LMFDB - Embedded newform 324.2.h.d.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(107,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("324.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.h (of order $6$, degree $2$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Root			$-0.535233 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	324.107
Dual form			324.2.h.d.215.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535233 + 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.35410 - 1.93649i) q^{7} +(-2.59808 - 1.11803i) q^{8} +O(q^{10})$	\(q+(0.535233 + 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.35410 - 1.93649i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(-2.50000 - 1.93649i) q^{10} +(-0.866025 + 1.50000i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(0.739674 - 5.42705i) q^{14} +(0.0729490 - 3.99933i) q^{16} +4.47214i q^{17} +(1.19682 - 4.30902i) q^{20} +(-2.42705 - 0.330792i) q^{22} +(3.46410 + 6.00000i) q^{23} +(1.73205 - 2.23607i) q^{26} +(7.50000 - 1.93649i) q^{28} +(-3.87298 - 2.23607i) q^{29} +(-3.35410 + 1.93649i) q^{31} +(5.27424 - 2.04508i) q^{32} +(-5.85410 + 2.39364i) q^{34} +8.66025 q^{35} -4.00000 q^{37} +(6.28115 - 0.739674i) q^{40} +(-7.74597 + 4.47214i) q^{41} +(6.70820 + 3.87298i) q^{43} +(-0.866025 - 3.35410i) q^{44} +(-6.00000 + 7.74597i) q^{46} +(1.73205 - 3.00000i) q^{47} +(4.00000 + 6.92820i) q^{49} +(3.85410 + 1.07047i) q^{52} -2.23607i q^{53} -3.87298i q^{55} +(6.54915 + 8.78115i) q^{56} +(0.854102 - 6.26662i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-4.33013 - 3.35410i) q^{62} +(5.50000 + 5.80948i) q^{64} +(3.87298 + 2.23607i) q^{65} +(6.70820 - 3.87298i) q^{67} +(-6.26662 - 6.38197i) q^{68} +(4.63525 + 11.3364i) q^{70} -10.3923 q^{71} +5.00000 q^{73} +(-2.14093 - 5.23607i) q^{74} +(5.80948 - 3.35410i) q^{77} +(6.70820 + 3.87298i) q^{79} +(4.33013 + 7.82624i) q^{80} +(-10.0000 - 7.74597i) q^{82} +(-6.06218 + 10.5000i) q^{83} +(-5.00000 - 8.66025i) q^{85} +(-1.47935 + 10.8541i) q^{86} +(3.92705 - 2.92887i) q^{88} +4.47214i q^{89} +7.74597i q^{91} +(-13.3510 - 3.70820i) q^{92} +(4.85410 + 0.661585i) q^{94} +(-5.50000 + 9.52628i) q^{97} +(-6.92820 + 8.94427i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4}+O(q^{10}) $ 8 * q + 2 * q^4	$ 8 q + 2 q^{4} - 20 q^{10} - 8 q^{13} + 14 q^{16} - 6 q^{22} + 60 q^{28} - 20 q^{34} - 32 q^{37} + 10 q^{40} - 48 q^{46} + 32 q^{49} + 4 q^{52} - 20 q^{58} + 16 q^{61} + 44 q^{64} - 30 q^{70} + 40 q^{73} - 80 q^{82} - 40 q^{85} + 18 q^{88} + 12 q^{94} - 44 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 20 * q^10 - 8 * q^13 + 14 * q^16 - 6 * q^22 + 60 * q^28 - 20 * q^34 - 32 * q^37 + 10 * q^40 - 48 * q^46 + 32 * q^49 + 4 * q^52 - 20 * q^58 + 16 * q^61 + 44 * q^64 - 30 * q^70 + 40 * q^73 - 80 * q^82 - 40 * q^85 + 18 * q^88 + 12 * q^94 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.535233	+	1.30902i	0.378467	+	0.925615i
$2$	0.535233	+	1.30902i	0.378467	+	0.925615i
$3$		0			0
$3$		0			0
$4$	−1.42705	+	1.40126i	−0.713525	+	0.700629i
$5$	−1.93649	+	1.11803i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$5$	−1.93649	+	1.11803i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$		0			0
$7$	−3.35410	−	1.93649i	−1.26773	−	0.731925i	−0.293173	−	0.956059i	$-0.594711\pi$
$7$	−3.35410	−	1.93649i	−1.26773	−	0.731925i	−0.974558	+	0.224134i	$0.928045\pi$
$8$	−2.59808	−	1.11803i	−0.918559	−	0.395285i
$9$		0			0
$10$	−2.50000	−	1.93649i	−0.790569	−	0.612372i
$11$	−0.866025	+	1.50000i	−0.261116	+	0.452267i	−0.966539	−	0.256520i	$-0.917424\pi$
$11$	−0.866025	+	1.50000i	−0.261116	+	0.452267i	0.705422	+	0.708787i	$0.250757\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.739674	−	5.42705i	0.197686	−	1.45044i
$15$		0			0
$16$	0.0729490	−	3.99933i	0.0182373	−	0.999834i
$17$			4.47214i			1.08465i	0.840168	+	0.542326i	$0.182456\pi$
$17$			4.47214i			1.08465i	−0.840168	+	0.542326i	$0.817544\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	1.19682	−	4.30902i	0.267617	−	0.963525i
$21$		0			0
$22$	−2.42705	−	0.330792i	−0.517449	−	0.0705251i
$23$	3.46410	+	6.00000i	0.722315	+	1.25109i	0.960070	+	0.279761i	$0.0902553\pi$
$23$	3.46410	+	6.00000i	0.722315	+	1.25109i	−0.237754	+	0.971325i	$0.576411\pi$
$24$		0			0
$25$		0			0
$26$	1.73205	−	2.23607i	0.339683	−	0.438529i
$27$		0			0
$28$	7.50000	−	1.93649i	1.41737	−	0.365963i
$29$	−3.87298	−	2.23607i	−0.719195	−	0.415227i	0.0952614	−	0.995452i	$-0.469631\pi$
$29$	−3.87298	−	2.23607i	−0.719195	−	0.415227i	−0.814456	+	0.580225i	$0.802965\pi$
$30$		0			0
$31$	−3.35410	+	1.93649i	−0.602414	+	0.347804i	−0.769991	−	0.638055i	$-0.779739\pi$
$31$	−3.35410	+	1.93649i	−0.602414	+	0.347804i	0.167576	+	0.985859i	$0.446406\pi$
$32$	5.27424	−	2.04508i	0.932363	−	0.361523i
$33$		0			0
$34$	−5.85410	+	2.39364i	−1.00397	+	0.410505i
$35$	8.66025			1.46385
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$		0			0
$40$	6.28115	−	0.739674i	0.993137	−	0.116953i
$41$	−7.74597	+	4.47214i	−1.20972	+	0.698430i	−0.962697	−	0.270580i	$-0.912784\pi$
$41$	−7.74597	+	4.47214i	−1.20972	+	0.698430i	−0.247019	+	0.969011i	$0.579451\pi$
$42$		0			0
$43$	6.70820	+	3.87298i	1.02299	+	0.590624i	0.914969	−	0.403524i	$-0.132215\pi$
$43$	6.70820	+	3.87298i	1.02299	+	0.590624i	0.108022	+	0.994148i	$0.465548\pi$
$44$	−0.866025	−	3.35410i	−0.130558	−	0.505650i
$45$		0			0
$46$	−6.00000	+	7.74597i	−0.884652	+	1.14208i
$47$	1.73205	−	3.00000i	0.252646	−	0.437595i	−0.711608	−	0.702577i	$-0.752033\pi$
$47$	1.73205	−	3.00000i	0.252646	−	0.437595i	0.964253	+	0.264982i	$0.0853660\pi$
$48$		0			0
$49$	4.00000	+	6.92820i	0.571429	+	0.989743i
$50$		0			0
$51$		0			0
$52$	3.85410	+	1.07047i	0.534468	+	0.148447i
$53$		−	2.23607i		−	0.307148i	−0.988137	−	0.153574i	$-0.950922\pi$
$53$		−	2.23607i		−	0.307148i	0.988137	−	0.153574i	$-0.0490783\pi$
$54$		0			0
$55$		−	3.87298i		−	0.522233i
$56$	6.54915	+	8.78115i	0.875167	+	1.17343i
$57$		0			0
$58$	0.854102	−	6.26662i	0.112149	−	0.822847i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	−4.33013	−	3.35410i	−0.549927	−	0.425971i
$63$		0			0
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$	3.87298	+	2.23607i	0.480384	+	0.277350i
$66$		0			0
$67$	6.70820	−	3.87298i	0.819538	−	0.473160i	−0.0307194	−	0.999528i	$-0.509780\pi$
$67$	6.70820	−	3.87298i	0.819538	−	0.473160i	0.850257	+	0.526368i	$0.176447\pi$
$68$	−6.26662	−	6.38197i	−0.759939	−	0.773927i
$69$		0			0
$70$	4.63525	+	11.3364i	0.554019	+	1.35496i
$71$	−10.3923			−1.23334			−0.616670	−	0.787222i	$-0.711519\pi$
$71$	−10.3923			−1.23334			−0.616670	+	0.787222i	$0.711519\pi$
$72$		0			0
$73$	5.00000			0.585206			0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000			0.585206			0.292603	+	0.956234i	$0.405479\pi$
$74$	−2.14093	−	5.23607i	−0.248878	−	0.608681i
$75$		0			0
$76$		0			0
$77$	5.80948	−	3.35410i	0.662051	−	0.382235i
$78$		0			0
$79$	6.70820	+	3.87298i	0.754732	+	0.435745i	0.827401	−	0.561611i	$-0.189818\pi$
$79$	6.70820	+	3.87298i	0.754732	+	0.435745i	−0.0726692	+	0.997356i	$0.523152\pi$
$80$	4.33013	+	7.82624i	0.484123	+	0.875000i
$81$		0			0
$82$	−10.0000	−	7.74597i	−1.10432	−	0.855399i
$83$	−6.06218	+	10.5000i	−0.665410	+	1.15252i	0.313763	+	0.949501i	$0.398410\pi$
$83$	−6.06218	+	10.5000i	−0.665410	+	1.15252i	−0.979174	+	0.203024i	$0.934923\pi$
$84$		0			0
$85$	−5.00000	−	8.66025i	−0.542326	−	0.939336i
$86$	−1.47935	+	10.8541i	−0.159522	+	1.17043i
$87$		0			0
$88$	3.92705	−	2.92887i	0.418625	−	0.312218i
$89$			4.47214i			0.474045i	0.971504	+	0.237023i	$0.0761716\pi$
$89$			4.47214i			0.474045i	−0.971504	+	0.237023i	$0.923828\pi$
$90$		0			0
$91$			7.74597i			0.811998i
$92$	−13.3510	−	3.70820i	−1.39194	−	0.386607i
$93$		0			0
$94$	4.85410	+	0.661585i	0.500662	+	0.0682372i
$95$		0			0
$96$		0			0
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	0.439187	+	0.898396i	$0.355267\pi$
$97$	−5.50000	+	9.52628i	−0.558440	+	0.967247i	−0.997627	+	0.0688512i	$0.978067\pi$
$98$	−6.92820	+	8.94427i	−0.699854	+	0.903508i
$99$		0			0
$100$		0			0
$101$	1.93649	+	1.11803i	0.192688	+	0.111249i	0.593240	−	0.805025i	$-0.297848\pi$
$101$	1.93649	+	1.11803i	0.192688	+	0.111249i	−0.400552	+	0.916274i	$0.631182\pi$
$102$		0			0
$103$	6.70820	−	3.87298i	0.660979	−	0.381616i	−0.131671	−	0.991293i	$-0.542034\pi$
$103$	6.70820	−	3.87298i	0.660979	−	0.381616i	0.792650	+	0.609677i	$0.208701\pi$
$104$	0.661585	+	5.61803i	0.0648737	+	0.550894i
$105$		0			0
$106$	2.92705	−	1.19682i	0.284300	−	0.116245i
$107$	−5.19615			−0.502331			−0.251166	−	0.967944i	$-0.580814\pi$
$107$	−5.19615			−0.502331			−0.251166	+	0.967944i	$0.580814\pi$
$108$		0			0
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	5.06980	−	2.07295i	0.483387	−	0.197648i
$111$		0			0
$112$	−7.98936	+	13.2729i	−0.754923	+	1.25417i
$113$	15.4919	−	8.94427i	1.45736	−	0.841406i	0.458478	−	0.888706i	$-0.348395\pi$
$113$	15.4919	−	8.94427i	1.45736	−	0.841406i	0.998881	+	0.0472996i	$0.0150615\pi$
$114$		0			0
$115$	−13.4164	−	7.74597i	−1.25109	−	0.722315i
$116$	8.66025	−	2.23607i	0.804084	−	0.207614i
$117$		0			0
$118$	3.00000	−	3.87298i	0.276172	−	0.356537i
$119$	8.66025	−	15.0000i	0.793884	−	1.37505i
$120$		0			0
$121$	4.00000	+	6.92820i	0.363636	+	0.629837i
$122$	5.60503	+	0.763932i	0.507456	+	0.0691632i
$123$		0			0
$124$	2.07295	−	7.46344i	0.186156	−	0.670236i
$125$		−	11.1803i		−	1.00000i
$126$		0			0
$127$			11.6190i			1.03102i	0.856885	+	0.515508i	$0.172397\pi$
$127$			11.6190i			1.03102i	−0.856885	+	0.515508i	$0.827603\pi$
$128$	−4.66092	+	10.3090i	−0.411971	+	0.911197i
$129$		0			0
$130$	−0.854102	+	6.26662i	−0.0749097	+	0.549619i
$131$	−9.52628	−	16.5000i	−0.832315	−	1.44161i	−0.896198	−	0.443654i	$-0.853682\pi$
$131$	−9.52628	−	16.5000i	−0.832315	−	1.44161i	0.0638831	−	0.997957i	$-0.479652\pi$
$132$		0			0
$133$		0			0
$134$	8.66025	+	6.70820i	0.748132	+	0.579501i
$135$		0			0
$136$	5.00000	−	11.6190i	0.428746	−	0.996317i
$137$	−3.87298	−	2.23607i	−0.330891	−	0.191040i	0.325345	−	0.945595i	$-0.394519\pi$
$137$	−3.87298	−	2.23607i	−0.330891	−	0.191040i	−0.656237	+	0.754555i	$0.727853\pi$
$138$		0			0
$139$	−13.4164	+	7.74597i	−1.13796	+	0.657004i	−0.945926	−	0.324383i	$-0.894843\pi$
$139$	−13.4164	+	7.74597i	−1.13796	+	0.657004i	−0.192039	+	0.981387i	$0.561510\pi$
$140$	−12.3586	+	12.1353i	−1.04449	+	1.02562i
$141$		0			0
$142$	−5.56231	−	13.6037i	−0.466778	−	1.14160i
$143$	3.46410			0.289683
$144$		0			0
$145$	10.0000			0.830455
$146$	2.67617	+	6.54508i	0.221481	+	0.541675i
$147$		0			0
$148$	5.70820	−	5.60503i	0.469211	−	0.460731i
$149$	−1.93649	+	1.11803i	−0.158644	+	0.0915929i	−0.577220	−	0.816589i	$-0.695863\pi$
$149$	−1.93649	+	1.11803i	−0.158644	+	0.0915929i	0.418576	+	0.908182i	$0.362529\pi$
$150$		0			0
$151$	−3.35410	−	1.93649i	−0.272953	−	0.157589i	0.357276	−	0.933999i	$-0.383706\pi$
$151$	−3.35410	−	1.93649i	−0.272953	−	0.157589i	−0.630229	+	0.776409i	$0.717039\pi$
$152$		0			0
$153$		0			0
$154$	7.50000	+	5.80948i	0.604367	+	0.468141i
$155$	4.33013	−	7.50000i	0.347804	−	0.602414i
$156$		0			0
$157$	−10.0000	−	17.3205i	−0.798087	−	1.38233i	−0.920860	−	0.389892i	$-0.872512\pi$
$157$	−10.0000	−	17.3205i	−0.798087	−	1.38233i	0.122774	−	0.992435i	$-0.460821\pi$
$158$	−1.47935	+	10.8541i	−0.117691	+	0.863506i
$159$		0			0
$160$	−7.92705	+	9.85707i	−0.626688	+	0.779270i
$161$		−	26.8328i		−	2.11472i
$162$		0			0
$163$		−	23.2379i		−	1.82013i	−0.414462	−	0.910066i	$-0.636030\pi$
$163$		−	23.2379i		−	1.82013i	0.414462	−	0.910066i	$-0.363970\pi$
$164$	4.78727	−	17.2361i	0.373823	−	1.34591i
$165$		0			0
$166$	−16.9894	−	2.31555i	−1.31863	−	0.179721i
$167$	−1.73205	−	3.00000i	−0.134030	−	0.232147i	0.791196	−	0.611562i	$-0.209459\pi$
$167$	−1.73205	−	3.00000i	−0.134030	−	0.232147i	−0.925227	+	0.379415i	$0.876125\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	8.66025	−	11.1803i	0.664211	−	0.857493i
$171$		0			0
$172$	−15.0000	+	3.87298i	−1.14374	+	0.295312i
$173$	13.5554	+	7.82624i	1.03060	+	0.595018i	0.917157	−	0.398527i	$-0.130478\pi$
$173$	13.5554	+	7.82624i	1.03060	+	0.595018i	0.113444	+	0.993544i	$0.463812\pi$
$174$		0			0
$175$		0			0
$176$	5.93583	+	3.57295i	0.447430	+	0.269321i
$177$		0			0
$178$	−5.85410	+	2.39364i	−0.438783	+	0.179411i
$179$	5.19615			0.388379			0.194189	−	0.980964i	$-0.437792\pi$
$179$	5.19615			0.388379			0.194189	+	0.980964i	$0.437792\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−10.1396	+	4.14590i	−0.751597	+	0.307314i
$183$		0			0
$184$	−2.29180	−	19.4614i	−0.168953	−	1.43472i
$185$	7.74597	−	4.47214i	0.569495	−	0.328798i
$186$		0			0
$187$	−6.70820	−	3.87298i	−0.490552	−	0.283221i
$188$	1.73205	+	6.70820i	0.126323	+	0.489246i
$189$		0			0
$190$		0			0
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	0.361588	+	0.932338i	$0.382235\pi$
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	−0.988222	+	0.153024i	$0.951099\pi$
$192$		0			0
$193$	12.5000	+	21.6506i	0.899770	+	1.55845i	0.827788	+	0.561041i	$0.189599\pi$
$193$	12.5000	+	21.6506i	0.899770	+	1.55845i	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−15.4138	−	2.10081i	−1.10665	−	0.150830i
$195$		0			0
$196$	−15.4164	−	4.28187i	−1.10117	−	0.305848i
$197$			24.5967i			1.75245i	0.481906	+	0.876223i	$0.339945\pi$
$197$			24.5967i			1.75245i	−0.481906	+	0.876223i	$0.660055\pi$
$198$		0			0
$199$		−	11.6190i		−	0.823646i	−0.911264	−	0.411823i	$-0.864892\pi$
$199$		−	11.6190i		−	0.823646i	0.911264	−	0.411823i	$-0.135108\pi$
$200$		0			0
$201$		0			0
$202$	−0.427051	+	3.13331i	−0.0300472	+	0.220459i
$203$	8.66025	+	15.0000i	0.607831	+	1.05279i
$204$		0			0
$205$	10.0000	−	17.3205i	0.698430	−	1.20972i
$206$	8.66025	+	6.70820i	0.603388	+	0.467383i
$207$		0			0
$208$	−7.00000	+	3.87298i	−0.485363	+	0.268543i
$209$		0			0
$210$		0			0
$211$	−13.4164	+	7.74597i	−0.923624	+	0.533254i	−0.884789	−	0.465991i	$-0.845698\pi$
$211$	−13.4164	+	7.74597i	−0.923624	+	0.533254i	−0.0388343	+	0.999246i	$0.512364\pi$
$212$	3.13331	+	3.19098i	0.215197	+	0.219158i
$213$		0			0
$214$	−2.78115	−	6.80185i	−0.190116	−	0.464965i
$215$	−17.3205			−1.18125
$216$		0			0
$217$	15.0000			1.01827
$218$	−2.14093	−	5.23607i	−0.145002	−	0.354631i
$219$		0			0
$220$	5.42705	+	5.52694i	0.365892	+	0.372627i
$221$	7.74597	−	4.47214i	0.521050	−	0.300828i
$222$		0			0
$223$	6.70820	+	3.87298i	0.449215	+	0.259354i	0.707498	−	0.706715i	$-0.249824\pi$
$223$	6.70820	+	3.87298i	0.449215	+	0.259354i	−0.258284	+	0.966069i	$0.583157\pi$
$224$	−21.6506	−	3.35410i	−1.44659	−	0.224105i
$225$		0			0
$226$	20.0000	+	15.4919i	1.33038	+	1.03051i
$227$	1.73205	−	3.00000i	0.114960	−	0.199117i	−0.802804	−	0.596244i	$-0.796659\pi$
$227$	1.73205	−	3.00000i	0.114960	−	0.199117i	0.917764	+	0.397127i	$0.129993\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$	2.95870	−	21.7082i	0.195091	−	1.43140i
$231$		0			0
$232$	7.56231	+	10.1396i	0.496490	+	0.665697i
$233$			4.47214i			0.292979i	0.989212	+	0.146490i	$0.0467975\pi$
$233$			4.47214i			0.292979i	−0.989212	+	0.146490i	$0.953202\pi$
$234$		0			0
$235$			7.74597i			0.505291i
$236$	6.67550	+	1.85410i	0.434538	+	0.120692i
$237$		0			0
$238$	24.2705	+	3.30792i	1.57322	+	0.214421i
$239$	−6.92820	−	12.0000i	−0.448148	−	0.776215i	0.550117	−	0.835087i	$-0.314583\pi$
$239$	−6.92820	−	12.0000i	−0.448148	−	0.776215i	−0.998266	+	0.0588719i	$0.981250\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−6.92820	+	8.94427i	−0.445362	+	0.574960i
$243$		0			0
$244$	2.00000	+	7.74597i	0.128037	+	0.495885i
$245$	−15.4919	−	8.94427i	−0.989743	−	0.571429i
$246$		0			0
$247$		0			0
$248$	10.8793	−	1.28115i	0.690835	−	0.0813533i
$249$		0			0
$250$	14.6353	−	5.98409i	0.925615	−	0.378467i
$251$	−10.3923			−0.655956			−0.327978	−	0.944685i	$-0.606367\pi$
$251$	−10.3923			−0.655956			−0.327978	+	0.944685i	$0.606367\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	−15.2094	+	6.21885i	−0.954323	+	0.390205i
$255$		0			0
$256$	−15.9894	−	0.583495i	−0.999335	−	0.0364684i
$257$	−19.3649	+	11.1803i	−1.20795	+	0.697410i	−0.962311	−	0.271951i	$-0.912331\pi$
$257$	−19.3649	+	11.1803i	−1.20795	+	0.697410i	−0.245639	+	0.969361i	$0.578998\pi$
$258$		0			0
$259$	13.4164	+	7.74597i	0.833655	+	0.481311i
$260$	−8.66025	+	2.23607i	−0.537086	+	0.138675i
$261$		0			0
$262$	16.5000	−	21.3014i	1.01937	−	1.31601i
$263$	−3.46410	+	6.00000i	−0.213606	+	0.369976i	−0.952840	−	0.303472i	$-0.901854\pi$
$263$	−3.46410	+	6.00000i	−0.213606	+	0.369976i	0.739235	+	0.673448i	$0.235187\pi$
$264$		0			0
$265$	2.50000	+	4.33013i	0.153574	+	0.265998i
$266$		0			0
$267$		0			0
$268$	−4.14590	+	14.9269i	−0.253251	+	0.911804i
$269$			4.47214i			0.272671i	0.990663	+	0.136335i	$0.0435325\pi$
$269$			4.47214i			0.272671i	−0.990663	+	0.136335i	$0.956467\pi$
$270$		0			0
$271$			11.6190i			0.705801i	0.935661	+	0.352900i	$0.114805\pi$
$271$			11.6190i			0.705801i	−0.935661	+	0.352900i	$0.885195\pi$
$272$	17.8856	+	0.326238i	1.08447	+	0.0197811i
$273$		0			0
$274$	0.854102	−	6.26662i	0.0515982	−	0.378580i
$275$		0			0
$276$		0			0
$277$	−10.0000	+	17.3205i	−0.600842	+	1.04069i	0.391852	+	0.920028i	$0.371834\pi$
$277$	−10.0000	+	17.3205i	−0.600842	+	1.04069i	−0.992694	+	0.120660i	$0.961499\pi$
$278$	−17.3205	−	13.4164i	−1.03882	−	0.804663i
$279$		0			0
$280$	−22.5000	−	9.68246i	−1.34463	−	0.578638i
$281$	−3.87298	−	2.23607i	−0.231043	−	0.133393i	0.380010	−	0.924982i	$-0.375920\pi$
$281$	−3.87298	−	2.23607i	−0.231043	−	0.133393i	−0.611053	+	0.791590i	$0.709254\pi$
$282$		0			0
$283$	26.8328	−	15.4919i	1.59505	−	0.920900i	0.602623	−	0.798026i	$-0.294122\pi$
$283$	26.8328	−	15.4919i	1.59505	−	0.920900i	0.992422	−	0.122874i	$-0.0392111\pi$
$284$	14.8303	−	14.5623i	0.880019	−	0.864114i
$285$		0			0
$286$	1.85410	+	4.53457i	0.109635	+	0.268135i
$287$	34.6410			2.04479
$288$		0			0
$289$	−3.00000			−0.176471
$290$	5.35233	+	13.0902i	0.314300	+	0.768681i
$291$		0			0
$292$	−7.13525	+	7.00629i	−0.417559	+	0.410012i
$293$	−19.3649	+	11.1803i	−1.13131	+	0.653162i	−0.944264	−	0.329189i	$-0.893225\pi$
$293$	−19.3649	+	11.1803i	−1.13131	+	0.653162i	−0.187046	+	0.982351i	$0.559891\pi$
$294$		0			0
$295$	6.70820	+	3.87298i	0.390567	+	0.225494i
$296$	10.3923	+	4.47214i	0.604040	+	0.259938i
$297$		0			0
$298$	−2.50000	−	1.93649i	−0.144821	−	0.112178i
$299$	6.92820	−	12.0000i	0.400668	−	0.693978i
$300$		0			0
$301$	−15.0000	−	25.9808i	−0.864586	−	1.49751i
$302$	0.739674	−	5.42705i	0.0425635	−	0.312292i
$303$		0			0
$304$		0			0
$305$			8.94427i			0.512148i
$306$		0			0
$307$			23.2379i			1.32626i	0.748506	+	0.663129i	$0.230772\pi$
$307$			23.2379i			1.32626i	−0.748506	+	0.663129i	$0.769228\pi$
$308$	−3.59045	+	12.9271i	−0.204585	+	0.736587i
$309$		0			0
$310$	12.1353	+	1.65396i	0.689236	+	0.0939387i
$311$	13.8564	+	24.0000i	0.785725	+	1.36092i	0.928565	+	0.371169i	$0.121043\pi$
$311$	13.8564	+	24.0000i	0.785725	+	1.36092i	−0.142840	+	0.989746i	$0.545624\pi$
$312$		0			0
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	−0.927990	−	0.372606i	$-0.878464\pi$
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	0.786681	+	0.617359i	$0.211798\pi$
$314$	17.3205	−	22.3607i	0.977453	−	1.26189i
$315$		0			0
$316$	−15.0000	+	3.87298i	−0.843816	+	0.217872i
$317$	13.5554	+	7.82624i	0.761349	+	0.439565i	0.829780	−	0.558091i	$-0.188466\pi$
$317$	13.5554	+	7.82624i	0.761349	+	0.439565i	−0.0684306	+	0.997656i	$0.521799\pi$
$318$		0			0
$319$	6.70820	−	3.87298i	0.375587	−	0.216845i
$320$	−17.1459	−	5.10081i	−0.958485	−	0.285144i
$321$		0			0
$322$	35.1246	−	14.3618i	1.95742	−	0.800352i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	30.4188	−	12.4377i	1.68474	−	0.688860i
$327$		0			0
$328$	25.1246	−	2.95870i	1.38727	−	0.163367i
$329$	−11.6190	+	6.70820i	−0.640573	+	0.369835i
$330$		0			0
$331$	6.70820	+	3.87298i	0.368716	+	0.212878i	0.672897	−	0.739736i	$-0.265050\pi$
$331$	6.70820	+	3.87298i	0.368716	+	0.212878i	−0.304181	+	0.952614i	$0.598383\pi$
$332$	−6.06218	−	23.4787i	−0.332705	−	1.28856i
$333$		0			0
$334$	3.00000	−	3.87298i	0.164153	−	0.211920i
$335$	−8.66025	+	15.0000i	−0.473160	+	0.819538i
$336$		0			0
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	0.969468	−	0.245220i	$-0.0788601\pi$
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	−0.697100	+	0.716974i	$0.745527\pi$
$338$	12.6113	+	1.71885i	0.685966	+	0.0934930i
$339$		0			0
$340$	19.2705	+	5.35233i	1.04509	+	0.290271i
$341$		−	6.70820i		−	0.363270i
$342$		0			0
$343$		−	3.87298i		−	0.209121i
$344$	−13.0983	−	17.5623i	−0.706213	−	0.946896i
$345$		0			0
$346$	−2.98936	+	21.9332i	−0.160709	+	1.17913i
$347$	16.4545	+	28.5000i	0.883323	+	1.52996i	0.847624	+	0.530598i	$0.178032\pi$
$347$	16.4545	+	28.5000i	0.883323	+	1.52996i	0.0356990	+	0.999363i	$0.488634\pi$
$348$		0			0
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	−0.568486	−	0.822693i	$-0.692471\pi$
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	0.996716	+	0.0809766i	$0.0258039\pi$
$350$		0			0
$351$		0			0
$352$	−1.50000	+	9.68246i	−0.0799503	+	0.516077i
$353$	−15.4919	−	8.94427i	−0.824552	−	0.476056i	0.0274314	−	0.999624i	$-0.491267\pi$
$353$	−15.4919	−	8.94427i	−0.824552	−	0.476056i	−0.851984	+	0.523568i	$0.824601\pi$
$354$		0			0
$355$	20.1246	−	11.6190i	1.06810	−	0.616670i
$356$	−6.26662	−	6.38197i	−0.332130	−	0.338244i
$357$		0			0
$358$	2.78115	+	6.80185i	0.146989	+	0.359489i
$359$	31.1769			1.64545			0.822727	−	0.568436i	$-0.192451\pi$
$359$	31.1769			1.64545			0.822727	+	0.568436i	$0.192451\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	−8.56373	−	20.9443i	−0.450100	−	1.10081i
$363$		0			0
$364$	−10.8541	−	11.0539i	−0.568910	−	0.579381i
$365$	−9.68246	+	5.59017i	−0.506803	+	0.292603i
$366$		0			0
$367$	−23.4787	−	13.5554i	−1.22558	−	0.707588i	−0.259477	−	0.965749i	$-0.583550\pi$
$367$	−23.4787	−	13.5554i	−1.22558	−	0.707588i	−0.966102	+	0.258161i	$0.916883\pi$
$368$	24.2487	−	13.4164i	1.26405	−	0.699379i
$369$		0			0
$370$	10.0000	+	7.74597i	0.519875	+	0.402694i
$371$	−4.33013	+	7.50000i	−0.224809	+	0.389381i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	1.47935	−	10.8541i	0.0764953	−	0.561252i
$375$		0			0
$376$	−7.85410	+	5.85774i	−0.405044	+	0.302090i
$377$			8.94427i			0.460653i
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	−24.2705	−	3.30792i	−1.24179	−	0.169248i
$383$	−12.1244	−	21.0000i	−0.619526	−	1.07305i	−0.989572	−	0.144037i	$-0.953992\pi$
$383$	−12.1244	−	21.0000i	−0.619526	−	1.07305i	0.370047	−	0.929013i	$-0.379342\pi$
$384$		0			0
$385$	−7.50000	+	12.9904i	−0.382235	+	0.662051i
$386$	−21.6506	+	27.9508i	−1.10199	+	1.42266i
$387$		0			0
$388$	−5.50000	−	21.3014i	−0.279220	−	1.08142i
$389$	1.93649	+	1.11803i	0.0981840	+	0.0566866i	0.548288	−	0.836290i	$-0.315280\pi$
$389$	1.93649	+	1.11803i	0.0981840	+	0.0566866i	−0.450104	+	0.892976i	$0.648613\pi$
$390$		0			0
$391$	−26.8328	+	15.4919i	−1.35699	+	0.783461i
$392$	−2.64634	−	22.4721i	−0.133660	−	1.13501i
$393$		0			0
$394$	−32.1976	+	13.1650i	−1.62209	+	0.663243i
$395$	−17.3205			−0.871489
$396$		0			0
$397$	14.0000			0.702640			0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000			0.702640			0.351320	+	0.936255i	$0.385733\pi$
$398$	15.2094	−	6.21885i	0.762378	−	0.311723i
$399$		0			0
$400$		0			0
$401$	15.4919	−	8.94427i	0.773630	−	0.446656i	−0.0605379	−	0.998166i	$-0.519282\pi$
$401$	15.4919	−	8.94427i	0.773630	−	0.446656i	0.834168	+	0.551510i	$0.185948\pi$
$402$		0			0
$403$	6.70820	+	3.87298i	0.334159	+	0.192927i
$404$	−4.33013	+	1.11803i	−0.215432	+	0.0556243i
$405$		0			0
$406$	−15.0000	+	19.3649i	−0.744438	+	0.961065i
$407$	3.46410	−	6.00000i	0.171709	−	0.297409i
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$	28.0252	+	3.81966i	1.38406	+	0.188640i
$411$		0			0
$412$	−4.14590	+	14.9269i	−0.204254	+	0.735394i
$413$			13.4164i			0.660178i
$414$		0			0
$415$		−	27.1109i		−	1.33082i
$416$	−8.81643	−	7.09017i	−0.432261	−	0.347624i
$417$		0			0
$418$		0			0
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	0.996239	−	0.0866469i	$-0.0276152\pi$
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	−0.573158	+	0.819445i	$0.694282\pi$
$420$		0			0
$421$	2.00000	−	3.46410i	0.0974740	−	0.168830i	−0.813164	−	0.582034i	$-0.802257\pi$
$421$	2.00000	−	3.46410i	0.0974740	−	0.168830i	0.910638	+	0.413204i	$0.135590\pi$
$422$	−17.3205	−	13.4164i	−0.843149	−	0.653101i
$423$		0			0
$424$	−2.50000	+	5.80948i	−0.121411	+	0.282133i
$425$		0			0
$426$		0			0
$427$	−13.4164	+	7.74597i	−0.649265	+	0.374854i
$428$	7.41517	−	7.28115i	0.358426	−	0.351948i
$429$		0			0
$430$	−9.27051	−	22.6728i	−0.447064	−	1.09338i
$431$	−10.3923			−0.500580			−0.250290	−	0.968171i	$-0.580526\pi$
$431$	−10.3923			−0.500580			−0.250290	+	0.968171i	$0.580526\pi$
$432$		0			0
$433$	−13.0000			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$434$	8.02850	+	19.6353i	0.385380	+	0.942522i
$435$		0			0
$436$	5.70820	−	5.60503i	0.273373	−	0.268432i
$437$		0			0
$438$		0			0
$439$	−3.35410	−	1.93649i	−0.160083	−	0.0924237i	0.417819	−	0.908530i	$-0.362795\pi$
$439$	−3.35410	−	1.93649i	−0.160083	−	0.0924237i	−0.577901	+	0.816107i	$0.696128\pi$
$440$	−4.33013	+	10.0623i	−0.206431	+	0.479702i
$441$		0			0
$442$	10.0000	+	7.74597i	0.475651	+	0.368438i
$443$	12.1244	−	21.0000i	0.576046	−	0.997740i	−0.419882	−	0.907579i	$-0.637928\pi$
$443$	12.1244	−	21.0000i	0.576046	−	0.997740i	0.995927	−	0.0901612i	$-0.0287382\pi$
$444$		0			0
$445$	−5.00000	−	8.66025i	−0.237023	−	0.410535i
$446$	−1.47935	+	10.8541i	−0.0700492	+	0.513957i
$447$		0			0
$448$	−7.19756	−	30.1363i	−0.340053	−	1.42381i
$449$			17.8885i			0.844213i	0.906546	+	0.422106i	$0.138709\pi$
$449$			17.8885i			0.844213i	−0.906546	+	0.422106i	$0.861291\pi$
$450$		0			0
$451$		−	15.4919i		−	0.729487i
$452$	−9.57454	+	34.4721i	−0.450349	+	1.62143i
$453$		0			0
$454$	4.85410	+	0.661585i	0.227814	+	0.0310497i
$455$	−8.66025	−	15.0000i	−0.405999	−	0.703211i
$456$		0			0
$457$	15.5000	−	26.8468i	0.725059	−	1.25584i	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	15.5000	−	26.8468i	0.725059	−	1.25584i	0.958950	−	0.283577i	$-0.0915211\pi$
$458$	1.73205	−	2.23607i	0.0809334	−	0.104485i
$459$		0			0
$460$	30.0000	−	7.74597i	1.39876	−	0.361158i
$461$	−32.9204	−	19.0066i	−1.53325	−	0.885225i	−0.999209	−	0.0397685i	$-0.987338\pi$
$461$	−32.9204	−	19.0066i	−1.53325	−	0.885225i	−0.534045	−	0.845456i	$-0.679329\pi$
$462$		0			0
$463$	−3.35410	+	1.93649i	−0.155878	+	0.0899964i	−0.575910	−	0.817513i	$-0.695352\pi$
$463$	−3.35410	+	1.93649i	−0.155878	+	0.0899964i	0.420032	+	0.907509i	$0.362019\pi$
$464$	−9.22531	+	15.3262i	−0.428274	+	0.711503i
$465$		0			0
$466$	−5.85410	+	2.39364i	−0.271186	+	0.110883i
$467$	5.19615			0.240449			0.120225	−	0.992747i	$-0.461639\pi$
$467$	5.19615			0.240449			0.120225	+	0.992747i	$0.461639\pi$
$468$		0			0
$469$	−30.0000			−1.38527
$470$	−10.1396	+	4.14590i	−0.467705	+	0.191236i
$471$		0			0
$472$	1.14590	+	9.73072i	0.0527442	+	0.447893i
$473$	−11.6190	+	6.70820i	−0.534240	+	0.308444i
$474$		0			0
$475$		0			0
$476$	8.66025	+	33.5410i	0.396942	+	1.53735i
$477$		0			0
$478$	12.0000	−	15.4919i	0.548867	−	0.708585i
$479$	−8.66025	+	15.0000i	−0.395697	+	0.685367i	−0.993190	−	0.116507i	$-0.962830\pi$
$479$	−8.66025	+	15.0000i	−0.395697	+	0.685367i	0.597493	+	0.801874i	$0.296164\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	−19.6176	−	2.67376i	−0.893558	−	0.121787i
$483$		0			0
$484$	−15.4164	−	4.28187i	−0.700746	−	0.194630i
$485$		−	24.5967i		−	1.11688i
$486$		0			0
$487$			23.2379i			1.05301i	0.850172	+	0.526505i	$0.176498\pi$
$487$			23.2379i			1.05301i	−0.850172	+	0.526505i	$0.823502\pi$
$488$	−9.06914	+	6.76393i	−0.410540	+	0.306189i
$489$		0			0
$490$	3.41641	−	25.0665i	0.154338	−	1.13239i
$491$	−4.33013	−	7.50000i	−0.195416	−	0.338470i	0.751621	−	0.659595i	$-0.229272\pi$
$491$	−4.33013	−	7.50000i	−0.195416	−	0.338470i	−0.947037	+	0.321125i	$0.895939\pi$
$492$		0			0
$493$	10.0000	−	17.3205i	0.450377	−	0.780076i
$494$		0			0
$495$		0			0
$496$	7.50000	+	13.5554i	0.336760	+	0.608657i
$497$	34.8569	+	20.1246i	1.56354	+	0.902712i
$498$		0			0
$499$	−33.5410	+	19.3649i	−1.50150	+	0.866893i	−0.501504	+	0.865155i	$0.667220\pi$
$499$	−33.5410	+	19.3649i	−1.50150	+	0.866893i	−0.999998	+	0.00173727i	$0.999447\pi$
$500$	15.6665	+	15.9549i	0.700629	+	0.713525i
$501$		0			0
$502$	−5.56231	−	13.6037i	−0.248258	−	0.607163i
$503$	−20.7846			−0.926740			−0.463370	−	0.886165i	$-0.653360\pi$
$503$	−20.7846			−0.926740			−0.463370	+	0.886165i	$0.653360\pi$
$504$		0			0
$505$	−5.00000			−0.222497
$506$	−6.42280	−	15.7082i	−0.285528	−	0.698315i
$507$		0			0
$508$	−16.2812	−	16.5808i	−0.722359	−	0.735656i
$509$	9.68246	−	5.59017i	0.429167	−	0.247780i	−0.269824	−	0.962910i	$-0.586966\pi$
$509$	9.68246	−	5.59017i	0.429167	−	0.247780i	0.698992	+	0.715130i	$0.253632\pi$
$510$		0			0
$511$	−16.7705	−	9.68246i	−0.741884	−	0.428327i
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$		0			0
$514$	−25.0000	−	19.3649i	−1.10270	−	0.854150i
$515$	−8.66025	+	15.0000i	−0.381616	+	0.660979i
$516$		0			0
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	−2.95870	+	21.7082i	−0.129998	+	0.953804i
$519$		0			0
$520$	−7.56231	−	10.1396i	−0.331629	−	0.444651i
$521$		−	22.3607i		−	0.979639i	−0.871824	−	0.489820i	$-0.837063\pi$
$521$		−	22.3607i		−	0.979639i	0.871824	−	0.489820i	$-0.162937\pi$
$522$		0			0
$523$		−	23.2379i		−	1.01612i	−0.861321	−	0.508061i	$-0.830362\pi$
$523$		−	23.2379i		−	1.01612i	0.861321	−	0.508061i	$-0.169638\pi$
$524$	36.7153	+	10.1976i	1.60391	+	0.445483i
$525$		0			0
$526$	−9.70820	−	1.32317i	−0.423298	−	0.0576929i
$527$	−8.66025	−	15.0000i	−0.377247	−	0.653410i
$528$		0			0
$529$	−12.5000	+	21.6506i	−0.543478	+	0.941332i
$530$	−4.33013	+	5.59017i	−0.188089	+	0.242821i
$531$		0			0
$532$		0			0
$533$	15.4919	+	8.94427i	0.671030	+	0.387419i
$534$		0			0
$535$	10.0623	−	5.80948i	0.435031	−	0.251166i
$536$	−21.7586	+	2.56231i	−0.939826	+	0.110675i
$537$		0			0
$538$	−5.85410	+	2.39364i	−0.252388	+	0.103197i
$539$	−13.8564			−0.596838
$540$		0			0
$541$	−4.00000			−0.171973			−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000			−0.171973			−0.0859867	+	0.996296i	$0.527404\pi$
$542$	−15.2094	+	6.21885i	−0.653300	+	0.267122i
$543$		0			0
$544$	9.14590	+	23.5871i	0.392127	+	1.01129i
$545$	7.74597	−	4.47214i	0.331801	−	0.191565i
$546$		0			0
$547$	6.70820	+	3.87298i	0.286822	+	0.165597i	0.636508	−	0.771270i	$-0.280378\pi$
$547$	6.70820	+	3.87298i	0.286822	+	0.165597i	−0.349686	+	0.936867i	$0.613712\pi$
$548$	8.66025	−	2.23607i	0.369948	−	0.0955201i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−15.0000	−	25.9808i	−0.637865	−	1.10481i
$554$	−28.0252	−	3.81966i	−1.19068	−	0.162282i
$555$		0			0
$556$	8.29180	−	29.8537i	0.351650	−	1.26608i
$557$		−	15.6525i		−	0.663217i	−0.943417	−	0.331608i	$-0.892409\pi$
$557$		−	15.6525i		−	0.663217i	0.943417	−	0.331608i	$-0.107591\pi$
$558$		0			0
$559$		−	15.4919i		−	0.655239i
$560$	0.631757	−	34.6353i	0.0266966	−	1.46361i
$561$		0			0
$562$	0.854102	−	6.26662i	0.0360281	−	0.264341i
$563$	−9.52628	−	16.5000i	−0.401485	−	0.695392i	0.592421	−	0.805629i	$-0.298172\pi$
$563$	−9.52628	−	16.5000i	−0.401485	−	0.695392i	−0.993905	+	0.110237i	$0.964839\pi$
$564$		0			0
$565$	−20.0000	+	34.6410i	−0.841406	+	1.45736i
$566$	34.6410	+	26.8328i	1.45607	+	1.12787i
$567$		0			0
$568$	27.0000	+	11.6190i	1.13289	+	0.487520i
$569$	30.9839	+	17.8885i	1.29891	+	0.749927i	0.980216	−	0.197930i	$-0.0634220\pi$
$569$	30.9839	+	17.8885i	1.29891	+	0.749927i	0.318695	+	0.947857i	$0.396755\pi$
$570$		0			0
$571$	6.70820	−	3.87298i	0.280730	−	0.162079i	−0.353024	−	0.935614i	$-0.614847\pi$
$571$	6.70820	−	3.87298i	0.280730	−	0.162079i	0.633754	+	0.773535i	$0.281513\pi$
$572$	−4.94345	+	4.85410i	−0.206696	+	0.202960i
$573$		0			0
$574$	18.5410	+	45.3457i	0.773887	+	1.89269i
$575$		0			0
$576$		0			0
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$	−1.60570	−	3.92705i	−0.0667883	−	0.163344i
$579$		0			0
$580$	−14.2705	+	14.0126i	−0.592551	+	0.581841i
$581$	40.6663	−	23.4787i	1.68712	−	0.974061i
$582$		0			0
$583$	3.35410	+	1.93649i	0.138913	+	0.0802013i
$584$	−12.9904	−	5.59017i	−0.537546	−	0.231323i
$585$		0			0
$586$	−25.0000	−	19.3649i	−1.03274	−	0.799957i
$587$	9.52628	−	16.5000i	0.393192	−	0.681028i	−0.599677	−	0.800242i	$-0.704704\pi$
$587$	9.52628	−	16.5000i	0.393192	−	0.681028i	0.992869	+	0.119214i	$0.0380376\pi$
$588$		0			0
$589$		0			0
$590$	−1.47935	+	10.8541i	−0.0609038	+	0.446856i
$591$		0			0
$592$	−0.291796	+	15.9973i	−0.0119927	+	0.657487i
$593$			4.47214i			0.183649i	0.995775	+	0.0918243i	$0.0292698\pi$
$593$			4.47214i			0.183649i	−0.995775	+	0.0918243i	$0.970730\pi$
$594$		0			0
$595$			38.7298i			1.58777i
$596$	1.19682	−	4.30902i	0.0490236	−	0.176504i
$597$		0			0
$598$	19.4164	+	2.64634i	0.793996	+	0.108217i
$599$	8.66025	+	15.0000i	0.353848	+	0.612883i	0.986920	−	0.161210i	$-0.0515395\pi$
$599$	8.66025	+	15.0000i	0.353848	+	0.612883i	−0.633072	+	0.774093i	$0.718206\pi$
$600$		0			0
$601$	15.5000	−	26.8468i	0.632258	−	1.09510i	−0.354831	−	0.934931i	$-0.615462\pi$
$601$	15.5000	−	26.8468i	0.632258	−	1.09510i	0.987089	−	0.160173i	$-0.0512051\pi$
$602$	25.9808	−	33.5410i	1.05890	−	1.36703i
$603$		0			0
$604$	7.50000	−	1.93649i	0.305171	−	0.0787947i
$605$	−15.4919	−	8.94427i	−0.629837	−	0.363636i
$606$		0			0
$607$	6.70820	−	3.87298i	0.272278	−	0.157200i	−0.357645	−	0.933858i	$-0.616420\pi$
$607$	6.70820	−	3.87298i	0.272278	−	0.157200i	0.629922	+	0.776658i	$0.283087\pi$
$608$		0			0
$609$		0			0
$610$	−11.7082	+	4.78727i	−0.474051	+	0.193831i
$611$	−6.92820			−0.280285
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$	−30.4188	+	12.4377i	−1.22760	+	0.501944i
$615$		0			0
$616$	−18.8435	+	2.21902i	−0.759225	+	0.0894069i
$617$	15.4919	−	8.94427i	0.623682	−	0.360083i	−0.154619	−	0.987974i	$-0.549415\pi$
$617$	15.4919	−	8.94427i	0.623682	−	0.360083i	0.778301	+	0.627891i	$0.216082\pi$
$618$		0			0
$619$	−33.5410	−	19.3649i	−1.34813	−	0.778342i	−0.360143	−	0.932897i	$-0.617272\pi$
$619$	−33.5410	−	19.3649i	−1.34813	−	0.778342i	−0.987984	+	0.154555i	$0.950606\pi$
$620$	4.33013	+	16.7705i	0.173902	+	0.673520i
$621$		0			0
$622$	−24.0000	+	30.9839i	−0.962312	+	1.24234i
$623$	8.66025	−	15.0000i	0.346966	−	0.600962i
$624$		0			0
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	−7.00629	−	0.954915i	−0.280028	−	0.0381661i
$627$		0			0
$628$	38.5410	+	10.7047i	1.53795	+	0.427163i
$629$		−	17.8885i		−	0.713263i
$630$		0			0
$631$			34.8569i			1.38763i	0.720154	+	0.693815i	$0.244071\pi$
$631$			34.8569i			1.38763i	−0.720154	+	0.693815i	$0.755929\pi$
$632$	−13.0983	−	17.5623i	−0.521022	−	0.698591i
$633$		0			0
$634$	−2.98936	+	21.9332i	−0.118723	+	0.871077i
$635$	−12.9904	−	22.5000i	−0.515508	−	0.892885i
$636$		0			0
$637$	8.00000	−	13.8564i	0.316972	−	0.549011i
$638$	8.66025	+	6.70820i	0.342863	+	0.265580i
$639$		0			0
$640$	−2.50000	−	25.1744i	−0.0988212	−	0.995105i
$641$	−38.7298	−	22.3607i	−1.52974	−	0.883194i	−0.999372	−	0.0354238i	$-0.988722\pi$
$641$	−38.7298	−	22.3607i	−1.52974	−	0.883194i	−0.530364	−	0.847770i	$-0.677945\pi$
$642$		0			0
$643$	26.8328	−	15.4919i	1.05818	−	0.610942i	0.133254	−	0.991082i	$-0.457457\pi$
$643$	26.8328	−	15.4919i	1.05818	−	0.610942i	0.924929	+	0.380140i	$0.124124\pi$
$644$	37.5997	+	38.2918i	1.48164	+	1.50891i
$645$		0			0
$646$		0			0
$647$	20.7846			0.817127			0.408564	−	0.912730i	$-0.366030\pi$
$647$	20.7846			0.817127			0.408564	+	0.912730i	$0.366030\pi$
$648$		0			0
$649$	6.00000			0.235521
$650$		0			0
$651$		0			0
$652$	32.5623	+	33.1617i	1.27524	+	1.29871i
$653$	9.68246	−	5.59017i	0.378904	−	0.218760i	−0.298437	−	0.954429i	$-0.596465\pi$
$653$	9.68246	−	5.59017i	0.378904	−	0.218760i	0.677341	+	0.735669i	$0.263132\pi$
$654$		0			0
$655$	36.8951	+	21.3014i	1.44161	+	0.832315i
$656$	17.3205	+	31.3050i	0.676252	+	1.22225i
$657$		0			0
$658$	−15.0000	−	11.6190i	−0.584761	−	0.452954i
$659$	4.33013	−	7.50000i	0.168678	−	0.292159i	−0.769277	−	0.638915i	$-0.779384\pi$
$659$	4.33013	−	7.50000i	0.168678	−	0.292159i	0.937955	+	0.346756i	$0.112717\pi$
$660$		0			0
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	0.978615	−	0.205702i	$-0.0659478\pi$
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	−0.667451	+	0.744654i	$0.732615\pi$
$662$	−1.47935	+	10.8541i	−0.0574965	+	0.421857i
$663$		0			0
$664$	27.4894	−	20.5021i	1.06679	−	0.795635i
$665$		0			0
$666$		0			0
$667$		−	30.9839i		−	1.19970i
$668$	6.67550	+	1.85410i	0.258283	+	0.0717374i
$669$		0			0
$670$	−24.2705	−	3.30792i	−0.937652	−	0.127796i
$671$	3.46410	+	6.00000i	0.133730	+	0.231627i
$672$		0			0
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	−0.997932	−	0.0642860i	$-0.979523\pi$
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	0.554639	+	0.832091i	$0.312856\pi$
$674$	−8.66025	+	11.1803i	−0.333581	+	0.430651i
$675$		0			0
$676$	4.50000	+	17.4284i	0.173077	+	0.670324i
$677$	19.3649	+	11.1803i	0.744254	+	0.429695i	0.823614	−	0.567151i	$-0.191954\pi$
$677$	19.3649	+	11.1803i	0.744254	+	0.429695i	−0.0793599	+	0.996846i	$0.525288\pi$
$678$		0			0
$679$	36.8951	−	21.3014i	1.41590	−	0.817473i
$680$	3.30792	+	28.0902i	0.126853	+	1.07721i
$681$		0			0
$682$	8.78115	−	3.59045i	0.336248	−	0.137486i
$683$	10.3923			0.397650			0.198825	−	0.980035i	$-0.436287\pi$
$683$	10.3923			0.397650			0.198825	+	0.980035i	$0.436287\pi$
$684$		0			0
$685$	10.0000			0.382080
$686$	5.06980	−	2.07295i	0.193566	−	0.0791456i
$687$		0			0
$688$	15.9787	−	26.5458i	0.609183	−	1.01205i
$689$	−3.87298	+	2.23607i	−0.147549	+	0.0851874i
$690$		0			0
$691$	−13.4164	−	7.74597i	−0.510384	−	0.294670i	0.222607	−	0.974908i	$-0.428543\pi$
$691$	−13.4164	−	7.74597i	−0.510384	−	0.294670i	−0.732992	+	0.680238i	$0.761877\pi$
$692$	−30.3109	+	7.82624i	−1.15225	+	0.297509i
$693$		0			0
$694$	−28.5000	+	36.7933i	−1.08185	+	1.39666i
$695$	17.3205	−	30.0000i	0.657004	−	1.13796i
$696$		0			0
$697$	−20.0000	−	34.6410i	−0.757554	−	1.31212i
$698$	22.4201	+	3.05573i	0.848615	+	0.115661i
$699$		0			0
$700$		0			0
$701$		−	15.6525i		−	0.591186i	−0.955314	−	0.295593i	$-0.904483\pi$
$701$		−	15.6525i		−	0.591186i	0.955314	−	0.295593i	$-0.0955172\pi$
$702$		0			0
$703$		0			0
$704$	−13.4774	+	3.21885i	−0.507947	+	0.121315i
$705$		0			0
$706$	3.41641	−	25.0665i	0.128578	−	0.943389i
$707$	−4.33013	−	7.50000i	−0.162851	−	0.282067i
$708$		0			0
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	0.391794	+	0.920053i	$0.371855\pi$
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	−0.992686	+	0.120723i	$0.961479\pi$
$710$	25.9808	+	20.1246i	0.975041	+	0.755263i
$711$		0			0
$712$	5.00000	−	11.6190i	0.187383	−	0.435439i
$713$	−23.2379	−	13.4164i	−0.870266	−	0.502448i
$714$		0			0
$715$	−6.70820	+	3.87298i	−0.250873	+	0.144841i
$716$	−7.41517	+	7.28115i	−0.277118	+	0.272109i
$717$		0			0
$718$	16.6869	+	40.8111i	0.622750	+	1.52306i
$719$	−20.7846			−0.775135			−0.387568	−	0.921841i	$-0.626685\pi$
$719$	−20.7846			−0.775135			−0.387568	+	0.921841i	$0.626685\pi$
$720$		0			0
$721$	−30.0000			−1.11726
$722$	10.1694	+	24.8713i	0.378467	+	0.925615i
$723$		0			0
$724$	22.8328	−	22.4201i	0.848575	−	0.833238i
$725$		0			0
$726$		0			0
$727$	36.8951	+	21.3014i	1.36836	+	0.790026i	0.990719	−	0.135925i	$-0.0434006\pi$
$727$	36.8951	+	21.3014i	1.36836	+	0.790026i	0.377645	+	0.925950i	$0.376734\pi$
$728$	8.66025	−	20.1246i	0.320970	−	0.745868i
$729$		0			0
$730$	−12.5000	−	9.68246i	−0.462646	−	0.358364i
$731$	−17.3205	+	30.0000i	−0.640622	+	1.10959i
$732$		0			0
$733$	−4.00000	−	6.92820i	−0.147743	−	0.255899i	0.782650	−	0.622462i	$-0.213868\pi$
$733$	−4.00000	−	6.92820i	−0.147743	−	0.255899i	−0.930393	+	0.366563i	$0.880534\pi$
$734$	5.17772	−	37.9894i	0.191113	−	1.40221i
$735$		0			0
$736$	30.5410	+	24.5611i	1.12576	+	0.905333i
$737$			13.4164i			0.494200i
$738$		0			0
$739$			23.2379i			0.854820i	0.904058	+	0.427410i	$0.140574\pi$
$739$			23.2379i			0.854820i	−0.904058	+	0.427410i	$0.859426\pi$
$740$	−4.78727	+	17.2361i	−0.175984	+	0.633610i
$741$		0			0
$742$	−12.1353	−	1.65396i	−0.445499	−	0.0607188i
$743$	−12.1244	−	21.0000i	−0.444799	−	0.770415i	0.553239	−	0.833023i	$-0.313392\pi$
$743$	−12.1244	−	21.0000i	−0.444799	−	0.770415i	−0.998038	+	0.0626075i	$0.980058\pi$
$744$		0			0
$745$	2.50000	−	4.33013i	0.0915929	−	0.158644i
$746$	−8.66025	+	11.1803i	−0.317074	+	0.409341i
$747$		0			0
$748$	15.0000	−	3.87298i	0.548454	−	0.141610i
$749$	17.4284	+	10.0623i	0.636821	+	0.367669i
$750$		0			0
$751$	−3.35410	+	1.93649i	−0.122393	+	0.0706636i	−0.559947	−	0.828529i	$-0.689178\pi$
$751$	−3.35410	+	1.93649i	−0.122393	+	0.0706636i	0.437554	+	0.899192i	$0.355845\pi$
$752$	−11.8717	−	7.14590i	−0.432915	−	0.260584i
$753$		0			0
$754$	−11.7082	+	4.78727i	−0.426388	+	0.174342i
$755$	8.66025			0.315179
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.4919	−	8.94427i	0.561582	−	0.324230i	−0.192198	−	0.981356i	$-0.561562\pi$
$761$	15.4919	−	8.94427i	0.561582	−	0.324230i	0.753780	+	0.657127i	$0.228228\pi$
$762$		0			0
$763$	13.4164	+	7.74597i	0.485707	+	0.280423i
$764$	−8.66025	−	33.5410i	−0.313317	−	1.21347i
$765$		0			0
$766$	21.0000	−	27.1109i	0.758761	−	0.979556i
$767$	−3.46410	+	6.00000i	−0.125081	+	0.216647i
$768$		0			0
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	0.749654	−	0.661830i	$-0.230220\pi$
$769$	−5.50000	−	9.52628i	−0.198335	−	0.343526i	−0.947989	+	0.318304i	$0.896887\pi$
$770$	−21.0189	−	2.86475i	−0.757468	−	0.103238i
$771$		0			0
$772$	−48.1763	−	13.3808i	−1.73390	−	0.481587i
$773$			4.47214i			0.160852i	0.996761	+	0.0804258i	$0.0256280\pi$
$773$			4.47214i			0.160852i	−0.996761	+	0.0804258i	$0.974372\pi$
$774$		0			0
$775$		0			0
$776$	24.9401	−	18.6008i	0.895298	−	0.667730i
$777$		0			0
$778$	−0.427051	+	3.13331i	−0.0153105	+	0.112335i
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$	−34.6410	−	26.8328i	−1.23876	−	0.959540i
$783$		0			0
$784$	28.0000	−	15.4919i	1.00000	−	0.553283i
$785$	38.7298	+	22.3607i	1.38233	+	0.798087i
$786$		0			0
$787$	−13.4164	+	7.74597i	−0.478243	+	0.276114i	−0.719684	−	0.694302i	$-0.755713\pi$
$787$	−13.4164	+	7.74597i	−0.478243	+	0.276114i	0.241441	+	0.970416i	$0.422380\pi$
$788$	−34.4664	−	35.1008i	−1.22781	−	1.25041i
$789$		0			0
$790$	−9.27051	−	22.6728i	−0.329830	−	0.806663i
$791$	−69.2820			−2.46339
$792$		0			0
$793$	−8.00000			−0.284088
$794$	7.49326	+	18.3262i	0.265926	+	0.650374i
$795$		0			0
$796$	16.2812	+	16.5808i	0.577070	+	0.587692i
$797$	−36.7933	+	21.2426i	−1.30329	+	0.752453i	−0.980966	−	0.194177i	$-0.937796\pi$
$797$	−36.7933	+	21.2426i	−1.30329	+	0.752453i	−0.322321	+	0.946631i	$0.604463\pi$
$798$		0			0
$799$	13.4164	+	7.74597i	0.474638	+	0.274033i
$800$		0			0
$801$		0			0
$802$	20.0000	+	15.4919i	0.706225	+	0.547039i
$803$	−4.33013	+	7.50000i	−0.152807	+	0.264669i
$804$		0			0
$805$	30.0000	+	51.9615i	1.05736	+	1.83140i
$806$	−1.47935	+	10.8541i	−0.0521078	+	0.382319i
$807$		0			0
$808$	−3.78115	−	5.06980i	−0.133020	−	0.178355i
$809$			4.47214i			0.157232i	0.996905	+	0.0786160i	$0.0250501\pi$
$809$			4.47214i			0.157232i	−0.996905	+	0.0786160i	$0.974950\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−33.3775	−	9.27051i	−1.17132	−	0.325331i
$813$		0			0
$814$	9.70820	+	1.32317i	0.340272	+	0.0463771i
$815$	25.9808	+	45.0000i	0.910066	+	1.57628i
$816$		0			0
$817$		0			0
$818$	−6.06218	+	7.82624i	−0.211959	+	0.273638i
$819$		0			0
$820$	10.0000	+	38.7298i	0.349215	+	1.35250i
$821$	−3.87298	−	2.23607i	−0.135168	−	0.0780393i	0.430891	−	0.902404i	$-0.358199\pi$
$821$	−3.87298	−	2.23607i	−0.135168	−	0.0780393i	−0.566059	+	0.824365i	$0.691533\pi$
$822$		0			0
$823$	−23.4787	+	13.5554i	−0.818417	+	0.472513i	−0.849870	−	0.526992i	$-0.823320\pi$
$823$	−23.4787	+	13.5554i	−0.818417	+	0.472513i	0.0314536	+	0.999505i	$0.489986\pi$
$824$	−21.7586	+	2.56231i	−0.757995	+	0.0892622i
$825$		0			0
$826$	−17.5623	+	7.18091i	−0.611071	+	0.249856i
$827$	31.1769			1.08413			0.542064	−	0.840337i	$-0.317643\pi$
$827$	31.1769			1.08413			0.542064	+	0.840337i	$0.317643\pi$
$828$		0			0
$829$	38.0000			1.31979			0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000			1.31979			0.659897	+	0.751356i	$0.270600\pi$
$830$	35.4886	−	14.5106i	1.23183	−	0.503672i
$831$		0			0
$832$	4.56231	−	15.3358i	0.158169	−	0.531672i
$833$	−30.9839	+	17.8885i	−1.07353	+	0.619801i
$834$		0			0
$835$	6.70820	+	3.87298i	0.232147	+	0.134030i
$836$		0			0
$837$		0			0
$838$	−15.0000	+	19.3649i	−0.518166	+	0.668950i
$839$	−19.0526	+	33.0000i	−0.657767	+	1.13929i	0.323425	+	0.946254i	$0.395166\pi$
$839$	−19.0526	+	33.0000i	−0.657767	+	1.13929i	−0.981192	+	0.193033i	$0.938168\pi$
$840$		0			0
$841$	−4.50000	−	7.79423i	−0.155172	−	0.268767i
$842$	5.60503	+	0.763932i	0.193162	+	0.0263268i
$843$		0			0
$844$	8.29180	−	29.8537i	0.285415	−	1.02761i
$845$			20.1246i			0.692308i
$846$		0			0
$847$		−	30.9839i		−	1.06462i
$848$	−8.94278	−	0.163119i	−0.307096	−	0.00560153i
$849$		0			0
$850$		0			0
$851$	−13.8564	−	24.0000i	−0.474991	−	0.822709i
$852$		0			0
$853$	−1.00000	+	1.73205i	−0.0342393	+	0.0593043i	−0.882637	−	0.470055i	$-0.844234\pi$
$853$	−1.00000	+	1.73205i	−0.0342393	+	0.0593043i	0.848398	+	0.529359i	$0.177568\pi$
$854$	−17.3205	−	13.4164i	−0.592696	−	0.459100i
$855$		0			0
$856$	13.5000	+	5.80948i	0.461421	+	0.198564i
$857$	−3.87298	−	2.23607i	−0.132299	−	0.0763826i	0.432390	−	0.901687i	$-0.357670\pi$
$857$	−3.87298	−	2.23607i	−0.132299	−	0.0763826i	−0.564689	+	0.825304i	$0.691004\pi$
$858$		0			0
$859$	−13.4164	+	7.74597i	−0.457762	+	0.264289i	−0.711103	−	0.703088i	$-0.751804\pi$
$859$	−13.4164	+	7.74597i	−0.457762	+	0.264289i	0.253341	+	0.967377i	$0.418471\pi$
$860$	24.7172	−	24.2705i	0.842851	−	0.827618i
$861$		0			0
$862$	−5.56231	−	13.6037i	−0.189453	−	0.463344i
$863$	20.7846			0.707516			0.353758	−	0.935337i	$-0.384904\pi$
$863$	20.7846			0.707516			0.353758	+	0.935337i	$0.384904\pi$
$864$		0			0
$865$	−35.0000			−1.19004
$866$	−6.95803	−	17.0172i	−0.236444	−	0.578269i
$867$		0			0
$868$	−21.4058	+	21.0189i	−0.726559	+	0.713427i
$869$	−11.6190	+	6.70820i	−0.394146	+	0.227560i
$870$		0			0
$871$	−13.4164	−	7.74597i	−0.454598	−	0.262462i
$872$	10.3923	+	4.47214i	0.351928	+	0.151446i
$873$		0			0
$874$		0			0
$875$	−21.6506	+	37.5000i	−0.731925	+	1.26773i
$876$		0			0
$877$	17.0000	+	29.4449i	0.574049	+	0.994282i	0.996144	+	0.0877308i	$0.0279615\pi$
$877$	17.0000	+	29.4449i	0.574049	+	0.994282i	−0.422095	+	0.906552i	$0.638705\pi$
$878$	0.739674	−	5.42705i	0.0249628	−	0.183154i
$879$		0			0
$880$	−15.4894	−	0.282530i	−0.522146	−	0.00952410i
$881$		−	22.3607i		−	0.753350i	−0.926345	−	0.376675i	$-0.877067\pi$
$881$		−	22.3607i		−	0.753350i	0.926345	−	0.376675i	$-0.122933\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−4.78727	+	17.2361i	−0.161013	+	0.579712i
$885$		0			0
$886$	33.9787	+	4.63109i	1.14154	+	0.155585i
$887$	19.0526	+	33.0000i	0.639722	+	1.10803i	0.985494	+	0.169713i	$0.0542840\pi$
$887$	19.0526	+	33.0000i	0.639722	+	1.10803i	−0.345771	+	0.938319i	$0.612383\pi$
$888$		0			0
$889$	22.5000	−	38.9711i	0.754626	−	1.30705i
$890$	8.66025	−	11.1803i	0.290292	−	0.374766i
$891$		0			0
$892$	−15.0000	+	3.87298i	−0.502237	+	0.129677i
$893$		0			0
$894$		0			0
$895$	−10.0623	+	5.80948i	−0.336346	+	0.194189i
$896$	35.5965	−	25.5517i	1.18920	−	0.853621i
$897$		0			0
$898$	−23.4164	+	9.57454i	−0.781416	+	0.319507i
$899$	17.3205			0.577671
$900$		0			0
$901$	10.0000			0.333148
$902$	20.2792	−	8.29180i	0.675224	−	0.276087i
$903$		0			0
$904$	−50.2492	+	5.91739i	−1.67126	+	0.196810i
$905$	30.9839	−	17.8885i	1.02994	−	0.594635i
$906$		0			0
$907$	−13.4164	−	7.74597i	−0.445485	−	0.257201i	0.260437	−	0.965491i	$-0.416133\pi$
$907$	−13.4164	−	7.74597i	−0.445485	−	0.257201i	−0.705921	+	0.708290i	$0.749467\pi$
$908$	1.73205	+	6.70820i	0.0574801	+	0.222620i
$909$		0			0
$910$	15.0000	−	19.3649i	0.497245	−	0.641941i
$911$	22.5167	−	39.0000i	0.746010	−	1.29213i	−0.203711	−	0.979031i	$-0.565300\pi$
$911$	22.5167	−	39.0000i	0.746010	−	1.29213i	0.949721	−	0.313097i	$-0.101366\pi$
$912$		0			0
$913$	−10.5000	−	18.1865i	−0.347499	−	0.601886i
$914$	43.4390	+	5.92047i	1.43683	+	0.195832i
$915$		0			0
$916$	3.85410	+	1.07047i	0.127343	+	0.0353692i
$917$			73.7902i			2.43677i
$918$		0			0
$919$		−	11.6190i		−	0.383274i	−0.981466	−	0.191637i	$-0.938620\pi$
$919$		−	11.6190i		−	0.383274i	0.981466	−	0.191637i	$-0.0613796\pi$
$920$	26.1966	+	35.1246i	0.863676	+	1.15802i
$921$		0			0
$922$	7.25987	−	53.2663i	0.239091	−	1.75423i
$923$	10.3923	+	18.0000i	0.342067	+	0.592477i
$924$		0			0
$925$		0			0
$926$	−4.33013	−	3.35410i	−0.142297	−	0.110223i
$927$		0			0
$928$	−25.0000	−	3.87298i	−0.820665	−	0.127137i
$929$	−38.7298	−	22.3607i	−1.27068	−	0.733630i	−0.295568	−	0.955322i	$-0.595509\pi$
$929$	−38.7298	−	22.3607i	−1.27068	−	0.733630i	−0.975117	+	0.221692i	$0.928842\pi$
$930$		0			0
$931$		0			0
$932$	−6.26662	−	6.38197i	−0.205270	−	0.209048i
$933$		0			0
$934$	2.78115	+	6.80185i	0.0910021	+	0.222563i
$935$	17.3205			0.566441
$936$		0			0
$937$	−31.0000			−1.01273			−0.506363	−	0.862320i	$-0.669010\pi$
$937$	−31.0000			−1.01273			−0.506363	+	0.862320i	$0.669010\pi$
$938$	−16.0570	−	39.2705i	−0.524279	−	1.28223i
$939$		0			0
$940$	−10.8541	−	11.0539i	−0.354022	−	0.360538i
$941$	−36.7933	+	21.2426i	−1.19943	+	0.692490i	−0.960428	−	0.278529i	$-0.910153\pi$
$941$	−36.7933	+	21.2426i	−1.19943	+	0.692490i	−0.239001	+	0.971019i	$0.576820\pi$
$942$		0			0
$943$	−53.6656	−	30.9839i	−1.74759	−	1.00897i
$944$	−12.1244	+	6.70820i	−0.394614	+	0.218333i
$945$		0			0
$946$	−15.0000	−	11.6190i	−0.487692	−	0.377765i
$947$	25.1147	−	43.5000i	0.816119	−	1.41356i	−0.0924021	−	0.995722i	$-0.529455\pi$
$947$	25.1147	−	43.5000i	0.816119	−	1.41356i	0.908521	−	0.417838i	$-0.137212\pi$
$948$		0			0
$949$	−5.00000	−	8.66025i	−0.162307	−	0.281124i
$950$		0			0
$951$		0			0
$952$	−39.2705	+	29.2887i	−1.27276	+	0.949252i
$953$		−	35.7771i		−	1.15893i	−0.814996	−	0.579467i	$-0.803261\pi$
$953$		−	35.7771i		−	1.15893i	0.814996	−	0.579467i	$-0.196739\pi$
$954$		0			0
$955$		−	38.7298i		−	1.25327i
$956$	26.7020	+	7.41641i	0.863604	+	0.239864i
$957$		0			0
$958$	−24.2705	−	3.30792i	−0.784145	−	0.106874i
$959$	8.66025	+	15.0000i	0.279654	+	0.484375i
$960$		0			0
$961$	−8.00000	+	13.8564i	−0.258065	+	0.446981i
$962$	−6.92820	+	8.94427i	−0.223374	+	0.288375i
$963$		0			0
$964$	−7.00000	−	27.1109i	−0.225455	−	0.873183i
$965$	−48.4123	−	27.9508i	−1.55845	−	0.899770i
$966$		0			0
$967$	−23.4787	+	13.5554i	−0.755025	+	0.435914i	−0.827507	−	0.561456i	$-0.810241\pi$
$967$	−23.4787	+	13.5554i	−0.755025	+	0.435914i	0.0724820	+	0.997370i	$0.476908\pi$
$968$	−2.64634	−	22.4721i	−0.0850565	−	0.722282i
$969$		0			0
$970$	32.1976	−	13.1650i	1.03380	−	0.422702i
$971$	36.3731			1.16727			0.583634	−	0.812017i	$-0.301630\pi$
$971$	36.3731			1.16727			0.583634	+	0.812017i	$0.301630\pi$
$972$		0			0
$973$	60.0000			1.92351
$974$	−30.4188	+	12.4377i	−0.974681	+	0.398529i
$975$		0			0
$976$	−13.7082	−	8.25137i	−0.438789	−	0.264120i
$977$	−42.6028	+	24.5967i	−1.36298	+	0.786920i	−0.990020	−	0.140926i	$-0.954992\pi$
$977$	−42.6028	+	24.5967i	−1.36298	+	0.786920i	−0.372965	+	0.927846i	$0.621659\pi$
$978$		0			0
$979$	−6.70820	−	3.87298i	−0.214395	−	0.123781i
$980$	34.6410	−	8.94427i	1.10657	−	0.285714i
$981$		0			0
$982$	7.50000	−	9.68246i	0.239335	−	0.308980i
$983$	12.1244	−	21.0000i	0.386707	−	0.669796i	−0.605298	−	0.795999i	$-0.706946\pi$
$983$	12.1244	−	21.0000i	0.386707	−	0.669796i	0.992004	+	0.126203i	$0.0402792\pi$
$984$		0			0
$985$	−27.5000	−	47.6314i	−0.876223	−	1.51766i
$986$	28.0252	+	3.81966i	0.892503	+	0.121643i
$987$		0			0
$988$		0			0
$989$			53.6656i			1.70647i
$990$		0			0
$991$			11.6190i			0.369088i	0.982824	+	0.184544i	$0.0590808\pi$
$991$			11.6190i			0.369088i	−0.982824	+	0.184544i	$0.940919\pi$
$992$	−13.7301	+	17.0729i	−0.435930	+	0.542067i
$993$		0			0
$994$	−7.68692	+	56.3996i	−0.243814	+	1.78889i
$995$	12.9904	+	22.5000i	0.411823	+	0.713298i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	−43.3013	−	33.5410i	−1.37068	−	1.06172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.h.d.107.3		8
3.2	odd	2	inner	324.2.h.d.107.2		8
4.3	odd	2	inner	324.2.h.d.107.4		8
9.2	odd	6		108.2.b.a.107.2	yes	4
9.4	even	3	inner	324.2.h.d.215.1		8
9.5	odd	6	inner	324.2.h.d.215.4		8
9.7	even	3		108.2.b.a.107.3	yes	4
12.11	even	2	inner	324.2.h.d.107.1		8
36.7	odd	6		108.2.b.a.107.1	✓	4
36.11	even	6		108.2.b.a.107.4	yes	4
36.23	even	6	inner	324.2.h.d.215.3		8
36.31	odd	6	inner	324.2.h.d.215.2		8
72.11	even	6		1728.2.c.c.1727.1		4
72.29	odd	6		1728.2.c.c.1727.2		4
72.43	odd	6		1728.2.c.c.1727.3		4
72.61	even	6		1728.2.c.c.1727.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.b.a.107.1	✓	4	36.7	odd	6
108.2.b.a.107.2	yes	4	9.2	odd	6
108.2.b.a.107.3	yes	4	9.7	even	3
108.2.b.a.107.4	yes	4	36.11	even	6
324.2.h.d.107.1		8	12.11	even	2	inner
324.2.h.d.107.2		8	3.2	odd	2	inner
324.2.h.d.107.3		8	1.1	even	1	trivial
324.2.h.d.107.4		8	4.3	odd	2	inner
324.2.h.d.215.1		8	9.4	even	3	inner
324.2.h.d.215.2		8	36.31	odd	6	inner
324.2.h.d.215.3		8	36.23	even	6	inner
324.2.h.d.215.4		8	9.5	odd	6	inner
1728.2.c.c.1727.1		4	72.11	even	6
1728.2.c.c.1727.2		4	72.29	odd	6
1728.2.c.c.1727.3		4	72.43	odd	6
1728.2.c.c.1727.4		4	72.61	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.535233 + 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.35410 - 1.93649i) q^{7} +(-2.59808 - 1.11803i) q^{8} +O(q^{10})\)	\(q+(0.535233 + 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.35410 - 1.93649i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(-2.50000 - 1.93649i) q^{10} +(-0.866025 + 1.50000i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(0.739674 - 5.42705i) q^{14} +(0.0729490 - 3.99933i) q^{16} +4.47214i q^{17} +(1.19682 - 4.30902i) q^{20} +(-2.42705 - 0.330792i) q^{22} +(3.46410 + 6.00000i) q^{23} +(1.73205 - 2.23607i) q^{26} +(7.50000 - 1.93649i) q^{28} +(-3.87298 - 2.23607i) q^{29} +(-3.35410 + 1.93649i) q^{31} +(5.27424 - 2.04508i) q^{32} +(-5.85410 + 2.39364i) q^{34} +8.66025 q^{35} -4.00000 q^{37} +(6.28115 - 0.739674i) q^{40} +(-7.74597 + 4.47214i) q^{41} +(6.70820 + 3.87298i) q^{43} +(-0.866025 - 3.35410i) q^{44} +(-6.00000 + 7.74597i) q^{46} +(1.73205 - 3.00000i) q^{47} +(4.00000 + 6.92820i) q^{49} +(3.85410 + 1.07047i) q^{52} -2.23607i q^{53} -3.87298i q^{55} +(6.54915 + 8.78115i) q^{56} +(0.854102 - 6.26662i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-4.33013 - 3.35410i) q^{62} +(5.50000 + 5.80948i) q^{64} +(3.87298 + 2.23607i) q^{65} +(6.70820 - 3.87298i) q^{67} +(-6.26662 - 6.38197i) q^{68} +(4.63525 + 11.3364i) q^{70} -10.3923 q^{71} +5.00000 q^{73} +(-2.14093 - 5.23607i) q^{74} +(5.80948 - 3.35410i) q^{77} +(6.70820 + 3.87298i) q^{79} +(4.33013 + 7.82624i) q^{80} +(-10.0000 - 7.74597i) q^{82} +(-6.06218 + 10.5000i) q^{83} +(-5.00000 - 8.66025i) q^{85} +(-1.47935 + 10.8541i) q^{86} +(3.92705 - 2.92887i) q^{88} +4.47214i q^{89} +7.74597i q^{91} +(-13.3510 - 3.70820i) q^{92} +(4.85410 + 0.661585i) q^{94} +(-5.50000 + 9.52628i) q^{97} +(-6.92820 + 8.94427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4}+O(q^{10}) \) 8 * q + 2 * q^4	\( 8 q + 2 q^{4} - 20 q^{10} - 8 q^{13} + 14 q^{16} - 6 q^{22} + 60 q^{28} - 20 q^{34} - 32 q^{37} + 10 q^{40} - 48 q^{46} + 32 q^{49} + 4 q^{52} - 20 q^{58} + 16 q^{61} + 44 q^{64} - 30 q^{70} + 40 q^{73} - 80 q^{82} - 40 q^{85} + 18 q^{88} + 12 q^{94} - 44 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 20 * q^10 - 8 * q^13 + 14 * q^16 - 6 * q^22 + 60 * q^28 - 20 * q^34 - 32 * q^37 + 10 * q^40 - 48 * q^46 + 32 * q^49 + 4 * q^52 - 20 * q^58 + 16 * q^61 + 44 * q^64 - 30 * q^70 + 40 * q^73 - 80 * q^82 - 40 * q^85 + 18 * q^88 + 12 * q^94 - 44 * q^97

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