LMFDB - Embedded newform 567.2.bd.a.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 3]))

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.16
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38665 - 0.244504i) q^{2} +(-0.0163608 + 0.00595485i) q^{4} +(-1.98299 + 0.721749i) q^{5} +(-2.18605 - 1.49037i) q^{7} +(-2.46004 + 1.42030i) q^{8} +O(q^{10})$	\(q+(1.38665 - 0.244504i) q^{2} +(-0.0163608 + 0.00595485i) q^{4} +(-1.98299 + 0.721749i) q^{5} +(-2.18605 - 1.49037i) q^{7} +(-2.46004 + 1.42030i) q^{8} +(-2.57325 + 1.48566i) q^{10} +(1.26664 - 3.48007i) q^{11} +(-2.27684 - 6.25557i) q^{13} +(-3.39569 - 1.53213i) q^{14} +(-3.03727 + 2.54857i) q^{16} +(1.61887 + 2.80397i) q^{17} +(-4.61385 - 2.66381i) q^{19} +(0.0281454 - 0.0236168i) q^{20} +(0.905502 - 5.13536i) q^{22} +(-0.689782 - 0.121627i) q^{23} +(-0.418902 + 0.351501i) q^{25} +(-4.68670 - 8.11761i) q^{26} +(0.0446405 + 0.0113661i) q^{28} +(-1.50083 + 4.12351i) q^{29} +(-0.513951 - 1.41207i) q^{31} +(0.0633067 - 0.0754460i) q^{32} +(2.93040 + 3.49232i) q^{34} +(5.41058 + 1.37761i) q^{35} +6.49662 q^{37} +(-7.04913 - 2.56567i) q^{38} +(3.85312 - 4.59197i) q^{40} +(-10.4849 + 3.81619i) q^{41} +(1.29121 + 7.32280i) q^{43} +0.0644796i q^{44} -0.986227 q^{46} +(5.63412 + 2.05065i) q^{47} +(2.55760 + 6.51603i) q^{49} +(-0.494929 + 0.589833i) q^{50} +(0.0745020 + 0.0887880i) q^{52} +(-0.766350 - 0.442452i) q^{53} +7.81514i q^{55} +(7.49453 + 0.561517i) q^{56} +(-1.07292 + 6.08484i) q^{58} +(-4.77604 - 4.00757i) q^{59} +(2.54368 - 6.98869i) q^{61} +(-1.05793 - 1.83239i) q^{62} +(4.03421 - 6.98746i) q^{64} +(9.02990 + 10.7614i) q^{65} +(1.82662 - 10.3593i) q^{67} +(-0.0431834 - 0.0362352i) q^{68} +(7.83942 + 0.587358i) q^{70} +(3.83248 + 2.21268i) q^{71} -3.06138i q^{73} +(9.00855 - 1.58845i) q^{74} +(0.0913491 + 0.0161073i) q^{76} +(-7.95554 + 5.71984i) q^{77} +(-1.65307 - 9.37505i) q^{79} +(4.18344 - 7.24593i) q^{80} +(-13.6058 + 7.85533i) q^{82} +(-11.4377 - 4.16299i) q^{83} +(-5.23397 - 4.39182i) q^{85} +(3.58091 + 9.83847i) q^{86} +(1.82677 + 10.3601i) q^{88} +(2.17916 - 3.77442i) q^{89} +(-4.34583 + 17.0683i) q^{91} +(0.0120097 - 0.00211763i) q^{92} +(8.31397 + 1.46598i) q^{94} +(11.0718 + 1.95226i) q^{95} +(-6.85869 + 1.20937i) q^{97} +(5.13970 + 8.41014i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	1.38665	−	0.244504i	0.980512	−	0.172891i	0.339654	−	0.940550i	$-0.389690\pi$
$2$	1.38665	−	0.244504i	0.980512	−	0.172891i	0.640858	+	0.767660i	$0.278579\pi$
$3$		0			0
$3$		0			0
$4$	−0.0163608	+	0.00595485i	−0.00818041	+	0.00297743i
$5$	−1.98299	+	0.721749i	−0.886819	+	0.322776i	−0.744958	−	0.667111i	$-0.767531\pi$
$5$	−1.98299	+	0.721749i	−0.886819	+	0.322776i	−0.141861	+	0.989887i	$0.545309\pi$
$6$		0			0
$7$	−2.18605	−	1.49037i	−0.826248	−	0.563307i
$7$	−2.18605	−	1.49037i	−0.826248	−	0.563307i
$8$	−2.46004	+	1.42030i	−0.869754	+	0.502153i
$9$		0			0
$10$	−2.57325	+	1.48566i	−0.813732	+	0.469808i
$11$	1.26664	−	3.48007i	0.381907	−	1.04928i	−0.588645	−	0.808392i	$-0.700338\pi$
$11$	1.26664	−	3.48007i	0.381907	−	1.04928i	0.970552	−	0.240890i	$-0.0774394\pi$
$12$		0			0
$13$	−2.27684	−	6.25557i	−0.631482	−	1.73498i	−0.676963	−	0.736017i	$-0.736704\pi$
$13$	−2.27684	−	6.25557i	−0.631482	−	1.73498i	0.0454806	−	0.998965i	$-0.485518\pi$
$14$	−3.39569	−	1.53213i	−0.907536	−	0.409478i
$15$		0			0
$16$	−3.03727	+	2.54857i	−0.759318	+	0.637143i
$17$	1.61887	+	2.80397i	0.392635	+	0.680063i	0.992796	−	0.119816i	$-0.0382303\pi$
$17$	1.61887	+	2.80397i	0.392635	+	0.680063i	−0.600161	+	0.799879i	$0.704897\pi$
$18$		0			0
$19$	−4.61385	−	2.66381i	−1.05849	−	0.611120i	−0.133476	−	0.991052i	$-0.542614\pi$
$19$	−4.61385	−	2.66381i	−1.05849	−	0.611120i	−0.925014	+	0.379932i	$0.875947\pi$
$20$	0.0281454	−	0.0236168i	0.00629351	−	0.00528088i
$21$		0			0
$22$	0.905502	−	5.13536i	0.193054	−	1.09486i
$23$	−0.689782	−	0.121627i	−0.143829	−	0.0253610i	0.101270	−	0.994859i	$-0.467709\pi$
$23$	−0.689782	−	0.121627i	−0.143829	−	0.0253610i	−0.245099	+	0.969498i	$0.578821\pi$
$24$		0			0
$25$	−0.418902	+	0.351501i	−0.0837805	+	0.0703002i
$26$	−4.68670	−	8.11761i	−0.919138	−	1.59199i
$27$		0			0
$28$	0.0446405	+	0.0113661i	0.00843625	+	0.00214799i
$29$	−1.50083	+	4.12351i	−0.278698	+	0.765716i	0.718813	+	0.695204i	$0.244686\pi$
$29$	−1.50083	+	4.12351i	−0.278698	+	0.765716i	−0.997511	+	0.0705128i	$0.977536\pi$
$30$		0			0
$31$	−0.513951	−	1.41207i	−0.0923084	−	0.253615i	0.884943	−	0.465699i	$-0.154197\pi$
$31$	−0.513951	−	1.41207i	−0.0923084	−	0.253615i	−0.977251	+	0.212084i	$0.931975\pi$
$32$	0.0633067	−	0.0754460i	0.0111911	−	0.0133371i
$33$		0			0
$34$	2.93040	+	3.49232i	0.502560	+	0.598927i
$35$	5.41058	+	1.37761i	0.914554	+	0.232859i
$36$		0			0
$37$	6.49662			1.06804			0.534019	−	0.845473i	$-0.320681\pi$
$37$	6.49662			1.06804			0.534019	+	0.845473i	$0.320681\pi$
$38$	−7.04913	−	2.56567i	−1.14352	−	0.416207i
$39$		0			0
$40$	3.85312	−	4.59197i	0.609232	−	0.726054i
$41$	−10.4849	+	3.81619i	−1.63746	+	0.595988i	−0.986593	−	0.163200i	$-0.947818\pi$
$41$	−10.4849	+	3.81619i	−1.63746	+	0.595988i	−0.650871	+	0.759188i	$0.725596\pi$
$42$		0			0
$43$	1.29121	+	7.32280i	0.196907	+	1.11672i	0.909676	+	0.415318i	$0.136330\pi$
$43$	1.29121	+	7.32280i	0.196907	+	1.11672i	−0.712769	+	0.701399i	$0.752559\pi$
$44$			0.0644796i			0.00972066i
$45$		0			0
$46$	−0.986227			−0.145411
$47$	5.63412	+	2.05065i	0.821821	+	0.299119i	0.718498	−	0.695529i	$-0.244830\pi$
$47$	5.63412	+	2.05065i	0.821821	+	0.299119i	0.103324	+	0.994648i	$0.467052\pi$
$48$		0			0
$49$	2.55760	+	6.51603i	0.365371	+	0.930862i
$50$	−0.494929	+	0.589833i	−0.0699935	+	0.0834150i
$51$		0			0
$52$	0.0745020	+	0.0887880i	0.0103316	+	0.0123127i
$53$	−0.766350	−	0.442452i	−0.105266	−	0.0607755i	0.446443	−	0.894812i	$-0.352691\pi$
$53$	−0.766350	−	0.442452i	−0.105266	−	0.0607755i	−0.551709	+	0.834037i	$0.686024\pi$
$54$		0			0
$55$			7.81514i			1.05379i
$56$	7.49453	+	0.561517i	1.00150	+	0.0750358i
$57$		0			0
$58$	−1.07292	+	6.08484i	−0.140881	+	0.798978i
$59$	−4.77604	−	4.00757i	−0.621787	−	0.521742i	0.276577	−	0.960992i	$-0.410800\pi$
$59$	−4.77604	−	4.00757i	−0.621787	−	0.521742i	−0.898365	+	0.439250i	$0.855244\pi$
$60$		0			0
$61$	2.54368	−	6.98869i	0.325684	−	0.894811i	−0.663506	−	0.748171i	$-0.730932\pi$
$61$	2.54368	−	6.98869i	0.325684	−	0.894811i	0.989190	−	0.146639i	$-0.0468456\pi$
$62$	−1.05793	−	1.83239i	−0.134357	−	0.232713i
$63$		0			0
$64$	4.03421	−	6.98746i	0.504277	−	0.873433i
$65$	9.02990	+	10.7614i	1.12002	+	1.33479i
$66$		0			0
$67$	1.82662	−	10.3593i	0.223157	−	1.26559i	−0.643019	−	0.765850i	$-0.722319\pi$
$67$	1.82662	−	10.3593i	0.223157	−	1.26559i	0.866177	−	0.499738i	$-0.166570\pi$
$68$	−0.0431834	−	0.0362352i	−0.00523675	−	0.00439416i
$69$		0			0
$70$	7.83942	+	0.587358i	0.936990	+	0.0702027i
$71$	3.83248	+	2.21268i	0.454832	+	0.262597i	0.709869	−	0.704334i	$-0.248754\pi$
$71$	3.83248	+	2.21268i	0.454832	+	0.262597i	−0.255037	+	0.966931i	$0.582088\pi$
$72$		0			0
$73$		−	3.06138i		−	0.358307i	−0.983821	−	0.179154i	$-0.942664\pi$
$73$		−	3.06138i		−	0.358307i	0.983821	−	0.179154i	$-0.0573359\pi$
$74$	9.00855	−	1.58845i	1.04722	−	0.184654i
$75$		0			0
$76$	0.0913491	+	0.0161073i	0.0104785	+	0.00184763i
$77$	−7.95554	+	5.71984i	−0.906618	+	0.651836i
$78$		0			0
$79$	−1.65307	−	9.37505i	−0.185985	−	1.05478i	−0.924683	−	0.380739i	$-0.875670\pi$
$79$	−1.65307	−	9.37505i	−0.185985	−	1.05478i	0.738697	−	0.674037i	$-0.235441\pi$
$80$	4.18344	−	7.24593i	0.467723	−	0.810120i
$81$		0			0
$82$	−13.6058	+	7.85533i	−1.50251	+	0.867476i
$83$	−11.4377	−	4.16299i	−1.25545	−	0.456947i	−0.373212	−	0.927746i	$-0.621744\pi$
$83$	−11.4377	−	4.16299i	−1.25545	−	0.456947i	−0.882241	+	0.470799i	$0.843966\pi$
$84$		0			0
$85$	−5.23397	−	4.39182i	−0.567704	−	0.476360i
$86$	3.58091	+	9.83847i	0.386140	+	1.06091i
$87$		0			0
$88$	1.82677	+	10.3601i	0.194734	+	1.10439i
$89$	2.17916	−	3.77442i	0.230991	−	0.400088i	−0.727109	−	0.686522i	$-0.759137\pi$
$89$	2.17916	−	3.77442i	0.230991	−	0.400088i	0.958100	+	0.286434i	$0.0924699\pi$
$90$		0			0
$91$	−4.34583	+	17.0683i	−0.455567	+	1.78924i
$92$	0.0120097	−	0.00211763i	0.00125210	−	0.000220778i
$93$		0			0
$94$	8.31397	+	1.46598i	0.857520	+	0.151204i
$95$	11.0718	+	1.95226i	1.13594	+	0.200298i
$96$		0			0
$97$	−6.85869	+	1.20937i	−0.696394	+	0.122793i	−0.510629	−	0.859801i	$-0.670587\pi$
$97$	−6.85869	+	1.20937i	−0.696394	+	0.122793i	−0.185765	+	0.982594i	$0.559476\pi$
$98$	5.13970	+	8.41014i	0.519188	+	0.849552i
$99$		0			0
$100$	0.00476045	−	0.00824535i	0.000476045	−	0.000824535i
$101$	−0.645643	−	3.66163i	−0.0642439	−	0.364345i	−0.999934	−	0.0115214i	$-0.996333\pi$
$101$	−0.645643	−	3.66163i	−0.0642439	−	0.364345i	0.935690	−	0.352824i	$-0.114779\pi$
$102$		0			0
$103$	−2.12266	−	5.83195i	−0.209152	−	0.574639i	0.790114	−	0.612960i	$-0.210021\pi$
$103$	−2.12266	−	5.83195i	−0.209152	−	0.574639i	−0.999265	+	0.0383208i	$0.987799\pi$
$104$	14.4859	+	12.1551i	1.42046	+	1.19191i
$105$		0			0
$106$	−1.17084	−	0.426152i	−0.113722	−	0.0413915i
$107$	−2.47461	+	1.42872i	−0.239230	+	0.138119i	−0.614823	−	0.788665i	$-0.710772\pi$
$107$	−2.47461	+	1.42872i	−0.239230	+	0.138119i	0.375593	+	0.926785i	$0.377439\pi$
$108$		0			0
$109$	2.81692	−	4.87905i	0.269812	−	0.467328i	−0.699001	−	0.715121i	$-0.746372\pi$
$109$	2.81692	−	4.87905i	0.269812	−	0.467328i	0.968813	+	0.247792i	$0.0797051\pi$
$110$	1.91084	+	10.8369i	0.182191	+	1.03326i
$111$		0			0
$112$	10.4379	−	1.04464i	0.986292	−	0.0987093i
$113$	−9.04367	−	1.59464i	−0.850757	−	0.150011i	−0.268765	−	0.963206i	$-0.586615\pi$
$113$	−9.04367	−	1.59464i	−0.850757	−	0.150011i	−0.581992	+	0.813194i	$0.697727\pi$
$114$		0			0
$115$	1.45561	−	0.256664i	0.135737	−	0.0239340i
$116$		−	0.0764013i		−	0.00709368i
$117$		0			0
$118$	−7.60258	−	4.38935i	−0.699874	−	0.404073i
$119$	0.640023	−	8.54234i	0.0586708	−	0.783075i
$120$		0			0
$121$	−2.08004	−	1.74536i	−0.189095	−	0.158669i
$122$	1.81843	−	10.3128i	0.164633	−	0.933680i
$123$		0			0
$124$	0.0168173	+	0.0200421i	0.00151024	+	0.00179984i
$125$	5.85261	−	10.1370i	0.523474	−	0.906683i
$126$		0			0
$127$	−0.958294	−	1.65981i	−0.0850349	−	0.147285i	0.820371	−	0.571831i	$-0.193767\pi$
$127$	−0.958294	−	1.65981i	−0.0850349	−	0.147285i	−0.905406	+	0.424547i	$0.860433\pi$
$128$	3.81822	−	10.4905i	0.337486	−	0.927235i
$129$		0			0
$130$	15.1525	+	12.7145i	1.32897	+	1.11513i
$131$	1.51205	−	8.57526i	0.132108	−	0.749224i	−0.844721	−	0.535206i	$-0.820234\pi$
$131$	1.51205	−	8.57526i	0.132108	−	0.749224i	0.976830	−	0.214018i	$-0.0686550\pi$
$132$		0			0
$133$	6.11604	+	12.6996i	0.530328	+	1.10119i
$134$		−	14.8114i		−	1.27951i
$135$		0			0
$136$	−7.96498	−	4.59858i	−0.682991	−	0.394325i
$137$	4.48477	+	5.34474i	0.383160	+	0.456632i	0.922809	−	0.385258i	$-0.125888\pi$
$137$	4.48477	+	5.34474i	0.383160	+	0.456632i	−0.539649	+	0.841890i	$0.681443\pi$
$138$		0			0
$139$	−6.76177	+	8.05836i	−0.573526	+	0.683501i	−0.972351	−	0.233526i	$-0.924974\pi$
$139$	−6.76177	+	8.05836i	−0.573526	+	0.683501i	0.398825	+	0.917027i	$0.369418\pi$
$140$	−0.0967249	+	0.00968035i	−0.00817475	+	0.000818139i
$141$		0			0
$142$	5.85533	+	2.13117i	0.491368	+	0.178843i
$143$	−24.6538			−2.06165
$144$		0			0
$145$		−	9.26009i		−	0.769009i
$146$	−0.748521	−	4.24507i	−0.0619480	−	0.351325i
$147$		0			0
$148$	−0.106290	+	0.0386864i	−0.00873699	+	0.00318000i
$149$	7.15261	−	8.52415i	0.585965	−	0.698326i	−0.388860	−	0.921297i	$-0.627131\pi$
$149$	7.15261	−	8.52415i	0.585965	−	0.698326i	0.974825	+	0.222971i	$0.0715756\pi$
$150$		0			0
$151$	18.9758	+	6.90663i	1.54423	+	0.562054i	0.967055	−	0.254567i	$-0.0819330\pi$
$151$	18.9758	+	6.90663i	1.54423	+	0.562054i	0.577175	+	0.816621i	$0.304155\pi$
$152$	15.1337			1.22750
$153$		0			0
$154$	−9.63305	+	9.87659i	−0.776253	+	0.795878i
$155$	2.03832	+	2.42917i	0.163722	+	0.195116i
$156$		0			0
$157$	−3.14481	+	3.74783i	−0.250983	+	0.299110i	−0.876795	−	0.480864i	$-0.840323\pi$
$157$	−3.14481	+	3.74783i	−0.250983	+	0.299110i	0.625812	+	0.779974i	$0.284768\pi$
$158$	−4.58448	−	12.5958i	−0.364722	−	1.00207i
$159$		0			0
$160$	−0.0710834	+	0.195300i	−0.00561963	+	0.0154398i
$161$	1.32663	+	1.29391i	0.104553	+	0.101975i
$162$		0			0
$163$	−4.68621	−	8.11676i	−0.367053	−	0.635754i	0.622051	−	0.782977i	$-0.286300\pi$
$163$	−4.68621	−	8.11676i	−0.367053	−	0.635754i	−0.989103	+	0.147223i	$0.952966\pi$
$164$	0.148817	−	0.124872i	0.0116206	−	0.00975086i
$165$		0			0
$166$	−16.8780	−	2.97605i	−1.30999	−	0.230986i
$167$	−1.49566	+	8.48231i	−0.115738	+	0.656381i	0.870645	+	0.491912i	$0.163702\pi$
$167$	−1.49566	+	8.48231i	−0.115738	+	0.656381i	−0.986382	+	0.164468i	$0.947409\pi$
$168$		0			0
$169$	−23.9896	+	20.1296i	−1.84535	+	1.54843i
$170$	−8.33152	−	4.81021i	−0.638999	−	0.368926i
$171$		0			0
$172$	−0.0647314	−	0.112118i	−0.00493572	−	0.00854892i
$173$	−6.49113	+	5.44671i	−0.493512	+	0.414106i	−0.855283	−	0.518161i	$-0.826617\pi$
$173$	−6.49113	+	5.44671i	−0.493512	+	0.414106i	0.361771	+	0.932267i	$0.382172\pi$
$174$		0			0
$175$	1.43961	−	0.144078i	0.108824	−	0.0108912i
$176$	5.02208	+	13.7981i	0.378554	+	1.04007i
$177$		0			0
$178$	2.09888	−	5.76663i	0.157318	−	0.432227i
$179$	4.18791	−	2.41789i	0.313019	−	0.180722i	−0.335258	−	0.942126i	$-0.608823\pi$
$179$	4.18791	−	2.41789i	0.313019	−	0.180722i	0.648277	+	0.761405i	$0.275490\pi$
$180$		0			0
$181$	3.95269	−	2.28209i	0.293801	−	0.169626i	−0.345854	−	0.938288i	$-0.612411\pi$
$181$	3.95269	−	2.28209i	0.293801	−	0.169626i	0.639655	+	0.768662i	$0.279077\pi$
$182$	−1.85289	+	24.7304i	−0.137345	+	1.83314i
$183$		0			0
$184$	1.86964	−	0.680492i	0.137831	−	0.0501665i
$185$	−12.8827	+	4.68892i	−0.947156	+	0.344737i
$186$		0			0
$187$	11.8086	−	2.08217i	0.863528	−	0.152263i
$188$	−0.104390			−0.00761344
$189$		0			0
$190$	15.8301			1.14844
$191$	10.1847	−	1.79584i	0.736940	−	0.129942i	0.207434	−	0.978249i	$-0.433489\pi$
$191$	10.1847	−	1.79584i	0.736940	−	0.129942i	0.529505	+	0.848307i	$0.322378\pi$
$192$		0			0
$193$	−9.77771	+	3.55879i	−0.703815	+	0.256168i	−0.669039	−	0.743228i	$-0.733294\pi$
$193$	−9.77771	+	3.55879i	−0.703815	+	0.256168i	−0.0347759	+	0.999395i	$0.511072\pi$
$194$	−9.21492	+	3.35396i	−0.661593	+	0.240800i
$195$		0			0
$196$	−0.0806464	−	0.0913776i	−0.00576046	−	0.00652697i
$197$	−12.2795	+	7.08959i	−0.874880	+	0.505112i	−0.868967	−	0.494870i	$-0.835216\pi$
$197$	−12.2795	+	7.08959i	−0.874880	+	0.505112i	−0.00591309	+	0.999983i	$0.501882\pi$
$198$		0			0
$199$	17.4224	−	10.0588i	1.23504	−	0.713050i	0.266963	−	0.963707i	$-0.413980\pi$
$199$	17.4224	−	10.0588i	1.23504	−	0.713050i	0.968076	+	0.250657i	$0.0806466\pi$
$200$	0.531277	−	1.45967i	0.0375670	−	0.103214i
$201$		0			0
$202$	−1.79057	−	4.91954i	−0.125984	−	0.346138i
$203$	9.42645	−	6.77738i	0.661607	−	0.475679i
$204$		0			0
$205$	18.0371	−	15.1349i	1.25976	−	1.05707i
$206$	−4.36933	−	7.56790i	−0.304425	−	0.527280i
$207$		0			0
$208$	22.8582	+	13.1972i	1.58493	+	0.915058i
$209$	−15.1144	+	12.6825i	−1.04548	+	0.877264i
$210$		0			0
$211$	0.582787	−	3.30515i	0.0401207	−	0.227536i	−0.958154	−	0.286254i	$-0.907590\pi$
$211$	0.582787	−	3.30515i	0.0401207	−	0.227536i	0.998275	+	0.0587176i	$0.0187011\pi$
$212$	0.0151729	+	0.00267538i	0.00104208	+	0.000183746i
$213$		0			0
$214$	−3.08210	+	2.58619i	−0.210688	+	0.176788i
$215$	−7.84567	−	13.5891i	−0.535070	−	0.926768i
$216$		0			0
$217$	−0.980985	+	3.85283i	−0.0665936	+	0.261547i
$218$	2.71314	−	7.45430i	0.183757	−	0.504869i
$219$		0			0
$220$	−0.0465380	−	0.127862i	−0.00313759	−	0.00862047i
$221$	13.8545	−	16.5112i	0.931956	−	1.11066i
$222$		0			0
$223$	−6.45098	−	7.68798i	−0.431990	−	0.514825i	0.505506	−	0.862823i	$-0.331306\pi$
$223$	−6.45098	−	7.68798i	−0.431990	−	0.514825i	−0.937495	+	0.347998i	$0.886862\pi$
$224$	−0.250834	+	0.0705780i	−0.0167595	+	0.00471569i
$225$		0			0
$226$	−12.9303			−0.860113
$227$	16.6785	+	6.07047i	1.10699	+	0.402911i	0.829889	−	0.557929i	$-0.188404\pi$
$227$	16.6785	+	6.07047i	1.10699	+	0.402911i	0.277102	+	0.960841i	$0.410626\pi$
$228$		0			0
$229$	−8.39720	+	10.0074i	−0.554903	+	0.661307i	−0.968459	−	0.249171i	$-0.919842\pi$
$229$	−8.39720	+	10.0074i	−0.554903	+	0.661307i	0.413557	+	0.910478i	$0.364286\pi$
$230$	1.95568	−	0.711808i	0.128953	−	0.0469352i
$231$		0			0
$232$	−2.16452	−	12.2756i	−0.142108	−	0.805934i
$233$			18.9719i			1.24289i	0.783457	+	0.621446i	$0.213455\pi$
$233$			18.9719i			1.24289i	−0.783457	+	0.621446i	$0.786545\pi$
$234$		0			0
$235$	−12.6525			−0.825355
$236$	0.102004	+	0.0371266i	0.00663992	+	0.00241674i
$237$		0			0
$238$	−1.20115	−	12.0017i	−0.0778589	−	0.777958i
$239$	13.6545	−	16.2728i	0.883236	−	1.05260i	−0.115008	−	0.993365i	$-0.536689\pi$
$239$	13.6545	−	16.2728i	0.883236	−	1.05260i	0.998244	−	0.0592349i	$-0.0188661\pi$
$240$		0			0
$241$	−7.57437	−	9.02679i	−0.487908	−	0.581466i	0.464776	−	0.885428i	$-0.346135\pi$
$241$	−7.57437	−	9.02679i	−0.487908	−	0.581466i	−0.952684	+	0.303962i	$0.901690\pi$
$242$	−3.31104	−	1.91163i	−0.212842	−	0.122884i
$243$		0			0
$244$			0.129488i			0.00828962i
$245$	−9.77462	−	11.0753i	−0.624477	−	0.707573i
$246$		0			0
$247$	−6.15863	+	34.9274i	−0.391865	+	2.22237i
$248$	3.26990	+	2.74377i	0.207639	+	0.174230i
$249$		0			0
$250$	5.63700	−	15.4875i	0.356515	−	0.979517i
$251$	13.6923	+	23.7157i	0.864248	+	1.49692i	0.867792	+	0.496927i	$0.165538\pi$
$251$	13.6923	+	23.7157i	0.864248	+	1.49692i	−0.00354445	+	0.999994i	$0.501128\pi$
$252$		0			0
$253$	−1.29698	+	2.24643i	−0.0815404	+	0.141232i
$254$	−1.73465	−	2.06728i	−0.108842	−	0.129713i
$255$		0			0
$256$	−0.0725551	+	0.411480i	−0.00453469	+	0.0257175i
$257$	−12.2349	−	10.2663i	−0.763190	−	0.640392i	0.175765	−	0.984432i	$-0.443760\pi$
$257$	−12.2349	−	10.2663i	−0.763190	−	0.640392i	−0.938955	+	0.344040i	$0.888204\pi$
$258$		0			0
$259$	−14.2019	−	9.68236i	−0.882463	−	0.601633i
$260$	−0.211819	−	0.122294i	−0.0131365	−	0.00758434i
$261$		0			0
$262$		−	12.2606i		−	0.757463i
$263$	−28.4125	+	5.00989i	−1.75199	+	0.308923i	−0.955338	−	0.295514i	$-0.904509\pi$
$263$	−28.4125	+	5.00989i	−1.75199	+	0.308923i	−0.796653	+	0.604437i	$0.793398\pi$
$264$		0			0
$265$	1.83900	+	0.324266i	0.112969	+	0.0199195i
$266$	11.5859	+	16.1145i	0.710378	+	0.988043i
$267$		0			0
$268$	0.0318030	+	0.180364i	0.00194268	+	0.0110175i
$269$	4.08105	−	7.06859i	0.248826	−	0.430979i	−0.714374	−	0.699764i	$-0.753289\pi$
$269$	4.08105	−	7.06859i	0.248826	−	0.430979i	0.963200	+	0.268784i	$0.0866219\pi$
$270$		0			0
$271$	10.1461	−	5.85783i	0.616329	−	0.355838i	−0.159109	−	0.987261i	$-0.550862\pi$
$271$	10.1461	−	5.85783i	0.616329	−	0.355838i	0.775438	+	0.631423i	$0.217529\pi$
$272$	−12.0631	−	4.39061i	−0.731432	−	0.266220i
$273$		0			0
$274$	7.52564	+	6.31476i	0.454640	+	0.381488i
$275$	0.692649	+	1.90304i	0.0417683	+	0.114757i
$276$		0			0
$277$	−1.65265	−	9.37262i	−0.0992979	−	0.563146i	−0.993345	−	0.115174i	$-0.963257\pi$
$277$	−1.65265	−	9.37262i	−0.0992979	−	0.563146i	0.894047	−	0.447972i	$-0.147854\pi$
$278$	−7.40592	+	12.8274i	−0.444178	+	0.769339i
$279$		0			0
$280$	−15.2668	+	4.29568i	−0.912367	+	0.256716i
$281$	−20.5328	+	3.62048i	−1.22488	+	0.215980i	−0.748426	−	0.663218i	$-0.769190\pi$
$281$	−20.5328	+	3.62048i	−1.22488	+	0.215980i	−0.476457	+	0.879198i	$0.658079\pi$
$282$		0			0
$283$	1.45014	+	0.255698i	0.0862017	+	0.0151997i	0.216583	−	0.976264i	$-0.430509\pi$
$283$	1.45014	+	0.255698i	0.0862017	+	0.0151997i	−0.130381	+	0.991464i	$0.541620\pi$
$284$	−0.0758787	−	0.0133795i	−0.00450258	−	0.000793925i
$285$		0			0
$286$	−34.1863	+	6.02796i	−2.02148	+	0.356441i
$287$	28.6080	+	7.28400i	1.68868	+	0.429961i
$288$		0			0
$289$	3.25849	−	5.64387i	0.191676	−	0.331992i
$290$	−2.26413	−	12.8405i	−0.132954	−	0.754022i
$291$		0			0
$292$	0.0182301	+	0.0500867i	0.00106683	+	0.00293110i
$293$	−4.11874	−	3.45603i	−0.240619	−	0.201904i	0.514501	−	0.857490i	$-0.327977\pi$
$293$	−4.11874	−	3.45603i	−0.240619	−	0.201904i	−0.755120	+	0.655586i	$0.772422\pi$
$294$		0			0
$295$	12.3633	+	4.49987i	0.719818	+	0.261992i
$296$	−15.9819	+	9.22716i	−0.928930	+	0.536318i
$297$		0			0
$298$	7.83400	−	13.5689i	0.453811	−	0.786024i
$299$	0.809676	+	4.59190i	0.0468248	+	0.265557i
$300$		0			0
$301$	8.09104	−	17.9323i	0.466360	−	1.03360i
$302$	28.0016	+	4.93743i	1.61131	+	0.284117i
$303$		0			0
$304$	20.8024	−	3.66803i	1.19310	−	0.210376i
$305$			15.6944i			0.898658i
$306$		0			0
$307$	−6.76941	−	3.90832i	−0.386351	−	0.223060i	0.294227	−	0.955736i	$-0.404938\pi$
$307$	−6.76941	−	3.90832i	−0.386351	−	0.223060i	−0.680578	+	0.732676i	$0.738271\pi$
$308$	0.0960984	−	0.140955i	0.00547571	−	0.00803167i
$309$		0			0
$310$	3.42038	+	2.87004i	0.194265	+	0.163007i
$311$	−2.15372	+	12.2144i	−0.122126	+	0.692612i	0.860847	+	0.508864i	$0.169934\pi$
$311$	−2.15372	+	12.2144i	−0.122126	+	0.692612i	−0.982973	+	0.183749i	$0.941177\pi$
$312$		0			0
$313$	−4.55606	−	5.42970i	−0.257524	−	0.306905i	0.621756	−	0.783211i	$-0.286420\pi$
$313$	−4.55606	−	5.42970i	−0.257524	−	0.306905i	−0.879279	+	0.476307i	$0.841975\pi$
$314$	−3.44439	+	5.96587i	−0.194378	+	0.336673i
$315$		0			0
$316$	0.0828727	+	0.143540i	0.00466196	+	0.00807475i
$317$	5.78906	−	15.9053i	0.325146	−	0.893332i	−0.664175	−	0.747578i	$-0.731217\pi$
$317$	5.78906	−	15.9053i	0.325146	−	0.893332i	0.989321	−	0.145754i	$-0.0465610\pi$
$318$		0			0
$319$	12.4491	+	10.4460i	0.697015	+	0.584865i
$320$	−2.95660	+	16.7677i	−0.165279	+	0.937345i
$321$		0			0
$322$	2.15594	+	1.46984i	0.120146	+	0.0819111i
$323$		−	17.2495i		−	0.959788i
$324$		0			0
$325$	3.15261	+	1.82016i	0.174875	+	0.100964i
$326$	−8.48274	−	10.1093i	−0.469815	−	0.559904i
$327$		0			0
$328$	20.3730	−	24.2797i	1.12491	−	1.34062i
$329$	−9.26022	−	12.8798i	−0.510533	−	0.710084i
$330$		0			0
$331$	−13.5894	−	4.94613i	−0.746940	−	0.271864i	−0.0596225	−	0.998221i	$-0.518990\pi$
$331$	−13.5894	−	4.94613i	−0.746940	−	0.271864i	−0.687318	+	0.726357i	$0.741212\pi$
$332$	0.211921			0.0116306
$333$		0			0
$334$			12.1277i			0.663599i
$335$	3.85463	+	21.8607i	0.210601	+	1.19438i
$336$		0			0
$337$	−14.9144	+	5.42839i	−0.812438	+	0.295703i	−0.714630	−	0.699502i	$-0.753405\pi$
$337$	−14.9144	+	5.42839i	−0.812438	+	0.295703i	−0.0978073	+	0.995205i	$0.531183\pi$
$338$	−28.3434	+	33.7784i	−1.54168	+	1.83730i
$339$		0			0
$340$	0.111785	+	0.0406863i	0.00606238	+	0.00220653i
$341$	−5.56510			−0.301367
$342$		0			0
$343$	4.12028	−	18.0561i	0.222474	−	0.974939i
$344$	−13.5770	−	16.1804i	−0.732023	−	0.872391i
$345$		0			0
$346$	−7.66921	+	9.13981i	−0.412299	+	0.491359i
$347$	−1.75821	−	4.83065i	−0.0943858	−	0.259323i	0.883511	−	0.468410i	$-0.155173\pi$
$347$	−1.75821	−	4.83065i	−0.0943858	−	0.259323i	−0.977897	+	0.209087i	$0.932951\pi$
$348$		0			0
$349$	−3.81124	+	10.4713i	−0.204011	+	0.560516i	−0.998932	−	0.0461967i	$-0.985290\pi$
$349$	−3.81124	+	10.4713i	−0.204011	+	0.560516i	0.794921	+	0.606713i	$0.207512\pi$
$350$	1.96101	−	0.551775i	0.104820	−	0.0294936i
$351$		0			0
$352$	−0.182371	−	0.315875i	−0.00972038	−	0.0168362i
$353$	−2.35970	+	1.98003i	−0.125594	+	0.105386i	−0.703421	−	0.710773i	$-0.748345\pi$
$353$	−2.35970	+	1.98003i	−0.125594	+	0.105386i	0.577827	+	0.816159i	$0.303901\pi$
$354$		0			0
$355$	−9.19676	−	1.62164i	−0.488113	−	0.0860676i
$356$	−0.0131768	+	0.0747292i	−0.000698368	+	0.00396064i
$357$		0			0
$358$	5.21599	−	4.37674i	0.275674	−	0.231318i
$359$	−18.9719	−	10.9534i	−1.00130	−	0.578099i	−0.0926653	−	0.995697i	$-0.529539\pi$
$359$	−18.9719	−	10.9534i	−1.00130	−	0.578099i	−0.908632	+	0.417598i	$0.862872\pi$
$360$		0			0
$361$	4.69176	+	8.12637i	0.246935	+	0.427704i
$362$	4.92303	−	4.13091i	0.258749	−	0.217116i
$363$		0			0
$364$	−0.0305378	−	0.305130i	−0.00160062	−	0.0159932i
$365$	2.20955	+	6.07068i	0.115653	+	0.317754i
$366$		0			0
$367$	2.26195	−	6.21467i	0.118073	−	0.324403i	−0.866551	−	0.499088i	$-0.833668\pi$
$367$	2.26195	−	6.21467i	0.118073	−	0.324403i	0.984624	+	0.174685i	$0.0558907\pi$
$368$	2.40503	−	1.38854i	0.125371	−	0.0723829i
$369$		0			0
$370$	−16.7174	+	9.65179i	−0.869096	+	0.501773i
$371$	1.01586	+	2.10937i	0.0527408	+	0.109513i
$372$		0			0
$373$	−23.1460	+	8.42445i	−1.19845	+	0.436201i	−0.862684	−	0.505743i	$-0.831218\pi$
$373$	−23.1460	+	8.42445i	−1.19845	+	0.436201i	−0.335769	+	0.941944i	$0.608996\pi$
$374$	15.8653	−	5.77449i	0.820375	−	0.298592i
$375$		0			0
$376$	−16.7727	+	2.95748i	−0.864986	+	0.152520i
$377$	29.2121			1.50450
$378$		0			0
$379$	2.06704			0.106176			0.0530882	−	0.998590i	$-0.483094\pi$
$379$	2.06704			0.106176			0.0530882	+	0.998590i	$0.483094\pi$
$380$	−0.192769	+	0.0339905i	−0.00988887	+	0.00174367i
$381$		0			0
$382$	13.6836	−	4.98041i	0.700112	−	0.254820i
$383$	−6.49822	+	2.36516i	−0.332044	+	0.120854i	−0.502662	−	0.864483i	$-0.667646\pi$
$383$	−6.49822	+	2.36516i	−0.332044	+	0.120854i	0.170618	+	0.985337i	$0.445424\pi$
$384$		0			0
$385$	11.6475	−	17.0843i	0.593609	−	0.870695i
$386$	−12.6881	+	7.32550i	−0.645810	+	0.372858i
$387$		0			0
$388$	0.105012	−	0.0606288i	0.00533118	−	0.00307796i
$389$	4.62127	−	12.6968i	0.234308	−	0.643755i	−0.765692	−	0.643207i	$-0.777603\pi$
$389$	4.62127	−	12.6968i	0.234308	−	0.643755i	1.00000		0.000547677i	$-0.000174331\pi$
$390$		0			0
$391$	−0.775631	−	2.13103i	−0.0392254	−	0.107771i
$392$	−15.5465	−	12.3971i	−0.785217	−	0.626149i
$393$		0			0
$394$	−15.2940	+	12.8332i	−0.770501	+	0.646527i
$395$	10.0445	+	17.3975i	0.505392	+	0.875364i
$396$		0			0
$397$	18.6484	+	10.7666i	0.935934	+	0.540362i	0.888683	−	0.458521i	$-0.151621\pi$
$397$	18.6484	+	10.7666i	0.935934	+	0.540362i	0.0472507	+	0.998883i	$0.484954\pi$
$398$	21.6994	−	18.2079i	1.08769	−	0.912681i
$399$		0			0
$400$	0.376494	−	2.13521i	0.0188247	−	0.106760i
$401$	−26.0547	−	4.59414i	−1.30111	−	0.229420i	−0.520188	−	0.854052i	$-0.674138\pi$
$401$	−26.0547	−	4.59414i	−1.30111	−	0.229420i	−0.780920	+	0.624631i	$0.785249\pi$
$402$		0			0
$403$	−7.66311	+	6.43011i	−0.381727	+	0.320307i
$404$	0.0323677	+	0.0560625i	0.00161035	+	0.00278921i
$405$		0			0
$406$	11.4141	−	11.7027i	0.566473	−	0.580794i
$407$	8.22890	−	22.6087i	0.407891	−	1.12067i
$408$		0			0
$409$	−8.57817	−	23.5683i	−0.424163	−	1.16538i	−0.949303	−	0.314362i	$-0.898209\pi$
$409$	−8.57817	−	23.5683i	−0.424163	−	1.16538i	0.525140	−	0.851016i	$-0.324013\pi$
$410$	21.3106	−	25.3970i	1.05246	−	1.25427i
$411$		0			0
$412$	0.0694568	+	0.0827754i	0.00342189	+	0.00407805i
$413$	4.46788	+	15.8788i	0.219850	+	0.781345i
$414$		0			0
$415$	25.6855			1.26085
$416$	−0.616097	−	0.224241i	−0.0302066	−	0.0109943i
$417$		0			0
$418$	−17.8575	+	21.2817i	−0.873437	+	1.04092i
$419$	22.3814	−	8.14616i	1.09340	−	0.397966i	0.268522	−	0.963273i	$-0.413465\pi$
$419$	22.3814	−	8.14616i	1.09340	−	0.397966i	0.824880	+	0.565307i	$0.191242\pi$
$420$		0			0
$421$	−1.34235	−	7.61285i	−0.0654222	−	0.371027i	−0.999888	−	0.0149744i	$-0.995233\pi$
$421$	−1.34235	−	7.61285i	−0.0654222	−	0.371027i	0.934466	−	0.356053i	$-0.115878\pi$
$422$		−	4.72559i		−	0.230038i
$423$		0			0
$424$	2.51366			0.122074
$425$	−1.66375	−	0.605555i	−0.0807037	−	0.0293737i
$426$		0			0
$427$	−15.9763	+	11.4866i	−0.773149	+	0.555875i
$428$	0.0319789	−	0.0381110i	0.00154576	−	0.00184216i
$429$		0			0
$430$	−14.2018	−	16.9251i	−0.684872	−	0.816199i
$431$	4.73254	+	2.73233i	0.227959	+	0.131612i	0.609630	−	0.792686i	$-0.291318\pi$
$431$	4.73254	+	2.73233i	0.227959	+	0.131612i	−0.381671	+	0.924298i	$0.624651\pi$
$432$		0			0
$433$			35.5423i			1.70805i	0.520229	+	0.854027i	$0.325846\pi$
$433$			35.5423i			1.70805i	−0.520229	+	0.854027i	$0.674154\pi$
$434$	−0.418253	+	5.58239i	−0.0200768	+	0.267963i
$435$		0			0
$436$	−0.0170331	+	0.0965996i	−0.000815738	+	0.00462628i
$437$	2.85856	+	2.39862i	0.136744	+	0.114741i
$438$		0			0
$439$	−1.38811	+	3.81379i	−0.0662506	+	0.182022i	−0.968400	−	0.249401i	$-0.919766\pi$
$439$	−1.38811	+	3.81379i	−0.0662506	+	0.182022i	0.902150	+	0.431423i	$0.141988\pi$
$440$	−11.0999	−	19.2255i	−0.529165	−	0.916541i
$441$		0			0
$442$	15.1744	−	26.2828i	0.721771	−	1.25014i
$443$	−5.32766	−	6.34926i	−0.253125	−	0.301662i	0.624486	−	0.781036i	$-0.285308\pi$
$443$	−5.32766	−	6.34926i	−0.253125	−	0.301662i	−0.877611	+	0.479373i	$0.840864\pi$
$444$		0			0
$445$	−1.59707	+	9.05744i	−0.0757084	+	0.429364i
$446$	−10.8250	−	9.08327i	−0.512579	−	0.430105i
$447$		0			0
$448$	−19.2329	+	9.26244i	−0.908668	+	0.437609i
$449$	−25.1276	−	14.5074i	−1.18585	−	0.684648i	−0.228486	−	0.973547i	$-0.573377\pi$
$449$	−25.1276	−	14.5074i	−1.18585	−	0.684648i	−0.957359	+	0.288899i	$0.906711\pi$
$450$		0			0
$451$			41.3219i			1.94577i
$452$	0.157458	−	0.0277641i	0.00740619	−	0.00130591i
$453$		0			0
$454$	24.6115	+	4.33968i	1.15508	+	0.203671i
$455$	−3.70129	−	36.9828i	−0.173519	−	1.73378i
$456$		0			0
$457$	−1.13908	−	6.46004i	−0.0532839	−	0.302188i	0.946506	−	0.322686i	$-0.104586\pi$
$457$	−1.13908	−	6.46004i	−0.0532839	−	0.302188i	−0.999790	+	0.0204982i	$0.993475\pi$
$458$	−9.19715	+	15.9299i	−0.429755	+	0.744357i
$459$		0			0
$460$	−0.0222866	+	0.0128672i	−0.00103912	+	0.000599936i
$461$	−20.7893	−	7.56669i	−0.968255	−	0.352416i	−0.190992	−	0.981592i	$-0.561170\pi$
$461$	−20.7893	−	7.56669i	−0.968255	−	0.352416i	−0.777263	+	0.629176i	$0.783393\pi$
$462$		0			0
$463$	12.6417	+	10.6077i	0.587511	+	0.492980i	0.887404	−	0.460993i	$-0.152507\pi$
$463$	12.6417	+	10.6077i	0.587511	+	0.492980i	−0.299893	+	0.953973i	$0.596951\pi$
$464$	−5.95062	−	16.3492i	−0.276251	−	0.758992i
$465$		0			0
$466$	4.63872	+	26.3075i	0.214884	+	1.21867i
$467$	−0.713130	+	1.23518i	−0.0329997	+	0.0571572i	−0.882054	−	0.471149i	$-0.843839\pi$
$467$	−0.713130	+	1.23518i	−0.0329997	+	0.0571572i	0.849054	+	0.528306i	$0.177173\pi$
$468$		0			0
$469$	−19.4322	+	19.9235i	−0.897298	+	0.919983i
$470$	−17.5446	+	3.09358i	−0.809271	+	0.142696i
$471$		0			0
$472$	17.4412	+	3.07535i	0.802796	+	0.141555i
$473$	27.1194	+	4.78188i	1.24695	+	0.219871i
$474$		0			0
$475$	2.86909	−	0.505897i	0.131643	−	0.0232122i
$476$	0.0403971	+	0.143571i	0.00185160	+	0.00658056i
$477$		0			0
$478$	14.9553	−	25.9033i	0.684038	−	1.18479i
$479$	−4.17371	−	23.6703i	−0.190702	−	1.08152i	−0.918408	−	0.395635i	$-0.870525\pi$
$479$	−4.17371	−	23.6703i	−0.190702	−	1.08152i	0.727706	−	0.685889i	$-0.240586\pi$
$480$		0			0
$481$	−14.7918	−	40.6400i	−0.674446	−	1.85303i
$482$	−12.7101	−	10.6651i	−0.578930	−	0.485780i
$483$		0			0
$484$	0.0444246	+	0.0161692i	0.00201930	+	0.000734965i
$485$	12.7278	−	7.34842i	0.577941	−	0.333674i
$486$		0			0
$487$	17.7620	−	30.7647i	0.804874	−	1.39408i	−0.111501	−	0.993764i	$-0.535566\pi$
$487$	17.7620	−	30.7647i	0.804874	−	1.39408i	0.916376	−	0.400319i	$-0.131101\pi$
$488$	3.66852	+	20.8052i	0.166066	+	0.941808i
$489$		0			0
$490$	−16.2620	−	12.9676i	−0.734640	−	0.585818i
$491$	30.5498	+	5.38675i	1.37869	+	0.243101i	0.813360	−	0.581761i	$-0.197636\pi$
$491$	30.5498	+	5.38675i	1.37869	+	0.243101i	0.565334	+	0.824862i	$0.308747\pi$
$492$		0			0
$493$	−13.9919	+	2.46714i	−0.630162	+	0.111115i
$494$			49.9379i			2.24681i
$495$		0			0
$496$	5.15977	+	2.97899i	0.231681	+	0.133761i
$497$	−5.08026	−	10.5488i	−0.227881	−	0.473180i
$498$		0			0
$499$	27.8976	+	23.4088i	1.24887	+	1.04792i	0.996777	+	0.0802188i	$0.0255619\pi$
$499$	27.8976	+	23.4088i	1.24887	+	1.04792i	0.252089	+	0.967704i	$0.418883\pi$
$500$	−0.0353891	+	0.200701i	−0.00158265	+	0.00897564i
$501$		0			0
$502$	24.7850	+	29.5376i	1.10621	+	1.31833i
$503$	−9.30116	+	16.1101i	−0.414718	+	0.718313i	−0.995399	−	0.0958185i	$-0.969453\pi$
$503$	−9.30116	+	16.1101i	−0.414718	+	0.718313i	0.580681	+	0.814131i	$0.302787\pi$
$504$		0			0
$505$	3.92308	+	6.79497i	0.174575	+	0.302372i
$506$	−1.24920	+	3.43214i	−0.0555336	+	0.152577i
$507$		0			0
$508$	0.0255624	+	0.0214494i	0.00113415	+	0.000951665i
$509$	−0.776316	+	4.40271i	−0.0344096	+	0.195147i	−0.997167	−	0.0752205i	$-0.976034\pi$
$509$	−0.776316	+	4.40271i	−0.0344096	+	0.195147i	0.962757	+	0.270367i	$0.0871450\pi$
$510$		0			0
$511$	−4.56259	+	6.69232i	−0.201837	+	0.296051i
$512$			22.9158i			1.01274i
$513$		0			0
$514$	−19.4757	−	11.2443i	−0.859034	−	0.495964i
$515$	8.41841	+	10.0327i	0.370959	+	0.442092i
$516$		0			0
$517$	14.2729	−	17.0097i	0.627719	−	0.748087i
$518$	−22.0605	−	9.95365i	−0.969283	−	0.437338i
$519$		0			0
$520$	−37.4983	−	13.6483i	−1.64441	−	0.598516i
$521$	34.6679			1.51883			0.759415	−	0.650607i	$-0.225485\pi$
$521$	34.6679			1.51883			0.759415	+	0.650607i	$0.225485\pi$
$522$		0			0
$523$			25.7209i			1.12470i	0.826901	+	0.562348i	$0.190102\pi$
$523$			25.7209i			1.12470i	−0.826901	+	0.562348i	$0.809898\pi$
$524$	0.0263260	+	0.149302i	0.00115006	+	0.00652231i
$525$		0			0
$526$	−38.1734	+	13.8940i	−1.66444	+	0.605806i
$527$	3.12738	−	3.72707i	0.136231	−	0.162354i
$528$		0			0
$529$	−21.1519	−	7.69867i	−0.919649	−	0.334725i
$530$	2.62934			0.114211
$531$		0			0
$532$	−0.175687	−	0.171355i	−0.00761702	−	0.00742919i
$533$	47.7448	+	56.9001i	2.06806	+	2.46462i
$534$		0			0
$535$	3.87595	−	4.61918i	0.167572	−	0.199704i
$536$	10.2198	+	28.0786i	0.441426	+	1.21281i
$537$		0			0
$538$	3.93070	−	10.7995i	0.169465	−	0.465600i
$539$	25.9158	−	0.647128i	1.11627	−	0.0278738i
$540$		0			0
$541$	13.1658	+	22.8039i	0.566044	+	0.980416i	0.996952	+	0.0780204i	$0.0248599\pi$
$541$	13.1658	+	22.8039i	0.566044	+	0.980416i	−0.430908	+	0.902396i	$0.641807\pi$
$542$	12.6368	−	10.6035i	0.542797	−	0.455461i
$543$		0			0
$544$	0.314034	+	0.0553727i	0.0134641	+	0.00237408i
$545$	−2.06447	+	11.7082i	−0.0884323	+	0.501524i
$546$		0			0
$547$	13.7395	−	11.5288i	0.587459	−	0.492937i	−0.299928	−	0.953962i	$-0.596963\pi$
$547$	13.7395	−	11.5288i	0.587459	−	0.492937i	0.887387	+	0.461025i	$0.152518\pi$
$548$	−0.105202	−	0.0607383i	−0.00449400	−	0.00259461i
$549$		0			0
$550$	1.42576	+	2.46950i	0.0607948	+	0.105300i
$551$	17.9089	−	15.0273i	0.762944	−	0.640186i
$552$		0			0
$553$	−10.3586	+	22.9580i	−0.440492	+	0.976273i
$554$	−4.58329	−	12.5925i	−0.194725	−	0.535004i
$555$		0			0
$556$	0.0626418	−	0.172107i	0.00265660	−	0.00729896i
$557$	−0.993267	+	0.573463i	−0.0420861	+	0.0242984i	−0.520895	−	0.853621i	$-0.674402\pi$
$557$	−0.993267	+	0.573463i	−0.0420861	+	0.0242984i	0.478809	+	0.877919i	$0.341069\pi$
$558$		0			0
$559$	42.8684	−	24.7501i	1.81314	−	1.04682i
$560$	−19.9443	+	9.60507i	−0.842801	+	0.405888i
$561$		0			0
$562$	−27.5866	+	10.0407i	−1.16367	+	0.423542i
$563$	8.48848	−	3.08955i	0.357747	−	0.130209i	−0.156893	−	0.987616i	$-0.550148\pi$
$563$	8.48848	−	3.08955i	0.357747	−	0.130209i	0.514640	+	0.857406i	$0.327926\pi$
$564$		0			0
$565$	19.0844	−	3.36510i	0.802888	−	0.141571i
$566$	2.07336			0.0871497
$567$		0			0
$568$	−12.5707			−0.527455
$569$	42.2332	−	7.44685i	1.77051	−	0.312188i	0.809172	−	0.587572i	$-0.199916\pi$
$569$	42.2332	−	7.44685i	1.77051	−	0.312188i	0.961334	+	0.275384i	$0.0888049\pi$
$570$		0			0
$571$	31.1144	−	11.3247i	1.30210	−	0.473925i	0.404419	−	0.914574i	$-0.367474\pi$
$571$	31.1144	−	11.3247i	1.30210	−	0.473925i	0.897680	+	0.440648i	$0.145251\pi$
$572$	0.403356	−	0.146810i	0.0168652	−	0.00613842i
$573$		0			0
$574$	41.4503	+	3.10561i	1.73010	+	0.129625i
$575$	0.331703	−	0.191509i	0.0138330	−	0.00798648i
$576$		0			0
$577$	36.2292	−	20.9170i	1.50824	−	0.870784i	0.508289	−	0.861187i	$-0.330278\pi$
$577$	36.2292	−	20.9170i	1.50824	−	0.870784i	0.999954	−	0.00959765i	$-0.00305507\pi$
$578$	3.13844	−	8.62281i	0.130542	−	0.358661i
$579$		0			0
$580$	0.0551425	+	0.151503i	0.00228967	+	0.00629081i
$581$	18.7990	+	26.1469i	0.779913	+	1.08476i
$582$		0			0
$583$	−2.51046	+	2.10653i	−0.103973	+	0.0872434i
$584$	4.34808	+	7.53110i	0.179925	+	0.311639i
$585$		0			0
$586$	−6.55628	−	3.78527i	−0.270838	−	0.156368i
$587$	10.1800	−	8.54200i	0.420172	−	0.352566i	−0.408057	−	0.912957i	$-0.633793\pi$
$587$	10.1800	−	8.54200i	0.420172	−	0.352566i	0.828228	+	0.560391i	$0.189349\pi$
$588$		0			0
$589$	−1.39019	+	7.88415i	−0.0572817	+	0.324861i
$590$	18.2438	+	3.21688i	0.751087	+	0.132437i
$591$		0			0
$592$	−19.7320	+	16.5571i	−0.810980	+	0.680493i
$593$	6.07625	+	10.5244i	0.249522	+	0.432184i	0.963393	−	0.268093i	$-0.0863933\pi$
$593$	6.07625	+	10.5244i	0.249522	+	0.432184i	−0.713872	+	0.700277i	$0.753060\pi$
$594$		0			0
$595$	4.89626	+	17.4013i	0.200727	+	0.713383i
$596$	−0.0662626	+	0.182055i	−0.00271422	+	0.00745726i
$597$		0			0
$598$	2.24548	+	6.16941i	0.0918245	+	0.252286i
$599$	−19.6946	+	23.4711i	−0.804700	+	0.959004i	−0.999763	−	0.0217865i	$-0.993065\pi$
$599$	−19.6946	+	23.4711i	−0.804700	+	0.959004i	0.195062	+	0.980791i	$0.437509\pi$
$600$		0			0
$601$	−0.739101	−	0.880827i	−0.0301486	−	0.0359297i	0.750759	−	0.660576i	$-0.229688\pi$
$601$	−0.739101	−	0.880827i	−0.0301486	−	0.0359297i	−0.780908	+	0.624646i	$0.785243\pi$
$602$	6.83493	−	26.8442i	0.278571	−	1.09409i
$603$		0			0
$604$	−0.351588			−0.0143059
$605$	5.38441	+	1.95976i	0.218907	+	0.0796758i
$606$		0			0
$607$	1.93858	−	2.31031i	0.0786845	−	0.0937725i	−0.725266	−	0.688469i	$-0.758283\pi$
$607$	1.93858	−	2.31031i	0.0786845	−	0.0937725i	0.803950	+	0.594696i	$0.202728\pi$
$608$	−0.493061	+	0.179460i	−0.0199963	+	0.00727805i
$609$		0			0
$610$	3.83735	+	21.7627i	0.155370	+	0.881145i
$611$		−	39.9137i		−	1.61473i
$612$		0			0
$613$	−40.0911			−1.61927			−0.809633	−	0.586937i	$-0.800334\pi$
$613$	−40.0911			−1.61927			−0.809633	+	0.586937i	$0.800334\pi$
$614$	−10.3424	−	3.76433i	−0.417386	−	0.151916i
$615$		0			0
$616$	11.4470	−	25.3703i	0.461213	−	1.02220i
$617$	−6.57249	+	7.83278i	−0.264598	+	0.315336i	−0.881942	−	0.471357i	$-0.843764\pi$
$617$	−6.57249	+	7.83278i	−0.264598	+	0.315336i	0.617344	+	0.786693i	$0.288209\pi$
$618$		0			0
$619$	25.0122	+	29.8084i	1.00533	+	1.19810i	0.980117	+	0.198419i	$0.0635805\pi$
$619$	25.0122	+	29.8084i	1.00533	+	1.19810i	0.0252085	+	0.999682i	$0.491975\pi$
$620$	−0.0478139	−	0.0276054i	−0.00192025	−	0.00110866i
$621$		0			0
$622$			17.4637i			0.700229i
$623$	−10.3890	+	5.00330i	−0.416228	+	0.200453i
$624$		0			0
$625$	−3.81449	+	21.6331i	−0.152580	+	0.865322i
$626$	−7.64526	−	6.41513i	−0.305566	−	0.256400i
$627$		0			0
$628$	0.0291338	−	0.0800445i	0.00116257	−	0.00319412i
$629$	10.5172	+	18.2163i	0.419349	+	0.726333i
$630$		0			0
$631$	5.94429	−	10.2958i	0.236639	−	0.409870i	−0.723109	−	0.690734i	$-0.757288\pi$
$631$	5.94429	−	10.2958i	0.236639	−	0.409870i	0.959748	+	0.280864i	$0.0906210\pi$
$632$	17.3820	+	20.7151i	0.691420	+	0.824002i
$633$		0			0
$634$	4.13850	−	23.4706i	0.164361	−	0.932137i
$635$	3.09825	+	2.59974i	0.122950	+	0.103168i
$636$		0			0
$637$	34.9383	−	30.8352i	1.38430	−	1.22173i
$638$	19.8167	+	11.4412i	0.784550	+	0.452960i
$639$		0			0
$640$			23.5583i			0.931222i
$641$	−49.2008	+	8.67542i	−1.94331	+	0.342659i	−0.943373	+	0.331734i	$0.892366\pi$
$641$	−49.2008	+	8.67542i	−1.94331	+	0.342659i	−0.999940	+	0.0109243i	$0.996523\pi$
$642$		0			0
$643$	7.32572	+	1.29172i	0.288898	+	0.0509406i	0.316219	−	0.948686i	$-0.397586\pi$
$643$	7.32572	+	1.29172i	0.288898	+	0.0509406i	−0.0273209	+	0.999627i	$0.508698\pi$
$644$	−0.0294098	−	0.0132696i	−0.00115891	−	0.000522896i
$645$		0			0
$646$	−4.21758	−	23.9191i	−0.165938	−	0.941083i
$647$	−9.06934	+	15.7086i	−0.356553	+	0.617567i	−0.987382	−	0.158354i	$-0.949381\pi$
$647$	−9.06934	+	15.7086i	−0.356553	+	0.617567i	0.630830	+	0.775921i	$0.282715\pi$
$648$		0			0
$649$	−19.9962	+	11.5448i	−0.784919	+	0.453173i
$650$	4.81662	+	1.75310i	0.188923	+	0.0687624i
$651$		0			0
$652$	0.125004	+	0.104891i	0.00489555	+	0.00410786i
$653$	7.59970	+	20.8800i	0.297399	+	0.817097i	0.994933	+	0.100545i	$0.0320587\pi$
$653$	7.59970	+	20.8800i	0.297399	+	0.817097i	−0.697533	+	0.716552i	$0.745719\pi$
$654$		0			0
$655$	3.19081	+	18.0960i	0.124675	+	0.707068i
$656$	22.1196	−	38.3123i	0.863625	−	1.49584i
$657$		0			0
$658$	−15.9899	−	15.5956i	−0.623350	−	0.607979i
$659$	−21.2896	+	3.75393i	−0.829324	+	0.146232i	−0.572167	−	0.820137i	$-0.693897\pi$
$659$	−21.2896	+	3.75393i	−0.829324	+	0.146232i	−0.257157	+	0.966370i	$0.582786\pi$
$660$		0			0
$661$	4.72263	+	0.832727i	0.183689	+	0.0323893i	0.264736	−	0.964321i	$-0.414715\pi$
$661$	4.72263	+	0.832727i	0.183689	+	0.0323893i	−0.0810468	+	0.996710i	$0.525826\pi$
$662$	−20.0531	−	3.53590i	−0.779386	−	0.137427i
$663$		0			0
$664$	34.0499	−	6.00391i	1.32139	−	0.232997i
$665$	−21.2939	−	20.7688i	−0.825743	−	0.805381i
$666$		0			0
$667$	1.53678	−	2.66178i	0.0595043	−	0.103065i
$668$	−0.0260407	−	0.147684i	−0.00100754	−	0.00571407i
$669$		0			0
$670$	10.6901	+	29.3707i	0.412993	+	1.13469i
$671$	−21.0992	−	17.7044i	−0.814527	−	0.683469i
$672$		0			0
$673$	−41.8330	−	15.2260i	−1.61255	−	0.586918i	−0.630604	−	0.776105i	$-0.717193\pi$
$673$	−41.8330	−	15.2260i	−1.61255	−	0.586918i	−0.981941	+	0.189186i	$0.939415\pi$
$674$	−19.3538	+	11.1739i	−0.745480	+	0.430403i
$675$		0			0
$676$	0.272620	−	0.472192i	0.0104854	−	0.0181612i
$677$	6.96679	+	39.5107i	0.267756	+	1.51852i	0.761072	+	0.648668i	$0.224673\pi$
$677$	6.96679	+	39.5107i	0.267756	+	1.51852i	−0.493316	+	0.869850i	$0.664215\pi$
$678$		0			0
$679$	16.7958	+	7.57824i	0.644564	+	0.290826i
$680$	19.1135	+	3.37022i	0.732968	+	0.129242i
$681$		0			0
$682$	−7.71686	+	1.36069i	−0.295494	+	0.0521035i
$683$		−	33.0102i		−	1.26310i	−0.775335	−	0.631550i	$-0.782419\pi$
$683$		−	33.0102i		−	1.26310i	0.775335	−	0.631550i	$-0.217581\pi$
$684$		0			0
$685$	−12.7508	−	7.36168i	−0.487183	−	0.281275i
$686$	1.29860	−	26.0450i	0.0495808	−	0.994402i
$687$		0			0
$688$	−22.5844	−	18.9506i	−0.861023	−	0.722484i
$689$	−1.02293	+	5.80135i	−0.0389707	+	0.221014i
$690$		0			0
$691$	−1.88171	−	2.24253i	−0.0715836	−	0.0853100i	0.729064	−	0.684445i	$-0.239956\pi$
$691$	−1.88171	−	2.24253i	−0.0715836	−	0.0853100i	−0.800648	+	0.599135i	$0.795511\pi$
$692$	0.0737660	−	0.127766i	0.00280416	−	0.00485695i
$693$		0			0
$694$	−3.61915	−	6.26854i	−0.137381	−	0.237951i
$695$	7.59239	−	20.8599i	0.287996	−	0.791262i
$696$		0			0
$697$	−27.6742	−	23.2214i	−1.04823	−	0.879574i
$698$	−2.72459	+	15.4519i	−0.103127	+	0.584864i
$699$		0			0
$700$	−0.0226952	+	0.0109299i	−0.000857797	+	0.000413110i
$701$		−	6.39386i		−	0.241493i	−0.992683	−	0.120746i	$-0.961471\pi$
$701$		−	6.39386i		−	0.241493i	0.992683	−	0.120746i	$-0.0385288\pi$
$702$		0			0
$703$	−29.9744	−	17.3058i	−1.13051	−	0.652699i
$704$	−19.2070	−	22.8900i	−0.723890	−	0.862699i
$705$		0			0
$706$	−2.78796	+	3.32257i	−0.104926	+	0.125046i
$707$	−4.04577	+	8.96673i	−0.152157	+	0.337229i
$708$		0			0
$709$	33.6905	+	12.2623i	1.26527	+	0.460521i	0.885535	−	0.464573i	$-0.153792\pi$
$709$	33.6905	+	12.2623i	1.26527	+	0.460521i	0.379737	+	0.925094i	$0.376014\pi$
$710$	−13.1492			−0.493481
$711$		0			0
$712$			12.3803i			0.463970i
$713$	0.182768	+	1.03653i	0.00684472	+	0.0388184i
$714$		0			0
$715$	48.8882	−	17.7938i	1.82831	−	0.665452i
$716$	−0.0541195	+	0.0644971i	−0.00202254	+	0.00241037i
$717$		0			0
$718$	−28.9856	−	10.5499i	−1.08173	−	0.393718i
$719$	35.6795			1.33062			0.665311	−	0.746566i	$-0.268299\pi$
$719$	35.6795			1.33062			0.665311	+	0.746566i	$0.268299\pi$
$720$		0			0
$721$	−4.05154	+	15.9125i	−0.150887	+	0.592611i
$722$	8.49278	+	10.1213i	0.316069	+	0.376676i
$723$		0			0
$724$	−0.0510798	+	0.0608745i	−0.00189836	+	0.00226238i
$725$	−0.820714	−	2.25489i	−0.0304805	−	0.0837446i
$726$		0			0
$727$	0.773622	−	2.12551i	0.0286921	−	0.0788308i	−0.924520	−	0.381135i	$-0.875533\pi$
$727$	0.773622	−	2.12551i	0.0286921	−	0.0788308i	0.953212	+	0.302304i	$0.0977557\pi$
$728$	−13.5512	−	48.1610i	−0.502242	−	1.78497i
$729$		0			0
$730$	4.54818	+	7.87768i	0.168336	+	0.291566i
$731$	−18.4426	+	15.4752i	−0.682125	+	0.572371i
$732$		0			0
$733$	15.8797	+	2.80002i	0.586530	+	0.103421i	0.459035	−	0.888418i	$-0.348195\pi$
$733$	15.8797	+	2.80002i	0.586530	+	0.103421i	0.127495	+	0.991839i	$0.459306\pi$
$734$	1.61703	−	9.17065i	0.0596858	−	0.338495i
$735$		0			0
$736$	−0.0528441	+	0.0443414i	−0.00194786	+	0.00163445i
$737$	−33.7374	−	19.4783i	−1.24273	−	0.717492i
$738$		0			0
$739$	−12.2994	−	21.3033i	−0.452442	−	0.783653i	0.546095	−	0.837723i	$-0.316114\pi$
$739$	−12.2994	−	21.3033i	−0.452442	−	0.783653i	−0.998537	+	0.0540705i	$0.982780\pi$
$740$	0.182850	−	0.153429i	0.00672170	−	0.00564018i
$741$		0			0
$742$	1.92439	+	2.67658i	0.0706467	+	0.0982602i
$743$	−8.41237	−	23.1128i	−0.308620	−	0.847926i	−0.992926	−	0.118732i	$-0.962117\pi$
$743$	−8.41237	−	23.1128i	−0.308620	−	0.847926i	0.684307	−	0.729194i	$-0.260105\pi$
$744$		0			0
$745$	−8.03125	+	22.0657i	−0.294242	+	0.808424i
$746$	−30.0356	+	17.3411i	−1.09968	+	0.634902i
$747$		0			0
$748$	−0.180799	+	0.104384i	−0.00661066	+	0.00381667i
$749$	7.53893	+	0.564844i	0.275467	+	0.0206389i
$750$		0			0
$751$	34.3971	−	12.5195i	1.25517	−	0.456843i	0.373022	−	0.927822i	$-0.378322\pi$
$751$	34.3971	−	12.5195i	1.25517	−	0.456843i	0.882144	+	0.470979i	$0.156099\pi$
$752$	−22.3386	+	8.13059i	−0.814605	+	0.296492i
$753$		0			0
$754$	40.5070	−	7.14247i	1.47518	−	0.260114i
$755$	−42.6137			−1.55087
$756$		0			0
$757$	−38.6682			−1.40542			−0.702709	−	0.711477i	$-0.748027\pi$
$757$	−38.6682			−1.40542			−0.702709	+	0.711477i	$0.748027\pi$
$758$	2.86626	−	0.505399i	0.104107	−	0.0183569i
$759$		0			0
$760$	−30.0099	+	10.9227i	−1.08857	+	0.396208i
$761$	−45.3555	+	16.5080i	−1.64413	+	0.598416i	−0.987755	−	0.156015i	$-0.950135\pi$
$761$	−45.3555	+	16.5080i	−1.64413	+	0.598416i	−0.656380	+	0.754431i	$0.727913\pi$
$762$		0			0
$763$	−13.4295	+	6.46757i	−0.486181	+	0.234142i
$764$	−0.155936	+	0.0900299i	−0.00564158	+	0.00325717i
$765$		0			0
$766$	−8.43249	+	4.86850i	−0.304678	+	0.175906i
$767$	−14.1954	+	39.0014i	−0.512565	+	1.40826i
$768$		0			0
$769$	16.2750	+	44.7151i	0.586891	+	1.61247i	0.776155	+	0.630543i	$0.217168\pi$
$769$	16.2750	+	44.7151i	0.586891	+	1.61247i	−0.189264	+	0.981926i	$0.560610\pi$
$770$	11.9738	−	26.5378i	0.431506	−	0.956356i
$771$		0			0
$772$	0.138779	−	0.116450i	0.00499477	−	0.00419111i
$773$	−1.79467	−	3.10845i	−0.0645496	−	0.111803i	0.831944	−	0.554859i	$-0.187228\pi$
$773$	−1.79467	−	3.10845i	−0.0645496	−	0.111803i	−0.896494	+	0.443056i	$0.853894\pi$
$774$		0			0
$775$	0.711639	+	0.410865i	0.0255628	+	0.0147587i
$776$	15.1549	−	12.7165i	0.544031	−	0.456496i
$777$		0			0
$778$	3.30367	−	18.7360i	0.118442	−	0.671719i
$779$	58.5413	+	10.3224i	2.09746	+	0.369839i
$780$		0			0
$781$	12.5547	−	10.5346i	0.449242	−	0.376959i
$782$	−1.59658	−	2.76535i	−0.0570935	−	0.0988888i
$783$		0			0
$784$	−24.3747	−	13.2727i	−0.870525	−	0.474027i
$785$	3.53112	−	9.70167i	0.126031	−	0.346267i
$786$		0			0
$787$	10.6009	+	29.1257i	0.377881	+	1.03822i	0.972233	+	0.234014i	$0.0751863\pi$
$787$	10.6009	+	29.1257i	0.377881	+	1.03822i	−0.594352	+	0.804205i	$0.702591\pi$
$788$	0.158686	−	0.189114i	0.00565294	−	0.00673692i
$789$		0			0
$790$	18.1819	+	21.6684i	0.646885	+	0.770927i
$791$	17.3933	+	16.9644i	0.618434	+	0.603184i
$792$		0			0
$793$	−49.5098			−1.75814
$794$	28.4913	+	10.3700i	1.01112	+	0.368017i
$795$		0			0
$796$	−0.225146	+	0.268318i	−0.00798007	+	0.00951028i
$797$	18.1049	−	6.58966i	0.641310	−	0.233418i	−0.000836476	−	1.00000i	$-0.500266\pi$
$797$	18.1049	−	6.58966i	0.641310	−	0.233418i	0.642147	+	0.766582i	$0.278044\pi$
$798$		0			0
$799$	3.37096	+	19.1177i	0.119256	+	0.676335i
$800$			0.0538568i			0.00190413i
$801$		0			0
$802$	−37.2521			−1.31542
$803$	−10.6538	−	3.87768i	−0.375965	−	0.136840i
$804$		0			0
$805$	−3.56456	−	1.60832i	−0.125634	−	0.0566859i
$806$	−9.05389	+	10.7900i	−0.318910	+	0.380062i
$807$		0			0
$808$	6.78892	+	8.09072i	0.238833	+	0.284630i
$809$	−10.9220	−	6.30585i	−0.383999	−	0.221702i	0.295558	−	0.955325i	$-0.404494\pi$
$809$	−10.9220	−	6.30585i	−0.383999	−	0.221702i	−0.679557	+	0.733623i	$0.737828\pi$
$810$		0			0
$811$		−	43.6085i		−	1.53130i	−0.643256	−	0.765652i	$-0.722417\pi$
$811$		−	43.6085i		−	1.53130i	0.643256	−	0.765652i	$-0.277583\pi$
$812$	−0.113866	+	0.167017i	−0.00399592	+	0.00586114i
$813$		0			0
$814$	5.88270	−	33.3624i	0.206188	−	1.16935i
$815$	15.1510	+	12.7132i	0.530715	+	0.445323i
$816$		0			0
$817$	13.5491	−	37.2258i	0.474023	−	1.30237i
$818$	−17.6575	−	30.5837i	−0.617380	−	1.06933i
$819$		0			0
$820$	−0.204975	+	0.355028i	−0.00715805	+	0.0123981i
$821$	−17.6656	−	21.0530i	−0.616532	−	0.734755i	0.363938	−	0.931423i	$-0.381432\pi$
$821$	−17.6656	−	21.0530i	−0.616532	−	0.734755i	−0.980470	+	0.196669i	$0.936988\pi$
$822$		0			0
$823$	−0.890725	+	5.05155i	−0.0310487	+	0.176086i	−0.996389	−	0.0849098i	$-0.972940\pi$
$823$	−0.890725	+	5.05155i	−0.0310487	+	0.176086i	0.965340	+	0.260996i	$0.0840509\pi$
$824$	13.5049	+	11.3320i	0.470467	+	0.394769i
$825$		0			0
$826$	10.0778	+	20.9260i	0.350653	+	0.728108i
$827$	−22.7209	−	13.1179i	−0.790082	−	0.456154i	0.0499094	−	0.998754i	$-0.484107\pi$
$827$	−22.7209	−	13.1179i	−0.790082	−	0.456154i	−0.839991	+	0.542600i	$0.817440\pi$
$828$		0			0
$829$			15.8622i			0.550916i	0.961313	+	0.275458i	$0.0888295\pi$
$829$			15.8622i			0.550916i	−0.961313	+	0.275458i	$0.911171\pi$
$830$	35.6169	−	6.28021i	1.23628	−	0.217989i
$831$		0			0
$832$	−52.8958	−	9.32696i	−1.83383	−	0.323354i
$833$	−14.1304	+	17.7201i	−0.489588	+	0.613964i
$834$		0			0
$835$	−3.15622	−	17.8998i	−0.109225	−	0.619448i
$836$	0.171761	−	0.297499i	0.00594049	−	0.0102892i
$837$		0			0
$838$	29.0435	−	16.7682i	1.00329	−	0.579249i
$839$	−43.7933	−	15.9395i	−1.51191	−	0.550291i	−0.552800	−	0.833314i	$-0.686440\pi$
$839$	−43.7933	−	15.9395i	−1.51191	−	0.550291i	−0.959113	+	0.283023i	$0.908663\pi$
$840$		0			0
$841$	7.46447	+	6.26343i	0.257395	+	0.215980i
$842$	−3.72275	−	10.2282i	−0.128294	−	0.352486i
$843$		0			0
$844$	0.0101468	+	0.0575454i	0.000349268	+	0.00198079i
$845$	33.0425	−	57.2312i	1.13670	−	1.96881i
$846$		0			0
$847$	1.94583	+	6.91547i	0.0668596	+	0.237618i
$848$	3.45523	−	0.609251i	0.118653	−	0.0209218i
$849$		0			0
$850$	−2.45510	−	0.432901i	−0.0842094	−	0.0148484i
$851$	−4.48125	−	0.790165i	−0.153615	−	0.0270865i
$852$		0			0
$853$	33.3113	−	5.87368i	1.14056	−	0.201111i	0.428708	−	0.903443i	$-0.358969\pi$
$853$	33.3113	−	5.87368i	1.14056	−	0.201111i	0.711850	+	0.702332i	$0.247858\pi$
$854$	−19.3451	+	19.8342i	−0.661976	+	0.678712i
$855$		0			0
$856$	4.05842	−	7.02939i	0.138714	−	0.240260i
$857$	7.64328	+	43.3472i	0.261089	+	1.48071i	0.779944	+	0.625849i	$0.215247\pi$
$857$	7.64328	+	43.3472i	0.261089	+	1.48071i	−0.518855	+	0.854862i	$0.673641\pi$
$858$		0			0
$859$	−15.9018	−	43.6898i	−0.542562	−	1.49068i	−0.843551	−	0.537048i	$-0.819539\pi$
$859$	−15.9018	−	43.6898i	−0.542562	−	1.49068i	0.300990	−	0.953627i	$-0.402683\pi$
$860$	0.209283	+	0.175609i	0.00713648	+	0.00598822i
$861$		0			0
$862$	7.23046	+	2.63167i	0.246271	+	0.0896351i
$863$	−6.24515	+	3.60564i	−0.212587	+	0.122737i	−0.602513	−	0.798109i	$-0.705834\pi$
$863$	−6.24515	+	3.60564i	−0.212587	+	0.122737i	0.389926	+	0.920846i	$0.372501\pi$
$864$		0			0
$865$	8.94069	−	15.4857i	0.303992	−	0.526530i
$866$	8.69024	+	49.2848i	0.295306	+	1.67477i
$867$		0			0
$868$	−0.00689330	−	0.0688770i	−0.000233974	−	0.00233784i
$869$	−34.7197	−	6.12203i	−1.17779	−	0.207676i
$870$		0			0
$871$	−68.9621	+	12.1599i	−2.33669	+	0.412022i
$872$			16.0035i			0.541947i
$873$		0			0
$874$	4.55031	+	2.62712i	0.153916	+	0.0888637i
$875$	−27.9020	+	13.4374i	−0.943259	+	0.454268i
$876$		0			0
$877$	−34.5295	−	28.9737i	−1.16598	−	0.978372i	−0.166008	−	0.986124i	$-0.553088\pi$
$877$	−34.5295	−	28.9737i	−1.16598	−	0.978372i	−0.999970	+	0.00775269i	$0.997532\pi$
$878$	−0.992333	+	5.62780i	−0.0334896	+	0.189929i
$879$		0			0
$880$	−19.9175	−	23.7367i	−0.671417	−	0.800164i
$881$	17.2527	−	29.8826i	0.581259	−	1.00677i	−0.414071	−	0.910245i	$-0.635894\pi$
$881$	17.2527	−	29.8826i	0.581259	−	1.00677i	0.995330	−	0.0965261i	$-0.0307731\pi$
$882$		0			0
$883$	−19.2076	−	33.2686i	−0.646388	−	1.11958i	−0.983979	−	0.178284i	$-0.942945\pi$
$883$	−19.2076	−	33.2686i	−0.646388	−	1.11958i	0.337591	−	0.941293i	$-0.390388\pi$
$884$	−0.128350	+	0.352638i	−0.00431687	+	0.0118605i
$885$		0			0
$886$	−8.94004	−	7.50158i	−0.300346	−	0.252021i
$887$	4.68652	−	26.5786i	0.157358	−	0.892422i	−0.799240	−	0.601012i	$-0.794764\pi$
$887$	4.68652	−	26.5786i	0.157358	−	0.892422i	0.956598	−	0.291410i	$-0.0941244\pi$
$888$		0			0
$889$	−0.378862	+	5.05664i	−0.0127066	+	0.169594i
$890$			12.9500i			0.434085i
$891$		0			0
$892$	0.151324	+	0.0873671i	0.00506671	+	0.00292527i
$893$	−20.5325	−	24.4697i	−0.687093	−	0.818846i
$894$		0			0
$895$	−6.55946	+	7.81726i	−0.219259	+	0.261302i
$896$	−23.9815	+	17.2421i	−0.801165	+	0.576018i
$897$		0			0
$898$	−38.3904	−	13.9730i	−1.28110	−	0.466284i
$899$	6.59404			0.219923
$900$		0			0
$901$		−	2.86510i		−	0.0954503i
$902$	10.1034	+	57.2992i	0.336406	+	1.90785i
$903$		0			0
$904$	24.5126	−	8.92187i	0.815278	−	0.296737i
$905$	−6.19104	+	7.37819i	−0.205797	+	0.245259i
$906$		0			0
$907$	34.2090	+	12.4511i	1.13589	+	0.413431i	0.840428	−	0.541923i	$-0.182304\pi$
$907$	34.2090	+	12.4511i	1.13589	+	0.413431i	0.295464	+	0.955354i	$0.404526\pi$
$908$	−0.309023			−0.0102553
$909$		0			0
$910$	−14.1749	−	50.3774i	−0.469892	−	1.66999i
$911$	−17.9098	−	21.3441i	−0.593378	−	0.707160i	0.382873	−	0.923801i	$-0.374935\pi$
$911$	−17.9098	−	21.3441i	−0.593378	−	0.707160i	−0.976251	+	0.216640i	$0.930490\pi$
$912$		0			0
$913$	−28.9750	+	34.5311i	−0.958933	+	1.14281i
$914$	−3.15902	−	8.67933i	−0.104491	−	0.287087i
$915$		0			0
$916$	0.0777926	−	0.213733i	0.00257034	−	0.00706195i
$917$	−16.0857	+	16.4924i	−0.531197	+	0.544627i
$918$		0			0
$919$	24.7371	+	42.8459i	0.816001	+	1.41336i	0.908607	+	0.417653i	$0.137147\pi$
$919$	24.7371	+	42.8459i	0.816001	+	1.41336i	−0.0926055	+	0.995703i	$0.529520\pi$
$920$	−3.21632	+	2.69881i	−0.106039	+	0.0889772i
$921$		0			0
$922$	−30.6776	−	5.40930i	−1.01031	−	0.178146i
$923$	5.11565	−	29.0123i	0.168384	−	0.954950i
$924$		0			0
$925$	−2.72145	+	2.28357i	−0.0894807	+	0.0750832i
$926$	20.1233	+	11.6182i	0.661293	+	0.381798i
$927$		0			0
$928$	0.216089	+	0.374278i	0.00709348	+	0.0122863i
$929$	23.8911	−	20.0470i	0.783840	−	0.657720i	−0.160372	−	0.987057i	$-0.551270\pi$
$929$	23.8911	−	20.0470i	0.783840	−	0.657720i	0.944213	+	0.329337i	$0.106825\pi$
$930$		0			0
$931$	5.55711	−	36.8770i	0.182127	−	1.20859i
$932$	−0.112975	−	0.310396i	−0.00370062	−	0.0101674i
$933$		0			0
$934$	−0.686858	+	1.88713i	−0.0224747	+	0.0617486i
$935$	−21.9134	+	12.6517i	−0.716646	+	0.413756i
$936$		0			0
$937$	−15.9634	+	9.21646i	−0.521501	+	0.301089i	−0.737548	−	0.675294i	$-0.764017\pi$
$937$	−15.9634	+	9.21646i	−0.521501	+	0.301089i	0.216048	+	0.976383i	$0.430683\pi$
$938$	−22.0744	+	32.3783i	−0.720754	+	1.05719i
$939$		0			0
$940$	0.207005	−	0.0753435i	0.00675175	−	0.00245743i
$941$	21.6113	−	7.86586i	0.704507	−	0.256420i	0.0351733	−	0.999381i	$-0.488802\pi$
$941$	21.6113	−	7.86586i	0.704507	−	0.256420i	0.669334	+	0.742961i	$0.266579\pi$
$942$		0			0
$943$	7.69644	−	1.35709i	0.250630	−	0.0441929i
$944$	24.7197			0.804558
$945$		0			0
$946$	38.7744			1.26066
$947$	−17.9325	+	3.16199i	−0.582728	+	0.102751i	−0.457238	−	0.889344i	$-0.651161\pi$
$947$	−17.9325	+	3.16199i	−0.582728	+	0.102751i	−0.125490	+	0.992095i	$0.540050\pi$
$948$		0			0
$949$	−19.1507	+	6.97027i	−0.621657	+	0.226265i
$950$	3.85473	−	1.40301i	0.125064	−	0.0455196i
$951$		0			0
$952$	10.5582	+	21.9235i	0.342194	+	0.710544i
$953$	20.4233	−	11.7914i	0.661576	−	0.381961i	−0.131301	−	0.991343i	$-0.541915\pi$
$953$	20.4233	−	11.7914i	0.661576	−	0.381961i	0.792877	+	0.609381i	$0.208582\pi$
$954$		0			0
$955$	−18.9000	+	10.9119i	−0.611590	+	0.353102i
$956$	−0.126497	+	0.347547i	−0.00409120	+	0.0112405i
$957$		0			0
$958$	−11.5750	−	31.8020i	−0.373971	−	1.02748i
$959$	−1.83827	−	18.3678i	−0.0593610	−	0.593128i
$960$		0			0
$961$	22.0176	−	18.4749i	0.710245	−	0.595966i
$962$	−30.4477	−	52.7370i	−0.981674	−	1.70031i
$963$		0			0
$964$	0.177676	+	0.102581i	0.00572256	+	0.00330392i
$965$	16.8205	−	14.1141i	0.541472	−	0.454349i
$966$		0			0
$967$	−6.40078	+	36.3006i	−0.205835	+	1.16735i	0.690285	+	0.723537i	$0.257485\pi$
$967$	−6.40078	+	36.3006i	−0.205835	+	1.16735i	−0.896120	+	0.443811i	$0.853626\pi$
$968$	7.59592	+	1.33936i	0.244142	+	0.0430488i
$969$		0			0
$970$	15.8524	−	13.3017i	0.508989	−	0.427092i
$971$	−6.28287	−	10.8822i	−0.201627	−	0.349228i	0.747426	−	0.664345i	$-0.231289\pi$
$971$	−6.28287	−	10.8822i	−0.201627	−	0.349228i	−0.949053	+	0.315117i	$0.897956\pi$
$972$		0			0
$973$	26.7915	−	7.53842i	0.858895	−	0.241671i
$974$	17.1077	−	47.0029i	0.548165	−	1.50607i
$975$		0			0
$976$	10.0854	+	27.7093i	0.322825	+	0.886953i
$977$	−10.4107	+	12.4070i	−0.333069	+	0.396936i	−0.906423	−	0.422372i	$-0.861198\pi$
$977$	−10.4107	+	12.4070i	−0.333069	+	0.396936i	0.573354	+	0.819308i	$0.305642\pi$
$978$		0			0
$979$	−10.3750	−	12.3645i	−0.331588	−	0.395171i
$980$	0.225872	+	0.122994i	0.00721523	+	0.00392891i
$981$		0			0
$982$	43.6791			1.39385
$983$	1.13238	+	0.412151i	0.0361172	+	0.0131456i	0.360016	−	0.932946i	$-0.382771\pi$
$983$	1.13238	+	0.412151i	0.0361172	+	0.0131456i	−0.323898	+	0.946092i	$0.604994\pi$
$984$		0			0
$985$	19.2332	−	22.9213i	0.612822	−	0.730333i
$986$	−18.7986	+	6.84215i	−0.598671	+	0.217898i
$987$		0			0
$988$	−0.107227	−	0.608114i	−0.00341134	−	0.0193467i
$989$		−	5.20818i		−	0.165610i
$990$		0			0
$991$	−53.5562			−1.70127			−0.850635	−	0.525757i	$-0.823782\pi$
$991$	−53.5562			−1.70127			−0.850635	+	0.525757i	$0.823782\pi$
$992$	−0.139071	−	0.0506179i	−0.00441552	−	0.00160712i
$993$		0			0
$994$	−9.62380	−	13.3854i	−0.305248	−	0.424560i
$995$	−27.2884	+	32.5211i	−0.865101	+	1.03099i
$996$		0			0
$997$	−1.75036	−	2.08600i	−0.0554344	−	0.0660641i	0.737615	−	0.675222i	$-0.235952\pi$
$997$	−1.75036	−	2.08600i	−0.0554344	−	0.0660641i	−0.793049	+	0.609158i	$0.791508\pi$
$998$	44.4078	+	25.6388i	1.40570	+	0.811584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.16		132
3.2	odd	2		189.2.bd.a.185.7	yes	132
7.5	odd	6		567.2.ba.a.341.7		132
21.5	even	6		189.2.ba.a.131.16	yes	132
27.7	even	9		189.2.ba.a.101.16	✓	132
27.20	odd	18		567.2.ba.a.143.7		132
189.47	even	18	inner	567.2.bd.a.467.16		132
189.61	odd	18		189.2.bd.a.47.7	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.16	✓	132	27.7	even	9
189.2.ba.a.131.16	yes	132	21.5	even	6
189.2.bd.a.47.7	yes	132	189.61	odd	18
189.2.bd.a.185.7	yes	132	3.2	odd	2
567.2.ba.a.143.7		132	27.20	odd	18
567.2.ba.a.341.7		132	7.5	odd	6
567.2.bd.a.17.16		132	1.1	even	1	trivial
567.2.bd.a.467.16		132	189.47	even	18	inner

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38665 - 0.244504i) q^{2} +(-0.0163608 + 0.00595485i) q^{4} +(-1.98299 + 0.721749i) q^{5} +(-2.18605 - 1.49037i) q^{7} +(-2.46004 + 1.42030i) q^{8} +O(q^{10})\)	\(q+(1.38665 - 0.244504i) q^{2} +(-0.0163608 + 0.00595485i) q^{4} +(-1.98299 + 0.721749i) q^{5} +(-2.18605 - 1.49037i) q^{7} +(-2.46004 + 1.42030i) q^{8} +(-2.57325 + 1.48566i) q^{10} +(1.26664 - 3.48007i) q^{11} +(-2.27684 - 6.25557i) q^{13} +(-3.39569 - 1.53213i) q^{14} +(-3.03727 + 2.54857i) q^{16} +(1.61887 + 2.80397i) q^{17} +(-4.61385 - 2.66381i) q^{19} +(0.0281454 - 0.0236168i) q^{20} +(0.905502 - 5.13536i) q^{22} +(-0.689782 - 0.121627i) q^{23} +(-0.418902 + 0.351501i) q^{25} +(-4.68670 - 8.11761i) q^{26} +(0.0446405 + 0.0113661i) q^{28} +(-1.50083 + 4.12351i) q^{29} +(-0.513951 - 1.41207i) q^{31} +(0.0633067 - 0.0754460i) q^{32} +(2.93040 + 3.49232i) q^{34} +(5.41058 + 1.37761i) q^{35} +6.49662 q^{37} +(-7.04913 - 2.56567i) q^{38} +(3.85312 - 4.59197i) q^{40} +(-10.4849 + 3.81619i) q^{41} +(1.29121 + 7.32280i) q^{43} +0.0644796i q^{44} -0.986227 q^{46} +(5.63412 + 2.05065i) q^{47} +(2.55760 + 6.51603i) q^{49} +(-0.494929 + 0.589833i) q^{50} +(0.0745020 + 0.0887880i) q^{52} +(-0.766350 - 0.442452i) q^{53} +7.81514i q^{55} +(7.49453 + 0.561517i) q^{56} +(-1.07292 + 6.08484i) q^{58} +(-4.77604 - 4.00757i) q^{59} +(2.54368 - 6.98869i) q^{61} +(-1.05793 - 1.83239i) q^{62} +(4.03421 - 6.98746i) q^{64} +(9.02990 + 10.7614i) q^{65} +(1.82662 - 10.3593i) q^{67} +(-0.0431834 - 0.0362352i) q^{68} +(7.83942 + 0.587358i) q^{70} +(3.83248 + 2.21268i) q^{71} -3.06138i q^{73} +(9.00855 - 1.58845i) q^{74} +(0.0913491 + 0.0161073i) q^{76} +(-7.95554 + 5.71984i) q^{77} +(-1.65307 - 9.37505i) q^{79} +(4.18344 - 7.24593i) q^{80} +(-13.6058 + 7.85533i) q^{82} +(-11.4377 - 4.16299i) q^{83} +(-5.23397 - 4.39182i) q^{85} +(3.58091 + 9.83847i) q^{86} +(1.82677 + 10.3601i) q^{88} +(2.17916 - 3.77442i) q^{89} +(-4.34583 + 17.0683i) q^{91} +(0.0120097 - 0.00211763i) q^{92} +(8.31397 + 1.46598i) q^{94} +(11.0718 + 1.95226i) q^{95} +(-6.85869 + 1.20937i) q^{97} +(5.13970 + 8.41014i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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