LMFDB - Embedded newform 990.2.bh.c.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(73,990)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			217.2
Character	$\chi$	$=$	990.217
Dual form			990.2.bh.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(1.90161 + 1.17638i) q^{5} +(-0.692077 - 1.35828i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-1.45937 + 1.69418i) q^{10} +(2.70495 - 1.91918i) q^{11} +(1.04553 + 0.165595i) q^{13} +(1.44982 - 0.471075i) q^{14} +(0.809017 + 0.587785i) q^{16} +(2.19616 - 0.347837i) q^{17} +(-1.91500 - 5.89375i) q^{19} +(-1.44502 - 1.70643i) q^{20} +(1.47241 + 2.97187i) q^{22} +(3.05791 - 3.05791i) q^{23} +(2.23228 + 4.47403i) q^{25} +(-0.327113 + 1.00675i) q^{26} +(0.238474 + 1.50566i) q^{28} +(-1.39938 + 4.30686i) q^{29} +(2.32781 - 1.69125i) q^{31} +(-0.707107 + 0.707107i) q^{32} +2.22353i q^{34} +(0.281782 - 3.39707i) q^{35} +(1.24018 - 0.631904i) q^{37} +(6.12076 - 0.969434i) q^{38} +(1.91147 - 1.16029i) q^{40} +(-2.38365 + 0.774496i) q^{41} +(6.40957 + 6.40957i) q^{43} +(-3.16562 + 0.989379i) q^{44} +(2.54190 + 3.49862i) q^{46} +(2.03678 - 3.99740i) q^{47} +(2.74855 - 3.78305i) q^{49} +(-4.76815 + 1.50490i) q^{50} +(-0.943185 - 0.480577i) q^{52} +(-0.594995 + 3.75665i) q^{53} +(7.40145 - 0.467516i) q^{55} -1.52443 q^{56} +(-4.03492 - 2.05589i) q^{58} +(-4.27154 - 1.38791i) q^{59} +(3.48115 - 4.79140i) q^{61} +(1.30628 + 2.56372i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(1.79339 + 1.54483i) q^{65} +(5.40776 + 5.40776i) q^{67} +(-2.19616 - 0.347837i) q^{68} +(3.31116 + 0.809731i) q^{70} +(7.19862 + 5.23010i) q^{71} +(-10.1633 + 5.17847i) q^{73} +(0.430117 + 1.32376i) q^{74} +6.19706i q^{76} +(-4.47882 - 2.34584i) q^{77} +(-4.69179 + 3.40879i) q^{79} +(0.846982 + 2.06945i) q^{80} +(-0.392075 - 2.47546i) q^{82} +(0.200087 + 1.26330i) q^{83} +(4.58543 + 1.92206i) q^{85} +(-7.33334 + 5.32798i) q^{86} +(-0.481987 - 3.28142i) q^{88} +10.5518i q^{89} +(-0.498662 - 1.53472i) q^{91} +(-3.85319 + 1.96330i) q^{92} +(3.62956 + 2.63703i) q^{94} +(3.29169 - 13.4604i) q^{95} +(6.92020 + 1.09605i) q^{97} +(3.30651 + 3.30651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$		0			0
$3$		0			0
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	1.90161	+	1.17638i	0.850428	+	0.526092i
$5$	1.90161	+	1.17638i	0.850428	+	0.526092i
$6$		0			0
$7$	−0.692077	−	1.35828i	−0.261581	−	0.513381i	0.722440	−	0.691433i	$-0.243020\pi$
$7$	−0.692077	−	1.35828i	−0.261581	−	0.513381i	−0.984021	+	0.178052i	$0.943020\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$		0			0
$10$	−1.45937	+	1.69418i	−0.461494	+	0.535746i
$11$	2.70495	−	1.91918i	0.815572	−	0.578656i
$11$	2.70495	−	1.91918i	0.815572	−	0.578656i
$12$		0			0
$13$	1.04553	+	0.165595i	0.289977	+	0.0459279i	0.299728	−	0.954025i	$-0.403104\pi$
$13$	1.04553	+	0.165595i	0.289977	+	0.0459279i	−0.00975110	+	0.999952i	$0.503104\pi$
$14$	1.44982	−	0.471075i	0.387481	−	0.125900i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	2.19616	−	0.347837i	0.532646	−	0.0843629i	0.115683	−	0.993286i	$-0.463094\pi$
$17$	2.19616	−	0.347837i	0.532646	−	0.0843629i	0.416963	+	0.908923i	$0.363094\pi$
$18$		0			0
$19$	−1.91500	−	5.89375i	−0.439330	−	1.35212i	−0.888583	−	0.458715i	$-0.848310\pi$
$19$	−1.91500	−	5.89375i	−0.439330	−	1.35212i	0.449253	−	0.893405i	$-0.351690\pi$
$20$	−1.44502	−	1.70643i	−0.323117	−	0.381570i
$21$		0			0
$22$	1.47241	+	2.97187i	0.313919	+	0.633605i
$23$	3.05791	−	3.05791i	0.637617	−	0.637617i	−0.312350	−	0.949967i	$-0.601116\pi$
$23$	3.05791	−	3.05791i	0.637617	−	0.637617i	0.949967	+	0.312350i	$0.101116\pi$
$24$		0			0
$25$	2.23228	+	4.47403i	0.446455	+	0.894806i
$26$	−0.327113	+	1.00675i	−0.0641522	+	0.197440i
$27$		0			0
$28$	0.238474	+	1.50566i	0.0450673	+	0.284544i
$29$	−1.39938	+	4.30686i	−0.259859	+	0.799763i	0.732975	+	0.680256i	$0.238131\pi$
$29$	−1.39938	+	4.30686i	−0.259859	+	0.799763i	−0.992833	+	0.119507i	$0.961869\pi$
$30$		0			0
$31$	2.32781	−	1.69125i	0.418087	−	0.303758i	−0.358781	−	0.933422i	$-0.616807\pi$
$31$	2.32781	−	1.69125i	0.418087	−	0.303758i	0.776868	+	0.629664i	$0.216807\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			2.22353i			0.381333i
$35$	0.281782	−	3.39707i	0.0476299	−	0.574209i
$36$		0			0
$37$	1.24018	−	0.631904i	0.203885	−	0.103884i	−0.349067	−	0.937098i	$-0.613501\pi$
$37$	1.24018	−	0.631904i	0.203885	−	0.103884i	0.552952	+	0.833213i	$0.313501\pi$
$38$	6.12076	−	0.969434i	0.992919	−	0.157263i
$39$		0			0
$40$	1.91147	−	1.16029i	0.302231	−	0.183458i
$41$	−2.38365	+	0.774496i	−0.372264	+	0.120956i	−0.489173	−	0.872187i	$-0.662701\pi$
$41$	−2.38365	+	0.774496i	−0.372264	+	0.120956i	0.116909	+	0.993143i	$0.462701\pi$
$42$		0			0
$43$	6.40957	+	6.40957i	0.977450	+	0.977450i	0.999751	−	0.0223009i	$-0.00709920\pi$
$43$	6.40957	+	6.40957i	0.977450	+	0.977450i	−0.0223009	+	0.999751i	$0.507099\pi$
$44$	−3.16562	+	0.989379i	−0.477235	+	0.149155i
$45$		0			0
$46$	2.54190	+	3.49862i	0.374782	+	0.515843i
$47$	2.03678	−	3.99740i	0.297095	−	0.583081i	−0.693413	−	0.720541i	$-0.743894\pi$
$47$	2.03678	−	3.99740i	0.297095	−	0.583081i	0.990507	+	0.137460i	$0.0438937\pi$
$48$		0			0
$49$	2.74855	−	3.78305i	0.392650	−	0.540436i
$50$	−4.76815	+	1.50490i	−0.674319	+	0.212825i
$51$		0			0
$52$	−0.943185	−	0.480577i	−0.130796	−	0.0666440i
$53$	−0.594995	+	3.75665i	−0.0817288	+	0.516016i	0.912530	+	0.409011i	$0.134126\pi$
$53$	−0.594995	+	3.75665i	−0.0817288	+	0.516016i	−0.994258	+	0.107005i	$0.965874\pi$
$54$		0			0
$55$	7.40145	−	0.467516i	0.998011	−	0.0630398i
$56$	−1.52443			−0.203711
$57$		0			0
$58$	−4.03492	−	2.05589i	−0.529811	−	0.269952i
$59$	−4.27154	−	1.38791i	−0.556107	−	0.180690i	0.0174620	−	0.999848i	$-0.494441\pi$
$59$	−4.27154	−	1.38791i	−0.556107	−	0.180690i	−0.573569	+	0.819158i	$0.694441\pi$
$60$		0			0
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	−0.525754	−	0.850636i	$-0.676217\pi$
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	0.971470	+	0.237161i	$0.0762169\pi$
$62$	1.30628	+	2.56372i	0.165898	+	0.325593i
$63$		0			0
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	1.79339	+	1.54483i	0.222443	+	0.191613i
$66$		0			0
$67$	5.40776	+	5.40776i	0.660663	+	0.660663i	0.955536	−	0.294873i	$-0.0952775\pi$
$67$	5.40776	+	5.40776i	0.660663	+	0.660663i	−0.294873	+	0.955536i	$0.595277\pi$
$68$	−2.19616	−	0.347837i	−0.266323	−	0.0421814i
$69$		0			0
$70$	3.31116	+	0.809731i	0.395759	+	0.0967814i
$71$	7.19862	+	5.23010i	0.854319	+	0.620699i	0.926334	−	0.376704i	$-0.122943\pi$
$71$	7.19862	+	5.23010i	0.854319	+	0.620699i	−0.0720143	+	0.997404i	$0.522943\pi$
$72$		0			0
$73$	−10.1633	+	5.17847i	−1.18953	+	0.606094i	−0.932801	−	0.360391i	$-0.882643\pi$
$73$	−10.1633	+	5.17847i	−1.18953	+	0.606094i	−0.256725	+	0.966485i	$0.582643\pi$
$74$	0.430117	+	1.32376i	0.0500001	+	0.153884i
$75$		0			0
$76$			6.19706i			0.710852i
$77$	−4.47882	−	2.34584i	−0.510409	−	0.267334i
$78$		0			0
$79$	−4.69179	+	3.40879i	−0.527868	+	0.383518i	−0.819560	−	0.572994i	$-0.805782\pi$
$79$	−4.69179	+	3.40879i	−0.527868	+	0.383518i	0.291692	+	0.956512i	$0.405782\pi$
$80$	0.846982	+	2.06945i	0.0946954	+	0.231372i
$81$		0			0
$82$	−0.392075	−	2.47546i	−0.0432974	−	0.273369i
$83$	0.200087	+	1.26330i	0.0219624	+	0.138665i	0.996233	−	0.0867161i	$-0.0276373\pi$
$83$	0.200087	+	1.26330i	0.0219624	+	0.138665i	−0.974271	+	0.225381i	$0.927637\pi$
$84$		0			0
$85$	4.58543	+	1.92206i	0.497360	+	0.208476i
$86$	−7.33334	+	5.32798i	−0.790774	+	0.574531i
$87$		0			0
$88$	−0.481987	−	3.28142i	−0.0513800	−	0.349800i
$89$			10.5518i			1.11849i	0.829004	+	0.559243i	$0.188908\pi$
$89$			10.5518i			1.11849i	−0.829004	+	0.559243i	$0.811092\pi$
$90$		0			0
$91$	−0.498662	−	1.53472i	−0.0522740	−	0.160883i
$92$	−3.85319	+	1.96330i	−0.401722	+	0.204688i
$93$		0			0
$94$	3.62956	+	2.63703i	0.374361	+	0.271989i
$95$	3.29169	−	13.4604i	0.337720	−	1.38101i
$96$		0			0
$97$	6.92020	+	1.09605i	0.702639	+	0.111287i	0.497523	−	0.867451i	$-0.334243\pi$
$97$	6.92020	+	1.09605i	0.702639	+	0.111287i	0.205116	+	0.978738i	$0.434243\pi$
$98$	3.30651	+	3.30651i	0.334008	+	0.334008i
$99$		0			0
$100$	−0.740470	−	4.94487i	−0.0740470	−	0.494487i
$101$	−10.3519	−	14.2481i	−1.03005	−	1.41774i	−0.904912	−	0.425599i	$-0.860063\pi$
$101$	−10.3519	−	14.2481i	−1.03005	−	1.41774i	−0.125136	−	0.992140i	$-0.539937\pi$
$102$		0			0
$103$	1.45835	+	2.86217i	0.143695	+	0.282018i	0.951625	−	0.307260i	$-0.0994122\pi$
$103$	1.45835	+	2.86217i	0.143695	+	0.282018i	−0.807930	+	0.589278i	$0.799412\pi$
$104$	0.622206	−	0.856394i	0.0610124	−	0.0839763i
$105$		0			0
$106$	−3.61732	−	1.17534i	−0.351345	−	0.114159i
$107$	14.7175	+	7.49892i	1.42279	+	0.724948i	0.984745	−	0.174006i	$-0.0556711\pi$
$107$	14.7175	+	7.49892i	1.42279	+	0.724948i	0.438045	+	0.898953i	$0.355671\pi$
$108$		0			0
$109$	1.88801			0.180839			0.0904195	−	0.995904i	$-0.471179\pi$
$109$	1.88801			0.180839			0.0904195	+	0.995904i	$0.471179\pi$
$110$	−0.696082	+	7.38346i	−0.0663688	+	0.703985i
$111$		0			0
$112$	0.238474	−	1.50566i	0.0225336	−	0.142272i
$113$	3.55455	+	1.81113i	0.334384	+	0.170377i	0.613118	−	0.789991i	$-0.289915\pi$
$113$	3.55455	+	1.81113i	0.334384	+	0.170377i	−0.278734	+	0.960368i	$0.589915\pi$
$114$		0			0
$115$	9.41221	−	2.21771i	0.877693	−	0.206803i
$116$	2.66178	−	3.66363i	0.247140	−	0.340160i
$117$		0			0
$118$	2.03903	−	4.00183i	0.187708	−	0.368398i
$119$	−1.99237	−	2.74226i	−0.182640	−	0.251383i
$120$		0			0
$121$	3.63346	−	10.3826i	0.330314	−	0.943871i
$122$	4.18783	+	4.18783i	0.379149	+	0.379149i
$123$		0			0
$124$	−2.73650	+	0.889144i	−0.245745	+	0.0798475i
$125$	−1.01821	+	11.1339i	−0.0910718	+	0.995844i
$126$		0			0
$127$	−16.7564	+	2.65395i	−1.48689	+	0.235500i	−0.846433	−	0.532495i	$-0.821254\pi$
$127$	−16.7564	+	2.65395i	−1.48689	+	0.235500i	−0.640456	+	0.767995i	$0.721254\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$		0			0
$130$	−1.80636	+	1.52964i	−0.158428	+	0.134159i
$131$		−	9.77651i		−	0.854177i	−0.904210	−	0.427089i	$-0.859539\pi$
$131$		−	9.77651i		−	0.854177i	0.904210	−	0.427089i	$-0.140461\pi$
$132$		0			0
$133$	−6.68003	+	6.68003i	−0.579232	+	0.579232i
$134$	−6.18714	+	4.49522i	−0.534488	+	0.388328i
$135$		0			0
$136$	0.687109	−	2.11471i	0.0589191	−	0.181334i
$137$	0.386515	+	2.44036i	0.0330222	+	0.208494i	0.998683	−	0.0513136i	$-0.0163408\pi$
$137$	0.386515	+	2.44036i	0.0330222	+	0.208494i	−0.965660	+	0.259808i	$0.916341\pi$
$138$		0			0
$139$	2.32161	−	7.14518i	0.196916	−	0.606046i	−0.803032	−	0.595935i	$-0.796781\pi$
$139$	2.32161	−	7.14518i	0.196916	−	0.606046i	0.999949	−	0.0101112i	$-0.00321854\pi$
$140$	−1.31774	+	3.14373i	−0.111369	+	0.265693i
$141$		0			0
$142$	−6.29183	+	6.29183i	−0.527998	+	0.527998i
$143$	3.14590	−	1.55864i	0.263074	−	0.130340i
$144$		0			0
$145$	−7.72757	+	6.54378i	−0.641740	+	0.543431i
$146$	−3.52482	−	10.8483i	−0.291716	−	0.897810i
$147$		0			0
$148$	−1.37475	+	0.217739i	−0.113004	+	0.0178981i
$149$	0.0269615	+	0.0195887i	0.00220877	+	0.00160477i	0.588889	−	0.808214i	$-0.299565\pi$
$149$	0.0269615	+	0.0195887i	0.00220877	+	0.00160477i	−0.586680	+	0.809819i	$0.699565\pi$
$150$		0			0
$151$	−20.1481	+	6.54653i	−1.63963	+	0.532749i	−0.976457	−	0.215714i	$-0.930792\pi$
$151$	−20.1481	+	6.54653i	−1.63963	+	0.532749i	−0.663176	+	0.748463i	$0.730792\pi$
$152$	−6.12076	−	0.969434i	−0.496459	−	0.0786315i
$153$		0			0
$154$	3.01760	−	4.05671i	0.243165	−	0.326899i
$155$	6.41615	−	0.477730i	0.515357	−	0.0383722i
$156$		0			0
$157$	−0.891858	+	1.75037i	−0.0711780	+	0.139695i	−0.923854	−	0.382746i	$-0.874978\pi$
$157$	−0.891858	+	1.75037i	−0.0711780	+	0.139695i	0.852676	+	0.522441i	$0.174978\pi$
$158$	−2.63286	−	5.16728i	−0.209459	−	0.411087i
$159$		0			0
$160$	−2.17647	+	0.512821i	−0.172065	+	0.0405420i
$161$	−6.26979	−	2.03718i	−0.494129	−	0.160552i
$162$		0			0
$163$	−0.340601	+	2.15047i	−0.0266779	+	0.168438i	−0.997430	−	0.0716458i	$-0.977175\pi$
$163$	−0.340601	+	2.15047i	−0.0266779	+	0.168438i	0.970752	+	0.240084i	$0.0771749\pi$
$164$	2.50632			0.195711
$165$		0			0
$166$	−1.27905			−0.0992732
$167$	3.35583	−	21.1879i	0.259682	−	1.63957i	−0.421053	−	0.907036i	$-0.638339\pi$
$167$	3.35583	−	21.1879i	0.259682	−	1.63957i	0.680735	−	0.732530i	$-0.261661\pi$
$168$		0			0
$169$	−11.2980	−	3.67095i	−0.869079	−	0.282381i
$170$	−2.61571	+	4.22830i	−0.200616	+	0.324296i
$171$		0			0
$172$	−4.11520	−	8.07653i	−0.313781	−	0.615830i
$173$	−5.98965	+	11.7553i	−0.455384	+	0.893742i	0.543151	+	0.839635i	$0.317231\pi$
$173$	−5.98965	+	11.7553i	−0.455384	+	0.893742i	−0.998535	+	0.0541069i	$0.982769\pi$
$174$		0			0
$175$	4.53207	−	6.12843i	0.342592	−	0.463266i
$176$	3.31642	+	0.0372739i	0.249984	+	0.00280962i
$177$		0			0
$178$	−10.4219	−	1.65066i	−0.781152	−	0.123722i
$179$	−12.8887	+	4.18779i	−0.963346	+	0.313010i	−0.748127	−	0.663555i	$-0.769047\pi$
$179$	−12.8887	+	4.18779i	−0.963346	+	0.313010i	−0.215219	+	0.976566i	$0.569047\pi$
$180$		0			0
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.0673204	−	0.997731i	$-0.521445\pi$
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.969702	+	0.244290i	$0.921445\pi$
$182$	1.59384	−	0.252439i	0.118143	−	0.0187120i
$183$		0			0
$184$	−1.33635	−	4.11287i	−0.0985173	−	0.303205i
$185$	3.10170	+	0.257282i	0.228042	+	0.0189158i
$186$		0			0
$187$	5.27292	−	5.15571i	0.385594	−	0.377023i
$188$	−3.17236	+	3.17236i	−0.231368	+	0.231368i
$189$		0			0
$190$	12.7798	+	5.35683i	0.927141	+	0.388626i
$191$	3.89136	−	11.9764i	0.281569	−	0.866580i	−0.705837	−	0.708374i	$-0.749429\pi$
$191$	3.89136	−	11.9764i	0.281569	−	0.866580i	0.987406	−	0.158206i	$-0.0505709\pi$
$192$		0			0
$193$	0.599973	+	3.78808i	0.0431870	+	0.272672i	0.999827	−	0.0186009i	$-0.00592120\pi$
$193$	0.599973	+	3.78808i	0.0431870	+	0.272672i	−0.956640	+	0.291273i	$0.905921\pi$
$194$	−2.16511	+	6.66354i	−0.155446	+	0.478414i
$195$		0			0
$196$	−3.78305	+	2.74855i	−0.270218	+	0.196325i
$197$	7.40013	−	7.40013i	0.527238	−	0.527238i	−0.392510	−	0.919748i	$-0.628393\pi$
$197$	7.40013	−	7.40013i	0.527238	−	0.527238i	0.919748	+	0.392510i	$0.128393\pi$
$198$		0			0
$199$			9.10742i			0.645608i	0.946466	+	0.322804i	$0.104625\pi$
$199$			9.10742i			0.645608i	−0.946466	+	0.322804i	$0.895375\pi$
$200$	4.99982	+	0.0421939i	0.353541	+	0.00298356i
$201$		0			0
$202$	15.6921	−	7.99551i	1.10409	−	0.562562i
$203$	6.81839	−	1.07993i	0.478557	−	0.0757960i
$204$		0			0
$205$	−5.44389	−	1.33128i	−0.380218	−	0.0929807i
$206$	−3.05507	+	0.992651i	−0.212857	+	0.0691613i
$207$		0			0
$208$	0.748516	+	0.748516i	0.0519002	+	0.0519002i
$209$	−16.4912	−	12.2671i	−1.14072	−	0.848530i
$210$		0			0
$211$	−14.7378	−	20.2849i	−1.01459	−	1.39647i	−0.915926	−	0.401347i	$-0.868542\pi$
$211$	−14.7378	−	20.2849i	−1.01459	−	1.39647i	−0.0986665	−	0.995121i	$-0.531458\pi$
$212$	1.72674	−	3.38892i	0.118593	−	0.232752i
$213$		0			0
$214$	−9.70891	+	13.3632i	−0.663687	+	0.913487i
$215$	4.64847	+	19.7286i	0.317023	+	1.34548i
$216$		0			0
$217$	−3.90821	−	1.99133i	−0.265307	−	0.135181i
$218$	−0.295350	+	1.86477i	−0.0200037	+	0.126298i
$219$		0			0
$220$	−7.18367	−	1.84254i	−0.484323	−	0.124224i
$221$	2.35374			0.158330
$222$		0			0
$223$	4.44282	+	2.26373i	0.297513	+	0.151590i	0.596375	−	0.802706i	$-0.296607\pi$
$223$	4.44282	+	2.26373i	0.297513	+	0.151590i	−0.298862	+	0.954296i	$0.596607\pi$
$224$	1.44982	+	0.471075i	0.0968702	+	0.0314750i
$225$		0			0
$226$	−2.34489	+	3.22746i	−0.155980	+	0.214688i
$227$	−0.926486	−	1.81833i	−0.0614931	−	0.120687i	0.858214	−	0.513292i	$-0.171574\pi$
$227$	−0.926486	−	1.81833i	−0.0614931	−	0.120687i	−0.919707	+	0.392605i	$0.871574\pi$
$228$		0			0
$229$	−0.895888	−	1.23308i	−0.0592020	−	0.0814845i	0.778389	−	0.627782i	$-0.216037\pi$
$229$	−0.895888	−	1.23308i	−0.0592020	−	0.0814845i	−0.837591	+	0.546297i	$0.816037\pi$
$230$	0.718013	+	9.64325i	0.0473444	+	0.635857i
$231$		0			0
$232$	3.20213	+	3.20213i	0.210230	+	0.210230i
$233$	−21.9164	−	3.47122i	−1.43579	−	0.227407i	−0.610457	−	0.792050i	$-0.709014\pi$
$233$	−21.9164	−	3.47122i	−1.43579	−	0.227407i	−0.825336	+	0.564642i	$0.809014\pi$
$234$		0			0
$235$	8.57562	−	5.20550i	0.559412	−	0.339569i
$236$	3.63358	+	2.63995i	0.236526	+	0.171846i
$237$		0			0
$238$	3.02018	−	1.53886i	0.195769	−	0.0997492i
$239$	−7.65870	−	23.5711i	−0.495400	−	1.52468i	−0.816332	−	0.577583i	$-0.803996\pi$
$239$	−7.65870	−	23.5711i	−0.495400	−	1.52468i	0.320932	−	0.947102i	$-0.396004\pi$
$240$		0			0
$241$		−	0.0562577i		−	0.00362387i	−0.999998	−	0.00181194i	$-0.999423\pi$
$241$		−	0.0562577i		−	0.00362387i	0.999998	−	0.00181194i	$-0.000576758\pi$
$242$	9.68636	+	5.21292i	0.622662	+	0.335099i
$243$		0			0
$244$	−4.79140	+	3.48115i	−0.306738	+	0.222858i
$245$	9.67697	−	3.96058i	0.618239	−	0.253032i
$246$		0			0
$247$	−1.02620	−	6.47920i	−0.0652958	−	0.412262i
$248$	−0.450114	−	2.84191i	−0.0285822	−	0.180461i
$249$		0			0
$250$	−10.8375	−	2.74740i	−0.685425	−	0.173761i
$251$	−6.81505	+	4.95143i	−0.430162	+	0.312531i	−0.781714	−	0.623637i	$-0.785654\pi$
$251$	−6.81505	+	4.95143i	−0.430162	+	0.312531i	0.351551	+	0.936169i	$0.385654\pi$
$252$		0			0
$253$	2.40278	−	14.1402i	0.151062	−	0.888984i
$254$		−	16.9653i		−	1.06449i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.35527	−	4.76675i	0.583566	−	0.297342i	−0.137175	−	0.990547i	$-0.543802\pi$
$257$	9.35527	−	4.76675i	0.583566	−	0.297342i	0.720740	+	0.693205i	$0.243802\pi$
$258$		0			0
$259$	−1.71660	−	1.24718i	−0.106664	−	0.0774963i
$260$	−1.22823	−	2.02341i	−0.0761719	−	0.125487i
$261$		0			0
$262$	9.65614	+	1.52938i	0.596558	+	0.0944856i
$263$	3.20922	+	3.20922i	0.197889	+	0.197889i	0.799095	−	0.601205i	$-0.205313\pi$
$263$	3.20922	+	3.20922i	0.197889	+	0.197889i	−0.601205	+	0.799095i	$0.705313\pi$
$264$		0			0
$265$	−5.55069	+	6.44376i	−0.340976	+	0.395837i
$266$	−5.55280	−	7.64278i	−0.340464	−	0.468609i
$267$		0			0
$268$	−3.47200	−	6.81417i	−0.212086	−	0.416242i
$269$	−15.2248	+	20.9551i	−0.928272	+	1.27766i	0.0322573	+	0.999480i	$0.489730\pi$
$269$	−15.2248	+	20.9551i	−0.928272	+	1.27766i	−0.960530	+	0.278178i	$0.910270\pi$
$270$		0			0
$271$	20.4415	+	6.64186i	1.24173	+	0.403464i	0.854952	−	0.518707i	$-0.173586\pi$
$271$	20.4415	+	6.64186i	1.24173	+	0.403464i	0.386783	+	0.922171i	$0.373586\pi$
$272$	1.98118	+	1.00946i	0.120127	+	0.0612077i
$273$		0			0
$274$	−2.47078			−0.149265
$275$	14.6247	+	7.81785i	0.881901	+	0.471434i
$276$		0			0
$277$	2.14809	−	13.5625i	0.129066	−	0.814893i	−0.835198	−	0.549950i	$-0.814647\pi$
$277$	2.14809	−	13.5625i	0.129066	−	0.814893i	0.964264	−	0.264943i	$-0.0853531\pi$
$278$	6.69403	+	3.41078i	0.401481	+	0.204565i
$279$		0			0
$280$	−2.89888	−	1.79331i	−0.173241	−	0.107170i
$281$	−5.82266	+	8.01420i	−0.347351	+	0.478087i	−0.946570	−	0.322498i	$-0.895478\pi$
$281$	−5.82266	+	8.01420i	−0.347351	+	0.478087i	0.599220	+	0.800585i	$0.295478\pi$
$282$		0			0
$283$	−0.935154	+	1.83534i	−0.0555891	+	0.109100i	−0.917130	−	0.398589i	$-0.869500\pi$
$283$	−0.935154	+	1.83534i	−0.0555891	+	0.109100i	0.861541	+	0.507689i	$0.169500\pi$
$284$	−5.23010	−	7.19862i	−0.310350	−	0.427160i
$285$		0			0
$286$	1.04732	+	3.35100i	0.0619292	+	0.198149i
$287$	2.70165	+	2.70165i	0.159473	+	0.159473i
$288$		0			0
$289$	−11.4658	+	3.72548i	−0.674461	+	0.219146i
$290$	−5.25436	−	8.65611i	−0.308547	−	0.508304i
$291$		0			0
$292$	11.2661	−	1.78438i	0.659300	−	0.104423i
$293$	17.5019	−	8.91767i	1.02247	−	0.520976i	0.139412	−	0.990234i	$-0.455479\pi$
$293$	17.5019	−	8.91767i	1.02247	−	0.520976i	0.883061	+	0.469259i	$0.155479\pi$
$294$		0			0
$295$	−6.49011	−	7.66420i	−0.377869	−	0.446227i
$296$		−	1.39189i		−	0.0809018i
$297$		0			0
$298$	−0.0235652	+	0.0235652i	−0.00136510	+	0.00136510i
$299$	3.70350	−	2.69075i	0.214179	−	0.155610i
$300$		0			0
$301$	4.27006	−	13.1419i	0.246122	−	0.757486i
$302$	−3.31407	−	20.9242i	−0.190703	−	1.20405i
$303$		0			0
$304$	1.91500	−	5.89375i	0.109833	−	0.338030i
$305$	12.2563	−	5.01624i	0.701793	−	0.287229i
$306$		0			0
$307$	8.35315	−	8.35315i	0.476740	−	0.476740i	−0.427348	−	0.904087i	$-0.640552\pi$
$307$	8.35315	−	8.35315i	0.476740	−	0.476740i	0.904087	+	0.427348i	$0.140552\pi$
$308$	3.53470	+	3.61506i	0.201408	+	0.205987i
$309$		0			0
$310$	−0.531858	+	6.41189i	−0.0302075	+	0.364171i
$311$	4.29712	+	13.2252i	0.243667	+	0.749931i	0.995853	+	0.0909796i	$0.0289998\pi$
$311$	4.29712	+	13.2252i	0.243667	+	0.749931i	−0.752185	+	0.658952i	$0.771000\pi$
$312$		0			0
$313$	29.8201	−	4.72303i	1.68553	−	0.266962i	0.761189	−	0.648530i	$-0.224616\pi$
$313$	29.8201	−	4.72303i	1.68553	−	0.266962i	0.924341	+	0.381569i	$0.124616\pi$
$314$	−1.58930	−	1.15470i	−0.0896895	−	0.0651633i
$315$		0			0
$316$	5.51553	−	1.79211i	0.310273	−	0.100814i
$317$	−30.2851	−	4.79669i	−1.70098	−	0.269409i	−0.770951	−	0.636894i	$-0.780219\pi$
$317$	−30.2851	−	4.79669i	−1.70098	−	0.269409i	−0.930029	+	0.367485i	$0.880219\pi$
$318$		0			0
$319$	4.48040	+	14.3355i	0.250854	+	0.802633i
$320$	−0.166032	−	2.22990i	−0.00928150	−	0.124655i
$321$		0			0
$322$	2.99291	−	5.87392i	0.166788	−	0.327341i
$323$	−6.25570	−	12.2775i	−0.348076	−	0.683139i
$324$		0			0
$325$	1.59303	+	5.04738i	0.0883654	+	0.279978i
$326$	−2.07071	−	0.672816i	−0.114686	−	0.0372638i
$327$		0			0
$328$	−0.392075	+	2.47546i	−0.0216487	+	0.136685i
$329$	−6.83919			−0.377057
$330$		0			0
$331$	14.2522			0.783372			0.391686	−	0.920099i	$-0.371892\pi$
$331$	14.2522			0.783372			0.391686	+	0.920099i	$0.371892\pi$
$332$	0.200087	−	1.26330i	0.0109812	−	0.0693325i
$333$		0			0
$334$	20.4020	+	6.62902i	1.11635	+	0.362724i
$335$	3.92191	+	16.6450i	0.214277	+	0.909415i
$336$		0			0
$337$	6.23713	+	12.2410i	0.339758	+	0.666812i	0.996155	−	0.0876027i	$-0.0279206\pi$
$337$	6.23713	+	12.2410i	0.339758	+	0.666812i	−0.656398	+	0.754415i	$0.727921\pi$
$338$	5.39316	−	10.5847i	0.293349	−	0.575730i
$339$		0			0
$340$	−3.76706	−	3.24496i	−0.204297	−	0.175983i
$341$	3.05077	−	9.04224i	0.165208	−	0.489665i
$342$		0			0
$343$	−17.5803	−	2.78444i	−0.949246	−	0.150346i
$344$	8.62085	−	2.80109i	0.464805	−	0.151024i
$345$		0			0
$346$	−10.6736	−	7.75484i	−0.573818	−	0.416903i
$347$	−17.5163	+	2.77431i	−0.940326	+	0.148933i	−0.607737	−	0.794139i	$-0.707922\pi$
$347$	−17.5163	+	2.77431i	−0.940326	+	0.148933i	−0.332589	+	0.943072i	$0.607922\pi$
$348$		0			0
$349$	−5.50175	−	16.9327i	−0.294502	−	0.906384i	−0.983388	−	0.181515i	$-0.941900\pi$
$349$	−5.50175	−	16.9327i	−0.294502	−	0.906384i	0.688886	−	0.724870i	$-0.258100\pi$
$350$	5.34400	+	5.43497i	0.285649	+	0.290511i
$351$		0			0
$352$	−0.555617	+	3.26975i	−0.0296145	+	0.174278i
$353$	−12.3974	+	12.3974i	−0.659845	+	0.659845i	−0.955343	−	0.295499i	$-0.904514\pi$
$353$	−12.3974	+	12.3974i	−0.659845	+	0.659845i	0.295499	+	0.955343i	$0.404514\pi$
$354$		0			0
$355$	7.53643	+	18.4139i	0.399992	+	0.977310i
$356$	3.26068	−	10.0353i	0.172816	−	0.531872i
$357$		0			0
$358$	−2.12000	−	13.3851i	−0.112045	−	0.707426i
$359$	−2.37480	+	7.30888i	−0.125337	+	0.385748i	−0.993962	−	0.109722i	$-0.965004\pi$
$359$	−2.37480	+	7.30888i	−0.125337	+	0.385748i	0.868625	+	0.495470i	$0.165004\pi$
$360$		0			0
$361$	−15.6978	+	11.4051i	−0.826200	+	0.600270i
$362$	12.1942	−	12.1942i	0.640915	−	0.640915i
$363$		0			0
$364$			1.61370i			0.0845810i
$365$	−25.4185	−	2.10844i	−1.33047	−	0.110361i
$366$		0			0
$367$	−32.2443	+	16.4293i	−1.68314	+	0.857603i	−0.692452	+	0.721464i	$0.743469\pi$
$367$	−32.2443	+	16.4293i	−1.68314	+	0.857603i	−0.990690	+	0.136139i	$0.956531\pi$
$368$	4.27129	−	0.676506i	0.222656	−	0.0352653i
$369$		0			0
$370$	−0.739328	+	3.02327i	−0.0384358	+	0.157172i
$371$	5.51436	−	1.79172i	0.286291	−	0.0930217i
$372$		0			0
$373$	11.5350	+	11.5350i	0.597259	+	0.597259i	0.939582	−	0.342323i	$-0.111214\pi$
$373$	11.5350	+	11.5350i	0.597259	+	0.597259i	−0.342323	+	0.939582i	$0.611214\pi$
$374$	4.26737	+	6.01453i	0.220660	+	0.311004i
$375$		0			0
$376$	−2.63703	−	3.62956i	−0.135995	−	0.187181i
$377$	−2.17629	+	4.27121i	−0.112085	+	0.219978i
$378$		0			0
$379$	−3.86753	+	5.32320i	−0.198662	+	0.273434i	−0.896712	−	0.442614i	$-0.854051\pi$
$379$	−3.86753	+	5.32320i	−0.198662	+	0.273434i	0.698050	+	0.716049i	$0.254051\pi$
$380$	−7.29008	+	11.7844i	−0.373973	+	0.604528i
$381$		0			0
$382$	11.2202	+	5.71697i	0.574074	+	0.292505i
$383$	−4.57876	+	28.9091i	−0.233963	+	1.47719i	0.538768	+	0.842454i	$0.318890\pi$
$383$	−4.57876	+	28.9091i	−0.233963	+	1.47719i	−0.772731	+	0.634733i	$0.781110\pi$
$384$		0			0
$385$	−5.75739	−	9.72967i	−0.293424	−	0.495870i
$386$	−3.83530			−0.195212
$387$		0			0
$388$	−6.24280	−	3.18087i	−0.316930	−	0.161484i
$389$	−4.21993	−	1.37114i	−0.213959	−	0.0695195i	0.200076	−	0.979780i	$-0.435881\pi$
$389$	−4.21993	−	1.37114i	−0.213959	−	0.0695195i	−0.414035	+	0.910261i	$0.635881\pi$
$390$		0			0
$391$	5.65199	−	7.77930i	0.285833	−	0.393416i
$392$	−2.12291	−	4.16644i	−0.107223	−	0.210437i
$393$		0			0
$394$	6.15139	+	8.46666i	0.309903	+	0.426544i
$395$	−12.9320	+	0.962884i	−0.650679	+	0.0484480i
$396$		0			0
$397$	6.59354	+	6.59354i	0.330920	+	0.330920i	0.852936	−	0.522016i	$-0.174820\pi$
$397$	6.59354	+	6.59354i	0.330920	+	0.330920i	−0.522016	+	0.852936i	$0.674820\pi$
$398$	−8.99529	−	1.42471i	−0.450893	−	0.0714145i
$399$		0			0
$400$	−0.823819	+	4.93167i	−0.0411909	+	0.246583i
$401$	7.12541	+	5.17691i	0.355826	+	0.258523i	0.751309	−	0.659951i	$-0.229423\pi$
$401$	7.12541	+	5.17691i	0.355826	+	0.258523i	−0.395483	+	0.918473i	$0.629423\pi$
$402$		0			0
$403$	2.71385	−	1.38278i	0.135187	−	0.0688811i
$404$	5.44229	+	16.7496i	0.270764	+	0.833326i
$405$		0			0
$406$			6.90338i			0.342609i
$407$	2.14188	−	4.08940i	0.106169	−	0.202704i
$408$		0			0
$409$	−14.0728	+	10.2245i	−0.695853	+	0.505567i	−0.878579	−	0.477597i	$-0.841508\pi$
$409$	−14.0728	+	10.2245i	−0.695853	+	0.505567i	0.182726	+	0.983164i	$0.441508\pi$
$410$	2.16650	−	5.16861i	0.106996	−	0.255259i
$411$		0			0
$412$	−0.502512	−	3.17274i	−0.0247570	−	0.156310i
$413$	1.07107	+	6.76247i	0.0527039	+	0.332759i
$414$		0			0
$415$	−1.10563	+	2.63768i	−0.0542731	+	0.129479i
$416$	−0.856394	+	0.622206i	−0.0419882	+	0.0305062i
$417$		0			0
$418$	14.6958	−	14.3691i	0.718796	−	0.702818i
$419$		−	16.4015i		−	0.801265i	−0.916239	−	0.400632i	$-0.868790\pi$
$419$		−	16.4015i		−	0.801265i	0.916239	−	0.400632i	$-0.131210\pi$
$420$		0			0
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	0.927229	+	0.374494i	$0.122184\pi$
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	−0.530022	+	0.847984i	$0.677816\pi$
$422$	22.3406	−	11.3831i	1.08752	−	0.554121i
$423$		0			0
$424$	3.07708	+	2.23563i	0.149436	+	0.108572i
$425$	6.45866	+	9.04920i	0.313291	+	0.438951i
$426$		0			0
$427$	−8.91727	−	1.41236i	−0.431537	−	0.0683488i
$428$	−11.6798	−	11.6798i	−0.564566	−	0.564566i
$429$		0			0
$430$	−20.2129	+	1.50500i	−0.974752	+	0.0725776i
$431$	5.58501	+	7.68711i	0.269020	+	0.370275i	0.922059	−	0.387050i	$-0.126506\pi$
$431$	5.58501	+	7.68711i	0.269020	+	0.370275i	−0.653038	+	0.757325i	$0.726506\pi$
$432$		0			0
$433$	11.3232	+	22.2230i	0.544158	+	1.06797i	0.985348	+	0.170557i	$0.0545566\pi$
$433$	11.3232	+	22.2230i	0.544158	+	1.06797i	−0.441190	+	0.897414i	$0.645443\pi$
$434$	2.57820	−	3.54858i	0.123757	−	0.170338i
$435$		0			0
$436$	−1.79561	−	0.583428i	−0.0859940	−	0.0279411i
$437$	−23.8784	−	12.1667i	−1.14226	−	0.582011i
$438$		0			0
$439$	−1.69115			−0.0807143			−0.0403571	−	0.999185i	$-0.512850\pi$
$439$	−1.69115			−0.0807143			−0.0403571	+	0.999185i	$0.512850\pi$
$440$	2.94363	−	6.80699i	0.140332	−	0.324510i
$441$		0			0
$442$	−0.368207	+	2.32477i	−0.0175138	+	0.110578i
$443$	18.0946	+	9.21964i	0.859698	+	0.438038i	0.827515	−	0.561444i	$-0.189754\pi$
$443$	18.0946	+	9.21964i	0.859698	+	0.438038i	0.0321835	+	0.999482i	$0.489754\pi$
$444$		0			0
$445$	−12.4129	+	20.0654i	−0.588426	+	0.951192i
$446$	−2.93087	+	4.03399i	−0.138781	+	0.191015i
$447$		0			0
$448$	−0.692077	+	1.35828i	−0.0326976	+	0.0641726i
$449$	24.7166	+	34.0195i	1.16645	+	1.60548i	0.683806	+	0.729664i	$0.260323\pi$
$449$	24.7166	+	34.0195i	1.16645	+	1.60548i	0.482643	+	0.875817i	$0.339677\pi$
$450$		0			0
$451$	−4.96125	+	6.66964i	−0.233616	+	0.314061i
$452$	−2.82091	−	2.82091i	−0.132684	−	0.132684i
$453$		0			0
$454$	1.94088	−	0.630630i	0.0910900	−	0.0295969i
$455$	0.857150	−	3.50507i	0.0401838	−	0.164320i
$456$		0			0
$457$	−9.99618	+	1.58324i	−0.467602	+	0.0740608i	−0.385789	−	0.922587i	$-0.626071\pi$
$457$	−9.99618	+	1.58324i	−0.467602	+	0.0740608i	−0.0818123	+	0.996648i	$0.526071\pi$
$458$	1.35805	−	0.691961i	0.0634575	−	0.0323332i
$459$		0			0
$460$	−9.63685	−	0.799364i	−0.449321	−	0.0372706i
$461$			27.4513i			1.27854i	0.768984	+	0.639268i	$0.220763\pi$
$461$			27.4513i			1.27854i	−0.768984	+	0.639268i	$0.779237\pi$
$462$		0			0
$463$	12.8080	−	12.8080i	0.595237	−	0.595237i	−0.343804	−	0.939041i	$-0.611716\pi$
$463$	12.8080	−	12.8080i	0.595237	−	0.595237i	0.939041	+	0.343804i	$0.111716\pi$
$464$	−3.66363	+	2.66178i	−0.170080	+	0.123570i
$465$		0			0
$466$	6.85697	−	21.1036i	0.317643	−	0.977604i
$467$	3.41594	+	21.5674i	0.158071	+	0.998021i	0.931395	+	0.364010i	$0.118593\pi$
$467$	3.41594	+	21.5674i	0.158071	+	0.998021i	−0.773324	+	0.634011i	$0.781407\pi$
$468$		0			0
$469$	3.60265	−	11.0878i	0.166355	−	0.511988i
$470$	3.79989	+	9.28436i	0.175276	+	0.428255i
$471$		0			0
$472$	−3.17587	+	3.17587i	−0.146181	+	0.146181i
$473$	29.6387	+	5.03639i	1.36279	+	0.231573i
$474$		0			0
$475$	22.0940	−	21.7242i	1.01374	−	0.996777i
$476$	1.04745	+	3.22372i	0.0480098	+	0.147759i
$477$		0			0
$478$	24.4789	−	3.87708i	1.11964	−	0.177334i
$479$	−5.27636	−	3.83350i	−0.241083	−	0.175157i	0.460683	−	0.887565i	$-0.347605\pi$
$479$	−5.27636	−	3.83350i	−0.241083	−	0.175157i	−0.701766	+	0.712408i	$0.747605\pi$
$480$		0			0
$481$	1.40128	−	0.455305i	0.0638931	−	0.0207601i
$482$	0.0555650	+	0.00880064i	0.00253092	+	0.000400858i
$483$		0			0
$484$	−6.66402	+	8.75162i	−0.302910	+	0.397801i
$485$	11.8702	+	10.2250i	0.538997	+	0.464294i
$486$		0			0
$487$	1.33144	−	2.61310i	0.0603334	−	0.118411i	−0.858871	−	0.512193i	$-0.828833\pi$
$487$	1.33144	−	2.61310i	0.0603334	−	0.118411i	0.919204	+	0.393782i	$0.128833\pi$
$488$	−2.68875	−	5.27698i	−0.121714	−	0.238878i
$489$		0			0
$490$	2.39801	+	10.1774i	0.108331	+	0.459768i
$491$	−12.6664	−	4.11555i	−0.571625	−	0.185732i	0.00892018	−	0.999960i	$-0.497161\pi$
$491$	−12.6664	−	4.11555i	−0.571625	−	0.185732i	−0.580545	+	0.814228i	$0.697161\pi$
$492$		0			0
$493$	−1.57518	+	9.94529i	−0.0709425	+	0.447913i
$494$	6.55996			0.295147
$495$		0			0
$496$	2.87733			0.129196
$497$	2.12193	−	13.3974i	0.0951818	−	0.600954i
$498$		0			0
$499$	−22.2265	−	7.22182i	−0.994994	−	0.323293i	−0.234130	−	0.972205i	$-0.575224\pi$
$499$	−22.2265	−	7.22182i	−0.994994	−	0.323293i	−0.760863	+	0.648912i	$0.775224\pi$
$500$	4.40894	−	10.2743i	0.197174	−	0.459481i
$501$		0			0
$502$	−3.82436	−	7.50572i	−0.170689	−	0.334997i
$503$	−10.5487	+	20.7030i	−0.470344	+	0.923103i	0.526972	+	0.849883i	$0.323327\pi$
$503$	−10.5487	+	20.7030i	−0.470344	+	0.923103i	−0.997316	+	0.0732197i	$0.976673\pi$
$504$		0			0
$505$	−2.92410	−	39.2721i	−0.130121	−	1.74758i
$506$	13.5902	+	4.58521i	0.604158	+	0.203837i
$507$		0			0
$508$	16.7564	+	2.65395i	0.743444	+	0.117750i
$509$	−21.9064	+	7.11784i	−0.970986	+	0.315493i	−0.751214	−	0.660059i	$-0.770531\pi$
$509$	−21.9064	+	7.11784i	−0.970986	+	0.315493i	−0.219772	+	0.975551i	$0.570531\pi$
$510$		0			0
$511$	14.0676	+	10.2207i	0.622314	+	0.452138i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$		0			0
$514$	3.24457	+	9.98577i	0.143112	+	0.440454i
$515$	−0.593772	+	7.15831i	−0.0261647	+	0.315433i
$516$		0			0
$517$	−2.16238	−	14.7217i	−0.0951014	−	0.647460i
$518$	1.50037	−	1.50037i	0.0659223	−	0.0659223i
$519$		0			0
$520$	2.19064	−	0.896582i	0.0960658	−	0.0393177i
$521$	9.62530	−	29.6236i	0.421692	−	1.29783i	−0.484435	−	0.874827i	$-0.660975\pi$
$521$	9.62530	−	29.6236i	0.421692	−	1.29783i	0.906127	−	0.423007i	$-0.139025\pi$
$522$		0			0
$523$	−0.813774	−	5.13797i	−0.0355838	−	0.224668i	0.963488	−	0.267753i	$-0.0862812\pi$
$523$	−0.813774	−	5.13797i	−0.0355838	−	0.224668i	−0.999071	+	0.0430856i	$0.986281\pi$
$524$	−3.02111	+	9.29801i	−0.131978	+	0.406185i
$525$		0			0
$526$	−3.67174	+	2.66768i	−0.160096	+	0.116316i
$527$	4.52395	−	4.52395i	0.197067	−	0.197067i
$528$		0			0
$529$			4.29842i			0.186888i
$530$	−5.49611	−	6.49037i	−0.238736	−	0.281924i
$531$		0			0
$532$	8.41733	−	4.28884i	0.364938	−	0.185945i
$533$	−2.62043	+	0.415035i	−0.113503	+	0.0179772i
$534$		0			0
$535$	19.1654	+	31.5733i	0.828591	+	1.36503i
$536$	7.27342	−	2.36328i	0.314164	−	0.102078i
$537$		0			0
$538$	−18.3155	−	18.3155i	−0.789636	−	0.789636i
$539$	0.174297	−	15.5079i	0.00750749	−	0.667973i
$540$		0			0
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	0.940974	−	0.338480i	$-0.109913\pi$
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	−0.612690	+	0.790323i	$0.709913\pi$
$542$	−9.75785	+	19.1509i	−0.419135	+	0.822600i
$543$		0			0
$544$	−1.30696	+	1.79888i	−0.0560354	+	0.0771262i
$545$	3.59027	+	2.22101i	0.153790	+	0.0951378i
$546$		0			0
$547$	4.19261	+	2.13624i	0.179263	+	0.0913391i	0.541319	−	0.840817i	$-0.317925\pi$
$547$	4.19261	+	2.13624i	0.179263	+	0.0913391i	−0.362056	+	0.932156i	$0.617925\pi$
$548$	0.386515	−	2.44036i	0.0165111	−	0.104247i
$549$		0			0
$550$	−10.0094	+	13.2216i	−0.426803	+	0.563773i
$551$	28.0634			1.19554
$552$		0			0
$553$	7.87716	+	4.01362i	0.334971	+	0.170676i
$554$	13.0595	+	4.24329i	0.554845	+	0.180280i
$555$		0			0
$556$	−4.41597	+	6.07806i	−0.187279	+	0.257767i
$557$	14.8729	+	29.1897i	0.630185	+	1.23681i	0.956551	+	0.291564i	$0.0941757\pi$
$557$	14.8729	+	29.1897i	0.630185	+	1.23681i	−0.326366	+	0.945243i	$0.605824\pi$
$558$		0			0
$559$	5.63999	+	7.76278i	0.238546	+	0.328331i
$560$	2.22471	−	2.58266i	0.0940112	−	0.109137i
$561$		0			0
$562$	−7.00467	−	7.00467i	−0.295474	−	0.295474i
$563$	−3.28421	−	0.520168i	−0.138413	−	0.0219225i	0.0868434	−	0.996222i	$-0.472322\pi$
$563$	−3.28421	−	0.520168i	−0.138413	−	0.0219225i	−0.225257	+	0.974299i	$0.572322\pi$
$564$		0			0
$565$	4.62881	+	7.62557i	0.194735	+	0.320810i
$566$	−1.66646	−	1.21075i	−0.0700464	−	0.0508917i
$567$		0			0
$568$	7.92816	−	4.03960i	0.332658	−	0.169498i
$569$	−2.18501	−	6.72478i	−0.0916005	−	0.281917i	0.894752	−	0.446563i	$-0.147352\pi$
$569$	−2.18501	−	6.72478i	−0.0916005	−	0.281917i	−0.986353	+	0.164645i	$0.947352\pi$
$570$		0			0
$571$			24.2620i			1.01533i	0.861553	+	0.507667i	$0.169492\pi$
$571$			24.2620i			1.01533i	−0.861553	+	0.507667i	$0.830508\pi$
$572$	−3.47358	+	0.510212i	−0.145238	+	0.0213330i
$573$		0			0
$574$	−3.09102	+	2.24576i	−0.129017	+	0.0937362i
$575$	20.5073	+	6.85507i	0.855212	+	0.285876i
$576$		0			0
$577$	1.00746	+	6.36086i	0.0419412	+	0.264806i	0.999744	−	0.0226195i	$-0.00720062\pi$
$577$	1.00746	+	6.36086i	0.0419412	+	0.264806i	−0.957803	+	0.287426i	$0.907201\pi$
$578$	−1.88596	−	11.9075i	−0.0784455	−	0.495286i
$579$		0			0
$580$	9.37150	−	3.83555i	0.389130	−	0.159263i
$581$	1.57744	−	1.14607i	0.0654430	−	0.0475471i
$582$		0			0
$583$	5.60028	+	11.3034i	0.231940	+	0.468141i
$584$			11.4066i			0.472007i
$585$		0			0
$586$	6.06998	+	18.6815i	0.250748	+	0.771724i
$587$	4.91253	−	2.50306i	0.202762	−	0.103312i	−0.349661	−	0.936876i	$-0.613703\pi$
$587$	4.91253	−	2.50306i	0.202762	−	0.103312i	0.552423	+	0.833564i	$0.313703\pi$
$588$		0			0
$589$	−14.4256	−	10.4808i	−0.594395	−	0.431853i
$590$	8.58511	−	5.21127i	0.353444	−	0.214544i
$591$		0			0
$592$	1.37475	+	0.217739i	0.0565019	+	0.00894903i
$593$	−11.4901	−	11.4901i	−0.471841	−	0.471841i	0.430669	−	0.902510i	$-0.358278\pi$
$593$	−11.4901	−	11.4901i	−0.471841	−	0.471841i	−0.902510	+	0.430669i	$0.858278\pi$
$594$		0			0
$595$	−0.562787	−	7.55850i	−0.0230720	−	0.309868i
$596$	−0.0195887	−	0.0269615i	−0.000802383	−	0.00110439i
$597$		0			0
$598$	2.07827	+	4.07883i	0.0849867	+	0.166796i
$599$	24.2507	−	33.3782i	0.990856	−	1.36380i	0.0600854	−	0.998193i	$-0.480863\pi$
$599$	24.2507	−	33.3782i	0.990856	−	1.36380i	0.930771	−	0.365603i	$-0.119137\pi$
$600$		0			0
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.991812	−	0.127705i	$-0.0407609\pi$
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.727330	+	0.686288i	$0.240761\pi$
$602$	12.3121	+	6.27334i	0.501804	+	0.255682i
$603$		0			0
$604$	21.1850			0.862006
$605$	19.1233	−	15.4694i	0.777471	−	0.628919i
$606$		0			0
$607$	2.64036	−	16.6706i	0.107169	−	0.676638i	−0.874353	−	0.485290i	$-0.838714\pi$
$607$	2.64036	−	16.6706i	0.107169	−	0.676638i	0.981522	−	0.191348i	$-0.0612858\pi$
$608$	5.52162	+	2.81341i	0.223931	+	0.114099i
$609$		0			0
$610$	3.03718	+	12.8901i	0.122972	+	0.521905i
$611$	2.79146	−	3.84212i	0.112930	−	0.155435i
$612$		0			0
$613$	−11.0412	+	21.6696i	−0.445949	+	0.875225i	0.553162	+	0.833074i	$0.313421\pi$
$613$	−11.0412	+	21.6696i	−0.445949	+	0.875225i	−0.999111	+	0.0421512i	$0.986579\pi$
$614$	6.94359	+	9.55703i	0.280221	+	0.385691i
$615$		0			0
$616$	−4.12350	+	2.92567i	−0.166141	+	0.117878i
$617$	2.46606	+	2.46606i	0.0992799	+	0.0992799i	0.755002	−	0.655722i	$-0.227636\pi$
$617$	2.46606	+	2.46606i	0.0992799	+	0.0992799i	−0.655722	+	0.755002i	$0.727636\pi$
$618$		0			0
$619$	28.7652	−	9.34637i	1.15617	−	0.375662i	0.332706	−	0.943031i	$-0.392038\pi$
$619$	28.7652	−	9.34637i	1.15617	−	0.375662i	0.823464	+	0.567369i	$0.192038\pi$
$620$	−6.24974	−	1.52835i	−0.250996	−	0.0613800i
$621$		0			0
$622$	−13.7346	+	2.17534i	−0.550706	+	0.0872233i
$623$	14.3323	−	7.30265i	0.574210	−	0.292574i
$624$		0			0
$625$	−15.0339	+	19.9745i	−0.601355	+	0.798982i
$626$			30.1918i			1.20671i
$627$		0			0
$628$	1.38910	−	1.38910i	0.0554312	−	0.0554312i
$629$	2.50383	−	1.81914i	0.0998344	−	0.0725339i
$630$		0			0
$631$	9.75833	−	30.0330i	0.388473	−	1.19560i	−0.545456	−	0.838139i	$-0.683644\pi$
$631$	9.75833	−	30.0330i	0.388473	−	1.19560i	0.933929	−	0.357458i	$-0.116356\pi$
$632$	0.907222	+	5.72797i	0.0360874	+	0.227847i
$633$		0			0
$634$	9.47527	−	29.1619i	0.376311	−	1.15817i
$635$	−34.9862	−	14.6650i	−1.38839	−	0.581964i
$636$		0			0
$637$	3.50014	−	3.50014i	0.138681	−	0.138681i
$638$	−14.8599	+	2.18268i	−0.588308	+	0.0864129i
$639$		0			0
$640$	2.22841	+	0.184844i	0.0880858	+	0.00730661i
$641$	1.51513	+	4.66309i	0.0598440	+	0.184181i	0.976509	−	0.215474i	$-0.0691298\pi$
$641$	1.51513	+	4.66309i	0.0598440	+	0.184181i	−0.916665	+	0.399655i	$0.869130\pi$
$642$		0			0
$643$	16.1752	−	2.56190i	0.637888	−	0.101031i	0.170890	−	0.985290i	$-0.445336\pi$
$643$	16.1752	−	2.56190i	0.637888	−	0.101031i	0.466998	+	0.884259i	$0.345336\pi$
$644$	5.33341	+	3.87495i	0.210166	+	0.152694i
$645$		0			0
$646$	13.1050	−	4.25806i	0.515608	−	0.167531i
$647$	−42.4816	−	6.72843i	−1.67012	−	0.264522i	−0.751523	−	0.659707i	$-0.770681\pi$
$647$	−42.4816	−	6.72843i	−1.67012	−	0.264522i	−0.918602	+	0.395185i	$0.870681\pi$
$648$		0			0
$649$	−14.2179	+	4.44366i	−0.558102	+	0.174429i
$650$	−5.23444	+	0.783833i	−0.205312	+	0.0307444i
$651$		0			0
$652$	0.988463	−	1.93997i	0.0387112	−	0.0759750i
$653$	−1.54616	−	3.03452i	−0.0605061	−	0.118750i	0.858773	−	0.512356i	$-0.171227\pi$
$653$	−1.54616	−	3.03452i	−0.0605061	−	0.118750i	−0.919279	+	0.393606i	$0.871227\pi$
$654$		0			0
$655$	11.5009	−	18.5911i	0.449376	−	0.726416i
$656$	−2.38365	−	0.774496i	−0.0930660	−	0.0302390i
$657$		0			0
$658$	1.06989	−	6.75499i	0.0417085	−	0.263337i
$659$	−1.70430			−0.0663902			−0.0331951	−	0.999449i	$-0.510568\pi$
$659$	−1.70430			−0.0663902			−0.0331951	+	0.999449i	$0.510568\pi$
$660$		0			0
$661$	−3.81557			−0.148409			−0.0742043	−	0.997243i	$-0.523642\pi$
$661$	−3.81557			−0.148409			−0.0742043	+	0.997243i	$0.523642\pi$
$662$	−2.22953	+	14.0767i	−0.0866533	+	0.547108i
$663$		0			0
$664$	1.21644	+	0.395247i	0.0472072	+	0.0153386i
$665$	−20.5611	+	4.84461i	−0.797324	+	0.187866i
$666$		0			0
$667$	8.89078	+	17.4491i	0.344252	+	0.675634i
$668$	−9.73899	+	19.1138i	−0.376813	+	0.739537i
$669$		0			0
$670$	−17.0536	+	1.26977i	−0.658839	+	0.0490555i
$671$	0.220754	−	19.6414i	0.00852212	−	0.758249i
$672$		0			0
$673$	−26.0401	−	4.12434i	−1.00377	−	0.158982i	−0.367153	−	0.930161i	$-0.619667\pi$
$673$	−26.0401	−	4.12434i	−1.00377	−	0.158982i	−0.636619	+	0.771179i	$0.719667\pi$
$674$	−13.0660	+	4.24541i	−0.503285	+	0.163527i
$675$		0			0
$676$	9.61068	+	6.98256i	0.369641	+	0.268560i
$677$	−11.6875	+	1.85111i	−0.449185	+	0.0711440i	−0.376929	−	0.926242i	$-0.623020\pi$
$677$	−11.6875	+	1.85111i	−0.449185	+	0.0711440i	−0.0722563	+	0.997386i	$0.523020\pi$
$678$		0			0
$679$	−3.30057	−	10.1581i	−0.126664	−	0.389832i
$680$	3.79431	−	3.21305i	0.145505	−	0.123215i
$681$		0			0
$682$	8.45367	+	4.42773i	0.323708	+	0.169546i
$683$	19.2371	−	19.2371i	0.736087	−	0.736087i	−0.235731	−	0.971818i	$-0.575748\pi$
$683$	19.2371	−	19.2371i	0.736087	−	0.736087i	0.971818	+	0.235731i	$0.0757484\pi$
$684$		0			0
$685$	−2.13578	+	5.09531i	−0.0816040	+	0.194682i
$686$	5.50033	−	16.9283i	0.210003	−	0.646324i
$687$		0			0
$688$	1.41800	+	8.95290i	0.0540608	+	0.341326i
$689$	−1.24417	+	3.82916i	−0.0473990	+	0.145879i
$690$		0			0
$691$	−2.86279	+	2.07994i	−0.108906	+	0.0791246i	−0.640905	−	0.767620i	$-0.721441\pi$
$691$	−2.86279	+	2.07994i	−0.108906	+	0.0791246i	0.531999	+	0.846745i	$0.321441\pi$
$692$	9.32909	−	9.32909i	0.354639	−	0.354639i
$693$		0			0
$694$		−	17.7347i		−	0.673199i
$695$	12.8202	−	10.8563i	0.486299	−	0.411803i
$696$		0			0
$697$	−4.96548	+	2.53004i	−0.188081	+	0.0958320i
$698$	17.5849	−	2.78517i	0.665596	−	0.105420i
$699$		0			0
$700$	−6.20404	+	4.42799i	−0.234491	+	0.167362i
$701$	−37.5991	+	12.2167i	−1.42010	+	0.461418i	−0.915634	−	0.402013i	$-0.868311\pi$
$701$	−37.5991	+	12.2167i	−1.42010	+	0.461418i	−0.504466	+	0.863432i	$0.668311\pi$
$702$		0			0
$703$	−6.09923	−	6.09923i	−0.230037	−	0.230037i
$704$	−3.14258	−	1.06028i	−0.118440	−	0.0399607i
$705$		0			0
$706$	−10.3053	−	14.1841i	−0.387847	−	0.533826i
$707$	−12.1886	+	23.9215i	−0.458400	+	0.899660i
$708$		0			0
$709$	−23.7291	+	32.6603i	−0.891166	+	1.22658i	0.0820353	+	0.996629i	$0.473858\pi$
$709$	−23.7291	+	32.6603i	−0.891166	+	1.22658i	−0.973201	+	0.229955i	$0.926142\pi$
$710$	−19.3662	+	4.56307i	−0.726800	+	0.171249i
$711$		0			0
$712$	9.40171	+	4.79041i	0.352344	+	0.179528i
$713$	1.94653	−	12.2899i	0.0728982	−	0.460261i
$714$		0			0
$715$	7.81584	+	0.736845i	0.292296	+	0.0275564i
$716$	13.5520			0.506461
$717$		0			0
$718$	−6.84740	−	3.48892i	−0.255543	−	0.130205i
$719$	6.32991	+	2.05671i	0.236066	+	0.0767024i	0.424661	−	0.905353i	$-0.360393\pi$
$719$	6.32991	+	2.05671i	0.236066	+	0.0767024i	−0.188595	+	0.982055i	$0.560393\pi$
$720$		0			0
$721$	2.87833	−	3.96168i	0.107195	−	0.147541i
$722$	−8.80903	−	17.2887i	−0.327838	−	0.643418i
$723$		0			0
$724$	10.1365	+	13.9517i	0.376720	+	0.518511i
$725$	−22.3928	+	3.35322i	−0.831648	+	0.124535i
$726$		0			0
$727$	13.3487	+	13.3487i	0.495074	+	0.495074i	0.909901	−	0.414826i	$-0.136158\pi$
$727$	13.3487	+	13.3487i	0.495074	+	0.495074i	−0.414826	+	0.909901i	$0.636158\pi$
$728$	−1.59384	−	0.252439i	−0.0590715	−	0.00935600i
$729$		0			0
$730$	6.05881	−	24.7758i	0.224247	−	0.916992i
$731$	16.3059	+	11.8469i	0.603096	+	0.438175i
$732$		0			0
$733$	−24.8515	+	12.6624i	−0.917909	+	0.467698i	−0.848084	−	0.529861i	$-0.822244\pi$
$733$	−24.8515	+	12.6624i	−0.917909	+	0.467698i	−0.0698250	+	0.997559i	$0.522244\pi$
$734$	−11.1829	−	34.4175i	−0.412769	−	1.27037i
$735$		0			0
$736$			4.32453i			0.159404i
$737$	25.0062	+	4.24920i	0.921115	+	0.156521i
$738$		0			0
$739$	−8.88327	+	6.45407i	−0.326776	+	0.237417i	−0.739061	−	0.673638i	$-0.764731\pi$
$739$	−8.88327	+	6.45407i	−0.326776	+	0.237417i	0.412285	+	0.911055i	$0.364731\pi$
$740$	−2.87039	−	1.20317i	−0.105518	−	0.0442294i
$741$		0			0
$742$	0.907029	+	5.72675i	0.0332981	+	0.210236i
$743$	−3.77987	−	23.8652i	−0.138670	−	0.875527i	−0.954711	−	0.297534i	$-0.903836\pi$
$743$	−3.77987	−	23.8652i	−0.138670	−	0.875527i	0.816041	−	0.577994i	$-0.196164\pi$
$744$		0			0
$745$	0.0282267	+	0.0689669i	0.00103415	+	0.00252675i
$746$	−13.1974	+	9.58850i	−0.483193	+	0.351060i
$747$		0			0
$748$	−6.60805	+	3.27395i	−0.241614	+	0.119708i
$749$		−	25.1802i		−	0.920065i
$750$		0			0
$751$	−15.1449	−	46.6112i	−0.552645	−	1.70087i	−0.702082	−	0.712096i	$-0.747746\pi$
$751$	−15.1449	−	46.6112i	−0.552645	−	1.70087i	0.149437	−	0.988771i	$-0.452254\pi$
$752$	3.99740	−	2.03678i	0.145770	−	0.0742737i
$753$		0			0
$754$	−3.87818	−	2.81766i	−0.141235	−	0.102613i
$755$	−46.0152	−	11.2528i	−1.67466	−	0.409532i
$756$		0			0
$757$	−49.9645	−	7.91360i	−1.81599	−	0.287625i	−0.846434	−	0.532493i	$-0.821255\pi$
$757$	−49.9645	−	7.91360i	−1.81599	−	0.287625i	−0.969556	+	0.244869i	$0.921255\pi$
$758$	−4.65265	−	4.65265i	−0.168992	−	0.168992i
$759$		0			0
$760$	−10.4989	−	9.04381i	−0.380836	−	0.328054i
$761$	−18.7749	−	25.8415i	−0.680591	−	0.936753i	0.319350	−	0.947637i	$-0.396536\pi$
$761$	−18.7749	−	25.8415i	−0.680591	−	0.936753i	−0.999941	+	0.0108837i	$0.996536\pi$
$762$		0			0
$763$	−1.30665	−	2.56445i	−0.0473040	−	0.0928392i
$764$	−7.40180	+	10.1877i	−0.267788	+	0.368578i
$765$		0			0
$766$	−27.8369	−	9.04477i	−1.00579	−	0.326801i
$767$	−4.23618	−	2.15844i	−0.152960	−	0.0779368i
$768$		0			0
$769$	41.4875			1.49608			0.748039	−	0.663655i	$-0.230996\pi$
$769$	41.4875			1.49608			0.748039	+	0.663655i	$0.230996\pi$
$770$	10.5105	−	4.16445i	0.378773	−	0.150076i
$771$		0			0
$772$	0.599973	−	3.78808i	0.0215935	−	0.136336i
$773$	19.4460	+	9.90821i	0.699422	+	0.356373i	0.767272	−	0.641322i	$-0.221614\pi$
$773$	19.4460	+	9.90821i	0.699422	+	0.356373i	−0.0678495	+	0.997696i	$0.521614\pi$
$774$		0			0
$775$	12.7630	+	6.63934i	0.458461	+	0.238492i
$776$	4.11829	−	5.66834i	0.147838	−	0.203482i
$777$		0			0
$778$	2.01440	−	3.95348i	0.0722197	−	0.141739i
$779$	9.12937	+	12.5655i	0.327094	+	0.450206i
$780$		0			0
$781$	29.5094	+	0.331662i	1.05593	+	0.0118678i
$782$	6.79935	+	6.79935i	0.243144	+	0.243144i
$783$		0			0
$784$	4.44724	−	1.44500i	0.158830	−	0.0516070i
$785$	−3.75506	+	2.27937i	−0.134024	+	0.0813541i
$786$		0			0
$787$	−29.9410	+	4.74219i	−1.06728	+	0.169041i	−0.665277	−	0.746596i	$-0.731687\pi$
$787$	−29.9410	+	4.74219i	−1.06728	+	0.169041i	−0.402005	+	0.915637i	$0.631687\pi$
$788$	−9.32471	+	4.75118i	−0.332179	+	0.169254i
$789$		0			0
$790$	1.07198	−	12.9234i	0.0381394	−	0.459794i
$791$		−	6.08151i		−	0.216234i
$792$		0			0
$793$	4.43308	−	4.43308i	0.157423	−	0.157423i
$794$	−7.54381	+	5.48090i	−0.267720	+	0.194510i
$795$		0			0
$796$	2.81435	−	8.66167i	0.0997519	−	0.307005i
$797$	−8.39878	−	53.0278i	−0.297500	−	1.87834i	−0.454505	−	0.890744i	$-0.650184\pi$
$797$	−8.39878	−	53.0278i	−0.297500	−	1.87834i	0.157004	−	0.987598i	$-0.449816\pi$
$798$		0			0
$799$	3.08264	−	9.48739i	0.109056	−	0.335640i
$800$	−4.74207	−	1.58516i	−0.167658	−	0.0560438i
$801$		0			0
$802$	−6.22783	+	6.22783i	−0.219912	+	0.219912i
$803$	−17.5528	+	33.5128i	−0.619424	+	1.18264i
$804$		0			0
$805$	−9.52624	−	11.2496i	−0.335756	−	0.396495i
$806$	0.941213	+	2.89676i	0.0331528	+	0.102034i
$807$		0			0
$808$	−17.3948	+	2.75506i	−0.611947	+	0.0969228i
$809$	25.4737	+	18.5077i	0.895608	+	0.650697i	0.937334	−	0.348432i	$-0.113286\pi$
$809$	25.4737	+	18.5077i	0.895608	+	0.650697i	−0.0417260	+	0.999129i	$0.513286\pi$
$810$		0			0
$811$	−6.48163	+	2.10601i	−0.227601	+	0.0739520i	−0.420597	−	0.907247i	$-0.638179\pi$
$811$	−6.48163	+	2.10601i	−0.227601	+	0.0739520i	0.192996	+	0.981199i	$0.438179\pi$
$812$	−6.81839	−	1.07993i	−0.239279	−	0.0378980i
$813$		0			0
$814$	3.70399	+	2.75524i	0.129825	+	0.0965710i
$815$	−3.17746	+	3.68869i	−0.111301	+	0.129209i
$816$		0			0
$817$	25.5021	−	50.0507i	0.892206	−	1.75105i
$818$	−7.89712	−	15.4990i	−0.276116	−	0.541908i
$819$		0			0
$820$	4.76606	+	2.94838i	0.166438	+	0.102962i
$821$	0.216685	+	0.0704052i	0.00756235	+	0.00245716i	0.312796	−	0.949820i	$-0.398734\pi$
$821$	0.216685	+	0.0704052i	0.00756235	+	0.00245716i	−0.305233	+	0.952278i	$0.598734\pi$
$822$		0			0
$823$	3.59018	−	22.6675i	0.125146	−	0.790139i	−0.842661	−	0.538445i	$-0.819012\pi$
$823$	3.59018	−	22.6675i	0.125146	−	0.790139i	0.967807	−	0.251695i	$-0.0809879\pi$
$824$	3.21229			0.111905
$825$		0			0
$826$	−6.84677			−0.238229
$827$	−6.32782	+	39.9523i	−0.220040	+	1.38928i	0.592124	+	0.805847i	$0.298290\pi$
$827$	−6.32782	+	39.9523i	−0.220040	+	1.38928i	−0.812164	+	0.583430i	$0.801710\pi$
$828$		0			0
$829$	−25.8477	−	8.39841i	−0.897726	−	0.291689i	−0.176428	−	0.984314i	$-0.556454\pi$
$829$	−25.8477	−	8.39841i	−0.897726	−	0.291689i	−0.721298	+	0.692625i	$0.756454\pi$
$830$	−2.43225	−	1.50464i	−0.0844247	−	0.0522268i
$831$		0			0
$832$	−0.480577	−	0.943185i	−0.0166610	−	0.0326990i
$833$	4.72036	−	9.26422i	0.163551	−	0.320986i
$834$		0			0
$835$	31.3064	−	36.3434i	1.08340	−	1.25772i
$836$	11.8933	+	16.7627i	0.411338	+	0.579750i
$837$		0			0
$838$	16.1996	+	2.56576i	0.559604	+	0.0886326i
$839$	20.9575	−	6.80951i	0.723533	−	0.235090i	0.0759789	−	0.997109i	$-0.475792\pi$
$839$	20.9575	−	6.80951i	0.723533	−	0.235090i	0.647554	+	0.762019i	$0.275792\pi$
$840$		0			0
$841$	6.87075	+	4.99189i	0.236922	+	0.172134i
$842$	−26.0493	+	4.12580i	−0.897718	+	0.142185i
$843$		0			0
$844$	7.74813	+	23.8463i	0.266701	+	0.820823i
$845$	−17.1661	−	20.2715i	−0.590531	−	0.697360i
$846$		0			0
$847$	−16.6171	+	2.25030i	−0.570969	+	0.0773212i
$848$	−2.68946	+	2.68946i	−0.0923566	+	0.0923566i
$849$		0			0
$850$	−9.94815	+	4.96354i	−0.341219	+	0.170248i
$851$	1.86005	−	5.72466i	0.0637619	−	0.196239i
$852$		0			0
$853$	5.72190	+	36.1266i	0.195914	+	1.23695i	0.868032	+	0.496508i	$0.165385\pi$
$853$	5.72190	+	36.1266i	0.195914	+	1.23695i	−0.672118	+	0.740444i	$0.734615\pi$
$854$	2.78994	−	8.58655i	0.0954697	−	0.293826i
$855$		0			0
$856$	13.3632	−	9.70891i	0.456744	−	0.331844i
$857$	8.98140	−	8.98140i	0.306799	−	0.306799i	−0.536868	−	0.843666i	$-0.680393\pi$
$857$	8.98140	−	8.98140i	0.306799	−	0.306799i	0.843666	+	0.536868i	$0.180393\pi$
$858$		0			0
$859$		−	54.6972i		−	1.86624i	−0.359559	−	0.933122i	$-0.617073\pi$
$859$		−	54.6972i		−	1.86624i	0.359559	−	0.933122i	$-0.382927\pi$
$860$	1.67552	−	20.1995i	0.0571348	−	0.688796i
$861$		0			0
$862$	−8.46615	+	4.31372i	−0.288358	+	0.146926i
$863$	14.0924	−	2.23202i	0.479711	−	0.0759788i	0.0881040	−	0.996111i	$-0.471919\pi$
$863$	14.0924	−	2.23202i	0.479711	−	0.0759788i	0.391607	+	0.920132i	$0.371919\pi$
$864$		0			0
$865$	−25.2187	+	15.3081i	−0.857462	+	0.520489i
$866$	−23.7208	+	7.70734i	−0.806064	+	0.261906i
$867$		0			0
$868$	3.10158	+	3.10158i	0.105274	+	0.105274i
$869$	−6.14895	+	18.2250i	−0.208589	+	0.618241i
$870$		0			0
$871$	4.75846	+	6.54946i	0.161234	+	0.221920i
$872$	0.857140	−	1.68223i	0.0290264	−	0.0569676i
$873$		0			0
$874$	15.7523	−	21.6812i	0.532829	−	0.733376i
$875$	15.8276	−	6.32249i	0.535070	−	0.213739i
$876$		0			0
$877$	13.7086	+	6.98490i	0.462908	+	0.235863i	0.669860	−	0.742488i	$-0.266354\pi$
$877$	13.7086	+	6.98490i	0.462908	+	0.235863i	−0.206952	+	0.978351i	$0.566354\pi$
$878$	0.264554	−	1.67033i	0.00892828	−	0.0563710i
$879$		0			0
$880$	6.26270	+	3.97223i	0.211115	+	0.133904i
$881$	27.4651			0.925323			0.462662	−	0.886535i	$-0.346894\pi$
$881$	27.4651			0.925323			0.462662	+	0.886535i	$0.346894\pi$
$882$		0			0
$883$	−48.3824	−	24.6520i	−1.62820	−	0.829607i	−0.998612	−	0.0526752i	$-0.983225\pi$
$883$	−48.3824	−	24.6520i	−1.62820	−	0.829607i	−0.629584	−	0.776932i	$-0.716775\pi$
$884$	−2.23854	−	0.727347i	−0.0752904	−	0.0244633i
$885$		0			0
$886$	−11.9367	+	16.4295i	−0.401023	+	0.551960i
$887$	26.8712	+	52.7376i	0.902246	+	1.77076i	0.551111	+	0.834432i	$0.314204\pi$
$887$	26.8712	+	52.7376i	0.902246	+	1.77076i	0.351134	+	0.936325i	$0.385796\pi$
$888$		0			0
$889$	15.2015	+	20.9231i	0.509843	+	0.701738i
$890$	−17.8766	−	15.3990i	−0.599224	−	0.516175i
$891$		0			0
$892$	−3.52584	−	3.52584i	−0.118054	−	0.118054i
$893$	−27.4601	−	4.34926i	−0.918918	−	0.145542i
$894$		0			0
$895$	−29.4358	−	7.19839i	−0.983929	−	0.240616i
$896$	−1.23329	−	0.896038i	−0.0412014	−	0.0299345i
$897$		0			0
$898$	−37.4672	+	19.0905i	−1.25030	+	0.637058i
$899$	4.02649	+	12.3922i	0.134291	+	0.413305i
$900$		0			0
$901$			8.45716i			0.281749i
$902$	−5.81141	−	5.94353i	−0.193499	−	0.197898i
$903$		0			0
$904$	3.22746	−	2.34489i	0.107344	−	0.0779899i
$905$	−14.6064	−	35.6882i	−0.485534	−	1.18632i
$906$		0			0
$907$	−2.36980	−	14.9623i	−0.0786880	−	0.496817i	−0.995284	−	0.0970022i	$-0.969075\pi$
$907$	−2.36980	−	14.9623i	−0.0786880	−	0.496817i	0.916596	−	0.399814i	$-0.130925\pi$
$908$	0.319245	+	2.01564i	0.0105945	+	0.0668912i
$909$		0			0
$910$	3.32782	+	1.39491i	0.110316	+	0.0462408i
$911$	−5.44856	+	3.95861i	−0.180519	+	0.131155i	−0.674375	−	0.738389i	$-0.735587\pi$
$911$	−5.44856	+	3.95861i	−0.180519	+	0.131155i	0.493856	+	0.869544i	$0.335587\pi$
$912$		0			0
$913$	2.96573	+	3.03315i	0.0981512	+	0.100383i
$914$		−	10.1208i		−	0.334766i
$915$		0			0
$916$	0.470996	+	1.44958i	0.0155622	+	0.0478954i
$917$	−13.2792	+	6.76610i	−0.438518	+	0.223436i
$918$		0			0
$919$	47.2044	+	34.2960i	1.55713	+	1.13132i	0.938315	+	0.345782i	$0.112386\pi$
$919$	47.2044	+	34.2960i	1.55713	+	1.13132i	0.618813	+	0.785538i	$0.287614\pi$
$920$	2.29706	−	9.39316i	0.0757318	−	0.309683i
$921$		0			0
$922$	−27.1134	−	4.29433i	−0.892931	−	0.141426i
$923$	6.66028	+	6.66028i	0.219226	+	0.219226i
$924$		0			0
$925$	5.59558	+	4.13802i	0.183982	+	0.136057i
$926$	10.6467	+	14.6539i	0.349872	+	0.481557i
$927$		0			0
$928$	−2.05589	−	4.03492i	−0.0674881	−	0.132453i
$929$	−5.89306	+	8.11110i	−0.193345	+	0.266117i	−0.894672	−	0.446723i	$-0.852591\pi$
$929$	−5.89306	+	8.11110i	−0.193345	+	0.266117i	0.701327	+	0.712839i	$0.252591\pi$
$930$		0			0
$931$	−27.5598	−	8.95473i	−0.903237	−	0.293480i
$932$	19.7711	+	10.0739i	0.647624	+	0.329981i
$933$		0			0
$934$	−21.8363			−0.714505
$935$	16.0921	−	3.60124i	0.526269	−	0.117773i
$936$		0			0
$937$	6.52746	−	41.2128i	0.213243	−	1.34636i	−0.616120	−	0.787652i	$-0.711297\pi$
$937$	6.52746	−	41.2128i	0.213243	−	1.34636i	0.829363	−	0.558710i	$-0.188703\pi$
$938$	10.3877	+	5.29282i	0.339172	+	0.172817i
$939$		0			0
$940$	−9.76448	+	2.30071i	−0.318482	+	0.0750410i
$941$	−14.4754	+	19.9237i	−0.471885	+	0.649494i	−0.976920	−	0.213605i	$-0.931480\pi$
$941$	−14.4754	+	19.9237i	−0.471885	+	0.649494i	0.505035	+	0.863099i	$0.331480\pi$
$942$		0			0
$943$	−4.92065	+	9.65732i	−0.160238	+	0.314486i
$944$	−2.63995	−	3.63358i	−0.0859232	−	0.118263i
$945$		0			0
$946$	−9.61089	+	28.4859i	−0.312477	+	0.926157i
$947$	6.72877	+	6.72877i	0.218656	+	0.218656i	0.807932	−	0.589276i	$-0.200587\pi$
$947$	6.72877	+	6.72877i	0.218656	+	0.218656i	−0.589276	+	0.807932i	$0.700587\pi$
$948$		0			0
$949$	−11.4836	+	3.73124i	−0.372772	+	0.121121i
$950$	18.0005	+	25.2204i	0.584014	+	0.818259i
$951$		0			0
$952$	−3.34789	+	0.530254i	−0.108506	+	0.0171856i
$953$	31.2897	−	15.9429i	1.01357	−	0.516441i	0.133384	−	0.991064i	$-0.457416\pi$
$953$	31.2897	−	15.9429i	1.01357	−	0.516441i	0.880189	+	0.474623i	$0.157416\pi$
$954$		0			0
$955$	21.4886	−	18.1967i	0.695354	−	0.588833i
$956$			24.7841i			0.801574i
$957$		0			0
$958$	4.61171	−	4.61171i	0.148998	−	0.148998i
$959$	3.04719	−	2.21391i	0.0983989	−	0.0714910i
$960$		0			0
$961$	−7.02117	+	21.6089i	−0.226489	+	0.697062i
$962$	0.230490	+	1.45526i	0.00743130	+	0.0469194i
$963$		0			0
$964$	−0.0173846	+	0.0535042i	−0.000559919	+	0.00172325i
$965$	−3.31529	+	7.90927i	−0.106723	+	0.254608i
$966$		0			0
$967$	−43.6347	+	43.6347i	−1.40320	+	1.40320i	−0.613512	+	0.789685i	$0.710244\pi$
$967$	−43.6347	+	43.6347i	−1.40320	+	1.40320i	−0.789685	+	0.613512i	$0.789756\pi$
$968$	−7.60139	−	7.95103i	−0.244318	−	0.255556i
$969$		0			0
$970$	−11.9560	+	10.1245i	−0.383885	+	0.325078i
$971$	−8.80597	−	27.1020i	−0.282597	−	0.869744i	−0.987109	−	0.160052i	$-0.948834\pi$
$971$	−8.80597	−	27.1020i	−0.282597	−	0.869744i	0.704512	−	0.709693i	$-0.251166\pi$
$972$		0			0
$973$	−11.3119	+	1.79163i	−0.362642	+	0.0574369i
$974$	2.37265	+	1.72383i	0.0760245	+	0.0552350i
$975$		0			0
$976$	5.63262	−	1.83015i	0.180296	−	0.0585817i
$977$	51.0116	+	8.07944i	1.63201	+	0.258484i	0.904140	−	0.427236i	$-0.140513\pi$
$977$	51.0116	+	8.07944i	1.63201	+	0.258484i	0.727865	+	0.685720i	$0.240513\pi$
$978$		0			0
$979$	20.2508	+	28.5420i	0.647219	+	0.912206i
$980$	−10.4272	+	0.776386i	−0.333086	+	0.0248007i
$981$		0			0
$982$	6.04634	−	11.8666i	0.192946	−	0.378679i
$983$	−24.7809	−	48.6352i	−0.790387	−	1.55122i	−0.833737	−	0.552161i	$-0.813803\pi$
$983$	−24.7809	−	48.6352i	−0.790387	−	1.55122i	0.0433506	−	0.999060i	$-0.486197\pi$
$984$		0			0
$985$	22.7775	−	5.36686i	0.725753	−	0.171002i
$986$	−9.57644	−	3.11157i	−0.304976	−	0.0990927i
$987$		0			0
$988$	−1.02620	+	6.47920i	−0.0326479	+	0.206131i
$989$	39.1997			1.24648
$990$		0			0
$991$	1.67436			0.0531879			0.0265939	−	0.999646i	$-0.491534\pi$
$991$	1.67436			0.0531879			0.0265939	+	0.999646i	$0.491534\pi$
$992$	−0.450114	+	2.84191i	−0.0142911	+	0.0902306i
$993$		0			0
$994$	12.9005	+	4.19162i	0.409178	+	0.132950i
$995$	−10.7138	+	17.3188i	−0.339649	+	0.549043i
$996$		0			0
$997$	−13.5579	−	26.6089i	−0.429384	−	0.842713i	−0.999772	−	0.0213379i	$-0.993207\pi$
$997$	−13.5579	−	26.6089i	−0.429384	−	0.842713i	0.570389	−	0.821375i	$-0.306793\pi$
$998$	10.6099	−	20.8231i	0.335850	−	0.659143i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bh.c.217.2		48
3.2	odd	2		110.2.k.a.107.6	yes	48
5.3	odd	4	inner	990.2.bh.c.613.6		48
11.7	odd	10	inner	990.2.bh.c.667.6		48
12.11	even	2		880.2.cm.c.657.1		48
15.2	even	4		550.2.bh.b.393.6		48
15.8	even	4		110.2.k.a.63.1	yes	48
15.14	odd	2		550.2.bh.b.107.1		48
33.29	even	10		110.2.k.a.7.1	✓	48
55.18	even	20	inner	990.2.bh.c.73.2		48
60.23	odd	4		880.2.cm.c.833.6		48
132.95	odd	10		880.2.cm.c.337.6		48
165.29	even	10		550.2.bh.b.7.6		48
165.62	odd	20		550.2.bh.b.293.1		48
165.128	odd	20		110.2.k.a.73.6	yes	48
660.623	even	20		880.2.cm.c.513.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.1	✓	48	33.29	even	10
110.2.k.a.63.1	yes	48	15.8	even	4
110.2.k.a.73.6	yes	48	165.128	odd	20
110.2.k.a.107.6	yes	48	3.2	odd	2
550.2.bh.b.7.6		48	165.29	even	10
550.2.bh.b.107.1		48	15.14	odd	2
550.2.bh.b.293.1		48	165.62	odd	20
550.2.bh.b.393.6		48	15.2	even	4
880.2.cm.c.337.6		48	132.95	odd	10
880.2.cm.c.513.1		48	660.623	even	20
880.2.cm.c.657.1		48	12.11	even	2
880.2.cm.c.833.6		48	60.23	odd	4
990.2.bh.c.73.2		48	55.18	even	20	inner
990.2.bh.c.217.2		48	1.1	even	1	trivial
990.2.bh.c.613.6		48	5.3	odd	4	inner
990.2.bh.c.667.6		48	11.7	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(1.90161 + 1.17638i) q^{5} +(-0.692077 - 1.35828i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-1.45937 + 1.69418i) q^{10} +(2.70495 - 1.91918i) q^{11} +(1.04553 + 0.165595i) q^{13} +(1.44982 - 0.471075i) q^{14} +(0.809017 + 0.587785i) q^{16} +(2.19616 - 0.347837i) q^{17} +(-1.91500 - 5.89375i) q^{19} +(-1.44502 - 1.70643i) q^{20} +(1.47241 + 2.97187i) q^{22} +(3.05791 - 3.05791i) q^{23} +(2.23228 + 4.47403i) q^{25} +(-0.327113 + 1.00675i) q^{26} +(0.238474 + 1.50566i) q^{28} +(-1.39938 + 4.30686i) q^{29} +(2.32781 - 1.69125i) q^{31} +(-0.707107 + 0.707107i) q^{32} +2.22353i q^{34} +(0.281782 - 3.39707i) q^{35} +(1.24018 - 0.631904i) q^{37} +(6.12076 - 0.969434i) q^{38} +(1.91147 - 1.16029i) q^{40} +(-2.38365 + 0.774496i) q^{41} +(6.40957 + 6.40957i) q^{43} +(-3.16562 + 0.989379i) q^{44} +(2.54190 + 3.49862i) q^{46} +(2.03678 - 3.99740i) q^{47} +(2.74855 - 3.78305i) q^{49} +(-4.76815 + 1.50490i) q^{50} +(-0.943185 - 0.480577i) q^{52} +(-0.594995 + 3.75665i) q^{53} +(7.40145 - 0.467516i) q^{55} -1.52443 q^{56} +(-4.03492 - 2.05589i) q^{58} +(-4.27154 - 1.38791i) q^{59} +(3.48115 - 4.79140i) q^{61} +(1.30628 + 2.56372i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(1.79339 + 1.54483i) q^{65} +(5.40776 + 5.40776i) q^{67} +(-2.19616 - 0.347837i) q^{68} +(3.31116 + 0.809731i) q^{70} +(7.19862 + 5.23010i) q^{71} +(-10.1633 + 5.17847i) q^{73} +(0.430117 + 1.32376i) q^{74} +6.19706i q^{76} +(-4.47882 - 2.34584i) q^{77} +(-4.69179 + 3.40879i) q^{79} +(0.846982 + 2.06945i) q^{80} +(-0.392075 - 2.47546i) q^{82} +(0.200087 + 1.26330i) q^{83} +(4.58543 + 1.92206i) q^{85} +(-7.33334 + 5.32798i) q^{86} +(-0.481987 - 3.28142i) q^{88} +10.5518i q^{89} +(-0.498662 - 1.53472i) q^{91} +(-3.85319 + 1.96330i) q^{92} +(3.62956 + 2.63703i) q^{94} +(3.29169 - 13.4604i) q^{95} +(6.92020 + 1.09605i) q^{97} +(3.30651 + 3.30651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47}+ \cdots + 72 q^{97}+O(q^{100}) \) 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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