LMFDB - Embedded newform 990.2.bh.c.937.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(73,990)] 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("990.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bh (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,8,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			937.1
Character	$\chi$	$=$	990.937
Dual form			990.2.bh.c.523.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(-1.69562 + 1.45770i) q^{5} +(-0.753160 + 0.119289i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.06861 + 0.849027i) q^{10} +(1.49880 - 2.95865i) q^{11} +(-0.760418 + 0.387452i) q^{13} +(0.448214 + 0.616914i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(1.29037 + 0.657479i) q^{17} +(-4.09783 + 2.97724i) q^{19} +(-0.182641 - 2.22860i) q^{20} +(-3.31662 + 0.00776159i) q^{22} +(1.65567 - 1.65567i) q^{23} +(0.750246 - 4.94339i) q^{25} +(0.690445 + 0.501638i) q^{26} +(0.346189 - 0.679435i) q^{28} +(0.552936 + 0.401731i) q^{29} +(-1.08804 + 3.34864i) q^{31} +(-0.707107 + 0.707107i) q^{32} -1.44822i q^{34} +(1.10318 - 1.30015i) q^{35} +(-1.26983 - 8.01741i) q^{37} +(4.51312 + 2.29955i) q^{38} +(-1.90278 + 1.17450i) q^{40} +(-7.30492 - 10.0544i) q^{41} +(-7.61267 - 7.61267i) q^{43} +(1.51263 + 2.95160i) q^{44} +(-2.22687 - 0.723555i) q^{46} +(-12.5361 - 1.98553i) q^{47} +(-6.10438 + 1.98343i) q^{49} +(-4.74520 + 1.57578i) q^{50} +(0.133507 - 0.842930i) q^{52} +(-3.72862 - 7.31784i) q^{53} +(1.77142 + 7.20153i) q^{55} -0.762548 q^{56} +(0.106918 - 0.675052i) q^{58} +(-0.254349 + 0.350081i) q^{59} +(12.0627 - 3.91939i) q^{61} +(3.47761 - 0.550800i) q^{62} +(0.951057 + 0.309017i) q^{64} +(0.724592 - 1.76543i) q^{65} +(-3.82631 - 3.82631i) q^{67} +(-1.29037 + 0.657479i) q^{68} +(-1.65927 - 0.392691i) q^{70} +(2.45595 + 7.55864i) q^{71} +(-0.179057 - 1.13052i) q^{73} +(-6.56708 + 4.77126i) q^{74} -5.06519i q^{76} +(-0.775899 + 2.40712i) q^{77} +(3.11720 - 9.59376i) q^{79} +(1.91033 + 1.16218i) q^{80} +(-5.64213 + 11.0733i) q^{82} +(0.108440 - 0.212826i) q^{83} +(-3.14639 + 0.766141i) q^{85} +(-3.32686 + 10.2390i) q^{86} +(1.94318 - 2.68776i) q^{88} +11.2102i q^{89} +(0.526498 - 0.382523i) q^{91} +(0.366287 + 2.31265i) q^{92} +(3.92217 + 12.0712i) q^{94} +(2.60843 - 11.0217i) q^{95} +(-12.6763 + 6.45889i) q^{97} +(4.53858 + 4.53858i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47}+ \cdots + 72 q^{97}+O(q^{100}) $ 48 * q + 8 * q^5 - 20 * q^7 - 12 * q^11 + 12 * q^16 + 20 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 20 * q^25 - 8 * q^26 - 20 * q^28 + 16 * q^31 + 20 * q^37 + 36 * q^38 + 20 * q^41 + 40 * q^46 - 40 * q^47 - 40 * q^50 + 40 * q^52 + 96 * q^55 + 8 * q^56 + 48 * q^58 + 80 * q^61 - 40 * q^62 - 20 * q^68 - 56 * q^70 + 56 * q^71 - 20 * q^73 + 96 * q^77 + 12 * q^80 - 80 * q^85 + 56 * q^86 - 4 * q^88 - 68 * q^91 + 12 * q^92 - 20 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$		0			0
$3$		0			0
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	−1.69562	+	1.45770i	−0.758304	+	0.651901i
$5$	−1.69562	+	1.45770i	−0.758304	+	0.651901i
$6$		0			0
$7$	−0.753160	+	0.119289i	−0.284668	+	0.0450869i	−0.297135	−	0.954835i	$-0.596031\pi$
$7$	−0.753160	+	0.119289i	−0.284668	+	0.0450869i	0.0124678	+	0.999922i	$0.496031\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$		0			0
$10$	2.06861	+	0.849027i	0.654152	+	0.268486i
$11$	1.49880	−	2.95865i	0.451904	−	0.892067i
$11$	1.49880	−	2.95865i	0.451904	−	0.892067i
$12$		0			0
$13$	−0.760418	+	0.387452i	−0.210902	+	0.107460i	−0.556251	−	0.831014i	$-0.687761\pi$
$13$	−0.760418	+	0.387452i	−0.210902	+	0.107460i	0.345349	+	0.938474i	$0.387761\pi$
$14$	0.448214	+	0.616914i	0.119790	+	0.164877i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.29037	+	0.657479i	0.312962	+	0.159462i	0.603415	−	0.797427i	$-0.293806\pi$
$17$	1.29037	+	0.657479i	0.312962	+	0.159462i	−0.290453	+	0.956889i	$0.593806\pi$
$18$		0			0
$19$	−4.09783	+	2.97724i	−0.940106	+	0.683027i	−0.948446	−	0.316939i	$-0.897345\pi$
$19$	−4.09783	+	2.97724i	−0.940106	+	0.683027i	0.00834049	+	0.999965i	$0.497345\pi$
$20$	−0.182641	−	2.22860i	−0.0408398	−	0.498329i
$21$		0			0
$22$	−3.31662	+	0.00776159i	−0.707105	+	0.00165478i
$23$	1.65567	−	1.65567i	0.345231	−	0.345231i	−0.513098	−	0.858330i	$-0.671502\pi$
$23$	1.65567	−	1.65567i	0.345231	−	0.345231i	0.858330	+	0.513098i	$0.171502\pi$
$24$		0			0
$25$	0.750246	−	4.94339i	0.150049	−	0.988679i
$26$	0.690445	+	0.501638i	0.135407	+	0.0983793i
$27$		0			0
$28$	0.346189	−	0.679435i	0.0654237	−	0.128401i
$29$	0.552936	+	0.401731i	0.102678	+	0.0745996i	0.637939	−	0.770087i	$-0.279787\pi$
$29$	0.552936	+	0.401731i	0.102678	+	0.0745996i	−0.535262	+	0.844686i	$0.679787\pi$
$30$		0			0
$31$	−1.08804	+	3.34864i	−0.195417	+	0.601433i	0.804554	+	0.593879i	$0.202404\pi$
$31$	−1.08804	+	3.34864i	−0.195417	+	0.601433i	−0.999971	+	0.00755335i	$0.997596\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	1.44822i		−	0.248368i
$35$	1.10318	−	1.30015i	0.186472	−	0.219765i
$36$		0			0
$37$	−1.26983	−	8.01741i	−0.208759	−	1.31805i	−0.840050	−	0.542509i	$-0.817475\pi$
$37$	−1.26983	−	8.01741i	−0.208759	−	1.31805i	0.631291	−	0.775546i	$-0.282525\pi$
$38$	4.51312	+	2.29955i	0.732124	+	0.373036i
$39$		0			0
$40$	−1.90278	+	1.17450i	−0.300855	+	0.185704i
$41$	−7.30492	−	10.0544i	−1.14084	−	1.57023i	−0.765624	−	0.643288i	$-0.777570\pi$
$41$	−7.30492	−	10.0544i	−1.14084	−	1.57023i	−0.375212	−	0.926939i	$-0.622430\pi$
$42$		0			0
$43$	−7.61267	−	7.61267i	−1.16092	−	1.16092i	−0.984274	−	0.176647i	$-0.943475\pi$
$43$	−7.61267	−	7.61267i	−1.16092	−	1.16092i	−0.176647	−	0.984274i	$-0.556525\pi$
$44$	1.51263	+	2.95160i	0.228037	+	0.444971i
$45$		0			0
$46$	−2.22687	−	0.723555i	−0.328335	−	0.106682i
$47$	−12.5361	−	1.98553i	−1.82858	−	0.289619i	−0.855114	−	0.518440i	$-0.826513\pi$
$47$	−12.5361	−	1.98553i	−1.82858	−	0.289619i	−0.973468	+	0.228821i	$0.926513\pi$
$48$		0			0
$49$	−6.10438	+	1.98343i	−0.872054	+	0.283347i
$50$	−4.74520	+	1.57578i	−0.671073	+	0.222849i
$51$		0			0
$52$	0.133507	−	0.842930i	0.0185141	−	0.116893i
$53$	−3.72862	−	7.31784i	−0.512166	−	1.00518i	−0.991810	−	0.127719i	$-0.959234\pi$
$53$	−3.72862	−	7.31784i	−0.512166	−	1.00518i	0.479644	−	0.877463i	$-0.340766\pi$
$54$		0			0
$55$	1.77142	+	7.20153i	0.238859	+	0.971054i
$56$	−0.762548			−0.101900
$57$		0			0
$58$	0.106918	−	0.675052i	0.0140390	−	0.0886386i
$59$	−0.254349	+	0.350081i	−0.0331134	+	0.0455767i	−0.825253	−	0.564764i	$-0.808967\pi$
$59$	−0.254349	+	0.350081i	−0.0331134	+	0.0455767i	0.792139	+	0.610340i	$0.208967\pi$
$60$		0			0
$61$	12.0627	−	3.91939i	1.54446	−	0.501827i	0.591860	−	0.806040i	$-0.298394\pi$
$61$	12.0627	−	3.91939i	1.54446	−	0.501827i	0.952604	+	0.304214i	$0.0983937\pi$
$62$	3.47761	−	0.550800i	0.441657	−	0.0699517i
$63$		0			0
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	0.724592	−	1.76543i	0.0898745	−	0.218975i
$66$		0			0
$67$	−3.82631	−	3.82631i	−0.467458	−	0.467458i	0.433632	−	0.901090i	$-0.357232\pi$
$67$	−3.82631	−	3.82631i	−0.467458	−	0.467458i	−0.901090	+	0.433632i	$0.857232\pi$
$68$	−1.29037	+	0.657479i	−0.156481	+	0.0797310i
$69$		0			0
$70$	−1.65927	−	0.392691i	−0.198321	−	0.0469355i
$71$	2.45595	+	7.55864i	0.291468	+	0.897045i	0.984385	+	0.176028i	$0.0563250\pi$
$71$	2.45595	+	7.55864i	0.291468	+	0.897045i	−0.692918	+	0.721017i	$0.743675\pi$
$72$		0			0
$73$	−0.179057	−	1.13052i	−0.0209571	−	0.132318i	0.974992	−	0.222242i	$-0.0713375\pi$
$73$	−0.179057	−	1.13052i	−0.0209571	−	0.132318i	−0.995949	+	0.0899243i	$0.971337\pi$
$74$	−6.56708	+	4.77126i	−0.763407	+	0.554648i
$75$		0			0
$76$		−	5.06519i		−	0.581017i
$77$	−0.775899	+	2.40712i	−0.0884219	+	0.274317i
$78$		0			0
$79$	3.11720	−	9.59376i	0.350713	−	1.07938i	−0.607741	−	0.794135i	$-0.707924\pi$
$79$	3.11720	−	9.59376i	0.350713	−	1.07938i	0.958454	−	0.285247i	$-0.0920757\pi$
$80$	1.91033	+	1.16218i	0.213581	+	0.129935i
$81$		0			0
$82$	−5.64213	+	11.0733i	−0.623070	+	1.22284i
$83$	0.108440	−	0.212826i	0.0119029	−	0.0233607i	−0.884979	−	0.465632i	$-0.845827\pi$
$83$	0.108440	−	0.212826i	0.0119029	−	0.0233607i	0.896881	+	0.442271i	$0.145827\pi$
$84$		0			0
$85$	−3.14639	+	0.766141i	−0.341274	+	0.0830996i
$86$	−3.32686	+	10.2390i	−0.358744	+	1.10410i
$87$		0			0
$88$	1.94318	−	2.68776i	0.207144	−	0.286516i
$89$			11.2102i			1.18828i	0.804361	+	0.594141i	$0.202508\pi$
$89$			11.2102i			1.18828i	−0.804361	+	0.594141i	$0.797492\pi$
$90$		0			0
$91$	0.526498	−	0.382523i	0.0551919	−	0.0400993i
$92$	0.366287	+	2.31265i	0.0381881	+	0.241110i
$93$		0			0
$94$	3.92217	+	12.0712i	0.404540	+	1.24505i
$95$	2.60843	−	11.0217i	0.267620	−	1.13080i
$96$		0			0
$97$	−12.6763	+	6.45889i	−1.28708	+	0.655800i	−0.957529	−	0.288337i	$-0.906898\pi$
$97$	−12.6763	+	6.45889i	−1.28708	+	0.655800i	−0.329552	+	0.944137i	$0.606898\pi$
$98$	4.53858	+	4.53858i	0.458466	+	0.458466i
$99$		0			0
$100$	3.55831	+	3.51261i	0.355831	+	0.351261i
$101$	8.91281	+	2.89595i	0.886858	+	0.288158i	0.716802	−	0.697277i	$-0.245605\pi$
$101$	8.91281	+	2.89595i	0.886858	+	0.288158i	0.170056	+	0.985434i	$0.445605\pi$
$102$		0			0
$103$	0.0976359	−	0.0154640i	0.00962035	−	0.00152371i	−0.151622	−	0.988438i	$-0.548450\pi$
$103$	0.0976359	−	0.0154640i	0.00962035	−	0.00152371i	0.161243	+	0.986915i	$0.448450\pi$
$104$	−0.811667	+	0.263727i	−0.0795905	+	0.0258605i
$105$		0			0
$106$	−4.82748	+	6.64446i	−0.468886	+	0.645367i
$107$	−1.02130	+	6.44826i	−0.0987332	+	0.623377i	0.887852	+	0.460129i	$0.152197\pi$
$107$	−1.02130	+	6.44826i	−0.0987332	+	0.623377i	−0.986585	+	0.163248i	$0.947803\pi$
$108$		0			0
$109$	11.8125			1.13143			0.565716	−	0.824600i	$-0.308600\pi$
$109$	11.8125			1.13143			0.565716	+	0.824600i	$0.308600\pi$
$110$	5.61240	−	4.84778i	0.535121	−	0.462217i
$111$		0			0
$112$	0.346189	+	0.679435i	0.0327118	+	0.0642006i
$113$	1.80338	−	11.3861i	0.169647	−	1.07111i	−0.745061	−	0.666997i	$-0.767580\pi$
$113$	1.80338	−	11.3861i	0.169647	−	1.07111i	0.914708	−	0.404115i	$-0.132420\pi$
$114$		0			0
$115$	−0.393922	+	5.22085i	−0.0367334	+	0.486847i
$116$	−0.650015	+	0.211203i	−0.0603524	+	0.0196097i
$117$		0			0
$118$	0.427397	+	0.0676930i	0.0393451	+	0.00623165i
$119$	−1.05029	−	0.341259i	−0.0962797	−	0.0312832i
$120$		0			0
$121$	−6.50722	−	8.86883i	−0.591565	−	0.806257i
$122$	−8.96853	−	8.96853i	−0.811973	−	0.811973i
$123$		0			0
$124$	−2.06957	−	2.84852i	−0.185853	−	0.255805i
$125$	5.93383	+	9.47574i	0.530738	+	0.847536i
$126$		0			0
$127$	−5.78299	−	2.94658i	−0.513157	−	0.261467i	0.178181	−	0.983998i	$-0.442979\pi$
$127$	−5.78299	−	2.94658i	−0.513157	−	0.261467i	−0.691339	+	0.722531i	$0.742979\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$		0			0
$130$	−1.90197	+	0.155873i	−0.166814	+	0.0136709i
$131$		−	1.56355i		−	0.136608i	−0.997665	−	0.0683040i	$-0.978241\pi$
$131$		−	1.56355i		−	0.136608i	0.997665	−	0.0683040i	$-0.0217588\pi$
$132$		0			0
$133$	2.73116	−	2.73116i	0.236822	−	0.236822i
$134$	−1.67216	+	5.14637i	−0.144452	+	0.444579i
$135$		0			0
$136$	1.17164	+	0.851243i	0.100467	+	0.0729935i
$137$	0.766306	−	1.50396i	0.0654700	−	0.128492i	−0.855952	−	0.517055i	$-0.827028\pi$
$137$	0.766306	−	1.50396i	0.0654700	−	0.128492i	0.921422	+	0.388563i	$0.127028\pi$
$138$		0			0
$139$	7.01947	+	5.09995i	0.595384	+	0.432572i	0.844237	−	0.535969i	$-0.180054\pi$
$139$	7.01947	+	5.09995i	0.595384	+	0.432572i	−0.248854	+	0.968541i	$0.580054\pi$
$140$	0.403404	+	1.65670i	0.0340939	+	0.140017i
$141$		0			0
$142$	5.61982	−	5.61982i	0.471605	−	0.471605i
$143$	0.00662403	+	2.83052i	0.000553929	+	0.236700i
$144$		0			0
$145$	−1.52317	+	0.124829i	−0.126492	+	0.0103665i
$146$	−0.926013	+	0.672788i	−0.0766374	+	0.0556803i
$147$		0			0
$148$	7.23261	+	3.68520i	0.594517	+	0.302922i
$149$	4.55529	+	14.0197i	0.373184	+	1.14854i	0.944696	+	0.327948i	$0.106357\pi$
$149$	4.55529	+	14.0197i	0.373184	+	1.14854i	−0.571512	+	0.820594i	$0.693643\pi$
$150$		0			0
$151$	6.72937	+	9.26219i	0.547629	+	0.753746i	0.989688	−	0.143240i	$-0.0457519\pi$
$151$	6.72937	+	9.26219i	0.547629	+	0.753746i	−0.442059	+	0.896986i	$0.645752\pi$
$152$	−4.51312	+	2.29955i	−0.366062	+	0.186518i
$153$		0			0
$154$	2.49701	−	0.401481i	0.201215	−	0.0323522i
$155$	−3.03639	−	7.26404i	−0.243889	−	0.583461i
$156$		0			0
$157$	0.814122	+	0.128944i	0.0649740	+	0.0102909i	0.188837	−	0.982008i	$-0.439528\pi$
$157$	0.814122	+	0.128944i	0.0649740	+	0.0102909i	−0.123863	+	0.992299i	$0.539528\pi$
$158$	−9.96328	+	1.57803i	−0.792636	+	0.125541i
$159$		0			0
$160$	0.168237	−	2.22973i	0.0133003	−	0.176276i
$161$	−1.04948	+	1.44449i	−0.0827108	+	0.113842i
$162$		0			0
$163$	4.05736	+	7.96301i	0.317797	+	0.623711i	0.993547	−	0.113419i	$-0.0361803\pi$
$163$	4.05736	+	7.96301i	0.317797	+	0.623711i	−0.675750	+	0.737131i	$0.736180\pi$
$164$	12.4279			0.970454
$165$		0			0
$166$	−0.238860			−0.0185391
$167$	−9.59049	−	18.8224i	−0.742134	−	1.45652i	−0.884418	−	0.466695i	$-0.845445\pi$
$167$	−9.59049	−	18.8224i	−0.742134	−	1.45652i	0.142284	−	0.989826i	$-0.454555\pi$
$168$		0			0
$169$	−7.21309	+	9.92797i	−0.554853	+	0.763690i
$170$	2.11107	+	2.45563i	0.161911	+	0.188338i
$171$		0			0
$172$	10.6334	−	1.68416i	0.810788	−	0.128416i
$173$	−2.42835	−	0.384613i	−0.184624	−	0.0292416i	0.0634376	−	0.997986i	$-0.479794\pi$
$173$	−2.42835	−	0.384613i	−0.184624	−	0.0292416i	−0.248062	+	0.968744i	$0.579794\pi$
$174$		0			0
$175$	0.0246365	+	3.81266i	0.00186234	+	0.288210i
$176$	−3.27700	−	0.511167i	−0.247013	−	0.0385307i
$177$		0			0
$178$	9.98839	−	5.08934i	0.748661	−	0.381462i
$179$	−9.35481	−	12.8758i	−0.699211	−	0.962382i	−0.999962	−	0.00867926i	$-0.997237\pi$
$179$	−9.35481	−	12.8758i	−0.699211	−	0.962382i	0.300751	−	0.953703i	$-0.402763\pi$
$180$		0			0
$181$	−1.59094	−	4.89640i	−0.118253	−	0.363947i	0.874358	−	0.485281i	$-0.161283\pi$
$181$	−1.59094	−	4.89640i	−0.118253	−	0.363947i	−0.992612	+	0.121334i	$0.961283\pi$
$182$	−0.579855	−	0.295451i	−0.0429817	−	0.0219003i
$183$		0			0
$184$	1.89429	−	1.37628i	0.139649	−	0.101461i
$185$	13.8401	+	11.7434i	1.01754	+	0.863395i
$186$		0			0
$187$	3.87926	−	2.83234i	0.283679	−	0.207121i
$188$	8.97488	−	8.97488i	0.654560	−	0.654560i
$189$		0			0
$190$	−11.0046	+	2.67960i	−0.798355	+	0.194398i
$191$	−21.7592	−	15.8090i	−1.57444	−	1.14390i	−0.922744	−	0.385413i	$-0.874059\pi$
$191$	−21.7592	−	15.8090i	−1.57444	−	1.14390i	−0.651693	−	0.758482i	$-0.725941\pi$
$192$		0			0
$193$	−4.39692	+	8.62943i	−0.316497	+	0.621160i	−0.993373	−	0.114937i	$-0.963333\pi$
$193$	−4.39692	+	8.62943i	−0.316497	+	0.621160i	0.676876	+	0.736097i	$0.263333\pi$
$194$	11.5098	+	8.36237i	0.826357	+	0.600383i
$195$		0			0
$196$	1.98343	−	6.10438i	0.141674	−	0.436027i
$197$	5.96449	−	5.96449i	0.424952	−	0.424952i	−0.461952	−	0.886905i	$-0.652851\pi$
$197$	5.96449	−	5.96449i	0.424952	−	0.424952i	0.886905	+	0.461952i	$0.152851\pi$
$198$		0			0
$199$		−	0.826885i		−	0.0586163i	−0.999570	−	0.0293082i	$-0.990670\pi$
$199$		−	0.826885i		−	0.0586163i	0.999570	−	0.0293082i	$-0.00933042\pi$
$200$	1.51433	−	4.76517i	0.107079	−	0.336948i
$201$		0			0
$202$	−1.46602	−	9.25610i	−0.103149	−	0.651257i
$203$	−0.464371	−	0.236609i	−0.0325924	−	0.0166067i
$204$		0			0
$205$	27.0426	+	6.40001i	1.88873	+	0.446996i
$206$	−0.0581043	−	0.0799737i	−0.00404832	−	0.00557203i
$207$		0			0
$208$	0.603471	+	0.603471i	0.0418432	+	0.0418432i
$209$	2.66682	+	16.5863i	0.184468	+	1.14730i
$210$		0			0
$211$	−13.8523	−	4.50087i	−0.953629	−	0.309853i	−0.209440	−	0.977822i	$-0.567164\pi$
$211$	−13.8523	−	4.50087i	−0.953629	−	0.309853i	−0.744190	+	0.667969i	$0.767164\pi$
$212$	8.11188	+	1.28480i	0.557126	+	0.0882402i
$213$		0			0
$214$	6.20910	−	2.01746i	0.424446	−	0.137911i
$215$	24.0051	+	1.81123i	1.63714	+	0.123525i
$216$		0			0
$217$	0.420011	−	2.65185i	0.0285122	−	0.180019i
$218$	−5.36276	−	10.5250i	−0.363212	−	0.712844i
$219$		0			0
$220$	−6.86738	−	2.79984i	−0.462999	−	0.188765i
$221$	−1.23597			−0.0831401
$222$		0			0
$223$	−0.210549	+	1.32935i	−0.0140994	+	0.0890201i	−0.993735	−	0.111766i	$-0.964349\pi$
$223$	−0.210549	+	1.32935i	−0.0140994	+	0.0890201i	0.979635	+	0.200786i	$0.0643494\pi$
$224$	0.448214	−	0.616914i	0.0299476	−	0.0412193i
$225$		0			0
$226$	−10.9638	+	3.56235i	−0.729300	+	0.236964i
$227$	−2.02684	+	0.321020i	−0.134526	+	0.0213068i	−0.223334	−	0.974742i	$-0.571694\pi$
$227$	−2.02684	+	0.321020i	−0.134526	+	0.0213068i	0.0888083	+	0.996049i	$0.471694\pi$
$228$		0			0
$229$	17.0466	+	5.53877i	1.12647	+	0.366012i	0.812234	−	0.583332i	$-0.198251\pi$
$229$	17.0466	+	5.53877i	1.12647	+	0.366012i	0.314237	+	0.949345i	$0.398251\pi$
$230$	4.83065	−	2.01923i	0.318524	−	0.133144i
$231$		0			0
$232$	0.483284	+	0.483284i	0.0317291	+	0.0317291i
$233$	21.9042	−	11.1608i	1.43499	−	0.731166i	0.448320	−	0.893873i	$-0.352023\pi$
$233$	21.9042	−	11.1608i	1.43499	−	0.731166i	0.986674	+	0.162707i	$0.0520226\pi$
$234$		0			0
$235$	24.1508	−	14.9072i	1.57542	−	0.972436i
$236$	−0.133719	−	0.411545i	−0.00870438	−	0.0267893i
$237$		0			0
$238$	0.172757	+	1.09074i	0.0111981	+	0.0707023i
$239$	−2.40071	+	1.74422i	−0.155289	+	0.112824i	−0.662717	−	0.748870i	$-0.730597\pi$
$239$	−2.40071	+	1.74422i	−0.155289	+	0.112824i	0.507427	+	0.861695i	$0.330597\pi$
$240$		0			0
$241$			21.2858i			1.37114i	0.728007	+	0.685570i	$0.240447\pi$
$241$			21.2858i			1.37114i	−0.728007	+	0.685570i	$0.759553\pi$
$242$	−4.94797	+	9.82434i	−0.318067	+	0.631532i
$243$		0			0
$244$	−3.91939	+	12.0627i	−0.250913	+	0.772232i
$245$	7.45945	−	12.2615i	0.476567	−	0.783356i
$246$		0			0
$247$	1.96252	−	3.85166i	0.124872	−	0.245075i
$248$	−1.59848	+	3.13720i	−0.101504	+	0.199212i
$249$		0			0
$250$	5.74904	−	9.58898i	0.363601	−	0.606460i
$251$	−4.10394	+	12.6306i	−0.259038	+	0.797238i	0.733969	+	0.679183i	$0.237666\pi$
$251$	−4.10394	+	12.6306i	−0.259038	+	0.797238i	−0.993007	+	0.118055i	$0.962334\pi$
$252$		0			0
$253$	−2.41704	−	7.38007i	−0.151958	−	0.463981i
$254$			6.49040i			0.407244i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.89548	−	18.2813i	−0.180615	−	1.14036i	−0.896796	−	0.442444i	$-0.854112\pi$
$257$	−2.89548	−	18.2813i	−0.180615	−	1.14036i	0.716181	−	0.697914i	$-0.245888\pi$
$258$		0			0
$259$	1.91277	+	5.88692i	0.118854	+	0.365795i
$260$	1.00236	+	1.62390i	0.0621636	+	0.100710i
$261$		0			0
$262$	−1.39313	+	0.709837i	−0.0860681	+	0.0438539i
$263$	17.4405	+	17.4405i	1.07543	+	1.07543i	0.996913	+	0.0785172i	$0.0250185\pi$
$263$	17.4405	+	17.4405i	1.07543	+	1.07543i	0.0785172	+	0.996913i	$0.474981\pi$
$264$		0			0
$265$	16.9895	+	6.97306i	1.04366	+	0.428352i
$266$	−3.67341	−	1.19356i	−0.225231	−	0.0731820i
$267$		0			0
$268$	5.34459	−	0.846501i	0.326473	−	0.0517083i
$269$	19.3677	−	6.29294i	1.18087	−	0.383687i	0.348179	−	0.937428i	$-0.386800\pi$
$269$	19.3677	−	6.29294i	1.18087	−	0.383687i	0.832689	+	0.553741i	$0.186800\pi$
$270$		0			0
$271$	4.38344	−	6.03328i	0.266275	−	0.366496i	−0.654853	−	0.755756i	$-0.727269\pi$
$271$	4.38344	−	6.03328i	0.266275	−	0.366496i	0.921128	+	0.389261i	$0.127269\pi$
$272$	0.226552	−	1.43039i	0.0137367	−	0.0867302i
$273$		0			0
$274$	−1.68793			−0.101972
$275$	−13.5013	−	9.62885i	−0.814159	−	0.580642i
$276$		0			0
$277$	−7.43406	−	14.5902i	−0.446669	−	0.876638i	−0.999072	−	0.0430609i	$-0.986289\pi$
$277$	−7.43406	−	14.5902i	−0.446669	−	0.876638i	0.552403	−	0.833577i	$-0.313711\pi$
$278$	1.35731	−	8.56972i	0.0814061	−	0.513978i
$279$		0			0
$280$	1.29299	−	1.11156i	0.0772709	−	0.0664286i
$281$	−3.98244	+	1.29397i	−0.237572	+	0.0771919i	−0.425383	−	0.905013i	$-0.639861\pi$
$281$	−3.98244	+	1.29397i	−0.237572	+	0.0771919i	0.187811	+	0.982205i	$0.439861\pi$
$282$		0			0
$283$	−27.3003	−	4.32395i	−1.62284	−	0.257032i	−0.722225	−	0.691658i	$-0.756881\pi$
$283$	−27.3003	−	4.32395i	−1.62284	−	0.257032i	−0.900611	+	0.434626i	$0.856881\pi$
$284$	−7.55864	−	2.45595i	−0.448523	−	0.145734i
$285$		0			0
$286$	2.51901	−	1.29093i	0.148952	−	0.0763345i
$287$	6.70114	+	6.70114i	0.395556	+	0.395556i
$288$		0			0
$289$	−8.75956	−	12.0565i	−0.515268	−	0.709206i
$290$	0.802728	+	1.30048i	0.0471378	+	0.0763670i
$291$		0			0
$292$	1.01986	+	0.519644i	0.0596827	+	0.0304099i
$293$	2.92476	+	18.4662i	0.170866	+	1.07881i	0.912822	+	0.408357i	$0.133898\pi$
$293$	2.92476	+	18.4662i	0.170866	+	1.07881i	−0.741956	+	0.670448i	$0.766102\pi$
$294$		0			0
$295$	−0.0790332	−	0.964368i	−0.00460149	−	0.0561477i
$296$		−	8.11735i		−	0.471812i
$297$		0			0
$298$	10.4236	−	10.4236i	0.603824	−	0.603824i
$299$	−0.617509	+	1.90050i	−0.0357115	+	0.109909i
$300$		0			0
$301$	6.64166	+	4.82545i	0.382819	+	0.278134i
$302$	5.19760	−	10.2009i	0.299088	−	0.586994i
$303$		0			0
$304$	4.09783	+	2.97724i	0.235026	+	0.170757i
$305$	−14.7404	+	24.2295i	−0.844031	+	1.38738i
$306$		0			0
$307$	7.13262	−	7.13262i	0.407080	−	0.407080i	−0.473639	−	0.880719i	$-0.657060\pi$
$307$	7.13262	−	7.13262i	0.407080	−	0.407080i	0.880719	+	0.473639i	$0.157060\pi$
$308$	−1.49134	−	2.04259i	−0.0849771	−	0.116387i
$309$		0			0
$310$	−5.09381	+	6.00325i	−0.289309	+	0.340962i
$311$	−18.5344	+	13.4660i	−1.05099	+	0.763589i	−0.972401	−	0.233318i	$-0.925042\pi$
$311$	−18.5344	+	13.4660i	−1.05099	+	0.763589i	−0.0785899	+	0.996907i	$0.525042\pi$
$312$		0			0
$313$	12.9044	+	6.57514i	0.729402	+	0.371649i	0.778919	−	0.627125i	$-0.215768\pi$
$313$	12.9044	+	6.57514i	0.729402	+	0.371649i	−0.0495173	+	0.998773i	$0.515768\pi$
$314$	−0.254714	−	0.783928i	−0.0143743	−	0.0442396i
$315$		0			0
$316$	5.92927	+	8.16094i	0.333547	+	0.459089i
$317$	1.99314	−	1.01556i	0.111946	−	0.0570393i	−0.397121	−	0.917766i	$-0.629991\pi$
$317$	1.99314	−	1.01556i	0.111946	−	0.0570393i	0.509067	+	0.860727i	$0.329991\pi$
$318$		0			0
$319$	2.01732	−	1.03383i	0.112948	−	0.0578834i
$320$	−2.06308	+	0.862376i	−0.115330	+	0.0482083i
$321$		0			0
$322$	1.76350	+	0.279311i	0.0982762	+	0.0155654i
$323$	−7.24520	+	1.14753i	−0.403134	+	0.0638501i
$324$		0			0
$325$	1.34483	+	4.04973i	0.0745977	+	0.224639i
$326$	5.25310	−	7.23027i	0.290942	−	0.400447i
$327$		0			0
$328$	−5.64213	−	11.0733i	−0.311535	−	0.611421i
$329$	9.67856			0.533596
$330$		0			0
$331$	1.96672			0.108101			0.0540503	−	0.998538i	$-0.482787\pi$
$331$	1.96672			0.108101			0.0540503	+	0.998538i	$0.482787\pi$
$332$	0.108440	+	0.212826i	0.00595143	+	0.0116803i
$333$		0			0
$334$	−12.4169	+	17.0904i	−0.679422	+	0.935144i
$335$	12.0655	+	0.910366i	0.659211	+	0.0497386i
$336$		0			0
$337$	−0.400422	+	0.0634205i	−0.0218123	+	0.00345474i	−0.167331	−	0.985901i	$-0.553515\pi$
$337$	−0.400422	+	0.0634205i	−0.0218123	+	0.00345474i	0.145519	+	0.989355i	$0.453515\pi$
$338$	12.1206	+	1.91971i	0.659272	+	0.104418i
$339$		0			0
$340$	1.22958	−	2.99581i	0.0666833	−	0.162470i
$341$	8.27669	+	8.23804i	0.448208	+	0.446115i
$342$		0			0
$343$	9.11701	−	4.64535i	0.492272	−	0.250825i
$344$	−6.32806	−	8.70983i	−0.341186	−	0.469602i
$345$		0			0
$346$	0.759756	+	2.33829i	0.0408447	+	0.125707i
$347$	−9.52619	−	4.85384i	−0.511393	−	0.260568i	0.179198	−	0.983813i	$-0.442650\pi$
$347$	−9.52619	−	4.85384i	−0.511393	−	0.260568i	−0.690591	+	0.723245i	$0.742650\pi$
$348$		0			0
$349$	−6.50852	+	4.72872i	−0.348393	+	0.253123i	−0.748195	−	0.663479i	$-0.769079\pi$
$349$	−6.50852	+	4.72872i	−0.348393	+	0.253123i	0.399801	+	0.916602i	$0.369079\pi$
$350$	3.38592	−	1.75286i	0.180985	−	0.0936944i
$351$		0			0
$352$	1.03227	+	3.15189i	0.0550203	+	0.167996i
$353$	−17.8934	+	17.8934i	−0.952372	+	0.952372i	−0.998916	−	0.0465446i	$-0.985179\pi$
$353$	−17.8934	+	17.8934i	−0.952372	+	0.952372i	0.0465446	+	0.998916i	$0.485179\pi$
$354$		0			0
$355$	−15.1825	−	9.23654i	−0.805806	−	0.490224i
$356$	−9.06926	−	6.58921i	−0.480670	−	0.349227i
$357$		0			0
$358$	−7.22542	+	14.1807i	−0.381875	+	0.749473i
$359$	13.1469	+	9.55175i	0.693864	+	0.504122i	0.877928	−	0.478792i	$-0.158925\pi$
$359$	13.1469	+	9.55175i	0.693864	+	0.504122i	−0.184064	+	0.982914i	$0.558925\pi$
$360$		0			0
$361$	2.05687	−	6.33038i	0.108256	−	0.333178i
$362$	−3.64046	+	3.64046i	−0.191338	+	0.191338i
$363$		0			0
$364$			0.650787i			0.0341105i
$365$	1.95157	+	1.65592i	0.102150	+	0.0866750i
$366$		0			0
$367$	1.34090	+	8.46611i	0.0699944	+	0.441927i	0.997652	+	0.0684942i	$0.0218195\pi$
$367$	1.34090	+	8.46611i	0.0699944	+	0.441927i	−0.927657	+	0.373433i	$0.878181\pi$
$368$	−2.08627	−	1.06301i	−0.108754	−	0.0554131i
$369$		0			0
$370$	4.18021	−	17.6630i	0.217319	−	0.918258i
$371$	3.68118	+	5.06672i	0.191118	+	0.263051i
$372$		0			0
$373$	23.2440	+	23.2440i	1.20353	+	1.20353i	0.973085	+	0.230446i	$0.0740184\pi$
$373$	23.2440	+	23.2440i	1.20353	+	1.20353i	0.230446	+	0.973085i	$0.425982\pi$
$374$	−4.28478	−	2.17059i	−0.221561	−	0.112238i
$375$		0			0
$376$	−12.0712	−	3.92217i	−0.622524	−	0.202270i
$377$	−0.576114	−	0.0912475i	−0.0296714	−	0.00469949i
$378$		0			0
$379$	−12.1822	+	3.95823i	−0.625757	+	0.203321i	−0.604695	−	0.796457i	$-0.706705\pi$
$379$	−12.1822	+	3.95823i	−0.625757	+	0.203321i	−0.0210622	+	0.999778i	$0.506705\pi$
$380$	7.38351	+	8.58863i	0.378766	+	0.440588i
$381$		0			0
$382$	−4.20743	+	26.5647i	−0.215271	+	1.35917i
$383$	−10.1184	−	19.8586i	−0.517028	−	1.01473i	−0.990959	−	0.134163i	$-0.957165\pi$
$383$	−10.1184	−	19.8586i	−0.517028	−	1.01473i	0.473931	−	0.880562i	$-0.342835\pi$
$384$		0			0
$385$	−2.19323	−	5.21259i	−0.111777	−	0.265658i
$386$	9.68504			0.492955
$387$		0			0
$388$	2.22558	−	14.0518i	0.112987	−	0.713370i
$389$	−8.06422	+	11.0995i	−0.408872	+	0.562765i	−0.962943	−	0.269705i	$-0.913074\pi$
$389$	−8.06422	+	11.0995i	−0.408872	+	0.562765i	0.554071	+	0.832470i	$0.313074\pi$
$390$		0			0
$391$	3.22501	−	1.04787i	0.163096	−	0.0529930i
$392$	−6.33950	+	1.00408i	−0.320193	+	0.0507136i
$393$		0			0
$394$	−8.02222	−	2.60658i	−0.404154	−	0.131318i
$395$	8.69920	+	20.8113i	0.437704	+	1.04713i
$396$		0			0
$397$	−0.807418	−	0.807418i	−0.0405232	−	0.0405232i	0.686555	−	0.727078i	$-0.259122\pi$
$397$	−0.807418	−	0.807418i	−0.0405232	−	0.0405232i	−0.727078	+	0.686555i	$0.759122\pi$
$398$	−0.736760	+	0.375398i	−0.0369304	+	0.0188170i
$399$		0			0
$400$	−4.93328	+	0.814066i	−0.246664	+	0.0407033i
$401$	−4.25930	−	13.1088i	−0.212700	−	0.654622i	−0.999309	−	0.0371709i	$-0.988165\pi$
$401$	−4.25930	−	13.1088i	−0.212700	−	0.654622i	0.786609	−	0.617451i	$-0.211835\pi$
$402$		0			0
$403$	−0.470073	−	2.96793i	−0.0234160	−	0.147843i
$404$	−7.58169	+	5.50842i	−0.377203	+	0.274054i
$405$		0			0
$406$			0.521176i			0.0258655i
$407$	−25.6239	−	8.25948i	−1.27013	−	0.409407i
$408$		0			0
$409$	6.24805	−	19.2295i	0.308946	−	0.950839i	−0.669229	−	0.743056i	$-0.733375\pi$
$409$	6.24805	−	19.2295i	0.308946	−	0.950839i	0.978175	−	0.207782i	$-0.0666246\pi$
$410$	−6.57461	−	27.0006i	−0.324697	−	1.33347i
$411$		0			0
$412$	−0.0448783	+	0.0880786i	−0.00221099	+	0.00433932i
$413$	0.149805	−	0.294008i	0.00737140	−	0.0144672i
$414$		0			0
$415$	0.126362	+	0.518944i	0.00620287	+	0.0254740i
$416$	0.263727	−	0.811667i	0.0129303	−	0.0397953i
$417$		0			0
$418$	13.5678	−	9.90618i	0.663623	−	0.484527i
$419$		−	19.4960i		−	0.952442i	−0.879326	−	0.476221i	$-0.842006\pi$
$419$		−	19.4960i		−	0.952442i	0.879326	−	0.476221i	$-0.157994\pi$
$420$		0			0
$421$	−2.31295	+	1.68045i	−0.112726	+	0.0819003i	−0.642720	−	0.766101i	$-0.722194\pi$
$421$	−2.31295	+	1.68045i	−0.112726	+	0.0819003i	0.529994	+	0.848001i	$0.322194\pi$
$422$	2.27849	+	14.3858i	0.110915	+	0.700290i
$423$		0			0
$424$	−2.53796	−	7.81103i	−0.123254	−	0.379337i
$425$	4.21827	−	5.88556i	0.204616	−	0.285491i
$426$		0			0
$427$	−8.61756	+	4.39087i	−0.417033	+	0.212489i
$428$	−4.61644	−	4.61644i	−0.223144	−	0.223144i
$429$		0			0
$430$	−9.28429	−	22.2110i	−0.447728	−	1.07111i
$431$	15.3238	+	4.97899i	0.738120	+	0.239830i	0.653861	−	0.756614i	$-0.273148\pi$
$431$	15.3238	+	4.97899i	0.738120	+	0.239830i	0.0842582	+	0.996444i	$0.473148\pi$
$432$		0			0
$433$	−24.1225	+	3.82063i	−1.15925	+	0.183608i	−0.706291	−	0.707922i	$-0.749633\pi$
$433$	−24.1225	+	3.82063i	−1.15925	+	0.183608i	−0.452963	+	0.891529i	$0.649633\pi$
$434$	−2.55349	+	0.829681i	−0.122572	+	0.0398259i
$435$		0			0
$436$	−6.94322	+	9.55652i	−0.332520	+	0.457674i
$437$	−1.85531	+	11.7140i	−0.0887517	+	0.560356i
$438$		0			0
$439$	−13.2566			−0.632702			−0.316351	−	0.948642i	$-0.602458\pi$
$439$	−13.2566			−0.632702			−0.316351	+	0.948642i	$0.602458\pi$
$440$	0.623048	+	7.38998i	0.0297026	+	0.352303i
$441$		0			0
$442$	0.561117	+	1.10125i	0.0266896	+	0.0523813i
$443$	0.340637	−	2.15069i	0.0161841	−	0.102183i	−0.978274	−	0.207316i	$-0.933527\pi$
$443$	0.340637	−	2.15069i	0.0161841	−	0.102183i	0.994458	+	0.105134i	$0.0335271\pi$
$444$		0			0
$445$	−16.3411	−	19.0083i	−0.774642	−	0.901078i
$446$	1.28005	−	0.415913i	0.0606121	−	0.0196941i
$447$		0			0
$448$	−0.753160	−	0.119289i	−0.0355834	−	0.00563586i
$449$	4.58948	+	1.49121i	0.216591	+	0.0703747i	0.415303	−	0.909683i	$-0.363676\pi$
$449$	4.58948	+	1.49121i	0.216591	+	0.0703747i	−0.198712	+	0.980058i	$0.563676\pi$
$450$		0			0
$451$	−40.6959	+	6.54326i	−1.91630	+	0.308110i
$452$	8.15153	+	8.15153i	0.383416	+	0.383416i
$453$		0			0
$454$	1.20620	+	1.66019i	0.0566096	+	0.0779164i
$455$	−0.335137	+	1.41609i	−0.0157115	+	0.0663871i
$456$		0			0
$457$	18.2443	+	9.29594i	0.853433	+	0.434846i	0.825257	−	0.564757i	$-0.191030\pi$
$457$	18.2443	+	9.29594i	0.853433	+	0.434846i	0.0281758	+	0.999603i	$0.491030\pi$
$458$	−2.80391	−	17.7032i	−0.131018	−	0.827215i
$459$		0			0
$460$	−3.99222	−	3.38743i	−0.186138	−	0.157940i
$461$		−	0.616244i		−	0.0287013i	−0.999897	−	0.0143507i	$-0.995432\pi$
$461$		−	0.616244i		−	0.0287013i	0.999897	−	0.0143507i	$-0.00456812\pi$
$462$		0			0
$463$	−13.5983	+	13.5983i	−0.631968	+	0.631968i	−0.948561	−	0.316593i	$-0.897461\pi$
$463$	−13.5983	+	13.5983i	−0.631968	+	0.631968i	0.316593	+	0.948561i	$0.397461\pi$
$464$	0.211203	−	0.650015i	0.00980484	−	0.0301762i
$465$		0			0
$466$	−19.8886	−	14.4499i	−0.921323	−	0.669380i
$467$	−0.705649	+	1.38491i	−0.0326535	+	0.0640862i	−0.906757	−	0.421654i	$-0.861450\pi$
$467$	−0.705649	+	1.38491i	−0.0326535	+	0.0640862i	0.874103	+	0.485740i	$0.161450\pi$
$468$		0			0
$469$	3.33825	+	2.42538i	0.154146	+	0.111994i
$470$	−24.2466	−	14.7508i	−1.11841	−	0.680404i
$471$		0			0
$472$	−0.305982	+	0.305982i	−0.0140840	+	0.0140840i
$473$	−33.9331	+	11.1134i	−1.56024	+	0.510994i
$474$		0			0
$475$	11.6433	+	22.4908i	0.534232	+	1.03195i
$476$	0.893428	−	0.649114i	0.0409502	−	0.0297521i
$477$		0			0
$478$	2.64401	+	1.34719i	0.120934	+	0.0616191i
$479$	−7.47583	−	23.0082i	−0.341579	−	1.05127i	−0.963390	−	0.268105i	$-0.913603\pi$
$479$	−7.47583	−	23.0082i	−0.341579	−	1.05127i	0.621810	−	0.783168i	$-0.286397\pi$
$480$		0			0
$481$	4.07197	+	5.60459i	0.185666	+	0.255547i
$482$	18.9658	−	9.66356i	0.863869	−	0.440163i
$483$		0			0
$484$	10.9999	−	0.0514844i	0.499995	−	0.00234020i
$485$	12.0790	−	29.4300i	0.548481	−	1.33635i
$486$		0			0
$487$	−18.5340	−	2.93550i	−0.839857	−	0.133020i	−0.278337	−	0.960483i	$-0.589783\pi$
$487$	−18.5340	−	2.93550i	−0.839857	−	0.133020i	−0.561520	+	0.827463i	$0.689783\pi$
$488$	12.5273	−	1.98412i	0.567083	−	0.0898171i
$489$		0			0
$490$	−14.3116	−	1.07983i	−0.646531	−	0.0487818i
$491$	−14.9190	+	20.5343i	−0.673285	+	0.926698i	−0.999829	−	0.0184843i	$-0.994116\pi$
$491$	−14.9190	+	20.5343i	−0.673285	+	0.926698i	0.326544	+	0.945182i	$0.394116\pi$
$492$		0			0
$493$	0.449365	+	0.881928i	0.0202384	+	0.0397200i
$494$	−4.32282			−0.194493
$495$		0			0
$496$	3.52096			0.158096
$497$	−2.75138	−	5.39989i	−0.123416	−	0.242218i
$498$		0			0
$499$	5.36524	−	7.38462i	0.240181	−	0.330581i	−0.671861	−	0.740677i	$-0.734505\pi$
$499$	5.36524	−	7.38462i	0.240181	−	0.330581i	0.912042	+	0.410096i	$0.134505\pi$
$500$	−11.1539	−	0.769128i	−0.498815	−	0.0343965i
$501$		0			0
$502$	13.1171	−	2.07755i	0.585446	−	0.0927255i
$503$	−22.1939	−	3.51517i	−0.989577	−	0.156734i	−0.359399	−	0.933184i	$-0.617018\pi$
$503$	−22.1939	−	3.51517i	−0.989577	−	0.156734i	−0.630178	+	0.776451i	$0.717018\pi$
$504$		0			0
$505$	−19.3341	+	8.08174i	−0.860358	+	0.359633i
$506$	−5.47838	+	5.50408i	−0.243544	+	0.244686i
$507$		0			0
$508$	5.78299	−	2.94658i	0.256579	−	0.130733i
$509$	−16.8593	−	23.2049i	−0.747276	−	1.02854i	−0.998167	−	0.0605220i	$-0.980723\pi$
$509$	−16.8593	−	23.2049i	−0.747276	−	1.02854i	0.250891	−	0.968015i	$-0.419277\pi$
$510$		0			0
$511$	0.269717	+	0.830104i	0.0119316	+	0.0367217i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$		0			0
$514$	−14.9743	+	10.8794i	−0.660486	+	0.479871i
$515$	−0.143011	+	0.168544i	−0.00630184	+	0.00742696i
$516$		0			0
$517$	−24.6636	+	34.1141i	−1.08470	+	1.50034i
$518$	4.37690	−	4.37690i	0.192310	−	0.192310i
$519$		0			0
$520$	0.991845	−	1.63034i	0.0434953	−	0.0714953i
$521$	27.5311	+	20.0025i	1.20616	+	0.876325i	0.994876	−	0.101100i	$-0.0322361\pi$
$521$	27.5311	+	20.0025i	1.20616	+	0.876325i	0.211282	+	0.977425i	$0.432236\pi$
$522$		0			0
$523$	12.9583	−	25.4321i	0.566628	−	1.11207i	−0.412903	−	0.910775i	$-0.635485\pi$
$523$	12.9583	−	25.4321i	0.566628	−	1.11207i	0.979531	−	0.201295i	$-0.0645149\pi$
$524$	1.26494	+	0.919032i	0.0552591	+	0.0401481i
$525$		0			0
$526$	7.62180	−	23.4575i	0.332326	−	1.02279i
$527$	−3.60563	+	3.60563i	−0.157064	+	0.157064i
$528$		0			0
$529$			17.5175i			0.761630i
$530$	−1.50003	−	18.3035i	−0.0651572	−	0.795052i
$531$		0			0
$532$	0.604220	+	3.81490i	0.0261963	+	0.165397i
$533$	9.45038	+	4.81521i	0.409341	+	0.208570i
$534$		0			0
$535$	−7.66786	−	12.4225i	−0.331510	−	0.537073i
$536$	−3.18063	−	4.37777i	−0.137382	−	0.189091i
$537$		0			0
$538$	−14.3998	−	14.3998i	−0.620819	−	0.620819i
$539$	−3.28094	+	21.0335i	−0.141320	+	0.905976i
$540$		0			0
$541$	29.0892	+	9.45165i	1.25064	+	0.406358i	0.858151	−	0.513398i	$-0.171613\pi$
$541$	29.0892	+	9.45165i	1.25064	+	0.406358i	0.392491	+	0.919756i	$0.371613\pi$
$542$	−7.36573	−	1.16662i	−0.316385	−	0.0501105i
$543$		0			0
$544$	−1.37734	+	0.447525i	−0.0590530	+	0.0191875i
$545$	−20.0295	+	17.2190i	−0.857970	+	0.737582i
$546$		0			0
$547$	0.0192582	−	0.121591i	0.000823420	−	0.00519887i	−0.987273	−	0.159033i	$-0.949162\pi$
$547$	0.0192582	−	0.121591i	0.000823420	−	0.00519887i	0.988097	+	0.153834i	$0.0491623\pi$
$548$	0.766306	+	1.50396i	0.0327350	+	0.0642460i
$549$		0			0
$550$	−2.44991	+	16.4012i	−0.104464	+	0.699348i
$551$	−3.46189			−0.147481
$552$		0			0
$553$	−1.20332	+	7.59748i	−0.0511705	+	0.323078i
$554$	−9.62494	+	13.2476i	−0.408924	+	0.562836i
$555$		0			0
$556$	−8.25188	+	2.68120i	−0.349958	+	0.113708i
$557$	35.5695	−	5.63365i	1.50713	−	0.238705i	0.652436	−	0.757844i	$-0.273747\pi$
$557$	35.5695	−	5.63365i	1.50713	−	0.238705i	0.854690	+	0.519138i	$0.173747\pi$
$558$		0			0
$559$	8.73836	+	2.83926i	0.369593	+	0.120088i
$560$	−1.57741	−	0.647424i	−0.0666579	−	0.0273587i
$561$		0			0
$562$	2.96093	+	2.96093i	0.124899	+	0.124899i
$563$	−10.5592	+	5.38016i	−0.445015	+	0.226747i	−0.662114	−	0.749403i	$-0.730341\pi$
$563$	−10.5592	+	5.38016i	−0.445015	+	0.226747i	0.217099	+	0.976150i	$0.430341\pi$
$564$		0			0
$565$	13.5396	+	21.9352i	0.569615	+	0.922822i
$566$	8.54143	+	26.2878i	0.359023	+	1.10496i
$567$		0			0
$568$	1.24328	+	7.84977i	0.0521669	+	0.329369i
$569$	−28.8735	+	20.9778i	−1.21044	+	0.879435i	−0.995270	−	0.0971424i	$-0.969030\pi$
$569$	−28.8735	+	20.9778i	−1.21044	+	0.879435i	−0.215168	+	0.976577i	$0.569030\pi$
$570$		0			0
$571$		−	31.2536i		−	1.30792i	−0.756528	−	0.653961i	$-0.773106\pi$
$571$		−	31.2536i		−	1.30792i	0.756528	−	0.653961i	$-0.226894\pi$
$572$	−2.29384	−	1.65838i	−0.0959101	−	0.0693404i
$573$		0			0
$574$	2.92851	−	9.01301i	0.122233	−	0.376196i
$575$	−6.94248	−	9.42680i	−0.289521	−	0.393125i
$576$		0			0
$577$	20.9695	−	41.1550i	0.872972	−	1.71330i	0.191454	−	0.981502i	$-0.438680\pi$
$577$	20.9695	−	41.1550i	0.872972	−	1.71330i	0.681518	−	0.731801i	$-0.261320\pi$
$578$	−6.76566	+	13.2784i	−0.281415	+	0.552307i
$579$		0			0
$580$	0.794308	−	1.30564i	0.0329819	−	0.0542139i
$581$	−0.0562850	+	0.173227i	−0.00233510	+	0.00718668i
$582$		0			0
$583$	−27.2394	+	0.0637459i	−1.12814	+	0.00264009i
$584$		−	1.14461i		−	0.0473645i
$585$		0			0
$586$	15.1257	−	10.9894i	0.624836	−	0.453970i
$587$	4.82637	+	30.4725i	0.199205	+	1.25773i	0.861216	+	0.508239i	$0.169703\pi$
$587$	4.82637	+	30.4725i	0.199205	+	1.25773i	−0.662011	+	0.749494i	$0.730297\pi$
$588$		0			0
$589$	−5.51112	−	16.9615i	−0.227082	−	0.698885i
$590$	−0.823378	+	0.508233i	−0.0338979	+	0.0209236i
$591$		0			0
$592$	−7.23261	+	3.68520i	−0.297259	+	0.151461i
$593$	−3.14365	−	3.14365i	−0.129094	−	0.129094i	0.639607	−	0.768702i	$-0.279097\pi$
$593$	−3.14365	−	3.14365i	−0.129094	−	0.129094i	−0.768702	+	0.639607i	$0.779097\pi$
$594$		0			0
$595$	2.27834	−	0.952355i	0.0934028	−	0.0390427i
$596$	−14.0197	−	4.55529i	−0.574271	−	0.186592i
$597$		0			0
$598$	1.97370	−	0.312603i	0.0807105	−	0.0127833i
$599$	−8.63991	+	2.80728i	−0.353017	+	0.114702i	−0.480157	−	0.877183i	$-0.659420\pi$
$599$	−8.63991	+	2.80728i	−0.353017	+	0.114702i	0.127140	+	0.991885i	$0.459420\pi$
$600$		0			0
$601$	−17.5277	+	24.1249i	−0.714971	+	0.984074i	0.284705	+	0.958615i	$0.408105\pi$
$601$	−17.5277	+	24.1249i	−0.714971	+	0.984074i	−0.999676	+	0.0254583i	$0.991895\pi$
$602$	1.28426	−	8.10847i	0.0523423	−	0.330476i
$603$		0			0
$604$	−11.4487			−0.465841
$605$	23.9618	+	5.55260i	0.974186	+	0.225745i
$606$		0			0
$607$	9.38932	+	18.4276i	0.381101	+	0.747952i	0.999274	−	0.0380895i	$-0.0121272\pi$
$607$	9.38932	+	18.4276i	0.381101	+	0.747952i	−0.618174	+	0.786041i	$0.712127\pi$
$608$	0.792370	−	5.00283i	0.0321349	−	0.202892i
$609$		0			0
$610$	28.2806	+	2.13382i	1.14505	+	0.0863958i
$611$	10.3020	−	3.34732i	0.416774	−	0.135418i
$612$		0			0
$613$	−12.4538	−	1.97249i	−0.503005	−	0.0796682i	−0.100225	−	0.994965i	$-0.531956\pi$
$613$	−12.4538	−	1.97249i	−0.503005	−	0.0796682i	−0.402780	+	0.915297i	$0.631956\pi$
$614$	−9.59336	−	3.11707i	−0.387156	−	0.125795i
$615$		0			0
$616$	−1.14290	+	2.25611i	−0.0460489	+	0.0909013i
$617$	−6.47501	−	6.47501i	−0.260674	−	0.260674i	0.564654	−	0.825328i	$-0.309010\pi$
$617$	−6.47501	−	6.47501i	−0.260674	−	0.260674i	−0.825328	+	0.564654i	$0.809010\pi$
$618$		0			0
$619$	−23.3769	−	32.1756i	−0.939598	−	1.29325i	−0.955996	−	0.293380i	$-0.905220\pi$
$619$	−23.3769	−	32.1756i	−0.939598	−	1.29325i	0.0163985	−	0.999866i	$-0.494780\pi$
$620$	7.66148	+	1.81320i	0.307692	+	0.0728198i
$621$		0			0
$622$	20.4128	+	10.4008i	0.818478	+	0.417035i
$623$	−1.33725	−	8.44309i	−0.0535759	−	0.338265i
$624$		0			0
$625$	−23.8743	−	7.41752i	−0.954971	−	0.296701i
$626$		−	14.4830i		−	0.578857i
$627$		0			0
$628$	−0.582847	+	0.582847i	−0.0232581	+	0.0232581i
$629$	3.63272	−	11.1804i	0.144846	−	0.445790i
$630$		0			0
$631$	−21.6416	−	15.7235i	−0.861537	−	0.625943i	0.0667657	−	0.997769i	$-0.478732\pi$
$631$	−21.6416	−	15.7235i	−0.861537	−	0.625943i	−0.928303	+	0.371825i	$0.878732\pi$
$632$	4.57962	−	8.98801i	0.182167	−	0.357524i
$633$		0			0
$634$	−1.80973	−	1.31485i	−0.0718737	−	0.0522193i
$635$	14.1010	−	3.43356i	0.559580	−	0.136257i
$636$		0			0
$637$	3.87339	−	3.87339i	0.153469	−	0.153469i
$638$	−1.83699	−	1.32810i	−0.0727273	−	0.0525799i
$639$		0			0
$640$	1.70500	+	1.44671i	0.0673961	+	0.0571862i
$641$	10.9993	−	7.99147i	0.434447	−	0.315644i	−0.348978	−	0.937131i	$-0.613471\pi$
$641$	10.9993	−	7.99147i	0.434447	−	0.315644i	0.783425	+	0.621487i	$0.213471\pi$
$642$		0			0
$643$	16.4511	+	8.38228i	0.648770	+	0.330565i	0.747220	−	0.664577i	$-0.231388\pi$
$643$	16.4511	+	8.38228i	0.648770	+	0.330565i	−0.0984497	+	0.995142i	$0.531388\pi$
$644$	−0.551745	−	1.69810i	−0.0217418	−	0.0669144i
$645$		0			0
$646$	4.31171	+	5.93456i	0.169642	+	0.233492i
$647$	−16.0422	+	8.17393i	−0.630686	+	0.321350i	−0.739950	−	0.672662i	$-0.765151\pi$
$647$	−16.0422	+	8.17393i	−0.630686	+	0.321350i	0.109264	+	0.994013i	$0.465151\pi$
$648$		0			0
$649$	0.654551	+	1.27723i	0.0256934	+	0.0501357i
$650$	2.99780	−	3.03679i	0.117583	−	0.119113i
$651$		0			0
$652$	−8.82707	−	1.39807i	−0.345695	−	0.0547527i
$653$	26.2280	−	4.15411i	1.02638	−	0.162563i	0.379531	−	0.925179i	$-0.376086\pi$
$653$	26.2280	−	4.15411i	1.02638	−	0.162563i	0.646851	+	0.762616i	$0.276086\pi$
$654$		0			0
$655$	2.27918	+	2.65118i	0.0890549	+	0.103590i
$656$	−7.30492	+	10.0544i	−0.285209	+	0.392557i
$657$		0			0
$658$	−4.39397	−	8.62366i	−0.171295	−	0.336185i
$659$	36.6251			1.42671			0.713356	−	0.700802i	$-0.247174\pi$
$659$	36.6251			1.42671			0.713356	+	0.700802i	$0.247174\pi$
$660$		0			0
$661$	7.39959			0.287811			0.143905	−	0.989591i	$-0.454034\pi$
$661$	7.39959			0.287811			0.143905	+	0.989591i	$0.454034\pi$
$662$	−0.892871	−	1.75236i	−0.0347024	−	0.0681073i
$663$		0			0
$664$	0.140398	−	0.193242i	0.00544851	−	0.00749923i
$665$	−0.649806	+	8.61222i	−0.0251984	+	0.333968i
$666$		0			0
$667$	1.58062	−	0.250345i	0.0612017	−	0.00969339i
$668$	20.8648	+	3.30466i	0.807283	+	0.127861i
$669$		0			0
$670$	−4.66650	−	11.1638i	−0.180283	−	0.431294i
$671$	6.48335	−	41.5635i	0.250287	−	1.60454i
$672$		0			0
$673$	−27.1875	+	13.8527i	−1.04800	+	0.533983i	−0.891183	−	0.453644i	$-0.850124\pi$
$673$	−27.1875	+	13.8527i	−1.04800	+	0.533983i	−0.156818	+	0.987627i	$0.550124\pi$
$674$	0.238296	+	0.327986i	0.00917881	+	0.0126335i
$675$		0			0
$676$	−3.79215	−	11.6710i	−0.145852	−	0.448886i
$677$	26.6676	+	13.5878i	1.02492	+	0.522223i	0.883847	−	0.467776i	$-0.154945\pi$
$677$	26.6676	+	13.5878i	1.02492	+	0.522223i	0.141074	+	0.989999i	$0.454945\pi$
$678$		0			0
$679$	8.77679	−	6.37671i	0.336822	−	0.244716i
$680$	−3.22750	+	0.264505i	−0.123769	+	0.0101433i
$681$		0			0
$682$	3.58261	−	11.1146i	0.137185	−	0.425599i
$683$	13.9351	−	13.9351i	0.533214	−	0.533214i	−0.388314	−	0.921527i	$-0.626942\pi$
$683$	13.9351	−	13.9351i	0.533214	−	0.533214i	0.921527	+	0.388314i	$0.126942\pi$
$684$		0			0
$685$	0.892954	+	3.66719i	0.0341180	+	0.140116i
$686$	−8.27807	−	6.01437i	−0.316058	−	0.229630i
$687$		0			0
$688$	−4.88763	+	9.59252i	−0.186339	+	0.365711i
$689$	5.67063	+	4.11995i	0.216034	+	0.156958i
$690$		0			0
$691$	−9.06481	+	27.8986i	−0.344841	+	1.06131i	0.616827	+	0.787099i	$0.288418\pi$
$691$	−9.06481	+	27.8986i	−0.344841	+	1.06131i	−0.961669	+	0.274214i	$0.911582\pi$
$692$	1.73851	−	1.73851i	0.0660882	−	0.0660882i
$693$		0			0
$694$			10.6915i			0.405844i
$695$	−19.3365	+	1.58469i	−0.733476	+	0.0601108i
$696$		0			0
$697$	−2.81556	−	17.7767i	−0.106647	−	0.673341i
$698$	7.16813	+	3.65234i	0.271318	+	0.138243i
$699$		0			0
$700$	−3.09899	−	2.22109i	−0.117131	−	0.0839494i
$701$	−4.36586	−	6.00910i	−0.164896	−	0.226960i	0.718570	−	0.695454i	$-0.244797\pi$
$701$	−4.36586	−	6.00910i	−0.164896	−	0.226960i	−0.883467	+	0.468494i	$0.844797\pi$
$702$		0			0
$703$	29.0734	+	29.0734i	1.09652	+	1.09652i
$704$	2.33971	−	2.35069i	0.0881813	−	0.0885950i
$705$		0			0
$706$	24.0666	+	7.81972i	0.905759	+	0.294299i
$707$	−7.05822	−	1.11791i	−0.265452	−	0.0420434i
$708$		0			0
$709$	−25.9291	+	8.42488i	−0.973788	+	0.316403i	−0.752344	−	0.658770i	$-0.771077\pi$
$709$	−25.9291	+	8.42488i	−0.973788	+	0.316403i	−0.221444	+	0.975173i	$0.571077\pi$
$710$	−1.33708	+	17.7210i	−0.0501798	+	0.665059i
$711$		0			0
$712$	−1.75367	+	11.0722i	−0.0657214	+	0.414949i
$713$	3.74281	+	7.34567i	0.140169	+	0.275098i
$714$		0			0
$715$	−4.13727	−	4.78983i	−0.154725	−	0.179130i
$716$	15.9154			0.594785
$717$		0			0
$718$	2.54212	−	16.0503i	0.0948712	−	0.598993i
$719$	1.00656	−	1.38541i	0.0375383	−	0.0516670i	−0.789835	−	0.613319i	$-0.789834\pi$
$719$	1.00656	−	1.38541i	0.0375383	−	0.0516670i	0.827374	+	0.561652i	$0.189834\pi$
$720$		0			0
$721$	−0.0716907	+	0.0232937i	−0.00266990	+	0.000867504i
$722$	−6.57421	+	1.04125i	−0.244667	+	0.0387514i
$723$		0			0
$724$	4.89640	+	1.59094i	0.181973	+	0.0591267i
$725$	2.40075	−	2.43198i	0.0891618	−	0.0903215i
$726$		0			0
$727$	−13.9556	−	13.9556i	−0.517583	−	0.517583i	0.399256	−	0.916839i	$-0.369268\pi$
$727$	−13.9556	−	13.9556i	−0.517583	−	0.517583i	−0.916839	+	0.399256i	$0.869268\pi$
$728$	0.579855	−	0.295451i	0.0214909	−	0.0109501i
$729$		0			0
$730$	0.589445	−	2.49064i	0.0218163	−	0.0921826i
$731$	−4.81803	−	14.8284i	−0.178201	−	0.548447i
$732$		0			0
$733$	−0.923038	−	5.82783i	−0.0340932	−	0.215256i	0.964760	−	0.263131i	$-0.0847551\pi$
$733$	−0.923038	−	5.82783i	−0.0340932	−	0.215256i	−0.998853	+	0.0478750i	$0.984755\pi$
$734$	6.93460	−	5.03828i	0.255961	−	0.185966i
$735$		0			0
$736$			2.34147i			0.0863079i
$737$	−17.0556	+	5.58585i	−0.628250	+	0.205757i
$738$		0			0
$739$	10.0720	−	30.9985i	0.370505	−	1.14030i	−0.575956	−	0.817480i	$-0.695370\pi$
$739$	10.0720	−	30.9985i	0.370505	−	1.14030i	0.946461	−	0.322817i	$-0.104630\pi$
$740$	−17.6357	+	4.29426i	−0.648300	+	0.157860i
$741$		0			0
$742$	2.84325	−	5.58020i	0.104379	−	0.204856i
$743$	−19.3261	+	37.9296i	−0.709007	+	1.39150i	0.202113	+	0.979362i	$0.435219\pi$
$743$	−19.3261	+	37.9296i	−0.709007	+	1.39150i	−0.911120	+	0.412142i	$0.864781\pi$
$744$		0			0
$745$	−28.1606	−	17.1319i	−1.03172	−	0.627665i
$746$	10.1580	−	31.2632i	0.371911	−	1.14463i
$747$		0			0
$748$	0.0112405	+	4.80319i	0.000410993	+	0.175622i
$749$		−	4.97840i		−	0.181907i
$750$		0			0
$751$	22.4102	−	16.2819i	0.817758	−	0.594136i	−0.0983111	−	0.995156i	$-0.531344\pi$
$751$	22.4102	−	16.2819i	0.817758	−	0.594136i	0.916070	+	0.401019i	$0.131344\pi$
$752$	1.98553	+	12.5361i	0.0724047	+	0.457146i
$753$		0			0
$754$	0.180248	+	0.554747i	0.00656425	+	0.0202027i
$755$	−24.9119	−	5.89576i	−0.906637	−	0.214569i
$756$		0			0
$757$	14.2535	−	7.26251i	0.518051	−	0.263960i	−0.175357	−	0.984505i	$-0.556108\pi$
$757$	14.2535	−	7.26251i	0.518051	−	0.263960i	0.693409	+	0.720544i	$0.256108\pi$
$758$	9.05740	+	9.05740i	0.328980	+	0.328980i
$759$		0			0
$760$	4.30048	−	10.4779i	0.155995	−	0.380074i
$761$	−6.47967	−	2.10537i	−0.234888	−	0.0763197i	0.189208	−	0.981937i	$-0.439408\pi$
$761$	−6.47967	−	2.10537i	−0.234888	−	0.0763197i	−0.424096	+	0.905617i	$0.639408\pi$
$762$		0			0
$763$	−8.89670	+	1.40910i	−0.322082	+	0.0510128i
$764$	25.5794	−	8.31126i	0.925431	−	0.300691i
$765$		0			0
$766$	−13.1004	+	18.0312i	−0.473338	+	0.651494i
$767$	0.0577717	−	0.364756i	0.00208602	−	0.0131706i
$768$		0			0
$769$	48.7563			1.75820			0.879098	−	0.476640i	$-0.158146\pi$
$769$	48.7563			1.75820			0.879098	+	0.476640i	$0.158146\pi$
$770$	−3.64875	+	4.32065i	−0.131492	+	0.155705i
$771$		0			0
$772$	−4.39692	−	8.62943i	−0.158248	−	0.310580i
$773$	−4.09258	+	25.8396i	−0.147200	+	0.929384i	0.797944	+	0.602731i	$0.205921\pi$
$773$	−4.09258	+	25.8396i	−0.147200	+	0.929384i	−0.945144	+	0.326653i	$0.894079\pi$
$774$		0			0
$775$	15.7373	+	7.89090i	0.565301	+	0.283449i
$776$	−13.5306	+	4.39636i	−0.485720	+	0.157820i
$777$		0			0
$778$	13.5508	+	2.14623i	0.485818	+	0.0769461i
$779$	59.8686	+	19.4525i	2.14501	+	0.696957i
$780$		0			0
$781$	26.0443	+	4.06256i	0.931939	+	0.145370i
$782$	−2.39778	−	2.39778i	−0.0857444	−	0.0857444i
$783$		0			0
$784$	3.77271	+	5.19269i	0.134740	+	0.185453i
$785$	−1.56840	+	0.968102i	−0.0559787	+	0.0345531i
$786$		0			0
$787$	20.7757	+	10.5858i	0.740574	+	0.377341i	0.783217	−	0.621749i	$-0.213578\pi$
$787$	20.7757	+	10.5858i	0.740574	+	0.377341i	−0.0426425	+	0.999090i	$0.513578\pi$
$788$	1.31953	+	8.33122i	0.0470065	+	0.296787i
$789$		0			0
$790$	14.5936	−	17.1992i	0.519218	−	0.611919i
$791$			8.79065i			0.312560i
$792$		0			0
$793$	−7.65408	+	7.65408i	−0.271804	+	0.271804i
$794$	−0.352855	+	1.08598i	−0.0125223	+	0.0385398i
$795$		0			0
$796$	0.668964	+	0.486031i	0.0237108	+	0.0172269i
$797$	16.0427	−	31.4855i	0.568261	−	1.11527i	−0.410804	−	0.911724i	$-0.634752\pi$
$797$	16.0427	−	31.4855i	0.568261	−	1.11527i	0.979064	−	0.203551i	$-0.0652482\pi$
$798$		0			0
$799$	−14.8709	−	10.8043i	−0.526093	−	0.382229i
$800$	2.96500	+	4.02601i	0.104829	+	0.142341i
$801$		0			0
$802$	−9.74633	+	9.74633i	−0.344155	+	0.344155i
$803$	−3.61319	−	1.16466i	−0.127507	−	0.0410998i
$804$		0			0
$805$	−0.326103	−	3.97913i	−0.0114936	−	0.140246i
$806$	−2.43103	+	1.76625i	−0.0856295	+	0.0622135i
$807$		0			0
$808$	8.35005	+	4.25456i	0.293754	+	0.149675i
$809$	−11.3255	−	34.8562i	−0.398182	−	1.22548i	−0.926455	−	0.376405i	$-0.877160\pi$
$809$	−11.3255	−	34.8562i	−0.398182	−	1.22548i	0.528273	−	0.849075i	$-0.322840\pi$
$810$		0			0
$811$	14.6687	+	20.1898i	0.515089	+	0.708960i	0.984767	−	0.173878i	$-0.0556299\pi$
$811$	14.6687	+	20.1898i	0.515089	+	0.708960i	−0.469678	+	0.882838i	$0.655630\pi$
$812$	0.464371	−	0.236609i	0.0162962	−	0.00830334i
$813$		0			0
$814$	4.27378	+	26.5808i	0.149796	+	0.931657i
$815$	−18.4874	−	7.58784i	−0.647585	−	0.265790i
$816$		0			0
$817$	53.8602	+	8.53061i	1.88433	+	0.298448i
$818$	−19.9702	+	3.16297i	−0.698241	+	0.110591i
$819$		0			0
$820$	−21.0729	+	18.1161i	−0.735899	+	0.632640i
$821$	−7.96168	+	10.9583i	−0.277865	+	0.382448i	−0.925025	−	0.379906i	$-0.875956\pi$
$821$	−7.96168	+	10.9583i	−0.277865	+	0.382448i	0.647160	+	0.762354i	$0.275956\pi$
$822$		0			0
$823$	3.90905	+	7.67193i	0.136261	+	0.267427i	0.949047	−	0.315136i	$-0.102050\pi$
$823$	3.90905	+	7.67193i	0.136261	+	0.267427i	−0.812786	+	0.582563i	$0.802050\pi$
$824$	0.0988529			0.00344371
$825$		0			0
$826$	−0.329973			−0.0114812
$827$	4.53336	+	8.89722i	0.157640	+	0.309387i	0.956295	−	0.292403i	$-0.0944547\pi$
$827$	4.53336	+	8.89722i	0.157640	+	0.309387i	−0.798655	+	0.601789i	$0.794455\pi$
$828$		0			0
$829$	−12.4310	+	17.1098i	−0.431746	+	0.594247i	−0.968353	−	0.249585i	$-0.919706\pi$
$829$	−12.4310	+	17.1098i	−0.431746	+	0.594247i	0.536607	+	0.843832i	$0.319706\pi$
$830$	0.405015	−	0.348185i	0.0140583	−	0.0120857i
$831$		0			0
$832$	−0.842930	+	0.133507i	−0.0292233	+	0.00462852i
$833$	−9.18100	−	1.45413i	−0.318103	−	0.0503825i
$834$		0			0
$835$	43.6991	+	17.9356i	1.51227	+	0.620687i
$836$	−14.9861	−	7.59169i	−0.518306	−	0.262564i
$837$		0			0
$838$	−17.3711	+	8.85100i	−0.600073	+	0.305753i
$839$	−23.3328	−	32.1148i	−0.805537	−	1.10873i	−0.991997	−	0.126264i	$-0.959701\pi$
$839$	−23.3328	−	32.1148i	−0.805537	−	1.10873i	0.186460	−	0.982463i	$-0.440299\pi$
$840$		0			0
$841$	−8.81714	−	27.1364i	−0.304039	−	0.935737i
$842$	2.54735	+	1.29794i	0.0877875	+	0.0447300i
$843$		0			0
$844$	11.7834	−	8.56117i	0.405603	−	0.294688i
$845$	−2.24131	−	27.3485i	−0.0771033	−	0.940819i
$846$		0			0
$847$	5.95893	+	5.90340i	0.204751	+	0.202843i
$848$	−5.80747	+	5.80747i	−0.199429	+	0.199429i
$849$		0			0
$850$	−7.15913	−	1.08652i	−0.245556	−	0.0372674i
$851$	−15.3766	−	11.1718i	−0.527104	−	0.382964i
$852$		0			0
$853$	16.5238	−	32.4298i	0.565764	−	1.11037i	−0.414012	−	0.910272i	$-0.635873\pi$
$853$	16.5238	−	32.4298i	0.565764	−	1.11037i	0.979775	−	0.200102i	$-0.0641273\pi$
$854$	7.82458	+	5.68489i	0.267752	+	0.194533i
$855$		0			0
$856$	−2.01746	+	6.20910i	−0.0689554	+	0.212223i
$857$	10.3508	−	10.3508i	0.353576	−	0.353576i	−0.507862	−	0.861438i	$-0.669564\pi$
$857$	10.3508	−	10.3508i	0.353576	−	0.353576i	0.861438	+	0.507862i	$0.169564\pi$
$858$		0			0
$859$		−	21.8229i		−	0.744588i	−0.928115	−	0.372294i	$-0.878571\pi$
$859$		−	21.8229i		−	0.744588i	0.928115	−	0.372294i	$-0.121429\pi$
$860$	−15.5752	+	18.3559i	−0.531109	+	0.625933i
$861$		0			0
$862$	−2.52053	−	15.9140i	−0.0858495	−	0.542032i
$863$	5.34286	+	2.72232i	0.181873	+	0.0926690i	0.542556	−	0.840019i	$-0.317456\pi$
$863$	5.34286	+	2.72232i	0.181873	+	0.0926690i	−0.360683	+	0.932688i	$0.617456\pi$
$864$		0			0
$865$	4.67821	−	2.88764i	0.159064	−	0.0981828i
$866$	14.3556	+	19.7588i	0.487823	+	0.671431i
$867$		0			0
$868$	1.89851	+	1.89851i	0.0644397	+	0.0644397i
$869$	−23.7125	−	23.6018i	−0.804392	−	0.800636i
$870$		0			0
$871$	4.39211	+	1.42708i	0.148821	+	0.0483548i
$872$	11.6671	+	1.84788i	0.395097	+	0.0625772i
$873$		0			0
$874$	11.2795	−	3.66494i	0.381536	−	0.123969i
$875$	−5.59947	−	6.42890i	−0.189297	−	0.217337i
$876$		0			0
$877$	4.44076	−	28.0379i	0.149954	−	0.946771i	−0.791876	−	0.610682i	$-0.790895\pi$
$877$	4.44076	−	28.0379i	0.149954	−	0.946771i	0.941830	−	0.336090i	$-0.109105\pi$
$878$	6.01836	+	11.8117i	0.203110	+	0.398625i
$879$		0			0
$880$	6.30166	−	3.91012i	0.212429	−	0.131810i
$881$	9.63291			0.324541			0.162270	−	0.986746i	$-0.448118\pi$
$881$	9.63291			0.324541			0.162270	+	0.986746i	$0.448118\pi$
$882$		0			0
$883$	−7.79859	+	49.2384i	−0.262443	+	1.65700i	0.406471	+	0.913663i	$0.366759\pi$
$883$	−7.79859	+	49.2384i	−0.262443	+	1.65700i	−0.668915	+	0.743339i	$0.733241\pi$
$884$	0.726483	−	0.999918i	0.0244343	−	0.0336309i
$885$		0			0
$886$	−2.07093	+	0.672885i	−0.0695742	+	0.0226060i
$887$	33.0342	−	5.23210i	1.10918	−	0.175677i	0.425144	−	0.905126i	$-0.360223\pi$
$887$	33.0342	−	5.23210i	1.10918	−	0.175677i	0.684035	+	0.729449i	$0.260223\pi$
$888$		0			0
$889$	4.70701	+	1.52940i	0.157868	+	0.0512944i
$890$	−9.51779	+	23.1896i	−0.319037	+	0.777317i
$891$		0			0
$892$	−0.951712	−	0.951712i	−0.0318657	−	0.0318657i
$893$	57.2823	−	29.1868i	1.91688	−	0.976698i
$894$		0			0
$895$	34.6312	+	8.19597i	1.15759	+	0.273961i
$896$	0.235640	+	0.725226i	0.00787219	+	0.0242281i
$897$		0			0
$898$	−0.754900	−	4.76625i	−0.0251913	−	0.159052i
$899$	−1.94687	+	1.41448i	−0.0649316	+	0.0471756i
$900$		0			0
$901$		−	11.8942i		−	0.396255i
$902$	24.3056	+	33.2897i	0.809289	+	1.10843i
$903$		0			0
$904$	3.56235	−	10.9638i	0.118482	−	0.364650i
$905$	9.83509	+	5.98333i	0.326929	+	0.198893i
$906$		0			0
$907$	−19.2581	+	37.7962i	−0.639456	+	1.25500i	0.312833	+	0.949808i	$0.398722\pi$
$907$	−19.2581	+	37.7962i	−0.639456	+	1.25500i	−0.952290	+	0.305196i	$0.901278\pi$
$908$	0.931635	−	1.82844i	0.0309174	−	0.0606788i
$909$		0			0
$910$	1.41389	−	0.344280i	0.0468700	−	0.0114128i
$911$	4.93516	−	15.1889i	0.163509	−	0.503229i	−0.835414	−	0.549621i	$-0.814772\pi$
$911$	4.93516	−	15.1889i	0.163509	−	0.503229i	0.998923	+	0.0463915i	$0.0147722\pi$
$912$		0			0
$913$	−0.467147	−	0.639819i	−0.0154603	−	0.0211749i
$914$		−	20.4761i		−	0.677288i
$915$		0			0
$916$	−14.5007	+	10.5354i	−0.479116	+	0.348098i
$917$	0.186514	+	1.17760i	0.00615923	+	0.0388879i
$918$		0			0
$919$	−7.78224	−	23.9513i	−0.256713	−	0.790080i	−0.993487	−	0.113942i	$-0.963652\pi$
$919$	−7.78224	−	23.9513i	−0.256713	−	0.790080i	0.736775	−	0.676138i	$-0.236348\pi$
$920$	−1.20579	+	5.09495i	−0.0397539	+	0.167976i
$921$		0			0
$922$	−0.549077	+	0.279769i	−0.0180829	+	0.00921369i
$923$	−4.79616	−	4.79616i	−0.157868	−	0.157868i
$924$		0			0
$925$	−40.5859	+	0.262256i	−1.33446	+	0.00862293i
$926$	18.2897	+	5.94269i	0.601037	+	0.195289i
$927$		0			0
$928$	−0.675052	+	0.106918i	−0.0221597	+	0.00350974i
$929$	8.61430	−	2.79896i	0.282626	−	0.0918308i	−0.164274	−	0.986415i	$-0.552528\pi$
$929$	8.61430	−	2.79896i	0.282626	−	0.0918308i	0.446900	+	0.894584i	$0.352528\pi$
$930$		0			0
$931$	19.1095	−	26.3020i	0.626289	−	0.862012i
$932$	−3.84574	+	24.2810i	−0.125971	+	0.795352i
$933$		0			0
$934$	1.55432			0.0508591
$935$	−2.44905	+	10.4573i	−0.0800926	+	0.341992i
$936$		0			0
$937$	−10.0962	−	19.8149i	−0.329829	−	0.647326i	0.665227	−	0.746641i	$-0.268335\pi$
$937$	−10.0962	−	19.8149i	−0.329829	−	0.647326i	−0.995056	+	0.0993152i	$0.968335\pi$
$938$	0.645497	−	4.07551i	0.0210762	−	0.133070i
$939$		0			0
$940$	−2.13533	+	28.3006i	−0.0696467	+	0.923064i
$941$	20.9430	−	6.80478i	0.682721	−	0.221829i	0.0529346	−	0.998598i	$-0.483143\pi$
$941$	20.9430	−	6.80478i	0.682721	−	0.221829i	0.629786	+	0.776769i	$0.283143\pi$
$942$		0			0
$943$	−28.7413	−	4.55217i	−0.935944	−	0.148239i
$944$	0.411545	+	0.133719i	0.0133947	+	0.00435219i
$945$		0			0
$946$	25.3074	+	25.1892i	0.822814	+	0.818972i
$947$	2.70333	+	2.70333i	0.0878464	+	0.0878464i	0.749664	−	0.661818i	$-0.230215\pi$
$947$	2.70333	+	2.70333i	0.0878464	+	0.0878464i	−0.661818	+	0.749664i	$0.730215\pi$
$948$		0			0
$949$	0.574182	+	0.790294i	0.0186387	+	0.0256540i
$950$	14.7535	−	20.5849i	0.478667	−	0.667862i
$951$		0			0
$952$	−0.983972	−	0.501359i	−0.0318907	−	0.0162491i
$953$	5.80899	+	36.6765i	0.188172	+	1.18807i	0.883168	+	0.469056i	$0.155406\pi$
$953$	5.80899	+	36.6765i	0.188172	+	1.18807i	−0.694997	+	0.719013i	$0.744594\pi$
$954$		0			0
$955$	59.9399	−	4.91228i	1.93961	−	0.158958i
$956$		−	2.96744i		−	0.0959740i
$957$		0			0
$958$	−17.1065	+	17.1065i	−0.552687	+	0.552687i
$959$	−0.397745	+	1.22413i	−0.0128439	+	0.0395294i
$960$		0			0
$961$	15.0500	+	10.9345i	0.485484	+	0.352725i
$962$	3.14509	−	6.17258i	0.101402	−	0.199012i
$963$		0			0
$964$	−17.2206	−	12.5115i	−0.554638	−	0.402968i
$965$	−5.12360	−	21.0416i	−0.164934	−	0.677353i
$966$		0			0
$967$	−16.6994	+	16.6994i	−0.537017	+	0.537017i	−0.922652	−	0.385634i	$-0.873983\pi$
$967$	−16.6994	+	16.6994i	−0.537017	+	0.537017i	0.385634	+	0.922652i	$0.373983\pi$
$968$	−5.03971	−	9.77759i	−0.161983	−	0.314264i
$969$		0			0
$970$	−31.7061	+	2.59842i	−1.01802	+	0.0834302i
$971$	21.9153	−	15.9224i	0.703294	−	0.510973i	−0.177709	−	0.984083i	$-0.556869\pi$
$971$	21.9153	−	15.9224i	0.703294	−	0.510973i	0.881003	+	0.473110i	$0.156869\pi$
$972$		0			0
$973$	−5.89515	−	3.00373i	−0.188990	−	0.0962951i
$974$	5.79872	+	17.8466i	0.185803	+	0.571843i
$975$		0			0
$976$	−7.45513	−	10.2611i	−0.238633	−	0.328450i
$977$	−36.0042	+	18.3451i	−1.15188	+	0.586911i	−0.922336	−	0.386388i	$-0.873722\pi$
$977$	−36.0042	+	18.3451i	−1.15188	+	0.586911i	−0.229541	+	0.973299i	$0.573722\pi$
$978$		0			0
$979$	33.1671	+	16.8018i	1.06003	+	0.536989i
$980$	5.53518	+	13.2419i	0.176815	+	0.422998i
$981$		0			0
$982$	25.0692	+	3.97058i	0.799992	+	0.126706i
$983$	−23.7573	+	3.76279i	−0.757740	+	0.120014i	−0.523338	−	0.852125i	$-0.675313\pi$
$983$	−23.7573	+	3.76279i	−0.757740	+	0.120014i	−0.234402	+	0.972140i	$0.575313\pi$
$984$		0			0
$985$	−1.41909	+	18.8079i	−0.0452159	+	0.599270i
$986$	0.581796	−	0.800773i	0.0185282	−	0.0255018i
$987$		0			0
$988$	1.96252	+	3.85166i	0.0624361	+	0.122538i
$989$	−25.2082			−0.801573
$990$		0			0
$991$	−4.81752			−0.153034			−0.0765169	−	0.997068i	$-0.524380\pi$
$991$	−4.81752			−0.153034			−0.0765169	+	0.997068i	$0.524380\pi$
$992$	−1.59848	−	3.13720i	−0.0507519	−	0.0996062i
$993$		0			0
$994$	−3.56224	+	4.90300i	−0.112987	+	0.155514i
$995$	1.20535	+	1.40208i	0.0382121	+	0.0444490i
$996$		0			0
$997$	−36.3270	+	5.75364i	−1.15049	+	0.182219i	−0.702409	−	0.711774i	$-0.747892\pi$
$997$	−36.3270	+	5.75364i	−1.15049	+	0.182219i	−0.448080	+	0.893993i	$0.647892\pi$
$998$	−9.01551	−	1.42792i	−0.285381	−	0.0451999i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bh.c.937.1		48
3.2	odd	2		110.2.k.a.57.6	yes	48
5.3	odd	4	inner	990.2.bh.c.343.3		48
11.6	odd	10	inner	990.2.bh.c.127.3		48
12.11	even	2		880.2.cm.c.497.2		48
15.2	even	4		550.2.bh.b.343.1		48
15.8	even	4		110.2.k.a.13.6	✓	48
15.14	odd	2		550.2.bh.b.57.1		48
33.17	even	10		110.2.k.a.17.6	yes	48
55.28	even	20	inner	990.2.bh.c.523.1		48
60.23	odd	4		880.2.cm.c.673.2		48
132.83	odd	10		880.2.cm.c.17.2		48
165.17	odd	20		550.2.bh.b.193.1		48
165.83	odd	20		110.2.k.a.83.6	yes	48
165.149	even	10		550.2.bh.b.457.1		48
660.83	even	20		880.2.cm.c.193.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.6	✓	48	15.8	even	4
110.2.k.a.17.6	yes	48	33.17	even	10
110.2.k.a.57.6	yes	48	3.2	odd	2
110.2.k.a.83.6	yes	48	165.83	odd	20
550.2.bh.b.57.1		48	15.14	odd	2
550.2.bh.b.193.1		48	165.17	odd	20
550.2.bh.b.343.1		48	15.2	even	4
550.2.bh.b.457.1		48	165.149	even	10
880.2.cm.c.17.2		48	132.83	odd	10
880.2.cm.c.193.2		48	660.83	even	20
880.2.cm.c.497.2		48	12.11	even	2
880.2.cm.c.673.2		48	60.23	odd	4
990.2.bh.c.127.3		48	11.6	odd	10	inner
990.2.bh.c.343.3		48	5.3	odd	4	inner
990.2.bh.c.523.1		48	55.28	even	20	inner
990.2.bh.c.937.1		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(-1.69562 + 1.45770i) q^{5} +(-0.753160 + 0.119289i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.06861 + 0.849027i) q^{10} +(1.49880 - 2.95865i) q^{11} +(-0.760418 + 0.387452i) q^{13} +(0.448214 + 0.616914i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(1.29037 + 0.657479i) q^{17} +(-4.09783 + 2.97724i) q^{19} +(-0.182641 - 2.22860i) q^{20} +(-3.31662 + 0.00776159i) q^{22} +(1.65567 - 1.65567i) q^{23} +(0.750246 - 4.94339i) q^{25} +(0.690445 + 0.501638i) q^{26} +(0.346189 - 0.679435i) q^{28} +(0.552936 + 0.401731i) q^{29} +(-1.08804 + 3.34864i) q^{31} +(-0.707107 + 0.707107i) q^{32} -1.44822i q^{34} +(1.10318 - 1.30015i) q^{35} +(-1.26983 - 8.01741i) q^{37} +(4.51312 + 2.29955i) q^{38} +(-1.90278 + 1.17450i) q^{40} +(-7.30492 - 10.0544i) q^{41} +(-7.61267 - 7.61267i) q^{43} +(1.51263 + 2.95160i) q^{44} +(-2.22687 - 0.723555i) q^{46} +(-12.5361 - 1.98553i) q^{47} +(-6.10438 + 1.98343i) q^{49} +(-4.74520 + 1.57578i) q^{50} +(0.133507 - 0.842930i) q^{52} +(-3.72862 - 7.31784i) q^{53} +(1.77142 + 7.20153i) q^{55} -0.762548 q^{56} +(0.106918 - 0.675052i) q^{58} +(-0.254349 + 0.350081i) q^{59} +(12.0627 - 3.91939i) q^{61} +(3.47761 - 0.550800i) q^{62} +(0.951057 + 0.309017i) q^{64} +(0.724592 - 1.76543i) q^{65} +(-3.82631 - 3.82631i) q^{67} +(-1.29037 + 0.657479i) q^{68} +(-1.65927 - 0.392691i) q^{70} +(2.45595 + 7.55864i) q^{71} +(-0.179057 - 1.13052i) q^{73} +(-6.56708 + 4.77126i) q^{74} -5.06519i q^{76} +(-0.775899 + 2.40712i) q^{77} +(3.11720 - 9.59376i) q^{79} +(1.91033 + 1.16218i) q^{80} +(-5.64213 + 11.0733i) q^{82} +(0.108440 - 0.212826i) q^{83} +(-3.14639 + 0.766141i) q^{85} +(-3.32686 + 10.2390i) q^{86} +(1.94318 - 2.68776i) q^{88} +11.2102i q^{89} +(0.526498 - 0.382523i) q^{91} +(0.366287 + 2.31265i) q^{92} +(3.92217 + 12.0712i) q^{94} +(2.60843 - 11.0217i) q^{95} +(-12.6763 + 6.45889i) q^{97} +(4.53858 + 4.53858i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47}+ \cdots + 72 q^{97}+O(q^{100}) \) 48 * q + 8 * q^5 - 20 * q^7 - 12 * q^11 + 12 * q^16 + 20 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 20 * q^25 - 8 * q^26 - 20 * q^28 + 16 * q^31 + 20 * q^37 + 36 * q^38 + 20 * q^41 + 40 * q^46 - 40 * q^47 - 40 * q^50 + 40 * q^52 + 96 * q^55 + 8 * q^56 + 48 * q^58 + 80 * q^61 - 40 * q^62 - 20 * q^68 - 56 * q^70 + 56 * q^71 - 20 * q^73 + 96 * q^77 + 12 * q^80 - 80 * q^85 + 56 * q^86 - 4 * q^88 - 68 * q^91 + 12 * q^92 - 20 * q^95 + 72 * q^97

Introduction

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