LMFDB - Embedded newform 216.2.t.a.133.5

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			133.5
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32716 + 0.488522i) q^{2} +(0.526029 - 1.65024i) q^{3} +(1.52269 - 1.29669i) q^{4} +(-0.114718 - 0.136716i) q^{5} +(0.108055 + 2.44711i) q^{6} +(2.42085 - 0.881117i) q^{7} +(-1.38739 + 2.46478i) q^{8} +(-2.44659 - 1.73615i) q^{9} +(0.219037 + 0.125401i) q^{10} +(0.599296 - 0.714213i) q^{11} +(-1.33887 - 3.19491i) q^{12} +(0.368417 - 0.0649618i) q^{13} +(-2.78240 + 2.35202i) q^{14} +(-0.285959 + 0.117396i) q^{15} +(0.637188 - 3.94892i) q^{16} +(-2.26254 - 3.91883i) q^{17} +(4.09515 + 1.10893i) q^{18} +(-1.97566 - 1.14065i) q^{19} +(-0.351958 - 0.0594221i) q^{20} +(-0.180617 - 4.45848i) q^{21} +(-0.446451 + 1.24064i) q^{22} +(4.40423 + 1.60301i) q^{23} +(3.33767 + 3.58608i) q^{24} +(0.862710 - 4.89267i) q^{25} +(-0.457212 + 0.266194i) q^{26} +(-4.15204 + 3.12419i) q^{27} +(2.54367 - 4.48076i) q^{28} +(1.58682 + 0.279799i) q^{29} +(0.322162 - 0.295500i) q^{30} +(8.17965 + 2.97715i) q^{31} +(1.08349 + 5.55212i) q^{32} +(-0.863376 - 1.36468i) q^{33} +(4.91718 + 4.09561i) q^{34} +(-0.398177 - 0.229888i) q^{35} +(-5.97665 + 0.528842i) q^{36} +(-3.82721 + 2.20964i) q^{37} +(3.17924 + 0.548665i) q^{38} +(0.0865954 - 0.642148i) q^{39} +(0.496133 - 0.0930767i) q^{40} +(0.238139 + 1.35055i) q^{41} +(2.41777 + 5.82886i) q^{42} +(-3.28437 + 3.91416i) q^{43} +(-0.0135696 - 1.86463i) q^{44} +(0.0433088 + 0.533654i) q^{45} +(-6.62821 + 0.0241177i) q^{46} +(-7.70413 + 2.80407i) q^{47} +(-6.18149 - 3.12876i) q^{48} +(-0.278168 + 0.233411i) q^{49} +(1.24522 + 6.91480i) q^{50} +(-7.65718 + 1.67231i) q^{51} +(0.476750 - 0.576640i) q^{52} -9.07829i q^{53} +(3.98418 - 6.17465i) q^{54} -0.166394 q^{55} +(-1.18691 + 7.18932i) q^{56} +(-2.92159 + 2.66029i) q^{57} +(-2.24265 + 0.403859i) q^{58} +(9.44865 + 11.2605i) q^{59} +(-0.283201 + 0.549558i) q^{60} +(5.07860 + 13.9533i) q^{61} +(-12.3101 + 0.0447920i) q^{62} +(-7.45257 - 2.04723i) q^{63} +(-4.15029 - 6.83923i) q^{64} +(-0.0511453 - 0.0429160i) q^{65} +(1.81251 + 1.38937i) q^{66} +(1.72274 - 0.303765i) q^{67} +(-8.52666 - 3.03337i) q^{68} +(4.96210 - 6.42480i) q^{69} +(0.640749 + 0.110579i) q^{70} +(2.77372 + 4.80422i) q^{71} +(7.67360 - 3.62158i) q^{72} +(-4.77001 + 8.26190i) q^{73} +(3.99985 - 4.80222i) q^{74} +(-7.62027 - 3.99737i) q^{75} +(-4.48738 + 0.824961i) q^{76} +(0.821500 - 2.25705i) q^{77} +(0.198778 + 0.894535i) q^{78} +(-0.704340 + 3.99451i) q^{79} +(-0.612976 + 0.365899i) q^{80} +(2.97157 + 8.49528i) q^{81} +(-0.975822 - 1.67606i) q^{82} +(15.0319 + 2.65052i) q^{83} +(-6.05629 - 6.55469i) q^{84} +(-0.276212 + 0.758885i) q^{85} +(2.44672 - 6.79919i) q^{86} +(1.29645 - 2.47145i) q^{87} +(0.928921 + 2.46803i) q^{88} +(8.16359 - 14.1397i) q^{89} +(-0.318179 - 0.687086i) q^{90} +(0.834643 - 0.481881i) q^{91} +(8.78489 - 3.27003i) q^{92} +(9.21575 - 11.9323i) q^{93} +(8.85474 - 7.48508i) q^{94} +(0.0706993 + 0.400955i) q^{95} +(9.73228 + 1.13257i) q^{96} +(-8.94677 - 7.50723i) q^{97} +(0.255147 - 0.445664i) q^{98} +(-2.70621 + 0.706917i) 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−1.32716	+	0.488522i	−0.938442	+	0.345437i
$2$	−1.32716	+	0.488522i	−0.938442	+	0.345437i
$3$	0.526029	−	1.65024i	0.303703	−	0.952767i
$3$	0.526029	−	1.65024i	0.303703	−	0.952767i
$4$	1.52269	−	1.29669i	0.761346	−	0.648345i
$5$	−0.114718	−	0.136716i	−0.0513035	−	0.0611411i	0.739782	−	0.672846i	$-0.234928\pi$
$5$	−0.114718	−	0.136716i	−0.0513035	−	0.0611411i	−0.791086	+	0.611705i	$0.790484\pi$
$6$	0.108055	+	2.44711i	0.0441131	+	0.999027i
$7$	2.42085	−	0.881117i	0.914995	−	0.333031i	0.158749	−	0.987319i	$-0.449254\pi$
$7$	2.42085	−	0.881117i	0.914995	−	0.333031i	0.756245	+	0.654288i	$0.227032\pi$
$8$	−1.38739	+	2.46478i	−0.490517	+	0.871432i
$9$	−2.44659	−	1.73615i	−0.815529	−	0.578717i
$10$	0.219037	+	0.125401i	0.0692657	+	0.0396552i
$11$	0.599296	−	0.714213i	0.180695	−	0.215343i	−0.668093	−	0.744078i	$-0.732889\pi$
$11$	0.599296	−	0.714213i	0.180695	−	0.215343i	0.848787	+	0.528735i	$0.177333\pi$
$12$	−1.33887	−	3.19491i	−0.386498	−	0.922290i
$13$	0.368417	−	0.0649618i	0.102180	−	0.0180172i	−0.122324	−	0.992490i	$-0.539035\pi$
$13$	0.368417	−	0.0649618i	0.102180	−	0.0180172i	0.224505	+	0.974473i	$0.427924\pi$
$14$	−2.78240	+	2.35202i	−0.743628	+	0.628603i
$15$	−0.285959	+	0.117396i	−0.0738342	+	0.0303115i
$16$	0.637188	−	3.94892i	0.159297	−	0.987231i
$17$	−2.26254	−	3.91883i	−0.548746	−	0.950456i	−0.998361	−	0.0572337i	$-0.981772\pi$
$17$	−2.26254	−	3.91883i	−0.548746	−	0.950456i	0.449615	−	0.893223i	$-0.351561\pi$
$18$	4.09515	+	1.10893i	0.965237	+	0.261378i
$19$	−1.97566	−	1.14065i	−0.453246	−	0.261682i	0.255954	−	0.966689i	$-0.417610\pi$
$19$	−1.97566	−	1.14065i	−0.453246	−	0.261682i	−0.709200	+	0.705007i	$0.750944\pi$
$20$	−0.351958	−	0.0594221i	−0.0787002	−	0.0132872i
$21$	−0.180617	−	4.45848i	−0.0394139	−	0.972919i
$22$	−0.446451	+	1.24064i	−0.0951837	+	0.264506i
$23$	4.40423	+	1.60301i	0.918345	+	0.334250i	0.757580	−	0.652742i	$-0.226382\pi$
$23$	4.40423	+	1.60301i	0.918345	+	0.334250i	0.160765	+	0.986993i	$0.448604\pi$
$24$	3.33767	+	3.58608i	0.681299	+	0.732005i
$25$	0.862710	−	4.89267i	0.172542	−	0.978534i
$26$	−0.457212	+	0.266194i	−0.0896666	+	0.0522050i
$27$	−4.15204	+	3.12419i	−0.799061	+	0.601251i
$28$	2.54367	−	4.48076i	0.480709	−	0.846785i
$29$	1.58682	+	0.279799i	0.294665	+	0.0519574i	0.319026	−	0.947746i	$-0.396644\pi$
$29$	1.58682	+	0.279799i	0.294665	+	0.0519574i	−0.0243613	+	0.999703i	$0.507755\pi$
$30$	0.322162	−	0.295500i	0.0588184	−	0.0539506i
$31$	8.17965	+	2.97715i	1.46911	+	0.534712i	0.947858	−	0.318692i	$-0.103244\pi$
$31$	8.17965	+	2.97715i	1.46911	+	0.534712i	0.521250	+	0.853404i	$0.325466\pi$
$32$	1.08349	+	5.55212i	0.191535	+	0.981486i
$33$	−0.863376	−	1.36468i	−0.150294	−	0.237560i
$34$	4.91718	+	4.09561i	0.843289	+	0.702391i
$35$	−0.398177	−	0.229888i	−0.0673043	−	0.0388581i
$36$	−5.97665	+	0.528842i	−0.996108	+	0.0881404i
$37$	−3.82721	+	2.20964i	−0.629190	+	0.363263i	−0.780438	−	0.625233i	$-0.785004\pi$
$37$	−3.82721	+	2.20964i	−0.629190	+	0.363263i	0.151248	+	0.988496i	$0.451671\pi$
$38$	3.17924	+	0.548665i	0.515740	+	0.0890052i
$39$	0.0865954	−	0.642148i	0.0138664	−	0.102826i
$40$	0.496133	−	0.0930767i	0.0784455	−	0.0147167i
$41$	0.238139	+	1.35055i	0.0371910	+	0.210921i	0.997740	−	0.0671892i	$-0.0214031\pi$
$41$	0.238139	+	1.35055i	0.0371910	+	0.210921i	−0.960549	+	0.278110i	$0.910292\pi$
$42$	2.41777	+	5.82886i	0.373070	+	0.899413i
$43$	−3.28437	+	3.91416i	−0.500862	+	0.596904i	−0.955945	−	0.293545i	$-0.905165\pi$
$43$	−3.28437	+	3.91416i	−0.500862	+	0.596904i	0.455083	+	0.890449i	$0.349609\pi$
$44$	−0.0135696	−	1.86463i	−0.00204570	−	0.281103i
$45$	0.0433088	+	0.533654i	0.00645609	+	0.0795525i
$46$	−6.62821	+	0.0241177i	−0.977276	+	0.00355596i
$47$	−7.70413	+	2.80407i	−1.12376	+	0.409016i	−0.836024	−	0.548693i	$-0.815126\pi$
$47$	−7.70413	+	2.80407i	−1.12376	+	0.409016i	−0.287738	+	0.957709i	$0.592903\pi$
$48$	−6.18149	−	3.12876i	−0.892222	−	0.451598i
$49$	−0.278168	+	0.233411i	−0.0397383	+	0.0333444i
$50$	1.24522	+	6.91480i	0.176101	+	0.977900i
$51$	−7.65718	+	1.67231i	−1.07222	+	0.234171i
$52$	0.476750	−	0.576640i	0.0661134	−	0.0799655i
$53$		−	9.07829i		−	1.24700i	−0.781824	−	0.623500i	$-0.785710\pi$
$53$		−	9.07829i		−	1.24700i	0.781824	−	0.623500i	$-0.214290\pi$
$54$	3.98418	−	6.17465i	0.542178	−	0.840264i
$55$	−0.166394			−0.0224366
$56$	−1.18691	+	7.18932i	−0.158607	+	0.960713i
$57$	−2.92159	+	2.66029i	−0.386974	+	0.352364i
$58$	−2.24265	+	0.403859i	−0.294474	+	0.0530292i
$59$	9.44865	+	11.2605i	1.23011	+	1.46599i	0.837641	+	0.546222i	$0.183934\pi$
$59$	9.44865	+	11.2605i	1.23011	+	1.46599i	0.392469	+	0.919765i	$0.371621\pi$
$60$	−0.283201	+	0.549558i	−0.0365611	+	0.0709476i
$61$	5.07860	+	13.9533i	0.650247	+	1.78654i	0.616827	+	0.787099i	$0.288418\pi$
$61$	5.07860	+	13.9533i	0.650247	+	1.78654i	0.0334206	+	0.999441i	$0.489360\pi$
$62$	−12.3101	+	0.0447920i	−1.56338	+	0.00568859i
$63$	−7.45257	−	2.04723i	−0.938935	−	0.257926i
$64$	−4.15029	−	6.83923i	−0.518786	−	0.854904i
$65$	−0.0511453	−	0.0429160i	−0.00634380	−	0.00532308i
$66$	1.81251	+	1.38937i	0.223105	+	0.171019i
$67$	1.72274	−	0.303765i	0.210466	−	0.0371108i	−0.0674209	−	0.997725i	$-0.521477\pi$
$67$	1.72274	−	0.303765i	0.210466	−	0.0371108i	0.277887	+	0.960614i	$0.410366\pi$
$68$	−8.52666	−	3.03337i	−1.03401	−	0.367850i
$69$	4.96210	−	6.42480i	0.597367	−	0.773456i
$70$	0.640749	+	0.110579i	0.0765842	+	0.0132167i
$71$	2.77372	+	4.80422i	0.329180	+	0.570156i	0.982349	−	0.187055i	$-0.0598944\pi$
$71$	2.77372	+	4.80422i	0.329180	+	0.570156i	−0.653169	+	0.757212i	$0.726561\pi$
$72$	7.67360	−	3.62158i	0.904343	−	0.426807i
$73$	−4.77001	+	8.26190i	−0.558287	+	0.966982i	0.439352	+	0.898315i	$0.355208\pi$
$73$	−4.77001	+	8.26190i	−0.558287	+	0.966982i	−0.997640	+	0.0686670i	$0.978125\pi$
$74$	3.99985	−	4.80222i	0.464974	−	0.558247i
$75$	−7.62027	−	3.99737i	−0.879913	−	0.461576i
$76$	−4.48738	+	0.824961i	−0.514738	+	0.0946295i
$77$	0.821500	−	2.25705i	0.0936186	−	0.257215i
$78$	0.198778	+	0.894535i	0.0225071	+	0.101286i
$79$	−0.704340	+	3.99451i	−0.0792444	+	0.449417i	0.919206	+	0.393776i	$0.128831\pi$
$79$	−0.704340	+	3.99451i	−0.0792444	+	0.449417i	−0.998451	+	0.0556413i	$0.982280\pi$
$80$	−0.612976	+	0.365899i	−0.0685328	+	0.0409088i
$81$	2.97157	+	8.49528i	0.330174	+	0.943920i
$82$	−0.975822	−	1.67606i	−0.107761	−	0.185090i
$83$	15.0319	+	2.65052i	1.64996	+	0.290933i	0.919813	−	0.392357i	$-0.128340\pi$
$83$	15.0319	+	2.65052i	1.64996	+	0.290933i	0.730148	+	0.683289i	$0.239451\pi$
$84$	−6.05629	−	6.55469i	−0.660795	−	0.715175i
$85$	−0.276212	+	0.758885i	−0.0299594	+	0.0823126i
$86$	2.44672	−	6.79919i	0.263837	−	0.733176i
$87$	1.29645	−	2.47145i	0.138994	−	0.264967i
$88$	0.928921	+	2.46803i	0.0990233	+	0.263092i
$89$	8.16359	−	14.1397i	0.865339	−	1.49881i	−0.00137211	−	0.999999i	$-0.500437\pi$
$89$	8.16359	−	14.1397i	0.865339	−	1.49881i	0.866711	−	0.498811i	$-0.166230\pi$
$90$	−0.318179	−	0.687086i	−0.0335390	−	0.0724252i
$91$	0.834643	−	0.481881i	0.0874943	−	0.0505149i
$92$	8.78489	−	3.27003i	0.915888	−	0.340924i
$93$	9.21575	−	11.9323i	0.955628	−	1.23732i
$94$	8.85474	−	7.48508i	0.913296	−	0.772027i
$95$	0.0706993	+	0.400955i	0.00725359	+	0.0411372i
$96$	9.73228	+	1.13257i	0.993297	+	0.115592i
$97$	−8.94677	−	7.50723i	−0.908407	−	0.762244i	0.0634084	−	0.997988i	$-0.479803\pi$
$97$	−8.94677	−	7.50723i	−0.908407	−	0.762244i	−0.971815	+	0.235744i	$0.924247\pi$
$98$	0.255147	−	0.445664i	0.0257737	−	0.0450189i
$99$	−2.70621	+	0.706917i	−0.271984	+	0.0710478i
$100$	−5.03064	−	8.56870i	−0.503064	−	0.856870i
$101$	−0.733566	−	2.01546i	−0.0729926	−	0.200545i	0.897831	−	0.440340i	$-0.145142\pi$
$101$	−0.733566	−	2.01546i	−0.0729926	−	0.200545i	−0.970824	+	0.239795i	$0.922920\pi$
$102$	9.34532	−	5.96012i	0.925324	−	0.590140i
$103$	8.97851	−	7.53386i	0.884679	−	0.742334i	−0.0824568	−	0.996595i	$-0.526277\pi$
$103$	8.97851	−	7.53386i	0.884679	−	0.742334i	0.967136	+	0.254261i	$0.0818322\pi$
$104$	−0.351022	+	0.998194i	−0.0344205	+	0.0978810i
$105$	−0.588823	+	0.536161i	−0.0574633	+	0.0523239i
$106$	4.43494	+	12.0483i	0.430760	+	1.17024i
$107$		−	7.40373i		−	0.715745i	−0.933770	−	0.357873i	$-0.883502\pi$
$107$		−	7.40373i		−	0.715745i	0.933770	−	0.357873i	$-0.116498\pi$
$108$	−2.27118	+	10.1411i	−0.218544	+	0.975827i
$109$			13.2321i			1.26741i	0.773575	+	0.633704i	$0.218466\pi$
$109$			13.2321i			1.26741i	−0.773575	+	0.633704i	$0.781534\pi$
$110$	0.220831	−	0.0812872i	0.0210554	−	0.00775043i
$111$	1.63321	+	7.47816i	0.155018	+	0.709795i
$112$	−1.93693	−	10.1212i	−0.183023	−	0.956362i
$113$	−7.02588	+	5.89541i	−0.660939	+	0.554594i	−0.910368	−	0.413799i	$-0.864201\pi$
$113$	−7.02588	+	5.89541i	−0.660939	+	0.554594i	0.249429	+	0.968393i	$0.419757\pi$
$114$	2.57780	−	4.95789i	0.241433	−	0.464349i
$115$	−0.286088	−	0.786020i	−0.0266778	−	0.0732968i
$116$	2.77905	−	1.63157i	0.258029	−	0.151487i
$117$	−1.01415	−	0.480692i	−0.0937579	−	0.0444400i
$118$	−18.0408	−	10.3285i	−1.66079	−	0.950818i
$119$	−8.93021	−	7.49334i	−0.818631	−	0.686913i
$120$	0.107381	−	0.867699i	0.00980254	−	0.0792098i
$121$	1.75919	+	9.97684i	0.159926	+	0.906985i
$122$	−13.5566	−	16.0373i	−1.22736	−	1.45194i
$123$	2.35400	+	0.317444i	0.212253	+	0.0286229i
$124$	16.3155	−	6.07319i	1.46518	−	0.545389i
$125$	−1.54067	+	0.889506i	−0.137802	+	0.0795598i
$126$	10.8908	−	0.923748i	0.970233	−	0.0822940i
$127$	−9.58464	+	16.6011i	−0.850500	+	1.47311i	0.0302583	+	0.999542i	$0.490367\pi$
$127$	−9.58464	+	16.6011i	−0.850500	+	1.47311i	−0.880758	+	0.473567i	$0.842966\pi$
$128$	8.84920	+	7.04923i	0.782166	+	0.623070i
$129$	4.73163	+	7.47896i	0.416597	+	0.658486i
$130$	0.0888433	+	0.0319707i	0.00779208	+	0.00280402i
$131$	0.312406	−	0.858328i	0.0272950	−	0.0749924i	−0.925297	−	0.379244i	$-0.876184\pi$
$131$	0.312406	−	0.858328i	0.0272950	−	0.0749924i	0.952592	+	0.304252i	$0.0984063\pi$
$132$	−3.08422	−	0.958456i	−0.268447	−	0.0834229i
$133$	−5.78780	−	1.02055i	−0.501866	−	0.0884926i
$134$	−2.13795	+	1.24474i	−0.184691	+	0.107529i
$135$	0.903439	+	0.209248i	0.0777557	+	0.0180092i
$136$	12.7981	−	0.139708i	1.09743	−	0.0119799i
$137$	0.995947	−	5.64830i	0.0850895	−	0.482566i	−0.912248	−	0.409639i	$-0.865655\pi$
$137$	0.995947	−	5.64830i	0.0850895	−	0.482566i	0.997337	−	0.0729275i	$-0.0232342\pi$
$138$	−3.44683	+	10.9508i	−0.293414	+	0.932196i
$139$	7.23743	−	19.8847i	0.613871	−	1.68660i	−0.107638	−	0.994190i	$-0.534329\pi$
$139$	7.23743	−	19.8847i	0.613871	−	1.68660i	0.721509	−	0.692406i	$-0.243449\pi$
$140$	−0.904395	+	0.166264i	−0.0764354	+	0.0140519i
$141$	0.574797	+	14.1887i	0.0484067	+	1.19490i
$142$	−6.02813	−	5.02094i	−0.505869	−	0.421348i
$143$	0.174394	−	0.302060i	0.0145836	−	0.0252595i
$144$	−8.41486	+	8.55513i	−0.701238	+	0.712927i
$145$	−0.143784	−	0.249041i	−0.0119406	−	0.0206817i
$146$	2.29443	−	13.2951i	0.189889	−	1.10031i
$147$	0.238859	+	0.581825i	0.0197008	+	0.0479882i
$148$	−2.96245	+	8.32732i	−0.243512	+	0.684501i
$149$	−7.83652	+	1.38179i	−0.641992	+	0.113201i	−0.485161	−	0.874425i	$-0.661239\pi$
$149$	−7.83652	+	1.38179i	−0.641992	+	0.113201i	−0.156831	+	0.987625i	$0.550128\pi$
$150$	12.0661	+	1.58247i	0.985193	+	0.129208i
$151$	−2.04551	−	1.71638i	−0.166461	−	0.139677i	0.555752	−	0.831348i	$-0.312430\pi$
$151$	−2.04551	−	1.71638i	−0.166461	−	0.139677i	−0.722213	+	0.691671i	$0.756875\pi$
$152$	5.55245	−	3.28704i	0.450363	−	0.266614i
$153$	−1.26818	+	13.5159i	−0.102527	+	1.09269i
$154$	0.0123597	+	3.39678i	0.000995972	+	0.273721i
$155$	−0.531330	−	1.45982i	−0.0426775	−	0.117255i
$156$	−0.700809	−	1.09008i	−0.0561096	−	0.0872764i
$157$	−7.93100	−	9.45180i	−0.632963	−	0.754336i	0.350278	−	0.936646i	$-0.386087\pi$
$157$	−7.93100	−	9.45180i	−0.632963	−	0.754336i	−0.983241	+	0.182310i	$0.941643\pi$
$158$	−1.01663	−	5.64543i	−0.0808791	−	0.449126i
$159$	−14.9814	−	4.77545i	−1.18810	−	0.378718i
$160$	0.634766	−	0.785058i	0.0501827	−	0.0620643i
$161$	12.0744			0.951597
$162$	−8.09387	−	9.82290i	−0.635914	−	0.771760i
$163$		−	13.6508i		−	1.06922i	−0.845100	−	0.534608i	$-0.820459\pi$
$163$		−	13.6508i		−	1.06922i	0.845100	−	0.534608i	$-0.179541\pi$
$164$	2.11386	+	1.74768i	0.165065	+	0.136471i
$165$	−0.0875282	+	0.274590i	−0.00681406	+	0.0213768i
$166$	−21.2445	+	3.82573i	−1.64889	+	0.296934i
$167$	−3.21110	+	2.69443i	−0.248482	+	0.208502i	−0.758519	−	0.651651i	$-0.774076\pi$
$167$	−3.21110	+	2.69443i	−0.248482	+	0.208502i	0.510036	+	0.860153i	$0.329632\pi$
$168$	11.2398	+	5.74047i	0.867166	+	0.442887i
$169$	−12.0845	+	4.39840i	−0.929576	+	0.338338i
$170$	−0.00415568	−	1.14210i	−0.000318726	−	0.0875947i
$171$	2.85328	+	6.22072i	0.218196	+	0.475710i
$172$	0.0743667	+	10.2189i	0.00567041	+	0.779182i
$173$	−12.8781	+	15.3475i	−0.979103	+	1.16685i	0.00687524	+	0.999976i	$0.497812\pi$
$173$	−12.8781	+	15.3475i	−0.979103	+	1.16685i	−0.985978	+	0.166873i	$0.946633\pi$
$174$	−0.513235	+	3.91335i	−0.0389082	+	0.296670i
$175$	−2.22253	−	12.6046i	−0.168007	−	0.952816i
$176$	−2.43851	−	2.82166i	−0.183809	−	0.212691i
$177$	23.5527	−	9.66921i	1.77033	−	0.726782i
$178$	−3.92679	+	22.7538i	−0.294325	+	1.70547i
$179$	−6.96829	+	4.02315i	−0.520835	+	0.300704i	−0.737276	−	0.675592i	$-0.763888\pi$
$179$	−6.96829	+	4.02315i	−0.520835	+	0.300704i	0.216441	+	0.976296i	$0.430555\pi$
$180$	0.757930	+	0.756433i	0.0564928	+	0.0563812i
$181$	6.99841	+	4.04053i	0.520188	+	0.300331i	0.737011	−	0.675880i	$-0.236236\pi$
$181$	6.99841	+	4.04053i	0.520188	+	0.300331i	−0.216824	+	0.976211i	$0.569570\pi$
$182$	−0.872293	+	1.04727i	−0.0646586	+	0.0776291i
$183$	25.6978	−	1.04104i	1.89964	−	0.0769562i
$184$	−10.0615	+	8.63146i	−0.741740	+	0.636319i
$185$	0.741143	+	0.269754i	0.0544899	+	0.0198327i
$186$	−6.40155	+	20.3382i	−0.469384	+	1.49127i
$187$	−4.15481	−	0.732605i	−0.303830	−	0.0535734i
$188$	−8.09501	+	14.2596i	−0.590389	+	1.03999i
$189$	−7.29869	+	11.2216i	−0.530901	+	0.816253i
$190$	−0.289705	−	0.497593i	−0.0210174	−	0.0360992i
$191$	2.88972	−	16.3884i	0.209093	−	1.18582i	−0.681776	−	0.731561i	$-0.738792\pi$
$191$	2.88972	−	16.3884i	0.209093	−	1.18582i	0.890868	−	0.454262i	$-0.150097\pi$
$192$	−13.4696	+	3.25134i	−0.972081	+	0.234645i
$193$	−0.775835	−	0.282381i	−0.0558458	−	0.0203262i	0.313946	−	0.949441i	$-0.398349\pi$
$193$	−0.775835	−	0.282381i	−0.0558458	−	0.0203262i	−0.369792	+	0.929115i	$0.620571\pi$
$194$	15.5412	+	5.59258i	1.11579	+	0.401524i
$195$	−0.0977257	+	0.0618270i	−0.00699829	+	0.00442752i
$196$	−0.120903	+	0.716111i	−0.00863594	+	0.0511508i
$197$	−13.0620	−	7.54137i	−0.930632	−	0.537301i	−0.0436205	−	0.999048i	$-0.513889\pi$
$197$	−13.0620	−	7.54137i	−0.930632	−	0.537301i	−0.887011	+	0.461748i	$0.847223\pi$
$198$	3.24622	−	2.26023i	0.230699	−	0.160628i
$199$	−7.77810	−	13.4721i	−0.551375	−	0.955009i	−0.998176	−	0.0603759i	$-0.980770\pi$
$199$	−7.77810	−	13.4721i	−0.551375	−	0.955009i	0.446801	−	0.894633i	$-0.352563\pi$
$200$	10.8624	+	8.91444i	0.768091	+	0.630346i
$201$	0.404925	−	3.00272i	0.0285612	−	0.211796i
$202$	1.95815	+	2.31647i	0.137775	+	0.162986i
$203$	4.08799	−	0.720823i	0.286921	−	0.0505918i
$204$	−9.49106	+	12.4754i	−0.664507	+	0.873453i
$205$	0.157323	−	0.187490i	0.0109879	−	0.0130949i
$206$	−8.23544	+	14.3848i	−0.573790	+	1.00224i
$207$	−7.99226	−	11.5683i	−0.555501	−	0.804052i
$208$	−0.0217786	−	1.49624i	−0.00151008	−	0.103746i
$209$	−1.99867	+	0.727455i	−0.138251	+	0.0503191i
$210$	0.519535	−	0.999223i	0.0358513	−	0.0689529i
$211$	3.55232	+	4.23349i	0.244552	+	0.291445i	0.874332	−	0.485328i	$-0.161300\pi$
$211$	3.55232	+	4.23349i	0.244552	+	0.291445i	−0.629781	+	0.776773i	$0.716855\pi$
$212$	−11.7717	−	13.8235i	−0.808486	−	0.949399i
$213$	9.38718	−	2.05014i	0.643199	−	0.140473i
$214$	3.61688	+	9.82591i	0.247245	+	0.671685i
$215$	0.911903			0.0621913
$216$	−1.93994	−	14.5683i	−0.131996	−	0.991250i
$217$	22.4249			1.52230
$218$	−6.46419	−	17.5611i	−0.437810	−	1.18939i
$219$	11.1249	+	12.2177i	0.751754	+	0.825593i
$220$	−0.253367	+	0.215762i	−0.0170820	+	0.0145466i
$221$	−1.08813	−	1.29679i	−0.0731957	−	0.0872312i
$222$	−5.82077	−	9.12683i	−0.390665	−	0.612553i
$223$	4.91216	−	1.78788i	0.328942	−	0.119725i	−0.172269	−	0.985050i	$-0.555110\pi$
$223$	4.91216	−	1.78788i	0.328942	−	0.119725i	0.501212	+	0.865325i	$0.332888\pi$
$224$	7.51503	+	12.4862i	0.502119	+	0.834267i
$225$	−10.6051	+	10.4725i	−0.707007	+	0.698170i
$226$	6.44441	−	11.2564i	0.428676	−	0.748767i
$227$	−5.65872	+	6.74381i	−0.375583	+	0.447602i	−0.920415	−	0.390943i	$-0.872149\pi$
$227$	−5.65872	+	6.74381i	−0.375583	+	0.447602i	0.544832	+	0.838545i	$0.316593\pi$
$228$	−0.999109	+	7.83921i	−0.0661676	+	0.519164i
$229$	8.50987	−	1.50052i	0.562348	−	0.0991572i	0.114754	−	0.993394i	$-0.463392\pi$
$229$	8.50987	−	1.50052i	0.562348	−	0.0991572i	0.447594	+	0.894237i	$0.352281\pi$
$230$	0.763672	+	0.903413i	0.0503550	+	0.0595693i
$231$	−3.29255	−	2.54295i	−0.216634	−	0.167314i
$232$	−2.89118	+	3.52297i	−0.189816	+	0.231295i
$233$	−0.420645	−	0.728579i	−0.0275574	−	0.0477308i	0.851918	−	0.523676i	$-0.175440\pi$
$233$	−0.420645	−	0.728579i	−0.0275574	−	0.0477308i	−0.879475	+	0.475945i	$0.842106\pi$
$234$	1.58076	+	0.142521i	0.103338	+	0.00931689i
$235$	1.26716	+	0.731597i	0.0826606	+	0.0477241i
$236$	28.9887	+	4.89425i	1.88701	+	0.318589i
$237$	6.22140	+	3.26356i	0.404123	+	0.211991i
$238$	15.5125	+	5.58224i	1.00552	+	0.361843i
$239$	12.9749	+	4.72248i	0.839276	+	0.305472i	0.725660	−	0.688053i	$-0.241534\pi$
$239$	12.9749	+	4.72248i	0.839276	+	0.305472i	0.113616	+	0.993525i	$0.463757\pi$
$240$	0.281378	+	1.20403i	0.0181629	+	0.0777199i
$241$	2.61837	−	14.8495i	0.168664	−	0.956542i	−0.776541	−	0.630066i	$-0.783028\pi$
$241$	2.61837	−	14.8495i	0.168664	−	0.956542i	0.945206	−	0.326476i	$-0.105861\pi$
$242$	−7.20862	−	12.3814i	−0.463387	−	0.795908i
$243$	15.5824	−	0.435036i	0.999611	−	0.0279076i
$244$	25.8263	+	14.6613i	1.65336	+	0.938591i
$245$	0.0638218	+	0.0112535i	0.00407743	+	0.000718960i
$246$	−3.27921	+	0.728684i	−0.209075	+	0.0464592i
$247$	−0.801963	−	0.291891i	−0.0510277	−	0.0185726i
$248$	−18.6864	+	16.0306i	−1.18659	+	1.01794i
$249$	12.2812	−	23.4119i	0.778289	−	1.48367i
$250$	1.61017	−	1.93316i	0.101836	−	0.122264i
$251$	−9.73582	−	5.62098i	−0.614520	−	0.354793i	0.160213	−	0.987083i	$-0.448782\pi$
$251$	−9.73582	−	5.62098i	−0.614520	−	0.354793i	−0.774732	+	0.632289i	$0.782115\pi$
$252$	−14.0026	+	6.54637i	−0.882080	+	0.412383i
$253$	3.78432	−	2.18488i	0.237918	−	0.137362i
$254$	4.61034	−	26.7146i	0.289278	−	1.67622i
$255$	1.10705	+	0.855011i	0.0693260	+	0.0535429i
$256$	−15.1880	−	5.03241i	−0.949249	−	0.314526i
$257$	1.23538	+	7.00619i	0.0770609	+	0.437034i	0.998789	+	0.0491976i	$0.0156664\pi$
$257$	1.23538	+	7.00619i	0.0770609	+	0.437034i	−0.921728	+	0.387837i	$0.873222\pi$
$258$	−9.93326	−	7.61426i	−0.618417	−	0.474043i
$259$	−7.31815	+	8.72143i	−0.454728	+	0.541923i
$260$	−0.133527		0.000971731i	−0.00828102		6.02642e-5i
$261$	−3.39652	−	3.43951i	−0.210239	−	0.212900i
$262$	0.00470023	+	1.29175i	0.000290381	+	0.0798048i
$263$	−18.0450	+	6.56783i	−1.11270	+	0.404990i	−0.831983	−	0.554801i	$-0.812795\pi$
$263$	−18.0450	+	6.56783i	−1.11270	+	0.404990i	−0.280717	+	0.959790i	$0.590572\pi$
$264$	4.56148	−	0.234688i	0.280739	−	0.0144441i
$265$	−1.24114	+	1.04144i	−0.0762429	+	0.0639754i
$266$	8.17989	−	1.47304i	0.501541	−	0.0903181i
$267$	−19.0397	−	20.9098i	−1.16521	−	1.27966i
$268$	2.22931	−	2.69640i	0.136177	−	0.164709i
$269$			16.5198i			1.00723i	0.863928	+	0.503616i	$0.167997\pi$
$269$			16.5198i			1.00723i	−0.863928	+	0.503616i	$0.832003\pi$
$270$	−1.30123	+	0.163645i	−0.0791902	+	0.00995911i
$271$	−1.17854			−0.0715913			−0.0357956	−	0.999359i	$-0.511397\pi$
$271$	−1.17854			−0.0715913			−0.0357956	+	0.999359i	$0.511397\pi$
$272$	−16.9168	+	6.43756i	−1.02573	+	0.390334i
$273$	−0.356173	−	1.63084i	−0.0215566	−	0.0987032i
$274$	1.43754	+	7.98272i	0.0868448	+	0.482254i
$275$	−2.97739	−	3.54832i	−0.179543	−	0.213972i
$276$	−0.775227	−	16.2173i	−0.0466632	−	0.976168i
$277$	−7.87030	−	21.6235i	−0.472880	−	1.29923i	−0.915428	−	0.402483i	$-0.868147\pi$
$277$	−7.87030	−	21.6235i	−0.472880	−	1.29923i	0.442547	−	0.896745i	$-0.354075\pi$
$278$	0.108889	+	29.9257i	0.00653073	+	1.79483i
$279$	−14.8434	−	21.4849i	−0.888654	−	1.28627i
$280$	1.11905	−	0.662476i	0.0668761	−	0.0395905i
$281$	16.4336	+	13.7895i	0.980348	+	0.822610i	0.984142	−	0.177383i	$-0.0567631\pi$
$281$	16.4336	+	13.7895i	0.980348	+	0.822610i	−0.00379366	+	0.999993i	$0.501208\pi$
$282$	−7.69433	−	18.5498i	−0.458191	−	1.10463i
$283$	−0.339199	+	0.0598100i	−0.0201633	+	0.00355534i	−0.183721	−	0.982978i	$-0.558814\pi$
$283$	−0.339199	+	0.0598100i	−0.0201633	+	0.00355534i	0.163557	+	0.986534i	$0.447703\pi$
$284$	10.4531	+	3.71870i	0.620278	+	0.220664i
$285$	0.698863	+	0.0942436i	0.0413971	+	0.00558251i
$286$	−0.0838858	+	0.486076i	−0.00496027	+	0.0287423i
$287$	1.76649	+	3.05966i	0.104273	+	0.180606i
$288$	6.98847	−	15.4648i	0.411800	−	0.911274i
$289$	−1.73816	+	3.01059i	−0.102245	+	0.177093i
$290$	0.312486	+	0.260275i	0.0183498	+	0.0152839i
$291$	−17.0950	+	10.8153i	−1.00213	+	0.634004i
$292$	3.44986	+	18.7656i	0.201888	+	1.09817i
$293$	9.01139	−	24.7586i	0.526451	−	1.44641i	−0.336770	−	0.941587i	$-0.609335\pi$
$293$	9.01139	−	24.7586i	0.526451	−	1.44641i	0.863221	−	0.504826i	$-0.168443\pi$
$294$	−0.601238	−	0.655486i	−0.0350649	−	0.0382287i
$295$	0.455551	−	2.58356i	0.0265232	−	0.150420i
$296$	−0.136442	−	12.4989i	−0.00793051	−	0.726482i
$297$	−0.256964	+	4.83776i	−0.0149106	+	0.280715i
$298$	9.72525	−	5.66216i	0.563369	−	0.328000i
$299$	1.72673	+	0.304468i	0.0998591	+	0.0176079i
$300$	−16.7867	+	3.79437i	−0.969180	+	0.219068i
$301$	−4.50213	+	12.3695i	−0.259499	+	0.712967i
$302$	3.55320	+	1.27864i	0.204464	+	0.0735773i
$303$	−3.71187	+	0.150371i	−0.213241	+	0.00863860i
$304$	−5.76318	+	7.07491i	−0.330541	+	0.405774i
$305$	1.32503	−	2.29502i	0.0758711	−	0.131413i
$306$	−4.91972	−	18.5572i	−0.281242	−	1.06085i
$307$	14.2917	−	8.25134i	0.815673	−	0.470929i	−0.0332493	−	0.999447i	$-0.510586\pi$
$307$	14.2917	−	8.25134i	0.815673	−	0.470929i	0.848922	+	0.528518i	$0.177252\pi$
$308$	−1.67581	−	4.50203i	−0.0954879	−	0.256527i
$309$	−7.70973	−	18.7797i	−0.438591	−	1.06834i
$310$	1.41831	+	1.67784i	0.0805547	+	0.0952950i
$311$	3.58763	+	20.3464i	0.203436	+	1.15374i	0.899882	+	0.436133i	$0.143652\pi$
$311$	3.58763	+	20.3464i	0.203436	+	1.15374i	−0.696447	+	0.717609i	$0.745237\pi$
$312$	1.46261	+	1.10435i	0.0828041	+	0.0625215i
$313$	−9.65918	−	8.10501i	−0.545969	−	0.458122i	0.327604	−	0.944815i	$-0.393759\pi$
$313$	−9.65918	−	8.10501i	−0.545969	−	0.458122i	−0.873573	+	0.486693i	$0.838203\pi$
$314$	15.1431	+	8.66956i	0.854574	+	0.489251i
$315$	0.575056	+	1.25374i	0.0324007	+	0.0706400i
$316$	4.10715	+	6.99572i	0.231045	+	0.393540i
$317$	−4.18467	−	11.4973i	−0.235034	−	0.645752i	−0.999999	−	0.00167879i	$-0.999466\pi$
$317$	−4.18467	−	11.4973i	−0.235034	−	0.645752i	0.764964	−	0.644073i	$-0.222757\pi$
$318$	22.2155	−	0.980952i	1.24579	−	0.0550091i
$319$	1.15081	−	0.965645i	0.0644331	−	0.0540658i
$320$	−0.458917	+	1.35199i	−0.0256542	+	0.0755787i
$321$	−12.2179	−	3.89458i	−0.681938	−	0.217374i
$322$	−16.0246	+	5.89861i	−0.893018	+	0.328717i
$323$			10.3230i			0.574388i
$324$	15.5405	+	9.08250i	0.863363	+	0.504583i
$325$		−	1.85859i		−	0.103096i
$326$	6.66873	+	18.1168i	0.369347	+	1.00340i
$327$	21.8362	+	6.96049i	1.20754	+	0.384916i
$328$	−3.65921	−	1.28678i	−0.202046	−	0.0710508i
$329$	−16.1798	+	13.5765i	−0.892022	+	0.748495i
$330$	−0.0179797	−	0.407184i	−0.000989748	−	0.0224147i
$331$	−6.93586	−	19.0561i	−0.381230	−	1.04742i	−0.970839	−	0.239731i	$-0.922941\pi$
$331$	−6.93586	−	19.0561i	−0.381230	−	1.04742i	0.589610	−	0.807688i	$-0.299282\pi$
$332$	26.3258	−	15.4557i	1.44482	−	0.848244i
$333$	13.1999	+	1.23853i	0.723349	+	0.0678712i
$334$	2.94535	−	5.14463i	0.161162	−	0.281502i
$335$	−0.239159	−	0.200678i	−0.0130666	−	0.0109642i
$336$	−17.7213	−	2.12764i	−0.966774	−	0.116072i
$337$	2.99094	+	16.9625i	0.162927	+	0.924006i	0.951176	+	0.308649i	$0.0998769\pi$
$337$	2.99094	+	16.9625i	0.162927	+	0.924006i	−0.788249	+	0.615357i	$0.789012\pi$
$338$	13.8893	−	11.7409i	0.755479	−	0.638621i
$339$	6.03303	+	14.6955i	0.327669	+	0.798153i
$340$	0.563454	+	1.51371i	0.0305576	+	0.0820924i
$341$	7.02835	−	4.05782i	0.380606	−	0.219743i
$342$	−6.82571	−	6.86198i	−0.369092	−	0.371054i
$343$	−9.48449	+	16.4276i	−0.512114	+	0.887008i
$344$	−5.09084	−	13.5257i	−0.274480	−	0.729258i
$345$	−1.44761	+	0.0586442i	−0.0779369	+	0.00315730i
$346$	9.59366	−	26.6598i	0.515758	−	1.43324i
$347$	−2.18170	+	5.99416i	−0.117120	+	0.321783i	−0.984376	−	0.176078i	$-0.943659\pi$
$347$	−2.18170	+	5.99416i	−0.117120	+	0.321783i	0.867257	+	0.497861i	$0.165881\pi$
$348$	−1.23061	−	5.44436i	−0.0659678	−	0.291848i
$349$	13.1972	+	2.32702i	0.706430	+	0.124563i	0.515310	−	0.857004i	$-0.327677\pi$
$349$	13.1972	+	2.32702i	0.706430	+	0.124563i	0.191120	+	0.981567i	$0.438788\pi$
$350$	9.10725	+	15.6425i	0.486803	+	0.836126i
$351$	−1.32673	+	1.42073i	−0.0708155	+	0.0758329i
$352$	4.61473	+	2.55352i	0.245966	+	0.136103i
$353$	−1.95983	+	11.1147i	−0.104311	+	0.591577i	0.887182	+	0.461419i	$0.152660\pi$
$353$	−1.95983	+	11.1147i	−0.104311	+	0.591577i	−0.991493	+	0.130158i	$0.958452\pi$
$354$	−26.5346	+	24.3386i	−1.41030	+	1.29358i
$355$	0.338617	−	0.930342i	0.0179719	−	0.0493774i
$356$	−5.90424	−	32.1161i	−0.312924	−	1.70215i
$357$	−17.0634	+	10.7953i	−0.903089	+	0.571347i
$358$	7.28263	−	8.74351i	0.384899	−	0.462109i
$359$	−13.5862	+	23.5320i	−0.717053	+	1.24197i	0.245109	+	0.969495i	$0.421176\pi$
$359$	−13.5862	+	23.5320i	−0.717053	+	1.24197i	−0.962162	+	0.272477i	$0.912157\pi$
$360$	−1.37543	−	0.633641i	−0.0724914	−	0.0333958i
$361$	−6.89786	−	11.9474i	−0.363045	−	0.628813i
$362$	−11.2619	−	1.94355i	−0.591911	−	0.102151i
$363$	17.3896	+	2.34503i	0.912715	+	0.123082i
$364$	0.646054	−	1.81603i	0.0338624	−	0.0951858i
$365$	1.67674	−	0.295654i	0.0877644	−	0.0154752i
$366$	−33.5965	+	13.9356i	−1.75612	+	0.728424i
$367$	17.5436	+	14.7209i	0.915771	+	0.768423i	0.973208	−	0.229926i	$-0.0738485\pi$
$367$	17.5436	+	14.7209i	0.915771	+	0.768423i	−0.0574375	+	0.998349i	$0.518293\pi$
$368$	9.13647	−	16.3705i	0.476272	−	0.853373i
$369$	1.76213	−	3.71769i	0.0917330	−	0.193535i
$370$	−1.11539	+	0.00405852i	−0.0579865	+	0.000210992i
$371$	−7.99904	−	21.9772i	−0.415289	−	1.14100i
$372$	−1.43977	−	30.1192i	−0.0746487	−	1.56161i
$373$	−18.2082	−	21.6997i	−0.942786	−	1.12357i	−0.992183	−	0.124790i	$-0.960174\pi$
$373$	−18.2082	−	21.6997i	−0.942786	−	1.12357i	0.0493967	−	0.998779i	$-0.484270\pi$
$374$	5.87198	−	1.05743i	0.303633	−	0.0546786i
$375$	0.657461	+	3.01038i	0.0339511	+	0.155455i
$376$	3.77722	−	22.8793i	0.194795	−	1.17991i
$377$	0.602788			0.0310451
$378$	4.20450	−	18.4584i	0.216256	−	0.949399i
$379$			9.20463i			0.472810i	0.971655	+	0.236405i	$0.0759692\pi$
$379$			9.20463i			0.472810i	−0.971655	+	0.236405i	$0.924031\pi$
$380$	0.627568	+	0.518857i	0.0321936	+	0.0266168i
$381$	22.3540	+	24.5496i	1.14523	+	1.25772i
$382$	4.17098	+	23.1617i	0.213406	+	1.18505i
$383$	18.0654	−	15.1587i	0.923100	−	0.774573i	−0.0514658	−	0.998675i	$-0.516389\pi$
$383$	18.0654	−	15.1587i	0.923100	−	0.774573i	0.974566	+	0.224102i	$0.0719449\pi$
$384$	16.2879	−	10.8952i	0.831187	−	0.555994i
$385$	−0.402815	+	0.146613i	−0.0205294	+	0.00747207i
$386$	1.16760	−	0.00424850i	0.0594295	−	0.000216243i
$387$	14.8311	−	3.87417i	0.753905	−	0.196935i
$388$	−23.3577	+	0.169983i	−1.18581	+	0.00862959i
$389$	−19.3453	+	23.0548i	−0.980844	+	1.16892i	0.00478250	+	0.999989i	$0.498478\pi$
$389$	−19.3453	+	23.0548i	−0.980844	+	1.16892i	−0.985627	+	0.168936i	$0.945967\pi$
$390$	0.0994936	−	0.129795i	0.00503805	−	0.00657244i
$391$	−3.68282	−	20.8863i	−0.186248	−	1.05627i
$392$	−0.189378	−	1.00946i	−0.00956505	−	0.0509852i
$393$	−1.25211	−	0.967050i	−0.0631607	−	0.0487812i
$394$	21.0195	+	3.62750i	1.05895	+	0.182751i
$395$	0.626912	−	0.361948i	0.0315434	−	0.0182116i
$396$	−3.20408	+	4.58553i	−0.161011	+	0.230432i
$397$	15.4854	+	8.94051i	0.777191	+	0.448711i	0.835434	−	0.549591i	$-0.185217\pi$
$397$	15.4854	+	8.94051i	0.777191	+	0.448711i	−0.0582431	+	0.998302i	$0.518550\pi$
$398$	16.9042	+	14.0798i	0.847329	+	0.705756i
$399$	−4.72870	+	9.01443i	−0.236731	+	0.451286i
$400$	−18.7711	−	6.52432i	−0.938554	−	0.326216i
$401$	−9.33220	−	3.39664i	−0.466028	−	0.169620i	0.0983243	−	0.995154i	$-0.468652\pi$
$401$	−9.33220	−	3.39664i	−0.466028	−	0.169620i	−0.564352	+	0.825534i	$0.690874\pi$
$402$	0.929496	+	4.18290i	0.0463590	+	0.208624i
$403$	3.20692	+	0.565467i	0.159748	+	0.0281679i
$404$	−3.73042	−	2.11771i	−0.185595	−	0.105360i
$405$	0.820545	−	1.38082i	0.0407732	−	0.0686136i
$406$	−5.07327	+	2.95372i	−0.251782	+	0.146590i
$407$	−0.715477	+	4.05767i	−0.0354649	+	0.201131i
$408$	6.50162	−	21.1934i	0.321878	−	1.04923i
$409$	−5.20287	−	1.89369i	−0.257265	−	0.0936369i	0.210168	−	0.977665i	$-0.432599\pi$
$409$	−5.20287	−	1.89369i	−0.257265	−	0.0936369i	−0.467433	+	0.884028i	$0.654821\pi$
$410$	−0.117199	+	0.325684i	−0.00578805	+	0.0160844i
$411$	−8.79715	−	4.61472i	−0.433931	−	0.227627i
$412$	3.90242	−	23.1141i	0.192259	−	1.13875i
$413$	32.7955	+	18.9345i	1.61376	+	0.931706i
$414$	16.2584	+	11.4486i	0.799054	+	0.562666i
$415$	−1.36206	−	2.35915i	−0.0668608	−	0.115806i
$416$	0.759851	+	1.97511i	0.0372547	+	0.0968377i
$417$	−29.0074	−	22.4034i	−1.42050	−	1.09710i
$418$	2.29717	−	1.94184i	0.112358	−	0.0949784i
$419$	4.02902	−	0.710424i	0.196830	−	0.0347065i	−0.0743638	−	0.997231i	$-0.523693\pi$
$419$	4.02902	−	0.710424i	0.196830	−	0.0347065i	0.271194	+	0.962525i	$0.412581\pi$
$420$	−0.201362	+	1.57993i	−0.00982548	+	0.0770927i
$421$	15.7920	−	18.8201i	0.769653	−	0.917237i	−0.228764	−	0.973482i	$-0.573468\pi$
$421$	15.7920	−	18.8201i	0.769653	−	0.917237i	0.998417	+	0.0562453i	$0.0179129\pi$
$422$	−6.78263	−	3.88312i	−0.330173	−	0.189027i
$423$	23.7171	+	6.51511i	1.15316	+	0.316776i
$424$	22.3760	+	12.5951i	1.08667	+	0.611674i
$425$	−21.1255	+	7.68904i	−1.02474	+	0.372973i
$426$	−11.4567	+	7.30670i	−0.555080	+	0.354011i
$427$	24.5890	+	29.3041i	1.18995	+	1.41812i
$428$	−9.60034	−	11.2736i	−0.464050	−	0.544930i
$429$	−0.406734	−	0.446684i	−0.0196373	−	0.0215661i
$430$	−1.21024	+	0.445485i	−0.0583629	+	0.0214832i
$431$	14.0058			0.674635			0.337318	−	0.941391i	$-0.390480\pi$
$431$	14.0058			0.674635			0.337318	+	0.941391i	$0.390480\pi$
$432$	9.69156	+	18.3868i	0.466285	+	0.884634i
$433$	12.4899			0.600227			0.300113	−	0.953904i	$-0.402976\pi$
$433$	12.4899			0.600227			0.300113	+	0.953904i	$0.402976\pi$
$434$	−29.7614	+	10.9551i	−1.42859	+	0.525860i
$435$	−0.486612	+	0.106275i	−0.0233313	+	0.00509550i
$436$	17.1580	+	20.1485i	0.821718	+	0.964937i
$437$	−6.87277	−	8.19065i	−0.328769	−	0.391812i
$438$	−20.7332	−	10.7800i	−0.990668	−	0.515087i
$439$	−10.1446	+	3.69232i	−0.484174	+	0.176225i	−0.572562	−	0.819861i	$-0.694050\pi$
$439$	−10.1446	+	3.69232i	−0.484174	+	0.176225i	0.0883886	+	0.996086i	$0.471828\pi$
$440$	0.230854	−	0.410125i	0.0110055	−	0.0195519i
$441$	1.08580	−	0.0881181i	0.0517047	−	0.00419610i
$442$	2.07763	+	1.18946i	0.0988228	+	0.0565769i
$443$	−18.6993	+	22.2849i	−0.888430	+	1.05879i	0.109469	+	0.993990i	$0.465085\pi$
$443$	−18.6993	+	22.2849i	−0.888430	+	1.05879i	−0.997898	+	0.0647991i	$0.979359\pi$
$444$	12.1837	+	9.26916i	0.578215	+	0.439895i
$445$	−2.86963	+	0.505994i	−0.136034	+	0.0239864i
$446$	−5.64579	+	4.77249i	−0.267336	+	0.225984i
$447$	−1.84195	+	13.6590i	−0.0871214	+	0.646048i
$448$	−16.0734	−	12.8999i	−0.759396	−	0.609461i
$449$	−15.0485	−	26.0648i	−0.710184	−	1.23007i	−0.964788	−	0.263029i	$-0.915278\pi$
$449$	−15.0485	−	26.0648i	−0.710184	−	1.23007i	0.254604	−	0.967045i	$-0.418055\pi$
$450$	8.95857	−	19.0795i	0.422311	−	0.899418i
$451$	1.10730	+	0.639299i	0.0521406	+	0.0301034i
$452$	−3.05373	+	18.0873i	−0.143635	+	0.850755i
$453$	−3.90844	+	2.47271i	−0.183635	+	0.116178i
$454$	4.21552	−	11.7145i	0.197844	−	0.549789i
$455$	−0.161629	−	0.0588282i	−0.00757729	−	0.00275791i
$456$	−2.50365	−	10.8920i	−0.117244	−	0.510062i
$457$	2.71160	−	15.3782i	0.126843	−	0.719363i	−0.853353	−	0.521334i	$-0.825435\pi$
$457$	2.71160	−	15.3782i	0.126843	−	0.719363i	0.980196	−	0.198029i	$-0.0634542\pi$
$458$	−10.5609	+	6.14868i	−0.493479	+	0.287309i
$459$	21.6373	+	9.20255i	1.00994	+	0.429538i
$460$	−1.45485	−	0.825900i	−0.0678327	−	0.0385078i
$461$	12.7088	+	2.24090i	0.591908	+	0.104369i	0.461575	−	0.887101i	$-0.347284\pi$
$461$	12.7088	+	2.24090i	0.591908	+	0.104369i	0.130332	+	0.991470i	$0.458396\pi$
$462$	5.61201	+	1.76641i	0.261094	+	0.0821809i
$463$	32.6243	+	11.8743i	1.51618	+	0.551845i	0.960191	−	0.279345i	$-0.0901172\pi$
$463$	32.6243	+	11.8743i	1.51618	+	0.551845i	0.555990	+	0.831189i	$0.312339\pi$
$464$	2.11601	−	6.08795i	0.0982332	−	0.282626i
$465$	−2.68855	+	0.108916i	−0.124678	+	0.00505084i
$466$	0.914189	+	0.761445i	0.0423490	+	0.0352732i
$467$	−12.4213	−	7.17141i	−0.574787	−	0.331853i	0.184272	−	0.982875i	$-0.441007\pi$
$467$	−12.4213	−	7.17141i	−0.574787	−	0.331853i	−0.759059	+	0.651022i	$0.774341\pi$
$468$	−2.16754	+	0.583088i	−0.100195	+	0.0269533i
$469$	3.90284	−	2.25330i	0.180216	−	0.104048i
$470$	−2.03913	−	0.351907i	−0.0940578	−	0.0162323i
$471$	−19.7697	+	8.11613i	−0.910939	+	0.373972i
$472$	−40.8635	+	7.66618i	−1.88090	+	0.352865i
$473$	0.827235	+	4.69148i	0.0380363	+	0.215715i
$474$	−9.85109	−	1.29197i	−0.452476	−	0.0593421i
$475$	−7.28522	+	8.68219i	−0.334269	+	0.398366i
$476$	−23.3145	+	0.169669i	−1.06862	+	0.00777675i
$477$	−15.7613	+	22.2108i	−0.721659	+	1.01696i
$478$	−19.5268	+	0.0710509i	−0.893133	+	0.00324979i
$479$	0.567163	−	0.206430i	0.0259143	−	0.00943204i	−0.329030	−	0.944319i	$-0.606722\pi$
$479$	0.567163	−	0.206430i	0.0259143	−	0.00943204i	0.354945	+	0.934887i	$0.384500\pi$
$480$	−0.961629	−	1.46048i	−0.0438921	−	0.0666615i
$481$	−1.26647	+	1.06269i	−0.0577459	+	0.0484546i
$482$	3.77932	+	20.9868i	0.172144	+	0.955922i
$483$	6.35149	−	19.9257i	0.289003	−	0.906650i
$484$	15.6156	+	12.9105i	0.709798	+	0.586843i
$485$			2.08438i			0.0946467i
$486$	−20.4678	+	8.18970i	−0.928436	+	0.371492i
$487$	−22.8735			−1.03650			−0.518249	−	0.855230i	$-0.673416\pi$
$487$	−22.8735			−1.03650			−0.518249	+	0.855230i	$0.673416\pi$
$488$	−41.4379	−	6.84110i	−1.87581	−	0.309682i
$489$	−22.5272	−	7.18074i	−1.01871	−	0.324724i
$490$	−0.0901992	+	0.0162432i	−0.00407478	+	0.000733792i
$491$	−5.76980	−	6.87618i	−0.260387	−	0.310318i	0.619973	−	0.784623i	$-0.287144\pi$
$491$	−5.76980	−	6.87618i	−0.260387	−	0.310318i	−0.880360	+	0.474306i	$0.842699\pi$
$492$	3.99605	−	2.56904i	0.180156	−	0.115821i
$493$	−2.49376	−	6.85154i	−0.112313	−	0.308578i
$494$	1.20693	−	0.00439157i	0.0543022	−	0.000197586i
$495$	0.407098	+	0.288885i	0.0182977	+	0.0129844i
$496$	16.9685	−	30.4038i	0.761908	−	1.36517i
$497$	10.9478	+	9.18633i	0.491078	+	0.412063i
$498$	−4.86184	+	37.0709i	−0.217864	+	1.66119i
$499$	−43.2976	+	7.63454i	−1.93827	+	0.341769i	−0.999992	−	0.00411738i	$-0.998689\pi$
$499$	−43.2976	+	7.63454i	−1.93827	+	0.341769i	−0.938276	+	0.345886i	$0.887578\pi$
$500$	−1.19255	+	3.35221i	−0.0533325	+	0.149916i
$501$	2.75733	+	6.71644i	0.123188	+	0.300068i
$502$	15.6669	+	2.70376i	0.699250	+	0.120675i
$503$	8.29388	+	14.3654i	0.369806	+	0.640523i	0.989535	−	0.144293i	$-0.0460909\pi$
$503$	8.29388	+	14.3654i	0.369806	+	0.640523i	−0.619729	+	0.784816i	$0.712758\pi$
$504$	15.3856	−	15.5286i	0.685329	−	0.691701i
$505$	−0.191391	+	0.331499i	−0.00851679	+	0.0147515i
$506$	−3.95503	+	4.74841i	−0.175823	+	0.211092i
$507$	0.901612	+	22.2560i	0.0400420	+	0.988424i
$508$	6.93201	+	37.7067i	0.307558	+	1.67296i
$509$	−9.18363	+	25.2318i	−0.407057	+	1.11838i	0.551672	+	0.834061i	$0.313990\pi$
$509$	−9.18363	+	25.2318i	−0.407057	+	1.11838i	−0.958730	+	0.284320i	$0.908232\pi$
$510$	−1.88692	−	0.593918i	−0.0835541	−	0.0262991i
$511$	−4.26777	+	24.2037i	−0.188795	+	1.07071i
$512$	22.6153	−	0.740862i	0.999464	−	0.0327418i
$513$	11.7666	−	1.43632i	0.519508	−	0.0634150i
$514$	−5.06222	−	8.69481i	−0.223285	−	0.383512i
$515$	−2.05999	−	0.363232i	−0.0907742	−	0.0160059i
$516$	16.9027	+	5.25271i	0.744101	+	0.231238i
$517$	−2.61435	+	7.18286i	−0.114979	+	0.315902i
$518$	5.45173	−	15.1498i	0.239535	−	0.665643i
$519$	18.5528	+	29.3252i	0.814379	+	1.28723i
$520$	0.176737	−	0.0665207i	0.00775044	−	0.00291713i
$521$	1.11230	−	1.92655i	0.0487306	−	0.0844039i	−0.840631	−	0.541608i	$-0.817816\pi$
$521$	1.11230	−	1.92655i	0.0487306	−	0.0844039i	0.889362	+	0.457204i	$0.151149\pi$
$522$	6.18799	+	2.90550i	0.270841	+	0.127170i
$523$	−3.08920	+	1.78355i	−0.135081	+	0.0779892i	−0.566018	−	0.824393i	$-0.691517\pi$
$523$	−3.08920	+	1.78355i	−0.135081	+	0.0779892i	0.430937	+	0.902382i	$0.358183\pi$
$524$	−0.637287	−	1.71206i	−0.0278400	−	0.0747918i
$525$	−21.9697	−	2.96267i	−0.958835	−	0.129302i
$526$	20.7400	−	17.5319i	0.904306	−	0.764428i
$527$	−6.83983	−	38.7906i	−0.297948	−	1.68974i
$528$	−5.93915	+	2.53985i	−0.258468	+	0.110533i
$529$	−0.791437	−	0.664094i	−0.0344103	−	0.0288737i
$530$	1.13843	−	1.98849i	0.0494501	−	0.0863743i
$531$	−3.56709	−	43.9540i	−0.154798	−	1.90744i
$532$	−10.1364	+	5.95101i	−0.439468	+	0.258009i
$533$	0.175469	+	0.482096i	0.00760039	+	0.0208819i
$534$	35.4836	+	18.4493i	1.53552	+	0.798379i
$535$	−1.01220	+	0.849341i	−0.0437614	+	0.0367202i
$536$	−1.64140	+	4.66762i	−0.0708976	+	0.201610i
$537$	2.97363	+	13.6157i	0.128322	+	0.587559i
$538$	−8.07030	−	21.9244i	−0.347935	−	0.945229i
$539$			0.338554i			0.0145825i
$540$	1.64699	−	0.852861i	0.0708752	−	0.0367013i
$541$		−	16.0298i		−	0.689174i	−0.938754	−	0.344587i	$-0.888019\pi$
$541$		−	16.0298i		−	0.689174i	0.938754	−	0.344587i	$-0.111981\pi$
$542$	1.56411	−	0.575743i	0.0671842	−	0.0247303i
$543$	10.3492	−	9.42362i	0.444128	−	0.404406i
$544$	19.3064	−	16.8079i	0.827755	−	0.720633i
$545$	1.80904	−	1.51796i	0.0774907	−	0.0650224i
$546$	1.26940	+	1.99039i	0.0543253	+	0.0851808i
$547$	11.0856	+	30.4574i	0.473985	+	1.30226i	0.914525	+	0.404530i	$0.132565\pi$
$547$	11.0856	+	30.4574i	0.473985	+	1.30226i	−0.440539	+	0.897733i	$0.645213\pi$
$548$	−5.80757	−	9.89205i	−0.248087	−	0.422568i
$549$	11.7998	−	42.9552i	0.503605	−	1.83328i
$550$	5.68490	+	3.25465i	0.242405	+	0.138779i
$551$	−2.81586	−	2.36279i	−0.119960	−	0.100658i
$552$	8.95136	+	21.1442i	0.380995	+	0.899957i
$553$	1.81453	+	10.2907i	0.0771616	+	0.437605i
$554$	21.0087	+	24.8529i	0.892572	+	1.05590i
$555$	0.835022	−	1.08117i	0.0354447	−	0.0458929i
$556$	−14.7639	−	39.6630i	−0.626128	−	1.68208i
$557$	29.5913	−	17.0845i	1.25382	−	0.723895i	0.281956	−	0.959427i	$-0.409017\pi$
$557$	29.5913	−	17.0845i	1.25382	−	0.723895i	0.971867	+	0.235532i	$0.0756833\pi$
$558$	30.1954	+	21.2626i	1.27828	+	0.900116i
$559$	−0.955747	+	1.65540i	−0.0404238	+	0.0700160i
$560$	−1.16152	+	1.42589i	−0.0490833	+	0.0602549i
$561$	−3.39453	+	6.47107i	−0.143317	+	0.273209i
$562$	−28.5465	−	10.2726i	−1.20416	−	0.433323i
$563$	−2.63340	+	7.23520i	−0.110984	+	0.304927i	−0.982734	−	0.185025i	$-0.940763\pi$
$563$	−2.63340	+	7.23520i	−0.110984	+	0.304927i	0.871749	+	0.489952i	$0.162986\pi$
$564$	19.2736	+	20.8597i	0.811564	+	0.878351i
$565$	1.61199	+	0.284237i	0.0678169	+	0.0119580i
$566$	0.420952	−	0.245084i	0.0176939	−	0.0103016i
$567$	14.6791	+	17.9475i	0.616462	+	0.753724i
$568$	−15.6896	+	0.171273i	−0.658321	+	0.00718644i
$569$	2.70678	−	15.3509i	0.113474	−	0.643544i	−0.874020	−	0.485890i	$-0.838496\pi$
$569$	2.70678	−	15.3509i	0.113474	−	0.643544i	0.987494	−	0.157654i	$-0.0503932\pi$
$570$	−0.973541	+	0.216334i	−0.0407771	+	0.00906122i
$571$	−7.83178	+	21.5176i	−0.327750	+	0.900485i	0.660930	+	0.750447i	$0.270162\pi$
$571$	−7.83178	+	21.5176i	−0.327750	+	0.900485i	−0.988680	+	0.150038i	$0.952060\pi$
$572$	−0.126129	−	0.686079i	−0.00527372	−	0.0286864i
$573$	−25.5247	−	13.3895i	−1.06631	−	0.559355i
$574$	−3.83912	−	3.19767i	−0.160242	−	0.133468i
$575$	11.6426	−	20.1655i	0.485528	−	0.840960i
$576$	−1.71989	+	23.9383i	−0.0716620	+	0.997429i
$577$	13.3039	+	23.0431i	0.553850	+	0.959297i	0.997992	+	0.0633405i	$0.0201754\pi$
$577$	13.3039	+	23.0431i	0.553850	+	0.959297i	−0.444141	+	0.895957i	$0.646491\pi$
$578$	0.836079	−	4.84466i	0.0347763	−	0.201511i
$579$	−0.874109	+	1.13177i	−0.0363267	+	0.0470349i
$580$	−0.541868	−	0.192770i	−0.0224998	−	0.00800433i
$581$	38.7253	−	6.82831i	1.60660	−	0.283286i
$582$	17.4042	−	22.7049i	0.721429	−	0.941148i
$583$	−6.48384	−	5.44058i	−0.268533	−	0.225326i
$584$	−13.7459	−	23.2195i	−0.568809	−	0.960830i
$585$	0.0506228	+	0.193794i	0.00209300	+	0.00801239i
$586$	0.135579	+	37.2608i	0.00560071	+	1.53923i
$587$	−14.1595	−	38.9028i	−0.584424	−	1.60569i	−0.780537	−	0.625110i	$-0.785054\pi$
$587$	−14.1595	−	38.9028i	−0.584424	−	1.60569i	0.196113	−	0.980581i	$-0.437168\pi$
$588$	1.11816	+	0.576215i	0.0461120	+	0.0237627i
$589$	−12.7643	−	15.2119i	−0.525944	−	0.626795i
$590$	0.657536	+	3.65133i	0.0270703	+	0.150323i
$591$	−19.3161	+	17.5885i	−0.794558	+	0.723495i
$592$	6.28705	+	16.5213i	0.258396	+	0.679022i
$593$	−12.1474			−0.498833			−0.249417	−	0.968396i	$-0.580239\pi$
$593$	−12.1474			−0.498833			−0.249417	+	0.968396i	$0.580239\pi$
$594$	−2.02232	−	6.54600i	−0.0829767	−	0.268585i
$595$			2.08052i			0.0852930i
$596$	−10.1409	+	12.2656i	−0.415386	+	0.502418i
$597$	−26.3237	+	5.74903i	−1.07736	+	0.235292i
$598$	−2.44038	+	0.439466i	−0.0997944	+	0.0179711i
$599$	25.1300	−	21.0866i	1.02679	−	0.861575i	0.0363204	−	0.999340i	$-0.488436\pi$
$599$	25.1300	−	21.0866i	1.02679	−	0.861575i	0.990465	+	0.137765i	$0.0439919\pi$
$600$	20.4249	−	13.2364i	0.833845	−	0.540373i
$601$	26.6419	−	9.69685i	1.08674	−	0.395543i	0.264331	−	0.964432i	$-0.414849\pi$
$601$	26.6419	−	9.69685i	1.08674	−	0.395543i	0.822414	+	0.568889i	$0.192627\pi$
$602$	−0.0677358	−	18.6157i	−0.00276071	−	0.758718i
$603$	−4.74221	−	2.24774i	−0.193118	−	0.0915352i
$604$	−5.34030	+	0.0388634i	−0.217294	+	0.00158133i
$605$	1.16218	−	1.38503i	0.0472493	−	0.0563095i
$606$	4.85277	−	2.01289i	0.197130	−	0.0817682i
$607$	−0.218532	−	1.23936i	−0.00886995	−	0.0503040i	0.980052	−	0.198744i	$-0.0636861\pi$
$607$	−0.218532	−	1.23936i	−0.00886995	−	0.0503040i	−0.988921	+	0.148440i	$0.952575\pi$
$608$	4.19240	−	12.2050i	0.170024	−	0.494976i
$609$	0.960871	−	7.12534i	0.0389365	−	0.288733i
$610$	−0.637357	+	3.69316i	−0.0258058	+	0.149532i
$611$	−2.65617	+	1.53354i	−0.107457	+	0.0620405i
$612$	15.5948	+	22.2250i	0.630384	+	0.898391i
$613$	−27.4944	−	15.8739i	−1.11049	−	0.641141i	−0.171532	−	0.985179i	$-0.554872\pi$
$613$	−27.4944	−	15.8739i	−1.11049	−	0.641141i	−0.938956	+	0.344038i	$0.888205\pi$
$614$	−14.9364	+	17.9327i	−0.602785	+	0.723703i
$615$	−0.226647	−	0.358246i	−0.00913929	−	0.0144459i
$616$	4.42340	+	5.15623i	0.178224	+	0.207750i
$617$	−29.6509	−	10.7920i	−1.19370	−	0.434471i	−0.332679	−	0.943040i	$-0.607953\pi$
$617$	−29.6509	−	10.7920i	−1.19370	−	0.434471i	−0.861021	+	0.508569i	$0.830175\pi$
$618$	19.4063	+	21.1573i	0.780637	+	0.851071i
$619$	−29.3688	−	5.17850i	−1.18043	−	0.208142i	−0.451208	−	0.892419i	$-0.649007\pi$
$619$	−29.3688	−	5.17850i	−1.18043	−	0.208142i	−0.729222	+	0.684277i	$0.760118\pi$
$620$	−2.70199	−	1.53388i	−0.108514	−	0.0616023i
$621$	−23.2946	+	7.10389i	−0.934781	+	0.285069i
$622$	−14.7010	−	25.2503i	−0.589458	−	1.01244i
$623$	7.30404	−	41.4233i	0.292630	−	1.65959i
$624$	−2.48062	−	0.751128i	−0.0993041	−	0.0300692i
$625$	−23.0443	−	8.38744i	−0.921772	−	0.335498i
$626$	16.7787	+	6.03791i	0.670612	+	0.241323i
$627$	0.149118	+	3.68094i	0.00595522	+	0.147003i
$628$	−24.3325	−	4.10813i	−0.970974	−	0.163932i
$629$	17.3184	+	9.99880i	0.690531	+	0.398678i
$630$	−1.37567	−	1.38298i	−0.0548079	−	0.0550992i
$631$	−15.5109	−	26.8656i	−0.617478	−	1.06950i	−0.989944	−	0.141458i	$-0.954821\pi$
$631$	−15.5109	−	26.8656i	−0.617478	−	1.06950i	0.372466	−	0.928046i	$-0.378512\pi$
$632$	−8.86839	−	7.27799i	−0.352766	−	0.289503i
$633$	8.85489	−	3.63524i	0.351950	−	0.144488i
$634$	11.1704	+	13.2144i	0.443633	+	0.524811i
$635$	3.36916	−	0.594074i	0.133701	−	0.0235751i
$636$	−29.0043	+	12.1547i	−1.15010	+	0.481963i
$637$	−0.0873191	+	0.104063i	−0.00345971	+	0.00412312i
$638$	−1.05557	+	1.84376i	−0.0417904	+	0.0729951i
$639$	1.55471	−	16.5695i	0.0615032	−	0.655481i
$640$	−0.0514231	−	2.01850i	−0.00203267	−	0.0797881i
$641$	34.7901	−	12.6626i	1.37413	−	0.500142i	0.453735	−	0.891137i	$-0.350091\pi$
$641$	34.7901	−	12.6626i	1.37413	−	0.500142i	0.920393	+	0.390995i	$0.127869\pi$
$642$	18.1177	−	0.800007i	0.715049	−	0.0315738i
$643$	21.1010	+	25.1472i	0.832143	+	0.991710i	0.999983	+	0.00589543i	$0.00187658\pi$
$643$	21.1010	+	25.1472i	0.832143	+	0.991710i	−0.167839	+	0.985814i	$0.553679\pi$
$644$	18.3856	−	15.6568i	0.724495	−	0.616963i
$645$	0.479688	−	1.50486i	0.0188877	−	0.0592538i
$646$	−5.04302	−	13.7003i	−0.198415	−	0.539030i
$647$	−32.3509			−1.27185			−0.635923	−	0.771752i	$-0.719380\pi$
$647$	−32.3509			−1.27185			−0.635923	+	0.771752i	$0.719380\pi$
$648$	−25.0617	−	4.46201i	−0.984518	−	0.175284i
$649$	13.7049			0.537965
$650$	0.907960	+	2.46664i	0.0356131	+	0.0967494i
$651$	11.7962	−	37.0065i	0.462328	−	1.45040i
$652$	−17.7009	−	20.7860i	−0.693221	−	0.814044i
$653$	−7.14706	−	8.51753i	−0.279686	−	0.333317i	0.607853	−	0.794050i	$-0.292031\pi$
$653$	−7.14706	−	8.51753i	−0.279686	−	0.333317i	−0.887539	+	0.460733i	$0.847587\pi$
$654$	−32.3804	+	1.42979i	−1.26617	+	0.0559094i
$655$	−0.153185	+	0.0557549i	−0.00598545	+	0.00217852i
$656$	5.48497	−	0.0798366i	0.214152	−	0.00311710i
$657$	26.0141	−	11.9320i	1.01491	−	0.465511i
$658$	14.8408	−	25.9223i	0.578553	−	1.01056i
$659$	21.7371	−	25.9052i	0.846757	−	1.00913i	−0.153025	−	0.988222i	$-0.548901\pi$
$659$	21.7371	−	25.9052i	0.846757	−	1.00913i	0.999782	−	0.0209028i	$-0.00665406\pi$
$660$	0.222780	+	0.531614i	0.00867170	+	0.0206930i
$661$	26.9698	−	4.75551i	1.04901	−	0.184968i	0.377532	−	0.925997i	$-0.376773\pi$
$661$	26.9698	−	4.75551i	1.04901	−	0.184968i	0.671473	+	0.741029i	$0.265662\pi$
$662$	18.5143	+	21.9022i	0.719579	+	0.851252i
$663$	−2.71240	+	1.11353i	−0.105341	+	0.0432460i
$664$	−27.3880	+	33.3729i	−1.06286	+	1.29512i
$665$	0.524441	+	0.908358i	0.0203369	+	0.0352246i
$666$	−18.1234	+	4.80470i	−0.702266	+	0.186178i
$667$	6.54020	+	3.77598i	0.253237	+	0.146207i
$668$	−1.39567	+	8.26660i	−0.0540003	+	0.319844i
$669$	−0.366491	−	9.04671i	−0.0141694	−	0.349766i
$670$	0.415437	+	0.149497i	0.0160497	+	0.00577557i
$671$	13.0092	+	4.73497i	0.502216	+	0.182792i
$672$	24.5583	−	5.83351i	0.947357	−	0.225032i
$673$	−3.55472	+	20.1598i	−0.137024	+	0.777103i	0.836404	+	0.548113i	$0.184654\pi$
$673$	−3.55472	+	20.1598i	−0.137024	+	0.777103i	−0.973429	+	0.228990i	$0.926458\pi$
$674$	−12.2560	−	21.0508i	−0.472083	−	0.810845i
$675$	11.7036	+	23.0098i	0.450473	+	0.885649i
$676$	−12.6976	+	22.3673i	−0.488370	+	0.860279i
$677$	32.7893	+	5.78165i	1.26020	+	0.222207i	0.763552	−	0.645747i	$-0.223454\pi$
$677$	32.7893	+	5.78165i	1.26020	+	0.222207i	0.496645	+	0.867954i	$0.334565\pi$
$678$	−15.1859	−	16.5560i	−0.583210	−	0.635831i
$679$	−28.2735	−	10.2907i	−1.08504	−	0.394922i
$680$	−1.48727	−	1.73367i	−0.0570343	−	0.0664833i
$681$	8.15224	+	12.8857i	0.312395	+	0.493781i
$682$	−7.34539	+	8.81887i	−0.281270	+	0.337692i
$683$	11.8895	+	6.86440i	0.454939	+	0.262659i	0.709914	−	0.704289i	$-0.248734\pi$
$683$	11.8895	+	6.86440i	0.454939	+	0.262659i	−0.254975	+	0.966948i	$0.582067\pi$
$684$	12.4110	+	5.77242i	0.474547	+	0.220714i
$685$	−0.886463	+	0.511800i	−0.0338700	+	0.0195549i
$686$	4.56216	−	26.4354i	0.174184	−	1.00931i
$687$	2.00022	−	14.8327i	0.0763133	−	0.565901i
$688$	13.3640	+	15.4638i	0.509496	+	0.589551i
$689$	−0.589743	−	3.34460i	−0.0224674	−	0.127419i
$690$	1.89256	−	0.785021i	0.0720486	−	0.0298852i
$691$	16.4903	−	19.6524i	0.627321	−	0.747612i	−0.354990	−	0.934870i	$-0.615516\pi$
$691$	16.4903	−	19.6524i	0.627321	−	0.747612i	0.982311	+	0.187258i	$0.0599600\pi$
$692$	0.291593	+	40.0684i	0.0110847	+	1.52317i
$693$	−5.92845	+	4.09583i	−0.225203	+	0.155588i
$694$	−0.0328242	−	9.02100i	−0.00124599	−	0.342432i
$695$	−3.54881	+	1.29166i	−0.134614	+	0.0489955i
$696$	4.29290	+	6.62434i	0.162722	+	0.251095i
$697$	4.75379	−	3.98890i	0.180063	−	0.151090i
$698$	−18.6516	+	3.35880i	−0.705972	+	0.127132i
$699$	−1.42360	+	0.310912i	−0.0538456	+	0.0117598i
$700$	−19.7284	−	16.3110i	−0.745665	−	0.616496i
$701$			0.366433i			0.0138400i	0.999976	+	0.00692000i	$0.00220272\pi$
$701$			0.366433i			0.0138400i	−0.999976	+	0.00692000i	$0.997797\pi$
$702$	1.06672	−	2.53367i	0.0402608	−	0.0956270i
$703$	10.0817			0.380237
$704$	−7.37192	−	1.13453i	−0.277840	−	0.0427593i
$705$	1.87388	−	1.70628i	0.0705742	−	0.0642623i
$706$	−2.82879	−	15.7084i	−0.106463	−	0.591193i
$707$	−3.55171	−	4.23276i	−0.133576	−	0.159189i
$708$	23.3256	−	45.2638i	0.876630	−	1.70112i
$709$	−2.32486	−	6.38749i	−0.0873118	−	0.239887i	0.888350	−	0.459166i	$-0.151852\pi$
$709$	−2.32486	−	6.38749i	−0.0873118	−	0.239887i	−0.975662	+	0.219279i	$0.929630\pi$
$710$	0.00509458	+	1.40013i	0.000191196	+	0.0525460i
$711$	8.65829	−	8.55007i	0.324711	−	0.320653i
$712$	23.5253	+	39.7388i	0.881647	+	1.48928i
$713$	31.2526	+	26.2241i	1.17042	+	0.982100i
$714$	17.3720	−	22.6629i	0.650132	−	0.848136i
$715$	−0.0613024	+	0.0108093i	−0.00229258	+	0.000404244i
$716$	−5.39380	+	15.1617i	−0.201576	+	0.566621i
$717$	14.6184	−	18.9275i	0.545934	−	0.706862i
$718$	6.53514	−	37.8679i	0.243889	−	1.41322i
$719$	−6.07495	−	10.5221i	−0.226558	−	0.392409i	0.730228	−	0.683203i	$-0.239414\pi$
$719$	−6.07495	−	10.5221i	−0.226558	−	0.392409i	−0.956786	+	0.290794i	$0.906080\pi$
$720$	2.13495	+	0.169015i	0.0795651	+	0.00629881i
$721$	15.0974	−	26.1495i	0.562257	−	0.973857i
$722$	14.9911	+	12.4864i	0.557912	+	0.464695i
$723$	−23.1279	−	12.1322i	−0.860137	−	0.451202i
$724$	15.8958	−	2.92228i	0.590761	−	0.108606i
$725$	2.73793	−	7.52240i	0.101684	−	0.279375i
$726$	−24.2243	+	5.38296i	−0.899047	+	0.199780i
$727$	0.337498	−	1.91405i	0.0125171	−	0.0709881i	−0.977909	−	0.209029i	$-0.932970\pi$
$727$	0.337498	−	1.91405i	0.0125171	−	0.0709881i	0.990426	+	0.138041i	$0.0440807\pi$
$728$	0.0297554	+	2.72577i	0.00110281	+	0.101024i
$729$	7.47888	−	25.9435i	0.276995	−	0.960871i
$730$	−2.08086	+	1.21150i	−0.0770160	+	0.0448397i
$731$	22.7700	+	4.01496i	0.842177	+	0.148499i
$732$	37.7800	−	34.9073i	1.39639	−	1.29021i
$733$	−14.2681	+	39.2014i	−0.527006	+	1.44794i	0.335572	+	0.942014i	$0.391070\pi$
$733$	−14.2681	+	39.2014i	−0.527006	+	1.44794i	−0.862579	+	0.505923i	$0.831152\pi$
$734$	−30.4746	−	10.9664i	−1.12484	−	0.404779i
$735$	0.0521431	−	0.0994017i	0.00192333	−	0.00366649i
$736$	−4.12817	+	26.1896i	−0.152166	+	0.965363i
$737$	0.815477	−	1.41245i	0.0300385	−	0.0520282i
$738$	−0.522457	+	5.79480i	−0.0192319	+	0.213309i
$739$	−22.3170	+	12.8847i	−0.820943	+	0.473971i	−0.850741	−	0.525584i	$-0.823847\pi$
$739$	−22.3170	+	12.8847i	−0.820943	+	0.473971i	0.0297988	+	0.999556i	$0.490513\pi$
$740$	1.47832	−	0.550280i	0.0543441	−	0.0202287i
$741$	−0.903546	+	1.16989i	−0.0331926	+	0.0429769i
$742$	21.3523	+	25.2595i	0.783868	+	0.927304i
$743$	−0.466716	−	2.64688i	−0.0171222	−	0.0971046i	0.975049	−	0.221989i	$-0.0712550\pi$
$743$	−0.466716	−	2.64688i	−0.0171222	−	0.0971046i	−0.992171	+	0.124885i	$0.960144\pi$
$744$	16.6247	+	39.2696i	0.609491	+	1.43969i
$745$	1.08790	+	0.912858i	0.0398576	+	0.0334445i
$746$	34.7660	+	19.9038i	1.27287	+	0.728731i
$747$	−32.1750	−	32.5823i	−1.17722	−	1.19212i
$748$	−7.27646	+	4.27197i	−0.266054	+	0.156199i
$749$	−6.52355	−	17.9233i	−0.238365	−	0.654903i
$750$	−2.34319	−	3.67406i	−0.0855612	−	0.134158i
$751$	−35.3934	+	29.6986i	−1.29153	+	1.08372i	−0.299982	+	0.953945i	$0.596981\pi$
$751$	−35.3934	+	29.6986i	−1.29153	+	1.08372i	−0.991544	+	0.129773i	$0.958575\pi$
$752$	6.16409	+	32.2097i	0.224781	+	1.17457i
$753$	−14.3973	+	13.1096i	−0.524667	+	0.477742i
$754$	−0.799994	+	0.294475i	−0.0291341	+	0.0107241i
$755$			0.476553i			0.0173435i
$756$	3.43732	+	26.5512i	0.125014	+	0.965659i
$757$			41.2974i			1.50098i	0.660883	+	0.750489i	$0.270182\pi$
$757$			41.2974i			1.50098i	−0.660883	+	0.750489i	$0.729818\pi$
$758$	−4.49666	−	12.2160i	−0.163326	−	0.443705i
$759$	−1.61491	−	7.39436i	−0.0586176	−	0.268398i
$760$	−1.08635	−	0.382024i	−0.0394062	−	0.0138575i
$761$	16.6555	−	13.9756i	0.603762	−	0.506616i	−0.288891	−	0.957362i	$-0.593286\pi$
$761$	16.6555	−	13.9756i	0.603762	−	0.506616i	0.892652	+	0.450746i	$0.148842\pi$
$762$	−41.6603	−	21.6608i	−1.50919	−	0.784688i
$763$	11.6591	+	32.0330i	0.422086	+	1.15967i
$764$	−16.8505	−	28.7016i	−0.609631	−	1.03839i
$765$	1.99331	−	1.37713i	0.0720684	−	0.0497904i
$766$	−16.5703	+	28.9433i	−0.598710	+	1.04576i
$767$	4.21254	+	3.53474i	0.152106	+	0.127632i
$768$	−16.2940	+	22.4166i	−0.587959	+	0.808890i
$769$	4.86149	+	27.5709i	0.175310	+	0.994232i	0.937786	+	0.347215i	$0.112873\pi$
$769$	4.86149	+	27.5709i	0.175310	+	0.994232i	−0.762476	+	0.647017i	$0.776016\pi$
$770$	0.462975	−	0.391362i	0.0166845	−	0.0141037i
$771$	12.2117	+	1.64679i	0.439795	+	0.0593076i
$772$	−1.54752	+	0.576039i	−0.0556964	+	0.0207321i
$773$	−23.6486	+	13.6535i	−0.850580	+	0.491083i	−0.860847	−	0.508864i	$-0.830065\pi$
$773$	−23.6486	+	13.6535i	−0.850580	+	0.491083i	0.0102662	+	0.999947i	$0.496732\pi$
$774$	−17.7905	+	12.3869i	−0.639468	+	0.445239i
$775$	21.6229	−	37.4519i	0.776717	−	1.34531i
$776$	30.9164	−	11.6364i	1.10983	−	0.417721i
$777$	10.5429	+	16.6644i	0.378224	+	0.597833i
$778$	14.4115	−	40.0479i	0.516676	−	1.43579i
$779$	1.07002	−	2.93986i	0.0383375	−	0.105331i
$780$	−0.0686358	+	0.220864i	−0.00245756	+	0.00790819i
$781$	5.09352	+	0.898125i	0.182260	+	0.0321374i
$782$	15.0911	+	25.9203i	0.539656	+	0.926907i
$783$	−7.46269	+	3.79579i	−0.266695	+	0.135650i
$784$	0.744476	+	1.24719i	0.0265884	+	0.0445426i
$785$	−0.382380	+	2.16858i	−0.0136477	+	0.0774001i
$786$	2.13418	+	0.671743i	0.0761235	+	0.0239603i
$787$	7.72182	−	21.2155i	0.275253	−	0.756252i	−0.722631	−	0.691234i	$-0.757067\pi$
$787$	7.72182	−	21.2155i	0.275253	−	0.756252i	0.997884	−	0.0650180i	$-0.0207105\pi$
$788$	−29.6683	+	5.45423i	−1.05689	+	0.194299i
$789$	1.34632	+	33.2334i	0.0479302	+	1.18314i
$790$	−0.655192	+	0.786622i	−0.0233107	+	0.0279868i
$791$	−11.8140	+	20.4625i	−0.420059	+	0.727564i
$792$	2.01218	−	7.65098i	0.0714997	−	0.271866i
$793$	2.77747	+	4.81073i	0.0986310	+	0.170834i
$794$	−24.9192	−	4.30050i	−0.884350	−	0.152619i
$795$	1.06575	+	2.59602i	0.0377984	+	0.0920712i
$796$	−29.3128	−	10.4280i	−1.03896	−	0.369612i
$797$	−19.2857	+	3.40058i	−0.683133	+	0.120455i	−0.504436	−	0.863449i	$-0.668299\pi$
$797$	−19.2857	+	3.40058i	−0.683133	+	0.120455i	−0.178697	+	0.983904i	$0.557188\pi$
$798$	1.87198	−	14.2736i	0.0662675	−	0.505281i
$799$	28.4196	+	23.8469i	1.00541	+	0.843641i
$800$	28.0994	−	0.511274i	0.993465	−	0.0180762i
$801$	−44.5216	+	20.4209i	−1.57309	+	0.721537i
$802$	14.0446	−	0.0511034i	0.495933	−	0.00180452i
$803$	3.04211	+	8.35812i	0.107354	+	0.294952i
$804$	−3.27702	−	5.09729i	−0.115572	−	0.179767i
$805$	−1.38515	−	1.65076i	−0.0488202	−	0.0581816i
$806$	−4.53233	+	0.816188i	−0.159645	+	0.0287490i
$807$	27.2617	+	8.68992i	0.959657	+	0.305900i
$808$	5.98540	+	0.988147i	0.210566	+	0.0347629i
$809$	−27.8483			−0.979094			−0.489547	−	0.871977i	$-0.662838\pi$
$809$	−27.8483			−0.979094			−0.489547	+	0.871977i	$0.662838\pi$
$810$	−0.414431	+	2.23342i	−0.0145616	+	0.0784744i
$811$		−	7.82601i		−	0.274808i	−0.990515	−	0.137404i	$-0.956124\pi$
$811$		−	7.82601i		−	0.274808i	0.990515	−	0.137404i	$-0.0438759\pi$
$812$	5.29007	−	6.39845i	0.185645	−	0.224541i
$813$	−0.619947	+	1.94488i	−0.0217425	+	0.0682098i
$814$	−1.03271	−	5.73470i	−0.0361965	−	0.201001i
$815$	−1.86628	+	1.56600i	−0.0653730	+	0.0548545i
$816$	1.72477	+	31.3032i	0.0603792	+	1.09583i
$817$	10.9535	−	3.98673i	0.383213	−	0.139478i
$818$	7.83013	−	0.0284911i	0.273774	−	0.000996167i
$819$	−2.87864	−	0.270101i	−0.100588	−	0.00943808i
$820$	−0.00356220	−	0.489489i	−0.000124397	−	0.0170937i
$821$	−9.82911	+	11.7139i	−0.343038	+	0.408817i	−0.909788	−	0.415073i	$-0.863756\pi$
$821$	−9.82911	+	11.7139i	−0.343038	+	0.408817i	0.566750	+	0.823890i	$0.308201\pi$
$822$	13.9296	+	1.82686i	0.485850	+	0.0637191i
$823$	−4.11133	−	23.3165i	−0.143312	−	0.812763i	−0.968707	−	0.248207i	$-0.920159\pi$
$823$	−4.11133	−	23.3165i	−0.143312	−	0.812763i	0.825395	−	0.564556i	$-0.190953\pi$
$824$	6.11262	+	32.5825i	0.212943	+	1.13506i
$825$	−7.42177	+	3.04689i	−0.258393	+	0.106079i
$826$	−52.7748	−	9.10774i	−1.83627	−	0.316899i
$827$	−0.0403168	+	0.0232769i	−0.00140195	+	0.000809419i	−0.500701	−	0.865620i	$-0.666924\pi$
$827$	−0.0403168	+	0.0232769i	−0.00140195	+	0.000809419i	0.499299	+	0.866430i	$0.333591\pi$
$828$	−27.1703	−	7.25147i	−0.944232	−	0.252006i
$829$	−6.44307	−	3.71991i	−0.223777	−	0.129198i	0.383921	−	0.923366i	$-0.374574\pi$
$829$	−6.44307	−	3.71991i	−0.223777	−	0.129198i	−0.607698	+	0.794168i	$0.707907\pi$
$830$	2.96016	+	2.46557i	0.102749	+	0.0855812i
$831$	−39.8239	+	1.61331i	−1.38148	+	0.0559649i
$832$	−1.97333	−	2.25008i	−0.0684128	−	0.0780074i
$833$	1.54406	+	0.561994i	0.0534987	+	0.0194719i
$834$	49.4419	+	15.5621i	1.71203	+	0.538872i
$835$	0.736742	+	0.129908i	0.0254960	+	0.00449564i
$836$	−2.10007	+	3.69934i	−0.0726325	+	0.127944i
$837$	−43.2634	+	13.1935i	−1.49540	+	0.456035i
$838$	−5.00008	+	2.91111i	−0.172725	+	0.100562i
$839$	−3.69536	+	20.9574i	−0.127578	+	0.723531i	0.852165	+	0.523273i	$0.175289\pi$
$839$	−3.69536	+	20.9574i	−0.127578	+	0.723531i	−0.979743	+	0.200258i	$0.935822\pi$
$840$	−0.504590	−	2.19519i	−0.0174100	−	0.0757411i
$841$	−24.8114	−	9.03060i	−0.855565	−	0.311400i
$842$	−11.7644	+	32.6920i	−0.405427	+	1.12664i
$843$	31.4005	−	19.8658i	1.08149	−	0.684214i
$844$	10.8986	+	1.84004i	0.375146	+	0.0633369i
$845$	1.98764	+	1.14756i	0.0683768	+	0.0394774i
$846$	−34.6591	+	2.93974i	−1.19160	+	0.101070i
$847$	13.0495	+	22.6024i	0.448385	+	0.776626i
$848$	−35.8495	−	5.78458i	−1.23108	−	0.198643i
$849$	−0.0797279	+	0.591222i	−0.00273626	+	0.0202907i
$850$	24.2806	−	20.5248i	0.832816	−	0.703996i
$851$	−20.3980	+	3.59671i	−0.699234	+	0.123294i
$852$	11.6354	−	15.2940i	0.398622	−	0.523964i
$853$	−11.8527	+	14.1255i	−0.405829	+	0.483648i	−0.929788	−	0.368095i	$-0.880010\pi$
$853$	−11.8527	+	14.1255i	−0.405829	+	0.483648i	0.523959	+	0.851744i	$0.324455\pi$
$854$	−46.9492	−	26.8788i	−1.60657	−	0.919774i
$855$	0.523147	−	1.10372i	0.0178912	−	0.0377463i
$856$	18.2486	+	10.2719i	0.623723	+	0.351085i
$857$	−18.6167	+	6.77591i	−0.635933	+	0.231461i	−0.639812	−	0.768532i	$-0.720988\pi$
$857$	−18.6167	+	6.77591i	−0.635933	+	0.231461i	0.00387866	+	0.999992i	$0.498765\pi$
$858$	0.758016	+	0.394122i	0.0258782	+	0.0134551i
$859$	5.06270	+	6.03349i	0.172737	+	0.205860i	0.845466	−	0.534029i	$-0.179323\pi$
$859$	5.06270	+	6.03349i	0.172737	+	0.205860i	−0.672729	+	0.739889i	$0.734878\pi$
$860$	1.38855	−	1.18246i	0.0473491	−	0.0403214i
$861$	5.97839	−	1.30567i	0.203743	−	0.0444971i
$862$	−18.5879	+	6.84214i	−0.633106	+	0.233044i
$863$	−3.41425			−0.116222			−0.0581111	−	0.998310i	$-0.518508\pi$
$863$	−3.41425			−0.116222			−0.0581111	+	0.998310i	$0.518508\pi$
$864$	−21.8446	−	19.6676i	−0.743167	−	0.669106i
$865$	3.57559			0.121574
$866$	−16.5761	+	6.10159i	−0.563278	+	0.207340i
$867$	4.05387	+	4.45205i	0.137677	+	0.151199i
$868$	34.1463	−	29.0782i	1.15900	−	0.986977i
$869$	2.43082	+	2.89694i	0.0824600	+	0.0982720i
$870$	0.593893	−	0.378765i	0.0201349	−	0.0128413i
$871$	0.614953	−	0.223825i	0.0208369	−	0.00758401i
$872$	−32.6143	−	18.3581i	−1.10446	−	0.621685i
$873$	8.85537	+	33.9000i	0.299709	+	1.14734i
$874$	13.1226	+	7.51278i	0.443877	+	0.254124i
$875$	−2.94597	+	3.51087i	−0.0995919	+	0.118689i
$876$	32.7824	+	4.17813i	1.10761	+	0.141166i
$877$	13.1746	−	2.32305i	0.444876	−	0.0784437i	0.0532774	−	0.998580i	$-0.483033\pi$
$877$	13.1746	−	2.32305i	0.444876	−	0.0784437i	0.391599	+	0.920136i	$0.371922\pi$
$878$	11.6597	−	9.85613i	0.393494	−	0.332628i
$879$	−36.1174	−	27.8947i	−1.21821	−	0.940865i
$880$	−0.106024	+	0.657078i	−0.00357408	+	0.0221501i
$881$	28.5441	+	49.4399i	0.961676	+	1.66567i	0.718292	+	0.695742i	$0.244924\pi$
$881$	28.5441	+	49.4399i	0.961676	+	1.66567i	0.243384	+	0.969930i	$0.421743\pi$
$882$	−1.39798	+	0.647383i	−0.0470724	+	0.0217985i
$883$	−17.0975	−	9.87122i	−0.575375	−	0.332193i	0.183918	−	0.982942i	$-0.441122\pi$
$883$	−17.0975	−	9.87122i	−0.575375	−	0.332193i	−0.759293	+	0.650749i	$0.774455\pi$
$884$	−3.33842	−	0.563635i	−0.112283	−	0.0189571i
$885$	−4.02385	−	2.11079i	−0.135260	−	0.0709536i
$886$	13.9302	−	38.7106i	0.467995	−	1.30051i
$887$	−53.6182	−	19.5154i	−1.80032	−	0.655264i	−0.998320	−	0.0579452i	$-0.981545\pi$
$887$	−53.6182	−	19.5154i	−1.80032	−	0.655264i	−0.802004	−	0.597319i	$-0.796233\pi$
$888$	−20.6979	−	6.34961i	−0.694577	−	0.213079i
$889$	−8.57547	+	48.6339i	−0.287612	+	1.63113i
$890$	3.56127	−	2.07341i	0.119374	−	0.0695010i
$891$	7.84829	+	2.96885i	0.262928	+	0.0994603i
$892$	5.16138	−	9.09194i	0.172816	−	0.304421i
$893$	18.4192	+	3.24779i	0.616373	+	0.108683i
$894$	−4.22816	−	19.0275i	−0.141411	−	0.636374i
$895$	1.34942	+	0.491147i	0.0451060	+	0.0164172i
$896$	27.6338	+	9.26794i	0.923180	+	0.309620i
$897$	1.41075	−	2.68935i	0.0471037	−	0.0897949i
$898$	32.7050	+	27.2406i	1.09138	+	0.909030i
$899$	12.1466	+	7.01286i	0.405113	+	0.233892i
$900$	−2.56866	+	29.6980i	−0.0856221	+	0.989934i
$901$	−35.5763	+	20.5400i	−1.18522	+	0.684286i
$902$	−1.78187	−	0.307511i	−0.0593298	−	0.0102390i
$903$	18.0444	+	13.9363i	0.600480	+	0.463772i
$904$	−4.78325	−	25.4965i	−0.159089	−	0.848001i
$905$	−0.250440	−	1.42031i	−0.00832490	−	0.0472128i
$906$	3.97914	−	5.19103i	0.132198	−	0.172461i
$907$	15.5646	−	18.5491i	0.516813	−	0.615914i	−0.443011	−	0.896516i	$-0.646090\pi$
$907$	15.5646	−	18.5491i	0.516813	−	0.615914i	0.959824	+	0.280602i	$0.0905342\pi$
$908$	0.128128	+	17.6064i	0.00425209	+	0.584288i
$909$	−1.70440	+	6.20457i	−0.0565314	+	0.205793i
$910$	0.243246		0.000885087i	0.00806354		2.93403e-5i
$911$	21.3962	−	7.78758i	0.708888	−	0.258014i	0.0376870	−	0.999290i	$-0.488001\pi$
$911$	21.3962	−	7.78758i	0.708888	−	0.258014i	0.671201	+	0.741275i	$0.265779\pi$
$912$	8.64369	+	13.2322i	0.286221	+	0.438163i
$913$	10.9016	−	9.14750i	0.360789	−	0.302738i
$914$	3.91388	+	21.7340i	0.129460	+	0.718897i
$915$	−3.09033	−	3.39387i	−0.102163	−	0.112198i
$916$	11.0122	−	13.3195i	0.363854	−	0.440089i
$917$		−	2.35315i		−	0.0777078i
$918$	−33.2118	−	1.64292i	−1.09615	−	0.0542246i
$919$	3.40847			0.112435			0.0562174	−	0.998419i	$-0.482096\pi$
$919$	3.40847			0.112435			0.0562174	+	0.998419i	$0.482096\pi$
$920$	2.33428	+	0.385374i	0.0769591	+	0.0127054i
$921$	−6.09882	−	27.9253i	−0.200963	−	0.920168i
$922$	−17.9613	+	3.23449i	−0.591524	+	0.106522i
$923$	1.33398	+	1.58977i	0.0439084	+	0.0523279i
$924$	−8.31095	+	0.397284i	−0.273410	+	0.0130697i
$925$	7.50928	+	20.6316i	0.246904	+	0.678362i
$926$	−49.0984	+	0.178652i	−1.61348	+	0.00587086i
$927$	−35.0466	+	2.84421i	−1.15108	+	0.0934162i
$928$	0.165819	+	9.11338i	0.00544328	+	0.299161i
$929$	−16.2267	−	13.6158i	−0.532381	−	0.446721i	0.336541	−	0.941669i	$-0.390743\pi$
$929$	−16.2267	−	13.6158i	−0.532381	−	0.446721i	−0.868923	+	0.494948i	$0.835187\pi$
$930$	3.51492	−	1.45796i	0.115259	−	0.0478084i
$931$	0.815804	−	0.143848i	0.0267369	−	0.00471443i
$932$	−1.58526	−	0.563955i	−0.0519268	−	0.0184730i
$933$	35.4637	+	4.78238i	1.16103	+	0.156568i
$934$	19.9883	+	3.44954i	0.654039	+	0.112872i
$935$	0.376473	+	0.652071i	0.0123120	+	0.0213250i
$936$	2.59182	−	1.83274i	0.0847163	−	0.0599051i
$937$	20.8301	−	36.0788i	0.680489	−	1.17864i	−0.294342	−	0.955700i	$-0.595101\pi$
$937$	20.8301	−	36.0788i	0.680489	−	1.17864i	0.974832	−	0.222942i	$-0.0715661\pi$
$938$	−4.07889	+	4.89711i	−0.133181	+	0.159896i
$939$	−18.4562	+	11.6765i	−0.602296	+	0.381048i
$940$	2.87815	−	0.529121i	0.0938750	−	0.0172580i
$941$	−17.2670	+	47.4407i	−0.562888	+	1.54652i	0.252493	+	0.967599i	$0.418749\pi$
$941$	−17.2670	+	47.4407i	−0.562888	+	1.54652i	−0.815382	+	0.578924i	$0.803473\pi$
$942$	22.2726	−	20.4293i	0.725679	−	0.665623i
$943$	−1.11613	+	6.32988i	−0.0363461	+	0.206129i
$944$	50.4873	−	30.1370i	1.64322	−	0.980874i
$945$	2.37146	−	0.289478i	0.0771437	−	0.00941673i
$946$	−3.38976	−	5.82221i	−0.110211	−	0.189296i
$947$	38.1758	+	6.73142i	1.24055	+	0.218742i	0.755149	−	0.655553i	$-0.227564\pi$
$947$	38.1758	+	6.73142i	1.24055	+	0.218742i	0.485396	+	0.874294i	$0.338675\pi$
$948$	13.7051	−	3.09783i	0.445121	−	0.100613i
$949$	−1.22064	+	3.35369i	−0.0396238	+	0.108865i
$950$	5.42719	−	15.0816i	0.176081	−	0.489312i
$951$	−21.1745	+	0.857801i	−0.686631	+	0.0278161i
$952$	30.8591	−	11.6148i	1.00015	−	0.376439i
$953$	−17.7159	+	30.6848i	−0.573873	+	0.993977i	0.422290	+	0.906461i	$0.361226\pi$
$953$	−17.7159	+	30.6848i	−0.573873	+	0.993977i	−0.996163	+	0.0875165i	$0.972107\pi$
$954$	10.0672	−	37.1770i	0.325938	−	1.20365i
$955$	−2.57205	+	1.48498i	−0.0832297	+	0.0480527i
$956$	25.8804	−	9.63354i	0.837031	−	0.311571i
$957$	−0.988186	−	2.40707i	−0.0319435	−	0.0778096i
$958$	−0.651868	+	0.551037i	−0.0210609	+	0.0178032i
$959$	−2.56577	−	14.5512i	−0.0828531	−	0.469883i
$960$	1.98971	+	1.46851i	0.0642176	+	0.0473960i
$961$	34.2959	+	28.7776i	1.10632	+	0.928311i
$962$	1.16165	−	2.02906i	0.0374532	−	0.0654194i
$963$	−12.8540	+	18.1139i	−0.414214	+	0.583711i
$964$	−15.2683	−	26.0065i	−0.491757	−	0.837612i
$965$	0.0503964	+	0.138463i	0.00162232	+	0.00445728i
$966$	1.30470	+	29.5473i	0.0419779	+	0.950670i
$967$	−1.48262	+	1.24406i	−0.0476777	+	0.0400064i	−0.666315	−	0.745670i	$-0.732129\pi$
$967$	−1.48262	+	1.24406i	−0.0476777	+	0.0400064i	0.618637	+	0.785677i	$0.287685\pi$
$968$	−27.0314	−	9.50577i	−0.868822	−	0.305527i
$969$	17.0355	+	5.43021i	0.547258	+	0.174443i
$970$	−1.01826	−	2.76630i	−0.0326945	−	0.0888204i
$971$		−	30.4220i		−	0.976288i	−0.872763	−	0.488144i	$-0.837674\pi$
$971$		−	30.4220i		−	0.976288i	0.872763	−	0.488144i	$-0.162326\pi$
$972$	23.1631	−	20.8680i	0.742956	−	0.669340i
$973$		−	54.5148i		−	1.74766i
$974$	30.3568	−	11.1742i	0.972693	−	0.358045i
$975$	−3.06711	−	0.977671i	−0.0982262	−	0.0313105i
$976$	58.3366	−	11.1641i	1.86731	−	0.357354i
$977$	2.40690	−	2.01963i	0.0770035	−	0.0646136i	−0.603473	−	0.797383i	$-0.706217\pi$
$977$	2.40690	−	2.01963i	0.0770035	−	0.0646136i	0.680477	+	0.732769i	$0.261773\pi$
$978$	33.4050	−	1.47504i	1.06817	−	0.0471665i
$979$	−5.20639	−	14.3044i	−0.166397	−	0.457172i
$980$	0.111773	−	0.0656215i	0.00357047	−	0.00209620i
$981$	22.9730	−	32.3736i	0.733470	−	1.03361i
$982$	11.0166	+	6.30710i	0.351554	+	0.201268i
$983$	44.9828	+	37.7451i	1.43473	+	1.20388i	0.942850	+	0.333218i	$0.108135\pi$
$983$	44.9828	+	37.7451i	1.43473	+	1.20388i	0.491880	+	0.870663i	$0.336310\pi$
$984$	−4.04835	+	5.36168i	−0.129057	+	0.170924i
$985$	0.467428	+	2.65092i	0.0148935	+	0.0844652i
$986$	6.65673	+	7.87482i	0.211994	+	0.250785i
$987$	13.8934	+	33.8422i	0.442231	+	1.07721i
$988$	−1.59964	+	0.595438i	−0.0508912	+	0.0189434i
$989$	−20.7395	+	11.9740i	−0.659479	+	0.380750i
$990$	−0.681409	−	0.184520i	−0.0216566	−	0.00586443i
$991$	10.3807	−	17.9799i	0.329754	−	0.571150i	−0.652709	−	0.757609i	$-0.726368\pi$
$991$	10.3807	−	17.9799i	0.329754	−	0.571150i	0.982463	+	0.186458i	$0.0597009\pi$
$992$	−7.66695	+	48.6401i	−0.243426	+	1.54433i
$993$	−35.0957	+	1.42176i	−1.11373	+	0.0451182i
$994$	−19.0172	−	6.84344i	−0.603190	−	0.217061i
$995$	−0.949553	+	2.60888i	−0.0301029	+	0.0827069i
$996$	−11.6575	−	51.5741i	−0.369383	−	1.63419i
$997$	32.5454	+	5.73863i	1.03072	+	0.181744i	0.663335	−	0.748323i	$-0.269141\pi$
$997$	32.5454	+	5.73863i	1.03072	+	0.181744i	0.367389	+	0.930067i	$0.380252\pi$
$998$	53.7331	−	31.2841i	1.70089	−	0.990280i
$999$	8.98740	−	21.1315i	0.284349	−	0.668570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.133.5	yes	204
3.2	odd	2		648.2.t.a.397.30		204
4.3	odd	2		864.2.bf.a.241.13		204
8.3	odd	2		864.2.bf.a.241.22		204
8.5	even	2	inner	216.2.t.a.133.28	yes	204
24.5	odd	2		648.2.t.a.397.7		204
27.13	even	9	inner	216.2.t.a.13.28	yes	204
27.14	odd	18		648.2.t.a.253.7		204
108.67	odd	18		864.2.bf.a.337.22		204
216.13	even	18	inner	216.2.t.a.13.5	✓	204
216.67	odd	18		864.2.bf.a.337.13		204
216.149	odd	18		648.2.t.a.253.30		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.5	✓	204	216.13	even	18	inner
216.2.t.a.13.28	yes	204	27.13	even	9	inner
216.2.t.a.133.5	yes	204	1.1	even	1	trivial
216.2.t.a.133.28	yes	204	8.5	even	2	inner
648.2.t.a.253.7		204	27.14	odd	18
648.2.t.a.253.30		204	216.149	odd	18
648.2.t.a.397.7		204	24.5	odd	2
648.2.t.a.397.30		204	3.2	odd	2
864.2.bf.a.241.13		204	4.3	odd	2
864.2.bf.a.241.22		204	8.3	odd	2
864.2.bf.a.337.13		204	216.67	odd	18
864.2.bf.a.337.22		204	108.67	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+(-1.32716 + 0.488522i) q^{2} +(0.526029 - 1.65024i) q^{3} +(1.52269 - 1.29669i) q^{4} +(-0.114718 - 0.136716i) q^{5} +(0.108055 + 2.44711i) q^{6} +(2.42085 - 0.881117i) q^{7} +(-1.38739 + 2.46478i) q^{8} +(-2.44659 - 1.73615i) q^{9} +(0.219037 + 0.125401i) q^{10} +(0.599296 - 0.714213i) q^{11} +(-1.33887 - 3.19491i) q^{12} +(0.368417 - 0.0649618i) q^{13} +(-2.78240 + 2.35202i) q^{14} +(-0.285959 + 0.117396i) q^{15} +(0.637188 - 3.94892i) q^{16} +(-2.26254 - 3.91883i) q^{17} +(4.09515 + 1.10893i) q^{18} +(-1.97566 - 1.14065i) q^{19} +(-0.351958 - 0.0594221i) q^{20} +(-0.180617 - 4.45848i) q^{21} +(-0.446451 + 1.24064i) q^{22} +(4.40423 + 1.60301i) q^{23} +(3.33767 + 3.58608i) q^{24} +(0.862710 - 4.89267i) q^{25} +(-0.457212 + 0.266194i) q^{26} +(-4.15204 + 3.12419i) q^{27} +(2.54367 - 4.48076i) q^{28} +(1.58682 + 0.279799i) q^{29} +(0.322162 - 0.295500i) q^{30} +(8.17965 + 2.97715i) q^{31} +(1.08349 + 5.55212i) q^{32} +(-0.863376 - 1.36468i) q^{33} +(4.91718 + 4.09561i) q^{34} +(-0.398177 - 0.229888i) q^{35} +(-5.97665 + 0.528842i) q^{36} +(-3.82721 + 2.20964i) q^{37} +(3.17924 + 0.548665i) q^{38} +(0.0865954 - 0.642148i) q^{39} +(0.496133 - 0.0930767i) q^{40} +(0.238139 + 1.35055i) q^{41} +(2.41777 + 5.82886i) q^{42} +(-3.28437 + 3.91416i) q^{43} +(-0.0135696 - 1.86463i) q^{44} +(0.0433088 + 0.533654i) q^{45} +(-6.62821 + 0.0241177i) q^{46} +(-7.70413 + 2.80407i) q^{47} +(-6.18149 - 3.12876i) q^{48} +(-0.278168 + 0.233411i) q^{49} +(1.24522 + 6.91480i) q^{50} +(-7.65718 + 1.67231i) q^{51} +(0.476750 - 0.576640i) q^{52} -9.07829i q^{53} +(3.98418 - 6.17465i) q^{54} -0.166394 q^{55} +(-1.18691 + 7.18932i) q^{56} +(-2.92159 + 2.66029i) q^{57} +(-2.24265 + 0.403859i) q^{58} +(9.44865 + 11.2605i) q^{59} +(-0.283201 + 0.549558i) q^{60} +(5.07860 + 13.9533i) q^{61} +(-12.3101 + 0.0447920i) q^{62} +(-7.45257 - 2.04723i) q^{63} +(-4.15029 - 6.83923i) q^{64} +(-0.0511453 - 0.0429160i) q^{65} +(1.81251 + 1.38937i) q^{66} +(1.72274 - 0.303765i) q^{67} +(-8.52666 - 3.03337i) q^{68} +(4.96210 - 6.42480i) q^{69} +(0.640749 + 0.110579i) q^{70} +(2.77372 + 4.80422i) q^{71} +(7.67360 - 3.62158i) q^{72} +(-4.77001 + 8.26190i) q^{73} +(3.99985 - 4.80222i) q^{74} +(-7.62027 - 3.99737i) q^{75} +(-4.48738 + 0.824961i) q^{76} +(0.821500 - 2.25705i) q^{77} +(0.198778 + 0.894535i) q^{78} +(-0.704340 + 3.99451i) q^{79} +(-0.612976 + 0.365899i) q^{80} +(2.97157 + 8.49528i) q^{81} +(-0.975822 - 1.67606i) q^{82} +(15.0319 + 2.65052i) q^{83} +(-6.05629 - 6.55469i) q^{84} +(-0.276212 + 0.758885i) q^{85} +(2.44672 - 6.79919i) q^{86} +(1.29645 - 2.47145i) q^{87} +(0.928921 + 2.46803i) q^{88} +(8.16359 - 14.1397i) q^{89} +(-0.318179 - 0.687086i) q^{90} +(0.834643 - 0.481881i) q^{91} +(8.78489 - 3.27003i) q^{92} +(9.21575 - 11.9323i) q^{93} +(8.85474 - 7.48508i) q^{94} +(0.0706993 + 0.400955i) q^{95} +(9.73228 + 1.13257i) q^{96} +(-8.94677 - 7.50723i) q^{97} +(0.255147 - 0.445664i) q^{98} +(-2.70621 + 0.706917i) 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

Related objects

Downloads

Learn more