LMFDB - Embedded newform 405.2.p.a.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(19,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.p (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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	405.289
Dual form			405.2.p.a.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73512 + 2.06784i) q^{2} +(-0.918006 - 5.20627i) q^{4} +(-1.79745 - 1.33011i) q^{5} +(-0.996499 - 0.175710i) q^{7} +(7.68312 + 4.43585i) q^{8} +(5.86923 - 1.40893i) q^{10} +(1.18249 - 0.430390i) q^{11} +(2.66452 + 3.17545i) q^{13} +(2.09238 - 1.75572i) q^{14} +(-12.5682 + 4.57445i) q^{16} +(-3.38700 + 1.95549i) q^{17} +(-0.433214 + 0.750349i) q^{19} +(-5.27482 + 10.5790i) q^{20} +(-1.16178 + 3.19197i) q^{22} +(-2.71843 + 0.479332i) q^{23} +(1.46164 + 4.78159i) q^{25} -11.1896 q^{26} +5.34934i q^{28} +(6.00558 + 5.03928i) q^{29} +(0.941551 + 5.33980i) q^{31} +(6.27953 - 17.2529i) q^{32} +(1.83323 - 10.3968i) q^{34} +(1.55744 + 1.64128i) q^{35} +(-6.44260 + 3.71964i) q^{37} +(-0.799919 - 2.19776i) q^{38} +(-7.90986 - 18.1926i) q^{40} +(2.73623 - 2.29597i) q^{41} +(1.45819 + 4.00634i) q^{43} +(-3.32626 - 5.76125i) q^{44} +(3.72562 - 6.45296i) q^{46} +(3.63443 + 0.640847i) q^{47} +(-5.61571 - 2.04395i) q^{49} +(-12.4237 - 5.27421i) q^{50} +(14.0862 - 16.7873i) q^{52} +0.485518i q^{53} +(-2.69792 - 0.799229i) q^{55} +(-6.87680 - 5.77032i) q^{56} +(-20.8408 + 3.67480i) q^{58} +(1.47979 + 0.538599i) q^{59} +(0.286481 - 1.62472i) q^{61} +(-12.6755 - 7.31822i) q^{62} +(11.4056 + 19.7550i) q^{64} +(-0.565650 - 9.25179i) q^{65} +(2.13105 + 2.53969i) q^{67} +(13.2901 + 15.8385i) q^{68} +(-6.09624 + 0.372721i) q^{70} +(4.95764 + 8.58688i) q^{71} +(4.55975 + 2.63257i) q^{73} +(3.48709 - 19.7763i) q^{74} +(4.30421 + 1.56660i) q^{76} +(-1.25397 + 0.221109i) q^{77} +(6.41639 + 5.38399i) q^{79} +(28.6752 + 8.49470i) q^{80} +9.64185i q^{82} +(-1.86155 + 2.21851i) q^{83} +(8.68897 + 0.990186i) q^{85} +(-10.8146 - 3.93619i) q^{86} +(10.9943 + 1.93860i) q^{88} +(-8.03383 + 13.9150i) q^{89} +(-2.09723 - 3.63251i) q^{91} +(4.99106 + 13.7128i) q^{92} +(-7.63133 + 6.40345i) q^{94} +(1.77672 - 0.772492i) q^{95} +(-1.05657 - 2.90290i) q^{97} +(13.9705 - 8.06587i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) $ 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−1.73512	+	2.06784i	−1.22692	+	1.46218i	−0.384698	+	0.923043i	$0.625694\pi$
$2$	−1.73512	+	2.06784i	−1.22692	+	1.46218i	−0.842218	+	0.539138i	$0.818750\pi$
$3$		0			0
$3$		0			0
$4$	−0.918006	−	5.20627i	−0.459003	−	2.60313i
$5$	−1.79745	−	1.33011i	−0.803843	−	0.594841i
$5$	−1.79745	−	1.33011i	−0.803843	−	0.594841i
$6$		0			0
$7$	−0.996499	−	0.175710i	−0.376641	−	0.0664120i	−0.0178769	−	0.999840i	$-0.505691\pi$
$7$	−0.996499	−	0.175710i	−0.376641	−	0.0664120i	−0.358764	+	0.933428i	$0.616802\pi$
$8$	7.68312	+	4.43585i	2.71639	+	1.56831i
$9$		0			0
$10$	5.86923	−	1.40893i	1.85601	−	0.445544i
$11$	1.18249	−	0.430390i	0.356533	−	0.129767i	−0.157543	−	0.987512i	$-0.550357\pi$
$11$	1.18249	−	0.430390i	0.356533	−	0.129767i	0.514076	+	0.857745i	$0.328135\pi$
$12$		0			0
$13$	2.66452	+	3.17545i	0.739004	+	0.880711i	0.996328	−	0.0856143i	$-0.0272853\pi$
$13$	2.66452	+	3.17545i	0.739004	+	0.880711i	−0.257324	+	0.966325i	$0.582841\pi$
$14$	2.09238	−	1.75572i	0.559213	−	0.469235i
$15$		0			0
$16$	−12.5682	+	4.57445i	−3.14205	+	1.14361i
$17$	−3.38700	+	1.95549i	−0.821469	+	0.474275i	−0.850923	−	0.525291i	$-0.823957\pi$
$17$	−3.38700	+	1.95549i	−0.821469	+	0.474275i	0.0294538	+	0.999566i	$0.490623\pi$
$18$		0			0
$19$	−0.433214	+	0.750349i	−0.0993861	+	0.172142i	−0.911431	−	0.411454i	$-0.865021\pi$
$19$	−0.433214	+	0.750349i	−0.0993861	+	0.172142i	0.812045	+	0.583595i	$0.198355\pi$
$20$	−5.27482	+	10.5790i	−1.17949	+	2.36555i
$21$		0			0
$22$	−1.16178	+	3.19197i	−0.247693	+	0.680530i
$23$	−2.71843	+	0.479332i	−0.566831	+	0.0999476i	−0.449717	−	0.893171i	$-0.648475\pi$
$23$	−2.71843	+	0.479332i	−0.566831	+	0.0999476i	−0.117114	+	0.993119i	$0.537364\pi$
$24$		0			0
$25$	1.46164	+	4.78159i	0.292328	+	0.956318i
$26$	−11.1896			−2.19445
$27$		0			0
$28$			5.34934i			1.01093i
$29$	6.00558	+	5.03928i	1.11521	+	0.935771i	0.998353	−	0.0573776i	$-0.0182739\pi$
$29$	6.00558	+	5.03928i	1.11521	+	0.935771i	0.116856	+	0.993149i	$0.462718\pi$
$30$		0			0
$31$	0.941551	+	5.33980i	0.169108	+	0.959057i	0.944728	+	0.327857i	$0.106326\pi$
$31$	0.941551	+	5.33980i	0.169108	+	0.959057i	−0.775620	+	0.631200i	$0.782563\pi$
$32$	6.27953	−	17.2529i	1.11008	−	3.04991i
$33$		0			0
$34$	1.83323	−	10.3968i	0.314397	−	1.78303i
$35$	1.55744	+	1.64128i	0.263256	+	0.277427i
$36$		0			0
$37$	−6.44260	+	3.71964i	−1.05916	+	0.611504i	−0.925199	−	0.379483i	$-0.876102\pi$
$37$	−6.44260	+	3.71964i	−1.05916	+	0.611504i	−0.133958	+	0.990987i	$0.542769\pi$
$38$	−0.799919	−	2.19776i	−0.129764	−	0.356524i
$39$		0			0
$40$	−7.90986	−	18.1926i	−1.25066	−	2.87650i
$41$	2.73623	−	2.29597i	0.427327	−	0.358570i	−0.403615	−	0.914929i	$-0.632246\pi$
$41$	2.73623	−	2.29597i	0.427327	−	0.358570i	0.830942	+	0.556359i	$0.187802\pi$
$42$		0			0
$43$	1.45819	+	4.00634i	0.222372	+	0.610962i	0.999839	−	0.0179623i	$-0.00571788\pi$
$43$	1.45819	+	4.00634i	0.222372	+	0.610962i	−0.777467	+	0.628924i	$0.783496\pi$
$44$	−3.32626	−	5.76125i	−0.501452	−	0.868540i
$45$		0			0
$46$	3.72562	−	6.45296i	0.549312	−	0.951436i
$47$	3.63443	+	0.640847i	0.530136	+	0.0934772i	0.432308	−	0.901726i	$-0.357699\pi$
$47$	3.63443	+	0.640847i	0.530136	+	0.0934772i	0.0978279	+	0.995203i	$0.468811\pi$
$48$		0			0
$49$	−5.61571	−	2.04395i	−0.802245	−	0.291993i
$50$	−12.4237	−	5.27421i	−1.75697	−	0.745886i
$51$		0			0
$52$	14.0862	−	16.7873i	1.95340	−	2.32798i
$53$			0.485518i			0.0666910i	0.999444	+	0.0333455i	$0.0106162\pi$
$53$			0.485518i			0.0666910i	−0.999444	+	0.0333455i	$0.989384\pi$
$54$		0			0
$55$	−2.69792	−	0.799229i	−0.363788	−	0.107768i
$56$	−6.87680	−	5.77032i	−0.918951	−	0.771091i
$57$		0			0
$58$	−20.8408	+	3.67480i	−2.73653	+	0.482525i
$59$	1.47979	+	0.538599i	0.192652	+	0.0701196i	0.436544	−	0.899683i	$-0.356202\pi$
$59$	1.47979	+	0.538599i	0.192652	+	0.0701196i	−0.243892	+	0.969802i	$0.578424\pi$
$60$		0			0
$61$	0.286481	−	1.62472i	0.0366802	−	0.208023i	−0.960960	−	0.276689i	$-0.910763\pi$
$61$	0.286481	−	1.62472i	0.0366802	−	0.208023i	0.997640	+	0.0686652i	$0.0218740\pi$
$62$	−12.6755	−	7.31822i	−1.60979	−	0.929415i
$63$		0			0
$64$	11.4056	+	19.7550i	1.42569	+	2.46938i
$65$	−0.565650	−	9.25179i	−0.0701602	−	1.14754i
$66$		0			0
$67$	2.13105	+	2.53969i	0.260349	+	0.310272i	0.880346	−	0.474332i	$-0.157310\pi$
$67$	2.13105	+	2.53969i	0.260349	+	0.310272i	−0.619997	+	0.784604i	$0.712866\pi$
$68$	13.2901	+	15.8385i	1.61166	+	1.92070i
$69$		0			0
$70$	−6.09624	+	0.372721i	−0.728640	+	0.0445487i
$71$	4.95764	+	8.58688i	0.588363	+	1.01907i	0.994447	+	0.105239i	$0.0335608\pi$
$71$	4.95764	+	8.58688i	0.588363	+	1.01907i	−0.406084	+	0.913836i	$0.633106\pi$
$72$		0			0
$73$	4.55975	+	2.63257i	0.533678	+	0.308119i	0.742513	−	0.669832i	$-0.233634\pi$
$73$	4.55975	+	2.63257i	0.533678	+	0.308119i	−0.208835	+	0.977951i	$0.566967\pi$
$74$	3.48709	−	19.7763i	0.405366	−	2.29894i
$75$		0			0
$76$	4.30421	+	1.56660i	0.493727	+	0.179702i
$77$	−1.25397	+	0.221109i	−0.142903	+	0.0251977i
$78$		0			0
$79$	6.41639	+	5.38399i	0.721901	+	0.605747i	0.927910	−	0.372803i	$-0.121603\pi$
$79$	6.41639	+	5.38399i	0.721901	+	0.605747i	−0.206010	+	0.978550i	$0.566048\pi$
$80$	28.6752	+	8.49470i	3.20599	+	0.949737i
$81$		0			0
$82$			9.64185i			1.06476i
$83$	−1.86155	+	2.21851i	−0.204331	+	0.243513i	−0.858472	−	0.512860i	$-0.828586\pi$
$83$	−1.86155	+	2.21851i	−0.204331	+	0.243513i	0.654141	+	0.756373i	$0.273030\pi$
$84$		0			0
$85$	8.68897	+	0.990186i	0.942451	+	0.107401i
$86$	−10.8146	−	3.93619i	−1.16617	−	0.424450i
$87$		0			0
$88$	10.9943	+	1.93860i	1.17200	+	0.206655i
$89$	−8.03383	+	13.9150i	−0.851584	+	1.47499i	0.0281944	+	0.999602i	$0.491024\pi$
$89$	−8.03383	+	13.9150i	−0.851584	+	1.47499i	−0.879778	+	0.475384i	$0.842309\pi$
$90$		0			0
$91$	−2.09723	−	3.63251i	−0.219850	−	0.380791i
$92$	4.99106	+	13.7128i	0.520354	+	1.42966i
$93$		0			0
$94$	−7.63133	+	6.40345i	−0.787112	+	0.660465i
$95$	1.77672	−	0.772492i	0.182288	−	0.0792561i
$96$		0			0
$97$	−1.05657	−	2.90290i	−0.107278	−	0.294745i	0.874425	−	0.485160i	$-0.161239\pi$
$97$	−1.05657	−	2.90290i	−0.107278	−	0.294745i	−0.981704	+	0.190416i	$0.939016\pi$
$98$	13.9705	−	8.06587i	1.41123	−	0.814776i
$99$		0			0
$100$	23.5525	−	11.9992i	2.35525	−	1.19992i
$101$	−1.48218	+	8.40586i	−0.147482	+	0.836415i	0.817858	+	0.575420i	$0.195162\pi$
$101$	−1.48218	+	8.40586i	−0.147482	+	0.836415i	−0.965340	+	0.260994i	$0.915950\pi$
$102$		0			0
$103$	5.45651	−	14.9916i	0.537646	−	1.47717i	−0.312136	−	0.950037i	$-0.601045\pi$
$103$	5.45651	−	14.9916i	0.537646	−	1.47717i	0.849782	−	0.527134i	$-0.176733\pi$
$104$	6.38599	+	36.2167i	0.626198	+	3.55134i
$105$		0			0
$106$	−1.00397	−	0.842432i	−0.0975143	−	0.0818242i
$107$			9.20342i			0.889728i	0.895598	+	0.444864i	$0.146748\pi$
$107$			9.20342i			0.889728i	−0.895598	+	0.444864i	$0.853252\pi$
$108$		0			0
$109$	−4.98029			−0.477025			−0.238512	−	0.971139i	$-0.576660\pi$
$109$	−4.98029			−0.477025			−0.238512	+	0.971139i	$0.576660\pi$
$110$	6.33389	−	4.19210i	0.603913	−	0.399701i
$111$		0			0
$112$	13.3280	−	2.35008i	1.25938	−	0.222062i
$113$	2.72188	−	7.47831i	0.256053	−	0.703500i	−0.743348	−	0.668904i	$-0.766764\pi$
$113$	2.72188	−	7.47831i	0.256053	−	0.703500i	0.999401	−	0.0345954i	$-0.0110143\pi$
$114$		0			0
$115$	5.52379	+	2.75422i	0.515096	+	0.256832i
$116$	20.7227	−	35.8928i	1.92405	−	3.33256i
$117$		0			0
$118$	−3.68134	+	2.12542i	−0.338895	+	0.195661i
$119$	3.71874	−	1.35351i	0.340897	−	0.124076i
$120$		0			0
$121$	−7.21345	+	6.05280i	−0.655768	+	0.550255i
$122$	2.86256	+	3.41147i	0.259164	+	0.308860i
$123$		0			0
$124$	26.9361	−	9.80394i	2.41893	−	0.880420i
$125$	3.73280	−	10.5388i	0.333872	−	0.942618i
$126$		0			0
$127$	−16.0918	−	9.29062i	−1.42792	−	0.824409i	−0.430962	−	0.902370i	$-0.641826\pi$
$127$	−16.0918	−	9.29062i	−1.42792	−	0.824409i	−0.996956	+	0.0779609i	$0.975159\pi$
$128$	−24.4777	−	4.31608i	−2.16354	−	0.381491i
$129$		0			0
$130$	20.1127	+	14.8833i	1.76400	+	1.30535i
$131$	−3.27027	−	18.5466i	−0.285725	−	1.62043i	−0.702685	−	0.711501i	$-0.748016\pi$
$131$	−3.27027	−	18.5466i	−0.285725	−	1.62043i	0.416960	−	0.908925i	$-0.363095\pi$
$132$		0			0
$133$	0.563541	−	0.671602i	0.0488652	−	0.0582353i
$134$	−8.94928			−0.773100
$135$		0			0
$136$	−34.6970			−2.97524
$137$	−10.2847	+	12.2568i	−0.878680	+	1.04717i	0.119840	+	0.992793i	$0.461762\pi$
$137$	−10.2847	+	12.2568i	−0.878680	+	1.04717i	−0.998520	+	0.0543771i	$0.982683\pi$
$138$		0			0
$139$	2.32924	+	13.2098i	0.197564	+	1.12044i	0.908720	+	0.417406i	$0.137061\pi$
$139$	2.32924	+	13.2098i	0.197564	+	1.12044i	−0.711156	+	0.703034i	$0.751828\pi$
$140$	7.11519	−	9.61517i	0.601344	−	0.812630i
$141$		0			0
$142$	−26.3583	−	4.64769i	−2.21194	−	0.390025i
$143$	4.51744	+	2.60814i	0.377767	+	0.218104i
$144$		0			0
$145$	−4.09194	−	17.0459i	−0.339818	−	1.41559i
$146$	−13.3554	+	4.86098i	−1.10530	+	0.402297i
$147$		0			0
$148$	25.2798	+	30.1273i	2.07798	+	2.47645i
$149$	−2.58412	+	2.16833i	−0.211699	+	0.177637i	−0.742471	−	0.669878i	$-0.766346\pi$
$149$	−2.58412	+	2.16833i	−0.211699	+	0.177637i	0.530772	+	0.847515i	$0.321902\pi$
$150$		0			0
$151$	21.6795	−	7.89070i	1.76426	−	0.642136i	0.764259	−	0.644910i	$-0.223105\pi$
$151$	21.6795	−	7.89070i	1.76426	−	0.642136i	0.999996	+	0.00277330i	$0.000882769\pi$
$152$	−6.65687	+	3.84335i	−0.539943	+	0.311737i
$153$		0			0
$154$	1.71857	−	2.97665i	0.138487	−	0.239866i
$155$	5.41011	−	10.8504i	0.434551	−	0.871523i
$156$		0			0
$157$	−3.12396	+	8.58300i	−0.249319	+	0.684998i	0.750393	+	0.660992i	$0.229864\pi$
$157$	−3.12396	+	8.58300i	−0.249319	+	0.684998i	−0.999712	+	0.0240060i	$0.992358\pi$
$158$	−22.2664	+	3.92617i	−1.77142	+	0.312349i
$159$		0			0
$160$	−34.2353	+	22.6587i	−2.70654	+	1.79133i
$161$	2.79313			0.220130
$162$		0			0
$163$		−	7.32494i		−	0.573734i	−0.957970	−	0.286867i	$-0.907386\pi$
$163$		−	7.32494i		−	0.573734i	0.957970	−	0.286867i	$-0.0926137\pi$
$164$	−14.4653	−	12.1378i	−1.12955	−	0.947806i
$165$		0			0
$166$	−1.35750	−	7.69875i	−0.105362	−	0.597539i
$167$	1.72047	−	4.72696i	0.133134	−	0.365783i	−0.855156	−	0.518371i	$-0.826539\pi$
$167$	1.72047	−	4.72696i	0.133134	−	0.365783i	0.988290	+	0.152588i	$0.0487608\pi$
$168$		0			0
$169$	−0.726391	+	4.11957i	−0.0558763	+	0.316890i
$170$	−17.1239	+	16.2493i	−1.31335	+	1.24626i
$171$		0			0
$172$	19.5195	−	11.2696i	1.48835	−	0.859297i
$173$	−6.55550	−	18.0111i	−0.498406	−	1.36936i	−0.892815	−	0.450423i	$-0.851273\pi$
$173$	−6.55550	−	18.0111i	−0.498406	−	1.36936i	0.394410	−	0.918935i	$-0.370949\pi$
$174$		0			0
$175$	−0.616349	−	5.02167i	−0.0465916	−	0.379603i
$176$	−12.8929	+	10.8185i	−0.971842	+	0.815472i
$177$		0			0
$178$	−14.8343	−	40.7568i	−1.11188	−	3.05485i
$179$	−6.81005	−	11.7953i	−0.509007	−	0.881626i	−0.999946	−	0.0104315i	$-0.996679\pi$
$179$	−6.81005	−	11.7953i	−0.509007	−	0.881626i	0.490939	−	0.871194i	$-0.336654\pi$
$180$		0			0
$181$	−4.25402	+	7.36817i	−0.316198	+	0.547672i	−0.979692	−	0.200511i	$-0.935740\pi$
$181$	−4.25402	+	7.36817i	−0.316198	+	0.547672i	0.663493	+	0.748182i	$0.269073\pi$
$182$	11.1504	+	1.96611i	0.826521	+	0.145738i
$183$		0			0
$184$	−23.0122	−	8.37577i	−1.69648	−	0.617470i
$185$	16.5277	+	1.88348i	1.21514	+	0.138477i
$186$		0			0
$187$	−3.16346	+	3.77007i	−0.231335	+	0.275695i
$188$		−	19.5101i		−	1.42292i
$189$		0			0
$190$	−1.48544	+	5.01434i	−0.107765	+	0.363778i
$191$	9.82022	+	8.24015i	0.710566	+	0.596236i	0.924758	−	0.380556i	$-0.124267\pi$
$191$	9.82022	+	8.24015i	0.710566	+	0.596236i	−0.214192	+	0.976792i	$0.568712\pi$
$192$		0			0
$193$	9.81499	−	1.73065i	0.706498	−	0.124575i	0.191157	−	0.981560i	$-0.438776\pi$
$193$	9.81499	−	1.73065i	0.706498	−	0.124575i	0.515342	+	0.856985i	$0.327665\pi$
$194$	7.83599	+	2.85207i	0.562591	+	0.204766i
$195$		0			0
$196$	−5.48611	+	31.1133i	−0.391865	+	2.22238i
$197$	17.0167	+	9.82458i	1.21239	+	0.699972i	0.963279	−	0.268503i	$-0.0865289\pi$
$197$	17.0167	+	9.82458i	1.21239	+	0.699972i	0.249109	+	0.968475i	$0.419862\pi$
$198$		0			0
$199$	1.80778	+	3.13117i	0.128150	+	0.221963i	0.922960	−	0.384896i	$-0.125763\pi$
$199$	1.80778	+	3.13117i	0.128150	+	0.221963i	−0.794810	+	0.606859i	$0.792429\pi$
$200$	−9.98048	+	43.2211i	−0.705727	+	3.05620i
$201$		0			0
$202$	−14.8102	−	17.6501i	−1.04204	−	1.24186i
$203$	−5.09911	−	6.07688i	−0.357887	−	0.426513i
$204$		0			0
$205$	−7.97211	+	0.487411i	−0.556796	+	0.0340422i
$206$	21.5326	+	37.2955i	1.50024	+	2.59850i
$207$		0			0
$208$	−48.0142	−	27.7210i	−3.32918	−	1.92210i
$209$	−0.189327	+	1.07373i	−0.0130960	+	0.0742714i
$210$		0			0
$211$	−17.2131	−	6.26505i	−1.18500	−	0.431304i	−0.327033	−	0.945013i	$-0.606049\pi$
$211$	−17.2131	−	6.26505i	−1.18500	−	0.431304i	−0.857964	+	0.513709i	$0.828271\pi$
$212$	2.52774	−	0.445708i	0.173606	−	0.0306114i
$213$		0			0
$214$	−19.0312	−	15.9690i	−1.30094	−	1.09162i
$215$	2.70784	−	9.14074i	0.184673	−	0.623393i
$216$		0			0
$217$		−	5.48655i		−	0.372451i
$218$	8.64139	−	10.2984i	0.585269	−	0.697496i
$219$		0			0
$220$	−1.68429	+	14.7798i	−0.113555	+	0.996455i
$221$	−15.2343	−	5.54482i	−1.02477	−	0.372985i
$222$		0			0
$223$	6.90273	+	1.21714i	0.462241	+	0.0815055i	0.399919	−	0.916551i	$-0.369038\pi$
$223$	6.90273	+	1.21714i	0.462241	+	0.0815055i	0.0623220	+	0.998056i	$0.480149\pi$
$224$	−9.28904	+	16.0891i	−0.620650	+	1.07500i
$225$		0			0
$226$	10.7411	+	18.6042i	0.714488	+	1.23753i
$227$	−4.59274	−	12.6185i	−0.304831	−	0.837516i	−0.993643	−	0.112576i	$-0.964090\pi$
$227$	−4.59274	−	12.6185i	−0.304831	−	0.837516i	0.688812	−	0.724940i	$-0.258132\pi$
$228$		0			0
$229$	7.11646	−	5.97142i	0.470269	−	0.394602i	−0.376624	−	0.926366i	$-0.622915\pi$
$229$	7.11646	−	5.97142i	0.470269	−	0.394602i	0.846893	+	0.531764i	$0.178471\pi$
$230$	−15.2797	+	6.64339i	−1.00751	+	0.438052i
$231$		0			0
$232$	23.7881	+	65.3573i	1.56177	+	4.29091i
$233$	−8.84302	+	5.10552i	−0.579325	+	0.334474i	−0.760865	−	0.648910i	$-0.775225\pi$
$233$	−8.84302	+	5.10552i	−0.579325	+	0.334474i	0.181540	+	0.983384i	$0.441892\pi$
$234$		0			0
$235$	−5.68030	−	5.98606i	−0.370542	−	0.390488i
$236$	1.44564	−	8.19861i	0.0941029	−	0.533684i
$237$		0			0
$238$	−3.65363	+	10.0383i	−0.236829	+	0.650683i
$239$	0.450136	+	2.55285i	0.0291169	+	0.165130i	0.995899	−	0.0904719i	$-0.0288375\pi$
$239$	0.450136	+	2.55285i	0.0291169	+	0.165130i	−0.966782	+	0.255602i	$0.917726\pi$
$240$		0			0
$241$	−12.7419	−	10.6918i	−0.820781	−	0.688717i	0.132374	−	0.991200i	$-0.457740\pi$
$241$	−12.7419	−	10.6918i	−0.820781	−	0.688717i	−0.953155	+	0.302483i	$0.902185\pi$
$242$		−	25.4186i		−	1.63397i
$243$		0			0
$244$	−8.72170			−0.558349
$245$	7.37528	+	11.1434i	0.471189	+	0.711925i
$246$		0			0
$247$	−3.53700	+	0.623669i	−0.225054	+	0.0396831i
$248$	−16.4525	+	45.2029i	−1.04474	+	2.87039i
$249$		0			0
$250$	15.3156	+	26.0049i	0.968646	+	1.64469i
$251$	6.10066	−	10.5667i	0.385070	−	0.666961i	−0.606709	−	0.794924i	$-0.707511\pi$
$251$	6.10066	−	10.5667i	0.385070	−	0.666961i	0.991779	+	0.127963i	$0.0408439\pi$
$252$		0			0
$253$	−3.00820	+	1.73679i	−0.189124	+	0.109191i
$254$	47.1327	−	17.1549i	2.95737	−	1.07639i
$255$		0			0
$256$	16.4481	−	13.8016i	1.02800	−	0.862597i
$257$	5.47165	+	6.52086i	0.341312	+	0.406760i	0.909209	−	0.416340i	$-0.136687\pi$
$257$	5.47165	+	6.52086i	0.341312	+	0.406760i	−0.567897	+	0.823100i	$0.692243\pi$
$258$		0			0
$259$	7.07362	−	2.57459i	0.439533	−	0.159977i
$260$	−47.6481	+	11.4381i	−2.95501	+	0.709362i
$261$		0			0
$262$	44.0257	+	25.4182i	2.71992	+	1.57034i
$263$	9.08152	+	1.60132i	0.559991	+	0.0987415i	0.446477	−	0.894795i	$-0.352678\pi$
$263$	9.08152	+	1.60132i	0.559991	+	0.0987415i	0.113514	+	0.993536i	$0.463789\pi$
$264$		0			0
$265$	0.645790	−	0.872693i	0.0396706	−	0.0536091i
$266$	0.410951	+	2.33062i	0.0251970	+	0.142899i
$267$		0			0
$268$	11.2660	−	13.4263i	0.688179	−	0.820140i
$269$	−7.15347			−0.436155			−0.218078	−	0.975931i	$-0.569979\pi$
$269$	−7.15347			−0.436155			−0.218078	+	0.975931i	$0.569979\pi$
$270$		0			0
$271$	17.3418			1.05344			0.526721	−	0.850038i	$-0.323421\pi$
$271$	17.3418			1.05344			0.526721	+	0.850038i	$0.323421\pi$
$272$	33.6233	−	40.0707i	2.03871	−	2.42964i
$273$		0			0
$274$	−7.49991	−	42.5341i	−0.453086	−	2.56958i
$275$	3.78632	+	5.02509i	0.228324	+	0.303025i
$276$		0			0
$277$	−10.3831	−	1.83081i	−0.623858	−	0.110003i	−0.147222	−	0.989104i	$-0.547033\pi$
$277$	−10.3831	−	1.83081i	−0.623858	−	0.110003i	−0.476636	+	0.879101i	$0.658144\pi$
$278$	−31.3572	−	18.1041i	−1.88068	−	1.08581i
$279$		0			0
$280$	4.68555	+	19.5187i	0.280015	+	1.16647i
$281$	−20.1528	+	7.33501i	−1.20221	+	0.437570i	−0.863996	−	0.503498i	$-0.832046\pi$
$281$	−20.1528	+	7.33501i	−1.20221	+	0.437570i	−0.338217	+	0.941068i	$0.609824\pi$
$282$		0			0
$283$	−10.4391	−	12.4408i	−0.620538	−	0.739528i	0.360625	−	0.932711i	$-0.382563\pi$
$283$	−10.4391	−	12.4408i	−0.620538	−	0.739528i	−0.981163	+	0.193183i	$0.938119\pi$
$284$	40.1545	−	33.6936i	2.38273	−	1.99935i
$285$		0			0
$286$	−13.2315	+	4.81588i	−0.782396	+	0.284769i
$287$	−3.13007	+	1.80715i	−0.184762	+	0.106673i
$288$		0			0
$289$	−0.852138	+	1.47595i	−0.0501257	+	0.0868203i
$290$	42.3481	+	21.1152i	2.48677	+	1.23993i
$291$		0			0
$292$	9.52000	−	26.1560i	0.557116	−	1.53066i
$293$	23.2745	−	4.10392i	1.35971	−	0.239753i	0.554223	−	0.832368i	$-0.313016\pi$
$293$	23.2745	−	4.10392i	1.35971	−	0.239753i	0.805486	+	0.592615i	$0.201904\pi$
$294$		0			0
$295$	−1.94345	−	2.93638i	−0.113152	−	0.170963i
$296$	−65.9990			−3.83611
$297$		0			0
$298$		−	9.10584i		−	0.527487i
$299$	−8.76538	−	7.35503i	−0.506915	−	0.425352i
$300$		0			0
$301$	−0.749131	−	4.24853i	−0.0431792	−	0.244881i
$302$	−21.2999	+	58.5210i	−1.22567	+	3.36751i
$303$		0			0
$304$	2.01229	−	11.4123i	0.115413	−	0.654538i
$305$	−2.67598	+	2.53929i	−0.153226	+	0.145399i
$306$		0			0
$307$	−5.34281	+	3.08468i	−0.304931	+	0.176052i	−0.644656	−	0.764473i	$-0.722999\pi$
$307$	−5.34281	+	3.08468i	−0.304931	+	0.176052i	0.339725	+	0.940525i	$0.389666\pi$
$308$	2.30230	+	6.32553i	0.131186	+	0.360430i
$309$		0			0
$310$	13.0496	+	30.0139i	0.741168	+	1.70468i
$311$	10.4699	−	8.78527i	0.593692	−	0.498167i	−0.295719	−	0.955275i	$-0.595559\pi$
$311$	10.4699	−	8.78527i	0.593692	−	0.498167i	0.889411	+	0.457108i	$0.151115\pi$
$312$		0			0
$313$	2.70332	+	7.42730i	0.152800	+	0.419816i	0.992348	−	0.123470i	$-0.0394022\pi$
$313$	2.70332	+	7.42730i	0.152800	+	0.419816i	−0.839548	+	0.543286i	$0.817180\pi$
$314$	−12.3278	−	21.3524i	−0.695698	−	1.20498i
$315$		0			0
$316$	22.1402	−	38.3480i	1.24549	−	2.15724i
$317$	5.53686	+	0.976298i	0.310981	+	0.0548344i	0.326961	−	0.945038i	$-0.393976\pi$
$317$	5.53686	+	0.976298i	0.310981	+	0.0548344i	−0.0159795	+	0.999872i	$0.505087\pi$
$318$		0			0
$319$	9.27038	+	3.37414i	0.519042	+	0.188916i
$320$	5.77535	−	50.6792i	0.322852	−	2.83305i
$321$		0			0
$322$	−4.84642	+	5.77574i	−0.270080	+	0.321869i
$323$		−	3.38858i		−	0.188546i
$324$		0			0
$325$	−11.2891	+	17.3820i	−0.626208	+	0.964179i
$326$	15.1468	+	12.7097i	0.838902	+	0.703923i
$327$		0			0
$328$	31.2073	−	5.50270i	1.72314	−	0.303836i
$329$	−3.50910	−	1.27721i	−0.193463	−	0.0704147i
$330$		0			0
$331$	4.33246	−	24.5706i	0.238133	−	1.35052i	−0.597780	−	0.801660i	$-0.703951\pi$
$331$	4.33246	−	24.5706i	0.238133	−	1.35052i	0.835914	−	0.548861i	$-0.184938\pi$
$332$	13.2591	+	7.65512i	0.727685	+	0.420129i
$333$		0			0
$334$	6.78935	+	11.7595i	0.371497	+	0.643451i
$335$	−0.452400	−	7.39948i	−0.0247173	−	0.404277i
$336$		0			0
$337$	−6.94135	−	8.27238i	−0.378119	−	0.450625i	0.543100	−	0.839668i	$-0.317250\pi$
$337$	−6.94135	−	8.27238i	−0.378119	−	0.450625i	−0.921220	+	0.389043i	$0.872806\pi$
$338$	−7.25822	−	8.65001i	−0.394795	−	0.470498i
$339$		0			0
$340$	−2.82135	−	46.1461i	−0.153009	−	2.50262i
$341$	3.41157	+	5.90901i	0.184747	+	0.319991i
$342$		0			0
$343$	11.3711	+	6.56508i	0.613979	+	0.354481i
$344$	−6.56810	+	37.2495i	−0.354128	+	2.00836i
$345$		0			0
$346$	48.6186	+	17.6957i	2.61375	+	0.951327i
$347$	−25.4825	+	4.49326i	−1.36797	+	0.241211i	−0.808919	−	0.587920i	$-0.799947\pi$
$347$	−25.4825	+	4.49326i	−1.36797	+	0.241211i	−0.559055	+	0.829131i	$0.688836\pi$
$348$		0			0
$349$	11.7162	+	9.83109i	0.627156	+	0.526246i	0.900044	−	0.435799i	$-0.143534\pi$
$349$	11.7162	+	9.83109i	0.627156	+	0.526246i	−0.272888	+	0.962046i	$0.587979\pi$
$350$	11.4534	+	7.43870i	0.612212	+	0.397615i
$351$		0			0
$352$		−	23.1039i		−	1.23144i
$353$	−22.2707	+	26.5412i	−1.18535	+	1.41265i	−0.296142	+	0.955144i	$0.595700\pi$
$353$	−22.2707	+	26.5412i	−1.18535	+	1.41265i	−0.889209	+	0.457502i	$0.848744\pi$
$354$		0			0
$355$	2.51036	−	22.0286i	0.133236	−	1.16916i
$356$	79.8203	+	29.0522i	4.23047	+	1.53976i
$357$		0			0
$358$	36.2071	+	6.38429i	1.91360	+	0.337420i
$359$	4.31838	−	7.47966i	0.227915	−	0.394761i	−0.729275	−	0.684221i	$-0.760142\pi$
$359$	4.31838	−	7.47966i	0.227915	−	0.394761i	0.957190	+	0.289460i	$0.0934757\pi$
$360$		0			0
$361$	9.12465	+	15.8044i	0.480245	+	0.831808i
$362$	−7.85494	−	21.5813i	−0.412846	−	1.13429i
$363$		0			0
$364$	−16.9866	+	14.2534i	−0.890338	+	0.747082i
$365$	−4.69431	−	10.7969i	−0.245711	−	0.565133i
$366$		0			0
$367$	9.36923	+	25.7417i	0.489070	+	1.34371i	0.901524	+	0.432729i	$0.142449\pi$
$367$	9.36923	+	25.7417i	0.489070	+	1.34371i	−0.412454	+	0.910978i	$0.635328\pi$
$368$	31.9731	−	18.4597i	1.66671	−	0.962276i
$369$		0			0
$370$	−32.5724	+	30.9086i	−1.69336	+	1.60686i
$371$	0.0853101	−	0.483818i	0.00442908	−	0.0251186i
$372$		0			0
$373$	−8.92883	+	24.5318i	−0.462317	+	1.27021i	0.461421	+	0.887181i	$0.347340\pi$
$373$	−8.92883	+	24.5318i	−0.462317	+	1.27021i	−0.923738	+	0.383025i	$0.874882\pi$
$374$	−2.30689	−	13.0831i	−0.119287	−	0.676508i
$375$		0			0
$376$	25.0810	+	21.0455i	1.29346	+	1.08534i
$377$			32.4977i			1.67372i
$378$		0			0
$379$	10.9442			0.562163			0.281082	−	0.959684i	$-0.409307\pi$
$379$	10.9442			0.562163			0.281082	+	0.959684i	$0.409307\pi$
$380$	−5.65285	−	8.54095i	−0.289985	−	0.438141i
$381$		0			0
$382$	−34.0785	+	6.00896i	−1.74361	+	0.307445i
$383$	0.753724	−	2.07084i	0.0385135	−	0.105815i	−0.918945	−	0.394385i	$-0.870958\pi$
$383$	0.753724	−	2.07084i	0.0385135	−	0.105815i	0.957459	+	0.288570i	$0.0931798\pi$
$384$		0			0
$385$	2.54804	+	1.27048i	0.129860	+	0.0647497i
$386$	−13.4515	+	23.2987i	−0.684663	+	1.18587i
$387$		0			0
$388$	−14.1433	+	8.16566i	−0.718019	+	0.414548i
$389$	−22.8822	+	8.32844i	−1.16017	+	0.422268i	−0.849159	−	0.528137i	$-0.822891\pi$
$389$	−22.8822	+	8.32844i	−1.16017	+	0.422268i	−0.311014	+	0.950405i	$0.600669\pi$
$390$		0			0
$391$	8.26999	−	6.93935i	0.418231	−	0.350938i
$392$	−34.0795	−	40.6144i	−1.72128	−	2.05134i
$393$		0			0
$394$	−49.8416	+	18.1409i	−2.51098	+	0.913923i
$395$	−4.37185	−	18.2119i	−0.219972	−	0.916342i
$396$		0			0
$397$	−9.65983	−	5.57711i	−0.484813	−	0.279907i	0.237607	−	0.971361i	$-0.423637\pi$
$397$	−9.65983	−	5.57711i	−0.484813	−	0.279907i	−0.722420	+	0.691454i	$0.756970\pi$
$398$	−9.61146	−	1.69476i	−0.481779	−	0.0849506i
$399$		0			0
$400$	−40.2433	−	53.4098i	−2.01217	−	2.67049i
$401$	−0.624022	−	3.53900i	−0.0311621	−	0.176729i	0.965254	−	0.261312i	$-0.0841553\pi$
$401$	−0.624022	−	3.53900i	−0.0311621	−	0.176729i	−0.996416	+	0.0845831i	$0.973044\pi$
$402$		0			0
$403$	−14.4475	+	17.2178i	−0.719680	+	0.857682i
$404$	45.1238			2.24500
$405$		0			0
$406$	21.4135			1.06274
$407$	−6.01739	+	7.17125i	−0.298271	+	0.355466i
$408$		0			0
$409$	1.50204	+	8.51848i	0.0742710	+	0.421212i	0.999160	+	0.0409749i	$0.0130464\pi$
$409$	1.50204	+	8.51848i	0.0742710	+	0.421212i	−0.924889	+	0.380237i	$0.875843\pi$
$410$	12.8247	−	17.3307i	0.633366	−	0.855904i
$411$		0			0
$412$	−83.0597	−	14.6457i	−4.09206	−	0.721540i
$413$	−1.37997	−	0.796726i	−0.0679039	−	0.0392043i
$414$		0			0
$415$	6.29688	−	1.51159i	0.309102	−	0.0742013i
$416$	71.5175	−	26.0303i	3.50644	−	1.27624i
$417$		0			0
$418$	−1.89179	−	2.25455i	−0.0925304	−	0.110273i
$419$	−28.1908	+	23.6549i	−1.37721	+	1.15562i	−0.406977	+	0.913438i	$0.633417\pi$
$419$	−28.1908	+	23.6549i	−1.37721	+	1.15562i	−0.970232	+	0.242177i	$0.922139\pi$
$420$		0			0
$421$	−34.0828	+	12.4051i	−1.66109	+	0.604588i	−0.990534	−	0.137269i	$-0.956168\pi$
$421$	−34.0828	+	12.4051i	−1.66109	+	0.604588i	−0.670558	+	0.741857i	$0.733945\pi$
$422$	42.8218	−	24.7232i	2.08453	−	1.20351i
$423$		0			0
$424$	−2.15368	+	3.73029i	−0.104592	+	0.181159i
$425$	−14.3009	−	13.3371i	−0.693696	−	0.646942i
$426$		0			0
$427$	−0.570956	+	1.56869i	−0.0276305	+	0.0759142i
$428$	47.9155	−	8.44879i	2.31608	−	0.408388i
$429$		0			0
$430$	14.2031	+	21.4597i	0.684935	+	1.03488i
$431$	19.3566			0.932373			0.466187	−	0.884686i	$-0.345628\pi$
$431$	19.3566			0.932373			0.466187	+	0.884686i	$0.345628\pi$
$432$		0			0
$433$		−	22.8003i		−	1.09571i	−0.836573	−	0.547855i	$-0.815444\pi$
$433$		−	22.8003i		−	1.09571i	0.836573	−	0.547855i	$-0.184556\pi$
$434$	11.3453	+	9.51981i	0.544591	+	0.456966i
$435$		0			0
$436$	4.57193	+	25.9287i	0.218956	+	1.24176i
$437$	0.817994	−	2.24742i	0.0391300	−	0.107509i
$438$		0			0
$439$	−3.36657	+	19.0928i	−0.160678	+	0.911248i	0.792732	+	0.609570i	$0.208658\pi$
$439$	−3.36657	+	19.0928i	−0.160678	+	0.911248i	−0.953410	+	0.301678i	$0.902453\pi$
$440$	−17.1832	−	18.1082i	−0.819177	−	0.863272i
$441$		0			0
$442$	37.8991	−	21.8810i	1.80268	−	1.04078i
$443$	1.33129	+	3.65769i	0.0632516	+	0.173782i	0.967292	−	0.253664i	$-0.0816356\pi$
$443$	1.33129	+	3.65769i	0.0632516	+	0.173782i	−0.904041	+	0.427446i	$0.859413\pi$
$444$		0			0
$445$	32.9488	−	14.3256i	1.56192	−	0.679101i
$446$	−14.4939	+	12.1618i	−0.686306	+	0.575879i
$447$		0			0
$448$	−7.89448	−	21.6899i	−0.372979	−	1.02475i
$449$	10.9458	+	18.9586i	0.516562	+	0.894712i	0.999815	+	0.0192309i	$0.00612178\pi$
$449$	10.9458	+	18.9586i	0.516562	+	0.894712i	−0.483253	+	0.875481i	$0.660545\pi$
$450$		0			0
$451$	2.24739	−	3.89260i	0.105826	−	0.183295i
$452$	−41.4328	−	7.30572i	−1.94883	−	0.343632i
$453$		0			0
$454$	34.0618	+	12.3975i	1.59860	+	0.581843i
$455$	−1.06196	+	9.31879i	−0.0497854	+	0.436872i
$456$		0			0
$457$	12.4055	−	14.7842i	0.580303	−	0.691578i	−0.393409	−	0.919364i	$-0.628704\pi$
$457$	12.4055	−	14.7842i	0.580303	−	0.691578i	0.973711	+	0.227786i	$0.0731486\pi$
$458$			25.0768i			1.17176i
$459$		0			0
$460$	9.26834	−	31.2867i	0.432138	−	1.45875i
$461$	−29.2721	−	24.5622i	−1.36334	−	1.14398i	−0.974936	−	0.222486i	$-0.928583\pi$
$461$	−29.2721	−	24.5622i	−1.36334	−	1.14398i	−0.388402	−	0.921490i	$-0.626973\pi$
$462$		0			0
$463$	21.9614	−	3.87239i	1.02063	−	0.179965i	0.361801	−	0.932255i	$-0.382162\pi$
$463$	21.9614	−	3.87239i	1.02063	−	0.179965i	0.658832	+	0.752290i	$0.271051\pi$
$464$	−98.5314	−	35.8625i	−4.57421	−	1.66487i
$465$		0			0
$466$	4.78632	−	27.1446i	0.221722	−	1.25745i
$467$	−26.1204	−	15.0806i	−1.20871	−	0.697847i	−0.246229	−	0.969212i	$-0.579192\pi$
$467$	−26.1204	−	15.0806i	−1.20871	−	0.697847i	−0.962477	+	0.271365i	$0.912525\pi$
$468$		0			0
$469$	−1.67734	−	2.90524i	−0.0774524	−	0.134152i
$470$	22.2342	−	1.35939i	1.02559	−	0.0627038i
$471$		0			0
$472$	8.98024	+	10.7022i	0.413349	+	0.492610i
$473$	3.44858	+	4.10986i	0.158566	+	0.188971i
$474$		0			0
$475$	−4.22106	−	0.974714i	−0.193676	−	0.0447230i
$476$	−10.4606	−	18.1182i	−0.479460	−	0.830448i
$477$		0			0
$478$	−6.05991	−	3.49869i	−0.277174	−	0.160026i
$479$	2.47679	−	14.0466i	0.113167	−	0.641804i	−0.874474	−	0.485073i	$-0.838793\pi$
$479$	2.47679	−	14.0466i	0.113167	−	0.641804i	0.987641	−	0.156731i	$-0.0500957\pi$
$480$		0			0
$481$	−28.9779	−	10.5471i	−1.32128	−	0.480907i
$482$	44.2176	−	7.79676i	2.01406	−	0.355133i
$483$		0			0
$484$	38.1345	+	31.9987i	1.73339	+	1.45448i
$485$	−1.96203	+	6.62315i	−0.0890914	+	0.300742i
$486$		0			0
$487$			20.9938i			0.951318i	0.879630	+	0.475659i	$0.157790\pi$
$487$			20.9938i			0.951318i	−0.879630	+	0.475659i	$0.842210\pi$
$488$	9.40806	−	11.2121i	0.425883	−	0.507548i
$489$		0			0
$490$	−35.8397	−	4.08425i	−1.61907	−	0.184508i
$491$	4.84651	+	1.76398i	0.218720	+	0.0796075i	0.449056	−	0.893504i	$-0.351760\pi$
$491$	4.84651	+	1.76398i	0.218720	+	0.0796075i	−0.230336	+	0.973111i	$0.573983\pi$
$492$		0			0
$493$	−30.1952	−	5.32423i	−1.35992	−	0.239791i
$494$	4.84748	−	8.39607i	0.218098	−	0.377757i
$495$		0			0
$496$	−36.2603	−	62.8047i	−1.62814	−	2.82001i
$497$	−3.43148	−	9.42792i	−0.153923	−	0.422900i
$498$		0			0
$499$	27.2570	−	22.8713i	1.22019	−	1.02386i	0.221376	−	0.975189i	$-0.428945\pi$
$499$	27.2570	−	22.8713i	1.22019	−	1.02386i	0.998815	−	0.0486726i	$-0.0154991\pi$
$500$	−58.2945	−	9.75930i	−2.60701	−	0.436449i
$501$		0			0
$502$	11.2647	+	30.9496i	0.502769	+	1.38135i
$503$	2.96137	−	1.70975i	0.132041	−	0.0762338i	−0.432525	−	0.901622i	$-0.642377\pi$
$503$	2.96137	−	1.70975i	0.132041	−	0.0762338i	0.564565	+	0.825388i	$0.309044\pi$
$504$		0			0
$505$	13.8448	−	13.1376i	0.616087	−	0.584618i
$506$	1.62820	−	9.23400i	0.0723825	−	0.410501i
$507$		0			0
$508$	−33.5971	+	92.3072i	−1.49063	+	4.09547i
$509$	3.45809	+	19.6118i	0.153277	+	0.869277i	0.960344	+	0.278817i	$0.0899424\pi$
$509$	3.45809	+	19.6118i	0.153277	+	0.869277i	−0.807067	+	0.590460i	$0.798946\pi$
$510$		0			0
$511$	−4.08121	−	3.42454i	−0.180542	−	0.151493i
$512$			8.24859i			0.364540i
$513$		0			0
$514$	−22.9780			−1.01352
$515$	−29.7483	+	19.6890i	−1.31087	+	0.867600i
$516$		0			0
$517$	4.57348	−	0.806427i	0.201141	−	0.0354666i
$518$	−6.94976	+	19.0943i	−0.305355	+	0.838955i
$519$		0			0
$520$	36.6936	−	73.5917i	1.60912	−	3.22721i
$521$	10.7424	−	18.6064i	0.470633	−	0.815160i	−0.528803	−	0.848744i	$-0.677359\pi$
$521$	10.7424	−	18.6064i	0.470633	−	0.815160i	0.999436	+	0.0335849i	$0.0106924\pi$
$522$		0			0
$523$	−28.7457	+	16.5963i	−1.25696	+	0.725707i	−0.972483	−	0.232976i	$-0.925154\pi$
$523$	−28.7457	+	16.5963i	−1.25696	+	0.725707i	−0.284479	+	0.958682i	$0.591820\pi$
$524$	−93.5566	+	34.0518i	−4.08704	+	1.48756i
$525$		0			0
$526$	−19.0688	+	16.0006i	−0.831439	+	0.697660i
$527$	−13.6310	−	16.2447i	−0.593774	−	0.707632i
$528$		0			0
$529$	−14.4529	+	5.26041i	−0.628385	+	0.228713i
$530$	0.684062	+	2.84961i	0.0297138	+	0.123779i
$531$		0			0
$532$	−4.01387	−	2.31741i	−0.174024	−	0.100473i
$533$	14.5815	+	2.57110i	0.631593	+	0.111367i
$534$		0			0
$535$	12.2415	−	16.5427i	0.529247	−	0.715202i
$536$	5.10744	+	28.9657i	0.220608	+	1.25113i
$537$		0			0
$538$	12.4121	−	14.7922i	0.535125	−	0.637737i
$539$	−7.52020			−0.323918
$540$		0			0
$541$	2.83444			0.121862			0.0609309	−	0.998142i	$-0.480593\pi$
$541$	2.83444			0.121862			0.0609309	+	0.998142i	$0.480593\pi$
$542$	−30.0902	+	35.8601i	−1.29248	+	1.54032i
$543$		0			0
$544$	12.4690	+	70.7151i	0.534603	+	3.03188i
$545$	8.95180	+	6.62431i	0.383453	+	0.283754i
$546$		0			0
$547$	33.2190	+	5.85741i	1.42034	+	0.250445i	0.830475	−	0.557055i	$-0.188069\pi$
$547$	33.2190	+	5.85741i	1.42034	+	0.250445i	0.589868	+	0.807500i	$0.299180\pi$
$548$	73.2537	+	42.2930i	3.12924	+	1.80667i
$549$		0			0
$550$	−16.9608	−	0.889661i	−0.723210	−	0.0379353i
$551$	−6.38292	+	2.32319i	−0.271922	+	0.0989714i
$552$		0			0
$553$	−5.44791	−	6.49256i	−0.231669	−	0.276092i
$554$	21.8017	−	18.2938i	0.926265	−	0.777229i
$555$		0			0
$556$	66.6355	−	24.2533i	2.82598	−	1.02857i
$557$	−14.3572	+	8.28915i	−0.608335	+	0.351222i	−0.772314	−	0.635242i	$-0.780901\pi$
$557$	−14.3572	+	8.28915i	−0.608335	+	0.351222i	0.163979	+	0.986464i	$0.447567\pi$
$558$		0			0
$559$	−8.83656	+	15.3054i	−0.373747	+	0.647349i
$560$	−27.0822	−	13.5035i	−1.14443	−	0.570626i
$561$		0			0
$562$	19.7999	−	54.3997i	0.835208	−	2.29471i
$563$	−13.2880	+	2.34303i	−0.560023	+	0.0987471i	−0.446492	−	0.894787i	$-0.647327\pi$
$563$	−13.2880	+	2.34303i	−0.560023	+	0.0987471i	−0.113530	+	0.993535i	$0.536216\pi$
$564$		0			0
$565$	−14.8394	+	9.82148i	−0.624297	+	0.413193i
$566$	43.8385			1.84267
$567$		0			0
$568$			87.9653i			3.69094i
$569$	14.0395	+	11.7805i	0.588565	+	0.493865i	0.887747	−	0.460331i	$-0.152269\pi$
$569$	14.0395	+	11.7805i	0.588565	+	0.493865i	−0.299182	+	0.954196i	$0.596714\pi$
$570$		0			0
$571$	1.67291	+	9.48757i	0.0700093	+	0.397043i	0.999596	+	0.0284379i	$0.00905327\pi$
$571$	1.67291	+	9.48757i	0.0700093	+	0.397043i	−0.929586	+	0.368605i	$0.879836\pi$
$572$	9.43167	−	25.9133i	0.394358	−	1.08349i
$573$		0			0
$574$	1.69417	−	9.60809i	0.0707131	−	0.401034i
$575$	−6.26532	−	12.2978i	−0.261282	−	0.512853i
$576$		0			0
$577$	16.3731	−	9.45304i	0.681623	−	0.393535i	−0.118843	−	0.992913i	$-0.537919\pi$
$577$	16.3731	−	9.45304i	0.681623	−	0.393535i	0.800466	+	0.599378i	$0.204585\pi$
$578$	−1.57345	−	4.32302i	−0.0654470	−	0.179814i
$579$		0			0
$580$	−84.9892	+	36.9520i	−3.52898	+	1.53435i
$581$	2.24484	−	1.88365i	0.0931318	−	0.0781468i
$582$		0			0
$583$	0.208962	+	0.574118i	0.00865432	+	0.0237776i
$584$	23.3554	+	40.4527i	0.966452	+	1.67394i
$585$		0			0
$586$	−31.8978	+	55.2485i	−1.31768	+	2.28230i
$587$	38.7578	+	6.83405i	1.59971	+	0.282071i	0.901158	−	0.433491i	$-0.142718\pi$
$587$	38.7578	+	6.83405i	1.59971	+	0.282071i	0.698549	+	0.715563i	$0.253830\pi$
$588$		0			0
$589$	−4.41461	−	1.60679i	−0.181901	−	0.0662065i
$590$	9.44406	+	1.07624i	0.388806	+	0.0443079i
$591$		0			0
$592$	63.9566	−	76.2206i	2.62860	−	3.13265i
$593$			1.34012i			0.0550322i	0.999621	+	0.0275161i	$0.00875976\pi$
$593$			1.34012i			0.0550322i	−0.999621	+	0.0275161i	$0.991240\pi$
$594$		0			0
$595$	−8.48456	−	2.51345i	−0.347833	−	0.103042i
$596$	13.6612	+	11.4631i	0.559583	+	0.469546i
$597$		0			0
$598$	30.4180	−	5.36351i	1.24388	−	0.219330i
$599$	30.9748	+	11.2739i	1.26559	+	0.460639i	0.885643	−	0.464367i	$-0.153718\pi$
$599$	30.9748	+	11.2739i	1.26559	+	0.460639i	0.379952	+	0.925006i	$0.375940\pi$
$600$		0			0
$601$	5.62780	−	31.9168i	0.229563	−	1.30192i	−0.624205	−	0.781261i	$-0.714577\pi$
$601$	5.62780	−	31.9168i	0.229563	−	1.30192i	0.853767	−	0.520655i	$-0.174312\pi$
$602$	10.0851	+	5.82264i	0.411038	+	0.237313i
$603$		0			0
$604$	−60.9831	−	105.626i	−2.48137	−	4.29785i
$605$	21.0167	−	1.28495i	0.854449	−	0.0522406i
$606$		0			0
$607$	13.3034	+	15.8543i	0.539967	+	0.643508i	0.965180	−	0.261585i	$-0.0842453\pi$
$607$	13.3034	+	15.8543i	0.539967	+	0.643508i	−0.425213	+	0.905093i	$0.639801\pi$
$608$	10.2253	+	12.1860i	0.414690	+	0.494209i
$609$		0			0
$610$	−0.607693	−	9.93946i	−0.0246048	−	0.402437i
$611$	7.64901	+	13.2485i	0.309446	+	0.535976i
$612$		0			0
$613$	29.2160	+	16.8679i	1.18002	+	0.681287i	0.956020	−	0.293301i	$-0.0947538\pi$
$613$	29.2160	+	16.8679i	1.18002	+	0.681287i	0.224004	+	0.974588i	$0.428087\pi$
$614$	2.89182	−	16.4003i	0.116704	−	0.661864i
$615$		0			0
$616$	−10.6152	−	3.86362i	−0.427699	−	0.155670i
$617$	30.2079	−	5.32646i	1.21612	−	0.214435i	0.471467	−	0.881884i	$-0.343725\pi$
$617$	30.2079	−	5.32646i	1.21612	−	0.214435i	0.744656	+	0.667448i	$0.232614\pi$
$618$		0			0
$619$	−22.9897	−	19.2906i	−0.924033	−	0.775356i	0.0507031	−	0.998714i	$-0.483854\pi$
$619$	−22.9897	−	19.2906i	−0.924033	−	0.775356i	−0.974737	+	0.223358i	$0.928298\pi$
$620$	−61.4565	−	18.2058i	−2.46815	−	0.731162i
$621$		0			0
$622$			36.8935i			1.47929i
$623$	10.4507	−	12.4547i	0.418698	−	0.498985i
$624$		0			0
$625$	−20.7272	+	13.9779i	−0.829089	+	0.559116i
$626$	−20.0490	−	7.29725i	−0.801320	−	0.291657i
$627$		0			0
$628$	47.5532	+	8.38492i	1.89758	+	0.334595i
$629$	14.5474	−	25.1968i	0.580043	−	1.00466i
$630$		0			0
$631$	22.1756	+	38.4093i	0.882797	+	1.52905i	0.848218	+	0.529647i	$0.177675\pi$
$631$	22.1756	+	38.4093i	0.882797	+	1.52905i	0.0345781	+	0.999402i	$0.488991\pi$
$632$	25.4153	+	69.8280i	1.01097	+	2.77761i
$633$		0			0
$634$	−11.6259	+	9.75533i	−0.461725	+	0.387433i
$635$	16.5667	+	38.1032i	0.657430	+	1.51208i
$636$		0			0
$637$	−8.47270	−	23.2785i	−0.335701	−	0.922330i
$638$	−23.0624	+	13.3151i	−0.913049	+	0.527149i
$639$		0			0
$640$	38.2566	+	40.3159i	1.51222	+	1.59362i
$641$	−5.79316	+	32.8547i	−0.228816	+	1.29768i	0.626437	+	0.779472i	$0.284512\pi$
$641$	−5.79316	+	32.8547i	−0.228816	+	1.29768i	−0.855254	+	0.518210i	$0.826599\pi$
$642$		0			0
$643$	5.56415	−	15.2874i	0.219429	−	0.602875i	−0.780318	−	0.625383i	$-0.784943\pi$
$643$	5.56415	−	15.2874i	0.219429	−	0.602875i	0.999747	+	0.0225078i	$0.00716506\pi$
$644$	−2.56411	−	14.5418i	−0.101040	−	0.573027i
$645$		0			0
$646$	7.00702	+	5.87959i	0.275688	+	0.231329i
$647$		−	39.9222i		−	1.56950i	−0.619811	−	0.784751i	$-0.712791\pi$
$647$		−	39.9222i		−	1.56950i	0.619811	−	0.784751i	$-0.287209\pi$
$648$		0			0
$649$	1.98164			0.0777861
$650$	−16.3551	−	53.5039i	−0.641499	−	2.09860i
$651$		0			0
$652$	−38.1356	+	6.72434i	−1.49351	+	0.263345i
$653$	−1.90591	+	5.23644i	−0.0745839	+	0.204918i	−0.971382	−	0.237522i	$-0.923665\pi$
$653$	−1.90591	+	5.23644i	−0.0745839	+	0.204918i	0.896798	+	0.442440i	$0.145887\pi$
$654$		0			0
$655$	−18.7908	+	37.6864i	−0.734218	+	1.47253i
$656$	−23.8867	+	41.3730i	−0.932619	+	1.61534i
$657$		0			0
$658$	8.72976	−	5.04013i	0.340322	−	0.196485i
$659$	−6.70045	+	2.43876i	−0.261012	+	0.0950007i	−0.469212	−	0.883086i	$-0.655462\pi$
$659$	−6.70045	+	2.43876i	−0.261012	+	0.0950007i	0.208199	+	0.978086i	$0.433240\pi$
$660$		0			0
$661$	−11.1617	+	9.36578i	−0.434140	+	0.364286i	−0.833511	−	0.552503i	$-0.813673\pi$
$661$	−11.1617	+	9.36578i	−0.434140	+	0.364286i	0.399371	+	0.916789i	$0.369228\pi$
$662$	43.2906	+	51.5917i	1.68254	+	2.00517i
$663$		0			0
$664$	−24.1435	+	8.78750i	−0.936948	+	0.341021i
$665$	−1.90624	+	0.457600i	−0.0739207	+	0.0177450i
$666$		0			0
$667$	−18.7412	−	10.8202i	−0.725663	−	0.418962i
$668$	−26.1892	−	4.61787i	−1.01329	−	0.178671i
$669$		0			0
$670$	16.0859	+	11.9035i	0.621451	+	0.459872i
$671$	−0.360501	−	2.04450i	−0.0139170	−	0.0789272i
$672$		0			0
$673$	−0.310596	+	0.370154i	−0.0119726	+	0.0142684i	−0.771998	−	0.635626i	$-0.780742\pi$
$673$	−0.310596	+	0.370154i	−0.0119726	+	0.0142684i	0.760025	+	0.649894i	$0.225187\pi$
$674$	29.1500			1.12282
$675$		0			0
$676$	22.1144			0.850555
$677$	25.1620	−	29.9869i	0.967055	−	1.15249i	−0.0212148	−	0.999775i	$-0.506753\pi$
$677$	25.1620	−	29.9869i	0.967055	−	1.15249i	0.988270	−	0.152717i	$-0.0488022\pi$
$678$		0			0
$679$	0.542802	+	3.07838i	0.0208308	+	0.118137i
$680$	62.3660	+	46.1507i	2.39163	+	1.76980i
$681$		0			0
$682$	−18.1383	−	3.19828i	−0.694553	−	0.122468i
$683$	0.184609	+	0.106584i	0.00706386	+	0.00407832i	0.503528	−	0.863979i	$-0.332035\pi$
$683$	0.184609	+	0.106584i	0.00706386	+	0.00407832i	−0.496464	+	0.868057i	$0.665368\pi$
$684$		0			0
$685$	34.7890	−	8.35126i	1.32922	−	0.319085i
$686$	−33.3056	+	12.1223i	−1.27162	+	0.462830i
$687$		0			0
$688$	−36.6537	−	43.6821i	−1.39741	−	1.66537i
$689$	−1.54174	+	1.29367i	−0.0587355	+	0.0492849i
$690$		0			0
$691$	20.5204	−	7.46881i	0.780633	−	0.284127i	0.0791962	−	0.996859i	$-0.474765\pi$
$691$	20.5204	−	7.46881i	0.780633	−	0.284127i	0.701436	+	0.712732i	$0.252542\pi$
$692$	−87.7526	+	50.6640i	−3.33585	+	1.92596i
$693$		0			0
$694$	34.9239	−	60.4900i	1.32569	−	2.29617i
$695$	13.3837	−	26.8421i	0.507674	−	1.01818i
$696$		0			0
$697$	−4.77788	+	13.1271i	−0.180975	+	0.497225i
$698$	−40.6582	+	7.16913i	−1.53893	+	0.271356i
$699$		0			0
$700$	−25.5784	+	7.81880i	−0.966772	+	0.295523i
$701$	35.4129			1.33753			0.668763	−	0.743476i	$-0.266824\pi$
$701$	35.4129			1.33753			0.668763	+	0.743476i	$0.266824\pi$
$702$		0			0
$703$		−	6.44560i		−	0.243100i
$704$	21.9893	+	18.4512i	0.828752	+	0.695405i
$705$		0			0
$706$	−16.2405	−	92.1044i	−0.611219	−	3.46639i
$707$	2.95398	−	8.11600i	0.111096	−	0.305234i
$708$		0			0
$709$	−1.16039	+	6.58093i	−0.0435795	+	0.247152i	−0.998813	−	0.0486997i	$-0.984492\pi$
$709$	−1.16039	+	6.58093i	−0.0435795	+	0.247152i	0.955234	+	0.295852i	$0.0956034\pi$
$710$	41.1958	+	43.4134i	1.54605	+	1.62927i
$711$		0			0
$712$	−123.450	+	71.2737i	−4.62647	+	2.67110i
$713$	−5.11907	−	14.0645i	−0.191711	−	0.526721i
$714$		0			0
$715$	−4.65075	−	10.6967i	−0.173928	−	0.400033i
$716$	−55.1581	+	46.2831i	−2.06135	+	1.72968i
$717$		0			0
$718$	7.97379	+	21.9078i	0.297579	+	0.817592i
$719$	1.59977	+	2.77089i	0.0596614	+	0.103337i	0.894313	−	0.447441i	$-0.147665\pi$
$719$	1.59977	+	2.77089i	0.0596614	+	0.103337i	−0.834652	+	0.550778i	$0.814331\pi$
$720$		0			0
$721$	−8.07159	+	13.9804i	−0.300602	+	0.520657i
$722$	−48.5132	−	8.55418i	−1.80547	−	0.318354i
$723$		0			0
$724$	42.2659	+	15.3835i	1.57080	+	0.571724i
$725$	−15.3178	+	36.0818i	−0.568889	+	1.34005i
$726$		0			0
$727$	25.4198	−	30.2941i	0.942768	−	1.12355i	−0.0494182	−	0.998778i	$-0.515737\pi$
$727$	25.4198	−	30.2941i	0.942768	−	1.12355i	0.992186	−	0.124769i	$-0.0398188\pi$
$728$		−	37.2120i		−	1.37917i
$729$		0			0
$730$	30.4713	+	9.02678i	1.12779	+	0.334096i
$731$	−12.7732	−	10.7180i	−0.472436	−	0.396421i
$732$		0			0
$733$	−47.0139	+	8.28983i	−1.73650	+	0.306192i	−0.950197	−	0.311650i	$-0.899118\pi$
$733$	−47.0139	+	8.28983i	−1.73650	+	0.306192i	−0.786302	+	0.617842i	$0.788007\pi$
$734$	−69.4864	−	25.2910i	−2.56479	−	0.933507i
$735$		0			0
$736$	−8.80059	+	49.9106i	−0.324394	+	1.83973i
$737$	3.61299	+	2.08596i	0.133086	+	0.0768374i
$738$		0			0
$739$	0.756718	+	1.31067i	0.0278363	+	0.0482139i	0.879608	−	0.475699i	$-0.157805\pi$
$739$	0.756718	+	1.31067i	0.0278363	+	0.0482139i	−0.851772	+	0.523913i	$0.824472\pi$
$740$	−5.36664	−	87.7770i	−0.197282	−	3.22675i
$741$		0			0
$742$	0.852432	+	1.01589i	0.0312938	+	0.0372945i
$743$	12.5490	+	14.9554i	0.460380	+	0.548659i	0.945429	−	0.325827i	$-0.105643\pi$
$743$	12.5490	+	14.9554i	0.460380	+	0.548659i	−0.485049	+	0.874487i	$0.661198\pi$
$744$		0			0
$745$	7.52892	−	0.460315i	0.275838	−	0.0168646i
$746$	−35.2351	−	61.0289i	−1.29005	−	2.23443i
$747$		0			0
$748$	22.5321	+	13.0089i	0.823855	+	0.475653i
$749$	1.61713	−	9.17119i	0.0590886	−	0.335108i
$750$		0			0
$751$	−20.9890	−	7.63937i	−0.765900	−	0.278765i	−0.0706193	−	0.997503i	$-0.522498\pi$
$751$	−20.9890	−	7.63937i	−0.765900	−	0.278765i	−0.695280	+	0.718739i	$0.744720\pi$
$752$	−48.6098	+	8.57121i	−1.77262	+	0.312560i
$753$		0			0
$754$	−67.1998	−	56.3874i	−2.44727	−	2.05351i
$755$	−49.4633	−	14.6529i	−1.80015	−	0.533275i
$756$		0			0
$757$		−	41.7562i		−	1.51766i	−0.651291	−	0.758828i	$-0.725772\pi$
$757$		−	41.7562i		−	1.51766i	0.651291	−	0.758828i	$-0.274228\pi$
$758$	−18.9894	+	22.6307i	−0.689727	+	0.821984i
$759$		0			0
$760$	17.0774	+	1.94613i	0.619464	+	0.0705934i
$761$	−31.4550	−	11.4487i	−1.14024	−	0.415014i	−0.298241	−	0.954490i	$-0.596400\pi$
$761$	−31.4550	−	11.4487i	−1.14024	−	0.415014i	−0.842001	+	0.539476i	$0.818622\pi$
$762$		0			0
$763$	4.96285	+	0.875084i	0.179667	+	0.0316802i
$764$	33.8854	−	58.6912i	1.22593	−	2.12337i
$765$		0			0
$766$	2.97435	+	5.15173i	0.107468	+	0.186140i
$767$	2.23263	+	6.13410i	0.0806155	+	0.221489i
$768$		0			0
$769$	11.6956	−	9.81375i	0.421753	−	0.353893i	−0.407076	−	0.913394i	$-0.633452\pi$
$769$	11.6956	−	9.81375i	0.421753	−	0.353893i	0.828830	+	0.559501i	$0.189007\pi$
$770$	−7.04831	+	3.06450i	−0.254003	+	0.110437i
$771$		0			0
$772$	−18.0204	−	49.5107i	−0.648570	−	1.78193i
$773$	23.3186	−	13.4630i	0.838711	−	0.484230i	−0.0181148	−	0.999836i	$-0.505766\pi$
$773$	23.3186	−	13.4630i	0.838711	−	0.484230i	0.856826	+	0.515606i	$0.172433\pi$
$774$		0			0
$775$	−24.1565	+	12.3070i	−0.867729	+	0.442079i
$776$	4.75908	−	26.9901i	0.170841	−	0.968887i
$777$		0			0
$778$	22.4815	−	61.7674i	0.806001	−	2.21447i
$779$	0.537404	+	3.04777i	0.0192545	+	0.109198i
$780$		0			0
$781$	9.55805	+	8.02015i	0.342014	+	0.286984i
$782$			29.1416i			1.04210i
$783$		0			0
$784$	79.9294			2.85462
$785$	17.0314	−	11.2723i	0.607878	−	0.402326i
$786$		0			0
$787$	25.7714	−	4.54419i	0.918650	−	0.161983i	0.305722	−	0.952121i	$-0.401102\pi$
$787$	25.7714	−	4.54419i	0.918650	−	0.161983i	0.612929	+	0.790138i	$0.289991\pi$
$788$	35.5280	−	97.6124i	1.26563	−	3.47730i
$789$		0			0
$790$	45.2450	+	22.5596i	1.60974	+	0.802635i
$791$	−4.02636	+	6.97386i	−0.143161	+	0.247962i
$792$		0			0
$793$	5.92253	−	3.41938i	0.210315	−	0.121426i
$794$	28.2935	−	10.2980i	1.00410	−	0.365462i
$795$		0			0
$796$	14.6422	−	12.2862i	0.518978	−	0.435474i
$797$	−22.9122	−	27.3057i	−0.811591	−	0.967216i	0.188298	−	0.982112i	$-0.439703\pi$
$797$	−22.9122	−	27.3057i	−0.811591	−	0.967216i	−0.999889	+	0.0148959i	$0.995258\pi$
$798$		0			0
$799$	−13.5630	+	4.93652i	−0.479824	+	0.174642i
$800$	91.6746	+	4.80870i	3.24119	+	0.170013i
$801$		0			0
$802$	8.40083	+	4.85022i	0.296643	+	0.171267i
$803$	6.52487	+	1.15051i	0.230258	+	0.0406006i
$804$		0			0
$805$	−5.02051	−	3.71516i	−0.176950	−	0.130942i
$806$	−10.5355	−	59.7500i	−0.371099	−	2.10461i
$807$		0			0
$808$	−48.6749	+	58.0085i	−1.71238	+	2.04073i
$809$	−5.37671			−0.189035			−0.0945175	−	0.995523i	$-0.530131\pi$
$809$	−5.37671			−0.189035			−0.0945175	+	0.995523i	$0.530131\pi$
$810$		0			0
$811$	25.4236			0.892744			0.446372	−	0.894847i	$-0.352716\pi$
$811$	25.4236			0.892744			0.446372	+	0.894847i	$0.352716\pi$
$812$	−26.9569	+	32.1259i	−0.946000	+	1.12740i
$813$		0			0
$814$	−4.38807	−	24.8860i	−0.153802	−	0.872253i
$815$	−9.74295	+	13.1662i	−0.341281	+	0.461192i
$816$		0			0
$817$	−3.63786	−	0.641454i	−0.127273	−	0.0224416i
$818$	−20.2210	−	11.6746i	−0.707012	−	0.408193i
$819$		0			0
$820$	9.85604	+	41.0575i	0.344188	+	1.43379i
$821$	−12.2590	+	4.46192i	−0.427843	+	0.155722i	−0.546961	−	0.837158i	$-0.684215\pi$
$821$	−12.2590	+	4.46192i	−0.427843	+	0.155722i	0.119118	+	0.992880i	$0.461993\pi$
$822$		0			0
$823$	−21.8976	−	26.0965i	−0.763302	−	0.909668i	0.234750	−	0.972056i	$-0.424573\pi$
$823$	−21.8976	−	26.0965i	−0.763302	−	0.909668i	−0.998052	+	0.0623879i	$0.980128\pi$
$824$	108.424	−	90.9783i	3.77712	−	3.16938i
$825$		0			0
$826$	4.04191	−	1.47114i	0.140636	−	0.0511874i
$827$	27.8760	−	16.0942i	0.969345	−	0.559651i	0.0703083	−	0.997525i	$-0.477602\pi$
$827$	27.8760	−	16.0942i	0.969345	−	0.559651i	0.899036	+	0.437874i	$0.144268\pi$
$828$		0			0
$829$	11.4430	−	19.8198i	0.397431	−	0.688371i	−0.595977	−	0.803001i	$-0.703235\pi$
$829$	11.4430	−	19.8198i	0.397431	−	0.688371i	0.993408	+	0.114630i	$0.0365684\pi$
$830$	−7.80012	+	15.6437i	−0.270746	+	0.543001i
$831$		0			0
$832$	−32.3407	+	88.8553i	−1.12121	+	3.08050i
$833$	23.0174	−	4.05858i	0.797504	−	0.140622i
$834$		0			0
$835$	−9.37982	+	6.20806i	−0.324602	+	0.214839i
$836$	5.76392			0.199350
$837$		0			0
$838$		−	99.3379i		−	3.43157i
$839$	14.3141	+	12.0109i	0.494176	+	0.414663i	0.855520	−	0.517769i	$-0.173237\pi$
$839$	14.3141	+	12.0109i	0.494176	+	0.414663i	−0.361344	+	0.932433i	$0.617682\pi$
$840$		0			0
$841$	5.63686	+	31.9682i	0.194375	+	1.10235i
$842$	33.4859	−	92.0019i	1.15400	−	3.17059i
$843$		0			0
$844$	−16.8158	+	95.3673i	−0.578824	+	3.28268i
$845$	6.78511	−	6.43854i	0.233415	−	0.221492i
$846$		0			0
$847$	8.25173	−	4.76414i	0.283533	−	0.163698i
$848$	−2.22098	−	6.10209i	−0.0762687	−	0.209547i
$849$		0			0
$850$	52.3926	−	6.43055i	1.79705	−	0.220566i
$851$	15.7308	−	13.1997i	0.539244	−	0.452480i
$852$		0			0
$853$	−7.32234	−	20.1180i	−0.250712	−	0.688826i	−0.999657	−	0.0261934i	$-0.991661\pi$
$853$	−7.32234	−	20.1180i	−0.250712	−	0.688826i	0.748945	−	0.662632i	$-0.230561\pi$
$854$	−2.25311	−	3.90251i	−0.0771000	−	0.133541i
$855$		0			0
$856$	−40.8250	+	70.7109i	−1.39537	+	2.41685i
$857$	5.92728	+	1.04514i	0.202472	+	0.0357013i	0.273964	−	0.961740i	$-0.411665\pi$
$857$	5.92728	+	1.04514i	0.202472	+	0.0357013i	−0.0714922	+	0.997441i	$0.522776\pi$
$858$		0			0
$859$	−21.9131	−	7.97570i	−0.747664	−	0.272128i	−0.0600417	−	0.998196i	$-0.519123\pi$
$859$	−21.9131	−	7.97570i	−0.747664	−	0.272128i	−0.687623	+	0.726068i	$0.741346\pi$
$860$	−50.0750	−	5.70649i	−1.70754	−	0.194590i
$861$		0			0
$862$	−33.5860	+	40.0262i	−1.14394	+	1.36330i
$863$		−	19.5769i		−	0.666405i	−0.942855	−	0.333203i	$-0.891871\pi$
$863$		−	19.5769i		−	0.666405i	0.942855	−	0.333203i	$-0.108129\pi$
$864$		0			0
$865$	−12.1735	+	41.0935i	−0.413911	+	1.39722i
$866$	47.1472	+	39.5612i	1.60213	+	1.34434i
$867$		0			0
$868$	−28.5644	+	5.03668i	−0.969540	+	0.170956i
$869$	9.90452	+	3.60495i	0.335988	+	0.122290i
$870$		0			0
$871$	−2.38642	+	13.5341i	−0.0808609	+	0.458585i
$872$	−38.2641	−	22.0918i	−1.29579	−	0.748123i
$873$		0			0
$874$	3.22798	+	5.59102i	0.109188	+	0.189119i
$875$	−5.57150	+	9.84601i	−0.188351	+	0.332856i
$876$		0			0
$877$	32.2415	+	38.4239i	1.08872	+	1.29748i	0.951739	+	0.306910i	$0.0992949\pi$
$877$	32.2415	+	38.4239i	1.08872	+	1.29748i	0.136979	+	0.990574i	$0.456261\pi$
$878$	−33.6393	−	40.0898i	−1.13527	−	1.35296i
$879$		0			0
$880$	37.5641	−	2.29665i	1.26629	−	0.0774200i
$881$	−4.92107	−	8.52354i	−0.165795	−	0.287165i	0.771142	−	0.636663i	$-0.219686\pi$
$881$	−4.92107	−	8.52354i	−0.165795	−	0.287165i	−0.936937	+	0.349497i	$0.886352\pi$
$882$		0			0
$883$	14.0540	+	8.11410i	0.472956	+	0.273061i	0.717476	−	0.696583i	$-0.245297\pi$
$883$	14.0540	+	8.11410i	0.472956	+	0.273061i	−0.244520	+	0.969644i	$0.578631\pi$
$884$	−14.8827	+	84.4039i	−0.500559	+	2.83881i
$885$		0			0
$886$	−9.87346	−	3.59365i	−0.331705	−	0.120731i
$887$	4.57011	−	0.805833i	0.153449	−	0.0270572i	−0.0963958	−	0.995343i	$-0.530731\pi$
$887$	4.57011	−	0.805833i	0.153449	−	0.0270572i	0.249845	+	0.968286i	$0.419620\pi$
$888$		0			0
$889$	14.4030	+	12.0856i	0.483062	+	0.405337i
$890$	−27.5470	+	92.9894i	−0.923379	+	3.11701i
$891$		0			0
$892$		−	37.0548i		−	1.24069i
$893$	−2.05534	+	2.44946i	−0.0687795	+	0.0819682i
$894$		0			0
$895$	−3.44835	+	30.2596i	−0.115266	+	1.01147i
$896$	23.6336	+	8.60194i	0.789544	+	0.287371i
$897$		0			0
$898$	−58.1955	−	10.2614i	−1.94201	−	0.342428i
$899$	−21.2542	+	36.8134i	−0.708867	+	1.22779i
$900$		0			0
$901$	−0.949424	−	1.64445i	−0.0316299	−	0.0547846i
$902$	4.14976	+	11.4014i	0.138172	+	0.379624i
$903$		0			0
$904$	54.0852	−	45.3829i	1.79885	−	1.50941i
$905$	17.4468	−	7.58561i	0.579952	−	0.252154i
$906$		0			0
$907$	−3.04461	−	8.36499i	−0.101094	−	0.277755i	0.878826	−	0.477142i	$-0.158327\pi$
$907$	−3.04461	−	8.36499i	−0.101094	−	0.277755i	−0.979921	+	0.199387i	$0.936105\pi$
$908$	−61.4789	+	35.4949i	−2.04025	+	1.17794i
$909$		0			0
$910$	−17.4271	−	18.3652i	−0.577703	−	0.608800i
$911$	−5.06913	+	28.7484i	−0.167948	+	0.952478i	0.778025	+	0.628233i	$0.216221\pi$
$911$	−5.06913	+	28.7484i	−0.167948	+	0.952478i	−0.945973	+	0.324245i	$0.894890\pi$
$912$		0			0
$913$	−1.24643	+	3.42455i	−0.0412509	+	0.113336i
$914$	9.04643	+	51.3049i	0.299229	+	1.69701i
$915$		0			0
$916$	−37.6218	−	31.5684i	−1.24306	−	1.04305i
$917$			19.0563i			0.629295i
$918$		0			0
$919$	−48.7206			−1.60714			−0.803572	−	0.595208i	$-0.797070\pi$
$919$	−48.7206			−1.60714			−0.803572	+	0.595208i	$0.797070\pi$
$920$	30.2226	+	45.6637i	0.996411	+	1.50549i
$921$		0			0
$922$	101.581	−	17.9115i	3.34540	−	0.589884i
$923$	−14.0575	+	38.6226i	−0.462707	+	1.27128i
$924$		0			0
$925$	−27.2025	−	25.3691i	−0.894414	−	0.834131i
$926$	−30.0982	+	52.1316i	−0.989088	+	1.71315i
$927$		0			0
$928$	124.654	−	71.9692i	4.09198	−	2.36251i
$929$	34.3831	−	12.5144i	1.12807	−	0.410585i	0.290480	−	0.956881i	$-0.406185\pi$
$929$	34.3831	−	12.5144i	1.12807	−	0.410585i	0.837592	+	0.546296i	$0.183963\pi$
$930$		0			0
$931$	3.96648	−	3.32827i	0.129996	−	0.109080i
$932$	34.6987	+	41.3522i	1.13659	+	1.35454i
$933$		0			0
$934$	76.5061	−	27.8460i	2.50336	−	0.911148i
$935$	10.7008	−	2.56876i	0.349952	−	0.0840075i
$936$		0			0
$937$	19.8545	+	11.4630i	0.648618	+	0.374480i	0.787927	−	0.615769i	$-0.211155\pi$
$937$	19.8545	+	11.4630i	0.648618	+	0.374480i	−0.139308	+	0.990249i	$0.544488\pi$
$938$	8.91795	+	1.57247i	0.291181	+	0.0513431i
$939$		0			0
$940$	−25.9505	+	35.0684i	−0.846412	+	1.14381i
$941$	−2.11146	−	11.9747i	−0.0688317	−	0.390364i	−0.999688	−	0.0249784i	$-0.992048\pi$
$941$	−2.11146	−	11.9747i	−0.0688317	−	0.390364i	0.930856	−	0.365385i	$-0.119063\pi$
$942$		0			0
$943$	−6.33770	+	7.55298i	−0.206384	+	0.245959i
$944$	−21.0621			−0.685512
$945$		0			0
$946$	−14.4822			−0.470857
$947$	8.24056	−	9.82072i	0.267782	−	0.319130i	−0.615351	−	0.788254i	$-0.710986\pi$
$947$	8.24056	−	9.82072i	0.267782	−	0.319130i	0.883133	+	0.469123i	$0.155430\pi$
$948$		0			0
$949$	3.78993	+	21.4938i	0.123026	+	0.697717i
$950$	9.33960	−	7.03722i	0.303017	−	0.228318i
$951$		0			0
$952$	34.5755	+	6.09660i	1.12060	+	0.197592i
$953$	−8.84797	−	5.10838i	−0.286614	−	0.165477i	0.349800	−	0.936824i	$-0.386250\pi$
$953$	−8.84797	−	5.10838i	−0.286614	−	0.165477i	−0.636414	+	0.771348i	$0.719583\pi$
$954$		0			0
$955$	−6.69108	−	27.8732i	−0.216518	−	0.901954i
$956$	12.8776	−	4.68706i	0.416491	−	0.151590i
$957$		0			0
$958$	24.7485	+	29.4941i	0.799586	+	0.952910i
$959$	12.4023	−	10.4068i	0.400492	−	0.336053i
$960$		0			0
$961$	1.50350	−	0.547231i	0.0485002	−	0.0176526i
$962$	72.0899	−	41.6211i	2.32427	−	1.34192i
$963$		0			0
$964$	−43.9670	+	76.1531i	−1.41608	+	2.45273i
$965$	−19.9439	−	9.94423i	−0.642016	−	0.320116i
$966$		0			0
$967$	−9.29181	+	25.5290i	−0.298804	+	0.820958i	0.695896	+	0.718143i	$0.255007\pi$
$967$	−9.29181	+	25.5290i	−0.298804	+	0.820958i	−0.994700	+	0.102816i	$0.967215\pi$
$968$	−82.2711	+	14.5066i	−2.64429	+	0.466260i
$969$		0			0
$970$	−10.2912	−	15.5491i	−0.330431	−	0.499252i
$971$	7.96515			0.255614			0.127807	−	0.991799i	$-0.459206\pi$
$971$	7.96515			0.255614			0.127807	+	0.991799i	$0.459206\pi$
$972$		0			0
$973$		−	13.5728i		−	0.435125i
$974$	−43.4117	−	36.4267i	−1.39100	−	1.16719i
$975$		0			0
$976$	3.83163	+	21.7303i	0.122648	+	0.695569i
$977$	14.7183	−	40.4381i	0.470879	−	1.29373i	−0.446168	−	0.894949i	$-0.647212\pi$
$977$	14.7183	−	40.4381i	0.470879	−	1.29373i	0.917047	−	0.398779i	$-0.130566\pi$
$978$		0			0
$979$	−3.51102	+	19.9120i	−0.112213	+	0.636390i
$980$	51.2449	−	48.6274i	1.63696	−	1.55334i
$981$		0			0
$982$	−12.0569	+	6.96105i	−0.384751	+	0.222136i
$983$	14.6729	+	40.3135i	0.467993	+	1.28580i	0.919345	+	0.393453i	$0.128720\pi$
$983$	14.6729	+	40.3135i	0.467993	+	1.28580i	−0.451352	+	0.892346i	$0.649058\pi$
$984$		0			0
$985$	−17.5189	−	40.2931i	−0.558197	−	1.28385i
$986$	63.4019	−	53.2005i	2.01913	−	1.69425i
$987$		0			0
$988$	6.49397	+	17.8420i	0.206601	+	0.567631i
$989$	−5.88435	−	10.1920i	−0.187111	−	0.324086i
$990$		0			0
$991$	18.5127	−	32.0649i	0.588075	−	1.01858i	−0.406410	−	0.913691i	$-0.633219\pi$
$991$	18.5127	−	32.0649i	0.588075	−	1.01858i	0.994484	−	0.104884i	$-0.0334473\pi$
$992$	98.0394	+	17.2870i	3.11276	+	0.548863i
$993$		0			0
$994$	25.4494	+	9.26283i	0.807206	+	0.293799i
$995$	0.915393	−	8.03265i	0.0290199	−	0.254652i
$996$		0			0
$997$	16.2659	−	19.3849i	0.515146	−	0.613927i	−0.444280	−	0.895888i	$-0.646540\pi$
$997$	16.2659	−	19.3849i	0.515146	−	0.613927i	0.959426	+	0.281961i	$0.0909849\pi$
$998$			96.0475i			3.04033i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.p.a.289.1		96
3.2	odd	2		135.2.p.a.124.16	yes	96
5.4	even	2	inner	405.2.p.a.289.16		96
15.2	even	4		675.2.l.h.151.16		96
15.8	even	4		675.2.l.h.151.1		96
15.14	odd	2		135.2.p.a.124.1	yes	96
27.5	odd	18		135.2.p.a.49.1	✓	96
27.22	even	9	inner	405.2.p.a.199.16		96
135.32	even	36		675.2.l.h.76.16		96
135.49	even	18	inner	405.2.p.a.199.1		96
135.59	odd	18		135.2.p.a.49.16	yes	96
135.113	even	36		675.2.l.h.76.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.1	✓	96	27.5	odd	18
135.2.p.a.49.16	yes	96	135.59	odd	18
135.2.p.a.124.1	yes	96	15.14	odd	2
135.2.p.a.124.16	yes	96	3.2	odd	2
405.2.p.a.199.1		96	135.49	even	18	inner
405.2.p.a.199.16		96	27.22	even	9	inner
405.2.p.a.289.1		96	1.1	even	1	trivial
405.2.p.a.289.16		96	5.4	even	2	inner
675.2.l.h.76.1		96	135.113	even	36
675.2.l.h.76.16		96	135.32	even	36
675.2.l.h.151.1		96	15.8	even	4
675.2.l.h.151.16		96	15.2	even	4

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.p (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73512 + 2.06784i) q^{2} +(-0.918006 - 5.20627i) q^{4} +(-1.79745 - 1.33011i) q^{5} +(-0.996499 - 0.175710i) q^{7} +(7.68312 + 4.43585i) q^{8} +(5.86923 - 1.40893i) q^{10} +(1.18249 - 0.430390i) q^{11} +(2.66452 + 3.17545i) q^{13} +(2.09238 - 1.75572i) q^{14} +(-12.5682 + 4.57445i) q^{16} +(-3.38700 + 1.95549i) q^{17} +(-0.433214 + 0.750349i) q^{19} +(-5.27482 + 10.5790i) q^{20} +(-1.16178 + 3.19197i) q^{22} +(-2.71843 + 0.479332i) q^{23} +(1.46164 + 4.78159i) q^{25} -11.1896 q^{26} +5.34934i q^{28} +(6.00558 + 5.03928i) q^{29} +(0.941551 + 5.33980i) q^{31} +(6.27953 - 17.2529i) q^{32} +(1.83323 - 10.3968i) q^{34} +(1.55744 + 1.64128i) q^{35} +(-6.44260 + 3.71964i) q^{37} +(-0.799919 - 2.19776i) q^{38} +(-7.90986 - 18.1926i) q^{40} +(2.73623 - 2.29597i) q^{41} +(1.45819 + 4.00634i) q^{43} +(-3.32626 - 5.76125i) q^{44} +(3.72562 - 6.45296i) q^{46} +(3.63443 + 0.640847i) q^{47} +(-5.61571 - 2.04395i) q^{49} +(-12.4237 - 5.27421i) q^{50} +(14.0862 - 16.7873i) q^{52} +0.485518i q^{53} +(-2.69792 - 0.799229i) q^{55} +(-6.87680 - 5.77032i) q^{56} +(-20.8408 + 3.67480i) q^{58} +(1.47979 + 0.538599i) q^{59} +(0.286481 - 1.62472i) q^{61} +(-12.6755 - 7.31822i) q^{62} +(11.4056 + 19.7550i) q^{64} +(-0.565650 - 9.25179i) q^{65} +(2.13105 + 2.53969i) q^{67} +(13.2901 + 15.8385i) q^{68} +(-6.09624 + 0.372721i) q^{70} +(4.95764 + 8.58688i) q^{71} +(4.55975 + 2.63257i) q^{73} +(3.48709 - 19.7763i) q^{74} +(4.30421 + 1.56660i) q^{76} +(-1.25397 + 0.221109i) q^{77} +(6.41639 + 5.38399i) q^{79} +(28.6752 + 8.49470i) q^{80} +9.64185i q^{82} +(-1.86155 + 2.21851i) q^{83} +(8.68897 + 0.990186i) q^{85} +(-10.8146 - 3.93619i) q^{86} +(10.9943 + 1.93860i) q^{88} +(-8.03383 + 13.9150i) q^{89} +(-2.09723 - 3.63251i) q^{91} +(4.99106 + 13.7128i) q^{92} +(-7.63133 + 6.40345i) q^{94} +(1.77672 - 0.772492i) q^{95} +(-1.05657 - 2.90290i) q^{97} +(13.9705 - 8.06587i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) \) 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Introduction

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