LMFDB - Embedded newform 567.2.bd.a.467.21

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			467.21
Character	$\chi$	$=$	567.467
Dual form			567.2.bd.a.17.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47573 + 0.436538i) q^{2} +(4.05929 + 1.47746i) q^{4} +(2.58032 + 0.939158i) q^{5} +(-2.62404 + 0.338290i) q^{7} +(5.05050 + 2.91591i) q^{8} +(5.97819 + 3.45151i) q^{10} +(-1.43170 - 3.93357i) q^{11} +(0.0398496 - 0.109486i) q^{13} +(-6.64408 - 0.307977i) q^{14} +(4.61245 + 3.87030i) q^{16} +(-2.57344 + 4.45733i) q^{17} +(4.51931 - 2.60922i) q^{19} +(9.08669 + 7.62463i) q^{20} +(-1.82736 - 10.3635i) q^{22} +(-7.39321 + 1.30362i) q^{23} +(1.94579 + 1.63271i) q^{25} +(0.146452 - 0.253662i) q^{26} +(-11.1515 - 2.50369i) q^{28} +(-1.21597 - 3.34086i) q^{29} +(-0.106042 + 0.291348i) q^{31} +(2.23240 + 2.66047i) q^{32} +(-8.31695 + 9.91175i) q^{34} +(-7.08855 - 1.59149i) q^{35} +1.91994 q^{37} +(12.3276 - 4.48688i) q^{38} +(10.2934 + 12.2672i) q^{40} +(6.29347 + 2.29063i) q^{41} +(0.411100 - 2.33146i) q^{43} -18.0828i q^{44} -18.8727 q^{46} +(4.74491 - 1.72700i) q^{47} +(6.77112 - 1.77537i) q^{49} +(4.10452 + 4.89157i) q^{50} +(0.323522 - 0.385559i) q^{52} +(-3.76047 + 2.17111i) q^{53} -11.4945i q^{55} +(-14.2391 - 5.94291i) q^{56} +(-1.55201 - 8.80190i) q^{58} +(-8.02306 + 6.73214i) q^{59} +(-0.395365 - 1.08626i) q^{61} +(-0.389715 + 0.675007i) q^{62} +(-1.65570 - 2.86775i) q^{64} +(0.205649 - 0.245083i) q^{65} +(1.92499 + 10.9172i) q^{67} +(-17.0319 + 14.2915i) q^{68} +(-16.8546 - 7.03452i) q^{70} +(5.47124 - 3.15882i) q^{71} +2.58177i q^{73} +(4.75325 + 0.838127i) q^{74} +(22.2002 - 3.91449i) q^{76} +(5.08753 + 9.83750i) q^{77} +(2.74201 - 15.5507i) q^{79} +(8.26674 + 14.3184i) q^{80} +(14.5810 + 8.41833i) q^{82} +(-10.6778 + 3.88640i) q^{83} +(-10.8264 + 9.08446i) q^{85} +(2.03554 - 5.59261i) q^{86} +(4.23912 - 24.0412i) q^{88} +(0.456832 + 0.791256i) q^{89} +(-0.0675288 + 0.300776i) q^{91} +(-31.9372 - 5.63140i) q^{92} +(12.5010 - 2.20427i) q^{94} +(14.1117 - 2.48828i) q^{95} +(5.88114 + 1.03700i) q^{97} +(17.5385 - 1.43948i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.47573	+	0.436538i	1.75061	+	0.308679i	0.954883	−	0.296982i	$-0.0959801\pi$
$2$	2.47573	+	0.436538i	1.75061	+	0.308679i	0.795723	+	0.605661i	$0.207091\pi$
$3$		0			0
$3$		0			0
$4$	4.05929	+	1.47746i	2.02965	+	0.738731i
$5$	2.58032	+	0.939158i	1.15395	+	0.420004i	0.846933	−	0.531699i	$-0.178446\pi$
$5$	2.58032	+	0.939158i	1.15395	+	0.420004i	0.307019	+	0.951703i	$0.400668\pi$
$6$		0			0
$7$	−2.62404	+	0.338290i	−0.991792	+	0.127862i
$7$	−2.62404	+	0.338290i	−0.991792	+	0.127862i
$8$	5.05050	+	2.91591i	1.78562	+	1.03093i
$9$		0			0
$10$	5.97819	+	3.45151i	1.89047	+	1.09146i
$11$	−1.43170	−	3.93357i	−0.431675	−	1.18602i	−0.944784	−	0.327694i	$-0.893729\pi$
$11$	−1.43170	−	3.93357i	−0.431675	−	1.18602i	0.513109	−	0.858323i	$-0.328494\pi$
$12$		0			0
$13$	0.0398496	−	0.109486i	0.0110523	−	0.0303659i	−0.934044	−	0.357158i	$-0.883746\pi$
$13$	0.0398496	−	0.109486i	0.0110523	−	0.0303659i	0.945096	+	0.326793i	$0.105968\pi$
$14$	−6.64408	−	0.307977i	−1.77571	−	0.0823103i
$15$		0			0
$16$	4.61245	+	3.87030i	1.15311	+	0.967575i
$17$	−2.57344	+	4.45733i	−0.624152	+	1.08106i	0.364553	+	0.931183i	$0.381222\pi$
$17$	−2.57344	+	4.45733i	−0.624152	+	1.08106i	−0.988704	+	0.149879i	$0.952111\pi$
$18$		0			0
$19$	4.51931	−	2.60922i	1.03680	−	0.598597i	0.117875	−	0.993028i	$-0.462392\pi$
$19$	4.51931	−	2.60922i	1.03680	−	0.598597i	0.918925	+	0.394432i	$0.129059\pi$
$20$	9.08669	+	7.62463i	2.03184	+	1.70492i
$21$		0			0
$22$	−1.82736	−	10.3635i	−0.389594	−	2.20950i
$23$	−7.39321	+	1.30362i	−1.54159	+	0.271824i	−0.878877	−	0.477049i	$-0.841706\pi$
$23$	−7.39321	+	1.30362i	−1.54159	+	0.271824i	−0.662714	+	0.748873i	$0.730595\pi$
$24$		0			0
$25$	1.94579	+	1.63271i	0.389158	+	0.326543i
$26$	0.146452	−	0.253662i	0.0287215	−	0.0497472i
$27$		0			0
$28$	−11.1515	−	2.50369i	−2.10744	−	0.473153i
$29$	−1.21597	−	3.34086i	−0.225801	−	0.620383i	0.774119	−	0.633040i	$-0.218193\pi$
$29$	−1.21597	−	3.34086i	−0.225801	−	0.620383i	−0.999920	+	0.0126573i	$0.995971\pi$
$30$		0			0
$31$	−0.106042	+	0.291348i	−0.0190457	+	0.0523276i	−0.948851	−	0.315724i	$-0.897753\pi$
$31$	−0.106042	+	0.291348i	−0.0190457	+	0.0523276i	0.929805	+	0.368051i	$0.119975\pi$
$32$	2.23240	+	2.66047i	0.394636	+	0.470309i
$33$		0			0
$34$	−8.31695	+	9.91175i	−1.42634	+	1.69985i
$35$	−7.08855	−	1.59149i	−1.19818	−	0.269011i
$36$		0			0
$37$	1.91994			0.315636			0.157818	−	0.987468i	$-0.449554\pi$
$37$	1.91994			0.315636			0.157818	+	0.987468i	$0.449554\pi$
$38$	12.3276	−	4.48688i	1.99980	−	0.727868i
$39$		0			0
$40$	10.2934	+	12.2672i	1.62753	+	1.93961i
$41$	6.29347	+	2.29063i	0.982874	+	0.357737i	0.782957	−	0.622076i	$-0.213710\pi$
$41$	6.29347	+	2.29063i	0.982874	+	0.357737i	0.199917	+	0.979813i	$0.435933\pi$
$42$		0			0
$43$	0.411100	−	2.33146i	0.0626921	−	0.355545i	−0.937284	−	0.348568i	$-0.886668\pi$
$43$	0.411100	−	2.33146i	0.0626921	−	0.355545i	0.999976	−	0.00697673i	$-0.00222078\pi$
$44$		−	18.0828i		−	2.72609i
$45$		0			0
$46$	−18.8727			−2.78262
$47$	4.74491	−	1.72700i	0.692116	−	0.251910i	0.0280749	−	0.999606i	$-0.491062\pi$
$47$	4.74491	−	1.72700i	0.692116	−	0.251910i	0.664041	+	0.747696i	$0.268840\pi$
$48$		0			0
$49$	6.77112	−	1.77537i	0.967303	−	0.253624i
$50$	4.10452	+	4.89157i	0.580466	+	0.691773i
$51$		0			0
$52$	0.323522	−	0.385559i	0.0448645	−	0.0534674i
$53$	−3.76047	+	2.17111i	−0.516541	+	0.298225i	−0.735518	−	0.677505i	$-0.763061\pi$
$53$	−3.76047	+	2.17111i	−0.516541	+	0.298225i	0.218977	+	0.975730i	$0.429728\pi$
$54$		0			0
$55$		−	11.4945i		−	1.54991i
$56$	−14.2391	−	5.94291i	−1.90278	−	0.794155i
$57$		0			0
$58$	−1.55201	−	8.80190i	−0.203789	−	1.15575i
$59$	−8.02306	+	6.73214i	−1.04451	+	0.876450i	−0.992506	−	0.122196i	$-0.961006\pi$
$59$	−8.02306	+	6.73214i	−1.04451	+	0.876450i	−0.0520070	+	0.998647i	$0.516562\pi$
$60$		0			0
$61$	−0.395365	−	1.08626i	−0.0506214	−	0.139081i	0.911805	−	0.410623i	$-0.134689\pi$
$61$	−0.395365	−	1.08626i	−0.0506214	−	0.139081i	−0.962427	+	0.271542i	$0.912466\pi$
$62$	−0.389715	+	0.675007i	−0.0494939	+	0.0857260i
$63$		0			0
$64$	−1.65570	−	2.86775i	−0.206962	−	0.358469i
$65$	0.205649	−	0.245083i	0.0255077	−	0.0303988i
$66$		0			0
$67$	1.92499	+	10.9172i	0.235175	+	1.33374i	0.842245	+	0.539095i	$0.181234\pi$
$67$	1.92499	+	10.9172i	0.235175	+	1.33374i	−0.607070	+	0.794648i	$0.707655\pi$
$68$	−17.0319	+	14.2915i	−2.06542	+	1.73309i
$69$		0			0
$70$	−16.8546	−	7.03452i	−2.01451	−	0.840786i
$71$	5.47124	−	3.15882i	0.649317	−	0.374883i	−0.138878	−	0.990310i	$-0.544350\pi$
$71$	5.47124	−	3.15882i	0.649317	−	0.374883i	0.788194	+	0.615426i	$0.211016\pi$
$72$		0			0
$73$			2.58177i			0.302173i	0.988521	+	0.151087i	$0.0482773\pi$
$73$			2.58177i			0.302173i	−0.988521	+	0.151087i	$0.951723\pi$
$74$	4.75325	+	0.838127i	0.552555	+	0.0974303i
$75$		0			0
$76$	22.2002	−	3.91449i	2.54654	−	0.449023i
$77$	5.08753	+	9.83750i	0.579778	+	1.12109i
$78$		0			0
$79$	2.74201	−	15.5507i	0.308501	−	1.74959i	−0.298052	−	0.954550i	$-0.596337\pi$
$79$	2.74201	−	15.5507i	0.308501	−	1.74959i	0.606552	−	0.795044i	$-0.292552\pi$
$80$	8.26674	+	14.3184i	0.924250	+	1.60085i
$81$		0			0
$82$	14.5810	+	8.41833i	1.61020	+	0.929649i
$83$	−10.6778	+	3.88640i	−1.17204	+	0.426588i	−0.853384	−	0.521282i	$-0.825454\pi$
$83$	−10.6778	+	3.88640i	−1.17204	+	0.426588i	−0.318657	+	0.947870i	$0.603232\pi$
$84$		0			0
$85$	−10.8264	+	9.08446i	−1.17429	+	0.985348i
$86$	2.03554	−	5.59261i	0.219498	−	0.603067i
$87$		0			0
$88$	4.23912	−	24.0412i	0.451891	−	2.56280i
$89$	0.456832	+	0.791256i	0.0484241	+	0.0838730i	0.889221	−	0.457477i	$-0.151247\pi$
$89$	0.456832	+	0.791256i	0.0484241	+	0.0838730i	−0.840797	+	0.541350i	$0.817913\pi$
$90$		0			0
$91$	−0.0675288	+	0.300776i	−0.00707894	+	0.0315299i
$92$	−31.9372	−	5.63140i	−3.32969	−	0.587114i
$93$		0			0
$94$	12.5010	−	2.20427i	1.28938	−	0.227353i
$95$	14.1117	−	2.48828i	1.44783	−	0.255292i
$96$		0			0
$97$	5.88114	+	1.03700i	0.597140	+	0.105292i	0.464045	−	0.885812i	$-0.346398\pi$
$97$	5.88114	+	1.03700i	0.597140	+	0.105292i	0.133094	+	0.991103i	$0.457509\pi$
$98$	17.5385	−	1.43948i	1.77165	−	0.145410i
$99$		0			0
$100$	5.48627	+	9.50249i	0.548627	+	0.950249i
$101$	−1.43057	+	8.11319i	−0.142347	+	0.807292i	0.827111	+	0.562038i	$0.189983\pi$
$101$	−1.43057	+	8.11319i	−0.142347	+	0.807292i	−0.969459	+	0.245254i	$0.921129\pi$
$102$		0			0
$103$	−0.337183	+	0.926404i	−0.0332237	+	0.0912813i	−0.955195	−	0.295976i	$-0.904355\pi$
$103$	−0.337183	+	0.926404i	−0.0332237	+	0.0912813i	0.921972	+	0.387257i	$0.126577\pi$
$104$	0.520511	−	0.436761i	0.0510403	−	0.0428279i
$105$		0			0
$106$	−10.2577	+	3.73349i	−0.996315	+	0.362629i
$107$	−11.2050	−	6.46919i	−1.08322	−	0.625400i	−0.151460	−	0.988463i	$-0.548397\pi$
$107$	−11.2050	−	6.46919i	−1.08322	−	0.625400i	−0.931764	+	0.363064i	$0.881731\pi$
$108$		0			0
$109$	1.89554	+	3.28318i	0.181560	+	0.314471i	0.942412	−	0.334454i	$-0.108552\pi$
$109$	1.89554	+	3.28318i	0.181560	+	0.314471i	−0.760852	+	0.648926i	$0.775219\pi$
$110$	5.01777	−	28.4572i	0.478426	−	2.71329i
$111$		0			0
$112$	−13.4125	−	8.59546i	−1.26736	−	0.812195i
$113$	−2.66007	+	0.469041i	−0.250238	+	0.0441237i	−0.297360	−	0.954765i	$-0.596106\pi$
$113$	−2.66007	+	0.469041i	−0.250238	+	0.0441237i	0.0471221	+	0.998889i	$0.484995\pi$
$114$		0			0
$115$	−20.3011	−	3.57964i	−1.89309	−	0.333803i
$116$		−	15.3581i		−	1.42596i
$117$		0			0
$118$	−22.8018	+	13.1646i	−2.09907	+	1.21190i
$119$	5.24493	−	12.5668i	0.480802	−	1.15199i
$120$		0			0
$121$	−4.99673	+	4.19276i	−0.454249	+	0.381160i
$122$	−0.504625	−	2.86187i	−0.0456866	−	0.259102i
$123$		0			0
$124$	−0.860909	+	1.02599i	−0.0773120	+	0.0921368i
$125$	−3.37741	−	5.84984i	−0.302084	−	0.523225i
$126$		0			0
$127$	0.619432	−	1.07289i	0.0549657	−	0.0952034i	−0.837233	−	0.546846i	$-0.815828\pi$
$127$	0.619432	−	1.07289i	0.0549657	−	0.0952034i	0.892199	+	0.451642i	$0.149162\pi$
$128$	−5.22285	−	14.3496i	−0.461639	−	1.26834i
$129$		0			0
$130$	0.616120	−	0.516986i	0.0540373	−	0.0453427i
$131$	−1.30100	−	7.37831i	−0.113669	−	0.644646i	−0.987401	−	0.158239i	$-0.949418\pi$
$131$	−1.30100	−	7.37831i	−0.113669	−	0.644646i	0.873732	−	0.486407i	$-0.161693\pi$
$132$		0			0
$133$	−10.9761	+	8.37553i	−0.951752	+	0.726250i
$134$			27.8683i			2.40745i
$135$		0			0
$136$	−25.9943	+	15.0078i	−2.22900	+	1.28691i
$137$	−10.4685	+	12.4759i	−0.894383	+	1.06588i	0.103078	+	0.994673i	$0.467131\pi$
$137$	−10.4685	+	12.4759i	−0.894383	+	1.06588i	−0.997461	+	0.0712111i	$0.977314\pi$
$138$		0			0
$139$	6.25623	+	7.45589i	0.530647	+	0.632400i	0.963064	−	0.269274i	$-0.0867836\pi$
$139$	6.25623	+	7.45589i	0.530647	+	0.632400i	−0.432417	+	0.901674i	$0.642339\pi$
$140$	−26.4231	−	16.9334i	−2.23316	−	1.43113i
$141$		0			0
$142$	14.9243	−	5.43199i	1.25242	−	0.455842i
$143$	−0.487724			−0.0407855
$144$		0			0
$145$		−	9.76248i		−	0.810730i
$146$	−1.12704	+	6.39177i	−0.0932746	+	0.528987i
$147$		0			0
$148$	7.79359	+	2.83664i	0.640630	+	0.233170i
$149$	10.7706	+	12.8359i	0.882365	+	1.05156i	0.998299	+	0.0583043i	$0.0185694\pi$
$149$	10.7706	+	12.8359i	0.882365	+	1.05156i	−0.115934	+	0.993257i	$0.536986\pi$
$150$		0			0
$151$	14.0649	−	5.11922i	1.14459	−	0.416596i	0.301020	−	0.953618i	$-0.402673\pi$
$151$	14.0649	−	5.11922i	1.14459	−	0.416596i	0.843568	+	0.537022i	$0.180451\pi$
$152$	30.4330			2.46844
$153$		0			0
$154$	8.30090	+	26.5759i	0.668906	+	2.14155i
$155$	−0.547243	+	0.652179i	−0.0439556	+	0.0523843i
$156$		0			0
$157$	−2.07640	−	2.47456i	−0.165715	−	0.197492i	0.676796	−	0.736171i	$-0.263368\pi$
$157$	−2.07640	−	2.47456i	−0.165715	−	0.197492i	−0.842511	+	0.538679i	$0.818924\pi$
$158$	13.5770	−	37.3024i	1.08013	−	2.96762i
$159$		0			0
$160$	3.26169	+	8.96143i	0.257860	+	0.708464i
$161$	18.9590	−	5.92180i	1.49418	−	0.466703i
$162$		0			0
$163$	3.85622	−	6.67918i	0.302043	−	0.523153i	−0.674556	−	0.738224i	$-0.735665\pi$
$163$	3.85622	−	6.67918i	0.302043	−	0.523153i	0.976599	+	0.215070i	$0.0689981\pi$
$164$	22.1627	+	18.5967i	1.73062	+	1.45216i
$165$		0			0
$166$	−28.1319	+	4.96042i	−2.18346	+	0.385003i
$167$	−0.286318	−	1.62379i	−0.0221559	−	0.125652i	0.971724	−	0.236121i	$-0.0758761\pi$
$167$	−0.286318	−	1.62379i	−0.0221559	−	0.125652i	−0.993880	+	0.110468i	$0.964765\pi$
$168$		0			0
$169$	9.94818	+	8.34751i	0.765245	+	0.642116i
$170$	−30.7691	+	17.7645i	−2.35988	+	1.36248i
$171$		0			0
$172$	5.11342	−	8.85670i	0.389894	−	0.675317i
$173$	14.0046	+	11.7513i	1.06475	+	0.893434i	0.994567	−	0.104100i	$-0.0331963\pi$
$173$	14.0046	+	11.7513i	1.06475	+	0.893434i	0.0701858	+	0.997534i	$0.477641\pi$
$174$		0			0
$175$	−5.65816	−	3.62606i	−0.427716	−	0.274104i
$176$	8.62046	−	23.6845i	0.649792	−	1.78529i
$177$		0			0
$178$	0.785580	+	2.15836i	0.0588817	+	0.161776i
$179$	−3.65498	−	2.11020i	−0.273186	−	0.157724i	0.357149	−	0.934048i	$-0.383749\pi$
$179$	−3.65498	−	2.11020i	−0.273186	−	0.157724i	−0.630335	+	0.776324i	$0.717082\pi$
$180$		0			0
$181$	−9.51249	−	5.49204i	−0.707058	−	0.408220i	0.102913	−	0.994690i	$-0.467184\pi$
$181$	−9.51249	−	5.49204i	−0.707058	−	0.408220i	−0.809971	+	0.586470i	$0.800517\pi$
$182$	−0.298483	+	0.715161i	−0.0221250	+	0.0530112i
$183$		0			0
$184$	−41.1406	−	14.9740i	−3.03293	−	1.10390i
$185$	4.95405	+	1.80313i	0.364229	+	0.132569i
$186$		0			0
$187$	21.2177	+	3.74125i	1.55159	+	0.273587i
$188$	21.8125			1.59084
$189$		0			0
$190$	36.0230			2.61338
$191$	10.0041	+	1.76400i	0.723872	+	0.127638i	0.523432	−	0.852068i	$-0.324652\pi$
$191$	10.0041	+	1.76400i	0.723872	+	0.127638i	0.200441	+	0.979706i	$0.435763\pi$
$192$		0			0
$193$	−8.12064	−	2.95567i	−0.584536	−	0.212754i	0.0327883	−	0.999462i	$-0.489561\pi$
$193$	−8.12064	−	2.95567i	−0.584536	−	0.212754i	−0.617325	+	0.786708i	$0.711784\pi$
$194$	14.1074	+	5.13469i	1.01285	+	0.368649i
$195$		0			0
$196$	30.1090	+	2.79733i	2.15064	+	0.199809i
$197$	−0.625155	−	0.360933i	−0.0445405	−	0.0257154i	0.477564	−	0.878597i	$-0.341520\pi$
$197$	−0.625155	−	0.360933i	−0.0445405	−	0.0257154i	−0.522105	+	0.852881i	$0.674853\pi$
$198$		0			0
$199$	18.8603	+	10.8890i	1.33697	+	0.771899i	0.986357	−	0.164622i	$-0.0526403\pi$
$199$	18.8603	+	10.8890i	1.33697	+	0.771899i	0.350612	+	0.936521i	$0.385974\pi$
$200$	5.06638	+	13.9198i	0.358247	+	0.984276i
$201$		0			0
$202$	−7.08343	+	19.4616i	−0.498388	+	1.36931i
$203$	4.32094	+	8.35519i	0.303271	+	0.586419i
$204$		0			0
$205$	14.0879	+	11.8211i	0.983939	+	0.825623i
$206$	−1.23919	+	2.14633i	−0.0863382	+	0.149542i
$207$		0			0
$208$	0.607548	−	0.350768i	0.0421259	−	0.0243214i
$209$	−16.7339	−	14.0414i	−1.15751	−	0.971263i
$210$		0			0
$211$	1.68157	+	9.53668i	0.115764	+	0.656532i	0.986369	+	0.164549i	$0.0526168\pi$
$211$	1.68157	+	9.53668i	0.115764	+	0.656532i	−0.870605	+	0.491983i	$0.836272\pi$
$212$	−18.4726	+	3.25722i	−1.26870	+	0.223706i
$213$		0			0
$214$	−24.9164	−	20.9074i	−1.70325	−	1.42920i
$215$	3.25038	−	5.62982i	0.221674	−	0.383951i
$216$		0			0
$217$	0.179698	−	0.800379i	0.0121987	−	0.0543333i
$218$	3.25962	+	8.95574i	0.220769	+	0.606559i
$219$		0			0
$220$	16.9826	−	46.6594i	1.14497	−	3.14577i
$221$	0.385465	+	0.459379i	0.0259292	+	0.0309012i
$222$		0			0
$223$	−18.0896	+	21.5583i	−1.21137	+	1.44365i	−0.349183	+	0.937055i	$0.613541\pi$
$223$	−18.0896	+	21.5583i	−1.21137	+	1.44365i	−0.862184	+	0.506596i	$0.830904\pi$
$224$	−6.75791	−	6.22597i	−0.451532	−	0.415990i
$225$		0			0
$226$	−6.79036			−0.451688
$227$	7.19954	−	2.62042i	0.477850	−	0.173923i	−0.0918550	−	0.995772i	$-0.529280\pi$
$227$	7.19954	−	2.62042i	0.477850	−	0.173923i	0.569705	+	0.821849i	$0.307057\pi$
$228$		0			0
$229$	9.13922	+	10.8917i	0.603937	+	0.719744i	0.978220	−	0.207571i	$-0.0665557\pi$
$229$	9.13922	+	10.8917i	0.603937	+	0.719744i	−0.374283	+	0.927314i	$0.622111\pi$
$230$	−48.6975	−	17.7244i	−3.21102	−	1.16871i
$231$		0			0
$232$	3.60037	−	20.4187i	0.236376	−	1.34055i
$233$			22.4909i			1.47343i	0.676204	+	0.736714i	$0.263624\pi$
$233$			22.4909i			1.47343i	−0.676204	+	0.736714i	$0.736376\pi$
$234$		0			0
$235$	13.8653			0.904472
$236$	−42.5144	+	15.4740i	−2.76745	+	1.00727i
$237$		0			0
$238$	18.4709	−	28.8223i	1.19729	−	1.86827i
$239$	15.3178	+	18.2550i	0.990825	+	1.18082i	0.983511	+	0.180846i	$0.0578835\pi$
$239$	15.3178	+	18.2550i	0.990825	+	1.18082i	0.00731345	+	0.999973i	$0.497672\pi$
$240$		0			0
$241$	8.71797	−	10.3897i	0.561574	−	0.669257i	−0.408305	−	0.912846i	$-0.633880\pi$
$241$	8.71797	−	10.3897i	0.561574	−	0.669257i	0.969879	+	0.243588i	$0.0783245\pi$
$242$	−14.2009	+	8.19887i	−0.912866	+	0.527044i
$243$		0			0
$244$		−	4.99357i		−	0.319681i
$245$	19.1390	+	1.77814i	1.22274	+	0.113601i
$246$		0			0
$247$	−0.105581	−	0.598777i	−0.00671793	−	0.0380993i
$248$	−1.38511	+	1.16224i	−0.0879544	+	0.0738025i
$249$		0			0
$250$	−5.80787	−	15.9570i	−0.367322	−	1.00921i
$251$	−4.77251	+	8.26623i	−0.301238	+	0.521760i	−0.976417	−	0.215895i	$-0.930733\pi$
$251$	−4.77251	+	8.26623i	−0.301238	+	0.521760i	0.675179	+	0.737654i	$0.264067\pi$
$252$		0			0
$253$	15.7128	+	27.2153i	0.987854	+	1.71101i
$254$	2.00190	−	2.38578i	0.125611	−	0.149697i
$255$		0			0
$256$	−5.51615	−	31.2837i	−0.344760	−	1.95523i
$257$	4.23694	−	3.55522i	0.264293	−	0.221768i	−0.501005	−	0.865445i	$-0.667036\pi$
$257$	4.23694	−	3.55522i	0.264293	−	0.221768i	0.765298	+	0.643676i	$0.222592\pi$
$258$		0			0
$259$	−5.03799	+	0.649496i	−0.313045	+	0.0403577i
$260$	1.19689	−	0.691025i	0.0742280	−	0.0428556i
$261$		0			0
$262$		−	18.8347i		−	1.16361i
$263$	8.23979	+	1.45290i	0.508087	+	0.0895895i	0.421815	−	0.906682i	$-0.361393\pi$
$263$	8.23979	+	1.45290i	0.508087	+	0.0895895i	0.0862727	+	0.996272i	$0.472504\pi$
$264$		0			0
$265$	−11.7422	+	2.07047i	−0.721319	+	0.127188i
$266$	−30.8302	+	15.9440i	−1.89032	+	0.977592i
$267$		0			0
$268$	−8.31559	+	47.1600i	−0.507955	+	2.88076i
$269$	−9.52435	−	16.4967i	−0.580710	−	1.00582i	−0.995395	−	0.0958542i	$-0.969442\pi$
$269$	−9.52435	−	16.4967i	−0.580710	−	1.00582i	0.414685	−	0.909965i	$-0.363892\pi$
$270$		0			0
$271$	−21.6453	−	12.4969i	−1.31486	−	0.759134i	−0.331962	−	0.943293i	$-0.607710\pi$
$271$	−21.6453	−	12.4969i	−1.31486	−	0.759134i	−0.982896	+	0.184159i	$0.941044\pi$
$272$	−29.1211	+	10.5992i	−1.76573	+	0.642671i
$273$		0			0
$274$	−31.3633	+	26.3170i	−1.89473	+	1.58987i
$275$	3.63660	−	9.99148i	0.219295	−	0.602509i
$276$		0			0
$277$	3.87669	−	21.9858i	0.232928	−	1.32100i	−0.614006	−	0.789301i	$-0.710443\pi$
$277$	3.87669	−	21.9858i	0.232928	−	1.32100i	0.846934	−	0.531698i	$-0.178446\pi$
$278$	12.2340	+	21.1899i	0.733745	+	1.27088i
$279$		0			0
$280$	−31.1601	−	28.7074i	−1.86217	−	1.71559i
$281$	−11.7375	−	2.06964i	−0.700200	−	0.123464i	−0.187795	−	0.982208i	$-0.560134\pi$
$281$	−11.7375	−	2.06964i	−0.700200	−	0.123464i	−0.512405	+	0.858744i	$0.671245\pi$
$282$		0			0
$283$	−3.98101	+	0.701959i	−0.236646	+	0.0417271i	−0.290713	−	0.956810i	$-0.593893\pi$
$283$	−3.98101	+	0.701959i	−0.236646	+	0.0417271i	0.0540671	+	0.998537i	$0.482782\pi$
$284$	26.8764	−	4.73903i	1.59482	−	0.281210i
$285$		0			0
$286$	−1.20747	−	0.212910i	−0.0713994	−	0.0125896i
$287$	−17.2892	−	3.88169i	−1.02055	−	0.229129i
$288$		0			0
$289$	−4.74522	−	8.21896i	−0.279130	−	0.483468i
$290$	4.26169	−	24.1693i	0.250255	−	1.41927i
$291$		0			0
$292$	−3.81447	+	10.4802i	−0.223225	+	0.613305i
$293$	1.36115	−	1.14214i	0.0795192	−	0.0667245i	−0.602162	−	0.798374i	$-0.705694\pi$
$293$	1.36115	−	1.14214i	0.0795192	−	0.0667245i	0.681681	+	0.731650i	$0.261249\pi$
$294$		0			0
$295$	−27.0246	+	9.83614i	−1.57343	+	0.572682i
$296$	9.69666	+	5.59837i	0.563607	+	0.325399i
$297$		0			0
$298$	21.0618	+	36.4801i	1.22008	+	2.11324i
$299$	−0.151888	+	0.861401i	−0.00878392	+	0.0498161i
$300$		0			0
$301$	−0.290030	+	6.25691i	−0.0167170	+	0.360642i
$302$	37.0557	−	6.53392i	2.13232	−	0.375985i
$303$		0			0
$304$	30.9435	+	5.45618i	1.77473	+	0.312933i
$305$		−	3.17420i		−	0.181754i
$306$		0			0
$307$	17.0250	−	9.82941i	0.971670	−	0.560994i	0.0719253	−	0.997410i	$-0.477086\pi$
$307$	17.0250	−	9.82941i	0.971670	−	0.560994i	0.899745	+	0.436416i	$0.143752\pi$
$308$	6.11723	+	47.4499i	0.348561	+	2.70371i
$309$		0			0
$310$	−1.63953	+	1.37573i	−0.0931189	+	0.0781360i
$311$	−4.59744	−	26.0734i	−0.260697	−	1.47849i	−0.781014	−	0.624514i	$-0.785297\pi$
$311$	−4.59744	−	26.0734i	−0.260697	−	1.47849i	0.520317	−	0.853973i	$-0.325814\pi$
$312$		0			0
$313$	3.24044	−	3.86181i	0.183161	−	0.218282i	−0.666649	−	0.745371i	$-0.732272\pi$
$313$	3.24044	−	3.86181i	0.183161	−	0.218282i	0.849810	+	0.527089i	$0.176717\pi$
$314$	−4.06038	−	7.03278i	−0.229140	−	0.396883i
$315$		0			0
$316$	34.1062	−	59.0737i	1.91862	−	3.32316i
$317$	−10.5704	−	29.0420i	−0.593694	−	1.63116i	−0.763592	−	0.645699i	$-0.776566\pi$
$317$	−10.5704	−	29.0420i	−0.593694	−	1.63116i	0.169897	−	0.985462i	$-0.445656\pi$
$318$		0			0
$319$	−11.4006	+	9.56625i	−0.638312	+	0.535607i
$320$	−1.57895	−	8.95466i	−0.0882659	−	0.500581i
$321$		0			0
$322$	49.5225	−	6.38443i	2.75978	−	0.355790i
$323$			26.8587i			1.49446i
$324$		0			0
$325$	0.256298	−	0.147974i	0.0142169	−	0.00820811i
$326$	12.4627	−	14.8525i	0.690244	−	0.822601i
$327$		0			0
$328$	25.1059	+	29.9200i	1.38624	+	1.65206i
$329$	−11.8666	+	6.13688i	−0.654225	+	0.338337i
$330$		0			0
$331$	−15.4130	+	5.60987i	−0.847174	+	0.308346i	−0.728888	−	0.684633i	$-0.759962\pi$
$331$	−15.4130	+	5.60987i	−0.847174	+	0.308346i	−0.118286	+	0.992980i	$0.537740\pi$
$332$	−49.0863			−2.69396
$333$		0			0
$334$		−	4.14505i		−	0.226807i
$335$	−5.28586	+	29.9776i	−0.288797	+	1.63785i
$336$		0			0
$337$	−1.34897	−	0.490985i	−0.0734831	−	0.0267457i	0.305017	−	0.952347i	$-0.401338\pi$
$337$	−1.34897	−	0.490985i	−0.0734831	−	0.0267457i	−0.378500	+	0.925601i	$0.623560\pi$
$338$	20.9850	+	25.0090i	1.14143	+	1.36031i
$339$		0			0
$340$	−57.3696	+	20.8808i	−3.11130	+	1.13242i
$341$	1.29786			0.0702829
$342$		0			0
$343$	−17.1671	+	6.94923i	−0.926934	+	0.375223i
$344$	8.87459	−	10.5763i	0.478486	−	0.570237i
$345$		0			0
$346$	29.5418	+	35.2066i	1.58818	+	1.89272i
$347$	−2.17743	+	5.98243i	−0.116890	+	0.321154i	−0.984316	−	0.176413i	$-0.943551\pi$
$347$	−2.17743	+	5.98243i	−0.116890	+	0.321154i	0.867426	+	0.497566i	$0.165773\pi$
$348$		0			0
$349$	−2.99689	−	8.23388i	−0.160420	−	0.440749i	0.833276	−	0.552856i	$-0.186462\pi$
$349$	−2.99689	−	8.23388i	−0.160420	−	0.440749i	−0.993696	+	0.112107i	$0.964240\pi$
$350$	−12.4252	−	11.4471i	−0.664153	−	0.611875i
$351$		0			0
$352$	7.26902	−	12.5903i	0.387440	−	0.671066i
$353$	1.68284	+	1.41207i	0.0895683	+	0.0751568i	0.686472	−	0.727156i	$-0.259158\pi$
$353$	1.68284	+	1.41207i	0.0895683	+	0.0751568i	−0.596904	+	0.802313i	$0.703603\pi$
$354$		0			0
$355$	17.0842	−	3.01240i	0.906733	−	0.159881i
$356$	0.685364	+	3.88689i	0.0363242	+	0.206005i
$357$		0			0
$358$	−8.12756	−	6.81983i	−0.429555	−	0.360439i
$359$	11.5360	−	6.66031i	0.608847	−	0.351518i	−0.163667	−	0.986516i	$-0.552332\pi$
$359$	11.5360	−	6.66031i	0.608847	−	0.351518i	0.772514	+	0.634998i	$0.218999\pi$
$360$		0			0
$361$	4.11608	−	7.12926i	0.216636	−	0.375224i
$362$	−21.1529	−	17.7494i	−1.11177	−	0.932887i
$363$		0			0
$364$	−0.718503	+	1.12116i	−0.0376598	+	0.0587650i
$365$	−2.42469	+	6.66179i	−0.126914	+	0.348694i
$366$		0			0
$367$	−3.64673	−	10.0193i	−0.190358	−	0.523003i	0.807395	−	0.590012i	$-0.200877\pi$
$367$	−3.64673	−	10.0193i	−0.190358	−	0.523003i	−0.997752	+	0.0670083i	$0.978655\pi$
$368$	−39.1462	−	22.6011i	−2.04064	−	1.17816i
$369$		0			0
$370$	11.4778	+	6.62669i	0.596701	+	0.344505i
$371$	9.13315	−	6.96920i	0.474169	−	0.361823i
$372$		0			0
$373$	13.1561	+	4.78843i	0.681197	+	0.247935i	0.659361	−	0.751826i	$-0.270827\pi$
$373$	13.1561	+	4.78843i	0.681197	+	0.247935i	0.0218355	+	0.999762i	$0.493049\pi$
$374$	50.8960	+	18.5246i	2.63177	+	0.957886i
$375$		0			0
$376$	28.9999	+	5.11347i	1.49556	+	0.263707i
$377$	−0.414234			−0.0213341
$378$		0			0
$379$	−34.6102			−1.77781			−0.888903	−	0.458095i	$-0.848532\pi$
$379$	−34.6102			−1.77781			−0.888903	+	0.458095i	$0.848532\pi$
$380$	60.9599	+	10.7489i	3.12718	+	0.551405i
$381$		0			0
$382$	23.9974	+	8.73436i	1.22782	+	0.446888i
$383$	15.9030	+	5.78823i	0.812607	+	0.295765i	0.714700	−	0.699431i	$-0.246563\pi$
$383$	15.9030	+	5.78823i	0.812607	+	0.295765i	0.0979068	+	0.995196i	$0.468785\pi$
$384$		0			0
$385$	3.88846	+	30.1619i	0.198174	+	1.53719i
$386$	−18.8143	−	10.8624i	−0.957620	−	0.552882i
$387$		0			0
$388$	22.3411	+	12.8987i	1.13420	+	0.654830i
$389$	−1.49572	−	4.10945i	−0.0758359	−	0.208357i	0.895982	−	0.444090i	$-0.146473\pi$
$389$	−1.49572	−	4.10945i	−0.0758359	−	0.208357i	−0.971818	+	0.235733i	$0.924251\pi$
$390$		0			0
$391$	13.2153	−	36.3088i	0.668327	−	1.83621i
$392$	39.3744	+	10.7775i	1.98871	+	0.544344i
$393$		0			0
$394$	−1.39015	−	1.16648i	−0.0700350	−	0.0587663i
$395$	21.6799	−	37.5506i	1.09083	−	1.88938i
$396$		0			0
$397$	9.37906	−	5.41500i	0.470721	−	0.271771i	−0.245820	−	0.969315i	$-0.579057\pi$
$397$	9.37906	−	5.41500i	0.470721	−	0.271771i	0.716542	+	0.697544i	$0.245724\pi$
$398$	41.9395	+	35.1914i	2.10224	+	1.76399i
$399$		0			0
$400$	2.65577	+	15.0616i	0.132788	+	0.753080i
$401$	−6.39743	+	1.12804i	−0.319472	+	0.0563316i	−0.331085	−	0.943601i	$-0.607415\pi$
$401$	−6.39743	+	1.12804i	−0.319472	+	0.0563316i	0.0116126	+	0.999933i	$0.496304\pi$
$402$		0			0
$403$	0.0276727	+	0.0232202i	0.00137848	+	0.00115668i
$404$	−17.7940	+	30.8202i	−0.885286	+	1.53336i
$405$		0			0
$406$	7.05013	+	22.5715i	0.349892	+	1.12020i
$407$	−2.74878	−	7.55222i	−0.136252	−	0.374350i
$408$		0			0
$409$	−5.29809	+	14.5564i	−0.261974	+	0.719766i	0.737061	+	0.675827i	$0.236213\pi$
$409$	−5.29809	+	14.5564i	−0.261974	+	0.719766i	−0.999034	+	0.0439398i	$0.986009\pi$
$410$	29.7174	+	35.4158i	1.46764	+	1.74906i
$411$		0			0
$412$	−2.73745	+	3.26237i	−0.134865	+	0.160725i
$413$	18.7754	−	20.3795i	0.923875	−	1.00281i
$414$		0			0
$415$	−31.2021			−1.53165
$416$	0.380244	−	0.138398i	0.0186430	−	0.00678550i
$417$		0			0
$418$	−35.2990	−	42.0677i	−1.72653	−	2.05760i
$419$	−14.7586	−	5.37170i	−0.721006	−	0.262425i	−0.0446532	−	0.999003i	$-0.514218\pi$
$419$	−14.7586	−	5.37170i	−0.721006	−	0.262425i	−0.676353	+	0.736578i	$0.736441\pi$
$420$		0			0
$421$	−2.01941	+	11.4527i	−0.0984202	+	0.558168i	0.895225	+	0.445614i	$0.147014\pi$
$421$	−2.01941	+	11.4527i	−0.0984202	+	0.558168i	−0.993646	+	0.112555i	$0.964097\pi$
$422$			24.3443i			1.18506i
$423$		0			0
$424$	−25.3230			−1.22980
$425$	−12.2849	+	4.47135i	−0.595907	+	0.216892i
$426$		0			0
$427$	1.40492	+	2.71663i	0.0679890	+	0.131467i
$428$	−35.9262	−	42.8152i	−1.73656	−	2.06955i
$429$		0			0
$430$	10.5047	−	12.5190i	0.506581	−	0.603720i
$431$	12.5999	−	7.27456i	0.606916	−	0.350403i	−0.164841	−	0.986320i	$-0.552711\pi$
$431$	12.5999	−	7.27456i	0.606916	−	0.350403i	0.771758	+	0.635917i	$0.219378\pi$
$432$		0			0
$433$		−	12.8056i		−	0.615396i	−0.951484	−	0.307698i	$-0.900441\pi$
$433$		−	12.8056i		−	0.615396i	0.951484	−	0.307698i	$-0.0995587\pi$
$434$	0.794279	−	1.90308i	0.0381266	−	0.0913507i
$435$		0			0
$436$	2.84379	+	16.1280i	0.136193	+	0.772389i
$437$	−30.0107	+	25.1820i	−1.43561	+	1.20462i
$438$		0			0
$439$	10.3334	+	28.3908i	0.493187	+	1.35502i	0.897748	+	0.440509i	$0.145202\pi$
$439$	10.3334	+	28.3908i	0.493187	+	1.35502i	−0.404561	+	0.914511i	$0.632576\pi$
$440$	33.5168	−	58.0528i	1.59785	−	2.76756i
$441$		0			0
$442$	0.753770	+	1.30557i	0.0358532	+	0.0620995i
$443$	16.6774	−	19.8753i	0.792367	−	0.944306i	−0.207054	−	0.978329i	$-0.566388\pi$
$443$	16.6774	−	19.8753i	0.792367	−	0.944306i	0.999421	+	0.0340234i	$0.0108321\pi$
$444$		0			0
$445$	0.435656	+	2.47073i	0.0206521	+	0.117124i
$446$	−54.1959	+	45.4758i	−2.56625	+	2.15334i
$447$		0			0
$448$	5.31473	+	6.96497i	0.251098	+	0.329064i
$449$	−4.52779	+	2.61412i	−0.213680	+	0.123368i	−0.603020	−	0.797726i	$-0.706036\pi$
$449$	−4.52779	+	2.61412i	−0.213680	+	0.123368i	0.389341	+	0.921094i	$0.372703\pi$
$450$		0			0
$451$		−	28.0353i		−	1.32013i
$452$	−11.4910	−	2.02617i	−0.540490	−	0.0953029i
$453$		0			0
$454$	18.9680	−	3.34458i	0.890214	−	0.156969i
$455$	−0.456722	+	0.712676i	−0.0214114	+	0.0334108i
$456$		0			0
$457$	6.70647	−	38.0343i	0.313715	−	1.77917i	−0.265620	−	0.964078i	$-0.585576\pi$
$457$	6.70647	−	38.0343i	0.313715	−	1.77917i	0.579335	−	0.815090i	$-0.303312\pi$
$458$	17.8716	+	30.9545i	0.835085	+	1.44641i
$459$		0			0
$460$	−77.1194	−	44.5249i	−3.59571	−	2.07598i
$461$	−15.4949	+	5.63970i	−0.721671	+	0.262667i	−0.676635	−	0.736318i	$-0.736563\pi$
$461$	−15.4949	+	5.63970i	−0.721671	+	0.262667i	−0.0450362	+	0.998985i	$0.514340\pi$
$462$		0			0
$463$	31.2960	−	26.2605i	1.45445	−	1.22043i	0.525198	−	0.850980i	$-0.323991\pi$
$463$	31.2960	−	26.2605i	1.45445	−	1.22043i	0.929251	−	0.369448i	$-0.120453\pi$
$464$	7.32153	−	20.1157i	0.339893	−	0.933850i
$465$		0			0
$466$	−9.81814	+	55.6814i	−0.454816	+	2.57939i
$467$	−19.3503	−	33.5157i	−0.895424	−	1.55092i	−0.833279	−	0.552852i	$-0.813539\pi$
$467$	−19.3503	−	33.5157i	−0.895424	−	1.55092i	−0.0621443	−	0.998067i	$-0.519794\pi$
$468$		0			0
$469$	−8.74441	−	27.9958i	−0.403779	−	1.29273i
$470$	34.3267	+	6.05273i	1.58337	+	0.279192i
$471$		0			0
$472$	−60.1508	+	10.6062i	−2.76866	+	0.488190i
$473$	−9.75955	+	1.72087i	−0.448744	+	0.0791258i
$474$		0			0
$475$	13.0537	+	2.30173i	0.598947	+	0.105610i
$476$	39.8576	−	43.2630i	1.82687	−	1.98296i
$477$		0			0
$478$	29.9537	+	51.8813i	1.37005	+	2.37300i
$479$	−5.01429	+	28.4374i	−0.229109	+	1.29934i	0.625564	+	0.780172i	$0.284869\pi$
$479$	−5.01429	+	28.4374i	−0.229109	+	1.29934i	−0.854673	+	0.519167i	$0.826242\pi$
$480$		0			0
$481$	0.0765089	−	0.210206i	0.00348850	−	0.00958459i
$482$	26.1188	−	21.9163i	1.18968	−	0.998260i
$483$		0			0
$484$	−26.4778	+	9.63714i	−1.20354	+	0.438052i
$485$	14.2013	+	8.19912i	0.644848	+	0.372303i
$486$		0			0
$487$	10.6879	+	18.5119i	0.484313	+	0.838854i	0.999838	−	0.0180204i	$-0.00573637\pi$
$487$	10.6879	+	18.5119i	0.484313	+	0.838854i	−0.515525	+	0.856875i	$0.672403\pi$
$488$	1.17063	−	6.63899i	0.0529921	−	0.300533i
$489$		0			0
$490$	46.6067	+	12.7571i	2.10548	+	0.576307i
$491$	17.7129	−	3.12326i	0.799372	−	0.140951i	0.240982	−	0.970530i	$-0.422531\pi$
$491$	17.7129	−	3.12326i	0.799372	−	0.140951i	0.558390	+	0.829579i	$0.311419\pi$
$492$		0			0
$493$	18.0206	+	3.17752i	0.811606	+	0.143108i
$494$		−	1.52850i		−	0.0687705i
$495$		0			0
$496$	−1.61672	+	0.933411i	−0.0725927	+	0.0419114i
$497$	−13.2881	+	10.1397i	−0.596054	+	0.454829i
$498$		0			0
$499$	−8.16488	+	6.85115i	−0.365510	+	0.306700i	−0.806983	−	0.590575i	$-0.798901\pi$
$499$	−8.16488	+	6.85115i	−0.365510	+	0.306700i	0.441472	+	0.897275i	$0.354456\pi$
$500$	−5.06696	−	28.7362i	−0.226602	−	1.28512i
$501$		0			0
$502$	−15.4240	+	18.3816i	−0.688405	+	0.820410i
$503$	−1.68293	−	2.91493i	−0.0750383	−	0.129970i	0.826065	−	0.563575i	$-0.190575\pi$
$503$	−1.68293	−	2.91493i	−0.0750383	−	0.129970i	−0.901103	+	0.433605i	$0.857241\pi$
$504$		0			0
$505$	−11.3109	+	19.5911i	−0.503328	+	0.871790i
$506$	27.0201	+	74.2370i	1.20119	+	3.30024i
$507$		0			0
$508$	4.09961	−	3.43998i	0.181891	−	0.152624i
$509$	−1.45437	−	8.24815i	−0.0644639	−	0.365593i	−0.999926	−	0.0121658i	$-0.996127\pi$
$509$	−1.45437	−	8.24815i	−0.0644639	−	0.365593i	0.935462	−	0.353427i	$-0.114984\pi$
$510$		0			0
$511$	−0.873387	−	6.77466i	−0.0386364	−	0.299693i
$512$		−	49.3168i		−	2.17951i
$513$		0			0
$514$	12.0415	−	6.95217i	0.531128	−	0.306647i
$515$	−1.74008	+	2.07375i	−0.0766771	+	0.0913802i
$516$		0			0
$517$	−13.5866	−	16.1919i	−0.597538	−	0.712118i
$518$	−12.7562	−	0.591297i	−0.560477	−	0.0259801i
$519$		0			0
$520$	1.75327	−	0.638139i	0.0768861	−	0.0279842i
$521$	16.2480			0.711838			0.355919	−	0.934517i	$-0.384168\pi$
$521$	16.2480			0.711838			0.355919	+	0.934517i	$0.384168\pi$
$522$		0			0
$523$			28.2596i			1.23571i	0.786294	+	0.617853i	$0.211997\pi$
$523$			28.2596i			1.23571i	−0.786294	+	0.617853i	$0.788003\pi$
$524$	5.62005	−	31.8729i	0.245513	−	1.39237i
$525$		0			0
$526$	19.7653	+	7.19397i	0.861806	+	0.313672i
$527$	−1.02574	−	1.22243i	−0.0446820	−	0.0532499i
$528$		0			0
$529$	31.3472	−	11.4094i	1.36292	−	0.496062i
$530$	−29.9744			−1.30201
$531$		0			0
$532$	−56.9299	+	17.7819i	−2.46822	+	0.770942i
$533$	0.501584	−	0.597765i	0.0217260	−	0.0258921i
$534$		0			0
$535$	−22.8367	−	27.2158i	−0.987319	−	1.17664i
$536$	−22.1113	+	60.7502i	−0.955062	+	2.62401i
$537$		0			0
$538$	−16.3783	−	44.9990i	−0.706119	−	1.94005i
$539$	−16.6778	−	24.0929i	−0.718363	−	1.03775i
$540$		0			0
$541$	3.36773	−	5.83309i	0.144790	−	0.250784i	−0.784504	−	0.620123i	$-0.787083\pi$
$541$	3.36773	−	5.83309i	0.144790	−	0.250784i	0.929295	+	0.369339i	$0.120416\pi$
$542$	−48.1325	−	40.3880i	−2.06747	−	1.73481i
$543$		0			0
$544$	−17.6036	+	3.10398i	−0.754746	+	0.133082i
$545$	1.80768	+	10.2518i	0.0774324	+	0.439141i
$546$		0			0
$547$	−31.5987	−	26.5144i	−1.35106	−	1.13368i	−0.978633	−	0.205615i	$-0.934080\pi$
$547$	−31.5987	−	26.5144i	−1.35106	−	1.13368i	−0.372429	−	0.928061i	$-0.621475\pi$
$548$	−60.9272	+	35.1764i	−2.60268	+	1.50266i
$549$		0			0
$550$	13.3649	−	23.1487i	0.569881	−	0.987063i
$551$	−14.2124	−	11.9256i	−0.605469	−	0.508049i
$552$		0			0
$553$	−1.93448	+	41.7332i	−0.0822627	+	1.77468i
$554$	19.1953	−	52.7386i	0.815530	−	2.24065i
$555$		0			0
$556$	14.3801	+	39.5090i	0.609852	+	1.67555i
$557$	5.64369	+	3.25839i	0.239131	+	0.138062i	0.614777	−	0.788701i	$-0.289246\pi$
$557$	5.64369	+	3.25839i	0.239131	+	0.138062i	−0.375646	+	0.926763i	$0.622579\pi$
$558$		0			0
$559$	−0.238880	−	0.137917i	−0.0101036	−	0.00583329i
$560$	−26.5360	−	34.7755i	−1.12135	−	1.46953i
$561$		0			0
$562$	−28.1554	−	10.2477i	−1.18766	−	0.432274i
$563$	−25.6976	−	9.35315i	−1.08302	−	0.394188i	−0.261991	−	0.965070i	$-0.584379\pi$
$563$	−25.6976	−	9.35315i	−1.08302	−	0.394188i	−0.821032	+	0.570882i	$0.806601\pi$
$564$		0			0
$565$	−7.30431	−	1.28795i	−0.307295	−	0.0541844i
$566$	−10.1623			−0.427155
$567$		0			0
$568$	36.8433			1.54591
$569$	−28.6452	−	5.05093i	−1.20087	−	0.211746i	−0.462796	−	0.886465i	$-0.653154\pi$
$569$	−28.6452	−	5.05093i	−1.20087	−	0.211746i	−0.738075	+	0.674719i	$0.764265\pi$
$570$		0			0
$571$	−16.3768	−	5.96065i	−0.685346	−	0.249446i	−0.0242047	−	0.999707i	$-0.507705\pi$
$571$	−16.3768	−	5.96065i	−0.685346	−	0.249446i	−0.661141	+	0.750262i	$0.729928\pi$
$572$	−1.97981	−	0.720593i	−0.0827801	−	0.0301295i
$573$		0			0
$574$	−41.1088	−	17.1574i	−1.71585	−	0.716136i
$575$	−16.5141	−	9.53441i	−0.688685	−	0.397612i
$576$		0			0
$577$	−19.6718	−	11.3575i	−0.818949	−	0.472821i	0.0311048	−	0.999516i	$-0.490097\pi$
$577$	−19.6718	−	11.3575i	−0.818949	−	0.472821i	−0.850054	+	0.526696i	$0.823431\pi$
$578$	−8.15999	−	22.4194i	−0.339411	−	0.932524i
$579$		0			0
$580$	14.4237	−	39.6287i	0.598911	−	1.64549i
$581$	26.7042	−	13.8102i	1.10788	−	0.572946i
$582$		0			0
$583$	13.9241	+	11.6837i	0.576677	+	0.483890i
$584$	−7.52821	+	13.0392i	−0.311519	+	0.539567i
$585$		0			0
$586$	3.86842	−	2.23344i	0.159803	−	0.0922624i
$587$	−1.35014	−	1.13291i	−0.0557264	−	0.0467600i	0.614499	−	0.788918i	$-0.289358\pi$
$587$	−1.35014	−	1.13291i	−0.0557264	−	0.0467600i	−0.670225	+	0.742158i	$0.733803\pi$
$588$		0			0
$589$	0.280955	+	1.59338i	0.0115766	+	0.0656539i
$590$	−71.1994	+	12.5544i	−2.93123	+	0.516856i
$591$		0			0
$592$	8.85562	+	7.43075i	0.363964	+	0.305402i
$593$	−20.7313	+	35.9077i	−0.851334	+	1.47455i	0.0286712	+	0.999589i	$0.490872\pi$
$593$	−20.7313	+	35.9077i	−0.851334	+	1.47455i	−0.880005	+	0.474965i	$0.842461\pi$
$594$		0			0
$595$	25.3358	−	27.5004i	1.03867	−	1.12741i
$596$	24.7565	+	68.0180i	1.01407	+	2.78613i
$597$		0			0
$598$	−0.752069	+	2.06629i	−0.0307544	+	0.0844970i
$599$	−13.6209	−	16.2328i	−0.556535	−	0.663253i	0.412274	−	0.911060i	$-0.364735\pi$
$599$	−13.6209	−	16.2328i	−0.556535	−	0.663253i	−0.968809	+	0.247807i	$0.920290\pi$
$600$		0			0
$601$	−5.31277	+	6.33151i	−0.216712	+	0.258268i	−0.863438	−	0.504455i	$-0.831693\pi$
$601$	−5.31277	+	6.33151i	−0.216712	+	0.258268i	0.646726	+	0.762723i	$0.276138\pi$
$602$	−3.44941	+	15.3638i	−0.140588	+	0.626182i
$603$		0			0
$604$	64.6571			2.63086
$605$	−16.8308	+	6.12592i	−0.684270	+	0.249054i
$606$		0			0
$607$	−10.1572	−	12.1049i	−0.412267	−	0.491321i	0.519452	−	0.854499i	$-0.326136\pi$
$607$	−10.1572	−	12.1049i	−0.412267	−	0.491321i	−0.931720	+	0.363179i	$0.881691\pi$
$608$	17.0307	+	6.19865i	0.690684	+	0.251389i
$609$		0			0
$610$	1.38566	−	7.85846i	0.0561037	−	0.318180i
$611$		−	0.588321i		−	0.0238009i
$612$		0			0
$613$	−18.8108			−0.759762			−0.379881	−	0.925035i	$-0.624035\pi$
$613$	−18.8108			−0.759762			−0.379881	+	0.925035i	$0.624035\pi$
$614$	46.4403	−	16.9029i	1.87418	−	0.682145i
$615$		0			0
$616$	−2.99069	+	64.5191i	−0.120498	+	2.59955i
$617$	1.65294	+	1.96989i	0.0665447	+	0.0793049i	0.798290	−	0.602273i	$-0.205738\pi$
$617$	1.65294	+	1.96989i	0.0665447	+	0.0793049i	−0.731745	+	0.681578i	$0.761294\pi$
$618$		0			0
$619$	−10.1248	+	12.0663i	−0.406951	+	0.484985i	−0.930126	−	0.367240i	$-0.880303\pi$
$619$	−10.1248	+	12.0663i	−0.406951	+	0.484985i	0.523175	+	0.852225i	$0.324747\pi$
$620$	−3.18499	+	1.83885i	−0.127912	+	0.0738501i
$621$		0			0
$622$		−	66.5577i		−	2.66872i
$623$	−1.46642	−	1.92174i	−0.0587508	−	0.0769930i
$624$		0			0
$625$	−5.42623	−	30.7737i	−0.217049	−	1.23095i
$626$	9.70829	−	8.14622i	0.388021	−	0.325588i
$627$		0			0
$628$	−4.77266	−	13.1128i	−0.190450	−	0.523257i
$629$	−4.94086	+	8.55781i	−0.197005	+	0.341222i
$630$		0			0
$631$	−21.8676	−	37.8758i	−0.870536	−	1.50781i	−0.861443	−	0.507855i	$-0.830439\pi$
$631$	−21.8676	−	37.8758i	−0.870536	−	1.50781i	−0.00909374	−	0.999959i	$-0.502895\pi$
$632$	59.1930	−	70.5435i	2.35457	−	2.80607i
$633$		0			0
$634$	−13.4916	−	76.5146i	−0.535819	−	3.03878i
$635$	2.60594	−	2.18665i	0.103414	−	0.0867744i
$636$		0			0
$637$	0.0754487	−	0.812090i	0.00298938	−	0.0321762i
$638$	−32.4009	+	18.7067i	−1.28276	+	0.740604i
$639$		0			0
$640$		−	41.9317i		−	1.65750i
$641$	−24.5241	−	4.32427i	−0.968645	−	0.170798i	−0.333125	−	0.942883i	$-0.608103\pi$
$641$	−24.5241	−	4.32427i	−0.968645	−	0.170798i	−0.635520	+	0.772084i	$0.719214\pi$
$642$		0			0
$643$	−22.2139	+	3.91690i	−0.876029	+	0.154468i	−0.593542	−	0.804803i	$-0.702271\pi$
$643$	−22.2139	+	3.91690i	−0.876029	+	0.154468i	−0.282488	+	0.959271i	$0.591160\pi$
$644$	85.7095	+	3.97294i	3.37743	+	0.156556i
$645$		0			0
$646$	−11.7249	+	66.4950i	−0.461308	+	2.61621i
$647$	−1.19357	−	2.06732i	−0.0469239	−	0.0812747i	0.841609	−	0.540087i	$-0.181609\pi$
$647$	−1.19357	−	2.06732i	−0.0469239	−	0.0812747i	−0.888533	+	0.458812i	$0.848275\pi$
$648$		0			0
$649$	37.9680	+	21.9208i	1.49038	+	0.860468i
$650$	0.699122	−	0.254459i	0.0274218	−	0.00998072i
$651$		0			0
$652$	25.5218	−	21.4153i	0.999509	−	0.838688i
$653$	12.6049	−	34.6318i	0.493269	−	1.35525i	−0.404403	−	0.914581i	$-0.632521\pi$
$653$	12.6049	−	34.6318i	0.493269	−	1.35525i	0.897672	−	0.440665i	$-0.145257\pi$
$654$		0			0
$655$	3.57242	−	20.2602i	0.139586	−	0.791633i
$656$	20.1628	+	34.9230i	0.787226	+	1.36352i
$657$		0			0
$658$	−32.0574	+	10.0130i	−1.24973	+	0.390349i
$659$	7.39431	+	1.30382i	0.288041	+	0.0507895i	0.315802	−	0.948825i	$-0.397726\pi$
$659$	7.39431	+	1.30382i	0.288041	+	0.0507895i	−0.0277605	+	0.999615i	$0.508838\pi$
$660$		0			0
$661$	−8.19948	+	1.44579i	−0.318923	+	0.0562347i	−0.330818	−	0.943695i	$-0.607325\pi$
$661$	−8.19948	+	1.44579i	−0.318923	+	0.0562347i	0.0118952	+	0.999929i	$0.496214\pi$
$662$	−40.6073	+	7.16016i	−1.57825	+	0.278288i
$663$		0			0
$664$	−65.2606	−	11.5072i	−2.53260	−	0.446566i
$665$	−36.1879	+	11.3032i	−1.40331	+	0.438318i
$666$		0			0
$667$	13.3452	+	23.1145i	0.516727	+	0.894998i
$668$	1.23684	−	7.01445i	0.0478546	−	0.271397i
$669$		0			0
$670$	−26.1727	+	71.9090i	−1.01114	+	2.77809i
$671$	−3.70683	+	3.11040i	−0.143100	+	0.120076i
$672$		0			0
$673$	36.7067	−	13.3601i	1.41494	−	0.514995i	0.482363	−	0.875971i	$-0.339779\pi$
$673$	36.7067	−	13.3601i	1.41494	−	0.514995i	0.932575	+	0.360976i	$0.117556\pi$
$674$	−3.12535	−	1.80442i	−0.120384	−	0.0695038i
$675$		0			0
$676$	28.0494	+	48.5830i	1.07882	+	1.86858i
$677$	3.32662	−	18.8662i	0.127852	−	0.725087i	−0.851720	−	0.523997i	$-0.824440\pi$
$677$	3.32662	−	18.8662i	0.127852	−	0.725087i	0.979573	−	0.201090i	$-0.0644484\pi$
$678$		0			0
$679$	−15.7831	−	0.731604i	−0.605701	−	0.0280764i
$680$	−81.1684	+	14.3122i	−3.11267	+	0.548847i
$681$		0			0
$682$	3.21315	+	0.566564i	0.123038	+	0.0216949i
$683$			41.1007i			1.57268i	0.617796	+	0.786338i	$0.288026\pi$
$683$			41.1007i			1.57268i	−0.617796	+	0.786338i	$0.711974\pi$
$684$		0			0
$685$	−38.7288	+	22.3601i	−1.47975	+	0.854335i
$686$	−45.5346	+	9.71034i	−1.73852	+	0.370743i
$687$		0			0
$688$	10.9196	−	9.16266i	0.416307	−	0.349323i
$689$	0.0878526	+	0.498237i	0.00334692	+	0.0189813i
$690$		0			0
$691$	27.2928	−	32.5263i	1.03827	−	1.23736i	0.0674047	−	0.997726i	$-0.478528\pi$
$691$	27.2928	−	32.5263i	1.03827	−	1.23736i	0.970863	−	0.239634i	$-0.0770274\pi$
$692$	39.4868	+	68.3932i	1.50106	+	2.59992i
$693$		0			0
$694$	−8.00228	+	13.8604i	−0.303763	+	0.526132i
$695$	9.14080	+	25.1141i	0.346730	+	0.952634i
$696$		0			0
$697$	−26.4060	+	22.1573i	−1.00020	+	0.839266i
$698$	−3.82508	−	21.6931i	−0.144781	−	0.821097i
$699$		0			0
$700$	−17.6107	−	23.0789i	−0.665624	−	0.872301i
$701$			18.1159i			0.684229i	0.939658	+	0.342114i	$0.111143\pi$
$701$			18.1159i			0.684229i	−0.939658	+	0.342114i	$0.888857\pi$
$702$		0			0
$703$	8.67679	−	5.00955i	0.327252	−	0.188939i
$704$	−8.91004	+	10.6186i	−0.335810	+	0.400202i
$705$		0			0
$706$	3.54983	+	4.23052i	0.133600	+	0.159218i
$707$	1.00927	−	21.7732i	0.0379574	−	0.818867i
$708$		0			0
$709$	8.87470	−	3.23013i	0.333296	−	0.121310i	−0.169951	−	0.985453i	$-0.554361\pi$
$709$	8.87470	−	3.23013i	0.333296	−	0.121310i	0.503247	+	0.864143i	$0.332139\pi$
$710$	43.6108			1.63668
$711$		0			0
$712$			5.32832i			0.199687i
$713$	0.404182	−	2.29223i	0.0151367	−	0.0858448i
$714$		0			0
$715$	−1.25848	−	0.458050i	−0.0470645	−	0.0171301i
$716$	−11.7189	−	13.9660i	−0.437955	−	0.521934i
$717$		0			0
$718$	31.4675	−	11.4532i	1.17436	−	0.427431i
$719$	14.5552			0.542817			0.271408	−	0.962464i	$-0.412511\pi$
$719$	14.5552			0.542817			0.271408	+	0.962464i	$0.412511\pi$
$720$		0			0
$721$	0.571388	−	2.54498i	0.0212796	−	0.0947801i
$722$	13.3025	−	15.8533i	0.495068	−	0.589999i
$723$		0			0
$724$	−30.4997	−	36.3481i	−1.13351	−	1.35087i
$725$	3.08864	−	8.48596i	0.114709	−	0.315161i
$726$		0			0
$727$	5.63920	+	15.4936i	0.209146	+	0.574625i	0.999265	−	0.0383287i	$-0.0122034\pi$
$727$	5.63920	+	15.4936i	0.209146	+	0.574625i	−0.790119	+	0.612954i	$0.789981\pi$
$728$	−1.21809	+	1.32216i	−0.0451454	+	0.0490025i
$729$		0			0
$730$	−8.91101	+	15.4343i	−0.329811	+	0.571250i
$731$	9.33416	+	7.83229i	0.345236	+	0.289688i
$732$		0			0
$733$	30.6823	−	5.41012i	1.13328	−	0.199827i	0.424614	−	0.905374i	$-0.360410\pi$
$733$	30.6823	−	5.41012i	1.13328	−	0.199827i	0.708663	+	0.705547i	$0.249299\pi$
$734$	−4.65451	−	26.3970i	−0.171801	−	0.974332i
$735$		0			0
$736$	−19.9728	−	16.7592i	−0.736209	−	0.617753i
$737$	40.1874	−	23.2022i	1.48032	−	0.854665i
$738$		0			0
$739$	2.09919	−	3.63590i	0.0772198	−	0.133749i	−0.824830	−	0.565381i	$-0.808729\pi$
$739$	2.09919	−	3.63590i	0.0772198	−	0.133749i	0.902049	+	0.431633i	$0.142062\pi$
$740$	17.4459	+	14.6388i	0.641324	+	0.538134i
$741$		0			0
$742$	25.6535	−	13.2669i	0.941771	−	0.487043i
$743$	15.8926	−	43.6646i	0.583044	−	1.60190i	−0.199906	−	0.979815i	$-0.564064\pi$
$743$	15.8926	−	43.6646i	0.583044	−	1.60190i	0.782950	−	0.622085i	$-0.213714\pi$
$744$		0			0
$745$	15.7367	+	43.2361i	0.576547	+	1.58405i
$746$	30.4806	+	17.5980i	1.11597	+	0.644308i
$747$		0			0
$748$	80.6011	+	46.5351i	2.94707	+	1.70149i
$749$	31.5907	+	13.1848i	1.15430	+	0.481764i
$750$		0			0
$751$	−48.5632	−	17.6756i	−1.77210	−	0.644990i	−0.999954	−	0.00954055i	$-0.996963\pi$
$751$	−48.5632	−	17.6756i	−1.77210	−	0.644990i	−0.772142	−	0.635450i	$-0.780815\pi$
$752$	28.5697	+	10.3985i	1.04183	+	0.379194i
$753$		0			0
$754$	−1.02553	−	0.180829i	−0.0373476	−	0.00658540i
$755$	41.0997			1.49577
$756$		0			0
$757$	−34.5687			−1.25642			−0.628210	−	0.778044i	$-0.716212\pi$
$757$	−34.5687			−1.25642			−0.628210	+	0.778044i	$0.716212\pi$
$758$	−85.6855	−	15.1087i	−3.11224	−	0.548772i
$759$		0			0
$760$	78.5268	+	28.5814i	2.84847	+	1.03676i
$761$	8.42366	+	3.06596i	0.305357	+	0.111141i	0.490154	−	0.871636i	$-0.336940\pi$
$761$	8.42366	+	3.06596i	0.305357	+	0.111141i	−0.184797	+	0.982777i	$0.559163\pi$
$762$		0			0
$763$	−6.08463	−	7.97393i	−0.220279	−	0.288675i
$764$	38.0034	+	21.9413i	1.37491	+	0.793807i
$765$		0			0
$766$	36.8448	+	21.2724i	1.33126	+	0.768602i
$767$	0.417359	+	1.14669i	0.0150700	+	0.0414044i
$768$		0			0
$769$	−2.93294	+	8.05819i	−0.105765	+	0.290586i	−0.981275	−	0.192614i	$-0.938303\pi$
$769$	−2.93294	+	8.05819i	−0.105765	+	0.290586i	0.875510	+	0.483200i	$0.160526\pi$
$770$	−3.54003	+	76.3701i	−0.127574	+	2.75219i
$771$		0			0
$772$	−28.5971	−	23.9959i	−1.02923	−	0.863630i
$773$	0.449480	−	0.778522i	0.0161667	−	0.0280015i	−0.857829	−	0.513935i	$-0.828187\pi$
$773$	0.449480	−	0.778522i	0.0161667	−	0.0280015i	0.873996	+	0.485934i	$0.161520\pi$
$774$		0			0
$775$	−0.682022	+	0.393766i	−0.0244990	+	0.0141445i
$776$	26.6789	+	22.3863i	0.957717	+	0.803620i
$777$		0			0
$778$	−1.90906	−	10.8268i	−0.0684432	−	0.388161i
$779$	34.4189	−	6.06897i	1.23318	−	0.217444i
$780$		0			0
$781$	−20.2586	−	16.9990i	−0.724911	−	0.608273i
$782$	48.5677	−	84.1218i	1.73678	−	3.00819i
$783$		0			0
$784$	38.1026	+	18.0175i	1.36081	+	0.643482i
$785$	−3.03377	−	8.33523i	−0.108280	−	0.297497i
$786$		0			0
$787$	−13.7718	+	37.8376i	−0.490911	+	1.34877i	0.408938	+	0.912562i	$0.365899\pi$
$787$	−13.7718	+	37.8376i	−0.490911	+	1.34877i	−0.899848	+	0.436203i	$0.856323\pi$
$788$	−2.00442	−	2.38878i	−0.0714046	−	0.0850966i
$789$		0			0
$790$	70.0658	−	83.5011i	2.49283	−	2.97084i
$791$	6.82143	−	2.13065i	0.242542	−	0.0757573i
$792$		0			0
$793$	−0.134685			−0.00478281
$794$	25.5839	−	9.31177i	0.907938	−	0.330462i
$795$		0			0
$796$	60.4713	+	72.0668i	2.14335	+	2.55434i
$797$	32.3110	+	11.7602i	1.14451	+	0.416569i	0.843542	−	0.537064i	$-0.180467\pi$
$797$	32.3110	+	11.7602i	1.14451	+	0.416569i	0.300972	+	0.953633i	$0.402689\pi$
$798$		0			0
$799$	−4.51291	+	25.5940i	−0.159655	+	0.905450i
$800$			8.82159i			0.311890i
$801$		0			0
$802$	−16.3307			−0.576658
$803$	10.1556	−	3.69633i	0.358383	−	0.130441i
$804$		0			0
$805$	54.4818	+	2.52543i	1.92023	+	0.0890096i
$806$	0.0583737	+	0.0695671i	0.00205613	+	0.00245040i
$807$		0			0
$808$	−30.8824	+	36.8042i	−1.08644	+	1.29477i
$809$	26.8173	−	15.4830i	0.942848	−	0.544353i	0.0519959	−	0.998647i	$-0.483442\pi$
$809$	26.8173	−	15.4830i	0.942848	−	0.544353i	0.890852	+	0.454294i	$0.150108\pi$
$810$		0			0
$811$			44.9726i			1.57920i	0.613622	+	0.789600i	$0.289712\pi$
$811$			44.9726i			1.57920i	−0.613622	+	0.789600i	$0.710288\pi$
$812$	5.19549	+	40.3002i	0.182326	+	1.41426i
$813$		0			0
$814$	−3.50842	−	19.8972i	−0.122970	−	0.697397i
$815$	16.2231	−	13.6128i	0.568270	−	0.476835i
$816$		0			0
$817$	−4.22542	−	11.6092i	−0.147829	−	0.406156i
$818$	−19.4710	+	33.7248i	−0.680789	+	1.17916i
$819$		0			0
$820$	39.7215	+	68.7996i	1.38713	+	2.40259i
$821$	−10.7469	+	12.8077i	−0.375071	+	0.446992i	−0.920252	−	0.391326i	$-0.872016\pi$
$821$	−10.7469	+	12.8077i	−0.375071	+	0.446992i	0.545181	+	0.838318i	$0.316461\pi$
$822$		0			0
$823$	−4.81216	−	27.2911i	−0.167741	−	0.951308i	−0.946193	−	0.323603i	$-0.895106\pi$
$823$	−4.81216	−	27.2911i	−0.167741	−	0.951308i	0.778452	−	0.627705i	$-0.216005\pi$
$824$	−4.40425	+	3.69561i	−0.153429	+	0.128743i
$825$		0			0
$826$	55.3792	−	42.2580i	1.92689	−	1.47034i
$827$	−12.2895	+	7.09535i	−0.427348	+	0.246730i	−0.698216	−	0.715887i	$-0.746023\pi$
$827$	−12.2895	+	7.09535i	−0.427348	+	0.246730i	0.270868	+	0.962616i	$0.412689\pi$
$828$		0			0
$829$		−	4.62117i		−	0.160500i	−0.996775	−	0.0802500i	$-0.974428\pi$
$829$		−	4.62117i		−	0.160500i	0.996775	−	0.0802500i	$-0.0255719\pi$
$830$	−77.2479	−	13.6209i	−2.68131	−	0.472788i
$831$		0			0
$832$	−0.379957	+	0.0669967i	−0.0131726	+	0.00232269i
$833$	−9.51168	+	34.7500i	−0.329560	+	1.20401i
$834$		0			0
$835$	0.786204	−	4.45878i	0.0272077	−	0.154303i
$836$	−47.1821	−	81.7217i	−1.63183	−	2.82640i
$837$		0			0
$838$	−34.1934	−	19.7416i	−1.18119	−	0.681962i
$839$	−26.3117	+	9.57669i	−0.908382	+	0.330624i	−0.753607	−	0.657325i	$-0.771688\pi$
$839$	−26.3117	+	9.57669i	−0.908382	+	0.330624i	−0.154776	+	0.987950i	$0.549465\pi$
$840$		0			0
$841$	12.5325	−	10.5160i	0.432156	−	0.362622i
$842$	−9.99904	+	27.4721i	−0.344590	+	0.946753i
$843$		0			0
$844$	−7.26407	+	41.1966i	−0.250040	+	1.41805i
$845$	17.8298	+	30.8821i	0.613364	+	1.06238i
$846$		0			0
$847$	11.6932	−	12.6923i	0.401784	−	0.436112i
$848$	−25.7478	−	4.54004i	−0.884184	−	0.155906i
$849$		0			0
$850$	−32.3661	+	5.70702i	−1.11015	+	0.195749i
$851$	−14.1945	+	2.50288i	−0.486582	+	0.0857975i
$852$		0			0
$853$	−26.0162	−	4.58736i	−0.890779	−	0.157068i	−0.290515	−	0.956870i	$-0.593827\pi$
$853$	−26.0162	−	4.58736i	−0.890779	−	0.157068i	−0.600264	+	0.799802i	$0.704938\pi$
$854$	2.29230	+	7.33895i	0.0784408	+	0.251134i
$855$		0			0
$856$	−37.7271	−	65.3453i	−1.28949	−	2.23345i
$857$	−1.78248	+	10.1089i	−0.0608882	+	0.345314i	0.939110	+	0.343616i	$0.111652\pi$
$857$	−1.78248	+	10.1089i	−0.0608882	+	0.345314i	−0.999999	+	0.00169852i	$0.999459\pi$
$858$		0			0
$859$	0.383066	−	1.05247i	0.0130700	−	0.0359097i	−0.932986	−	0.359913i	$-0.882807\pi$
$859$	0.383066	−	1.05247i	0.0130700	−	0.0359097i	0.946056	+	0.324003i	$0.105029\pi$
$860$	21.5121	−	18.0508i	0.733556	−	0.615526i
$861$		0			0
$862$	34.3696	−	12.5095i	1.17063	−	0.426076i
$863$	−22.3865	−	12.9249i	−0.762046	−	0.439968i	0.0679836	−	0.997686i	$-0.478343\pi$
$863$	−22.3865	−	12.9249i	−0.762046	−	0.439968i	−0.830030	+	0.557719i	$0.811677\pi$
$864$		0			0
$865$	25.1001	+	43.4746i	0.853428	+	1.47818i
$866$	5.59012	−	31.7031i	0.189960	−	1.07732i
$867$		0			0
$868$	1.91197	−	2.98348i	0.0648966	−	0.101266i
$869$	−65.0957	+	11.4781i	−2.20822	+	0.389369i
$870$		0			0
$871$	1.27199	+	0.224285i	0.0430996	+	0.00759962i
$872$			22.1089i			0.748702i
$873$		0			0
$874$	−85.2914	+	49.2430i	−2.88502	+	1.66567i
$875$	10.8414	+	14.2076i	0.366505	+	0.480306i
$876$		0			0
$877$	14.6459	−	12.2894i	0.494557	−	0.414982i	−0.361099	−	0.932527i	$-0.617598\pi$
$877$	14.6459	−	12.2894i	0.494557	−	0.414982i	0.855656	+	0.517545i	$0.173154\pi$
$878$	13.1891	+	74.7989i	0.445110	+	2.52434i
$879$		0			0
$880$	44.4870	−	53.0176i	1.49966	−	1.78722i
$881$	−17.8333	−	30.8881i	−0.600818	−	1.04065i	−0.992697	−	0.120631i	$-0.961508\pi$
$881$	−17.8333	−	30.8881i	−0.600818	−	1.04065i	0.391879	−	0.920017i	$-0.371825\pi$
$882$		0			0
$883$	−22.8393	+	39.5588i	−0.768602	+	1.33126i	0.169718	+	0.985493i	$0.445714\pi$
$883$	−22.8393	+	39.5588i	−0.768602	+	1.33126i	−0.938321	+	0.345766i	$0.887619\pi$
$884$	0.885999	+	2.43426i	0.0297994	+	0.0818731i
$885$		0			0
$886$	49.9651	−	41.9257i	1.67861	−	1.40852i
$887$	7.00402	+	39.7218i	0.235172	+	1.33373i	0.842251	+	0.539085i	$0.181230\pi$
$887$	7.00402	+	39.7218i	0.235172	+	1.33373i	−0.607080	+	0.794641i	$0.707659\pi$
$888$		0			0
$889$	−1.26246	+	3.02484i	−0.0423417	+	0.101450i
$890$			6.30704i			0.211413i
$891$		0			0
$892$	−105.282	+	60.7848i	−3.52511	+	2.03523i
$893$	16.9375	−	20.1854i	0.566793	−	0.675478i
$894$		0			0
$895$	−7.44919	−	8.87759i	−0.248999	−	0.296745i
$896$	18.5593	+	35.8871i	0.620022	+	1.19891i
$897$		0			0
$898$	−12.3508	+	4.49531i	−0.412150	+	0.150010i
$899$	1.10230			0.0367637
$900$		0			0
$901$		−	22.3489i		−	0.744550i
$902$	12.2385	−	69.4079i	0.407497	−	2.31103i
$903$		0			0
$904$	−14.8023	−	5.38761i	−0.492319	−	0.179189i
$905$	−19.3873	−	23.1049i	−0.644457	−	0.768034i
$906$		0			0
$907$	−32.3007	+	11.7565i	−1.07253	+	0.390367i	−0.817121	−	0.576467i	$-0.804431\pi$
$907$	−32.3007	+	11.7565i	−1.07253	+	0.390367i	−0.255405	+	0.966834i	$0.582209\pi$
$908$	33.0966			1.09835
$909$		0			0
$910$	−1.44183	+	1.56502i	−0.0477962	+	0.0518798i
$911$	−2.82347	+	3.36488i	−0.0935458	+	0.111484i	−0.810787	−	0.585342i	$-0.800960\pi$
$911$	−2.82347	+	3.36488i	−0.0935458	+	0.111484i	0.717241	+	0.696825i	$0.245405\pi$
$912$		0			0
$913$	30.5749	+	36.4377i	1.01188	+	1.20591i
$914$	33.2068	−	91.2350i	1.09838	−	3.01778i
$915$		0			0
$916$	21.0067	+	57.7154i	0.694081	+	1.90697i
$917$	5.90987	+	18.9208i	0.195161	+	0.624821i
$918$		0			0
$919$	−11.3040	+	19.5792i	−0.372886	+	0.645857i	−0.990008	−	0.141010i	$-0.954965\pi$
$919$	−11.3040	+	19.5792i	−0.372886	+	0.645857i	0.617122	+	0.786867i	$0.288298\pi$
$920$	−92.0929	−	77.2752i	−3.03621	−	2.54769i
$921$		0			0
$922$	−40.8232	+	7.19824i	−1.34444	+	0.237061i
$923$	−0.127820	−	0.724901i	−0.00420724	−	0.0238604i
$924$		0			0
$925$	3.73580	+	3.13471i	0.122832	+	0.103069i
$926$	88.9442	−	51.3520i	2.92289	−	1.68753i
$927$		0			0
$928$	6.17373	−	10.6932i	0.202663	−	0.351022i
$929$	−12.2360	−	10.2672i	−0.401449	−	0.336856i	0.419605	−	0.907707i	$-0.362169\pi$
$929$	−12.2360	−	10.2672i	−0.401449	−	0.336856i	−0.821053	+	0.570851i	$0.806613\pi$
$930$		0			0
$931$	25.9684	−	25.6908i	0.851081	−	0.841982i
$932$	−33.2294	+	91.2971i	−1.08847	+	2.99054i
$933$		0			0
$934$	−33.2752	−	91.4228i	−1.08880	−	2.99145i
$935$	51.2346	+	29.5803i	1.67555	+	0.967380i
$936$		0			0
$937$	51.5494	+	29.7620i	1.68404	+	0.972283i	0.958925	+	0.283660i	$0.0915487\pi$
$937$	51.5494	+	29.7620i	1.68404	+	0.972283i	0.725119	+	0.688623i	$0.241785\pi$
$938$	−9.42756	−	73.1273i	−0.307821	−	2.38769i
$939$		0			0
$940$	56.2833	+	20.4854i	1.83576	+	0.668161i
$941$	−38.2145	−	13.9089i	−1.24576	−	0.453418i	−0.366790	−	0.930304i	$-0.619543\pi$
$941$	−38.2145	−	13.9089i	−1.24576	−	0.453418i	−0.878965	+	0.476886i	$0.841766\pi$
$942$		0			0
$943$	−49.5150	−	8.73083i	−1.61243	−	0.284315i
$944$	−63.0613			−2.05247
$945$		0			0
$946$	−24.9132			−0.809999
$947$	38.9630	+	6.87023i	1.26613	+	0.223253i	0.766080	−	0.642745i	$-0.222204\pi$
$947$	38.9630	+	6.87023i	1.26613	+	0.223253i	0.500048	+	0.865998i	$0.333316\pi$
$948$		0			0
$949$	0.282668	+	0.102883i	0.00917578	+	0.00333971i
$950$	31.3128	+	11.3969i	1.01592	+	0.369765i
$951$		0			0
$952$	63.1331	−	48.1747i	2.04616	−	1.56135i
$953$	10.2234	+	5.90251i	0.331170	+	0.191201i	0.656360	−	0.754447i	$-0.272095\pi$
$953$	10.2234	+	5.90251i	0.331170	+	0.191201i	−0.325190	+	0.945649i	$0.605428\pi$
$954$		0			0
$955$	24.1571	+	13.9471i	0.781706	+	0.451318i
$956$	35.2082	+	96.7339i	1.13872	+	3.12860i
$957$		0			0
$958$	−24.8280	+	68.2145i	−0.802158	+	2.20391i
$959$	23.2492	−	36.2785i	0.750757	−	1.17149i
$960$		0			0
$961$	23.6737	+	19.8646i	0.763669	+	0.640794i
$962$	0.281178	−	0.487015i	0.00906556	−	0.0157020i
$963$		0			0
$964$	50.7391	−	29.2942i	1.63420	−	0.943504i
$965$	−18.1780	−	15.2531i	−0.585170	−	0.491016i
$966$		0			0
$967$	−3.86189	−	21.9019i	−0.124190	−	0.704317i	−0.981786	−	0.189992i	$-0.939154\pi$
$967$	−3.86189	−	21.9019i	−0.124190	−	0.704317i	0.857596	−	0.514325i	$-0.171957\pi$
$968$	−37.4617	+	6.60551i	−1.20406	+	0.212309i
$969$		0			0
$970$	31.5794	+	26.4982i	1.01395	+	0.850807i
$971$	1.25978	−	2.18201i	0.0404284	−	0.0700240i	−0.845103	−	0.534603i	$-0.820461\pi$
$971$	1.25978	−	2.18201i	0.0404284	−	0.0700240i	0.885532	+	0.464579i	$0.153794\pi$
$972$		0			0
$973$	−18.9388	−	17.4481i	−0.607151	−	0.559360i
$974$	18.3791	+	50.4961i	0.588904	+	1.61800i
$975$		0			0
$976$	2.38054	−	6.54049i	0.0761993	−	0.209356i
$977$	−11.6467	−	13.8800i	−0.372611	−	0.444060i	0.546857	−	0.837226i	$-0.315824\pi$
$977$	−11.6467	−	13.8800i	−0.372611	−	0.444060i	−0.919468	+	0.393166i	$0.871380\pi$
$978$		0			0
$979$	2.45842	−	2.92983i	0.0785713	−	0.0936377i
$980$	75.0636	+	35.4951i	2.39782	+	1.13385i
$981$		0			0
$982$	45.2158			1.44289
$983$	−37.9664	+	13.8186i	−1.21094	+	0.440746i	−0.867030	−	0.498256i	$-0.833974\pi$
$983$	−37.9664	+	13.8186i	−1.21094	+	0.440746i	−0.343910	+	0.939002i	$0.611752\pi$
$984$		0			0
$985$	−1.27412	−	1.51844i	−0.0405970	−	0.0483816i
$986$	43.2270	+	15.7333i	1.37663	+	0.501052i
$987$		0			0
$988$	0.456087	−	2.58660i	0.0145101	−	0.0822907i
$989$			17.7729i			0.565145i
$990$		0			0
$991$	26.2787			0.834772			0.417386	−	0.908729i	$-0.362946\pi$
$991$	26.2787			0.834772			0.417386	+	0.908729i	$0.362946\pi$
$992$	−1.01185	+	0.368283i	−0.0321263	+	0.0116930i
$993$		0			0
$994$	−37.3242	+	19.3024i	−1.18385	+	0.612236i
$995$	38.4390	+	45.8098i	1.21860	+	1.45227i
$996$		0			0
$997$	8.82324	−	10.5151i	0.279435	−	0.333017i	−0.608012	−	0.793928i	$-0.708033\pi$
$997$	8.82324	−	10.5151i	0.279435	−	0.333017i	0.887447	+	0.460911i	$0.152477\pi$
$998$	−23.2048	+	13.3973i	−0.734536	+	0.424085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.467.21		132
3.2	odd	2		189.2.bd.a.47.2	yes	132
7.3	odd	6		567.2.ba.a.143.2		132
21.17	even	6		189.2.ba.a.101.21	✓	132
27.4	even	9		189.2.ba.a.131.21	yes	132
27.23	odd	18		567.2.ba.a.341.2		132
189.31	odd	18		189.2.bd.a.185.2	yes	132
189.185	even	18	inner	567.2.bd.a.17.21		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.21	✓	132	21.17	even	6
189.2.ba.a.131.21	yes	132	27.4	even	9
189.2.bd.a.47.2	yes	132	3.2	odd	2
189.2.bd.a.185.2	yes	132	189.31	odd	18
567.2.ba.a.143.2		132	7.3	odd	6
567.2.ba.a.341.2		132	27.23	odd	18
567.2.bd.a.17.21		132	189.185	even	18	inner
567.2.bd.a.467.21		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)

\(f(q)\)	\(=\)	\(q+(2.47573 + 0.436538i) q^{2} +(4.05929 + 1.47746i) q^{4} +(2.58032 + 0.939158i) q^{5} +(-2.62404 + 0.338290i) q^{7} +(5.05050 + 2.91591i) q^{8} +(5.97819 + 3.45151i) q^{10} +(-1.43170 - 3.93357i) q^{11} +(0.0398496 - 0.109486i) q^{13} +(-6.64408 - 0.307977i) q^{14} +(4.61245 + 3.87030i) q^{16} +(-2.57344 + 4.45733i) q^{17} +(4.51931 - 2.60922i) q^{19} +(9.08669 + 7.62463i) q^{20} +(-1.82736 - 10.3635i) q^{22} +(-7.39321 + 1.30362i) q^{23} +(1.94579 + 1.63271i) q^{25} +(0.146452 - 0.253662i) q^{26} +(-11.1515 - 2.50369i) q^{28} +(-1.21597 - 3.34086i) q^{29} +(-0.106042 + 0.291348i) q^{31} +(2.23240 + 2.66047i) q^{32} +(-8.31695 + 9.91175i) q^{34} +(-7.08855 - 1.59149i) q^{35} +1.91994 q^{37} +(12.3276 - 4.48688i) q^{38} +(10.2934 + 12.2672i) q^{40} +(6.29347 + 2.29063i) q^{41} +(0.411100 - 2.33146i) q^{43} -18.0828i q^{44} -18.8727 q^{46} +(4.74491 - 1.72700i) q^{47} +(6.77112 - 1.77537i) q^{49} +(4.10452 + 4.89157i) q^{50} +(0.323522 - 0.385559i) q^{52} +(-3.76047 + 2.17111i) q^{53} -11.4945i q^{55} +(-14.2391 - 5.94291i) q^{56} +(-1.55201 - 8.80190i) q^{58} +(-8.02306 + 6.73214i) q^{59} +(-0.395365 - 1.08626i) q^{61} +(-0.389715 + 0.675007i) q^{62} +(-1.65570 - 2.86775i) q^{64} +(0.205649 - 0.245083i) q^{65} +(1.92499 + 10.9172i) q^{67} +(-17.0319 + 14.2915i) q^{68} +(-16.8546 - 7.03452i) q^{70} +(5.47124 - 3.15882i) q^{71} +2.58177i q^{73} +(4.75325 + 0.838127i) q^{74} +(22.2002 - 3.91449i) q^{76} +(5.08753 + 9.83750i) q^{77} +(2.74201 - 15.5507i) q^{79} +(8.26674 + 14.3184i) q^{80} +(14.5810 + 8.41833i) q^{82} +(-10.6778 + 3.88640i) q^{83} +(-10.8264 + 9.08446i) q^{85} +(2.03554 - 5.59261i) q^{86} +(4.23912 - 24.0412i) q^{88} +(0.456832 + 0.791256i) q^{89} +(-0.0675288 + 0.300776i) q^{91} +(-31.9372 - 5.63140i) q^{92} +(12.5010 - 2.20427i) q^{94} +(14.1117 - 2.48828i) q^{95} +(5.88114 + 1.03700i) q^{97} +(17.5385 - 1.43948i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) \) 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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