953263i	$0.402298\pi$
$468$		0			0
$469$	−3.59494	−	3.59494i	−0.165999	−	0.165999i
$470$		0			0
$471$	−7.04500	−	17.5558i	−0.324616	−	0.808928i
$472$		0			0
$473$	14.7158	+	25.4885i	0.676633	+	1.17196i
$474$		0			0
$475$	−0.703645	−	2.62604i	−0.0322855	−	0.120491i
$476$		0			0
$477$	18.0911	+	33.0024i	0.828332	+	1.51108i
$478$		0			0
$479$	−12.8097	+	22.1870i	−0.585288	+	1.01375i	0.409551	+	0.912287i	$0.365685\pi$
$479$	−12.8097	+	22.1870i	−0.585288	+	1.01375i	−0.994839	+	0.101462i	$0.967648\pi$
$480$		0			0
$481$	−24.9716	−	43.2521i	−1.13861	−	1.97212i
$482$		0			0
$483$	0.785890	−	0.589317i	0.0357592	−	0.0268148i
$484$		0			0
$485$	−4.91202	+	4.91202i	−0.223043	+	0.223043i
$486$		0			0
$487$	−24.8039			−1.12397			−0.561986	−	0.827147i	$-0.689962\pi$
$487$	−24.8039			−1.12397			−0.561986	+	0.827147i	$0.689962\pi$
$488$		0			0
$489$	−3.62704	+	25.3745i	−0.164020	+	1.14747i
$490$		0			0
$491$	−9.75039	+	36.3890i	−0.440029	+	1.64221i	0.288708	+	0.957417i	$0.406774\pi$
$491$	−9.75039	+	36.3890i	−0.440029	+	1.64221i	−0.728737	+	0.684793i	$0.759892\pi$
$492$		0			0
$493$	−1.92324	−	7.17764i	−0.0866185	−	0.323265i
$494$		0			0
$495$	−2.38044	+	8.15654i	−0.106993	+	0.366609i
$496$		0			0
$497$	1.87197	+	1.08078i	0.0839692	+	0.0484796i
$498$		0			0
$499$	−5.39127	+	20.1205i	−0.241346	+	0.900717i	0.733838	+	0.679324i	$0.237727\pi$
$499$	−5.39127	+	20.1205i	−0.241346	+	0.900717i	−0.975185	+	0.221393i	$0.928940\pi$
$500$		0			0
$501$	21.1616	+	9.04137i	0.945430	+	0.403939i
$502$		0			0
$503$		−	4.55397i		−	0.203051i	−0.994833	−	0.101526i	$-0.967628\pi$
$503$		−	4.55397i		−	0.203051i	0.994833	−	0.101526i	$-0.0323724\pi$
$504$		0			0
$505$			11.1880i			0.497858i
$506$		0			0
$507$	−2.64498	−	21.9688i	−0.117468	−	0.975668i
$508$		0			0
$509$	−1.99603	+	7.44927i	−0.0884723	+	0.330183i	−0.995949	−	0.0899191i	$-0.971339\pi$
$509$	−1.99603	+	7.44927i	−0.0884723	+	0.330183i	0.907477	+	0.420102i	$0.138006\pi$
$510$		0			0
$511$	−7.20399	−	4.15923i	−0.318686	−	0.183993i
$512$		0			0
$513$	3.61149	+	1.63858i	0.159451	+	0.0723451i
$514$		0			0
$515$	1.25446	+	4.68172i	0.0552782	+	0.206301i
$516$		0			0
$517$	−1.60868	+	6.00367i	−0.0707496	+	0.264041i
$518$		0			0
$519$	10.2706	+	8.06322i	0.450828	+	0.353936i
$520$		0			0
$521$	−41.5553			−1.82057			−0.910286	−	0.413980i	$-0.864138\pi$
$521$	−41.5553			−1.82057			−0.910286	+	0.413980i	$0.864138\pi$
$522$		0			0
$523$	−7.94661	+	7.94661i	−0.347481	+	0.347481i	−0.859171	−	0.511689i	$-0.829020\pi$
$523$	−7.94661	+	7.94661i	−0.347481	+	0.347481i	0.511689	+	0.859171i	$0.329020\pi$
$524$		0			0
$525$	−4.04011	−	1.72615i	−0.176325	−	0.0753356i
$526$		0			0
$527$	−2.08567	−	3.61248i	−0.0908531	−	0.157362i
$528$		0			0
$529$	−11.1829	+	19.3693i	−0.486211	+	0.842142i
$530$		0			0
$531$	33.7209	+	20.4781i	1.46336	+	0.888675i
$532$		0			0
$533$	−8.33153	−	31.0937i	−0.360879	−	1.34682i
$534$		0			0
$535$	−6.71295	−	11.6272i	−0.290226	−	0.502686i
$536$		0			0
$537$	−36.6260	−	5.23535i	−1.58053	−	0.225922i
$538$		0			0
$539$	10.8441	+	10.8441i	0.467089	+	0.467089i
$540$		0			0
$541$	23.7454	−	23.7454i	1.02090	−	1.02090i	0.0211185	−	0.999777i	$-0.493277\pi$
$541$	23.7454	−	23.7454i	1.02090	−	1.02090i	0.999777	−	0.0211185i	$-0.00672274\pi$
$542$		0			0
$543$	−1.07066	+	7.49021i	−0.0459462	+	0.321436i
$544$		0			0
$545$	−12.1230	+	6.99924i	−0.519294	+	0.299814i
$546$		0			0
$547$	−0.683605	+	0.183171i	−0.0292288	+	0.00783185i	−0.273404	−	0.961899i	$-0.588150\pi$
$547$	−0.683605	+	0.183171i	−0.0292288	+	0.00783185i	0.244175	+	0.969731i	$0.421483\pi$
$548$		0			0
$549$	1.70257	+	0.0377324i	0.0726638	+	0.00161038i
$550$		0			0
$551$	5.69010	+	3.28518i	0.242406	+	0.139953i
$552$		0			0
$553$	−0.599525	+	0.346136i	−0.0254944	+	0.0147192i
$554$		0			0
$555$	−8.02746	+	18.7885i	−0.340747	+	0.797527i
$556$		0			0
$557$	11.0432	+	11.0432i	0.467916	+	0.467916i	0.901239	−	0.433322i	$-0.142659\pi$
$557$	11.0432	+	11.0432i	0.467916	+	0.467916i	−0.433322	+	0.901239i	$0.642659\pi$
$558$		0			0
$559$			63.2626i			2.67572i
$560$		0			0
$561$	−2.18061	+	2.77755i	−0.0920652	+	0.117268i
$562$		0			0
$563$	43.2988	+	11.6019i	1.82483	+	0.488961i	0.997364	−	0.0725616i	$-0.0231174\pi$
$563$	43.2988	+	11.6019i	1.82483	+	0.488961i	0.827462	+	0.561522i	$0.189784\pi$
$564$		0			0
$565$	−8.96703	+	2.40271i	−0.377246	+	0.101083i
$566$		0			0
$567$	5.68674	−	2.95539i	0.238820	−	0.124115i
$568$		0			0
$569$	−12.4715	+	21.6013i	−0.522833	+	0.905574i	0.476814	+	0.879004i	$0.341792\pi$
$569$	−12.4715	+	21.6013i	−0.522833	+	0.905574i	−0.999647	+	0.0265695i	$0.991542\pi$
$570$		0			0
$571$	34.6227	+	9.27714i	1.44892	+	0.388236i	0.895647	−	0.444766i	$-0.146713\pi$
$571$	34.6227	+	9.27714i	1.44892	+	0.388236i	0.553270	+	0.833002i	$0.313380\pi$
$572$		0			0
$573$	−8.61470	+	1.03719i	−0.359884	+	0.0433291i
$574$		0			0
$575$	−2.83695			−0.118309
$576$		0			0
$577$	−20.2125			−0.841457			−0.420729	−	0.907187i	$-0.638226\pi$
$577$	−20.2125			−0.841457			−0.420729	+	0.907187i	$0.638226\pi$
$578$		0			0
$579$	−3.91312	+	9.15877i	−0.162624	+	0.380626i
$580$		0			0
$581$	−7.95381	−	2.13122i	−0.329980	−	0.0884178i
$582$		0			0
$583$	14.8155	−	25.6612i	0.613596	−	1.06278i
$584$		0			0
$585$	−13.1974	+	12.6251i	−0.545644	+	0.521983i
$586$		0			0
$587$	−1.58919	+	0.425823i	−0.0655930	+	0.0175756i	−0.291466	−	0.956581i	$-0.594143\pi$
$587$	−1.58919	+	0.425823i	−0.0655930	+	0.0175756i	0.225873	+	0.974157i	$0.427476\pi$
$588$		0			0
$589$	3.56262	+	0.954602i	0.146795	+	0.0393337i
$590$		0			0
$591$	−1.24988	−	0.178658i	−0.0514131	−	0.00734902i
$592$		0			0
$593$		−	35.7642i		−	1.46866i	−0.678793	−	0.734329i	$-0.737497\pi$
$593$		−	35.7642i		−	1.46866i	0.678793	−	0.734329i	$-0.262503\pi$
$594$		0			0
$595$	0.521182	+	0.521182i	0.0213664	+	0.0213664i
$596$		0			0
$597$	−22.5055	−	30.0125i	−0.921090	−	1.22833i
$598$		0			0
$599$	24.2410	−	13.9955i	0.990460	−	0.571842i	0.0850481	−	0.996377i	$-0.472896\pi$
$599$	24.2410	−	13.9955i	0.990460	−	0.571842i	0.905412	+	0.424535i	$0.139562\pi$
$600$		0			0
$601$	9.43704	+	5.44848i	0.384945	+	0.222248i	0.679968	−	0.733242i	$-0.261994\pi$
$601$	9.43704	+	5.44848i	0.384945	+	0.222248i	−0.295023	+	0.955490i	$0.595327\pi$
$602$		0			0
$603$	−18.3072	−	11.1176i	−0.745527	−	0.452745i
$604$		0			0
$605$	−6.27927	+	1.68253i	−0.255289	+	0.0684044i
$606$		0			0
$607$	−36.6954	+	21.1861i	−1.48942	+	0.859916i	−0.999927	−	0.0120914i	$-0.996151\pi$
$607$	−36.6954	+	21.1861i	−1.48942	+	0.859916i	−0.489492	+	0.872008i	$0.662818\pi$
$608$		0			0
$609$	9.85397	−	3.95432i	0.399303	−	0.160237i
$610$		0			0
$611$	−9.44695	+	9.44695i	−0.382183	+	0.382183i
$612$		0			0
$613$	11.5060	+	11.5060i	0.464722	+	0.464722i	0.900200	−	0.435477i	$-0.143420\pi$
$613$	11.5060	+	11.5060i	0.464722	+	0.464722i	−0.435477	+	0.900200i	$0.643420\pi$
$614$		0			0
$615$	−8.13205	+	10.3582i	−0.327916	+	0.417684i
$616$		0			0
$617$	0.520100	+	0.900840i	0.0209384	+	0.0362665i	0.876305	−	0.481757i	$-0.160001\pi$
$617$	0.520100	+	0.900840i	0.0209384	+	0.0362665i	−0.855366	+	0.518024i	$0.826668\pi$
$618$		0			0
$619$	−4.73131	−	17.6575i	−0.190167	−	0.709714i	−0.993465	−	0.114136i	$-0.963590\pi$
$619$	−4.73131	−	17.6575i	−0.190167	−	0.709714i	0.803298	−	0.595578i	$-0.203077\pi$
$620$		0			0
$621$	2.62699	−	3.19765i	0.105418	−	0.128317i
$622$		0			0
$623$	1.55069	−	2.68588i	0.0621272	−	0.107608i
$624$		0			0
$625$	2.74947	+	4.76221i	0.109979	+	0.190489i
$626$		0			0
$627$	−0.373227	−	3.09996i	−0.0149052	−	0.123801i
$628$		0			0
$629$	−6.00428	+	6.00428i	−0.239406	+	0.239406i
$630$		0			0
$631$	−18.9729			−0.755301			−0.377650	−	0.925948i	$-0.623268\pi$
$631$	−18.9729			−0.755301			−0.377650	+	0.925948i	$0.623268\pi$
$632$		0			0
$633$	−3.74054	+	1.50105i	−0.148673	+	0.0596614i
$634$		0			0
$635$	2.23971	−	8.35872i	0.0888803	−	0.331706i
$636$		0			0
$637$	8.53175	+	31.8409i	0.338040	+	1.26158i
$638$		0			0
$639$	8.74183	+	2.55125i	0.345821	+	0.100926i
$640$		0			0
$641$	6.62975	+	3.82769i	0.261859	+	0.151185i	0.625182	−	0.780479i	$-0.285025\pi$
$641$	6.62975	+	3.82769i	0.261859	+	0.151185i	−0.363323	+	0.931663i	$0.618358\pi$
$642$		0			0
$643$	−4.91116	+	18.3287i	−0.193677	+	0.722813i	0.798928	+	0.601427i	$0.205401\pi$
$643$	−4.91116	+	18.3287i	−0.193677	+	0.722813i	−0.992605	+	0.121387i	$0.961266\pi$
$644$		0			0
$645$	20.7056	−	15.5266i	0.815284	−	0.611359i
$646$		0			0
$647$		−	1.59451i		−	0.0626865i	−0.999509	−	0.0313432i	$-0.990022\pi$
$647$		−	1.59451i		−	0.0626865i	0.999509	−	0.0313432i	$-0.00997849\pi$
$648$		0			0
$649$		−	31.0610i		−	1.21925i
$650$		0			0
$651$	4.76857	−	3.57582i	0.186895	−	0.140147i
$652$		0			0
$653$	−0.359845	+	1.34296i	−0.0140818	+	0.0525540i	−0.972609	−	0.232446i	$-0.925327\pi$
$653$	−0.359845	+	1.34296i	−0.0140818	+	0.0525540i	0.958527	+	0.285000i	$0.0919937\pi$
$654$		0			0
$655$	−6.27121	−	3.62069i	−0.245037	−	0.141472i
$656$		0			0
$657$	−33.6417	−	9.81813i	−1.31249	−	0.383042i
$658$		0			0
$659$	−7.51827	−	28.0586i	−0.292870	−	1.09301i	−0.942894	−	0.333093i	$-0.891908\pi$
$659$	−7.51827	−	28.0586i	−0.292870	−	1.09301i	0.650024	−	0.759914i	$-0.274759\pi$
$660$		0			0
$661$	0.0811214	−	0.302749i	0.00315526	−	0.0117756i	−0.964330	−	0.264702i	$-0.914726\pi$
$661$	0.0811214	−	0.302749i	0.00315526	−	0.0117756i	0.967486	+	0.252926i	$0.0813931\pi$
$662$		0			0
$663$	−7.04435	+	2.82684i	−0.273580	+	0.109786i
$664$		0			0
$665$	−0.651712			−0.0252723
$666$		0			0
$667$	4.84807	−	4.84807i	0.187718	−	0.187718i
$668$		0			0
$669$	3.91125	+	32.4862i	0.151218	+	1.25599i
$670$		0			0
$671$	−0.670391	−	1.16115i	−0.0258802	−	0.0448257i
$672$		0			0
$673$	−14.6918	+	25.4470i	−0.566329	+	0.980911i	0.430595	+	0.902545i	$0.358304\pi$
$673$	−14.6918	+	25.4470i	−0.566329	+	0.980911i	−0.996925	+	0.0783659i	$0.975030\pi$
$674$		0			0
$675$	−18.2604	−	3.02442i	−0.702843	−	0.116410i
$676$		0			0
$677$	−1.89270	−	7.06366i	−0.0727424	−	0.271478i	0.919969	−	0.391990i	$-0.128213\pi$
$677$	−1.89270	−	7.06366i	−0.0727424	−	0.271478i	−0.992712	+	0.120511i	$0.961547\pi$
$678$		0			0
$679$	−2.06261	−	3.57254i	−0.0791556	−	0.137102i
$680$		0			0
$681$	−8.72736	+	11.1165i	−0.334433	+	0.425985i
$682$		0			0
$683$	20.6264	+	20.6264i	0.789247	+	0.789247i	0.981371	−	0.192123i	$-0.0615374\pi$
$683$	20.6264	+	20.6264i	0.789247	+	0.789247i	−0.192123	+	0.981371i	$0.561537\pi$
$684$		0			0
$685$	−4.62083	+	4.62083i	−0.176553	+	0.176553i
$686$		0			0
$687$	−12.1698	+	4.88363i	−0.464305	+	0.186322i
$688$		0			0
$689$	55.1583	−	31.8456i	2.10136	−	1.21322i
$690$		0			0
$691$	−1.74504	+	0.467582i	−0.0663844	+	0.0177876i	−0.291858	−	0.956462i	$-0.594274\pi$
$691$	−1.74504	+	0.467582i	−0.0663844	+	0.0177876i	0.225474	+	0.974249i	$0.427607\pi$
$692$		0			0
$693$	−4.31279	−	2.61908i	−0.163829	−	0.0994907i
$694$		0			0
$695$	−15.4593	−	8.92542i	−0.586404	−	0.338560i
$696$		0			0
$697$	−4.73979	+	2.73652i	−0.179532	+	0.103653i
$698$		0			0
$699$	7.04467	+	9.39449i	0.266454	+	0.355332i
$700$		0			0
$701$	−31.2193	−	31.2193i	−1.17914	−	1.17914i	−0.979964	−	0.199174i	$-0.936174\pi$
$701$	−31.2193	−	31.2193i	−1.17914	−	1.17914i	−0.199174	−	0.979964i	$-0.563826\pi$
$702$		0			0
$703$		−	7.50805i		−	0.283171i
$704$		0			0
$705$	5.41053	+	0.773384i	0.203772	+	0.0291273i
$706$		0			0
$707$	−6.41751	−	1.71957i	−0.241355	−	0.0646709i
$708$		0			0
$709$	18.6747	−	5.00387i	0.701344	−	0.187924i	0.109511	−	0.993986i	$-0.465071\pi$
$709$	18.6747	−	5.00387i	0.701344	−	0.187924i	0.591832	+	0.806061i	$0.298405\pi$
$710$		0			0
$711$	−2.10746	+	2.01607i	−0.0790359	+	0.0756087i
$712$		0			0
$713$	1.92438	−	3.33312i	0.0720686	−	0.124826i
$714$		0			0
$715$	13.8893	+	3.72162i	0.519430	+	0.139181i
$716$		0			0
$717$	12.9084	−	30.2125i	0.482074	−	1.12831i
$718$		0			0
$719$	5.23889			0.195378			0.0976889	−	0.995217i	$-0.468855\pi$
$719$	5.23889			0.195378			0.0976889	+	0.995217i	$0.468855\pi$
$720$		0			0
$721$	−2.87828			−0.107193
$722$		0			0
$723$	−0.176282	+	0.0212238i	−0.00655599	+	0.000789323i
$724$		0			0
$725$	−29.6200	−	7.93665i	−1.10006	−	0.294760i
$726$		0			0
$727$	−20.0812	+	34.7817i	−0.744772	+	1.28998i	0.205530	+	0.978651i	$0.434108\pi$
$727$	−20.0812	+	34.7817i	−0.744772	+	1.28998i	−0.950301	+	0.311332i	$0.899225\pi$
$728$		0			0
$729$	20.3179	−	17.7815i	0.752516	−	0.658574i
$730$		0			0
$731$	10.3894	−	2.78383i	0.384266	−	0.102964i
$732$		0			0
$733$	46.0065	+	12.3274i	1.69929	+	0.455324i	0.972761	−	0.231811i	$-0.0744652\pi$
$733$	46.0065	+	12.3274i	1.69929	+	0.455324i	0.726530	+	0.687135i	$0.241132\pi$
$734$		0			0
$735$	8.32747	−	10.6072i	0.307164	−	0.391251i
$736$		0			0
$737$			16.8631i			0.621161i
$738$		0			0
$739$	−9.18363	−	9.18363i	−0.337825	−	0.337825i	0.517723	−	0.855548i	$-0.326780\pi$
$739$	−9.18363	−	9.18363i	−0.337825	−	0.337825i	−0.855548	+	0.517723i	$0.826780\pi$
$740$		0			0
$741$	2.63689	−	6.17172i	0.0968686	−	0.226724i
$742$		0			0
$743$	42.0760	−	24.2926i	1.54362	−	0.891208i	0.545011	−	0.838429i	$-0.316525\pi$
$743$	42.0760	−	24.2926i	1.54362	−	0.891208i	0.998606	−	0.0527792i	$-0.0168079\pi$
$744$		0			0
$745$	11.9859	+	6.92004i	0.439128	+	0.253531i
$746$		0			0
$747$	−34.6824	−	0.768633i	−1.26896	−	0.0281228i
$748$		0			0
$749$	7.70120	−	2.06353i	0.281396	−	0.0753998i
$750$		0			0
$751$	25.5639	−	14.7593i	0.932839	−	0.538575i	0.0451310	−	0.998981i	$-0.485629\pi$
$751$	25.5639	−	14.7593i	0.932839	−	0.538575i	0.887708	+	0.460406i	$0.152296\pi$
$752$		0			0
$753$	−2.28464	+	15.9832i	−0.0832571	+	0.582459i
$754$		0			0
$755$	−8.13448	+	8.13448i	−0.296044	+	0.296044i
$756$		0			0
$757$	30.3982	+	30.3982i	1.10484	+	1.10484i	0.993818	+	0.111022i	$0.0354123\pi$
$757$	30.3982	+	30.3982i	1.10484	+	1.10484i	0.111022	+	0.993818i	$0.464588\pi$
$758$		0			0
$759$	−3.22540	−	0.461041i	−0.117075	−	0.0167347i
$760$		0			0
$761$	2.97086	+	5.14568i	0.107694	+	0.186531i	0.914836	−	0.403827i	$-0.132320\pi$
$761$	2.97086	+	5.14568i	0.107694	+	0.186531i	−0.807142	+	0.590357i	$0.798987\pi$
$762$		0			0
$763$	−2.15153	−	8.02963i	−0.0778907	−	0.290692i
$764$		0			0
$765$	2.65412	+	1.61180i	0.0959598	+	0.0582747i
$766$		0			0
$767$	33.3825	−	57.8201i	1.20537	−	2.08776i
$768$		0			0
$769$	−6.00863	−	10.4073i	−0.216677	−	0.375295i	0.737113	−	0.675769i	$-0.236188\pi$
$769$	−6.00863	−	10.4073i	−0.216677	−	0.375295i	−0.953790	+	0.300474i	$0.902855\pi$
$770$		0			0
$771$	26.3132	+	11.2424i	0.947648	+	0.404887i
$772$		0			0
$773$	−22.2746	+	22.2746i	−0.801163	+	0.801163i	−0.983277	−	0.182114i	$-0.941706\pi$
$773$	−22.2746	+	22.2746i	−0.801163	+	0.801163i	0.182114	+	0.983277i	$0.441706\pi$
$774$		0			0
$775$	−17.2139			−0.618340
$776$		0			0
$777$	−9.54343	−	7.49236i	−0.342368	−	0.268787i
$778$		0			0
$779$	1.25249	−	4.67437i	0.0448753	−	0.167477i
$780$		0			0
$781$	−1.85565	−	6.92536i	−0.0664002	−	0.247809i
$782$		0			0
$783$	36.3736	−	26.0367i	1.29989	−	0.930477i
$784$		0			0
$785$	11.3417	+	6.54815i	0.404803	+	0.233713i
$786$		0			0
$787$	−1.60408	+	5.98650i	−0.0571792	+	0.213396i	−0.988604	−	0.150537i	$-0.951900\pi$
$787$	−1.60408	+	5.98650i	−0.0571792	+	0.213396i	0.931425	+	0.363933i	$0.118566\pi$
$788$		0			0
$789$	−5.32914	−	44.2630i	−0.189723	−	1.57581i
$790$		0			0
$791$		−	5.51285i		−	0.196014i
$792$		0			0
$793$		−	2.88198i		−	0.102342i
$794$		0			0
$795$	−23.9605	−	10.2372i	−0.849791	−	0.363077i
$796$		0			0
$797$	8.87494	−	33.1217i	0.314367	−	1.17323i	−0.610211	−	0.792239i	$-0.708915\pi$
$797$	8.87494	−	33.1217i	0.314367	−	1.17323i	0.924578	−	0.380993i	$-0.124418\pi$
$798$		0			0
$799$	1.96715	+	1.13573i	0.0695927	+	0.0401794i
$800$		0			0
$801$	3.66051	−	12.5427i	0.129338	−	0.443174i
$802$		0			0
$803$	7.14118	+	26.6513i	0.252007	+	0.940503i
$804$		0			0
$805$	−0.176014	+	0.656892i	−0.00620367	+	0.0231524i
$806$		0			0
$807$	1.60309	−	11.2150i	0.0564313	−	0.394788i
$808$		0			0
$809$	12.8401			0.451432			0.225716	−	0.974193i	$-0.427528\pi$
$809$	12.8401			0.451432			0.225716	+	0.974193i	$0.427528\pi$
$810$		0			0
$811$	37.1183	−	37.1183i	1.30340	−	1.30340i	0.377314	−	0.926086i	$-0.376848\pi$
$811$	37.1183	−	37.1183i	1.30340	−	1.30340i	0.926086	−	0.377314i	$-0.123152\pi$
$812$		0			0
$813$	8.49466	−	6.36991i	0.297921	−	0.223402i
$814$		0			0
$815$	−8.87287	−	15.3683i	−0.310803	−	0.538327i
$816$		0			0
$817$	−4.75519	+	8.23624i	−0.166363	+	0.288149i
$818$		0			0
$819$	−5.21344	−	9.51055i	−0.182172	−	0.332326i
$820$		0			0
$821$	7.26977	+	27.1312i	0.253717	+	0.946884i	0.968800	+	0.247844i	$0.0797222\pi$
$821$	7.26977	+	27.1312i	0.253717	+	0.946884i	−0.715083	+	0.699040i	$0.753611\pi$
$822$		0			0
$823$	−9.61847	−	16.6597i	−0.335279	−	0.580720i	0.648260	−	0.761419i	$-0.275497\pi$
$823$	−9.61847	−	16.6597i	−0.335279	−	0.580720i	−0.983538	+	0.180700i	$0.942164\pi$
$824$		0			0
$825$	5.42715	+	13.5242i	0.188949	+	0.470852i
$826$		0			0
$827$	28.7848	+	28.7848i	1.00095	+	1.00095i	1.00000		0.000945916i	$0.000301094\pi$
$827$	28.7848	+	28.7848i	1.00095	+	1.00095i	0.000945916		1.00000i	$0.499699\pi$
$828$		0			0
$829$	−23.5696	+	23.5696i	−0.818606	+	0.818606i	−0.985906	−	0.167300i	$-0.946495\pi$
$829$	−23.5696	+	23.5696i	−0.818606	+	0.818606i	0.167300	+	0.985906i	$0.446495\pi$
$830$		0			0
$831$	−0.974201	−	0.764827i	−0.0337946	−	0.0265315i
$832$		0			0
$833$	4.85369	−	2.80228i	0.168171	−	0.0970933i
$834$		0			0
$835$	−15.3889	+	4.12343i	−0.532553	+	0.142697i
$836$		0			0
$837$	15.9399	−	19.4025i	0.550963	−	0.670649i
$838$		0			0
$839$	−5.76796	−	3.33013i	−0.199132	−	0.114969i	0.397119	−	0.917767i	$-0.370010\pi$
$839$	−5.76796	−	3.33013i	−0.199132	−	0.114969i	−0.596251	+	0.802798i	$0.703344\pi$
$840$		0			0
$841$	39.0658	−	22.5546i	1.34710	−	0.777747i
$842$		0			0
$843$	−17.8002	+	2.14310i	−0.613072	+	0.0738121i
$844$		0			0
$845$	10.8323	+	10.8323i	0.372643	+	0.372643i
$846$		0			0
$847$		−	3.86044i		−	0.132646i
$848$		0			0
$849$	16.9400	+	42.2135i	0.581378	+	1.44877i
$850$		0			0
$851$	−7.56773	−	2.02777i	−0.259418	−	0.0695109i
$852$		0			0
$853$	10.9887	−	2.94440i	0.376245	−	0.100814i	−0.0657407	−	0.997837i	$-0.520941\pi$
$853$	10.9887	−	2.94440i	0.376245	−	0.100814i	0.441985	+	0.897022i	$0.354274\pi$
$854$		0			0
$855$	−2.66716	+	0.651683i	−0.0912148	+	0.0222871i
$856$		0			0
$857$	15.7885	−	27.3465i	0.539326	−	0.934140i	−0.459615	−	0.888118i	$-0.652013\pi$
$857$	15.7885	−	27.3465i	0.539326	−	0.934140i	0.998940	−	0.0460211i	$-0.0146542\pi$
$858$		0			0
$859$	27.2537	+	7.30262i	0.929886	+	0.249162i	0.691806	−	0.722084i	$-0.256815\pi$
$859$	27.2537	+	7.30262i	0.929886	+	0.249162i	0.238080	+	0.971246i	$0.423482\pi$
$860$		0			0
$861$	−4.69168	−	6.25664i	−0.159892	−	0.213226i
$862$		0			0
$863$	−29.1288			−0.991557			−0.495779	−	0.868449i	$-0.665117\pi$
$863$	−29.1288			−0.991557			−0.495779	+	0.868449i	$0.665117\pi$
$864$		0			0
$865$	−9.03998			−0.307369
$866$		0			0
$867$	−16.8908	−	22.5249i	−0.573640	−	0.764984i
$868$		0			0
$869$	2.21795	+	0.594298i	0.0752388	+	0.0201602i
$870$		0			0
$871$	−18.1235	+	31.3907i	−0.614090	+	1.06363i
$872$		0			0
$873$	−12.0137	−	12.5582i	−0.406601	−	0.425032i
$874$		0			0
$875$	7.06198	−	1.89225i	0.238739	−	0.0639698i
$876$		0			0
$877$	−32.2138	−	8.63165i	−1.08778	−	0.291470i	−0.330001	−	0.943980i	$-0.607049\pi$
$877$	−32.2138	−	8.63165i	−1.08778	−	0.291470i	−0.757780	+	0.652510i	$0.773716\pi$
$878$		0			0
$879$	12.9969	+	32.3875i	0.438373	+	1.09240i
$880$		0			0
$881$		−	10.4223i		−	0.351136i	−0.984467	−	0.175568i	$-0.943824\pi$
$881$		−	10.4223i		−	0.351136i	0.984467	−	0.175568i	$-0.0561763\pi$
$882$		0			0
$883$	−7.73247	−	7.73247i	−0.260218	−	0.260218i	0.564924	−	0.825143i	$-0.308905\pi$
$883$	−7.73247	−	7.73247i	−0.260218	−	0.260218i	−0.825143	+	0.564924i	$0.808905\pi$
$884$		0			0
$885$	−27.1174	+	3.26486i	−0.911542	+	0.109747i
$886$		0			0
$887$	22.0565	−	12.7343i	0.740584	−	0.427577i	−0.0816974	−	0.996657i	$-0.526034\pi$
$887$	22.0565	−	12.7343i	0.740584	−	0.427577i	0.822282	+	0.569081i	$0.192701\pi$
$888$		0			0
$889$	4.45039	+	2.56943i	0.149261	+	0.0861761i
$890$		0			0
$891$	−20.2692	−	6.40609i	−0.679044	−	0.214612i
$892$		0			0
$893$	−1.94000	+	0.519821i	−0.0649196	+	0.0173951i
$894$		0			0
$895$	22.1829	−	12.8073i	0.741492	−	0.428100i
$896$		0			0
$897$	−5.50860	−	4.32470i	−0.183927	−	0.144398i
$898$		0			0
$899$	29.4168	−	29.4168i	0.981104	−	0.981104i
$900$		0			0
$901$	−7.65711	−	7.65711i	−0.255095	−	0.255095i
$902$		0			0
$903$	5.72376	+	14.2633i	0.190475	+	0.474654i
$904$		0			0
$905$	−2.61915	−	4.53651i	−0.0870637	−	0.150799i
$906$		0			0
$907$	9.44656	+	35.2550i	0.313668	+	1.17062i	0.925223	+	0.379423i	$0.123877\pi$
$907$	9.44656	+	35.2550i	0.313668	+	1.17062i	−0.611555	+	0.791202i	$0.709456\pi$
$908$		0			0
$909$	−27.9834	−	0.620169i	−0.928150	−	0.0205697i
$910$		0			0
$911$	−4.86150	+	8.42037i	−0.161069	+	0.278979i	−0.935252	−	0.353982i	$-0.884827\pi$
$911$	−4.86150	+	8.42037i	−0.161069	+	0.278979i	0.774183	+	0.632961i	$0.218161\pi$
$912$		0			0
$913$	13.6563	+	23.6534i	0.451957	+	0.782813i
$914$		0			0
$915$	−0.943263	+	0.707327i	−0.0311833	+	0.0233835i
$916$		0			0
$917$	3.04073	−	3.04073i	0.100414	−	0.100414i
$918$		0			0
$919$	26.5741			0.876599			0.438300	−	0.898829i	$-0.355581\pi$
$919$	26.5741			0.876599			0.438300	+	0.898829i	$0.355581\pi$
$920$		0			0
$921$	2.05432	−	14.3718i	0.0676921	−	0.473568i
$922$		0			0
$923$	3.98867	−	14.8859i	0.131289	−	0.489976i
$924$		0			0
$925$	9.06934	+	33.8472i	0.298198	+	1.11289i
$926$		0			0
$927$	−11.7795	+	2.87815i	−0.386888	+	0.0945308i
$928$		0			0
$929$	20.9365	+	12.0877i	0.686904	+	0.396584i	0.802451	−	0.596718i	$-0.203529\pi$
$929$	20.9365	+	12.0877i	0.686904	+	0.396584i	−0.115547	+	0.993302i	$0.536862\pi$
$930$		0			0
$931$	−1.28259	+	4.78670i	−0.0420353	+	0.156878i
$932$		0			0
$933$	41.5475	+	17.7513i	1.36020	+	0.581153i
$934$		0			0
$935$		−	2.44476i		−	0.0799521i
$936$		0			0
$937$		−	1.33551i		−	0.0436291i	−0.999762	−	0.0218146i	$-0.993056\pi$
$937$		−	1.33551i		−	0.0436291i	0.999762	−	0.0218146i	$-0.00694434\pi$
$938$		0			0
$939$	0.128790	+	1.06971i	0.00420289	+	0.0349086i
$940$		0			0
$941$	5.71431	−	21.3261i	0.186281	−	0.695211i	−0.808071	−	0.589085i	$-0.799488\pi$
$941$	5.71431	−	21.3261i	0.186281	−	0.695211i	0.994353	−	0.106126i	$-0.0338448\pi$
$942$		0			0
$943$	−4.37325	−	2.52490i	−0.142413	−	0.0822220i
$944$		0			0
$945$	−1.83323	+	4.04052i	−0.0596351	+	0.131438i
$946$		0			0
$947$	−6.28700	−	23.4634i	−0.204300	−	0.762458i	−0.989662	−	0.143421i	$-0.954190\pi$
$947$	−6.28700	−	23.4634i	−0.204300	−	0.762458i	0.785362	−	0.619037i	$-0.212477\pi$
$948$		0			0
$949$	−15.3498	+	57.2863i	−0.498277	+	1.85959i
$950$		0			0
$951$	19.3279	+	15.1740i	0.626752	+	0.492051i
$952$		0			0
$953$	15.2157			0.492885			0.246442	−	0.969157i	$-0.420738\pi$
$953$	15.2157			0.492885			0.246442	+	0.969157i	$0.420738\pi$
$954$		0			0
$955$	4.24772	−	4.24772i	0.137453	−	0.137453i
$956$		0			0
$957$	−32.3859	−	13.8370i	−1.04689	−	0.447287i
$958$		0			0
$959$	−1.94033	−	3.36075i	−0.0626566	−	0.108524i
$960$		0			0
$961$	−3.82339	+	6.62230i	−0.123335	+	0.213623i
$962$		0			0
$963$	29.4540	−	16.1459i	0.949142	−	0.520295i
$964$		0			0
$965$	−1.78463	−	6.66032i	−0.0574492	−	0.214403i
$966$		0			0
$967$	16.3260	+	28.2775i	0.525010	+	0.909344i	0.999576	+	0.0291241i	$0.00927179\pi$
$967$	16.3260	+	28.2775i	0.525010	+	0.909344i	−0.474566	+	0.880220i	$0.657395\pi$
$968$		0			0
$969$	−1.12960	−	0.161465i	−0.0362878	−	0.00518701i
$970$		0			0
$971$	−23.6028	−	23.6028i	−0.757449	−	0.757449i	0.218408	−	0.975858i	$-0.429914\pi$
$971$	−23.6028	−	23.6028i	−0.757449	−	0.757449i	−0.975858	+	0.218408i	$0.929914\pi$
$972$		0			0
$973$	7.49574	−	7.49574i	0.240303	−	0.240303i
$974$		0			0
$975$	−4.43232	+	31.0081i	−0.141948	+	0.993054i
$976$		0			0
$977$	30.2605	−	17.4709i	0.968119	−	0.558944i	0.0694570	−	0.997585i	$-0.477873\pi$
$977$	30.2605	−	17.4709i	0.968119	−	0.558944i	0.898662	+	0.438641i	$0.144540\pi$
$978$		0			0
$979$	−9.93644	+	2.66246i	−0.317570	+	0.0850926i
$980$		0			0
$981$	−16.8345	−	30.7101i	−0.537484	−	0.980499i
$982$		0			0
$983$	28.8301	+	16.6450i	0.919536	+	0.530895i	0.883487	−	0.468455i	$-0.155189\pi$
$983$	28.8301	+	16.6450i	0.919536	+	0.530895i	0.0360492	+	0.999350i	$0.488523\pi$
$984$		0			0
$985$	0.756999	−	0.437053i	0.0241200	−	0.0139257i
$986$		0			0
$987$	−1.27520	+	2.98465i	−0.0405902	+	0.0950025i
$988$		0			0
$989$	7.01742	+	7.01742i	0.223141	+	0.223141i
$990$		0			0
$991$		−	10.4637i		−	0.332390i	−0.986093	−	0.166195i	$-0.946852\pi$
$991$		−	10.4637i		−	0.332390i	0.986093	−	0.166195i	$-0.0531482\pi$
$992$		0			0
$993$	11.4680	−	14.6074i	0.363925	−	0.463550i
$994$		0			0
$995$	25.0862	+	6.72182i	0.795286	+	0.213096i
$996$		0			0
$997$	−27.8961	+	7.47474i	−0.883479	+	0.236727i	−0.671907	−	0.740635i	$-0.734525\pi$
$997$	−27.8961	+	7.47474i	−0.883479	+	0.236727i	−0.211571	+	0.977363i	$0.567858\pi$
$998$		0			0
$999$	−46.5488	−	21.1198i	−1.47274	−	0.668200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.8		88
3.2	odd	2		1728.2.z.a.143.8		88
4.3	odd	2		144.2.u.a.11.1	✓	88
9.4	even	3		1728.2.z.a.719.8		88
9.5	odd	6	inner	576.2.y.a.527.4		88
12.11	even	2		432.2.v.a.251.22		88
16.3	odd	4	inner	576.2.y.a.47.4		88
16.13	even	4		144.2.u.a.83.7	yes	88
36.23	even	6		144.2.u.a.59.7	yes	88
36.31	odd	6		432.2.v.a.395.16		88
48.29	odd	4		432.2.v.a.35.16		88
48.35	even	4		1728.2.z.a.1007.8		88
144.13	even	12		432.2.v.a.179.22		88
144.67	odd	12		1728.2.z.a.1583.8		88
144.77	odd	12		144.2.u.a.131.1	yes	88
144.131	even	12	inner	576.2.y.a.239.8		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.1	✓	88	4.3	odd	2
144.2.u.a.59.7	yes	88	36.23	even	6
144.2.u.a.83.7	yes	88	16.13	even	4
144.2.u.a.131.1	yes	88	144.77	odd	12
432.2.v.a.35.16		88	48.29	odd	4
432.2.v.a.179.22		88	144.13	even	12
432.2.v.a.251.22		88	12.11	even	2
432.2.v.a.395.16		88	36.31	odd	6
576.2.y.a.47.4		88	16.3	odd	4	inner
576.2.y.a.239.8		88	144.131	even	12	inner
576.2.y.a.335.8		88	1.1	even	1	trivial
576.2.y.a.527.4		88	9.5	odd	6	inner
1728.2.z.a.143.8		88	3.2	odd	2
1728.2.z.a.719.8		88	9.4	even	3
1728.2.z.a.1007.8		88	48.35	even	4
1728.2.z.a.1583.8		88	144.67	odd	12

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03912 - 1.38573i) q^{3} +(1.15827 + 0.310357i) q^{5} +(-0.356047 + 0.616691i) q^{7} +(-0.840471 + 2.87986i) q^{9} +O(q^{10})\)	\(q+(-1.03912 - 1.38573i) q^{3} +(1.15827 + 0.310357i) q^{5} +(-0.356047 + 0.616691i) q^{7} +(-0.840471 + 2.87986i) q^{9} +(2.28146 - 0.611314i) q^{11} +(4.90394 + 1.31401i) q^{13} +(-0.773508 - 1.92754i) q^{15} -0.863180i q^{17} +(0.539682 + 0.539682i) q^{19} +(1.22454 - 0.147431i) q^{21} +(0.689728 - 0.398215i) q^{23} +(-3.08486 - 1.78104i) q^{25} +(4.86405 - 1.82785i) q^{27} +(8.31534 - 2.22809i) q^{29} +(4.18508 - 2.41626i) q^{31} +(-3.21781 - 2.52625i) q^{33} +(-0.603793 + 0.603793i) q^{35} +(-6.95600 - 6.95600i) q^{37} +(-3.27492 - 8.16093i) q^{39} +(-3.17027 - 5.49108i) q^{41} +(3.22509 + 12.0362i) q^{43} +(-1.86728 + 3.07481i) q^{45} +(-1.31575 + 2.27895i) q^{47} +(3.24646 + 5.62304i) q^{49} +(-1.19613 + 0.896946i) q^{51} +(8.87081 - 8.87081i) q^{53} +2.83227 q^{55} +(0.187058 - 1.30864i) q^{57} +(3.40363 - 12.7025i) q^{59} +(-0.146922 - 0.548319i) q^{61} +(-1.47674 - 1.54368i) q^{63} +(5.27228 + 3.04395i) q^{65} +(-1.84784 + 6.89625i) q^{67} +(-1.26852 - 0.541982i) q^{69} -3.03550i q^{71} +11.6817i q^{73} +(0.737491 + 6.12548i) q^{75} +(-0.435313 + 1.62461i) q^{77} +(0.841919 + 0.486082i) q^{79} +(-7.58722 - 4.84088i) q^{81} +(2.99289 + 11.1696i) q^{83} +(0.267894 - 0.999796i) q^{85} +(-11.7281 - 9.20754i) q^{87} -4.35531 q^{89} +(-2.55637 + 2.55637i) q^{91} +(-7.69706 - 3.28860i) q^{93} +(0.457603 + 0.792591i) q^{95} +(-2.89654 + 5.01695i) q^{97} +(-0.156998 + 7.08407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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