LMFDB - Embedded newform 648.2.v.b.35.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("648.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.13
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.505867 - 1.32064i) q^{2} +(-1.48820 + 1.33614i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(-0.199218 - 0.0351275i) q^{7} +(2.51739 + 1.28947i) q^{8} +O(q^{10})$	\(q+(-0.505867 - 1.32064i) q^{2} +(-1.48820 + 1.33614i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(-0.199218 - 0.0351275i) q^{7} +(2.51739 + 1.28947i) q^{8} +(0.0809654 + 4.83625i) q^{10} +(-1.37658 - 3.78212i) q^{11} +(1.09713 + 1.30751i) q^{13} +(0.0543868 + 0.280866i) q^{14} +(0.429466 - 3.97688i) q^{16} +(-1.57350 + 0.908459i) q^{17} +(-3.24004 + 5.61192i) q^{19} +(6.34601 - 2.55343i) q^{20} +(-4.29847 + 3.73122i) q^{22} +(1.37566 + 7.80173i) q^{23} +(5.13093 + 4.30536i) q^{25} +(1.17176 - 2.11035i) q^{26} +(0.343411 - 0.213906i) q^{28} +(3.08543 + 2.58898i) q^{29} +(7.51214 - 1.32459i) q^{31} +(-5.46929 + 1.44460i) q^{32} +(1.99573 + 1.61847i) q^{34} +(0.599188 + 0.345941i) q^{35} +(1.53384 - 0.885560i) q^{37} +(9.05037 + 1.44006i) q^{38} +(-6.58240 - 7.08912i) q^{40} +(6.61260 + 7.88059i) q^{41} +(3.47909 - 1.26628i) q^{43} +(7.10206 + 3.78924i) q^{44} +(9.60741 - 5.76339i) q^{46} +(-0.523875 + 2.97105i) q^{47} +(-6.53939 - 2.38014i) q^{49} +(3.09028 - 8.95407i) q^{50} +(-3.37977 - 0.479915i) q^{52} -9.46508 q^{53} +13.7659i q^{55} +(-0.456214 - 0.345316i) q^{56} +(1.85830 - 5.38442i) q^{58} +(-1.23077 + 3.38152i) q^{59} +(-8.13039 - 1.43361i) q^{61} +(-5.54946 - 9.25079i) q^{62} +(4.67453 + 6.49221i) q^{64} +(-1.99664 - 5.48571i) q^{65} +(-1.26475 + 1.06125i) q^{67} +(1.12785 - 3.45438i) q^{68} +(0.153756 - 0.966313i) q^{70} +(2.24594 + 3.89008i) q^{71} +(-4.05026 + 7.01525i) q^{73} +(-1.94543 - 1.57767i) q^{74} +(-2.67648 - 12.6808i) q^{76} +(0.141383 + 0.801822i) q^{77} +(-0.380899 + 0.453938i) q^{79} +(-6.03238 + 12.2792i) q^{80} +(7.06236 - 12.7194i) q^{82} +(8.02454 - 9.56328i) q^{83} +(6.11986 - 1.07910i) q^{85} +(-3.43227 - 3.95406i) q^{86} +(1.41154 - 11.2961i) q^{88} +(-10.7122 - 6.18471i) q^{89} +(-0.172639 - 0.299020i) q^{91} +(-12.4714 - 9.77245i) q^{92} +(4.18870 - 0.811100i) q^{94} +(16.9781 - 14.2463i) q^{95} +(-8.24324 + 3.00029i) q^{97} +(0.164739 + 9.84024i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.505867	−	1.32064i	−0.357702	−	0.933836i
$2$	−0.505867	−	1.32064i	−0.357702	−	0.933836i
$3$		0			0
$3$		0			0
$4$	−1.48820	+	1.33614i	−0.744099	+	0.668069i
$5$	−3.21396	−	1.16979i	−1.43733	−	0.523144i	−0.498306	−	0.867001i	$-0.666044\pi$
$5$	−3.21396	−	1.16979i	−1.43733	−	0.523144i	−0.939022	+	0.343857i	$0.888266\pi$
$6$		0			0
$7$	−0.199218	−	0.0351275i	−0.0752973	−	0.0132770i	0.135873	−	0.990726i	$-0.456616\pi$
$7$	−0.199218	−	0.0351275i	−0.0752973	−	0.0132770i	−0.211170	+	0.977449i	$0.567727\pi$
$8$	2.51739	+	1.28947i	0.890033	+	0.455897i
$9$		0			0
$10$	0.0809654	+	4.83625i	0.0256035	+	1.52936i
$11$	−1.37658	−	3.78212i	−0.415054	−	1.14035i	−0.954469	−	0.298311i	$-0.903577\pi$
$11$	−1.37658	−	3.78212i	−0.415054	−	1.14035i	0.539414	−	0.842040i	$-0.318646\pi$
$12$		0			0
$13$	1.09713	+	1.30751i	0.304290	+	0.362639i	0.896422	−	0.443202i	$-0.146158\pi$
$13$	1.09713	+	1.30751i	0.304290	+	0.362639i	−0.592131	+	0.805842i	$0.701713\pi$
$14$	0.0543868	+	0.280866i	0.0145355	+	0.0750646i
$15$		0			0
$16$	0.429466	−	3.97688i	0.107366	−	0.994220i
$17$	−1.57350	+	0.908459i	−0.381629	+	0.220334i	−0.678527	−	0.734576i	$-0.737381\pi$
$17$	−1.57350	+	0.908459i	−0.381629	+	0.220334i	0.296898	+	0.954909i	$0.404048\pi$
$18$		0			0
$19$	−3.24004	+	5.61192i	−0.743317	+	1.28746i	0.207661	+	0.978201i	$0.433415\pi$
$19$	−3.24004	+	5.61192i	−0.743317	+	1.28746i	−0.950977	+	0.309261i	$0.899918\pi$
$20$	6.34601	−	2.55343i	1.41901	−	0.570963i
$21$		0			0
$22$	−4.29847	+	3.73122i	−0.916436	+	0.795498i
$23$	1.37566	+	7.80173i	0.286844	+	1.62677i	0.698623	+	0.715490i	$0.253796\pi$
$23$	1.37566	+	7.80173i	0.286844	+	1.62677i	−0.411779	+	0.911284i	$0.635092\pi$
$24$		0			0
$25$	5.13093	+	4.30536i	1.02619	+	0.861072i
$26$	1.17176	−	2.11035i	0.229800	−	0.413874i
$27$		0			0
$28$	0.343411	−	0.213906i	0.0648986	−	0.0404245i
$29$	3.08543	+	2.58898i	0.572949	+	0.480761i	0.882623	−	0.470081i	$-0.155775\pi$
$29$	3.08543	+	2.58898i	0.572949	+	0.480761i	−0.309674	+	0.950843i	$0.600220\pi$
$30$		0			0
$31$	7.51214	−	1.32459i	1.34922	−	0.237904i	0.548103	−	0.836411i	$-0.315350\pi$
$31$	7.51214	−	1.32459i	1.34922	−	0.237904i	0.801117	+	0.598507i	$0.204239\pi$
$32$	−5.46929	+	1.44460i	−0.966843	+	0.255371i
$33$		0			0
$34$	1.99573	+	1.61847i	0.342265	+	0.277565i
$35$	0.599188	+	0.345941i	0.101281	+	0.0584747i
$36$		0			0
$37$	1.53384	−	0.885560i	0.252161	−	0.145585i	−0.368592	−	0.929591i	$-0.620160\pi$
$37$	1.53384	−	0.885560i	0.252161	−	0.145585i	0.620753	+	0.784006i	$0.286827\pi$
$38$	9.05037	+	1.44006i	1.46816	+	0.233608i
$39$		0			0
$40$	−6.58240	−	7.08912i	−1.04077	−	1.12089i
$41$	6.61260	+	7.88059i	1.03271	+	1.23074i	0.972584	+	0.232551i	$0.0747072\pi$
$41$	6.61260	+	7.88059i	1.03271	+	1.23074i	0.0601305	+	0.998191i	$0.480848\pi$
$42$		0			0
$43$	3.47909	−	1.26628i	0.530556	−	0.193107i	−0.0628305	−	0.998024i	$-0.520013\pi$
$43$	3.47909	−	1.26628i	0.530556	−	0.193107i	0.593387	+	0.804918i	$0.297791\pi$
$44$	7.10206	+	3.78924i	1.07068	+	0.571250i
$45$		0			0
$46$	9.60741	−	5.76339i	1.41654	−	0.849765i
$47$	−0.523875	+	2.97105i	−0.0764151	+	0.433371i	0.922466	+	0.386078i	$0.126171\pi$
$47$	−0.523875	+	2.97105i	−0.0764151	+	0.433371i	−0.998881	+	0.0472931i	$0.984941\pi$
$48$		0			0
$49$	−6.53939	−	2.38014i	−0.934199	−	0.340021i
$50$	3.09028	−	8.95407i	0.437032	−	1.26630i
$51$		0			0
$52$	−3.37977	−	0.479915i	−0.468690	−	0.0665523i
$53$	−9.46508			−1.30013			−0.650064	−	0.759879i	$-0.725258\pi$
$53$	−9.46508			−1.30013			−0.650064	+	0.759879i	$0.725258\pi$
$54$		0			0
$55$			13.7659i			1.85619i
$56$	−0.456214	−	0.345316i	−0.0609642	−	0.0461447i
$57$		0			0
$58$	1.85830	−	5.38442i	0.244007	−	0.707010i
$59$	−1.23077	+	3.38152i	−0.160233	+	0.440237i	−0.993665	−	0.112386i	$-0.964151\pi$
$59$	−1.23077	+	3.38152i	−0.160233	+	0.440237i	0.833432	+	0.552623i	$0.186373\pi$
$60$		0			0
$61$	−8.13039	−	1.43361i	−1.04099	−	0.183555i	−0.373082	−	0.927798i	$-0.621699\pi$
$61$	−8.13039	−	1.43361i	−1.04099	−	0.183555i	−0.667908	+	0.744244i	$0.732810\pi$
$62$	−5.54946	−	9.25079i	−0.704782	−	1.17485i
$63$		0			0
$64$	4.67453	+	6.49221i	0.584316	+	0.811526i
$65$	−1.99664	−	5.48571i	−0.247652	−	0.680419i
$66$		0			0
$67$	−1.26475	+	1.06125i	−0.154514	+	0.129653i	−0.716767	−	0.697312i	$-0.754379\pi$
$67$	−1.26475	+	1.06125i	−0.154514	+	0.129653i	0.562253	+	0.826965i	$0.309935\pi$
$68$	1.12785	−	3.45438i	0.136772	−	0.418905i
$69$		0			0
$70$	0.153756	−	0.966313i	0.0183773	−	0.115497i
$71$	2.24594	+	3.89008i	0.266544	+	0.461668i	0.967967	−	0.251078i	$-0.0807849\pi$
$71$	2.24594	+	3.89008i	0.266544	+	0.461668i	−0.701423	+	0.712745i	$0.747452\pi$
$72$		0			0
$73$	−4.05026	+	7.01525i	−0.474047	+	0.821073i	−0.999558	−	0.0297132i	$-0.990541\pi$
$73$	−4.05026	+	7.01525i	−0.474047	+	0.821073i	0.525512	+	0.850786i	$0.323874\pi$
$74$	−1.94543	−	1.57767i	−0.226151	−	0.183401i
$75$		0			0
$76$	−2.67648	−	12.6808i	−0.307013	−	1.45459i
$77$	0.141383	+	0.801822i	0.0161121	+	0.0913761i
$78$		0			0
$79$	−0.380899	+	0.453938i	−0.0428545	+	0.0510720i	−0.787046	−	0.616894i	$-0.788391\pi$
$79$	−0.380899	+	0.453938i	−0.0428545	+	0.0510720i	0.744191	+	0.667966i	$0.232835\pi$
$80$	−6.03238	+	12.2792i	−0.674441	+	1.37285i
$81$		0			0
$82$	7.06236	−	12.7194i	0.779907	−	1.40462i
$83$	8.02454	−	9.56328i	0.880808	−	1.04971i	−0.117586	−	0.993063i	$-0.537516\pi$
$83$	8.02454	−	9.56328i	0.880808	−	1.04971i	0.998394	−	0.0566436i	$-0.0180399\pi$
$84$		0			0
$85$	6.11986	−	1.07910i	0.663792	−	0.117044i
$86$	−3.43227	−	3.95406i	−0.370111	−	0.426378i
$87$		0			0
$88$	1.41154	−	11.2961i	0.150471	−	1.20417i
$89$	−10.7122	−	6.18471i	−1.13549	−	0.655578i	−0.190183	−	0.981749i	$-0.560908\pi$
$89$	−10.7122	−	6.18471i	−1.13549	−	0.655578i	−0.945311	+	0.326171i	$0.894241\pi$
$90$		0			0
$91$	−0.172639	−	0.299020i	−0.0180975	−	0.0313458i
$92$	−12.4714	−	9.77245i	−1.30024	−	1.01885i
$93$		0			0
$94$	4.18870	−	0.811100i	0.432032	−	0.0836586i
$95$	16.9781	−	14.2463i	1.74192	−	1.46164i
$96$		0			0
$97$	−8.24324	+	3.00029i	−0.836974	+	0.304634i	−0.724718	−	0.689046i	$-0.758030\pi$
$97$	−8.24324	+	3.00029i	−0.836974	+	0.304634i	−0.112256	+	0.993679i	$0.535808\pi$
$98$	0.164739	+	9.84024i	0.0166412	+	0.994015i
$99$		0			0
$100$	−13.3884	+	0.448406i	−1.33884	+	0.0448406i
$101$	−1.79803	+	10.1971i	−0.178910	+	1.01465i	0.754623	+	0.656159i	$0.227820\pi$
$101$	−1.79803	+	10.1971i	−0.178910	+	1.01465i	−0.933533	+	0.358491i	$0.883291\pi$
$102$		0			0
$103$	2.22000	−	6.09941i	0.218744	−	0.600993i	−0.780979	−	0.624558i	$-0.785279\pi$
$103$	2.22000	−	6.09941i	0.218744	−	0.600993i	0.999722	+	0.0235646i	$0.00750153\pi$
$104$	1.07592	+	4.70625i	0.105502	+	0.461486i
$105$		0			0
$106$	4.78807	+	12.5000i	0.465058	+	1.21411i
$107$			2.26037i			0.218518i	0.994013	+	0.109259i	$0.0348478\pi$
$107$			2.26037i			0.218518i	−0.994013	+	0.109259i	$0.965152\pi$
$108$		0			0
$109$			3.00655i			0.287975i	0.989580	+	0.143987i	$0.0459925\pi$
$109$			3.00655i			0.287975i	−0.989580	+	0.143987i	$0.954008\pi$
$110$	18.1798	−	6.96371i	1.73338	−	0.663963i
$111$		0			0
$112$	−0.225255	+	0.777180i	−0.0212846	+	0.0734366i
$113$	−1.92611	+	5.29194i	−0.181193	+	0.497824i	−0.996723	−	0.0808910i	$-0.974223\pi$
$113$	−1.92611	+	5.29194i	−0.181193	+	0.497824i	0.815530	+	0.578715i	$0.196446\pi$
$114$		0			0
$115$	4.70506	−	26.6837i	0.438749	−	2.48827i
$116$	−8.05096	+	0.269644i	−0.747513	+	0.0250358i
$117$		0			0
$118$	5.08839	−	0.0851866i	0.468424	−	0.00784206i
$119$	0.345381	−	0.125708i	0.0316610	−	0.0115237i
$120$		0			0
$121$	−3.98297	+	3.34211i	−0.362088	+	0.303828i
$122$	2.21961	+	11.4626i	0.200954	+	1.03777i
$123$		0			0
$124$	−9.40971	+	12.0085i	−0.845017	+	1.07840i
$125$	−2.90369	−	5.02934i	−0.259714	−	0.449838i
$126$		0			0
$127$	9.60934	+	5.54795i	0.852691	+	0.492301i	0.861558	−	0.507660i	$-0.169489\pi$
$127$	9.60934	+	5.54795i	0.852691	+	0.492301i	−0.00886716	+	0.999961i	$0.502823\pi$
$128$	6.20920	−	9.45758i	0.548821	−	0.835940i
$129$		0			0
$130$	−6.23464	+	5.41188i	−0.546814	+	0.474654i
$131$	−7.26270	+	1.28061i	−0.634545	+	0.111887i	−0.481662	−	0.876357i	$-0.659967\pi$
$131$	−7.26270	+	1.28061i	−0.634545	+	0.111887i	−0.152883	+	0.988244i	$0.548856\pi$
$132$		0			0
$133$	0.842608	−	1.00418i	0.0730633	−	0.0870735i
$134$	2.04134	+	1.13344i	0.176345	+	0.0979139i
$135$		0			0
$136$	−5.13254	+	0.257970i	−0.440112	+	0.0221207i
$137$	−7.46073	+	8.89135i	−0.637413	+	0.759640i	−0.983959	−	0.178393i	$-0.942910\pi$
$137$	−7.46073	+	8.89135i	−0.637413	+	0.759640i	0.346546	+	0.938033i	$0.387354\pi$
$138$		0			0
$139$	1.37040	+	7.77191i	0.116236	+	0.659205i	0.986131	+	0.165969i	$0.0530751\pi$
$139$	1.37040	+	7.77191i	0.116236	+	0.659205i	−0.869895	+	0.493236i	$0.835814\pi$
$140$	−1.35393	+	0.285769i	−0.114428	+	0.0241519i
$141$		0			0
$142$	4.00126	−	4.93395i	0.335779	−	0.414048i
$143$	3.43488	−	5.94939i	0.287239	−	0.497513i
$144$		0			0
$145$	−6.88789	−	11.9302i	−0.572008	−	0.990747i
$146$	11.3135	+	1.80016i	0.936315	+	0.148983i
$147$		0			0
$148$	−1.09942	+	3.36731i	−0.0903717	+	0.276791i
$149$	−5.38903	+	4.52193i	−0.441486	+	0.370451i	−0.836265	−	0.548325i	$-0.815266\pi$
$149$	−5.38903	+	4.52193i	−0.441486	+	0.370451i	0.394779	+	0.918776i	$0.370821\pi$
$150$		0			0
$151$	2.14375	+	5.88990i	0.174456	+	0.479313i	0.995846	−	0.0910533i	$-0.0290234\pi$
$151$	2.14375	+	5.88990i	0.174456	+	0.479313i	−0.821390	+	0.570367i	$0.806801\pi$
$152$	−15.3929	+	9.94946i	−1.24853	+	0.807008i
$153$		0			0
$154$	0.987400	−	0.592332i	0.0795670	−	0.0477314i
$155$	−25.6932	−	4.53041i	−2.06373	−	0.363891i
$156$		0			0
$157$	−1.70377	+	4.68108i	−0.135976	+	0.373591i	−0.988928	−	0.148399i	$-0.952588\pi$
$157$	−1.70377	+	4.68108i	−0.135976	+	0.373591i	0.852952	+	0.521990i	$0.174810\pi$
$158$	0.792174	+	0.273400i	0.0630220	+	0.0217505i
$159$		0			0
$160$	19.2680	+	1.75501i	1.52327	+	0.138746i
$161$		−	1.60257i		−	0.126300i
$162$		0			0
$163$	6.53033			0.511495			0.255747	−	0.966744i	$-0.417679\pi$
$163$	6.53033			0.511495			0.255747	+	0.966744i	$0.417679\pi$
$164$	−20.3704	−	2.89252i	−1.59066	−	0.225868i
$165$		0			0
$166$	−16.6890	−	5.75982i	−1.29532	−	0.447048i
$167$	11.5164	+	4.19163i	0.891167	+	0.324358i	0.746708	−	0.665152i	$-0.231633\pi$
$167$	11.5164	+	4.19163i	0.891167	+	0.324358i	0.144460	+	0.989511i	$0.453856\pi$
$168$		0			0
$169$	1.75154	−	9.93346i	0.134734	−	0.764113i
$170$	−4.52094	−	7.53628i	−0.346740	−	0.578006i
$171$		0			0
$172$	−3.48564	+	6.53303i	−0.265778	+	0.498139i
$173$	−22.9308	+	8.34612i	−1.74339	+	0.634543i	−0.999433	−	0.0336797i	$-0.989277\pi$
$173$	−22.9308	+	8.34612i	−1.74339	+	0.634543i	−0.743961	+	0.668223i	$0.767055\pi$
$174$		0			0
$175$	−0.870937	−	1.03794i	−0.0658367	−	0.0784611i
$176$	−15.6322	+	3.85020i	−1.17832	+	0.290219i
$177$		0			0
$178$	−2.74883	+	17.2757i	−0.206034	+	1.29487i
$179$	12.4964	−	7.21481i	0.934026	−	0.539260i	0.0459437	−	0.998944i	$-0.485371\pi$
$179$	12.4964	−	7.21481i	0.934026	−	0.539260i	0.888083	+	0.459684i	$0.152037\pi$
$180$		0			0
$181$	−17.7079	−	10.2237i	−1.31622	−	0.759919i	−0.333100	−	0.942892i	$-0.608095\pi$
$181$	−17.7079	−	10.2237i	−1.31622	−	0.759919i	−0.983118	+	0.182973i	$0.941428\pi$
$182$	−0.307566	+	0.379259i	−0.0227983	+	0.0281126i
$183$		0			0
$184$	−6.59704	+	21.4139i	−0.486340	+	1.57865i
$185$	−5.96560	+	1.05190i	−0.438600	+	0.0773370i
$186$		0			0
$187$	5.60194	+	4.70059i	0.409655	+	0.343741i
$188$	−3.19010	−	5.12147i	−0.232662	−	0.373522i
$189$		0			0
$190$	−27.4030	−	15.2153i	−1.98802	−	1.10383i
$191$	−15.9522	−	13.3855i	−1.15426	−	0.968538i	−0.154448	−	0.988001i	$-0.549360\pi$
$191$	−15.9522	−	13.3855i	−1.15426	−	0.968538i	−0.999811	+	0.0194633i	$0.993804\pi$
$192$		0			0
$193$	0.989078	+	5.60934i	0.0711954	+	0.403769i	0.999490	+	0.0319244i	$0.0101636\pi$
$193$	0.989078	+	5.60934i	0.0711954	+	0.403769i	−0.928295	+	0.371845i	$0.878725\pi$
$194$	8.13229	+	9.36863i	0.583865	+	0.672628i
$195$		0			0
$196$	12.9121	−	5.19541i	0.922294	−	0.371101i
$197$	13.4024	−	23.2137i	0.954885	−	1.65391i	0.220254	−	0.975443i	$-0.429312\pi$
$197$	13.4024	−	23.2137i	0.954885	−	1.65391i	0.734631	−	0.678467i	$-0.237355\pi$
$198$		0			0
$199$	−22.2890	+	12.8685i	−1.58002	+	0.912226i	−0.585168	+	0.810912i	$0.698971\pi$
$199$	−22.2890	+	12.8685i	−1.58002	+	0.912226i	−0.994854	+	0.101314i	$0.967695\pi$
$200$	7.36493	+	17.4545i	0.520779	+	1.23422i
$201$		0			0
$202$	14.3763	−	2.78383i	1.01151	−	0.195869i
$203$	−0.523728	−	0.624155i	−0.0367585	−	0.0438071i
$204$		0			0
$205$	−12.0340	−	33.0633i	−0.840494	−	2.30924i
$206$	−9.17818	+	0.153655i	−0.639474	+	0.0107057i
$207$		0			0
$208$	5.67100	−	3.80164i	0.393213	−	0.263596i
$209$	25.6851	+	4.52898i	1.77668	+	0.313276i
$210$		0			0
$211$	−2.22400	−	0.809471i	−0.153107	−	0.0557263i	0.264330	−	0.964432i	$-0.414849\pi$
$211$	−2.22400	−	0.809471i	−0.153107	−	0.0557263i	−0.417437	+	0.908706i	$0.637071\pi$
$212$	14.0859	−	12.6467i	0.967424	−	0.868576i
$213$		0			0
$214$	2.98514	−	1.14344i	0.204060	−	0.0781643i
$215$	−12.6629			−0.863606
$216$		0			0
$217$	−1.54308			−0.104751
$218$	3.97058	−	1.52091i	0.268921	−	0.103009i
$219$		0			0
$220$	−18.3931	−	20.4864i	−1.24007	−	1.38119i
$221$	−2.91416	−	1.06067i	−0.196028	−	0.0713482i
$222$		0			0
$223$	19.7258	+	3.47820i	1.32094	+	0.232917i	0.789277	−	0.614038i	$-0.210456\pi$
$223$	19.7258	+	3.47820i	1.32094	+	0.232917i	0.531664	+	0.846955i	$0.321567\pi$
$224$	1.14033	−	0.0956676i	0.0761913	−	0.00639206i
$225$		0			0
$226$	7.96312	−	0.133313i	0.529699	−	0.00886788i
$227$	8.81116	+	24.2085i	0.584817	+	1.60677i	0.779843	+	0.625975i	$0.215299\pi$
$227$	8.81116	+	24.2085i	0.584817	+	1.60677i	−0.195026	+	0.980798i	$0.562479\pi$
$228$		0			0
$229$	1.43440	+	1.70946i	0.0947880	+	0.112964i	0.811353	−	0.584556i	$-0.198731\pi$
$229$	1.43440	+	1.70946i	0.0947880	+	0.112964i	−0.716565	+	0.697520i	$0.754287\pi$
$230$	−37.6198	+	7.28469i	−2.48057	+	0.480338i
$231$		0			0
$232$	4.42881	+	10.4960i	0.290766	+	0.689099i
$233$	7.43882	−	4.29480i	0.487333	−	0.281362i	−0.236134	−	0.971720i	$-0.575881\pi$
$233$	7.43882	−	4.29480i	0.487333	−	0.281362i	0.723467	+	0.690358i	$0.242547\pi$
$234$		0			0
$235$	5.15920	−	8.93600i	0.336549	−	0.582921i
$236$	−2.68655	−	6.67686i	−0.174879	−	0.434626i
$237$		0			0
$238$	−0.340733	−	0.392533i	−0.0220864	−	0.0254442i
$239$	0.254336	+	1.44241i	0.0164516	+	0.0933018i	0.991928	−	0.126802i	$-0.0404714\pi$
$239$	0.254336	+	1.44241i	0.0164516	+	0.0933018i	−0.975476	+	0.220104i	$0.929360\pi$
$240$		0			0
$241$	1.54665	+	1.29779i	0.0996285	+	0.0835982i	0.691241	−	0.722624i	$-0.257064\pi$
$241$	1.54665	+	1.29779i	0.0996285	+	0.0835982i	−0.591613	+	0.806222i	$0.701509\pi$
$242$	6.42858	+	3.56942i	0.413245	+	0.229451i
$243$		0			0
$244$	14.0151	−	8.72984i	0.897227	−	0.558871i
$245$	18.2331	+	15.2994i	1.16487	+	0.977442i
$246$		0			0
$247$	−10.8924	+	1.92063i	−0.693068	+	0.122207i
$248$	20.6190	+	6.35216i	1.30931	+	0.403363i
$249$		0			0
$250$	−5.17309	+	6.37892i	−0.327175	+	0.403438i
$251$	0.0195920	+	0.0113115i	0.00123664	+	0.000713973i	0.500618	−	0.865668i	$-0.333106\pi$
$251$	0.0195920	+	0.0113115i	0.00123664	+	0.000713973i	−0.499382	+	0.866382i	$0.666439\pi$
$252$		0			0
$253$	27.6134	−	15.9426i	1.73604	−	1.00230i
$254$	2.46582	−	15.4970i	0.154720	−	0.972370i
$255$		0			0
$256$	−15.6311	−	3.41586i	−0.976945	−	0.213492i
$257$	10.5865	+	12.6165i	0.660369	+	0.786997i	0.987439	−	0.158003i	$-0.0505056\pi$
$257$	10.5865	+	12.6165i	0.660369	+	0.786997i	−0.327070	+	0.945000i	$0.606061\pi$
$258$		0			0
$259$	−0.336675	+	0.122540i	−0.0209200	+	0.00761425i
$260$	10.3011	+	5.49604i	0.638845	+	0.340850i
$261$		0			0
$262$	5.36519	+	8.94362i	0.331462	+	0.552538i
$263$	−1.02766	+	5.82816i	−0.0633684	+	0.359380i	0.936592	+	0.350423i	$0.113962\pi$
$263$	−1.02766	+	5.82816i	−0.0633684	+	0.359380i	−0.999960	+	0.00895677i	$0.997149\pi$
$264$		0			0
$265$	30.4204	+	11.0721i	1.86871	+	0.680155i
$266$	−1.75241	−	0.604803i	−0.107447	−	0.0370828i
$267$		0			0
$268$	0.464221	−	3.26924i	0.0283568	−	0.199701i
$269$	4.98736			0.304085			0.152042	−	0.988374i	$-0.451415\pi$
$269$	4.98736			0.304085			0.152042	+	0.988374i	$0.451415\pi$
$270$		0			0
$271$		−	7.03519i		−	0.427358i	−0.976904	−	0.213679i	$-0.931455\pi$
$271$		−	7.03519i		−	0.427358i	0.976904	−	0.213679i	$-0.0685446\pi$
$272$	2.93707	+	6.64776i	0.178086	+	0.403079i
$273$		0			0
$274$	15.5164	+	5.35513i	0.937382	+	0.323515i
$275$	9.22026	−	25.3325i	0.556003	−	1.52760i
$276$		0			0
$277$	−22.4822	−	3.96421i	−1.35082	−	0.238187i	−0.549037	−	0.835798i	$-0.685006\pi$
$277$	−22.4822	−	3.96421i	−1.35082	−	0.238187i	−0.801786	+	0.597611i	$0.796117\pi$
$278$	9.57069	−	5.74136i	0.574012	−	0.344344i
$279$		0			0
$280$	1.06231	+	1.64350i	0.0634851	+	0.0982182i
$281$	−8.38379	−	23.0343i	−0.500135	−	1.37411i	−0.891143	−	0.453722i	$-0.850096\pi$
$281$	−8.38379	−	23.0343i	−0.500135	−	1.37411i	0.391008	−	0.920387i	$-0.372126\pi$
$282$		0			0
$283$	−8.31451	+	6.97670i	−0.494246	+	0.414722i	−0.855545	−	0.517728i	$-0.826778\pi$
$283$	−8.31451	+	6.97670i	−0.494246	+	0.414722i	0.361299	+	0.932450i	$0.382333\pi$
$284$	−8.54009	−	2.78832i	−0.506761	−	0.165456i
$285$		0			0
$286$	−9.59461	−	1.52666i	−0.567341	−	0.0902730i
$287$	−1.04052	−	1.80224i	−0.0614202	−	0.106383i
$288$		0			0
$289$	−6.84941	+	11.8635i	−0.402906	+	0.697854i
$290$	−12.2711	+	15.1315i	−0.720587	+	0.888553i
$291$		0			0
$292$	−3.34577	−	15.8518i	−0.195796	−	0.927656i
$293$	2.84714	+	16.1469i	0.166332	+	0.943313i	0.947681	+	0.319219i	$0.103421\pi$
$293$	2.84714	+	16.1469i	0.166332	+	0.943313i	−0.781349	+	0.624094i	$0.785468\pi$
$294$		0			0
$295$	7.91132	−	9.42834i	0.460615	−	0.548939i
$296$	5.00317	−	0.251467i	0.290803	−	0.0146162i
$297$		0			0
$298$	8.69799	+	4.82949i	0.503861	+	0.279765i
$299$	−8.69159	+	10.3582i	−0.502648	+	0.599032i
$300$		0			0
$301$	−0.737579	+	0.130055i	−0.0425133	+	0.00749625i
$302$	6.69401	−	5.81063i	0.385197	−	0.334364i
$303$		0			0
$304$	20.9264	+	15.2954i	1.20021	+	0.877250i
$305$	24.4538	+	14.1184i	1.40022	+	0.808416i
$306$		0			0
$307$	7.29100	+	12.6284i	0.416119	+	0.720740i	0.995545	−	0.0942851i	$-0.0300565\pi$
$307$	7.29100	+	12.6284i	0.416119	+	0.720740i	−0.579426	+	0.815025i	$0.696723\pi$
$308$	−1.28175	−	1.00436i	−0.0730346	−	0.0572289i
$309$		0			0
$310$	7.01429	+	36.2234i	0.398385	+	2.05735i
$311$	18.0464	−	15.1428i	1.02332	−	0.858667i	0.0332788	−	0.999446i	$-0.489405\pi$
$311$	18.0464	−	15.1428i	1.02332	−	0.858667i	0.990041	+	0.140779i	$0.0449606\pi$
$312$		0			0
$313$	4.27277	−	1.55516i	0.241511	−	0.0879028i	−0.218429	−	0.975853i	$-0.570093\pi$
$313$	4.27277	−	1.55516i	0.241511	−	0.0879028i	0.459940	+	0.887950i	$0.347871\pi$
$314$	7.04392	−	0.117925i	0.397511	−	0.00665488i
$315$		0			0
$316$	−0.0396708	−	1.18448i	−0.00223166	−	0.0666324i
$317$	1.85951	−	10.5458i	0.104440	−	0.592310i	−0.887002	−	0.461765i	$-0.847216\pi$
$317$	1.85951	−	10.5458i	0.104440	−	0.592310i	0.991442	−	0.130545i	$-0.0416726\pi$
$318$		0			0
$319$	5.54450	−	15.2334i	0.310432	−	0.852906i
$320$	−7.42927	−	26.3339i	−0.415309	−	1.47211i
$321$		0			0
$322$	−2.11642	+	0.810686i	−0.117944	+	0.0451778i
$323$		−	11.7738i		−	0.655111i
$324$		0			0
$325$			11.4323i			0.634151i
$326$	−3.30347	−	8.62423i	−0.182963	−	0.477652i
$327$		0			0
$328$	6.48472	+	28.3653i	0.358059	+	1.56621i
$329$	0.208731	−	0.573483i	0.0115077	−	0.0316172i
$330$		0			0
$331$	−2.53127	+	14.3556i	−0.139131	+	0.789053i	0.832762	+	0.553631i	$0.186758\pi$
$331$	−2.53127	+	14.3556i	−0.139131	+	0.789053i	−0.971893	+	0.235422i	$0.924353\pi$
$332$	0.835760	+	24.9540i	0.0458683	+	1.36953i
$333$		0			0
$334$	−0.290119	−	17.3295i	−0.0158746	−	0.948228i
$335$	5.30631	−	1.93134i	0.289915	−	0.105520i
$336$		0			0
$337$	19.2969	−	16.1920i	1.05117	−	0.882035i	0.0579523	−	0.998319i	$-0.481543\pi$
$337$	19.2969	−	16.1920i	1.05117	−	0.882035i	0.993216	+	0.116285i	$0.0370984\pi$
$338$	−14.0046	+	2.71185i	−0.761750	+	0.147505i
$339$		0			0
$340$	−7.66574	+	9.78289i	−0.415733	+	0.530552i
$341$	−15.3508	−	26.5884i	−0.831293	−	1.43984i
$342$		0			0
$343$	2.44548	+	1.41190i	0.132044	+	0.0762354i
$344$	10.3911	+	1.29845i	0.560249	+	0.0700075i
$345$		0			0
$346$	22.6222	+	26.0613i	1.21617	+	1.40107i
$347$	8.71967	−	1.53751i	0.468097	−	0.0825380i	0.0653753	−	0.997861i	$-0.479176\pi$
$347$	8.71967	−	1.53751i	0.468097	−	0.0825380i	0.402721	+	0.915323i	$0.368064\pi$
$348$		0			0
$349$	−19.6221	+	23.3847i	−1.05035	+	1.25175i	−0.0834696	+	0.996510i	$0.526600\pi$
$349$	−19.6221	+	23.3847i	−1.05035	+	1.25175i	−0.966877	+	0.255244i	$0.917844\pi$
$350$	−0.930174	+	1.67526i	−0.0497199	+	0.0895463i
$351$		0			0
$352$	12.9926	+	18.6969i	0.692506	+	0.996548i
$353$	8.90806	−	10.6162i	0.474128	−	0.565044i	−0.474979	−	0.879997i	$-0.657544\pi$
$353$	8.90806	−	10.6162i	0.474128	−	0.565044i	0.949107	+	0.314953i	$0.101989\pi$
$354$		0			0
$355$	−2.66780	−	15.1298i	−0.141592	−	0.803008i
$356$	24.2055	−	5.10895i	1.28289	−	0.270774i
$357$		0			0
$358$	−15.8497	−	12.8536i	−0.837684	−	0.679333i
$359$	−9.49643	+	16.4483i	−0.501202	+	0.868108i	0.498797	+	0.866719i	$0.333775\pi$
$359$	−9.49643	+	16.4483i	−0.501202	+	0.868108i	−0.999999	+	0.00138897i	$0.999558\pi$
$360$		0			0
$361$	−11.4957	−	19.9112i	−0.605039	−	1.04796i
$362$	−4.54397	+	28.5576i	−0.238826	+	1.50096i
$363$		0			0
$364$	0.656454	+	0.214331i	0.0344075	+	0.0112340i
$365$	21.2237	−	17.8088i	1.11090	−	0.932156i
$366$		0			0
$367$	−6.89218	−	18.9361i	−0.359769	−	0.988456i	−0.979109	−	0.203334i	$-0.934822\pi$
$367$	−6.89218	−	18.9361i	−0.359769	−	0.988456i	0.619341	−	0.785122i	$-0.287400\pi$
$368$	31.6173	−	2.12024i	1.64817	−	0.110525i
$369$		0			0
$370$	4.40698	+	7.34632i	0.229108	+	0.381917i
$371$	1.88561	+	0.332485i	0.0978962	+	0.0172617i
$372$		0			0
$373$	4.70270	−	12.9206i	0.243496	−	0.669001i	−0.756393	−	0.654118i	$-0.773040\pi$
$373$	4.70270	−	12.9206i	0.243496	−	0.669001i	0.999889	−	0.0148833i	$-0.00473766\pi$
$374$	3.37396	−	9.77604i	0.174464	−	0.505507i
$375$		0			0
$376$	−5.14988	+	6.80377i	−0.265585	+	0.350877i
$377$			6.87469i			0.354065i
$378$		0			0
$379$	−23.0899			−1.18605			−0.593026	−	0.805184i	$-0.702067\pi$
$379$	−23.0899			−1.18605			−0.593026	+	0.805184i	$0.702067\pi$
$380$	−6.23172	+	43.8865i	−0.319680	+	2.25133i
$381$		0			0
$382$	−9.60775	+	27.8384i	−0.491575	+	1.42434i
$383$	1.72830	+	0.629049i	0.0883119	+	0.0321429i	0.385798	−	0.922583i	$-0.373926\pi$
$383$	1.72830	+	0.629049i	0.0883119	+	0.0321429i	−0.297486	+	0.954726i	$0.596148\pi$
$384$		0			0
$385$	0.483562	−	2.74241i	0.0246446	−	0.139766i
$386$	6.90760	−	4.14380i	0.351588	−	0.210914i
$387$		0			0
$388$	8.25876	−	15.4791i	0.419275	−	0.785834i
$389$	27.9217	−	10.1627i	1.41569	−	0.515268i	0.482894	−	0.875679i	$-0.339586\pi$
$389$	27.9217	−	10.1627i	1.41569	−	0.515268i	0.932794	+	0.360411i	$0.117364\pi$
$390$		0			0
$391$	−9.25214	−	11.0263i	−0.467901	−	0.557623i
$392$	−13.3931	−	14.4241i	−0.676454	−	0.728528i
$393$		0			0
$394$	−37.4369	−	5.95681i	−1.88604	−	0.300100i
$395$	1.75521	−	1.01337i	0.0883140	−	0.0509881i
$396$		0			0
$397$	13.2935	+	7.67501i	0.667182	+	0.385198i	0.795008	−	0.606599i	$-0.207467\pi$
$397$	13.2935	+	7.67501i	0.667182	+	0.385198i	−0.127826	+	0.991797i	$0.540800\pi$
$398$	28.2700	+	22.9260i	1.41705	+	1.14918i
$399$		0			0
$400$	19.3255	−	18.5561i	0.966273	−	0.927804i
$401$	−16.6682	+	2.93905i	−0.832368	+	0.146769i	−0.573564	−	0.819161i	$-0.694440\pi$
$401$	−16.6682	+	2.93905i	−0.832368	+	0.146769i	−0.258804	+	0.965930i	$0.583328\pi$
$402$		0			0
$403$	9.97375	+	8.36897i	0.496828	+	0.416888i
$404$	−10.9489	−	17.5777i	−0.544730	−	0.874525i
$405$		0			0
$406$	−0.559349	+	1.00740i	−0.0277600	+	0.0499963i
$407$	−5.46074	−	4.58210i	−0.270679	−	0.227126i
$408$		0			0
$409$	0.249722	+	1.41624i	0.0123480	+	0.0700287i	0.990359	−	0.138524i	$-0.0442358\pi$
$409$	0.249722	+	1.41624i	0.0123480	+	0.0700287i	−0.978011	+	0.208553i	$0.933125\pi$
$410$	−37.5771	+	32.6183i	−1.85580	+	1.61090i
$411$		0			0
$412$	4.84586	+	12.0434i	0.238738	+	0.593334i
$413$	0.363977	−	0.630426i	0.0179101	−	0.0310212i
$414$		0			0
$415$	−36.9776	+	21.3490i	−1.81516	+	1.04798i
$416$	−7.88938	−	5.56625i	−0.386809	−	0.272908i
$417$		0			0
$418$	−7.01208	−	36.2119i	−0.342972	−	1.77118i
$419$	17.2769	+	20.5898i	0.844029	+	1.00588i	0.999836	+	0.0180876i	$0.00575778\pi$
$419$	17.2769	+	20.5898i	0.844029	+	1.00588i	−0.155807	+	0.987788i	$0.549798\pi$
$420$		0			0
$421$	13.1300	+	36.0744i	0.639917	+	1.75816i	0.651986	+	0.758231i	$0.273936\pi$
$421$	13.1300	+	36.0744i	0.639917	+	1.75816i	−0.0120688	+	0.999927i	$0.503842\pi$
$422$	0.0560266	+	3.34660i	0.00272733	+	0.162910i
$423$		0			0
$424$	−23.8273	−	12.2049i	−1.15716	−	0.592724i
$425$	−11.9847	−	2.11323i	−0.581345	−	0.102507i
$426$		0			0
$427$	1.56936	+	0.571201i	0.0759467	+	0.0276424i
$428$	−3.02016	−	3.36387i	−0.145985	−	0.162599i
$429$		0			0
$430$	6.40576	+	16.7232i	0.308913	+	0.806466i
$431$	−7.70543			−0.371157			−0.185579	−	0.982629i	$-0.559416\pi$
$431$	−7.70543			−0.371157			−0.185579	+	0.982629i	$0.559416\pi$
$432$		0			0
$433$	−18.8564			−0.906183			−0.453091	−	0.891464i	$-0.649679\pi$
$433$	−18.8564			−0.906183			−0.453091	+	0.891464i	$0.649679\pi$
$434$	0.780594	+	2.03786i	0.0374697	+	0.0978205i
$435$		0			0
$436$	−4.01716	−	4.47434i	−0.192387	−	0.214282i
$437$	−48.2399	−	17.5579i	−2.30763	−	0.839907i
$438$		0			0
$439$	−16.3164	−	2.87702i	−0.778738	−	0.137313i	−0.229870	−	0.973221i	$-0.573830\pi$
$439$	−16.3164	−	2.87702i	−0.778738	−	0.137313i	−0.548868	+	0.835909i	$0.684941\pi$
$440$	−17.7507	+	34.6542i	−0.846232	+	1.65207i
$441$		0			0
$442$	0.0734129	+	4.38512i	0.00349189	+	0.208579i
$443$	2.23622	+	6.14396i	0.106246	+	0.291908i	0.981411	−	0.191915i	$-0.0614699\pi$
$443$	2.23622	+	6.14396i	0.106246	+	0.291908i	−0.875166	+	0.483824i	$0.839248\pi$
$444$		0			0
$445$	27.1939	+	32.4084i	1.28911	+	1.53631i
$446$	−5.38519	−	27.8103i	−0.254996	−	1.31686i
$447$		0			0
$448$	−0.703196	−	1.45757i	−0.0332229	−	0.0688637i
$449$	−9.04053	+	5.21955i	−0.426649	+	0.246326i	−0.697918	−	0.716178i	$-0.745890\pi$
$449$	−9.04053	+	5.21955i	−0.426649	+	0.246326i	0.271269	+	0.962504i	$0.412557\pi$
$450$		0			0
$451$	20.7026	−	35.8579i	0.974846	−	1.68848i
$452$	−4.20434	−	10.4490i	−0.197755	−	0.491480i
$453$		0			0
$454$	27.5135	−	23.8827i	1.29127	−	1.12087i
$455$	0.205066	+	1.16299i	0.00961366	+	0.0545218i
$456$		0			0
$457$	20.6728	+	17.3466i	0.967034	+	0.811438i	0.982083	−	0.188449i	$-0.0603460\pi$
$457$	20.6728	+	17.3466i	0.967034	+	0.811438i	−0.0150490	+	0.999887i	$0.504790\pi$
$458$	1.53196	−	2.75909i	0.0715840	−	0.128924i
$459$		0			0
$460$	28.6511	+	45.9972i	1.33586	+	2.14463i
$461$	−3.79701	−	3.18607i	−0.176844	−	0.148390i	0.550069	−	0.835119i	$-0.314601\pi$
$461$	−3.79701	−	3.18607i	−0.176844	−	0.148390i	−0.726913	+	0.686729i	$0.759046\pi$
$462$		0			0
$463$	2.96473	−	0.522762i	0.137783	−	0.0242948i	−0.104331	−	0.994543i	$-0.533270\pi$
$463$	2.96473	−	0.522762i	0.137783	−	0.0242948i	0.242114	+	0.970248i	$0.422159\pi$
$464$	11.6211	−	11.1585i	0.539498	−	0.518020i
$465$		0			0
$466$	−9.43496	−	7.65143i	−0.437066	−	0.354446i
$467$	29.0602	+	16.7779i	1.34475	+	0.776390i	0.987500	−	0.157620i	$-0.0503822\pi$
$467$	29.0602	+	16.7779i	1.34475	+	0.776390i	0.357247	+	0.934010i	$0.383716\pi$
$468$		0			0
$469$	0.289241	−	0.166993i	0.0133559	−	0.00771104i
$470$	−14.4111	−	2.29304i	−0.664737	−	0.105770i
$471$		0			0
$472$	−7.45871	+	6.92557i	−0.343315	+	0.318775i
$473$	−9.57848	−	11.4152i	−0.440419	−	0.524871i
$474$		0			0
$475$	−40.7858	+	14.8448i	−1.87138	+	0.681126i
$476$	−0.346031	+	0.648556i	−0.0158603	+	0.0297265i
$477$		0			0
$478$	1.77625	−	1.06555i	0.0812438	−	0.0487373i
$479$	2.69060	−	15.2592i	0.122937	−	0.697208i	−0.859575	−	0.511009i	$-0.829272\pi$
$479$	2.69060	−	15.2592i	0.122937	−	0.697208i	0.982512	−	0.186199i	$-0.0596170\pi$
$480$		0			0
$481$	2.84070	+	1.03393i	0.129525	+	0.0471432i
$482$	0.931523	−	2.69908i	0.0424297	−	0.122940i
$483$		0			0
$484$	1.46193	−	10.2955i	0.0664512	−	0.467978i
$485$	30.0031			1.36237
$486$		0			0
$487$		−	42.9742i		−	1.94735i	−0.227945	−	0.973674i	$-0.573201\pi$
$487$		−	42.9742i		−	1.94735i	0.227945	−	0.973674i	$-0.426799\pi$
$488$	−18.6188	−	14.0929i	−0.842833	−	0.637953i
$489$		0			0
$490$	10.9815	−	31.8189i	0.496094	−	1.43743i
$491$	4.27635	−	11.7492i	0.192989	−	0.530233i	−0.805024	−	0.593243i	$-0.797848\pi$
$491$	4.27635	−	11.7492i	0.192989	−	0.530233i	0.998013	+	0.0630092i	$0.0200697\pi$
$492$		0			0
$493$	−7.20689	−	1.27077i	−0.324582	−	0.0572325i
$494$	8.04658	+	13.4134i	0.362033	+	0.603498i
$495$		0			0
$496$	−2.04154	−	30.4437i	−0.0916678	−	1.36696i
$497$	−0.310783	−	0.853868i	−0.0139405	−	0.0383012i
$498$		0			0
$499$	0.451535	−	0.378883i	0.0202135	−	0.0169611i	−0.632625	−	0.774458i	$-0.718023\pi$
$499$	0.451535	−	0.378883i	0.0202135	−	0.0169611i	0.652838	+	0.757497i	$0.273578\pi$
$500$	11.0412	+	3.60492i	0.493776	+	0.161217i
$501$		0			0
$502$	0.00502745	−	0.0315962i	0.000224386	−	0.00141021i
$503$	5.40120	+	9.35516i	0.240828	+	0.417126i	0.960950	−	0.276721i	$-0.0892478\pi$
$503$	5.40120	+	9.35516i	0.240828	+	0.417126i	−0.720123	+	0.693847i	$0.755914\pi$
$504$		0			0
$505$	17.7072	−	30.6698i	0.787961	−	1.36479i
$506$	−35.0232	−	28.4026i	−1.55697	−	1.26265i
$507$		0			0
$508$	−21.7134	+	4.58296i	−0.963378	+	0.203336i
$509$	4.10539	+	23.2828i	0.181968	+	1.03199i	0.929789	+	0.368093i	$0.119989\pi$
$509$	4.10539	+	23.2828i	0.181968	+	1.03199i	−0.747821	+	0.663901i	$0.768900\pi$
$510$		0			0
$511$	1.05331	−	1.25529i	0.0465958	−	0.0555307i
$512$	3.39612	+	22.3711i	0.150089	+	0.988673i
$513$		0			0
$514$	11.3066	−	20.3633i	0.498711	−	0.898187i
$515$	−14.2700	+	17.0064i	−0.628812	+	0.749389i
$516$		0			0
$517$	11.9580	−	2.10852i	0.525912	−	0.0927325i
$518$	0.332144	+	0.382639i	0.0145936	+	0.0168122i
$519$		0			0
$520$	2.04735	−	16.3843i	0.0897821	−	0.718499i
$521$	−29.7943	−	17.2017i	−1.30531	−	0.753622i	−0.324002	−	0.946056i	$-0.605028\pi$
$521$	−29.7943	−	17.2017i	−1.30531	−	0.753622i	−0.981310	+	0.192434i	$0.938362\pi$
$522$		0			0
$523$	15.1865	+	26.3038i	0.664059	+	1.15018i	0.979539	+	0.201252i	$0.0645011\pi$
$523$	15.1865	+	26.3038i	0.664059	+	1.15018i	−0.315480	+	0.948932i	$0.602166\pi$
$524$	9.09726	−	11.6098i	0.397416	−	0.507175i
$525$		0			0
$526$	8.21678	−	1.59110i	0.358269	−	0.0693751i
$527$	−10.6170	+	8.90871i	−0.462483	+	0.388070i
$528$		0			0
$529$	−37.3617	+	13.5985i	−1.62442	+	0.591241i
$530$	−0.766345	−	45.7755i	−0.0332879	−	1.98836i
$531$		0			0
$532$	0.0877580	+	2.62026i	0.00380479	+	0.113603i
$533$	−3.04907	+	17.2921i	−0.132070	+	0.749005i
$534$		0			0
$535$	2.64415	−	7.26473i	0.114316	−	0.314082i
$536$	−4.55234	+	1.04073i	−0.196631	+	0.0449528i
$537$		0			0
$538$	−2.52294	−	6.58652i	−0.108772	−	0.283965i
$539$			28.0092i			1.20644i
$540$		0			0
$541$			4.15389i			0.178590i	0.996005	+	0.0892948i	$0.0284613\pi$
$541$			4.15389i			0.178590i	−0.996005	+	0.0892948i	$0.971539\pi$
$542$	−9.29098	+	3.55887i	−0.399082	+	0.152867i
$543$		0			0
$544$	7.29355	−	7.24170i	0.312708	−	0.310485i
$545$	3.51702	−	9.66293i	0.150652	−	0.413914i
$546$		0			0
$547$	2.83365	−	16.0704i	0.121158	−	0.687122i	−0.862358	−	0.506300i	$-0.831013\pi$
$547$	2.83365	−	16.0704i	0.121158	−	0.687122i	0.983516	−	0.180823i	$-0.0578760\pi$
$548$	−0.777039	−	23.2007i	−0.0331935	−	0.991083i
$549$		0			0
$550$	−38.1194	+	0.638170i	−1.62542	+	0.0272117i
$551$	−24.5260	+	8.92675i	−1.04484	+	0.380292i
$552$		0			0
$553$	0.0918277	−	0.0770526i	0.00390491	−	0.00327661i
$554$	6.13767	+	31.6963i	0.260765	+	1.34665i
$555$		0			0
$556$	−12.4238	−	9.73510i	−0.526886	−	0.412860i
$557$	14.8098	+	25.6513i	0.627511	+	1.08688i	0.988049	+	0.154137i	$0.0492598\pi$
$557$	14.8098	+	25.6513i	0.627511	+	1.08688i	−0.360538	+	0.932745i	$0.617407\pi$
$558$		0			0
$559$	5.47271	+	3.15967i	0.231471	+	0.133640i
$560$	1.63310	−	2.23433i	0.0690109	−	0.0944175i
$561$		0			0
$562$	−26.1790	+	22.7243i	−1.10429	+	0.958565i
$563$	−22.0013	+	3.87943i	−0.927246	+	0.163498i	−0.616824	−	0.787101i	$-0.711581\pi$
$563$	−22.0013	+	3.87943i	−0.927246	+	0.163498i	−0.310421	+	0.950599i	$0.600470\pi$
$564$		0			0
$565$	12.3809	−	14.7550i	0.520868	−	0.620746i
$566$	13.4198	+	7.45122i	0.564075	+	0.313198i
$567$		0			0
$568$	0.637766	+	12.6889i	0.0267601	+	0.532416i
$569$	1.10991	−	1.32274i	0.0465299	−	0.0554522i	−0.742278	−	0.670093i	$-0.766254\pi$
$569$	1.10991	−	1.32274i	0.0465299	−	0.0554522i	0.788807	+	0.614640i	$0.210699\pi$
$570$		0			0
$571$	2.73361	+	15.5031i	0.114398	+	0.648783i	0.987047	+	0.160434i	$0.0512894\pi$
$571$	2.73361	+	15.5031i	0.114398	+	0.648783i	−0.872649	+	0.488349i	$0.837599\pi$
$572$	2.83743	+	13.4433i	0.118639	+	0.562095i
$573$		0			0
$574$	−1.85375	+	2.28585i	−0.0773740	+	0.0954097i
$575$	−26.5309	+	45.9528i	−1.10641	+	1.91637i
$576$		0			0
$577$	9.83883	+	17.0414i	0.409596	+	0.709441i	0.994844	−	0.101413i	$-0.0323364\pi$
$577$	9.83883	+	17.0414i	0.409596	+	0.709441i	−0.585248	+	0.810854i	$0.699003\pi$
$578$	19.1324	+	3.04426i	0.795801	+	0.126625i
$579$		0			0
$580$	26.1909	+	8.55128i	1.08752	+	0.355073i
$581$	−1.93457	+	1.62330i	−0.0802594	+	0.0673456i
$582$		0			0
$583$	13.0294	+	35.7981i	0.539624	+	1.48260i
$584$	−19.2421	+	12.4375i	−0.796242	+	0.514666i
$585$		0			0
$586$	19.8841	−	11.9282i	0.821403	−	0.492751i
$587$	1.96505	+	0.346492i	0.0811063	+	0.0143012i	0.214054	−	0.976822i	$-0.431333\pi$
$587$	1.96505	+	0.346492i	0.0811063	+	0.0143012i	−0.132948	+	0.991123i	$0.542444\pi$
$588$		0			0
$589$	−16.9061	+	46.4492i	−0.696605	+	1.91391i
$590$	−16.4536	−	5.67855i	−0.677382	−	0.233782i
$591$		0			0
$592$	−2.86304	−	6.48019i	−0.117670	−	0.266334i
$593$		−	21.4365i		−	0.880291i	−0.897927	−	0.440145i	$-0.854927\pi$
$593$		−	21.4365i		−	0.880291i	0.897927	−	0.440145i	$-0.145073\pi$
$594$		0			0
$595$	−1.25709			−0.0515358
$596$	1.97801	−	13.9300i	0.0810225	−	0.570596i
$597$		0			0
$598$	18.0763	+	6.23861i	0.739196	+	0.255116i
$599$	−39.6839	−	14.4438i	−1.62144	−	0.590156i	−0.637785	−	0.770215i	$-0.720149\pi$
$599$	−39.6839	−	14.4438i	−1.62144	−	0.590156i	−0.983656	+	0.180059i	$0.942371\pi$
$600$		0			0
$601$	−3.07096	+	17.4163i	−0.125267	+	0.710424i	0.855882	+	0.517171i	$0.173015\pi$
$601$	−3.07096	+	17.4163i	−0.125267	+	0.710424i	−0.981149	+	0.193253i	$0.938096\pi$
$602$	0.544873	+	0.908288i	0.0222074	+	0.0370191i
$603$		0			0
$604$	−11.0600	−	5.90099i	−0.450027	−	0.240108i
$605$	16.7107	−	6.08218i	0.679385	−	0.247276i
$606$		0			0
$607$	−25.0286	−	29.8279i	−1.01588	−	1.21068i	−0.977395	−	0.211420i	$-0.932191\pi$
$607$	−25.0286	−	29.8279i	−1.01588	−	1.21068i	−0.0384848	−	0.999259i	$-0.512253\pi$
$608$	9.61376	−	35.3738i	0.389889	−	1.43460i
$609$		0			0
$610$	6.27501	−	39.4367i	0.254068	−	1.59675i
$611$	−4.45944	+	2.57466i	−0.180410	+	0.104160i
$612$		0			0
$613$	2.98975	+	1.72613i	0.120755	+	0.0697178i	0.559161	−	0.829059i	$-0.311123\pi$
$613$	2.98975	+	1.72613i	0.120755	+	0.0697178i	−0.438406	+	0.898777i	$0.644457\pi$
$614$	12.9893	−	16.0171i	0.524206	−	0.646397i
$615$		0			0
$616$	−0.678010	+	2.20081i	−0.0273178	+	0.0886732i
$617$	−3.45250	+	0.608769i	−0.138992	+	0.0245081i	−0.242711	−	0.970099i	$-0.578037\pi$
$617$	−3.45250	+	0.608769i	−0.138992	+	0.0245081i	0.103719	+	0.994607i	$0.466926\pi$
$618$		0			0
$619$	−5.42408	−	4.55134i	−0.218012	−	0.182934i	0.527241	−	0.849716i	$-0.323227\pi$
$619$	−5.42408	−	4.55134i	−0.218012	−	0.182934i	−0.745253	+	0.666782i	$0.767671\pi$
$620$	44.2898	−	27.5876i	1.77872	−	1.10794i
$621$		0			0
$622$	−29.1273	−	16.1727i	−1.16790	−	0.648466i
$623$	1.91682	+	1.60840i	0.0767956	+	0.0644391i
$624$		0			0
$625$	−2.36634	−	13.4202i	−0.0946535	−	0.536807i
$626$	−4.21526	−	4.85610i	−0.168476	−	0.194089i
$627$		0			0
$628$	−3.71902	−	9.24285i	−0.148405	−	0.368830i
$629$	−1.60899	+	2.78685i	−0.0641546	+	0.111119i
$630$		0			0
$631$	6.49028	−	3.74717i	0.258374	−	0.149172i	−0.365219	−	0.930922i	$-0.619006\pi$
$631$	6.49028	−	3.74717i	0.258374	−	0.149172i	0.623593	+	0.781749i	$0.285672\pi$
$632$	−1.54421	+	0.651582i	−0.0614255	+	0.0259185i
$633$		0			0
$634$	−14.8679	+	2.87901i	−0.590479	+	0.114340i
$635$	−24.3941	−	29.0718i	−0.968051	−	1.15368i
$636$		0			0
$637$	−4.06252	−	11.1617i	−0.160963	−	0.442242i
$638$	−22.9226	+	0.383756i	−0.907516	+	0.0151930i
$639$		0			0
$640$	−31.0195	+	23.1329i	−1.22615	+	0.914407i
$641$	−21.3252	−	3.76021i	−0.842295	−	0.148519i	−0.264178	−	0.964474i	$-0.585101\pi$
$641$	−21.3252	−	3.76021i	−0.842295	−	0.148519i	−0.578116	+	0.815955i	$0.696212\pi$
$642$		0			0
$643$	−22.2522	−	8.09915i	−0.877543	−	0.319399i	−0.136325	−	0.990664i	$-0.543529\pi$
$643$	−22.2522	−	8.09915i	−0.877543	−	0.319399i	−0.741218	+	0.671265i	$0.765751\pi$
$644$	2.14126	+	2.38494i	0.0843773	+	0.0939798i
$645$		0			0
$646$	−15.5490	+	5.95596i	−0.611766	+	0.234334i
$647$	18.8024			0.739198			0.369599	−	0.929191i	$-0.379495\pi$
$647$	18.8024			0.739198			0.369599	+	0.929191i	$0.379495\pi$
$648$		0			0
$649$	14.4836			0.568530
$650$	15.0980	−	5.78323i	0.592193	−	0.226837i
$651$		0			0
$652$	−9.71842	+	8.72542i	−0.380603	+	0.341714i
$653$	−10.1057	−	3.67818i	−0.395467	−	0.143938i	0.136629	−	0.990622i	$-0.456373\pi$
$653$	−10.1057	−	3.67818i	−0.395467	−	0.143938i	−0.532096	+	0.846684i	$0.678595\pi$
$654$		0			0
$655$	24.8401	+	4.37998i	0.970582	+	0.171140i
$656$	34.1800	−	22.9131i	1.33451	−	0.894605i
$657$		0			0
$658$	−0.862957	+	0.0144471i	−0.0336416	+	0.000563205i
$659$	−8.25777	−	22.6880i	−0.321677	−	0.883800i	−0.990143	−	0.140058i	$-0.955271\pi$
$659$	−8.25777	−	22.6880i	−0.321677	−	0.883800i	0.668466	−	0.743742i	$-0.266951\pi$
$660$		0			0
$661$	−1.20921	−	1.44108i	−0.0470329	−	0.0560516i	0.742015	−	0.670383i	$-0.233870\pi$
$661$	−1.20921	−	1.44108i	−0.0470329	−	0.0560516i	−0.789048	+	0.614331i	$0.789426\pi$
$662$	20.2391	−	3.91909i	0.786614	−	0.152320i
$663$		0			0
$664$	32.5325	−	13.7271i	1.26251	−	0.532715i
$665$	−3.88279	+	2.24173i	−0.150568	+	0.0869305i
$666$		0			0
$667$	−15.9540	+	27.6332i	−0.617743	+	1.06996i
$668$	−22.7393	+	9.14956i	−0.879811	+	0.354007i
$669$		0			0
$670$	−5.23490	−	6.03075i	−0.202242	−	0.232988i
$671$	5.77005	+	32.7236i	0.222750	+	1.26328i
$672$		0			0
$673$	−20.7393	−	17.4023i	−0.799439	−	0.670809i	0.148623	−	0.988894i	$-0.452516\pi$
$673$	−20.7393	−	17.4023i	−0.799439	−	0.670809i	−0.948062	+	0.318085i	$0.896960\pi$
$674$	−31.1455	−	17.2933i	−1.19968	−	0.666113i
$675$		0			0
$676$	10.6659	+	17.1233i	0.410225	+	0.658587i
$677$	18.1567	+	15.2353i	0.697820	+	0.585540i	0.921153	−	0.389202i	$-0.127249\pi$
$677$	18.1567	+	15.2353i	0.697820	+	0.585540i	−0.223333	+	0.974742i	$0.571694\pi$
$678$		0			0
$679$	1.74759	−	0.308148i	0.0670665	−	0.0118256i
$680$	16.7976	+	5.17487i	0.644157	+	0.198447i
$681$		0			0
$682$	−27.3483	+	33.7231i	−1.04722	+	1.29133i
$683$	−18.0209	−	10.4044i	−0.689551	−	0.398113i	0.113893	−	0.993493i	$-0.463668\pi$
$683$	−18.0209	−	10.4044i	−0.689551	−	0.398113i	−0.803444	+	0.595380i	$0.797001\pi$
$684$		0			0
$685$	34.3795	−	19.8490i	1.31357	−	0.758392i
$686$	0.627528	−	3.94384i	0.0239591	−	0.150577i
$687$		0			0
$688$	−3.54171	−	14.3797i	−0.135026	−	0.548222i
$689$	−10.3845	−	12.3757i	−0.395617	−	0.471478i
$690$		0			0
$691$	17.7551	−	6.46235i	0.675438	−	0.245839i	0.0185503	−	0.999828i	$-0.494095\pi$
$691$	17.7551	−	6.46235i	0.675438	−	0.245839i	0.656887	+	0.753989i	$0.271873\pi$
$692$	22.9739	−	43.0594i	0.873338	−	1.63687i
$693$		0			0
$694$	−6.44150	−	10.7378i	−0.244516	−	0.407601i
$695$	4.68707	−	26.5817i	0.177791	−	1.00830i
$696$		0			0
$697$	−17.5641	−	6.39281i	−0.665288	−	0.242145i
$698$	40.8090	+	14.0842i	1.54464	+	0.533097i
$699$		0			0
$700$	2.68296	+	0.380971i	0.101406	+	0.0143993i
$701$	7.59328			0.286794			0.143397	−	0.989665i	$-0.454197\pi$
$701$	7.59328			0.286794			0.143397	+	0.989665i	$0.454197\pi$
$702$		0			0
$703$			11.4770i			0.432864i
$704$	18.1194	−	26.6167i	0.682902	−	1.00315i
$705$		0			0
$706$	−18.5265	−	6.39398i	−0.697255	−	0.240641i
$707$	0.716398	−	1.96829i	0.0269429	−	0.0740251i
$708$		0			0
$709$	47.1054	+	8.30595i	1.76908	+	0.311937i	0.960879	−	0.276969i	$-0.0893299\pi$
$709$	47.1054	+	8.30595i	1.76908	+	0.311937i	0.808202	+	0.588906i	$0.200441\pi$
$710$	−18.6316	+	11.1769i	−0.699230	+	0.419461i
$711$		0			0
$712$	−18.9919	−	29.3824i	−0.711751	−	1.10115i
$713$	20.6682	+	56.7855i	0.774032	+	2.12663i
$714$		0			0
$715$	−17.9991	+	15.1030i	−0.673128	+	0.564821i
$716$	−8.95716	+	27.4340i	−0.334745	+	1.02526i
$717$		0			0
$718$	26.5263	+	4.22075i	0.989951	+	0.157517i
$719$	3.52716	+	6.10922i	0.131541	+	0.227835i	0.924271	−	0.381738i	$-0.124674\pi$
$719$	3.52716	+	6.10922i	0.131541	+	0.227835i	−0.792730	+	0.609573i	$0.791341\pi$
$720$		0			0
$721$	−0.656522	+	1.13713i	−0.0244502	+	0.0423489i
$722$	−20.4803	+	25.2542i	−0.762198	+	0.939864i
$723$		0			0
$724$	40.0131	−	8.44538i	1.48707	−	0.313870i
$725$	4.68461	+	26.5677i	0.173982	+	0.986701i
$726$		0			0
$727$	18.2911	−	21.7985i	0.678380	−	0.808462i	−0.311518	−	0.950240i	$-0.600837\pi$
$727$	18.2911	−	21.7985i	0.678380	−	0.808462i	0.989898	+	0.141778i	$0.0452819\pi$
$728$	−0.0490234	−	0.975364i	−0.00181693	−	0.0361494i
$729$		0			0
$730$	−34.2555	−	19.0201i	−1.26785	−	0.703965i
$731$	−4.32397	+	5.15310i	−0.159928	+	0.190594i
$732$		0			0
$733$	−14.2179	+	2.50701i	−0.525152	+	0.0925984i	−0.429938	−	0.902858i	$-0.641465\pi$
$733$	−14.2179	+	2.50701i	−0.525152	+	0.0925984i	−0.0952137	+	0.995457i	$0.530353\pi$
$734$	−21.5213	+	18.6812i	−0.794366	+	0.689537i
$735$		0			0
$736$	−18.7942	−	40.6827i	−0.692765	−	1.49958i
$737$	5.75483	+	3.32255i	0.211982	+	0.122388i
$738$		0			0
$739$	−7.63499	−	13.2242i	−0.280858	−	0.486460i	0.690738	−	0.723105i	$-0.257286\pi$
$739$	−7.63499	−	13.2242i	−0.280858	−	0.486460i	−0.971596	+	0.236645i	$0.923952\pi$
$740$	7.47252	−	9.53631i	0.274695	−	0.350562i
$741$		0			0
$742$	−0.514776	−	2.65842i	−0.0188980	−	0.0975936i
$743$	9.41012	−	7.89602i	0.345224	−	0.289677i	−0.453645	−	0.891182i	$-0.649877\pi$
$743$	9.41012	−	7.89602i	0.345224	−	0.289677i	0.798869	+	0.601505i	$0.205432\pi$
$744$		0			0
$745$	22.6098	−	8.22931i	0.828360	−	0.301498i
$746$	−19.4424	+	0.325492i	−0.711836	+	0.0119171i
$747$		0			0
$748$	−14.6174	+	0.489569i	−0.534466	+	0.0179004i
$749$	0.0794011	−	0.450306i	0.00290125	−	0.0164538i
$750$		0			0
$751$	−8.22636	+	22.6017i	−0.300184	+	0.824749i	0.694283	+	0.719702i	$0.255722\pi$
$751$	−8.22636	+	22.6017i	−0.300184	+	0.824749i	−0.994467	+	0.105047i	$0.966501\pi$
$752$	11.5905	+	3.35935i	0.422662	+	0.122503i
$753$		0			0
$754$	9.07902	−	3.47768i	0.330638	−	0.126650i
$755$		−	21.4376i		−	0.780196i
$756$		0			0
$757$			2.57077i			0.0934361i	0.998908	+	0.0467180i	$0.0148762\pi$
$757$			2.57077i			0.0934361i	−0.998908	+	0.0467180i	$0.985124\pi$
$758$	11.6804	+	30.4936i	0.424253	+	1.10758i
$759$		0			0
$760$	61.1108	−	13.9708i	2.21672	−	0.506775i
$761$	8.41063	−	23.1080i	0.304885	−	0.837665i	−0.688748	−	0.725001i	$-0.741839\pi$
$761$	8.41063	−	23.1080i	0.304885	−	0.837665i	0.993633	−	0.112664i	$-0.0359384\pi$
$762$		0			0
$763$	0.105613	−	0.598958i	0.00382343	−	0.0216837i
$764$	41.6248	−	1.39410i	1.50593	−	0.0504369i
$765$		0			0
$766$	−0.0435389	−	2.60068i	−0.00157313	−	0.0939664i
$767$	−5.77171	+	2.10073i	−0.208404	+	0.0758530i
$768$		0			0
$769$	17.5940	−	14.7631i	0.634455	−	0.532371i	−0.267855	−	0.963459i	$-0.586315\pi$
$769$	17.5940	−	14.7631i	0.634455	−	0.532371i	0.902310	+	0.431088i	$0.141870\pi$
$770$	−3.86637	+	0.748683i	−0.139334	+	0.0269807i
$771$		0			0
$772$	−8.96680	−	7.02626i	−0.322722	−	0.252881i
$773$	−1.98617	−	3.44015i	−0.0714375	−	0.123733i	0.828094	−	0.560589i	$-0.189425\pi$
$773$	−1.98617	−	3.44015i	−0.0714375	−	0.123733i	−0.899532	+	0.436856i	$0.856092\pi$
$774$		0			0
$775$	44.2471	+	25.5461i	1.58940	+	0.917642i
$776$	−24.6202	−	3.07649i	−0.883815	−	0.110440i
$777$		0			0
$778$	−27.5459	−	31.7337i	−0.987570	−	1.13771i
$779$	−65.6503	+	11.5759i	−2.35217	+	0.414751i
$780$		0			0
$781$	11.6210	−	13.8494i	0.415833	−	0.495571i
$782$	−9.88143	+	17.7966i	−0.353359	+	0.636405i
$783$		0			0
$784$	−12.2740	+	24.9842i	−0.438357	+	0.892292i
$785$	10.9517	−	13.0518i	0.390884	−	0.465837i
$786$		0			0
$787$	2.43923	+	13.8335i	0.0869490	+	0.493112i	0.996919	+	0.0784382i	$0.0249933\pi$
$787$	2.43923	+	13.8335i	0.0869490	+	0.493112i	−0.909970	+	0.414674i	$0.863896\pi$
$788$	11.0713	+	52.4541i	0.394397	+	1.86860i
$789$		0			0
$790$	−2.22620	−	1.80537i	−0.0792046	−	0.0642322i
$791$	0.569609	−	0.986591i	0.0202529	−	0.0350791i
$792$		0			0
$793$	−7.04567	−	12.2035i	−0.250199	−	0.433358i
$794$	3.41121	−	21.4385i	0.121059	−	0.760825i
$795$		0			0
$796$	15.9762	−	48.9321i	0.566262	−	1.73435i
$797$	18.0786	−	15.1698i	0.640378	−	0.537341i	−0.263756	−	0.964589i	$-0.584961\pi$
$797$	18.0786	−	15.1698i	0.640378	−	0.537341i	0.904134	+	0.427248i	$0.140517\pi$
$798$		0			0
$799$	−1.87476	−	5.15085i	−0.0663241	−	0.182224i
$800$	−34.2821	−	16.1351i	−1.21205	−	0.570463i
$801$		0			0
$802$	12.3133	+	20.5259i	0.434798	+	0.724796i
$803$	32.1080	+	5.66151i	1.13307	+	0.199790i
$804$		0			0
$805$	−1.87466	+	5.15060i	−0.0660732	+	0.181535i
$806$	6.00704	−	17.4053i	0.211589	−	0.613077i
$807$		0			0
$808$	−17.6752	+	23.3516i	−0.621812	+	0.821507i
$809$		−	30.1592i		−	1.06034i	−0.847891	−	0.530170i	$-0.822128\pi$
$809$		−	30.1592i		−	1.06034i	0.847891	−	0.530170i	$-0.177872\pi$
$810$		0			0
$811$	−19.2303			−0.675266			−0.337633	−	0.941278i	$-0.609626\pi$
$811$	−19.2303			−0.675266			−0.337633	+	0.941278i	$0.609626\pi$
$812$	1.61337	+	0.229092i	0.0566181	+	0.00803956i
$813$		0			0
$814$	−3.28892	+	9.52962i	−0.115277	+	0.334013i
$815$	−20.9882	−	7.63909i	−0.735185	−	0.267586i
$816$		0			0
$817$	−4.16611	+	23.6272i	−0.145754	+	0.826610i
$818$	1.74403	−	1.04622i	0.0609785	−	0.0365804i
$819$		0			0
$820$	62.0861	+	33.1255i	2.16814	+	1.15679i
$821$	4.28889	−	1.56103i	0.149683	−	0.0544802i	−0.266092	−	0.963948i	$-0.585733\pi$
$821$	4.28889	−	1.56103i	0.149683	−	0.0544802i	0.415775	+	0.909467i	$0.363510\pi$
$822$		0			0
$823$	9.86833	+	11.7606i	0.343988	+	0.409949i	0.910106	−	0.414375i	$-0.136000\pi$
$823$	9.86833	+	11.7606i	0.343988	+	0.409949i	−0.566118	+	0.824324i	$0.691555\pi$
$824$	13.4536	−	12.4920i	0.468680	−	0.435179i
$825$		0			0
$826$	−1.01669	−	0.161772i	−0.0353752	−	0.00562876i
$827$	−30.5131	+	17.6168i	−1.06104	+	0.612594i	−0.925721	−	0.378207i	$-0.876541\pi$
$827$	−30.5131	+	17.6168i	−1.06104	+	0.612594i	−0.135324	+	0.990801i	$0.543207\pi$
$828$		0			0
$829$	−32.1764	−	18.5771i	−1.11753	−	0.645208i	−0.176763	−	0.984253i	$-0.556563\pi$
$829$	−32.1764	−	18.5771i	−1.11753	−	0.645208i	−0.940770	+	0.339045i	$0.889896\pi$
$830$	46.9002	+	38.0344i	1.62793	+	1.32019i
$831$		0			0
$832$	−3.36006	+	13.2348i	−0.116489	+	0.458835i
$833$	12.4520	−	2.19562i	0.431435	−	0.0760737i
$834$		0			0
$835$	−32.1100	−	26.9435i	−1.11121	−	0.932418i
$836$	−44.2759	+	27.5789i	−1.53131	+	0.953835i
$837$		0			0
$838$	18.4519	−	33.2322i	0.637411	−	1.14799i
$839$	−12.7067	−	10.6622i	−0.438683	−	0.368099i	0.396533	−	0.918020i	$-0.370213\pi$
$839$	−12.7067	−	10.6622i	−0.438683	−	0.368099i	−0.835216	+	0.549921i	$0.814658\pi$
$840$		0			0
$841$	−2.21876	−	12.5832i	−0.0765090	−	0.433904i
$842$	40.9994	−	35.5889i	1.41293	−	1.22647i
$843$		0			0
$844$	4.39132	−	1.76692i	0.151155	−	0.0608200i
$845$	−17.2494	+	29.8769i	−0.593398	+	1.02779i
$846$		0			0
$847$	0.910879	−	0.525896i	0.0312982	−	0.0180700i
$848$	−4.06493	+	37.6415i	−0.139590	+	1.29261i
$849$		0			0
$850$	3.27185	+	16.8966i	0.112224	+	0.579548i
$851$	9.01893	+	10.7483i	0.309165	+	0.368449i
$852$		0			0
$853$	6.77920	+	18.6257i	0.232115	+	0.637732i	0.999996	−	0.00286126i	$-0.000910768\pi$
$853$	6.77920	+	18.6257i	0.232115	+	0.637732i	−0.767880	+	0.640593i	$0.778689\pi$
$854$	−0.0395350	−	2.36152i	−0.00135286	−	0.0808095i
$855$		0			0
$856$	−2.91468	+	5.69023i	−0.0996216	+	0.194488i
$857$	17.6147	+	3.10595i	0.601708	+	0.106097i	0.466201	−	0.884679i	$-0.345623\pi$
$857$	17.6147	+	3.10595i	0.601708	+	0.106097i	0.135507	+	0.990776i	$0.456734\pi$
$858$		0			0
$859$	7.25730	+	2.64144i	0.247616	+	0.0901249i	0.462847	−	0.886438i	$-0.346828\pi$
$859$	7.25730	+	2.64144i	0.247616	+	0.0901249i	−0.215231	+	0.976563i	$0.569050\pi$
$860$	18.8450	−	16.9195i	0.642608	−	0.576949i
$861$		0			0
$862$	3.89792	+	10.1761i	0.132764	+	0.346600i
$863$	8.69446			0.295963			0.147981	−	0.988990i	$-0.452722\pi$
$863$	8.69446			0.295963			0.147981	+	0.988990i	$0.452722\pi$
$864$		0			0
$865$	83.4618			2.83779
$866$	9.53884	+	24.9026i	0.324143	+	0.846226i
$867$		0			0
$868$	2.29641	−	2.06177i	0.0779453	−	0.0699812i
$869$	2.24118	+	0.815725i	0.0760270	+	0.0276716i
$870$		0			0
$871$	−2.77521	−	0.489344i	−0.0940344	−	0.0165808i
$872$	−3.87685	+	7.56866i	−0.131287	+	0.256307i
$873$		0			0
$874$	1.21525	+	72.5896i	0.0411064	+	2.45538i
$875$	0.401800	+	1.10394i	0.0135833	+	0.0373198i
$876$		0			0
$877$	−27.2022	−	32.4183i	−0.918553	−	1.09469i	−0.995223	−	0.0976318i	$-0.968873\pi$
$877$	−27.2022	−	32.4183i	−0.918553	−	1.09469i	0.0766700	−	0.997057i	$-0.475571\pi$
$878$	4.45440	+	23.0035i	0.150329	+	0.776331i
$879$		0			0
$880$	54.7453	+	5.91198i	1.84546	+	0.199293i
$881$	−23.5185	+	13.5784i	−0.792359	+	0.457468i	−0.840792	−	0.541358i	$-0.817910\pi$
$881$	−23.5185	+	13.5784i	−0.792359	+	0.457468i	0.0484336	+	0.998826i	$0.484577\pi$
$882$		0			0
$883$	4.48989	−	7.77672i	0.151097	−	0.261707i	−0.780534	−	0.625113i	$-0.785053\pi$
$883$	4.48989	−	7.77672i	0.151097	−	0.261707i	0.931631	+	0.363406i	$0.118386\pi$
$884$	5.75404	−	2.31524i	0.193529	−	0.0778699i
$885$		0			0
$886$	6.98275	−	6.06127i	0.234590	−	0.203632i
$887$	1.66173	+	9.42413i	0.0557954	+	0.316431i	0.999913	−	0.0131769i	$-0.00419445\pi$
$887$	1.66173	+	9.42413i	0.0557954	+	0.316431i	−0.944118	+	0.329608i	$0.893083\pi$
$888$		0			0
$889$	−1.71947	−	1.44280i	−0.0576691	−	0.0483901i
$890$	29.0435	−	52.3078i	0.973540	−	1.75336i
$891$		0			0
$892$	−34.0033	+	21.1802i	−1.13852	+	0.709166i
$893$	−14.9759	−	12.5663i	−0.501149	−	0.420514i
$894$		0			0
$895$	−48.6028	+	8.56999i	−1.62461	+	0.286463i
$896$	−1.56921	+	1.66601i	−0.0524235	+	0.0556574i
$897$		0			0
$898$	11.4665	+	9.29892i	0.382641	+	0.310309i
$899$	26.6075	+	15.3618i	0.887409	+	0.512346i
$900$		0			0
$901$	14.8933	−	8.59864i	0.496167	−	0.286462i
$902$	−57.8282	−	9.20139i	−1.92547	−	0.306373i
$903$		0			0
$904$	−11.6726	+	10.8382i	−0.388224	+	0.360474i
$905$	44.9530	+	53.5729i	1.49429	+	1.78082i
$906$		0			0
$907$	22.4084	−	8.15601i	0.744060	−	0.270816i	0.0579560	−	0.998319i	$-0.481542\pi$
$907$	22.4084	−	8.15601i	0.744060	−	0.270816i	0.686104	+	0.727503i	$0.259319\pi$
$908$	−45.4586	−	24.2541i	−1.50860	−	0.804899i
$909$		0			0
$910$	1.43216	−	0.859137i	0.0474756	−	0.0284801i
$911$	−4.55164	+	25.8136i	−0.150802	+	0.855243i	0.811721	+	0.584045i	$0.198531\pi$
$911$	−4.55164	+	25.8136i	−0.150802	+	0.855243i	−0.962524	+	0.271198i	$0.912580\pi$
$912$		0			0
$913$	−47.2159	−	17.1852i	−1.56262	−	0.568746i
$914$	12.4509	−	36.0765i	0.411840	−	1.19330i
$915$		0			0
$916$	−4.41875	−	0.627446i	−0.145999	−	0.0207314i
$917$	1.49185			0.0492651
$918$		0			0
$919$		−	28.4248i		−	0.937649i	−0.883291	−	0.468824i	$-0.844678\pi$
$919$		−	28.4248i		−	0.937649i	0.883291	−	0.468824i	$-0.155322\pi$
$920$	46.2523	−	61.1063i	1.52489	−	2.01462i
$921$		0			0
$922$	−2.28688	+	6.62623i	−0.0753145	+	0.218223i
$923$	−2.62224	+	7.20454i	−0.0863120	+	0.237140i
$924$		0			0
$925$	11.6827	+	2.05997i	0.384123	+	0.0677313i
$926$	−2.19014	−	3.65090i	−0.0719725	−	0.119976i
$927$		0			0
$928$	−20.6151	−	9.70267i	−0.676725	−	0.318506i
$929$	−0.817461	−	2.24596i	−0.0268200	−	0.0736874i	0.925560	−	0.378601i	$-0.123595\pi$
$929$	−0.817461	−	2.24596i	−0.0268200	−	0.0736874i	−0.952380	+	0.304913i	$0.901372\pi$
$930$		0			0
$931$	34.5451	−	28.9868i	1.13217	−	0.950003i
$932$	−5.33198	+	16.3308i	−0.174655	+	0.534934i
$933$		0			0
$934$	7.45706	−	46.8656i	0.244002	−	1.53349i
$935$	−12.5057	−	21.6606i	−0.408982	−	0.708377i
$936$		0			0
$937$	−25.1607	+	43.5796i	−0.821965	+	1.42368i	0.0822523	+	0.996612i	$0.473789\pi$
$937$	−25.1607	+	43.5796i	−0.821965	+	1.42368i	−0.904217	+	0.427073i	$0.859545\pi$
$938$	−0.366856	−	0.297508i	−0.0119783	−	0.00971398i
$939$		0			0
$940$	4.26183	+	20.1920i	0.139005	+	0.658589i
$941$	−7.57703	−	42.9715i	−0.247004	−	1.40083i	−0.815792	−	0.578346i	$-0.803698\pi$
$941$	−7.57703	−	42.9715i	−0.247004	−	1.40083i	0.568787	−	0.822485i	$-0.307413\pi$
$942$		0			0
$943$	−52.3856	+	62.4307i	−1.70591	+	2.03302i
$944$	12.9193	+	6.34688i	0.420488	+	0.206573i
$945$		0			0
$946$	−10.2300	+	18.4243i	−0.332605	+	0.599026i
$947$	19.4528	−	23.1830i	0.632132	−	0.753345i	−0.350974	−	0.936385i	$-0.614149\pi$
$947$	19.4528	−	23.1830i	0.632132	−	0.753345i	0.983105	+	0.183040i	$0.0585938\pi$
$948$		0			0
$949$	−13.6162	+	2.40091i	−0.442001	+	0.0779367i
$950$	40.2368	+	46.3539i	1.30546	+	1.50392i
$951$		0			0
$952$	1.03156	+	0.128901i	0.0334329	+	0.00417771i
$953$	−27.2578	−	15.7373i	−0.882965	−	0.509780i	−0.0113304	−	0.999936i	$-0.503607\pi$
$953$	−27.2578	−	15.7373i	−0.882965	−	0.509780i	−0.871635	+	0.490156i	$0.836940\pi$
$954$		0			0
$955$	35.6115	+	61.6810i	1.15236	+	1.99595i
$956$	−2.30576	−	1.80677i	−0.0745737	−	0.0584350i
$957$		0			0
$958$	−21.5130	+	4.16577i	−0.695053	+	0.134590i
$959$	1.79864	−	1.50924i	0.0580812	−	0.0487359i
$960$		0			0
$961$	25.5472	−	9.29843i	0.824104	−	0.299949i
$962$	−0.0715624	−	4.27459i	−0.00230727	−	0.137818i
$963$		0			0
$964$	−4.03575	+	0.135166i	−0.129983	+	0.00435340i
$965$	3.38287	−	19.1852i	0.108899	−	0.617594i
$966$		0			0
$967$	−2.57740	+	7.08136i	−0.0828837	+	0.227721i	−0.974211	−	0.225640i	$-0.927553\pi$
$967$	−2.57740	+	7.08136i	−0.0828837	+	0.227721i	0.891327	+	0.453361i	$0.149775\pi$
$968$	−14.3362	+	3.27748i	−0.460784	+	0.105342i
$969$		0			0
$970$	−15.1776	−	39.6235i	−0.487323	−	1.27223i
$971$			15.5087i			0.497696i	0.968543	+	0.248848i	$0.0800520\pi$
$971$			15.5087i			0.497696i	−0.968543	+	0.248848i	$0.919948\pi$
$972$		0			0
$973$		−	1.59644i		−	0.0511796i
$974$	−56.7536	+	21.7392i	−1.81850	+	0.696570i
$975$		0			0
$976$	−9.19301	+	31.7179i	−0.294261	+	1.01526i
$977$	7.54941	−	20.7418i	0.241527	−	0.663590i	−0.758403	−	0.651786i	$-0.774020\pi$
$977$	7.54941	−	20.7418i	0.241527	−	0.663590i	0.999930	−	0.0118046i	$-0.00375761\pi$
$978$		0			0
$979$	−8.64507	+	49.0287i	−0.276298	+	1.56696i
$980$	−47.5766	+	1.59344i	−1.51978	+	0.0509006i
$981$		0			0
$982$	−17.6798	+	0.295983i	−0.564184	+	0.00944520i
$983$	13.7881	−	5.01845i	0.439771	−	0.160064i	−0.112639	−	0.993636i	$-0.535930\pi$
$983$	13.7881	−	5.01845i	0.439771	−	0.160064i	0.552410	+	0.833572i	$0.313708\pi$
$984$		0			0
$985$	−70.2301	+	58.9300i	−2.23772	+	1.87767i
$986$	1.96749	+	10.1606i	0.0626577	+	0.323578i
$987$		0			0
$988$	13.6439	−	17.4121i	0.434069	−	0.553951i
$989$	14.6652	+	25.4010i	0.466328	+	0.807703i
$990$		0			0
$991$	−10.0032	−	5.77533i	−0.317761	−	0.183460i	0.332633	−	0.943056i	$-0.392063\pi$
$991$	−10.0032	−	5.77533i	−0.317761	−	0.183460i	−0.650394	+	0.759597i	$0.725396\pi$
$992$	−39.1726	+	18.0966i	−1.24373	+	0.574568i
$993$		0			0
$994$	−0.970441	+	0.842377i	−0.0307805	+	0.0267186i
$995$	86.6893	−	15.2857i	2.74824	−	0.484588i
$996$		0			0
$997$	−27.6917	+	33.0016i	−0.877004	+	1.04517i	0.121612	+	0.992578i	$0.461194\pi$
$997$	−27.6917	+	33.0016i	−0.877004	+	1.04517i	−0.998616	+	0.0525950i	$0.983251\pi$
$998$	−0.728786	−	0.404653i	−0.0230693	−	0.0128091i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.13		192
3.2	odd	2		216.2.v.b.11.20	yes	192
8.3	odd	2	inner	648.2.v.b.35.30		192
12.11	even	2		864.2.bh.b.335.26		192
24.5	odd	2		864.2.bh.b.335.25		192
24.11	even	2		216.2.v.b.11.3	✓	192
27.5	odd	18	inner	648.2.v.b.611.30		192
27.22	even	9		216.2.v.b.59.3	yes	192
108.103	odd	18		864.2.bh.b.815.25		192
216.59	even	18	inner	648.2.v.b.611.13		192
216.157	even	18		864.2.bh.b.815.26		192
216.211	odd	18		216.2.v.b.59.20	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.3	✓	192	24.11	even	2
216.2.v.b.11.20	yes	192	3.2	odd	2
216.2.v.b.59.3	yes	192	27.22	even	9
216.2.v.b.59.20	yes	192	216.211	odd	18
648.2.v.b.35.13		192	1.1	even	1	trivial
648.2.v.b.35.30		192	8.3	odd	2	inner
648.2.v.b.611.13		192	216.59	even	18	inner
648.2.v.b.611.30		192	27.5	odd	18	inner
864.2.bh.b.335.25		192	24.5	odd	2
864.2.bh.b.335.26		192	12.11	even	2
864.2.bh.b.815.25		192	108.103	odd	18
864.2.bh.b.815.26		192	216.157	even	18

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.505867 - 1.32064i) q^{2} +(-1.48820 + 1.33614i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(-0.199218 - 0.0351275i) q^{7} +(2.51739 + 1.28947i) q^{8} +O(q^{10})\)	\(q+(-0.505867 - 1.32064i) q^{2} +(-1.48820 + 1.33614i) q^{4} +(-3.21396 - 1.16979i) q^{5} +(-0.199218 - 0.0351275i) q^{7} +(2.51739 + 1.28947i) q^{8} +(0.0809654 + 4.83625i) q^{10} +(-1.37658 - 3.78212i) q^{11} +(1.09713 + 1.30751i) q^{13} +(0.0543868 + 0.280866i) q^{14} +(0.429466 - 3.97688i) q^{16} +(-1.57350 + 0.908459i) q^{17} +(-3.24004 + 5.61192i) q^{19} +(6.34601 - 2.55343i) q^{20} +(-4.29847 + 3.73122i) q^{22} +(1.37566 + 7.80173i) q^{23} +(5.13093 + 4.30536i) q^{25} +(1.17176 - 2.11035i) q^{26} +(0.343411 - 0.213906i) q^{28} +(3.08543 + 2.58898i) q^{29} +(7.51214 - 1.32459i) q^{31} +(-5.46929 + 1.44460i) q^{32} +(1.99573 + 1.61847i) q^{34} +(0.599188 + 0.345941i) q^{35} +(1.53384 - 0.885560i) q^{37} +(9.05037 + 1.44006i) q^{38} +(-6.58240 - 7.08912i) q^{40} +(6.61260 + 7.88059i) q^{41} +(3.47909 - 1.26628i) q^{43} +(7.10206 + 3.78924i) q^{44} +(9.60741 - 5.76339i) q^{46} +(-0.523875 + 2.97105i) q^{47} +(-6.53939 - 2.38014i) q^{49} +(3.09028 - 8.95407i) q^{50} +(-3.37977 - 0.479915i) q^{52} -9.46508 q^{53} +13.7659i q^{55} +(-0.456214 - 0.345316i) q^{56} +(1.85830 - 5.38442i) q^{58} +(-1.23077 + 3.38152i) q^{59} +(-8.13039 - 1.43361i) q^{61} +(-5.54946 - 9.25079i) q^{62} +(4.67453 + 6.49221i) q^{64} +(-1.99664 - 5.48571i) q^{65} +(-1.26475 + 1.06125i) q^{67} +(1.12785 - 3.45438i) q^{68} +(0.153756 - 0.966313i) q^{70} +(2.24594 + 3.89008i) q^{71} +(-4.05026 + 7.01525i) q^{73} +(-1.94543 - 1.57767i) q^{74} +(-2.67648 - 12.6808i) q^{76} +(0.141383 + 0.801822i) q^{77} +(-0.380899 + 0.453938i) q^{79} +(-6.03238 + 12.2792i) q^{80} +(7.06236 - 12.7194i) q^{82} +(8.02454 - 9.56328i) q^{83} +(6.11986 - 1.07910i) q^{85} +(-3.43227 - 3.95406i) q^{86} +(1.41154 - 11.2961i) q^{88} +(-10.7122 - 6.18471i) q^{89} +(-0.172639 - 0.299020i) q^{91} +(-12.4714 - 9.77245i) q^{92} +(4.18870 - 0.811100i) q^{94} +(16.9781 - 14.2463i) q^{95} +(-8.24324 + 3.00029i) q^{97} +(0.164739 + 9.84024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

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