LMFDB - Embedded newform 216.2.v.b.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.491528 - 1.32605i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(-1.51680 + 1.30358i) q^{4} +(0.715441 + 0.260399i) q^{5} +(1.07262 + 2.20215i) q^{6} +(-3.32699 - 0.586638i) q^{7} +(2.47416 + 1.37060i) q^{8} +(2.94222 - 0.585931i) q^{9} +O(q^{10})$	\(q+(-0.491528 - 1.32605i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(-1.51680 + 1.30358i) q^{4} +(0.715441 + 0.260399i) q^{5} +(1.07262 + 2.20215i) q^{6} +(-3.32699 - 0.586638i) q^{7} +(2.47416 + 1.37060i) q^{8} +(2.94222 - 0.585931i) q^{9} +(-0.00635759 - 1.07670i) q^{10} +(1.95175 + 5.36238i) q^{11} +(2.39294 - 2.50477i) q^{12} +(3.36983 + 4.01601i) q^{13} +(0.857399 + 4.70010i) q^{14} +(-1.27746 - 0.327249i) q^{15} +(0.601369 - 3.95454i) q^{16} +(-2.95820 + 1.70792i) q^{17} +(-2.22316 - 3.61353i) q^{18} +(1.27164 - 2.20255i) q^{19} +(-1.42463 + 0.537659i) q^{20} +(5.83441 + 0.445715i) q^{21} +(6.15143 - 5.22386i) q^{22} +(0.947065 + 5.37107i) q^{23} +(-4.49763 - 1.94198i) q^{24} +(-3.38617 - 2.84134i) q^{25} +(3.66905 - 6.44253i) q^{26} +(-4.97190 + 1.51004i) q^{27} +(5.81111 - 3.44718i) q^{28} +(3.27434 + 2.74749i) q^{29} +(0.193959 + 1.85482i) q^{30} +(2.33080 - 0.410982i) q^{31} +(-5.53949 + 1.14632i) q^{32} +(-4.27562 - 8.91136i) q^{33} +(3.71882 + 3.08323i) q^{34} +(-2.22751 - 1.28605i) q^{35} +(-3.69896 + 4.72416i) q^{36} +(-9.07767 + 5.24099i) q^{37} +(-3.54573 - 0.603643i) q^{38} +(-6.49112 - 6.34960i) q^{39} +(1.41321 + 1.62485i) q^{40} +(1.88727 + 2.24916i) q^{41} +(-2.27674 - 7.95579i) q^{42} +(-5.95761 + 2.16839i) q^{43} +(-9.95069 - 5.58941i) q^{44} +(2.25756 + 0.346954i) q^{45} +(6.65678 - 3.89588i) q^{46} +(0.625921 - 3.54977i) q^{47} +(-0.364446 + 6.91861i) q^{48} +(4.14688 + 1.50934i) q^{49} +(-2.10335 + 5.88682i) q^{50} +(4.80874 - 3.44671i) q^{51} +(-10.3465 - 1.69865i) q^{52} +8.06569 q^{53} +(4.44621 + 5.85075i) q^{54} +4.34470i q^{55} +(-7.42745 - 6.01142i) q^{56} +(-1.81756 + 4.01265i) q^{57} +(2.03388 - 5.69239i) q^{58} +(-1.63379 + 4.48880i) q^{59} +(2.36424 - 1.16889i) q^{60} +(-2.62747 - 0.463294i) q^{61} +(-1.69063 - 2.88874i) q^{62} +(-10.1325 + 0.223366i) q^{63} +(4.24289 + 6.78217i) q^{64} +(1.36515 + 3.75071i) q^{65} +(-9.71529 + 10.0499i) q^{66} +(2.16648 - 1.81790i) q^{67} +(2.26060 - 6.44682i) q^{68} +(-2.54534 - 9.09710i) q^{69} +(-0.610483 + 3.58591i) q^{70} +(3.03884 + 5.26343i) q^{71} +(8.08260 + 2.58294i) q^{72} +(1.40736 - 2.43763i) q^{73} +(11.4117 + 9.46132i) q^{74} +(6.31965 + 4.32206i) q^{75} +(0.942366 + 4.99851i) q^{76} +(-3.34767 - 18.9856i) q^{77} +(-5.22931 + 11.7285i) q^{78} +(7.42577 - 8.84969i) q^{79} +(1.46000 - 2.67264i) q^{80} +(8.31337 - 3.44788i) q^{81} +(2.05484 - 3.60813i) q^{82} +(5.47239 - 6.52174i) q^{83} +(-9.43067 + 6.92955i) q^{84} +(-2.56116 + 0.451602i) q^{85} +(5.80373 + 6.83425i) q^{86} +(-6.11092 - 4.17931i) q^{87} +(-2.52077 + 15.9424i) q^{88} +(-7.79000 - 4.49756i) q^{89} +(-0.649578 - 3.16417i) q^{90} +(-8.85545 - 15.3381i) q^{91} +(-8.43812 - 6.91227i) q^{92} +(-3.94772 + 1.10456i) q^{93} +(-5.01483 + 0.914812i) q^{94} +(1.48333 - 1.24466i) q^{95} +(9.35354 - 2.91742i) q^{96} +(13.6755 - 4.97747i) q^{97} +(-0.0368503 - 6.24084i) q^{98} +(8.88446 + 14.6337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.491528	−	1.32605i	−0.347563	−	0.937657i
$2$	−0.491528	−	1.32605i	−0.347563	−	0.937657i
$3$	−1.72369	+	0.169964i	−0.995174	+	0.0981288i
$3$	−1.72369	+	0.169964i	−0.995174	+	0.0981288i
$4$	−1.51680	+	1.30358i	−0.758400	+	0.651789i
$5$	0.715441	+	0.260399i	0.319955	+	0.116454i	0.497005	−	0.867748i	$-0.334433\pi$
$5$	0.715441	+	0.260399i	0.319955	+	0.116454i	−0.177050	+	0.984202i	$0.556655\pi$
$6$	1.07262	+	2.20215i	0.437896	+	0.899025i
$7$	−3.32699	−	0.586638i	−1.25748	−	0.221728i	−0.495091	−	0.868841i	$-0.664865\pi$
$7$	−3.32699	−	0.586638i	−1.25748	−	0.221728i	−0.762394	+	0.647113i	$0.775976\pi$
$8$	2.47416	+	1.37060i	0.874746	+	0.484582i
$9$	2.94222	−	0.585931i	0.980741	−	0.195310i
$10$	−0.00635759	−	1.07670i	−0.00201045	−	0.340483i
$11$	1.95175	+	5.36238i	0.588474	+	1.61682i	0.773296	+	0.634046i	$0.218607\pi$
$11$	1.95175	+	5.36238i	0.588474	+	1.61682i	−0.184822	+	0.982772i	$0.559171\pi$
$12$	2.39294	−	2.50477i	0.690781	−	0.723064i
$13$	3.36983	+	4.01601i	0.934622	+	1.11384i	0.993300	+	0.115563i	$0.0368671\pi$
$13$	3.36983	+	4.01601i	0.934622	+	1.11384i	−0.0586778	+	0.998277i	$0.518688\pi$
$14$	0.857399	+	4.70010i	0.229150	+	1.25615i
$15$	−1.27746	−	0.327249i	−0.329838	−	0.0844952i
$16$	0.601369	−	3.95454i	0.150342	−	0.988634i
$17$	−2.95820	+	1.70792i	−0.717470	+	0.414231i	−0.813821	−	0.581116i	$-0.802616\pi$
$17$	−2.95820	+	1.70792i	−0.717470	+	0.414231i	0.0963510	+	0.995347i	$0.469283\pi$
$18$	−2.22316	−	3.61353i	−0.524003	−	0.851716i
$19$	1.27164	−	2.20255i	0.291735	−	0.505299i	−0.682485	−	0.730899i	$-0.739101\pi$
$19$	1.27164	−	2.20255i	0.291735	−	0.505299i	0.974220	+	0.225600i	$0.0724342\pi$
$20$	−1.42463	+	0.537659i	−0.318557	+	0.120224i
$21$	5.83441	+	0.445715i	1.27317	+	0.0972629i
$22$	6.15143	−	5.22386i	1.31149	−	1.11373i
$23$	0.947065	+	5.37107i	0.197477	+	1.11995i	0.908847	+	0.417129i	$0.136964\pi$
$23$	0.947065	+	5.37107i	0.197477	+	1.11995i	−0.711371	+	0.702817i	$0.751925\pi$
$24$	−4.49763	−	1.94198i	−0.918076	−	0.396405i
$25$	−3.38617	−	2.84134i	−0.677235	−	0.568268i
$26$	3.66905	−	6.44253i	0.719559	−	1.26348i
$27$	−4.97190	+	1.51004i	−0.956843	+	0.290607i
$28$	5.81111	−	3.44718i	1.09820	−	0.651456i
$29$	3.27434	+	2.74749i	0.608029	+	0.510197i	0.894015	−	0.448037i	$-0.147877\pi$
$29$	3.27434	+	2.74749i	0.608029	+	0.510197i	−0.285986	+	0.958234i	$0.592321\pi$
$30$	0.193959	+	1.85482i	0.0354119	+	0.338642i
$31$	2.33080	−	0.410982i	0.418623	−	0.0738146i	0.0396309	−	0.999214i	$-0.487382\pi$
$31$	2.33080	−	0.410982i	0.418623	−	0.0738146i	0.378992	+	0.925400i	$0.376271\pi$
$32$	−5.53949	+	1.14632i	−0.979253	+	0.202643i
$33$	−4.27562	−	8.91136i	−0.744290	−	1.55127i
$34$	3.71882	+	3.08323i	0.637772	+	0.528769i
$35$	−2.22751	−	1.28605i	−0.376517	−	0.217382i
$36$	−3.69896	+	4.72416i	−0.616494	+	0.787360i
$37$	−9.07767	+	5.24099i	−1.49236	+	0.861614i	−0.999962	−	0.00875627i	$-0.997213\pi$
$37$	−9.07767	+	5.24099i	−1.49236	+	0.861614i	−0.492398	+	0.870370i	$0.663879\pi$
$38$	−3.54573	−	0.603643i	−0.575193	−	0.0979238i
$39$	−6.49112	−	6.34960i	−1.03941	−	1.01675i
$40$	1.41321	+	1.62485i	0.223448	+	0.256912i
$41$	1.88727	+	2.24916i	0.294742	+	0.351259i	0.893010	−	0.450036i	$-0.148589\pi$
$41$	1.88727	+	2.24916i	0.294742	+	0.351259i	−0.598269	+	0.801296i	$0.704144\pi$
$42$	−2.27674	−	7.95579i	−0.351308	−	1.22760i
$43$	−5.95761	+	2.16839i	−0.908528	+	0.330677i	−0.753665	−	0.657259i	$-0.771716\pi$
$43$	−5.95761	+	2.16839i	−0.908528	+	0.330677i	−0.154863	+	0.987936i	$0.549494\pi$
$44$	−9.95069	−	5.58941i	−1.50012	−	0.842635i
$45$	2.25756	+	0.346954i	0.336538	+	0.0517208i
$46$	6.65678	−	3.89588i	0.981489	−	0.574417i
$47$	0.625921	−	3.54977i	0.0913000	−	0.517788i	−0.904519	−	0.426434i	$-0.859770\pi$
$47$	0.625921	−	3.54977i	0.0913000	−	0.517788i	0.995819	−	0.0913536i	$-0.0291193\pi$
$48$	−0.364446	+	6.91861i	−0.0526032	+	0.998615i
$49$	4.14688	+	1.50934i	0.592412	+	0.215620i
$50$	−2.10335	+	5.88682i	−0.297458	+	0.832522i
$51$	4.80874	−	3.44671i	0.673359	−	0.482637i
$52$	−10.3465	−	1.69865i	−1.43481	−	0.235560i
$53$	8.06569			1.10791			0.553954	−	0.832548i	$-0.313118\pi$
$53$	8.06569			1.10791			0.553954	+	0.832548i	$0.313118\pi$
$54$	4.44621	+	5.85075i	0.605052	+	0.796186i
$55$			4.34470i			0.585839i
$56$	−7.42745	−	6.01142i	−0.992534	−	0.803310i
$57$	−1.81756	+	4.01265i	−0.240742	+	0.531488i
$58$	2.03388	−	5.69239i	0.267061	−	0.747448i
$59$	−1.63379	+	4.48880i	−0.212701	+	0.584392i	−0.999460	−	0.0328691i	$-0.989536\pi$
$59$	−1.63379	+	4.48880i	−0.212701	+	0.584392i	0.786758	+	0.617261i	$0.211758\pi$
$60$	2.36424	−	1.16889i	0.305222	−	0.150904i
$61$	−2.62747	−	0.463294i	−0.336413	−	0.0593187i	0.00289009	−	0.999996i	$-0.499080\pi$
$61$	−2.62747	−	0.463294i	−0.336413	−	0.0593187i	−0.339303	+	0.940677i	$0.610191\pi$
$62$	−1.69063	−	2.88874i	−0.214711	−	0.366870i
$63$	−10.1325	+	0.223366i	−1.27657	+	0.0281415i
$64$	4.24289	+	6.78217i	0.530361	+	0.847772i
$65$	1.36515	+	3.75071i	0.169326	+	0.465219i
$66$	−9.71529	+	10.0499i	−1.19587	+	1.23705i
$67$	2.16648	−	1.81790i	0.264678	−	0.222091i	−0.500784	−	0.865572i	$-0.666955\pi$
$67$	2.16648	−	1.81790i	0.264678	−	0.222091i	0.765462	+	0.643481i	$0.222510\pi$
$68$	2.26060	−	6.44682i	0.274138	−	0.781792i
$69$	−2.54534	−	9.09710i	−0.306422	−	1.09516i
$70$	−0.610483	+	3.58591i	−0.0729666	+	0.428598i
$71$	3.03884	+	5.26343i	0.360644	+	0.624654i	0.988067	−	0.154025i	$-0.0492235\pi$
$71$	3.03884	+	5.26343i	0.360644	+	0.624654i	−0.627423	+	0.778679i	$0.715890\pi$
$72$	8.08260	+	2.58294i	0.952544	+	0.304402i
$73$	1.40736	−	2.43763i	0.164720	−	0.285303i	−0.771836	−	0.635822i	$-0.780661\pi$
$73$	1.40736	−	2.43763i	0.164720	−	0.285303i	0.936556	+	0.350519i	$0.113995\pi$
$74$	11.4117	+	9.46132i	1.32659	+	1.09986i
$75$	6.31965	+	4.32206i	0.729730	+	0.499069i
$76$	0.942366	+	4.99851i	0.108097	+	0.573369i
$77$	−3.34767	−	18.9856i	−0.381502	−	2.16360i
$78$	−5.22931	+	11.7285i	−0.592102	+	1.32800i
$79$	7.42577	−	8.84969i	0.835464	−	0.995667i	−0.164493	−	0.986378i	$-0.552599\pi$
$79$	7.42577	−	8.84969i	0.835464	−	0.995667i	0.999957	−	0.00928911i	$-0.00295686\pi$
$80$	1.46000	−	2.67264i	0.163233	−	0.298810i
$81$	8.31337	−	3.44788i	0.923708	−	0.383098i
$82$	2.05484	−	3.60813i	0.226919	−	0.398451i
$83$	5.47239	−	6.52174i	0.600673	−	0.715854i	−0.376947	−	0.926235i	$-0.623026\pi$
$83$	5.47239	−	6.52174i	0.600673	−	0.715854i	0.977620	+	0.210381i	$0.0674704\pi$
$84$	−9.43067	+	6.92955i	−1.02897	+	0.756076i
$85$	−2.56116	+	0.451602i	−0.277797	+	0.0489831i
$86$	5.80373	+	6.83425i	0.625832	+	0.736956i
$87$	−6.11092	−	4.17931i	−0.655159	−	0.448069i
$88$	−2.52077	+	15.9424i	−0.268715	+	1.69947i
$89$	−7.79000	−	4.49756i	−0.825739	−	0.476740i	0.0266528	−	0.999645i	$-0.491515\pi$
$89$	−7.79000	−	4.49756i	−0.825739	−	0.476740i	−0.852391	+	0.522904i	$0.824848\pi$
$90$	−0.649578	−	3.16417i	−0.0684716	−	0.333533i
$91$	−8.85545	−	15.3381i	−0.928303	−	1.60787i
$92$	−8.43812	−	6.91227i	−0.879735	−	0.720654i
$93$	−3.94772	+	1.10456i	−0.409360	+	0.114537i
$94$	−5.01483	+	0.914812i	−0.517240	+	0.0943557i
$95$	1.48333	−	1.24466i	0.152186	−	0.127699i
$96$	9.35354	−	2.91742i	0.954641	−	0.297758i
$97$	13.6755	−	4.97747i	1.38854	−	0.505386i	0.463781	−	0.885950i	$-0.346492\pi$
$97$	13.6755	−	4.97747i	1.38854	−	0.505386i	0.924755	+	0.380564i	$0.124270\pi$
$98$	−0.0368503	−	6.24084i	−0.00372244	−	0.630420i
$99$	8.88446	+	14.6337i	0.892922	+	1.47075i
$100$	8.84006	−	0.104399i	0.884006	−	0.0104399i
$101$	0.867234	−	4.91833i	0.0862930	−	0.489392i	−0.910777	−	0.412898i	$-0.864516\pi$
$101$	0.867234	−	4.91833i	0.0862930	−	0.489392i	0.997070	−	0.0764934i	$-0.0243724\pi$
$102$	−6.93414	−	4.68247i	−0.686582	−	0.463633i
$103$	−1.64778	+	4.52724i	−0.162360	+	0.446082i	−0.994019	−	0.109205i	$-0.965169\pi$
$103$	−1.64778	+	4.52724i	−0.162360	+	0.446082i	0.831659	+	0.555287i	$0.187392\pi$
$104$	2.83313	+	14.5549i	0.277811	+	1.42723i
$105$	4.05811	+	1.83816i	0.396031	+	0.179386i
$106$	−3.96451	−	10.6955i	−0.385067	−	1.03884i
$107$		−	2.56818i		−	0.248275i	−0.992265	−	0.124138i	$-0.960384\pi$
$107$		−	2.56818i		−	0.248275i	0.992265	−	0.124138i	$-0.0396164\pi$
$108$	5.57293	−	8.77168i	0.536256	−	0.844056i
$109$			7.69169i			0.736730i	0.929681	+	0.368365i	$0.120082\pi$
$109$			7.69169i			0.736730i	−0.929681	+	0.368365i	$0.879918\pi$
$110$	5.76127	−	2.13554i	0.549316	−	0.203616i
$111$	14.7563	−	10.5767i	1.40061	−	1.00390i
$112$	−4.32063	+	12.8039i	−0.408261	+	1.20986i
$113$	−2.07354	+	5.69700i	−0.195062	+	0.535928i	−0.998207	−	0.0598551i	$-0.980936\pi$
$113$	−2.07354	+	5.69700i	−0.195062	+	0.535928i	0.803145	+	0.595783i	$0.203158\pi$
$114$	6.21434	+	0.437848i	0.582026	+	0.0410082i
$115$	−0.721054	+	4.08930i	−0.0672386	+	0.381329i
$116$	−8.54809	+	0.100951i	−0.793670	+	0.00937308i
$117$	12.2679	+	9.84150i	1.13417	+	0.909847i
$118$	6.75541	−	0.0398886i	0.621886	−	0.00367205i
$119$	10.8438	−	3.94684i	0.994054	−	0.361806i
$120$	−2.71210	−	2.56055i	−0.247580	−	0.233745i
$121$	−16.5193	+	13.8613i	−1.50175	+	1.26012i
$122$	0.677125	+	3.71187i	0.0613040	+	0.336057i
$123$	−3.63534	−	3.55609i	−0.327788	−	0.320641i
$124$	−2.99961	+	3.66175i	−0.269372	+	0.328835i
$125$	−3.58612	−	6.21133i	−0.320752	−	0.555559i
$126$	5.27659	+	13.3264i	0.470076	+	1.18721i
$127$	−2.68591	−	1.55071i	−0.238336	−	0.137603i	0.376076	−	0.926589i	$-0.377273\pi$
$127$	−2.68591	−	1.55071i	−0.238336	−	0.137603i	−0.614412	+	0.788986i	$0.710607\pi$
$128$	6.90798	−	8.95990i	0.610585	−	0.791951i
$129$	9.90054	−	4.75022i	0.871694	−	0.418234i
$130$	4.30261	−	3.65383i	0.377364	−	0.320462i
$131$	15.9872	−	2.81898i	1.39681	−	0.246295i	0.575978	−	0.817465i	$-0.304621\pi$
$131$	15.9872	−	2.81898i	1.39681	−	0.246295i	0.820832	+	0.571170i	$0.193510\pi$
$132$	18.1019	+	7.94315i	1.57557	+	0.691363i
$133$	−5.52284	+	6.58187i	−0.478891	+	0.570720i
$134$	−3.47550	−	1.97931i	−0.300238	−	0.170987i
$135$	−3.95031	−	0.214337i	−0.339989	−	0.0184472i
$136$	−9.65994	+	0.171133i	−0.828333	+	0.0146745i
$137$	0.0788460	−	0.0939650i	0.00673627	−	0.00802797i	−0.762666	−	0.646793i	$-0.776110\pi$
$137$	0.0788460	−	0.0939650i	0.00673627	−	0.00802797i	0.769402	+	0.638765i	$0.220554\pi$
$138$	−10.8121	+	7.84671i	−0.920385	+	0.667957i
$139$	2.78791	+	15.8110i	0.236467	+	1.34107i	0.839502	+	0.543357i	$0.182847\pi$
$139$	2.78791	+	15.8110i	0.236467	+	1.34107i	−0.603035	+	0.797715i	$0.706042\pi$
$140$	5.05515	−	0.953044i	0.427238	−	0.0805469i
$141$	−0.475561	+	6.22510i	−0.0400494	+	0.524248i
$142$	5.48588	−	6.61677i	0.460365	−	0.555267i
$143$	−14.9583	+	25.9085i	−1.25088	+	2.16658i
$144$	−0.547723	−	11.9875i	−0.0456436	−	0.998958i
$145$	1.62715	+	2.81830i	0.135127	+	0.234047i
$146$	−3.92417	−	0.668070i	−0.324766	−	0.0552899i
$147$	−7.40448	−	1.89682i	−0.610711	−	0.156447i
$148$	6.93697	−	19.7830i	0.570215	−	1.62615i
$149$	−14.4253	+	12.1043i	−1.18177	+	0.991623i	−0.181805	+	0.983335i	$0.558194\pi$
$149$	−14.4253	+	12.1043i	−1.18177	+	0.991623i	−0.999966	+	0.00828872i	$0.997362\pi$
$150$	2.62497	−	10.5046i	0.214328	−	0.857694i
$151$	−5.65105	−	15.5261i	−0.459876	−	1.26350i	−0.925578	−	0.378557i	$-0.876420\pi$
$151$	−5.65105	−	15.5261i	−0.459876	−	1.26350i	0.465702	−	0.884942i	$-0.345802\pi$
$152$	6.16506	−	3.70653i	0.500053	−	0.300639i
$153$	−7.70298	+	6.75839i	−0.622749	+	0.546383i
$154$	−23.5303	+	13.7711i	−1.89612	+	1.10971i
$155$	1.77457	+	0.312904i	0.142537	+	0.0251330i
$156$	18.1229	+	1.16940i	1.45100	+	0.0936271i
$157$	3.99126	−	10.9659i	0.318537	−	0.875174i	−0.672320	−	0.740260i	$-0.734702\pi$
$157$	3.99126	−	10.9659i	0.318537	−	0.875174i	0.990857	−	0.134913i	$-0.0430755\pi$
$158$	−15.3851	−	5.49705i	−1.22397	−	0.437322i
$159$	−13.9028	+	1.37088i	−1.10256	+	0.108718i
$160$	−4.26168	−	0.622353i	−0.336915	−	0.0492014i
$161$		−	18.4251i		−	1.45210i
$162$	−8.65831	−	9.32919i	−0.680261	−	0.732970i
$163$	2.29194			0.179518			0.0897591	−	0.995964i	$-0.471390\pi$
$163$	2.29194			0.179518			0.0897591	+	0.995964i	$0.471390\pi$
$164$	−5.79456	−	0.951323i	−0.452479	−	0.0742859i
$165$	−0.738442	−	7.48892i	−0.0574876	−	0.583011i
$166$	−11.3380	−	4.05103i	−0.879997	−	0.314421i
$167$	7.85034	+	2.85729i	0.607478	+	0.221104i	0.627399	−	0.778698i	$-0.284119\pi$
$167$	7.85034	+	2.85729i	0.607478	+	0.221104i	−0.0199215	+	0.999802i	$0.506342\pi$
$168$	13.8244	+	9.09944i	1.06657	+	0.702037i
$169$	−2.51513	+	14.2640i	−0.193471	+	1.09723i
$170$	1.85773	+	3.17424i	0.142481	+	0.243453i
$171$	2.45091	−	7.22549i	0.187426	−	0.552547i
$172$	6.20984	−	11.0552i	0.473496	−	0.842954i
$173$	4.31220	−	1.56951i	0.327850	−	0.119328i	−0.172851	−	0.984948i	$-0.555298\pi$
$173$	4.31220	−	1.56951i	0.327850	−	0.119328i	0.500701	+	0.865620i	$0.333076\pi$
$174$	−2.53828	+	10.1576i	−0.192426	+	0.770047i
$175$	9.59894	+	11.4396i	0.725611	+	0.864750i
$176$	22.3794	−	4.49348i	1.68691	−	0.338709i
$177$	2.05321	−	8.01499i	0.154329	−	0.602444i
$178$	−2.13497	+	12.5406i	−0.160023	+	0.939956i
$179$	−8.01534	+	4.62766i	−0.599094	+	0.345887i	−0.768685	−	0.639627i	$-0.779089\pi$
$179$	−8.01534	+	4.62766i	−0.599094	+	0.345887i	0.169591	+	0.985515i	$0.445755\pi$
$180$	−3.87655	+	2.41665i	−0.288941	+	0.180126i
$181$	−10.1708	−	5.87212i	−0.755990	−	0.436471i	0.0718639	−	0.997414i	$-0.477105\pi$
$181$	−10.1708	−	5.87212i	−0.755990	−	0.436471i	−0.827854	+	0.560943i	$0.810439\pi$
$182$	−15.9863	+	19.2818i	−1.18499	+	1.42927i
$183$	4.60769	+	0.352000i	0.340610	+	0.0260206i
$184$	−5.01843	+	14.5869i	−0.369963	+	1.07536i
$185$	−7.85928	+	1.38580i	−0.577826	+	0.101886i
$186$	3.40511	+	4.69194i	0.249675	+	0.344030i
$187$	−14.9322	−	12.5296i	−1.09195	−	0.916254i
$188$	3.67801	+	6.20024i	0.268246	+	0.452199i
$189$	17.4273	−	2.10717i	1.26765	−	0.153274i
$190$	−2.37957	−	1.35518i	−0.172632	−	0.0983148i
$191$	9.19786	+	7.71792i	0.665534	+	0.558449i	0.911740	−	0.410768i	$-0.134740\pi$
$191$	9.19786	+	7.71792i	0.665534	+	0.558449i	−0.246206	+	0.969218i	$0.579184\pi$
$192$	−8.46616	−	10.9692i	−0.610992	−	0.791637i
$193$	0.0875504	+	0.496523i	0.00630202	+	0.0357405i	0.987797	−	0.155749i	$-0.0497792\pi$
$193$	0.0875504	+	0.496523i	0.00630202	+	0.0357405i	−0.981495	+	0.191490i	$0.938668\pi$
$194$	−13.3222	−	15.6878i	−0.956482	−	1.12632i
$195$	−2.99058	−	6.23305i	−0.214160	−	0.446358i
$196$	−8.25754	+	3.11641i	−0.589824	+	0.222601i
$197$	−1.86464	+	3.22964i	−0.132850	+	0.230103i	−0.924774	−	0.380517i	$-0.875746\pi$
$197$	−1.86464	+	3.22964i	−0.132850	+	0.230103i	0.791924	+	0.610619i	$0.209079\pi$
$198$	15.0381	−	18.9741i	1.06871	−	1.34843i
$199$	22.4920	−	12.9857i	1.59441	−	0.920534i	0.601876	−	0.798590i	$-0.294420\pi$
$199$	22.4920	−	12.9857i	1.59441	−	0.920534i	0.992537	−	0.121945i	$-0.0389130\pi$
$200$	−4.48357	−	11.6710i	−0.317036	−	0.825265i
$201$	−3.42537	+	3.50171i	−0.241607	+	0.246992i
$202$	−6.94820	+	1.26750i	−0.488874	+	0.0891811i
$203$	−9.28190	−	11.0617i	−0.651462	−	0.776382i
$204$	−2.80085	+	11.4966i	−0.196099	+	0.804920i
$205$	0.764549	+	2.10058i	0.0533984	+	0.146711i
$206$	6.81326	−	0.0402302i	0.474702	−	0.00280297i
$207$	5.93355	+	15.2480i	0.412411	+	1.05981i
$208$	17.9079	−	10.9110i	1.24169	−	0.756542i
$209$	14.2928	+	2.52021i	0.988655	+	0.174327i
$210$	0.442809	−	6.28476i	0.0305567	−	0.433689i
$211$	−5.28560	−	1.92380i	−0.363875	−	0.132440i	0.153611	−	0.988131i	$-0.450910\pi$
$211$	−5.28560	−	1.92380i	−0.363875	−	0.132440i	−0.517486	+	0.855692i	$0.673132\pi$
$212$	−12.2340	+	10.5143i	−0.840237	+	0.722122i
$213$	−6.13262	−	8.55603i	−0.420200	−	0.586250i
$214$	−3.40552	+	1.26233i	−0.232797	+	0.0862912i
$215$	−4.82697			−0.329196
$216$	−14.3709	−	3.07844i	−0.977817	−	0.209461i
$217$	−7.99564			−0.542779
$218$	10.1995	−	3.78068i	0.690800	−	0.256060i
$219$	−2.01155	+	4.44092i	−0.135928	+	0.300090i
$220$	−5.66365	−	6.59004i	−0.381843	−	0.444300i
$221$	−16.8277	−	6.12476i	−1.13195	−	0.411996i
$222$	−21.2784	−	14.3688i	−1.42811	−	0.964371i
$223$	1.15220	+	0.203163i	0.0771568	+	0.0136048i	0.212093	−	0.977249i	$-0.431972\pi$
$223$	1.15220	+	0.203163i	0.0771568	+	0.0136048i	−0.134937	+	0.990854i	$0.543083\pi$
$224$	19.1023	−	0.564124i	1.27633	−	0.0376921i
$225$	−11.6277	−	6.37579i	−0.775181	−	0.425053i
$226$	8.57369	−	0.0506250i	0.570313	−	0.00336752i
$227$	−3.74301	−	10.2838i	−0.248432	−	0.682563i	−0.999744	−	0.0226152i	$-0.992801\pi$
$227$	−3.74301	−	10.2838i	−0.248432	−	0.682563i	0.751312	−	0.659947i	$-0.229421\pi$
$228$	−2.47392	−	8.45572i	−0.163839	−	0.559994i
$229$	−3.60038	−	4.29076i	−0.237920	−	0.283542i	0.633852	−	0.773455i	$-0.281473\pi$
$229$	−3.60038	−	4.29076i	−0.237920	−	0.283542i	−0.871771	+	0.489913i	$0.837029\pi$
$230$	5.77702	−	1.05385i	0.380925	−	0.0694890i
$231$	8.99720	+	32.1563i	0.591973	+	2.11573i
$232$	4.33549	+	11.2855i	0.284639	+	0.740932i
$233$	−12.0089	+	6.93335i	−0.786730	+	0.454219i	−0.838810	−	0.544424i	$-0.816748\pi$
$233$	−12.0089	+	6.93335i	−0.786730	+	0.454219i	0.0520803	+	0.998643i	$0.483415\pi$
$234$	7.02028	−	21.1052i	0.458930	−	1.37969i
$235$	1.37217	−	2.37666i	0.0895103	−	0.155036i
$236$	−3.37337	−	8.93839i	−0.219588	−	0.581840i
$237$	−11.2956	+	16.5162i	−0.733728	+	1.07285i
$238$	−10.5637	−	12.4395i	−0.684746	−	0.806331i
$239$	−3.00765	−	17.0573i	−0.194549	−	1.10334i	−0.913060	−	0.407826i	$-0.866287\pi$
$239$	−3.00765	−	17.0573i	−0.194549	−	1.10334i	0.718511	−	0.695516i	$-0.244824\pi$
$240$	−2.06234	+	4.85495i	−0.133123	+	0.313386i
$241$	−1.47032	−	1.23374i	−0.0947115	−	0.0794724i	0.594202	−	0.804316i	$-0.297468\pi$
$241$	−1.47032	−	1.23374i	−0.0947115	−	0.0794724i	−0.688914	+	0.724843i	$0.741912\pi$
$242$	26.5005	+	15.0921i	1.70351	+	0.970159i
$243$	−13.7437	+	7.35606i	−0.881657	+	0.471891i
$244$	4.58929	−	2.72239i	0.293799	−	0.174283i
$245$	2.57382	+	2.15969i	0.164435	+	0.137977i
$246$	−2.92866	+	6.56855i	−0.186725	+	0.418795i
$247$	13.1307	−	2.31529i	0.835484	−	0.147318i
$248$	6.33004	+	2.17776i	0.401958	+	0.138288i
$249$	−8.32425	+	12.1716i	−0.527528	+	0.771343i
$250$	−6.47384	+	7.80840i	−0.409442	+	0.493847i
$251$	18.6528	+	10.7692i	1.17735	+	0.679746i	0.955401	−	0.295311i	$-0.0954234\pi$
$251$	18.6528	+	10.7692i	1.17735	+	0.679746i	0.221953	+	0.975057i	$0.428757\pi$
$252$	15.0778	−	13.5473i	0.949811	−	0.853399i
$253$	−26.9533	+	15.5615i	−1.69454	+	0.978342i
$254$	−0.736115	+	4.32386i	−0.0461880	+	0.271303i
$255$	4.33789	−	1.21373i	0.271649	−	0.0760065i
$256$	−15.2767	−	4.75627i	−0.954794	−	0.297267i
$257$	−5.79174	−	6.90232i	−0.361279	−	0.430555i	0.554534	−	0.832161i	$-0.312897\pi$
$257$	−5.79174	−	6.90232i	−0.361279	−	0.430555i	−0.915813	+	0.401606i	$0.868452\pi$
$258$	−11.1654	−	10.7937i	−0.695128	−	0.671987i
$259$	33.2759	−	12.1114i	2.06766	−	0.752568i
$260$	−6.96001	−	3.90951i	−0.431641	−	0.242457i
$261$	11.2437	+	6.16521i	0.695966	+	0.381617i
$262$	−11.5963	−	19.8142i	−0.716419	−	1.22413i
$263$	1.07833	−	6.11552i	0.0664927	−	0.377099i	−0.933343	−	0.358985i	$-0.883123\pi$
$263$	1.07833	−	6.11552i	0.0664927	−	0.377099i	0.999836	−	0.0181137i	$-0.00576609\pi$
$264$	1.63540	−	27.9083i	0.100652	−	1.71763i
$265$	5.77052	+	2.10030i	0.354480	+	0.129020i
$266$	11.4425	+	4.08838i	0.701584	+	0.250674i
$267$	14.1920	+	6.42838i	0.868535	+	0.393411i
$268$	−0.916355	+	5.58156i	−0.0559753	+	0.340948i
$269$	−1.29437			−0.0789188			−0.0394594	−	0.999221i	$-0.512564\pi$
$269$	−1.29437			−0.0789188			−0.0394594	+	0.999221i	$0.512564\pi$
$270$	1.65747	+	5.34365i	0.100870	+	0.325204i
$271$			3.86099i			0.234539i	0.993100	+	0.117269i	$0.0374141\pi$
$271$			3.86099i			0.234539i	−0.993100	+	0.117269i	$0.962586\pi$
$272$	4.97506	+	12.7254i	0.301657	+	0.771591i
$273$	17.8710	+	24.9330i	1.08160	+	1.50902i
$274$	−0.163357	−	0.0583671i	−0.00986876	−	0.00352608i
$275$	8.62737	−	23.7035i	0.520250	−	1.42938i
$276$	15.7195	+	10.4804i	0.946206	+	0.630849i
$277$	24.2259	+	4.27169i	1.45560	+	0.256661i	0.844780	−	0.535113i	$-0.179731\pi$
$277$	24.2259	+	4.27169i	1.45560	+	0.256661i	0.610815	+	0.791774i	$0.290842\pi$
$278$	19.5958	−	11.4684i	1.17528	−	0.687831i
$279$	6.61692	−	2.57489i	0.396144	−	0.154154i
$280$	−3.74853	−	6.23492i	−0.224017	−	0.372608i
$281$	1.24545	+	3.42184i	0.0742972	+	0.204130i	0.971282	−	0.237932i	$-0.0764694\pi$
$281$	1.24545	+	3.42184i	0.0742972	+	0.204130i	−0.896985	+	0.442062i	$0.854247\pi$
$282$	8.48853	−	2.42919i	0.505484	−	0.144656i
$283$	2.81306	−	2.36044i	0.167219	−	0.140314i	−0.555338	−	0.831625i	$-0.687411\pi$
$283$	2.81306	−	2.36044i	0.167219	−	0.140314i	0.722557	+	0.691311i	$0.242967\pi$
$284$	−11.4706	−	4.02221i	−0.680655	−	0.238674i
$285$	−2.34525	+	2.39752i	−0.138921	+	0.142017i
$286$	41.7083	+	7.10064i	2.46626	+	0.419869i
$287$	−4.95948	−	8.59007i	−0.292749	−	0.507056i
$288$	−15.6268	+	6.61849i	−0.920816	+	0.389998i
$289$	−2.66602	+	4.61769i	−0.156825	+	0.271629i
$290$	2.93741	−	3.54295i	0.172491	−	0.208049i
$291$	−22.7263	+	10.9040i	−1.33224	+	0.639202i
$292$	1.04295	+	5.53201i	0.0610338	+	0.323736i
$293$	−5.15756	−	29.2500i	−0.301308	−	1.70880i	−0.640394	−	0.768046i	$-0.721229\pi$
$293$	−5.15756	−	29.2500i	−0.301308	−	1.70880i	0.339086	−	0.940755i	$-0.389882\pi$
$294$	1.12424	+	10.7510i	0.0655668	+	0.627012i
$295$	−2.33776	+	2.78603i	−0.136110	+	0.162209i
$296$	−29.6429	+	0.525145i	−1.72296	+	0.0305235i
$297$	−17.8013	−	23.7140i	−1.03293	−	1.37603i
$298$	23.1413	+	13.1791i	1.34054	+	0.763444i
$299$	−18.3788	+	21.9030i	−1.06287	+	1.26668i
$300$	−15.2198	+	1.68244i	−0.878715	+	0.0971359i
$301$	21.0930	−	3.71926i	1.21578	−	0.214375i
$302$	−17.8107	+	15.1251i	−1.02489	+	0.870351i
$303$	−0.658905	+	8.62508i	−0.0378531	+	0.495498i
$304$	−7.94533	−	6.35330i	−0.455696	−	0.364387i
$305$	−1.75916	−	1.01565i	−0.100729	−	0.0581559i
$306$	12.7482	+	6.89257i	0.728764	+	0.394022i
$307$	4.62536	+	8.01136i	0.263983	+	0.457232i	0.967297	−	0.253648i	$-0.0816303\pi$
$307$	4.62536	+	8.01136i	0.263983	+	0.457232i	−0.703314	+	0.710880i	$0.748297\pi$
$308$	29.8269	+	24.4334i	1.69955	+	1.39222i
$309$	2.07080	−	8.08362i	0.117803	−	0.459861i
$310$	−0.457323	−	2.50696i	−0.0259742	−	0.142386i
$311$	−20.0930	+	16.8601i	−1.13937	+	0.956046i	−0.999418	−	0.0341122i	$-0.989140\pi$
$311$	−20.0930	+	16.8601i	−1.13937	+	0.956046i	−0.139953	+	0.990158i	$0.544695\pi$
$312$	−7.35725	−	24.6067i	−0.416522	−	1.39308i
$313$	18.7936	−	6.84033i	1.06228	−	0.386638i	0.248995	−	0.968505i	$-0.419900\pi$
$313$	18.7936	−	6.84033i	1.06228	−	0.386638i	0.813284	+	0.581866i	$0.197677\pi$
$314$	−16.5031	+	0.0974458i	−0.931324	+	0.00549918i
$315$	−7.30736	−	2.47869i	−0.411723	−	0.139658i
$316$	0.272845	+	23.1033i	0.0153487	+	1.29966i
$317$	−4.07115	+	23.0886i	−0.228659	+	1.29679i	0.626907	+	0.779094i	$0.284320\pi$
$317$	−4.07115	+	23.0886i	−0.228659	+	1.29679i	−0.855566	+	0.517694i	$0.826791\pi$
$318$	8.65144	+	17.7619i	0.485149	+	0.996037i
$319$	−8.34243	+	22.9206i	−0.467086	+	1.28331i
$320$	1.26946	+	5.95709i	0.0709652	+	0.333011i
$321$	0.436498	+	4.42675i	0.0243629	+	0.247077i
$322$	−24.4325	+	9.05645i	−1.36157	+	0.504696i
$323$			8.68745i			0.483383i
$324$	−8.11514	+	16.0669i	−0.450841	+	0.892604i
$325$		−	23.1737i		−	1.28545i
$326$	−1.12655	−	3.03921i	−0.0623939	−	0.168327i
$327$	−1.30731	−	13.2581i	−0.0722945	−	0.733175i
$328$	1.58669	+	8.15146i	0.0876102	+	0.450089i
$329$	−4.16487	+	11.4429i	−0.229617	+	0.630866i
$330$	−9.56769	+	4.66022i	−0.526684	+	0.256537i
$331$	−3.95158	+	22.4105i	−0.217198	+	1.23179i	0.659853	+	0.751395i	$0.270619\pi$
$331$	−3.95158	+	22.4105i	−0.217198	+	1.23179i	−0.877051	+	0.480397i	$0.840492\pi$
$332$	0.201072	+	17.0259i	0.0110353	+	0.934416i
$333$	−23.6377	+	20.7391i	−1.29534	+	1.13649i
$334$	−0.0697602	−	11.8144i	−0.00381711	−	0.646453i
$335$	2.02337	−	0.736446i	0.110548	−	0.0402363i
$336$	5.27123	−	22.8044i	0.287569	−	1.24408i
$337$	24.5647	−	20.6122i	1.33812	−	1.12282i	0.356018	−	0.934479i	$-0.384134\pi$
$337$	24.5647	−	20.6122i	1.33812	−	1.12282i	0.982104	−	0.188338i	$-0.0603101\pi$
$338$	20.1510	−	3.67598i	1.09607	−	0.199947i
$339$	2.60585	−	10.1723i	0.141531	−	0.552483i
$340$	3.29607	−	4.02366i	0.178755	−	0.218214i
$341$	6.75296	+	11.6965i	0.365693	+	0.633400i
$342$	−10.7860	+	0.301500i	−0.583242	+	0.0163033i
$343$	7.56875	+	4.36982i	0.408674	+	0.235948i
$344$	−17.7121	−	2.80059i	−0.954971	−	0.150997i
$345$	0.547840	−	7.17124i	0.0294947	−	0.386087i
$346$	−4.20081	−	4.94672i	−0.225837	−	0.265937i
$347$	14.5793	−	2.57072i	0.782658	−	0.138004i	0.231979	−	0.972721i	$-0.425480\pi$
$347$	14.5793	−	2.57072i	0.782658	−	0.138004i	0.550679	+	0.834717i	$0.314369\pi$
$348$	14.7171	−	1.62688i	0.788920	−	0.0872097i
$349$	16.2504	−	19.3665i	0.869864	−	1.03666i	−0.129121	−	0.991629i	$-0.541216\pi$
$349$	16.2504	−	19.3665i	0.869864	−	1.03666i	0.998985	−	0.0450350i	$-0.0143399\pi$
$350$	10.4513	−	18.3515i	0.558643	−	0.980929i
$351$	−22.8188	−	14.8786i	−1.21798	−	0.794162i
$352$	−16.9587	−	27.4675i	−0.903901	−	1.46402i
$353$	0.289344	−	0.344827i	0.0154002	−	0.0183533i	−0.758289	−	0.651918i	$-0.773965\pi$
$353$	0.289344	−	0.344827i	0.0154002	−	0.0183533i	0.773690	+	0.633565i	$0.218409\pi$
$354$	−11.6375	+	1.21693i	−0.618524	+	0.0646793i
$355$	0.803519	+	4.55698i	0.0426464	+	0.241860i
$356$	17.6788	−	3.33297i	0.936975	−	0.176647i
$357$	−18.0206	+	8.64620i	−0.953753	+	0.457605i
$358$	10.0762	+	8.35409i	0.532546	+	0.441527i
$359$	1.58856	−	2.75146i	0.0838408	−	0.145216i	−0.821056	−	0.570848i	$-0.806615\pi$
$359$	1.58856	−	2.75146i	0.0838408	−	0.145216i	0.904897	+	0.425631i	$0.139948\pi$
$360$	5.11003	+	3.95264i	0.269322	+	0.208323i
$361$	6.26585	+	10.8528i	0.329782	+	0.571199i
$362$	−2.78747	+	16.3733i	−0.146506	+	0.860561i
$363$	26.1182	−	26.7003i	1.37085	−	1.40140i
$364$	33.4263	+	11.7211i	1.75202	+	0.614350i
$365$	1.64164	−	1.37750i	0.0859275	−	0.0721017i
$366$	−1.79804	−	6.28303i	−0.0939850	−	0.328419i
$367$	−11.2504	−	30.9103i	−0.587268	−	1.61351i	−0.775476	−	0.631377i	$-0.782490\pi$
$367$	−11.2504	−	30.9103i	−0.587268	−	1.61351i	0.188208	−	0.982129i	$-0.439732\pi$
$368$	21.8096	−	0.515207i	1.13691	−	0.0268570i
$369$	6.87061	+	5.51172i	0.357670	+	0.286928i
$370$	5.70070	+	9.74062i	0.296365	+	0.506391i
$371$	−26.8345	−	4.73164i	−1.39318	−	0.245655i
$372$	4.54803	−	6.82156i	0.235804	−	0.353681i
$373$	4.07881	−	11.2064i	0.211193	−	0.580247i	−0.788188	−	0.615434i	$-0.788981\pi$
$373$	4.07881	−	11.2064i	0.211193	−	0.580247i	0.999381	+	0.0351875i	$0.0112029\pi$
$374$	−9.27523	+	25.9594i	−0.479611	+	1.34233i
$375$	7.23706	+	10.0969i	0.373720	+	0.521402i
$376$	6.41396	−	7.92480i	0.330775	−	0.408691i
$377$			22.4083i			1.15409i
$378$	−11.3602	−	22.0737i	−0.584307	−	1.13535i
$379$	1.35817			0.0697646			0.0348823	−	0.999391i	$-0.488894\pi$
$379$	1.35817			0.0697646			0.0348823	+	0.999391i	$0.488894\pi$
$380$	−0.627401	+	3.82153i	−0.0321850	+	0.196040i
$381$	4.89324	+	2.21644i	0.250688	+	0.113551i
$382$	5.71332	−	15.9904i	0.292319	−	0.818138i
$383$	27.9805	+	10.1841i	1.42973	+	0.520381i	0.936855	−	0.349717i	$-0.113722\pi$
$383$	27.9805	+	10.1841i	1.42973	+	0.520381i	0.492879	+	0.870098i	$0.335944\pi$
$384$	−10.3844	+	16.6182i	−0.529925	+	0.848044i
$385$	2.54877	−	14.4548i	0.129897	−	0.736683i
$386$	0.615379	−	0.360151i	0.0313220	−	0.0183312i
$387$	−16.2581	+	9.87065i	−0.826446	+	0.501753i
$388$	−14.2545	+	25.3769i	−0.723661	+	1.28832i
$389$	−5.43932	+	1.97975i	−0.275784	+	0.100377i	−0.476210	−	0.879332i	$-0.657990\pi$
$389$	−5.43932	+	1.97975i	−0.275784	+	0.100377i	0.200426	+	0.979709i	$0.435768\pi$
$390$	−6.79536	+	7.02937i	−0.344096	+	0.355946i
$391$	−11.9750	−	14.2712i	−0.605600	−	0.721726i
$392$	8.19132	+	9.41808i	0.413724	+	0.475685i
$393$	−27.0779	+	7.57630i	−1.36590	+	0.382174i
$394$	5.19918	+	0.885135i	0.261931	+	0.0445924i
$395$	7.61715	−	4.39776i	0.383260	−	0.221275i
$396$	−32.5522	−	10.6149i	−1.63581	−	0.533417i
$397$	13.5494	+	7.82276i	0.680026	+	0.392613i	0.799865	−	0.600180i	$-0.204904\pi$
$397$	13.5494	+	7.82276i	0.680026	+	0.392613i	−0.119839	+	0.992793i	$0.538238\pi$
$398$	−28.2751	−	23.4425i	−1.41730	−	1.17507i
$399$	8.40099	−	12.2838i	0.420576	−	0.614959i
$400$	−13.2725	+	11.6821i	−0.663626	+	0.584103i
$401$	32.9174	−	5.80423i	1.64382	−	0.289850i	0.726251	−	0.687429i	$-0.241261\pi$
$401$	32.9174	−	5.80423i	1.64382	−	0.289850i	0.917568	+	0.397580i	$0.130150\pi$
$402$	6.32710	+	2.82101i	0.315567	+	0.140699i
$403$	9.50489	+	7.97555i	0.473472	+	0.397290i
$404$	5.09600	+	8.59063i	0.253536	+	0.427400i
$405$	6.84555	−	0.301961i	0.340158	−	0.0150045i
$406$	−10.1061	+	17.7454i	−0.501556	+	0.880689i
$407$	−45.8215	−	38.4488i	−2.27129	−	1.90584i
$408$	16.6217	−	1.93682i	0.822895	−	0.0958870i
$409$	−4.03315	−	22.8731i	−0.199426	−	1.13100i	−0.905973	−	0.423336i	$-0.860859\pi$
$409$	−4.03315	−	22.8731i	−0.199426	−	1.13100i	0.706547	−	0.707666i	$-0.250252\pi$
$410$	2.40967	−	2.04632i	0.119005	−	0.101061i
$411$	−0.119936	+	0.175368i	−0.00591598	+	0.00865025i
$412$	−3.40225	−	9.01492i	−0.167617	−	0.444133i
$413$	8.06891	−	13.9758i	0.397045	−	0.687702i
$414$	17.3030	−	15.3630i	0.850398	−	0.755049i
$415$	5.61343	−	3.24091i	0.275552	−	0.159090i
$416$	−23.2708	−	18.3837i	−1.14094	−	0.901336i
$417$	−7.49279	−	26.7794i	−0.366924	−	1.31139i
$418$	−3.68340	−	20.1917i	−0.180161	−	0.987608i
$419$	1.20391	+	1.43476i	0.0588147	+	0.0700926i	0.794650	−	0.607068i	$-0.207655\pi$
$419$	1.20391	+	1.43476i	0.0588147	+	0.0700926i	−0.735835	+	0.677161i	$0.763210\pi$
$420$	−8.55153	+	2.50195i	−0.417272	+	0.122083i
$421$	6.15422	+	16.9086i	0.299938	+	0.824073i	0.994509	+	0.104649i	$0.0333719\pi$
$421$	6.15422	+	16.9086i	0.299938	+	0.824073i	−0.694571	+	0.719424i	$0.744406\pi$
$422$	0.0469692	+	7.95455i	0.00228642	+	0.387221i
$423$	−0.238323	−	10.8110i	−0.0115877	−	0.525648i
$424$	19.9558	+	11.0549i	0.969138	+	0.536872i
$425$	14.8698	+	2.62194i	0.721290	+	0.127183i
$426$	−8.33135	+	12.3377i	−0.403655	+	0.597762i
$427$	8.46978	+	3.08275i	0.409881	+	0.149185i
$428$	3.34782	+	3.89541i	0.161823	+	0.188292i
$429$	21.3800	−	47.2007i	1.03223	−	2.27887i
$430$	2.37259	+	6.40078i	0.114416	+	0.308673i
$431$	−28.7176			−1.38328			−0.691640	−	0.722242i	$-0.743111\pi$
$431$	−28.7176			−1.38328			−0.691640	+	0.722242i	$0.743111\pi$
$432$	2.98155	+	20.5696i	0.143450	+	0.989658i
$433$	−6.95359			−0.334168			−0.167084	−	0.985943i	$-0.553435\pi$
$433$	−6.95359			−0.334168			−0.167084	+	0.985943i	$0.553435\pi$
$434$	3.93008	+	10.6026i	0.188650	+	0.508941i
$435$	−3.28371	−	4.58133i	−0.157442	−	0.219658i
$436$	−10.0267	−	11.6668i	−0.480193	−	0.558737i
$437$	13.0344	+	4.74412i	0.623519	+	0.226942i
$438$	6.87760	+	0.484579i	0.328625	+	0.0231541i
$439$	−32.5793	−	5.74462i	−1.55493	−	0.274176i	−0.670877	−	0.741568i	$-0.734082\pi$
$439$	−32.5793	−	5.74462i	−1.55493	−	0.274176i	−0.884050	+	0.467393i	$0.845193\pi$
$440$	−5.95486	+	10.7495i	−0.283887	+	0.512460i
$441$	13.0854	+	2.01103i	0.623116	+	0.0957636i
$442$	0.149535	+	25.3247i	0.00711265	+	1.20458i
$443$	6.00559	+	16.5002i	0.285334	+	0.783949i	0.996703	+	0.0811307i	$0.0258531\pi$
$443$	6.00559	+	16.5002i	0.285334	+	0.783949i	−0.711369	+	0.702818i	$0.751925\pi$
$444$	−8.59480	+	35.2788i	−0.407891	+	1.67426i
$445$	−4.40212	−	5.24625i	−0.208681	−	0.248696i
$446$	−0.296933	−	1.62773i	−0.0140602	−	0.0770751i
$447$	22.8076	−	23.3159i	1.07876	−	1.10280i
$448$	−10.1374	−	25.0533i	−0.478946	−	1.18366i
$449$	35.9869	−	20.7770i	1.69833	−	0.980529i	0.750974	−	0.660332i	$-0.229584\pi$
$449$	35.9869	−	20.7770i	1.69833	−	0.980529i	0.947351	−	0.320197i	$-0.103749\pi$
$450$	−2.73925	+	18.5528i	−0.129129	+	0.874586i
$451$	−8.37736	+	14.5100i	−0.394475	+	0.683250i
$452$	−4.28134	−	11.3442i	−0.201377	−	0.533588i
$453$	12.3796	+	25.8018i	0.581642	+	1.21227i
$454$	−11.7971	+	10.0182i	−0.553664	+	0.470178i
$455$	−2.34152	−	13.2794i	−0.109772	−	0.622550i
$456$	−9.99669	+	7.43675i	−0.468138	+	0.348258i
$457$	13.2175	+	11.0908i	0.618287	+	0.518804i	0.897265	−	0.441493i	$-0.145551\pi$
$457$	13.2175	+	11.0908i	0.618287	+	0.518804i	−0.278978	+	0.960298i	$0.589996\pi$
$458$	−3.92007	+	6.88330i	−0.183173	+	0.321635i
$459$	12.1289	−	12.9586i	0.566127	−	0.604856i
$460$	−4.23702	−	7.14260i	−0.197552	−	0.333025i
$461$	12.7382	+	10.6886i	0.593276	+	0.497817i	0.889276	−	0.457370i	$-0.151209\pi$
$461$	12.7382	+	10.6886i	0.593276	+	0.497817i	−0.296001	+	0.955188i	$0.595653\pi$
$462$	38.2183	−	27.7364i	1.77808	−	1.29041i
$463$	−22.8699	+	4.03258i	−1.06285	+	0.187410i	−0.677622	−	0.735410i	$-0.736990\pi$
$463$	−22.8699	+	4.03258i	−1.06285	+	0.187410i	−0.385232	+	0.922820i	$0.625878\pi$
$464$	12.8341	−	11.2962i	0.595810	−	0.524414i
$465$	−3.11199	−	0.237737i	−0.144315	−	0.0110248i
$466$	15.0967	+	12.5164i	0.699339	+	0.579813i
$467$	−19.4081	−	11.2053i	−0.898099	−	0.518518i	−0.0215159	−	0.999769i	$-0.506849\pi$
$467$	−19.4081	−	11.2053i	−0.898099	−	0.518518i	−0.876583	+	0.481251i	$0.840183\pi$
$468$	−31.4371	+	1.06456i	−1.45318	+	0.0492093i
$469$	−8.27432	+	4.77718i	−0.382073	+	0.220590i
$470$	−3.82603	−	0.651362i	−0.176481	−	0.0300451i
$471$	−5.01589	+	19.5802i	−0.231120	+	0.902207i
$472$	−10.1946	+	8.86671i	−0.469245	+	0.408123i
$473$	−23.2555	−	27.7148i	−1.06929	−	1.27433i
$474$	27.4534	+	6.86031i	1.26098	+	0.315104i
$475$	−10.5642	+	3.84505i	−0.484718	+	0.176423i
$476$	−11.3029	+	20.1224i	−0.518070	+	0.922307i
$477$	23.7311	−	4.72594i	1.08657	−	0.216386i
$478$	−21.1404	+	12.3724i	−0.966938	+	0.565901i
$479$	5.11572	−	29.0127i	0.233743	−	1.32562i	−0.611502	−	0.791243i	$-0.709434\pi$
$479$	5.11572	−	29.0127i	0.233743	−	1.32562i	0.845245	−	0.534379i	$-0.179455\pi$
$480$	7.45160	+	0.348413i	0.340117	+	0.0159028i
$481$	−51.6380	−	18.7947i	−2.35449	−	0.856965i
$482$	−0.913299	+	2.55613i	−0.0415996	+	0.116429i
$483$	3.13160	+	31.7592i	0.142493	+	1.44509i
$484$	6.98715	−	42.5591i	0.317598	−	1.93450i
$485$	11.0801			0.503123
$486$	16.5099	+	14.6090i	0.748903	+	0.662680i
$487$			27.2531i			1.23496i	0.786587	+	0.617479i	$0.211846\pi$
$487$			27.2531i			1.23496i	−0.786587	+	0.617479i	$0.788154\pi$
$488$	−5.86577	−	4.74748i	−0.265531	−	0.214908i
$489$	−3.95059	+	0.389547i	−0.178652	+	0.0176159i
$490$	1.59875	−	4.47455i	0.0722240	−	0.202140i
$491$	−5.33019	+	14.6446i	−0.240548	+	0.660900i	0.759399	+	0.650625i	$0.225493\pi$
$491$	−5.33019	+	14.6446i	−0.240548	+	0.660900i	−0.999947	+	0.0102751i	$0.996729\pi$
$492$	10.1497	+	0.654922i	0.457585	+	0.0295261i
$493$	−14.3787	−	2.53534i	−0.647582	−	0.114186i
$494$	−9.52427	−	16.2738i	−0.428517	−	0.732195i
$495$	2.54569	+	12.7831i	0.114420	+	0.574556i
$496$	−0.223576	−	9.46437i	−0.0100388	−	0.424963i
$497$	−7.02247	−	19.2941i	−0.315001	−	0.865458i
$498$	20.2317	+	5.05568i	0.906604	+	0.226550i
$499$	4.83664	−	4.05842i	0.216518	−	0.181680i	−0.528077	−	0.849196i	$-0.677087\pi$
$499$	4.83664	−	4.05842i	0.216518	−	0.181680i	0.744595	+	0.667516i	$0.232642\pi$
$500$	13.5364	+	4.74658i	0.605365	+	0.212273i
$501$	−14.0172	−	3.59081i	−0.626243	−	0.160426i
$502$	5.11209	−	30.0279i	0.228164	−	1.34021i
$503$	3.45933	+	5.99174i	0.154244	+	0.267159i	0.932784	−	0.360437i	$-0.117372\pi$
$503$	3.45933	+	5.99174i	0.154244	+	0.267159i	−0.778539	+	0.627596i	$0.784039\pi$
$504$	−25.3755	−	13.3350i	−1.13031	−	0.593987i
$505$	1.90118	−	3.29294i	0.0846015	−	0.146534i
$506$	33.8835	+	28.0924i	1.50631	+	1.24886i
$507$	1.91094	−	25.0142i	0.0848677	−	1.11092i
$508$	6.09546	−	1.14917i	0.270442	−	0.0509863i
$509$	6.85834	+	38.8956i	0.303991	+	1.72402i	0.628218	+	0.778037i	$0.283785\pi$
$509$	6.85834	+	38.8956i	0.303991	+	1.72402i	−0.324227	+	0.945979i	$0.605104\pi$
$510$	−3.74165	−	5.15567i	−0.165683	−	0.228297i
$511$	−6.11230	+	7.28435i	−0.270392	+	0.322241i
$512$	1.20189	+	22.5955i	0.0531166	+	0.998588i
$513$	−2.99655	+	12.8711i	−0.132301	+	0.568272i
$514$	−6.30600	+	11.0728i	−0.278146	+	0.488400i
$515$	−2.35778	+	2.80989i	−0.103896	+	0.123818i
$516$	−8.82486	+	20.1113i	−0.388493	+	0.885349i
$517$	20.2569	−	3.57183i	0.890896	−	0.157089i
$518$	−32.4164	−	38.1723i	−1.42429	−	1.67719i
$519$	−7.16614	+	3.43827i	−0.314559	+	0.150923i
$520$	−1.76316	+	11.1509i	−0.0773195	+	0.489001i
$521$	0.808019	+	0.466510i	0.0353999	+	0.0204382i	0.517596	−	0.855625i	$-0.326827\pi$
$521$	0.808019	+	0.466510i	0.0353999	+	0.0204382i	−0.482196	+	0.876064i	$0.660161\pi$
$522$	2.64878	−	17.9400i	0.115934	−	0.785213i
$523$	−18.5482	−	32.1264i	−0.811057	−	1.40479i	−0.912125	−	0.409912i	$-0.865560\pi$
$523$	−18.5482	−	32.1264i	−0.811057	−	1.40479i	0.101069	−	0.994879i	$-0.467774\pi$
$524$	−20.5747	+	25.1164i	−0.898809	+	1.09722i
$525$	−18.4899	−	18.0868i	−0.806966	−	0.789373i
$526$	−8.63949	+	1.57603i	−0.376700	+	0.0687182i
$527$	−6.19304	+	5.19658i	−0.269773	+	0.226367i
$528$	−37.8115	+	11.5491i	−1.64553	+	0.502609i
$529$	−6.33854	+	2.30704i	−0.275589	+	0.100306i
$530$	−0.0512783	−	8.68434i	−0.00222739	−	0.377223i
$531$	−2.17685	+	14.1643i	−0.0944672	+	0.614680i
$532$	−0.202926	−	17.1828i	−0.00879795	−	0.744970i
$533$	−2.67286	+	15.1585i	−0.115774	+	0.656590i
$534$	1.54859	−	21.9790i	0.0670138	−	0.951123i
$535$	0.668751	−	1.83738i	0.0289126	−	0.0794368i
$536$	7.85183	−	1.52836i	0.339147	−	0.0660153i
$537$	13.0294	−	9.33897i	0.562261	−	0.403006i
$538$	0.636216	+	1.71639i	0.0274292	+	0.0739988i
$539$			25.1830i			1.08471i
$540$	6.27124	−	4.82443i	0.269871	−	0.207611i
$541$		−	25.5189i		−	1.09714i	−0.836104	−	0.548571i	$-0.815172\pi$
$541$		−	25.5189i		−	1.09714i	0.836104	−	0.548571i	$-0.184828\pi$
$542$	5.11986	−	1.89779i	0.219917	−	0.0815169i
$543$	18.5294	+	8.39305i	0.795172	+	0.360180i
$544$	14.4291	−	12.8521i	0.618643	−	0.551027i
$545$	−2.00291	+	5.50295i	−0.0857952	+	0.235720i
$546$	24.2783	−	35.9530i	1.03901	−	1.53865i
$547$	−3.90042	+	22.1204i	−0.166770	+	0.945800i	0.780451	+	0.625218i	$0.214990\pi$
$547$	−3.90042	+	22.1204i	−0.166770	+	0.945800i	−0.947221	+	0.320582i	$0.896121\pi$
$548$	0.00289704	+	0.245308i	0.000123755	+	0.0104790i
$549$	−8.00206	+	0.176402i	−0.341520	+	0.00752864i
$550$	−35.6726	+	0.210636i	−1.52108	+	0.00898153i
$551$	10.2153	−	3.71805i	0.435185	−	0.158394i
$552$	6.17097	−	25.9963i	0.262654	−	1.10648i
$553$	−29.8970	+	25.0866i	−1.27135	+	1.06679i
$554$	−6.24326	−	34.2244i	−0.265251	−	1.45405i
$555$	13.3114	−	3.72449i	0.565039	−	0.158096i
$556$	−24.8396	−	20.3479i	−1.05343	−	0.862942i
$557$	12.6918	+	21.9828i	0.537768	+	0.931441i	0.999024	+	0.0441741i	$0.0140656\pi$
$557$	12.6918	+	21.9828i	0.537768	+	0.931441i	−0.461256	+	0.887267i	$0.652601\pi$
$558$	−6.66682	−	7.50871i	−0.282229	−	0.317869i
$559$	−28.7844	−	16.6187i	−1.21745	−	0.702896i
$560$	−6.42529	+	8.03536i	−0.271518	+	0.339556i
$561$	27.8680	+	19.0592i	1.17659	+	0.804680i
$562$	3.92535	−	3.33345i	0.165581	−	0.140613i
$563$	−24.4865	+	4.31763i	−1.03198	+	0.181966i	−0.663896	−	0.747825i	$-0.731098\pi$
$563$	−24.4865	+	4.31763i	−1.03198	+	0.181966i	−0.368087	+	0.929791i	$0.619987\pi$
$564$	−7.39357	−	10.0622i	−0.311326	−	0.423694i
$565$	−2.96699	+	3.53592i	−0.124822	+	0.148757i
$566$	−4.51275	−	2.57003i	−0.189685	−	0.108026i
$567$	−29.6812	+	6.59413i	−1.24649	+	0.276927i
$568$	0.304491	+	17.1876i	0.0127761	+	0.721175i
$569$	−7.57957	+	9.03298i	−0.317752	+	0.378682i	−0.901152	−	0.433503i	$-0.857277\pi$
$569$	−7.57957	+	9.03298i	−0.317752	+	0.378682i	0.583400	+	0.812185i	$0.301722\pi$
$570$	4.33198	+	1.93146i	0.181447	+	0.0809001i
$571$	−5.98228	−	33.9272i	−0.250351	−	1.41981i	−0.807731	−	0.589551i	$-0.799305\pi$
$571$	−5.98228	−	33.9272i	−0.250351	−	1.41981i	0.557380	−	0.830257i	$-0.311807\pi$
$572$	−11.0850	−	58.7974i	−0.463488	−	2.45844i
$573$	−17.1660	−	11.7400i	−0.717122	−	0.490446i
$574$	−8.95311	+	10.7988i	−0.373696	+	0.450732i
$575$	12.0541	−	20.8783i	0.502691	−	0.870686i
$576$	16.4574	+	17.4686i	0.685726	+	0.727860i
$577$	21.3516	+	36.9821i	0.888880	+	1.53958i	0.841201	+	0.540722i	$0.181849\pi$
$577$	21.3516	+	36.9821i	0.888880	+	1.53958i	0.0476781	+	0.998863i	$0.484818\pi$
$578$	7.43369	+	1.26555i	0.309201	+	0.0526399i
$579$	−0.235301	−	0.840972i	−0.00977877	−	0.0349496i
$580$	−6.14194	−	2.15369i	−0.255030	−	0.0894271i
$581$	−22.0325	+	18.4875i	−0.914062	+	0.766989i
$582$	25.6298	+	24.7766i	1.06239	+	1.02702i
$583$	15.7422	+	43.2513i	0.651974	+	1.79128i
$584$	6.82306	−	4.10213i	0.282340	−	0.169747i
$585$	6.21423	+	10.2356i	0.256927	+	0.423188i
$586$	−36.2518	+	21.2163i	−1.49755	+	0.876439i
$587$	−0.937739	−	0.165349i	−0.0387046	−	0.00682467i	0.154262	−	0.988030i	$-0.450700\pi$
$587$	−0.937739	−	0.165349i	−0.0387046	−	0.00682467i	−0.192967	+	0.981205i	$0.561811\pi$
$588$	13.7038	−	6.77522i	0.565134	−	0.279405i
$589$	2.05873	−	5.65631i	0.0848285	−	0.233064i
$590$	4.84348	+	1.73057i	0.199403	+	0.0712463i
$591$	2.66513	−	5.88383i	0.109629	−	0.242028i
$592$	15.2667	+	39.0497i	0.627456	+	1.60493i
$593$		−	11.5209i		−	0.473108i	−0.971618	−	0.236554i	$-0.923982\pi$
$593$		−	11.5209i		−	0.473108i	0.971618	−	0.236554i	$-0.0760180\pi$
$594$	−22.6961	+	35.2614i	−0.931230	+	1.44679i
$595$	8.78588			0.360186
$596$	6.10147	−	37.1644i	0.249926	−	1.52231i
$597$	−36.5621	+	26.2062i	−1.49639	+	1.07255i
$598$	38.0781	+	13.6052i	1.55713	+	0.556359i
$599$	45.3618	+	16.5103i	1.85343	+	0.674594i	0.983360	+	0.181668i	$0.0581495\pi$
$599$	45.3618	+	16.5103i	1.85343	+	0.674594i	0.870071	+	0.492926i	$0.164073\pi$
$600$	9.71195	+	19.3552i	0.396489	+	0.790172i
$601$	4.24537	−	24.0767i	0.173172	−	0.982109i	−0.767060	−	0.641575i	$-0.778281\pi$
$601$	4.24537	−	24.0767i	0.173172	−	0.982109i	0.940232	−	0.340534i	$-0.110608\pi$
$602$	−15.2997	−	26.1422i	−0.623570	−	1.06548i
$603$	5.30912	−	6.61807i	0.216204	−	0.269508i
$604$	28.8111	+	16.1835i	1.17231	+	0.658496i
$605$	−15.4281	+	5.61535i	−0.627240	+	0.228297i
$606$	11.7611	−	3.36573i	0.477763	−	0.136723i
$607$	18.4241	+	21.9570i	0.747812	+	0.891207i	0.997012	−	0.0772447i	$-0.0246123\pi$
$607$	18.4241	+	21.9570i	0.747812	+	0.891207i	−0.249201	+	0.968452i	$0.580168\pi$
$608$	−4.51942	+	13.6587i	−0.183287	+	0.553934i
$609$	17.8792	+	17.4894i	0.724503	+	0.708708i
$610$	−0.482124	+	2.83194i	−0.0195206	+	0.114662i
$611$	16.3652	−	9.44843i	0.662064	−	0.382243i
$612$	2.87380	−	20.2926i	0.116166	−	0.820278i
$613$	32.4005	+	18.7064i	1.30864	+	0.755546i	0.981870	−	0.189556i	$-0.0607049\pi$
$613$	32.4005	+	18.7064i	1.30864	+	0.755546i	0.326774	+	0.945102i	$0.394038\pi$
$614$	8.34994	−	10.0712i	0.336976	−	0.406442i
$615$	−1.67487	−	3.49081i	−0.0675373	−	0.140763i
$616$	17.7390	−	51.5615i	0.714726	−	2.07747i
$617$	6.61066	−	1.16564i	0.266135	−	0.0469268i	−0.0389880	−	0.999240i	$-0.512413\pi$
$617$	6.61066	−	1.16564i	0.266135	−	0.0469268i	0.305123	+	0.952313i	$0.401302\pi$
$618$	−11.7371	+	1.22735i	−0.472136	+	0.0493714i
$619$	−5.88154	−	4.93520i	−0.236399	−	0.198362i	0.516890	−	0.856052i	$-0.327090\pi$
$619$	−5.88154	−	4.93520i	−0.236399	−	0.198362i	−0.753289	+	0.657689i	$0.771534\pi$
$620$	−3.09956	+	1.83867i	−0.124481	+	0.0738428i
$621$	−12.8192	−	25.2743i	−0.514418	−	1.01422i
$622$	32.2335	+	18.3571i	1.29245	+	0.736053i
$623$	23.2788	+	19.5333i	0.932647	+	0.782583i
$624$	−29.0133	+	21.8509i	−1.16146	+	0.874737i
$625$	2.88969	+	16.3882i	0.115588	+	0.655530i
$626$	−18.3082	−	21.5590i	−0.731743	−	0.861673i
$627$	−25.0648	−	1.91480i	−1.00099	−	0.0764697i
$628$	8.24095	+	21.8360i	0.328850	+	0.871351i
$629$	17.9024	−	31.0079i	0.713815	−	1.23636i
$630$	0.304917	+	10.9082i	0.0121482	+	0.434595i
$631$	2.13355	−	1.23181i	0.0849353	−	0.0490374i	−0.456931	−	0.889502i	$-0.651051\pi$
$631$	2.13355	−	1.23181i	0.0849353	−	0.0490374i	0.541866	+	0.840465i	$0.317718\pi$
$632$	30.5019	−	11.7177i	1.21330	−	0.466105i
$633$	9.43771	+	2.41768i	0.375115	+	0.0960940i
$634$	32.6177	−	5.95018i	1.29542	−	0.236312i
$635$	−1.51780	−	1.80885i	−0.0602322	−	0.0717820i
$636$	19.3007	−	20.2027i	0.765321	−	0.801088i
$637$	7.91276	+	21.7401i	0.313515	+	0.861375i
$638$	34.4944	−	0.203679i	1.36565	−	0.00806372i
$639$	12.0250	+	13.7056i	0.475700	+	0.542187i
$640$	7.27540	−	4.61144i	0.287586	−	0.182283i
$641$	−34.3110	−	6.04995i	−1.35520	−	0.238959i	−0.551592	−	0.834114i	$-0.685979\pi$
$641$	−34.3110	−	6.04995i	−1.35520	−	0.238959i	−0.803610	+	0.595156i	$0.797090\pi$
$642$	5.65552	−	2.75469i	0.223206	−	0.108719i
$643$	45.2740	+	16.4784i	1.78543	+	0.649844i	0.999503	+	0.0315285i	$0.0100375\pi$
$643$	45.2740	+	16.4784i	1.78543	+	0.649844i	0.785930	+	0.618316i	$0.212185\pi$
$644$	24.0185	+	27.9472i	0.946463	+	1.10127i
$645$	8.32020	−	0.820411i	0.327608	−	0.0323036i
$646$	11.5200	−	4.27012i	0.453247	−	0.168006i
$647$	−0.709735			−0.0279025			−0.0139513	−	0.999903i	$-0.504441\pi$
$647$	−0.709735			−0.0279025			−0.0139513	+	0.999903i	$0.504441\pi$
$648$	25.2942	+	2.86374i	0.993652	+	0.112498i
$649$	−27.2594			−1.07002
$650$	−30.7294	+	11.3905i	−1.20531	+	0.446773i
$651$	13.7820	−	1.35897i	0.540160	−	0.0532623i
$652$	−3.47641	+	2.98772i	−0.136147	+	0.117008i
$653$	0.660215	+	0.240299i	0.0258362	+	0.00940361i	0.354906	−	0.934902i	$-0.384513\pi$
$653$	0.660215	+	0.240299i	0.0258362	+	0.00940361i	−0.329070	+	0.944306i	$0.606735\pi$
$654$	−16.9383	+	8.25028i	−0.662339	+	0.322612i
$655$	12.1720	+	2.14625i	0.475598	+	0.0838608i
$656$	10.0293	−	6.11069i	0.391579	−	0.238582i
$657$	2.71250	−	7.99667i	0.105825	−	0.311980i
$658$	17.2209	−	0.101684i	0.671342	−	0.00396407i
$659$	−12.8249	−	35.2362i	−0.499589	−	1.37261i	−0.891673	−	0.452680i	$-0.850468\pi$
$659$	−12.8249	−	35.2362i	−0.499589	−	1.37261i	0.392084	−	0.919929i	$-0.371754\pi$
$660$	10.8825	+	10.3966i	0.423599	+	0.404686i
$661$	2.70452	+	3.22312i	0.105194	+	0.125365i	0.816072	−	0.577950i	$-0.196147\pi$
$661$	2.70452	+	3.22312i	0.105194	+	0.125365i	−0.710879	+	0.703314i	$0.751703\pi$
$662$	31.6597	−	5.77541i	1.23049	−	0.224468i
$663$	30.0467	+	7.69711i	1.16692	+	0.298931i
$664$	22.4783	−	8.63532i	0.872326	−	0.335115i
$665$	−5.66518	+	3.27079i	−0.219686	+	0.126836i
$666$	39.1196	+	21.1508i	1.51585	+	0.819578i
$667$	−11.6560	+	20.1887i	−0.451321	+	0.781711i
$668$	−15.6321	+	5.89959i	−0.604824	+	0.228262i
$669$	−2.02056	−	0.154359i	−0.0781194	−	0.00596786i
$670$	−1.97110	−	2.32110i	−0.0761504	−	0.0896718i
$671$	−2.64380	−	14.9937i	−0.102063	−	0.578826i
$672$	−32.8306	+	4.21908i	−1.26647	+	0.162755i
$673$	−30.4222	−	25.5272i	−1.17269	−	0.984002i	−0.172689	−	0.984976i	$-0.555245\pi$
$673$	−30.4222	−	25.5272i	−1.17269	−	0.984002i	−1.00000		0.000974390i	$0.999690\pi$
$674$	−39.4069	−	22.4424i	−1.51790	−	0.864449i
$675$	21.1262	+	9.01360i	0.813150	+	0.346934i
$676$	−14.7793	−	24.9143i	−0.568434	−	0.958243i
$677$	2.47156	+	2.07389i	0.0949899	+	0.0797060i	0.689046	−	0.724718i	$-0.258030\pi$
$677$	2.47156	+	2.07389i	0.0949899	+	0.0797060i	−0.594056	+	0.804424i	$0.702474\pi$
$678$	−14.7698	+	1.54448i	−0.567230	+	0.0593154i
$679$	−48.4182	+	8.53744i	−1.85812	+	0.327637i
$680$	−6.95567	−	2.39300i	−0.266738	−	0.0917675i
$681$	8.19968	+	17.0900i	0.314213	+	0.654890i
$682$	12.1908	−	14.7039i	0.466810	−	0.563041i
$683$	10.7853	+	6.22690i	0.412689	+	0.238266i	0.691944	−	0.721951i	$-0.256754\pi$
$683$	10.7853	+	6.22690i	0.412689	+	0.238266i	−0.279256	+	0.960217i	$0.590088\pi$
$684$	5.70144	+	14.1546i	0.218000	+	0.541214i
$685$	0.0808781	−	0.0466950i	0.00309019	−	0.00178412i
$686$	2.07433	−	12.1844i	0.0791985	−	0.465203i
$687$	6.93521	+	6.78402i	0.264595	+	0.258826i
$688$	4.99227	+	24.8636i	0.190328	+	0.947916i
$689$	27.1800	+	32.3918i	1.03547	+	1.23403i
$690$	−9.77868	+	2.79840i	−0.372268	+	0.106533i
$691$	−33.7240	+	12.2745i	−1.28292	+	0.466945i	−0.891397	−	0.453222i	$-0.850274\pi$
$691$	−33.7240	+	12.2745i	−1.28292	+	0.466945i	−0.391524	+	0.920168i	$0.628052\pi$
$692$	−4.49477	+	8.00193i	−0.170865	+	0.304188i
$693$	−20.9738	−	53.8983i	−0.796729	−	2.04743i
$694$	−10.5750	−	18.0693i	−0.401423	−	0.685899i
$695$	−2.12259	+	12.0378i	−0.0805144	+	0.456620i
$696$	−9.39118	−	18.7159i	−0.355972	−	0.709425i
$697$	−9.42430	−	3.43016i	−0.356971	−	0.129927i
$698$	−33.6684	−	12.0296i	−1.27437	−	0.455328i
$699$	19.5212	−	13.9920i	0.738361	−	0.529227i
$700$	−29.4720	−	4.83858i	−1.11394	−	0.182881i
$701$	35.4138			1.33756			0.668781	−	0.743459i	$-0.266816\pi$
$701$	35.4138			1.33756			0.668781	+	0.743459i	$0.266816\pi$
$702$	−8.51368	+	37.5720i	−0.321328	+	1.41806i
$703$			26.6587i			1.00545i
$704$	−28.0875	+	35.9891i	−1.05859	+	1.35639i
$705$	−1.96125	+	4.32985i	−0.0738648	+	0.163072i
$706$	−0.599477	−	0.214192i	−0.0225616	−	0.00806121i
$707$	−5.77056	+	15.8545i	−0.217024	+	0.596269i
$708$	7.33385	+	14.8337i	0.275623	+	0.557484i
$709$	−2.07523	−	0.365919i	−0.0779368	−	0.0137424i	0.134544	−	0.990908i	$-0.457043\pi$
$709$	−2.07523	−	0.365919i	−0.0779368	−	0.0137424i	−0.212481	+	0.977165i	$0.568154\pi$
$710$	5.64782	−	3.30539i	0.211959	−	0.124049i
$711$	16.6630	−	30.3887i	0.624910	−	1.13967i
$712$	−13.1093	−	21.8047i	−0.491292	−	0.817164i
$713$	4.41483	+	12.1296i	0.165337	+	0.454259i
$714$	20.3229	+	19.6464i	0.760566	+	0.735246i
$715$	−17.4483	+	14.6409i	−0.652530	+	0.547538i
$716$	6.12516	−	17.4678i	0.228908	−	0.652804i
$717$	8.08339	+	28.8903i	0.301880	+	1.07893i
$718$	−4.42938	−	0.754081i	−0.165303	−	0.0281420i
$719$	−2.79238	−	4.83654i	−0.104138	−	0.180373i	0.809248	−	0.587468i	$-0.199875\pi$
$719$	−2.79238	−	4.83654i	−0.104138	−	0.180373i	−0.913386	+	0.407095i	$0.866542\pi$
$720$	2.72967	−	8.71897i	0.101729	−	0.324937i
$721$	8.13800	−	14.0954i	0.303075	−	0.524941i
$722$	11.3114	−	13.6433i	0.420969	−	0.507749i
$723$	2.74407	+	1.87669i	0.102053	+	0.0697949i
$724$	23.0819	−	4.35161i	0.857830	−	0.161726i
$725$	−3.28091	−	18.6070i	−0.121850	−	0.691046i
$726$	−48.2438	−	21.5100i	−1.79049	−	0.798313i
$727$	−3.41147	+	4.06563i	−0.126524	+	0.150786i	−0.825588	−	0.564274i	$-0.809156\pi$
$727$	−3.41147	+	4.06563i	−0.126524	+	0.150786i	0.699063	+	0.715060i	$0.253601\pi$
$728$	−0.887312	−	50.0861i	−0.0328860	−	1.85632i
$729$	22.4396	−	15.0155i	0.831095	−	0.556130i
$730$	−2.63354	−	1.49981i	−0.0974719	−	0.0555106i
$731$	13.9204	−	16.5897i	0.514864	−	0.613591i
$732$	−7.44780	+	5.47257i	−0.275279	+	0.202272i
$733$	−44.4108	+	7.83081i	−1.64035	+	0.289238i	−0.916294	−	0.400505i	$-0.868835\pi$
$733$	−44.4108	+	7.83081i	−1.64035	+	0.289238i	−0.724054	+	0.689743i	$0.757723\pi$
$734$	−35.4586	+	30.1119i	−1.30880	+	1.11145i
$735$	−4.80354	−	3.28518i	−0.177181	−	0.121176i
$736$	−11.4032	−	28.6674i	−0.420329	−	1.05669i
$737$	13.9767	+	8.06943i	0.514837	+	0.297241i
$738$	3.93170	−	11.8199i	0.144728	−	0.435097i
$739$	9.87524	+	17.1044i	0.363267	+	0.629196i	0.988496	−	0.151244i	$-0.0483280\pi$
$739$	9.87524	+	17.1044i	0.363267	+	0.629196i	−0.625230	+	0.780441i	$0.714995\pi$
$740$	10.1145	−	12.3472i	0.371815	−	0.453891i
$741$	−22.2397	+	6.22259i	−0.816996	+	0.228592i
$742$	6.91551	+	37.9095i	0.253876	+	1.39170i
$743$	8.50460	−	7.13621i	0.312004	−	0.261802i	−0.473316	−	0.880893i	$-0.656943\pi$
$743$	8.50460	−	7.13621i	0.312004	−	0.261802i	0.785320	+	0.619091i	$0.212499\pi$
$744$	−11.2812	−	2.67791i	−0.413588	−	0.0981771i
$745$	−13.4724	+	4.90356i	−0.493592	+	0.179653i
$746$	−16.8651	+	0.0995832i	−0.617475	+	0.00364600i
$747$	12.2797	−	22.3949i	0.449291	−	0.819386i
$748$	38.9824	−	0.460374i	1.42534	−	0.0168330i
$749$	−1.50659	+	8.54431i	−0.0550497	+	0.312202i
$750$	9.83176	−	14.5596i	0.359005	−	0.531641i
$751$	−1.58243	+	4.34770i	−0.0577439	+	0.158650i	−0.965210	−	0.261474i	$-0.915791\pi$
$751$	−1.58243	+	4.34770i	−0.0577439	+	0.158650i	0.907467	+	0.420124i	$0.138014\pi$
$752$	−13.6613	−	4.60995i	−0.498176	−	0.168108i
$753$	−33.9821	−	15.3925i	−1.23837	−	0.560933i
$754$	29.7145	−	11.0143i	1.08214	−	0.401118i
$755$		−	12.5796i		−	0.457817i
$756$	−23.6869	+	25.9140i	−0.861484	+	0.942484i
$757$		−	11.0029i		−	0.399907i	−0.979805	−	0.199954i	$-0.935921\pi$
$757$		−	11.0029i		−	0.399907i	0.979805	−	0.199954i	$-0.0640792\pi$
$758$	−0.667579	−	1.80100i	−0.0242476	−	0.0654152i
$759$	43.8142	−	31.4043i	1.59036	−	1.13990i
$760$	5.37591	−	1.04643i	0.195005	−	0.0379578i
$761$	−3.02165	+	8.30192i	−0.109535	+	0.300944i	−0.982334	−	0.187135i	$-0.940080\pi$
$761$	−3.02165	+	8.30192i	−0.109535	+	0.300944i	0.872799	+	0.488079i	$0.162302\pi$
$762$	0.533935	−	7.57811i	0.0193424	−	0.274526i
$763$	4.51224	−	25.5902i	0.163354	−	0.926427i
$764$	−24.0122	+	0.283580i	−0.868732	+	0.0102595i
$765$	−7.27090	+	2.82938i	−0.262880	+	0.102296i
$766$	−0.248642	−	42.1091i	−0.00898379	−	1.52147i
$767$	−23.5326	+	8.56518i	−0.849714	+	0.309271i
$768$	27.1407	+	5.60185i	0.979357	+	0.202139i
$769$	38.6343	−	32.4180i	1.39319	−	1.16902i	0.429158	−	0.903229i	$-0.358810\pi$
$769$	38.6343	−	32.4180i	1.39319	−	1.16902i	0.964030	−	0.265794i	$-0.0856342\pi$
$770$	−20.4205	+	3.72514i	−0.735903	+	0.134245i
$771$	11.1563	+	10.9131i	0.401785	+	0.393025i
$772$	−0.780053	−	0.638998i	−0.0280747	−	0.0229980i
$773$	−10.6364	−	18.4228i	−0.382565	−	0.662622i	0.608863	−	0.793275i	$-0.291626\pi$
$773$	−10.6364	−	18.4228i	−0.382565	−	0.662622i	−0.991428	+	0.130653i	$0.958293\pi$
$774$	21.0803	+	16.7073i	0.757714	+	0.600532i
$775$	−9.06022	−	5.23092i	−0.325453	−	0.187900i
$776$	40.6574	+	6.42865i	1.45952	+	0.230775i
$777$	−55.2989	+	26.5321i	−1.98384	+	0.951833i
$778$	5.29882	+	6.23969i	0.189972	+	0.223704i
$779$	7.35380	−	1.29667i	0.263477	−	0.0464582i
$780$	12.6614	+	5.55584i	0.453350	+	0.198931i
$781$	−22.2934	+	26.5683i	−0.797722	+	0.950688i
$782$	−13.0383	+	22.8941i	−0.466247	+	0.818690i
$783$	−20.4285	−	8.71590i	−0.730055	−	0.311481i
$784$	8.46255	−	15.4913i	0.302234	−	0.553261i
$785$	5.71102	−	6.80613i	0.203835	−	0.242921i
$786$	23.3561	+	32.1826i	0.833084	+	1.14792i
$787$	−0.282984	−	1.60488i	−0.0100873	−	0.0572079i	0.979349	−	0.202179i	$-0.0648022\pi$
$787$	−0.282984	−	1.60488i	−0.0100873	−	0.0572079i	−0.989436	+	0.144971i	$0.953691\pi$
$788$	−1.38181	−	7.32942i	−0.0492250	−	0.261100i
$789$	−0.819292	+	10.7245i	−0.0291676	+	0.381804i
$790$	−9.57568	−	7.93907i	−0.340687	−	0.282459i
$791$	10.2407	−	17.7374i	0.364118	−	0.630671i
$792$	1.92448	+	48.3832i	0.0683834	+	1.71922i
$793$	−6.99353	−	12.1131i	−0.248347	−	0.430150i
$794$	3.71343	−	21.8123i	0.131785	−	0.774088i
$795$	−10.3036	−	2.63948i	−0.365430	−	0.0936129i
$796$	−17.1879	+	49.0168i	−0.609209	+	1.73735i
$797$	6.03133	−	5.06088i	0.213641	−	0.179266i	−0.529687	−	0.848193i	$-0.677691\pi$
$797$	6.03133	−	5.06088i	0.213641	−	0.179266i	0.743328	+	0.668927i	$0.233246\pi$
$798$	−20.4182	−	5.10229i	−0.722797	−	0.180619i
$799$	4.21113	+	11.5700i	0.148979	+	0.409316i
$800$	22.0148	+	11.8579i	0.778339	+	0.419241i
$801$	−25.5552	−	8.66843i	−0.902948	−	0.306284i
$802$	−23.8765	−	40.7971i	−0.843110	−	1.44060i
$803$	15.8183	+	2.78919i	0.558216	+	0.0984285i
$804$	0.630848	−	9.77664i	0.0222483	−	0.344796i
$805$	4.79788	−	13.1821i	0.169103	−	0.464607i
$806$	5.90403	−	16.5241i	0.207961	−	0.582038i
$807$	2.23109	−	0.219995i	0.0785379	−	0.00774421i
$808$	8.88675	−	10.9801i	0.312635	−	0.386278i
$809$			3.21158i			0.112913i	0.998405	+	0.0564566i	$0.0179802\pi$
$809$			3.21158i			0.112913i	−0.998405	+	0.0564566i	$0.982020\pi$
$810$	−3.76519	−	8.92910i	−0.132295	−	0.313736i
$811$	20.5556			0.721806			0.360903	−	0.932603i	$-0.382469\pi$
$811$	20.5556			0.721806			0.360903	+	0.932603i	$0.382469\pi$
$812$	28.4986	+	4.67877i	1.00011	+	0.164193i
$813$	−0.656230	−	6.65516i	−0.0230150	−	0.233407i
$814$	−28.4624	+	79.6601i	−0.997605	+	2.79208i
$815$	1.63974	+	0.596818i	0.0574377	+	0.0209056i
$816$	−10.7383	−	21.0891i	−0.375917	−	0.738266i
$817$	−2.79996	+	15.8794i	−0.0979581	+	0.555548i
$818$	−28.3484	+	16.5909i	−0.991179	+	0.580087i
$819$	−35.0418	−	39.9394i	−1.22446	−	1.39560i
$820$	−3.89794	−	2.18951i	−0.136122	−	0.0764611i
$821$	−13.9182	+	5.06579i	−0.485747	+	0.176797i	−0.573272	−	0.819365i	$-0.694326\pi$
$821$	−13.9182	+	5.06579i	−0.485747	+	0.176797i	0.0875255	+	0.996162i	$0.472104\pi$
$822$	0.291497	+	0.0728420i	0.0101671	+	0.00254066i
$823$	6.69751	+	7.98178i	0.233460	+	0.278227i	0.870037	−	0.492986i	$-0.164095\pi$
$823$	6.69751	+	7.98178i	0.233460	+	0.278227i	−0.636577	+	0.771213i	$0.719650\pi$
$824$	−10.2819	+	8.94263i	−0.358187	+	0.311531i
$825$	−10.8422	+	42.3239i	−0.377476	+	1.47353i
$826$	−22.4986	−	3.83028i	−0.782827	−	0.133272i
$827$	−39.8873	+	23.0289i	−1.38702	+	0.800794i	−0.992978	−	0.118300i	$-0.962256\pi$
$827$	−39.8873	+	23.0289i	−1.38702	+	0.800794i	−0.394038	+	0.919094i	$0.628922\pi$
$828$	−28.8770	−	15.3933i	−1.00354	−	0.534954i
$829$	0.902728	+	0.521190i	0.0313531	+	0.0181017i	0.515595	−	0.856833i	$-0.327571\pi$
$829$	0.902728	+	0.521190i	0.0313531	+	0.0181017i	−0.484242	+	0.874934i	$0.660904\pi$
$830$	−7.05676	−	5.85067i	−0.244944	−	0.203080i
$831$	−42.4841	−	3.24553i	−1.47376	−	0.112586i
$832$	−12.9394	+	39.8942i	−0.448594	+	1.38308i
$833$	−14.8452	+	2.61760i	−0.514354	+	0.0906945i
$834$	−31.8279	+	23.0986i	−1.10211	+	0.799840i
$835$	4.87242	+	4.08844i	0.168617	+	0.141486i
$836$	−24.9646	+	14.8091i	−0.863420	+	0.512185i
$837$	−10.9679	+	5.56295i	−0.379106	+	0.192284i
$838$	1.31081	−	2.30166i	0.0452810	−	0.0795095i
$839$	8.47456	+	7.11100i	0.292574	+	0.245499i	0.777246	−	0.629197i	$-0.216616\pi$
$839$	8.47456	+	7.11100i	0.292574	+	0.245499i	−0.484671	+	0.874696i	$0.661061\pi$
$840$	7.52102	+	10.1100i	0.259500	+	0.348827i
$841$	−1.86324	−	10.5670i	−0.0642498	−	0.364379i
$842$	19.3966	−	16.4718i	0.668450	−	0.567656i
$843$	−2.72836	−	5.68652i	−0.0939697	−	0.195854i
$844$	10.5250	−	3.97217i	0.362286	−	0.136728i
$845$	−5.51376	+	9.55011i	−0.189679	+	0.328534i
$846$	−14.2187	+	5.62993i	−0.488850	+	0.193561i
$847$	63.0911	−	36.4257i	2.16784	−	1.25160i
$848$	4.85045	−	31.8961i	0.166565	−	1.09531i
$849$	−4.44766	+	4.54679i	−0.152643	+	0.156045i
$850$	−3.83209	−	21.0068i	−0.131440	−	0.720526i
$851$	−36.7469	−	43.7932i	−1.25967	−	1.50121i
$852$	20.4554	+	4.98345i	0.700791	+	0.170730i
$853$	−6.84425	−	18.8044i	−0.234343	−	0.643851i	−1.00000		0.000602347i	$-0.999808\pi$
$853$	−6.84425	−	18.8044i	−0.234343	−	0.643851i	0.765657	−	0.643249i	$-0.222414\pi$
$854$	−0.0752647	−	12.7466i	−0.00257550	−	0.436179i
$855$	3.63499	−	4.53119i	0.124314	−	0.154963i
$856$	3.51995	−	6.35407i	0.120310	−	0.217178i
$857$	29.9891	+	5.28788i	1.02441	+	0.180631i	0.660517	−	0.750811i	$-0.270337\pi$
$857$	29.9891	+	5.28788i	1.02441	+	0.180631i	0.363890	+	0.931442i	$0.381448\pi$
$858$	−73.0991	−	5.15039i	−2.49556	−	0.175831i
$859$	−27.6630	−	10.0685i	−0.943851	−	0.343533i	−0.176165	−	0.984361i	$-0.556369\pi$
$859$	−27.6630	−	10.0685i	−0.943851	−	0.343533i	−0.767685	+	0.640827i	$0.778592\pi$
$860$	7.32155	−	6.29233i	0.249663	−	0.214567i
$861$	10.0086	+	13.9637i	0.341093	+	0.475882i
$862$	14.1155	+	38.0809i	0.480776	+	1.29704i
$863$	−4.08631			−0.139100			−0.0695498	−	0.997578i	$-0.522156\pi$
$863$	−4.08631			−0.139100			−0.0695498	+	0.997578i	$0.522156\pi$
$864$	25.8108	−	14.0642i	0.878101	−	0.478475i
$865$	3.49382			0.118794
$866$	3.41788	+	9.22078i	0.116144	+	0.313335i
$867$	3.81056	−	8.41259i	0.129413	−	0.285707i
$868$	12.1278	−	10.4229i	0.411644	−	0.353777i
$869$	61.9486	+	22.5474i	2.10146	+	0.764869i
$870$	−4.46102	+	6.60621i	−0.151243	+	0.223971i
$871$	14.6014	+	2.57461i	0.494748	+	0.0872374i
$872$	−10.5423	+	19.0304i	−0.357006	+	0.644452i
$873$	37.3199	−	22.6577i	1.26309	−	0.766848i
$874$	−0.115827	−	19.6161i	−0.00391790	−	0.663523i
$875$	8.28717	+	22.7688i	0.280157	+	0.769726i
$876$	−2.73796	−	9.35821i	−0.0925070	−	0.316185i
$877$	−34.0441	−	40.5721i	−1.14959	−	1.37002i	−0.917697	−	0.397282i	$-0.869954\pi$
$877$	−34.0441	−	40.5721i	−1.14959	−	1.37002i	−0.231890	−	0.972742i	$-0.574491\pi$
$878$	8.39602	+	46.0254i	0.283352	+	1.55328i
$879$	13.8615	+	49.5413i	0.467536	+	1.67099i
$880$	17.1813	+	2.61277i	0.579180	+	0.0880763i
$881$	−36.3618	+	20.9935i	−1.22506	+	0.707288i	−0.965992	−	0.258571i	$-0.916748\pi$
$881$	−36.3618	+	20.9935i	−1.22506	+	0.707288i	−0.259067	+	0.965859i	$0.583415\pi$
$882$	−3.76513	−	18.3404i	−0.126778	−	0.617552i
$883$	15.5284	−	26.8959i	0.522571	−	0.905120i	−0.477084	−	0.878858i	$-0.658306\pi$
$883$	15.5284	−	26.8959i	0.522571	−	0.905120i	0.999655	−	0.0262620i	$-0.00836041\pi$
$884$	33.5083	−	12.6461i	1.12701	−	0.425335i
$885$	3.55605	−	5.19960i	0.119535	−	0.174783i
$886$	18.9282	−	16.0740i	0.635904	−	0.540017i
$887$	3.83931	+	21.7738i	0.128911	+	0.731092i	0.978908	+	0.204304i	$0.0654929\pi$
$887$	3.83931	+	21.7738i	0.128911	+	0.731092i	−0.849996	+	0.526789i	$0.823396\pi$
$888$	51.0059	−	5.94341i	1.71165	−	0.199448i
$889$	8.02628	+	6.73485i	0.269193	+	0.225880i
$890$	−4.79300	+	8.41610i	−0.160662	+	0.282108i
$891$	34.7144	+	37.8500i	1.16298	+	1.26802i
$892$	−2.01249	+	1.19382i	−0.0673832	+	0.0399720i
$893$	−7.02260	−	5.89266i	−0.235002	−	0.197190i
$894$	−42.1285	−	18.7835i	−1.40899	−	0.628214i
$895$	−6.93953	+	1.22363i	−0.231963	+	0.0409013i
$896$	−28.2390	+	25.7570i	−0.943400	+	0.860482i
$897$	27.9567	−	40.8778i	0.933446	−	1.36487i
$898$	−45.2399	−	37.5078i	−1.50967	−	1.25165i
$899$	8.76098	+	5.05815i	0.292195	+	0.168699i
$900$	25.9483	−	5.48683i	0.864942	−	0.182894i
$901$	−23.8599	+	13.7755i	−0.794890	+	0.458930i
$902$	23.3587	+	3.97670i	0.777759	+	0.132410i
$903$	−35.7257	+	9.99591i	−1.18888	+	0.332643i
$904$	−12.9386	+	11.2533i	−0.430331	+	0.374278i
$905$	−5.74752	−	6.84962i	−0.191054	−	0.227689i
$906$	28.1295	−	29.0982i	0.934540	−	0.966722i
$907$	−17.8490	+	6.49651i	−0.592666	+	0.215713i	−0.620902	−	0.783888i	$-0.713233\pi$
$907$	−17.8490	+	6.49651i	−0.592666	+	0.215713i	0.0282353	+	0.999601i	$0.491011\pi$
$908$	19.0832	+	10.7192i	0.633298	+	0.355730i
$909$	−0.330204	−	14.9790i	−0.0109522	−	0.496821i
$910$	−16.4582	+	9.63219i	−0.545585	+	0.319304i
$911$	1.05476	−	5.98186i	0.0349458	−	0.198188i	−0.962337	−	0.271861i	$-0.912361\pi$
$911$	1.05476	−	5.98186i	0.0349458	−	0.198188i	0.997282	+	0.0736730i	$0.0234721\pi$
$912$	14.7751	+	9.60070i	0.489253	+	0.317911i
$913$	45.6528	+	16.6162i	1.51089	+	0.549917i
$914$	8.21013	−	22.9784i	0.271567	−	0.760058i
$915$	3.20487	+	1.45167i	0.105950	+	0.0479908i
$916$	11.0544	+	1.81486i	0.365248	+	0.0599646i
$917$	−54.8431			−1.81108
$918$	−23.1454	−	9.71394i	−0.763912	−	0.320608i
$919$			0.413428i			0.0136377i	0.999977	+	0.00681886i	$0.00217053\pi$
$919$			0.413428i			0.0136377i	−0.999977	+	0.00681886i	$0.997829\pi$
$920$	−7.38881	+	9.12928i	−0.243602	+	0.300983i
$921$	−9.33433	−	13.0230i	−0.307577	−	0.429121i
$922$	7.91241	−	22.1451i	0.260581	−	0.729312i
$923$	−10.8976	+	29.9409i	−0.358698	+	0.985515i
$924$	−55.5652	−	37.0461i	−1.82796	−	1.21873i
$925$	45.6300	+	8.04580i	1.50031	+	0.264544i
$926$	16.5886	+	28.3444i	0.545134	+	0.931456i
$927$	−2.19549	+	14.2856i	−0.0721093	+	0.469202i
$928$	−21.2877	−	11.4663i	−0.698802	−	0.376399i
$929$	9.19985	+	25.2764i	0.301837	+	0.829291i	0.994181	+	0.107723i	$0.0343561\pi$
$929$	9.19985	+	25.2764i	0.301837	+	0.829291i	−0.692344	+	0.721568i	$0.743422\pi$
$930$	1.21438	+	4.24349i	0.0398210	+	0.139150i
$931$	8.59775	−	7.21437i	0.281780	−	0.236441i
$932$	9.17696	−	26.1711i	0.300601	−	0.857261i
$933$	31.7686	−	32.4766i	1.04006	−	1.06324i
$934$	−5.31909	+	31.2437i	−0.174046	+	1.02233i
$935$	−7.42039	−	12.8525i	−0.242673	−	0.420322i
$936$	16.8639	+	41.1638i	0.551213	+	1.34548i
$937$	16.3866	−	28.3824i	0.535326	−	0.927211i	−0.463822	−	0.885928i	$-0.653522\pi$
$937$	16.3866	−	28.3824i	0.535326	−	0.927211i	0.999148	−	0.0412827i	$-0.0131444\pi$
$938$	10.4018	+	8.62402i	0.339632	+	0.281584i
$939$	−31.2318	+	14.9849i	−1.01921	+	0.489012i
$940$	1.01686	+	5.39365i	0.0331664	+	0.175922i
$941$	−2.14333	−	12.1554i	−0.0698705	−	0.396255i	−0.999607	−	0.0280300i	$-0.991077\pi$
$941$	−2.14333	−	12.1554i	−0.0698705	−	0.396255i	0.929737	−	0.368225i	$-0.120034\pi$
$942$	28.4297	−	2.97290i	0.926290	−	0.0968623i
$943$	−10.2930	+	12.2667i	−0.335187	+	0.399460i
$944$	16.7686	+	9.16031i	0.545772	+	0.298143i
$945$	13.0169	+	3.03050i	0.423440	+	0.0985822i
$946$	−25.3204	+	44.4605i	−0.823238	+	1.44553i
$947$	6.78558	−	8.08674i	0.220502	−	0.262784i	−0.644441	−	0.764654i	$-0.722910\pi$
$947$	6.78558	−	8.08674i	0.220502	−	0.262784i	0.864943	+	0.501870i	$0.167354\pi$
$948$	−4.39703	−	39.7765i	−0.142809	−	1.29188i
$949$	14.5321	−	2.56240i	0.471732	−	0.0831791i
$950$	10.2913	+	12.1187i	0.333894	+	0.393181i
$951$	3.09317	−	40.4897i	0.100303	−	1.31297i
$952$	32.2389	+	5.09753i	1.04487	+	0.165212i
$953$	−3.50537	−	2.02383i	−0.113550	−	0.0655581i	0.442149	−	0.896941i	$-0.354216\pi$
$953$	−3.50537	−	2.02383i	−0.113550	−	0.0655581i	−0.555699	+	0.831383i	$0.687549\pi$
$954$	−17.9313	−	29.1456i	−0.580547	−	0.943623i
$955$	4.57078	+	7.91683i	0.147907	+	0.256183i
$956$	26.7975	+	21.9517i	0.866692	+	0.709970i
$957$	10.4841	−	40.9260i	0.338903	−	1.32295i
$958$	−40.9867	+	7.47685i	−1.32422	+	0.241566i
$959$	−0.317444	+	0.266367i	−0.0102508	+	0.00860143i
$960$	−3.20065	−	10.0524i	−0.103301	−	0.324440i
$961$	−23.8668	+	8.68679i	−0.769896	+	0.280219i
$962$	0.458869	+	77.7126i	0.0147945	+	2.50555i
$963$	−1.50477	−	7.55615i	−0.0484907	−	0.243494i
$964$	3.83846	−	0.0453314i	0.123628	−	0.00146003i
$965$	−0.0666570	+	0.378031i	−0.00214577	+	0.0121692i
$966$	40.5749	−	19.7632i	1.30548	−	0.635870i
$967$	5.69598	−	15.6496i	0.183170	−	0.503256i	−0.813791	−	0.581158i	$-0.802600\pi$
$967$	5.69598	−	15.6496i	0.183170	−	0.503256i	0.996961	+	0.0779019i	$0.0248221\pi$
$968$	−59.8697	+	11.6537i	−1.92428	+	0.374564i
$969$	−1.47655	−	14.9745i	−0.0474337	−	0.481050i
$970$	−5.44619	−	14.6928i	−0.174867	−	0.471757i
$971$		−	0.618203i		−	0.0198391i	−0.999951	−	0.00991953i	$-0.996842\pi$
$971$		−	0.618203i		−	0.0198391i	0.999951	−	0.00991953i	$-0.00315754\pi$
$972$	11.2572	−	29.0736i	0.361075	−	0.932537i
$973$		−	54.2386i		−	1.73881i
$974$	36.1389	−	13.3957i	1.15797	−	0.429225i
$975$	3.93870	+	39.9443i	0.126139	+	1.27924i
$976$	−3.41219	+	10.1118i	−0.109222	+	0.323671i
$977$	−18.4051	+	50.5677i	−0.588833	+	1.61780i	0.183809	+	0.982962i	$0.441157\pi$
$977$	−18.4051	+	50.5677i	−0.588833	+	1.61780i	−0.772642	+	0.634842i	$0.781065\pi$
$978$	2.45838	+	5.04719i	0.0786104	+	0.161391i
$979$	8.91351	−	50.5510i	0.284877	−	1.61562i
$980$	−6.71929	+	0.0793535i	−0.214640	+	0.00253485i
$981$	4.50680	+	22.6307i	0.143891	+	0.722542i
$982$	22.0393	−	0.130135i	0.703303	−	0.00415279i
$983$	−14.7088	+	5.35358i	−0.469139	+	0.170753i	−0.565762	−	0.824568i	$-0.691418\pi$
$983$	−14.7088	+	5.35358i	−0.469139	+	0.170753i	0.0966232	+	0.995321i	$0.469196\pi$
$984$	−4.12041	−	13.7809i	−0.131354	−	0.439320i
$985$	−2.17503	+	1.82507i	−0.0693023	+	0.0581515i
$986$	3.70552	+	20.3130i	0.118008	+	0.646896i
$987$	5.23407	−	20.4319i	0.166602	−	0.650354i
$988$	−16.8984	+	20.6287i	−0.537611	+	0.656286i
$989$	−17.2888	−	29.9452i	−0.549753	−	0.952201i
$990$	15.6997	−	9.65894i	0.498968	−	0.306981i
$991$	−13.5526	−	7.82457i	−0.430511	−	0.248556i	0.269053	−	0.963125i	$-0.413289\pi$
$991$	−13.5526	−	7.82457i	−0.430511	−	0.248556i	−0.699564	+	0.714570i	$0.746623\pi$
$992$	−12.4403	+	4.94847i	−0.394980	+	0.157114i
$993$	3.00232	−	39.3004i	0.0952757	−	1.24716i
$994$	−22.1331	+	18.7957i	−0.702020	+	0.596164i
$995$	19.4731	−	3.43364i	0.617340	−	0.108854i
$996$	−3.24037	−	29.3132i	−0.102675	−	0.928823i
$997$	−5.45472	+	6.50068i	−0.172753	+	0.205879i	−0.845473	−	0.534018i	$-0.820681\pi$
$997$	−5.45472	+	6.50068i	−0.172753	+	0.205879i	0.672720	+	0.739897i	$0.265126\pi$
$998$	−7.75901	−	4.41879i	−0.245607	−	0.139874i
$999$	37.2192	−	39.7653i	1.17756	−	1.25812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.13	✓	192
3.2	odd	2		648.2.v.b.35.20		192
4.3	odd	2		864.2.bh.b.335.32		192
8.3	odd	2	inner	216.2.v.b.11.30	yes	192
8.5	even	2		864.2.bh.b.335.31		192
24.11	even	2		648.2.v.b.35.3		192
27.5	odd	18	inner	216.2.v.b.59.30	yes	192
27.22	even	9		648.2.v.b.611.3		192
108.59	even	18		864.2.bh.b.815.31		192
216.5	odd	18		864.2.bh.b.815.32		192
216.59	even	18	inner	216.2.v.b.59.13	yes	192
216.211	odd	18		648.2.v.b.611.20		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.13	✓	192	1.1	even	1	trivial
216.2.v.b.11.30	yes	192	8.3	odd	2	inner
216.2.v.b.59.13	yes	192	216.59	even	18	inner
216.2.v.b.59.30	yes	192	27.5	odd	18	inner
648.2.v.b.35.3		192	24.11	even	2
648.2.v.b.35.20		192	3.2	odd	2
648.2.v.b.611.3		192	27.22	even	9
648.2.v.b.611.20		192	216.211	odd	18
864.2.bh.b.335.31		192	8.5	even	2
864.2.bh.b.335.32		192	4.3	odd	2
864.2.bh.b.815.31		192	108.59	even	18
864.2.bh.b.815.32		192	216.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.491528 - 1.32605i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(-1.51680 + 1.30358i) q^{4} +(0.715441 + 0.260399i) q^{5} +(1.07262 + 2.20215i) q^{6} +(-3.32699 - 0.586638i) q^{7} +(2.47416 + 1.37060i) q^{8} +(2.94222 - 0.585931i) q^{9} +O(q^{10})\)	\(q+(-0.491528 - 1.32605i) q^{2} +(-1.72369 + 0.169964i) q^{3} +(-1.51680 + 1.30358i) q^{4} +(0.715441 + 0.260399i) q^{5} +(1.07262 + 2.20215i) q^{6} +(-3.32699 - 0.586638i) q^{7} +(2.47416 + 1.37060i) q^{8} +(2.94222 - 0.585931i) q^{9} +(-0.00635759 - 1.07670i) q^{10} +(1.95175 + 5.36238i) q^{11} +(2.39294 - 2.50477i) q^{12} +(3.36983 + 4.01601i) q^{13} +(0.857399 + 4.70010i) q^{14} +(-1.27746 - 0.327249i) q^{15} +(0.601369 - 3.95454i) q^{16} +(-2.95820 + 1.70792i) q^{17} +(-2.22316 - 3.61353i) q^{18} +(1.27164 - 2.20255i) q^{19} +(-1.42463 + 0.537659i) q^{20} +(5.83441 + 0.445715i) q^{21} +(6.15143 - 5.22386i) q^{22} +(0.947065 + 5.37107i) q^{23} +(-4.49763 - 1.94198i) q^{24} +(-3.38617 - 2.84134i) q^{25} +(3.66905 - 6.44253i) q^{26} +(-4.97190 + 1.51004i) q^{27} +(5.81111 - 3.44718i) q^{28} +(3.27434 + 2.74749i) q^{29} +(0.193959 + 1.85482i) q^{30} +(2.33080 - 0.410982i) q^{31} +(-5.53949 + 1.14632i) q^{32} +(-4.27562 - 8.91136i) q^{33} +(3.71882 + 3.08323i) q^{34} +(-2.22751 - 1.28605i) q^{35} +(-3.69896 + 4.72416i) q^{36} +(-9.07767 + 5.24099i) q^{37} +(-3.54573 - 0.603643i) q^{38} +(-6.49112 - 6.34960i) q^{39} +(1.41321 + 1.62485i) q^{40} +(1.88727 + 2.24916i) q^{41} +(-2.27674 - 7.95579i) q^{42} +(-5.95761 + 2.16839i) q^{43} +(-9.95069 - 5.58941i) q^{44} +(2.25756 + 0.346954i) q^{45} +(6.65678 - 3.89588i) q^{46} +(0.625921 - 3.54977i) q^{47} +(-0.364446 + 6.91861i) q^{48} +(4.14688 + 1.50934i) q^{49} +(-2.10335 + 5.88682i) q^{50} +(4.80874 - 3.44671i) q^{51} +(-10.3465 - 1.69865i) q^{52} +8.06569 q^{53} +(4.44621 + 5.85075i) q^{54} +4.34470i q^{55} +(-7.42745 - 6.01142i) q^{56} +(-1.81756 + 4.01265i) q^{57} +(2.03388 - 5.69239i) q^{58} +(-1.63379 + 4.48880i) q^{59} +(2.36424 - 1.16889i) q^{60} +(-2.62747 - 0.463294i) q^{61} +(-1.69063 - 2.88874i) q^{62} +(-10.1325 + 0.223366i) q^{63} +(4.24289 + 6.78217i) q^{64} +(1.36515 + 3.75071i) q^{65} +(-9.71529 + 10.0499i) q^{66} +(2.16648 - 1.81790i) q^{67} +(2.26060 - 6.44682i) q^{68} +(-2.54534 - 9.09710i) q^{69} +(-0.610483 + 3.58591i) q^{70} +(3.03884 + 5.26343i) q^{71} +(8.08260 + 2.58294i) q^{72} +(1.40736 - 2.43763i) q^{73} +(11.4117 + 9.46132i) q^{74} +(6.31965 + 4.32206i) q^{75} +(0.942366 + 4.99851i) q^{76} +(-3.34767 - 18.9856i) q^{77} +(-5.22931 + 11.7285i) q^{78} +(7.42577 - 8.84969i) q^{79} +(1.46000 - 2.67264i) q^{80} +(8.31337 - 3.44788i) q^{81} +(2.05484 - 3.60813i) q^{82} +(5.47239 - 6.52174i) q^{83} +(-9.43067 + 6.92955i) q^{84} +(-2.56116 + 0.451602i) q^{85} +(5.80373 + 6.83425i) q^{86} +(-6.11092 - 4.17931i) q^{87} +(-2.52077 + 15.9424i) q^{88} +(-7.79000 - 4.49756i) q^{89} +(-0.649578 - 3.16417i) q^{90} +(-8.85545 - 15.3381i) q^{91} +(-8.43812 - 6.91227i) q^{92} +(-3.94772 + 1.10456i) q^{93} +(-5.01483 + 0.914812i) q^{94} +(1.48333 - 1.24466i) q^{95} +(9.35354 - 2.91742i) q^{96} +(13.6755 - 4.97747i) q^{97} +(-0.0368503 - 6.24084i) q^{98} +(8.88446 + 14.6337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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