LMFDB - Embedded newform 216.2.t.a.157.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] 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("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			157.13
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.644492 + 1.25882i) q^{2} +(0.195652 + 1.72096i) q^{3} +(-1.16926 - 1.62260i) q^{4} +(1.34802 + 3.70366i) q^{5} +(-2.29248 - 0.862856i) q^{6} +(0.00177522 + 0.0100678i) q^{7} +(2.79614 - 0.426137i) q^{8} +(-2.92344 + 0.673422i) q^{9} +(-5.53104 - 0.690061i) q^{10} +(0.343808 - 0.944604i) q^{11} +(2.56367 - 2.32972i) q^{12} +(2.57400 - 3.06757i) q^{13} +(-0.0138176 - 0.00425391i) q^{14} +(-6.11013 + 3.04453i) q^{15} +(-1.26566 + 3.79448i) q^{16} +(-0.948987 + 1.64369i) q^{17} +(1.03642 - 4.11410i) q^{18} +(-3.76245 + 2.17225i) q^{19} +(4.43337 - 6.51785i) q^{20} +(-0.0169790 + 0.00502488i) q^{21} +(0.967506 + 1.04158i) q^{22} +(1.19728 - 6.79010i) q^{23} +(1.28044 + 4.72869i) q^{24} +(-8.06972 + 6.77130i) q^{25} +(2.20260 + 5.21723i) q^{26} +(-1.73091 - 4.89938i) q^{27} +(0.0142603 - 0.0146523i) q^{28} +(3.82827 + 4.56236i) q^{29} +(0.105409 - 9.65373i) q^{30} +(1.38501 - 7.85480i) q^{31} +(-3.96087 - 4.03875i) q^{32} +(1.69290 + 0.406867i) q^{33} +(-1.45750 - 2.25395i) q^{34} +(-0.0348946 + 0.0201464i) q^{35} +(4.51096 + 3.95617i) q^{36} +(6.65823 + 3.84413i) q^{37} +(-0.309608 - 6.13625i) q^{38} +(5.78279 + 3.82958i) q^{39} +(5.34753 + 9.78152i) q^{40} +(4.44753 + 3.73192i) q^{41} +(0.00461738 - 0.0246120i) q^{42} +(-1.42511 + 3.91546i) q^{43} +(-1.93471 + 0.546626i) q^{44} +(-6.43499 - 9.91964i) q^{45} +(7.77588 + 5.88332i) q^{46} +(1.37530 + 7.79973i) q^{47} +(-6.77780 - 1.43576i) q^{48} +(6.57775 - 2.39411i) q^{49} +(-3.32298 - 14.5224i) q^{50} +(-3.01441 - 1.31158i) q^{51} +(-7.98712 - 0.589779i) q^{52} +2.25567i q^{53} +(7.28300 + 0.978700i) q^{54} +3.96195 q^{55} +(0.00925402 + 0.0273944i) q^{56} +(-4.47450 - 6.05004i) q^{57} +(-8.21048 + 1.87871i) q^{58} +(2.24610 + 6.17111i) q^{59} +(12.0844 + 6.35444i) q^{60} +(-0.106836 + 0.0188381i) q^{61} +(8.99516 + 6.80584i) q^{62} +(-0.0119696 - 0.0282371i) q^{63} +(7.63681 - 2.38308i) q^{64} +(14.8311 + 5.39806i) q^{65} +(-1.60323 + 1.86883i) q^{66} +(2.47342 - 2.94771i) q^{67} +(3.77667 - 0.382080i) q^{68} +(11.9198 + 0.731973i) q^{69} +(-0.00287143 - 0.0569102i) q^{70} +(0.442665 - 0.766718i) q^{71} +(-7.88738 + 3.12877i) q^{72} +(-7.26116 - 12.5767i) q^{73} +(-9.13025 + 5.90401i) q^{74} +(-13.2320 - 12.5629i) q^{75} +(7.92398 + 3.56502i) q^{76} +(0.0101204 + 0.00178450i) q^{77} +(-8.54772 + 4.81137i) q^{78} +(2.46319 - 2.06686i) q^{79} +(-15.7596 + 0.427473i) q^{80} +(8.09301 - 3.93742i) q^{81} +(-7.56422 + 3.19345i) q^{82} +(-9.76904 - 11.6423i) q^{83} +(0.0280062 + 0.0216747i) q^{84} +(-7.36694 - 1.29899i) q^{85} +(-4.01039 - 4.31744i) q^{86} +(-7.10265 + 7.48096i) q^{87} +(0.558804 - 2.78776i) q^{88} +(-1.45362 - 2.51775i) q^{89} +(16.6344 - 1.70737i) q^{90} +(0.0354530 + 0.0204688i) q^{91} +(-12.4175 + 5.99669i) q^{92} +(13.7888 + 0.846748i) q^{93} +(-10.7048 - 3.29560i) q^{94} +(-13.1172 - 11.0066i) q^{95} +(6.17560 - 7.60671i) q^{96} +(-12.0217 - 4.37554i) q^{97} +(-1.22556 + 9.82319i) q^{98} +(-0.368984 + 2.99302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.644492	+	1.25882i	−0.455725	+	0.890121i
$2$	−0.644492	+	1.25882i	−0.455725	+	0.890121i
$3$	0.195652	+	1.72096i	0.112960	+	0.993600i
$3$	0.195652	+	1.72096i	0.112960	+	0.993600i
$4$	−1.16926	−	1.62260i	−0.584630	−	0.811300i
$5$	1.34802	+	3.70366i	0.602854	+	1.65633i	0.745462	+	0.666548i	$0.232229\pi$
$5$	1.34802	+	3.70366i	0.602854	+	1.65633i	−0.142608	+	0.989779i	$0.545549\pi$
$6$	−2.29248	−	0.862856i	−0.935902	−	0.352260i
$7$	0.00177522	+	0.0100678i	0.000670970	+	0.00380526i	0.985141	−	0.171745i	$-0.0549406\pi$
$7$	0.00177522	+	0.0100678i	0.000670970	+	0.00380526i	−0.984470	+	0.175550i	$0.943829\pi$
$8$	2.79614	−	0.426137i	0.988585	−	0.150662i
$9$	−2.92344	+	0.673422i	−0.974480	+	0.224474i
$10$	−5.53104	−	0.690061i	−1.74907	−	0.218216i
$11$	0.343808	−	0.944604i	0.103662	−	0.284809i	−0.877009	−	0.480474i	$-0.840465\pi$
$11$	0.343808	−	0.944604i	0.103662	−	0.284809i	0.980671	+	0.195666i	$0.0626867\pi$
$12$	2.56367	−	2.32972i	0.740067	−	0.672533i
$13$	2.57400	−	3.06757i	0.713899	−	0.850792i	−0.280124	−	0.959964i	$-0.590376\pi$
$13$	2.57400	−	3.06757i	0.713899	−	0.850792i	0.994023	+	0.109172i	$0.0348200\pi$
$14$	−0.0138176	−	0.00425391i	−0.00369292	−	0.00113691i
$15$	−6.11013	+	3.04453i	−1.57763	+	0.786094i
$16$	−1.26566	+	3.79448i	−0.316415	+	0.948621i
$17$	−0.948987	+	1.64369i	−0.230163	+	0.398654i	−0.957856	−	0.287249i	$-0.907259\pi$
$17$	−0.948987	+	1.64369i	−0.230163	+	0.398654i	0.727693	+	0.685903i	$0.240593\pi$
$18$	1.03642	−	4.11410i	0.244285	−	0.969703i
$19$	−3.76245	+	2.17225i	−0.863166	+	0.498349i	−0.865071	−	0.501649i	$-0.832727\pi$
$19$	−3.76245	+	2.17225i	−0.863166	+	0.498349i	0.00190536	+	0.999998i	$0.499394\pi$
$20$	4.43337	−	6.51785i	0.991332	−	1.45743i
$21$	−0.0169790	+	0.00502488i	−0.00370511	+	0.00109652i
$22$	0.967506	+	1.04158i	0.206273	+	0.222066i
$23$	1.19728	−	6.79010i	0.249650	−	1.41583i	−0.559792	−	0.828633i	$-0.689119\pi$
$23$	1.19728	−	6.79010i	0.249650	−	1.41583i	0.809442	−	0.587200i	$-0.199770\pi$
$24$	1.28044	+	4.72869i	0.261369	+	0.965239i
$25$	−8.06972	+	6.77130i	−1.61394	+	1.35426i
$26$	2.20260	+	5.21723i	0.431966	+	1.02318i
$27$	−1.73091	−	4.89938i	−0.333115	−	0.942886i
$28$	0.0142603	−	0.0146523i	0.00269494	−	0.00276903i
$29$	3.82827	+	4.56236i	0.710892	+	0.847208i	0.993712	−	0.111965i	$-0.0357143\pi$
$29$	3.82827	+	4.56236i	0.710892	+	0.847208i	−0.282820	+	0.959173i	$0.591270\pi$
$30$	0.105409	−	9.65373i	0.0192450	−	1.76252i
$31$	1.38501	−	7.85480i	0.248756	−	1.41076i	−0.562850	−	0.826559i	$-0.690295\pi$
$31$	1.38501	−	7.85480i	0.248756	−	1.41076i	0.811606	−	0.584205i	$-0.198594\pi$
$32$	−3.96087	−	4.03875i	−0.700189	−	0.713957i
$33$	1.69290	+	0.406867i	0.294696	+	0.0708264i
$34$	−1.45750	−	2.25395i	−0.249959	−	0.386550i
$35$	−0.0348946	+	0.0201464i	−0.00589826	+	0.00340536i
$36$	4.51096	+	3.95617i	0.751826	+	0.659361i
$37$	6.65823	+	3.84413i	1.09461	+	0.631971i	0.934799	−	0.355177i	$-0.115579\pi$
$37$	6.65823	+	3.84413i	1.09461	+	0.631971i	0.159807	+	0.987148i	$0.448913\pi$
$38$	−0.309608	−	6.13625i	−0.0502250	−	0.995432i
$39$	5.78279	+	3.82958i	0.925988	+	0.613224i
$40$	5.34753	+	9.78152i	0.845519	+	1.54659i
$41$	4.44753	+	3.73192i	0.694588	+	0.582828i	0.920228	−	0.391382i	$-0.128003\pi$
$41$	4.44753	+	3.73192i	0.694588	+	0.582828i	−0.225641	+	0.974211i	$0.572447\pi$
$42$	0.00461738	−	0.0246120i	0.000712477	−	0.00379771i
$43$	−1.42511	+	3.91546i	−0.217327	+	0.597102i	−0.999668	−	0.0257481i	$-0.991803\pi$
$43$	−1.42511	+	3.91546i	−0.217327	+	0.597102i	0.782341	+	0.622850i	$0.214025\pi$
$44$	−1.93471	+	0.546626i	−0.291669	+	0.0824069i
$45$	−6.43499	−	9.91964i	−0.959272	−	1.47873i
$46$	7.77588	+	5.88332i	1.14649	+	0.867448i
$47$	1.37530	+	7.79973i	0.200608	+	1.13771i	0.904202	+	0.427105i	$0.140466\pi$
$47$	1.37530	+	7.79973i	0.200608	+	1.13771i	−0.703594	+	0.710602i	$0.748422\pi$
$48$	−6.77780	−	1.43576i	−0.978292	−	0.207234i
$49$	6.57775	−	2.39411i	0.939679	−	0.342015i
$50$	−3.32298	−	14.5224i	−0.469941	−	2.05377i
$51$	−3.01441	−	1.31158i	−0.422102	−	0.183658i
$52$	−7.98712	−	0.589779i	−1.10761	−	0.0817876i
$53$			2.25567i			0.309840i	0.987927	+	0.154920i	$0.0495120\pi$
$53$			2.25567i			0.309840i	−0.987927	+	0.154920i	$0.950488\pi$
$54$	7.28300	+	0.978700i	0.991091	+	0.133184i
$55$	3.96195			0.534230
$56$	0.00925402	+	0.0273944i	0.00123662	+	0.00366074i
$57$	−4.47450	−	6.05004i	−0.592663	−	0.801348i
$58$	−8.21048	+	1.87871i	−1.07809	+	0.246686i
$59$	2.24610	+	6.17111i	0.292417	+	0.803410i	0.995712	+	0.0925111i	$0.0294894\pi$
$59$	2.24610	+	6.17111i	0.292417	+	0.803410i	−0.703294	+	0.710899i	$0.748288\pi$
$60$	12.0844	+	6.35444i	1.56009	+	0.820355i
$61$	−0.106836	+	0.0188381i	−0.0136789	+	0.00241197i	−0.180483	−	0.983578i	$-0.557766\pi$
$61$	−0.106836	+	0.0188381i	−0.0136789	+	0.00241197i	0.166805	+	0.985990i	$0.446655\pi$
$62$	8.99516	+	6.80584i	1.14239	+	0.864343i
$63$	−0.0119696	−	0.0282371i	−0.00150803	−	0.00355754i
$64$	7.63681	−	2.38308i	0.954602	−	0.297885i
$65$	14.8311	+	5.39806i	1.83957	+	0.669547i
$66$	−1.60323	+	1.86883i	−0.197344	+	0.230037i
$67$	2.47342	−	2.94771i	0.302177	−	0.360120i	−0.593494	−	0.804839i	$-0.702252\pi$
$67$	2.47342	−	2.94771i	0.302177	−	0.360120i	0.895670	+	0.444718i	$0.146696\pi$
$68$	3.77667	−	0.382080i	0.457989	−	0.0463340i
$69$	11.9198	+	0.731973i	1.43497	+	0.0881192i
$70$	−0.00287143	−	0.0569102i	−0.000343202	−	0.00680207i
$71$	0.442665	−	0.766718i	0.0525346	−	0.0909926i	−0.838562	−	0.544806i	$-0.816603\pi$
$71$	0.442665	−	0.766718i	0.0525346	−	0.0909926i	0.891097	+	0.453813i	$0.149937\pi$
$72$	−7.88738	+	3.12877i	−0.929537	+	0.368729i
$73$	−7.26116	−	12.5767i	−0.849854	−	1.47199i	−0.881338	−	0.472486i	$-0.843357\pi$
$73$	−7.26116	−	12.5767i	−0.849854	−	1.47199i	0.0314838	−	0.999504i	$-0.489977\pi$
$74$	−9.13025	+	5.90401i	−1.06137	+	0.686327i
$75$	−13.2320	−	12.5629i	−1.52790	−	1.45064i
$76$	7.92398	+	3.56502i	0.908943	+	0.408936i
$77$	0.0101204	+	0.00178450i	0.00115333	+	0.000203362i
$78$	−8.54772	+	4.81137i	−0.967839	+	0.544780i
$79$	2.46319	−	2.06686i	0.277131	−	0.232540i	−0.493619	−	0.869678i	$-0.664326\pi$
$79$	2.46319	−	2.06686i	0.277131	−	0.232540i	0.770750	+	0.637138i	$0.219882\pi$
$80$	−15.7596	+	0.427473i	−1.76198	+	0.0477930i
$81$	8.09301	−	3.93742i	0.899223	−	0.437491i
$82$	−7.56422	+	3.19345i	−0.835328	+	0.352658i
$83$	−9.76904	−	11.6423i	−1.07229	−	1.27791i	−0.958712	−	0.284378i	$-0.908213\pi$
$83$	−9.76904	−	11.6423i	−1.07229	−	1.27791i	−0.113579	−	0.993529i	$-0.536232\pi$
$84$	0.0280062	+	0.0216747i	0.00305573	+	0.00236490i
$85$	−7.36694	−	1.29899i	−0.799057	−	0.140895i
$86$	−4.01039	−	4.31744i	−0.432452	−	0.465562i
$87$	−7.10265	+	7.48096i	−0.761483	+	0.802043i
$88$	0.558804	−	2.78776i	0.0595687	−	0.297176i
$89$	−1.45362	−	2.51775i	−0.154084	−	0.266881i	0.778641	−	0.627469i	$-0.215909\pi$
$89$	−1.45362	−	2.51775i	−0.154084	−	0.266881i	−0.932725	+	0.360588i	$0.882576\pi$
$90$	16.6344	−	1.70737i	1.75341	−	0.179973i
$91$	0.0354530	+	0.0204688i	0.00371649	+	0.00214572i
$92$	−12.4175	+	5.99669i	−1.29462	+	0.625198i
$93$	13.7888	+	0.846748i	1.42983	+	0.0878037i
$94$	−10.7048	−	3.29560i	−1.10412	−	0.339915i
$95$	−13.1172	−	11.0066i	−1.34579	−	1.12925i
$96$	6.17560	−	7.60671i	0.630294	−	0.776356i
$97$	−12.0217	−	4.37554i	−1.22062	−	0.444269i	−0.350244	−	0.936658i	$-0.613901\pi$
$97$	−12.0217	−	4.37554i	−1.22062	−	0.444269i	−0.870375	+	0.492389i	$0.836124\pi$
$98$	−1.22556	+	9.82319i	−0.123800	+	0.992292i
$99$	−0.368984	+	2.99302i	−0.0370843	+	0.300810i
$100$	20.4227	+	5.17651i	2.04227	+	0.517651i
$101$	−8.25225	+	1.45509i	−0.821129	+	0.144787i	−0.568403	−	0.822751i	$-0.692438\pi$
$101$	−8.25225	+	1.45509i	−0.821129	+	0.144787i	−0.252727	+	0.967538i	$0.581327\pi$
$102$	3.59381	−	2.94930i	0.355840	−	0.292024i
$103$	6.53199	−	2.37745i	0.643617	−	0.234257i	0.000469418	−	1.00000i	$-0.499851\pi$
$103$	6.53199	−	2.37745i	0.643617	−	0.234257i	0.643147	+	0.765743i	$0.277628\pi$
$104$	5.89006	−	9.67424i	0.577568	−	0.948638i
$105$	−0.0414985	−	0.0561107i	−0.00404984	−	0.00547584i
$106$	−2.83949	−	1.45376i	−0.275795	−	0.141202i
$107$			14.2756i			1.38007i	0.723776	+	0.690035i	$0.242405\pi$
$107$			14.2756i			1.38007i	−0.723776	+	0.690035i	$0.757595\pi$
$108$	−5.92585	+	8.53723i	−0.570215	+	0.821496i
$109$		−	4.88426i		−	0.467827i	−0.972257	−	0.233914i	$-0.924847\pi$
$109$		−	4.88426i		−	0.467827i	0.972257	−	0.233914i	$-0.0751533\pi$
$110$	−2.55345	+	4.98739i	−0.243462	+	0.475529i
$111$	−5.31292	+	12.2107i	−0.504280	+	1.15899i
$112$	−0.0404488	−	0.00600633i	−0.00382206	−	0.000567545i
$113$	4.20463	−	1.53036i	0.395538	−	0.143964i	−0.136591	−	0.990628i	$-0.543614\pi$
$113$	4.20463	−	1.53036i	0.395538	−	0.143964i	0.532129	+	0.846663i	$0.321392\pi$
$114$	10.4997	−	1.73340i	0.983387	−	0.162348i
$115$	26.7622	−	4.71889i	2.49559	−	0.440039i
$116$	2.92663	−	11.5463i	0.271731	−	1.07205i
$117$	−5.45916	+	10.7013i	−0.504700	+	0.989331i
$118$	−9.21591	−	1.14979i	−0.848394	−	0.105847i
$119$	−0.0182330	−	0.00663627i	−0.00167142	−	0.000608346i
$120$	−15.7874	+	11.1167i	−1.44118	+	1.01481i
$121$	7.65242	+	6.42114i	0.695674	+	0.583740i
$122$	0.0451412	−	0.146628i	0.00408689	−	0.0132751i
$123$	−5.55233	+	8.38420i	−0.500637	+	0.755978i
$124$	−14.3646	+	6.93699i	−1.28998	+	0.622960i
$125$	−18.8902	−	10.9063i	−1.68959	−	0.975485i
$126$	0.0432597	+	0.00313096i	0.00385388	+	0.000278928i
$127$	−0.733337	−	1.27018i	−0.0650731	−	0.112710i	0.831653	−	0.555295i	$-0.187395\pi$
$127$	−0.733337	−	1.27018i	−0.0650731	−	0.112710i	−0.896726	+	0.442585i	$0.854061\pi$
$128$	−1.92199	+	11.1493i	−0.169882	+	0.985464i
$129$	−7.01720	−	1.68650i	−0.617830	−	0.148488i
$130$	−16.3537	+	15.1906i	−1.43431	+	1.33231i
$131$	−11.2373	−	1.98143i	−0.981805	−	0.173119i	−0.340366	−	0.940293i	$-0.610551\pi$
$131$	−11.2373	−	1.98143i	−0.981805	−	0.173119i	−0.641439	+	0.767174i	$0.721662\pi$
$132$	−1.31926	−	3.22263i	−0.114826	−	0.280494i
$133$	−0.0285489	−	0.0340233i	−0.00247551	−	0.00295019i
$134$	2.11654	+	5.01337i	0.182841	+	0.433089i
$135$	15.8123	−	13.0152i	1.36091	−	1.12017i
$136$	−1.95306	+	5.00040i	−0.167474	+	0.428781i
$137$	3.27137	−	2.74501i	0.279492	−	0.234522i	−0.492255	−	0.870451i	$-0.663827\pi$
$137$	3.27137	−	2.74501i	0.279492	−	0.234522i	0.771748	+	0.635929i	$0.219383\pi$
$138$	−8.60362	+	14.5331i	−0.732389	+	1.23714i
$139$	1.04893	+	0.184955i	0.0889693	+	0.0156877i	0.217956	−	0.975959i	$-0.430061\pi$
$139$	1.04893	+	0.184955i	0.0889693	+	0.0156877i	−0.128986	+	0.991646i	$0.541172\pi$
$140$	0.0734904	+	0.0330636i	0.00621107	+	0.00279438i
$141$	−13.1540	+	3.89288i	−1.10776	+	0.327840i
$142$	0.679866	+	1.05138i	0.0570531	+	0.0882297i
$143$	−2.01268	−	3.48606i	−0.168309	−	0.291519i
$144$	1.14479	−	11.9453i	0.0953993	−	0.995439i
$145$	−11.7368	+	20.3288i	−0.974690	+	1.68821i
$146$	20.5116	−	1.03492i	1.69755	−	0.0856506i
$147$	5.40712	+	10.8517i	0.445972	+	0.895030i
$148$	−1.54772	−	15.2984i	−0.127222	−	1.25752i
$149$	1.34236	−	1.59976i	0.109970	−	0.131058i	−0.708251	−	0.705960i	$-0.750516\pi$
$149$	1.34236	−	1.59976i	0.109970	−	0.131058i	0.818222	+	0.574903i	$0.194960\pi$
$150$	24.3423	−	8.56008i	1.98754	−	0.698927i
$151$	9.89970	+	3.60320i	0.805626	+	0.293224i	0.711816	−	0.702366i	$-0.247873\pi$
$151$	9.89970	+	3.60320i	0.805626	+	0.293224i	0.0938105	+	0.995590i	$0.470095\pi$
$152$	−9.59467	+	7.67725i	−0.778231	+	0.622707i
$153$	1.66741	−	5.44431i	0.134802	−	0.440146i
$154$	−0.00876888	+	0.0115897i	−0.000706616	+	0.000933922i
$155$	30.9586	−	5.45883i	2.48665	−	0.438464i
$156$	−0.547711	−	13.8609i	−0.0438520	−	1.10976i
$157$	−7.61747	−	20.9288i	−0.607940	−	1.67030i	−0.734720	−	0.678371i	$-0.762686\pi$
$157$	−7.61747	−	20.9288i	−0.607940	−	1.67030i	0.126779	−	0.991931i	$-0.459536\pi$
$158$	1.01430	+	4.43280i	0.0806937	+	0.352654i
$159$	−3.88193	+	0.441328i	−0.307857	+	0.0349996i
$160$	9.61883	−	20.1140i	0.760436	−	1.59015i
$161$	0.0704866			0.00555512
$162$	−0.259371	+	12.7253i	−0.0203781	+	0.999792i
$163$		−	8.64571i		−	0.677184i	−0.940933	−	0.338592i	$-0.890049\pi$
$163$		−	8.64571i		−	0.677184i	0.940933	−	0.338592i	$-0.109951\pi$
$164$	0.855093	−	11.5801i	0.0667715	−	0.904258i
$165$	0.775166	+	6.81838i	0.0603466	+	0.530810i
$166$	20.9516	−	4.79411i	1.62616	−	0.372095i
$167$	−7.93163	+	2.88688i	−0.613768	+	0.223393i	−0.630151	−	0.776473i	$-0.717007\pi$
$167$	−7.93163	+	2.88688i	−0.613768	+	0.223393i	0.0163833	+	0.999866i	$0.494785\pi$
$168$	−0.0453343	+	0.0212856i	−0.00349762	+	0.00164222i
$169$	−0.527105	−	2.98936i	−0.0405465	−	0.229951i
$170$	6.38313	−	8.43647i	0.489564	−	0.647048i
$171$	9.53646	−	8.88417i	0.729271	−	0.679389i
$172$	8.01955	−	2.26581i	0.611485	−	0.172766i
$173$	4.65008	−	12.7760i	0.353539	−	0.971340i	−0.627685	−	0.778467i	$-0.715997\pi$
$173$	4.65008	−	12.7760i	0.353539	−	0.971340i	0.981224	−	0.192872i	$-0.0617803\pi$
$174$	−4.83959	−	13.7624i	−0.366888	−	1.04332i
$175$	−0.0824974	−	0.0692236i	−0.00623622	−	0.00523281i
$176$	3.14914	+	2.50012i	0.237375	+	0.188454i
$177$	−10.1808	+	5.07285i	−0.765236	+	0.381299i
$178$	4.10624	−	0.207183i	0.307776	−	0.0155290i
$179$	−0.257187	−	0.148487i	−0.0192231	−	0.0110985i	0.490358	−	0.871521i	$-0.336866\pi$
$179$	−0.257187	−	0.148487i	−0.0192231	−	0.0110985i	−0.509581	+	0.860423i	$0.670199\pi$
$180$	−8.57143	+	22.0401i	−0.638877	+	1.64277i
$181$	−1.63626	+	0.944694i	−0.121622	+	0.0702186i	−0.559577	−	0.828778i	$-0.689036\pi$
$181$	−1.63626	+	0.944694i	−0.121622	+	0.0702186i	0.437955	+	0.898997i	$0.355703\pi$
$182$	−0.0486158	+	0.0314370i	−0.00360364	+	0.00233027i
$183$	−0.0533224	−	0.180175i	−0.00394170	−	0.0133189i
$184$	0.454243	−	19.4963i	0.0334873	−	1.43728i
$185$	−5.26192	+	29.8418i	−0.386864	+	2.19401i
$186$	−9.95269	+	16.8119i	−0.729767	+	1.23271i
$187$	1.22637	+	1.46153i	0.0896811	+	0.106878i
$188$	11.0477	−	11.3515i	0.805740	−	0.827892i
$189$	0.0462531	−	0.0261239i	0.00336442	−	0.00190024i
$190$	22.3092	−	9.41849i	1.61848	−	0.683289i
$191$	10.6897	−	8.96976i	0.773483	−	0.649029i	−0.168116	−	0.985767i	$-0.553768\pi$
$191$	10.6897	−	8.96976i	0.773483	−	0.649029i	0.941598	+	0.336738i	$0.109324\pi$
$192$	5.59536	+	12.6764i	0.403810	+	0.914843i
$193$	1.65530	−	9.38768i	0.119151	−	0.675740i	−0.865460	−	0.500979i	$-0.832974\pi$
$193$	1.65530	−	9.38768i	0.119151	−	0.675740i	0.984611	−	0.174761i	$-0.0559153\pi$
$194$	13.2559	−	12.3132i	0.951720	−	0.884034i
$195$	−6.38814	+	26.5799i	−0.457465	+	1.90342i
$196$	−11.5758	−	7.87372i	−0.826841	−	0.562409i
$197$	−7.61046	+	4.39390i	−0.542223	+	0.313052i	−0.745979	−	0.665969i	$-0.768018\pi$
$197$	−7.61046	+	4.39390i	−0.542223	+	0.313052i	0.203757	+	0.979022i	$0.434685\pi$
$198$	−3.52987	−	2.39346i	−0.250857	−	0.170096i
$199$	4.70991	−	8.15780i	0.333876	−	0.578291i	−0.649392	−	0.760454i	$-0.724977\pi$
$199$	4.70991	−	8.15780i	0.333876	−	0.578291i	0.983268	+	0.182163i	$0.0583098\pi$
$200$	−19.6786	+	22.3723i	−1.39149	+	1.58196i
$201$	5.55684	+	3.67995i	0.391949	+	0.259563i
$202$	3.48680	−	11.3259i	0.245331	−	0.796887i
$203$	−0.0391368	+	0.0466414i	−0.00274686	+	0.00327358i
$204$	1.39646	+	6.42476i	0.0977718	+	0.449823i
$205$	−7.82640	+	21.5029i	−0.546619	+	1.50182i
$206$	−1.21703	+	9.75486i	−0.0847946	+	0.679653i
$207$	1.07243	+	20.6567i	0.0745393	+	1.43574i
$208$	8.38205	+	13.6495i	0.581190	+	0.946423i
$209$	0.758358	+	4.30086i	0.0524567	+	0.297497i
$210$	0.0973787	−	0.0160763i	0.00671977	−	0.00110937i
$211$	4.12560	+	11.3350i	0.284018	+	0.780333i	0.996873	+	0.0790214i	$0.0251795\pi$
$211$	4.12560	+	11.3350i	0.284018	+	0.780333i	−0.712855	+	0.701311i	$0.752598\pi$
$212$	3.66005	−	2.63747i	0.251373	−	0.181142i
$213$	1.40610	+	0.611800i	0.0963445	+	0.0419198i
$214$	−17.9704	−	9.20048i	−1.22843	−	0.628932i
$215$	−16.4226			−1.12001
$216$	−6.92769	−	12.9618i	−0.471370	−	0.881936i
$217$	0.0815391			0.00553524
$218$	6.14841	+	3.14786i	0.416423	+	0.213200i
$219$	20.2234	−	14.9569i	1.36657	−	1.01069i
$220$	−4.63255	−	6.42866i	−0.312327	−	0.433420i
$221$	2.59946	+	7.14195i	0.174858	+	0.480420i
$222$	−11.9469	−	14.5577i	−0.801827	−	0.977049i
$223$	0.616341	+	3.49544i	0.0412732	+	0.234072i	0.998465	−	0.0553815i	$-0.0176375\pi$
$223$	0.616341	+	3.49544i	0.0412732	+	0.234072i	−0.957192	+	0.289454i	$0.906526\pi$
$224$	0.0336298	−	0.0470468i	0.00224699	−	0.00314345i
$225$	19.0314	−	25.2298i	1.26876	−	1.68199i
$226$	−0.783400	+	6.27918i	−0.0521110	+	0.417685i
$227$	3.72066	−	10.2224i	0.246949	−	0.678486i	−0.752846	−	0.658197i	$-0.771319\pi$
$227$	3.72066	−	10.2224i	0.246949	−	0.678486i	0.999794	−	0.0202886i	$-0.00645849\pi$
$228$	−4.58494	+	14.3344i	−0.303645	+	0.949319i
$229$	5.05083	−	6.01935i	0.333769	−	0.397770i	−0.572892	−	0.819631i	$-0.694179\pi$
$229$	5.05083	−	6.01935i	0.333769	−	0.397770i	0.906661	+	0.421861i	$0.138623\pi$
$230$	−11.3078	+	36.7301i	−0.745612	+	2.42191i
$231$	−0.00109098	+	0.0177660i	−7.17811e−5	+	0.00116892i
$232$	12.6486	+	11.1256i	0.830420	+	0.730433i
$233$	12.0985	−	20.9553i	0.792602	−	1.37283i	−0.131749	−	0.991283i	$-0.542059\pi$
$233$	12.0985	−	20.9553i	0.792602	−	1.37283i	0.924351	−	0.381544i	$-0.124608\pi$
$234$	−9.95258	−	13.7690i	−0.650620	−	0.900106i
$235$	−27.0336	+	15.6079i	−1.76348	+	1.01814i
$236$	7.38696	−	10.8602i	0.480850	−	0.706936i
$237$	4.03893	+	3.83468i	0.262357	+	0.249089i
$238$	0.0201049	−	0.0186751i	0.00130321	−	0.00121052i
$239$	−5.23764	+	29.7041i	−0.338795	+	1.92140i	0.0471684	+	0.998887i	$0.484980\pi$
$239$	−5.23764	+	29.7041i	−0.338795	+	1.92140i	−0.385963	+	0.922514i	$0.626131\pi$
$240$	−3.81908	−	27.0381i	−0.246520	−	1.74530i
$241$	−1.91756	+	1.60903i	−0.123521	+	0.103647i	−0.702456	−	0.711727i	$-0.747913\pi$
$241$	−1.91756	+	1.60903i	−0.123521	+	0.103647i	0.578935	+	0.815374i	$0.303469\pi$
$242$	−13.0150	+	5.49465i	−0.836635	+	0.353209i
$243$	8.35958	+	13.1574i	0.536267	+	0.844048i
$244$	0.155486	+	0.151325i	0.00995396	+	0.00968762i
$245$	17.7339	+	21.1344i	1.13298	+	1.35023i
$246$	−6.97578	−	12.3929i	−0.444759	−	0.790145i
$247$	−3.02101	+	17.1330i	−0.192222	+	1.09015i
$248$	0.525470	−	22.5534i	0.0333674	−	1.43214i
$249$	18.1246	−	19.0900i	1.14860	−	1.20978i
$250$	25.9036	−	16.7504i	1.63829	−	1.05939i
$251$	14.5027	−	8.37314i	0.915402	−	0.528508i	0.0332368	−	0.999448i	$-0.489418\pi$
$251$	14.5027	−	8.37314i	0.915402	−	0.528508i	0.882165	+	0.470940i	$0.156085\pi$
$252$	−0.0318219	+	0.0524384i	−0.00200459	+	0.00330331i
$253$	−6.00232	−	3.46544i	−0.377363	−	0.217870i
$254$	2.07156	−	0.104521i	0.129981	−	0.00655825i
$255$	0.794157	−	12.9324i	0.0497320	−	0.809858i
$256$	−12.7962	−	9.60505i	−0.799763	−	0.600316i
$257$	−20.4870	−	17.1907i	−1.27795	−	1.07232i	−0.993524	−	0.113626i	$-0.963753\pi$
$257$	−20.4870	−	17.1907i	−1.27795	−	1.07232i	−0.284423	−	0.958699i	$-0.591802\pi$
$258$	6.64552	−	7.74646i	0.413732	−	0.482274i
$259$	−0.0268820	+	0.0738578i	−0.00167037	+	0.00458930i
$260$	−8.58247	−	30.3766i	−0.532262	−	1.88388i
$261$	−14.2641	−	10.7597i	−0.882927	−	0.666011i
$262$	9.73660	−	12.8687i	0.601529	−	0.795031i
$263$	−0.762315	−	4.32330i	−0.0470064	−	0.266586i	0.952242	−	0.305343i	$-0.0987713\pi$
$263$	−0.762315	−	4.32330i	−0.0470064	−	0.266586i	−0.999249	+	0.0387571i	$0.987660\pi$
$264$	4.90696	+	0.416251i	0.302003	+	0.0256185i
$265$	−8.35424	+	3.04070i	−0.513197	+	0.186788i
$266$	0.0612288	−	0.0140103i	0.00375418	−	0.000859024i
$267$	4.04855	−	2.99424i	0.247767	−	0.183244i
$268$	−7.67503	−	0.566734i	−0.468827	−	0.0346188i
$269$		−	0.741050i		−	0.0451826i	−0.999745	−	0.0225913i	$-0.992808\pi$
$269$		−	0.741050i		−	0.0451826i	0.999745	−	0.0225913i	$-0.00719165\pi$
$270$	6.19288	+	28.2931i	0.376887	+	1.72186i
$271$	−14.1450			−0.859245			−0.429622	−	0.903009i	$-0.641353\pi$
$271$	−14.1450			−0.859245			−0.429622	+	0.903009i	$0.641353\pi$
$272$	−5.03587	−	5.68127i	−0.305345	−	0.344478i
$273$	−0.0282897	+	0.0650182i	−0.00171217	+	0.00393508i
$274$	1.34710	+	5.88721i	0.0813813	+	0.355659i
$275$	3.62176	+	9.95071i	0.218400	+	0.600050i
$276$	−12.7496	−	20.1969i	−0.767437	−	1.21571i
$277$	8.42697	−	1.48590i	0.506327	−	0.0892792i	0.0853514	−	0.996351i	$-0.472799\pi$
$277$	8.42697	−	1.48590i	0.506327	−	0.0892792i	0.420976	+	0.907072i	$0.361688\pi$
$278$	−0.908854	+	1.20122i	−0.0545094	+	0.0720442i
$279$	1.24059	+	23.8958i	0.0742724	+	1.43060i
$280$	−0.0889851	+	0.0712021i	−0.00531788	+	0.00425514i
$281$	−17.6483	−	6.42344i	−1.05281	−	0.383191i	−0.243086	−	0.970005i	$-0.578160\pi$
$281$	−17.6483	−	6.42344i	−1.05281	−	0.383191i	−0.809722	+	0.586814i	$0.800382\pi$
$282$	3.57719	−	19.0674i	0.213018	−	1.13545i
$283$	−16.5234	+	19.6918i	−0.982214	+	1.17056i	0.00313343	+	0.999995i	$0.499003\pi$
$283$	−16.5234	+	19.6918i	−0.982214	+	1.17056i	−0.985347	+	0.170562i	$0.945442\pi$
$284$	−1.76167	+	0.178225i	−0.104536	+	0.0105757i
$285$	16.3756	−	24.7276i	0.970005	−	1.46474i
$286$	5.68549	−	0.286864i	0.336190	−	0.0169626i
$287$	−0.0296768	+	0.0514017i	−0.00175177	+	0.00303415i
$288$	14.2991	+	9.13972i	0.842585	+	0.538563i
$289$	6.69885	+	11.6027i	0.394050	+	0.682514i
$290$	−18.0260	−	27.8763i	−1.05852	−	1.63695i
$291$	5.17808	−	21.5450i	0.303544	−	1.26299i
$292$	−11.9168	+	26.4874i	−0.697375	+	1.55006i
$293$	14.3663	+	2.53317i	0.839288	+	0.147989i	0.576738	−	0.816929i	$-0.304325\pi$
$293$	14.3663	+	2.53317i	0.839288	+	0.147989i	0.262550	+	0.964918i	$0.415436\pi$
$294$	−17.1452	−	0.187208i	−0.999925	−	0.0109182i
$295$	−19.8279	+	16.6376i	−1.15442	+	0.968678i
$296$	20.2555	+	7.91142i	1.17733	+	0.459842i
$297$	−5.22308	−	0.0494167i	−0.303074	−	0.00286745i
$298$	1.14868	+	2.72083i	0.0665410	+	0.157613i
$299$	−17.7473	−	21.1504i	−1.02635	−	1.22316i
$300$	−4.91284	+	36.1596i	−0.283643	+	2.08767i
$301$	−0.0419499	−	0.00739689i	−0.00241795	−	0.000426350i
$302$	−10.9161	+	10.1397i	−0.628149	+	0.583476i
$303$	−4.11874	−	13.9171i	−0.236615	−	0.799518i
$304$	−3.48059	−	17.0259i	−0.199626	−	0.976502i
$305$	−0.213787	−	0.370290i	−0.0122414	−	0.0212028i
$306$	5.77878	+	5.60778i	0.330351	+	0.320575i
$307$	−8.07578	−	4.66255i	−0.460909	−	0.266106i	0.251517	−	0.967853i	$-0.419070\pi$
$307$	−8.07578	−	4.66255i	−0.460909	−	0.266106i	−0.712426	+	0.701747i	$0.752404\pi$
$308$	−0.00893785	−	0.0185079i	−0.000509281	−	0.00105458i
$309$	5.36951	+	10.7762i	0.305461	+	0.613035i
$310$	−13.0809	+	42.4895i	−0.742942	+	2.41324i
$311$	−6.15253	−	5.16259i	−0.348878	−	0.292743i	0.451461	−	0.892291i	$-0.350903\pi$
$311$	−6.15253	−	5.16259i	−0.348878	−	0.292743i	−0.800339	+	0.599547i	$0.795347\pi$
$312$	17.8014	+	8.24379i	1.00781	+	0.466713i
$313$	31.0694	+	11.3083i	1.75615	+	0.639185i	0.999886	−	0.0150840i	$-0.00480156\pi$
$313$	31.0694	+	11.3083i	1.75615	+	0.639185i	0.756261	+	0.654269i	$0.227024\pi$
$314$	31.2550	+	3.89943i	1.76382	+	0.220057i
$315$	0.0884452	−	0.0823956i	0.00498332	−	0.00464247i
$316$	−6.23381	−	1.58007i	−0.350679	−	0.0888861i
$317$	−25.6721	+	4.52669i	−1.44189	+	0.254244i	−0.839240	−	0.543762i	$-0.817000\pi$
$317$	−25.6721	+	4.52669i	−1.44189	+	0.254244i	−0.602650	+	0.798006i	$0.705888\pi$
$318$	1.94632	−	5.17109i	0.109144	−	0.289980i
$319$	5.62581	−	2.04763i	0.314985	−	0.114645i
$320$	19.1207	+	25.0717i	1.06888	+	1.40155i
$321$	−24.5677	+	2.79305i	−1.37124	+	0.155893i
$322$	−0.0454280	+	0.0887300i	−0.00253161	+	0.00494473i
$323$		−	8.24576i		−	0.458806i
$324$	−15.8517	−	8.52784i	−0.880649	−	0.473769i
$325$			42.1838i			2.33993i
$326$	10.8834	+	5.57209i	0.602776	+	0.308609i
$327$	8.40564	−	0.955617i	0.464833	−	0.0528457i
$328$	14.0262	+	8.53972i	0.774469	+	0.471527i
$329$	−0.0760844	+	0.0276925i	−0.00419467	+	0.00152674i
$330$	−9.08271	−	3.41860i	−0.499987	−	0.188188i
$331$	−2.73256	+	0.481823i	−0.150195	+	0.0264834i	−0.248240	−	0.968699i	$-0.579852\pi$
$331$	−2.73256	+	0.481823i	−0.150195	+	0.0264834i	0.0980451	+	0.995182i	$0.468741\pi$
$332$	−7.46822	+	29.4641i	−0.409872	+	1.61705i
$333$	−22.0537	−	6.75429i	−1.20853	−	0.370133i
$334$	1.47781	−	11.8451i	0.0808621	−	0.648133i
$335$	14.2516	+	5.18714i	0.778645	+	0.283404i
$336$	0.00242278	−	0.0707862i	0.000132173	−	0.00386170i
$337$	−10.0326	−	8.41837i	−0.546512	−	0.458578i	0.327246	−	0.944939i	$-0.393879\pi$
$337$	−10.0326	−	8.41837i	−0.546512	−	0.458578i	−0.873758	+	0.486361i	$0.838324\pi$
$338$	4.10278	+	1.26309i	0.223162	+	0.0687029i
$339$	3.45634	+	6.93660i	0.187723	+	0.376744i
$340$	6.50613	+	13.4725i	0.352844	+	0.730646i
$341$	−6.94350	−	4.00883i	−0.376012	−	0.217090i
$342$	5.03741	+	17.7305i	0.272392	+	0.958754i
$343$	0.0715611	+	0.123947i	0.00386393	+	0.00669253i
$344$	−2.31629	+	11.5555i	−0.124886	+	0.623029i
$345$	13.3571	+	45.1335i	0.719124	+	2.42991i
$346$	13.0857	+	14.0876i	0.703493	+	0.757356i
$347$	−14.2864	−	2.51907i	−0.766932	−	0.135231i	−0.223523	−	0.974699i	$-0.571756\pi$
$347$	−14.2864	−	2.51907i	−0.766932	−	0.135231i	−0.543409	+	0.839468i	$0.682867\pi$
$348$	20.4434	+	2.77756i	1.09588	+	0.148893i
$349$	−15.0245	−	17.9055i	−0.804242	−	0.958459i	0.195510	−	0.980702i	$-0.437364\pi$
$349$	−15.0245	−	17.9055i	−0.804242	−	0.958459i	−0.999753	+	0.0222430i	$0.992919\pi$
$350$	0.140309	−	0.0592355i	0.00749983	−	0.00316627i
$351$	−19.4846	−	7.30130i	−1.04001	−	0.389714i
$352$	−5.17680	+	2.35290i	−0.275924	+	0.125410i
$353$	−26.1780	+	21.9660i	−1.39332	+	1.16913i	−0.429340	+	0.903143i	$0.641254\pi$
$353$	−26.1780	+	21.9660i	−1.39332	+	1.16913i	−0.963976	+	0.265988i	$0.914302\pi$
$354$	0.175635	−	16.0852i	0.00933487	−	0.854920i
$355$	3.43638	+	0.605927i	0.182384	+	0.0321593i
$356$	−2.38564	+	5.30255i	−0.126438	+	0.281035i
$357$	0.00785346	−	0.0326768i	0.000415649	−	0.00172944i
$358$	0.352674	−	0.228054i	0.0186394	−	0.0120530i
$359$	−13.5391	−	23.4504i	−0.714565	−	1.23766i	−0.963127	−	0.269047i	$-0.913291\pi$
$359$	−13.5391	−	23.4504i	−0.714565	−	1.23766i	0.248562	−	0.968616i	$-0.420042\pi$
$360$	−22.2203	−	24.9945i	−1.17111	−	1.31733i
$361$	−0.0626343	+	0.108486i	−0.00329654	+	0.00570978i
$362$	−0.134646	−	2.66860i	−0.00707682	−	0.140259i
$363$	−9.55334	+	14.4259i	−0.501420	+	0.757161i
$364$	−0.00824113	−	0.0814595i	−0.000431953	−	0.00426964i
$365$	36.7916	−	43.8465i	1.92576	−	2.29503i
$366$	0.261174	+	0.0489982i	0.0136518	+	0.00256118i
$367$	4.30354	+	1.56636i	0.224643	+	0.0817633i	0.451890	−	0.892074i	$-0.350750\pi$
$367$	4.30354	+	1.56636i	0.224643	+	0.0817633i	−0.227247	+	0.973837i	$0.572972\pi$
$368$	24.2496	+	13.1370i	1.26410	+	0.684814i
$369$	−15.5152	−	7.91498i	−0.807691	−	0.412038i
$370$	−34.1742	−	25.8566i	−1.77663	−	1.34422i
$371$	−0.0227096	+	0.00400432i	−0.00117902	+	0.000207894i
$372$	−14.7488	−	23.3638i	−0.764689	−	1.21136i
$373$	−5.86591	−	16.1165i	−0.303725	−	0.834479i	−0.993845	−	0.110783i	$-0.964664\pi$
$373$	−5.86591	−	16.1165i	−0.303725	−	0.834479i	0.690119	−	0.723696i	$-0.257558\pi$
$374$	−2.63019	+	0.601836i	−0.136004	+	0.0311202i
$375$	15.0734	−	34.6432i	0.778385	−	1.78897i
$376$	7.16929	+	21.2231i	0.369728	+	1.09450i
$377$	23.8493			1.22830
$378$	0.00307560	+	0.0750611i	0.000158192	+	0.00386072i
$379$		−	0.380673i		−	0.0195538i	−0.999952	−	0.00977692i	$-0.996888\pi$
$379$		−	0.380673i		−	0.0195538i	0.999952	−	0.00977692i	$-0.00311214\pi$
$380$	−2.52194	+	34.1535i	−0.129373	+	1.75204i
$381$	2.04245	−	1.51056i	0.104638	−	0.0773884i
$382$	4.40187	+	19.2374i	0.225219	+	0.984272i
$383$	34.6697	−	12.6187i	1.77154	−	0.644788i	0.771578	−	0.636135i	$-0.219468\pi$
$383$	34.6697	−	12.6187i	1.77154	−	0.644788i	0.999963	−	0.00865253i	$-0.00275422\pi$
$384$	−19.5635	−	1.12630i	−0.998347	−	0.0574764i
$385$	0.00703334	+	0.0398880i	0.000358452	+	0.00203288i
$386$	10.7506	+	8.13401i	0.547190	+	0.414010i
$387$	1.52947	−	12.4063i	0.0777473	−	0.630649i
$388$	6.95675	+	24.6226i	0.353176	+	1.25002i
$389$	−2.44660	+	6.72197i	−0.124047	+	0.340817i	−0.986136	−	0.165941i	$-0.946934\pi$
$389$	−2.44660	+	6.72197i	−0.124047	+	0.340817i	0.862088	+	0.506758i	$0.169156\pi$
$390$	−29.3422	−	25.1720i	−1.48580	−	1.27464i
$391$	10.0246	+	8.41167i	0.506968	+	0.425397i
$392$	17.3721	−	9.49728i	0.877424	−	0.479685i
$393$	1.21138	−	19.7266i	0.0611060	−	0.995077i
$394$	−0.626255	−	12.4120i	−0.0315503	−	0.625309i
$395$	10.9754	+	6.33665i	0.552233	+	0.318832i
$396$	5.28791	−	2.90091i	0.265728	−	0.145776i
$397$	22.6986	−	13.1051i	1.13921	−	0.657724i	0.192976	−	0.981203i	$-0.438186\pi$
$397$	22.6986	−	13.1051i	1.13921	−	0.657724i	0.946235	+	0.323479i	$0.104853\pi$
$398$	7.23371	+	11.1866i	0.362593	+	0.560732i
$399$	0.0529672	−	0.0557885i	0.00265168	−	0.00279292i
$400$	−15.4801	−	39.1906i	−0.774003	−	1.95953i
$401$	3.00071	−	17.0179i	0.149848	−	0.849832i	−0.813497	−	0.581569i	$-0.802439\pi$
$401$	3.00071	−	17.0179i	0.149848	−	0.849832i	0.963346	−	0.268263i	$-0.0864497\pi$
$402$	−8.21373	+	4.62337i	−0.409664	+	0.230593i
$403$	−20.5302	−	24.4669i	−1.02268	−	1.21878i
$404$	12.0101	+	11.6887i	0.597523	+	0.581535i
$405$	25.4924	+	24.6660i	1.26673	+	1.22566i
$406$	−0.0334898	−	0.0793262i	−0.00166207	−	0.00393689i
$407$	5.92033	−	4.96775i	0.293460	−	0.246242i
$408$	−8.98763	−	2.38281i	−0.444954	−	0.117967i
$409$	−4.27076	+	24.2207i	−0.211176	+	1.19764i	0.676245	+	0.736677i	$0.263606\pi$
$409$	−4.27076	+	24.2207i	−0.211176	+	1.19764i	−0.887421	+	0.460960i	$0.847505\pi$
$410$	−22.0242	−	23.7105i	−1.08770	−	1.17098i
$411$	5.36412	+	5.09285i	0.264592	+	0.251212i
$412$	−11.4953	−	7.81895i	−0.566331	−	0.385212i
$413$	−0.0581420	+	0.0335683i	−0.00286098	+	0.00165179i
$414$	−26.6943	−	11.9631i	−1.31195	−	0.587954i
$415$	29.9502	−	51.8753i	1.47020	−	2.54646i
$416$	−22.5844	+	1.75450i	−1.10729	+	0.0860216i
$417$	−0.113075	+	1.84136i	−0.00553731	+	0.0901720i
$418$	−5.90277	−	1.81723i	−0.288714	−	0.0888838i
$419$	−8.86909	+	10.5698i	−0.433283	+	0.516367i	−0.937867	−	0.346996i	$-0.887202\pi$
$419$	−8.86909	+	10.5698i	−0.433283	+	0.516367i	0.504583	+	0.863363i	$0.331646\pi$
$420$	−0.0425226	+	0.132943i	−0.00207489	+	0.00648697i
$421$	−12.5029	+	34.3515i	−0.609355	+	1.67419i	0.122281	+	0.992496i	$0.460979\pi$
$421$	−12.5029	+	34.3515i	−0.609355	+	1.67419i	−0.731637	+	0.681695i	$0.761243\pi$
$422$	−16.9276	−	2.11192i	−0.824024	−	0.102807i
$423$	−9.27312	−	21.8759i	−0.450875	−	1.06364i
$424$	0.961226	+	6.30718i	0.0466813	+	0.306304i
$425$	−3.47188	−	19.6900i	−0.168411	−	0.955106i
$426$	−1.67637	+	1.37573i	−0.0812203	+	0.0666544i
$427$	−0.000379315	−	0.00104216i	−1.83563e−5	−	5.04336e-5i
$428$	23.1635	−	16.6918i	1.11965	−	0.806830i
$429$	5.60561	−	4.14581i	0.270641	−	0.200162i
$430$	10.5842	−	20.6731i	0.510418	−	0.996947i
$431$	7.44743			0.358730			0.179365	−	0.983783i	$-0.442596\pi$
$431$	7.44743			0.358730			0.179365	+	0.983783i	$0.442596\pi$
$432$	20.7814	−	0.366975i	0.999844	−	0.0176561i
$433$	20.9407			1.00634			0.503172	−	0.864186i	$-0.332166\pi$
$433$	20.9407			1.00634			0.503172	+	0.864186i	$0.332166\pi$
$434$	−0.0525513	+	0.102643i	−0.00252254	+	0.00492703i
$435$	−37.2815	−	16.2213i	−1.78751	−	0.777751i
$436$	−7.92519	+	5.71097i	−0.379548	+	0.273506i
$437$	10.2451	+	28.1482i	0.490090	+	1.34651i
$438$	5.79420	+	35.0972i	0.276858	+	1.67701i
$439$	4.88555	+	27.7073i	0.233174	+	1.32240i	0.846424	+	0.532509i	$0.178751\pi$
$439$	4.88555	+	27.7073i	0.233174	+	1.32240i	−0.613250	+	0.789889i	$0.710138\pi$
$440$	11.0782	−	1.68834i	0.528132	−	0.0804882i
$441$	−17.6174	+	11.4286i	−0.838925	+	0.544220i
$442$	−10.6658	−	1.33068i	−0.507319	−	0.0632939i
$443$	−5.98423	+	16.4415i	−0.284319	+	0.781161i	0.712515	+	0.701657i	$0.247556\pi$
$443$	−5.98423	+	16.4415i	−0.284319	+	0.781161i	−0.996835	+	0.0795043i	$0.974666\pi$
$444$	26.0253	−	5.65675i	1.23510	−	0.268457i
$445$	7.36537	−	8.77771i	0.349152	−	0.416103i
$446$	−4.79736	−	1.47692i	−0.227162	−	0.0699342i
$447$	3.01577	+	1.99716i	0.142641	+	0.0944624i
$448$	0.0375493	+	0.0726552i	0.00177404	+	0.00343264i
$449$	−2.99357	+	5.18501i	−0.141275	+	0.244696i	−0.927977	−	0.372637i	$-0.878454\pi$
$449$	−2.99357	+	5.18501i	−0.141275	+	0.244696i	0.786702	+	0.617333i	$0.211787\pi$
$450$	19.4942	+	40.2175i	0.918967	+	1.89587i
$451$	5.05428	−	2.91809i	0.237997	−	0.137408i
$452$	−7.39947	−	5.03304i	−0.348042	−	0.236734i
$453$	−4.26407	+	17.7420i	−0.200344	+	0.833593i
$454$	10.4703	+	11.2719i	0.491394	+	0.529017i
$455$	−0.0280181	+	0.158899i	−0.00131351	+	0.00744928i
$456$	−15.0895	−	15.0100i	−0.706630	−	0.702909i
$457$	18.6279	−	15.6306i	0.871375	−	0.731170i	−0.0930125	−	0.995665i	$-0.529650\pi$
$457$	18.6279	−	15.6306i	0.871375	−	0.731170i	0.964387	+	0.264495i	$0.0852052\pi$
$458$	4.32206	+	10.2375i	0.201957	+	0.478368i
$459$	9.69570	+	1.80436i	0.452556	+	0.0842201i
$460$	−38.9488	−	37.9067i	−1.81600	−	1.76741i
$461$	−10.3010	−	12.2762i	−0.479764	−	0.571761i	0.470819	−	0.882230i	$-0.343958\pi$
$461$	−10.3010	−	12.2762i	−0.479764	−	0.571761i	−0.950584	+	0.310469i	$0.899514\pi$
$462$	−0.0216611	−	0.0128234i	−0.00100776	−	0.000596598i
$463$	0.124840	−	0.708003i	0.00580181	−	0.0329037i	−0.981769	−	0.190076i	$-0.939127\pi$
$463$	0.124840	−	0.708003i	0.00580181	−	0.0329037i	0.987571	+	0.157172i	$0.0502377\pi$
$464$	−22.1571	+	8.75192i	−1.02862	+	0.406298i
$465$	15.4516	+	52.2106i	0.716550	+	2.42121i
$466$	18.5816	+	28.7354i	0.860774	+	1.33114i
$467$	−16.8793	+	9.74528i	−0.781082	+	0.450958i	−0.836814	−	0.547488i	$-0.815584\pi$
$467$	−16.8793	+	9.74528i	−0.781082	+	0.450958i	0.0557318	+	0.998446i	$0.482251\pi$
$468$	23.7470	−	3.65452i	1.09771	−	0.168930i
$469$	0.0340678	+	0.0196690i	0.00157310	+	0.000908231i
$470$	−2.22456	−	44.0896i	−0.102611	−	2.03370i
$471$	34.5274	−	17.2042i	1.59094	−	0.792726i
$472$	8.91015	+	16.2981i	0.410123	+	0.750183i
$473$	3.20859	+	2.69233i	0.147531	+	0.123794i
$474$	−7.43024	+	2.61287i	−0.341282	+	0.120013i
$475$	15.6530	−	43.0062i	0.718207	−	1.97326i
$476$	0.0105511	+	0.0373444i	0.000483610	+	0.00171168i
$477$	−1.51902	−	6.59432i	−0.0695511	−	0.301933i
$478$	−34.0166	−	25.7373i	−1.55588	−	1.17720i
$479$	1.69552	+	9.61575i	0.0774701	+	0.439355i	0.998729	+	0.0504046i	$0.0160511\pi$
$479$	1.69552	+	9.61575i	0.0774701	+	0.439355i	−0.921259	+	0.388950i	$0.872838\pi$
$480$	36.4975	+	12.6183i	1.66588	+	0.575944i
$481$	28.9304	−	10.5298i	1.31911	−	0.480118i
$482$	−0.789623	−	3.45087i	−0.0359663	−	0.157183i
$483$	0.0137909	+	0.121305i	0.000627507	+	0.00551957i
$484$	1.47127	−	19.9248i	0.0668760	−	0.905672i
$485$		−	50.4227i		−	2.28958i
$486$	−21.9505	+	2.04336i	−0.995695	+	0.0926889i
$487$	−40.7197			−1.84519			−0.922594	−	0.385773i	$-0.873935\pi$
$487$	−40.7197			−1.84519			−0.922594	+	0.385773i	$0.873935\pi$
$488$	−0.290701	+	0.0982007i	−0.0131594	+	0.00444534i
$489$	14.8790	−	1.69155i	0.672850	−	0.0764947i
$490$	−38.0338	+	8.70284i	−1.71819	+	0.393154i
$491$	4.27622	+	11.7488i	0.192983	+	0.530217i	0.998012	−	0.0630180i	$-0.0200726\pi$
$491$	4.27622	+	11.7488i	0.192983	+	0.530217i	−0.805029	+	0.593235i	$0.797850\pi$
$492$	20.0963	−	0.794101i	0.906013	−	0.0358008i
$493$	−11.1321	+	1.96289i	−0.501365	+	0.0884041i
$494$	−19.6203	−	14.8450i	−0.882761	−	0.667907i
$495$	−11.5825	+	2.66807i	−0.520596	+	0.119921i
$496$	28.0520	+	15.1969i	1.25957	+	0.682362i
$497$	0.00850497	+	0.00309555i	0.000381500	+	0.000138855i
$498$	12.3497	+	35.1190i	0.553405	+	1.57372i
$499$	2.94192	−	3.50604i	0.131698	−	0.156952i	−0.696165	−	0.717882i	$-0.745112\pi$
$499$	2.94192	−	3.50604i	0.131698	−	0.156952i	0.827863	+	0.560930i	$0.189556\pi$
$500$	4.39106	+	43.4035i	0.196374	+	1.94106i
$501$	−6.52006	−	13.0852i	−0.291295	−	0.584605i
$502$	1.19341	+	23.6527i	0.0532644	+	1.05567i
$503$	−9.68900	+	16.7818i	−0.432011	+	0.748265i	−0.997046	−	0.0768015i	$-0.975529\pi$
$503$	−9.68900	+	16.7818i	−0.432011	+	0.748265i	0.565035	+	0.825067i	$0.308863\pi$
$504$	−0.0455016	−	0.0738541i	−0.00202680	−	0.00328972i
$505$	−16.5134	−	28.6020i	−0.734836	−	1.27277i
$506$	8.23081	−	5.32240i	0.365904	−	0.236609i
$507$	5.04145	−	1.49200i	0.223899	−	0.0662622i
$508$	−1.20353	+	2.67508i	−0.0533979	+	0.118688i
$509$	2.30682	+	0.406755i	0.102248	+	0.0180291i	0.224538	−	0.974465i	$-0.427913\pi$
$509$	2.30682	+	0.406755i	0.102248	+	0.0180291i	−0.122290	+	0.992494i	$0.539024\pi$
$510$	15.7677	+	9.33453i	0.698207	+	0.413340i
$511$	0.113729	−	0.0954301i	0.00503108	−	0.00422158i
$512$	20.3381	−	9.91776i	0.898825	−	0.438307i
$513$	17.1552	+	14.6737i	0.757420	+	0.647860i
$514$	34.8437	−	14.7103i	1.53689	−	0.648842i
$515$	17.6105	+	20.9874i	0.776014	+	0.924817i
$516$	5.46842	+	13.3581i	0.240734	+	0.588056i
$517$	7.84049	+	1.38249i	0.344824	+	0.0608018i
$518$	−0.0756484	−	0.0814404i	−0.00332380	−	0.00357829i
$519$	22.8968	+	5.50296i	1.00506	+	0.241553i
$520$	43.7701	+	8.77368i	1.91944	+	0.384751i
$521$	−3.33988	−	5.78485i	−0.146323	−	0.253439i	0.783543	−	0.621338i	$-0.213411\pi$
$521$	−3.33988	−	5.78485i	−0.146323	−	0.253439i	−0.929866	+	0.367899i	$0.880077\pi$
$522$	22.7377	−	11.0214i	0.995201	−	0.482394i
$523$	−25.4719	−	14.7062i	−1.11381	−	0.643057i	−0.173994	−	0.984747i	$-0.555667\pi$
$523$	−25.4719	−	14.7062i	−1.11381	−	0.643057i	−0.939813	+	0.341690i	$0.889001\pi$
$524$	9.92422	+	20.5504i	0.433542	+	0.897749i
$525$	0.102990	−	0.155519i	0.00449487	−	0.00678740i
$526$	5.93357	+	1.82672i	0.258716	+	0.0796486i
$527$	11.5965	+	9.73065i	0.505153	+	0.423874i
$528$	−3.68648	+	5.90871i	−0.160433	+	0.257144i
$529$	−23.0590	−	8.39280i	−1.00257	−	0.364904i
$530$	1.55655	−	12.4762i	0.0676122	−	0.541932i
$531$	−10.7221	−	16.5283i	−0.465299	−	0.717267i
$532$	−0.0218251	+	0.0861056i	−0.000946236	+	0.00373315i
$533$	22.8959	−	4.03716i	0.991731	−	0.174869i
$534$	1.15995	+	7.02617i	0.0501960	+	0.304052i
$535$	−52.8718	+	19.2438i	−2.28585	+	0.831980i
$536$	5.65991	−	9.29623i	0.244471	−	0.401536i
$537$	0.205222	−	0.471662i	0.00885598	−	0.0203537i
$538$	0.932850	+	0.477601i	0.0402180	+	0.0205908i
$539$		−	7.03648i		−	0.303083i
$540$	−39.6072	−	10.4389i	−1.70442	−	0.449220i
$541$			1.09392i			0.0470312i	0.999723	+	0.0235156i	$0.00748594\pi$
$541$			1.09392i			0.0470312i	−0.999723	+	0.0235156i	$0.992514\pi$
$542$	9.11631	−	17.8060i	0.391579	−	0.764832i
$543$	−1.94592	−	2.63111i	−0.0835076	−	0.112912i
$544$	10.3973	−	2.67773i	0.445780	−	0.114807i
$545$	18.0896	−	6.58409i	0.774875	−	0.282031i
$546$	−0.0636139	−	0.0775153i	−0.00272242	−	0.00331735i
$547$	11.4033	−	2.01070i	0.487568	−	0.0859714i	0.0755403	−	0.997143i	$-0.475932\pi$
$547$	11.4033	−	2.01070i	0.487568	−	0.0859714i	0.412028	+	0.911171i	$0.364821\pi$
$548$	−8.27914	−	2.09850i	−0.353667	−	0.0896435i
$549$	0.299643	−	0.127018i	0.0127884	−	0.00542098i
$550$	−14.8604	−	1.85400i	−0.633648	−	0.0790549i
$551$	−24.3143	−	8.84968i	−1.03582	−	0.377009i
$552$	33.6413	−	3.03276i	1.43187	−	0.129083i
$553$	0.0251814	+	0.0211297i	0.00107082	+	0.000898528i
$554$	−3.56063	+	11.5657i	−0.151277	+	0.491379i
$555$	−52.3862	−	3.21695i	−2.22367	−	0.136552i
$556$	−0.926368	−	1.91826i	−0.0392867	−	0.0813523i
$557$	11.9979	+	6.92697i	0.508366	+	0.293505i	0.732162	−	0.681131i	$-0.238512\pi$
$557$	11.9979	+	6.92697i	0.508366	+	0.293505i	−0.223796	+	0.974636i	$0.571845\pi$
$558$	−30.8800	−	13.8389i	−1.30726	−	0.585849i
$559$	8.34273	+	14.4500i	0.352860	+	0.611171i
$560$	−0.0322805	−	0.157905i	−0.00136410	−	0.00667272i
$561$	−2.27530	+	2.39649i	−0.0960633	+	0.101180i
$562$	19.4601	−	18.0762i	0.820876	−	0.762496i
$563$	−29.5384	−	5.20841i	−1.24489	−	0.219508i	−0.487882	−	0.872910i	$-0.662230\pi$
$563$	−29.5384	−	5.20841i	−1.24489	−	0.219508i	−0.757012	+	0.653401i	$0.773341\pi$
$564$	21.6970	+	16.7918i	0.913609	+	0.707064i
$565$	11.3359	+	13.5096i	0.476903	+	0.568351i
$566$	−14.1393	−	33.4912i	−0.594318	−	1.40774i
$567$	0.0540079	+	0.0744888i	0.00226812	+	0.00312823i
$568$	0.911026	−	2.33249i	0.0382258	−	0.0978690i
$569$	−13.1491	+	11.0334i	−0.551241	+	0.462546i	−0.875361	−	0.483470i	$-0.839376\pi$
$569$	−13.1491	+	11.0334i	−0.551241	+	0.462546i	0.324120	+	0.946016i	$0.394932\pi$
$570$	20.5737	+	36.5507i	0.861739	+	1.53094i
$571$	16.7116	+	2.94670i	0.699357	+	0.123316i	0.512012	−	0.858978i	$-0.328900\pi$
$571$	16.7116	+	2.94670i	0.699357	+	0.123316i	0.187346	+	0.982294i	$0.440012\pi$
$572$	−3.30314	+	7.34189i	−0.138111	+	0.306980i
$573$	17.5281	+	16.6417i	0.732248	+	0.695218i
$574$	−0.0455791	−	0.0704858i	−0.00190244	−	0.00294202i
$575$	36.3161	+	62.9013i	1.51449	+	2.62317i
$576$	−20.7210	+	12.1096i	−0.863373	+	0.504566i
$577$	−4.49809	+	7.79092i	−0.187258	+	0.324340i	−0.944335	−	0.328985i	$-0.893293\pi$
$577$	−4.49809	+	7.79092i	−0.187258	+	0.324340i	0.757077	+	0.653326i	$0.226627\pi$
$578$	−18.9231	+	0.954775i	−0.787098	+	0.0397134i
$579$	16.4797	+	1.01199i	0.684874	+	0.0420570i
$580$	46.7089	−	4.72547i	1.93948	−	0.196214i
$581$	0.0998698	−	0.119020i	0.00414330	−	0.00493779i
$582$	23.7841	+	20.4039i	0.985882	+	0.845768i
$583$	2.13072	+	0.775517i	0.0882453	+	0.0321186i
$584$	−25.6626	−	32.0720i	−1.06193	−	1.32715i
$585$	−46.9929	−	5.79335i	−1.94292	−	0.239526i
$586$	−12.4478	+	16.4520i	−0.514212	+	0.679626i
$587$	−29.2734	+	5.16169i	−1.20824	+	0.213046i	−0.741258	−	0.671220i	$-0.765771\pi$
$587$	−29.2734	+	5.16169i	−1.20824	+	0.213046i	−0.466984	+	0.884266i	$0.654660\pi$
$588$	11.2856	−	21.4620i	0.465409	−	0.885079i
$589$	11.8516	+	32.5619i	0.488336	+	1.34169i
$590$	−8.16482	−	35.6826i	−0.336140	−	1.46903i
$591$	−9.05075	−	12.2376i	−0.372298	−	0.503390i
$592$	−23.0136	+	20.3992i	−0.945851	+	0.838401i
$593$	−21.5451			−0.884750			−0.442375	−	0.896830i	$-0.645864\pi$
$593$	−21.5451			−0.884750			−0.442375	+	0.896830i	$0.645864\pi$
$594$	3.42844	−	6.54307i	0.140670	−	0.268465i
$595$		−	0.0764747i		−	0.00313516i
$596$	−4.16535	−	0.307574i	−0.170619	−	0.0125987i
$597$	14.9608	+	6.50949i	0.612304	+	0.266416i
$598$	38.0626	−	8.70942i	1.55650	−	0.356155i
$599$	−10.2586	+	3.73384i	−0.419156	+	0.152560i	−0.542983	−	0.839743i	$-0.682705\pi$
$599$	−10.2586	+	3.73384i	−0.419156	+	0.152560i	0.123827	+	0.992304i	$0.460483\pi$
$600$	−42.3521	−	29.4889i	−1.72902	−	1.20388i
$601$	−2.62710	−	14.8990i	−0.107162	−	0.607744i	−0.990335	−	0.138697i	$-0.955709\pi$
$601$	−2.62710	−	14.8990i	−0.107162	−	0.607744i	0.883173	−	0.469047i	$-0.155403\pi$
$602$	0.0363477	−	0.0480401i	0.00148142	−	0.00195797i
$603$	−5.24585	+	10.2831i	−0.213628	+	0.418761i
$604$	−5.72879	−	20.2763i	−0.233101	−	0.825032i
$605$	−13.4661	+	36.9978i	−0.547475	+	1.50417i
$606$	20.1737	+	3.78473i	0.819499	+	0.153744i
$607$	−18.8283	−	15.7988i	−0.764216	−	0.641253i	0.175005	−	0.984568i	$-0.444006\pi$
$607$	−18.8283	−	15.7988i	−0.764216	−	0.641253i	−0.939221	+	0.343314i	$0.888450\pi$
$608$	23.6758	+	6.59161i	0.960179	+	0.267325i
$609$	−0.0879254	−	0.0582275i	−0.00356292	−	0.00235950i
$610$	0.603913	−	0.0304707i	0.0244517	−	0.00123372i
$611$	27.4663	+	15.8577i	1.11117	+	0.641532i
$612$	−10.7836	+	3.66028i	−0.435900	+	0.147958i
$613$	15.6018	−	9.00768i	0.630149	−	0.363817i	−0.150661	−	0.988586i	$-0.548140\pi$
$613$	15.6018	−	9.00768i	0.630149	−	0.363817i	0.780810	+	0.624769i	$0.214807\pi$
$614$	11.0741	−	7.16098i	0.446914	−	0.288994i
$615$	−38.5369	−	9.26187i	−1.55396	−	0.373475i
$616$	0.0290585		0.000677033i	0.00117080		2.72784e-5i
$617$	−4.06887	+	23.0757i	−0.163807	+	0.928994i	0.786480	+	0.617616i	$0.211902\pi$
$617$	−4.06887	+	23.0757i	−0.163807	+	0.928994i	−0.950286	+	0.311378i	$0.899210\pi$
$618$	−17.0259	−	0.185906i	−0.684882	−	0.00747822i
$619$	21.6871	+	25.8457i	0.871679	+	1.03883i	0.998897	+	0.0469514i	$0.0149506\pi$
$619$	21.6871	+	25.8457i	0.871679	+	1.03883i	−0.127219	+	0.991875i	$0.540605\pi$
$620$	−45.0561	−	43.8506i	−1.80950	−	1.76108i
$621$	−35.3397	+	5.88716i	−1.41813	+	0.236244i
$622$	10.4640	−	4.41769i	0.419569	−	0.177133i
$623$	0.0227676	−	0.0191043i	0.000912166	−	0.000765398i
$624$	−21.8503	+	17.0958i	−0.874714	+	0.684378i
$625$	5.78239	−	32.7936i	0.231296	−	1.31174i
$626$	−34.2592	+	31.8227i	−1.36927	+	1.27189i
$627$	−7.25326	+	2.14658i	−0.289667	+	0.0857263i
$628$	−25.0523	+	36.8313i	−0.999695	+	1.46973i
$629$	−12.6372	+	7.29606i	−0.503876	+	0.290913i
$630$	0.0467191	+	0.164440i	0.00186133	+	0.00655145i
$631$	−3.55095	+	6.15043i	−0.141361	+	0.244845i	−0.928009	−	0.372557i	$-0.878481\pi$
$631$	−3.55095	+	6.15043i	−0.141361	+	0.244845i	0.786648	+	0.617401i	$0.211815\pi$
$632$	6.00667	−	6.82890i	0.238932	−	0.271639i
$633$	−18.6999	+	9.31773i	−0.743256	+	0.370346i
$634$	10.8472	−	35.2340i	0.430797	−	1.39932i
$635$	3.71575	−	4.42826i	0.147455	−	0.175730i
$636$	5.25509	+	5.78280i	0.208378	+	0.229303i
$637$	9.58703	−	26.3402i	0.379852	−	1.04363i
$638$	−1.04819	+	8.40157i	−0.0414983	+	0.332621i
$639$	−0.777779	+	2.53955i	−0.0307685	+	0.100463i
$640$	−43.8840	+	7.91104i	−1.73467	+	0.312711i
$641$	−0.826096	−	4.68502i	−0.0326288	−	0.185047i	0.964137	−	0.265404i	$-0.0855052\pi$
$641$	−0.826096	−	4.68502i	−0.0326288	−	0.185047i	−0.996766	+	0.0803565i	$0.974394\pi$
$642$	12.3177	−	32.7265i	0.486143	−	1.29161i
$643$	5.88956	+	16.1814i	0.232262	+	0.638134i	0.999997	−	0.00263392i	$-0.000838403\pi$
$643$	5.88956	+	16.1814i	0.232262	+	0.638134i	−0.767735	+	0.640768i	$0.778616\pi$
$644$	−0.0824172	−	0.114372i	−0.00324769	−	0.00450687i
$645$	−3.21313	−	28.2628i	−0.126517	−	1.11284i
$646$	10.3799	+	5.31433i	0.408393	+	0.209089i
$647$	38.9704			1.53208			0.766042	−	0.642791i	$-0.222224\pi$
$647$	38.9704			1.53208			0.766042	+	0.642791i	$0.222224\pi$
$648$	20.9513	−	14.4583i	0.823045	−	0.567976i
$649$	6.60148			0.259131
$650$	−53.1018	−	27.1871i	−2.08282	−	1.06637i
$651$	0.0159533	+	0.140326i	0.000625260	+	0.00549981i
$652$	−14.0285	+	10.1091i	−0.549399	+	0.395902i
$653$	−7.50821	−	20.6286i	−0.293819	−	0.807261i	−0.995499	−	0.0947692i	$-0.969789\pi$
$653$	−7.50821	−	20.6286i	−0.293819	−	0.807261i	0.701680	−	0.712492i	$-0.252434\pi$
$654$	−4.21441	+	11.1971i	−0.164797	+	0.437840i
$655$	−7.80953	−	44.2901i	−0.305144	−	1.73056i
$656$	−19.7898	+	12.1527i	−0.772661	+	0.474485i
$657$	29.6970	+	31.8774i	1.15859	+	1.24366i
$658$	0.0141759	−	0.113624i	0.000552636	−	0.00442953i
$659$	10.8064	−	29.6905i	0.420960	−	1.15658i	−0.530199	−	0.847873i	$-0.677883\pi$
$659$	10.8064	−	29.6905i	0.420960	−	1.15658i	0.951158	−	0.308703i	$-0.0998950\pi$
$660$	10.1571	−	9.23025i	0.395366	−	0.359287i
$661$	0.564964	−	0.673298i	0.0219746	−	0.0261883i	−0.754945	−	0.655788i	$-0.772337\pi$
$661$	0.564964	−	0.673298i	0.0219746	−	0.0261883i	0.776920	+	0.629600i	$0.216781\pi$
$662$	1.15458	−	3.75033i	0.0448741	−	0.145761i
$663$	−11.7825	+	5.87092i	−0.457593	+	0.228008i
$664$	−32.2768	−	28.3905i	−1.25258	−	1.10177i
$665$	0.0875262	−	0.151600i	0.00339412	−	0.00587879i
$666$	22.7158	−	23.4085i	0.880221	−	0.907062i
$667$	35.5624	−	20.5319i	1.37698	−	0.795000i
$668$	13.9584	+	9.49435i	0.540066	+	0.367347i
$669$	−5.89494	+	1.74459i	−0.227912	+	0.0674498i
$670$	−15.7147	+	14.5971i	−0.607111	+	0.563934i
$671$	−0.0189365	+	0.107394i	−0.000731036	+	0.00414591i
$672$	0.0875457	+	0.0486710i	0.00337715	+	0.00187752i
$673$	2.60760	−	2.18804i	0.100516	−	0.0843426i	−0.591145	−	0.806565i	$-0.701324\pi$
$673$	2.60760	−	2.18804i	0.100516	−	0.0843426i	0.691661	+	0.722223i	$0.256879\pi$
$674$	17.0632	−	7.20371i	0.657249	−	0.277477i
$675$	47.1432	+	27.8161i	1.81454	+	1.07064i
$676$	−4.23421	+	4.35062i	−0.162854	+	0.167331i
$677$	12.0910	+	14.4095i	0.464695	+	0.553802i	0.946595	−	0.322424i	$-0.104498\pi$
$677$	12.0910	+	14.4095i	0.464695	+	0.553802i	−0.481900	+	0.876226i	$0.660053\pi$
$678$	−10.9595	−	0.119667i	−0.420898	−	0.00459578i
$679$	0.0227108	−	0.128799i	0.000871561	−	0.00494287i
$680$	−21.1526	−	0.492833i	−0.811163	−	0.0188993i
$681$	18.3204	+	4.40308i	0.702038	+	0.168726i
$682$	9.52143	−	6.15696i	0.364594	−	0.235762i
$683$	−19.4488	+	11.2288i	−0.744188	+	0.429657i	−0.823590	−	0.567186i	$-0.808032\pi$
$683$	−19.4488	+	11.2288i	−0.744188	+	0.429657i	0.0794021	+	0.996843i	$0.474699\pi$
$684$	−25.5661	−	5.08595i	−0.977543	−	0.194466i
$685$	14.5765	+	8.41573i	0.556938	+	0.321548i
$686$	−0.202148	+	0.0101995i	−0.00771805	+	0.000389418i
$687$	11.3473	+	7.51461i	0.432926	+	0.286700i
$688$	−13.0534	−	10.3632i	−0.497658	−	0.395093i
$689$	6.91944	+	5.80610i	0.263610	+	0.221195i
$690$	−65.4236	−	12.2739i	−2.49063	−	0.467261i
$691$	−14.6665	+	40.2960i	−0.557941	+	1.53293i	0.264677	+	0.964337i	$0.414735\pi$
$691$	−14.6665	+	40.2960i	−0.557941	+	1.53293i	−0.822618	+	0.568594i	$0.807488\pi$
$692$	−26.1674	+	7.39323i	−0.994737	+	0.281049i
$693$	−0.0307881	+	0.00159842i	−0.00116954	+	6.07191e-5i
$694$	12.3785	−	16.3605i	0.469882	−	0.621034i
$695$	0.728974	+	4.13422i	0.0276515	+	0.156820i
$696$	−16.6721	+	23.9445i	−0.631954	+	0.907615i
$697$	−10.3548	+	3.76883i	−0.392215	+	0.142755i
$698$	32.2230	−	7.37320i	1.21966	−	0.279080i
$699$	38.4304	+	16.7212i	1.45357	+	0.632455i
$700$	−0.0158612	+	0.214801i	−0.000599495	+	0.00811870i
$701$			30.9274i			1.16811i	0.811714	+	0.584055i	$0.198535\pi$
$701$			30.9274i			1.16811i	−0.811714	+	0.584055i	$0.801465\pi$
$702$	21.7487	−	19.8220i	0.820851	−	0.748132i
$703$	−33.4017			−1.25977
$704$	0.374529	−	8.03308i	0.0141156	−	0.302758i
$705$	−32.1498	−	43.4702i	−1.21083	−	1.63718i
$706$	−10.7797	−	47.1103i	−0.405699	−	1.77302i
$707$	−0.0292991	−	0.0804987i	−0.00110191	−	0.00302746i
$708$	20.1352	+	10.5879i	0.756728	+	0.397917i
$709$	10.5402	−	1.85852i	0.395845	−	0.0697982i	0.0278175	−	0.999613i	$-0.491144\pi$
$709$	10.5402	−	1.85852i	0.395845	−	0.0697982i	0.368028	+	0.929815i	$0.380033\pi$
$710$	−2.97747	+	3.93528i	−0.111743	+	0.147688i
$711$	−5.80913	+	7.70112i	−0.217859	+	0.288815i
$712$	−5.13744	−	6.42054i	−0.192534	−	0.240620i
$713$	−51.6766	−	18.8088i	−1.93531	−	0.704394i
$714$	0.0360727	+	0.0309460i	0.00134999	+	0.00115812i
$715$	10.1981	−	12.1536i	0.381386	−	0.454518i
$716$	0.0597837	+	0.590932i	0.00223422	+	0.0220842i
$717$	−52.1445	−	3.20211i	−1.94737	−	0.119585i
$718$	38.2456	−	1.92970i	1.42731	−	0.0720158i
$719$	7.98318	−	13.8273i	0.297723	−	0.515671i	−0.677892	−	0.735161i	$-0.737106\pi$
$719$	7.98318	−	13.8273i	0.297723	−	0.515671i	0.975615	+	0.219491i	$0.0704397\pi$
$720$	45.7844	−	11.8626i	1.70629	−	0.442092i
$721$	0.0355314	+	0.0615422i	0.00132326	+	0.00229195i
$722$	−0.0961969	−	0.148764i	−0.00358008	−	0.00553641i
$723$	−3.14426	−	2.98525i	−0.116936	−	0.111023i
$724$	3.44607	+	1.55040i	0.128072	+	0.0576201i
$725$	−61.7861	−	10.8946i	−2.29468	−	0.404614i
$726$	−12.0025	−	21.3233i	−0.445455	−	0.791382i
$727$	18.0652	−	15.1585i	0.670002	−	0.562198i	−0.243064	−	0.970010i	$-0.578153\pi$
$727$	18.0652	−	15.1585i	0.670002	−	0.562198i	0.913066	+	0.407812i	$0.133708\pi$
$728$	0.107854	+	0.0421259i	0.00399735	+	0.00156129i
$729$	−21.0079	+	16.9608i	−0.778069	+	0.628178i
$730$	31.4830	+	74.5728i	1.16524	+	2.76006i
$731$	−5.08341	−	6.05817i	−0.188017	−	0.224069i
$732$	−0.230005	+	0.297193i	−0.00850122	+	0.0109846i
$733$	5.12011	+	0.902813i	0.189115	+	0.0333462i	0.267404	−	0.963585i	$-0.413834\pi$
$733$	5.12011	+	0.902813i	0.189115	+	0.0333462i	−0.0782882	+	0.996931i	$0.524945\pi$
$734$	−4.74536	+	4.40788i	−0.175155	+	0.162698i
$735$	−32.9020	+	34.6544i	−1.21361	+	1.27825i
$736$	−32.1658	+	22.0592i	−1.18565	+	0.813112i
$737$	−1.93404	−	3.34985i	−0.0712412	−	0.123393i
$738$	19.9630	−	14.4298i	0.734848	−	0.531167i
$739$	10.5638	+	6.09903i	0.388596	+	0.224356i	0.681552	−	0.731770i	$-0.261305\pi$
$739$	10.5638	+	6.09903i	0.388596	+	0.224356i	−0.292955	+	0.956126i	$0.594639\pi$
$740$	54.5739	−	26.3549i	2.00617	−	0.968824i
$741$	−30.0763	−	1.84694i	−1.10488	−	0.0678489i
$742$	0.00959544	−	0.0311681i	0.000352260	−	0.00114422i
$743$	−11.5486	−	9.69040i	−0.423676	−	0.355506i	0.405883	−	0.913925i	$-0.366964\pi$
$743$	−11.5486	−	9.69040i	−0.423676	−	0.355506i	−0.829559	+	0.558419i	$0.811408\pi$
$744$	38.9163	−	3.50830i	1.42674	−	0.128621i
$745$	7.73451	+	2.81513i	0.283371	+	0.103138i
$746$	24.0683	+	3.00279i	0.881202	+	0.109940i
$747$	36.3994	+	27.4568i	1.33178	+	1.00459i
$748$	0.937534	−	3.69882i	0.0342796	−	0.135242i
$749$	−0.143723	+	0.0253422i	−0.00525153	+	0.000925986i
$750$	33.8949	+	41.3019i	1.23767	+	1.50813i
$751$	−1.35242	+	0.492239i	−0.0493504	+	0.0179621i	−0.366577	−	0.930388i	$-0.619471\pi$
$751$	−1.35242	+	0.492239i	−0.0493504	+	0.0179621i	0.317227	+	0.948350i	$0.397248\pi$
$752$	−31.3366	−	4.65324i	−1.14273	−	0.169686i
$753$	17.2474	+	23.3204i	0.628529	+	0.849843i
$754$	−15.3707	+	30.0220i	−0.559768	+	1.09334i
$755$			41.5223i			1.51115i
$756$	−0.0964706	−	0.0445046i	−0.00350860	−	0.00161862i
$757$		−	15.3476i		−	0.557818i	−0.960318	−	0.278909i	$-0.910027\pi$
$757$		−	15.3476i		−	0.557818i	0.960318	−	0.278909i	$-0.0899727\pi$
$758$	0.479199	+	0.245340i	0.0174053	+	0.00891116i
$759$	4.78953	−	11.0078i	0.173849	−	0.399558i
$760$	−41.3678	−	25.1863i	−1.50057	−	0.913603i
$761$	−3.86991	+	1.40853i	−0.140284	+	0.0510593i	−0.411208	−	0.911541i	$-0.634893\pi$
$761$	−3.86991	+	1.40853i	−0.140284	+	0.0510593i	0.270924	+	0.962601i	$0.412671\pi$
$762$	0.585182	+	3.54462i	0.0211989	+	0.128408i
$763$	0.0491736	−	0.00867063i	0.00178020	−	0.000313898i
$764$	−27.0534	−	6.85719i	−0.978759	−	0.248084i
$765$	22.4116	−	1.16354i	0.810292	−	0.0420679i
$766$	−6.45961	+	51.7757i	−0.233395	+	1.87073i
$767$	24.7118	+	8.99435i	0.892291	+	0.324767i
$768$	14.0263	−	23.9011i	0.506132	−	0.862456i
$769$	36.4911	+	30.6197i	1.31590	+	1.10417i	0.987156	+	0.159757i	$0.0510710\pi$
$769$	36.4911	+	30.6197i	1.31590	+	1.10417i	0.328748	+	0.944418i	$0.393373\pi$
$770$	−0.0547448	−	0.0168538i	−0.00197287	−	0.000607369i
$771$	25.5762	−	38.6209i	0.921104	−	1.39090i
$772$	−17.1679	+	8.29075i	−0.617887	+	0.298391i
$773$	4.04314	+	2.33431i	0.145422	+	0.0839592i	0.570945	−	0.820988i	$-0.306577\pi$
$773$	4.04314	+	2.33431i	0.145422	+	0.0839592i	−0.425524	+	0.904947i	$0.639910\pi$
$774$	14.6316	+	9.92110i	0.525922	+	0.356607i
$775$	42.0105	+	72.7644i	1.50906	+	2.61377i
$776$	−35.4790	−	7.11174i	−1.27362	−	0.255297i
$777$	−0.132366	−	0.0318126i	−0.00474861	−	0.00114127i
$778$	−6.88494	−	7.41208i	−0.246837	−	0.265736i
$779$	−24.8403	−	4.38001i	−0.889996	−	0.156930i
$780$	50.5979	−	20.7134i	1.81170	−	0.741658i
$781$	−0.572053	−	0.681746i	−0.0204697	−	0.0243948i
$782$	−17.0496	+	7.19797i	−0.609692	+	0.257399i
$783$	15.7263	−	26.6532i	0.562013	−	0.952508i
$784$	0.759198	+	27.9893i	0.0271142	+	0.999617i
$785$	67.2447	−	56.4250i	2.40007	−	2.01390i
$786$	24.0516	+	14.2386i	0.857891	+	0.507873i
$787$	−16.1106	−	2.84073i	−0.574279	−	0.101261i	−0.121037	−	0.992648i	$-0.538622\pi$
$787$	−16.1106	−	2.84073i	−0.574279	−	0.101261i	−0.453243	+	0.891387i	$0.649733\pi$
$788$	16.0281	+	7.21111i	0.570979	+	0.256885i
$789$	7.29111	−	2.15778i	0.259570	−	0.0768191i
$790$	−15.0503	+	9.73215i	−0.535465	+	0.346254i
$791$	0.0228715	+	0.0396145i	0.000813215	+	0.00140853i
$792$	0.243706	+	8.52615i	0.00865971	+	0.302963i
$793$	−0.217209	+	0.376216i	−0.00771330	+	0.0133598i
$794$	1.86784	+	37.0196i	0.0662872	+	1.31378i
$795$	−6.86746	−	13.7824i	−0.243564	−	0.488813i
$796$	−18.7439	+	1.89630i	−0.664362	+	0.0672125i
$797$	−6.71611	+	8.00395i	−0.237897	+	0.283514i	−0.871762	−	0.489929i	$-0.837023\pi$
$797$	−6.71611	+	8.00395i	−0.237897	+	0.283514i	0.633866	+	0.773443i	$0.281467\pi$
$798$	0.0360907	+	0.102631i	0.00127760	+	0.00363311i
$799$	−14.1255	−	5.14126i	−0.499725	−	0.181885i
$800$	59.3107	+	5.77138i	2.09695	+	0.204049i
$801$	5.94509	+	6.38159i	0.210059	+	0.225482i
$802$	19.4885	+	14.7452i	0.688164	+	0.520672i
$803$	−14.3764	+	2.53495i	−0.507333	+	0.0894566i
$804$	−0.526310	−	13.3193i	−0.0185615	−	0.469737i
$805$	0.0950175	+	0.261058i	0.00334893	+	0.00920110i
$806$	44.0310	−	10.0751i	1.55092	−	0.354880i
$807$	1.27532	−	0.144988i	0.0448934	−	0.00510383i
$808$	−22.4544	+	7.58524i	−0.789942	+	0.266848i
$809$	5.87774			0.206650			0.103325	−	0.994648i	$-0.467052\pi$
$809$	5.87774			0.206650			0.103325	+	0.994648i	$0.467052\pi$
$810$	−47.4798	+	16.1933i	−1.66827	+	0.568976i
$811$		−	40.3341i		−	1.41632i	−0.706052	−	0.708160i	$-0.749525\pi$
$811$		−	40.3341i		−	1.41632i	0.706052	−	0.708160i	$-0.250475\pi$
$812$	0.121441	+	0.00896738i	0.00426176	+	0.000314693i
$813$	−2.76750	−	24.3430i	−0.0970603	−	0.853745i
$814$	2.43790	+	10.6543i	0.0854484	+	0.373433i
$815$	32.0208	−	11.6546i	1.12164	−	0.408243i
$816$	8.79199	−	9.77812i	0.307781	−	0.342303i
$817$	−3.14346	−	17.8274i	−0.109976	−	0.623703i
$818$	−27.7371	−	20.9862i	−0.969803	−	0.733764i
$819$	−0.117429	−	0.0359645i	−0.00410330	−	0.00125670i
$820$	44.0416	−	12.4433i	1.53800	−	0.434540i
$821$	−8.31903	+	22.8563i	−0.290336	+	0.797692i	0.705681	+	0.708530i	$0.250641\pi$
$821$	−8.31903	+	22.8563i	−0.290336	+	0.797692i	−0.996017	+	0.0891622i	$0.971581\pi$
$822$	−9.86812	+	3.47016i	−0.344190	+	0.121036i
$823$	−22.0384	−	18.4924i	−0.768211	−	0.644605i	0.172039	−	0.985090i	$-0.444964\pi$
$823$	−22.0384	−	18.4924i	−0.768211	−	0.644605i	−0.940250	+	0.340485i	$0.889409\pi$
$824$	17.2513	−	9.43122i	0.600976	−	0.328552i
$825$	−16.4162	+	8.17981i	−0.571539	+	0.284784i
$826$	−0.00478443	−	0.0948249i	−0.000166472	−	0.00329938i
$827$	12.6598	+	7.30915i	0.440225	+	0.254164i	0.703693	−	0.710504i	$-0.251533\pi$
$827$	12.6598	+	7.30915i	0.440225	+	0.254164i	−0.263468	+	0.964668i	$0.584866\pi$
$828$	32.2636	−	25.8932i	1.12124	−	0.899851i
$829$	38.2098	−	22.0604i	1.32708	−	0.766191i	0.342234	−	0.939615i	$-0.388816\pi$
$829$	38.2098	−	22.0604i	1.32708	−	0.766191i	0.984847	+	0.173424i	$0.0554830\pi$
$830$	45.9990	+	71.1351i	1.59665	+	2.46914i
$831$	4.20594	+	14.2118i	0.145903	+	0.493002i
$832$	12.3469	−	29.5605i	0.428051	−	1.02483i
$833$	−2.30702	+	13.0838i	−0.0799336	+	0.453326i
$834$	−2.24507	−	1.32908i	−0.0777405	−	0.0460224i
$835$	−21.3840	−	25.4845i	−0.740025	−	0.881927i
$836$	6.09186	−	6.25934i	0.210691	−	0.216484i
$837$	−40.8810	+	6.81028i	−1.41305	+	0.235398i
$838$	−7.58939	−	17.9767i	−0.262171	−	0.620995i
$839$	−28.2388	+	23.6951i	−0.974911	+	0.818047i	−0.983314	−	0.181917i	$-0.941770\pi$
$839$	−28.2388	+	23.6951i	−0.974911	+	0.818047i	0.00840301	+	0.999965i	$0.497325\pi$
$840$	−0.139946	−	0.139209i	−0.00482861	−	0.00480318i
$841$	−1.12364	+	6.37246i	−0.0387461	+	0.219740i
$842$	−35.1844	−	37.8782i	−1.21253	−	1.30537i
$843$	7.60159	−	31.6288i	0.261813	−	1.08935i
$844$	13.5683	−	19.9478i	0.467038	−	0.686630i
$845$	10.3610	−	5.98194i	0.356430	−	0.205785i
$846$	33.5143	+	2.42562i	1.15224	+	0.0833946i
$847$	−0.0510619	+	0.0884417i	−0.00175451	+	0.00303889i
$848$	−8.55911	−	2.85491i	−0.293921	−	0.0980381i
$849$	−37.1218	−	24.5834i	−1.27402	−	0.843701i
$850$	27.0238	+	8.31958i	0.926909	+	0.285359i
$851$	34.0738	−	40.6075i	1.16803	−	1.39201i
$852$	−0.651393	−	2.99689i	−0.0223164	−	0.102672i
$853$	12.7574	−	35.0506i	0.436804	−	1.20011i	−0.504756	−	0.863262i	$-0.668417\pi$
$853$	12.7574	−	35.0506i	0.436804	−	1.20011i	0.941560	−	0.336846i	$-0.109360\pi$
$854$	0.00155636		0.000194174i	5.32574e−5		6.64448e-6i
$855$	45.7593	+	23.3438i	1.56494	+	0.798340i
$856$	6.08334	+	39.9165i	0.207924	+	1.36432i
$857$	−2.38265	−	13.5127i	−0.0813899	−	0.461585i	−0.998077	−	0.0619803i	$-0.980258\pi$
$857$	−2.38265	−	13.5127i	−0.0813899	−	0.461585i	0.916687	−	0.399605i	$-0.130853\pi$
$858$	1.60606	+	9.72840i	0.0548301	+	0.332122i
$859$	10.4655	+	28.7538i	0.357079	+	0.981067i	0.980038	+	0.198812i	$0.0637083\pi$
$859$	10.4655	+	28.7538i	0.357079	+	0.981067i	−0.622958	+	0.782255i	$0.714069\pi$
$860$	19.2023	+	26.6473i	0.654794	+	0.908667i
$861$	−0.0942669	−	0.0410158i	−0.00321261	−	0.00139782i
$862$	−4.79981	+	9.37498i	−0.163482	+	0.319313i
$863$	−7.80840			−0.265801			−0.132900	−	0.991129i	$-0.542429\pi$
$863$	−7.80840			−0.265801			−0.132900	+	0.991129i	$0.542429\pi$
$864$	−12.9315	+	26.3965i	−0.439937	+	0.898028i
$865$	53.5863			1.82199
$866$	−13.4961	+	26.3606i	−0.458616	+	0.895768i
$867$	−18.6573	+	13.7986i	−0.633634	+	0.468625i
$868$	−0.0953405	−	0.132305i	−0.00323607	−	0.00449074i
$869$	−1.10550	−	3.03735i	−0.0375016	−	0.103035i
$870$	44.4473	−	36.4762i	1.50690	−	1.23666i
$871$	−2.67573	−	15.1748i	−0.0906636	−	0.514179i
$872$	−2.08136	−	13.6571i	−0.0704839	−	0.462487i
$873$	38.0913	+	4.69596i	1.28920	+	0.158934i
$874$	−42.0364	−	5.24453i	−1.42190	−	0.177399i
$875$	0.0762675	−	0.209543i	0.00257831	−	0.00708385i
$876$	−47.9154	−	15.3260i	−1.61891	−	0.517817i
$877$	−22.5373	+	26.8589i	−0.761029	+	0.906959i	−0.997913	−	0.0645787i	$-0.979430\pi$
$877$	−22.5373	+	26.8589i	−0.761029	+	0.906959i	0.236883	+	0.971538i	$0.423874\pi$
$878$	−38.0273	−	11.7071i	−1.28336	−	0.395096i
$879$	−1.54869	+	25.2195i	−0.0522359	+	0.850633i
$880$	−5.01448	+	15.0336i	−0.169038	+	0.506781i
$881$	−17.3596	+	30.0677i	−0.584859	+	1.01301i	0.410034	+	0.912070i	$0.365517\pi$
$881$	−17.3596	+	30.0677i	−0.584859	+	1.01301i	−0.994893	+	0.100936i	$0.967816\pi$
$882$	−3.03231	−	29.5428i	−0.102103	−	0.994759i
$883$	−48.4749	+	27.9870i	−1.63131	+	0.941837i	−0.647620	+	0.761963i	$0.724236\pi$
$883$	−48.4749	+	27.9870i	−1.63131	+	0.941837i	−0.983690	+	0.179874i	$0.942431\pi$
$884$	8.54909	−	12.5687i	0.287537	−	0.422731i
$885$	−32.5121	−	30.8679i	−1.09288	−	1.03761i
$886$	−16.8402	−	18.1295i	−0.565756	−	0.609073i
$887$	5.13500	−	29.1221i	0.172417	−	0.977823i	−0.768667	−	0.639649i	$-0.779080\pi$
$887$	5.13500	−	29.1221i	0.172417	−	0.977823i	0.941084	−	0.338174i	$-0.109809\pi$
$888$	−9.65223	+	36.4069i	−0.323908	+	1.22173i
$889$	0.0114860	−	0.00963792i	0.000385229	−	0.000323245i
$890$	6.30264	+	14.9289i	0.211265	+	0.500416i
$891$	−0.936863	−	8.99840i	−0.0313861	−	0.301458i
$892$	4.95104	−	5.08716i	0.165773	−	0.170331i
$893$	−22.1175	−	26.3586i	−0.740134	−	0.882057i
$894$	−4.45771	+	2.50917i	−0.149088	+	0.0839191i
$895$	0.203252	−	1.15270i	0.00679396	−	0.0385305i
$896$	−0.115660		0.000442194i	−0.00386394		1.47726e-5i
$897$	32.9269	−	34.6807i	1.09940	−	1.15795i
$898$	−4.59767	−	7.11007i	−0.153426	−	0.237266i
$899$	41.1386	−	23.7514i	1.37205	−	0.792154i
$900$	−63.1905	−	1.38012i	−2.10635	−	0.0460040i
$901$	−3.70763	−	2.14060i	−0.123519	−	0.0713138i
$902$	0.415911	+	8.24312i	0.0138483	+	0.274466i
$903$	0.00452220	−	0.0736415i	0.000150489	−	0.00245063i
$904$	11.1046	−	6.07085i	0.369333	−	0.201913i
$905$	−5.70454	−	4.78668i	−0.189625	−	0.159115i
$906$	−19.5859	−	16.8023i	−0.650697	−	0.558219i
$907$	11.8324	−	32.5093i	0.392889	−	1.07945i	−0.572787	−	0.819704i	$-0.694138\pi$
$907$	11.8324	−	32.5093i	0.392889	−	1.07945i	0.965676	−	0.259749i	$-0.0836399\pi$
$908$	−20.9373	+	5.91553i	−0.694829	+	0.196314i
$909$	23.1451	−	9.81113i	0.767673	−	0.325414i
$910$	−0.181967	−	0.137679i	−0.00603216	−	0.00456400i
$911$	−2.10465	−	11.9361i	−0.0697303	−	0.395460i	−0.999619	−	0.0276180i	$-0.991208\pi$
$911$	−2.10465	−	11.9361i	−0.0697303	−	0.395460i	0.929888	−	0.367842i	$-0.119903\pi$
$912$	28.6200	−	9.32114i	0.947702	−	0.308654i
$913$	−14.3560	+	5.22516i	−0.475115	+	0.172928i
$914$	7.67066	+	33.5230i	0.253723	+	1.10884i
$915$	0.595428	−	0.440368i	0.0196843	−	0.0145581i
$916$	−15.6727	−	1.15729i	−0.517842	−	0.0382381i
$917$		−	0.116652i		−	0.00385218i
$918$	−8.52016	+	11.0423i	−0.281207	+	0.364449i
$919$	11.2018			0.369514			0.184757	−	0.982784i	$-0.440850\pi$
$919$	11.2018			0.369514			0.184757	+	0.982784i	$0.440850\pi$
$920$	72.8199	−	24.5991i	2.40080	−	0.811007i
$921$	6.44404	−	14.8104i	0.212338	−	0.488018i
$922$	22.0925	−	5.05516i	0.727577	−	0.166483i
$923$	−1.21254	−	3.33144i	−0.0399114	−	0.109656i
$924$	0.0301027	−	0.0190028i	0.000990307	−	0.000625148i
$925$	−79.7598	+	14.0638i	−2.62249	+	0.462415i
$926$	0.810790	+	0.613453i	0.0266442	+	0.0201593i
$927$	−17.4949	+	11.3491i	−0.574607	+	0.372754i
$928$	3.26295	−	33.5323i	0.107112	−	1.10075i
$929$	33.5582	+	12.2142i	1.10101	+	0.400734i	0.827687	−	0.561189i	$-0.189656\pi$
$929$	33.5582	+	12.2142i	1.10101	+	0.400734i	0.273320	+	0.961923i	$0.411878\pi$
$930$	−75.6822	−	14.1985i	−2.48172	−	0.465588i
$931$	−19.5479	+	23.2962i	−0.640656	+	0.763504i
$932$	−48.1484	+	4.87110i	−1.57715	+	0.159558i
$933$	7.68087	−	11.5984i	0.251460	−	0.379713i
$934$	−1.38898	−	27.5288i	−0.0454488	−	0.900770i
$935$	−3.75984	+	6.51224i	−0.122960	+	0.212973i
$936$	−10.7044	+	32.2486i	−0.349884	+	1.05408i
$937$	−13.9023	−	24.0795i	−0.454169	−	0.786643i	0.544471	−	0.838779i	$-0.316730\pi$
$937$	−13.9023	−	24.0795i	−0.454169	−	0.786643i	−0.998640	+	0.0521363i	$0.983397\pi$
$938$	−0.0467162	+	0.0302087i	−0.00152534	+	0.000986348i
$939$	−13.3825	+	55.6819i	−0.436720	+	1.81711i
$940$	56.9346	+	25.6151i	1.85700	+	0.835471i
$941$	17.4040	+	3.06880i	0.567355	+	0.100040i	0.449965	−	0.893046i	$-0.351436\pi$
$941$	17.4040	+	3.06880i	0.567355	+	0.100040i	0.117390	+	0.993086i	$0.462547\pi$
$942$	−0.595651	+	54.5518i	−0.0194073	+	1.77739i
$943$	30.6650	−	25.7310i	0.998591	−	0.837917i
$944$	−26.2590	+	0.712264i	−0.854657	+	0.0231822i
$945$	0.159104	+	0.136090i	0.00517567	+	0.00442701i
$946$	−5.45708	+	2.30386i	−0.177425	+	0.0749050i
$947$	31.1472	+	37.1197i	1.01215	+	1.20623i	0.978383	+	0.206800i	$0.0663049\pi$
$947$	31.1472	+	37.1197i	1.01215	+	1.20623i	0.0337637	+	0.999430i	$0.489251\pi$
$948$	1.49959	−	11.0373i	0.0487045	−	0.358475i
$949$	−57.2701	−	10.0983i	−1.85907	−	0.327804i
$950$	44.0488	+	47.4214i	1.42913	+	1.53855i
$951$	−12.8131	−	43.2951i	−0.415493	−	1.40394i
$952$	−0.0538100	−	0.0107862i	−0.00174399	−	0.000349582i
$953$	6.84000	+	11.8472i	0.221569	+	0.383770i	0.955285	−	0.295688i	$-0.0955487\pi$
$953$	6.84000	+	11.8472i	0.221569	+	0.383770i	−0.733715	+	0.679457i	$0.762215\pi$
$954$	9.28007	+	2.33781i	0.300453	+	0.0756895i
$955$	47.6310	+	27.4998i	1.54130	+	0.889871i
$956$	54.3221	−	26.2333i	1.75690	−	0.848445i
$957$	4.62460	+	9.28120i	0.149492	+	0.300018i
$958$	−13.1973	−	4.06292i	−0.426384	−	0.131267i
$959$	0.0334435	+	0.0280625i	0.00107995	+	0.000906184i
$960$	−39.4065	+	37.8114i	−1.27184	+	1.22036i
$961$	−30.6492	−	11.1554i	−0.988684	−	0.359852i
$962$	−5.39028	+	43.2046i	−0.173789	+	1.39297i
$963$	−9.61347	−	41.7337i	−0.309790	−	1.34485i
$964$	4.85294	+	1.23007i	0.156303	+	0.0396178i
$965$	37.0002	−	6.52413i	1.19108	−	0.210019i
$966$	−0.161589	−	0.0608198i	−0.00519905	−	0.00195685i
$967$	28.0120	−	10.1955i	0.900806	−	0.327867i	0.150230	−	0.988651i	$-0.451999\pi$
$967$	28.0120	−	10.1955i	0.900806	−	0.327867i	0.750576	+	0.660785i	$0.229776\pi$
$968$	24.1335	+	14.6934i	0.775681	+	0.472265i
$969$	14.1907	−	1.61330i	0.455870	−	0.0518268i
$970$	63.4731	+	32.4970i	2.03800	+	1.04342i
$971$		−	31.5563i		−	1.01269i	−0.862331	−	0.506345i	$-0.830996\pi$
$971$		−	31.5563i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$972$	11.5747	−	28.9487i	0.371258	−	0.928530i
$973$			0.0108888i			0.000349078i
$974$	26.2435	−	51.2589i	0.840897	−	1.64244i
$975$	−72.5968	+	8.25336i	−2.32496	+	0.264319i
$976$	0.0637373	−	0.429230i	0.00204018	−	0.0137393i
$977$	26.2819	−	9.56585i	0.840834	−	0.306039i	0.114536	−	0.993419i	$-0.463462\pi$
$977$	26.2819	−	9.56585i	0.840834	−	0.306039i	0.726297	+	0.687381i	$0.241240\pi$
$978$	−7.46000	+	19.8201i	−0.238545	+	0.633778i
$979$	−2.87804	+	0.507477i	−0.0919827	+	0.0162190i
$980$	13.5572	−	53.4867i	0.433069	−	1.70857i
$981$	3.28917	+	14.2788i	0.105015	+	0.455888i
$982$	−17.5457	−	2.18902i	−0.559905	−	0.0698546i
$983$	23.5384	+	8.56727i	0.750758	+	0.273253i	0.688925	−	0.724833i	$-0.258083\pi$
$983$	23.5384	+	8.56727i	0.750758	+	0.273253i	0.0618331	+	0.998087i	$0.480305\pi$
$984$	−11.9523	+	25.8095i	−0.381025	+	0.822776i
$985$	−26.5326	−	22.2635i	−0.845398	−	0.709373i
$986$	4.70362	−	15.2784i	0.149794	−	0.486563i
$987$	−0.0625439	−	0.125521i	−0.00199079	−	0.00399536i
$988$	31.3323	−	15.1310i	0.996813	−	0.481382i
$989$	24.8801	+	14.3645i	0.791141	+	0.456766i
$990$	4.10623	−	16.2999i	0.130505	−	0.518044i
$991$	11.3147	+	19.5976i	0.359422	+	0.622537i	0.987864	−	0.155319i	$-0.0496405\pi$
$991$	11.3147	+	19.5976i	0.359422	+	0.622537i	−0.628442	+	0.777856i	$0.716307\pi$
$992$	−37.2095	+	25.5181i	−1.18140	+	0.810201i
$993$	−1.36383	−	4.60836i	−0.0432799	−	0.146242i
$994$	−0.00937813	+	0.00871117i	−0.000297456	+	0.000276302i
$995$	36.5628	+	6.44700i	1.15912	+	0.204384i
$996$	−52.1679	−	7.08782i	−1.65300	−	0.224586i
$997$	−6.16806	−	7.35081i	−0.195344	−	0.232802i	0.659477	−	0.751725i	$-0.270778\pi$
$997$	−6.16806	−	7.35081i	−0.195344	−	0.232802i	−0.854821	+	0.518922i	$0.826333\pi$
$998$	2.51744	+	5.96297i	0.0796881	+	0.188754i
$999$	7.30904	−	39.2751i	0.231248	−	1.24261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.157.13	yes	204
3.2	odd	2		648.2.t.a.37.22		204
4.3	odd	2		864.2.bf.a.49.16		204
8.3	odd	2		864.2.bf.a.49.19		204
8.5	even	2	inner	216.2.t.a.157.4	✓	204
24.5	odd	2		648.2.t.a.37.31		204
27.11	odd	18		648.2.t.a.613.31		204
27.16	even	9	inner	216.2.t.a.205.4	yes	204
108.43	odd	18		864.2.bf.a.529.19		204
216.43	odd	18		864.2.bf.a.529.16		204
216.173	odd	18		648.2.t.a.613.22		204
216.205	even	18	inner	216.2.t.a.205.13	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.4	✓	204	8.5	even	2	inner
216.2.t.a.157.13	yes	204	1.1	even	1	trivial
216.2.t.a.205.4	yes	204	27.16	even	9	inner
216.2.t.a.205.13	yes	204	216.205	even	18	inner
648.2.t.a.37.22		204	3.2	odd	2
648.2.t.a.37.31		204	24.5	odd	2
648.2.t.a.613.22		204	216.173	odd	18
648.2.t.a.613.31		204	27.11	odd	18
864.2.bf.a.49.16		204	4.3	odd	2
864.2.bf.a.49.19		204	8.3	odd	2
864.2.bf.a.529.16		204	216.43	odd	18
864.2.bf.a.529.19		204	108.43	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.644492 + 1.25882i) q^{2} +(0.195652 + 1.72096i) q^{3} +(-1.16926 - 1.62260i) q^{4} +(1.34802 + 3.70366i) q^{5} +(-2.29248 - 0.862856i) q^{6} +(0.00177522 + 0.0100678i) q^{7} +(2.79614 - 0.426137i) q^{8} +(-2.92344 + 0.673422i) q^{9} +(-5.53104 - 0.690061i) q^{10} +(0.343808 - 0.944604i) q^{11} +(2.56367 - 2.32972i) q^{12} +(2.57400 - 3.06757i) q^{13} +(-0.0138176 - 0.00425391i) q^{14} +(-6.11013 + 3.04453i) q^{15} +(-1.26566 + 3.79448i) q^{16} +(-0.948987 + 1.64369i) q^{17} +(1.03642 - 4.11410i) q^{18} +(-3.76245 + 2.17225i) q^{19} +(4.43337 - 6.51785i) q^{20} +(-0.0169790 + 0.00502488i) q^{21} +(0.967506 + 1.04158i) q^{22} +(1.19728 - 6.79010i) q^{23} +(1.28044 + 4.72869i) q^{24} +(-8.06972 + 6.77130i) q^{25} +(2.20260 + 5.21723i) q^{26} +(-1.73091 - 4.89938i) q^{27} +(0.0142603 - 0.0146523i) q^{28} +(3.82827 + 4.56236i) q^{29} +(0.105409 - 9.65373i) q^{30} +(1.38501 - 7.85480i) q^{31} +(-3.96087 - 4.03875i) q^{32} +(1.69290 + 0.406867i) q^{33} +(-1.45750 - 2.25395i) q^{34} +(-0.0348946 + 0.0201464i) q^{35} +(4.51096 + 3.95617i) q^{36} +(6.65823 + 3.84413i) q^{37} +(-0.309608 - 6.13625i) q^{38} +(5.78279 + 3.82958i) q^{39} +(5.34753 + 9.78152i) q^{40} +(4.44753 + 3.73192i) q^{41} +(0.00461738 - 0.0246120i) q^{42} +(-1.42511 + 3.91546i) q^{43} +(-1.93471 + 0.546626i) q^{44} +(-6.43499 - 9.91964i) q^{45} +(7.77588 + 5.88332i) q^{46} +(1.37530 + 7.79973i) q^{47} +(-6.77780 - 1.43576i) q^{48} +(6.57775 - 2.39411i) q^{49} +(-3.32298 - 14.5224i) q^{50} +(-3.01441 - 1.31158i) q^{51} +(-7.98712 - 0.589779i) q^{52} +2.25567i q^{53} +(7.28300 + 0.978700i) q^{54} +3.96195 q^{55} +(0.00925402 + 0.0273944i) q^{56} +(-4.47450 - 6.05004i) q^{57} +(-8.21048 + 1.87871i) q^{58} +(2.24610 + 6.17111i) q^{59} +(12.0844 + 6.35444i) q^{60} +(-0.106836 + 0.0188381i) q^{61} +(8.99516 + 6.80584i) q^{62} +(-0.0119696 - 0.0282371i) q^{63} +(7.63681 - 2.38308i) q^{64} +(14.8311 + 5.39806i) q^{65} +(-1.60323 + 1.86883i) q^{66} +(2.47342 - 2.94771i) q^{67} +(3.77667 - 0.382080i) q^{68} +(11.9198 + 0.731973i) q^{69} +(-0.00287143 - 0.0569102i) q^{70} +(0.442665 - 0.766718i) q^{71} +(-7.88738 + 3.12877i) q^{72} +(-7.26116 - 12.5767i) q^{73} +(-9.13025 + 5.90401i) q^{74} +(-13.2320 - 12.5629i) q^{75} +(7.92398 + 3.56502i) q^{76} +(0.0101204 + 0.00178450i) q^{77} +(-8.54772 + 4.81137i) q^{78} +(2.46319 - 2.06686i) q^{79} +(-15.7596 + 0.427473i) q^{80} +(8.09301 - 3.93742i) q^{81} +(-7.56422 + 3.19345i) q^{82} +(-9.76904 - 11.6423i) q^{83} +(0.0280062 + 0.0216747i) q^{84} +(-7.36694 - 1.29899i) q^{85} +(-4.01039 - 4.31744i) q^{86} +(-7.10265 + 7.48096i) q^{87} +(0.558804 - 2.78776i) q^{88} +(-1.45362 - 2.51775i) q^{89} +(16.6344 - 1.70737i) q^{90} +(0.0354530 + 0.0204688i) q^{91} +(-12.4175 + 5.99669i) q^{92} +(13.7888 + 0.846748i) q^{93} +(-10.7048 - 3.29560i) q^{94} +(-13.1172 - 11.0066i) q^{95} +(6.17560 - 7.60671i) q^{96} +(-12.0217 - 4.37554i) q^{97} +(-1.22556 + 9.82319i) q^{98} +(-0.368984 + 2.99302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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