LMFDB - Embedded newform 432.2.y.e.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			181.2
Character	$\chi$	$=$	432.181
Dual form			432.2.y.e.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30272 + 0.550382i) q^{2} +(1.39416 - 1.43399i) q^{4} +(0.0468197 - 0.174734i) q^{5} +(4.04791 + 2.33706i) q^{7} +(-1.02696 + 2.63540i) q^{8} +O(q^{10})$	\(q+(-1.30272 + 0.550382i) q^{2} +(1.39416 - 1.43399i) q^{4} +(0.0468197 - 0.174734i) q^{5} +(4.04791 + 2.33706i) q^{7} +(-1.02696 + 2.63540i) q^{8} +(0.0351772 + 0.253398i) q^{10} +(0.598734 - 0.160430i) q^{11} +(-4.41237 - 1.18229i) q^{13} +(-6.55957 - 0.816641i) q^{14} +(-0.112639 - 3.99841i) q^{16} +4.34691 q^{17} +(-1.23918 + 1.23918i) q^{19} +(-0.185292 - 0.310745i) q^{20} +(-0.691685 + 0.538528i) q^{22} +(3.86311 - 2.23037i) q^{23} +(4.30179 + 2.48364i) q^{25} +(6.39880 - 0.888296i) q^{26} +(8.99475 - 2.54642i) q^{28} +(2.31752 + 8.64910i) q^{29} +(-2.25376 - 3.90364i) q^{31} +(2.34739 + 5.14682i) q^{32} +(-5.66281 + 2.39246i) q^{34} +(0.597886 - 0.597886i) q^{35} +(2.79692 + 2.79692i) q^{37} +(0.932282 - 2.29633i) q^{38} +(0.412412 + 0.302833i) q^{40} +(-3.67211 + 2.12009i) q^{41} +(-0.0131254 + 0.00351694i) q^{43} +(0.604676 - 1.08224i) q^{44} +(-3.80500 + 5.03173i) q^{46} +(1.17465 - 2.03456i) q^{47} +(7.42373 + 12.8583i) q^{49} +(-6.97097 - 0.867859i) q^{50} +(-7.84695 + 4.67899i) q^{52} +(0.519418 + 0.519418i) q^{53} -0.112130i q^{55} +(-10.3161 + 8.26782i) q^{56} +(-7.77939 - 9.99184i) q^{58} +(2.95679 - 11.0349i) q^{59} +(0.588805 + 2.19745i) q^{61} +(5.08451 + 3.84491i) q^{62} +(-5.89071 - 5.41290i) q^{64} +(-0.413172 + 0.715636i) q^{65} +(7.04291 + 1.88714i) q^{67} +(6.06029 - 6.23342i) q^{68} +(-0.449812 + 1.10794i) q^{70} +7.55145i q^{71} -2.92707i q^{73} +(-5.18298 - 2.10423i) q^{74} +(0.0493539 + 3.50458i) q^{76} +(2.79856 + 0.749872i) q^{77} +(1.45885 - 2.52680i) q^{79} +(-0.703931 - 0.167523i) q^{80} +(3.61687 - 4.78295i) q^{82} +(-1.99394 - 7.44148i) q^{83} +(0.203521 - 0.759552i) q^{85} +(0.0151631 - 0.0118056i) q^{86} +(-0.192077 + 1.74266i) q^{88} -3.18821i q^{89} +(-15.0978 - 15.0978i) q^{91} +(2.18747 - 8.64914i) q^{92} +(-0.410459 + 3.29697i) q^{94} +(0.158508 + 0.274544i) q^{95} +(8.03868 - 13.9234i) q^{97} +(-16.7480 - 12.6648i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.30272	+	0.550382i	−0.921162	+	0.389179i
$2$	−1.30272	+	0.550382i	−0.921162	+	0.389179i
$3$		0			0
$3$		0			0
$4$	1.39416	−	1.43399i	0.697080	−	0.716994i
$5$	0.0468197	−	0.174734i	0.0209384	−	0.0781432i	−0.954666	−	0.297679i	$-0.903788\pi$
$5$	0.0468197	−	0.174734i	0.0209384	−	0.0781432i	0.975604	+	0.219536i	$0.0704542\pi$
$6$		0			0
$7$	4.04791	+	2.33706i	1.52997	+	0.883327i	0.999362	+	0.0357075i	$0.0113685\pi$
$7$	4.04791	+	2.33706i	1.52997	+	0.883327i	0.530605	+	0.847619i	$0.321965\pi$
$8$	−1.02696	+	2.63540i	−0.363085	+	0.931756i
$9$		0			0
$10$	0.0351772	+	0.253398i	0.0111240	+	0.0801314i
$11$	0.598734	−	0.160430i	0.180525	−	0.0483716i	−0.167424	−	0.985885i	$-0.553545\pi$
$11$	0.598734	−	0.160430i	0.180525	−	0.0483716i	0.347949	+	0.937513i	$0.386878\pi$
$12$		0			0
$13$	−4.41237	−	1.18229i	−1.22377	−	0.327909i	−0.411621	−	0.911355i	$-0.635037\pi$
$13$	−4.41237	−	1.18229i	−1.22377	−	0.327909i	−0.812152	+	0.583446i	$0.801704\pi$
$14$	−6.55957	−	0.816641i	−1.75312	−	0.218257i
$15$		0			0
$16$	−0.112639	−	3.99841i	−0.0281598	−	0.999603i
$17$	4.34691			1.05428			0.527141	−	0.849778i	$-0.323264\pi$
$17$	4.34691			1.05428			0.527141	+	0.849778i	$0.323264\pi$
$18$		0			0
$19$	−1.23918	+	1.23918i	−0.284287	+	0.284287i	−0.834816	−	0.550529i	$-0.814426\pi$
$19$	−1.23918	+	1.23918i	−0.284287	+	0.284287i	0.550529	+	0.834816i	$0.314426\pi$
$20$	−0.185292	−	0.310745i	−0.0414325	−	0.0694848i
$21$		0			0
$22$	−0.691685	+	0.538528i	−0.147468	+	0.114815i
$23$	3.86311	−	2.23037i	0.805515	−	0.465064i	−0.0398812	−	0.999204i	$-0.512698\pi$
$23$	3.86311	−	2.23037i	0.805515	−	0.465064i	0.845396	+	0.534140i	$0.179365\pi$
$24$		0			0
$25$	4.30179	+	2.48364i	0.860357	+	0.496728i
$26$	6.39880	−	0.888296i	1.25491	−	0.174209i
$27$		0			0
$28$	8.99475	−	2.54642i	1.69985	−	0.481227i
$29$	2.31752	+	8.64910i	0.430353	+	1.60610i	0.751949	+	0.659221i	$0.229114\pi$
$29$	2.31752	+	8.64910i	0.430353	+	1.60610i	−0.321597	+	0.946877i	$0.604220\pi$
$30$		0			0
$31$	−2.25376	−	3.90364i	−0.404788	−	0.701114i	0.589509	−	0.807762i	$-0.299321\pi$
$31$	−2.25376	−	3.90364i	−0.404788	−	0.701114i	−0.994297	+	0.106648i	$0.965988\pi$
$32$	2.34739	+	5.14682i	0.414964	+	0.909838i
$33$		0			0
$34$	−5.66281	+	2.39246i	−0.971164	+	0.410304i
$35$	0.597886	−	0.597886i	0.101061	−	0.101061i
$36$		0			0
$37$	2.79692	+	2.79692i	0.459811	+	0.459811i	0.898593	−	0.438783i	$-0.144590\pi$
$37$	2.79692	+	2.79692i	0.459811	+	0.459811i	−0.438783	+	0.898593i	$0.644590\pi$
$38$	0.932282	−	2.29633i	0.151236	−	0.372513i
$39$		0			0
$40$	0.412412	+	0.302833i	0.0652080	+	0.0478821i
$41$	−3.67211	+	2.12009i	−0.573487	+	0.331103i	−0.758541	−	0.651626i	$-0.774087\pi$
$41$	−3.67211	+	2.12009i	−0.573487	+	0.331103i	0.185054	+	0.982728i	$0.440754\pi$
$42$		0			0
$43$	−0.0131254	+	0.00351694i	−0.00200161	+	0.000536329i	−0.259820	−	0.965657i	$-0.583663\pi$
$43$	−0.0131254	+	0.00351694i	−0.00200161	+	0.000536329i	0.257818	+	0.966193i	$0.416996\pi$
$44$	0.604676	−	1.08224i	0.0911583	−	0.163154i
$45$		0			0
$46$	−3.80500	+	5.03173i	−0.561017	+	0.741889i
$47$	1.17465	−	2.03456i	0.171341	−	0.296771i	−0.767548	−	0.640991i	$-0.778523\pi$
$47$	1.17465	−	2.03456i	0.171341	−	0.296771i	0.938889	+	0.344221i	$0.111857\pi$
$48$		0			0
$49$	7.42373	+	12.8583i	1.06053	+	1.83690i
$50$	−6.97097	−	0.867859i	−0.985845	−	0.122734i
$51$		0			0
$52$	−7.84695	+	4.67899i	−1.08818	+	0.648859i
$53$	0.519418	+	0.519418i	0.0713476	+	0.0713476i	0.741880	−	0.670533i	$-0.233934\pi$
$53$	0.519418	+	0.519418i	0.0713476	+	0.0713476i	−0.670533	+	0.741880i	$0.733934\pi$
$54$		0			0
$55$		−	0.112130i		−	0.0151196i
$56$	−10.3161	+	8.26782i	−1.37855	+	1.10483i
$57$		0			0
$58$	−7.77939	−	9.99184i	−1.02148	−	1.31199i
$59$	2.95679	−	11.0349i	0.384942	−	1.43662i	−0.453317	−	0.891350i	$-0.649759\pi$
$59$	2.95679	−	11.0349i	0.384942	−	1.43662i	0.838258	−	0.545273i	$-0.183574\pi$
$60$		0			0
$61$	0.588805	+	2.19745i	0.0753887	+	0.281355i	0.993321	−	0.115382i	$-0.0368093\pi$
$61$	0.588805	+	2.19745i	0.0753887	+	0.281355i	−0.917932	+	0.396737i	$0.870143\pi$
$62$	5.08451	+	3.84491i	0.645734	+	0.488304i
$63$		0			0
$64$	−5.89071	−	5.41290i	−0.736339	−	0.676613i
$65$	−0.413172	+	0.715636i	−0.0512477	+	0.0887637i
$66$		0			0
$67$	7.04291	+	1.88714i	0.860428	+	0.230551i	0.661944	−	0.749553i	$-0.269732\pi$
$67$	7.04291	+	1.88714i	0.860428	+	0.230551i	0.198484	+	0.980104i	$0.436398\pi$
$68$	6.06029	−	6.23342i	0.734918	−	0.755913i
$69$		0			0
$70$	−0.449812	+	1.10794i	−0.0537628	+	0.132425i
$71$			7.55145i			0.896193i	0.893985	+	0.448096i	$0.147898\pi$
$71$			7.55145i			0.896193i	−0.893985	+	0.448096i	$0.852102\pi$
$72$		0			0
$73$		−	2.92707i		−	0.342588i	−0.985220	−	0.171294i	$-0.945205\pi$
$73$		−	2.92707i		−	0.342588i	0.985220	−	0.171294i	$-0.0547948\pi$
$74$	−5.18298	−	2.10423i	−0.602509	−	0.244612i
$75$		0			0
$76$	0.0493539	+	3.50458i	0.00566128	+	0.402003i
$77$	2.79856	+	0.749872i	0.318925	+	0.0854558i
$78$		0			0
$79$	1.45885	−	2.52680i	0.164133	−	0.284287i	−0.772214	−	0.635362i	$-0.780851\pi$
$79$	1.45885	−	2.52680i	0.164133	−	0.284287i	0.936347	+	0.351076i	$0.114184\pi$
$80$	−0.703931	−	0.167523i	−0.0787019	−	0.0187296i
$81$		0			0
$82$	3.61687	−	4.78295i	0.399416	−	0.528188i
$83$	−1.99394	−	7.44148i	−0.218863	−	0.816808i	−0.984771	−	0.173858i	$-0.944377\pi$
$83$	−1.99394	−	7.44148i	−0.218863	−	0.816808i	0.765908	−	0.642950i	$-0.222290\pi$
$84$		0			0
$85$	0.203521	−	0.759552i	0.0220750	−	0.0823850i
$86$	0.0151631	−	0.0118056i	0.00163508	−	0.00127303i
$87$		0			0
$88$	−0.192077	+	1.74266i	−0.0204754	+	0.185768i
$89$		−	3.18821i		−	0.337950i	−0.985620	−	0.168975i	$-0.945954\pi$
$89$		−	3.18821i		−	0.337950i	0.985620	−	0.168975i	$-0.0540457\pi$
$90$		0			0
$91$	−15.0978	−	15.0978i	−1.58268	−	1.58268i
$92$	2.18747	−	8.64914i	0.228060	−	0.901736i
$93$		0			0
$94$	−0.410459	+	3.29697i	−0.0423357	+	0.340056i
$95$	0.158508	+	0.274544i	0.0162626	+	0.0281676i
$96$		0			0
$97$	8.03868	−	13.9234i	0.816204	−	1.41371i	−0.0922553	−	0.995735i	$-0.529408\pi$
$97$	8.03868	−	13.9234i	0.816204	−	1.41371i	0.908460	−	0.417972i	$-0.137259\pi$
$98$	−16.7480	−	12.6648i	−1.69180	−	1.27934i
$99$		0			0
$100$	9.55888	−	2.70612i	0.955888	−	0.270612i
$101$	−17.0308	+	4.56339i	−1.69463	+	0.454074i	−0.971578	−	0.236720i	$-0.923928\pi$
$101$	−17.0308	+	4.56339i	−1.69463	+	0.454074i	−0.723051	+	0.690795i	$0.757261\pi$
$102$		0			0
$103$	−8.05916	+	4.65296i	−0.794093	+	0.458470i	−0.841401	−	0.540411i	$-0.818269\pi$
$103$	−8.05916	+	4.65296i	−0.794093	+	0.458470i	0.0473086	+	0.998880i	$0.484936\pi$
$104$	7.64715	−	10.4142i	0.749864	−	1.02120i
$105$		0			0
$106$	−0.962535	−	0.390778i	−0.0934897	−	0.0379557i
$107$	−9.51927	−	9.51927i	−0.920263	−	0.920263i	0.0767848	−	0.997048i	$-0.475535\pi$
$107$	−9.51927	−	9.51927i	−0.920263	−	0.920263i	−0.997048	+	0.0767848i	$0.975535\pi$
$108$		0			0
$109$	−6.35255	+	6.35255i	−0.608464	+	0.608464i	−0.942544	−	0.334081i	$-0.891574\pi$
$109$	−6.35255	+	6.35255i	−0.608464	+	0.608464i	0.334081	+	0.942544i	$0.391574\pi$
$110$	0.0617145	+	0.146074i	0.00588425	+	0.0139276i
$111$		0			0
$112$	8.88859	−	16.4485i	0.839893	−	1.55423i
$113$	−5.34598	−	9.25951i	−0.502908	−	0.871062i	−0.999994	−	0.00336088i	$-0.998930\pi$
$113$	−5.34598	−	9.25951i	−0.502908	−	0.871062i	0.497087	−	0.867701i	$-0.334403\pi$
$114$		0			0
$115$	−0.208851	−	0.779441i	−0.0194754	−	0.0726832i
$116$	15.6337	+	8.73493i	1.45155	+	0.811018i
$117$		0			0
$118$	2.22154	+	16.0028i	0.204509	+	1.47317i
$119$	17.5959	+	10.1590i	1.61302	+	0.931275i
$120$		0			0
$121$	−9.19353	+	5.30789i	−0.835776	+	0.482535i
$122$	−1.97648	−	2.53859i	−0.178942	−	0.229833i
$123$		0			0
$124$	−8.73987	−	2.21042i	−0.784864	−	0.198502i
$125$	1.27495	−	1.27495i	0.114035	−	0.114035i
$126$		0			0
$127$	−11.5283			−1.02297			−0.511484	−	0.859293i	$-0.670904\pi$
$127$	−11.5283			−1.02297			−0.511484	+	0.859293i	$0.670904\pi$
$128$	10.6531	+	3.80936i	0.941611	+	0.336703i
$129$		0			0
$130$	0.144375	−	1.15968i	0.0126625	−	0.101710i
$131$	3.42289	+	0.917160i	0.299059	+	0.0801327i	0.405229	−	0.914215i	$-0.367192\pi$
$131$	3.42289	+	0.917160i	0.299059	+	0.0801327i	−0.106169	+	0.994348i	$0.533859\pi$
$132$		0			0
$133$	−7.91213	+	2.12005i	−0.686069	+	0.183832i
$134$	−10.2136	+	1.41787i	−0.882320	+	0.122486i
$135$		0			0
$136$	−4.46410	+	11.4559i	−0.382793	+	0.982333i
$137$	−13.0194	−	7.51678i	−1.11233	−	0.642202i	−0.172895	−	0.984940i	$-0.555312\pi$
$137$	−13.0194	−	7.51678i	−1.11233	−	0.642202i	−0.939431	+	0.342739i	$0.888646\pi$
$138$		0			0
$139$	2.61562	−	9.76161i	0.221854	−	0.827969i	−0.761787	−	0.647828i	$-0.775678\pi$
$139$	2.61562	−	9.76161i	0.221854	−	0.827969i	0.983641	−	0.180142i	$-0.0576556\pi$
$140$	−0.0238125	−	1.69091i	−0.00201253	−	0.142908i
$141$		0			0
$142$	−4.15618	−	9.83743i	−0.348779	−	0.825539i
$143$	−2.83152			−0.236783
$144$		0			0
$145$	1.61979			0.134517
$146$	1.61101	+	3.81316i	0.133328	+	0.315579i
$147$		0			0
$148$	7.91010	−	0.111395i	0.650206	−	0.00915664i
$149$	−1.37943	+	5.14811i	−0.113007	+	0.421749i	−0.999130	−	0.0417013i	$-0.986722\pi$
$149$	−1.37943	+	5.14811i	−0.113007	+	0.421749i	0.886123	+	0.463451i	$0.153389\pi$
$150$		0			0
$151$	−9.86458	−	5.69532i	−0.802768	−	0.463479i	0.0416699	−	0.999131i	$-0.486732\pi$
$151$	−9.86458	−	5.69532i	−0.802768	−	0.463479i	−0.844438	+	0.535653i	$0.820066\pi$
$152$	−1.99315	−	4.53832i	−0.161666	−	0.368107i
$153$		0			0
$154$	−4.05846	+	0.563404i	−0.327040	+	0.0454004i
$155$	−0.787617	+	0.211041i	−0.0632629	+	0.0169512i
$156$		0			0
$157$	−5.47145	−	1.46607i	−0.436670	−	0.117005i	0.0337857	−	0.999429i	$-0.489244\pi$
$157$	−5.47145	−	1.46607i	−0.436670	−	0.117005i	−0.470455	+	0.882424i	$0.655910\pi$
$158$	−0.509765	+	4.09463i	−0.0405548	+	0.325751i
$159$		0			0
$160$	1.00923	−	0.169196i	0.0797864	−	0.0133761i
$161$	20.8501			1.64321
$162$		0			0
$163$	15.0117	−	15.0117i	1.17581	−	1.17581i	0.195004	−	0.980802i	$-0.437528\pi$
$163$	15.0117	−	15.0117i	1.17581	−	1.17581i	0.980802	−	0.195004i	$-0.0624721\pi$
$164$	−2.07932	+	8.22150i	−0.162367	+	0.641991i
$165$		0			0
$166$	6.69320	+	8.59673i	0.519493	+	0.667236i
$167$	−7.81918	+	4.51441i	−0.605066	+	0.349335i	−0.771032	−	0.636796i	$-0.780259\pi$
$167$	−7.81918	+	4.51441i	−0.605066	+	0.349335i	0.165966	+	0.986132i	$0.446926\pi$
$168$		0			0
$169$	6.81291	+	3.93343i	0.524070	+	0.302572i
$170$	0.152912	+	1.10150i	0.0117278	+	0.0844810i
$171$		0			0
$172$	−0.0132557	+	0.0237249i	−0.00101073	+	0.00180900i
$173$	1.34114	+	5.00520i	0.101965	+	0.380539i	0.997983	−	0.0634788i	$-0.0202195\pi$
$173$	1.34114	+	5.00520i	0.101965	+	0.380539i	−0.896018	+	0.444017i	$0.853553\pi$
$174$		0			0
$175$	11.6088	+	20.1071i	0.877546	+	1.51995i
$176$	−0.708908	−	2.37592i	−0.0534359	−	0.179091i
$177$		0			0
$178$	1.75473	+	4.15335i	0.131523	+	0.311306i
$179$	−1.96093	+	1.96093i	−0.146566	+	0.146566i	−0.776582	−	0.630016i	$-0.783048\pi$
$179$	−1.96093	+	1.96093i	−0.146566	+	0.146566i	0.630016	+	0.776582i	$0.283048\pi$
$180$		0			0
$181$	−0.224256	−	0.224256i	−0.0166688	−	0.0166688i	0.698723	−	0.715392i	$-0.253752\pi$
$181$	−0.224256	−	0.224256i	−0.0166688	−	0.0166688i	−0.715392	+	0.698723i	$0.753752\pi$
$182$	27.9778	+	11.3587i	2.07385	+	0.841960i
$183$		0			0
$184$	1.91067	+	12.4714i	0.140856	+	0.919401i
$185$	0.619667	−	0.357765i	0.0455588	−	0.0263034i
$186$		0			0
$187$	2.60265	−	0.697377i	0.190324	−	0.0509972i
$188$	−1.27988	−	4.52093i	−0.0933446	−	0.329723i
$189$		0			0
$190$	−0.357596	−	0.270414i	−0.0259427	−	0.0196179i
$191$	10.3893	−	17.9947i	0.751741	−	1.30205i	−0.195237	−	0.980756i	$-0.562548\pi$
$191$	10.3893	−	17.9947i	0.751741	−	1.30205i	0.946978	−	0.321298i	$-0.104119\pi$
$192$		0			0
$193$	7.69572	+	13.3294i	0.553950	+	0.959469i	0.997984	+	0.0634596i	$0.0202134\pi$
$193$	7.69572	+	13.3294i	0.553950	+	0.959469i	−0.444035	+	0.896010i	$0.646453\pi$
$194$	−2.80896	+	22.5626i	−0.201672	+	1.61990i
$195$		0			0
$196$	28.7885	+	7.28095i	2.05632	+	0.520068i
$197$	0.905158	+	0.905158i	0.0644898	+	0.0644898i	0.738616	−	0.674126i	$-0.235480\pi$
$197$	0.905158	+	0.905158i	0.0644898	+	0.0644898i	−0.674126	+	0.738616i	$0.735480\pi$
$198$		0			0
$199$			16.5201i			1.17108i	0.810645	+	0.585538i	$0.199117\pi$
$199$			16.5201i			1.17108i	−0.810645	+	0.585538i	$0.800883\pi$
$200$	−10.9631	+	8.78635i	−0.775212	+	0.621289i
$201$		0			0
$202$	19.6748	−	15.3183i	1.38431	−	1.07779i
$203$	−10.8324	+	40.4270i	−0.760284	+	2.83742i
$204$		0			0
$205$	0.198524	+	0.740902i	0.0138655	+	0.0517469i
$206$	7.93793	−	10.4971i	0.553062	−	0.731369i
$207$		0			0
$208$	−4.23029	+	17.7757i	−0.293318	+	1.23252i
$209$	−0.543137	+	0.940741i	−0.0375696	+	0.0650724i
$210$		0			0
$211$	−25.2027	−	6.75305i	−1.73503	−	0.464899i	−0.753695	−	0.657224i	$-0.771730\pi$
$211$	−25.2027	−	6.75305i	−1.73503	−	0.464899i	−0.981331	+	0.192325i	$0.938397\pi$
$212$	1.46899	−	0.0206873i	0.100891	−	0.00142081i
$213$		0			0
$214$	17.6402	+	7.16171i	1.20586	+	0.489565i
$215$			0.00245811i			0.000167642i
$216$		0			0
$217$		−	21.0688i		−	1.43024i
$218$	4.77926	−	11.7719i	0.323693	−	0.797295i
$219$		0			0
$220$	−0.160793	−	0.156328i	−0.0108407	−	0.0105396i
$221$	−19.1802	−	5.13932i	−1.29020	−	0.345708i
$222$		0			0
$223$	6.47927	−	11.2224i	0.433884	−	0.751510i	−0.563320	−	0.826239i	$-0.690476\pi$
$223$	6.47927	−	11.2224i	0.433884	−	0.751510i	0.997204	+	0.0747295i	$0.0238093\pi$
$224$	−2.52641	+	26.3199i	−0.168803	+	1.75857i
$225$		0			0
$226$	12.0606	+	9.12022i	0.802258	+	0.606668i
$227$	−3.52089	−	13.1401i	−0.233690	−	0.872142i	−0.978735	−	0.205128i	$-0.934239\pi$
$227$	−3.52089	−	13.1401i	−0.233690	−	0.872142i	0.745045	−	0.667014i	$-0.232428\pi$
$228$		0			0
$229$	4.35071	−	16.2371i	0.287503	−	1.07298i	−0.659488	−	0.751715i	$-0.729227\pi$
$229$	4.35071	−	16.2371i	0.287503	−	1.07298i	0.946991	−	0.321260i	$-0.104106\pi$
$230$	0.701064	+	0.900446i	0.0462268	+	0.0593736i
$231$		0			0
$232$	−25.1739	−	2.77467i	−1.65275	−	0.182166i
$233$			10.0493i			0.658351i	0.944269	+	0.329176i	$0.106771\pi$
$233$			10.0493i			0.658351i	−0.944269	+	0.329176i	$0.893229\pi$
$234$		0			0
$235$	−0.300509	−	0.300509i	−0.0196030	−	0.0196030i
$236$	−11.7017	−	19.6244i	−0.761714	−	1.27744i
$237$		0			0
$238$	−28.5139	−	3.54987i	−1.84828	−	0.230104i
$239$	3.38365	+	5.86066i	0.218870	+	0.379094i	0.954463	−	0.298330i	$-0.0964295\pi$
$239$	3.38365	+	5.86066i	0.218870	+	0.379094i	−0.735593	+	0.677424i	$0.763096\pi$
$240$		0			0
$241$	−1.07804	+	1.86722i	−0.0694428	+	0.120278i	−0.898656	−	0.438654i	$-0.855455\pi$
$241$	−1.07804	+	1.86722i	−0.0694428	+	0.120278i	0.829213	+	0.558932i	$0.188789\pi$
$242$	9.05524	−	11.9747i	0.582093	−	0.769760i
$243$		0			0
$244$	3.97200	+	2.21926i	0.254281	+	0.142073i
$245$	2.59435	−	0.695154i	0.165747	−	0.0444118i
$246$		0			0
$247$	6.93279	−	4.00265i	0.441123	−	0.254683i
$248$	12.6022	−	1.93071i	0.800239	−	0.122600i
$249$		0			0
$250$	−0.959196	+	2.36262i	−0.0606649	+	0.149425i
$251$	−3.65289	−	3.65289i	−0.230568	−	0.230568i	0.582362	−	0.812930i	$-0.302129\pi$
$251$	−3.65289	−	3.65289i	−0.230568	−	0.230568i	−0.812930	+	0.582362i	$0.802129\pi$
$252$		0			0
$253$	1.95516	−	1.95516i	0.122920	−	0.122920i
$254$	15.0181	−	6.34495i	0.942320	−	0.398118i
$255$		0			0
$256$	−15.9746	+	0.900756i	−0.998414	+	0.0562972i
$257$	5.09689	+	8.82807i	0.317935	+	0.550680i	0.980057	−	0.198716i	$-0.0636772\pi$
$257$	5.09689	+	8.82807i	0.317935	+	0.550680i	−0.662122	+	0.749396i	$0.730344\pi$
$258$		0			0
$259$	4.78511	+	17.8583i	0.297332	+	1.10966i
$260$	0.450184	+	1.59019i	0.0279192	+	0.0986196i
$261$		0			0
$262$	−4.96385	+	0.689093i	−0.306668	+	0.0425723i
$263$	−14.5937	−	8.42569i	−0.899888	−	0.519550i	−0.0227239	−	0.999742i	$-0.507234\pi$
$263$	−14.5937	−	8.42569i	−0.899888	−	0.519550i	−0.877164	+	0.480191i	$0.840567\pi$
$264$		0			0
$265$	0.115079	−	0.0664408i	0.00706924	−	0.00408143i
$266$	9.14045	−	7.11652i	0.560437	−	0.436342i
$267$		0			0
$268$	12.5251	−	7.46846i	0.765091	−	0.456209i
$269$	−18.2219	+	18.2219i	−1.11101	+	1.11101i	−0.117993	+	0.993014i	$0.537646\pi$
$269$	−18.2219	+	18.2219i	−1.11101	+	1.11101i	−0.993014	+	0.117993i	$0.962354\pi$
$270$		0			0
$271$	9.95663			0.604822			0.302411	−	0.953178i	$-0.402208\pi$
$271$	9.95663			0.604822			0.302411	+	0.953178i	$0.402208\pi$
$272$	−0.489632	−	17.3808i	−0.0296883	−	1.05386i
$273$		0			0
$274$	21.0978	+	2.62659i	1.27456	+	0.158678i
$275$	2.97408	+	0.796902i	0.179344	+	0.0480550i
$276$		0			0
$277$	2.63740	−	0.706690i	0.158466	−	0.0424609i	−0.178714	−	0.983901i	$-0.557194\pi$
$277$	2.63740	−	0.706690i	0.158466	−	0.0424609i	0.337180	+	0.941440i	$0.390527\pi$
$278$	1.96520	+	14.1562i	0.117865	+	0.849035i
$279$		0			0
$280$	0.961666	+	2.18967i	0.0574706	+	0.130858i
$281$	21.8517	+	12.6161i	1.30356	+	0.752612i	0.981013	−	0.193941i	$-0.0621271\pi$
$281$	21.8517	+	12.6161i	1.30356	+	0.752612i	0.322549	+	0.946553i	$0.395460\pi$
$282$		0			0
$283$	−2.31429	+	8.63704i	−0.137570	+	0.513419i	0.862404	+	0.506221i	$0.168958\pi$
$283$	−2.31429	+	8.63704i	−0.137570	+	0.513419i	−0.999974	+	0.00719814i	$0.997709\pi$
$284$	10.8287	+	10.5279i	0.642564	+	0.624718i
$285$		0			0
$286$	3.68867	−	1.55842i	0.218116	−	0.0921510i
$287$	−19.8192			−1.16989
$288$		0			0
$289$	1.89565			0.111509
$290$	−2.11014	+	0.891505i	−0.123912	+	0.0523510i
$291$		0			0
$292$	−4.19739	−	4.08081i	−0.245634	−	0.238811i
$293$	5.38845	−	20.1100i	0.314796	−	1.17484i	−0.609383	−	0.792876i	$-0.708583\pi$
$293$	5.38845	−	20.1100i	0.314796	−	1.17484i	0.924179	−	0.381960i	$-0.124751\pi$
$294$		0			0
$295$	−1.78973	−	1.03330i	−0.104202	−	0.0601612i
$296$	−10.2433	+	4.49869i	−0.595382	+	0.261481i
$297$		0			0
$298$	−1.03641	−	7.46576i	−0.0600378	−	0.432480i
$299$	−19.6824	+	5.27390i	−1.13827	+	0.304997i
$300$		0			0
$301$	−0.0613498	−	0.0164386i	−0.00353615	−	0.000947507i
$302$	15.9854	+	1.99012i	0.919856	+	0.114518i
$303$		0			0
$304$	5.09433	+	4.81517i	0.292180	+	0.276169i
$305$	0.411536			0.0235645
$306$		0			0
$307$	11.4523	−	11.4523i	0.653619	−	0.653619i	−0.300243	−	0.953863i	$-0.597068\pi$
$307$	11.4523	−	11.4523i	0.653619	−	0.653619i	0.953863	+	0.300243i	$0.0970679\pi$
$308$	4.97694	−	2.96766i	0.283588	−	0.169098i
$309$		0			0
$310$	0.909891	−	0.708418i	0.0516783	−	0.0402354i
$311$	15.6387	−	9.02903i	0.886792	−	0.511989i	0.0138999	−	0.999903i	$-0.495575\pi$
$311$	15.6387	−	9.02903i	0.886792	−	0.511989i	0.872892	+	0.487914i	$0.162242\pi$
$312$		0			0
$313$	−22.1825	−	12.8070i	−1.25383	−	0.723897i	−0.281959	−	0.959426i	$-0.590984\pi$
$313$	−22.1825	−	12.8070i	−1.25383	−	0.723897i	−0.971867	+	0.235529i	$0.924318\pi$
$314$	7.93467	−	1.10151i	0.447779	−	0.0621617i
$315$		0			0
$316$	−1.58953	−	5.61472i	−0.0894180	−	0.315853i
$317$	0.887719	+	3.31301i	0.0498593	+	0.186077i	0.986364	−	0.164577i	$-0.0526259\pi$
$317$	0.887719	+	3.31301i	0.0498593	+	0.186077i	−0.936505	+	0.350654i	$0.885959\pi$
$318$		0			0
$319$	2.77516	+	4.80671i	0.155379	+	0.269124i
$320$	−1.22162	+	0.775875i	−0.0682905	+	0.0433727i
$321$		0			0
$322$	−27.1618	+	11.4755i	−1.51367	+	0.639504i
$323$	−5.38660	+	5.38660i	−0.299719	+	0.299719i
$324$		0			0
$325$	−16.0447	−	16.0447i	−0.890001	−	0.890001i
$326$	−11.2939	+	27.8182i	−0.625510	+	1.54071i
$327$		0			0
$328$	−1.81620	−	11.8547i	−0.100283	−	0.654568i
$329$	9.50978	−	5.49047i	0.524291	−	0.302700i
$330$		0			0
$331$	15.2234	−	4.07910i	0.836753	−	0.224207i	0.185096	−	0.982721i	$-0.440741\pi$
$331$	15.2234	−	4.07910i	0.836753	−	0.224207i	0.651658	+	0.758513i	$0.274074\pi$
$332$	−13.4508	−	7.51532i	−0.738211	−	0.412457i
$333$		0			0
$334$	7.70156	−	10.1845i	0.421410	−	0.557273i
$335$	0.659494	−	1.14228i	0.0360320	−	0.0624093i
$336$		0			0
$337$	−8.67225	−	15.0208i	−0.472407	−	0.818233i	0.527094	−	0.849807i	$-0.323282\pi$
$337$	−8.67225	−	15.0208i	−0.472407	−	0.818233i	−0.999501	+	0.0315734i	$0.989948\pi$
$338$	−11.0402	−	1.37446i	−0.600508	−	0.0747609i
$339$		0			0
$340$	−0.805446	−	1.35078i	−0.0436815	−	0.0732565i
$341$	−1.97567	−	1.97567i	−0.106988	−	0.106988i
$342$		0			0
$343$			36.6800i			1.98053i
$344$	0.00421069	−	0.0382025i	0.000227025	−	0.00205974i
$345$		0			0
$346$	−4.50190	−	5.78224i	−0.242024	−	0.310855i
$347$	1.85473	−	6.92193i	0.0995669	−	0.371589i	−0.898105	−	0.439780i	$-0.855056\pi$
$347$	1.85473	−	6.92193i	0.0995669	−	0.371589i	0.997672	+	0.0681917i	$0.0217230\pi$
$348$		0			0
$349$	0.294768	+	1.10009i	0.0157786	+	0.0588865i	0.973366	−	0.229256i	$-0.0736291\pi$
$349$	0.294768	+	1.10009i	0.0157786	+	0.0588865i	−0.957588	+	0.288142i	$0.906962\pi$
$350$	−26.1897	−	19.8046i	−1.39990	−	1.05860i
$351$		0			0
$352$	2.23117	+	2.70498i	0.118922	+	0.144176i
$353$	12.2507	−	21.2188i	0.652037	−	1.12936i	−0.330591	−	0.943774i	$-0.607248\pi$
$353$	12.2507	−	21.2188i	0.652037	−	1.12936i	0.982628	−	0.185587i	$-0.0594187\pi$
$354$		0			0
$355$	1.31949	+	0.353557i	0.0700314	+	0.0187649i
$356$	−4.57185	−	4.44487i	−0.242308	−	0.235578i
$357$		0			0
$358$	1.47528	−	3.63379i	0.0779709	−	0.192052i
$359$			11.6859i			0.616757i	0.951264	+	0.308378i	$0.0997863\pi$
$359$			11.6859i			0.616757i	−0.951264	+	0.308378i	$0.900214\pi$
$360$		0			0
$361$			15.9289i			0.838362i
$362$	0.415570	+	0.168717i	0.0218419	+	0.00886755i
$363$		0			0
$364$	−42.6988	+	0.601314i	−2.23803	+	0.0315174i
$365$	−0.511458	−	0.137045i	−0.0267709	−	0.00717325i
$366$		0			0
$367$	−5.61911	+	9.73258i	−0.293315	+	0.508037i	−0.974592	−	0.223990i	$-0.928092\pi$
$367$	−5.61911	+	9.73258i	−0.293315	+	0.508037i	0.681276	+	0.732026i	$0.261425\pi$
$368$	−9.35307	−	15.1951i	−0.487563	−	0.792099i
$369$		0			0
$370$	−0.610345	+	0.807121i	−0.0317303	+	0.0419602i
$371$	0.888646	+	3.31647i	0.0461362	+	0.172183i
$372$		0			0
$373$	3.09978	−	11.5685i	0.160501	−	0.598996i	−0.838071	−	0.545561i	$-0.816316\pi$
$373$	3.09978	−	11.5685i	0.160501	−	0.598996i	0.998571	−	0.0534347i	$-0.0170169\pi$
$374$	−3.00670	+	2.34094i	−0.155473	+	0.121047i
$375$		0			0
$376$	4.15556	+	5.18509i	0.214307	+	0.267401i
$377$		−	40.9031i		−	2.10661i
$378$		0			0
$379$	11.6135	+	11.6135i	0.596544	+	0.596544i	0.939391	−	0.342847i	$-0.111391\pi$
$379$	11.6135	+	11.6135i	0.596544	+	0.596544i	−0.342847	+	0.939391i	$0.611391\pi$
$380$	0.614679	+	0.155460i	0.0315323	+	0.00797491i
$381$		0			0
$382$	−3.63033	+	29.1602i	−0.185744	+	1.49196i
$383$	14.5294	+	25.1657i	0.742418	+	1.28591i	0.951391	+	0.307985i	$0.0996546\pi$
$383$	14.5294	+	25.1657i	0.742418	+	1.28591i	−0.208973	+	0.977921i	$0.567012\pi$
$384$		0			0
$385$	0.262056	−	0.453894i	0.0133556	−	0.0231326i
$386$	−17.3616	−	13.1289i	−0.883683	−	0.668241i
$387$		0			0
$388$	−8.75878	−	30.9388i	−0.444660	−	1.57068i
$389$	13.6478	−	3.65693i	0.691973	−	0.185414i	0.104341	−	0.994542i	$-0.466727\pi$
$389$	13.6478	−	3.65693i	0.691973	−	0.185414i	0.587632	+	0.809128i	$0.300060\pi$
$390$		0			0
$391$	16.7926	−	9.69522i	0.849239	−	0.490308i
$392$	−41.5106	+	6.35961i	−2.09660	+	0.321209i
$393$		0			0
$394$	−1.67735	−	0.680985i	−0.0845037	−	0.0343075i
$395$	−0.373213	−	0.373213i	−0.0187784	−	0.0187784i
$396$		0			0
$397$	−1.83996	+	1.83996i	−0.0923450	+	0.0923450i	−0.751770	−	0.659425i	$-0.770800\pi$
$397$	−1.83996	+	1.83996i	−0.0923450	+	0.0923450i	0.659425	+	0.751770i	$0.270800\pi$
$398$	−9.09235	−	21.5210i	−0.455758	−	1.07875i
$399$		0			0
$400$	9.44606	−	17.4801i	0.472303	−	0.874004i
$401$	−14.5786	−	25.2509i	−0.728021	−	1.26097i	−0.957718	−	0.287708i	$-0.907107\pi$
$401$	−14.5786	−	25.2509i	−0.728021	−	1.26097i	0.229697	−	0.973262i	$-0.426226\pi$
$402$		0			0
$403$	5.32922	+	19.8889i	0.265467	+	0.990737i
$404$	−17.1998	+	30.7841i	−0.855723	+	1.53156i
$405$		0			0
$406$	−8.13873	−	58.6270i	−0.403918	−	2.90961i
$407$	2.12332	+	1.22590i	0.105249	+	0.0607656i
$408$		0			0
$409$	9.18277	−	5.30167i	0.454059	−	0.262151i	−0.255484	−	0.966813i	$-0.582235\pi$
$409$	9.18277	−	5.30167i	0.454059	−	0.262151i	0.709543	+	0.704662i	$0.248901\pi$
$410$	−0.666401	−	0.855924i	−0.0329112	−	0.0422711i
$411$		0			0
$412$	−4.56347	+	18.0437i	−0.224826	+	0.888949i
$413$	37.7581	−	37.7581i	1.85796	−	1.85796i
$414$		0			0
$415$	−1.39363			−0.0684107
$416$	−4.27253	−	25.4850i	−0.209478	−	1.24950i
$417$		0			0
$418$	0.189789	−	1.52445i	0.00928287	−	0.0745635i
$419$	13.8275	+	3.70507i	0.675519	+	0.181005i	0.580240	−	0.814446i	$-0.302959\pi$
$419$	13.8275	+	3.70507i	0.675519	+	0.181005i	0.0952792	+	0.995451i	$0.469626\pi$
$420$		0			0
$421$	−19.2855	+	5.16753i	−0.939918	+	0.251850i	−0.696079	−	0.717966i	$-0.745074\pi$
$421$	−19.2855	+	5.16753i	−0.939918	+	0.251850i	−0.243839	+	0.969816i	$0.578407\pi$
$422$	36.5488	−	5.07379i	1.77917	−	0.246988i
$423$		0			0
$424$	−1.90230	+	0.835456i	−0.0923838	+	0.0405733i
$425$	18.6995	+	10.7962i	0.907059	+	0.523691i
$426$		0			0
$427$	−2.75215	+	10.2712i	−0.133186	+	0.497056i
$428$	−26.9219	+	0.379133i	−1.30132	+	0.0183261i
$429$		0			0
$430$	−0.00135290	−	0.00320223i	−6.52427e−5	−	0.000154425i
$431$	8.92159			0.429738			0.214869	−	0.976643i	$-0.431068\pi$
$431$	8.92159			0.429738			0.214869	+	0.976643i	$0.431068\pi$
$432$		0			0
$433$	−29.8178			−1.43295			−0.716476	−	0.697612i	$-0.754246\pi$
$433$	−29.8178			−1.43295			−0.716476	+	0.697612i	$0.754246\pi$
$434$	11.5959	+	27.4467i	0.556619	+	1.31748i
$435$		0			0
$436$	0.253009	+	17.9659i	0.0121169	+	0.860412i
$437$	−2.02326	+	7.55091i	−0.0967857	+	0.361209i
$438$		0			0
$439$	−27.0574	−	15.6216i	−1.29138	−	0.745579i	−0.312481	−	0.949924i	$-0.601160\pi$
$439$	−27.0574	−	15.6216i	−1.29138	−	0.745579i	−0.978899	+	0.204345i	$0.934493\pi$
$440$	0.295509	+	0.115153i	0.0140878	+	0.00548971i
$441$		0			0
$442$	27.8150	−	3.86134i	1.32303	−	0.183665i
$443$	10.6006	−	2.84043i	0.503651	−	0.134953i	0.00195701	−	0.999998i	$-0.499377\pi$
$443$	10.6006	−	2.84043i	0.503651	−	0.134953i	0.501694	+	0.865045i	$0.332710\pi$
$444$		0			0
$445$	−0.557087	−	0.149271i	−0.0264085	−	0.00707613i
$446$	−2.26406	+	18.1858i	−0.107206	+	0.861121i
$447$		0			0
$448$	−11.1948	−	35.6779i	−0.528904	−	1.68562i
$449$	−27.4967			−1.29765			−0.648824	−	0.760938i	$-0.724739\pi$
$449$	−27.4967			−1.29765			−0.648824	+	0.760938i	$0.724739\pi$
$450$		0			0
$451$	−1.85849	+	1.85849i	−0.0875128	+	0.0875128i
$452$	−20.7312	−	5.24317i	−0.975113	−	0.246618i
$453$		0			0
$454$	11.8188	+	15.1801i	0.554685	+	0.712437i
$455$	−3.34497	+	1.93122i	−0.156815	+	0.0905370i
$456$		0			0
$457$	16.8184	+	9.71008i	0.786729	+	0.454218i	0.838810	−	0.544424i	$-0.183252\pi$
$457$	16.8184	+	9.71008i	0.786729	+	0.454218i	−0.0520805	+	0.998643i	$0.516585\pi$
$458$	3.26883	+	23.5469i	0.152742	+	1.10027i
$459$		0			0
$460$	−1.40888	−	0.787176i	−0.0656893	−	0.0367023i
$461$	1.08101	+	4.03437i	0.0503475	+	0.187900i	0.986520	−	0.163642i	$-0.0523242\pi$
$461$	1.08101	+	4.03437i	0.0503475	+	0.187900i	−0.936172	+	0.351542i	$0.885658\pi$
$462$		0			0
$463$	−0.773244	−	1.33930i	−0.0359357	−	0.0622425i	0.847498	−	0.530798i	$-0.178108\pi$
$463$	−0.773244	−	1.33930i	−0.0359357	−	0.0622425i	−0.883434	+	0.468556i	$0.844774\pi$
$464$	34.3216	−	10.2406i	1.59334	−	0.475409i
$465$		0			0
$466$	−5.53095	−	13.0914i	−0.256216	−	0.606448i
$467$	2.13196	−	2.13196i	0.0986553	−	0.0986553i	−0.656056	−	0.754712i	$-0.727777\pi$
$467$	2.13196	−	2.13196i	0.0986553	−	0.0986553i	0.754712	+	0.656056i	$0.227777\pi$
$468$		0			0
$469$	24.0987	+	24.0987i	1.11277	+	1.11277i
$470$	0.556873	+	0.226084i	0.0256866	+	0.0104285i
$471$		0			0
$472$	26.0449	+	19.1247i	1.19882	+	0.880288i
$473$	−0.00729441	+	0.00421143i	−0.000335397	+	0.000193642i
$474$		0			0
$475$	−8.40836	+	2.25301i	−0.385802	+	0.103375i
$476$	39.0994	−	11.0690i	1.79212	−	0.507349i
$477$		0			0
$478$	−7.63355	−	5.77250i	−0.349151	−	0.264028i
$479$	−14.5113	+	25.1343i	−0.663037	+	1.14841i	0.316777	+	0.948500i	$0.397399\pi$
$479$	−14.5113	+	25.1343i	−0.663037	+	1.14841i	−0.979814	+	0.199914i	$0.935934\pi$
$480$		0			0
$481$	−9.03428	−	15.6478i	−0.411928	−	0.713480i
$482$	0.376701	−	3.02580i	0.0171583	−	0.137822i
$483$		0			0
$484$	−5.20581	+	20.5835i	−0.236628	+	0.935612i
$485$	−2.05652	−	2.05652i	−0.0933817	−	0.0933817i
$486$		0			0
$487$			3.59517i			0.162913i	0.996677	+	0.0814564i	$0.0259571\pi$
$487$			3.59517i			0.162913i	−0.996677	+	0.0814564i	$0.974043\pi$
$488$	−6.39585	−	0.704951i	−0.289526	−	0.0319116i
$489$		0			0
$490$	−2.99711	+	2.33347i	−0.135396	+	0.105416i
$491$	5.35801	−	19.9964i	0.241804	−	0.902424i	−0.733159	−	0.680057i	$-0.761955\pi$
$491$	5.35801	−	19.9964i	0.241804	−	0.902424i	0.974963	−	0.222367i	$-0.0713782\pi$
$492$		0			0
$493$	10.0741	+	37.5969i	0.453713	+	1.69328i
$494$	−6.82850	+	9.03002i	−0.307229	+	0.406280i
$495$		0			0
$496$	−15.3545	+	9.45119i	−0.689437	+	0.424371i
$497$	−17.6482	+	30.5676i	−0.791631	+	1.37115i
$498$		0			0
$499$	−14.7412	−	3.94988i	−0.659905	−	0.176821i	−0.0867019	−	0.996234i	$-0.527633\pi$
$499$	−14.7412	−	3.94988i	−0.659905	−	0.176821i	−0.573203	+	0.819413i	$0.694299\pi$
$500$	−0.0507787	−	3.60575i	−0.00227089	−	0.161254i
$501$		0			0
$502$	6.76918	+	2.74821i	0.302123	+	0.122659i
$503$		−	11.1260i		−	0.496085i	−0.968749	−	0.248042i	$-0.920213\pi$
$503$		−	11.1260i		−	0.496085i	0.968749	−	0.248042i	$-0.0797872\pi$
$504$		0			0
$505$			3.18951i			0.141931i
$506$	−1.47094	+	3.62311i	−0.0653913	+	0.161067i
$507$		0			0
$508$	−16.0722	+	16.5314i	−0.713091	+	0.733462i
$509$	24.1806	+	6.47918i	1.07179	+	0.287185i	0.751227	−	0.660044i	$-0.229462\pi$
$509$	24.1806	+	6.47918i	1.07179	+	0.287185i	0.320560	+	0.947228i	$0.396129\pi$
$510$		0			0
$511$	6.84076	−	11.8485i	0.302617	−	0.524149i
$512$	20.3147	−	9.96558i	0.897792	−	0.440420i
$513$		0			0
$514$	−11.4986	−	8.69527i	−0.507183	−	0.383532i
$515$	0.435701	+	1.62606i	0.0191993	+	0.0716526i
$516$		0			0
$517$	0.376900	−	1.40661i	0.0165760	−	0.0618626i
$518$	−16.0625	−	20.6307i	−0.705746	−	0.906460i
$519$		0			0
$520$	−1.46168	−	1.82380i	−0.0640988	−	0.0799791i
$521$			44.7974i			1.96261i	0.192458	+	0.981305i	$0.438354\pi$
$521$			44.7974i			1.96261i	−0.192458	+	0.981305i	$0.561646\pi$
$522$		0			0
$523$	7.02267	+	7.02267i	0.307080	+	0.307080i	0.843776	−	0.536696i	$-0.180328\pi$
$523$	7.02267	+	7.02267i	0.307080	+	0.307080i	−0.536696	+	0.843776i	$0.680328\pi$
$524$	6.08725	−	3.62971i	0.265923	−	0.158565i
$525$		0			0
$526$	23.6489	+	2.94419i	1.03114	+	0.128373i
$527$	−9.79692	−	16.9688i	−0.426761	−	0.739171i
$528$		0			0
$529$	−1.55091	+	2.68626i	−0.0674309	+	0.116794i
$530$	−0.113348	+	0.149891i	−0.00492351	+	0.00651085i
$531$		0			0
$532$	−7.99065	+	14.3016i	−0.346438	+	0.620052i
$533$	18.7093	−	5.01314i	0.810389	−	0.217143i
$534$		0			0
$535$	−2.10903	+	1.21765i	−0.0911812	+	0.0526435i
$536$	−12.2062	+	16.6229i	−0.527226	+	0.718000i
$537$		0			0
$538$	13.7090	−	33.7670i	0.591038	−	1.45580i
$539$	6.50770	+	6.50770i	0.280306	+	0.280306i
$540$		0			0
$541$	14.9663	−	14.9663i	0.643452	−	0.643452i	−0.307950	−	0.951402i	$-0.599643\pi$
$541$	14.9663	−	14.9663i	0.643452	−	0.643452i	0.951402	+	0.307950i	$0.0996431\pi$
$542$	−12.9707	+	5.47995i	−0.557140	+	0.235384i
$543$		0			0
$544$	10.2039	+	22.3728i	0.437489	+	0.959225i
$545$	0.812579	+	1.40743i	0.0348071	+	0.0602876i
$546$		0			0
$547$	1.38173	+	5.15670i	0.0590787	+	0.220485i	0.989154	−	0.146885i	$-0.0469249\pi$
$547$	1.38173	+	5.15670i	0.0590787	+	0.220485i	−0.930075	+	0.367370i	$0.880258\pi$
$548$	−28.9301	+	8.19013i	−1.23583	+	0.349865i
$549$		0			0
$550$	−4.31299	+	0.598739i	−0.183907	+	0.0255303i
$551$	−13.5896	−	7.84596i	−0.578937	−	0.334249i
$552$		0			0
$553$	11.8106	−	6.81883i	0.502236	−	0.289966i
$554$	−3.04685	+	2.37220i	−0.129448	+	0.100785i
$555$		0			0
$556$	−10.3514	−	17.3600i	−0.438999	−	0.736228i
$557$	−7.66230	+	7.66230i	−0.324662	+	0.324662i	−0.850552	−	0.525890i	$-0.823732\pi$
$557$	−7.66230	+	7.66230i	−0.324662	+	0.324662i	0.525890	+	0.850552i	$0.323732\pi$
$558$		0			0
$559$	0.0620723			0.00262538
$560$	−2.45794	−	2.32325i	−0.103867	−	0.0981752i
$561$		0			0
$562$	−35.4103	−	4.40844i	−1.49369	−	0.185959i
$563$	21.3157	+	5.71152i	0.898349	+	0.240712i	0.678307	−	0.734779i	$-0.262714\pi$
$563$	21.3157	+	5.71152i	0.898349	+	0.240712i	0.220042	+	0.975490i	$0.429381\pi$
$564$		0			0
$565$	−1.86825	+	0.500595i	−0.0785977	+	0.0210602i
$566$	−1.73880	−	12.5254i	−0.0730873	−	0.526482i
$567$		0			0
$568$	−19.9011	−	7.75503i	−0.835033	−	0.325394i
$569$	−38.6354	−	22.3061i	−1.61968	−	0.935122i	−0.987002	−	0.160706i	$-0.948623\pi$
$569$	−38.6354	−	22.3061i	−1.61968	−	0.935122i	−0.632676	−	0.774416i	$-0.718044\pi$
$570$		0			0
$571$	−2.53873	+	9.47469i	−0.106243	+	0.396503i	−0.998483	−	0.0550573i	$-0.982466\pi$
$571$	−2.53873	+	9.47469i	−0.106243	+	0.396503i	0.892240	+	0.451561i	$0.149133\pi$
$572$	−3.94758	+	4.06036i	−0.165057	+	0.169772i
$573$		0			0
$574$	25.8188	−	10.9081i	1.07766	−	0.455295i
$575$	22.1577			0.924041
$576$		0			0
$577$	−0.565932			−0.0235600			−0.0117800	−	0.999931i	$-0.503750\pi$
$577$	−0.565932			−0.0235600			−0.0117800	+	0.999931i	$0.503750\pi$
$578$	−2.46951	+	1.04333i	−0.102718	+	0.0433969i
$579$		0			0
$580$	2.25825	−	2.32276i	0.0937688	−	0.0964475i
$581$	9.31992	−	34.7824i	0.386655	−	1.44302i
$582$		0			0
$583$	0.394324	+	0.227663i	0.0163312	+	0.00942884i
$584$	7.71402	+	3.00598i	0.319209	+	0.124389i
$585$		0			0
$586$	4.04852	+	29.1633i	0.167243	+	1.20473i
$587$	39.9093	−	10.6937i	1.64723	−	0.441375i	0.688397	−	0.725334i	$-0.258315\pi$
$587$	39.9093	−	10.6937i	1.64723	−	0.441375i	0.958836	+	0.283960i	$0.0916482\pi$
$588$		0			0
$589$	7.63012	+	2.04448i	0.314394	+	0.0842415i
$590$	2.90023	+	0.361068i	0.119401	+	0.0148649i
$591$		0			0
$592$	10.8682	−	11.4983i	0.446680	−	0.472576i
$593$	12.9281			0.530893			0.265447	−	0.964126i	$-0.414481\pi$
$593$	12.9281			0.530893			0.265447	+	0.964126i	$0.414481\pi$
$594$		0			0
$595$	2.59896	−	2.59896i	0.106547	−	0.106547i
$596$	5.45917	+	9.15537i	0.223616	+	0.375018i
$597$		0			0
$598$	22.7381	−	17.7033i	0.929829	−	0.723941i
$599$	−39.9617	+	23.0719i	−1.63279	+	0.942692i	−0.649563	+	0.760308i	$0.725048\pi$
$599$	−39.9617	+	23.0719i	−1.63279	+	0.942692i	−0.983227	+	0.182384i	$0.941619\pi$
$600$		0			0
$601$	28.4107	+	16.4029i	1.15890	+	0.669090i	0.951040	−	0.309069i	$-0.100017\pi$
$601$	28.4107	+	16.4029i	1.15890	+	0.669090i	0.207858	+	0.978159i	$0.433351\pi$
$602$	0.0889692	−	0.0123509i	0.00362611	−	0.000503385i
$603$		0			0
$604$	−21.9198	+	6.20550i	−0.891905	+	0.252498i
$605$	0.497028	+	1.85493i	0.0202071	+	0.0754138i
$606$		0			0
$607$	−6.36706	−	11.0281i	−0.258431	−	0.447616i	0.707391	−	0.706823i	$-0.249872\pi$
$607$	−6.36706	−	11.0281i	−0.258431	−	0.447616i	−0.965822	+	0.259207i	$0.916539\pi$
$608$	−9.28667	−	3.46899i	−0.376624	−	0.140686i
$609$		0			0
$610$	−0.536116	+	0.226502i	−0.0217067	+	0.00917080i
$611$	−7.58845	+	7.58845i	−0.306996	+	0.306996i
$612$		0			0
$613$	29.9303	+	29.9303i	1.20888	+	1.20888i	0.971392	+	0.237483i	$0.0763225\pi$
$613$	29.9303	+	29.9303i	1.20888	+	1.20888i	0.237483	+	0.971392i	$0.423677\pi$
$614$	−8.61603	+	21.2223i	−0.347715	+	0.856464i
$615$		0			0
$616$	−4.85022	+	6.60525i	−0.195421	+	0.266133i
$617$	−2.50740	+	1.44765i	−0.100944	+	0.0582802i	−0.549622	−	0.835413i	$-0.685228\pi$
$617$	−2.50740	+	1.44765i	−0.100944	+	0.0582802i	0.448678	+	0.893693i	$0.351895\pi$
$618$		0			0
$619$	−5.55188	+	1.48762i	−0.223149	+	0.0597926i	−0.368661	−	0.929564i	$-0.620184\pi$
$619$	−5.55188	+	1.48762i	−0.223149	+	0.0597926i	0.145512	+	0.989356i	$0.453517\pi$
$620$	−0.795433	+	1.42366i	−0.0319454	+	0.0571755i
$621$		0			0
$622$	−15.4035	+	20.3696i	−0.617624	+	0.816746i
$623$	7.45105	−	12.9056i	0.298520	−	0.517052i
$624$		0			0
$625$	12.2551	+	21.2265i	0.490204	+	0.849059i
$626$	35.9463	+	4.47517i	1.43670	+	0.178864i
$627$		0			0
$628$	−9.73041	+	5.80206i	−0.388286	+	0.231527i
$629$	12.1580	+	12.1580i	0.484770	+	0.484770i
$630$		0			0
$631$		−	33.4420i		−	1.33130i	−0.746262	−	0.665652i	$-0.768154\pi$
$631$		−	33.4420i		−	1.33130i	0.746262	−	0.665652i	$-0.231846\pi$
$632$	5.16095	+	6.43956i	0.205292	+	0.256152i
$633$		0			0
$634$	−2.97987	−	3.82734i	−0.118346	−	0.152003i
$635$	−0.539750	+	2.01438i	−0.0214193	+	0.0799381i
$636$		0			0
$637$	−17.5540	−	65.5126i	−0.695516	−	2.59570i
$638$	−6.26078	−	4.73440i	−0.247867	−	0.187437i
$639$		0			0
$640$	1.16440	−	1.68310i	0.0460269	−	0.0665305i
$641$	−9.42170	+	16.3189i	−0.372135	+	0.644557i	−0.989894	−	0.141811i	$-0.954707\pi$
$641$	−9.42170	+	16.3189i	−0.372135	+	0.644557i	0.617759	+	0.786368i	$0.288041\pi$
$642$		0			0
$643$	−11.8825	−	3.18391i	−0.468601	−	0.125561i	0.0167890	−	0.999859i	$-0.494656\pi$
$643$	−11.8825	−	3.18391i	−0.468601	−	0.125561i	−0.485390	+	0.874298i	$0.661322\pi$
$644$	29.0683	−	29.8987i	1.14545	−	1.17817i
$645$		0			0
$646$	4.05255	−	9.98193i	0.159445	−	0.392734i
$647$		−	8.72393i		−	0.342973i	−0.985186	−	0.171487i	$-0.945143\pi$
$647$		−	8.72393i		−	0.342973i	0.985186	−	0.171487i	$-0.0548570\pi$
$648$		0			0
$649$		−	7.08134i		−	0.277967i
$650$	29.7325	+	12.0710i	1.16620	+	0.473466i
$651$		0			0
$652$	−0.597884	−	42.4553i	−0.0234149	−	1.66268i
$653$	−18.9252	−	5.07099i	−0.740600	−	0.198443i	−0.131255	−	0.991349i	$-0.541901\pi$
$653$	−18.9252	−	5.07099i	−0.740600	−	0.198443i	−0.609345	+	0.792906i	$0.708567\pi$
$654$		0			0
$655$	0.320517	−	0.555152i	0.0125237	−	0.0216916i
$656$	8.89063	+	14.4438i	0.347121	+	0.563935i
$657$		0			0
$658$	−9.36672	+	12.3866i	−0.365153	+	0.482878i
$659$	10.0113	+	37.3628i	0.389986	+	1.45545i	0.830155	+	0.557533i	$0.188252\pi$
$659$	10.0113	+	37.3628i	0.389986	+	1.45545i	−0.440168	+	0.897915i	$0.645081\pi$
$660$		0			0
$661$	7.13570	−	26.6308i	0.277546	−	1.03582i	−0.676569	−	0.736379i	$-0.736534\pi$
$661$	7.13570	−	26.6308i	0.277546	−	1.03582i	0.954116	−	0.299438i	$-0.0967992\pi$
$662$	−17.5868	+	13.6926i	−0.683529	+	0.532178i
$663$		0			0
$664$	21.6590	+	2.38726i	0.840532	+	0.0926436i
$665$			1.48177i			0.0574608i
$666$		0			0
$667$	28.2435	+	28.2435i	1.09359	+	1.09359i
$668$	−4.42758	+	17.5064i	−0.171308	+	0.677343i
$669$		0			0
$670$	−0.230447	+	1.85104i	−0.00890296	+	0.0715120i
$671$	0.705075	+	1.22123i	0.0272191	+	0.0471449i
$672$		0			0
$673$	10.0608	−	17.4258i	0.387815	−	0.671716i	−0.604340	−	0.796726i	$-0.706563\pi$
$673$	10.0608	−	17.4258i	0.387815	−	0.671716i	0.992155	+	0.125011i	$0.0398965\pi$
$674$	19.5647	+	14.7948i	0.753603	+	0.569875i
$675$		0			0
$676$	15.1388	−	4.28579i	0.582261	−	0.164838i
$677$	−19.5932	+	5.24998i	−0.753027	+	0.201773i	−0.614860	−	0.788636i	$-0.710788\pi$
$677$	−19.5932	+	5.24998i	−0.753027	+	0.201773i	−0.138167	+	0.990409i	$0.544121\pi$
$678$		0			0
$679$	65.0798	−	37.5738i	2.49753	−	1.44195i
$680$	1.79272	+	1.31639i	0.0687476	+	0.0504812i
$681$		0			0
$682$	3.66111	+	1.48637i	0.140191	+	0.0569161i
$683$	18.4322	+	18.4322i	0.705287	+	0.705287i	0.965540	−	0.260253i	$-0.0838061\pi$
$683$	18.4322	+	18.4322i	0.705287	+	0.705287i	−0.260253	+	0.965540i	$0.583806\pi$
$684$		0			0
$685$	−1.92300	+	1.92300i	−0.0734741	+	0.0734741i
$686$	−20.1880	−	47.7838i	−0.770782	−	1.82439i
$687$		0			0
$688$	0.0155406	+	0.0520847i	0.000592481	+	0.00198571i
$689$	−1.67776	−	2.90597i	−0.0639177	−	0.110709i
$690$		0			0
$691$	−4.19392	−	15.6519i	−0.159544	−	0.595427i	−0.998673	−	0.0514946i	$-0.983601\pi$
$691$	−4.19392	−	15.6519i	−0.159544	−	0.595427i	0.839129	−	0.543932i	$-0.183065\pi$
$692$	9.04716	+	5.05487i	0.343921	+	0.192157i
$693$		0			0
$694$	1.39352	+	10.0381i	0.0528972	+	0.381043i
$695$	−1.58322	−	0.914072i	−0.0600549	−	0.0346727i
$696$		0			0
$697$	−15.9623	+	9.21585i	−0.604616	+	0.349075i
$698$	−0.989471	−	1.27087i	−0.0374520	−	0.0481033i
$699$		0			0
$700$	45.0179	+	11.3856i	1.70152	+	0.430334i
$701$	−2.97647	+	2.97647i	−0.112420	+	0.112420i	−0.761079	−	0.648659i	$-0.775330\pi$
$701$	−2.97647	+	2.97647i	−0.112420	+	0.112420i	0.648659	+	0.761079i	$0.275330\pi$
$702$		0			0
$703$	−6.93177			−0.261437
$704$	−4.39536	−	2.29584i	−0.165657	−	0.0865278i
$705$		0			0
$706$	−4.28076	+	34.3847i	−0.161108	+	1.29408i
$707$	−79.6042	−	21.3299i	−2.99382	−	0.802192i
$708$		0			0
$709$	−37.3329	+	10.0033i	−1.40207	+	0.375682i	−0.879086	−	0.476663i	$-0.841846\pi$
$709$	−37.3329	+	10.0033i	−1.40207	+	0.375682i	−0.522980	+	0.852345i	$0.675180\pi$
$710$	−1.91352	+	0.265639i	−0.0718132	+	0.00996926i
$711$		0			0
$712$	8.40222	+	3.27416i	0.314887	+	0.122704i
$713$	−17.4131	−	10.0535i	−0.652125	−	0.376505i
$714$		0			0
$715$	−0.132571	+	0.494761i	−0.00495787	+	0.0185030i
$716$	0.0780995	+	5.54578i	0.00291872	+	0.207256i
$717$		0			0
$718$	−6.43169	−	15.2234i	−0.240029	−	0.568133i
$719$	−38.3674			−1.43086			−0.715431	−	0.698683i	$-0.753770\pi$
$719$	−38.3674			−1.43086			−0.715431	+	0.698683i	$0.753770\pi$
$720$		0			0
$721$	−43.4970			−1.61991
$722$	−8.76696	−	20.7509i	−0.326273	−	0.772267i
$723$		0			0
$724$	−0.634230	+	0.00893166i	−0.0235710	+	0.000331943i
$725$	−11.5118	+	42.9625i	−0.427536	+	1.59559i
$726$		0			0
$727$	14.8899	+	8.59667i	0.552235	+	0.318833i	0.750023	−	0.661412i	$-0.230042\pi$
$727$	14.8899	+	8.59667i	0.552235	+	0.318833i	−0.197788	+	0.980245i	$0.563376\pi$
$728$	55.2937	−	24.2840i	2.04932	−	0.900025i
$729$		0			0
$730$	0.741714	−	0.102966i	0.0274521	−	0.00381096i
$731$	−0.0570550	+	0.0152878i	−0.00211026	+	0.000565441i
$732$		0			0
$733$	−12.7311	−	3.41130i	−0.470235	−	0.125999i	0.0159168	−	0.999873i	$-0.494933\pi$
$733$	−12.7311	−	3.41130i	−0.470235	−	0.125999i	−0.486152	+	0.873874i	$0.661600\pi$
$734$	1.96349	−	15.7715i	0.0724737	−	0.582136i
$735$		0			0
$736$	20.5475	+	14.6472i	0.757393	+	0.539903i
$737$	4.51959			0.166481
$738$		0			0
$739$	−15.2048	+	15.2048i	−0.559316	+	0.559316i	−0.929113	−	0.369797i	$-0.879427\pi$
$739$	−15.2048	+	15.2048i	−0.559316	+	0.559316i	0.369797	+	0.929113i	$0.379427\pi$
$740$	0.350884	−	1.38737i	0.0128988	−	0.0510009i
$741$		0			0
$742$	−2.98298	−	3.83134i	−0.109509	−	0.140653i
$743$	36.6127	−	21.1384i	1.34319	−	0.775491i	0.355916	−	0.934518i	$-0.384169\pi$
$743$	36.6127	−	21.1384i	1.34319	−	0.775491i	0.987274	+	0.159027i	$0.0508356\pi$
$744$		0			0
$745$	0.834963	+	0.482066i	0.0305907	+	0.0176615i
$746$	2.32897	+	16.7766i	0.0852696	+	0.614236i
$747$		0			0
$748$	2.62847	−	4.70442i	0.0961065	−	0.172010i
$749$	−16.2860	−	60.7803i	−0.595079	−	2.22086i
$750$		0			0
$751$	−9.72823	−	16.8498i	−0.354988	−	0.614857i	0.632128	−	0.774864i	$-0.282182\pi$
$751$	−9.72823	−	16.8498i	−0.354988	−	0.614857i	−0.987116	+	0.160007i	$0.948848\pi$
$752$	−8.26731	−	4.46758i	−0.301478	−	0.162916i
$753$		0			0
$754$	22.5123	+	53.2852i	0.819850	+	1.94053i
$755$	−1.45702	+	1.45702i	−0.0530264	+	0.0530264i
$756$		0			0
$757$	26.9716	+	26.9716i	0.980300	+	0.980300i	0.999810	−	0.0195093i	$-0.00621039\pi$
$757$	26.9716	+	26.9716i	0.980300	+	0.980300i	−0.0195093	+	0.999810i	$0.506210\pi$
$758$	−21.5210	−	8.73726i	−0.781677	−	0.317352i
$759$		0			0
$760$	−0.886316	+	0.135788i	−0.0321501	+	0.00492553i
$761$	−15.0417	+	8.68435i	−0.545263	+	0.314808i	−0.747209	−	0.664589i	$-0.768607\pi$
$761$	−15.0417	+	8.68435i	−0.545263	+	0.314808i	0.201946	+	0.979397i	$0.435273\pi$
$762$		0			0
$763$	−40.5609	+	10.8683i	−1.46840	+	0.393457i
$764$	−11.3199	−	39.9856i	−0.409541	−	1.44663i
$765$		0			0
$766$	−32.7785	−	24.7871i	−1.18434	−	0.895595i
$767$	−26.0930	+	45.1944i	−0.942163	+	1.63187i
$768$		0			0
$769$	15.0664	+	26.0957i	0.543307	+	0.941036i	0.998711	+	0.0507510i	$0.0161615\pi$
$769$	15.0664	+	26.0957i	0.543307	+	0.941036i	−0.455404	+	0.890285i	$0.650505\pi$
$770$	−0.0915702	+	0.735527i	−0.00329996	+	0.0265066i
$771$		0			0
$772$	29.8432	+	7.54771i	1.07408	+	0.271648i
$773$	9.37945	+	9.37945i	0.337355	+	0.337355i	0.855371	−	0.518016i	$-0.173329\pi$
$773$	9.37945	+	9.37945i	0.337355	+	0.337355i	−0.518016	+	0.855371i	$0.673329\pi$
$774$		0			0
$775$		−	22.3901i		−	0.804278i
$776$	28.4384	+	35.4839i	1.02088	+	1.27380i
$777$		0			0
$778$	−15.7666	+	12.2755i	−0.565260	+	0.440097i
$779$	1.92322	−	7.17757i	0.0689067	−	0.257163i
$780$		0			0
$781$	1.21148	+	4.52131i	0.0433502	+	0.161785i
$782$	−16.5400	+	21.8725i	−0.591469	+	0.782159i
$783$		0			0
$784$	50.5765	−	31.1315i	1.80630	−	1.11184i
$785$	−0.512344	+	0.887406i	−0.0182863	+	0.0316729i
$786$		0			0
$787$	12.6850	+	3.39895i	0.452173	+	0.121159i	0.477716	−	0.878514i	$-0.341465\pi$
$787$	12.6850	+	3.39895i	0.452173	+	0.121159i	−0.0255430	+	0.999674i	$0.508131\pi$
$788$	2.55992	−	0.0360505i	0.0911934	−	0.00128425i
$789$		0			0
$790$	0.691602	+	0.280783i	0.0246061	+	0.00998979i
$791$		−	49.9756i		−	1.77693i
$792$		0			0
$793$		−	10.3921i		−	0.369035i
$794$	1.38427	−	3.40964i	0.0491260	−	0.121003i
$795$		0			0
$796$	23.6896	+	23.0316i	0.839654	+	0.816334i
$797$	16.0687	+	4.30559i	0.569181	+	0.152512i	0.531921	−	0.846794i	$-0.321470\pi$
$797$	16.0687	+	4.30559i	0.569181	+	0.152512i	0.0372602	+	0.999306i	$0.488137\pi$
$798$		0			0
$799$	5.10611	−	8.84405i	0.180641	−	0.312880i
$800$	−2.68486	+	27.9706i	−0.0949240	+	0.988910i
$801$		0			0
$802$	32.8895	+	24.8710i	1.16137	+	0.878227i
$803$	−0.469592	−	1.75254i	−0.0165715	−	0.0618458i
$804$		0			0
$805$	0.976194	−	3.64320i	0.0344063	−	0.128406i
$806$	−17.8890	−	22.9766i	−0.630112	−	0.809315i
$807$		0			0
$808$	5.46356	−	49.5695i	0.192207	−	1.74385i
$809$			6.67548i			0.234697i	0.993091	+	0.117349i	$0.0374395\pi$
$809$			6.67548i			0.234697i	−0.993091	+	0.117349i	$0.962560\pi$
$810$		0			0
$811$	−18.4521	−	18.4521i	−0.647940	−	0.647940i	0.304555	−	0.952495i	$-0.401492\pi$
$811$	−18.4521	−	18.4521i	−0.647940	−	0.647940i	−0.952495	+	0.304555i	$0.901492\pi$
$812$	42.8697	+	71.8952i	1.50443	+	2.52303i
$813$		0			0
$814$	−3.44081	−	0.428367i	−0.120600	−	0.0150143i
$815$	−1.92020	−	3.32589i	−0.0672618	−	0.116501i
$816$		0			0
$817$	0.0119066	−	0.0206229i	0.000416560	−	0.000721502i
$818$	−9.04463	+	11.9606i	−0.316238	+	0.418194i
$819$		0			0
$820$	1.33922	+	0.748255i	0.0467676	+	0.0261302i
$821$	−12.3271	+	3.30305i	−0.430220	+	0.115277i	−0.467430	−	0.884030i	$-0.654820\pi$
$821$	−12.3271	+	3.30305i	−0.430220	+	0.115277i	0.0372093	+	0.999307i	$0.488153\pi$
$822$		0			0
$823$	−7.14088	+	4.12279i	−0.248915	+	0.143711i	−0.619268	−	0.785180i	$-0.712570\pi$
$823$	−7.14088	+	4.12279i	−0.248915	+	0.143711i	0.370352	+	0.928891i	$0.379237\pi$
$824$	−3.98600	−	26.0175i	−0.138859	−	0.906364i
$825$		0			0
$826$	−28.4069	+	69.9697i	−0.988402	+	2.43456i
$827$	24.9396	+	24.9396i	0.867236	+	0.867236i	0.992166	−	0.124930i	$-0.0398705\pi$
$827$	24.9396	+	24.9396i	0.867236	+	0.867236i	−0.124930	+	0.992166i	$0.539870\pi$
$828$		0			0
$829$	22.7949	−	22.7949i	0.791701	−	0.791701i	−0.190069	−	0.981771i	$-0.560871\pi$
$829$	22.7949	−	22.7949i	0.791701	−	0.791701i	0.981771	+	0.190069i	$0.0608713\pi$
$830$	1.81551	−	0.767030i	0.0630173	−	0.0266240i
$831$		0			0
$832$	19.5924	+	30.8483i	0.679244	+	1.06947i
$833$	32.2703	+	55.8938i	1.11810	+	1.93661i
$834$		0			0
$835$	0.422726	+	1.57764i	0.0146291	+	0.0545964i
$836$	0.591791	+	2.09039i	0.0204675	+	0.0722978i
$837$		0			0
$838$	−20.0526	+	2.78375i	−0.692706	+	0.0961629i
$839$	−29.5746	−	17.0749i	−1.02103	−	0.589492i	−0.106628	−	0.994299i	$-0.534005\pi$
$839$	−29.5746	−	17.0749i	−1.02103	−	0.589492i	−0.914402	+	0.404807i	$0.867339\pi$
$840$		0			0
$841$	−44.3213	+	25.5889i	−1.52832	+	0.882377i
$842$	22.2795	−	17.3462i	0.767802	−	0.597791i
$843$		0			0
$844$	−44.8204	+	26.7255i	−1.54278	+	0.919931i
$845$	1.00628	−	1.00628i	0.0346171	−	0.0346171i
$846$		0			0
$847$	−49.6195			−1.70495
$848$	2.01834	−	2.13536i	0.0693102	−	0.0733284i
$849$		0			0
$850$	−30.3022	−	3.77251i	−1.03936	−	0.129396i
$851$	17.0430	+	4.56665i	0.584225	+	0.156543i
$852$		0			0
$853$	−21.8060	+	5.84290i	−0.746624	+	0.200057i	−0.612020	−	0.790842i	$-0.709643\pi$
$853$	−21.8060	+	5.84290i	−0.746624	+	0.200057i	−0.134604	+	0.990900i	$0.542976\pi$
$854$	−2.06778	−	14.8952i	−0.0707580	−	0.509702i
$855$		0			0
$856$	34.8630	−	15.3112i	1.19159	−	0.523327i
$857$	44.1400	+	25.4842i	1.50779	+	0.870525i	0.999959	+	0.00907074i	$0.00288735\pi$
$857$	44.1400	+	25.4842i	1.50779	+	0.870525i	0.507835	+	0.861454i	$0.330446\pi$
$858$		0			0
$859$	−4.66973	+	17.4277i	−0.159329	+	0.594624i	0.839367	+	0.543566i	$0.182926\pi$
$859$	−4.66973	+	17.4277i	−0.159329	+	0.594624i	−0.998696	+	0.0510584i	$0.983741\pi$
$860$	0.00352490	+	0.00342700i	0.000120198	+	0.000116860i
$861$		0			0
$862$	−11.6223	+	4.91028i	−0.395858	+	0.167245i
$863$	45.5523			1.55062			0.775309	−	0.631583i	$-0.217594\pi$
$863$	45.5523			1.55062			0.775309	+	0.631583i	$0.217594\pi$
$864$		0			0
$865$	0.937369			0.0318715
$866$	38.8443	−	16.4112i	1.31998	−	0.557675i
$867$		0			0
$868$	−30.2123	−	29.3732i	−1.02547	−	0.996992i
$869$	0.468086	−	1.74692i	0.0158787	−	0.0592603i
$870$		0			0
$871$	−28.8448	−	16.6536i	−0.977369	−	0.564284i
$872$	−10.2177	−	23.2653i	−0.346016	−	0.787864i
$873$		0			0
$874$	−1.52014	−	10.9503i	−0.0514196	−	0.370399i
$875$	8.14054	−	2.18125i	0.275201	−	0.0737398i
$876$		0			0
$877$	18.7798	+	5.03203i	0.634148	+	0.169919i	0.561551	−	0.827442i	$-0.310205\pi$
$877$	18.7798	+	5.03203i	0.634148	+	0.169919i	0.0725968	+	0.997361i	$0.476871\pi$
$878$	43.8461	+	5.45867i	1.47973	+	0.184221i
$879$		0			0
$880$	−0.448343	+	0.0126303i	−0.0151136	+	0.000425766i
$881$	−51.8921			−1.74829			−0.874145	−	0.485666i	$-0.838577\pi$
$881$	−51.8921			−1.74829			−0.874145	+	0.485666i	$0.838577\pi$
$882$		0			0
$883$	−1.40472	+	1.40472i	−0.0472726	+	0.0472726i	−0.730348	−	0.683075i	$-0.760642\pi$
$883$	−1.40472	+	1.40472i	−0.0472726	+	0.0472726i	0.683075	+	0.730348i	$0.260642\pi$
$884$	−34.1100	+	20.3391i	−1.14724	+	0.684079i
$885$		0			0
$886$	−12.2463	+	9.53468i	−0.411423	+	0.320324i
$887$	−6.52145	+	3.76516i	−0.218969	+	0.126422i	−0.605473	−	0.795866i	$-0.707016\pi$
$887$	−6.52145	+	3.76516i	−0.218969	+	0.126422i	0.386504	+	0.922288i	$0.373683\pi$
$888$		0			0
$889$	−46.6654	−	26.9423i	−1.56511	−	0.903616i
$890$	0.807885	−	0.112152i	0.0270804	−	0.00375936i
$891$		0			0
$892$	−7.05968	−	24.9371i	−0.236376	−	0.834954i
$893$	1.06558	+	3.97679i	0.0356582	+	0.133078i
$894$		0			0
$895$	0.250830	+	0.434449i	0.00838431	+	0.0145220i
$896$	34.2202	+	40.3169i	1.14322	+	1.34689i
$897$		0			0
$898$	35.8205	−	15.1337i	1.19535	−	0.505017i
$899$	28.5398	−	28.5398i	0.951855	−	0.951855i
$900$		0			0
$901$	2.25787	+	2.25787i	0.0752204	+	0.0752204i
$902$	1.39821	−	3.44397i	0.0465554	−	0.114672i
$903$		0			0
$904$	29.8927	−	4.57969i	0.994215	−	0.152318i
$905$	−0.0496848	+	0.0286855i	−0.00165158	+	0.000953539i
$906$		0			0
$907$	19.2960	−	5.17036i	0.640714	−	0.171679i	0.0761873	−	0.997094i	$-0.475725\pi$
$907$	19.2960	−	5.17036i	0.640714	−	0.171679i	0.564527	+	0.825415i	$0.309059\pi$
$908$	−23.7515	−	13.2705i	−0.788221	−	0.440398i
$909$		0			0
$910$	3.29465	−	4.35685i	0.109217	−	0.144428i
$911$	20.6774	−	35.8143i	0.685073	−	1.18658i	−0.288341	−	0.957528i	$-0.593104\pi$
$911$	20.6774	−	35.8143i	0.685073	−	1.18658i	0.973414	−	0.229053i	$-0.0735629\pi$
$912$		0			0
$913$	−2.38768	−	4.13558i	−0.0790206	−	0.136868i
$914$	−27.2539	−	3.39300i	−0.901478	−	0.112230i
$915$		0			0
$916$	−17.2182	−	28.8759i	−0.568904	−	0.954087i
$917$	11.7121	+	11.7121i	0.386767	+	0.386767i
$918$		0			0
$919$		−	8.25699i		−	0.272373i	−0.990683	−	0.136187i	$-0.956515\pi$
$919$		−	8.25699i		−	0.272373i	0.990683	−	0.136187i	$-0.0434847\pi$
$920$	2.26862	+	0.250048i	0.0747943	+	0.00824384i
$921$		0			0
$922$	−3.62870	−	4.66069i	−0.119505	−	0.153492i
$923$	8.92803	−	33.3198i	0.293870	−	1.09674i
$924$		0			0
$925$	5.08522	+	18.9783i	0.167201	+	0.624002i
$926$	1.74445	+	1.31915i	0.0573261	+	0.0433500i
$927$		0			0
$928$	−39.0752	+	32.2307i	−1.28271	+	1.05802i
$929$	2.79783	−	4.84599i	0.0917939	−	0.158992i	−0.816472	−	0.577385i	$-0.804073\pi$
$929$	2.79783	−	4.84599i	0.0917939	−	0.158992i	0.908266	+	0.418393i	$0.137407\pi$
$930$		0			0
$931$	−25.1330	−	6.73438i	−0.823702	−	0.220710i
$932$	14.4106	+	14.0103i	0.472034	+	0.458923i
$933$		0			0
$934$	−1.60395	+	3.95074i	−0.0524830	+	0.129272i
$935$		−	0.487421i		−	0.0159404i
$936$		0			0
$937$			3.12869i			0.102210i	0.998693	+	0.0511049i	$0.0162743\pi$
$937$			3.12869i			0.102210i	−0.998693	+	0.0511049i	$0.983726\pi$
$938$	−44.6574	−	18.1304i	−1.45811	−	0.591978i
$939$		0			0
$940$	−0.849883	+	0.0119686i	−0.0277201	+	0.000390374i
$941$	−12.9126	−	3.45992i	−0.420939	−	0.112790i	0.0421307	−	0.999112i	$-0.486585\pi$
$941$	−12.9126	−	3.45992i	−0.420939	−	0.112790i	−0.463070	+	0.886322i	$0.653252\pi$
$942$		0			0
$943$	−9.45717	+	16.3803i	−0.307968	+	0.533416i
$944$	−44.4552	−	10.5795i	−1.44689	−	0.344334i
$945$		0			0
$946$	0.00718468	−	0.00950102i	0.000233594	−	0.000308905i
$947$	−5.84975	−	21.8316i	−0.190091	−	0.709431i	−0.993483	−	0.113980i	$-0.963640\pi$
$947$	−5.84975	−	21.8316i	−0.190091	−	0.709431i	0.803392	−	0.595451i	$-0.203027\pi$
$948$		0			0
$949$	−3.46066	+	12.9154i	−0.112338	+	0.419250i
$950$	9.71372	−	7.56285i	0.315155	−	0.245371i
$951$		0			0
$952$	−44.8434	+	35.9395i	−1.45338	+	1.16481i
$953$		−	13.2051i		−	0.427754i	−0.976861	−	0.213877i	$-0.931391\pi$
$953$		−	13.2051i		−	0.427754i	0.976861	−	0.213877i	$-0.0686092\pi$
$954$		0			0
$955$	−2.65786	−	2.65786i	−0.0860065	−	0.0860065i
$956$	13.1215	+	3.31858i	0.424378	+	0.107330i
$957$		0			0
$958$	5.07068	−	40.7297i	0.163826	−	1.31592i
$959$	−35.1344	−	60.8545i	−1.13455	−	1.96509i
$960$		0			0
$961$	5.34109	−	9.25104i	0.172293	−	0.298421i
$962$	20.3814	+	15.4124i	0.657123	+	0.496917i
$963$		0			0
$964$	1.17461	+	4.14911i	0.0378317	+	0.133634i
$965$	2.68940	−	0.720623i	0.0865749	−	0.0231977i
$966$		0			0
$967$	−26.0110	+	15.0175i	−0.836457	+	0.482929i	−0.856058	−	0.516879i	$-0.827094\pi$
$967$	−26.0110	+	15.0175i	−0.836457	+	0.482929i	0.0196013	+	0.999808i	$0.493760\pi$
$968$	−4.54705	−	29.6797i	−0.146148	−	0.953941i
$969$		0			0
$970$	3.81094	+	1.54720i	0.122362	+	0.0496775i
$971$	−29.4184	−	29.4184i	−0.944081	−	0.944081i	0.0544362	−	0.998517i	$-0.482664\pi$
$971$	−29.4184	−	29.4184i	−0.944081	−	0.944081i	−0.998517	+	0.0544362i	$0.982664\pi$
$972$		0			0
$973$	33.4013	−	33.4013i	1.07080	−	1.07080i
$974$	−1.97872	−	4.68350i	−0.0634022	−	0.150069i
$975$		0			0
$976$	8.71999	−	2.60180i	0.279120	−	0.0832817i
$977$	1.26388	+	2.18911i	0.0404352	+	0.0700358i	0.885535	−	0.464573i	$-0.153792\pi$
$977$	1.26388	+	2.18911i	0.0404352	+	0.0700358i	−0.845100	+	0.534609i	$0.820459\pi$
$978$		0			0
$979$	−0.511486	−	1.90889i	−0.0163472	−	0.0610084i
$980$	2.62010	−	4.68942i	0.0836959	−	0.149798i
$981$		0			0
$982$	4.02565	+	28.9986i	0.128464	+	0.925383i
$983$	−17.8779	−	10.3218i	−0.570215	−	0.329214i	0.187020	−	0.982356i	$-0.440117\pi$
$983$	−17.8779	−	10.3218i	−0.570215	−	0.329214i	−0.757235	+	0.653142i	$0.773450\pi$
$984$		0			0
$985$	0.200541	−	0.115782i	0.00638976	−	0.00368913i
$986$	−33.8163	−	43.4336i	−1.07693	−	1.38321i
$987$		0			0
$988$	3.92567	−	15.5219i	0.124892	−	0.493817i
$989$	−0.0428609	+	0.0428609i	−0.00136290	+	0.00136290i
$990$		0			0
$991$	32.9680			1.04726			0.523631	−	0.851945i	$-0.324577\pi$
$991$	32.9680			1.04726			0.523631	+	0.851945i	$0.324577\pi$
$992$	14.8008	−	20.7631i	0.469927	−	0.659229i
$993$		0			0
$994$	6.16683	−	49.5343i	0.195600	−	1.57113i
$995$	2.88661	+	0.773465i	0.0915117	+	0.0245205i
$996$		0			0
$997$	−8.34081	+	2.23491i	−0.264156	+	0.0707804i	−0.388466	−	0.921463i	$-0.626995\pi$
$997$	−8.34081	+	2.23491i	−0.264156	+	0.0707804i	0.124310	+	0.992243i	$0.460328\pi$
$998$	21.3776	−	2.96768i	0.676695	−	0.0939402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.181.2		72
3.2	odd	2		144.2.x.e.133.17	yes	72
4.3	odd	2		1728.2.bc.e.1585.11		72
9.4	even	3	inner	432.2.y.e.37.10		72
9.5	odd	6		144.2.x.e.85.9	yes	72
12.11	even	2		576.2.bb.e.241.15		72
16.3	odd	4		1728.2.bc.e.721.8		72
16.13	even	4	inner	432.2.y.e.397.10		72
36.23	even	6		576.2.bb.e.49.14		72
36.31	odd	6		1728.2.bc.e.1009.8		72
48.29	odd	4		144.2.x.e.61.9	yes	72
48.35	even	4		576.2.bb.e.529.14		72
144.13	even	12	inner	432.2.y.e.253.2		72
144.67	odd	12		1728.2.bc.e.145.11		72
144.77	odd	12		144.2.x.e.13.17	✓	72
144.131	even	12		576.2.bb.e.337.15		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.17	✓	72	144.77	odd	12
144.2.x.e.61.9	yes	72	48.29	odd	4
144.2.x.e.85.9	yes	72	9.5	odd	6
144.2.x.e.133.17	yes	72	3.2	odd	2
432.2.y.e.37.10		72	9.4	even	3	inner
432.2.y.e.181.2		72	1.1	even	1	trivial
432.2.y.e.253.2		72	144.13	even	12	inner
432.2.y.e.397.10		72	16.13	even	4	inner
576.2.bb.e.49.14		72	36.23	even	6
576.2.bb.e.241.15		72	12.11	even	2
576.2.bb.e.337.15		72	144.131	even	12
576.2.bb.e.529.14		72	48.35	even	4
1728.2.bc.e.145.11		72	144.67	odd	12
1728.2.bc.e.721.8		72	16.3	odd	4
1728.2.bc.e.1009.8		72	36.31	odd	6
1728.2.bc.e.1585.11		72	4.3	odd	2

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30272 + 0.550382i) q^{2} +(1.39416 - 1.43399i) q^{4} +(0.0468197 - 0.174734i) q^{5} +(4.04791 + 2.33706i) q^{7} +(-1.02696 + 2.63540i) q^{8} +O(q^{10})\)	\(q+(-1.30272 + 0.550382i) q^{2} +(1.39416 - 1.43399i) q^{4} +(0.0468197 - 0.174734i) q^{5} +(4.04791 + 2.33706i) q^{7} +(-1.02696 + 2.63540i) q^{8} +(0.0351772 + 0.253398i) q^{10} +(0.598734 - 0.160430i) q^{11} +(-4.41237 - 1.18229i) q^{13} +(-6.55957 - 0.816641i) q^{14} +(-0.112639 - 3.99841i) q^{16} +4.34691 q^{17} +(-1.23918 + 1.23918i) q^{19} +(-0.185292 - 0.310745i) q^{20} +(-0.691685 + 0.538528i) q^{22} +(3.86311 - 2.23037i) q^{23} +(4.30179 + 2.48364i) q^{25} +(6.39880 - 0.888296i) q^{26} +(8.99475 - 2.54642i) q^{28} +(2.31752 + 8.64910i) q^{29} +(-2.25376 - 3.90364i) q^{31} +(2.34739 + 5.14682i) q^{32} +(-5.66281 + 2.39246i) q^{34} +(0.597886 - 0.597886i) q^{35} +(2.79692 + 2.79692i) q^{37} +(0.932282 - 2.29633i) q^{38} +(0.412412 + 0.302833i) q^{40} +(-3.67211 + 2.12009i) q^{41} +(-0.0131254 + 0.00351694i) q^{43} +(0.604676 - 1.08224i) q^{44} +(-3.80500 + 5.03173i) q^{46} +(1.17465 - 2.03456i) q^{47} +(7.42373 + 12.8583i) q^{49} +(-6.97097 - 0.867859i) q^{50} +(-7.84695 + 4.67899i) q^{52} +(0.519418 + 0.519418i) q^{53} -0.112130i q^{55} +(-10.3161 + 8.26782i) q^{56} +(-7.77939 - 9.99184i) q^{58} +(2.95679 - 11.0349i) q^{59} +(0.588805 + 2.19745i) q^{61} +(5.08451 + 3.84491i) q^{62} +(-5.89071 - 5.41290i) q^{64} +(-0.413172 + 0.715636i) q^{65} +(7.04291 + 1.88714i) q^{67} +(6.06029 - 6.23342i) q^{68} +(-0.449812 + 1.10794i) q^{70} +7.55145i q^{71} -2.92707i q^{73} +(-5.18298 - 2.10423i) q^{74} +(0.0493539 + 3.50458i) q^{76} +(2.79856 + 0.749872i) q^{77} +(1.45885 - 2.52680i) q^{79} +(-0.703931 - 0.167523i) q^{80} +(3.61687 - 4.78295i) q^{82} +(-1.99394 - 7.44148i) q^{83} +(0.203521 - 0.759552i) q^{85} +(0.0151631 - 0.0118056i) q^{86} +(-0.192077 + 1.74266i) q^{88} -3.18821i q^{89} +(-15.0978 - 15.0978i) q^{91} +(2.18747 - 8.64914i) q^{92} +(-0.410459 + 3.29697i) q^{94} +(0.158508 + 0.274544i) q^{95} +(8.03868 - 13.9234i) q^{97} +(-16.7480 - 12.6648i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

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