LMFDB - Embedded newform 567.2.ba.a.341.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] 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("567.143"); 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([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (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			341.10
Character	$\chi$	$=$	567.341
Dual form			567.2.ba.a.143.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.204899 - 0.244189i) q^{2} +(0.329652 - 1.86955i) q^{4} +(2.18935 + 1.83708i) q^{5} +(0.468007 + 2.60403i) q^{7} +(-1.07619 + 0.621337i) q^{8} -0.911030i q^{10} +(2.19030 + 2.61029i) q^{11} +(1.17022 + 3.21516i) q^{13} +(0.539981 - 0.647845i) q^{14} +(-3.19557 - 1.16309i) q^{16} -4.66323 q^{17} +5.52060i q^{19} +(4.15623 - 3.48749i) q^{20} +(0.188615 - 1.06969i) q^{22} +(-0.470293 - 1.29212i) q^{23} +(0.550137 + 3.11998i) q^{25} +(0.545329 - 0.944538i) q^{26} +(5.02264 - 0.0165384i) q^{28} +(2.81504 - 7.73427i) q^{29} +(2.17942 + 0.384290i) q^{31} +(1.22079 + 3.35410i) q^{32} +(0.955489 + 1.13871i) q^{34} +(-3.75918 + 6.56089i) q^{35} +(0.882419 + 1.52840i) q^{37} +(1.34807 - 1.13116i) q^{38} +(-3.49759 - 0.616720i) q^{40} +(4.96713 - 1.80789i) q^{41} +(-1.57831 - 8.95103i) q^{43} +(5.60210 - 3.23437i) q^{44} +(-0.219159 + 0.379594i) q^{46} +(-0.532155 - 3.01800i) q^{47} +(-6.56194 + 2.43741i) q^{49} +(0.649143 - 0.773618i) q^{50} +(6.39667 - 1.12790i) q^{52} +(1.30996 - 0.756305i) q^{53} +9.73859i q^{55} +(-2.12164 - 2.51163i) q^{56} +(-2.46542 + 0.897340i) q^{58} +(6.44995 - 2.34759i) q^{59} +(9.69333 - 1.70919i) q^{61} +(-0.352721 - 0.610930i) q^{62} +(-2.83176 + 4.90475i) q^{64} +(-3.34449 + 9.18891i) q^{65} +(-7.34743 - 6.16523i) q^{67} +(-1.53724 + 8.71812i) q^{68} +(2.37235 - 0.426368i) q^{70} +(9.64722 + 5.56983i) q^{71} +(-5.11937 - 2.95567i) q^{73} +(0.192410 - 0.528643i) q^{74} +(10.3210 + 1.81988i) q^{76} +(-5.77220 + 6.92523i) q^{77} +(8.75642 - 7.34751i) q^{79} +(-4.85952 - 8.41694i) q^{80} +(-1.45922 - 0.842484i) q^{82} +(6.72578 + 2.44798i) q^{83} +(-10.2094 - 8.56673i) q^{85} +(-1.86235 + 2.21946i) q^{86} +(-3.97904 - 1.44825i) q^{88} -12.2586 q^{89} +(-7.82471 + 4.55201i) q^{91} +(-2.57071 + 0.453286i) q^{92} +(-0.627925 + 0.748331i) q^{94} +(-10.1418 + 12.0865i) q^{95} +(2.47531 - 0.436465i) q^{97} +(1.93972 + 1.10293i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.204899	−	0.244189i	−0.144885	−	0.172668i	0.688721	−	0.725026i	$-0.258172\pi$
$2$	−0.204899	−	0.244189i	−0.144885	−	0.172668i	−0.833607	+	0.552359i	$0.813728\pi$
$3$		0			0
$3$		0			0
$4$	0.329652	−	1.86955i	0.164826	−	0.934774i
$5$	2.18935	+	1.83708i	0.979106	+	0.821568i	0.983954	−	0.178420i	$-0.0570987\pi$
$5$	2.18935	+	1.83708i	0.979106	+	0.821568i	−0.00484794	+	0.999988i	$0.501543\pi$
$6$		0			0
$7$	0.468007	+	2.60403i	0.176890	+	0.984231i
$7$	0.468007	+	2.60403i	0.176890	+	0.984231i
$8$	−1.07619	+	0.621337i	−0.380489	+	0.219676i
$9$		0			0
$10$		−	0.911030i		−	0.288093i
$11$	2.19030	+	2.61029i	0.660399	+	0.787033i	0.987443	−	0.157976i	$-0.0504970\pi$
$11$	2.19030	+	2.61029i	0.660399	+	0.787033i	−0.327044	+	0.945009i	$0.606053\pi$
$12$		0			0
$13$	1.17022	+	3.21516i	0.324562	+	0.891726i	0.989462	+	0.144794i	$0.0462518\pi$
$13$	1.17022	+	3.21516i	0.324562	+	0.891726i	−0.664900	+	0.746932i	$0.731526\pi$
$14$	0.539981	−	0.647845i	0.144316	−	0.173144i
$15$		0			0
$16$	−3.19557	−	1.16309i	−0.798893	−	0.290773i
$17$	−4.66323			−1.13100			−0.565499	−	0.824749i	$-0.691317\pi$
$17$	−4.66323			−1.13100			−0.565499	+	0.824749i	$0.691317\pi$
$18$		0			0
$19$			5.52060i			1.26651i	0.773942	+	0.633256i	$0.218282\pi$
$19$			5.52060i			1.26651i	−0.773942	+	0.633256i	$0.781718\pi$
$20$	4.15623	−	3.48749i	0.929362	−	0.779827i
$21$		0			0
$22$	0.188615	−	1.06969i	0.0402129	−	0.228059i
$23$	−0.470293	−	1.29212i	−0.0980628	−	0.269425i	0.880955	−	0.473200i	$-0.156901\pi$
$23$	−0.470293	−	1.29212i	−0.0980628	−	0.269425i	−0.979018	+	0.203775i	$0.934679\pi$
$24$		0			0
$25$	0.550137	+	3.11998i	0.110027	+	0.623997i
$26$	0.545329	−	0.944538i	0.106948	−	0.185239i
$27$		0			0
$28$	5.02264	−	0.0165384i	0.949189	−	0.00312546i
$29$	2.81504	−	7.73427i	0.522741	−	1.43622i	−0.344717	−	0.938707i	$-0.612025\pi$
$29$	2.81504	−	7.73427i	0.522741	−	1.43622i	0.867458	−	0.497511i	$-0.165753\pi$
$30$		0			0
$31$	2.17942	+	0.384290i	0.391435	+	0.0690206i	0.365902	−	0.930653i	$-0.380761\pi$
$31$	2.17942	+	0.384290i	0.391435	+	0.0690206i	0.0255331	+	0.999674i	$0.491872\pi$
$32$	1.22079	+	3.35410i	0.215808	+	0.592927i
$33$		0			0
$34$	0.955489	+	1.13871i	0.163865	+	0.195287i
$35$	−3.75918	+	6.56089i	−0.635418	+	1.10899i
$36$		0			0
$37$	0.882419	+	1.52840i	0.145069	+	0.251267i	0.929399	−	0.369077i	$-0.120326\pi$
$37$	0.882419	+	1.52840i	0.145069	+	0.251267i	−0.784330	+	0.620344i	$0.786993\pi$
$38$	1.34807	−	1.13116i	0.218686	−	0.183499i
$39$		0			0
$40$	−3.49759	−	0.616720i	−0.553018	−	0.0975120i
$41$	4.96713	−	1.80789i	0.775735	−	0.282344i	0.0763420	−	0.997082i	$-0.475676\pi$
$41$	4.96713	−	1.80789i	0.775735	−	0.282344i	0.699393	+	0.714737i	$0.253454\pi$
$42$		0			0
$43$	−1.57831	−	8.95103i	−0.240690	−	1.36502i	−0.830293	−	0.557327i	$-0.811827\pi$
$43$	−1.57831	−	8.95103i	−0.240690	−	1.36502i	0.589603	−	0.807693i	$-0.299284\pi$
$44$	5.60210	−	3.23437i	0.844548	−	0.487600i
$45$		0			0
$46$	−0.219159	+	0.379594i	−0.0323132	+	0.0559681i
$47$	−0.532155	−	3.01800i	−0.0776228	−	0.440221i	−0.998706	−	0.0508551i	$-0.983805\pi$
$47$	−0.532155	−	3.01800i	−0.0776228	−	0.440221i	0.921083	−	0.389366i	$-0.127306\pi$
$48$		0			0
$49$	−6.56194	+	2.43741i	−0.937420	+	0.348201i
$50$	0.649143	−	0.773618i	0.0918027	−	0.109406i
$51$		0			0
$52$	6.39667	−	1.12790i	0.887058	−	0.156412i
$53$	1.30996	−	0.756305i	0.179937	−	0.103886i	−0.407326	−	0.913283i	$-0.633539\pi$
$53$	1.30996	−	0.756305i	0.179937	−	0.103886i	0.587263	+	0.809396i	$0.300205\pi$
$54$		0			0
$55$			9.73859i			1.31315i
$56$	−2.12164	−	2.51163i	−0.283516	−	0.335631i
$57$		0			0
$58$	−2.46542	+	0.897340i	−0.323726	+	0.117827i
$59$	6.44995	−	2.34759i	0.839713	−	0.305630i	0.113874	−	0.993495i	$-0.463674\pi$
$59$	6.44995	−	2.34759i	0.839713	−	0.305630i	0.725839	+	0.687865i	$0.241452\pi$
$60$		0			0
$61$	9.69333	−	1.70919i	1.24110	−	0.218840i	0.485715	−	0.874117i	$-0.338559\pi$
$61$	9.69333	−	1.70919i	1.24110	−	0.218840i	0.755388	+	0.655277i	$0.227448\pi$
$62$	−0.352721	−	0.610930i	−0.0447956	−	0.0775882i
$63$		0			0
$64$	−2.83176	+	4.90475i	−0.353970	+	0.613094i
$65$	−3.34449	+	9.18891i	−0.414833	+	1.13974i
$66$		0			0
$67$	−7.34743	−	6.16523i	−0.897632	−	0.753203i	0.0720942	−	0.997398i	$-0.477032\pi$
$67$	−7.34743	−	6.16523i	−0.897632	−	0.753203i	−0.969726	+	0.244195i	$0.921476\pi$
$68$	−1.53724	+	8.71812i	−0.186418	+	1.05723i
$69$		0			0
$70$	2.37235	−	0.426368i	0.283550	−	0.0509608i
$71$	9.64722	+	5.56983i	1.14491	+	0.661017i	0.947643	−	0.319332i	$-0.103459\pi$
$71$	9.64722	+	5.56983i	1.14491	+	0.661017i	0.197272	+	0.980349i	$0.436792\pi$
$72$		0			0
$73$	−5.11937	−	2.95567i	−0.599176	−	0.345935i	0.169541	−	0.985523i	$-0.445771\pi$
$73$	−5.11937	−	2.95567i	−0.599176	−	0.345935i	−0.768718	+	0.639588i	$0.779105\pi$
$74$	0.192410	−	0.528643i	0.0223673	−	0.0614535i
$75$		0			0
$76$	10.3210	+	1.81988i	1.18390	+	0.208754i
$77$	−5.77220	+	6.92523i	−0.657804	+	0.789203i
$78$		0			0
$79$	8.75642	−	7.34751i	0.985175	−	0.826660i	0.000312673	−	1.00000i	$-0.499900\pi$
$79$	8.75642	−	7.34751i	0.985175	−	0.826660i	0.984862	+	0.173340i	$0.0554560\pi$
$80$	−4.85952	−	8.41694i	−0.543311	−	0.941042i
$81$		0			0
$82$	−1.45922	−	0.842484i	−0.161144	−	0.0930367i
$83$	6.72578	+	2.44798i	0.738250	+	0.268701i	0.683653	−	0.729807i	$-0.260390\pi$
$83$	6.72578	+	2.44798i	0.738250	+	0.268701i	0.0545974	+	0.998508i	$0.482612\pi$
$84$		0			0
$85$	−10.2094	−	8.56673i	−1.10737	−	0.929192i
$86$	−1.86235	+	2.21946i	−0.200822	+	0.239331i
$87$		0			0
$88$	−3.97904	−	1.44825i	−0.424167	−	0.154384i
$89$	−12.2586			−1.29941			−0.649703	−	0.760188i	$-0.725107\pi$
$89$	−12.2586			−1.29941			−0.649703	+	0.760188i	$0.725107\pi$
$90$		0			0
$91$	−7.82471	+	4.55201i	−0.820252	+	0.477181i
$92$	−2.57071	+	0.453286i	−0.268015	+	0.0472583i
$93$		0			0
$94$	−0.627925	+	0.748331i	−0.0647655	+	0.0771845i
$95$	−10.1418	+	12.0865i	−1.04053	+	1.24005i
$96$		0			0
$97$	2.47531	−	0.436465i	0.251330	−	0.0443163i	−0.0465636	−	0.998915i	$-0.514827\pi$
$97$	2.47531	−	0.436465i	0.251330	−	0.0443163i	0.297894	+	0.954599i	$0.403716\pi$
$98$	1.93972	+	1.10293i	0.195941	+	0.111413i
$99$		0			0
$100$	6.01431			0.601431
$101$	−8.75323	−	3.18591i	−0.870979	−	0.317010i	−0.132415	−	0.991194i	$-0.542273\pi$
$101$	−8.75323	−	3.18591i	−0.870979	−	0.317010i	−0.738563	+	0.674184i	$0.764495\pi$
$102$		0			0
$103$	−7.24467	+	8.63386i	−0.713838	+	0.850719i	−0.994017	−	0.109229i	$-0.965162\pi$
$103$	−7.24467	+	8.63386i	−0.713838	+	0.850719i	0.280178	+	0.959948i	$0.409606\pi$
$104$	−3.25708	−	2.73301i	−0.319383	−	0.267994i
$105$		0			0
$106$	−0.453090	−	0.164911i	−0.0440080	−	0.0160176i
$107$	−5.79854	−	3.34779i	−0.560566	−	0.323643i	0.192807	−	0.981237i	$-0.438241\pi$
$107$	−5.79854	−	3.34779i	−0.560566	−	0.323643i	−0.753373	+	0.657594i	$0.771574\pi$
$108$		0			0
$109$	−8.30492	−	14.3845i	−0.795467	−	1.37779i	−0.922542	−	0.385896i	$-0.873892\pi$
$109$	−8.30492	−	14.3845i	−0.795467	−	1.37779i	0.127076	−	0.991893i	$-0.459441\pi$
$110$	2.37806	−	1.99543i	0.226739	−	0.190256i
$111$		0			0
$112$	1.53318	−	8.86569i	0.144872	−	0.837729i
$113$	−10.4246	−	1.83814i	−0.980666	−	0.172918i	−0.339739	−	0.940520i	$-0.610339\pi$
$113$	−10.4246	−	1.83814i	−0.980666	−	0.172918i	−0.640927	+	0.767602i	$0.721450\pi$
$114$		0			0
$115$	1.34409	−	3.69286i	0.125337	−	0.344361i
$116$	−13.5316	−	7.81247i	−1.25638	−	0.725370i
$117$		0			0
$118$	−1.89484	−	1.09399i	−0.174434	−	0.100710i
$119$	−2.18242	−	12.1432i	−0.200062	−	1.11316i
$120$		0			0
$121$	−0.106102	+	0.601736i	−0.00964566	+	0.0547033i
$122$	−2.40352	−	2.01679i	−0.217604	−	0.182592i
$123$		0			0
$124$	1.43690	−	3.94784i	0.129037	−	0.354527i
$125$	2.61776	−	4.53409i	0.234139	−	0.405541i
$126$		0			0
$127$	8.48685	+	14.6997i	0.753086	+	1.30438i	0.946320	+	0.323231i	$0.104769\pi$
$127$	8.48685	+	14.6997i	0.753086	+	1.30438i	−0.193234	+	0.981153i	$0.561898\pi$
$128$	8.80818	−	1.55312i	0.778540	−	0.137278i
$129$		0			0
$130$	2.92911	−	1.06611i	0.256900	−	0.0935039i
$131$	15.0308	−	5.47076i	1.31325	−	0.477982i	0.411958	−	0.911203i	$-0.364845\pi$
$131$	15.0308	−	5.47076i	1.31325	−	0.477982i	0.901288	+	0.433221i	$0.142623\pi$
$132$		0			0
$133$	−14.3758	+	2.58368i	−1.24654	+	0.224033i
$134$			3.05741i			0.264120i
$135$		0			0
$136$	5.01850	−	2.89743i	0.430333	−	0.248453i
$137$	−12.8335	+	2.26289i	−1.09644	+	0.193332i	−0.692475	−	0.721442i	$-0.743480\pi$
$137$	−12.8335	+	2.26289i	−1.09644	+	0.193332i	−0.403965	+	0.914774i	$0.632368\pi$
$138$		0			0
$139$	2.63292	−	3.13779i	0.223321	−	0.266144i	−0.642737	−	0.766087i	$-0.722201\pi$
$139$	2.63292	−	3.13779i	0.223321	−	0.266144i	0.866058	+	0.499943i	$0.166646\pi$
$140$	11.0267	+	9.19078i	0.931925	+	0.776763i
$141$		0			0
$142$	−0.616615	−	3.49699i	−0.0517451	−	0.293461i
$143$	−5.82938	+	10.0968i	−0.487477	+	0.844335i
$144$		0			0
$145$	20.3716	−	11.7615i	1.69177	−	0.976743i
$146$	0.327211	+	1.85570i	0.0270802	+	0.153579i
$147$		0			0
$148$	3.14830	−	1.14589i	0.258789	−	0.0941913i
$149$	−1.46897	−	0.259019i	−0.120343	−	0.0212197i	0.113152	−	0.993578i	$-0.463905\pi$
$149$	−1.46897	−	0.259019i	−0.120343	−	0.0212197i	−0.233495	+	0.972358i	$0.575016\pi$
$150$		0			0
$151$	−3.72109	+	3.12237i	−0.302818	+	0.254095i	−0.781516	−	0.623885i	$-0.785553\pi$
$151$	−3.72109	+	3.12237i	−0.302818	+	0.254095i	0.478698	+	0.877980i	$0.341109\pi$
$152$	−3.43015	−	5.94120i	−0.278222	−	0.481895i
$153$		0			0
$154$	2.87378	−	0.00946270i	0.231576	−	0.000762526i
$155$	4.06553	+	4.84511i	0.326551	+	0.389169i
$156$		0			0
$157$	−7.70444	−	21.1678i	−0.614882	−	1.68937i	−0.719177	−	0.694827i	$-0.755481\pi$
$157$	−7.70444	−	21.1678i	−0.614882	−	1.68937i	0.104295	−	0.994546i	$-0.466741\pi$
$158$	−3.58836	−	0.632725i	−0.285475	−	0.0503369i
$159$		0			0
$160$	−3.48902	+	9.58599i	−0.275831	+	0.757839i
$161$	3.14462	−	1.82938i	0.247830	−	0.144175i
$162$		0			0
$163$	−4.81306	+	8.33646i	−0.376988	+	0.652962i	−0.990622	−	0.136628i	$-0.956374\pi$
$163$	−4.81306	+	8.33646i	−0.376988	+	0.652962i	0.613635	+	0.789590i	$0.289707\pi$
$164$	−1.74251	−	9.88225i	−0.136067	−	0.771674i
$165$		0			0
$166$	−0.780334	−	2.14395i	−0.0605657	−	0.166403i
$167$	1.75065	−	9.92841i	0.135469	−	0.768284i	−0.839063	−	0.544035i	$-0.816896\pi$
$167$	1.75065	−	9.92841i	0.135469	−	0.768284i	0.974532	−	0.224249i	$-0.0719929\pi$
$168$		0			0
$169$	0.990731	−	0.831322i	0.0762101	−	0.0639479i
$170$			4.24834i			0.325833i
$171$		0			0
$172$	−17.2547			−1.31566
$173$	11.6153	+	4.22763i	0.883097	+	0.321421i	0.743459	−	0.668782i	$-0.233184\pi$
$173$	11.6153	+	4.22763i	0.883097	+	0.321421i	0.139638	+	0.990203i	$0.455406\pi$
$174$		0			0
$175$	−7.86706	+	2.89275i	−0.594694	+	0.218671i
$176$	−3.96323	−	10.8889i	−0.298740	−	0.820781i
$177$		0			0
$178$	2.51177	+	2.99341i	0.188265	+	0.224365i
$179$			15.7838i			1.17974i	0.807500	+	0.589868i	$0.200820\pi$
$179$			15.7838i			1.17974i	−0.807500	+	0.589868i	$0.799180\pi$
$180$		0			0
$181$	−11.3602	+	6.55879i	−0.844393	+	0.487511i	−0.858755	−	0.512386i	$-0.828762\pi$
$181$	−11.3602	+	6.55879i	−0.844393	+	0.487511i	0.0143618	+	0.999897i	$0.495428\pi$
$182$	2.71482	+	0.978004i	0.201236	+	0.0724945i
$183$		0			0
$184$	1.30896	+	1.09835i	0.0964981	+	0.0809715i
$185$	−0.875863	+	4.96727i	−0.0643947	+	0.365201i
$186$		0			0
$187$	−10.2138	−	12.1724i	−0.746910	−	0.890133i
$188$	−5.81773			−0.424301
$189$		0			0
$190$	5.02943			0.364874
$191$	11.4242	+	13.6149i	0.826629	+	0.985138i	1.00000		0.000281329i	$8.95499e-5\pi$
$191$	11.4242	+	13.6149i	0.826629	+	0.985138i	−0.173371	+	0.984857i	$0.555466\pi$
$192$		0			0
$193$	−2.36579	+	13.4170i	−0.170293	+	0.965780i	0.773144	+	0.634230i	$0.218683\pi$
$193$	−2.36579	+	13.4170i	−0.170293	+	0.965780i	−0.943438	+	0.331550i	$0.892428\pi$
$194$	−0.613769	−	0.515013i	−0.0440660	−	0.0369758i
$195$		0			0
$196$	2.39369	+	13.0714i	0.170978	+	0.933668i
$197$	−7.98620	+	4.61083i	−0.568993	+	0.328508i	−0.756747	−	0.653708i	$-0.773213\pi$
$197$	−7.98620	+	4.61083i	−0.568993	+	0.328508i	0.187754	+	0.982216i	$0.439879\pi$
$198$		0			0
$199$			0.268183i			0.0190110i	0.999955	+	0.00950548i	$0.00302573\pi$
$199$			0.268183i			0.0190110i	−0.999955	+	0.00950548i	$0.996974\pi$
$200$	−2.53061	−	3.01587i	−0.178941	−	0.213254i
$201$		0			0
$202$	1.01556	+	2.79023i	0.0714546	+	0.196320i
$203$	21.4577	+	3.71077i	1.50604	+	0.260445i
$204$		0			0
$205$	14.1960	+	5.16692i	0.991492	+	0.360874i
$206$	3.59272			0.250316
$207$		0			0
$208$		−	11.6354i		−	0.806767i
$209$	−14.4104	+	12.0917i	−0.996787	+	0.836404i
$210$		0			0
$211$	−2.27165	+	12.8832i	−0.156387	+	0.886914i	0.801120	+	0.598503i	$0.204238\pi$
$211$	−2.27165	+	12.8832i	−0.156387	+	0.886914i	−0.957507	+	0.288410i	$0.906873\pi$
$212$	−0.982118	−	2.69835i	−0.0674521	−	0.185323i
$213$		0			0
$214$	0.370621	+	2.10190i	0.0253351	+	0.143683i
$215$	12.9883	−	22.4964i	0.885795	−	1.53424i
$216$		0			0
$217$	0.0192796	+	5.85512i	0.00130878	+	0.397471i
$218$	−1.81088	+	4.97534i	−0.122648	+	0.336973i
$219$		0			0
$220$	18.2068	+	3.21034i	1.22750	+	0.216441i
$221$	−5.45702	−	14.9930i	−0.367079	−	1.00854i
$222$		0			0
$223$	−9.50475	−	11.3273i	−0.636485	−	0.758534i	0.347325	−	0.937745i	$-0.387090\pi$
$223$	−9.50475	−	11.3273i	−0.636485	−	0.758534i	−0.983811	+	0.179211i	$0.942646\pi$
$224$	−8.16284	+	4.74872i	−0.545403	+	0.317287i
$225$		0			0
$226$	1.68714	+	2.92221i	0.112227	+	0.194383i
$227$	7.02467	−	5.89440i	0.466244	−	0.391225i	−0.379178	−	0.925324i	$-0.623793\pi$
$227$	7.02467	−	5.89440i	0.466244	−	0.391225i	0.845422	+	0.534099i	$0.179349\pi$
$228$		0			0
$229$	12.5995	+	2.22163i	0.832599	+	0.146810i	0.573670	−	0.819087i	$-0.305519\pi$
$229$	12.5995	+	2.22163i	0.832599	+	0.146810i	0.258929	+	0.965896i	$0.416630\pi$
$230$	−1.17716	+	0.428451i	−0.0776196	+	0.0282512i
$231$		0			0
$232$	1.77607	+	10.0726i	0.116605	+	0.661299i
$233$	14.7803	−	8.53340i	0.968289	−	0.559042i	0.0695746	−	0.997577i	$-0.477836\pi$
$233$	14.7803	−	8.53340i	0.968289	−	0.559042i	0.898714	+	0.438535i	$0.144502\pi$
$234$		0			0
$235$	4.37924	−	7.58507i	0.285670	−	0.494796i
$236$	−2.26270	−	12.8324i	−0.147289	−	0.835317i
$237$		0			0
$238$	−2.51805	+	3.02105i	−0.163221	+	0.195825i
$239$	4.33839	−	5.17029i	0.280627	−	0.334438i	−0.607257	−	0.794505i	$-0.707730\pi$
$239$	4.33839	−	5.17029i	0.280627	−	0.334438i	0.887884	+	0.460067i	$0.152175\pi$
$240$		0			0
$241$	−2.76527	+	0.487591i	−0.178126	+	0.0314085i	−0.262000	−	0.965068i	$-0.584382\pi$
$241$	−2.76527	+	0.487591i	−0.178126	+	0.0314085i	0.0838734	+	0.996476i	$0.473271\pi$
$242$	0.168677	−	0.0973859i	0.0108430	−	0.00626021i
$243$		0			0
$244$		−	18.6856i		−	1.19622i
$245$	−18.8441	−	6.71848i	−1.20390	−	0.429228i
$246$		0			0
$247$	−17.7496	+	6.46034i	−1.12938	+	0.411061i
$248$	−2.58423	+	0.940584i	−0.164099	+	0.0597272i
$249$		0			0
$250$	−1.64355	+	0.289802i	−0.103947	+	0.0183287i
$251$	11.4184	+	19.7772i	0.720720	+	1.24832i	0.960712	+	0.277549i	$0.0895220\pi$
$251$	11.4184	+	19.7772i	0.720720	+	1.24832i	−0.239992	+	0.970775i	$0.577145\pi$
$252$		0			0
$253$	2.34273	−	4.05772i	0.147286	−	0.255107i
$254$	1.85055	−	5.08434i	0.116114	−	0.319020i
$255$		0			0
$256$	6.49298	+	5.44825i	0.405811	+	0.340516i
$257$	−2.17396	+	12.3291i	−0.135608	+	0.769069i	0.838827	+	0.544398i	$0.183242\pi$
$257$	−2.17396	+	12.3291i	−0.135608	+	0.769069i	−0.974435	+	0.224671i	$0.927869\pi$
$258$		0			0
$259$	−3.56701	+	3.01315i	−0.221643	+	0.187228i
$260$	16.0766	+	9.28182i	0.997027	+	0.575634i
$261$		0			0
$262$	−4.41569	−	2.54940i	−0.272802	−	0.157502i
$263$	−4.35051	+	11.9529i	−0.268264	+	0.737049i	0.730282	+	0.683146i	$0.239389\pi$
$263$	−4.35051	+	11.9529i	−0.268264	+	0.737049i	−0.998546	+	0.0539035i	$0.982834\pi$
$264$		0			0
$265$	4.25735	+	0.750685i	0.261527	+	0.0461142i
$266$	3.57649	+	2.98102i	0.219289	+	0.182778i
$267$		0			0
$268$	−13.9483	+	11.7040i	−0.852027	+	0.714936i
$269$	−9.79421	−	16.9641i	−0.597163	−	1.03432i	−0.993238	−	0.116099i	$-0.962961\pi$
$269$	−9.79421	−	16.9641i	−0.597163	−	1.03432i	0.396074	−	0.918218i	$-0.370372\pi$
$270$		0			0
$271$	16.1584	+	9.32907i	0.981555	+	0.566701i	0.902739	−	0.430188i	$-0.141553\pi$
$271$	16.1584	+	9.32907i	0.981555	+	0.566701i	0.0788154	+	0.996889i	$0.474886\pi$
$272$	14.9017	+	5.42376i	0.903546	+	0.328864i
$273$		0			0
$274$	3.18214	+	2.67013i	0.192240	+	0.161309i
$275$	−6.93911	+	8.26971i	−0.418444	+	0.498682i
$276$		0			0
$277$	2.50916	+	0.913261i	0.150761	+	0.0548725i	0.416298	−	0.909228i	$-0.363327\pi$
$277$	2.50916	+	0.913261i	0.150761	+	0.0548725i	−0.265537	+	0.964101i	$0.585549\pi$
$278$	−1.30570			−0.0783104
$279$		0			0
$280$	−0.0309404	−	9.39647i	−0.00184904	−	0.561546i
$281$	−17.0926	+	3.01388i	−1.01966	+	0.179793i	−0.658396	−	0.752672i	$-0.728765\pi$
$281$	−17.0926	+	3.01388i	−1.01966	+	0.179793i	−0.361261	+	0.932465i	$0.617654\pi$
$282$		0			0
$283$	0.702594	−	0.837319i	0.0417649	−	0.0497734i	−0.744758	−	0.667335i	$-0.767435\pi$
$283$	0.702594	−	0.837319i	0.0417649	−	0.0497734i	0.786523	+	0.617562i	$0.211879\pi$
$284$	13.5933	−	16.1998i	0.806613	−	0.961284i
$285$		0			0
$286$	3.65995	−	0.645349i	0.216418	−	0.0381603i
$287$	7.03244	+	12.0884i	0.415112	+	0.713558i
$288$		0			0
$289$	4.74568			0.279158
$290$	−7.04615	−	2.56459i	−0.413764	−	0.150598i
$291$		0			0
$292$	−7.21337	+	8.59656i	−0.422130	+	0.503075i
$293$	16.1311	+	13.5356i	0.942391	+	0.790760i	0.978000	−	0.208606i	$-0.0668926\pi$
$293$	16.1311	+	13.5356i	0.942391	+	0.790760i	−0.0356088	+	0.999366i	$0.511337\pi$
$294$		0			0
$295$	18.4339	+	6.70940i	1.07326	+	0.390636i
$296$	−1.89930	−	1.09656i	−0.110394	−	0.0637362i
$297$		0			0
$298$	0.237741	+	0.411779i	0.0137720	+	0.0238537i
$299$	3.60402	−	3.02414i	0.208426	−	0.174890i
$300$		0			0
$301$	22.5701	−	8.29911i	1.30092	−	0.478353i
$302$	1.52489	+	0.268880i	0.0877478	+	0.0154723i
$303$		0			0
$304$	6.42097	−	17.6415i	0.368268	−	1.01181i
$305$	24.3620	+	14.0654i	1.39496	+	0.805383i
$306$		0			0
$307$	19.7567	+	11.4065i	1.12757	+	0.651004i	0.943323	−	0.331876i	$-0.107682\pi$
$307$	19.7567	+	11.4065i	1.12757	+	0.651004i	0.184249	+	0.982880i	$0.441015\pi$
$308$	11.0442	+	13.0743i	0.629303	+	0.744979i
$309$		0			0
$310$	0.350100	−	1.98552i	0.0198843	−	0.112770i
$311$	−17.2454	−	14.4706i	−0.977895	−	0.820551i	0.00587548	−	0.999983i	$-0.498130\pi$
$311$	−17.2454	−	14.4706i	−0.977895	−	0.820551i	−0.983770	+	0.179431i	$0.942574\pi$
$312$		0			0
$313$	0.482843	−	1.32660i	0.0272919	−	0.0749839i	−0.925298	−	0.379240i	$-0.876186\pi$
$313$	0.482843	−	1.32660i	0.0272919	−	0.0749839i	0.952590	+	0.304256i	$0.0984078\pi$
$314$	−3.59031	+	6.21859i	−0.202613	+	0.350935i
$315$		0			0
$316$	−10.8500	−	18.7927i	−0.610358	−	1.05717i
$317$	−6.75056	+	1.19031i	−0.379149	+	0.0668542i	−0.359975	−	0.932962i	$-0.617215\pi$
$317$	−6.75056	+	1.19031i	−0.379149	+	0.0668542i	−0.0191741	+	0.999816i	$0.506104\pi$
$318$		0			0
$319$	26.3545	−	9.59225i	1.47557	−	0.537063i
$320$	−15.2101	+	5.53604i	−0.850273	+	0.309474i
$321$		0			0
$322$	−1.09104	−	0.393043i	−0.0608014	−	0.0219034i
$323$		−	25.7438i		−	1.43242i
$324$		0			0
$325$	−9.38747	+	5.41986i	−0.520723	+	0.300640i
$326$	3.02186	−	0.532836i	0.167365	−	0.0295110i
$327$		0			0
$328$	−4.22225	+	5.03188i	−0.233135	+	0.277839i
$329$	7.60992	−	2.79819i	0.419548	−	0.154269i
$330$		0			0
$331$	0.516799	+	2.93091i	0.0284058	+	0.161098i	0.995711	−	0.0925176i	$-0.0294914\pi$
$331$	0.516799	+	2.93091i	0.0284058	+	0.161098i	−0.967305	+	0.253615i	$0.918380\pi$
$332$	6.79379	−	11.7672i	0.372858	−	0.645808i
$333$		0			0
$334$	−2.78311	+	1.60683i	−0.152285	+	0.0879219i
$335$	−4.76007	−	26.9957i	−0.260070	−	1.47493i
$336$		0			0
$337$	23.6884	−	8.62186i	1.29039	−	0.469663i	0.396534	−	0.918020i	$-0.370213\pi$
$337$	23.6884	−	8.62186i	1.29039	−	0.469663i	0.893854	+	0.448357i	$0.147991\pi$
$338$	−0.405999	−	0.0715886i	−0.0220834	−	0.00389391i
$339$		0			0
$340$	−19.3815	+	16.2630i	−1.05111	+	0.881984i
$341$	3.77046	+	6.53063i	0.204182	+	0.353653i
$342$		0			0
$343$	−9.41811	−	15.9468i	−0.508530	−	0.861044i
$344$	7.26016	+	8.65232i	0.391442	+	0.466502i
$345$		0			0
$346$	−1.34763	−	3.70257i	−0.0724488	−	0.199051i
$347$	2.26682	+	0.399701i	0.121689	+	0.0214571i	0.234161	−	0.972198i	$-0.424766\pi$
$347$	2.26682	+	0.399701i	0.121689	+	0.0214571i	−0.112472	+	0.993655i	$0.535877\pi$
$348$		0			0
$349$	2.39148	−	6.57053i	0.128013	−	0.351712i	−0.859084	−	0.511834i	$-0.828966\pi$
$349$	2.39148	−	6.57053i	0.128013	−	0.351712i	0.987097	+	0.160121i	$0.0511886\pi$
$350$	2.31833	+	1.32833i	0.123920	+	0.0710022i
$351$		0			0
$352$	−6.08129	+	10.5331i	−0.324134	+	0.561416i
$353$	3.83541	+	21.7517i	0.204138	+	1.15772i	0.898790	+	0.438379i	$0.144447\pi$
$353$	3.83541	+	21.7517i	0.204138	+	1.15772i	−0.694652	+	0.719346i	$0.744442\pi$
$354$		0			0
$355$	10.8889	+	29.9170i	0.577923	+	1.58783i
$356$	−4.04106	+	22.9180i	−0.214176	+	1.21465i
$357$		0			0
$358$	3.85423	−	3.23408i	0.203702	−	0.170926i
$359$		−	32.6065i		−	1.72090i	−0.509532	−	0.860451i	$-0.670182\pi$
$359$		−	32.6065i		−	1.72090i	0.509532	−	0.860451i	$-0.329818\pi$
$360$		0			0
$361$	−11.4770			−0.604055
$362$	3.92926	+	1.43014i	0.206518	+	0.0751662i
$363$		0			0
$364$	5.93078	+	16.1292i	0.310857	+	0.845402i
$365$	−5.77827	−	15.8757i	−0.302449	−	0.830971i
$366$		0			0
$367$	2.73420	+	3.25850i	0.142724	+	0.170092i	0.832671	−	0.553768i	$-0.186811\pi$
$367$	2.73420	+	3.25850i	0.142724	+	0.170092i	−0.689947	+	0.723860i	$0.742366\pi$
$368$			4.67605i			0.243756i
$369$		0			0
$370$	1.39241	−	0.803911i	0.0723882	−	0.0417933i
$371$	2.58251	+	3.05721i	0.134077	+	0.158723i
$372$		0			0
$373$	−18.6688	−	15.6650i	−0.966633	−	0.811101i	0.0153863	−	0.999882i	$-0.495102\pi$
$373$	−18.6688	−	15.6650i	−0.966633	−	0.811101i	−0.982019	+	0.188780i	$0.939547\pi$
$374$	−0.879557	+	4.98821i	−0.0454808	+	0.257934i
$375$		0			0
$376$	2.44789	+	2.91729i	0.126241	+	0.150448i
$377$	28.1612			1.45037
$378$		0			0
$379$	−17.8518			−0.916987			−0.458493	−	0.888698i	$-0.651611\pi$
$379$	−17.8518			−0.916987			−0.458493	+	0.888698i	$0.651611\pi$
$380$	19.2531	+	22.9449i	0.987661	+	1.17705i
$381$		0			0
$382$	0.983789	−	5.57934i	0.0503350	−	0.285464i
$383$	−20.9677	−	17.5940i	−1.07140	−	0.899009i	−0.0762189	−	0.997091i	$-0.524285\pi$
$383$	−20.9677	−	17.5940i	−1.07140	−	0.899009i	−0.995178	+	0.0980821i	$0.968729\pi$
$384$		0			0
$385$	−25.3596	+	4.55773i	−1.29244	+	0.232283i
$386$	3.76104	−	2.17144i	0.191432	−	0.110523i
$387$		0			0
$388$		−	4.77160i		−	0.242241i
$389$	−10.4768	−	12.4858i	−0.531197	−	0.633056i	0.431993	−	0.901877i	$-0.357810\pi$
$389$	−10.4768	−	12.4858i	−0.531197	−	0.633056i	−0.963190	+	0.268821i	$0.913366\pi$
$390$		0			0
$391$	2.19308	+	6.02544i	0.110909	+	0.304720i
$392$	5.54742	−	6.70028i	0.280187	−	0.338415i
$393$		0			0
$394$	2.76228	+	1.00539i	0.139162	+	0.0506506i
$395$	32.6688			1.64375
$396$		0			0
$397$			4.55646i			0.228682i	0.993442	+	0.114341i	$0.0364757\pi$
$397$			4.55646i			0.228682i	−0.993442	+	0.114341i	$0.963524\pi$
$398$	0.0654872	−	0.0549503i	0.00328258	−	0.00275441i
$399$		0			0
$400$	1.87083	−	10.6100i	0.0935414	−	0.530499i
$401$	−12.8930	−	35.4232i	−0.643844	−	1.76895i	−0.639299	−	0.768958i	$-0.720775\pi$
$401$	−12.8930	−	35.4232i	−0.643844	−	1.76895i	−0.00454521	−	0.999990i	$-0.501447\pi$
$402$		0			0
$403$	1.31485	+	7.45689i	0.0654974	+	0.371454i
$404$	−8.84173	+	15.3143i	−0.439893	+	0.761916i
$405$		0			0
$406$	−3.49053	−	6.00007i	−0.173232	−	0.297778i
$407$	−2.05680	+	5.65101i	−0.101952	+	0.280110i
$408$		0			0
$409$	−0.986288	−	0.173909i	−0.0487688	−	0.00859926i	0.149211	−	0.988805i	$-0.452327\pi$
$409$	−0.986288	−	0.173909i	−0.0487688	−	0.00859926i	−0.197979	+	0.980206i	$0.563438\pi$
$410$	−1.64704	−	4.52520i	−0.0813415	−	0.223484i
$411$		0			0
$412$	13.7532	+	16.3904i	0.677571	+	0.807498i
$413$	9.13182	+	15.6972i	0.449348	+	0.772408i
$414$		0			0
$415$	10.2279	+	17.7153i	0.502069	+	0.869610i
$416$	−9.35538	+	7.85009i	−0.458685	+	0.384883i
$417$		0			0
$418$	5.90534	+	1.04127i	0.288840	+	0.0509302i
$419$	2.20646	−	0.803084i	0.107792	−	0.0392332i	−0.287561	−	0.957762i	$-0.592844\pi$
$419$	2.20646	−	0.803084i	0.107792	−	0.0392332i	0.395353	+	0.918529i	$0.370622\pi$
$420$		0			0
$421$	1.14047	+	6.46793i	0.0555831	+	0.315228i	0.999905	−	0.0137960i	$-0.00439155\pi$
$421$	1.14047	+	6.46793i	0.0555831	+	0.315228i	−0.944322	+	0.329024i	$0.893280\pi$
$422$	3.61138	−	2.08503i	0.175799	−	0.101498i
$423$		0			0
$424$	−0.939840	+	1.62785i	−0.0456426	+	0.0790554i
$425$	−2.56542	−	14.5492i	−0.124441	−	0.705740i
$426$		0			0
$427$	8.98734	+	24.4418i	0.434928	+	1.18282i
$428$	−8.17035	+	9.73704i	−0.394929	+	0.470658i
$429$		0			0
$430$	−8.15466	+	1.43789i	−0.393253	+	0.0693411i
$431$	−13.3456	+	7.70506i	−0.642833	+	0.371140i	−0.785705	−	0.618602i	$-0.787700\pi$
$431$	−13.3456	+	7.70506i	−0.642833	+	0.371140i	0.142872	+	0.989741i	$0.454366\pi$
$432$		0			0
$433$		−	9.87188i		−	0.474412i	−0.971459	−	0.237206i	$-0.923768\pi$
$433$		−	9.87188i		−	0.474412i	0.971459	−	0.237206i	$-0.0762317\pi$
$434$	1.42580	−	1.20441i	0.0684408	−	0.0578138i
$435$		0			0
$436$	−29.6303	+	10.7845i	−1.41903	+	0.516486i
$437$	7.13327	−	2.59630i	0.341231	−	0.124198i
$438$		0			0
$439$	−34.7691	+	6.13074i	−1.65944	+	0.292604i	−0.923258	−	0.384180i	$-0.874484\pi$
$439$	−34.7691	+	6.13074i	−1.65944	+	0.292604i	−0.736182	+	0.676784i	$0.763373\pi$
$440$	−6.05094	−	10.4805i	−0.288467	−	0.499640i
$441$		0			0
$442$	−2.54299	+	4.40460i	−0.120958	+	0.209505i
$443$	−1.52210	+	4.18193i	−0.0723170	+	0.198689i	−0.970585	−	0.240759i	$-0.922604\pi$
$443$	−1.52210	+	4.18193i	−0.0723170	+	0.198689i	0.898268	+	0.439448i	$0.144826\pi$
$444$		0			0
$445$	−26.8383	−	22.5200i	−1.27226	−	1.06755i
$446$	−0.818494	+	4.64191i	−0.0387568	+	0.219801i
$447$		0			0
$448$	−14.0974	−	5.07853i	−0.666040	−	0.239938i
$449$	−4.96216	−	2.86491i	−0.234179	−	0.135203i	0.378319	−	0.925675i	$-0.376502\pi$
$449$	−4.96216	−	2.86491i	−0.234179	−	0.135203i	−0.612498	+	0.790472i	$0.709835\pi$
$450$		0			0
$451$	15.5986	+	9.00585i	0.734509	+	0.424069i
$452$	−6.87299	+	18.8834i	−0.323278	+	0.888200i
$453$		0			0
$454$	−2.87869	−	0.507591i	−0.135104	−	0.0238224i
$455$	−25.4934	−	4.40868i	−1.19515	−	0.206682i
$456$		0			0
$457$	31.3062	−	26.2690i	1.46444	−	1.22881i	0.543327	−	0.839521i	$-0.317165\pi$
$457$	31.3062	−	26.2690i	1.46444	−	1.22881i	0.921115	−	0.389291i	$-0.127280\pi$
$458$	−2.03913	−	3.53187i	−0.0952821	−	0.165033i
$459$		0			0
$460$	−6.46090	−	3.73020i	−0.301241	−	0.173922i
$461$	−25.5016	−	9.28183i	−1.18773	−	0.432298i	−0.328803	−	0.944399i	$-0.606645\pi$
$461$	−25.5016	−	9.28183i	−1.18773	−	0.432298i	−0.858925	+	0.512101i	$0.828867\pi$
$462$		0			0
$463$	−9.76642	−	8.19500i	−0.453884	−	0.380854i	0.386991	−	0.922084i	$-0.373515\pi$
$463$	−9.76642	−	8.19500i	−0.453884	−	0.380854i	−0.840875	+	0.541230i	$0.817959\pi$
$464$	−17.9913	+	21.4412i	−0.835227	+	0.995385i
$465$		0			0
$466$	−5.11222	−	1.86070i	−0.236819	−	0.0861951i
$467$	−22.5443			−1.04323			−0.521613	−	0.853182i	$-0.674670\pi$
$467$	−22.5443			−1.04323			−0.521613	+	0.853182i	$0.674670\pi$
$468$		0			0
$469$	12.6158	−	22.0183i	0.582543	−	1.01671i
$470$	−2.74949	+	0.484810i	−0.126825	+	0.0223626i
$471$		0			0
$472$	−5.48271	+	6.53404i	−0.252362	+	0.300754i
$473$	19.9078	−	23.7252i	0.915364	−	1.09089i
$474$		0			0
$475$	−17.2242	+	3.03709i	−0.790300	+	0.139351i
$476$	−23.4217	+	0.0771223i	−1.07353	+	0.00353489i
$477$		0			0
$478$	−2.15146			−0.0984053
$479$	30.6612	+	11.1598i	1.40095	+	0.509903i	0.928460	−	0.371433i	$-0.121134\pi$
$479$	30.6612	+	11.1598i	1.40095	+	0.509903i	0.472489	+	0.881337i	$0.343356\pi$
$480$		0			0
$481$	−3.88141	+	4.62569i	−0.176977	+	0.210913i
$482$	0.685664	+	0.575340i	0.0312311	+	0.0262060i
$483$		0			0
$484$	1.09000	+	0.396726i	0.0495453	+	0.0180330i
$485$	6.22115	+	3.59178i	0.282488	+	0.163094i
$486$		0			0
$487$	3.41485	+	5.91469i	0.154741	+	0.268020i	0.932965	−	0.359967i	$-0.117212\pi$
$487$	3.41485	+	5.91469i	0.154741	+	0.268020i	−0.778223	+	0.627988i	$0.783879\pi$
$488$	−9.36984	+	7.86223i	−0.424153	+	0.355906i
$489$		0			0
$490$	2.22055	+	5.97813i	0.100314	+	0.270064i
$491$	2.93823	+	0.518089i	0.132601	+	0.0233810i	0.239554	−	0.970883i	$-0.422999\pi$
$491$	2.93823	+	0.518089i	0.132601	+	0.0233810i	−0.106954	+	0.994264i	$0.534110\pi$
$492$		0			0
$493$	−13.1272	+	36.0667i	−0.591219	+	1.62436i
$494$	5.21442	+	3.01055i	0.234608	+	0.135451i
$495$		0			0
$496$	−6.51752	−	3.76289i	−0.292645	−	0.168959i
$497$	−9.98903	+	27.7284i	−0.448069	+	1.24379i
$498$		0			0
$499$	5.31326	−	30.1330i	0.237854	−	1.34894i	−0.598664	−	0.801000i	$-0.704302\pi$
$499$	5.31326	−	30.1330i	0.237854	−	1.34894i	0.836518	−	0.547939i	$-0.184587\pi$
$500$	−7.61374	−	6.38869i	−0.340497	−	0.285711i
$501$		0			0
$502$	2.48976	−	6.84055i	0.111123	−	0.305309i
$503$	−4.53519	+	7.85518i	−0.202214	+	0.350245i	−0.949242	−	0.314548i	$-0.898147\pi$
$503$	−4.53519	+	7.85518i	−0.202214	+	0.350245i	0.747027	+	0.664793i	$0.231480\pi$
$504$		0			0
$505$	−13.3111	−	23.0555i	−0.592335	−	1.02595i
$506$	−1.47087	+	0.259355i	−0.0653883	+	0.0115297i
$507$		0			0
$508$	30.2794	−	11.0208i	1.34343	−	0.488969i
$509$	7.01260	−	2.55238i	0.310828	−	0.113132i	−0.181896	−	0.983318i	$-0.558223\pi$
$509$	7.01260	−	2.55238i	0.310828	−	0.113132i	0.492724	+	0.870186i	$0.336001\pi$
$510$		0			0
$511$	5.30075	−	14.7143i	0.234491	−	0.650920i
$512$		−	20.5900i		−	0.909956i
$513$		0			0
$514$	3.45607	−	1.99536i	0.152441	−	0.0880117i
$515$	−31.7222	+	5.59348i	−1.39785	+	0.246478i
$516$		0			0
$517$	6.71229	−	7.99940i	0.295206	−	0.351813i
$518$	1.46665	+	0.253634i	0.0644410	+	0.0111440i
$519$		0			0
$520$	−2.11011	−	11.9670i	−0.0925345	−	0.524789i
$521$	−7.87991	+	13.6484i	−0.345225	+	0.597947i	−0.985395	−	0.170286i	$-0.945531\pi$
$521$	−7.87991	+	13.6484i	−0.345225	+	0.597947i	0.640170	+	0.768234i	$0.278864\pi$
$522$		0			0
$523$	4.87781	−	2.81620i	0.213292	−	0.123144i	−0.389549	−	0.921006i	$-0.627369\pi$
$523$	4.87781	−	2.81620i	0.213292	−	0.123144i	0.602840	+	0.797862i	$0.294036\pi$
$524$	−5.27292	−	29.9042i	−0.230348	−	1.30637i
$525$		0			0
$526$	3.81019	−	1.38679i	0.166132	−	0.0604671i
$527$	−10.1631	−	1.79203i	−0.442712	−	0.0780622i
$528$		0			0
$529$	16.1706	−	13.5688i	0.703071	−	0.589946i
$530$	−0.689016	−	1.19341i	−0.0299290	−	0.0518385i
$531$		0			0
$532$	0.0913019	+	27.7280i	0.00395844	+	1.20216i
$533$	11.6253	+	13.8545i	0.503548	+	0.600105i
$534$		0			0
$535$	−6.54487	−	17.9819i	−0.282959	−	0.777424i
$536$	11.7379	+	2.06971i	0.507000	+	0.0893977i
$537$		0			0
$538$	−2.13561	+	5.86755i	−0.0920729	+	0.252968i
$539$	−20.7349	−	11.7899i	−0.893117	−	0.507829i
$540$		0			0
$541$	−0.446747	+	0.773788i	−0.0192071	+	0.0332677i	−0.875469	−	0.483274i	$-0.839448\pi$
$541$	−0.446747	+	0.773788i	−0.0192071	+	0.0332677i	0.856262	+	0.516542i	$0.172781\pi$
$542$	−1.03279	−	5.85722i	−0.0443620	−	0.251589i
$543$		0			0
$544$	−5.69283	−	15.6409i	−0.244078	−	0.670599i
$545$	8.24321	−	46.7496i	0.353100	−	2.00253i
$546$		0			0
$547$	4.87449	−	4.09018i	0.208418	−	0.174884i	−0.532603	−	0.846365i	$-0.678786\pi$
$547$	4.87449	−	4.09018i	0.208418	−	0.174884i	0.741021	+	0.671481i	$0.234342\pi$
$548$			24.7388i			1.05679i
$549$		0			0
$550$	3.44118			0.146733
$551$	42.6978	+	15.5407i	1.81899	+	0.662058i
$552$		0			0
$553$	23.2312	+	19.3633i	0.987891	+	0.823411i
$554$	−0.291117	−	0.799836i	−0.0123684	−	0.0339818i
$555$		0			0
$556$	−4.99831	−	5.95675i	−0.211975	−	0.252622i
$557$			17.2809i			0.732217i	0.930572	+	0.366109i	$0.119310\pi$
$557$			17.2809i			0.732217i	−0.930572	+	0.366109i	$0.880690\pi$
$558$		0			0
$559$	26.9320	−	15.5492i	1.13910	−	0.657662i
$560$	19.6437	−	16.5935i	0.830096	−	0.701204i
$561$		0			0
$562$	4.23820	+	3.55627i	0.178778	+	0.150012i
$563$	0.323777	−	1.83623i	0.0136456	−	0.0773878i	−0.977225	−	0.212208i	$-0.931935\pi$
$563$	0.323777	−	1.83623i	0.0136456	−	0.0773878i	0.990870	+	0.134820i	$0.0430457\pi$
$564$		0			0
$565$	−19.4463	−	23.1752i	−0.818113	−	0.974989i
$566$	−0.348424			−0.0146454
$567$		0			0
$568$	−13.8429			−0.580837
$569$	−16.5138	−	19.6804i	−0.692296	−	0.825046i	0.299336	−	0.954148i	$-0.403235\pi$
$569$	−16.5138	−	19.6804i	−0.692296	−	0.825046i	−0.991631	+	0.129102i	$0.958791\pi$
$570$		0			0
$571$	−0.379935	+	2.15472i	−0.0158998	+	0.0901722i	−0.991725	−	0.128380i	$-0.959022\pi$
$571$	−0.379935	+	2.15472i	−0.0158998	+	0.0901722i	0.975825	+	0.218552i	$0.0701334\pi$
$572$	16.9547	+	14.2267i	0.708914	+	0.594849i
$573$		0			0
$574$	1.51092	−	4.19415i	0.0630648	−	0.175060i
$575$	3.77267	−	2.17815i	0.157331	−	0.0908351i
$576$		0			0
$577$		−	14.2718i		−	0.594142i	−0.954855	−	0.297071i	$-0.903990\pi$
$577$		−	14.2718i		−	0.594142i	0.954855	−	0.297071i	$-0.0960098\pi$
$578$	−0.972385	−	1.15884i	−0.0404459	−	0.0482015i
$579$		0			0
$580$	−15.2732	−	41.9629i	−0.634187	−	1.74241i
$581$	−3.22691	+	18.6598i	−0.133875	+	0.774139i
$582$		0			0
$583$	4.84337	+	1.76284i	0.200592	+	0.0730095i
$584$	7.34586			0.303974
$585$		0			0
$586$		−	6.71248i		−	0.277290i
$587$	−20.9075	+	17.5435i	−0.862947	+	0.724098i	−0.962601	−	0.270924i	$-0.912671\pi$
$587$	−20.9075	+	17.5435i	−0.862947	+	0.724098i	0.0996541	+	0.995022i	$0.468226\pi$
$588$		0			0
$589$	−2.12151	+	12.0317i	−0.0874154	+	0.495757i
$590$	−2.13873	−	5.87610i	−0.0880500	−	0.241915i
$591$		0			0
$592$	−1.04217	−	5.91043i	−0.0428328	−	0.242917i
$593$	−9.81715	+	17.0038i	−0.403142	+	0.698262i	−0.994103	−	0.108438i	$-0.965415\pi$
$593$	−9.81715	+	17.0038i	−0.403142	+	0.698262i	0.590961	+	0.806700i	$0.298749\pi$
$594$		0			0
$595$	17.5299	−	30.5949i	0.718657	−	1.25427i
$596$	−0.968498	+	2.66093i	−0.0396712	+	0.108996i
$597$		0			0
$598$	−1.47692	−	0.260421i	−0.0603958	−	0.0106494i
$599$	−6.60034	−	18.1343i	−0.269682	−	0.740946i	−0.998422	−	0.0561554i	$-0.982116\pi$
$599$	−6.60034	−	18.1343i	−0.269682	−	0.740946i	0.728740	−	0.684791i	$-0.240106\pi$
$600$		0			0
$601$	13.5997	+	16.2075i	0.554743	+	0.661116i	0.968425	−	0.249305i	$-0.0802021\pi$
$601$	13.5997	+	16.2075i	0.554743	+	0.661116i	−0.413683	+	0.910421i	$0.635758\pi$
$602$	−6.65113	−	3.81089i	−0.271080	−	0.155320i
$603$		0			0
$604$	4.61075	+	7.98605i	0.187609	+	0.324948i
$605$	−1.33773	+	1.12249i	−0.0543866	+	0.0456357i
$606$		0			0
$607$	−14.7116	−	2.59404i	−0.597123	−	0.105289i	−0.133086	−	0.991105i	$-0.542489\pi$
$607$	−14.7116	−	2.59404i	−0.597123	−	0.105289i	−0.464038	+	0.885816i	$0.653600\pi$
$608$	−18.5167	+	6.73951i	−0.750949	+	0.273323i
$609$		0			0
$610$	−1.55713	−	8.83091i	−0.0630463	−	0.357553i
$611$	9.08063	−	5.24270i	0.367363	−	0.212097i
$612$		0			0
$613$	−2.79443	+	4.84009i	−0.112866	+	0.195490i	−0.916925	−	0.399060i	$-0.869336\pi$
$613$	−2.79443	+	4.84009i	−0.112866	+	0.195490i	0.804059	+	0.594550i	$0.202670\pi$
$614$	−1.26277	−	7.16153i	−0.0509613	−	0.289016i
$615$		0			0
$616$	1.90907	−	11.0393i	0.0769187	−	0.444787i
$617$	−4.78146	+	5.69832i	−0.192494	+	0.229406i	−0.853655	−	0.520838i	$-0.825619\pi$
$617$	−4.78146	+	5.69832i	−0.192494	+	0.229406i	0.661161	+	0.750244i	$0.270064\pi$
$618$		0			0
$619$	15.1027	−	2.66302i	0.607030	−	0.107036i	0.138320	−	0.990388i	$-0.455830\pi$
$619$	15.1027	−	2.66302i	0.607030	−	0.107036i	0.468710	+	0.883352i	$0.344719\pi$
$620$	10.3984	−	6.00351i	0.417609	−	0.241107i
$621$		0			0
$622$			7.17613i			0.287737i
$623$	−5.73710	−	31.9217i	−0.229852	−	1.27892i
$624$		0			0
$625$	28.9459	−	10.5355i	1.15784	−	0.421418i
$626$	−0.422875	+	0.153914i	−0.0169015	+	0.00615164i
$627$		0			0
$628$	−42.1140	+	7.42583i	−1.68053	+	0.296323i
$629$	−4.11492	−	7.12725i	−0.164073	−	0.284182i
$630$		0			0
$631$	−12.0123	+	20.8060i	−0.478203	+	0.828272i	−0.999688	−	0.0249886i	$-0.992045\pi$
$631$	−12.0123	+	20.8060i	−0.478203	+	0.828272i	0.521485	+	0.853261i	$0.325378\pi$
$632$	−4.85827	+	13.3480i	−0.193252	+	0.530954i
$633$		0			0
$634$	1.67384	+	1.40452i	0.0664767	+	0.0557806i
$635$	−8.42380	+	47.7737i	−0.334288	+	1.89584i
$636$		0			0
$637$	−15.5156	−	18.2454i	−0.614750	−	0.722909i
$638$	−7.74232	−	4.47003i	−0.306521	−	0.176970i
$639$		0			0
$640$	22.1374	+	12.7810i	0.875056	+	0.505214i
$641$	15.3856	−	42.2717i	0.607696	−	1.66963i	−0.127552	−	0.991832i	$-0.540712\pi$
$641$	15.3856	−	42.2717i	0.607696	−	1.66963i	0.735248	−	0.677798i	$-0.237066\pi$
$642$		0			0
$643$	5.46038	+	0.962813i	0.215337	+	0.0379696i	0.280276	−	0.959920i	$-0.409574\pi$
$643$	5.46038	+	0.962813i	0.215337	+	0.0379696i	−0.0649390	+	0.997889i	$0.520685\pi$
$644$	−2.38348	−	6.48206i	−0.0939222	−	0.255429i
$645$		0			0
$646$	−6.28635	+	5.27488i	−0.247333	+	0.207537i
$647$	17.8595	+	30.9335i	0.702127	+	1.21612i	0.967718	+	0.252035i	$0.0810997\pi$
$647$	17.8595	+	30.9335i	0.702127	+	1.21612i	−0.265591	+	0.964086i	$0.585567\pi$
$648$		0			0
$649$	20.2552	+	11.6943i	0.795086	+	0.459043i
$650$	3.24695	+	1.18179i	0.127356	+	0.0463538i
$651$		0			0
$652$	13.9988	+	11.7464i	0.548235	+	0.460023i
$653$	−17.1210	+	20.4041i	−0.669998	+	0.798473i	−0.988784	−	0.149354i	$-0.952281\pi$
$653$	−17.1210	+	20.4041i	−0.669998	+	0.798473i	0.318786	+	0.947827i	$0.396725\pi$
$654$		0			0
$655$	42.9578	+	15.6354i	1.67850	+	0.610925i
$656$	−17.9755			−0.701827
$657$		0			0
$658$	−2.24255	−	1.28491i	−0.0874237	−	0.0500910i
$659$	−27.7440	+	4.89202i	−1.08075	+	0.190566i	−0.685549	−	0.728027i	$-0.740438\pi$
$659$	−27.7440	+	4.89202i	−1.08075	+	0.190566i	−0.395205	+	0.918593i	$0.629327\pi$
$660$		0			0
$661$	−21.3442	+	25.4370i	−0.830193	+	0.989386i	0.169799	+	0.985479i	$0.445688\pi$
$661$	−21.3442	+	25.4370i	−0.830193	+	0.989386i	−0.999992	+	0.00390705i	$0.998756\pi$
$662$	0.609805	−	0.726737i	0.0237007	−	0.0282454i
$663$		0			0
$664$	−8.75922	+	1.54449i	−0.339924	+	0.0599377i
$665$	−36.2201	−	20.7530i	−1.40455	−	0.804765i
$666$		0			0
$667$	−11.3175			−0.438215
$668$	−17.9845	−	6.54584i	−0.695843	−	0.253266i
$669$		0			0
$670$	−5.61671	+	6.69373i	−0.216992	+	0.258602i
$671$	25.6927	+	21.5588i	0.991857	+	0.832267i
$672$		0			0
$673$	2.51415	+	0.915077i	0.0969135	+	0.0352736i	0.390022	−	0.920806i	$-0.372467\pi$
$673$	2.51415	+	0.915077i	0.0969135	+	0.0352736i	−0.293108	+	0.956079i	$0.594690\pi$
$674$	−6.95908	−	4.01783i	−0.268054	−	0.154761i
$675$		0			0
$676$	−1.22760	−	2.12627i	−0.0472154	−	0.0817795i
$677$	30.4165	−	25.5225i	1.16900	−	0.980909i	0.169013	−	0.985614i	$-0.445942\pi$
$677$	30.4165	−	25.5225i	1.16900	−	0.980909i	0.999989	+	0.00470491i	$0.00149763\pi$
$678$		0			0
$679$	2.29503	+	6.24152i	0.0880752	+	0.239528i
$680$	16.3101	+	2.87591i	0.625463	+	0.110286i
$681$		0			0
$682$	0.822144	−	2.25882i	0.0314815	−	0.0864947i
$683$	16.9924	+	9.81058i	0.650197	+	0.375392i	0.788532	−	0.614994i	$-0.210842\pi$
$683$	16.9924	+	9.81058i	0.650197	+	0.375392i	−0.138335	+	0.990386i	$0.544175\pi$
$684$		0			0
$685$	−32.2541	−	18.6219i	−1.23237	−	0.711507i
$686$	−1.96426	+	5.56727i	−0.0749958	+	0.212559i
$687$		0			0
$688$	−5.36728	+	30.4394i	−0.204626	+	1.16049i
$689$	3.96459	+	3.32668i	0.151039	+	0.126737i
$690$		0			0
$691$	1.90749	−	5.24080i	0.0725645	−	0.199369i	−0.898108	−	0.439775i	$-0.855058\pi$
$691$	1.90749	−	5.24080i	0.0725645	−	0.199369i	0.970673	+	0.240406i	$0.0772804\pi$
$692$	11.7328	−	20.3218i	0.446013	−	0.772517i
$693$		0			0
$694$	−0.366866	−	0.635430i	−0.0139260	−	0.0241206i
$695$	11.5288	−	2.03283i	0.437311	−	0.0771097i
$696$		0			0
$697$	−23.1628	+	8.43059i	−0.877355	+	0.319331i
$698$	−2.09446	+	0.762322i	−0.0792765	+	0.0288543i
$699$		0			0
$700$	2.81474	+	15.6614i	0.106387	+	0.591947i
$701$			46.9342i			1.77268i	0.463033	+	0.886341i	$0.346761\pi$
$701$			46.9342i			1.77268i	−0.463033	+	0.886341i	$0.653239\pi$
$702$		0			0
$703$	−8.43766	+	4.87149i	−0.318232	+	0.183732i
$704$	−19.0052	+	3.35113i	−0.716286	+	0.126301i
$705$		0			0
$706$	4.52564	−	5.39345i	0.170325	−	0.202985i
$707$	4.19964	−	24.2847i	0.157944	−	0.913320i
$708$		0			0
$709$	−3.01382	−	17.0922i	−0.113186	−	0.641911i	−0.987632	−	0.156788i	$-0.949886\pi$
$709$	−3.01382	−	17.0922i	−0.113186	−	0.641911i	0.874446	−	0.485123i	$-0.161225\pi$
$710$	5.07428	−	8.78891i	0.190434	−	0.329842i
$711$		0			0
$712$	13.1925	−	7.61670i	0.494410	−	0.285448i
$713$	−0.528416	−	2.99680i	−0.0197893	−	0.112231i
$714$		0			0
$715$	−31.3111	+	11.3963i	−1.17097	+	0.426198i
$716$	29.5086	+	5.20315i	1.10279	+	0.194451i
$717$		0			0
$718$	−7.96213	+	6.68102i	−0.297144	+	0.249334i
$719$	−13.3361	−	23.0988i	−0.497353	−	0.861441i	0.502642	−	0.864495i	$-0.332361\pi$
$719$	−13.3361	−	23.0988i	−0.497353	−	0.861441i	−0.999995	+	0.00305366i	$0.999028\pi$
$720$		0			0
$721$	−25.8734	−	14.8246i	−0.963575	−	0.552098i
$722$	2.35163	+	2.80257i	0.0875187	+	0.104301i
$723$		0			0
$724$	8.51707	+	23.4005i	0.316534	+	0.869671i
$725$	25.6795	+	4.52798i	0.953711	+	0.168165i
$726$		0			0
$727$	−11.6117	+	31.9029i	−0.430654	+	1.18321i	0.514758	+	0.857336i	$0.327882\pi$
$727$	−11.6117	+	31.9029i	−0.430654	+	1.18321i	−0.945412	+	0.325878i	$0.894340\pi$
$728$	5.59251	−	9.76059i	0.207272	−	0.361752i
$729$		0			0
$730$	−2.69270	+	4.66390i	−0.0996614	+	0.172619i
$731$	7.36001	+	41.7407i	0.272220	+	1.54384i
$732$		0			0
$733$	5.22487	+	14.3552i	0.192985	+	0.530222i	0.998013	−	0.0630153i	$-0.0200717\pi$
$733$	5.22487	+	14.3552i	0.192985	+	0.530222i	−0.805027	+	0.593238i	$0.797849\pi$
$734$	0.235454	−	1.33532i	0.00869076	−	0.0492877i
$735$		0			0
$736$	3.75977	−	3.15482i	0.138587	−	0.116288i
$737$		−	32.6826i		−	1.20388i
$738$		0			0
$739$	−31.0643			−1.14272			−0.571359	−	0.820701i	$-0.693583\pi$
$739$	−31.0643			−1.14272			−0.571359	+	0.820701i	$0.693583\pi$
$740$	8.99781	+	3.27494i	0.330766	+	0.120389i
$741$		0			0
$742$	0.217385	−	1.25704i	0.00798044	−	0.0461474i
$743$	10.8218	+	29.7328i	0.397015	+	1.09079i	0.963731	+	0.266876i	$0.0859915\pi$
$743$	10.8218	+	29.7328i	0.397015	+	1.09079i	−0.566716	+	0.823913i	$0.691786\pi$
$744$		0			0
$745$	−2.74025	−	3.26571i	−0.100395	−	0.119646i
$746$			7.76844i			0.284423i
$747$		0			0
$748$	−26.1239	+	15.0826i	−0.955183	+	0.551475i
$749$	6.00399	−	16.6664i	0.219381	−	0.608976i
$750$		0			0
$751$	−16.1329	−	13.5371i	−0.588698	−	0.493976i	0.299093	−	0.954224i	$-0.403316\pi$
$751$	−16.1329	−	13.5371i	−0.588698	−	0.493976i	−0.887790	+	0.460248i	$0.847760\pi$
$752$	−1.80968	+	10.2632i	−0.0659921	+	0.374260i
$753$		0			0
$754$	−5.77019	−	6.87664i	−0.210138	−	0.250433i
$755$	−13.8828			−0.505247
$756$		0			0
$757$	−13.1053			−0.476322			−0.238161	−	0.971226i	$-0.576545\pi$
$757$	−13.1053			−0.476322			−0.238161	+	0.971226i	$0.576545\pi$
$758$	3.65782	+	4.35922i	0.132858	+	0.158334i
$759$		0			0
$760$	3.40467	−	19.3088i	0.123500	−	0.700405i
$761$	7.76470	+	6.51536i	0.281470	+	0.236182i	0.772582	−	0.634915i	$-0.218965\pi$
$761$	7.76470	+	6.51536i	0.281470	+	0.236182i	−0.491112	+	0.871097i	$0.663409\pi$
$762$		0			0
$763$	33.5710	−	28.3583i	1.21535	−	1.02664i
$764$	29.2197	−	16.8700i	1.05713	−	0.610335i
$765$		0			0
$766$			8.72505i			0.315249i
$767$	15.0958	+	17.9904i	0.545077	+	0.649597i
$768$		0			0
$769$	7.15123	+	19.6478i	0.257880	+	0.708519i	0.999298	+	0.0374752i	$0.0119315\pi$
$769$	7.15123	+	19.6478i	0.257880	+	0.708519i	−0.741418	+	0.671044i	$0.765846\pi$
$770$	6.30909	+	5.25865i	0.227364	+	0.189509i
$771$		0			0
$772$	24.3039	+	8.84590i	0.874717	+	0.318371i
$773$	−21.1888			−0.762108			−0.381054	−	0.924553i	$-0.624439\pi$
$773$	−21.1888			−0.762108			−0.381054	+	0.924553i	$0.624439\pi$
$774$		0			0
$775$			7.01116i			0.251848i
$776$	−2.39271	+	2.00772i	−0.0858932	+	0.0720730i
$777$		0			0
$778$	−0.902204	+	5.11665i	−0.0323456	+	0.183441i
$779$	9.98062	+	27.4215i	0.357593	+	0.982478i
$780$		0			0
$781$	6.59139	+	37.3816i	0.235858	+	1.33762i
$782$	1.02199	−	1.77013i	0.0365462	−	0.0632998i
$783$		0			0
$784$	23.8041	−	0.156764i	0.850145	−	0.00559873i
$785$	22.0192	−	60.4974i	0.785900	−	2.15924i
$786$		0			0
$787$	−21.4804	−	3.78757i	−0.765693	−	0.135012i	−0.222857	−	0.974851i	$-0.571538\pi$
$787$	−21.4804	−	3.78757i	−0.765693	−	0.135012i	−0.542836	+	0.839839i	$0.682650\pi$
$788$	5.98751	+	16.4505i	0.213296	+	0.586027i
$789$		0			0
$790$	−6.69381	−	7.97737i	−0.238155	−	0.283822i
$791$	−0.0922183	−	28.0063i	−0.00327891	−	0.995789i
$792$		0			0
$793$	16.8387	+	29.1655i	0.597960	+	1.03570i
$794$	1.11264	−	0.933613i	0.0394860	−	0.0331327i
$795$		0			0
$796$	0.501380	+	0.0884069i	0.0177710	+	0.00313350i
$797$	−14.4170	+	5.24735i	−0.510676	+	0.185871i	−0.584490	−	0.811401i	$-0.698705\pi$
$797$	−14.4170	+	5.24735i	−0.510676	+	0.185871i	0.0738137	+	0.997272i	$0.476483\pi$
$798$		0			0
$799$	2.48156	+	14.0736i	0.0877913	+	0.497889i
$800$	−9.79314	+	5.65407i	−0.346240	+	0.199902i
$801$		0			0
$802$	−6.00818	+	10.4065i	−0.212156	+	0.367466i
$803$	−3.49777	−	19.8368i	−0.123434	−	0.700026i
$804$		0			0
$805$	10.2454	+	1.77177i	0.361102	+	0.0624467i
$806$	1.55148	−	1.84898i	0.0546485	−	0.0651275i
$807$		0			0
$808$	11.3996	−	2.01006i	0.401038	−	0.0707137i
$809$	11.6471	−	6.72444i	0.409489	−	0.236419i	−0.281081	−	0.959684i	$-0.590693\pi$
$809$	11.6471	−	6.72444i	0.409489	−	0.236419i	0.690570	+	0.723265i	$0.257360\pi$
$810$		0			0
$811$			3.07886i			0.108113i	0.998538	+	0.0540566i	$0.0172152\pi$
$811$			3.07886i			0.108113i	−0.998538	+	0.0540566i	$0.982785\pi$
$812$	14.0110	−	38.8930i	0.491691	−	1.36488i
$813$		0			0
$814$	1.80135	−	0.655637i	0.0631373	−	0.0229801i
$815$	−25.8522	+	9.40944i	−0.905564	+	0.329598i
$816$		0			0
$817$	49.4151	−	8.71321i	1.72881	−	0.304837i
$818$	0.159623	+	0.276474i	0.00558107	+	0.00966670i
$819$		0			0
$820$	14.3395	−	24.8368i	0.500759	−	0.867340i
$821$	1.54402	−	4.24217i	0.0538868	−	0.148053i	−0.909829	−	0.414984i	$-0.863787\pi$
$821$	1.54402	−	4.24217i	0.0538868	−	0.148053i	0.963716	+	0.266931i	$0.0860095\pi$
$822$		0			0
$823$	23.4546	+	19.6807i	0.817575	+	0.686027i	0.952403	−	0.304842i	$-0.0986036\pi$
$823$	23.4546	+	19.6807i	0.817575	+	0.686027i	−0.134828	+	0.990869i	$0.543048\pi$
$824$	2.43208	−	13.7930i	0.0847256	−	0.480503i
$825$		0			0
$826$	1.96198	−	5.44622i	0.0682660	−	0.189498i
$827$	−12.8966	−	7.44587i	−0.448459	−	0.258918i	0.258720	−	0.965952i	$-0.416699\pi$
$827$	−12.8966	−	7.44587i	−0.448459	−	0.258918i	−0.707179	+	0.707034i	$0.750033\pi$
$828$		0			0
$829$	21.8853	+	12.6355i	0.760107	+	0.438848i	0.829334	−	0.558753i	$-0.188720\pi$
$829$	21.8853	+	12.6355i	0.760107	+	0.438848i	−0.0692275	+	0.997601i	$0.522053\pi$
$830$	2.23019	−	6.12739i	0.0774109	−	0.212685i
$831$		0			0
$832$	−19.0834	−	3.36491i	−0.661597	−	0.116657i
$833$	30.5998	−	11.3662i	1.06022	−	0.393815i
$834$		0			0
$835$	22.0721	−	18.5207i	0.763836	−	0.640934i
$836$	17.8557	+	30.9270i	0.617552	+	1.06963i
$837$		0			0
$838$	−0.648204	−	0.374241i	−0.0223918	−	0.0129279i
$839$	16.6975	+	6.07738i	0.576460	+	0.209814i	0.613764	−	0.789490i	$-0.289655\pi$
$839$	16.6975	+	6.07738i	0.576460	+	0.209814i	−0.0373037	+	0.999304i	$0.511877\pi$
$840$		0			0
$841$	−29.6792	−	24.9038i	−1.02342	−	0.858751i
$842$	1.34572	−	1.60376i	0.0463764	−	0.0552692i
$843$		0			0
$844$	23.3368	+	8.49391i	0.803287	+	0.292373i
$845$	3.69626			0.127155
$846$		0			0
$847$	−1.61659	+	0.00532307i	−0.0555468	+	0.000182903i
$848$	−5.06571	+	0.893222i	−0.173957	+	0.0306734i
$849$		0			0
$850$	−3.02710	+	3.60756i	−0.103829	+	0.123738i
$851$	1.55987	−	1.85898i	0.0534717	−	0.0637251i
$852$		0			0
$853$	13.7587	−	2.42603i	0.471089	−	0.0830656i	0.0669361	−	0.997757i	$-0.478678\pi$
$853$	13.7587	−	2.42603i	0.471089	−	0.0830656i	0.404152	+	0.914692i	$0.367567\pi$
$854$	4.12692	−	7.20270i	0.141220	−	0.246471i
$855$		0			0
$856$	8.32042			0.284386
$857$	−20.0805	−	7.30871i	−0.685937	−	0.249661i	−0.0245424	−	0.999699i	$-0.507813\pi$
$857$	−20.0805	−	7.30871i	−0.685937	−	0.249661i	−0.661395	+	0.750038i	$0.730035\pi$
$858$		0			0
$859$	7.97036	−	9.49870i	0.271945	−	0.324092i	−0.612737	−	0.790287i	$-0.709931\pi$
$859$	7.97036	−	9.49870i	0.271945	−	0.324092i	0.884682	+	0.466196i	$0.154376\pi$
$860$	−37.7765	−	31.6982i	−1.28817	−	1.08090i
$861$		0			0
$862$	4.61598	+	1.68008i	0.157221	+	0.0572237i
$863$	−9.03144	−	5.21430i	−0.307434	−	0.177497i	0.338344	−	0.941023i	$-0.390133\pi$
$863$	−9.03144	−	5.21430i	−0.307434	−	0.177497i	−0.645778	+	0.763526i	$0.723467\pi$
$864$		0			0
$865$	17.6635	+	30.5941i	0.600577	+	1.04023i
$866$	−2.41060	+	2.02274i	−0.0819156	+	0.0687354i
$867$		0			0
$868$	10.9528	+	1.89411i	0.371762	+	0.0642901i
$869$	38.3583	+	6.76360i	1.30122	+	0.229440i
$870$		0			0
$871$	11.2241	−	30.8379i	0.380313	−	1.04490i
$872$	17.8753	+	10.3203i	0.605333	+	0.349489i
$873$		0			0
$874$	−2.09559	−	1.20989i	−0.0708843	−	0.0409250i
$875$	13.0320	+	4.69473i	0.440563	+	0.158711i
$876$		0			0
$877$	7.13778	−	40.4804i	0.241026	−	1.36693i	−0.588518	−	0.808484i	$-0.700289\pi$
$877$	7.13778	−	40.4804i	0.241026	−	1.36693i	0.829544	−	0.558441i	$-0.188600\pi$
$878$	8.62121	+	7.23405i	0.290952	+	0.244137i
$879$		0			0
$880$	11.3269	−	31.1203i	0.381829	−	1.04907i
$881$	−14.4200	+	24.9761i	−0.485821	+	0.841467i	−0.999867	−	0.0162958i	$-0.994813\pi$
$881$	−14.4200	+	24.9761i	−0.485821	+	0.841467i	0.514046	+	0.857762i	$0.328146\pi$
$882$		0			0
$883$	24.3484	+	42.1726i	0.819388	+	1.41922i	0.906134	+	0.422991i	$0.139020\pi$
$883$	24.3484	+	42.1726i	0.819388	+	1.41922i	−0.0867455	+	0.996231i	$0.527647\pi$
$884$	−29.8291	+	5.25967i	−1.00326	+	0.176902i
$885$		0			0
$886$	1.33306	−	0.485193i	0.0447849	−	0.0163004i
$887$	7.47224	−	2.71967i	0.250893	−	0.0913177i	−0.213512	−	0.976940i	$-0.568490\pi$
$887$	7.47224	−	2.71967i	0.250893	−	0.0913177i	0.464405	+	0.885623i	$0.346268\pi$
$888$		0			0
$889$	−34.3064	+	28.9796i	−1.15060	+	0.971943i
$890$			11.1679i			0.374350i
$891$		0			0
$892$	−24.3102	+	14.0355i	−0.813967	+	0.469944i
$893$	16.6612	−	2.93782i	0.557545	−	0.0983103i
$894$		0			0
$895$	−28.9961	+	34.5562i	−0.969233	+	1.15509i
$896$	8.16665	+	22.2099i	0.272829	+	0.741980i
$897$		0			0
$898$	0.317163	+	1.79872i	0.0105839	+	0.0600241i
$899$	9.10736	−	15.7744i	0.303748	−	0.526106i
$900$		0			0
$901$	−6.10863	+	3.52682i	−0.203508	+	0.117495i
$902$	−0.997004	−	5.65429i	−0.0331966	−	0.188267i
$903$		0			0
$904$	12.3609	−	4.49902i	0.411119	−	0.149635i
$905$	−36.9204	−	6.51005i	−1.22727	−	0.216402i
$906$		0			0
$907$	33.1849	−	27.8455i	1.10189	−	0.924593i	0.104337	−	0.994542i	$-0.466728\pi$
$907$	33.1849	−	27.8455i	1.10189	−	0.924593i	0.997551	+	0.0699485i	$0.0222835\pi$
$908$	−8.70416	−	15.0761i	−0.288858	−	0.500316i
$909$		0			0
$910$	4.14702	+	7.12854i	0.137472	+	0.236309i
$911$	32.8056	+	39.0962i	1.08690	+	1.29531i	0.952551	+	0.304379i	$0.0984490\pi$
$911$	32.8056	+	39.0962i	1.08690	+	1.29531i	0.134346	+	0.990934i	$0.457107\pi$
$912$		0			0
$913$	8.34149	+	22.9181i	0.276063	+	0.758477i
$914$	−12.8292	−	2.26213i	−0.424352	−	0.0748247i
$915$		0			0
$916$	8.30690	−	22.8230i	0.274468	−	0.754094i
$917$	21.2805	+	36.5802i	0.702745	+	1.20799i
$918$		0			0
$919$	19.5951	−	33.9398i	0.646384	−	1.11957i	−0.337596	−	0.941291i	$-0.609614\pi$
$919$	19.5951	−	33.9398i	0.646384	−	1.11957i	0.983980	−	0.178279i	$-0.0570529\pi$
$920$	0.848017	+	4.80935i	0.0279583	+	0.158559i
$921$		0			0
$922$	2.95873	+	8.12904i	0.0974406	+	0.267716i
$923$	−6.61849	+	37.5353i	−0.217850	+	1.23549i
$924$		0			0
$925$	−4.28312	+	3.59396i	−0.140828	+	0.118169i
$926$			4.06400i			0.133551i
$927$		0			0
$928$	29.3781			0.964384
$929$	28.7454	+	10.4625i	0.943107	+	0.343263i	0.767392	−	0.641178i	$-0.221554\pi$
$929$	28.7454	+	10.4625i	0.943107	+	0.343263i	0.175715	+	0.984441i	$0.443776\pi$
$930$		0			0
$931$	−13.4560	−	36.2259i	−0.441001	−	1.18725i
$932$	−11.0813	−	30.4455i	−0.362979	−	0.997275i
$933$		0			0
$934$	4.61930	+	5.50507i	0.151148	+	0.180131i
$935$		−	45.4133i		−	1.48517i
$936$		0			0
$937$	4.39414	−	2.53696i	0.143550	−	0.0828787i	−0.426505	−	0.904485i	$-0.640255\pi$
$937$	4.39414	−	2.53696i	0.143550	−	0.0828787i	0.570055	+	0.821607i	$0.306922\pi$
$938$	−7.96158	+	1.43089i	−0.259955	+	0.0467202i
$939$		0			0
$940$	−12.7370	−	10.6876i	−0.415436	−	0.348592i
$941$	2.52700	−	14.3313i	0.0823778	−	0.467188i	−0.915514	−	0.402286i	$-0.868216\pi$
$941$	2.52700	−	14.3313i	0.0823778	−	0.467188i	0.997892	−	0.0649013i	$-0.0206733\pi$
$942$		0			0
$943$	−4.67201	−	5.56788i	−0.152142	−	0.181315i
$944$	−23.3417			−0.759709
$945$		0			0
$946$	−9.87254			−0.320984
$947$	35.0139	+	41.7280i	1.13780	+	1.35598i	0.925489	+	0.378774i	$0.123654\pi$
$947$	35.0139	+	41.7280i	1.13780	+	1.35598i	0.212310	+	0.977202i	$0.431901\pi$
$948$		0			0
$949$	3.51215	−	19.9184i	0.114009	−	0.646578i
$950$	4.27084	+	3.58366i	0.138564	+	0.116269i
$951$		0			0
$952$	9.89370	+	11.7123i	0.320657	+	0.379598i
$953$	−19.6055	+	11.3192i	−0.635084	+	0.366666i	−0.782718	−	0.622376i	$-0.786167\pi$
$953$	−19.6055	+	11.3192i	−0.635084	+	0.366666i	0.147634	+	0.989042i	$0.452834\pi$
$954$		0			0
$955$			50.7950i			1.64369i
$956$	−8.23594	−	9.81521i	−0.266369	−	0.317447i
$957$		0			0
$958$	−3.55736	−	9.77376i	−0.114933	−	0.315776i
$959$	−11.8988	−	32.3598i	−0.384232	−	1.04495i
$960$		0			0
$961$	−24.5283	−	8.92757i	−0.791235	−	0.287986i
$962$	1.92484			0.0620592
$963$		0			0
$964$			5.33053i			0.171685i
$965$	−29.8277	+	25.0284i	−0.960189	+	0.805694i
$966$		0			0
$967$	5.14316	−	29.1683i	0.165393	−	0.937990i	−0.783265	−	0.621687i	$-0.786447\pi$
$967$	5.14316	−	29.1683i	0.165393	−	0.937990i	0.948658	−	0.316303i	$-0.102441\pi$
$968$	−0.259695	−	0.713505i	−0.00834690	−	0.0229329i
$969$		0			0
$970$	−0.397633	−	2.25509i	−0.0127672	−	0.0724065i
$971$	7.12855	−	12.3470i	0.228766	−	0.396234i	−0.728677	−	0.684858i	$-0.759864\pi$
$971$	7.12855	−	12.3470i	0.228766	−	0.396234i	0.957443	+	0.288623i	$0.0931976\pi$
$972$		0			0
$973$	9.40313	+	5.38769i	0.301450	+	0.172722i
$974$	0.744603	−	2.04578i	0.0238586	−	0.0655510i
$975$		0			0
$976$	−32.9637	−	5.81238i	−1.05514	−	0.186050i
$977$	−6.86194	−	18.8530i	−0.219533	−	0.603162i	0.780217	−	0.625508i	$-0.215108\pi$
$977$	−6.86194	−	18.8530i	−0.219533	−	0.603162i	−0.999750	+	0.0223468i	$0.992886\pi$
$978$		0			0
$979$	−26.8499	−	31.9985i	−0.858126	−	1.02268i
$980$	−18.7725	+	33.0152i	−0.599666	+	1.05463i
$981$		0			0
$982$	−0.475528	−	0.823639i	−0.0151747	−	0.0262834i
$983$	12.8242	−	10.7608i	0.409029	−	0.343216i	−0.414942	−	0.909848i	$-0.636198\pi$
$983$	12.8242	−	10.7608i	0.409029	−	0.343216i	0.823971	+	0.566632i	$0.191754\pi$
$984$		0			0
$985$	−25.9551	−	4.57658i	−0.826997	−	0.145822i
$986$	11.4968	−	4.18450i	0.366133	−	0.133262i
$987$		0			0
$988$	6.22671	+	35.3134i	0.198098	+	1.12347i
$989$	−10.8235	+	6.24897i	−0.344168	+	0.198706i
$990$		0			0
$991$	−11.0601	+	19.1566i	−0.351335	+	0.608531i	−0.986484	−	0.163859i	$-0.947606\pi$
$991$	−11.0601	+	19.1566i	−0.351335	+	0.608531i	0.635148	+	0.772390i	$0.280939\pi$
$992$	1.37167	+	7.77913i	0.0435506	+	0.246988i
$993$		0			0
$994$	8.81770	−	3.24230i	0.279680	−	0.102840i
$995$	−0.492673	+	0.587145i	−0.0156188	+	0.0186138i
$996$		0			0
$997$	−43.9525	+	7.75001i	−1.39199	+	0.245445i	−0.818847	−	0.574011i	$-0.805387\pi$
$997$	−43.9525	+	7.75001i	−1.39199	+	0.245445i	−0.573141	+	0.819457i	$0.694275\pi$
$998$	−8.44683	+	4.87678i	−0.267380	+	0.154372i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.341.10		132
3.2	odd	2		189.2.ba.a.131.13	yes	132
7.3	odd	6		567.2.bd.a.17.13		132
21.17	even	6		189.2.bd.a.185.10	yes	132
27.7	even	9		189.2.bd.a.47.10	yes	132
27.20	odd	18		567.2.bd.a.467.13		132
189.101	even	18	inner	567.2.ba.a.143.10		132
189.115	odd	18		189.2.ba.a.101.13	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.13	✓	132	189.115	odd	18
189.2.ba.a.131.13	yes	132	3.2	odd	2
189.2.bd.a.47.10	yes	132	27.7	even	9
189.2.bd.a.185.10	yes	132	21.17	even	6
567.2.ba.a.143.10		132	189.101	even	18	inner
567.2.ba.a.341.10		132	1.1	even	1	trivial
567.2.bd.a.17.13		132	7.3	odd	6
567.2.bd.a.467.13		132	27.20	odd	18

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.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.204899 - 0.244189i) q^{2} +(0.329652 - 1.86955i) q^{4} +(2.18935 + 1.83708i) q^{5} +(0.468007 + 2.60403i) q^{7} +(-1.07619 + 0.621337i) q^{8} -0.911030i q^{10} +(2.19030 + 2.61029i) q^{11} +(1.17022 + 3.21516i) q^{13} +(0.539981 - 0.647845i) q^{14} +(-3.19557 - 1.16309i) q^{16} -4.66323 q^{17} +5.52060i q^{19} +(4.15623 - 3.48749i) q^{20} +(0.188615 - 1.06969i) q^{22} +(-0.470293 - 1.29212i) q^{23} +(0.550137 + 3.11998i) q^{25} +(0.545329 - 0.944538i) q^{26} +(5.02264 - 0.0165384i) q^{28} +(2.81504 - 7.73427i) q^{29} +(2.17942 + 0.384290i) q^{31} +(1.22079 + 3.35410i) q^{32} +(0.955489 + 1.13871i) q^{34} +(-3.75918 + 6.56089i) q^{35} +(0.882419 + 1.52840i) q^{37} +(1.34807 - 1.13116i) q^{38} +(-3.49759 - 0.616720i) q^{40} +(4.96713 - 1.80789i) q^{41} +(-1.57831 - 8.95103i) q^{43} +(5.60210 - 3.23437i) q^{44} +(-0.219159 + 0.379594i) q^{46} +(-0.532155 - 3.01800i) q^{47} +(-6.56194 + 2.43741i) q^{49} +(0.649143 - 0.773618i) q^{50} +(6.39667 - 1.12790i) q^{52} +(1.30996 - 0.756305i) q^{53} +9.73859i q^{55} +(-2.12164 - 2.51163i) q^{56} +(-2.46542 + 0.897340i) q^{58} +(6.44995 - 2.34759i) q^{59} +(9.69333 - 1.70919i) q^{61} +(-0.352721 - 0.610930i) q^{62} +(-2.83176 + 4.90475i) q^{64} +(-3.34449 + 9.18891i) q^{65} +(-7.34743 - 6.16523i) q^{67} +(-1.53724 + 8.71812i) q^{68} +(2.37235 - 0.426368i) q^{70} +(9.64722 + 5.56983i) q^{71} +(-5.11937 - 2.95567i) q^{73} +(0.192410 - 0.528643i) q^{74} +(10.3210 + 1.81988i) q^{76} +(-5.77220 + 6.92523i) q^{77} +(8.75642 - 7.34751i) q^{79} +(-4.85952 - 8.41694i) q^{80} +(-1.45922 - 0.842484i) q^{82} +(6.72578 + 2.44798i) q^{83} +(-10.2094 - 8.56673i) q^{85} +(-1.86235 + 2.21946i) q^{86} +(-3.97904 - 1.44825i) q^{88} -12.2586 q^{89} +(-7.82471 + 4.55201i) q^{91} +(-2.57071 + 0.453286i) q^{92} +(-0.627925 + 0.748331i) q^{94} +(-10.1418 + 12.0865i) q^{95} +(2.47531 - 0.436465i) q^{97} +(1.93972 + 1.10293i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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