LMFDB - Embedded newform 567.2.bd.a.467.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(17,567)] 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("567.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([11, 3])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			467.18
Character	$\chi$	$=$	567.467
Dual form			567.2.bd.a.17.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63190 + 0.287749i) q^{2} +(0.700923 + 0.255115i) q^{4} +(3.60525 + 1.31220i) q^{5} +(2.03118 + 1.69538i) q^{7} +(-1.79971 - 1.03907i) q^{8} +(5.50583 + 3.17879i) q^{10} +(-0.982995 - 2.70076i) q^{11} +(-1.44158 + 3.96072i) q^{13} +(2.82685 + 3.35116i) q^{14} +(-3.78076 - 3.17244i) q^{16} +(1.59416 - 2.76117i) q^{17} +(-1.96303 + 1.13336i) q^{19} +(2.19224 + 1.83951i) q^{20} +(-0.827014 - 4.69023i) q^{22} +(-2.25312 + 0.397286i) q^{23} +(7.44573 + 6.24771i) q^{25} +(-3.49221 + 6.04869i) q^{26} +(0.991186 + 1.70651i) q^{28} +(-0.356349 - 0.979061i) q^{29} +(2.96755 - 8.15327i) q^{31} +(-2.58538 - 3.08114i) q^{32} +(3.39605 - 4.04725i) q^{34} +(5.09824 + 8.77758i) q^{35} +0.0244697 q^{37} +(-3.52960 + 1.28467i) q^{38} +(-5.12495 - 6.10768i) q^{40} +(2.99981 + 1.09184i) q^{41} +(-0.110557 + 0.627001i) q^{43} -2.14380i q^{44} -3.79119 q^{46} +(-10.0976 + 3.67521i) q^{47} +(1.25140 + 6.88723i) q^{49} +(10.3529 + 12.3382i) q^{50} +(-2.02088 + 2.40839i) q^{52} +(-1.91685 + 1.10670i) q^{53} -11.0268i q^{55} +(-1.89394 - 5.16172i) q^{56} +(-0.299804 - 1.70027i) q^{58} +(8.38964 - 7.03975i) q^{59} +(-2.60670 - 7.16186i) q^{61} +(7.18884 - 12.4514i) q^{62} +(1.60294 + 2.77637i) q^{64} +(-10.3945 + 12.3877i) q^{65} +(-1.88769 - 10.7056i) q^{67} +(1.82180 - 1.52867i) q^{68} +(5.79410 + 15.7912i) q^{70} +(-3.88604 + 2.24361i) q^{71} -2.22546i q^{73} +(0.0399322 + 0.00704112i) q^{74} +(-1.66507 + 0.293597i) q^{76} +(2.58216 - 7.15227i) q^{77} +(-2.19643 + 12.4566i) q^{79} +(-9.46771 - 16.3986i) q^{80} +(4.58122 + 2.64497i) q^{82} +(-4.16888 + 1.51735i) q^{83} +(9.37059 - 7.86286i) q^{85} +(-0.360837 + 0.991392i) q^{86} +(-1.03715 + 5.88198i) q^{88} +(-2.36580 - 4.09769i) q^{89} +(-9.64302 + 5.60091i) q^{91} +(-1.68062 - 0.296338i) q^{92} +(-17.5358 + 3.09203i) q^{94} +(-8.56442 + 1.51014i) q^{95} +(-13.0174 - 2.29533i) q^{97} +(0.0603728 + 11.5994i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	1.63190	+	0.287749i	1.15393	+	0.203469i	0.717691	−	0.696362i	$-0.245199\pi$
$2$	1.63190	+	0.287749i	1.15393	+	0.203469i	0.436239	+	0.899831i	$0.356310\pi$
$3$		0			0
$3$		0			0
$4$	0.700923	+	0.255115i	0.350461	+	0.127558i
$5$	3.60525	+	1.31220i	1.61232	+	0.586835i	0.981896	−	0.189418i	$-0.0606603\pi$
$5$	3.60525	+	1.31220i	1.61232	+	0.586835i	0.630420	+	0.776254i	$0.282882\pi$
$6$		0			0
$7$	2.03118	+	1.69538i	0.767715	+	0.640792i
$7$	2.03118	+	1.69538i	0.767715	+	0.640792i
$8$	−1.79971	−	1.03907i	−0.636295	−	0.367365i
$9$		0			0
$10$	5.50583	+	3.17879i	1.74110	+	1.00522i
$11$	−0.982995	−	2.70076i	−0.296384	−	0.814309i	−0.995097	−	0.0989062i	$-0.968466\pi$
$11$	−0.982995	−	2.70076i	−0.296384	−	0.814309i	0.698713	−	0.715402i	$-0.253757\pi$
$12$		0			0
$13$	−1.44158	+	3.96072i	−0.399823	+	1.09851i	0.562547	+	0.826765i	$0.309821\pi$
$13$	−1.44158	+	3.96072i	−0.399823	+	1.09851i	−0.962371	+	0.271740i	$0.912401\pi$
$14$	2.82685	+	3.35116i	0.755507	+	0.895635i
$15$		0			0
$16$	−3.78076	−	3.17244i	−0.945191	−	0.793109i
$17$	1.59416	−	2.76117i	0.386642	−	0.669683i	−0.605354	−	0.795957i	$-0.706968\pi$
$17$	1.59416	−	2.76117i	0.386642	−	0.669683i	0.991995	+	0.126273i	$0.0403017\pi$
$18$		0			0
$19$	−1.96303	+	1.13336i	−0.450351	+	0.260010i	−0.707978	−	0.706234i	$-0.750393\pi$
$19$	−1.96303	+	1.13336i	−0.450351	+	0.260010i	0.257628	+	0.966244i	$0.417059\pi$
$20$	2.19224	+	1.83951i	0.490200	+	0.411326i
$21$		0			0
$22$	−0.827014	−	4.69023i	−0.176320	−	0.999960i
$23$	−2.25312	+	0.397286i	−0.469808	+	0.0828398i	−0.403540	−	0.914962i	$-0.632220\pi$
$23$	−2.25312	+	0.397286i	−0.469808	+	0.0828398i	−0.0662680	+	0.997802i	$0.521109\pi$
$24$		0			0
$25$	7.44573	+	6.24771i	1.48915	+	1.24954i
$26$	−3.49221	+	6.04869i	−0.684880	+	1.18625i
$27$		0			0
$28$	0.991186	+	1.70651i	0.187317	+	0.322501i
$29$	−0.356349	−	0.979061i	−0.0661723	−	0.181807i	0.902199	−	0.431320i	$-0.141952\pi$
$29$	−0.356349	−	0.979061i	−0.0661723	−	0.181807i	−0.968372	+	0.249513i	$0.919730\pi$
$30$		0			0
$31$	2.96755	−	8.15327i	0.532988	−	1.46437i	−0.322511	−	0.946566i	$-0.604527\pi$
$31$	2.96755	−	8.15327i	0.532988	−	1.46437i	0.855498	−	0.517805i	$-0.173251\pi$
$32$	−2.58538	−	3.08114i	−0.457035	−	0.544673i
$33$		0			0
$34$	3.39605	−	4.04725i	0.582417	−	0.694098i
$35$	5.09824	+	8.77758i	0.861760	+	1.48368i
$36$		0			0
$37$	0.0244697			0.00402279			0.00201140	−	0.999998i	$-0.499360\pi$
$37$	0.0244697			0.00402279			0.00201140	+	0.999998i	$0.499360\pi$
$38$	−3.52960	+	1.28467i	−0.572577	+	0.208401i
$39$		0			0
$40$	−5.12495	−	6.10768i	−0.810326	−	0.965709i
$41$	2.99981	+	1.09184i	0.468492	+	0.170517i	0.565469	−	0.824770i	$-0.308695\pi$
$41$	2.99981	+	1.09184i	0.468492	+	0.170517i	−0.0969772	+	0.995287i	$0.530917\pi$
$42$		0			0
$43$	−0.110557	+	0.627001i	−0.0168598	+	0.0956167i	−0.992077	−	0.125635i	$-0.959903\pi$
$43$	−0.110557	+	0.627001i	−0.0168598	+	0.0956167i	0.975217	+	0.221252i	$0.0710143\pi$
$44$		−	2.14380i		−	0.323190i
$45$		0			0
$46$	−3.79119			−0.558980
$47$	−10.0976	+	3.67521i	−1.47288	+	0.536084i	−0.948881	−	0.315635i	$-0.897783\pi$
$47$	−10.0976	+	3.67521i	−1.47288	+	0.536084i	−0.523999	+	0.851719i	$0.675560\pi$
$48$		0			0
$49$	1.25140	+	6.88723i	0.178772	+	0.983891i
$50$	10.3529	+	12.3382i	1.46413	+	1.74488i
$51$		0			0
$52$	−2.02088	+	2.40839i	−0.280245	+	0.333983i
$53$	−1.91685	+	1.10670i	−0.263300	+	0.152016i	−0.625839	−	0.779952i	$-0.715243\pi$
$53$	−1.91685	+	1.10670i	−0.263300	+	0.152016i	0.362539	+	0.931969i	$0.381910\pi$
$54$		0			0
$55$		−	11.0268i		−	1.48685i
$56$	−1.89394	−	5.16172i	−0.253088	−	0.689764i
$57$		0			0
$58$	−0.299804	−	1.70027i	−0.0393661	−	0.223257i
$59$	8.38964	−	7.03975i	1.09224	−	0.916497i	0.0953596	−	0.995443i	$-0.469600\pi$
$59$	8.38964	−	7.03975i	1.09224	−	0.916497i	0.996879	+	0.0789460i	$0.0251555\pi$
$60$		0			0
$61$	−2.60670	−	7.16186i	−0.333754	−	0.916982i	−0.987126	−	0.159945i	$-0.948868\pi$
$61$	−2.60670	−	7.16186i	−0.333754	−	0.916982i	0.653372	−	0.757037i	$-0.273354\pi$
$62$	7.18884	−	12.4514i	0.912984	−	1.58133i
$63$		0			0
$64$	1.60294	+	2.77637i	0.200367	+	0.347046i
$65$	−10.3945	+	12.3877i	−1.28928	+	1.53651i
$66$		0			0
$67$	−1.88769	−	10.7056i	−0.230618	−	1.30790i	−0.851649	−	0.524113i	$-0.824397\pi$
$67$	−1.88769	−	10.7056i	−0.230618	−	1.30790i	0.621031	−	0.783786i	$-0.286714\pi$
$68$	1.82180	−	1.52867i	0.220926	−	0.185379i
$69$		0			0
$70$	5.79410	+	15.7912i	0.692527	+	1.88741i
$71$	−3.88604	+	2.24361i	−0.461188	+	0.266267i	−0.712544	−	0.701628i	$-0.752457\pi$
$71$	−3.88604	+	2.24361i	−0.461188	+	0.266267i	0.251356	+	0.967895i	$0.419124\pi$
$72$		0			0
$73$		−	2.22546i		−	0.260470i	−0.991483	−	0.130235i	$-0.958427\pi$
$73$		−	2.22546i		−	0.260470i	0.991483	−	0.130235i	$-0.0415732\pi$
$74$	0.0399322	+	0.00704112i	0.00464202	+	0.000818514i
$75$		0			0
$76$	−1.66507	+	0.293597i	−0.190997	+	0.0336779i
$77$	2.58216	−	7.15227i	0.294264	−	0.815077i
$78$		0			0
$79$	−2.19643	+	12.4566i	−0.247118	+	1.40147i	0.568405	+	0.822749i	$0.307561\pi$
$79$	−2.19643	+	12.4566i	−0.247118	+	1.40147i	−0.815523	+	0.578725i	$0.803551\pi$
$80$	−9.46771	−	16.3986i	−1.05852	−	1.83342i
$81$		0			0
$82$	4.58122	+	2.64497i	0.505912	+	0.292088i
$83$	−4.16888	+	1.51735i	−0.457594	+	0.166550i	−0.560524	−	0.828138i	$-0.689400\pi$
$83$	−4.16888	+	1.51735i	−0.457594	+	0.166550i	0.102931	+	0.994689i	$0.467178\pi$
$84$		0			0
$85$	9.37059	−	7.86286i	1.01638	−	0.852846i
$86$	−0.360837	+	0.991392i	−0.0389101	+	0.106905i
$87$		0			0
$88$	−1.03715	+	5.88198i	−0.110561	+	0.627022i
$89$	−2.36580	−	4.09769i	−0.250774	−	0.434354i	0.712965	−	0.701200i	$-0.247352\pi$
$89$	−2.36580	−	4.09769i	−0.250774	−	0.434354i	−0.963739	+	0.266846i	$0.914019\pi$
$90$		0			0
$91$	−9.64302	+	5.60091i	−1.01086	+	0.587135i
$92$	−1.68062	−	0.296338i	−0.175216	−	0.0308954i
$93$		0			0
$94$	−17.5358	+	3.09203i	−1.80868	+	0.318918i
$95$	−8.56442	+	1.51014i	−0.878691	+	0.154937i
$96$		0			0
$97$	−13.0174	−	2.29533i	−1.32172	−	0.233055i	−0.532117	−	0.846671i	$-0.678603\pi$
$97$	−13.0174	−	2.29533i	−1.32172	−	0.233055i	−0.789605	+	0.613616i	$0.789714\pi$
$98$	0.0603728	+	11.5994i	0.00609857	+	1.17171i
$99$		0			0
$100$	3.62500	+	6.27868i	0.362500	+	0.627868i
$101$	−0.471291	+	2.67282i	−0.0468952	+	0.265956i	−0.999236	−	0.0390800i	$-0.987557\pi$
$101$	−0.471291	+	2.67282i	−0.0468952	+	0.265956i	0.952341	+	0.305036i	$0.0986684\pi$
$102$		0			0
$103$	3.33939	−	9.17490i	0.329040	−	0.904029i	−0.659316	−	0.751866i	$-0.729154\pi$
$103$	3.33939	−	9.17490i	0.329040	−	0.904029i	0.988355	−	0.152163i	$-0.0486239\pi$
$104$	6.70988	−	5.63026i	0.657958	−	0.552092i
$105$		0			0
$106$	−3.44657	+	1.25445i	−0.334761	+	0.121843i
$107$	−12.2288	−	7.06029i	−1.18220	−	0.682544i	−0.225678	−	0.974202i	$-0.572460\pi$
$107$	−12.2288	−	7.06029i	−1.18220	−	0.682544i	−0.956523	+	0.291658i	$0.905793\pi$
$108$		0			0
$109$	2.48897	+	4.31103i	0.238400	+	0.412922i	0.960255	−	0.279123i	$-0.0900436\pi$
$109$	2.48897	+	4.31103i	0.238400	+	0.412922i	−0.721855	+	0.692044i	$0.756710\pi$
$110$	3.17294	−	17.9947i	0.302528	−	1.71572i
$111$		0			0
$112$	−2.30094	−	12.8536i	−0.217419	−	1.21455i
$113$	−7.89136	+	1.39146i	−0.742357	+	0.130898i	−0.532020	−	0.846732i	$-0.678567\pi$
$113$	−7.89136	+	1.39146i	−0.742357	+	0.130898i	−0.210336	+	0.977629i	$0.567456\pi$
$114$		0			0
$115$	−8.64438	−	1.52424i	−0.806092	−	0.142136i
$116$		−	0.777156i		−	0.0721571i
$117$		0			0
$118$	15.7168	−	9.07408i	1.44684	−	0.835336i
$119$	7.91927	−	2.90574i	0.725958	−	0.266369i
$120$		0			0
$121$	2.09869	−	1.76101i	0.190790	−	0.160091i
$122$	−2.19307	−	12.4375i	−0.198551	−	1.12604i
$123$		0			0
$124$	4.16005	−	4.95775i	0.373583	−	0.445219i
$125$	9.05388	+	15.6818i	0.809804	+	1.40262i
$126$		0			0
$127$	−3.39217	+	5.87541i	−0.301006	+	0.521358i	−0.976364	−	0.216132i	$-0.930656\pi$
$127$	−3.39217	+	5.87541i	−0.301006	+	0.521358i	0.675358	+	0.737490i	$0.263989\pi$
$128$	4.56825	+	12.5512i	0.403780	+	1.10938i
$129$		0			0
$130$	−20.5274	+	17.2246i	−1.80037	+	1.51069i
$131$	−3.49094	−	19.7981i	−0.305005	−	1.72977i	−0.623482	−	0.781837i	$-0.714283\pi$
$131$	−3.49094	−	19.7981i	−0.305005	−	1.72977i	0.318478	−	0.947930i	$-0.396828\pi$
$132$		0			0
$133$	−5.90875	−	1.02602i	−0.512353	−	0.0889675i
$134$		−	18.0137i		−	1.55615i
$135$		0			0
$136$	−5.73808	+	3.31288i	−0.492036	+	0.284077i
$137$	−12.0468	+	14.3569i	−1.02923	+	1.22659i	−0.0556027	+	0.998453i	$0.517708\pi$
$137$	−12.0468	+	14.3569i	−1.02923	+	1.22659i	−0.973629	+	0.228138i	$0.926736\pi$
$138$		0			0
$139$	8.49230	+	10.1207i	0.720308	+	0.858429i	0.994661	−	0.103200i	$-0.0329081\pi$
$139$	8.49230	+	10.1207i	0.720308	+	0.858429i	−0.274353	+	0.961629i	$0.588464\pi$
$140$	1.33418	+	7.45304i	0.112759	+	0.629897i
$141$		0			0
$142$	−6.98723	+	2.54314i	−0.586355	+	0.213416i
$143$	12.1140			1.01302
$144$		0			0
$145$		−	3.99736i		−	0.331963i
$146$	0.640372	−	3.63173i	0.0529976	−	0.300564i
$147$		0			0
$148$	0.0171514	+	0.00624259i	0.00140983	+	0.000513138i
$149$	8.49738	+	10.1268i	0.696132	+	0.829618i	0.992083	−	0.125585i	$-0.0400808\pi$
$149$	8.49738	+	10.1268i	0.696132	+	0.829618i	−0.295951	+	0.955203i	$0.595636\pi$
$150$		0			0
$151$	11.8035	−	4.29612i	0.960556	−	0.349614i	0.186304	−	0.982492i	$-0.440349\pi$
$151$	11.8035	−	4.29612i	0.960556	−	0.349614i	0.774251	+	0.632878i	$0.218127\pi$
$152$	4.71053			0.382075
$153$		0			0
$154$	6.27188	−	10.9288i	0.505403	−	0.880668i
$155$	21.3975	−	25.5006i	1.71869	−	2.04825i
$156$		0			0
$157$	11.6576	+	13.8930i	0.930376	+	1.10878i	0.993843	+	0.110794i	$0.0353395\pi$
$157$	11.6576	+	13.8930i	0.930376	+	1.10878i	−0.0634678	+	0.997984i	$0.520216\pi$
$158$	−7.16872	+	19.6959i	−0.570313	+	1.56692i
$159$		0			0
$160$	−5.27787	−	14.5008i	−0.417252	−	1.14639i
$161$	−5.25004	−	3.01292i	−0.413761	−	0.237452i
$162$		0			0
$163$	2.93944	−	5.09126i	0.230235	−	0.398779i	−0.727642	−	0.685957i	$-0.759384\pi$
$163$	2.93944	−	5.09126i	0.230235	−	0.398779i	0.957877	+	0.287178i	$0.0927172\pi$
$164$	1.82409	+	1.53059i	0.142438	+	0.119519i
$165$		0			0
$166$	−7.23982	+	1.27657i	−0.561919	+	0.0990814i
$167$	1.43991	+	8.16616i	0.111424	+	0.631916i	0.988459	+	0.151490i	$0.0484070\pi$
$167$	1.43991	+	8.16616i	0.111424	+	0.631916i	−0.877035	+	0.480427i	$0.840482\pi$
$168$		0			0
$169$	−3.65055	−	3.06317i	−0.280811	−	0.235629i
$170$	17.5544	−	10.1350i	1.34636	−	0.777322i
$171$		0			0
$172$	−0.237449	+	0.411274i	−0.0181053	+	0.0313594i
$173$	14.9572	+	12.5506i	1.13718	+	0.954205i	0.999343	−	0.0362507i	$-0.0115415\pi$
$173$	14.9572	+	12.5506i	1.13718	+	0.954205i	0.137834	+	0.990455i	$0.455986\pi$
$174$		0			0
$175$	4.53142	+	25.3135i	0.342543	+	1.91352i
$176$	−4.85151	+	13.3294i	−0.365696	+	1.00474i
$177$		0			0
$178$	−2.68165	−	7.36778i	−0.200998	−	0.552239i
$179$	−2.56681	−	1.48195i	−0.191853	−	0.110766i	0.400997	−	0.916079i	$-0.368664\pi$
$179$	−2.56681	−	1.48195i	−0.191853	−	0.110766i	−0.592850	+	0.805313i	$0.701997\pi$
$180$		0			0
$181$	22.0624	+	12.7377i	1.63988	+	0.946787i	0.980872	+	0.194653i	$0.0623581\pi$
$181$	22.0624	+	12.7377i	1.63988	+	0.946787i	0.659011	+	0.752134i	$0.270975\pi$
$182$	−17.3481	+	6.36538i	−1.28593	+	0.471833i
$183$		0			0
$184$	4.46778	+	1.62614i	0.329369	+	0.119880i
$185$	0.0882194	+	0.0321092i	0.00648602	+	0.00236072i
$186$		0			0
$187$	−9.02431	−	1.59123i	−0.659923	−	0.116362i
$188$	−8.01521			−0.584569
$189$		0			0
$190$	−14.4108			−1.04547
$191$	22.3269	+	3.93683i	1.61552	+	0.284859i	0.907094	−	0.420929i	$-0.138296\pi$
$191$	22.3269	+	3.93683i	1.61552	+	0.284859i	0.708423	+	0.705788i	$0.249407\pi$
$192$		0			0
$193$	14.0257	+	5.10496i	1.00960	+	0.367463i	0.793277	−	0.608860i	$-0.208373\pi$
$193$	14.0257	+	5.10496i	1.00960	+	0.367463i	0.216318	+	0.976323i	$0.430595\pi$
$194$	−20.5827	−	7.49150i	−1.47775	−	0.537859i
$195$		0			0
$196$	−0.879902	+	5.14667i	−0.0628501	+	0.367619i
$197$	−16.5142	−	9.53447i	−1.17659	−	0.679303i	−0.221364	−	0.975191i	$-0.571051\pi$
$197$	−16.5142	−	9.53447i	−1.17659	−	0.679303i	−0.955222	+	0.295889i	$0.904384\pi$
$198$		0			0
$199$	−5.02974	−	2.90392i	−0.356549	−	0.205854i	0.311017	−	0.950404i	$-0.399330\pi$
$199$	−5.02974	−	2.90392i	−0.356549	−	0.205854i	−0.667566	+	0.744551i	$0.732664\pi$
$200$	−6.90840	−	18.9807i	−0.488498	−	1.34214i
$201$		0			0
$202$	−1.53820	+	4.22617i	−0.108227	+	0.297352i
$203$	0.936066	−	2.59280i	0.0656990	−	0.181979i
$204$		0			0
$205$	9.38235	+	7.87273i	0.655292	+	0.549855i
$206$	8.08962	−	14.0116i	0.563631	−	0.976237i
$207$		0			0
$208$	18.0154	−	10.4012i	1.24914	−	0.721194i
$209$	4.99057	+	4.18759i	0.345205	+	0.289662i
$210$		0			0
$211$	0.180568	+	1.02405i	0.0124308	+	0.0704985i	0.990392	−	0.138288i	$-0.0441599\pi$
$211$	0.180568	+	1.02405i	0.0124308	+	0.0704985i	−0.977961	+	0.208786i	$0.933049\pi$
$212$	−1.62590	+	0.286690i	−0.111667	+	0.0196900i
$213$		0			0
$214$	−17.9246	−	15.0405i	−1.22530	−	1.02815i
$215$	−1.22134	+	2.11542i	−0.0832946	+	0.144271i
$216$		0			0
$217$	19.8505	−	11.5297i	1.34754	−	0.782685i
$218$	2.82127	+	7.75138i	0.191081	+	0.524990i
$219$		0			0
$220$	2.81310	−	7.72893i	0.189659	−	0.521084i
$221$	8.63811	+	10.2945i	0.581062	+	0.692483i
$222$		0			0
$223$	4.95104	−	5.90042i	0.331546	−	0.395122i	−0.574358	−	0.818604i	$-0.694748\pi$
$223$	4.95104	−	5.90042i	0.331546	−	0.395122i	0.905904	+	0.423483i	$0.139193\pi$
$224$	−0.0276935	−	10.6415i	−0.00185035	−	0.711018i
$225$		0			0
$226$	−13.2783			−0.883261
$227$	−3.04716	+	1.10908i	−0.202247	+	0.0736119i	−0.441158	−	0.897430i	$-0.645432\pi$
$227$	−3.04716	+	1.10908i	−0.202247	+	0.0736119i	0.238910	+	0.971042i	$0.423210\pi$
$228$		0			0
$229$	−14.0510	−	16.7453i	−0.928514	−	1.10656i	−0.994073	−	0.108711i	$-0.965328\pi$
$229$	−14.0510	−	16.7453i	−0.928514	−	1.10656i	0.0655597	−	0.997849i	$-0.479117\pi$
$230$	−13.6682	−	4.97481i	−0.901254	−	0.328030i
$231$		0			0
$232$	−0.375982	+	2.13230i	−0.0246844	+	0.139992i
$233$			9.31495i			0.610243i	0.952313	+	0.305121i	$0.0986970\pi$
$233$			9.31495i			0.610243i	−0.952313	+	0.305121i	$0.901303\pi$
$234$		0			0
$235$	−41.2268			−2.68934
$236$	7.67644	−	2.79399i	0.499693	−	0.181874i
$237$		0			0
$238$	13.7596	−	2.46313i	0.891902	−	0.159661i
$239$	3.92573	+	4.67850i	0.253934	+	0.302627i	0.877919	−	0.478810i	$-0.158932\pi$
$239$	3.92573	+	4.67850i	0.253934	+	0.302627i	−0.623984	+	0.781437i	$0.714487\pi$
$240$		0			0
$241$	0.213906	−	0.254923i	0.0137789	−	0.0164210i	−0.759111	−	0.650961i	$-0.774366\pi$
$241$	0.213906	−	0.254923i	0.0137789	−	0.0164210i	0.772890	+	0.634540i	$0.218810\pi$
$242$	3.93158	−	2.26990i	0.252731	−	0.145915i
$243$		0			0
$244$		−	5.68492i		−	0.363939i
$245$	−4.52584	+	26.4723i	−0.289145	+	1.69125i
$246$		0			0
$247$	−1.65903	−	9.40885i	−0.105562	−	0.598671i
$248$	−13.8125	+	11.5901i	−0.877096	+	0.735971i
$249$		0			0
$250$	10.2626	+	28.1964i	0.649067	+	1.78330i
$251$	−6.85299	+	11.8697i	−0.432557	+	0.749210i	−0.997093	−	0.0761982i	$-0.975722\pi$
$251$	−6.85299	+	11.8697i	−0.432557	+	0.749210i	0.564536	+	0.825409i	$0.309055\pi$
$252$		0			0
$253$	3.28778	+	5.69460i	0.206701	+	0.358016i
$254$	−7.22633	+	8.61200i	−0.453420	+	0.540365i
$255$		0			0
$256$	2.72997	+	15.4824i	0.170623	+	0.967652i
$257$	−0.0315889	+	0.0265062i	−0.00197046	+	0.00165341i	−0.643772	−	0.765217i	$-0.722632\pi$
$257$	−0.0315889	+	0.0265062i	−0.00197046	+	0.00165341i	0.641802	+	0.766871i	$0.278187\pi$
$258$		0			0
$259$	0.0497024	+	0.0414853i	0.00308836	+	0.00257777i
$260$	−10.4461	+	6.03104i	−0.647837	+	0.374029i
$261$		0			0
$262$		−	33.3131i		−	2.05809i
$263$	−13.7378	−	2.42234i	−0.847109	−	0.149368i	−0.266787	−	0.963755i	$-0.585962\pi$
$263$	−13.7378	−	2.42234i	−0.847109	−	0.149368i	−0.580322	+	0.814387i	$0.697073\pi$
$264$		0			0
$265$	−8.36295	+	1.47461i	−0.513732	+	0.0905848i
$266$	−9.34726	−	3.37460i	−0.573117	−	0.206910i
$267$		0			0
$268$	1.40804	−	7.98538i	0.0860096	−	0.487785i
$269$	11.2526	+	19.4900i	0.686081	+	1.18833i	0.973096	+	0.230401i	$0.0740038\pi$
$269$	11.2526	+	19.4900i	0.686081	+	1.18833i	−0.287015	+	0.957926i	$0.592663\pi$
$270$		0			0
$271$	5.53035	+	3.19295i	0.335945	+	0.193958i	0.658477	−	0.752601i	$-0.271201\pi$
$271$	5.53035	+	3.19295i	0.335945	+	0.193958i	−0.322533	+	0.946558i	$0.604534\pi$
$272$	−14.7868	+	5.38196i	−0.896582	+	0.326329i
$273$		0			0
$274$	−23.7905	+	19.9626i	−1.43723	+	1.20598i
$275$	9.55442	−	26.2506i	0.576153	−	1.58297i
$276$		0			0
$277$	1.08917	−	6.17699i	0.0654418	−	0.371139i	−0.934445	−	0.356107i	$-0.884104\pi$
$277$	1.08917	−	6.17699i	0.0654418	−	0.371139i	0.999887	−	0.0150321i	$-0.00478504\pi$
$278$	10.9464	+	18.9597i	0.656521	+	1.13713i
$279$		0			0
$280$	−0.0548963	−	21.0945i	−0.00328068	−	1.26064i
$281$	6.25888	+	1.10361i	0.373373	+	0.0658358i	0.357186	−	0.934033i	$-0.383736\pi$
$281$	6.25888	+	1.10361i	0.373373	+	0.0658358i	0.0161870	+	0.999869i	$0.494847\pi$
$282$		0			0
$283$	−0.572909	+	0.101019i	−0.0340559	+	0.00600498i	−0.190650	−	0.981658i	$-0.561060\pi$
$283$	−0.572909	+	0.101019i	−0.0340559	+	0.00600498i	0.156594	+	0.987663i	$0.449949\pi$
$284$	−3.29619	+	0.581207i	−0.195593	+	0.0344883i
$285$		0			0
$286$	19.7689	+	3.48579i	1.16896	+	0.206119i
$287$	4.24208	+	7.30354i	0.250402	+	0.431114i
$288$		0			0
$289$	3.41728	+	5.91890i	0.201016	+	0.348170i
$290$	1.15023	−	6.52331i	0.0675441	−	0.383062i
$291$		0			0
$292$	0.567747	−	1.55987i	0.0332249	−	0.0912847i
$293$	7.63328	−	6.40508i	0.445941	−	0.374189i	−0.391986	−	0.919971i	$-0.628212\pi$
$293$	7.63328	−	6.40508i	0.445941	−	0.374189i	0.837927	+	0.545782i	$0.183767\pi$
$294$		0			0
$295$	39.4843	−	14.3711i	2.29887	−	0.836719i
$296$	−0.0440385	−	0.0254256i	−0.00255968	−	0.00147783i
$297$		0			0
$298$	10.9529	+	18.9710i	0.634486	+	1.09896i
$299$	1.67452	−	9.49669i	0.0968401	−	0.549208i
$300$		0			0
$301$	−1.28756	+	1.08612i	−0.0742139	+	0.0626027i
$302$	20.4984	−	3.61442i	1.17955	−	0.207986i
$303$		0			0
$304$	11.0173	+	1.94264i	0.631884	+	0.111418i
$305$		−	29.2408i		−	1.67432i
$306$		0			0
$307$	1.93850	−	1.11920i	0.110636	−	0.0638759i	−0.443661	−	0.896195i	$-0.646320\pi$
$307$	1.93850	−	1.11920i	0.110636	−	0.0638759i	0.554297	+	0.832319i	$0.312987\pi$
$308$	3.63454	−	4.35444i	0.207097	−	0.248117i
$309$		0			0
$310$	42.2564	−	35.4573i	2.40000	−	2.01384i
$311$	−0.646712	−	3.66769i	−0.0366717	−	0.207976i	0.960966	−	0.276665i	$-0.0892293\pi$
$311$	−0.646712	−	3.66769i	−0.0366717	−	0.207976i	−0.997638	+	0.0686896i	$0.978118\pi$
$312$		0			0
$313$	−9.35374	+	11.1474i	−0.528705	+	0.630086i	−0.962616	−	0.270870i	$-0.912689\pi$
$313$	−9.35374	+	11.1474i	−0.528705	+	0.630086i	0.433911	+	0.900956i	$0.357133\pi$
$314$	15.0263	+	26.0264i	0.847986	+	1.46875i
$315$		0			0
$316$	−4.71738	+	8.17075i	−0.265374	+	0.459641i
$317$	0.419059	+	1.15136i	0.0235367	+	0.0646666i	0.950905	−	0.309484i	$-0.100156\pi$
$317$	0.419059	+	1.15136i	0.0235367	+	0.0646666i	−0.927368	+	0.374151i	$0.877934\pi$
$318$		0			0
$319$	−2.29391	+	1.92482i	−0.128435	+	0.107769i
$320$	2.13583	+	12.1129i	0.119396	+	0.677131i
$321$		0			0
$322$	−7.70060	−	6.42749i	−0.429138	−	0.358190i
$323$			7.22704i			0.402123i
$324$		0			0
$325$	−35.4790	+	20.4838i	−1.96802	+	1.13624i
$326$	6.26189	−	7.46263i	0.346814	−	0.413317i
$327$		0			0
$328$	−4.26431	−	5.08200i	−0.235457	−	0.280607i
$329$	−26.7408	−	9.65413i	−1.47427	−	0.532249i
$330$		0			0
$331$	−19.2551	+	7.00827i	−1.05835	+	0.385210i	−0.811810	−	0.583922i	$-0.801517\pi$
$331$	−19.2551	+	7.00827i	−1.05835	+	0.385210i	−0.246545	+	0.969131i	$0.579295\pi$
$332$	−3.30916			−0.181614
$333$		0			0
$334$			13.7407i			0.751858i
$335$	7.24235	−	41.0734i	0.395692	−	2.24408i
$336$		0			0
$337$	18.8694	+	6.86790i	1.02788	+	0.374119i	0.800274	−	0.599634i	$-0.204687\pi$
$337$	18.8694	+	6.86790i	1.02788	+	0.374119i	0.227608	+	0.973753i	$0.426909\pi$
$338$	−5.07591	−	6.04924i	−0.276093	−	0.329035i
$339$		0			0
$340$	8.57399	−	3.12068i	0.464990	−	0.169242i
$341$	−24.9371			−1.35042
$342$		0			0
$343$	−9.13463	+	16.1108i	−0.493224	+	0.869903i
$344$	0.850466	−	1.01355i	0.0458540	−	0.0546467i
$345$		0			0
$346$	20.7973	+	24.7853i	1.11807	+	1.33247i
$347$	0.215717	−	0.592678i	0.0115803	−	0.0318166i	−0.933768	−	0.357879i	$-0.883500\pi$
$347$	0.215717	−	0.592678i	0.0115803	−	0.0318166i	0.945348	+	0.326063i	$0.105722\pi$
$348$		0			0
$349$	−0.582328	−	1.59993i	−0.0311713	−	0.0856425i	0.923131	−	0.384486i	$-0.125621\pi$
$349$	−0.582328	−	1.59993i	−0.0311713	−	0.0856425i	−0.954302	+	0.298844i	$0.903399\pi$
$350$	0.110896	+	42.6132i	0.00592765	+	2.27777i
$351$		0			0
$352$	−5.77999	+	10.0112i	−0.308074	+	0.533600i
$353$	−18.3149	−	15.3681i	−0.974806	−	0.817960i	0.00849145	−	0.999964i	$-0.497297\pi$
$353$	−18.3149	−	15.3681i	−0.974806	−	0.817960i	−0.983298	+	0.182004i	$0.941742\pi$
$354$		0			0
$355$	−16.9542	+	2.98948i	−0.899836	+	0.158665i
$356$	−0.612862	−	3.47571i	−0.0324816	−	0.184212i
$357$		0			0
$358$	−3.76236	−	3.15700i	−0.198847	−	0.166852i
$359$	10.8355	−	6.25585i	0.571873	−	0.330171i	−0.186024	−	0.982545i	$-0.559560\pi$
$359$	10.8355	−	6.25585i	0.571873	−	0.330171i	0.757897	+	0.652374i	$0.226227\pi$
$360$		0			0
$361$	−6.93100	+	12.0048i	−0.364789	+	0.631834i
$362$	32.3384	+	27.1351i	1.69967	+	1.42619i
$363$		0			0
$364$	−8.18789	+	1.46573i	−0.429162	+	0.0768250i
$365$	2.92025	−	8.02333i	0.152853	−	0.419960i
$366$		0			0
$367$	−4.50874	−	12.3877i	−0.235354	−	0.646630i	−0.999998	−	0.00217674i	$-0.999307\pi$
$367$	−4.50874	−	12.3877i	−0.235354	−	0.646630i	0.764643	−	0.644454i	$-0.222915\pi$
$368$	9.77888	+	5.64584i	0.509759	+	0.294310i
$369$		0			0
$370$	0.134726	+	0.0777842i	0.00700408	+	0.00404381i
$371$	−5.76975	−	1.00189i	−0.299550	−	0.0520154i
$372$		0			0
$373$	10.5249	+	3.83075i	0.544959	+	0.198349i	0.599805	−	0.800146i	$-0.295245\pi$
$373$	10.5249	+	3.83075i	0.544959	+	0.198349i	−0.0548464	+	0.998495i	$0.517467\pi$
$374$	−14.2689	−	5.19347i	−0.737829	−	0.268548i
$375$		0			0
$376$	21.9915	+	3.87769i	1.13412	+	0.199977i
$377$	4.39149			0.226173
$378$		0			0
$379$	−6.24758			−0.320917			−0.160458	−	0.987043i	$-0.551297\pi$
$379$	−6.24758			−0.320917			−0.160458	+	0.987043i	$0.551297\pi$
$380$	−6.38826	−	1.12642i	−0.327711	−	0.0577842i
$381$		0			0
$382$	35.3025	+	12.8491i	1.80623	+	0.657415i
$383$	13.4741	+	4.90417i	0.688494	+	0.250591i	0.662490	−	0.749070i	$-0.269500\pi$
$383$	13.4741	+	4.90417i	0.688494	+	0.250591i	0.0260038	+	0.999662i	$0.491722\pi$
$384$		0			0
$385$	18.6946	−	22.3974i	0.952763	−	1.14148i
$386$	21.4197	+	12.3667i	1.09023	+	0.629447i
$387$		0			0
$388$	−8.53865	−	4.92979i	−0.433484	−	0.250272i
$389$	2.95313	+	8.11366i	0.149730	+	0.411379i	0.991769	−	0.128037i	$-0.0408675\pi$
$389$	2.95313	+	8.11366i	0.149730	+	0.411379i	−0.842040	+	0.539415i	$0.818645\pi$
$390$		0			0
$391$	−2.49487	+	6.85459i	−0.126171	+	0.346652i
$392$	4.90412	−	13.6953i	0.247696	−	0.691719i
$393$		0			0
$394$	−24.2060	−	20.3113i	−1.21948	−	1.02327i
$395$	−24.2642	+	42.0269i	−1.22087	+	2.11460i
$396$		0			0
$397$	0.00629478	−	0.00363429i	0.000315926	−	0.000182400i	−0.499842	−	0.866117i	$-0.666609\pi$
$397$	0.00629478	−	0.00363429i	0.000315926	−	0.000182400i	0.500158	+	0.865934i	$0.333275\pi$
$398$	−7.37245	−	6.18622i	−0.369548	−	0.310087i
$399$		0			0
$400$	−8.33008	−	47.2422i	−0.416504	−	2.36211i
$401$	−14.9200	+	2.63081i	−0.745071	+	0.131376i	−0.533280	−	0.845939i	$-0.679041\pi$
$401$	−14.9200	+	2.63081i	−0.745071	+	0.131376i	−0.211791	+	0.977315i	$0.567930\pi$
$402$		0			0
$403$	28.0148	+	23.5072i	1.39552	+	1.17098i
$404$	−1.01222	+	1.75321i	−0.0503596	+	0.0872254i
$405$		0			0
$406$	2.27364	−	3.96184i	0.112839	−	0.196623i
$407$	−0.0240536	−	0.0660867i	−0.00119229	−	0.00327580i
$408$		0			0
$409$	3.50114	−	9.61931i	0.173120	−	0.475644i	−0.822540	−	0.568708i	$-0.807444\pi$
$409$	3.50114	−	9.61931i	0.173120	−	0.475644i	0.995660	+	0.0930631i	$0.0296658\pi$
$410$	13.0457	+	15.5473i	0.644282	+	0.767826i
$411$		0			0
$412$	4.68131	−	5.57897i	0.230631	−	0.274856i
$413$	28.9759	−	0.0754068i	1.42581	−	0.00371052i
$414$		0			0
$415$	−17.0209			−0.835524
$416$	15.9306	−	5.79825i	0.781060	−	0.284283i
$417$		0			0
$418$	6.93916	+	8.26977i	0.339405	+	0.404488i
$419$	37.4662	+	13.6366i	1.83034	+	0.666190i	0.992795	+	0.119827i	$0.0382340\pi$
$419$	37.4662	+	13.6366i	1.83034	+	0.666190i	0.837548	+	0.546363i	$0.183988\pi$
$420$		0			0
$421$	3.81518	−	21.6370i	0.185940	−	1.05452i	−0.738801	−	0.673924i	$-0.764608\pi$
$421$	3.81518	−	21.6370i	0.185940	−	1.05452i	0.924741	−	0.380597i	$-0.124281\pi$
$422$			1.72311i			0.0838795i
$423$		0			0
$424$	4.59972			0.223382
$425$	29.1207	−	10.5991i	1.41256	−	0.514131i
$426$		0			0
$427$	6.84735	−	18.9664i	0.331367	−	0.917847i
$428$	−6.77024	−	8.06846i	−0.327252	−	0.390004i
$429$		0			0
$430$	−2.60182	+	3.10072i	−0.125471	+	0.149530i
$431$	−5.61933	+	3.24432i	−0.270673	+	0.156273i	−0.629194	−	0.777249i	$-0.716615\pi$
$431$	−5.61933	+	3.24432i	−0.270673	+	0.156273i	0.358520	+	0.933522i	$0.383281\pi$
$432$		0			0
$433$		−	1.48559i		−	0.0713927i	−0.999363	−	0.0356963i	$-0.988635\pi$
$433$		−	1.48559i		−	0.0713927i	0.999363	−	0.0356963i	$-0.0113649\pi$
$434$	35.7117	−	13.1034i	1.71422	−	0.628981i
$435$		0			0
$436$	0.644770	+	3.65667i	0.0308789	+	0.175123i
$437$	3.97268	−	3.33348i	0.190039	−	0.159462i
$438$		0			0
$439$	4.31238	+	11.8482i	0.205819	+	0.565483i	0.999056	−	0.0434295i	$-0.0138284\pi$
$439$	4.31238	+	11.8482i	0.205819	+	0.565483i	−0.793238	+	0.608912i	$0.791606\pi$
$440$	−11.4576	+	19.8451i	−0.546217	+	0.946076i
$441$		0			0
$442$	11.1343	+	19.2852i	0.529606	+	0.917305i
$443$	0.999759	−	1.19147i	0.0475000	−	0.0566083i	−0.741771	−	0.670653i	$-0.766014\pi$
$443$	0.999759	−	1.19147i	0.0475000	−	0.0566083i	0.789271	+	0.614045i	$0.210458\pi$
$444$		0			0
$445$	−3.15230	−	17.8776i	−0.149434	−	0.847480i
$446$	9.77746	−	8.20426i	0.462976	−	0.388483i
$447$		0			0
$448$	−1.45113	+	8.35689i	−0.0685595	+	0.394826i
$449$	3.71332	−	2.14388i	0.175242	−	0.101176i	−0.409813	−	0.912169i	$-0.634406\pi$
$449$	3.71332	−	2.14388i	0.175242	−	0.101176i	0.585055	+	0.810993i	$0.301073\pi$
$450$		0			0
$451$		−	9.17503i		−	0.432035i
$452$	−5.88622	−	1.03790i	−0.276864	−	0.0488186i
$453$		0			0
$454$	−5.29180	+	0.933088i	−0.248357	+	0.0437920i
$455$	−42.1151	+	7.53908i	−1.97438	+	0.353438i
$456$		0			0
$457$	2.62834	−	14.9061i	0.122949	−	0.697277i	−0.859556	−	0.511041i	$-0.829260\pi$
$457$	2.62834	−	14.9061i	0.122949	−	0.697277i	0.982505	−	0.186236i	$-0.0596288\pi$
$458$	−18.1114	−	31.3698i	−0.846289	−	1.46582i
$459$		0			0
$460$	−5.67019	−	3.27368i	−0.264374	−	0.152636i
$461$	6.54769	−	2.38316i	0.304956	−	0.110995i	−0.185009	−	0.982737i	$-0.559232\pi$
$461$	6.54769	−	2.38316i	0.304956	−	0.110995i	0.489966	+	0.871742i	$0.337009\pi$
$462$		0			0
$463$	−30.9400	+	25.9617i	−1.43790	+	1.20654i	−0.497051	+	0.867721i	$0.665584\pi$
$463$	−30.9400	+	25.9617i	−1.43790	+	1.20654i	−0.940851	+	0.338822i	$0.889972\pi$
$464$	−1.75874	+	4.83209i	−0.0816473	+	0.224324i
$465$		0			0
$466$	−2.68036	+	15.2011i	−0.124165	+	0.704177i
$467$	−4.21489	−	7.30040i	−0.195042	−	0.337822i	0.751872	−	0.659309i	$-0.229151\pi$
$467$	−4.21489	−	7.30040i	−0.195042	−	0.337822i	−0.946914	+	0.321486i	$0.895818\pi$
$468$		0			0
$469$	14.3158	−	24.9454i	0.661042	−	1.15187i
$470$	−67.2782	−	11.8630i	−3.10331	−	0.547197i
$471$		0			0
$472$	−22.4137	+	3.95214i	−1.03167	+	0.181912i
$473$	1.80205	−	0.317751i	0.0828585	−	0.0146102i
$474$		0			0
$475$	−21.6971	−	3.82578i	−0.995531	−	0.175539i
$476$	6.29209	−	0.0163745i	0.288398	−	0.000750525i
$477$		0			0
$478$	5.06018	+	8.76448i	0.231447	+	0.400878i
$479$	−3.99718	+	22.6691i	−0.182636	+	1.03578i	0.746320	+	0.665588i	$0.231819\pi$
$479$	−3.99718	+	22.6691i	−0.182636	+	1.03578i	−0.928956	+	0.370191i	$0.879292\pi$
$480$		0			0
$481$	−0.0352751	+	0.0969176i	−0.00160841	+	0.00441906i
$482$	0.422427	−	0.354458i	0.0192410	−	0.0161451i
$483$		0			0
$484$	1.92028	−	0.698923i	0.0872852	−	0.0317692i
$485$	−43.9192	−	25.3568i	−1.99427	−	1.15139i
$486$		0			0
$487$	−13.2168	−	22.8922i	−0.598912	−	1.03735i	−0.992982	−	0.118265i	$-0.962267\pi$
$487$	−13.2168	−	22.8922i	−0.598912	−	1.03735i	0.394070	−	0.919080i	$-0.371067\pi$
$488$	−2.75032	+	15.5978i	−0.124501	+	0.706080i
$489$		0			0
$490$	−15.0031	+	41.8979i	−0.677771	+	1.89275i
$491$	12.8648	−	2.26841i	0.580580	−	0.102372i	0.124357	−	0.992238i	$-0.460313\pi$
$491$	12.8648	−	2.26841i	0.580580	−	0.102372i	0.456223	+	0.889866i	$0.349202\pi$
$492$		0			0
$493$	−3.27144	−	0.576843i	−0.147338	−	0.0259797i
$494$		−	15.8317i		−	0.712303i
$495$		0			0
$496$	−37.0854	+	21.4112i	−1.66518	+	0.961393i
$497$	−11.6970	−	2.03113i	−0.524682	−	0.0911084i
$498$		0			0
$499$	19.8121	−	16.6244i	0.886913	−	0.744208i	−0.0806756	−	0.996740i	$-0.525708\pi$
$499$	19.8121	−	16.6244i	0.886913	−	0.744208i	0.967589	+	0.252532i	$0.0812633\pi$
$500$	2.34541	+	13.3015i	0.104890	+	0.594861i
$501$		0			0
$502$	−14.5989	+	17.3983i	−0.651581	+	0.776524i
$503$	−11.7401	−	20.3345i	−0.523467	−	0.906672i	−0.999627	−	0.0273131i	$-0.991305\pi$
$503$	−11.7401	−	20.3345i	−0.523467	−	0.906672i	0.476160	−	0.879359i	$-0.342028\pi$
$504$		0			0
$505$	−5.20641	+	9.01776i	−0.231682	+	0.401285i
$506$	3.72672	+	10.2391i	0.165673	+	0.455183i
$507$		0			0
$508$	−3.87655	+	3.25281i	−0.171994	+	0.144320i
$509$	−4.92895	−	27.9535i	−0.218472	−	1.23902i	−0.874779	−	0.484522i	$-0.838993\pi$
$509$	−4.92895	−	27.9535i	−0.218472	−	1.23902i	0.656307	−	0.754494i	$-0.272118\pi$
$510$		0			0
$511$	3.77299	−	4.52031i	0.166907	−	0.199967i
$512$		−	0.661943i		−	0.0292540i
$513$		0			0
$514$	−0.0591771	+	0.0341659i	−0.00261019	+	0.00150699i
$515$	24.0787	−	28.6958i	1.06103	−	1.26449i
$516$		0			0
$517$	19.8517	+	23.6583i	0.873076	+	1.04049i
$518$	0.0691722	+	0.0820018i	0.00303925	+	0.00360295i
$519$		0			0
$520$	31.5789	−	11.4938i	1.38482	−	0.504035i
$521$	15.0773			0.660549			0.330275	−	0.943885i	$-0.392859\pi$
$521$	15.0773			0.660549			0.330275	+	0.943885i	$0.392859\pi$
$522$		0			0
$523$		−	4.77566i		−	0.208825i	−0.994534	−	0.104412i	$-0.966704\pi$
$523$		−	4.77566i		−	0.208825i	0.994534	−	0.104412i	$-0.0332962\pi$
$524$	2.60391	−	14.7675i	0.113752	−	0.645122i
$525$		0			0
$526$	−21.7217	−	7.90606i	−0.947112	−	0.344721i
$527$	−17.7818	−	21.1916i	−0.774590	−	0.923120i
$528$		0			0
$529$	−16.6942	+	6.07620i	−0.725836	+	0.264183i
$530$	−14.0718			−0.611242
$531$		0			0
$532$	−3.87982	−	2.22657i	−0.168212	−	0.0965342i
$533$	−8.64896	+	10.3074i	−0.374628	+	0.446464i
$534$		0			0
$535$	−34.8233	−	41.5008i	−1.50554	−	1.79423i
$536$	−7.72653	+	21.2285i	−0.333735	+	0.916930i
$537$		0			0
$538$	12.7549	+	35.0437i	0.549902	+	1.51084i
$539$	17.3706	−	10.1498i	0.748206	−	0.437185i
$540$		0			0
$541$	−10.3759	+	17.9716i	−0.446094	+	0.772657i	−0.998128	−	0.0611643i	$-0.980519\pi$
$541$	−10.3759	+	17.9716i	−0.446094	+	0.772657i	0.552034	+	0.833822i	$0.313852\pi$
$542$	8.10622	+	6.80193i	0.348192	+	0.292168i
$543$		0			0
$544$	−12.6291	+	2.22685i	−0.541468	+	0.0954753i
$545$	3.31642	+	18.8084i	0.142060	+	0.805662i
$546$		0			0
$547$	−9.38962	−	7.87883i	−0.401471	−	0.336874i	0.419591	−	0.907713i	$-0.362174\pi$
$547$	−9.38962	−	7.87883i	−0.401471	−	0.336874i	−0.821062	+	0.570839i	$0.806618\pi$
$548$	−12.1066	+	6.98973i	−0.517167	+	0.298586i
$549$		0			0
$550$	23.1454	−	40.0891i	0.986925	−	1.70940i
$551$	1.80915	+	1.51806i	0.0770724	+	0.0646714i
$552$		0			0
$553$	−25.5799	+	21.5778i	−1.08777	+	0.917581i
$554$	3.55484	−	9.76683i	0.151031	−	0.414953i
$555$		0			0
$556$	3.37050	+	9.26036i	0.142941	+	0.392727i
$557$	18.6030	+	10.7404i	0.788233	+	0.455086i	0.839340	−	0.543607i	$-0.182942\pi$
$557$	18.6030	+	10.7404i	0.788233	+	0.455086i	−0.0511072	+	0.998693i	$0.516275\pi$
$558$		0			0
$559$	−2.32400	−	1.34176i	−0.0982945	−	0.0567504i
$560$	8.57108	−	49.3598i	0.362194	−	2.08583i
$561$		0			0
$562$	9.89631	+	3.60196i	0.417451	+	0.151940i
$563$	15.1623	+	5.51864i	0.639016	+	0.232583i	0.641151	−	0.767415i	$-0.278457\pi$
$563$	15.1623	+	5.51864i	0.639016	+	0.232583i	−0.00213467	+	0.999998i	$0.500679\pi$
$564$		0			0
$565$	−30.2762	−	5.33851i	−1.27373	−	0.224593i
$566$	−0.964001			−0.0405200
$567$		0			0
$568$	9.32501			0.391269
$569$	−26.1637	−	4.61337i	−1.09684	−	0.193403i	−0.404190	−	0.914675i	$-0.632446\pi$
$569$	−26.1637	−	4.61337i	−1.09684	−	0.193403i	−0.692651	+	0.721272i	$0.743558\pi$
$570$		0			0
$571$	−27.8574	−	10.1393i	−1.16580	−	0.424315i	−0.314631	−	0.949214i	$-0.601881\pi$
$571$	−27.8574	−	10.1393i	−1.16580	−	0.424315i	−0.851164	+	0.524899i	$0.824103\pi$
$572$	8.49098	+	3.09046i	0.355026	+	0.129219i
$573$		0			0
$574$	4.82108	+	13.1393i	0.201228	+	0.548424i
$575$	−19.2582	−	11.1187i	−0.803124	−	0.463684i
$576$		0			0
$577$	31.4355	+	18.1493i	1.30868	+	0.755564i	0.981875	−	0.189529i	$-0.0606962\pi$
$577$	31.4355	+	18.1493i	1.30868	+	0.755564i	0.326800	+	0.945093i	$0.394029\pi$
$578$	3.87351	+	10.6424i	0.161117	+	0.442665i
$579$		0			0
$580$	1.01979	−	2.80184i	0.0423443	−	0.116340i
$581$	−11.0402	−	3.98581i	−0.458026	−	0.165359i
$582$		0			0
$583$	4.87317	+	4.08908i	0.201826	+	0.169352i
$584$	−2.31240	+	4.00519i	−0.0956876	+	0.165736i
$585$		0			0
$586$	14.2998	−	8.25601i	0.590720	−	0.341053i
$587$	−27.4601	−	23.0418i	−1.13340	−	0.951035i	−0.134196	−	0.990955i	$-0.542845\pi$
$587$	−27.4601	−	23.0418i	−1.13340	−	0.951035i	−0.999203	+	0.0399198i	$0.987290\pi$
$588$		0			0
$589$	3.41518	+	19.3684i	0.140720	+	0.798063i
$590$	68.5699	−	12.0907i	2.82298	−	0.497767i
$591$		0			0
$592$	−0.0925142	−	0.0776286i	−0.00380231	−	0.00319052i
$593$	−9.90996	+	17.1646i	−0.406953	+	0.704864i	−0.994547	−	0.104293i	$-0.966742\pi$
$593$	−9.90996	+	17.1646i	−0.406953	+	0.704864i	0.587593	+	0.809156i	$0.300076\pi$
$594$		0			0
$595$	32.3639	−	0.0842236i	1.32679	−	0.00345283i
$596$	3.37251	+	9.26590i	0.138143	+	0.379546i
$597$		0			0
$598$	5.46532	−	15.0158i	0.223493	−	0.614043i
$599$	−11.8996	−	14.1814i	−0.486205	−	0.579436i	0.466043	−	0.884762i	$-0.345679\pi$
$599$	−11.8996	−	14.1814i	−0.486205	−	0.579436i	−0.952248	+	0.305326i	$0.901235\pi$
$600$		0			0
$601$	27.1016	−	32.2984i	1.10550	−	1.31748i	0.161741	−	0.986833i	$-0.448289\pi$
$601$	27.1016	−	32.2984i	1.10550	−	1.31748i	0.943755	−	0.330646i	$-0.107266\pi$
$602$	−2.41371	+	1.40194i	−0.0983754	+	0.0571389i
$603$		0			0
$604$	9.36935			0.381234
$605$	9.87708	−	3.59496i	0.401561	−	0.146156i
$606$		0			0
$607$	26.4848	+	31.5633i	1.07498	+	1.28111i	0.957623	+	0.288025i	$0.0929988\pi$
$607$	26.4848	+	31.5633i	1.07498	+	1.28111i	0.117360	+	0.993089i	$0.462557\pi$
$608$	8.56722	+	3.11821i	0.347447	+	0.126460i
$609$		0			0
$610$	8.41400	−	47.7182i	0.340673	−	1.93205i
$611$		−	45.2917i		−	1.83231i
$612$		0			0
$613$	−33.7892			−1.36473			−0.682366	−	0.731011i	$-0.739049\pi$
$613$	−33.7892			−1.36473			−0.682366	+	0.731011i	$0.739049\pi$
$614$	3.48550	−	1.26862i	0.140663	−	0.0511972i
$615$		0			0
$616$	−12.0788	+	10.1890i	−0.486669	+	0.410527i
$617$	−12.0622	−	14.3752i	−0.485607	−	0.578724i	0.466487	−	0.884528i	$-0.345519\pi$
$617$	−12.0622	−	14.3752i	−0.485607	−	0.578724i	−0.952095	+	0.305803i	$0.901075\pi$
$618$		0			0
$619$	−9.30674	+	11.0913i	−0.374069	+	0.445798i	−0.919933	−	0.392076i	$-0.871757\pi$
$619$	−9.30674	+	11.0913i	−0.374069	+	0.445798i	0.545864	+	0.837874i	$0.316202\pi$
$620$	21.5036	−	12.4151i	0.863605	−	0.498602i
$621$		0			0
$622$		−	6.17140i		−	0.247451i
$623$	2.14175	−	12.3341i	0.0858074	−	0.494154i
$624$		0			0
$625$	3.62476	+	20.5571i	0.144991	+	0.822282i
$626$	−18.4720	+	15.4999i	−0.738291	+	0.619500i
$627$		0			0
$628$	4.62676	+	12.7119i	0.184628	+	0.507260i
$629$	0.0390087	−	0.0675651i	0.00155538	−	0.00269400i
$630$		0			0
$631$	3.09835	+	5.36650i	0.123343	+	0.213637i	0.921084	−	0.389363i	$-0.127305\pi$
$631$	3.09835	+	5.36650i	0.123343	+	0.213637i	−0.797741	+	0.603001i	$0.793972\pi$
$632$	16.8961	−	20.1360i	0.672092	−	0.800968i
$633$		0			0
$634$	0.352563	+	1.99948i	0.0140021	+	0.0794097i
$635$	−19.9393	+	16.7311i	−0.791269	+	0.663953i
$636$		0			0
$637$	−29.0824	−	4.97208i	−1.15229	−	0.197001i
$638$	−4.29731	+	2.48105i	−0.170132	+	0.0982259i
$639$		0			0
$640$			51.2445i			2.02562i
$641$	8.28416	+	1.46072i	0.327205	+	0.0576950i	0.334838	−	0.942276i	$-0.391319\pi$
$641$	8.28416	+	1.46072i	0.327205	+	0.0576950i	−0.00763285	+	0.999971i	$0.502430\pi$
$642$		0			0
$643$	−12.6614	+	2.23255i	−0.499317	+	0.0880430i	−0.417634	−	0.908615i	$-0.637141\pi$
$643$	−12.6614	+	2.23255i	−0.499317	+	0.0880430i	−0.0816827	+	0.996658i	$0.526029\pi$
$644$	−2.91123	−	3.45119i	−0.114719	−	0.135996i
$645$		0			0
$646$	−2.07957	+	11.7938i	−0.0818196	+	0.464022i
$647$	3.45841	+	5.99014i	0.135964	+	0.235497i	0.925965	−	0.377609i	$-0.123253\pi$
$647$	3.45841	+	5.99014i	0.135964	+	0.235497i	−0.790001	+	0.613105i	$0.789920\pi$
$648$		0			0
$649$	−27.2596	−	15.7383i	−1.07003	−	0.617784i
$650$	−63.7926	+	23.2186i	−2.50215	+	0.910708i
$651$		0			0
$652$	3.35918	−	2.81869i	0.131556	−	0.110388i
$653$	−2.61548	+	7.18597i	−0.102352	+	0.281209i	−0.980290	−	0.197565i	$-0.936697\pi$
$653$	−2.61548	+	7.18597i	−0.102352	+	0.281209i	0.877938	+	0.478774i	$0.158919\pi$
$654$		0			0
$655$	13.3934	−	75.9579i	0.523325	−	2.96792i
$656$	−7.87778	−	13.6447i	−0.307576	−	0.532736i
$657$		0			0
$658$	−40.8605	−	23.4492i	−1.59291	−	0.914146i
$659$	5.58789	+	0.985295i	0.217673	+	0.0383817i	0.281421	−	0.959584i	$-0.409194\pi$
$659$	5.58789	+	0.985295i	0.217673	+	0.0383817i	−0.0637479	+	0.997966i	$0.520305\pi$
$660$		0			0
$661$	47.1559	−	8.31485i	1.83415	−	0.323410i	0.853790	−	0.520618i	$-0.174298\pi$
$661$	47.1559	−	8.31485i	1.83415	−	0.323410i	0.980362	+	0.197208i	$0.0631874\pi$
$662$	−33.4390	+	5.89620i	−1.29965	+	0.229162i
$663$		0			0
$664$	9.07941	+	1.60094i	0.352349	+	0.0621287i
$665$	−19.9562	−	11.4526i	−0.773866	−	0.444111i
$666$		0			0
$667$	1.19186	+	2.06437i	0.0461491	+	0.0799327i
$668$	−1.07404	+	6.09119i	−0.0415559	+	0.235675i
$669$		0			0
$670$	23.6376	−	64.9439i	0.913202	−	2.50900i
$671$	−16.7800	+	14.0801i	−0.647787	+	0.543557i
$672$		0			0
$673$	−17.7107	+	6.44618i	−0.682699	+	0.248482i	−0.660006	−	0.751260i	$-0.729446\pi$
$673$	−17.7107	+	6.44618i	−0.682699	+	0.248482i	−0.0226931	+	0.999742i	$0.507224\pi$
$674$	28.8168	+	16.6374i	1.10998	+	0.640849i
$675$		0			0
$676$	−1.77729	−	3.07836i	−0.0683573	−	0.118398i
$677$	2.26261	−	12.8319i	0.0869591	−	0.493169i	−0.909958	−	0.414701i	$-0.863886\pi$
$677$	2.26261	−	12.8319i	0.0869591	−	0.493169i	0.996917	−	0.0784680i	$-0.0250028\pi$
$678$		0			0
$679$	−22.5494	−	26.7317i	−0.865365	−	1.02587i
$680$	−25.0344	+	4.41424i	−0.960025	+	0.169278i
$681$		0			0
$682$	−40.6949	−	7.17561i	−1.55829	−	0.274768i
$683$			41.4953i			1.58777i	0.608066	+	0.793886i	$0.291946\pi$
$683$			41.4953i			1.58777i	−0.608066	+	0.793886i	$0.708054\pi$
$684$		0			0
$685$	−62.2710	+	35.9522i	−2.37925	+	1.37366i
$686$	−19.5427	+	23.6628i	−0.746143	+	0.903451i
$687$		0			0
$688$	2.40711	−	2.01981i	0.0917703	−	0.0770044i
$689$	−1.62001	−	9.18751i	−0.0617173	−	0.350016i
$690$		0			0
$691$	−4.14114	+	4.93522i	−0.157536	+	0.187745i	−0.839039	−	0.544071i	$-0.816882\pi$
$691$	−4.14114	+	4.93522i	−0.157536	+	0.187745i	0.681503	+	0.731815i	$0.261327\pi$
$692$	7.28201	+	12.6128i	0.276821	+	0.479467i
$693$		0			0
$694$	0.522571	−	0.905120i	0.0198365	−	0.0343579i
$695$	17.3364	+	47.6314i	0.657608	+	1.80676i
$696$		0			0
$697$	7.79696	−	6.54243i	0.295331	−	0.247812i
$698$	−0.489925	−	2.77850i	−0.0185439	−	0.105168i
$699$		0			0
$700$	−3.28169	+	18.8989i	−0.124036	+	0.714310i
$701$			10.7905i			0.407550i	0.979018	+	0.203775i	$0.0653211\pi$
$701$			10.7905i			0.407550i	−0.979018	+	0.203775i	$0.934679\pi$
$702$		0			0
$703$	−0.0480348	+	0.0277329i	−0.00181167	+	0.00104597i
$704$	5.92261	−	7.05830i	0.223217	−	0.266020i
$705$		0			0
$706$	−25.4661	−	30.3493i	−0.958428	−	1.14221i
$707$	−5.48871	+	4.62997i	−0.206424	+	0.174128i
$708$		0			0
$709$	−43.7116	+	15.9097i	−1.64163	+	0.597503i	−0.987322	−	0.158730i	$-0.949260\pi$
$709$	−43.7116	+	15.9097i	−1.64163	+	0.597503i	−0.654303	+	0.756232i	$0.727038\pi$
$710$	−28.5278			−1.07063
$711$		0			0
$712$			9.83289i			0.368503i
$713$	−3.44706	+	19.5493i	−0.129093	+	0.732126i
$714$		0			0
$715$	43.6740	+	15.8960i	1.63332	+	0.594478i
$716$	−1.42107	−	1.69357i	−0.0531079	−	0.0632915i
$717$		0			0
$718$	19.4825	−	7.09106i	0.727081	−	0.264636i
$719$	15.8232			0.590106			0.295053	−	0.955481i	$-0.404663\pi$
$719$	15.8232			0.590106			0.295053	+	0.955481i	$0.404663\pi$
$720$		0			0
$721$	22.3378	−	12.9744i	0.831903	−	0.483191i
$722$	−14.7651	+	17.5964i	−0.549500	+	0.654869i
$723$		0			0
$724$	12.2144	+	14.5566i	0.453946	+	0.540992i
$725$	3.46361	−	9.51619i	0.128635	−	0.353422i
$726$		0			0
$727$	−11.4600	−	31.4861i	−0.425028	−	1.16775i	−0.948795	−	0.315893i	$-0.897696\pi$
$727$	−11.4600	−	31.4861i	−0.425028	−	1.16775i	0.523767	−	0.851862i	$-0.324526\pi$
$728$	23.1744	−	0.0603089i	0.858900	−	0.00223520i
$729$		0			0
$730$	7.07427	−	12.2530i	0.261831	−	0.453504i
$731$	1.55501	+	1.30481i	0.0575142	+	0.0482601i
$732$		0			0
$733$	5.74109	−	1.01231i	0.212052	−	0.0373905i	−0.0666128	−	0.997779i	$-0.521219\pi$
$733$	5.74109	−	1.01231i	0.212052	−	0.0373905i	0.278665	+	0.960388i	$0.410108\pi$
$734$	−3.79329	−	21.5128i	−0.140013	−	0.794053i
$735$		0			0
$736$	7.04927	+	5.91504i	0.259839	+	0.218031i
$737$	−27.0576	+	15.6217i	−0.996681	+	0.575434i
$738$		0			0
$739$	22.7016	−	39.3204i	0.835093	−	1.44642i	−0.0588624	−	0.998266i	$-0.518747\pi$
$739$	22.7016	−	39.3204i	0.835093	−	1.44642i	0.893955	−	0.448157i	$-0.147919\pi$
$740$	0.0536434	+	0.0450122i	0.00197197	+	0.00165468i
$741$		0			0
$742$	−9.12737	−	3.29522i	−0.335076	−	0.120971i
$743$	−8.03623	+	22.0794i	−0.294821	+	0.810013i	0.700524	+	0.713629i	$0.252950\pi$
$743$	−8.03623	+	22.0794i	−0.294821	+	0.810013i	−0.995344	+	0.0963839i	$0.969272\pi$
$744$		0			0
$745$	17.3468	+	47.6599i	0.635537	+	1.74612i
$746$	16.0733	+	9.27994i	0.588486	+	0.339763i
$747$		0			0
$748$	−5.91940	−	3.41757i	−0.216435	−	0.124959i
$749$	−12.8690	−	35.0731i	−0.470224	−	1.28154i
$750$		0			0
$751$	−21.6249	−	7.87082i	−0.789103	−	0.287210i	−0.0841402	−	0.996454i	$-0.526814\pi$
$751$	−21.6249	−	7.87082i	−0.789103	−	0.287210i	−0.704963	+	0.709244i	$0.749037\pi$
$752$	49.8358	+	18.1388i	1.81733	+	0.661452i
$753$		0			0
$754$	7.16649	+	1.26364i	0.260988	+	0.0460192i
$755$	48.1920			1.75389
$756$		0			0
$757$	−0.0748603			−0.00272084			−0.00136042	−	0.999999i	$-0.500433\pi$
$757$	−0.0748603			−0.00272084			−0.00136042	+	0.999999i	$0.500433\pi$
$758$	−10.1954	−	1.79773i	−0.370315	−	0.0652966i
$759$		0			0
$760$	16.9826	+	6.18118i	0.616025	+	0.224215i
$761$	−2.80845	−	1.02219i	−0.101806	−	0.0370544i	0.290615	−	0.956840i	$-0.406140\pi$
$761$	−2.80845	−	1.02219i	−0.101806	−	0.0370544i	−0.392421	+	0.919786i	$0.628362\pi$
$762$		0			0
$763$	−2.25326	+	12.9762i	−0.0815734	+	0.469771i
$764$	14.6451	+	8.45534i	0.529840	+	0.305903i
$765$		0			0
$766$	20.5772	+	11.8803i	0.743486	+	0.429252i
$767$	15.7881	+	43.3774i	0.570074	+	1.56627i
$768$		0			0
$769$	5.62460	−	15.4535i	0.202828	−	0.557266i	−0.796019	−	0.605272i	$-0.793064\pi$
$769$	5.62460	−	15.4535i	0.202828	−	0.557266i	0.998847	+	0.0480060i	$0.0152867\pi$
$770$	36.9525	−	31.1711i	1.33168	−	1.12333i
$771$		0			0
$772$	8.52862	+	7.15636i	0.306952	+	0.257563i
$773$	19.5197	−	33.8091i	0.702074	−	1.21603i	−0.265663	−	0.964066i	$-0.585591\pi$
$773$	19.5197	−	33.8091i	0.702074	−	1.21603i	0.967737	−	0.251962i	$-0.0810759\pi$
$774$		0			0
$775$	73.0348	−	42.1667i	2.62349	−	1.51467i
$776$	21.0427	+	17.6569i	0.755388	+	0.633846i
$777$		0			0
$778$	2.48453	+	14.0905i	0.0890747	+	0.505168i
$779$	−7.12618	+	1.25654i	−0.255322	+	0.0450201i
$780$		0			0
$781$	9.87939	+	8.28979i	0.353512	+	0.296632i
$782$	−6.04378	+	10.4681i	−0.216125	+	0.374340i
$783$		0			0
$784$	17.1181	−	30.0090i	0.611360	−	1.07175i
$785$	23.7981	+	65.3847i	0.849390	+	2.33368i
$786$		0			0
$787$	1.64760	−	4.52676i	0.0587308	−	0.161361i	−0.906857	−	0.421438i	$-0.861526\pi$
$787$	1.64760	−	4.52676i	0.0587308	−	0.161361i	0.965588	+	0.260076i	$0.0837478\pi$
$788$	−9.14278	−	10.8959i	−0.325698	−	0.388152i
$789$		0			0
$790$	−51.6900	+	61.6018i	−1.83905	+	2.19169i
$791$	−18.3878	−	10.5525i	−0.653796	−	0.375204i
$792$		0			0
$793$	32.1239			1.14075
$794$	0.0113182	−	0.00411950i	0.000401669	−	0.000146196i
$795$		0			0
$796$	−2.78463	−	3.31859i	−0.0986984	−	0.117624i
$797$	−16.1079	−	5.86280i	−0.570572	−	0.207671i	0.0405913	−	0.999176i	$-0.487076\pi$
$797$	−16.1079	−	5.86280i	−0.570572	−	0.207671i	−0.611163	+	0.791505i	$0.709298\pi$
$798$		0			0
$799$	−5.94927	+	33.7400i	−0.210470	+	1.19364i
$800$		−	39.0940i		−	1.38218i
$801$		0			0
$802$	−25.1051			−0.886491
$803$	−6.01042	+	2.18761i	−0.212103	+	0.0771992i
$804$		0			0
$805$	−14.9742	−	17.7515i	−0.527769	−	0.625657i
$806$	38.9533	+	46.4228i	1.37207	+	1.63517i
$807$		0			0
$808$	3.62542	−	4.32061i	0.127542	−	0.151999i
$809$	1.45376	−	0.839326i	0.0511113	−	0.0295091i	−0.474227	−	0.880403i	$-0.657272\pi$
$809$	1.45376	−	0.839326i	0.0511113	−	0.0295091i	0.525338	+	0.850894i	$0.323939\pi$
$810$		0			0
$811$		−	24.2899i		−	0.852933i	−0.904503	−	0.426467i	$-0.859758\pi$
$811$		−	24.2899i		−	0.852933i	0.904503	−	0.426467i	$-0.140242\pi$
$812$	1.31757	−	1.57855i	0.0462377	−	0.0553961i
$813$		0			0
$814$	−0.0202368	−	0.114768i	−0.000709299	−	0.00402263i
$815$	17.2782	−	14.4981i	0.605229	−	0.507848i
$816$		0			0
$817$	−0.493589	−	1.35612i	−0.0172685	−	0.0474448i
$818$	8.48147	−	14.6903i	0.296548	−	0.513636i
$819$		0			0
$820$	4.56785	+	7.91175i	0.159516	+	0.276290i
$821$	−1.25319	+	1.49349i	−0.0437366	+	0.0521233i	−0.787469	−	0.616354i	$-0.788609\pi$
$821$	−1.25319	+	1.49349i	−0.0437366	+	0.0521233i	0.743733	+	0.668477i	$0.233054\pi$
$822$		0			0
$823$	4.76626	+	27.0308i	0.166141	+	0.942234i	0.947880	+	0.318628i	$0.103222\pi$
$823$	4.76626	+	27.0308i	0.166141	+	0.942234i	−0.781739	+	0.623606i	$0.785667\pi$
$824$	−15.5433	+	13.0423i	−0.541475	+	0.454352i
$825$		0			0
$826$	47.3076	+	8.21472i	1.64604	+	0.285827i
$827$	39.0581	−	22.5502i	1.35818	−	0.784147i	0.368804	−	0.929507i	$-0.379767\pi$
$827$	39.0581	−	22.5502i	1.35818	−	0.784147i	0.989379	+	0.145360i	$0.0464340\pi$
$828$		0			0
$829$		−	35.8296i		−	1.24441i	−0.782853	−	0.622207i	$-0.786236\pi$
$829$		−	35.8296i		−	1.24441i	0.782853	−	0.622207i	$-0.213764\pi$
$830$	−27.7765	−	4.89774i	−0.964136	−	0.170003i
$831$		0			0
$832$	−13.3072	+	2.34641i	−0.461343	+	0.0813473i
$833$	21.0118	+	7.52405i	0.728016	+	0.260693i
$834$		0			0
$835$	−5.52441	+	31.3305i	−0.191180	+	1.08424i
$836$	2.42969	+	4.20835i	0.0840326	+	0.145549i
$837$		0			0
$838$	57.2173	+	33.0344i	1.97654	+	1.14115i
$839$	30.2589	−	11.0133i	1.04465	−	0.380222i	0.238010	−	0.971263i	$-0.423505\pi$
$839$	30.2589	−	11.0133i	1.04465	−	0.380222i	0.806642	+	0.591040i	$0.201283\pi$
$840$		0			0
$841$	21.3837	−	17.9431i	0.737369	−	0.618726i
$842$	12.4520	−	34.2116i	0.429124	−	1.17901i
$843$		0			0
$844$	−0.134686	+	0.763845i	−0.00463610	+	0.0262926i
$845$	−9.14163	−	15.8338i	−0.314482	−	0.544698i
$846$		0			0
$847$	7.24838	−	0.0188631i	0.249057	−	0.000648145i
$848$	10.7581	+	1.89694i	0.369435	+	0.0651413i
$849$		0			0
$850$	50.5721	−	8.91722i	1.73461	−	0.305858i
$851$	−0.0551332	+	0.00972146i	−0.00188994	+	0.000333247i
$852$		0			0
$853$	29.8196	+	5.25801i	1.02100	+	0.180031i	0.658998	−	0.752145i	$-0.270981\pi$
$853$	29.8196	+	5.25801i	1.02100	+	0.180031i	0.362007	+	0.932175i	$0.382092\pi$
$854$	16.6318	−	28.9810i	0.569127	−	0.991708i
$855$		0			0
$856$	14.6722	+	25.4130i	0.501485	+	0.868598i
$857$	−8.06670	+	45.7485i	−0.275553	+	1.56274i	0.461646	+	0.887064i	$0.347259\pi$
$857$	−8.06670	+	45.7485i	−0.275553	+	1.56274i	−0.737199	+	0.675675i	$0.763852\pi$
$858$		0			0
$859$	−15.7677	+	43.3213i	−0.537986	+	1.47810i	0.311373	+	0.950288i	$0.399211\pi$
$859$	−15.7677	+	43.3213i	−0.537986	+	1.47810i	−0.849359	+	0.527816i	$0.823011\pi$
$860$	−1.39574	+	1.17116i	−0.0475943	+	0.0399364i
$861$		0			0
$862$	−10.1037	+	3.67746i	−0.344135	+	0.125255i
$863$	−2.45633	−	1.41816i	−0.0836143	−	0.0482748i	0.457610	−	0.889153i	$-0.348706\pi$
$863$	−2.45633	−	1.41816i	−0.0836143	−	0.0482748i	−0.541224	+	0.840878i	$0.682039\pi$
$864$		0			0
$865$	37.4556	+	64.8750i	1.27353	+	2.20582i
$866$	0.427475	−	2.42433i	0.0145262	−	0.0823821i
$867$		0			0
$868$	16.8551	−	3.01725i	0.572098	−	0.102412i
$869$	35.8012	−	6.31272i	1.21447	−	0.214144i
$870$		0			0
$871$	45.1232	+	7.95643i	1.52894	+	0.269593i
$872$		−	10.3448i		−	0.350320i
$873$		0			0
$874$	7.44223	−	4.29678i	0.251737	−	0.145341i
$875$	−8.19644	+	47.2023i	−0.277090	+	1.59573i
$876$		0			0
$877$	−37.7331	+	31.6619i	−1.27416	+	1.06915i	−0.280136	+	0.959960i	$0.590380\pi$
$877$	−37.7331	+	31.6619i	−1.27416	+	1.06915i	−0.994021	+	0.109185i	$0.965176\pi$
$878$	3.62810	+	20.5760i	0.122442	+	0.694405i
$879$		0			0
$880$	−34.9818	+	41.6897i	−1.17924	+	1.40536i
$881$	−13.9157	−	24.1027i	−0.468833	−	0.812042i	0.530533	−	0.847664i	$-0.321992\pi$
$881$	−13.9157	−	24.1027i	−0.468833	−	0.812042i	−0.999365	+	0.0356225i	$0.988659\pi$
$882$		0			0
$883$	20.7815	−	35.9946i	0.699354	−	1.21132i	−0.269337	−	0.963046i	$-0.586805\pi$
$883$	20.7815	−	35.9946i	0.699354	−	1.21132i	0.968691	−	0.248270i	$-0.0798621\pi$
$884$	3.42837	+	9.41936i	0.115308	+	0.316807i
$885$		0			0
$886$	1.97435	−	1.65668i	0.0663297	−	0.0556572i
$887$	−4.60475	−	26.1148i	−0.154612	−	0.876850i	−0.959139	−	0.282934i	$-0.908692\pi$
$887$	−4.60475	−	26.1148i	−0.154612	−	0.876850i	0.804527	−	0.593916i	$-0.202419\pi$
$888$		0			0
$889$	−16.8511	+	6.18302i	−0.565169	+	0.207372i
$890$		−	30.0816i		−	1.00834i
$891$		0			0
$892$	4.97559	−	2.87266i	0.166595	−	0.0961836i
$893$	15.6565	−	18.6587i	0.523925	−	0.624389i
$894$		0			0
$895$	−7.30939	−	8.71099i	−0.244326	−	0.291176i
$896$	−12.0000	+	33.2386i	−0.400891	+	1.11042i
$897$		0			0
$898$	6.67667	−	2.43011i	0.222803	−	0.0810938i
$899$	−9.04003			−0.301502
$900$		0			0
$901$			7.05703i			0.235104i
$902$	2.64010	−	14.9728i	0.0879058	−	0.498538i
$903$		0			0
$904$	15.6480	+	5.69541i	0.520445	+	0.189426i
$905$	62.8259	+	74.8730i	2.08840	+	2.48886i
$906$		0			0
$907$	12.1012	−	4.40449i	0.401815	−	0.146249i	−0.133204	−	0.991089i	$-0.542527\pi$
$907$	12.1012	−	4.40449i	0.401815	−	0.146249i	0.535019	+	0.844840i	$0.320304\pi$
$908$	−2.41877			−0.0802695
$909$		0			0
$910$	−70.8970	+	0.184502i	−2.35021	+	0.00611619i
$911$	1.43534	−	1.71057i	0.0475550	−	0.0566738i	−0.741743	−	0.670685i	$-0.766000\pi$
$911$	1.43534	−	1.71057i	0.0475550	−	0.0566738i	0.789298	+	0.614011i	$0.210445\pi$
$912$		0			0
$913$	8.19597	+	9.76757i	0.271247	+	0.323260i
$914$	8.57840	−	23.5690i	0.283748	−	0.779592i
$915$		0			0
$916$	−5.57667	−	15.3218i	−0.184258	−	0.506245i
$917$	26.4745	−	46.1320i	0.874265	−	1.52341i
$918$		0			0
$919$	−9.06589	+	15.7026i	−0.299056	+	0.517980i	−0.975920	−	0.218128i	$-0.930005\pi$
$919$	−9.06589	+	15.7026i	−0.299056	+	0.517980i	0.676864	+	0.736108i	$0.263338\pi$
$920$	13.9736	+	11.7253i	0.460697	+	0.386570i
$921$		0			0
$922$	11.3709	−	2.00500i	0.374482	−	0.0660313i
$923$	−3.28424	−	18.6258i	−0.108102	−	0.613077i
$924$		0			0
$925$	0.182195	+	0.152880i	0.00599053	+	0.00502665i
$926$	−57.9615	+	33.4641i	−1.90473	+	1.09970i
$927$		0			0
$928$	−2.09532	+	3.62921i	−0.0687824	+	0.119135i
$929$	−14.7593	−	12.3845i	−0.484237	−	0.406323i	0.367719	−	0.929937i	$-0.380139\pi$
$929$	−14.7593	−	12.3845i	−0.484237	−	0.406323i	−0.851956	+	0.523614i	$0.824583\pi$
$930$		0			0
$931$	−10.2622	−	12.1016i	−0.336331	−	0.396613i
$932$	−2.37638	+	6.52906i	−0.0778410	+	0.213866i
$933$		0			0
$934$	−4.77761	−	13.1264i	−0.156328	−	0.429508i
$935$	−30.4469	−	17.5785i	−0.995720	−	0.574879i
$936$		0			0
$937$	26.1439	+	15.0942i	0.854085	+	0.493106i	0.862027	−	0.506862i	$-0.169195\pi$
$937$	26.1439	+	15.0942i	0.854085	+	0.493106i	−0.00794190	+	0.999968i	$0.502528\pi$
$938$	30.5400	−	36.5891i	0.997166	−	1.19468i
$939$		0			0
$940$	−28.8968	−	10.5176i	−0.942510	−	0.343046i
$941$	−2.92209	−	1.06355i	−0.0952573	−	0.0346708i	0.293952	−	0.955820i	$-0.405029\pi$
$941$	−2.92209	−	1.06355i	−0.0952573	−	0.0346708i	−0.389209	+	0.921149i	$0.627252\pi$
$942$		0			0
$943$	−7.19271	−	1.26827i	−0.234227	−	0.0413005i
$944$	−54.0524			−1.75926
$945$		0			0
$946$	3.03221			0.0985856
$947$	−49.0430	−	8.64760i	−1.59368	−	0.281009i	−0.694802	−	0.719201i	$-0.744508\pi$
$947$	−49.0430	−	8.64760i	−1.59368	−	0.281009i	−0.898881	+	0.438192i	$0.855619\pi$
$948$		0			0
$949$	8.81441	+	3.20818i	0.286128	+	0.104142i
$950$	−34.3067	−	12.4866i	−1.11306	−	0.405119i
$951$		0			0
$952$	−17.2717	−	2.99914i	−0.559778	−	0.0972026i
$953$	24.6725	+	14.2447i	0.799222	+	0.461431i	0.843199	−	0.537602i	$-0.180670\pi$
$953$	24.6725	+	14.2447i	0.799222	+	0.461431i	−0.0439773	+	0.999033i	$0.514003\pi$
$954$		0			0
$955$	75.3281	+	43.4907i	2.43756	+	1.40733i
$956$	1.55808	+	4.28078i	0.0503918	+	0.138450i
$957$		0			0
$958$	−13.0460	+	35.8436i	−0.421498	+	1.15806i
$959$	−48.8096	+	8.73749i	−1.57615	+	0.282148i
$960$		0			0
$961$	−33.9221	−	28.4641i	−1.09426	−	0.918196i
$962$	−0.0854535	+	0.148010i	−0.00275513	+	0.00477202i
$963$		0			0
$964$	0.214966	−	0.124111i	0.00692359	−	0.00399734i
$965$	43.8676	+	36.8093i	1.41215	+	1.18493i
$966$		0			0
$967$	0.546444	+	3.09904i	0.0175725	+	0.0996584i	0.992333	−	0.123597i	$-0.0394429\pi$
$967$	0.546444	+	3.09904i	0.0175725	+	0.0996584i	−0.974760	+	0.223255i	$0.928332\pi$
$968$	−5.60683	+	0.988636i	−0.180210	+	0.0317760i
$969$		0			0
$970$	−64.3755	−	54.0175i	−2.06697	−	1.73440i
$971$	−11.2478	+	19.4817i	−0.360958	+	0.625197i	−0.988119	−	0.153693i	$-0.950883\pi$
$971$	−11.2478	+	19.4817i	−0.360958	+	0.625197i	0.627161	+	0.778890i	$0.284217\pi$
$972$		0			0
$973$	0.0909659	+	34.9547i	0.00291623	+	1.12060i
$974$	−14.9814	−	41.1610i	−0.480034	−	1.31888i
$975$		0			0
$976$	−12.8652	+	35.3469i	−0.411805	+	1.13143i
$977$	28.7374	+	34.2480i	0.919392	+	1.09569i	0.995131	+	0.0985613i	$0.0314241\pi$
$977$	28.7374	+	34.2480i	0.919392	+	1.09569i	−0.0757387	+	0.997128i	$0.524131\pi$
$978$		0			0
$979$	−8.74128	+	10.4175i	−0.279373	+	0.332943i
$980$	−9.92575	+	17.4004i	−0.317066	+	0.555836i
$981$		0			0
$982$	21.6468			0.690778
$983$	0.767586	−	0.279378i	0.0244822	−	0.00891078i	−0.329750	−	0.944068i	$-0.606964\pi$
$983$	0.767586	−	0.279378i	0.0244822	−	0.00891078i	0.354232	+	0.935157i	$0.384742\pi$
$984$		0			0
$985$	−47.0266	−	56.0441i	−1.49839	−	1.78571i
$986$	−5.17268	−	1.88270i	−0.164732	−	0.0599574i
$987$		0			0
$988$	1.23748	−	7.01812i	0.0393696	−	0.223276i
$989$		−	1.45663i		−	0.0463181i
$990$		0			0
$991$	−10.8376			−0.344267			−0.172134	−	0.985074i	$-0.555066\pi$
$991$	−10.8376			−0.344267			−0.172134	+	0.985074i	$0.555066\pi$
$992$	−32.7936	+	11.9359i	−1.04120	+	0.378965i
$993$		0			0
$994$	−18.5039	−	6.68040i	−0.586909	−	0.211889i
$995$	−14.3229	−	17.0694i	−0.454068	−	0.541137i
$996$		0			0
$997$	32.7273	−	39.0028i	1.03648	−	1.23523i	0.0650587	−	0.997881i	$-0.479277\pi$
$997$	32.7273	−	39.0028i	1.03648	−	1.23523i	0.971424	−	0.237351i	$-0.0762790\pi$
$998$	37.1151	−	21.4284i	1.17486	−	0.678305i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.467.18		132
3.2	odd	2		189.2.bd.a.47.5	yes	132
7.3	odd	6		567.2.ba.a.143.5		132
21.17	even	6		189.2.ba.a.101.18	✓	132
27.4	even	9		189.2.ba.a.131.18	yes	132
27.23	odd	18		567.2.ba.a.341.5		132
189.31	odd	18		189.2.bd.a.185.5	yes	132
189.185	even	18	inner	567.2.bd.a.17.18		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.18	✓	132	21.17	even	6
189.2.ba.a.131.18	yes	132	27.4	even	9
189.2.bd.a.47.5	yes	132	3.2	odd	2
189.2.bd.a.185.5	yes	132	189.31	odd	18
567.2.ba.a.143.5		132	7.3	odd	6
567.2.ba.a.341.5		132	27.23	odd	18
567.2.bd.a.17.18		132	189.185	even	18	inner
567.2.bd.a.467.18		132	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.63190 + 0.287749i) q^{2} +(0.700923 + 0.255115i) q^{4} +(3.60525 + 1.31220i) q^{5} +(2.03118 + 1.69538i) q^{7} +(-1.79971 - 1.03907i) q^{8} +(5.50583 + 3.17879i) q^{10} +(-0.982995 - 2.70076i) q^{11} +(-1.44158 + 3.96072i) q^{13} +(2.82685 + 3.35116i) q^{14} +(-3.78076 - 3.17244i) q^{16} +(1.59416 - 2.76117i) q^{17} +(-1.96303 + 1.13336i) q^{19} +(2.19224 + 1.83951i) q^{20} +(-0.827014 - 4.69023i) q^{22} +(-2.25312 + 0.397286i) q^{23} +(7.44573 + 6.24771i) q^{25} +(-3.49221 + 6.04869i) q^{26} +(0.991186 + 1.70651i) q^{28} +(-0.356349 - 0.979061i) q^{29} +(2.96755 - 8.15327i) q^{31} +(-2.58538 - 3.08114i) q^{32} +(3.39605 - 4.04725i) q^{34} +(5.09824 + 8.77758i) q^{35} +0.0244697 q^{37} +(-3.52960 + 1.28467i) q^{38} +(-5.12495 - 6.10768i) q^{40} +(2.99981 + 1.09184i) q^{41} +(-0.110557 + 0.627001i) q^{43} -2.14380i q^{44} -3.79119 q^{46} +(-10.0976 + 3.67521i) q^{47} +(1.25140 + 6.88723i) q^{49} +(10.3529 + 12.3382i) q^{50} +(-2.02088 + 2.40839i) q^{52} +(-1.91685 + 1.10670i) q^{53} -11.0268i q^{55} +(-1.89394 - 5.16172i) q^{56} +(-0.299804 - 1.70027i) q^{58} +(8.38964 - 7.03975i) q^{59} +(-2.60670 - 7.16186i) q^{61} +(7.18884 - 12.4514i) q^{62} +(1.60294 + 2.77637i) q^{64} +(-10.3945 + 12.3877i) q^{65} +(-1.88769 - 10.7056i) q^{67} +(1.82180 - 1.52867i) q^{68} +(5.79410 + 15.7912i) q^{70} +(-3.88604 + 2.24361i) q^{71} -2.22546i q^{73} +(0.0399322 + 0.00704112i) q^{74} +(-1.66507 + 0.293597i) q^{76} +(2.58216 - 7.15227i) q^{77} +(-2.19643 + 12.4566i) q^{79} +(-9.46771 - 16.3986i) q^{80} +(4.58122 + 2.64497i) q^{82} +(-4.16888 + 1.51735i) q^{83} +(9.37059 - 7.86286i) q^{85} +(-0.360837 + 0.991392i) q^{86} +(-1.03715 + 5.88198i) q^{88} +(-2.36580 - 4.09769i) q^{89} +(-9.64302 + 5.60091i) q^{91} +(-1.68062 - 0.296338i) q^{92} +(-17.5358 + 3.09203i) q^{94} +(-8.56442 + 1.51014i) q^{95} +(-13.0174 - 2.29533i) q^{97} +(0.0603728 + 11.5994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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