LMFDB - Embedded newform 864.2.bn.a.35.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34272 + 0.443967i) q^{2} +(1.60579 - 1.19224i) q^{4} +(3.31478 + 2.54352i) q^{5} +(-0.681945 + 0.182727i) q^{7} +(-1.62680 + 2.31376i) q^{8} +(-5.58006 - 1.94358i) q^{10} +(0.665115 - 5.05205i) q^{11} +(4.20726 - 0.553897i) q^{13} +(0.834536 - 0.548111i) q^{14} +(1.15711 - 3.82898i) q^{16} +3.27263 q^{17} +(1.06932 + 0.442925i) q^{19} +(8.35533 + 0.132325i) q^{20} +(1.34988 + 7.07877i) q^{22} +(1.52244 - 5.68183i) q^{23} +(3.22418 + 12.0328i) q^{25} +(-5.40326 + 2.61161i) q^{26} +(-0.877204 + 1.10647i) q^{28} +(-2.15735 - 2.81151i) q^{29} +(-2.35537 + 1.35987i) q^{31} +(0.146271 + 5.65496i) q^{32} +(-4.39422 + 1.45294i) q^{34} +(-2.72527 - 1.12884i) q^{35} +(-3.40926 - 8.23069i) q^{37} +(-1.63244 - 0.119984i) q^{38} +(-11.2776 + 3.53181i) q^{40} +(5.03584 + 1.34935i) q^{41} +(2.10768 + 0.277481i) q^{43} +(-4.95524 - 8.90550i) q^{44} +(0.478331 + 8.30501i) q^{46} +(0.497855 + 0.287437i) q^{47} +(-5.63052 + 3.25078i) q^{49} +(-9.67133 - 14.7253i) q^{50} +(6.09559 - 5.90553i) q^{52} +(1.89053 + 4.56414i) q^{53} +(15.0547 - 15.0547i) q^{55} +(0.686605 - 1.87512i) q^{56} +(4.14493 + 2.81728i) q^{58} +(-7.22375 + 9.41417i) q^{59} +(-4.29798 + 3.29796i) q^{61} +(2.55886 - 2.87163i) q^{62} +(-2.70702 - 7.52809i) q^{64} +(15.3550 + 8.86522i) q^{65} +(3.81142 - 0.501783i) q^{67} +(5.25514 - 3.90177i) q^{68} +(4.16044 + 0.305791i) q^{70} +(-0.140021 + 0.140021i) q^{71} +(0.0572828 + 0.0572828i) q^{73} +(8.23183 + 9.53790i) q^{74} +(2.24517 - 0.563643i) q^{76} +(0.469572 + 3.56676i) q^{77} +(-4.30540 + 7.45718i) q^{79} +(13.5747 - 9.74912i) q^{80} +(-7.36078 + 0.423947i) q^{82} +(5.51068 + 7.18166i) q^{83} +(10.8480 + 8.32400i) q^{85} +(-2.95321 + 0.563160i) q^{86} +(10.6072 + 9.75762i) q^{88} +(2.41213 + 2.41213i) q^{89} +(-2.76791 + 1.14651i) q^{91} +(-4.32941 - 10.9389i) q^{92} +(-0.796092 - 0.164916i) q^{94} +(2.41796 + 4.18803i) q^{95} +(1.15407 - 1.99891i) q^{97} +(6.11696 - 6.86465i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34272	+	0.443967i	−0.949446	+	0.313932i
$2$	−1.34272	+	0.443967i	−0.949446	+	0.313932i
$3$		0			0
$3$		0			0
$4$	1.60579	−	1.19224i	0.802894	−	0.596122i
$5$	3.31478	+	2.54352i	1.48242	+	1.13750i	0.958268	+	0.285870i	$0.0922825\pi$
$5$	3.31478	+	2.54352i	1.48242	+	1.13750i	0.524147	+	0.851628i	$0.324384\pi$
$6$		0			0
$7$	−0.681945	+	0.182727i	−0.257751	+	0.0690642i	−0.385381	−	0.922758i	$-0.625930\pi$
$7$	−0.681945	+	0.182727i	−0.257751	+	0.0690642i	0.127629	+	0.991822i	$0.459263\pi$
$8$	−1.62680	+	2.31376i	−0.575162	+	0.818039i
$9$		0			0
$10$	−5.58006	−	1.94358i	−1.76457	−	0.614615i
$11$	0.665115	−	5.05205i	0.200540	−	1.52325i	−0.534466	−	0.845190i	$-0.679487\pi$
$11$	0.665115	−	5.05205i	0.200540	−	1.52325i	0.735006	−	0.678061i	$-0.237179\pi$
$12$		0			0
$13$	4.20726	−	0.553897i	1.16689	−	0.153623i	0.477910	−	0.878409i	$-0.341394\pi$
$13$	4.20726	−	0.553897i	1.16689	−	0.153623i	0.688975	+	0.724785i	$0.258061\pi$
$14$	0.834536	−	0.548111i	0.223039	−	0.146489i
$15$		0			0
$16$	1.15711	−	3.82898i	0.289277	−	0.957246i
$17$	3.27263			0.793729			0.396864	−	0.917877i	$-0.370098\pi$
$17$	3.27263			0.793729			0.396864	+	0.917877i	$0.370098\pi$
$18$		0			0
$19$	1.06932	+	0.442925i	0.245318	+	0.101614i	0.501955	−	0.864894i	$-0.332614\pi$
$19$	1.06932	+	0.442925i	0.245318	+	0.101614i	−0.256637	+	0.966508i	$0.582614\pi$
$20$	8.35533	+	0.132325i	1.86831	+	0.0295887i
$21$		0			0
$22$	1.34988	+	7.07877i	0.287795	+	1.50920i
$23$	1.52244	−	5.68183i	0.317451	−	1.18474i	−0.604235	−	0.796806i	$-0.706521\pi$
$23$	1.52244	−	5.68183i	0.317451	−	1.18474i	0.921686	−	0.387937i	$-0.126812\pi$
$24$		0			0
$25$	3.22418	+	12.0328i	0.644836	+	2.40656i
$26$	−5.40326	+	2.61161i	−1.05967	+	0.512179i
$27$		0			0
$28$	−0.877204	+	1.10647i	−0.165776	+	0.209102i
$29$	−2.15735	−	2.81151i	−0.400609	−	0.522084i	0.548872	−	0.835906i	$-0.315057\pi$
$29$	−2.15735	−	2.81151i	−0.400609	−	0.522084i	−0.949482	+	0.313822i	$0.898391\pi$
$30$		0			0
$31$	−2.35537	+	1.35987i	−0.423036	+	0.244240i	−0.696376	−	0.717678i	$-0.745205\pi$
$31$	−2.35537	+	1.35987i	−0.423036	+	0.244240i	0.273339	+	0.961918i	$0.411872\pi$
$32$	0.146271	+	5.65496i	0.0258573	+	0.999666i
$33$		0			0
$34$	−4.39422	+	1.45294i	−0.753602	+	0.249177i
$35$	−2.72527	−	1.12884i	−0.460655	−	0.190809i
$36$		0			0
$37$	−3.40926	−	8.23069i	−0.560480	−	1.35312i	−0.909383	−	0.415959i	$-0.863446\pi$
$37$	−3.40926	−	8.23069i	−0.560480	−	1.35312i	0.348904	−	0.937158i	$-0.386554\pi$
$38$	−1.63244	−	0.119984i	−0.264816	−	0.0194639i
$39$		0			0
$40$	−11.2776	+	3.53181i	−1.78315	+	0.558429i
$41$	5.03584	+	1.34935i	0.786465	+	0.210733i	0.629633	−	0.776893i	$-0.283205\pi$
$41$	5.03584	+	1.34935i	0.786465	+	0.210733i	0.156832	+	0.987625i	$0.449872\pi$
$42$		0			0
$43$	2.10768	+	0.277481i	0.321418	+	0.0423155i	0.289509	−	0.957175i	$-0.406508\pi$
$43$	2.10768	+	0.277481i	0.321418	+	0.0423155i	0.0319091	+	0.999491i	$0.489841\pi$
$44$	−4.95524	−	8.90550i	−0.747031	−	1.34255i
$45$		0			0
$46$	0.478331	+	8.30501i	0.0705261	+	1.22451i
$47$	0.497855	+	0.287437i	0.0726197	+	0.0419270i	0.535870	−	0.844300i	$-0.319984\pi$
$47$	0.497855	+	0.287437i	0.0726197	+	0.0419270i	−0.463251	+	0.886227i	$0.653317\pi$
$48$		0			0
$49$	−5.63052	+	3.25078i	−0.804360	+	0.464397i
$50$	−9.67133	−	14.7253i	−1.36773	−	2.08247i
$51$		0			0
$52$	6.09559	−	5.90553i	0.845307	−	0.818949i
$53$	1.89053	+	4.56414i	0.259684	+	0.626933i	0.998918	−	0.0465164i	$-0.0148120\pi$
$53$	1.89053	+	4.56414i	0.259684	+	0.626933i	−0.739233	+	0.673449i	$0.764812\pi$
$54$		0			0
$55$	15.0547	−	15.0547i	2.02998	−	2.02998i
$56$	0.686605	−	1.87512i	0.0917514	−	0.250574i
$57$		0			0
$58$	4.14493	+	2.81728i	0.544256	+	0.369927i
$59$	−7.22375	+	9.41417i	−0.940452	+	1.22562i	0.0336326	+	0.999434i	$0.489292\pi$
$59$	−7.22375	+	9.41417i	−0.940452	+	1.22562i	−0.974084	+	0.226186i	$0.927374\pi$
$60$		0			0
$61$	−4.29798	+	3.29796i	−0.550300	+	0.422260i	−0.846127	−	0.532982i	$-0.821072\pi$
$61$	−4.29798	+	3.29796i	−0.550300	+	0.422260i	0.295827	+	0.955242i	$0.404405\pi$
$62$	2.55886	−	2.87163i	0.324975	−	0.364697i
$63$		0			0
$64$	−2.70702	−	7.52809i	−0.338377	−	0.941011i
$65$	15.3550	+	8.86522i	1.90456	+	1.09960i
$66$		0			0
$67$	3.81142	−	0.501783i	0.465639	−	0.0613025i	0.105943	−	0.994372i	$-0.466214\pi$
$67$	3.81142	−	0.501783i	0.465639	−	0.0613025i	0.359696	+	0.933070i	$0.382881\pi$
$68$	5.25514	−	3.90177i	0.637280	−	0.473159i
$69$		0			0
$70$	4.16044	+	0.305791i	0.497268	+	0.0365490i
$71$	−0.140021	+	0.140021i	−0.0166175	+	0.0166175i	−0.715367	−	0.698749i	$-0.753740\pi$
$71$	−0.140021	+	0.140021i	−0.0166175	+	0.0166175i	0.698749	+	0.715367i	$0.253740\pi$
$72$		0			0
$73$	0.0572828	+	0.0572828i	0.00670445	+	0.00670445i	0.710451	−	0.703747i	$-0.248491\pi$
$73$	0.0572828	+	0.0572828i	0.00670445	+	0.00670445i	−0.703747	+	0.710451i	$0.748491\pi$
$74$	8.23183	+	9.53790i	0.956931	+	1.10876i
$75$		0			0
$76$	2.24517	−	0.563643i	0.257539	−	0.0646542i
$77$	0.469572	+	3.56676i	0.0535127	+	0.406470i
$78$		0			0
$79$	−4.30540	+	7.45718i	−0.484396	+	0.838998i	−0.999839	−	0.0179254i	$-0.994294\pi$
$79$	−4.30540	+	7.45718i	−0.484396	+	0.838998i	0.515444	+	0.856924i	$0.327627\pi$
$80$	13.5747	−	9.74912i	1.51769	−	1.08998i
$81$		0			0
$82$	−7.36078	+	0.423947i	−0.812862	+	0.0468172i
$83$	5.51068	+	7.18166i	0.604876	+	0.788290i	0.990958	−	0.134175i	$-0.0428384\pi$
$83$	5.51068	+	7.18166i	0.604876	+	0.788290i	−0.386082	+	0.922465i	$0.626172\pi$
$84$		0			0
$85$	10.8480	+	8.32400i	1.17664	+	0.902864i
$86$	−2.95321	+	0.563160i	−0.318453	+	0.0607271i
$87$		0			0
$88$	10.6072	+	9.75762i	1.13074	+	1.04017i
$89$	2.41213	+	2.41213i	0.255686	+	0.255686i	0.823297	−	0.567611i	$-0.192132\pi$
$89$	2.41213	+	2.41213i	0.255686	+	0.255686i	−0.567611	+	0.823297i	$0.692132\pi$
$90$		0			0
$91$	−2.76791	+	1.14651i	−0.290156	+	0.120187i
$92$	−4.32941	−	10.9389i	−0.451372	−	1.14046i
$93$		0			0
$94$	−0.796092	−	0.164916i	−0.0821106	−	0.0170098i
$95$	2.41796	+	4.18803i	0.248078	+	0.429683i
$96$		0			0
$97$	1.15407	−	1.99891i	0.117178	−	0.202958i	−0.801470	−	0.598035i	$-0.795949\pi$
$97$	1.15407	−	1.99891i	0.117178	−	0.202958i	0.918648	+	0.395076i	$0.129282\pi$
$98$	6.11696	−	6.86465i	0.617907	−	0.693434i
$99$		0			0
$100$	19.5234	+	15.4781i	1.95234	+	1.54781i
$101$	1.43922	−	10.9319i	0.143208	−	1.08777i	−0.757343	−	0.653017i	$-0.773503\pi$
$101$	1.43922	−	10.9319i	0.143208	−	1.08777i	0.900550	−	0.434752i	$-0.143164\pi$
$102$		0			0
$103$	1.09443	−	4.08448i	0.107838	−	0.402456i	−0.890814	−	0.454368i	$-0.849865\pi$
$103$	1.09443	−	4.08448i	0.107838	−	0.402456i	0.998652	+	0.0519123i	$0.0165316\pi$
$104$	−5.56281	+	10.6357i	−0.545478	+	1.04292i
$105$		0			0
$106$	−4.56477	−	5.28903i	−0.443370	−	0.513716i
$107$	0.436533	−	0.180818i	0.0422012	−	0.0174803i	−0.361483	−	0.932379i	$-0.617729\pi$
$107$	0.436533	−	0.180818i	0.0422012	−	0.0174803i	0.403684	+	0.914898i	$0.367729\pi$
$108$		0			0
$109$	−1.95414	+	4.71771i	−0.187173	+	0.451874i	−0.989413	−	0.145126i	$-0.953641\pi$
$109$	−1.95414	+	4.71771i	−0.187173	+	0.451874i	0.802241	+	0.597001i	$0.203641\pi$
$110$	−13.5305	+	26.8980i	−1.29008	+	2.56463i
$111$		0			0
$112$	−0.0894261	+	2.82259i	−0.00844998	+	0.266710i
$113$	4.63361	+	8.02564i	0.435893	+	0.754989i	0.997368	−	0.0725046i	$-0.0230992\pi$
$113$	4.63361	+	8.02564i	0.435893	+	0.754989i	−0.561475	+	0.827494i	$0.689766\pi$
$114$		0			0
$115$	19.4984	−	14.9617i	1.81824	−	1.39518i
$116$	−6.81625	−	1.94260i	−0.632873	−	0.180366i
$117$		0			0
$118$	5.51988	−	15.8477i	0.508146	−	1.45890i
$119$	−2.23175	+	0.597996i	−0.204584	+	0.0548182i
$120$		0			0
$121$	−14.4556	−	3.87338i	−1.31415	−	0.352125i
$122$	4.30680	−	6.33639i	0.389919	−	0.573670i
$123$		0			0
$124$	−2.16092	+	4.99184i	−0.194056	+	0.448280i
$125$	−11.9236	+	28.7862i	−1.06648	+	2.57472i
$126$		0			0
$127$			15.5152i			1.37675i	0.725355	+	0.688375i	$0.241676\pi$
$127$			15.5152i			1.37675i	−0.725355	+	0.688375i	$0.758324\pi$
$128$	6.97698	+	8.90628i	0.616684	+	0.787211i
$129$		0			0
$130$	−24.5533	−	5.08639i	−2.15347	−	0.446106i
$131$	0.620380	+	4.71225i	0.0542028	+	0.411711i	0.996940	+	0.0781740i	$0.0249090\pi$
$131$	0.620380	+	4.71225i	0.0542028	+	0.411711i	−0.942737	+	0.333537i	$0.891758\pi$
$132$		0			0
$133$	−0.810150	−	0.106658i	−0.0702489	−	0.00924844i
$134$	−4.89489	+	2.36589i	−0.422854	+	0.204382i
$135$		0			0
$136$	−5.32392	+	7.57209i	−0.456523	+	0.649301i
$137$	−5.82142	−	21.7258i	−0.497357	−	1.85616i	−0.516405	−	0.856344i	$-0.672730\pi$
$137$	−5.82142	−	21.7258i	−0.497357	−	1.85616i	0.0190478	−	0.999819i	$-0.493937\pi$
$138$		0			0
$139$	7.45496	−	9.71549i	0.632321	−	0.824057i	−0.361808	−	0.932252i	$-0.617841\pi$
$139$	7.45496	−	9.71549i	0.632321	−	0.824057i	0.994130	+	0.108195i	$0.0345072\pi$
$140$	−5.72206	+	1.43650i	−0.483602	+	0.121407i
$141$		0			0
$142$	0.125844	−	0.250174i	0.0105606	−	0.0209941i
$143$		−	21.6237i		−	1.80827i
$144$		0			0
$145$		−	14.8068i		−	1.22964i
$146$	−0.102346	−	0.0514831i	−0.00847025	−	0.00426077i
$147$		0			0
$148$	−15.2875	−	9.15206i	−1.25663	−	0.752295i
$149$	−9.40409	+	12.2556i	−0.770413	+	1.00402i	0.229118	+	0.973399i	$0.426416\pi$
$149$	−9.40409	+	12.2556i	−0.770413	+	1.00402i	−0.999531	+	0.0306231i	$0.990251\pi$
$150$		0			0
$151$	−2.35190	−	8.77740i	−0.191395	−	0.714295i	−0.993171	−	0.116670i	$-0.962778\pi$
$151$	−2.35190	−	8.77740i	−0.191395	−	0.714295i	0.801776	−	0.597625i	$-0.203889\pi$
$152$	−2.76439	+	1.75359i	−0.224222	+	0.142235i
$153$		0			0
$154$	−2.21402	−	4.58068i	−0.178411	−	0.369121i
$155$	−11.2664	−	1.48325i	−0.904939	−	0.119137i
$156$		0			0
$157$	−0.490917	−	3.72889i	−0.0391795	−	0.297598i	−0.999805	−	0.0197511i	$-0.993713\pi$
$157$	−0.490917	−	3.72889i	−0.0391795	−	0.297598i	0.960625	−	0.277847i	$-0.0896207\pi$
$158$	2.47021	−	11.9243i	0.196519	−	0.948650i
$159$		0			0
$160$	−13.8987	+	19.1170i	−1.09879	+	1.51133i
$161$			4.15289i			0.327293i
$162$		0			0
$163$	−0.486214	+	1.17383i	−0.0380832	+	0.0919411i	−0.941777	−	0.336239i	$-0.890845\pi$
$163$	−0.486214	+	1.17383i	−0.0380832	+	0.0919411i	0.903693	+	0.428180i	$0.140845\pi$
$164$	9.69523	−	3.83718i	0.757071	−	0.299633i
$165$		0			0
$166$	−10.5877	−	7.19639i	−0.821766	−	0.558548i
$167$	−1.89723	−	0.508362i	−0.146812	−	0.0393383i	0.184664	−	0.982802i	$-0.440880\pi$
$167$	−1.89723	−	0.508362i	−0.146812	−	0.0393383i	−0.331477	+	0.943463i	$0.607547\pi$
$168$		0			0
$169$	4.83724	−	1.29613i	0.372095	−	0.0997026i
$170$	−18.2614	−	6.36062i	−1.40059	−	0.487837i
$171$		0			0
$172$	3.71531	−	2.06729i	0.283290	−	0.157630i
$173$	−5.75436	+	4.41547i	−0.437496	+	0.335702i	−0.803911	−	0.594749i	$-0.797251\pi$
$173$	−5.75436	+	4.41547i	−0.437496	+	0.335702i	0.366416	+	0.930451i	$0.380585\pi$
$174$		0			0
$175$	−4.39743	−	7.61657i	−0.332415	−	0.575759i
$176$	−18.5746	−	8.39247i	−1.40011	−	0.632606i
$177$		0			0
$178$	−4.30973	−	2.16791i	−0.323028	−	0.162492i
$179$	−0.274410	+	0.662483i	−0.0205103	+	0.0495163i	−0.933803	−	0.357788i	$-0.883531\pi$
$179$	−0.274410	+	0.662483i	−0.0205103	+	0.0495163i	0.913293	+	0.407304i	$0.133531\pi$
$180$		0			0
$181$	3.53686	−	1.46501i	0.262892	−	0.108894i	−0.247344	−	0.968928i	$-0.579558\pi$
$181$	3.53686	−	1.46501i	0.262892	−	0.108894i	0.510237	+	0.860034i	$0.329558\pi$
$182$	3.20752	−	2.76830i	0.237757	−	0.205200i
$183$		0			0
$184$	10.6697	+	12.7658i	0.786581	+	0.941107i
$185$	9.63397	−	35.9545i	0.708304	−	2.64343i
$186$		0			0
$187$	2.17667	−	16.5335i	0.159174	−	1.20905i
$188$	1.14214	−	0.132003i	0.0832995	−	0.00962728i
$189$		0			0
$190$	−5.10599	−	4.54985i	−0.370427	−	0.330081i
$191$	−1.37402	+	2.37986i	−0.0994203	+	0.172201i	−0.911445	−	0.411422i	$-0.865032\pi$
$191$	−1.37402	+	2.37986i	−0.0994203	+	0.172201i	0.812025	+	0.583623i	$0.198365\pi$
$192$		0			0
$193$	−6.77073	−	11.7272i	−0.487368	−	0.844145i	0.512527	−	0.858671i	$-0.328709\pi$
$193$	−6.77073	−	11.7272i	−0.487368	−	0.844145i	−0.999894	+	0.0145258i	$0.995376\pi$
$194$	−0.662143	+	3.19634i	−0.0475391	+	0.229484i
$195$		0			0
$196$	−5.16569	+	11.9330i	−0.368978	+	0.852358i
$197$	14.1506	−	5.86137i	1.00819	−	0.417605i	0.183395	−	0.983039i	$-0.441291\pi$
$197$	14.1506	−	5.86137i	1.00819	−	0.417605i	0.824794	+	0.565434i	$0.191291\pi$
$198$		0			0
$199$	−3.90190	−	3.90190i	−0.276598	−	0.276598i	0.555151	−	0.831749i	$-0.312660\pi$
$199$	−3.90190	−	3.90190i	−0.276598	−	0.276598i	−0.831749	+	0.555151i	$0.812660\pi$
$200$	−33.0862	−	12.1150i	−2.33955	−	0.856662i
$201$		0			0
$202$	2.92095	+	15.3175i	0.205518	+	1.07773i
$203$	1.98493	+	1.52309i	0.139315	+	0.106900i
$204$		0			0
$205$	13.2606	+	17.2816i	0.926161	+	1.20700i
$206$	0.343857	+	5.97021i	0.0239576	+	0.415964i
$207$		0			0
$208$	2.74739	−	16.7505i	0.190497	−	1.16144i
$209$	2.94890	−	5.10764i	0.203980	−	0.353303i
$210$		0			0
$211$	1.75092	+	13.2996i	0.120539	+	0.915582i	0.939696	+	0.342012i	$0.111108\pi$
$211$	1.75092	+	13.2996i	0.120539	+	0.915582i	−0.819157	+	0.573569i	$0.805558\pi$
$212$	8.47736	+	5.07507i	0.582227	+	0.348557i
$213$		0			0
$214$	−0.505864	+	0.436594i	−0.0345802	+	0.0298449i
$215$	6.28072	+	6.28072i	0.428341	+	0.428341i
$216$		0			0
$217$	1.35775	−	1.35775i	0.0921699	−	0.0921699i
$218$	0.529354	−	7.20213i	0.0358524	−	0.487790i
$219$		0			0
$220$	6.22577	−	42.1236i	0.419741	−	2.83997i
$221$	13.7688	−	1.81270i	0.926190	−	0.121935i
$222$		0			0
$223$	−16.8744	−	9.74243i	−1.12999	−	0.652402i	−0.186060	−	0.982538i	$-0.559572\pi$
$223$	−16.8744	−	9.74243i	−1.12999	−	0.652402i	−0.943933	+	0.330137i	$0.892905\pi$
$224$	−1.13306	−	3.82965i	−0.0757059	−	0.255879i
$225$		0			0
$226$	−9.78475	−	8.71902i	−0.650872	−	0.579980i
$227$	−15.4649	+	11.8666i	−1.02644	+	0.787616i	−0.977447	−	0.211183i	$-0.932269\pi$
$227$	−15.4649	+	11.8666i	−1.02644	+	0.787616i	−0.0489951	+	0.998799i	$0.515602\pi$
$228$		0			0
$229$	−7.80039	+	10.1657i	−0.515464	+	0.671766i	−0.976476	−	0.215628i	$-0.930820\pi$
$229$	−7.80039	+	10.1657i	−0.515464	+	0.671766i	0.461011	+	0.887394i	$0.347487\pi$
$230$	−19.5384	+	28.7459i	−1.28832	+	1.89545i
$231$		0			0
$232$	10.0148	−	0.417818i	0.657501	−	0.0274311i
$233$	−9.69820	+	9.69820i	−0.635350	+	0.635350i	−0.949405	−	0.314055i	$-0.898313\pi$
$233$	−9.69820	+	9.69820i	−0.635350	+	0.635350i	0.314055	+	0.949405i	$0.398313\pi$
$234$		0			0
$235$	0.919180	+	2.21910i	0.0599607	+	0.144758i
$236$	−0.375810	+	23.7296i	−0.0244632	+	1.54467i
$237$		0			0
$238$	2.73113	−	1.79376i	0.177033	−	0.116272i
$239$	−18.6229	+	10.7520i	−1.20462	+	0.695486i	−0.961578	−	0.274530i	$-0.911478\pi$
$239$	−18.6229	+	10.7520i	−1.20462	+	0.695486i	−0.243039	+	0.970017i	$0.578144\pi$
$240$		0			0
$241$	18.8890	+	10.9056i	1.21675	+	0.702491i	0.964221	−	0.265099i	$-0.0854046\pi$
$241$	18.8890	+	10.9056i	1.21675	+	0.702491i	0.252528	+	0.967589i	$0.418738\pi$
$242$	21.1295	−	1.21696i	1.35826	−	0.0782295i
$243$		0			0
$244$	−2.96967	+	10.4201i	−0.190114	+	0.667076i
$245$	−26.9324	−	3.54571i	−1.72065	−	0.226527i
$246$		0			0
$247$	4.74423	+	1.27121i	0.301868	+	0.0808854i
$248$	0.685298	−	7.66201i	0.0435165	−	0.486538i
$249$		0			0
$250$	3.22998	−	43.9455i	0.204282	−	2.77935i
$251$	−7.58144	−	18.3032i	−0.478536	−	1.15529i	−0.960295	−	0.278985i	$-0.910002\pi$
$251$	−7.58144	−	18.3032i	−0.478536	−	1.15529i	0.481759	−	0.876304i	$-0.339998\pi$
$252$		0			0
$253$	−27.6923	−	11.4705i	−1.74100	−	0.721145i
$254$	−6.88822	−	20.8325i	−0.432206	−	1.30715i
$255$		0			0
$256$	−13.3222	−	8.86108i	−0.832638	−	0.553818i
$257$	−19.7920	+	11.4269i	−1.23459	+	0.712790i	−0.967983	−	0.251016i	$-0.919235\pi$
$257$	−19.7920	+	11.4269i	−1.23459	+	0.712790i	−0.266605	+	0.963806i	$0.585902\pi$
$258$		0			0
$259$	3.82890	+	4.98992i	0.237916	+	0.310058i
$260$	35.2264	−	4.07127i	2.18465	−	0.252489i
$261$		0			0
$262$	−2.92508	−	6.05180i	−0.180712	−	0.373882i
$263$	−7.95273	−	29.6800i	−0.490386	−	1.83015i	−0.554472	−	0.832202i	$-0.687080\pi$
$263$	−7.95273	−	29.6800i	−0.490386	−	1.83015i	0.0640860	−	0.997944i	$-0.479587\pi$
$264$		0			0
$265$	−5.34230	+	19.9377i	−0.328175	+	1.22477i
$266$	1.13516	−	0.216467i	0.0696009	−	0.0132725i
$267$		0			0
$268$	5.52208	−	5.34990i	0.337315	−	0.326797i
$269$	−1.00756	−	0.417343i	−0.0614317	−	0.0254459i	0.351756	−	0.936092i	$-0.385585\pi$
$269$	−1.00756	−	0.417343i	−0.0614317	−	0.0254459i	−0.413188	+	0.910646i	$0.635585\pi$
$270$		0			0
$271$	−21.0778			−1.28038			−0.640191	−	0.768216i	$-0.721145\pi$
$271$	−21.0778			−1.28038			−0.640191	+	0.768216i	$0.721145\pi$
$272$	3.78678	−	12.5308i	0.229607	−	0.759793i
$273$		0			0
$274$	17.4621	+	26.5872i	1.05492	+	1.60619i
$275$	62.9348	−	8.28553i	3.79511	−	0.499636i
$276$		0			0
$277$	−1.10339	+	8.38105i	−0.0662960	+	0.503568i	0.925793	+	0.378031i	$0.123399\pi$
$277$	−1.10339	+	8.38105i	−0.0662960	+	0.503568i	−0.992089	+	0.125537i	$0.959935\pi$
$278$	−5.69656	+	16.3549i	−0.341657	+	0.980903i
$279$		0			0
$280$	7.04536	−	4.46922i	0.421041	−	0.267087i
$281$	9.59718	−	2.57156i	0.572519	−	0.153406i	0.0390676	−	0.999237i	$-0.487561\pi$
$281$	9.59718	−	2.57156i	0.572519	−	0.153406i	0.533452	+	0.845830i	$0.320895\pi$
$282$		0			0
$283$	4.74003	+	3.63716i	0.281766	+	0.216207i	0.739969	−	0.672641i	$-0.234840\pi$
$283$	4.74003	+	3.63716i	0.281766	+	0.216207i	−0.458203	+	0.888847i	$0.651507\pi$
$284$	−0.0579048	+	0.391784i	−0.00343602	+	0.0232481i
$285$		0			0
$286$	9.60021	+	29.0346i	0.567672	+	1.71685i
$287$	−3.68073			−0.217266
$288$		0			0
$289$	−6.28991			−0.369995
$290$	6.57373	+	19.8814i	0.386023	+	1.16747i
$291$		0			0
$292$	0.160279	+	0.0236889i	0.00937963	+	0.00138629i
$293$	4.47989	+	3.43754i	0.261718	+	0.200823i	0.731282	−	0.682075i	$-0.238922\pi$
$293$	4.47989	+	3.43754i	0.261718	+	0.200823i	−0.469564	+	0.882898i	$0.655589\pi$
$294$		0			0
$295$	−47.8903	+	12.8322i	−2.78828	+	0.747117i
$296$	24.5901	+	5.50149i	1.42927	+	0.319768i
$297$		0			0
$298$	7.18595	−	20.6310i	0.416271	−	1.19512i
$299$	3.25817	−	24.7482i	0.188425	−	1.43123i
$300$		0			0
$301$	−1.48803	+	0.195902i	−0.0857684	+	0.0112916i
$302$	7.05481	+	10.7414i	0.405959	+	0.618099i
$303$		0			0
$304$	2.93327	−	3.58188i	0.168234	−	0.205435i
$305$	−22.6353			−1.29609
$306$		0			0
$307$	13.9643	+	5.78421i	0.796986	+	0.330122i	0.743749	−	0.668459i	$-0.233046\pi$
$307$	13.9643	+	5.78421i	0.796986	+	0.330122i	0.0532375	+	0.998582i	$0.483046\pi$
$308$	5.00648	+	5.16761i	0.285271	+	0.294452i
$309$		0			0
$310$	15.7861	−	3.01032i	0.896591	−	0.170974i
$311$	6.29559	−	23.4954i	0.356990	−	1.33230i	−0.520972	−	0.853574i	$-0.674430\pi$
$311$	6.29559	−	23.4954i	0.356990	−	1.33230i	0.877962	−	0.478731i	$-0.158903\pi$
$312$		0			0
$313$	−8.32744	−	31.0784i	−0.470695	−	1.75666i	−0.637283	−	0.770630i	$-0.719942\pi$
$313$	−8.32744	−	31.0784i	−0.470695	−	1.75666i	0.166588	−	0.986027i	$-0.446725\pi$
$314$	2.31467	+	4.78890i	0.130624	+	0.270253i
$315$		0			0
$316$	1.97722	+	17.1077i	0.111227	+	0.962385i
$317$	−5.36484	−	6.99159i	−0.301319	−	0.392687i	0.618014	−	0.786167i	$-0.287938\pi$
$317$	−5.36484	−	6.99159i	−0.301319	−	0.392687i	−0.919333	+	0.393480i	$0.871271\pi$
$318$		0			0
$319$	−15.6388	+	9.02905i	−0.875603	+	0.505530i
$320$	10.1747	−	31.8393i	0.568782	−	1.77987i
$321$		0			0
$322$	−1.84374	−	5.57616i	−0.102748	−	0.310747i
$323$	3.49947	+	1.44953i	0.194716	+	0.0806540i
$324$		0			0
$325$	20.2299	+	48.8394i	1.12215	+	2.70912i
$326$	0.131710	−	1.79198i	0.00729474	−	0.0992486i
$327$		0			0
$328$	−11.3144	+	9.45661i	−0.624733	+	0.522154i
$329$	−0.392033	−	0.105045i	−0.0216135	−	0.00579131i
$330$		0			0
$331$	−6.05875	−	0.797650i	−0.333019	−	0.0438428i	−0.0378374	−	0.999284i	$-0.512047\pi$
$331$	−6.05875	−	0.797650i	−0.333019	−	0.0438428i	−0.295182	+	0.955441i	$0.595380\pi$
$332$	17.4113	+	4.96214i	0.955568	+	0.272333i
$333$		0			0
$334$	2.77315	−	0.159721i	0.151740	−	0.00873953i
$335$	13.9103	+	8.03112i	0.760002	+	0.438787i
$336$		0			0
$337$	−7.43132	+	4.29047i	−0.404810	+	0.233717i	−0.688557	−	0.725182i	$-0.741756\pi$
$337$	−7.43132	+	4.29047i	−0.404810	+	0.233717i	0.283748	+	0.958899i	$0.408422\pi$
$338$	−5.91961	+	3.88791i	−0.321984	+	0.211475i
$339$		0			0
$340$	27.3439	+	0.433050i	1.48293	+	0.0234854i
$341$	5.30355	+	12.8039i	0.287203	+	0.693370i
$342$		0			0
$343$	6.74023	−	6.74023i	0.363938	−	0.363938i
$344$	−4.07081	+	4.42527i	−0.219483	+	0.238594i
$345$		0			0
$346$	5.76616	−	8.48348i	0.309991	−	0.456075i
$347$	5.23723	−	6.82530i	0.281150	−	0.366401i	−0.631337	−	0.775509i	$-0.717493\pi$
$347$	5.23723	−	6.82530i	0.281150	−	0.366401i	0.912486	+	0.409108i	$0.134160\pi$
$348$		0			0
$349$	1.72655	−	1.32483i	0.0924199	−	0.0709163i	−0.561518	−	0.827465i	$-0.689782\pi$
$349$	1.72655	−	1.32483i	0.0924199	−	0.0709163i	0.653938	+	0.756548i	$0.273116\pi$
$350$	9.28602	+	8.27461i	0.496359	+	0.442296i
$351$		0			0
$352$	28.6664	+	3.02223i	1.52793	+	0.161085i
$353$	18.1756	+	10.4937i	0.967387	+	0.558521i	0.898439	−	0.439099i	$-0.144702\pi$
$353$	18.1756	+	10.4937i	0.967387	+	0.558521i	0.0689486	+	0.997620i	$0.478036\pi$
$354$		0			0
$355$	−0.820287	+	0.107993i	−0.0435363	+	0.00573167i
$356$	6.74923	+	0.997521i	0.357708	+	0.0528685i
$357$		0			0
$358$	0.0743345	−	1.01136i	0.00392870	−	0.0534519i
$359$	−24.5834	+	24.5834i	−1.29746	+	1.29746i	−0.367401	+	0.930062i	$0.619752\pi$
$359$	−24.5834	+	24.5834i	−1.29746	+	1.29746i	−0.930062	+	0.367401i	$0.880248\pi$
$360$		0			0
$361$	−12.4878	−	12.4878i	−0.657251	−	0.657251i
$362$	−4.09859	+	3.53735i	−0.215417	+	0.185919i
$363$		0			0
$364$	−3.07776	+	5.14107i	−0.161319	+	0.269466i
$365$	0.0441800	+	0.335580i	0.00231249	+	0.0175651i
$366$		0			0
$367$	11.1995	−	19.3981i	0.584609	−	1.01257i	−0.410315	−	0.911944i	$-0.634581\pi$
$367$	11.1995	−	19.3981i	0.584609	−	1.01257i	0.994924	−	0.100628i	$-0.0320853\pi$
$368$	−19.9940	−	12.4039i	−1.04226	−	0.646597i
$369$		0			0
$370$	3.02687	+	52.5539i	0.157359	+	2.73215i
$371$	−2.12323	−	2.76704i	−0.110232	−	0.143658i
$372$		0			0
$373$	3.13684	+	2.40698i	0.162420	+	0.124629i	0.686773	−	0.726871i	$-0.259026\pi$
$373$	3.13684	+	2.40698i	0.162420	+	0.124629i	−0.524354	+	0.851500i	$0.675693\pi$
$374$	4.41765	+	23.1662i	0.228431	+	1.19789i
$375$		0			0
$376$	−1.47497	+	0.684317i	−0.0760660	+	0.0352909i
$377$	−10.6338	−	10.6338i	−0.547670	−	0.547670i
$378$		0			0
$379$	−21.0622	+	8.72423i	−1.08189	+	0.448134i	−0.851172	−	0.524887i	$-0.824108\pi$
$379$	−21.0622	+	8.72423i	−1.08189	+	0.448134i	−0.230718	+	0.973021i	$0.574108\pi$
$380$	8.87589	+	3.84229i	0.455323	+	0.197105i
$381$		0			0
$382$	0.788336	−	3.80551i	0.0403348	−	0.194707i
$383$	−16.7028	−	28.9302i	−0.853475	−	1.47826i	−0.878053	−	0.478564i	$-0.841157\pi$
$383$	−16.7028	−	28.9302i	−0.853475	−	1.47826i	0.0245777	−	0.999698i	$-0.492176\pi$
$384$		0			0
$385$	−7.51559	+	13.0174i	−0.383030	+	0.663427i
$386$	14.2977	+	12.7404i	0.727733	+	0.648470i
$387$		0			0
$388$	−0.529995	−	4.58575i	−0.0269064	−	0.232806i
$389$	−4.05917	+	30.8325i	−0.205808	+	1.56327i	0.507024	+	0.861932i	$0.330746\pi$
$389$	−4.05917	+	30.8325i	−0.205808	+	1.56327i	−0.712832	+	0.701335i	$0.752588\pi$
$390$		0			0
$391$	4.98238	−	18.5945i	0.251970	−	0.940364i
$392$	1.63821	−	18.3161i	0.0827420	−	0.925102i
$393$		0			0
$394$	−16.3980	+	14.1526i	−0.826121	+	0.712996i
$395$	−33.2390	+	13.7680i	−1.67243	+	0.692745i
$396$		0			0
$397$	−0.939961	+	2.26927i	−0.0471753	+	0.113891i	−0.945711	−	0.325010i	$-0.894632\pi$
$397$	−0.939961	+	2.26927i	−0.0471753	+	0.113891i	0.898535	+	0.438901i	$0.144632\pi$
$398$	6.97146	+	3.50684i	0.349448	+	0.175782i
$399$		0			0
$400$	49.8041	+	1.57791i	2.49021	+	0.0788955i
$401$	3.51481	+	6.08782i	0.175521	+	0.304011i	0.940341	−	0.340232i	$-0.110506\pi$
$401$	3.51481	+	6.08782i	0.175521	+	0.304011i	−0.764820	+	0.644243i	$0.777172\pi$
$402$		0			0
$403$	−9.15642	+	7.02597i	−0.456114	+	0.349989i
$404$	−10.7225	−	19.2703i	−0.533463	−	0.958732i
$405$		0			0
$406$	−3.34141	−	1.16384i	−0.165831	−	0.0577604i
$407$	−43.8494	+	11.7494i	−2.17353	+	0.582397i
$408$		0			0
$409$	27.9547	+	7.49043i	1.38227	+	0.370378i	0.871945	−	0.489604i	$-0.162859\pi$
$409$	27.9547	+	7.49043i	1.38227	+	0.370378i	0.510324	+	0.859982i	$0.329525\pi$
$410$	−25.4777	−	17.3170i	−1.25825	−	0.855226i
$411$		0			0
$412$	−3.11227	−	7.86365i	−0.153331	−	0.387414i
$413$	3.20598	−	7.73992i	0.157756	−	0.380856i
$414$		0			0
$415$			37.8222i			1.85662i
$416$	3.74767	+	23.7109i	0.183745	+	1.16252i
$417$		0			0
$418$	−1.69192	+	8.16734i	−0.0827545	+	0.399478i
$419$	−0.486408	−	3.69464i	−0.0237626	−	0.180495i	0.975448	−	0.220232i	$-0.0706814\pi$
$419$	−0.486408	−	3.69464i	−0.0237626	−	0.180495i	−0.999210	+	0.0397369i	$0.987348\pi$
$420$		0			0
$421$	8.43183	+	1.11007i	0.410942	+	0.0541015i	0.333163	−	0.942869i	$-0.391884\pi$
$421$	8.43183	+	1.11007i	0.410942	+	0.0541015i	0.0777786	+	0.996971i	$0.475217\pi$
$422$	−8.25557	−	17.0803i	−0.401875	−	0.831454i
$423$		0			0
$424$	−13.6359	−	3.05072i	−0.662216	−	0.148156i
$425$	10.5515	+	39.3789i	0.511825	+	1.91016i
$426$		0			0
$427$	2.32836	−	3.03438i	0.112677	−	0.146844i
$428$	0.485400	−	0.810809i	0.0234627	−	0.0391919i
$429$		0			0
$430$	−11.2217	−	5.64481i	−0.541157	−	0.272217i
$431$			30.9185i			1.48929i	0.667460	+	0.744646i	$0.267382\pi$
$431$			30.9185i			1.48929i	−0.667460	+	0.744646i	$0.732618\pi$
$432$		0			0
$433$		−	7.78344i		−	0.374048i	−0.982355	−	0.187024i	$-0.940116\pi$
$433$		−	7.78344i		−	0.374048i	0.982355	−	0.187024i	$-0.0598843\pi$
$434$	−1.22028	+	2.42587i	−0.0585752	+	0.116445i
$435$		0			0
$436$	2.48673	+	9.90545i	0.119093	+	0.474385i
$437$	4.14460	−	5.40134i	0.198263	−	0.258381i
$438$		0			0
$439$	−0.716161	−	2.67275i	−0.0341805	−	0.127563i	0.946727	−	0.322036i	$-0.104367\pi$
$439$	−0.716161	−	2.67275i	−0.0341805	−	0.127563i	−0.980908	+	0.194473i	$0.937700\pi$
$440$	10.3420	+	59.3241i	0.493035	+	2.82817i
$441$		0			0
$442$	−17.6829	+	8.54683i	−0.841088	+	0.406531i
$443$	25.7814	+	3.39419i	1.22491	+	0.161263i	0.715100	−	0.699022i	$-0.246381\pi$
$443$	25.7814	+	3.39419i	1.22491	+	0.161263i	0.509813	+	0.860285i	$0.329714\pi$
$444$		0			0
$445$	1.86038	+	14.1310i	0.0881906	+	0.669874i
$446$	26.9829	+	5.58968i	1.27768	+	0.264679i
$447$		0			0
$448$	3.22162	+	4.63910i	0.152207	+	0.219177i
$449$		−	32.2988i		−	1.52427i	−0.647417	−	0.762136i	$-0.724151\pi$
$449$		−	32.2988i		−	1.52427i	0.647417	−	0.762136i	$-0.275849\pi$
$450$		0			0
$451$	10.1664	−	24.5438i	0.478716	−	1.15572i
$452$	17.0091	+	7.36309i	0.800042	+	0.346330i
$453$		0			0
$454$	15.4966	−	22.7995i	0.727293	−	1.07003i
$455$	−12.0912	−	3.23982i	−0.566844	−	0.151885i
$456$		0			0
$457$	34.2613	−	9.18028i	1.60267	−	0.429435i	0.656825	−	0.754043i	$-0.271899\pi$
$457$	34.2613	−	9.18028i	1.60267	−	0.429435i	0.945849	+	0.324607i	$0.105232\pi$
$458$	5.96052	−	17.1127i	0.278517	−	0.799626i
$459$		0			0
$460$	13.4724	−	47.2721i	0.628152	−	2.20407i
$461$	21.2164	−	16.2799i	0.988147	−	0.758232i	0.0177735	−	0.999842i	$-0.494342\pi$
$461$	21.2164	−	16.2799i	0.988147	−	0.758232i	0.970373	+	0.241610i	$0.0776756\pi$
$462$		0			0
$463$	8.97808	+	15.5505i	0.417247	+	0.722693i	0.995661	−	0.0930503i	$-0.0296617\pi$
$463$	8.97808	+	15.5505i	0.417247	+	0.722693i	−0.578415	+	0.815743i	$0.696328\pi$
$464$	−13.2615	+	5.00723i	−0.615650	+	0.232455i
$465$		0			0
$466$	8.71628	−	17.3276i	0.403774	−	0.802687i
$467$	1.89271	−	4.56940i	0.0875841	−	0.211447i	−0.874018	−	0.485893i	$-0.838495\pi$
$467$	1.89271	−	4.56940i	0.0875841	−	0.211447i	0.961602	+	0.274446i	$0.0884945\pi$
$468$		0			0
$469$	−2.50749	+	1.03864i	−0.115785	+	0.0479598i
$470$	−2.21940	−	2.57154i	−0.102374	−	0.118616i
$471$		0			0
$472$	−10.0306	−	32.0291i	−0.461694	−	1.47426i
$473$	2.80370	−	10.4635i	0.128914	−	0.481114i
$474$		0			0
$475$	−1.88197	+	14.2950i	−0.0863505	+	0.655897i
$476$	−2.87076	+	3.62105i	−0.131581	+	0.165971i
$477$		0			0
$478$	20.2319	−	22.7048i	0.925383	−	1.03849i
$479$	10.5230	−	18.2264i	0.480809	−	0.832785i	−0.518949	−	0.854805i	$-0.673676\pi$
$479$	10.5230	−	18.2264i	0.480809	−	0.832785i	0.999758	+	0.0220202i	$0.00700982\pi$
$480$		0			0
$481$	−18.9026	−	32.7403i	−0.861886	−	1.49283i
$482$	−30.2044	−	6.25704i	−1.37577	−	0.285000i
$483$		0			0
$484$	−27.8307	+	11.0148i	−1.26503	+	0.500675i
$485$	8.90975	−	3.69054i	0.404571	−	0.167579i
$486$		0			0
$487$	23.3607	+	23.3607i	1.05857	+	1.05857i	0.998174	+	0.0603997i	$0.0192375\pi$
$487$	23.3607	+	23.3607i	1.05857	+	1.05857i	0.0603997	+	0.998174i	$0.480762\pi$
$488$	−0.638722	−	15.3096i	−0.0289136	−	0.693035i
$489$		0			0
$490$	37.7368	−	7.19617i	1.70477	−	0.325090i
$491$	33.6634	+	25.8309i	1.51921	+	1.16573i	0.935270	+	0.353934i	$0.115156\pi$
$491$	33.6634	+	25.8309i	1.51921	+	1.16573i	0.583940	+	0.811797i	$0.301510\pi$
$492$		0			0
$493$	−7.06019	−	9.20103i	−0.317975	−	0.414393i
$494$	−6.93455	+	0.399399i	−0.312000	+	0.0179698i
$495$		0			0
$496$	2.48151	+	10.5922i	0.111423	+	0.475603i
$497$	0.0699012	−	0.121072i	0.00313550	−	0.00543084i
$498$		0			0
$499$	−3.65147	−	27.7356i	−0.163462	−	1.24162i	−0.854751	−	0.519039i	$-0.826290\pi$
$499$	−3.65147	−	27.7356i	−0.163462	−	1.24162i	0.691288	−	0.722579i	$-0.257043\pi$
$500$	15.1734	+	60.4404i	0.678573	+	2.70298i
$501$		0			0
$502$	18.3058	+	21.2102i	0.817026	+	0.946656i
$503$	−15.4913	−	15.4913i	−0.690725	−	0.690725i	0.271667	−	0.962391i	$-0.412425\pi$
$503$	−15.4913	−	15.4913i	−0.690725	−	0.690725i	−0.962391	+	0.271667i	$0.912425\pi$
$504$		0			0
$505$	32.5763	−	32.5763i	1.44963	−	1.44963i
$506$	42.2755	+	3.10723i	1.87937	+	0.138133i
$507$		0			0
$508$	18.4979	+	24.9141i	0.820711	+	1.10538i
$509$	−19.3181	+	2.54328i	−0.856261	+	0.112729i	−0.545860	−	0.837877i	$-0.683797\pi$
$509$	−19.3181	+	2.54328i	−0.856261	+	0.112729i	−0.310401	+	0.950606i	$0.600463\pi$
$510$		0			0
$511$	−0.0495309	−	0.0285967i	−0.00219112	−	0.00126504i
$512$	21.8220	+	5.98332i	0.964405	+	0.264428i
$513$		0			0
$514$	21.5019	−	24.1301i	0.948407	−	1.06433i
$515$	14.0168	−	10.7555i	0.617653	−	0.473942i
$516$		0			0
$517$	1.78328	−	2.32401i	0.0784284	−	0.102210i
$518$	−7.35649	−	5.00015i	−0.323226	−	0.219694i
$519$		0			0
$520$	−45.4916	+	21.1059i	−1.99494	+	0.925555i
$521$	30.1843	−	30.1843i	1.32240	−	1.32240i	0.410572	−	0.911828i	$-0.365329\pi$
$521$	30.1843	−	30.1843i	1.32240	−	1.32240i	0.911828	−	0.410572i	$-0.134671\pi$
$522$		0			0
$523$	14.2906	+	34.5006i	0.624886	+	1.50861i	0.845903	+	0.533337i	$0.179062\pi$
$523$	14.2906	+	34.5006i	0.624886	+	1.50861i	−0.221017	+	0.975270i	$0.570938\pi$
$524$	6.61435	+	6.82723i	0.288949	+	0.298249i
$525$		0			0
$526$	23.8552	+	36.3211i	1.04014	+	1.58368i
$527$	−7.70824	+	4.45035i	−0.335776	+	0.193860i
$528$		0			0
$529$	−10.0468	−	5.80050i	−0.436815	−	0.252195i
$530$	−1.67848	−	29.1426i	−0.0729085	−	1.26587i
$531$		0			0
$532$	−1.42809	+	0.794626i	−0.0619156	+	0.0344514i
$533$	21.9345	+	2.88773i	0.950088	+	0.125081i
$534$		0			0
$535$	1.90693	+	0.510959i	0.0824436	+	0.0220907i
$536$	−5.03942	+	9.63503i	−0.217670	+	0.416170i
$537$		0			0
$538$	1.53815	+	0.113054i	0.0663143	+	0.00487408i
$539$	12.6782	+	30.6078i	0.546087	+	1.31837i
$540$		0			0
$541$	−15.8282	−	6.55627i	−0.680509	−	0.281876i	0.0155308	−	0.999879i	$-0.495056\pi$
$541$	−15.8282	−	6.55627i	−0.680509	−	0.281876i	−0.696040	+	0.718003i	$0.745056\pi$
$542$	28.3015	−	9.35782i	1.21565	−	0.401953i
$543$		0			0
$544$	0.478691	+	18.5066i	0.0205237	+	0.793463i
$545$	−18.4771	+	10.6678i	−0.791474	+	0.456957i
$546$		0			0
$547$	3.59785	+	4.68881i	0.153833	+	0.200479i	0.863912	−	0.503643i	$-0.168007\pi$
$547$	3.59785	+	4.68881i	0.153833	+	0.200479i	−0.710079	+	0.704122i	$0.751341\pi$
$548$	−35.2505	−	27.9465i	−1.50583	−	1.19382i
$549$		0			0
$550$	−80.8253	+	39.0661i	−3.44640	+	1.66578i
$551$	−1.06160	−	3.96194i	−0.0452256	−	0.168784i
$552$		0			0
$553$	1.57342	−	5.87210i	0.0669088	−	0.249707i
$554$	−2.23937	−	11.7433i	−0.0951416	−	0.498923i
$555$		0			0
$556$	0.387839	−	24.4891i	0.0164480	−	1.03857i
$557$	−25.3053	−	10.4818i	−1.07222	−	0.444128i	−0.224447	−	0.974486i	$-0.572058\pi$
$557$	−25.3053	−	10.4818i	−1.07222	−	0.444128i	−0.847774	+	0.530358i	$0.822058\pi$
$558$		0			0
$559$	9.02126			0.381559
$560$	−7.47575	+	9.12882i	−0.315908	+	0.385763i
$561$		0			0
$562$	−11.7446	+	7.71370i	−0.495417	+	0.325383i
$563$	−5.66165	+	0.745370i	−0.238610	+	0.0314136i	−0.248883	−	0.968534i	$-0.580063\pi$
$563$	−5.66165	+	0.745370i	−0.238610	+	0.0314136i	0.0102727	+	0.999947i	$0.496730\pi$
$564$		0			0
$565$	−5.05400	+	38.3889i	−0.212623	+	1.61504i
$566$	−7.97931	−	2.77926i	−0.335395	−	0.116821i
$567$		0			0
$568$	−0.0961891	−	0.551763i	−0.00403600	−	0.0231515i
$569$	10.0612	−	2.69590i	0.421788	−	0.113018i	−0.0416807	−	0.999131i	$-0.513271\pi$
$569$	10.0612	−	2.69590i	0.421788	−	0.113018i	0.463469	+	0.886113i	$0.346605\pi$
$570$		0			0
$571$	−7.19131	−	5.51809i	−0.300947	−	0.230925i	0.447238	−	0.894415i	$-0.352408\pi$
$571$	−7.19131	−	5.51809i	−0.300947	−	0.230925i	−0.748185	+	0.663490i	$0.769074\pi$
$572$	−25.7808	−	34.7231i	−1.07795	−	1.45185i
$573$		0			0
$574$	4.94218	−	1.63412i	0.206283	−	0.0682068i
$575$	73.2770			3.05586
$576$		0			0
$577$	−10.1091			−0.420845			−0.210423	−	0.977610i	$-0.567484\pi$
$577$	−10.1091			−0.420845			−0.210423	+	0.977610i	$0.567484\pi$
$578$	8.44559	−	2.79251i	0.351290	−	0.116153i
$579$		0			0
$580$	−17.6533	−	23.7766i	−0.733015	−	0.987269i
$581$	−5.07026	−	3.89055i	−0.210350	−	0.161407i
$582$		0			0
$583$	24.3157	−	6.51537i	1.00705	−	0.269839i
$584$	−0.225727	+	0.0393510i	−0.00934065	+	0.00162836i
$585$		0			0
$586$	−7.54138	−	2.62673i	−0.311531	−	0.108509i
$587$	−2.88035	+	21.8785i	−0.118885	+	0.903021i	0.823225	+	0.567716i	$0.192173\pi$
$587$	−2.88035	+	21.8785i	−0.118885	+	0.903021i	−0.942110	+	0.335305i	$0.891161\pi$
$588$		0			0
$589$	−3.12095	+	0.410882i	−0.128597	+	0.0169301i
$590$	58.6061	−	38.4917i	2.41278	−	1.58468i
$591$		0			0
$592$	−35.4601	+	3.53022i	−1.45740	+	0.145091i
$593$	13.8523			0.568845			0.284422	−	0.958699i	$-0.408198\pi$
$593$	13.8523			0.568845			0.284422	+	0.958699i	$0.408198\pi$
$594$		0			0
$595$	−8.91879	−	3.69428i	−0.365635	−	0.151451i
$596$	−0.489241	+	30.8919i	−0.0200401	+	1.26538i
$597$		0			0
$598$	6.61258	+	34.6764i	0.270409	+	1.41802i
$599$	6.23971	−	23.2869i	0.254948	−	0.951478i	−0.713172	−	0.700989i	$-0.752742\pi$
$599$	6.23971	−	23.2869i	0.254948	−	0.951478i	0.968119	−	0.250489i	$-0.0805913\pi$
$600$		0			0
$601$	−9.05439	−	33.7914i	−0.369336	−	1.37838i	−0.861446	−	0.507849i	$-0.830441\pi$
$601$	−9.05439	−	33.7914i	−0.369336	−	1.37838i	0.492110	−	0.870533i	$-0.336226\pi$
$602$	1.91103	−	0.923675i	0.0778876	−	0.0376462i
$603$		0			0
$604$	−14.2415	−	11.2906i	−0.579476	−	0.459408i
$605$	−38.0653	−	49.6077i	−1.54757	−	2.01684i
$606$		0			0
$607$	15.8254	−	9.13679i	0.642332	−	0.370851i	−0.143180	−	0.989697i	$-0.545733\pi$
$607$	15.8254	−	9.13679i	0.642332	−	0.370851i	0.785512	+	0.618846i	$0.212399\pi$
$608$	−2.34832	+	6.11173i	−0.0952368	+	0.247863i
$609$		0			0
$610$	30.3928	−	10.0493i	1.23057	−	0.406885i
$611$	2.25382	+	0.933563i	0.0911798	+	0.0377679i
$612$		0			0
$613$	−1.15710	−	2.79348i	−0.0467348	−	0.112828i	0.898788	−	0.438383i	$-0.144449\pi$
$613$	−1.15710	−	2.79348i	−0.0467348	−	0.112828i	−0.945523	+	0.325555i	$0.894449\pi$
$614$	−21.3182	−	1.56688i	−0.860331	−	0.0632341i
$615$		0			0
$616$	−9.01654	−	4.71593i	−0.363287	−	0.190010i
$617$	−2.32983	−	0.624276i	−0.0937954	−	0.0251324i	0.211616	−	0.977353i	$-0.432127\pi$
$617$	−2.32983	−	0.624276i	−0.0937954	−	0.0251324i	−0.305412	+	0.952220i	$0.598794\pi$
$618$		0			0
$619$	−6.16432	−	0.811548i	−0.247765	−	0.0326189i	0.00562074	−	0.999984i	$-0.498211\pi$
$619$	−6.16432	−	0.811548i	−0.247765	−	0.0326189i	−0.253386	+	0.967365i	$0.581544\pi$
$620$	−19.8598	+	11.0505i	−0.797590	+	0.443799i
$621$		0			0
$622$	1.97799	+	34.3428i	0.0793102	+	1.37702i
$623$	−2.08571	−	1.20418i	−0.0835620	−	0.0482446i
$624$		0			0
$625$	−58.8009	+	33.9487i	−2.35204	+	1.35795i
$626$	24.9792	+	38.0325i	0.998369	+	1.52008i
$627$		0			0
$628$	−5.23406	−	5.40251i	−0.208862	−	0.215584i
$629$	−11.1572	−	26.9360i	−0.444869	−	1.07401i
$630$		0			0
$631$	−19.8310	+	19.8310i	−0.789458	+	0.789458i	−0.981405	−	0.191947i	$-0.938520\pi$
$631$	−19.8310	+	19.8310i	−0.789458	+	0.789458i	0.191947	+	0.981405i	$0.438520\pi$
$632$	−10.2501	−	22.0931i	−0.407727	−	0.878815i
$633$		0			0
$634$	10.3075	+	7.00593i	0.409363	+	0.278241i
$635$	−39.4632	+	51.4295i	−1.56605	+	2.04092i
$636$		0			0
$637$	−21.8885	+	16.7956i	−0.867253	+	0.665467i
$638$	16.9899	−	19.0666i	0.672636	−	0.754853i
$639$		0			0
$640$	0.473853	+	47.2685i	0.0187307	+	1.86845i
$641$	−32.7883	−	18.9303i	−1.29506	−	0.747702i	−0.315512	−	0.948922i	$-0.602176\pi$
$641$	−32.7883	−	18.9303i	−1.29506	−	0.747702i	−0.979546	+	0.201220i	$0.935510\pi$
$642$		0			0
$643$	8.33708	−	1.09760i	0.328783	−	0.0432850i	0.0356718	−	0.999364i	$-0.488643\pi$
$643$	8.33708	−	1.09760i	0.328783	−	0.0432850i	0.293111	+	0.956079i	$0.405310\pi$
$644$	4.95126	+	6.66865i	0.195107	+	0.262782i
$645$		0			0
$646$	−5.34235	−	0.392661i	−0.210192	−	0.0154490i
$647$	−8.24716	+	8.24716i	−0.324229	+	0.324229i	−0.850387	−	0.526158i	$-0.823632\pi$
$647$	−8.24716	+	8.24716i	−0.324229	+	0.324229i	0.526158	+	0.850387i	$0.323632\pi$
$648$		0			0
$649$	42.7562	+	42.7562i	1.67833	+	1.67833i
$650$	−48.8461	−	56.5961i	−1.91590	−	2.21988i
$651$		0			0
$652$	0.618730	+	2.46460i	0.0242313	+	0.0965212i
$653$	−4.12727	−	31.3497i	−0.161512	−	1.22681i	−0.859664	−	0.510859i	$-0.829327\pi$
$653$	−4.12727	−	31.3497i	−0.161512	−	1.22681i	0.698152	−	0.715950i	$-0.254006\pi$
$654$		0			0
$655$	−9.92929	+	17.1980i	−0.387970	+	0.671983i
$656$	10.9936	−	17.7208i	0.429229	−	0.691880i
$657$		0			0
$658$	0.573026	−	0.0330037i	0.0223389	−	0.00128662i
$659$	−5.19357	−	6.76840i	−0.202313	−	0.263659i	0.681167	−	0.732128i	$-0.261473\pi$
$659$	−5.19357	−	6.76840i	−0.202313	−	0.263659i	−0.883480	+	0.468468i	$0.844806\pi$
$660$		0			0
$661$	−33.7257	−	25.8786i	−1.31178	−	1.00656i	−0.998378	−	0.0569392i	$-0.981866\pi$
$661$	−33.7257	−	25.8786i	−1.31178	−	1.00656i	−0.313398	−	0.949622i	$-0.601467\pi$
$662$	8.48933	−	1.61886i	0.329947	−	0.0629190i
$663$		0			0
$664$	−25.5815	+	1.06727i	−0.992754	+	0.0414179i
$665$	−2.41418	−	2.41418i	−0.0936180	−	0.0936180i
$666$		0			0
$667$	−19.2590	+	7.97732i	−0.745710	+	0.308883i
$668$	−3.65265	+	1.44564i	−0.141325	+	0.0559337i
$669$		0			0
$670$	−22.2432	−	4.60783i	−0.859329	−	0.178016i
$671$	13.8028	+	23.9071i	0.532851	+	0.922925i
$672$		0			0
$673$	12.3032	−	21.3097i	0.474252	−	0.821428i	−0.525314	−	0.850909i	$-0.676052\pi$
$673$	12.3032	−	21.3097i	0.474252	−	0.821428i	0.999565	+	0.0294806i	$0.00938532\pi$
$674$	8.07334	−	9.06015i	0.310974	−	0.348984i
$675$		0			0
$676$	6.22227	−	7.84848i	0.239318	−	0.301865i
$677$	−6.14666	+	46.6886i	−0.236235	+	1.79439i	0.303791	+	0.952739i	$0.401748\pi$
$677$	−6.14666	+	46.6886i	−0.236235	+	1.79439i	−0.540026	+	0.841648i	$0.681586\pi$
$678$		0			0
$679$	−0.421759	+	1.57402i	−0.0161856	+	0.0604055i
$680$	−36.9074	+	11.5583i	−1.41533	+	0.443241i
$681$		0			0
$682$	−12.8057	−	14.8374i	−0.490355	−	0.568155i
$683$	−42.4306	+	17.5753i	−1.62356	+	0.672501i	−0.994489	−	0.104845i	$-0.966565\pi$
$683$	−42.4306	+	17.5753i	−1.62356	+	0.672501i	−0.629073	+	0.777346i	$0.716565\pi$
$684$		0			0
$685$	35.9634	−	86.8233i	1.37409	−	3.31735i
$686$	−6.05780	+	12.0427i	−0.231288	+	0.459791i
$687$		0			0
$688$	3.50128	−	7.74919i	0.133485	−	0.295435i
$689$	10.4820	+	18.1554i	0.399333	+	0.691665i
$690$		0			0
$691$	−23.6372	+	18.1375i	−0.899202	+	0.689982i	−0.951170	−	0.308667i	$-0.900117\pi$
$691$	−23.6372	+	18.1375i	−0.899202	+	0.689982i	0.0519680	+	0.998649i	$0.483451\pi$
$692$	−3.97595	+	13.9509i	−0.151143	+	0.530334i
$693$		0			0
$694$	−4.00193	+	11.4896i	−0.151911	+	0.436140i
$695$	49.4231	−	13.2429i	1.87473	−	0.502331i
$696$		0			0
$697$	16.4804	+	4.41591i	0.624240	+	0.167265i
$698$	−1.73009	+	2.54540i	−0.0654848	+	0.0963447i
$699$		0			0
$700$	−16.1422	−	6.98779i	−0.610116	−	0.264114i
$701$	−14.9000	+	35.9718i	−0.562765	+	1.35864i	0.344780	+	0.938683i	$0.387953\pi$
$701$	−14.9000	+	35.9718i	−0.562765	+	1.35864i	−0.907546	+	0.419953i	$0.862047\pi$
$702$		0			0
$703$		−	10.3113i		−	0.388897i
$704$	−39.8327	+	8.66893i	−1.50125	+	0.326723i
$705$		0			0
$706$	−29.0635	−	6.02070i	−1.09382	−	0.226592i
$707$	1.01609	+	7.71797i	0.0382140	+	0.290264i
$708$		0			0
$709$	−3.48182	−	0.458391i	−0.130763	−	0.0172152i	0.0648607	−	0.997894i	$-0.479340\pi$
$709$	−3.48182	−	0.458391i	−0.130763	−	0.0172152i	−0.195623	+	0.980679i	$0.562673\pi$
$710$	1.05347	−	0.509184i	0.0395360	−	0.0191093i
$711$		0			0
$712$	−9.50518	+	1.65704i	−0.356222	+	0.0621002i
$713$	4.14065	+	15.4531i	0.155069	+	0.578724i
$714$		0			0
$715$	55.0004	−	71.6779i	2.05690	−	2.68060i
$716$	0.349199	+	1.39097i	0.0130502	+	0.0519830i
$717$		0			0
$718$	22.0944	−	43.9229i	0.824556	−	1.63919i
$719$		−	9.36057i		−	0.349091i	−0.984649	−	0.174545i	$-0.944154\pi$
$719$		−	9.36057i		−	0.349091i	0.984649	−	0.174545i	$-0.0558455\pi$
$720$		0			0
$721$			2.98538i			0.111181i
$722$	22.3117	+	11.2234i	0.830356	+	0.417692i
$723$		0			0
$724$	3.93279	−	6.56930i	0.146161	−	0.244146i
$725$	26.8747	−	35.0238i	0.998101	−	1.30075i
$726$		0			0
$727$	4.13266	+	15.4233i	0.153272	+	0.572019i	0.999247	+	0.0387966i	$0.0123524\pi$
$727$	4.13266	+	15.4233i	0.153272	+	0.572019i	−0.845975	+	0.533222i	$0.820981\pi$
$728$	1.85010	−	8.26944i	0.0685694	−	0.306486i
$729$		0			0
$730$	−0.208308	−	0.430975i	−0.00770981	−	0.0159511i
$731$	6.89765	+	0.908093i	0.255119	+	0.0335870i
$732$		0			0
$733$	−2.57675	−	19.5723i	−0.0951744	−	0.722921i	−0.970793	−	0.239918i	$-0.922879\pi$
$733$	−2.57675	−	19.5723i	−0.0951744	−	0.722921i	0.875619	−	0.483003i	$-0.160454\pi$
$734$	−6.42567	+	31.0184i	−0.237176	+	1.14491i
$735$		0			0
$736$	32.3532	+	7.77826i	1.19256	+	0.286710i
$737$		−	19.5892i		−	0.721578i
$738$		0			0
$739$	−13.4889	+	32.5651i	−0.496197	+	1.19793i	0.455319	+	0.890328i	$0.349525\pi$
$739$	−13.4889	+	32.5651i	−0.496197	+	1.19793i	−0.951516	+	0.307598i	$0.900475\pi$
$740$	−27.3964	−	69.2213i	−1.00711	−	2.54463i
$741$		0			0
$742$	4.07937	+	2.77272i	0.149758	+	0.101790i
$743$	−11.1598	−	2.99025i	−0.409412	−	0.109702i	0.0482343	−	0.998836i	$-0.484641\pi$
$743$	−11.1598	−	2.99025i	−0.409412	−	0.109702i	−0.457646	+	0.889135i	$0.651307\pi$
$744$		0			0
$745$	−62.3450	+	16.7053i	−2.28414	+	0.612035i
$746$	−5.28052	−	1.83925i	−0.193334	−	0.0673397i
$747$		0			0
$748$	−16.2167	−	29.1444i	−0.592940	−	1.06562i
$749$	−0.264651	+	0.203074i	−0.00967015	+	0.00742017i
$750$		0			0
$751$	12.2793	+	21.2684i	0.448079	+	0.776095i	0.998261	−	0.0589497i	$-0.0187751\pi$
$751$	12.2793	+	21.2684i	0.448079	+	0.776095i	−0.550182	+	0.835045i	$0.685442\pi$
$752$	1.67666	−	1.57368i	0.0611416	−	0.0573864i
$753$		0			0
$754$	18.9993	+	9.55717i	0.691913	+	0.348052i
$755$	14.5295	−	35.0773i	0.528782	−	1.27659i
$756$		0			0
$757$	24.9075	−	10.3170i	0.905278	−	0.374979i	0.119031	−	0.992891i	$-0.462021\pi$
$757$	24.9075	−	10.3170i	0.905278	−	0.374979i	0.786247	+	0.617912i	$0.212021\pi$
$758$	24.4073	−	21.0651i	0.886513	−	0.765118i
$759$		0			0
$760$	−13.6237	−	1.21851i	−0.494182	−	0.0442002i
$761$	−6.72681	+	25.1048i	−0.243847	+	0.910048i	0.730113	+	0.683326i	$0.239467\pi$
$761$	−6.72681	+	25.1048i	−0.243847	+	0.910048i	−0.973960	+	0.226722i	$0.927199\pi$
$762$		0			0
$763$	0.470564	−	3.57429i	0.0170356	−	0.129398i
$764$	0.631004	+	5.45972i	0.0228289	+	0.197526i
$765$		0			0
$766$	35.2712	+	31.4296i	1.27440	+	1.13560i
$767$	−25.1777	+	43.6091i	−0.909115	+	1.57463i
$768$		0			0
$769$	3.15099	+	5.45767i	0.113628	+	0.196809i	0.917230	−	0.398357i	$-0.130420\pi$
$769$	3.15099	+	5.45767i	0.113628	+	0.196809i	−0.803603	+	0.595166i	$0.797086\pi$
$770$	4.31204	−	20.8154i	0.155395	−	0.750133i
$771$		0			0
$772$	−24.8541	−	10.7591i	−0.894518	−	0.387228i
$773$	6.65957	−	2.75849i	0.239528	−	0.0992158i	−0.259690	−	0.965692i	$-0.583620\pi$
$773$	6.65957	−	2.75849i	0.239528	−	0.0992158i	0.499219	+	0.866476i	$0.333620\pi$
$774$		0			0
$775$	−23.9572	−	23.9572i	−0.860569	−	0.860569i
$776$	2.74756	+	5.92208i	0.0986315	+	0.212590i
$777$		0			0
$778$	−8.23825	−	43.2015i	−0.295356	−	1.54885i
$779$	4.78724	+	3.67338i	0.171521	+	0.131612i
$780$		0			0
$781$	0.614264	+	0.800525i	0.0219801	+	0.0286450i
$782$	1.56540	+	27.1792i	0.0559786	+	0.971926i
$783$		0			0
$784$	5.93207	+	25.3207i	0.211860	+	0.904309i
$785$	7.85722	−	13.6091i	0.280436	−	0.485730i
$786$		0			0
$787$	5.70110	+	43.3041i	0.203222	+	1.54363i	0.723919	+	0.689885i	$0.242339\pi$
$787$	5.70110	+	43.3041i	0.203222	+	1.54363i	−0.520697	+	0.853741i	$0.674328\pi$
$788$	15.7347	−	26.2831i	0.560524	−	0.936296i
$789$		0			0
$790$	38.5180	−	33.2436i	1.37041	−	1.18275i
$791$	−4.62637	−	4.62637i	−0.164495	−	0.164495i
$792$		0			0
$793$	−16.2560	+	16.2560i	−0.577268	+	0.577268i
$794$	0.254625	−	3.46430i	0.00903630	−	0.122943i
$795$		0			0
$796$	−10.9176	−	1.61360i	−0.386965	−	0.0571926i
$797$	−14.3743	+	1.89241i	−0.509164	+	0.0670327i	−0.380732	−	0.924686i	$-0.624328\pi$
$797$	−14.3743	+	1.89241i	−0.509164	+	0.0670327i	−0.128432	+	0.991718i	$0.540995\pi$
$798$		0			0
$799$	1.62929	+	0.940674i	0.0576403	+	0.0332786i
$800$	−67.5735	+	19.9927i	−2.38908	+	0.706848i
$801$		0			0
$802$	−7.42218	−	6.61378i	−0.262086	−	0.233541i
$803$	0.327495	−	0.251296i	0.0115571	−	0.00886805i
$804$		0			0
$805$	−10.5630	+	13.7659i	−0.372295	+	0.485185i
$806$	9.17521	−	13.4991i	0.323183	−	0.475484i
$807$		0			0
$808$	22.9526	+	21.1141i	0.807470	+	0.742793i
$809$	−9.54703	+	9.54703i	−0.335656	+	0.335656i	−0.854729	−	0.519074i	$-0.826277\pi$
$809$	−9.54703	+	9.54703i	−0.335656	+	0.335656i	0.519074	+	0.854729i	$0.326277\pi$
$810$		0			0
$811$	−12.9403	−	31.2405i	−0.454394	−	1.09700i	−0.970634	−	0.240560i	$-0.922669\pi$
$811$	−12.9403	−	31.2405i	−0.454394	−	1.09700i	0.516241	−	0.856444i	$-0.327331\pi$
$812$	5.00328	+	0.0792377i	0.175581	+	0.00278070i
$813$		0			0
$814$	53.6611	−	35.2438i	1.88082	−	1.23530i
$815$	−4.59734	+	2.65428i	−0.161038	+	0.0929753i
$816$		0			0
$817$	2.13087	+	1.23026i	0.0745498	+	0.0430414i
$818$	−40.8607	+	2.35339i	−1.42866	+	0.0822845i
$819$		0			0
$820$	41.8975	+	11.9406i	1.46313	+	0.416985i
$821$	−35.7513	−	4.70675i	−1.24773	−	0.164267i	−0.522419	−	0.852689i	$-0.674970\pi$
$821$	−35.7513	−	4.70675i	−1.24773	−	0.164267i	−0.725310	+	0.688422i	$0.758304\pi$
$822$		0			0
$823$	41.6234	+	11.1529i	1.45090	+	0.388767i	0.896336	−	0.443375i	$-0.146219\pi$
$823$	41.6234	+	11.1529i	1.45090	+	0.388767i	0.554563	+	0.832142i	$0.312886\pi$
$824$	7.67011	+	9.17692i	0.267201	+	0.319693i
$825$		0			0
$826$	−0.868464	+	11.8159i	−0.0302177	+	0.411127i
$827$	17.1956	+	41.5138i	0.597950	+	1.44358i	0.875667	+	0.482915i	$0.160422\pi$
$827$	17.1956	+	41.5138i	0.597950	+	1.44358i	−0.277718	+	0.960663i	$0.589578\pi$
$828$		0			0
$829$	−31.6468	−	13.1086i	−1.09914	−	0.455279i	−0.241955	−	0.970287i	$-0.577789\pi$
$829$	−31.6468	−	13.1086i	−1.09914	−	0.455279i	−0.857185	+	0.515009i	$0.827789\pi$
$830$	−16.7918	−	50.7846i	−0.582851	−	1.76276i
$831$		0			0
$832$	−15.5589	−	30.1732i	−0.539408	−	1.04607i
$833$	−18.4266	+	10.6386i	−0.638443	+	0.368605i
$834$		0			0
$835$	−4.99589	−	6.51077i	−0.172890	−	0.225314i
$836$	−1.35425	−	11.7176i	−0.0468379	−	0.405262i
$837$		0			0
$838$	2.29341	+	4.74491i	0.0792244	+	0.163910i
$839$	11.4882	+	42.8744i	0.396616	+	1.48019i	0.819011	+	0.573778i	$0.194523\pi$
$839$	11.4882	+	42.8744i	0.396616	+	1.48019i	−0.422395	+	0.906412i	$0.638810\pi$
$840$		0			0
$841$	4.25531	−	15.8810i	0.146735	−	0.547622i
$842$	−11.8144	+	2.25294i	−0.407151	+	0.0776413i
$843$		0			0
$844$	18.6680	+	19.2688i	0.642578	+	0.663259i
$845$	19.3311	+	8.00722i	0.665011	+	0.275457i
$846$		0			0
$847$	10.5657			0.363043
$848$	19.6636	−	1.95760i	0.675249	−	0.0672244i
$849$		0			0
$850$	−31.6507	−	48.1903i	−1.08561	−	1.65291i
$851$	−51.9558	+	6.84011i	−1.78102	+	0.234476i
$852$		0			0
$853$	3.30226	−	25.0831i	0.113067	−	0.858830i	−0.837092	−	0.547063i	$-0.815746\pi$
$853$	3.30226	−	25.0831i	0.113067	−	0.858830i	0.950159	−	0.311767i	$-0.100921\pi$
$854$	−1.77917	+	5.10804i	−0.0608820	+	0.174793i
$855$		0			0
$856$	−0.291784	+	1.30419i	−0.00997296	+	0.0445763i
$857$	15.1930	−	4.07096i	0.518984	−	0.139061i	0.0101874	−	0.999948i	$-0.496757\pi$
$857$	15.1930	−	4.07096i	0.518984	−	0.139061i	0.508797	+	0.860887i	$0.330091\pi$
$858$		0			0
$859$	−27.0298	−	20.7407i	−0.922244	−	0.707663i	0.0342501	−	0.999413i	$-0.489096\pi$
$859$	−27.0298	−	20.7407i	−0.922244	−	0.707663i	−0.956495	+	0.291750i	$0.905762\pi$
$860$	17.5737	+	2.59735i	0.599257	+	0.0885688i
$861$		0			0
$862$	−13.7268	−	41.5149i	−0.467536	−	1.41400i
$863$	2.03418			0.0692444			0.0346222	−	0.999400i	$-0.488977\pi$
$863$	2.03418			0.0692444			0.0346222	+	0.999400i	$0.488977\pi$
$864$		0			0
$865$	−30.3053			−1.03041
$866$	3.45559	+	10.4510i	0.117426	+	0.355139i
$867$		0			0
$868$	0.561487	−	3.79902i	0.0190581	−	0.128947i
$869$	34.8104	+	26.7110i	1.18086	+	0.906109i
$870$		0			0
$871$	15.7577	−	4.22226i	0.533930	−	0.143066i
$872$	−7.73667	−	12.1962i	−0.261997	−	0.413016i
$873$		0			0
$874$	−3.16701	+	9.09255i	−0.107126	+	0.307560i
$875$	2.87126	−	21.8094i	0.0970663	−	0.737291i
$876$		0			0
$877$	38.3089	−	5.04346i	1.29360	−	0.170306i	0.547875	−	0.836560i	$-0.315437\pi$
$877$	38.3089	−	5.04346i	1.29360	−	0.170306i	0.745725	+	0.666254i	$0.232103\pi$
$878$	2.14821	+	3.27080i	0.0724987	+	0.110384i
$879$		0			0
$880$	−40.2243	−	75.0641i	−1.35596	−	2.53041i
$881$	24.0834			0.811392			0.405696	−	0.914008i	$-0.367029\pi$
$881$	24.0834			0.811392			0.405696	+	0.914008i	$0.367029\pi$
$882$		0			0
$883$	19.6149	+	8.12476i	0.660094	+	0.273420i	0.687478	−	0.726205i	$-0.258718\pi$
$883$	19.6149	+	8.12476i	0.660094	+	0.273420i	−0.0273840	+	0.999625i	$0.508718\pi$
$884$	19.9486	−	19.3266i	0.670944	−	0.650024i
$885$		0			0
$886$	−36.1241	+	6.88865i	−1.21361	+	0.231429i
$887$	2.20271	−	8.22064i	0.0739599	−	0.276022i	−0.919036	−	0.394175i	$-0.871031\pi$
$887$	2.20271	−	8.22064i	0.0739599	−	0.276022i	0.992995	+	0.118153i	$0.0376972\pi$
$888$		0			0
$889$	−2.83504	−	10.5805i	−0.0950841	−	0.354859i
$890$	−8.77167	−	18.1480i	−0.294027	−	0.608323i
$891$		0			0
$892$	−38.7120	+	4.47412i	−1.29618	+	0.149805i
$893$	0.405052	+	0.527874i	0.0135545	+	0.0176646i
$894$		0			0
$895$	−2.59465	+	1.49802i	−0.0867295	+	0.0500733i
$896$	−6.38533	−	4.79871i	−0.213319	−	0.160314i
$897$		0			0
$898$	14.3396	+	43.3681i	0.478518	+	1.44721i
$899$	8.90464	+	3.68842i	0.296986	+	0.123016i
$900$		0			0
$901$	6.18700	+	14.9367i	0.206119	+	0.497615i
$902$	−2.75396	+	37.4690i	−0.0916968	+	1.24758i
$903$		0			0
$904$	−26.1074	−	2.33507i	−0.868320	−	0.0776634i
$905$	15.4502	+	4.13987i	0.513582	+	0.137614i
$906$		0			0
$907$	−14.0354	−	1.84779i	−0.466036	−	0.0613549i	−0.106148	−	0.994350i	$-0.533852\pi$
$907$	−14.0354	−	1.84779i	−0.466036	−	0.0613549i	−0.359888	+	0.932995i	$0.617185\pi$
$908$	−10.6854	+	37.4932i	−0.354608	+	1.24426i
$909$		0			0
$910$	17.6734	−	1.01791i	0.585869	−	0.0337434i
$911$	−10.7904	−	6.22981i	−0.357500	−	0.206403i	0.310483	−	0.950579i	$-0.399509\pi$
$911$	−10.7904	−	6.22981i	−0.357500	−	0.206403i	−0.667984	+	0.744176i	$0.732842\pi$
$912$		0			0
$913$	39.9473	−	23.0636i	1.32206	−	0.763294i
$914$	−41.9275	+	27.5374i	−1.38684	+	0.910856i
$915$		0			0
$916$	−0.405810	+	25.6239i	−0.0134083	+	0.846637i
$917$	−1.28412	−	3.10014i	−0.0424054	−	0.102376i
$918$		0			0
$919$	8.09555	−	8.09555i	0.267048	−	0.267048i	−0.560862	−	0.827909i	$-0.689530\pi$
$919$	8.09555	−	8.09555i	0.267048	−	0.267048i	0.827909	+	0.560862i	$0.189530\pi$
$920$	2.89766	+	69.4544i	0.0955329	+	2.28984i
$921$		0			0
$922$	−21.2599	+	31.2787i	−0.700159	+	1.03011i
$923$	−0.511549	+	0.666664i	−0.0168378	+	0.0219435i
$924$		0			0
$925$	88.0463	−	67.5603i	2.89494	−	2.22137i
$926$	−18.9589	−	16.8940i	−0.623029	−	0.555170i
$927$		0			0
$928$	15.5834	−	12.6110i	0.511551	−	0.413975i
$929$	−8.44700	−	4.87688i	−0.277137	−	0.160005i	0.354989	−	0.934870i	$-0.384484\pi$
$929$	−8.44700	−	4.87688i	−0.277137	−	0.160005i	−0.632127	+	0.774865i	$0.717818\pi$
$930$		0			0
$931$	−7.46066	+	0.982214i	−0.244513	+	0.0321908i
$932$	−4.01062	+	27.1359i	−0.131372	+	0.888865i
$933$		0			0
$934$	−0.512713	+	6.97572i	−0.0167765	+	0.228253i
$935$	49.2684	−	49.2684i	1.61125	−	1.61125i
$936$		0			0
$937$	−0.190702	−	0.190702i	−0.00622997	−	0.00622997i	0.703985	−	0.710215i	$-0.251402\pi$
$937$	−0.190702	−	0.190702i	−0.00622997	−	0.00622997i	−0.710215	+	0.703985i	$0.751402\pi$
$938$	2.90573	−	2.50784i	0.0948755	−	0.0818838i
$939$		0			0
$940$	4.12171	+	2.46751i	0.134435	+	0.0804813i
$941$	0.226723	+	1.72213i	0.00739097	+	0.0561400i	0.994743	−	0.102404i	$-0.0326534\pi$
$941$	0.226723	+	1.72213i	0.00739097	+	0.0561400i	−0.987352	+	0.158544i	$0.949320\pi$
$942$		0			0
$943$	15.3335	−	26.5584i	0.499328	−	0.864862i
$944$	27.6880	+	38.5528i	0.901169	+	1.25479i
$945$		0			0
$946$	0.880885	+	15.2943i	0.0286401	+	0.497262i
$947$	1.58884	+	2.07062i	0.0516303	+	0.0672860i	0.818455	−	0.574571i	$-0.194831\pi$
$947$	1.58884	+	2.07062i	0.0516303	+	0.0672860i	−0.766825	+	0.641857i	$0.778164\pi$
$948$		0			0
$949$	0.272733	+	0.209275i	0.00885328	+	0.00679336i
$950$	−3.81953	−	20.0296i	−0.123922	−	0.649847i
$951$		0			0
$952$	2.24700	−	6.13657i	0.0728257	−	0.198887i
$953$	−32.7952	−	32.7952i	−1.06234	−	1.06234i	−0.997923	−	0.0644170i	$-0.979481\pi$
$953$	−32.7952	−	32.7952i	−1.06234	−	1.06234i	−0.0644170	−	0.997923i	$-0.520519\pi$
$954$		0			0
$955$	−10.6078	+	4.39389i	−0.343260	+	0.142183i
$956$	−17.0855	+	39.4684i	−0.552585	+	1.27650i
$957$		0			0
$958$	−6.03754	+	29.1448i	−0.195064	+	0.941625i
$959$	7.93978	+	13.7521i	0.256389	+	0.444078i
$960$		0			0
$961$	−11.8015	+	20.4408i	−0.380693	+	0.659380i
$962$	39.9165	+	35.5689i	1.28696	+	1.14679i
$963$		0			0
$964$	43.3339	−	5.00829i	1.39569	−	0.161306i
$965$	7.38501	−	56.0947i	0.237732	−	1.80575i
$966$		0			0
$967$	−6.93757	+	25.8914i	−0.223097	+	0.832610i	0.760061	+	0.649852i	$0.225169\pi$
$967$	−6.93757	+	25.8914i	−0.223097	+	0.832610i	−0.983158	+	0.182758i	$0.941498\pi$
$968$	32.4786	−	27.1457i	1.04390	−	0.872497i
$969$		0			0
$970$	−10.3248	+	8.91099i	−0.331510	+	0.286115i
$971$	14.4324	−	5.97811i	0.463159	−	0.191847i	−0.138887	−	0.990308i	$-0.544352\pi$
$971$	14.4324	−	5.97811i	0.463159	−	0.191847i	0.602046	+	0.798462i	$0.294352\pi$
$972$		0			0
$973$	−3.30859	+	7.98765i	−0.106069	+	0.256072i
$974$	−41.7382	−	20.9955i	−1.33738	−	0.672738i
$975$		0			0
$976$	7.65459	+	20.2730i	0.245018	+	0.648922i
$977$	14.0912	+	24.4067i	0.450819	+	0.780841i	0.998437	−	0.0558872i	$-0.0177987\pi$
$977$	14.0912	+	24.4067i	0.450819	+	0.780841i	−0.547618	+	0.836728i	$0.684465\pi$
$978$		0			0
$979$	13.7906	−	10.5819i	0.440749	−	0.338198i
$980$	−47.4750	+	26.4163i	−1.51653	+	0.843838i
$981$		0			0
$982$	−56.6686	−	19.7382i	−1.80837	−	0.629870i
$983$	23.4618	−	6.28657i	0.748315	−	0.200510i	0.135544	−	0.990771i	$-0.456722\pi$
$983$	23.4618	−	6.28657i	0.748315	−	0.200510i	0.612770	+	0.790261i	$0.290055\pi$
$984$		0			0
$985$	61.8147	+	16.5632i	1.96958	+	0.527747i
$986$	13.5648	+	9.21990i	0.431991	+	0.293621i
$987$		0			0
$988$	9.13383	−	3.61499i	0.290586	−	0.115008i
$989$	4.78542	−	11.5530i	0.152167	−	0.367365i
$990$		0			0
$991$		−	30.2498i		−	0.960917i	−0.877017	−	0.480459i	$-0.840470\pi$
$991$		−	30.2498i		−	0.960917i	0.877017	−	0.480459i	$-0.159530\pi$
$992$	−8.03455	−	13.1206i	−0.255097	−	0.416580i
$993$		0			0
$994$	−0.0401056	+	0.193600i	−0.00127207	+	0.00614062i
$995$	−3.00938	−	22.8585i	−0.0954037	−	0.724663i
$996$		0			0
$997$	52.8202	+	6.95391i	1.67283	+	0.220233i	0.906498	−	0.422209i	$-0.138745\pi$
$997$	52.8202	+	6.95391i	1.67283	+	0.220233i	0.766334	+	0.642442i	$0.222079\pi$
$998$	17.2166	+	35.6200i	0.544982	+	1.12753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.4		368
3.2	odd	2		288.2.bf.a.227.43	yes	368
9.4	even	3		288.2.bf.a.131.28	yes	368
9.5	odd	6	inner	864.2.bn.a.611.19		368
32.11	odd	8	inner	864.2.bn.a.683.19		368
96.11	even	8		288.2.bf.a.11.28	✓	368
288.139	odd	24		288.2.bf.a.203.43	yes	368
288.203	even	24	inner	864.2.bn.a.395.4		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.28	✓	368	96.11	even	8
288.2.bf.a.131.28	yes	368	9.4	even	3
288.2.bf.a.203.43	yes	368	288.139	odd	24
288.2.bf.a.227.43	yes	368	3.2	odd	2
864.2.bn.a.35.4		368	1.1	even	1	trivial
864.2.bn.a.395.4		368	288.203	even	24	inner
864.2.bn.a.611.19		368	9.5	odd	6	inner
864.2.bn.a.683.19		368	32.11	odd	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34272 + 0.443967i) q^{2} +(1.60579 - 1.19224i) q^{4} +(3.31478 + 2.54352i) q^{5} +(-0.681945 + 0.182727i) q^{7} +(-1.62680 + 2.31376i) q^{8} +(-5.58006 - 1.94358i) q^{10} +(0.665115 - 5.05205i) q^{11} +(4.20726 - 0.553897i) q^{13} +(0.834536 - 0.548111i) q^{14} +(1.15711 - 3.82898i) q^{16} +3.27263 q^{17} +(1.06932 + 0.442925i) q^{19} +(8.35533 + 0.132325i) q^{20} +(1.34988 + 7.07877i) q^{22} +(1.52244 - 5.68183i) q^{23} +(3.22418 + 12.0328i) q^{25} +(-5.40326 + 2.61161i) q^{26} +(-0.877204 + 1.10647i) q^{28} +(-2.15735 - 2.81151i) q^{29} +(-2.35537 + 1.35987i) q^{31} +(0.146271 + 5.65496i) q^{32} +(-4.39422 + 1.45294i) q^{34} +(-2.72527 - 1.12884i) q^{35} +(-3.40926 - 8.23069i) q^{37} +(-1.63244 - 0.119984i) q^{38} +(-11.2776 + 3.53181i) q^{40} +(5.03584 + 1.34935i) q^{41} +(2.10768 + 0.277481i) q^{43} +(-4.95524 - 8.90550i) q^{44} +(0.478331 + 8.30501i) q^{46} +(0.497855 + 0.287437i) q^{47} +(-5.63052 + 3.25078i) q^{49} +(-9.67133 - 14.7253i) q^{50} +(6.09559 - 5.90553i) q^{52} +(1.89053 + 4.56414i) q^{53} +(15.0547 - 15.0547i) q^{55} +(0.686605 - 1.87512i) q^{56} +(4.14493 + 2.81728i) q^{58} +(-7.22375 + 9.41417i) q^{59} +(-4.29798 + 3.29796i) q^{61} +(2.55886 - 2.87163i) q^{62} +(-2.70702 - 7.52809i) q^{64} +(15.3550 + 8.86522i) q^{65} +(3.81142 - 0.501783i) q^{67} +(5.25514 - 3.90177i) q^{68} +(4.16044 + 0.305791i) q^{70} +(-0.140021 + 0.140021i) q^{71} +(0.0572828 + 0.0572828i) q^{73} +(8.23183 + 9.53790i) q^{74} +(2.24517 - 0.563643i) q^{76} +(0.469572 + 3.56676i) q^{77} +(-4.30540 + 7.45718i) q^{79} +(13.5747 - 9.74912i) q^{80} +(-7.36078 + 0.423947i) q^{82} +(5.51068 + 7.18166i) q^{83} +(10.8480 + 8.32400i) q^{85} +(-2.95321 + 0.563160i) q^{86} +(10.6072 + 9.75762i) q^{88} +(2.41213 + 2.41213i) q^{89} +(-2.76791 + 1.14651i) q^{91} +(-4.32941 - 10.9389i) q^{92} +(-0.796092 - 0.164916i) q^{94} +(2.41796 + 4.18803i) q^{95} +(1.15407 - 1.99891i) q^{97} +(6.11696 - 6.86465i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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