LMFDB - Embedded newform 576.2.r.e.481.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(97,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.r (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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			481.3
Root			$-0.673288 + 0.180407i$ of defining polynomial
Character	$\chi$	$=$	576.481
Dual form			576.2.r.e.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.492881 - 1.66044i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(2.17731 + 3.77121i) q^{7} +(-2.51414 + 1.63680i) q^{9} +O(q^{10})$	\(q+(-0.492881 - 1.66044i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(2.17731 + 3.77121i) q^{7} +(-2.51414 + 1.63680i) q^{9} +(-5.05328 + 2.91751i) q^{11} +(3.48133 + 2.00994i) q^{13} +(-0.698664 + 2.91751i) q^{15} +1.70739 q^{17} +2.00000i q^{19} +(5.18872 - 5.47405i) q^{21} +(-3.32123 + 5.75253i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(3.95698 + 3.36783i) q^{27} +(4.06108 - 2.34467i) q^{29} +(2.43071 - 4.21012i) q^{31} +(7.33502 + 6.95269i) q^{33} -7.54241i q^{35} +5.75194i q^{37} +(1.62152 - 6.77121i) q^{39} +(0.646305 - 1.11943i) q^{41} +(-3.06782 + 1.77121i) q^{43} +(5.18872 - 0.277894i) q^{45} +(5.30669 + 9.19145i) q^{47} +(-5.98133 + 10.3600i) q^{49} +(-0.841540 - 2.83502i) q^{51} +0.506816i q^{53} +10.1066 q^{55} +(3.32088 - 0.985762i) q^{57} +(1.62152 + 0.936184i) q^{59} +(-1.06108 + 0.612617i) q^{61} +(-11.6468 - 5.91751i) q^{63} +(-3.48133 - 6.02983i) q^{65} +(-1.36811 - 0.789879i) q^{67} +(11.1887 + 2.67939i) q^{69} -9.88549 q^{71} -7.96265 q^{73} +(-2.38309 + 2.51414i) q^{75} +(-22.0051 - 12.7046i) q^{77} +(1.03339 + 1.78988i) q^{79} +(3.64177 - 8.23028i) q^{81} +(1.33577 - 0.771205i) q^{83} +(-2.56108 - 1.47864i) q^{85} +(-5.89482 - 5.58755i) q^{87} +3.96265 q^{89} +17.5051i q^{91} +(-8.18872 - 1.96097i) q^{93} +(1.73205 - 3.00000i) q^{95} +(-3.06108 - 5.30195i) q^{97} +(7.92925 - 15.6062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{5} - 4 q^{9}+O(q^{10}) $ 12 * q - 18 * q^5 - 4 * q^9	$ 12 q - 18 q^{5} - 4 q^{9} - 6 q^{13} - 6 q^{21} - 12 q^{25} + 18 q^{29} + 30 q^{33} + 18 q^{41} - 6 q^{45} - 24 q^{49} + 8 q^{57} + 18 q^{61} + 6 q^{65} + 66 q^{69} - 90 q^{77} - 20 q^{81} - 48 q^{89} - 30 q^{93} - 6 q^{97}+O(q^{100}) $ 12 * q - 18 * q^5 - 4 * q^9 - 6 * q^13 - 6 * q^21 - 12 * q^25 + 18 * q^29 + 30 * q^33 + 18 * q^41 - 6 * q^45 - 24 * q^49 + 8 * q^57 + 18 * q^61 + 6 * q^65 + 66 * q^69 - 90 * q^77 - 20 * q^81 - 48 * q^89 - 30 * q^93 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.492881	−	1.66044i	−0.284565	−	0.958657i
$3$	−0.492881	−	1.66044i	−0.284565	−	0.958657i
$4$		0			0
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	2.17731	+	3.77121i	0.822944	+	1.42538i	0.903480	+	0.428630i	$0.141004\pi$
$7$	2.17731	+	3.77121i	0.822944	+	1.42538i	−0.0805357	+	0.996752i	$0.525663\pi$
$8$		0			0
$9$	−2.51414	+	1.63680i	−0.838046	+	0.545600i
$10$		0			0
$11$	−5.05328	+	2.91751i	−1.52362	+	0.879663i	−0.524011	+	0.851712i	$0.675565\pi$
$11$	−5.05328	+	2.91751i	−1.52362	+	0.879663i	−0.999609	+	0.0279511i	$0.991102\pi$
$12$		0			0
$13$	3.48133	+	2.00994i	0.965546	+	0.557458i	0.897876	−	0.440249i	$-0.145110\pi$
$13$	3.48133	+	2.00994i	0.965546	+	0.557458i	0.0676707	+	0.997708i	$0.478443\pi$
$14$		0			0
$15$	−0.698664	+	2.91751i	−0.180394	+	0.753298i
$16$		0			0
$17$	1.70739			0.414103			0.207051	−	0.978330i	$-0.433613\pi$
$17$	1.70739			0.414103			0.207051	+	0.978330i	$0.433613\pi$
$18$		0			0
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$		0			0
$21$	5.18872	−	5.47405i	1.13227	−	1.19453i
$22$		0			0
$23$	−3.32123	+	5.75253i	−0.692523	+	1.19949i	0.278485	+	0.960441i	$0.410168\pi$
$23$	−3.32123	+	5.75253i	−0.692523	+	1.19949i	−0.971008	+	0.239045i	$0.923166\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$		0			0
$27$	3.95698	+	3.36783i	0.761522	+	0.648139i
$28$		0			0
$29$	4.06108	−	2.34467i	0.754124	−	0.435394i	−0.0730578	−	0.997328i	$-0.523276\pi$
$29$	4.06108	−	2.34467i	0.754124	−	0.435394i	0.827182	+	0.561934i	$0.189942\pi$
$30$		0			0
$31$	2.43071	−	4.21012i	0.436569	−	0.756160i	−0.560853	−	0.827915i	$-0.689527\pi$
$31$	2.43071	−	4.21012i	0.436569	−	0.756160i	0.997422	+	0.0717553i	$0.0228601\pi$
$32$		0			0
$33$	7.33502	+	6.95269i	1.27686	+	1.21031i
$34$		0			0
$35$		−	7.54241i		−	1.27490i
$36$		0			0
$37$			5.75194i			0.945613i	0.881166	+	0.472807i	$0.156759\pi$
$37$			5.75194i			0.945613i	−0.881166	+	0.472807i	$0.843241\pi$
$38$		0			0
$39$	1.62152	−	6.77121i	0.259651	−	1.08426i
$40$		0			0
$41$	0.646305	−	1.11943i	0.100936	−	0.174826i	−0.811135	−	0.584860i	$-0.801150\pi$
$41$	0.646305	−	1.11943i	0.100936	−	0.174826i	0.912071	+	0.410033i	$0.134483\pi$
$42$		0			0
$43$	−3.06782	+	1.77121i	−0.467838	+	0.270106i	−0.715334	−	0.698783i	$-0.753726\pi$
$43$	−3.06782	+	1.77121i	−0.467838	+	0.270106i	0.247496	+	0.968889i	$0.420392\pi$
$44$		0			0
$45$	5.18872	−	0.277894i	0.773488	−	0.0414260i
$46$		0			0
$47$	5.30669	+	9.19145i	0.774060	+	1.34071i	0.935322	+	0.353799i	$0.115110\pi$
$47$	5.30669	+	9.19145i	0.774060	+	1.34071i	−0.161262	+	0.986912i	$0.551556\pi$
$48$		0			0
$49$	−5.98133	+	10.3600i	−0.854475	+	1.47999i
$50$		0			0
$51$	−0.841540	−	2.83502i	−0.117839	−	0.396982i
$52$		0			0
$53$			0.506816i			0.0696166i	0.999394	+	0.0348083i	$0.0110821\pi$
$53$			0.506816i			0.0696166i	−0.999394	+	0.0348083i	$0.988918\pi$
$54$		0			0
$55$	10.1066			1.36277
$56$		0			0
$57$	3.32088	−	0.985762i	0.439862	−	0.130567i
$58$		0			0
$59$	1.62152	+	0.936184i	0.211104	+	0.121881i	0.601824	−	0.798629i	$-0.294441\pi$
$59$	1.62152	+	0.936184i	0.211104	+	0.121881i	−0.390721	+	0.920509i	$0.627774\pi$
$60$		0			0
$61$	−1.06108	+	0.612617i	−0.135858	+	0.0784376i	−0.566388	−	0.824138i	$-0.691660\pi$
$61$	−1.06108	+	0.612617i	−0.135858	+	0.0784376i	0.430531	+	0.902576i	$0.358326\pi$
$62$		0			0
$63$	−11.6468	−	5.91751i	−1.46735	−	0.745536i
$64$		0			0
$65$	−3.48133	−	6.02983i	−0.431805	−	0.747909i
$66$		0			0
$67$	−1.36811	−	0.789879i	−0.167141	−	0.0964990i	0.414096	−	0.910233i	$-0.364098\pi$
$67$	−1.36811	−	0.789879i	−0.167141	−	0.0964990i	−0.581237	+	0.813734i	$0.697431\pi$
$68$		0			0
$69$	11.1887	+	2.67939i	1.34696	+	0.322561i
$70$		0			0
$71$	−9.88549			−1.17319			−0.586596	−	0.809880i	$-0.699532\pi$
$71$	−9.88549			−1.17319			−0.586596	+	0.809880i	$0.699532\pi$
$72$		0			0
$73$	−7.96265			−0.931958			−0.465979	−	0.884796i	$-0.654298\pi$
$73$	−7.96265			−0.931958			−0.465979	+	0.884796i	$0.654298\pi$
$74$		0			0
$75$	−2.38309	+	2.51414i	−0.275175	+	0.290308i
$76$		0			0
$77$	−22.0051	−	12.7046i	−2.50771	−	1.44783i
$78$		0			0
$79$	1.03339	+	1.78988i	0.116265	+	0.201377i	0.918285	−	0.395921i	$-0.129574\pi$
$79$	1.03339	+	1.78988i	0.116265	+	0.201377i	−0.802020	+	0.597298i	$0.796241\pi$
$80$		0			0
$81$	3.64177	−	8.23028i	0.404641	−	0.914476i
$82$		0			0
$83$	1.33577	−	0.771205i	0.146619	−	0.0846508i	−0.424896	−	0.905242i	$-0.639689\pi$
$83$	1.33577	−	0.771205i	0.146619	−	0.0846508i	0.571515	+	0.820592i	$0.306356\pi$
$84$		0			0
$85$	−2.56108	−	1.47864i	−0.277789	−	0.160381i
$86$		0			0
$87$	−5.89482	−	5.58755i	−0.631991	−	0.599049i
$88$		0			0
$89$	3.96265			0.420040			0.210020	−	0.977697i	$-0.432647\pi$
$89$	3.96265			0.420040			0.210020	+	0.977697i	$0.432647\pi$
$90$		0			0
$91$			17.5051i			1.83503i
$92$		0			0
$93$	−8.18872	−	1.96097i	−0.849130	−	0.203343i
$94$		0			0
$95$	1.73205	−	3.00000i	0.177705	−	0.307794i
$96$		0			0
$97$	−3.06108	−	5.30195i	−0.310806	−	0.538332i	0.667731	−	0.744403i	$-0.267266\pi$
$97$	−3.06108	−	5.30195i	−0.310806	−	0.538332i	−0.978537	+	0.206071i	$0.933932\pi$
$98$		0			0
$99$	7.92925	−	15.6062i	0.796919	−	1.56848i
$100$		0			0
$101$	−10.0051	+	5.77643i	−0.995541	+	0.574776i	−0.906926	−	0.421290i	$-0.861577\pi$
$101$	−10.0051	+	5.77643i	−0.995541	+	0.574776i	−0.0886151	+	0.996066i	$0.528244\pi$
$102$		0			0
$103$	0.110533	−	0.191448i	0.0108911	−	0.0188639i	−0.860528	−	0.509402i	$-0.829867\pi$
$103$	0.110533	−	0.191448i	0.0108911	−	0.0188639i	0.871420	+	0.490538i	$0.163200\pi$
$104$		0			0
$105$	−12.5237	+	3.71751i	−1.22219	+	0.362792i
$106$		0			0
$107$		−	0.329957i		−	0.0318982i	−0.999873	−	0.0159491i	$-0.994923\pi$
$107$		−	0.329957i		−	0.0318982i	0.999873	−	0.0159491i	$-0.00507697\pi$
$108$		0			0
$109$			17.9253i			1.71693i	0.512873	+	0.858465i	$0.328581\pi$
$109$			17.9253i			1.71693i	−0.512873	+	0.858465i	$0.671419\pi$
$110$		0			0
$111$	9.55077	−	2.83502i	0.906519	−	0.269088i
$112$		0			0
$113$	9.04241	−	15.6619i	0.850638	−	1.47335i	−0.0299946	−	0.999550i	$-0.509549\pi$
$113$	9.04241	−	15.6619i	0.850638	−	1.47335i	0.880633	−	0.473799i	$-0.157118\pi$
$114$		0			0
$115$	9.96368	−	5.75253i	0.929118	−	0.536426i
$116$		0			0
$117$	−12.0424	+	0.644960i	−1.11332	+	0.0596266i
$118$		0			0
$119$	3.71751	+	6.43892i	0.340784	+	0.590254i
$120$		0			0
$121$	11.5237	−	19.9597i	1.04761	−	1.81452i
$122$		0			0
$123$	−2.17731	−	0.521405i	−0.196321	−	0.0470135i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$	4.57568			0.406026			0.203013	−	0.979176i	$-0.434927\pi$
$127$	4.57568			0.406026			0.203013	+	0.979176i	$0.434927\pi$
$128$		0			0
$129$	4.45305	+	4.22094i	0.392069	+	0.371633i
$130$		0			0
$131$	−11.7281	−	6.77121i	−1.02469	−	0.591603i	−0.109228	−	0.994017i	$-0.534838\pi$
$131$	−11.7281	−	6.77121i	−1.02469	−	0.591603i	−0.915458	+	0.402414i	$0.868171\pi$
$132$		0			0
$133$	−7.54241	+	4.35461i	−0.654010	+	0.377593i
$134$		0			0
$135$	−3.01885	−	8.47859i	−0.259821	−	0.729721i
$136$		0			0
$137$	11.1887	+	19.3794i	0.955917	+	1.65570i	0.732257	+	0.681029i	$0.238467\pi$
$137$	11.1887	+	19.3794i	0.955917	+	1.65570i	0.223660	+	0.974667i	$0.428200\pi$
$138$		0			0
$139$	9.99602	+	5.77121i	0.847851	+	0.489507i	0.859925	−	0.510420i	$-0.170510\pi$
$139$	9.99602	+	5.77121i	0.847851	+	0.489507i	−0.0120739	+	0.999927i	$0.503843\pi$
$140$		0			0
$141$	12.6463	−	13.3417i	1.06501	−	1.12358i
$142$		0			0
$143$	−23.4561			−1.96150
$144$		0			0
$145$	−8.12217			−0.674509
$146$		0			0
$147$	20.1502	+	4.82542i	1.66196	+	0.397994i
$148$		0			0
$149$	−1.93892	−	1.11943i	−0.158842	−	0.0917076i	0.418472	−	0.908230i	$-0.362566\pi$
$149$	−1.93892	−	1.11943i	−0.158842	−	0.0917076i	−0.577314	+	0.816522i	$0.695899\pi$
$150$		0			0
$151$	−8.51738	−	14.7525i	−0.693134	−	1.20054i	−0.970806	−	0.239868i	$-0.922896\pi$
$151$	−8.51738	−	14.7525i	−0.693134	−	1.20054i	0.277671	−	0.960676i	$-0.410437\pi$
$152$		0			0
$153$	−4.29261	+	2.79466i	−0.347037	+	0.225935i
$154$		0			0
$155$	−7.29214	+	4.21012i	−0.585719	+	0.338165i
$156$		0			0
$157$	−0.0424108	−	0.0244859i	−0.00338475	−	0.00195419i	0.498307	−	0.867001i	$-0.333955\pi$
$157$	−0.0424108	−	0.0244859i	−0.00338475	−	0.00195419i	−0.501691	+	0.865047i	$0.667289\pi$
$158$		0			0
$159$	0.841540	−	0.249800i	0.0667384	−	0.0198104i
$160$		0			0
$161$	−28.9253			−2.27963
$162$		0			0
$163$		−	19.0848i		−	1.49484i	−0.664353	−	0.747419i	$-0.731293\pi$
$163$		−	19.0848i		−	1.49484i	0.664353	−	0.747419i	$-0.268707\pi$
$164$		0			0
$165$	−4.98133	−	16.7813i	−0.387796	−	1.30643i
$166$		0			0
$167$	9.99602	−	17.3136i	0.773515	−	1.33977i	−0.162110	−	0.986773i	$-0.551830\pi$
$167$	9.99602	−	17.3136i	0.773515	−	1.33977i	0.935625	−	0.352995i	$-0.114837\pi$
$168$		0			0
$169$	1.57976	+	2.73622i	0.121520	+	0.210478i
$170$		0			0
$171$	−3.27360	−	5.02827i	−0.250339	−	0.384522i
$172$		0			0
$173$	10.5000	−	6.06218i	0.798300	−	0.460899i	−0.0445762	−	0.999006i	$-0.514194\pi$
$173$	10.5000	−	6.06218i	0.798300	−	0.460899i	0.842876	+	0.538107i	$0.180860\pi$
$174$		0			0
$175$	4.35461	−	7.54241i	0.329178	−	0.570153i
$176$		0			0
$177$	0.755264	−	3.15386i	0.0567691	−	0.237059i
$178$		0			0
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$		0			0
$181$		−	5.75194i		−	0.427538i	−0.976884	−	0.213769i	$-0.931426\pi$
$181$		−	5.75194i		−	0.427538i	0.976884	−	0.213769i	$-0.0685740\pi$
$182$		0			0
$183$	1.54020	+	1.45992i	0.113855	+	0.107921i
$184$		0			0
$185$	4.98133	−	8.62791i	0.366234	−	0.634337i
$186$		0			0
$187$	−8.62791	+	4.98133i	−0.630935	+	0.364271i
$188$		0			0
$189$	−4.08522	+	22.2554i	−0.297156	+	1.61884i
$190$		0			0
$191$	−0.110533	−	0.191448i	−0.00799786	−	0.0138527i	0.861999	−	0.506910i	$-0.169212\pi$
$191$	−0.110533	−	0.191448i	−0.00799786	−	0.0138527i	−0.869997	+	0.493058i	$0.835879\pi$
$192$		0			0
$193$	−9.02374	+	15.6296i	−0.649543	+	1.12504i	0.333689	+	0.942683i	$0.391706\pi$
$193$	−9.02374	+	15.6296i	−0.649543	+	1.12504i	−0.983232	+	0.182358i	$0.941627\pi$
$194$		0			0
$195$	−8.29631	+	8.75253i	−0.594111	+	0.626782i
$196$		0			0
$197$		−	9.82080i		−	0.699703i	−0.936805	−	0.349852i	$-0.886232\pi$
$197$		−	9.82080i		−	0.699703i	0.936805	−	0.349852i	$-0.113768\pi$
$198$		0			0
$199$	−0.604760			−0.0428703			−0.0214352	−	0.999770i	$-0.506824\pi$
$199$	−0.604760			−0.0428703			−0.0214352	+	0.999770i	$0.506824\pi$
$200$		0			0
$201$	−0.637233	+	2.66098i	−0.0449469	+	0.187691i
$202$		0			0
$203$	17.6844	+	10.2101i	1.24120	+	0.716610i
$204$		0			0
$205$	−1.93892	+	1.11943i	−0.135420	+	0.0781846i
$206$		0			0
$207$	−1.06573	−	19.8988i	−0.0740734	−	1.38306i
$208$		0			0
$209$	−5.83502	−	10.1066i	−0.403617	−	0.699085i
$210$		0			0
$211$	−0.363941	−	0.210121i	−0.0250547	−	0.0144654i	0.487420	−	0.873167i	$-0.337938\pi$
$211$	−0.363941	−	0.210121i	−0.0250547	−	0.0144654i	−0.512475	+	0.858702i	$0.671271\pi$
$212$		0			0
$213$	4.87237	+	16.4143i	0.333849	+	1.12469i
$214$		0			0
$215$	6.13564			0.418447
$216$		0			0
$217$	21.1696			1.43709
$218$		0			0
$219$	3.92464	+	13.2215i	0.265203	+	0.893428i
$220$		0			0
$221$	5.94398	+	3.43176i	0.399835	+	0.230845i
$222$		0			0
$223$	11.3933	+	19.7339i	0.762955	+	1.32148i	0.941321	+	0.337513i	$0.109586\pi$
$223$	11.3933	+	19.7339i	0.762955	+	1.32148i	−0.178366	+	0.983964i	$0.557081\pi$
$224$		0			0
$225$	5.34916	+	2.71781i	0.356611	+	0.181188i
$226$		0			0
$227$	10.2494	−	5.91751i	0.680279	−	0.392759i	−0.119681	−	0.992812i	$-0.538187\pi$
$227$	10.2494	−	5.91751i	0.680279	−	0.392759i	0.799960	+	0.600053i	$0.204854\pi$
$228$		0			0
$229$	13.5848	+	7.84320i	0.897710	+	0.518293i	0.876457	−	0.481481i	$-0.159901\pi$
$229$	13.5848	+	7.84320i	0.897710	+	0.518293i	0.0212537	+	0.999774i	$0.493234\pi$
$230$		0			0
$231$	−10.2494	+	42.8000i	−0.674363	+	2.81603i
$232$		0			0
$233$	−0.829557			−0.0543461			−0.0271731	−	0.999631i	$-0.508651\pi$
$233$	−0.829557			−0.0543461			−0.0271731	+	0.999631i	$0.508651\pi$
$234$		0			0
$235$		−	18.3829i		−	1.19917i
$236$		0			0
$237$	2.46265	−	2.59808i	0.159967	−	0.168763i
$238$		0			0
$239$	3.60698	−	6.24747i	0.233316	−	0.404115i	−0.725466	−	0.688258i	$-0.758376\pi$
$239$	3.60698	−	6.24747i	0.233316	−	0.404115i	0.958782	+	0.284143i	$0.0917090\pi$
$240$		0			0
$241$	10.4627	+	18.1218i	0.673959	+	1.16733i	0.976772	+	0.214281i	$0.0687408\pi$
$241$	10.4627	+	18.1218i	0.673959	+	1.16733i	−0.302813	+	0.953050i	$0.597926\pi$
$242$		0			0
$243$	−15.4609	−	1.99040i	−0.991815	−	0.127684i
$244$		0			0
$245$	17.9440	−	10.3600i	1.14640	−	0.661874i
$246$		0			0
$247$	−4.01989	+	6.96265i	−0.255779	+	0.443023i
$248$		0			0
$249$	−1.93892	−	1.83785i	−0.122874	−	0.116469i
$250$		0			0
$251$		−	20.2553i		−	1.27850i	−0.768999	−	0.639250i	$-0.779245\pi$
$251$		−	20.2553i		−	1.27850i	0.768999	−	0.639250i	$-0.220755\pi$
$252$		0			0
$253$		−	38.7588i		−	2.43675i
$254$		0			0
$255$	−1.19289	+	4.98133i	−0.0747018	+	0.311943i
$256$		0			0
$257$	3.37237	−	5.84111i	0.210363	−	0.364359i	−0.741465	−	0.670991i	$-0.765869\pi$
$257$	3.37237	−	5.84111i	0.210363	−	0.364359i	0.951828	+	0.306632i	$0.0992022\pi$
$258$		0			0
$259$	−21.6917	+	12.5237i	−1.34786	+	0.778187i
$260$		0			0
$261$	−6.37237	+	12.5420i	−0.394440	+	0.776330i
$262$		0			0
$263$	13.2067	+	22.8747i	0.814361	+	1.41051i	0.909786	+	0.415078i	$0.136246\pi$
$263$	13.2067	+	22.8747i	0.814361	+	1.41051i	−0.0954250	+	0.995437i	$0.530421\pi$
$264$		0			0
$265$	0.438916	−	0.760225i	0.0269624	−	0.0467002i
$266$		0			0
$267$	−1.95312	−	6.57976i	−0.119529	−	0.402675i
$268$		0			0
$269$			23.1704i			1.41272i	0.707851	+	0.706362i	$0.249665\pi$
$269$			23.1704i			1.41272i	−0.707851	+	0.706362i	$0.750335\pi$
$270$		0			0
$271$	−17.7626			−1.07900			−0.539502	−	0.841984i	$-0.681387\pi$
$271$	−17.7626			−1.07900			−0.539502	+	0.841984i	$0.681387\pi$
$272$		0			0
$273$	29.0661	−	8.62791i	1.75916	−	0.522185i
$274$		0			0
$275$	10.1066	+	5.83502i	0.609448	+	0.351865i
$276$		0			0
$277$	9.04241	−	5.22064i	0.543306	−	0.313678i	−0.203112	−	0.979156i	$-0.565106\pi$
$277$	9.04241	−	5.22064i	0.543306	−	0.313678i	0.746418	+	0.665478i	$0.231772\pi$
$278$		0			0
$279$	0.779979	+	14.5634i	0.0466961	+	0.871889i
$280$		0			0
$281$	13.4440	+	23.2857i	0.802001	+	1.38911i	0.918297	+	0.395891i	$0.129564\pi$
$281$	13.4440	+	23.2857i	0.802001	+	1.38911i	−0.116297	+	0.993215i	$0.537102\pi$
$282$		0			0
$283$	−16.1317	−	9.31362i	−0.958927	−	0.553637i	−0.0630847	−	0.998008i	$-0.520094\pi$
$283$	−16.1317	−	9.31362i	−0.958927	−	0.553637i	−0.895843	+	0.444371i	$0.853427\pi$
$284$		0			0
$285$	−5.83502	−	1.39733i	−0.345637	−	0.0827706i
$286$		0			0
$287$	5.62882			0.332259
$288$		0			0
$289$	−14.0848			−0.828519
$290$		0			0
$291$	−7.29484	+	7.69598i	−0.427631	+	0.451147i
$292$		0			0
$293$	1.00506	+	0.580274i	0.0587165	+	0.0339000i	0.529071	−	0.848578i	$-0.322541\pi$
$293$	1.00506	+	0.580274i	0.0587165	+	0.0339000i	−0.470354	+	0.882478i	$0.655874\pi$
$294$		0			0
$295$	−1.62152	−	2.80855i	−0.0944084	−	0.163520i
$296$		0			0
$297$	−29.8214	−	5.47405i	−1.73041	−	0.317636i
$298$		0			0
$299$	−23.1245	+	13.3510i	−1.33733	+	0.772106i
$300$		0			0
$301$	−13.3592	−	7.71291i	−0.770009	−	0.444565i
$302$		0			0
$303$	14.5227	+	13.7657i	0.834309	+	0.790821i
$304$		0			0
$305$	2.12217			0.121515
$306$		0			0
$307$			19.0848i			1.08923i	0.838687	+	0.544614i	$0.183324\pi$
$307$			19.0848i			1.08923i	−0.838687	+	0.544614i	$0.816676\pi$
$308$		0			0
$309$	−0.372368	−	0.0891719i	−0.0211833	−	0.00507281i
$310$		0			0
$311$	5.56009	−	9.63036i	0.315284	−	0.546088i	−0.664214	−	0.747543i	$-0.731234\pi$
$311$	5.56009	−	9.63036i	0.315284	−	0.546088i	0.979498	+	0.201455i	$0.0645669\pi$
$312$		0			0
$313$	−13.4627	−	23.3180i	−0.760954	−	1.31801i	−0.942359	−	0.334603i	$-0.891398\pi$
$313$	−13.4627	−	23.3180i	−0.760954	−	1.31801i	0.181405	−	0.983408i	$-0.441935\pi$
$314$		0			0
$315$	12.3454	+	18.9627i	0.695586	+	1.06842i
$316$		0			0
$317$	19.4440	−	11.2260i	1.09208	−	0.630514i	0.157953	−	0.987447i	$-0.449511\pi$
$317$	19.4440	−	11.2260i	1.09208	−	0.630514i	0.934130	+	0.356932i	$0.116177\pi$
$318$		0			0
$319$	−13.6812	+	23.6965i	−0.765999	+	1.32675i
$320$		0			0
$321$	−0.547875	+	0.162630i	−0.0305794	+	0.00907710i
$322$		0			0
$323$			3.41478i			0.190003i
$324$		0			0
$325$		−	8.03978i		−	0.445967i
$326$		0			0
$327$	29.7639	−	8.83502i	1.64595	−	0.488578i
$328$		0			0
$329$	−23.1086	+	40.0252i	−1.27402	+	2.20666i
$330$		0			0
$331$	19.5634	−	11.2949i	1.07530	−	0.620826i	0.145677	−	0.989332i	$-0.453464\pi$
$331$	19.5634	−	11.2949i	1.07530	−	0.620826i	0.929625	+	0.368506i	$0.120131\pi$
$332$		0			0
$333$	−9.41478	−	14.4612i	−0.515927	−	0.792467i
$334$		0			0
$335$	1.36811	+	2.36964i	0.0747478	+	0.129467i
$336$		0			0
$337$	7.04241	−	12.1978i	0.383625	−	0.664457i	−0.607953	−	0.793973i	$-0.708009\pi$
$337$	7.04241	−	12.1978i	0.383625	−	0.664457i	0.991577	+	0.129516i	$0.0413423\pi$
$338$		0			0
$339$	−30.4625	−	7.29494i	−1.65450	−	0.396207i
$340$		0			0
$341$			28.3665i			1.53613i
$342$		0			0
$343$	−21.6104			−1.16685
$344$		0			0
$345$	−14.4627	−	13.7088i	−0.778643	−	0.738057i
$346$		0			0
$347$	6.05745	+	3.49727i	0.325181	+	0.187743i	0.653699	−	0.756754i	$-0.273216\pi$
$347$	6.05745	+	3.49727i	0.325181	+	0.187743i	−0.328519	+	0.944497i	$0.606549\pi$
$348$		0			0
$349$	8.16458	−	4.71382i	0.437040	−	0.252325i	−0.265301	−	0.964166i	$-0.585471\pi$
$349$	8.16458	−	4.71382i	0.437040	−	0.252325i	0.702341	+	0.711840i	$0.252138\pi$
$350$		0			0
$351$	7.00639	+	19.6778i	0.373974	+	1.05033i
$352$		0			0
$353$	3.81128	+	6.60134i	0.202854	+	0.351354i	0.949447	−	0.313928i	$-0.101645\pi$
$353$	3.81128	+	6.60134i	0.202854	+	0.351354i	−0.746593	+	0.665281i	$0.768312\pi$
$354$		0			0
$355$	14.8282	+	8.56108i	0.787001	+	0.454375i
$356$		0			0
$357$	8.85916	−	9.34633i	0.468876	−	0.494660i
$358$		0			0
$359$	−10.8344			−0.571820			−0.285910	−	0.958257i	$-0.592296\pi$
$359$	−10.8344			−0.571820			−0.285910	+	0.958257i	$0.592296\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$		0			0
$363$	−38.8218	−	9.29675i	−2.03761	−	0.487953i
$364$		0			0
$365$	11.9440	+	6.89586i	0.625176	+	0.360946i
$366$		0			0
$367$	−11.4747	−	19.8747i	−0.598973	−	1.03745i	−0.992973	−	0.118341i	$-0.962243\pi$
$367$	−11.4747	−	19.8747i	−0.598973	−	1.03745i	0.394000	−	0.919110i	$-0.371091\pi$
$368$		0			0
$369$	0.207389	+	3.87228i	0.0107963	+	0.201583i
$370$		0			0
$371$	−1.91131	+	1.10349i	−0.0992302	+	0.0572906i
$372$		0			0
$373$	0.0984305	+	0.0568289i	0.00509654	+	0.00294249i	0.502546	−	0.864550i	$-0.332397\pi$
$373$	0.0984305	+	0.0568289i	0.00509654	+	0.00294249i	−0.497450	+	0.867493i	$0.665730\pi$
$374$		0			0
$375$	20.1318	−	5.97586i	1.03960	−	0.308592i
$376$		0			0
$377$	18.8506			0.970856
$378$		0			0
$379$		−	16.2070i		−	0.832497i	−0.909251	−	0.416249i	$-0.863345\pi$
$379$		−	16.2070i		−	0.832497i	0.909251	−	0.416249i	$-0.136655\pi$
$380$		0			0
$381$	−2.25526	−	7.59765i	−0.115541	−	0.389239i
$382$		0			0
$383$	7.03874	−	12.1914i	0.359663	−	0.622954i	−0.628242	−	0.778018i	$-0.716225\pi$
$383$	7.03874	−	12.1914i	0.359663	−	0.622954i	0.987904	+	0.155064i	$0.0495585\pi$
$384$		0			0
$385$	22.0051	+	38.1139i	1.12148	+	1.94246i
$386$		0			0
$387$	4.81380	−	9.47446i	0.244699	−	0.481614i
$388$		0			0
$389$	25.0051	−	14.4367i	1.26781	−	0.731969i	0.293234	−	0.956041i	$-0.405268\pi$
$389$	25.0051	−	14.4367i	1.26781	−	0.731969i	0.974573	+	0.224072i	$0.0719350\pi$
$390$		0			0
$391$	−5.67063	+	9.82181i	−0.286776	+	0.496710i
$392$		0			0
$393$	−5.46265	+	22.8112i	−0.275554	+	1.15067i
$394$		0			0
$395$		−	3.57976i		−	0.180117i
$396$		0			0
$397$			2.85934i			0.143506i	0.997422	+	0.0717531i	$0.0228594\pi$
$397$			2.85934i			0.143506i	−0.997422	+	0.0717531i	$0.977141\pi$
$398$		0			0
$399$	10.9481	+	10.3774i	0.548090	+	0.519521i
$400$		0			0
$401$	−10.7739	+	18.6610i	−0.538025	+	0.931886i	0.460986	+	0.887408i	$0.347496\pi$
$401$	−10.7739	+	18.6610i	−0.538025	+	0.931886i	−0.999010	+	0.0444786i	$0.985837\pi$
$402$		0			0
$403$	16.9242	−	9.77121i	0.843056	−	0.486738i
$404$		0			0
$405$	−12.5903	+	9.19156i	−0.625616	+	0.456732i
$406$		0			0
$407$	−16.7813	−	29.0661i	−0.831821	−	1.44076i
$408$		0			0
$409$	10.4627	−	18.1218i	0.517345	−	0.896068i	−0.482452	−	0.875922i	$-0.660254\pi$
$409$	10.4627	−	18.1218i	0.517345	−	0.896068i	0.999797	−	0.0201454i	$-0.00641290\pi$
$410$		0			0
$411$	26.6637	−	28.1300i	1.31522	−	1.38755i
$412$		0			0
$413$			8.15344i			0.401204i
$414$		0			0
$415$	−2.67153			−0.131140
$416$		0			0
$417$	4.65591	−	19.4423i	0.228001	−	0.952095i
$418$		0			0
$419$	10.9678	+	6.33229i	0.535814	+	0.309353i	0.743381	−	0.668868i	$-0.233221\pi$
$419$	10.9678	+	6.33229i	0.535814	+	0.309353i	−0.207567	+	0.978221i	$0.566554\pi$
$420$		0			0
$421$	23.1086	−	13.3417i	1.12624	−	0.650236i	0.183255	−	0.983065i	$-0.441337\pi$
$421$	23.1086	−	13.3417i	1.12624	−	0.650236i	0.942987	+	0.332829i	$0.108003\pi$
$422$		0			0
$423$	−28.3863	−	14.4226i	−1.38019	−	0.701250i
$424$		0			0
$425$	−1.70739	−	2.95729i	−0.0828205	−	0.143449i
$426$		0			0
$427$	−4.62061	−	2.66771i	−0.223607	−	0.129100i
$428$		0			0
$429$	11.5611	+	38.9476i	0.558174	+	1.88041i
$430$		0			0
$431$	23.6772			1.14049			0.570246	−	0.821474i	$-0.306848\pi$
$431$	23.6772			1.14049			0.570246	+	0.821474i	$0.306848\pi$
$432$		0			0
$433$	7.96265			0.382661			0.191330	−	0.981526i	$-0.438720\pi$
$433$	7.96265			0.382661			0.191330	+	0.981526i	$0.438720\pi$
$434$		0			0
$435$	4.00326	+	13.4864i	0.191942	+	0.646623i
$436$		0			0
$437$	−11.5051	−	6.64245i	−0.550362	−	0.317752i
$438$		0			0
$439$	5.33903	+	9.24747i	0.254818	+	0.441358i	0.964846	−	0.262816i	$-0.0846511\pi$
$439$	5.33903	+	9.24747i	0.254818	+	0.441358i	−0.710028	+	0.704173i	$0.751318\pi$
$440$		0			0
$441$	−1.91932	−	35.8366i	−0.0913960	−	1.70650i
$442$		0			0
$443$	11.1566	−	6.44125i	0.530065	−	0.306033i	−0.210978	−	0.977491i	$-0.567665\pi$
$443$	11.1566	−	6.44125i	0.530065	−	0.306033i	0.741043	+	0.671458i	$0.234332\pi$
$444$		0			0
$445$	−5.94398	−	3.43176i	−0.281772	−	0.162681i
$446$		0			0
$447$	−0.903100	+	3.77121i	−0.0427152	+	0.178372i
$448$		0			0
$449$	−0.547875			−0.0258558			−0.0129279	−	0.999916i	$-0.504115\pi$
$449$	−0.547875			−0.0258558			−0.0129279	+	0.999916i	$0.504115\pi$
$450$		0			0
$451$			7.54241i			0.355158i
$452$		0			0
$453$	−20.2977	+	21.4139i	−0.953668	+	1.00611i
$454$		0			0
$455$	15.1598	−	26.2576i	0.710704	−	1.23098i
$456$		0			0
$457$	−9.90157	−	17.1500i	−0.463176	−	0.802244i	0.535941	−	0.844255i	$-0.319957\pi$
$457$	−9.90157	−	17.1500i	−0.463176	−	0.802244i	−0.999117	+	0.0420111i	$0.986624\pi$
$458$		0			0
$459$	6.75611	+	5.75020i	0.315348	+	0.268396i
$460$		0			0
$461$	−12.1833	+	7.03400i	−0.567431	+	0.327606i	−0.756122	−	0.654430i	$-0.772909\pi$
$461$	−12.1833	+	7.03400i	−0.567431	+	0.327606i	0.188692	+	0.982036i	$0.439575\pi$
$462$		0			0
$463$	6.22954	−	10.7899i	0.289511	−	0.501448i	−0.684182	−	0.729311i	$-0.739841\pi$
$463$	6.22954	−	10.7899i	0.289511	−	0.501448i	0.973693	+	0.227863i	$0.0731739\pi$
$464$		0			0
$465$	10.5848	+	10.0331i	0.490859	+	0.465274i
$466$		0			0
$467$			29.3401i			1.35770i	0.734278	+	0.678849i	$0.237521\pi$
$467$			29.3401i			1.35770i	−0.734278	+	0.678849i	$0.762479\pi$
$468$		0			0
$469$		−	6.87923i		−	0.317653i
$470$		0			0
$471$	−0.0197539	+	0.0824893i	−0.000910213	+	0.00380091i
$472$		0			0
$473$	10.3350	−	17.9008i	0.475205	−	0.823079i
$474$		0			0
$475$	3.46410	−	2.00000i	0.158944	−	0.0917663i
$476$		0			0
$477$	−0.829557	−	1.27421i	−0.0379828	−	0.0583419i
$478$		0			0
$479$	−9.96368	−	17.2576i	−0.455252	−	0.788520i	0.543451	−	0.839441i	$-0.317118\pi$
$479$	−9.96368	−	17.2576i	−0.455252	−	0.788520i	−0.998703	+	0.0509214i	$0.983784\pi$
$480$		0			0
$481$	−11.5611	+	20.0244i	−0.527140	+	0.913033i
$482$		0			0
$483$	14.2567	+	48.0288i	0.648704	+	2.18539i
$484$		0			0
$485$			10.6039i			0.481499i
$486$		0			0
$487$	7.46828			0.338420			0.169210	−	0.985580i	$-0.445878\pi$
$487$	7.46828			0.338420			0.169210	+	0.985580i	$0.445878\pi$
$488$		0			0
$489$	−31.6892	+	9.40654i	−1.43304	+	0.425379i
$490$		0			0
$491$	30.2186	+	17.4467i	1.36375	+	0.787359i	0.990120	−	0.140220i	$-0.0447811\pi$
$491$	30.2186	+	17.4467i	1.36375	+	0.787359i	0.373626	+	0.927580i	$0.378114\pi$
$492$		0			0
$493$	6.93385	−	4.00326i	0.312285	−	0.180298i
$494$		0			0
$495$	−25.4093	+	16.5424i	−1.14206	+	0.743526i
$496$		0			0
$497$	−21.5237	−	37.2802i	−0.965472	−	1.67225i
$498$		0			0
$499$	−32.4480	−	18.7339i	−1.45257	−	0.838643i	−0.453945	−	0.891030i	$-0.649984\pi$
$499$	−32.4480	−	18.7339i	−1.45257	−	0.838643i	−0.998627	+	0.0523870i	$0.983317\pi$
$500$		0			0
$501$	−33.6751	−	8.06427i	−1.50449	−	0.360285i
$502$		0			0
$503$	−10.8991			−0.485968			−0.242984	−	0.970030i	$-0.578126\pi$
$503$	−10.8991			−0.485968			−0.242984	+	0.970030i	$0.578126\pi$
$504$		0			0
$505$	20.0101			0.890439
$506$		0			0
$507$	3.76470	−	3.97173i	0.167196	−	0.176391i
$508$		0			0
$509$	4.06108	+	2.34467i	0.180004	+	0.103926i	0.587295	−	0.809373i	$-0.300193\pi$
$509$	4.06108	+	2.34467i	0.180004	+	0.103926i	−0.407290	+	0.913299i	$0.633526\pi$
$510$		0			0
$511$	−17.3371	−	30.0288i	−0.766950	−	1.32840i
$512$		0			0
$513$	−6.73566	+	7.91396i	−0.297387	+	0.349410i
$514$		0			0
$515$	−0.331598	+	0.191448i	−0.0146119	+	0.00843621i
$516$		0			0
$517$	−53.6323	−	30.9646i	−2.35875	−	1.36182i
$518$		0			0
$519$	−15.2411	−	14.4467i	−0.669012	−	0.634140i
$520$		0			0
$521$	−26.4249			−1.15770			−0.578848	−	0.815435i	$-0.696498\pi$
$521$	−26.4249			−1.15770			−0.578848	+	0.815435i	$0.696498\pi$
$522$		0			0
$523$		−	13.8880i		−	0.607278i	−0.952787	−	0.303639i	$-0.901798\pi$
$523$		−	13.8880i		−	0.607278i	0.952787	−	0.303639i	$-0.0982017\pi$
$524$		0			0
$525$	−14.6700	−	3.51307i	−0.640253	−	0.153323i
$526$		0			0
$527$	4.15018	−	7.18832i	0.180785	−	0.313128i
$528$		0			0
$529$	−10.5611	−	18.2923i	−0.459178	−	0.795319i
$530$		0			0
$531$	−5.60907	+	0.300407i	−0.243413	+	0.0130366i
$532$		0			0
$533$	4.50000	−	2.59808i	0.194917	−	0.112535i
$534$		0			0
$535$	−0.285751	+	0.494936i	−0.0123541	+	0.0213979i
$536$		0			0
$537$	9.96265	−	2.95729i	0.429920	−	0.127616i
$538$		0			0
$539$		−	69.8023i		−	3.00660i
$540$		0			0
$541$			25.0161i			1.07553i	0.843096	+	0.537763i	$0.180731\pi$
$541$			25.0161i			1.07553i	−0.843096	+	0.537763i	$0.819269\pi$
$542$		0			0
$543$	−9.55077	+	2.83502i	−0.409863	+	0.121662i
$544$		0			0
$545$	15.5237	−	26.8879i	0.664964	−	1.15175i
$546$		0			0
$547$	−12.4236	+	7.17277i	−0.531195	+	0.306686i	−0.741503	−	0.670950i	$-0.765887\pi$
$547$	−12.4236	+	7.17277i	−0.531195	+	0.306686i	0.210308	+	0.977635i	$0.432553\pi$
$548$		0			0
$549$	1.66498	−	3.27699i	0.0710596	−	0.139858i
$550$		0			0
$551$	4.68934	+	8.12217i	0.199772	+	0.346016i
$552$		0			0
$553$	−4.50000	+	7.79423i	−0.191359	+	0.331444i
$554$		0			0
$555$	−16.7813	−	4.01867i	−0.712329	−	0.170583i
$556$		0			0
$557$		−	32.9912i		−	1.39788i	−0.715179	−	0.698941i	$-0.753655\pi$
$557$		−	32.9912i		−	1.39788i	0.715179	−	0.698941i	$-0.246345\pi$
$558$		0			0
$559$	−14.2401			−0.602292
$560$		0			0
$561$	12.5237	+	11.8709i	0.528753	+	0.501192i
$562$		0			0
$563$	−21.6459	−	12.4973i	−0.912266	−	0.526697i	−0.0311065	−	0.999516i	$-0.509903\pi$
$563$	−21.6459	−	12.4973i	−0.912266	−	0.526697i	−0.881160	+	0.472819i	$0.843236\pi$
$564$		0			0
$565$	−27.1272	+	15.6619i	−1.14125	+	0.658902i
$566$		0			0
$567$	38.9673	−	4.18598i	1.63647	−	0.175795i
$568$		0			0
$569$	2.79261	+	4.83694i	0.117072	+	0.202775i	0.918606	−	0.395174i	$-0.129316\pi$
$569$	2.79261	+	4.83694i	0.117072	+	0.202775i	−0.801534	+	0.597949i	$0.795982\pi$
$570$		0			0
$571$	−4.83221	−	2.78988i	−0.202222	−	0.116753i	0.395470	−	0.918479i	$-0.370582\pi$
$571$	−4.83221	−	2.78988i	−0.202222	−	0.116753i	−0.597691	+	0.801726i	$0.703915\pi$
$572$		0			0
$573$	−0.263409	+	0.277894i	−0.0110041	+	0.0116092i
$574$		0			0
$575$	13.2849			0.554019
$576$		0			0
$577$	−9.04748			−0.376651			−0.188326	−	0.982107i	$-0.560306\pi$
$577$	−9.04748			−0.376651			−0.188326	+	0.982107i	$0.560306\pi$
$578$		0			0
$579$	30.3996	+	7.27988i	1.26337	+	0.302541i
$580$		0			0
$581$	5.81675	+	3.35830i	0.241319	+	0.139326i
$582$		0			0
$583$	−1.47864	−	2.56108i	−0.0612391	−	0.106069i
$584$		0			0
$585$	18.6222	+	9.46159i	0.769932	+	0.391189i
$586$		0			0
$587$	6.24617	−	3.60623i	0.257807	−	0.148845i	−0.365527	−	0.930801i	$-0.619111\pi$
$587$	6.24617	−	3.60623i	0.257807	−	0.148845i	0.623334	+	0.781956i	$0.285778\pi$
$588$		0			0
$589$	8.42024	+	4.86143i	0.346950	+	0.200312i
$590$		0			0
$591$	−16.3069	+	4.84049i	−0.670775	+	0.199111i
$592$		0			0
$593$	−25.0475			−1.02858			−0.514288	−	0.857617i	$-0.671944\pi$
$593$	−25.0475			−1.02858			−0.514288	+	0.857617i	$0.671944\pi$
$594$		0			0
$595$		−	12.8778i		−	0.527940i
$596$		0			0
$597$	0.298075	+	1.00417i	0.0121994	+	0.0410979i
$598$		0			0
$599$	−20.1026	+	34.8187i	−0.821369	+	1.42265i	0.0832941	+	0.996525i	$0.473456\pi$
$599$	−20.1026	+	34.8187i	−0.821369	+	1.42265i	−0.904663	+	0.426128i	$0.859877\pi$
$600$		0			0
$601$	5.48133	+	9.49394i	0.223588	+	0.387266i	0.955895	−	0.293709i	$-0.0948897\pi$
$601$	5.48133	+	9.49394i	0.223588	+	0.387266i	−0.732307	+	0.680975i	$0.761556\pi$
$602$		0			0
$603$	4.73249	−	0.253460i	0.192722	−	0.0103217i
$604$		0			0
$605$	−34.5712	+	19.9597i	−1.40552	+	0.811477i
$606$		0			0
$607$	14.2370	−	24.6592i	0.577861	−	1.00088i	−0.417863	−	0.908510i	$-0.637221\pi$
$607$	14.2370	−	24.6592i	0.577861	−	1.00088i	0.995724	−	0.0923747i	$-0.0294458\pi$
$608$		0			0
$609$	8.23699	−	34.3964i	0.333780	−	1.39381i
$610$		0			0
$611$			42.6646i			1.72602i
$612$		0			0
$613$			14.3632i			0.580125i	0.957008	+	0.290063i	$0.0936761\pi$
$613$			14.3632i			0.580125i	−0.957008	+	0.290063i	$0.906324\pi$
$614$		0			0
$615$	2.81441	+	2.66771i	0.113488	+	0.107572i
$616$		0			0
$617$	0.316348	−	0.547931i	0.0127357	−	0.0220589i	−0.859587	−	0.510989i	$-0.829279\pi$
$617$	0.316348	−	0.547931i	0.0127357	−	0.0220589i	0.872323	+	0.488930i	$0.162613\pi$
$618$		0			0
$619$	28.9516	−	16.7152i	1.16366	−	0.671840i	0.211482	−	0.977382i	$-0.432171\pi$
$619$	28.9516	−	16.7152i	1.16366	−	0.671840i	0.952179	+	0.305542i	$0.0988376\pi$
$620$		0			0
$621$	−32.5156	+	11.5773i	−1.30481	+	0.464583i
$622$		0			0
$623$	8.62791	+	14.9440i	0.345670	+	0.598718i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$		0			0
$627$	−13.9054	+	14.6700i	−0.555327	+	0.585865i
$628$		0			0
$629$			9.82080i			0.391581i
$630$		0			0
$631$	7.59765			0.302458			0.151229	−	0.988499i	$-0.451677\pi$
$631$	7.59765			0.302458			0.151229	+	0.988499i	$0.451677\pi$
$632$		0			0
$633$	−0.169515	+	0.707868i	−0.00673761	+	0.0281352i
$634$		0			0
$635$	−6.86352	−	3.96265i	−0.272370	−	0.157253i
$636$		0			0
$637$	−41.6459	+	24.0443i	−1.65007	+	0.952669i
$638$		0			0
$639$	24.8535	−	16.1806i	0.983188	−	0.640094i
$640$		0			0
$641$	11.8774	+	20.5723i	0.469130	+	0.812558i	0.999377	−	0.0352856i	$-0.0112341\pi$
$641$	11.8774	+	20.5723i	0.469130	+	0.812558i	−0.530247	+	0.847843i	$0.677901\pi$
$642$		0			0
$643$	12.4236	+	7.17277i	0.489939	+	0.282867i	0.724549	−	0.689223i	$-0.242048\pi$
$643$	12.4236	+	7.17277i	0.489939	+	0.282867i	−0.234610	+	0.972090i	$0.575381\pi$
$644$		0			0
$645$	−3.02414	−	10.1879i	−0.119075	−	0.401147i
$646$		0			0
$647$	−28.5781			−1.12352			−0.561761	−	0.827299i	$-0.689876\pi$
$647$	−28.5781			−1.12352			−0.561761	+	0.827299i	$0.689876\pi$
$648$		0			0
$649$	−10.9253			−0.428856
$650$		0			0
$651$	−10.4341	−	35.1510i	−0.408945	−	1.37768i
$652$		0			0
$653$	14.7443	+	8.51265i	0.576990	+	0.333126i	0.759936	−	0.649997i	$-0.225230\pi$
$653$	14.7443	+	8.51265i	0.576990	+	0.333126i	−0.182946	+	0.983123i	$0.558563\pi$
$654$		0			0
$655$	11.7281	+	20.3136i	0.458254	+	0.793719i
$656$		0			0
$657$	20.0192	−	13.0333i	0.781023	−	0.508476i
$658$		0			0
$659$	10.8209	−	6.24747i	0.421524	−	0.243367i	−0.274205	−	0.961671i	$-0.588415\pi$
$659$	10.8209	−	6.24747i	0.421524	−	0.243367i	0.695729	+	0.718304i	$0.255081\pi$
$660$		0			0
$661$	30.1272	+	17.3940i	1.17181	+	0.676547i	0.954107	−	0.299467i	$-0.0968090\pi$
$661$	30.1272	+	17.3940i	1.17181	+	0.676547i	0.217707	+	0.976014i	$0.430142\pi$
$662$		0			0
$663$	2.76856	−	11.5611i	0.107522	−	0.448995i
$664$		0			0
$665$	15.0848			0.584964
$666$		0			0
$667$			31.1487i			1.20608i
$668$		0			0
$669$	27.1514	−	28.6444i	1.04973	−	1.10746i
$670$		0			0
$671$	3.57463	−	6.19145i	0.137997	−	0.239018i
$672$		0			0
$673$	−13.0237	−	22.5578i	−0.502028	−	0.869538i	−0.999997	−	0.00234354i	$-0.999254\pi$
$673$	−13.0237	−	22.5578i	−0.502028	−	0.869538i	0.497969	−	0.867195i	$-0.334079\pi$
$674$		0			0
$675$	1.87627	−	10.2215i	0.0722178	−	0.393427i
$676$		0			0
$677$	−28.8829	+	16.6755i	−1.11006	+	0.640893i	−0.938845	−	0.344340i	$-0.888103\pi$
$677$	−28.8829	+	16.6755i	−1.11006	+	0.640893i	−0.171215	+	0.985234i	$0.554769\pi$
$678$		0			0
$679$	13.3298	−	23.0880i	0.511552	−	0.886034i
$680$		0			0
$681$	−14.8774	−	14.1020i	−0.570104	−	0.540388i
$682$		0			0
$683$			26.4249i			1.01112i	0.862791	+	0.505560i	$0.168714\pi$
$683$			26.4249i			1.01112i	−0.862791	+	0.505560i	$0.831286\pi$
$684$		0			0
$685$		−	38.7588i		−	1.48090i
$686$		0			0
$687$	6.32748	−	26.4226i	0.241409	−	1.00808i
$688$		0			0
$689$	−1.01867	+	1.76439i	−0.0388084	+	0.0672181i
$690$		0			0
$691$	17.6521	−	10.1914i	0.671518	−	0.387701i	−0.125134	−	0.992140i	$-0.539936\pi$
$691$	17.6521	−	10.1914i	0.671518	−	0.387701i	0.796651	+	0.604439i	$0.206603\pi$
$692$		0			0
$693$	76.1187	−	4.07672i	2.89151	−	0.154862i
$694$		0			0
$695$	−9.99602	−	17.3136i	−0.379171	−	0.656743i
$696$		0			0
$697$	1.10349	−	1.91131i	0.0417978	−	0.0723960i
$698$		0			0
$699$	0.408873	+	1.37743i	0.0154650	+	0.0520993i
$700$		0			0
$701$		−	49.8696i		−	1.88355i	−0.336247	−	0.941774i	$-0.609158\pi$
$701$		−	49.8696i		−	1.88355i	0.336247	−	0.941774i	$-0.390842\pi$
$702$		0			0
$703$	−11.5039			−0.433877
$704$		0			0
$705$	−30.5237	+	9.06058i	−1.14959	+	0.341241i
$706$		0			0
$707$	−43.5682	−	25.1541i	−1.63855	−	0.946017i
$708$		0			0
$709$	8.57469	−	4.95060i	0.322029	−	0.185924i	−0.330267	−	0.943887i	$-0.607139\pi$
$709$	8.57469	−	4.95060i	0.322029	−	0.185924i	0.652297	+	0.757964i	$0.273806\pi$
$710$		0			0
$711$	−5.52775	−	2.80855i	−0.207307	−	0.105329i
$712$		0			0
$713$	16.1459	+	27.9655i	0.604669	+	1.04732i
$714$		0			0
$715$	35.1842	+	20.3136i	1.31582	+	0.759686i
$716$		0			0
$717$	−12.1514	−	2.90992i	−0.453801	−	0.108673i
$718$		0			0
$719$	−25.5562			−0.953084			−0.476542	−	0.879152i	$-0.658110\pi$
$719$	−25.5562			−0.953084			−0.476542	+	0.879152i	$0.658110\pi$
$720$		0			0
$721$	0.962653			0.0358511
$722$		0			0
$723$	24.9334	−	26.3045i	0.927285	−	0.978277i
$724$		0			0
$725$	−8.12217	−	4.68934i	−0.301650	−	0.174158i
$726$		0			0
$727$	20.0702	+	34.7627i	0.744364	+	1.28928i	0.950491	+	0.310751i	$0.100580\pi$
$727$	20.0702	+	34.7627i	0.744364	+	1.28928i	−0.206128	+	0.978525i	$0.566086\pi$
$728$		0			0
$729$	4.31542	+	26.6529i	0.159830	+	0.987144i
$730$		0			0
$731$	−5.23796	+	3.02414i	−0.193733	+	0.111852i
$732$		0			0
$733$	40.9965	+	23.6694i	1.51424	+	0.874247i	0.999861	+	0.0166852i	$0.00531131\pi$
$733$	40.9965	+	23.6694i	1.51424	+	0.874247i	0.514380	+	0.857562i	$0.328022\pi$
$734$		0			0
$735$	−26.0464	−	24.6887i	−0.960735	−	0.910657i
$736$		0			0
$737$	9.21792			0.339546
$738$		0			0
$739$			37.9627i			1.39648i	0.715864	+	0.698239i	$0.246033\pi$
$739$			37.9627i			1.39648i	−0.715864	+	0.698239i	$0.753967\pi$
$740$		0			0
$741$	13.5424	+	3.24304i	0.497493	+	0.119136i
$742$		0			0
$743$	−7.25980	+	12.5743i	−0.266336	+	0.461308i	−0.967913	−	0.251286i	$-0.919146\pi$
$743$	−7.25980	+	12.5743i	−0.266336	+	0.461308i	0.701577	+	0.712594i	$0.252480\pi$
$744$		0			0
$745$	1.93892	+	3.35830i	0.0710364	+	0.123039i
$746$		0			0
$747$	−2.09599	+	4.12530i	−0.0766883	+	0.150937i
$748$		0			0
$749$	1.24434	−	0.718418i	0.0454671	−	0.0262504i
$750$		0			0
$751$	−18.3216	+	31.7339i	−0.668563	+	1.15798i	0.309743	+	0.950820i	$0.399757\pi$
$751$	−18.3216	+	31.7339i	−0.668563	+	1.15798i	−0.978306	+	0.207165i	$0.933576\pi$
$752$		0			0
$753$	−33.6327	+	9.98343i	−1.22564	+	0.363816i
$754$		0			0
$755$			29.5051i			1.07380i
$756$		0			0
$757$			2.02727i			0.0736822i	0.999321	+	0.0368411i	$0.0117295\pi$
$757$			2.02727i			0.0736822i	−0.999321	+	0.0368411i	$0.988270\pi$
$758$		0			0
$759$	−64.3568	+	19.1035i	−2.33600	+	0.693413i
$760$		0			0
$761$	8.60349	−	14.9017i	0.311876	−	0.540186i	−0.666892	−	0.745154i	$-0.732376\pi$
$761$	8.60349	−	14.9017i	0.311876	−	0.540186i	0.978769	+	0.204968i	$0.0657092\pi$
$762$		0			0
$763$	−67.5999	+	39.0288i	−2.44728	+	1.41294i
$764$		0			0
$765$	8.85916	−	0.474473i	0.320304	−	0.0171546i
$766$		0			0
$767$	3.76336	+	6.51832i	0.135887	+	0.235363i
$768$		0			0
$769$	−13.4253	+	23.2533i	−0.484129	+	0.838536i	−0.999834	−	0.0182304i	$-0.994197\pi$
$769$	−13.4253	+	23.2533i	−0.484129	+	0.838536i	0.515705	+	0.856766i	$0.327530\pi$
$770$		0			0
$771$	−11.3610	−	2.72065i	−0.409157	−	0.0979818i
$772$		0			0
$773$			4.41305i			0.158726i	0.996846	+	0.0793632i	$0.0252887\pi$
$773$			4.41305i			0.158726i	−0.996846	+	0.0793632i	$0.974711\pi$
$774$		0			0
$775$	−9.72286			−0.349255
$776$		0			0
$777$	31.4864	+	29.8452i	1.12957	+	1.07069i
$778$		0			0
$779$	2.23887	+	1.29261i	0.0802157	+	0.0463126i
$780$		0			0
$781$	49.9541	−	28.8410i	1.78750	−	1.03201i
$782$		0			0
$783$	23.9661	+	4.39924i	0.856478	+	0.157216i
$784$		0			0
$785$	0.0424108	+	0.0734576i	0.00151371	+	0.00262182i
$786$		0			0
$787$	29.7765	+	17.1914i	1.06142	+	0.612809i	0.925824	−	0.377956i	$-0.123373\pi$
$787$	29.7765	+	17.1914i	1.06142	+	0.612809i	0.135593	+	0.990765i	$0.456706\pi$
$788$		0			0
$789$	31.4728	−	33.2035i	1.12046	−	1.18208i
$790$		0			0
$791$	78.7524			2.80011
$792$		0			0
$793$	−4.92531			−0.174903
$794$		0			0
$795$	−1.47864	−	0.354094i	−0.0524420	−	0.0125584i
$796$		0			0
$797$	−19.8269	−	11.4471i	−0.702304	−	0.405475i	0.105901	−	0.994377i	$-0.466227\pi$
$797$	−19.8269	−	11.4471i	−0.702304	−	0.405475i	−0.808205	+	0.588901i	$0.799561\pi$
$798$		0			0
$799$	9.06058	+	15.6934i	0.320540	+	0.555192i
$800$		0			0
$801$	−9.96265	+	6.48607i	−0.352013	+	0.229174i
$802$		0			0
$803$	40.2375	−	23.2311i	1.41995	−	0.819809i
$804$		0			0
$805$	43.3880	+	25.0501i	1.52922	+	0.882898i
$806$		0			0
$807$	38.4731	−	11.4202i	1.35432	−	0.402012i
$808$		0			0
$809$	34.7922			1.22323			0.611614	−	0.791156i	$-0.290520\pi$
$809$	34.7922			1.22323			0.611614	+	0.791156i	$0.290520\pi$
$810$		0			0
$811$		−	11.6810i		−	0.410174i	−0.978744	−	0.205087i	$-0.934252\pi$
$811$		−	11.6810i		−	0.410174i	0.978744	−	0.205087i	$-0.0657478\pi$
$812$		0			0
$813$	8.75486	+	29.4938i	0.307047	+	1.03439i
$814$		0			0
$815$	−16.5279	+	28.6272i	−0.578948	+	1.00277i
$816$		0			0
$817$	−3.54241	−	6.13564i	−0.123933	−	0.214659i
$818$		0			0
$819$	−28.6523	−	44.0101i	−1.00119	−	1.53784i
$820$		0			0
$821$	−13.9389	+	8.04764i	−0.486472	+	0.280864i	−0.723109	−	0.690733i	$-0.757288\pi$
$821$	−13.9389	+	8.04764i	−0.486472	+	0.280864i	0.236638	+	0.971598i	$0.423954\pi$
$822$		0			0
$823$	6.40163	−	11.0880i	0.223147	−	0.386502i	−0.732615	−	0.680643i	$-0.761700\pi$
$823$	6.40163	−	11.0880i	0.223147	−	0.386502i	0.955762	+	0.294142i	$0.0950337\pi$
$824$		0			0
$825$	4.70739	−	19.6573i	0.163890	−	0.684380i
$826$		0			0
$827$		−	25.9253i		−	0.901511i	−0.892647	−	0.450756i	$-0.851155\pi$
$827$		−	25.9253i		−	0.901511i	0.892647	−	0.450756i	$-0.148845\pi$
$828$		0			0
$829$			49.0708i			1.70430i	0.523299	+	0.852149i	$0.324701\pi$
$829$			49.0708i			1.70430i	−0.523299	+	0.852149i	$0.675299\pi$
$830$		0			0
$831$	−13.1254	−	12.4412i	−0.455315	−	0.431582i
$832$		0			0
$833$	−10.2125	+	17.6885i	−0.353841	+	0.612870i
$834$		0			0
$835$	−29.9881	+	17.3136i	−1.03778	+	0.599162i
$836$		0			0
$837$	23.7973	−	8.47314i	0.822554	−	0.292875i
$838$		0			0
$839$	15.1275	+	26.2016i	0.522259	+	0.904579i	0.999665	+	0.0258959i	$0.00824385\pi$
$839$	15.1275	+	26.2016i	0.522259	+	0.904579i	−0.477406	+	0.878683i	$0.658423\pi$
$840$		0			0
$841$	−3.50506	+	6.07095i	−0.120864	+	0.209343i
$842$		0			0
$843$	32.0382	−	33.8000i	1.10345	−	1.16413i
$844$		0			0
$845$		−	5.47244i		−	0.188258i
$846$		0			0
$847$	100.363			3.44851
$848$		0			0
$849$	−7.51374	+	31.3762i	−0.257871	+	1.07683i
$850$		0			0
$851$	−33.0882	−	19.1035i	−1.13425	−	0.654859i
$852$		0			0
$853$	−25.9389	+	14.9758i	−0.888132	+	0.512763i	−0.873331	−	0.487127i	$-0.838045\pi$
$853$	−25.9389	+	14.9758i	−0.888132	+	0.512763i	−0.0148007	+	0.999890i	$0.504711\pi$
$854$		0			0
$855$	0.555788	+	10.3774i	0.0190076	+	0.354901i
$856$		0			0
$857$	−11.9016	−	20.6141i	−0.406550	−	0.704165i	0.587951	−	0.808897i	$-0.299935\pi$
$857$	−11.9016	−	20.6141i	−0.406550	−	0.704165i	−0.994501	+	0.104732i	$0.966602\pi$
$858$		0			0
$859$	−28.5000	−	16.4545i	−0.972406	−	0.561419i	−0.0724371	−	0.997373i	$-0.523078\pi$
$859$	−28.5000	−	16.4545i	−0.972406	−	0.561419i	−0.899969	+	0.435954i	$0.856411\pi$
$860$		0			0
$861$	−2.77434	−	9.34633i	−0.0945492	−	0.318522i
$862$		0			0
$863$	−36.3906			−1.23875			−0.619375	−	0.785095i	$-0.712614\pi$
$863$	−36.3906			−1.23875			−0.619375	+	0.785095i	$0.712614\pi$
$864$		0			0
$865$	−21.0000			−0.714021
$866$		0			0
$867$	6.94214	+	23.3870i	0.235767	+	0.794265i
$868$		0			0
$869$	−10.4440	−	6.02983i	−0.354288	−	0.204548i
$870$		0			0
$871$	−3.17523	−	5.49965i	−0.107588	−	0.186349i
$872$		0			0
$873$	16.3742	+	8.31945i	0.554183	+	0.281571i
$874$		0			0
$875$	−45.7234	+	26.3984i	−1.54573	+	0.892430i
$876$		0			0
$877$	−42.3529	−	24.4525i	−1.43016	−	0.825701i	−0.433024	−	0.901383i	$-0.642553\pi$
$877$	−42.3529	−	24.4525i	−1.43016	−	0.825701i	−0.997132	+	0.0756818i	$0.975887\pi$
$878$		0			0
$879$	0.468135	−	1.95486i	0.0157898	−	0.0659357i
$880$		0			0
$881$	39.9627			1.34638			0.673188	−	0.739471i	$-0.264924\pi$
$881$	39.9627			1.34638			0.673188	+	0.739471i	$0.264924\pi$
$882$		0			0
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$		0			0
$885$	−3.86422	+	4.07672i	−0.129894	+	0.137037i
$886$		0			0
$887$	−22.5949	+	39.1354i	−0.758661	+	1.31404i	0.184873	+	0.982762i	$0.440813\pi$
$887$	−22.5949	+	39.1354i	−0.758661	+	1.31404i	−0.943534	+	0.331277i	$0.892521\pi$
$888$		0			0
$889$	9.96265	+	17.2558i	0.334137	+	0.578742i
$890$		0			0
$891$	5.60907	+	52.2148i	0.187911	+	1.74926i
$892$		0			0
$893$	−18.3829	+	10.6134i	−0.615160	+	0.355163i
$894$		0			0
$895$	5.19615	−	9.00000i	0.173688	−	0.300837i
$896$		0			0
$897$	33.5661	+	31.8165i	1.12074	+	1.06232i
$898$		0			0
$899$		−	22.7969i		−	0.760318i
$900$		0			0
$901$			0.865333i			0.0288284i
$902$		0			0
$903$	−6.22237	+	25.9837i	−0.207068	+	0.864682i
$904$		0			0
$905$	−4.98133	+	8.62791i	−0.165585	+	0.286801i
$906$		0			0
$907$	34.9726	−	20.1914i	1.16125	−	0.670446i	0.209644	−	0.977778i	$-0.432769\pi$
$907$	34.9726	−	20.1914i	1.16125	−	0.670446i	0.951602	+	0.307332i	$0.0994361\pi$
$908$		0			0
$909$	15.6992	−	30.8990i	0.520711	−	1.02486i
$910$		0			0
$911$	4.26071	+	7.37976i	0.141164	+	0.244503i	0.927935	−	0.372742i	$-0.121582\pi$
$911$	4.26071	+	7.37976i	0.141164	+	0.244503i	−0.786771	+	0.617244i	$0.788249\pi$
$912$		0			0
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$		0			0
$915$	−1.04598	−	3.52374i	−0.0345789	−	0.116491i
$916$		0			0
$917$		−	58.9720i		−	1.94743i
$918$		0			0
$919$	−2.00834			−0.0662490			−0.0331245	−	0.999451i	$-0.510546\pi$
$919$	−2.00834			−0.0662490			−0.0331245	+	0.999451i	$0.510546\pi$
$920$		0			0
$921$	31.6892	−	9.40654i	1.04420	−	0.309956i
$922$		0			0
$923$	−34.4146	−	19.8693i	−1.13277	−	0.654006i
$924$		0			0
$925$	9.96265	−	5.75194i	0.327570	−	0.189123i
$926$		0			0
$927$	0.0354682	+	0.662247i	0.00116493	+	0.0217510i
$928$		0			0
$929$	−14.9864	−	25.9572i	−0.491688	−	0.851628i	0.508267	−	0.861200i	$-0.330286\pi$
$929$	−14.9864	−	25.9572i	−0.491688	−	0.851628i	−0.999954	+	0.00957195i	$0.996953\pi$
$930$		0			0
$931$	−20.7199	−	11.9627i	−0.679068	−	0.392060i
$932$		0			0
$933$	−18.7311	−	4.48559i	−0.613230	−	0.146852i
$934$		0			0
$935$	17.2558			0.564326
$936$		0			0
$937$	−45.0475			−1.47164			−0.735818	−	0.677179i	$-0.763202\pi$
$937$	−45.0475			−1.47164			−0.735818	+	0.677179i	$0.763202\pi$
$938$		0			0
$939$	−32.0827	+	33.8470i	−1.04698	+	1.10455i
$940$		0			0
$941$	46.3880	+	26.7821i	1.51220	+	0.873072i	0.999898	+	0.0142686i	$0.00454200\pi$
$941$	46.3880	+	26.7821i	1.51220	+	0.873072i	0.512306	+	0.858803i	$0.328791\pi$
$942$		0			0
$943$	4.29305	+	7.43578i	0.139801	+	0.242142i
$944$		0			0
$945$	25.4016	−	29.8452i	0.826313	−	0.970864i
$946$		0			0
$947$	20.6417	−	11.9175i	0.670766	−	0.387267i	−0.125601	−	0.992081i	$-0.540086\pi$
$947$	20.6417	−	11.9175i	0.670766	−	0.387267i	0.796367	+	0.604814i	$0.206752\pi$
$948$		0			0
$949$	−27.7206	−	16.0045i	−0.899849	−	0.519528i
$950$		0			0
$951$	−28.2237	−	26.7525i	−0.915215	−	0.867510i
$952$		0			0
$953$	−32.4732			−1.05191			−0.525955	−	0.850513i	$-0.676292\pi$
$953$	−32.4732			−1.05191			−0.525955	+	0.850513i	$0.676292\pi$
$954$		0			0
$955$			0.382896i			0.0123902i
$956$		0			0
$957$	46.0899	+	11.0373i	1.48987	+	0.356784i
$958$		0			0
$959$	−48.7225	+	84.3899i	−1.57333	+	2.72509i
$960$		0			0
$961$	3.68325	+	6.37958i	0.118815	+	0.205793i
$962$		0			0
$963$	0.540074	+	0.829557i	0.0174036	+	0.0267321i
$964$		0			0
$965$	27.0712	−	15.6296i	0.871453	−	0.503134i
$966$		0			0
$967$	−4.83221	+	8.36964i	−0.155393	+	0.269149i	−0.933202	−	0.359352i	$-0.882998\pi$
$967$	−4.83221	+	8.36964i	−0.155393	+	0.269149i	0.777809	+	0.628501i	$0.216331\pi$
$968$		0			0
$969$	5.67004	−	1.68308i	0.182148	−	0.0540683i
$970$		0			0
$971$			49.8133i			1.59858i	0.600943	+	0.799292i	$0.294792\pi$
$971$			49.8133i			1.59858i	−0.600943	+	0.799292i	$0.705208\pi$
$972$		0			0
$973$			50.2627i			1.61135i
$974$		0			0
$975$	−13.3496	+	3.96265i	−0.427529	+	0.126906i
$976$		0			0
$977$	3.59029	−	6.21856i	0.114863	−	0.198949i	−0.802862	−	0.596165i	$-0.796690\pi$
$977$	3.59029	−	6.21856i	0.114863	−	0.198949i	0.917725	+	0.397216i	$0.130024\pi$
$978$		0			0
$979$	−20.0244	+	11.5611i	−0.639982	+	0.369494i
$980$		0			0
$981$	−29.3401	−	45.0666i	−0.936757	−	1.43887i
$982$		0			0
$983$	2.38174	+	4.12530i	0.0759658	+	0.131577i	0.901506	−	0.432767i	$-0.142463\pi$
$983$	2.38174	+	4.12530i	0.0759658	+	0.131577i	−0.825540	+	0.564344i	$0.809129\pi$
$984$		0			0
$985$	−8.50506	+	14.7312i	−0.270994	+	0.469375i
$986$		0			0
$987$	77.8493	+	18.6428i	2.47797	+	0.593406i
$988$		0			0
$989$		−	23.5303i		−	0.748220i
$990$		0			0
$991$	28.5781			0.907815			0.453907	−	0.891049i	$-0.350030\pi$
$991$	28.5781			0.907815			0.453907	+	0.891049i	$0.350030\pi$
$992$		0			0
$993$	−28.3970	−	26.9169i	−0.901153	−	0.854181i
$994$		0			0
$995$	0.907140	+	0.523738i	0.0287583	+	0.0166036i
$996$		0			0
$997$	−32.2494	+	18.6192i	−1.02135	+	0.589676i	−0.914494	−	0.404599i	$-0.867411\pi$
$997$	−32.2494	+	18.6192i	−1.02135	+	0.589676i	−0.106854	+	0.994275i	$0.534078\pi$
$998$		0			0
$999$	−19.3716	+	22.7603i	−0.612889	+	0.720105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.r.e.481.3	yes	12
3.2	odd	2		1728.2.r.f.1441.6		12
4.3	odd	2	inner	576.2.r.e.481.4	yes	12
8.3	odd	2		576.2.r.f.481.3	yes	12
8.5	even	2		576.2.r.f.481.4	yes	12
9.2	odd	6		1728.2.r.e.289.6		12
9.4	even	3		5184.2.d.q.2593.7		12
9.5	odd	6		5184.2.d.r.2593.1		12
9.7	even	3		576.2.r.f.97.4	yes	12
12.11	even	2		1728.2.r.f.1441.1		12
24.5	odd	2		1728.2.r.e.1441.6		12
24.11	even	2		1728.2.r.e.1441.1		12
36.7	odd	6		576.2.r.f.97.3	yes	12
36.11	even	6		1728.2.r.e.289.1		12
36.23	even	6		5184.2.d.r.2593.6		12
36.31	odd	6		5184.2.d.q.2593.12		12
72.5	odd	6		5184.2.d.r.2593.7		12
72.11	even	6		1728.2.r.f.289.1		12
72.13	even	6		5184.2.d.q.2593.1		12
72.29	odd	6		1728.2.r.f.289.6		12
72.43	odd	6	inner	576.2.r.e.97.4	yes	12
72.59	even	6		5184.2.d.r.2593.12		12
72.61	even	6	inner	576.2.r.e.97.3	✓	12
72.67	odd	6		5184.2.d.q.2593.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.r.e.97.3	✓	12	72.61	even	6	inner
576.2.r.e.97.4	yes	12	72.43	odd	6	inner
576.2.r.e.481.3	yes	12	1.1	even	1	trivial
576.2.r.e.481.4	yes	12	4.3	odd	2	inner
576.2.r.f.97.3	yes	12	36.7	odd	6
576.2.r.f.97.4	yes	12	9.7	even	3
576.2.r.f.481.3	yes	12	8.3	odd	2
576.2.r.f.481.4	yes	12	8.5	even	2
1728.2.r.e.289.1		12	36.11	even	6
1728.2.r.e.289.6		12	9.2	odd	6
1728.2.r.e.1441.1		12	24.11	even	2
1728.2.r.e.1441.6		12	24.5	odd	2
1728.2.r.f.289.1		12	72.11	even	6
1728.2.r.f.289.6		12	72.29	odd	6
1728.2.r.f.1441.1		12	12.11	even	2
1728.2.r.f.1441.6		12	3.2	odd	2
5184.2.d.q.2593.1		12	72.13	even	6
5184.2.d.q.2593.6		12	72.67	odd	6
5184.2.d.q.2593.7		12	9.4	even	3
5184.2.d.q.2593.12		12	36.31	odd	6
5184.2.d.r.2593.1		12	9.5	odd	6
5184.2.d.r.2593.6		12	36.23	even	6
5184.2.d.r.2593.7		12	72.5	odd	6
5184.2.d.r.2593.12		12	72.59	even	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.492881 - 1.66044i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(2.17731 + 3.77121i) q^{7} +(-2.51414 + 1.63680i) q^{9} +O(q^{10})\)	\(q+(-0.492881 - 1.66044i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(2.17731 + 3.77121i) q^{7} +(-2.51414 + 1.63680i) q^{9} +(-5.05328 + 2.91751i) q^{11} +(3.48133 + 2.00994i) q^{13} +(-0.698664 + 2.91751i) q^{15} +1.70739 q^{17} +2.00000i q^{19} +(5.18872 - 5.47405i) q^{21} +(-3.32123 + 5.75253i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(3.95698 + 3.36783i) q^{27} +(4.06108 - 2.34467i) q^{29} +(2.43071 - 4.21012i) q^{31} +(7.33502 + 6.95269i) q^{33} -7.54241i q^{35} +5.75194i q^{37} +(1.62152 - 6.77121i) q^{39} +(0.646305 - 1.11943i) q^{41} +(-3.06782 + 1.77121i) q^{43} +(5.18872 - 0.277894i) q^{45} +(5.30669 + 9.19145i) q^{47} +(-5.98133 + 10.3600i) q^{49} +(-0.841540 - 2.83502i) q^{51} +0.506816i q^{53} +10.1066 q^{55} +(3.32088 - 0.985762i) q^{57} +(1.62152 + 0.936184i) q^{59} +(-1.06108 + 0.612617i) q^{61} +(-11.6468 - 5.91751i) q^{63} +(-3.48133 - 6.02983i) q^{65} +(-1.36811 - 0.789879i) q^{67} +(11.1887 + 2.67939i) q^{69} -9.88549 q^{71} -7.96265 q^{73} +(-2.38309 + 2.51414i) q^{75} +(-22.0051 - 12.7046i) q^{77} +(1.03339 + 1.78988i) q^{79} +(3.64177 - 8.23028i) q^{81} +(1.33577 - 0.771205i) q^{83} +(-2.56108 - 1.47864i) q^{85} +(-5.89482 - 5.58755i) q^{87} +3.96265 q^{89} +17.5051i q^{91} +(-8.18872 - 1.96097i) q^{93} +(1.73205 - 3.00000i) q^{95} +(-3.06108 - 5.30195i) q^{97} +(7.92925 - 15.6062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{5} - 4 q^{9}+O(q^{10}) \) 12 * q - 18 * q^5 - 4 * q^9	\( 12 q - 18 q^{5} - 4 q^{9} - 6 q^{13} - 6 q^{21} - 12 q^{25} + 18 q^{29} + 30 q^{33} + 18 q^{41} - 6 q^{45} - 24 q^{49} + 8 q^{57} + 18 q^{61} + 6 q^{65} + 66 q^{69} - 90 q^{77} - 20 q^{81} - 48 q^{89} - 30 q^{93} - 6 q^{97}+O(q^{100}) \) 12 * q - 18 * q^5 - 4 * q^9 - 6 * q^13 - 6 * q^21 - 12 * q^25 + 18 * q^29 + 30 * q^33 + 18 * q^41 - 6 * q^45 - 24 * q^49 + 8 * q^57 + 18 * q^61 + 6 * q^65 + 66 * q^69 - 90 * q^77 - 20 * q^81 - 48 * q^89 - 30 * q^93 - 6 * q^97

Introduction

L-functions

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Representations

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Database

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