LMFDB - Embedded newform 216.2.t.a.13.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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([0, 9, 8]))

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

//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);

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: 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:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.26
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00198 + 0.998014i) q^{2} +(-0.281905 + 1.70896i) q^{3} +(0.00793474 + 1.99998i) q^{4} +(2.06932 - 2.46612i) q^{5} +(-1.98803 + 1.43100i) q^{6} +(3.77263 + 1.37313i) q^{7} +(-1.98806 + 2.01187i) q^{8} +(-2.84106 - 0.963527i) q^{9} +O(q^{10})$	\(q+(1.00198 + 0.998014i) q^{2} +(-0.281905 + 1.70896i) q^{3} +(0.00793474 + 1.99998i) q^{4} +(2.06932 - 2.46612i) q^{5} +(-1.98803 + 1.43100i) q^{6} +(3.77263 + 1.37313i) q^{7} +(-1.98806 + 2.01187i) q^{8} +(-2.84106 - 0.963527i) q^{9} +(4.53465 - 0.405796i) q^{10} +(-1.90102 - 2.26554i) q^{11} +(-3.42012 - 0.550246i) q^{12} +(-5.98096 - 1.05461i) q^{13} +(2.40971 + 5.14099i) q^{14} +(3.63114 + 4.23159i) q^{15} +(-3.99987 + 0.0317387i) q^{16} +(0.333117 - 0.576975i) q^{17} +(-1.88507 - 3.80085i) q^{18} +(0.785955 - 0.453771i) q^{19} +(4.94862 + 4.11904i) q^{20} +(-3.41014 + 6.06017i) q^{21} +(0.356261 - 4.16727i) q^{22} +(2.52077 - 0.917484i) q^{23} +(-2.87775 - 3.96467i) q^{24} +(-0.931421 - 5.28235i) q^{25} +(-4.94030 - 7.02578i) q^{26} +(2.44753 - 4.58362i) q^{27} +(-2.71630 + 7.55610i) q^{28} +(2.05474 - 0.362306i) q^{29} +(-0.584853 + 7.86390i) q^{30} +(-6.54016 + 2.38042i) q^{31} +(-4.03948 - 3.96013i) q^{32} +(4.40762 - 2.61008i) q^{33} +(0.909607 - 0.245663i) q^{34} +(11.1931 - 6.46233i) q^{35} +(1.90450 - 5.68972i) q^{36} +(4.94847 + 2.85700i) q^{37} +(1.24038 + 0.329724i) q^{38} +(3.48834 - 9.92390i) q^{39} +(0.847567 + 9.06600i) q^{40} +(0.999412 - 5.66795i) q^{41} +(-9.46503 + 2.66881i) q^{42} +(1.91659 + 2.28410i) q^{43} +(4.51597 - 3.81998i) q^{44} +(-8.25524 + 5.01255i) q^{45} +(3.44142 + 1.59646i) q^{46} +(5.49754 + 2.00094i) q^{47} +(1.07335 - 6.84455i) q^{48} +(6.98497 + 5.86109i) q^{49} +(4.33860 - 6.22239i) q^{50} +(0.892118 + 0.731934i) q^{51} +(2.06174 - 11.9702i) q^{52} -2.21497i q^{53} +(7.02690 - 2.15003i) q^{54} -9.52091 q^{55} +(-10.2628 + 4.86017i) q^{56} +(0.553910 + 1.47108i) q^{57} +(2.42040 + 1.68763i) q^{58} +(-5.51061 + 6.56729i) q^{59} +(-8.43430 + 7.29580i) q^{60} +(-1.47289 + 4.04672i) q^{61} +(-8.92882 - 4.14203i) q^{62} +(-9.39523 - 7.53617i) q^{63} +(-0.0952148 - 7.99943i) q^{64} +(-14.9773 + 12.5675i) q^{65} +(7.02125 + 1.78361i) q^{66} +(-5.42498 - 0.956570i) q^{67} +(1.15658 + 0.661650i) q^{68} +(0.857322 + 4.56652i) q^{69} +(17.6648 + 4.69572i) q^{70} +(0.0541491 - 0.0937891i) q^{71} +(7.58669 - 3.80028i) q^{72} +(-6.43487 - 11.1455i) q^{73} +(2.10695 + 7.80130i) q^{74} +(9.28988 - 0.102635i) q^{75} +(0.913771 + 1.56830i) q^{76} +(-4.06096 - 11.1574i) q^{77} +(13.3994 - 6.46216i) q^{78} +(2.85410 + 16.1864i) q^{79} +(-8.19875 + 9.92985i) q^{80} +(7.14323 + 5.47488i) q^{81} +(6.65808 - 4.68175i) q^{82} +(6.91953 - 1.22010i) q^{83} +(-12.1473 - 6.77213i) q^{84} +(-0.733565 - 2.01545i) q^{85} +(-0.359180 + 4.20142i) q^{86} +(0.0399230 + 3.61359i) q^{87} +(8.33731 + 0.679450i) q^{88} +(-6.44771 - 11.1678i) q^{89} +(-13.2742 - 3.21636i) q^{90} +(-21.1159 - 12.1913i) q^{91} +(1.85496 + 5.03421i) q^{92} +(-2.22433 - 11.8479i) q^{93} +(3.51147 + 7.49153i) q^{94} +(0.507338 - 2.87726i) q^{95} +(7.90644 - 5.78690i) q^{96} +(-5.56275 + 4.66770i) q^{97} +(1.14936 + 12.8438i) q^{98} +(3.21799 + 8.26822i) 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}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.00198	+	0.998014i	0.708508	+	0.705703i
$2$	1.00198	+	0.998014i	0.708508	+	0.705703i
$3$	−0.281905	+	1.70896i	−0.162758	+	0.986666i
$3$	−0.281905	+	1.70896i	−0.162758	+	0.986666i
$4$	0.00793474	+	1.99998i	0.00396737	+	0.999992i
$5$	2.06932	−	2.46612i	0.925429	−	1.10288i	−0.0690154	−	0.997616i	$-0.521986\pi$
$5$	2.06932	−	2.46612i	0.925429	−	1.10288i	0.994444	−	0.105267i	$-0.0335698\pi$
$6$	−1.98803	+	1.43100i	−0.811608	+	0.584202i
$7$	3.77263	+	1.37313i	1.42592	+	0.518993i	0.935760	−	0.352639i	$-0.114716\pi$
$7$	3.77263	+	1.37313i	1.42592	+	0.518993i	0.490162	+	0.871632i	$0.336938\pi$
$8$	−1.98806	+	2.01187i	−0.702886	+	0.711302i
$9$	−2.84106	−	0.963527i	−0.947020	−	0.321176i
$10$	4.53465	−	0.405796i	1.43398	−	0.128324i
$11$	−1.90102	−	2.26554i	−0.573178	−	0.683087i	0.399102	−	0.916906i	$-0.369322\pi$
$11$	−1.90102	−	2.26554i	−0.573178	−	0.683087i	−0.972280	+	0.233820i	$0.924877\pi$
$12$	−3.42012	−	0.550246i	−0.987304	−	0.158842i
$13$	−5.98096	−	1.05461i	−1.65882	−	0.292495i	−0.735787	−	0.677213i	$-0.763187\pi$
$13$	−5.98096	−	1.05461i	−1.65882	−	0.292495i	−0.923034	+	0.384719i	$0.874299\pi$
$14$	2.40971	+	5.14099i	0.644022	+	1.37399i
$15$	3.63114	+	4.23159i	0.937556	+	1.09259i
$16$	−3.99987	+	0.0317387i	−0.999969	+	0.00793467i
$17$	0.333117	−	0.576975i	0.0807927	−	0.139937i	−0.822798	−	0.568334i	$-0.807588\pi$
$17$	0.333117	−	0.576975i	0.0807927	−	0.139937i	0.903591	+	0.428397i	$0.140921\pi$
$18$	−1.88507	−	3.80085i	−0.444316	−	0.895870i
$19$	0.785955	−	0.453771i	0.180310	−	0.104102i	−0.407128	−	0.913371i	$-0.633470\pi$
$19$	0.785955	−	0.453771i	0.180310	−	0.104102i	0.587438	+	0.809269i	$0.300136\pi$
$20$	4.94862	+	4.11904i	1.10655	+	0.921046i
$21$	−3.41014	+	6.06017i	−0.744153	+	1.32244i
$22$	0.356261	−	4.16727i	0.0759551	−	0.888466i
$23$	2.52077	−	0.917484i	0.525616	−	0.191309i	−0.0655637	−	0.997848i	$-0.520885\pi$
$23$	2.52077	−	0.917484i	0.525616	−	0.191309i	0.591180	+	0.806540i	$0.298662\pi$
$24$	−2.87775	−	3.96467i	−0.587417	−	0.809284i
$25$	−0.931421	−	5.28235i	−0.186284	−	1.05647i
$26$	−4.94030	−	7.02578i	−0.968873	−	1.37787i
$27$	2.44753	−	4.58362i	0.471028	−	0.882118i
$28$	−2.71630	+	7.55610i	−0.513332	+	1.42797i
$29$	2.05474	−	0.362306i	0.381555	−	0.0672785i	0.0204189	−	0.999792i	$-0.493500\pi$
$29$	2.05474	−	0.362306i	0.381555	−	0.0672785i	0.361136	+	0.932513i	$0.382389\pi$
$30$	−0.584853	+	7.86390i	−0.106779	+	1.43575i
$31$	−6.54016	+	2.38042i	−1.17465	+	0.427537i	−0.854308	−	0.519766i	$-0.826019\pi$
$31$	−6.54016	+	2.38042i	−1.17465	+	0.427537i	−0.320339	+	0.947303i	$0.603797\pi$
$32$	−4.03948	−	3.96013i	−0.714085	−	0.700059i
$33$	4.40762	−	2.61008i	0.767268	−	0.454357i
$34$	0.909607	−	0.245663i	0.155996	−	0.0421309i
$35$	11.1931	−	6.46233i	1.89198	−	1.09233i
$36$	1.90450	−	5.68972i	0.317416	−	0.948286i
$37$	4.94847	+	2.85700i	0.813523	+	0.469688i	0.848178	−	0.529712i	$-0.177700\pi$
$37$	4.94847	+	2.85700i	0.813523	+	0.469688i	−0.0346549	+	0.999399i	$0.511033\pi$
$38$	1.24038	+	0.329724i	0.201217	+	0.0534882i
$39$	3.48834	−	9.92390i	0.558581	−	1.58910i
$40$	0.847567	+	9.06600i	0.134012	+	1.43346i
$41$	0.999412	−	5.66795i	0.156082	−	0.885184i	−0.801708	−	0.597716i	$-0.796075\pi$
$41$	0.999412	−	5.66795i	0.156082	−	0.885184i	0.957790	−	0.287469i	$-0.0928137\pi$
$42$	−9.46503	+	2.66881i	−1.46049	+	0.411807i
$43$	1.91659	+	2.28410i	0.292277	+	0.348323i	0.892123	−	0.451793i	$-0.149216\pi$
$43$	1.91659	+	2.28410i	0.292277	+	0.348323i	−0.599845	+	0.800116i	$0.704771\pi$
$44$	4.51597	−	3.81998i	0.680807	−	0.575883i
$45$	−8.25524	+	5.01255i	−1.23062	+	0.747226i
$46$	3.44142	+	1.59646i	0.507410	+	0.235385i
$47$	5.49754	+	2.00094i	0.801899	+	0.291867i	0.710273	−	0.703926i	$-0.248571\pi$
$47$	5.49754	+	2.00094i	0.801899	+	0.291867i	0.0916258	+	0.995794i	$0.470794\pi$
$48$	1.07335	−	6.84455i	0.154924	−	0.987926i
$49$	6.98497	+	5.86109i	0.997853	+	0.837298i
$50$	4.33860	−	6.22239i	0.613570	−	0.879979i
$51$	0.892118	+	0.731934i	0.124922	+	0.102491i
$52$	2.06174	−	11.9702i	0.285911	−	1.65997i
$53$		−	2.21497i		−	0.304249i	−0.988361	−	0.152125i	$-0.951389\pi$
$53$		−	2.21497i		−	0.304249i	0.988361	−	0.152125i	$-0.0486115\pi$
$54$	7.02690	−	2.15003i	0.956240	−	0.292582i
$55$	−9.52091			−1.28380
$56$	−10.2628	+	4.86017i	−1.37142	+	0.649468i
$57$	0.553910	+	1.47108i	0.0733672	+	0.194850i
$58$	2.42040	+	1.68763i	0.317814	+	0.221597i
$59$	−5.51061	+	6.56729i	−0.717420	+	0.854988i	−0.994377	−	0.105894i	$-0.966229\pi$
$59$	−5.51061	+	6.56729i	−0.717420	+	0.854988i	0.276957	+	0.960882i	$0.410674\pi$
$60$	−8.43430	+	7.29580i	−1.08886	+	0.941883i
$61$	−1.47289	+	4.04672i	−0.188584	+	0.518129i	−0.997568	−	0.0697010i	$-0.977795\pi$
$61$	−1.47289	+	4.04672i	−0.188584	+	0.518129i	0.808984	+	0.587830i	$0.200018\pi$
$62$	−8.92882	−	4.14203i	−1.13396	−	0.526039i
$63$	−9.39523	−	7.53617i	−1.18369	−	0.949468i
$64$	−0.0952148	−	7.99943i	−0.0119019	−	0.999929i
$65$	−14.9773	+	12.5675i	−1.85771	+	1.55880i
$66$	7.02125	+	1.78361i	0.864257	+	0.219547i
$67$	−5.42498	−	0.956570i	−0.662767	−	0.116864i	−0.167862	−	0.985811i	$-0.553686\pi$
$67$	−5.42498	−	0.956570i	−0.662767	−	0.116864i	−0.494905	+	0.868947i	$0.664797\pi$
$68$	1.15658	+	0.661650i	0.140257	+	0.0802369i
$69$	0.857322	+	4.56652i	0.103209	+	0.549745i
$70$	17.6648	+	4.69572i	2.11134	+	0.561246i
$71$	0.0541491	−	0.0937891i	0.00642632	−	0.0111307i	−0.862794	−	0.505555i	$-0.831288\pi$
$71$	0.0541491	−	0.0937891i	0.00642632	−	0.0111307i	0.869221	+	0.494424i	$0.164621\pi$
$72$	7.58669	−	3.80028i	0.894100	−	0.447867i
$73$	−6.43487	−	11.1455i	−0.753144	−	1.30448i	−0.946292	−	0.323314i	$-0.895203\pi$
$73$	−6.43487	−	11.1455i	−0.753144	−	1.30448i	0.193148	−	0.981170i	$-0.438130\pi$
$74$	2.10695	+	7.80130i	0.244928	+	0.906883i
$75$	9.28988	−	0.102635i	1.07270	−	0.0118512i
$76$	0.913771	+	1.56830i	0.104817	+	0.179896i
$77$	−4.06096	−	11.1574i	−0.462789	−	1.27150i
$78$	13.3994	−	6.46216i	1.51719	−	0.731695i
$79$	2.85410	+	16.1864i	0.321111	+	1.82111i	0.535703	+	0.844407i	$0.320047\pi$
$79$	2.85410	+	16.1864i	0.321111	+	1.82111i	−0.214592	+	0.976704i	$0.568842\pi$
$80$	−8.19875	+	9.92985i	−0.916648	+	1.11019i
$81$	7.14323	+	5.47488i	0.793692	+	0.608319i
$82$	6.65808	−	4.68175i	0.735262	−	0.517013i
$83$	6.91953	−	1.22010i	0.759517	−	0.133923i	0.219540	−	0.975603i	$-0.429544\pi$
$83$	6.91953	−	1.22010i	0.759517	−	0.133923i	0.539977	+	0.841680i	$0.318433\pi$
$84$	−12.1473	−	6.77213i	−1.32538	−	0.738900i
$85$	−0.733565	−	2.01545i	−0.0795663	−	0.218607i
$86$	−0.359180	+	4.20142i	−0.0387313	+	0.453050i
$87$	0.0399230	+	3.61359i	0.00428019	+	0.387418i
$88$	8.33731	+	0.679450i	0.888760	+	0.0724296i
$89$	−6.44771	−	11.1678i	−0.683456	−	1.18378i	−0.973919	−	0.226895i	$-0.927143\pi$
$89$	−6.44771	−	11.1678i	−0.683456	−	1.18378i	0.290463	−	0.956886i	$-0.406191\pi$
$90$	−13.2742	−	3.21636i	−1.39922	−	0.339035i
$91$	−21.1159	−	12.1913i	−2.21354	−	1.27799i
$92$	1.85496	+	5.03421i	0.193392	+	0.524853i
$93$	−2.22433	−	11.8479i	−0.230653	−	1.22857i
$94$	3.51147	+	7.49153i	0.362180	+	0.772693i
$95$	0.507338	−	2.87726i	0.0520518	−	0.295200i
$96$	7.90644	−	5.78690i	0.806947	−	0.590623i
$97$	−5.56275	+	4.66770i	−0.564812	+	0.473934i	−0.879920	−	0.475122i	$-0.842404\pi$
$97$	−5.56275	+	4.66770i	−0.564812	+	0.473934i	0.315108	+	0.949056i	$0.397959\pi$
$98$	1.14936	+	12.8438i	0.116103	+	1.29742i
$99$	3.21799	+	8.26822i	0.323420	+	0.830987i
$100$	10.5572	−	1.90474i	1.05572	−	0.190474i
$101$	−0.296560	+	0.814791i	−0.0295088	+	0.0810748i	−0.953572	−	0.301164i	$-0.902625\pi$
$101$	−0.296560	+	0.814791i	−0.0295088	+	0.0810748i	0.924063	+	0.382239i	$0.124847\pi$
$102$	0.163405	+	1.62373i	0.0161795	+	0.160773i
$103$	6.97212	+	5.85030i	0.686984	+	0.576448i	0.918038	−	0.396493i	$-0.129773\pi$
$103$	6.97212	+	5.85030i	0.686984	+	0.576448i	−0.231054	+	0.972941i	$0.574217\pi$
$104$	14.0123	−	9.93628i	1.37401	−	0.974332i
$105$	7.88845	+	20.9502i	0.769833	+	2.04453i
$106$	2.21057	−	2.21936i	0.214709	−	0.215563i
$107$			5.28107i			0.510540i	0.966870	+	0.255270i	$0.0821644\pi$
$107$			5.28107i			0.510540i	−0.966870	+	0.255270i	$0.917836\pi$
$108$	9.18659	+	4.85866i	0.883980	+	0.467525i
$109$			12.2897i			1.17714i	0.808448	+	0.588568i	$0.200308\pi$
$109$			12.2897i			1.17714i	−0.808448	+	0.588568i	$0.799692\pi$
$110$	−9.53978	−	9.50201i	−0.909583	−	0.905981i
$111$	−6.27748	+	7.65131i	−0.595832	+	0.726230i
$112$	−15.1336	−	5.37259i	−1.42999	−	0.507662i
$113$	−13.0045	−	10.9120i	−1.22336	−	1.02652i	−0.998642	−	0.0520948i	$-0.983410\pi$
$113$	−13.0045	−	10.9120i	−1.22336	−	1.02652i	−0.224716	−	0.974424i	$-0.572145\pi$
$114$	−0.913153	+	2.02681i	−0.0855246	+	0.189828i
$115$	2.95365	−	8.11508i	0.275429	−	0.756736i
$116$	0.740910	+	4.10657i	0.0687917	+	0.381285i
$117$	15.9761	+	8.75902i	1.47699	+	0.809771i
$118$	−12.0758	+	1.08064i	−1.11166	+	0.0994805i
$119$	2.04899	−	1.71930i	0.187830	−	0.157608i
$120$	−15.7323	−	1.10730i	−1.43616	−	0.101082i
$121$	0.391308	−	2.21922i	0.0355735	−	0.201747i
$122$	−5.51449	+	2.58478i	−0.499258	+	0.234015i
$123$	9.40453	+	3.30577i	0.847978	+	0.298072i
$124$	−4.81270	−	13.0613i	−0.432194	−	1.17294i
$125$	−1.01439	−	0.585657i	−0.0907297	−	0.0523828i
$126$	−1.89264	−	16.9277i	−0.168610	−	1.50804i
$127$	−2.28246	−	3.95334i	−0.202536	−	0.350802i	0.746809	−	0.665038i	$-0.231585\pi$
$127$	−2.28246	−	3.95334i	−0.202536	−	0.350802i	−0.949345	+	0.314237i	$0.898251\pi$
$128$	7.88815	−	8.11031i	0.697220	−	0.716857i
$129$	−4.44373	+	2.63147i	−0.391249	+	0.231688i
$130$	−27.5495	−	2.35521i	−2.41625	−	0.206566i
$131$	3.72780	+	10.2420i	0.325699	+	0.894851i	0.989186	+	0.146664i	$0.0468535\pi$
$131$	3.72780	+	10.2420i	0.325699	+	0.894851i	−0.663487	+	0.748188i	$0.730924\pi$
$132$	5.25510	+	8.79446i	0.457398	+	0.765459i
$133$	3.58820	−	0.632697i	0.311137	−	0.0548618i
$134$	−4.48106	−	6.37267i	−0.387105	−	0.550515i
$135$	−6.23903	−	15.5209i	−0.536970	−	1.33583i
$136$	0.498540	+	1.81725i	0.0427495	+	0.155828i
$137$	2.28158	+	12.9395i	0.194928	+	1.10549i	0.912521	+	0.409030i	$0.134133\pi$
$137$	2.28158	+	12.9395i	0.194928	+	1.10549i	−0.717593	+	0.696463i	$0.754756\pi$
$138$	−3.69843	+	5.43119i	−0.314832	+	0.462334i
$139$	−1.55226	−	4.26479i	−0.131661	−	0.361735i	0.856292	−	0.516493i	$-0.172763\pi$
$139$	−1.55226	−	4.26479i	−0.131661	−	0.361735i	−0.987953	+	0.154757i	$0.950540\pi$
$140$	13.0134	+	22.3347i	1.09983	+	1.88763i
$141$	−4.96931	+	8.83098i	−0.418491	+	0.743703i
$142$	0.147859	−	0.0399333i	0.0124081	−	0.00335113i
$143$	8.98065	+	15.5549i	0.751000	+	1.30077i
$144$	11.3945	+	3.76382i	0.949538	+	0.313651i
$145$	3.35842	−	5.81696i	0.278902	−	0.483072i
$146$	4.67576	−	17.5897i	0.386969	−	1.45573i
$147$	−11.9854	+	10.2847i	−0.988542	+	0.848271i
$148$	−5.67469	+	9.91952i	−0.466456	+	0.815380i
$149$	6.86426	+	1.21035i	0.562342	+	0.0991561i	0.447591	−	0.894238i	$-0.352282\pi$
$149$	6.86426	+	1.21035i	0.562342	+	0.0991561i	0.114751	+	0.993394i	$0.463393\pi$
$150$	9.41072	+	9.16860i	0.768382	+	0.748613i
$151$	−2.62150	+	2.19970i	−0.213334	+	0.179009i	−0.743193	−	0.669077i	$-0.766690\pi$
$151$	−2.62150	+	2.19970i	−0.213334	+	0.179009i	0.529858	+	0.848086i	$0.322245\pi$
$152$	−0.649600	+	2.48336i	−0.0526895	+	0.201427i
$153$	−1.50234	+	1.31825i	−0.121457	+	0.106575i
$154$	7.06623	−	15.2324i	0.569413	−	1.22746i
$155$	−7.66328	+	21.0547i	−0.615529	+	1.69115i
$156$	19.8753	+	6.89788i	1.59130	+	0.552272i
$157$	11.7526	−	14.0062i	0.937957	−	1.11781i	−0.0548984	−	0.998492i	$-0.517484\pi$
$157$	11.7526	−	14.0062i	0.937957	−	1.11781i	0.992856	−	0.119322i	$-0.0380721\pi$
$158$	−13.2945	+	19.0669i	−1.05765	+	1.51688i
$159$	3.78528	+	0.624411i	0.300192	+	0.0495190i
$160$	−18.1251	+	1.76706i	−1.43292	+	0.139698i
$161$	10.7697			0.848775
$162$	1.69338	+	12.6148i	0.133045	+	0.991110i
$163$			6.82738i			0.534761i	0.963591	+	0.267381i	$0.0861581\pi$
$163$			6.82738i			0.534761i	−0.963591	+	0.267381i	$0.913842\pi$
$164$	11.3437	+	1.95383i	0.885797	+	0.152569i
$165$	2.68400	−	16.2708i	0.208949	−	1.26668i
$166$	8.15092	+	5.68327i	0.632634	+	0.441107i
$167$	−11.3859	−	9.55388i	−0.881065	−	0.739301i	0.0853330	−	0.996352i	$-0.472805\pi$
$167$	−11.3859	−	9.55388i	−0.881065	−	0.739301i	−0.966398	+	0.257051i	$0.917249\pi$
$168$	−5.41269	−	18.9087i	−0.417598	−	1.45884i
$169$	22.4437	+	8.16885i	1.72644	+	0.628373i
$170$	1.27643	−	2.75156i	0.0978979	−	0.211035i
$171$	−2.67016	+	0.531902i	−0.204193	+	0.0406755i
$172$	−4.55296	+	3.85128i	−0.347160	+	0.293657i
$173$	1.51792	+	1.80898i	0.115405	+	0.137534i	0.820654	−	0.571425i	$-0.193609\pi$
$173$	1.51792	+	1.80898i	0.115405	+	0.137534i	−0.705249	+	0.708960i	$0.749165\pi$
$174$	−3.56641	+	3.66060i	−0.270369	+	0.277509i
$175$	3.73943	−	21.2073i	0.282674	−	1.60312i
$176$	7.67573	+	9.00155i	0.578580	+	0.678517i
$177$	−9.66973	−	11.2687i	−0.726821	−	0.847010i
$178$	4.68510	−	17.6248i	0.351163	−	1.32104i
$179$	−19.3988	−	11.1999i	−1.44993	−	0.837119i	−0.451455	−	0.892294i	$-0.649095\pi$
$179$	−19.3988	−	11.1999i	−1.44993	−	0.837119i	−0.998477	+	0.0551751i	$0.982428\pi$
$180$	−10.0905	−	16.4706i	−0.752103	−	1.22764i
$181$	4.50340	−	2.60004i	0.334735	−	0.193259i	−0.323206	−	0.946329i	$-0.604761\pi$
$181$	4.50340	−	2.60004i	0.334735	−	0.193259i	0.657941	+	0.753069i	$0.271427\pi$
$182$	−8.99067	−	33.2894i	−0.666433	−	2.46757i
$183$	−6.50045	−	3.65789i	−0.480527	−	0.270399i
$184$	−3.16559	+	6.89546i	−0.233370	+	0.508340i
$185$	17.2857	−	6.29147i	1.27087	−	0.462558i
$186$	9.59563	−	14.0913i	0.703586	−	1.03322i
$187$	−1.94042	+	0.342149i	−0.141898	+	0.0250204i
$188$	−3.95823	+	11.0109i	−0.288684	+	0.803051i
$189$	15.5275	−	13.9315i	1.12946	−	1.01337i
$190$	3.37989	−	2.37663i	0.245203	−	0.172419i
$191$	0.464890	+	2.63652i	0.0336383	+	0.190772i	0.996997	−	0.0774456i	$-0.0246764\pi$
$191$	0.464890	+	2.63652i	0.0336383	+	0.190772i	−0.963358	+	0.268218i	$0.913565\pi$
$192$	13.6975	+	2.09236i	0.988533	+	0.151003i
$193$	22.3288	−	8.12704i	1.60727	−	0.584997i	0.626369	−	0.779527i	$-0.284540\pi$
$193$	22.3288	−	8.12704i	1.60727	−	0.584997i	0.980897	+	0.194530i	$0.0623181\pi$
$194$	−10.2322	−	0.874753i	−0.734630	−	0.0628036i
$195$	−17.2550	−	29.1384i	−1.23566	−	2.08664i
$196$	−11.6667	+	14.0163i	−0.833333	+	1.00117i
$197$	−15.7503	+	9.09343i	−1.12216	+	0.647880i	−0.941952	−	0.335749i	$-0.891011\pi$
$197$	−15.7503	+	9.09343i	−1.12216	+	0.647880i	−0.180209	+	0.983628i	$0.557677\pi$
$198$	−5.02744	+	11.4962i	−0.357285	+	0.817000i
$199$	3.43558	−	5.95060i	0.243542	−	0.421827i	−0.718179	−	0.695859i	$-0.755024\pi$
$199$	3.43558	−	5.95060i	0.243542	−	0.421827i	0.961721	+	0.274032i	$0.0883573\pi$
$200$	12.4791	+	8.62775i	0.882407	+	0.610074i
$201$	3.16407	−	9.00139i	0.223176	−	0.634909i
$202$	−1.11032	+	0.520435i	−0.0781219	+	0.0366177i
$203$	8.24926	+	1.45457i	0.578985	+	0.102091i
$204$	−1.45678	+	1.79003i	−0.101995	+	0.125327i
$205$	−11.9097	−	14.1935i	−0.831812	−	0.991315i
$206$	1.14725	+	12.8202i	0.0799327	+	0.893224i
$207$	−8.04567	+	0.177799i	−0.559213	+	0.0123579i
$208$	23.9566	+	4.02846i	1.66109	+	0.279323i
$209$	−2.52215	−	0.917988i	−0.174461	−	0.0634985i
$210$	−13.0046	+	28.8645i	−0.897401	+	1.99184i
$211$	−12.6911	+	15.1247i	−0.873694	+	1.04123i	0.125100	+	0.992144i	$0.460075\pi$
$211$	−12.6911	+	15.1247i	−0.873694	+	1.04123i	−0.998795	+	0.0490841i	$0.984370\pi$
$212$	4.42990	−	0.0175752i	0.304247	−	0.00120707i
$213$	0.145016	+	0.118978i	0.00993636	+	0.00815225i
$214$	−5.27058	+	5.29153i	−0.360289	+	0.361722i
$215$	9.59892			0.654641
$216$	4.35578	+	14.0366i	0.296373	+	0.955072i
$217$	−27.9422			−1.89684
$218$	−12.2653	+	12.3140i	−0.830708	+	0.834011i
$219$	20.8612	−	7.85492i	1.40967	−	0.530786i
$220$	−0.0755459	−	19.0417i	−0.00509331	−	1.28379i
$221$	−2.60084	+	3.09956i	−0.174951	+	0.208499i
$222$	−13.9260	+	1.40145i	−0.934654	+	0.0940593i
$223$	−17.5001	−	6.36950i	−1.17189	−	0.426533i	−0.318559	−	0.947903i	$-0.603199\pi$
$223$	−17.5001	−	6.36950i	−1.17189	−	0.426533i	−0.853331	+	0.521370i	$0.825421\pi$
$224$	−9.80170	−	20.4868i	−0.654904	−	1.36883i
$225$	−2.44347	+	15.9049i	−0.162898	+	1.06033i
$226$	−2.13986	−	23.9123i	−0.142342	−	1.59062i
$227$	−9.26931	−	11.0467i	−0.615226	−	0.733198i	0.365016	−	0.931001i	$-0.381064\pi$
$227$	−9.26931	−	11.0467i	−0.615226	−	0.733198i	−0.980242	+	0.197804i	$0.936619\pi$
$228$	−2.93775	+	1.11948i	−0.194557	+	0.0741396i
$229$	23.1876	+	4.08860i	1.53228	+	0.270182i	0.875246	−	0.483679i	$-0.160700\pi$
$229$	23.1876	+	4.08860i	1.53228	+	0.270182i	0.657034	+	0.753861i	$0.271811\pi$
$230$	11.0585	−	5.18338i	0.729174	−	0.341782i
$231$	20.2123	−	3.79467i	1.32987	−	0.249671i
$232$	−3.35604	+	4.85415i	−0.220335	+	0.318690i
$233$	−9.79013	+	16.9570i	−0.641373	+	1.11089i	0.343754	+	0.939060i	$0.388302\pi$
$233$	−9.79013	+	16.9570i	−0.641373	+	1.11089i	−0.985127	+	0.171831i	$0.945032\pi$
$234$	7.26616	+	24.7208i	0.475004	+	1.61605i
$235$	16.3107	−	9.41701i	1.06400	−	0.614298i
$236$	−13.1782	−	10.9690i	−0.857827	−	0.714022i
$237$	−28.4664	+	0.314497i	−1.84909	+	0.0204288i
$238$	3.76894	+	0.322207i	0.244304	+	0.0208856i
$239$	12.2840	−	4.47102i	0.794587	−	0.289206i	0.0873458	−	0.996178i	$-0.472161\pi$
$239$	12.2840	−	4.47102i	0.794587	−	0.289206i	0.707242	+	0.706972i	$0.249939\pi$
$240$	−14.6584	−	16.8106i	−0.946196	−	1.08512i
$241$	−1.01014	−	5.72879i	−0.0650688	−	0.369024i	−0.999903	−	0.0139387i	$-0.995563\pi$
$241$	−1.01014	−	5.72879i	−0.0650688	−	0.369024i	0.934834	−	0.355085i	$-0.115548\pi$
$242$	2.60690	−	1.83309i	0.167578	−	0.117835i
$243$	−11.3700	+	10.6641i	−0.729388	+	0.684100i
$244$	−8.10506	−	2.91364i	−0.518873	−	0.186527i
$245$	28.9083	−	5.09731i	1.84688	−	0.325655i
$246$	6.12396	+	12.6982i	0.390449	+	0.809606i
$247$	−5.17931	+	1.88512i	−0.329552	+	0.119947i
$248$	8.21315	−	17.8904i	0.521536	−	1.13604i
$249$	0.134444	+	12.1691i	0.00852007	+	0.771187i
$250$	−0.431904	−	1.59919i	−0.0273160	−	0.101142i
$251$	1.79969	−	1.03905i	0.113595	−	0.0655844i	−0.442126	−	0.896953i	$-0.645776\pi$
$251$	1.79969	−	1.03905i	0.113595	−	0.0655844i	0.555721	+	0.831369i	$0.312442\pi$
$252$	14.9977	−	18.8501i	0.944764	−	1.18744i
$253$	−6.87062	−	3.96675i	−0.431952	−	0.249388i
$254$	1.65850	−	6.23910i	0.104064	−	0.391476i
$255$	3.65112	−	0.685463i	0.228642	−	0.0429254i
$256$	15.9980	−	0.253902i	0.999874	−	0.0158688i
$257$	−0.774820	+	4.39422i	−0.0483319	+	0.274104i	−0.999391	−	0.0349064i	$-0.988887\pi$
$257$	−0.774820	+	4.39422i	−0.0483319	+	0.274104i	0.951059	+	0.309010i	$0.0999978\pi$
$258$	−7.07878	−	1.79822i	−0.440706	−	0.111952i
$259$	14.7457	+	17.5733i	0.916255	+	1.09195i
$260$	−25.2536	−	29.8547i	−1.56616	−	1.85151i
$261$	−6.18672	−	0.950464i	−0.382949	−	0.0588323i
$262$	−6.48652	+	13.9827i	−0.400738	+	0.863856i
$263$	−15.8933	−	5.78468i	−0.980021	−	0.356699i	−0.198173	−	0.980167i	$-0.563501\pi$
$263$	−15.8933	−	5.78468i	−0.980021	−	0.356699i	−0.781849	+	0.623468i	$0.785723\pi$
$264$	−3.51148	+	14.0565i	−0.216117	+	0.865121i
$265$	−5.46238	−	4.58348i	−0.335551	−	0.281561i
$266$	4.22675	+	2.94713i	0.259159	+	0.180700i
$267$	20.9029	−	7.87060i	1.27923	−	0.481673i
$268$	1.87008	−	10.8575i	0.114233	−	0.663225i
$269$		−	18.9889i		−	1.15777i	−0.815408	−	0.578886i	$-0.803488\pi$
$269$		−	18.9889i		−	1.15777i	0.815408	−	0.578886i	$-0.196512\pi$
$270$	9.23869	−	21.7783i	0.562249	−	1.32538i
$271$	5.10354			0.310018			0.155009	−	0.987913i	$-0.450459\pi$
$271$	5.10354			0.310018			0.155009	+	0.987913i	$0.450459\pi$
$272$	−1.31411	+	2.31840i	−0.0796798	+	0.140574i
$273$	26.7870	−	32.6493i	1.62122	−	1.97603i
$274$	−10.6277	+	15.2422i	−0.642041	+	0.920812i
$275$	−10.1968	+	12.1520i	−0.614887	+	0.732794i
$276$	−9.12617	+	1.75086i	−0.549331	+	0.105390i
$277$	−2.28588	+	6.28041i	−0.137345	+	0.377353i	−0.989229	−	0.146378i	$-0.953238\pi$
$277$	−2.28588	+	6.28041i	−0.137345	+	0.377353i	0.851883	+	0.523732i	$0.175461\pi$
$278$	2.70099	−	5.82242i	0.161995	−	0.349206i
$279$	20.8746	−	0.461301i	1.24973	−	0.0276174i
$280$	−9.25120	+	35.3665i	−0.552865	+	2.11355i
$281$	3.73413	−	3.13331i	0.222759	−	0.186917i	−0.524577	−	0.851363i	$-0.675777\pi$
$281$	3.73413	−	3.13331i	0.222759	−	0.186917i	0.747337	+	0.664445i	$0.231332\pi$
$282$	−13.7926	+	3.88904i	−0.821337	+	0.231589i
$283$	7.48836	+	1.32040i	0.445137	+	0.0784896i	0.391724	−	0.920083i	$-0.371879\pi$
$283$	7.48836	+	1.32040i	0.445137	+	0.0784896i	0.0534129	+	0.998573i	$0.482990\pi$
$284$	0.188006	+	0.107553i	0.0111561	+	0.00638211i
$285$	4.77408	+	1.67813i	0.282792	+	0.0994040i
$286$	−6.52561	+	24.5486i	−0.385867	+	1.45159i
$287$	11.5532	−	20.0108i	0.681965	−	1.18120i
$288$	7.66070	+	15.1431i	0.451411	+	0.892316i
$289$	8.27807	+	14.3380i	0.486945	+	0.843414i
$290$	9.17049	−	2.47673i	0.538510	−	0.145439i
$291$	−6.40873	−	10.8223i	−0.375686	−	0.634417i
$292$	22.2398	−	12.9581i	1.30149	−	0.758313i
$293$	−1.06412	−	2.92364i	−0.0621664	−	0.170801i	0.904721	−	0.426005i	$-0.140079\pi$
$293$	−1.06412	−	2.92364i	−0.0621664	−	0.170801i	−0.966887	+	0.255204i	$0.917857\pi$
$294$	−22.2735	−	1.65652i	−1.29902	−	0.0966104i
$295$	4.79250	+	27.1796i	0.279030	+	1.58246i
$296$	−15.5858	+	4.27576i	−0.905904	+	0.248524i
$297$	−15.0372	+	3.16854i	−0.872546	+	0.183857i
$298$	5.66992	+	8.06339i	0.328449	+	0.467099i
$299$	−16.0442	+	2.82902i	−0.927860	+	0.163607i
$300$	0.278980	+	18.5788i	0.0161069	+	1.07265i
$301$	4.09423	+	11.2488i	0.235988	+	0.648370i
$302$	−4.82202	−	0.412235i	−0.277476	−	0.0237215i
$303$	−1.30884	−	0.736502i	−0.0751909	−	0.0423109i
$304$	−3.12932	+	1.83997i	−0.179479	+	0.105530i
$305$	6.93183	+	12.0063i	0.396915	+	0.687477i
$306$	−2.82095	−	0.178487i	−0.161263	−	0.0102034i
$307$	16.5604	+	9.56114i	0.945151	+	0.545683i	0.891571	−	0.452880i	$-0.149603\pi$
$307$	16.5604	+	9.56114i	0.945151	+	0.545683i	0.0535799	+	0.998564i	$0.482937\pi$
$308$	22.2824	−	8.21039i	1.26966	−	0.467830i
$309$	−11.9634	+	10.2658i	−0.680573	+	0.584002i
$310$	−28.6913	+	13.4483i	−1.62956	+	0.763815i
$311$	−0.197557	+	1.12040i	−0.0112024	+	0.0635321i	−0.989897	−	0.141792i	$-0.954714\pi$
$311$	−0.197557	+	1.12040i	−0.0112024	+	0.0635321i	0.978694	+	0.205324i	$0.0658248\pi$
$312$	13.0305	+	26.7474i	0.737709	+	1.51427i
$313$	13.0225	−	10.9271i	0.736073	−	0.617639i	−0.195707	−	0.980662i	$-0.562700\pi$
$313$	13.0225	−	10.9271i	0.736073	−	0.617639i	0.931780	+	0.363024i	$0.118256\pi$
$314$	25.7542	−	2.30469i	1.45339	−	0.130061i
$315$	−38.0268	+	7.57502i	−2.14257	+	0.426804i
$316$	−32.3499	+	5.83658i	−1.81982	+	0.328333i
$317$	−6.93833	+	19.0629i	−0.389695	+	1.07068i	0.577444	+	0.816431i	$0.304050\pi$
$317$	−6.93833	+	19.0629i	−0.389695	+	1.07068i	−0.967139	+	0.254249i	$0.918172\pi$
$318$	3.16961	+	4.40341i	0.177743	+	0.246931i
$319$	−4.72691	−	3.96635i	−0.264656	−	0.222073i
$320$	−19.9246	−	16.3186i	−1.11382	−	0.912237i
$321$	−9.02511	−	1.48876i	−0.503732	−	0.0830945i
$322$	10.7911	+	10.7484i	0.601364	+	0.598983i
$323$		−	0.604635i		−	0.0336428i
$324$	−10.8930	+	14.3298i	−0.605166	+	0.796099i
$325$			32.5758i			1.80698i
$326$	−6.81382	+	6.84091i	−0.377383	+	0.378883i
$327$	−21.0025	−	3.46452i	−1.16144	−	0.191588i
$328$	9.41626	+	13.2789i	0.519926	+	0.733205i
$329$	17.9927	+	15.0976i	0.991968	+	0.832360i
$330$	18.9278	−	13.6244i	1.04194	−	0.749998i
$331$	−1.29048	+	3.54556i	−0.0709312	+	0.194882i	−0.970093	−	0.242735i	$-0.921955\pi$
$331$	−1.29048	+	3.54556i	−0.0709312	+	0.194882i	0.899161	+	0.437617i	$0.144178\pi$
$332$	2.49509	+	13.8293i	0.136936	+	0.758980i
$333$	−11.3061	−	12.8849i	−0.619570	−	0.706087i
$334$	−1.87352	−	20.9361i	−0.102515	−	1.14557i
$335$	−13.5850	+	11.3992i	−0.742230	+	0.622805i
$336$	13.4478	−	24.3482i	0.733636	−	1.32830i
$337$	−0.768414	+	4.35789i	−0.0418582	+	0.237389i	−0.998558	−	0.0536876i	$-0.982902\pi$
$337$	−0.768414	+	4.35789i	−0.0418582	+	0.237389i	0.956700	+	0.291077i	$0.0940136\pi$
$338$	14.3356	+	30.5842i	0.779752	+	1.66356i
$339$	22.3142	−	19.1479i	1.21194	−	1.03997i
$340$	4.02506	−	1.48311i	0.218289	−	0.0804330i
$341$	17.8259	+	10.2918i	0.965327	+	0.557332i
$342$	−3.20630	−	2.13191i	−0.173377	−	0.115280i
$343$	4.25209	+	7.36483i	0.229591	+	0.397664i
$344$	−8.40562	−	0.685016i	−0.453200	−	0.0369336i
$345$	13.0357	+	7.33534i	0.701817	+	0.394921i
$346$	−0.284466	+	3.32747i	−0.0152930	+	0.178886i
$347$	−1.68666	−	4.63407i	−0.0905448	−	0.248770i	0.886152	−	0.463396i	$-0.153369\pi$
$347$	−1.68666	−	4.63407i	−0.0905448	−	0.248770i	−0.976696	+	0.214626i	$0.931147\pi$
$348$	−7.22681	+	0.108518i	−0.387398	+	0.00581719i
$349$	−5.14891	+	0.907892i	−0.275615	+	0.0485983i	−0.309747	−	0.950819i	$-0.600244\pi$
$349$	−5.14891	+	0.907892i	−0.275615	+	0.0485983i	0.0341322	+	0.999417i	$0.489133\pi$
$350$	24.9121	−	17.5174i	1.33161	−	0.936343i
$351$	−19.4725	+	24.8333i	−1.03937	+	1.32550i
$352$	−1.29273	+	16.6799i	−0.0689030	+	0.889040i
$353$	−3.88735	−	22.0463i	−0.206903	−	1.17340i	−0.894417	−	0.447233i	$-0.852409\pi$
$353$	−3.88735	−	22.0463i	−0.206903	−	1.17340i	0.687515	−	0.726170i	$-0.258702\pi$
$354$	1.55747	−	20.9416i	0.0827784	−	1.11303i
$355$	−0.119243	−	0.327618i	−0.00632877	−	0.0173882i
$356$	22.2842	−	12.9839i	1.18106	−	0.688147i
$357$	2.36060	+	3.98631i	0.124936	+	0.210978i
$358$	−8.25957	−	30.5823i	−0.436532	−	1.61633i
$359$	13.8239	+	23.9436i	0.729595	+	1.26370i	0.957054	+	0.289908i	$0.0936248\pi$
$359$	13.8239	+	23.9436i	0.729595	+	1.26370i	−0.227459	+	0.973788i	$0.573042\pi$
$360$	6.32735	−	26.5737i	0.333481	−	1.40056i
$361$	−9.08818	+	15.7412i	−0.478325	+	0.828484i
$362$	7.10720	+	1.88927i	0.373546	+	0.0992977i
$363$	3.68224	+	1.29434i	0.193267	+	0.0679351i
$364$	24.2148	−	42.3281i	1.26920	−	2.21860i
$365$	−40.8020	−	7.19449i	−2.13567	−	0.376577i
$366$	−2.86271	−	10.1527i	−0.149636	−	0.530689i
$367$	−8.02667	+	6.73517i	−0.418989	+	0.351573i	−0.827778	−	0.561055i	$-0.810395\pi$
$367$	−8.02667	+	6.73517i	−0.418989	+	0.351573i	0.408790	+	0.912629i	$0.365951\pi$
$368$	−10.0536	+	3.74983i	−0.524082	+	0.195473i
$369$	−8.30061	+	15.1400i	−0.432112	+	0.788157i
$370$	23.5989	+	10.9474i	1.22685	+	0.569129i
$371$	3.04143	−	8.35626i	0.157903	−	0.433835i
$372$	23.6780	−	4.54264i	1.22764	−	0.235525i
$373$	15.7921	−	18.8203i	0.817683	−	0.974477i	−0.182278	−	0.983247i	$-0.558347\pi$
$373$	15.7921	−	18.8203i	0.817683	−	0.974477i	0.999962	+	0.00876993i	$0.00279159\pi$
$374$	−2.28574	−	1.59374i	−0.118193	−	0.0824105i
$375$	1.28682	−	1.56845i	0.0664513	−	0.0809942i
$376$	−14.9551	+	7.08233i	−0.771250	+	0.365243i
$377$	−12.6714			−0.652610
$378$	29.4622	+	1.53756i	1.51537	+	0.0790833i
$379$		−	15.3787i		−	0.789950i	−0.918692	−	0.394975i	$-0.870753\pi$
$379$		−	15.3787i		−	0.789950i	0.918692	−	0.394975i	$-0.129247\pi$
$380$	5.75849	+	0.991838i	0.295405	+	0.0508802i
$381$	7.39951	−	2.78616i	0.379089	−	0.142739i
$382$	−2.16548	+	3.10572i	−0.110795	+	0.158902i
$383$	−4.86989	−	4.08632i	−0.248840	−	0.208801i	0.509833	−	0.860273i	$-0.329707\pi$
$383$	−4.86989	−	4.08632i	−0.248840	−	0.208801i	−0.758672	+	0.651472i	$0.774152\pi$
$384$	11.6365	+	15.7668i	0.593820	+	0.804598i
$385$	−35.9189	−	13.0734i	−1.83060	−	0.666283i
$386$	30.4840	+	14.1414i	1.55159	+	0.719777i
$387$	−3.24435	−	8.33596i	−0.164920	−	0.423741i
$388$	−9.37947	−	11.0884i	−0.476171	−	0.562927i
$389$	−3.44454	−	4.10505i	−0.174645	−	0.208134i	0.671620	−	0.740896i	$-0.265599\pi$
$389$	−3.44454	−	4.10505i	−0.174645	−	0.208134i	−0.846265	+	0.532762i	$0.821154\pi$
$390$	11.7913	−	46.4169i	0.597076	−	2.35041i
$391$	0.310344	−	1.76005i	0.0156948	−	0.0890095i
$392$	−25.6783	+	2.40062i	−1.29695	+	0.121250i
$393$	−18.5541	+	3.48336i	−0.935930	+	0.175712i
$394$	−24.8569	−	6.60755i	−1.25227	−	0.332884i
$395$	45.8236	+	26.4563i	2.30564	+	1.33116i
$396$	−16.5108	+	6.50153i	−0.829698	+	0.326714i
$397$	17.1815	−	9.91973i	0.862314	−	0.497857i	−0.00247280	−	0.999997i	$-0.500787\pi$
$397$	17.1815	−	9.91973i	0.862314	−	0.497857i	0.864786	+	0.502140i	$0.167454\pi$
$398$	9.38117	−	2.53363i	0.470236	−	0.127000i
$399$	0.0697177	+	6.31044i	0.00349025	+	0.315917i
$400$	3.89322	+	21.0992i	0.194661	+	1.05496i
$401$	−15.7999	+	5.75068i	−0.789007	+	0.287175i	−0.704923	−	0.709284i	$-0.749019\pi$
$401$	−15.7999	+	5.75068i	−0.789007	+	0.287175i	−0.0840838	+	0.996459i	$0.526796\pi$
$402$	12.1539	−	5.86144i	0.606179	−	0.292342i
$403$	41.6269	−	7.33994i	2.07358	−	0.365628i
$404$	−1.63192	−	0.586650i	−0.0811912	−	0.0291869i
$405$	28.2833	−	6.28680i	1.40541	−	0.312393i
$406$	6.81393	+	9.69033i	0.338170	+	0.480923i
$407$	−2.93446	−	16.6422i	−0.145456	−	0.824921i
$408$	−3.24614	+	0.339691i	−0.160708	+	0.0168172i
$409$	19.2384	−	7.00221i	0.951278	−	0.346237i	0.180668	−	0.983544i	$-0.442174\pi$
$409$	19.2384	−	7.00221i	0.951278	−	0.346237i	0.770610	+	0.637307i	$0.219952\pi$
$410$	2.23195	−	26.1077i	0.110228	−	1.28937i
$411$	−22.7562	+	0.251410i	−1.12248	+	0.0124011i
$412$	−11.6452	+	13.9906i	−0.573718	+	0.689265i
$413$	−29.8072	+	17.2092i	−1.46672	+	0.846809i
$414$	−8.23906	−	7.85154i	−0.404928	−	0.385882i
$415$	11.3098	−	19.5892i	0.555177	−	0.961595i
$416$	19.9836	+	27.9454i	0.979776	+	1.37014i
$417$	7.72594	−	1.45047i	0.378341	−	0.0710299i
$418$	−1.61098	−	3.43695i	−0.0787958	−	0.168107i
$419$	−5.37400	−	0.947582i	−0.262537	−	0.0462924i	0.0408300	−	0.999166i	$-0.487000\pi$
$419$	−5.37400	−	0.947582i	−0.262537	−	0.0462924i	−0.303367	+	0.952874i	$0.598111\pi$
$420$	−41.8376	+	15.9430i	−2.04146	+	0.777939i
$421$	17.5035	+	20.8599i	0.853069	+	1.01665i	0.999623	+	0.0274450i	$0.00873711\pi$
$421$	17.5035	+	20.8599i	0.853069	+	1.01665i	−0.146555	+	0.989203i	$0.546818\pi$
$422$	−27.8110	+	2.48874i	−1.35382	+	0.121150i
$423$	−13.6909	−	10.9818i	−0.665673	−	0.533955i
$424$	4.45622	+	4.40349i	0.216413	+	0.213852i
$425$	−3.35806	−	1.22223i	−0.162890	−	0.0592871i
$426$	0.0265619	+	0.263942i	0.00128693	+	0.0127880i
$427$	−11.1133	+	13.2443i	−0.537811	+	0.640938i
$428$	−10.5620	+	0.0419039i	−0.510536	+	0.00202550i
$429$	−29.1144	+	10.9625i	−1.40566	+	0.529275i
$430$	9.61794	+	9.57986i	0.463818	+	0.461982i
$431$	14.9537			0.720297			0.360148	−	0.932895i	$-0.382726\pi$
$431$	14.9537			0.720297			0.360148	+	0.932895i	$0.382726\pi$
$432$	−9.64435	+	18.4116i	−0.464014	+	0.885828i
$433$	−5.13521			−0.246782			−0.123391	−	0.992358i	$-0.539377\pi$
$433$	−5.13521			−0.246782			−0.123391	+	0.992358i	$0.539377\pi$
$434$	−27.9976	−	27.8868i	−1.34393	−	1.33861i
$435$	8.99417	+	7.37923i	0.431237	+	0.353807i
$436$	−24.5791	+	0.0975152i	−1.17713	+	0.00467013i
$437$	1.56488	−	1.86495i	0.0748584	−	0.0892127i
$438$	28.7419	+	12.9493i	1.37334	+	0.618742i
$439$	4.31312	+	1.56985i	0.205854	+	0.0749247i	0.442889	−	0.896576i	$-0.353953\pi$
$439$	4.31312	+	1.56985i	0.205854	+	0.0749247i	−0.237035	+	0.971501i	$0.576176\pi$
$440$	18.9282	−	19.1548i	0.902365	−	0.913170i
$441$	−14.1974	−	23.3819i	−0.676067	−	1.11342i
$442$	−5.69940	+	0.510027i	−0.271093	+	0.0242595i
$443$	−25.3124	−	30.1662i	−1.20263	−	1.43324i	−0.872020	−	0.489471i	$-0.837190\pi$
$443$	−25.3124	−	30.1662i	−1.20263	−	1.43324i	−0.330610	−	0.943767i	$-0.607254\pi$
$444$	−15.3523	−	12.4942i	−0.728588	−	0.592946i
$445$	−40.8834	−	7.20886i	−1.93806	−	0.341733i
$446$	−11.1779	−	23.8474i	−0.529288	−	1.12921i
$447$	−4.00352	+	11.3895i	−0.189360	+	0.538706i
$448$	10.6250	−	30.3097i	0.501985	−	1.43200i
$449$	18.6512	−	32.3048i	0.880203	−	1.52456i	0.0290891	−	0.999577i	$-0.490739\pi$
$449$	18.6512	−	32.3048i	0.880203	−	1.52456i	0.851114	−	0.524980i	$-0.175927\pi$
$450$	−18.3217	+	13.4978i	−0.863691	+	0.636294i
$451$	−14.7409	+	8.51065i	−0.694120	+	0.400751i
$452$	21.7207	−	26.0953i	1.02166	−	1.22742i
$453$	−3.02017	−	5.10013i	−0.141900	−	0.239625i
$454$	1.73712	−	20.3195i	0.0815271	−	0.953643i
$455$	−73.7606	+	26.8467i	−3.45795	+	1.25859i
$456$	−4.06083	−	1.81021i	−0.190166	−	0.0847709i
$457$	2.36388	+	13.4062i	0.110578	+	0.627116i	0.988845	+	0.148947i	$0.0475884\pi$
$457$	2.36388	+	13.4062i	0.110578	+	0.627116i	−0.878268	+	0.478169i	$0.841300\pi$
$458$	19.1531	+	27.2383i	0.894964	+	1.27276i
$459$	−1.82932	−	2.93905i	−0.0853854	−	0.137183i
$460$	16.2535	+	5.84286i	0.757822	+	0.272425i
$461$	28.5492	−	5.03400i	1.32967	−	0.234457i	0.536729	−	0.843755i	$-0.319660\pi$
$461$	28.5492	−	5.03400i	1.32967	−	0.234457i	0.792941	+	0.609298i	$0.208549\pi$
$462$	24.0395	+	16.3700i	1.11842	+	0.761600i
$463$	5.15703	−	1.87701i	0.239667	−	0.0872318i	−0.219394	−	0.975636i	$-0.570408\pi$
$463$	5.15703	−	1.87701i	0.239667	−	0.0872318i	0.459061	+	0.888405i	$0.348186\pi$
$464$	−8.20720	+	1.51439i	−0.381009	+	0.0703039i
$465$	−33.8212	−	19.0316i	−1.56842	−	0.882571i
$466$	−26.7329	+	7.21992i	−1.23838	+	0.334456i
$467$	23.4850	−	13.5591i	1.08676	−	0.627440i	0.154046	−	0.988064i	$-0.450770\pi$
$467$	23.4850	−	13.5591i	1.08676	−	0.627440i	0.932711	+	0.360624i	$0.117436\pi$
$468$	−17.3911	+	32.0215i	−0.803905	+	1.48019i
$469$	−19.1530	−	11.0580i	−0.884402	−	0.510610i
$470$	25.7414	+	6.84268i	1.18736	+	0.315629i
$471$	20.6228	+	24.0330i	0.950249	+	1.10738i
$472$	−2.25707	−	24.1428i	−0.103890	−	1.11126i
$473$	1.53127	−	8.68424i	0.0704077	−	0.399302i
$474$	−28.8367	−	28.0948i	−1.32451	−	1.29043i
$475$	−3.12903	−	3.72904i	−0.143570	−	0.171100i
$476$	3.45484	+	4.08430i	0.158352	+	0.187204i
$477$	−2.13418	+	6.29285i	−0.0977174	+	0.288130i
$478$	16.7705	+	7.77975i	0.767065	+	0.355838i
$479$	34.7152	+	12.6353i	1.58618	+	0.577322i	0.976536	−	0.215355i	$-0.0690909\pi$
$479$	34.7152	+	12.6353i	1.58618	+	0.577322i	0.609642	+	0.792677i	$0.291313\pi$
$480$	2.08975	−	31.4732i	0.0953836	−	1.43655i
$481$	−26.5836	−	22.3063i	−1.21211	−	1.01708i
$482$	4.70527	−	6.74828i	0.214319	−	0.307376i
$483$	−3.03605	+	18.4050i	−0.138145	+	0.837457i
$484$	4.44151	+	0.765002i	0.201887	+	0.0347728i
$485$			23.3774i			1.06151i
$486$	−22.0355	−	0.662255i	−0.999549	−	0.0300405i
$487$	41.5808			1.88420			0.942102	−	0.335326i	$-0.108847\pi$
$487$	41.5808			1.88420			0.942102	+	0.335326i	$0.108847\pi$
$488$	−5.21327	−	11.0084i	−0.235994	−	0.498326i
$489$	−11.6677	−	1.92467i	−0.527631	−	0.0870368i
$490$	34.0528	+	23.7435i	1.53835	+	1.07262i
$491$	16.9792	−	20.2350i	0.766261	−	0.913194i	−0.231966	−	0.972724i	$-0.574516\pi$
$491$	16.9792	−	20.2350i	0.766261	−	0.913194i	0.998227	+	0.0595299i	$0.0189602\pi$
$492$	−6.53687	+	18.8351i	−0.294705	+	0.849154i
$493$	0.475427	−	1.30622i	0.0214121	−	0.0588294i
$494$	−7.07095	−	3.28018i	−0.318137	−	0.147582i
$495$	27.0495	+	9.17366i	1.21578	+	0.412325i
$496$	26.0843	−	9.72897i	1.17122	−	0.436844i
$497$	0.333069	−	0.279478i	0.0149402	−	0.0125363i
$498$	−12.0102	+	12.3274i	−0.538192	+	0.552405i
$499$	−0.289107	−	0.0509773i	−0.0129422	−	0.00228206i	0.167173	−	0.985928i	$-0.446536\pi$
$499$	−0.289107	−	0.0509773i	−0.0129422	−	0.00228206i	−0.180116	+	0.983645i	$0.557647\pi$
$500$	1.16326	−	2.03341i	0.0520224	−	0.0909368i
$501$	19.5369	−	16.7647i	0.872844	−	0.748989i
$502$	2.84025	+	0.755006i	0.126766	+	0.0336976i
$503$	−7.59691	+	13.1582i	−0.338729	+	0.586696i	−0.984194	−	0.177094i	$-0.943330\pi$
$503$	−7.59691	+	13.1582i	−0.338729	+	0.586696i	0.645465	+	0.763790i	$0.276664\pi$
$504$	33.8401	−	3.91957i	1.50736	−	0.174592i
$505$	1.39570	+	2.41742i	0.0621077	+	0.107574i
$506$	−2.92536	−	10.8316i	−0.130048	−	0.481523i
$507$	−20.2872	+	36.0525i	−0.900986	+	1.60115i
$508$	7.88850	−	4.59625i	0.349996	−	0.203926i
$509$	−0.262015	−	0.719880i	−0.0116136	−	0.0319081i	0.933750	−	0.357925i	$-0.116516\pi$
$509$	−0.262015	−	0.719880i	−0.0116136	−	0.0319081i	−0.945364	+	0.326017i	$0.894293\pi$
$510$	4.34246	+	2.95705i	0.192287	+	0.130940i
$511$	−8.97219	−	50.8838i	−0.396906	−	2.25097i
$512$	16.2831	+	15.7118i	0.719618	+	0.694371i
$513$	−0.156263	−	4.71314i	−0.00689918	−	0.208090i
$514$	−5.16185	+	3.62965i	−0.227679	+	0.160097i
$515$	28.8551	−	5.08794i	1.27151	−	0.224201i
$516$	−5.29815	−	8.86651i	−0.233238	−	0.390326i
$517$	−5.91770	−	16.2587i	−0.260260	−	0.715059i
$518$	−2.76343	+	32.3245i	−0.121418	+	1.42026i
$519$	−3.51938	+	2.08409i	−0.154484	+	0.0914814i
$520$	4.49179	−	55.1173i	0.196978	−	2.41705i
$521$	−18.2983	−	31.6937i	−0.801665	−	1.38852i	−0.918519	−	0.395376i	$-0.870614\pi$
$521$	−18.2983	−	31.6937i	−0.801665	−	1.38852i	0.116854	−	0.993149i	$-0.462719\pi$
$522$	−5.25041	−	7.12679i	−0.229804	−	0.311931i
$523$	−24.8785	−	14.3636i	−1.08786	−	0.628078i	−0.154856	−	0.987937i	$-0.549491\pi$
$523$	−24.8785	−	14.3636i	−1.08786	−	0.628078i	−0.933007	+	0.359859i	$0.882825\pi$
$524$	−20.4543	+	7.53681i	−0.893552	+	0.329247i
$525$	35.1882	+	12.3690i	1.53574	+	0.539826i
$526$	−10.1516	−	21.6579i	−0.442630	−	0.944328i
$527$	−0.805192	+	4.56647i	−0.0350747	+	0.198919i
$528$	−17.5471	+	10.5799i	−0.763639	+	0.460431i
$529$	−12.1065	+	10.1586i	−0.526371	+	0.441678i
$530$	−0.898824	−	10.0441i	−0.0390424	−	0.436287i
$531$	21.9837	−	13.3484i	0.954012	−	0.579272i
$532$	1.29386	+	7.17133i	0.0560957	+	0.310917i
$533$	−11.9549	+	32.8458i	−0.517824	+	1.42271i
$534$	28.7993	+	12.9752i	1.24627	+	0.561490i
$535$	13.0237	+	10.9282i	0.563066	+	0.472468i
$536$	12.7097	−	9.01262i	0.548975	−	0.389286i
$537$	24.6087	−	29.9943i	1.06194	−	1.29435i
$538$	18.9512	−	19.0265i	0.817043	−	0.820291i
$539$		−	26.9668i		−	1.16154i
$540$	30.9920	−	12.6011i	1.33369	−	0.542265i
$541$			8.42593i			0.362259i	0.983459	+	0.181129i	$0.0579753\pi$
$541$			8.42593i			0.362259i	−0.983459	+	0.181129i	$0.942025\pi$
$542$	5.11365	+	5.09341i	0.219650	+	0.218781i
$543$	3.17382	+	8.42908i	0.136202	+	0.361726i
$544$	−3.63052	+	1.01149i	−0.155657	+	0.0433674i
$545$	30.3078	+	25.4313i	1.29824	+	1.08936i
$546$	59.4245	−	5.98021i	2.54314	−	0.255929i
$547$	8.83678	−	24.2789i	0.377833	−	1.03809i	−0.594419	−	0.804155i	$-0.702618\pi$
$547$	8.83678	−	24.2789i	0.377833	−	1.03809i	0.972253	−	0.233933i	$-0.0751598\pi$
$548$	−25.8606	+	4.66579i	−1.10471	+	0.199313i
$549$	8.08368	−	10.0778i	0.345003	−	0.430110i
$550$	−22.3448	+	1.99959i	−0.952787	+	0.0852629i
$551$	1.45053	−	1.21714i	0.0617945	−	0.0518518i
$552$	−10.8916	−	7.35371i	−0.463579	−	0.312995i
$553$	−11.4585	+	64.9843i	−0.487264	+	2.76341i
$554$	−8.55835	+	4.01151i	−0.363610	+	0.170433i
$555$	5.87892	+	31.3140i	0.249546	+	1.32921i
$556$	8.51721	−	3.13833i	0.361210	−	0.133095i
$557$	−12.1279	−	7.00204i	−0.513875	−	0.296686i	0.220550	−	0.975376i	$-0.429215\pi$
$557$	−12.1279	−	7.00204i	−0.513875	−	0.296686i	−0.734425	+	0.678690i	$0.762548\pi$
$558$	21.3763	+	20.3709i	0.904932	+	0.862370i
$559$	−9.05423	−	15.6824i	−0.382953	−	0.663294i
$560$	−44.5658	+	26.2038i	−1.88325	+	1.10731i
$561$	−0.0377019	−	3.41255i	−0.00159177	−	0.144078i
$562$	6.86861	+	0.587199i	0.289735	+	0.0247695i
$563$	9.88635	+	27.1625i	0.416660	+	1.14476i	0.953582	+	0.301132i	$0.0973645\pi$
$563$	9.88635	+	27.1625i	0.416660	+	1.14476i	−0.536923	+	0.843632i	$0.680413\pi$
$564$	−17.7013	−	9.86846i	−0.745357	−	0.415537i
$565$	−53.8209	+	9.49007i	−2.26426	+	0.399250i
$566$	6.18542	+	8.79650i	0.259993	+	0.369745i
$567$	19.4311	+	30.4632i	0.816029	+	1.27934i
$568$	0.0810392	+	0.295399i	0.00340033	+	0.0123947i
$569$	4.85589	+	27.5391i	0.203570	+	1.15450i	0.899675	+	0.436560i	$0.143804\pi$
$569$	4.85589	+	27.5391i	0.203570	+	1.15450i	−0.696105	+	0.717940i	$0.745085\pi$
$570$	3.10874	+	6.44606i	0.130211	+	0.269996i
$571$	3.61107	+	9.92133i	0.151118	+	0.415195i	0.992034	−	0.125972i	$-0.0402050\pi$
$571$	3.61107	+	9.92133i	0.151118	+	0.415195i	−0.840915	+	0.541167i	$0.817983\pi$
$572$	−31.0384	+	18.0846i	−1.29778	+	0.756155i
$573$	−4.63676	+	0.0512269i	−0.193703	+	0.00214003i
$574$	31.5471	−	8.52014i	1.31675	−	0.355624i
$575$	−7.19437	−	12.4610i	−0.300026	−	0.519660i
$576$	−7.43716	+	22.8186i	−0.309882	+	0.950775i
$577$	−10.7516	+	18.6224i	−0.447597	+	0.775260i	−0.998229	−	0.0594876i	$-0.981053\pi$
$577$	−10.7516	+	18.6224i	−0.447597	+	0.775260i	0.550632	+	0.834748i	$0.314387\pi$
$578$	−6.01509	+	22.6281i	−0.250195	+	0.941204i
$579$	7.59412	+	40.4501i	0.315601	+	1.68105i
$580$	11.6605	+	6.67064i	0.484175	+	0.276983i
$581$	27.7802	+	4.89840i	1.15252	+	0.203220i
$582$	4.37943	−	17.2398i	0.181533	−	0.714613i
$583$	−5.01810	+	4.21069i	−0.207829	+	0.174389i
$584$	35.2162	+	9.21189i	1.45726	+	0.381191i
$585$	54.6605	−	21.2738i	2.25993	−	0.879565i
$586$	1.85161	−	3.99143i	0.0764891	−	0.164885i
$587$	0.845987	−	2.32433i	0.0349176	−	0.0959354i	−0.921009	−	0.389542i	$-0.872633\pi$
$587$	0.845987	−	2.32433i	0.0349176	−	0.0959354i	0.955926	+	0.293607i	$0.0948556\pi$
$588$	−20.6644	−	23.8891i	−0.852186	−	0.985169i
$589$	−4.06010	+	4.83864i	−0.167294	+	0.199373i
$590$	−22.3237	+	32.0165i	−0.919051	+	1.31810i
$591$	−11.1002	−	29.4800i	−0.456600	−	1.21265i
$592$	−19.8839	−	11.2706i	−0.817224	−	0.463218i
$593$	22.0990			0.907496			0.453748	−	0.891130i	$-0.350087\pi$
$593$	22.0990			0.907496			0.453748	+	0.891130i	$0.350087\pi$
$594$	−18.2292	−	11.8325i	−0.747955	−	0.485494i
$595$		−	8.61084i		−	0.353010i
$596$	−2.36622	+	13.7380i	−0.0969243	+	0.562731i
$597$	9.20080	+	7.54876i	0.376564	+	0.308950i
$598$	−18.8994	−	13.1777i	−0.772854	−	0.538876i
$599$	3.16314	+	2.65419i	0.129242	+	0.108447i	0.705118	−	0.709090i	$-0.250894\pi$
$599$	3.16314	+	2.65419i	0.129242	+	0.108447i	−0.575875	+	0.817538i	$0.695339\pi$
$600$	−18.2624	+	18.8940i	−0.745558	+	0.771346i
$601$	−13.5544	−	4.93340i	−0.552895	−	0.201237i	0.0504372	−	0.998727i	$-0.483939\pi$
$601$	−13.5544	−	4.93340i	−0.552895	−	0.201237i	−0.603332	+	0.797490i	$0.706161\pi$
$602$	−7.12413	+	15.3572i	−0.290358	+	0.625913i
$603$	14.4910	+	7.94479i	0.590119	+	0.323537i
$604$	−4.42016	−	5.22550i	−0.179854	−	0.212623i
$605$	−4.66312	−	5.55729i	−0.189583	−	0.225936i
$606$	−0.576395	−	2.04420i	−0.0234145	−	0.0830401i
$607$	4.07551	−	23.1134i	0.165420	−	0.938143i	−0.783211	−	0.621757i	$-0.786419\pi$
$607$	4.07551	−	23.1134i	0.165420	−	0.938143i	0.948630	−	0.316386i	$-0.102470\pi$
$608$	−4.97184	−	1.27948i	−0.201635	−	0.0518900i
$609$	−4.81130	+	13.6876i	−0.194964	+	0.554649i
$610$	−5.03687	+	18.9481i	−0.203937	+	0.767187i
$611$	−30.7704	−	17.7653i	−1.24484	−	0.718707i
$612$	−2.64841	−	2.99419i	−0.107056	−	0.121033i
$613$	−7.92829	+	4.57740i	−0.320220	+	0.184879i	−0.651491	−	0.758657i	$-0.725856\pi$
$613$	−7.92829	+	4.57740i	−0.320220	+	0.184879i	0.331270	+	0.943536i	$0.392523\pi$
$614$	7.05105	+	26.1076i	0.284557	+	1.05362i
$615$	27.6134	−	16.3520i	1.11348	−	0.659376i
$616$	30.5206	+	14.0115i	1.22971	+	0.564539i
$617$	12.1692	−	4.42922i	0.489913	−	0.178314i	−0.0852386	−	0.996361i	$-0.527165\pi$
$617$	12.1692	−	4.42922i	0.489913	−	0.178314i	0.575152	+	0.818047i	$0.304943\pi$
$618$	−22.2325	−	1.65348i	−0.894323	−	0.0665125i
$619$	7.64583	−	1.34817i	0.307312	−	0.0541874i	−0.0178655	−	0.999840i	$-0.505687\pi$
$619$	7.64583	−	1.34817i	0.307312	−	0.0541874i	0.325178	+	0.945653i	$0.394576\pi$
$620$	−42.1698	−	15.1594i	−1.69358	−	0.608815i
$621$	1.96427	−	13.7998i	0.0788233	−	0.553767i
$622$	−1.31612	+	0.925457i	−0.0527718	+	0.0371074i
$623$	−8.99010	−	50.9854i	−0.360181	−	2.04269i
$624$	−13.6379	+	39.8051i	−0.545955	+	1.59348i
$625$	21.6584	−	7.88302i	0.866337	−	0.315321i
$626$	23.9537	+	2.04781i	0.957383	+	0.0818468i
$627$	2.27981	−	4.05146i	0.0910467	−	0.161800i
$628$	28.1054	+	23.3938i	1.12153	+	0.933515i
$629$	3.29684	−	1.90343i	0.131453	−	0.0758947i
$630$	−45.6622	−	30.3613i	−1.81922	−	1.20962i
$631$	−9.90352	+	17.1534i	−0.394253	+	0.682866i	−0.993006	−	0.118068i	$-0.962330\pi$
$631$	−9.90352	+	17.1534i	−0.394253	+	0.682866i	0.598752	+	0.800934i	$0.295663\pi$
$632$	−38.2390	−	26.4375i	−1.52106	−	1.05163i
$633$	−22.2698	−	25.9523i	−0.885144	−	1.03151i
$634$	−25.9771	+	12.1761i	−1.03168	+	0.483576i
$635$	−14.4725	−	2.55190i	−0.574325	−	0.101269i
$636$	−1.21878	+	7.57545i	−0.0483276	+	0.300386i
$637$	−35.5957	−	42.4213i	−1.41035	−	1.68079i
$638$	−0.777805	−	8.69173i	−0.0307936	−	0.344109i
$639$	−0.244209	+	0.214286i	−0.00966077	+	0.00847703i
$640$	−3.67790	−	36.2360i	−0.145382	−	1.43235i
$641$	38.5686	+	14.0378i	1.52337	+	0.554460i	0.961986	−	0.273097i	$-0.0880481\pi$
$641$	38.5686	+	14.0378i	1.52337	+	0.554460i	0.561381	+	0.827558i	$0.310270\pi$
$642$	−7.55719	−	10.4989i	−0.298258	−	0.414358i
$643$	−19.9574	+	23.7843i	−0.787044	+	0.937962i	−0.999229	−	0.0392673i	$-0.987498\pi$
$643$	−19.9574	+	23.7843i	−0.787044	+	0.937962i	0.212185	+	0.977230i	$0.431942\pi$
$644$	0.0854551	+	21.5393i	0.00336740	+	0.848768i
$645$	−2.70599	+	16.4041i	−0.106548	+	0.645912i
$646$	0.603435	−	0.605834i	0.0237418	−	0.0238362i
$647$	−44.6478			−1.75528			−0.877642	−	0.479316i	$-0.840885\pi$
$647$	−44.6478			−1.75528			−0.877642	+	0.479316i	$0.840885\pi$
$648$	−25.2159	+	3.48683i	−0.990574	+	0.136976i
$649$	25.3542			0.995240
$650$	−32.5112	+	32.6404i	−1.27519	+	1.28026i
$651$	7.87707	−	47.7521i	0.308727	−	1.87155i
$652$	−13.6546	+	0.0541734i	−0.534757	+	0.00212160i
$653$	19.0947	−	22.7562i	0.747235	−	0.890520i	−0.249735	−	0.968314i	$-0.580343\pi$
$653$	19.0947	−	22.7562i	0.747235	−	0.890520i	0.996969	+	0.0777946i	$0.0247878\pi$
$654$	−17.5865	−	24.4322i	−0.687685	−	0.955374i
$655$	32.9721	+	12.0009i	1.28833	+	0.468913i
$656$	−3.81763	+	22.7028i	−0.149053	+	0.886395i
$657$	7.54282	+	37.8652i	0.294274	+	1.47726i
$658$	2.96066	+	33.0845i	0.115419	+	1.28977i
$659$	−6.09764	−	7.26689i	−0.237530	−	0.283078i	0.634090	−	0.773259i	$-0.281375\pi$
$659$	−6.09764	−	7.26689i	−0.237530	−	0.283078i	−0.871620	+	0.490182i	$0.836930\pi$
$660$	32.5627	+	5.23885i	1.26750	+	0.203922i
$661$	−9.86777	−	1.73995i	−0.383812	−	0.0676764i	−0.0215866	−	0.999767i	$-0.506872\pi$
$661$	−9.86777	−	1.73995i	−0.383812	−	0.0676764i	−0.362225	+	0.932091i	$0.617983\pi$
$662$	−4.83156	+	2.26467i	−0.187784	+	0.0880190i
$663$	−4.56382	−	5.31850i	−0.177244	−	0.206554i
$664$	−11.3018	+	16.3468i	−0.438594	+	0.634379i
$665$	5.86484	−	10.1582i	0.227429	−	0.393918i
$666$	1.53080	−	24.1941i	0.0593174	−	0.937501i
$667$	4.84711	−	2.79848i	0.187681	−	0.108357i
$668$	19.0173	−	22.8474i	0.735800	−	0.883991i
$669$	15.8186	−	28.1112i	0.611580	−	1.08684i
$670$	−24.9885	−	2.13627i	−0.965392	−	0.0825315i
$671$	11.9680	−	4.35599i	0.462019	−	0.168161i
$672$	37.7742	−	10.9753i	1.45717	−	0.423383i
$673$	−1.67987	−	9.52699i	−0.0647541	−	0.367239i	−0.999915	−	0.0130162i	$-0.995857\pi$
$673$	−1.67987	−	9.52699i	−0.0647541	−	0.367239i	0.935161	−	0.354222i	$-0.115254\pi$
$674$	−5.11917	+	3.59964i	−0.197183	+	0.138653i
$675$	−26.4920	−	8.65946i	−1.01968	−	0.333303i
$676$	−16.1595	+	44.9519i	−0.621518	+	1.72892i
$677$	5.70943	−	1.00673i	0.219431	−	0.0386916i	−0.0628516	−	0.998023i	$-0.520019\pi$
$677$	5.70943	−	1.00673i	0.219431	−	0.0386916i	0.282283	+	0.959331i	$0.408908\pi$
$678$	41.4683	+	3.08408i	1.59258	+	0.118443i
$679$	−27.3956	+	9.97117i	−1.05135	+	0.382658i
$680$	5.51320	+	2.53101i	0.211421	+	0.0970599i
$681$	21.4915	−	12.7267i	0.823554	−	0.487689i
$682$	7.58987	+	28.1027i	0.290631	+	1.07611i
$683$	−4.25094	+	2.45428i	−0.162658	+	0.0939105i	−0.579119	−	0.815243i	$-0.696603\pi$
$683$	−4.25094	+	2.45428i	−0.162658	+	0.0939105i	0.416461	+	0.909153i	$0.363270\pi$
$684$	−1.08498	−	5.33607i	−0.0414853	−	0.204030i
$685$	36.6316	+	21.1493i	1.39962	+	0.808072i
$686$	−3.08969	+	11.6231i	−0.117965	+	0.443771i
$687$	−13.5239	+	38.4740i	−0.515971	+	1.46787i
$688$	−7.73862	−	9.07530i	−0.295032	−	0.345993i
$689$	−2.33592	+	13.2476i	−0.0889913	+	0.504695i
$690$	5.74073	+	20.3597i	0.218546	+	0.775079i
$691$	−28.6850	−	34.1855i	−1.09123	−	1.30048i	−0.950602	−	0.310414i	$-0.899532\pi$
$691$	−28.6850	−	34.1855i	−1.09123	−	1.30048i	−0.140628	−	0.990063i	$-0.544912\pi$
$692$	−3.60589	+	3.05016i	−0.137076	+	0.115950i
$693$	0.786971	+	35.6117i	0.0298946	+	1.35278i
$694$	2.93486	−	6.32657i	0.111406	−	0.240153i
$695$	−13.7296	−	4.99717i	−0.520794	−	0.189554i
$696$	−7.34944	−	7.10373i	−0.278580	−	0.269266i
$697$	−2.93734	−	2.46472i	−0.111260	−	0.0933581i
$698$	−6.06520	−	4.22900i	−0.229571	−	0.160070i
$699$	−26.2189	−	21.5112i	−0.991689	−	0.813627i
$700$	42.4440	+	7.31052i	1.60423	+	0.276312i
$701$			25.9103i			0.978619i	0.872110	+	0.489310i	$0.162751\pi$
$701$			25.9103i			0.978619i	−0.872110	+	0.489310i	$0.837249\pi$
$702$	−44.2951	+	5.44863i	−1.67181	+	0.205645i
$703$	5.18569			0.195582
$704$	−17.9421	+	15.4228i	−0.676217	+	0.581267i
$705$	11.4952	+	30.5290i	0.432933	+	1.14979i
$706$	18.1074	−	25.9696i	0.681482	−	0.977378i
$707$	−2.23762	+	2.66669i	−0.0841545	+	0.100291i
$708$	22.4606	−	19.4287i	0.844120	−	0.730176i
$709$	4.93718	−	13.5648i	0.185420	−	0.509436i	−0.811802	−	0.583933i	$-0.801513\pi$
$709$	4.93718	−	13.5648i	0.185420	−	0.509436i	0.997221	+	0.0744971i	$0.0237351\pi$
$710$	0.207488	−	0.447274i	0.00778689	−	0.0167859i
$711$	7.48737	−	48.7365i	0.280798	−	1.82776i
$712$	35.2865	+	9.23028i	1.32242	+	0.345919i
$713$	−14.3022	+	12.0010i	−0.535622	+	0.449440i
$714$	−1.61312	+	6.35012i	−0.0603696	+	0.237647i
$715$	56.9442	+	10.0408i	2.12959	+	0.375505i
$716$	22.2457	−	38.8861i	0.831360	−	1.45324i
$717$	4.17784	+	22.2533i	0.156024	+	0.831063i
$718$	−10.0448	+	37.7875i	−0.374870	+	1.41022i
$719$	−25.1097	+	43.4913i	−0.936433	+	1.62195i	−0.164376	+	0.986398i	$0.552561\pi$
$719$	−25.1097	+	43.4913i	−0.936433	+	1.62195i	−0.772058	+	0.635553i	$0.780772\pi$
$720$	32.8608	−	20.3116i	1.22465	−	0.756967i
$721$	18.2700	+	31.6447i	0.680412	+	1.17851i
$722$	−24.8161	+	6.70225i	−0.923561	+	0.249432i
$723$	10.0750	−	0.111309i	0.374694	−	0.00413961i
$724$	5.23577	+	8.98610i	0.194586	+	0.333966i
$725$	−3.82765	−	10.5164i	−0.142156	−	0.390569i
$726$	2.39777	+	4.97183i	0.0889894	+	0.184522i
$727$	−1.87025	−	10.6067i	−0.0693637	−	0.393381i	−0.999648	−	0.0265409i	$-0.991551\pi$
$727$	−1.87025	−	10.6067i	−0.0693637	−	0.393381i	0.930284	−	0.366840i	$-0.119560\pi$
$728$	66.5068	−	18.2453i	2.46491	−	0.676217i
$729$	−15.0191	−	22.4371i	−0.556265	−	0.831005i
$730$	−33.7026	−	47.9297i	−1.24739	−	1.77396i
$731$	1.95632	−	0.344952i	0.0723571	−	0.0127585i
$732$	7.26414	−	13.0298i	0.268490	−	0.481596i
$733$	−4.17468	−	11.4699i	−0.154195	−	0.423649i	0.838409	−	0.545042i	$-0.183486\pi$
$733$	−4.17468	−	11.4699i	−0.154195	−	0.423649i	−0.992605	+	0.121393i	$0.961264\pi$
$734$	−14.7644	−	1.26221i	−0.544963	−	0.0465890i
$735$	0.561680	+	50.8400i	0.0207179	+	1.87526i
$736$	−13.8159	−	6.27641i	−0.509262	−	0.231352i
$737$	8.14582	+	14.1090i	0.300055	+	0.519711i
$738$	−23.4270	+	6.88588i	−0.862360	+	0.253473i
$739$	−4.76903	−	2.75340i	−0.175432	−	0.101285i	0.409713	−	0.912215i	$-0.365629\pi$
$739$	−4.76903	−	2.75340i	−0.175432	−	0.101285i	−0.585145	+	0.810929i	$0.698962\pi$
$740$	12.7200	+	34.5211i	0.467596	+	1.26902i
$741$	−1.76150	−	9.38264i	−0.0647105	−	0.344680i
$742$	11.3871	−	5.33743i	0.418034	−	0.195943i
$743$	1.48636	−	8.42955i	0.0545292	−	0.309250i	−0.945329	−	0.326120i	$-0.894259\pi$
$743$	1.48636	−	8.42955i	0.0545292	−	0.309250i	0.999858	+	0.0168693i	$0.00536992\pi$
$744$	28.2585	+	19.0793i	1.03601	+	0.699481i
$745$	17.1892	−	14.4235i	0.629765	−	0.528436i
$746$	34.6063	−	3.09684i	1.26703	−	0.113384i
$747$	−20.8344	−	3.20078i	−0.762290	−	0.117110i
$748$	−0.699689	−	3.87810i	−0.0255832	−	0.141797i
$749$	−7.25157	+	19.9235i	−0.264967	+	0.727990i
$750$	2.85470	−	0.287284i	0.104239	−	0.0104901i
$751$	−22.4279	−	18.8192i	−0.818405	−	0.686723i	0.134193	−	0.990955i	$-0.457156\pi$
$751$	−22.4279	−	18.8192i	−0.818405	−	0.686723i	−0.952598	+	0.304232i	$0.901600\pi$
$752$	−22.0530	−	7.82903i	−0.804190	−	0.285495i
$753$	1.26835	+	3.36851i	0.0462213	+	0.122755i
$754$	−12.6965	−	12.6462i	−0.462380	−	0.460549i
$755$			11.0168i			0.400943i
$756$	27.9861	+	30.9443i	1.01784	+	1.12543i
$757$		−	51.3515i		−	1.86640i	−0.359356	−	0.933201i	$-0.617004\pi$
$757$		−	51.3515i		−	1.86640i	0.359356	−	0.933201i	$-0.382996\pi$
$758$	15.3482	−	15.4092i	0.557470	−	0.559686i
$759$	8.71587	−	10.6233i	0.316366	−	0.385602i
$760$	4.78004	+	6.74086i	0.173390	+	0.244517i
$761$	−25.3587	−	21.2785i	−0.919254	−	0.771345i	0.0546033	−	0.998508i	$-0.482611\pi$
$761$	−25.3587	−	21.2785i	−0.919254	−	0.771345i	−0.973857	+	0.227163i	$0.927055\pi$
$762$	10.1948	+	4.59314i	0.369319	+	0.166392i
$763$	−16.8753	+	46.3644i	−0.610925	+	1.67850i
$764$	−5.26932	+	0.950693i	−0.190637	+	0.0343949i
$765$	0.142157	+	6.43283i	0.00513971	+	0.232580i
$766$	−0.801331	−	8.95464i	−0.0289533	−	0.323544i
$767$	39.8846	−	33.4672i	1.44015	−	1.20843i
$768$	−4.07601	+	27.4114i	−0.147080	+	0.989125i
$769$	−1.38866	+	7.87547i	−0.0500763	+	0.283997i	−0.999555	−	0.0298353i	$-0.990502\pi$
$769$	−1.38866	+	7.87547i	−0.0500763	+	0.283997i	0.949479	+	0.313832i	$0.101613\pi$
$770$	−22.9426	−	48.9469i	−0.826795	−	1.76392i
$771$	−7.29110	−	2.56289i	−0.262583	−	0.0923001i
$772$	16.4311	+	44.5929i	0.591369	+	1.60493i
$773$	−33.6805	−	19.4455i	−1.21140	−	0.699405i	−0.248339	−	0.968673i	$-0.579885\pi$
$773$	−33.6805	−	19.4455i	−1.21140	−	0.699405i	−0.963065	+	0.269268i	$0.913218\pi$
$774$	5.06863	−	11.5904i	0.182188	−	0.416608i
$775$	18.6659	+	32.3303i	0.670498	+	1.16134i
$776$	1.66830	−	20.4712i	0.0598886	−	0.734873i
$777$	−34.1888	+	20.2458i	−1.22652	+	0.726314i
$778$	0.645526	−	7.55089i	0.0231432	−	0.270712i
$779$	−1.78646	−	4.90825i	−0.0640065	−	0.175856i
$780$	58.1394	−	34.7410i	2.08173	−	1.24393i
$781$	−0.315422	+	0.0556173i	−0.0112867	+	0.00199014i
$782$	2.06751	−	1.45381i	0.0739342	−	0.0519881i
$783$	3.36837	−	10.3049i	0.120376	−	0.368267i
$784$	−28.1250	−	23.2219i	−1.00447	−	0.829354i
$785$	−10.2211	−	57.9665i	−0.364805	−	2.06891i
$786$	−22.0673	−	15.0270i	−0.787114	−	0.535995i
$787$	−13.9143	−	38.2291i	−0.495990	−	1.36272i	−0.895120	−	0.445826i	$-0.852910\pi$
$787$	−13.9143	−	38.2291i	−0.495990	−	1.36272i	0.399130	−	0.916894i	$-0.369312\pi$
$788$	−18.3117	−	31.4282i	−0.652327	−	1.11958i
$789$	14.3662	−	25.5302i	0.511449	−	0.908898i
$790$	19.5107	+	72.2413i	0.694159	+	2.57023i
$791$	−34.0775	−	59.0239i	−1.21166	−	2.09865i
$792$	−23.0321	−	9.96358i	−0.818411	−	0.354040i
$793$	13.0770	−	22.6500i	0.464377	−	0.804324i
$794$	27.1156	+	7.20797i	0.962295	+	0.255801i
$795$	9.37283	−	8.04285i	0.332420	−	0.285251i
$796$	11.9284	+	6.82389i	0.422790	+	0.241866i
$797$	30.0489	+	5.29843i	1.06439	+	0.187680i	0.678302	−	0.734783i	$-0.262716\pi$
$797$	30.0489	+	5.29843i	1.06439	+	0.187680i	0.386085	+	0.922463i	$0.373827\pi$
$798$	−6.22805	+	6.39253i	−0.220471	+	0.226293i
$799$	2.98582	−	2.50540i	0.105631	−	0.0886347i
$800$	−17.1564	+	25.0265i	−0.606569	+	0.884820i
$801$	7.55788	+	37.9408i	0.267045	+	1.34057i
$802$	−21.5704	−	10.0064i	−0.761678	−	0.353339i
$803$	−13.0179	+	35.7663i	−0.459390	+	1.26216i
$804$	18.0277	+	6.25666i	0.635789	+	0.220655i
$805$	22.2861	−	26.5595i	0.785481	−	0.936099i
$806$	49.0347	+	34.1897i	1.72717	+	1.20428i
$807$	32.4511	+	5.35306i	1.14233	+	0.188437i
$808$	−1.04967	−	2.21650i	−0.0369273	−	0.0779760i
$809$	−36.6344			−1.28800			−0.643999	−	0.765027i	$-0.722726\pi$
$809$	−36.6344			−1.28800			−0.643999	+	0.765027i	$0.722726\pi$
$810$	34.6137	+	21.9279i	1.21620	+	0.770469i
$811$			43.6168i			1.53159i	0.643084	+	0.765796i	$0.277655\pi$
$811$			43.6168i			1.53159i	−0.643084	+	0.765796i	$0.722345\pi$
$812$	−2.84366	+	16.5099i	−0.0997928	+	0.579385i
$813$	−1.43871	+	8.72172i	−0.0504579	+	0.305884i
$814$	13.6688	−	19.6038i	0.479093	−	0.687112i
$815$	16.8371	+	14.1280i	0.589779	+	0.494884i
$816$	−3.59159	−	2.89933i	−0.125731	−	0.101497i
$817$	2.54281	+	0.925509i	0.0889618	+	0.0323794i
$818$	26.2648	+	12.1841i	0.918329	+	0.426008i
$819$	48.2448	+	54.9818i	1.68581	+	1.92122i
$820$	28.2922	−	23.9319i	0.988007	−	0.835738i
$821$	−15.4483	−	18.4106i	−0.539150	−	0.642534i	0.425847	−	0.904795i	$-0.359976\pi$
$821$	−15.4483	−	18.4106i	−0.539150	−	0.642534i	−0.964997	+	0.262261i	$0.915532\pi$
$822$	−23.0522	−	22.4591i	−0.804037	−	0.783350i
$823$	−0.238830	+	1.35447i	−0.00832510	+	0.0472140i	−0.988687	−	0.149991i	$-0.952075\pi$
$823$	−0.238830	+	1.35447i	−0.00832510	+	0.0472140i	0.980362	+	0.197205i	$0.0631865\pi$
$824$	−25.6310	+	2.39621i	−0.892900	+	0.0834758i
$825$	−17.8927	−	20.8515i	−0.622945	−	0.725956i
$826$	−47.0413	−	12.5047i	−1.63678	−	0.435095i
$827$	−0.632823	−	0.365361i	−0.0220054	−	0.0127048i	0.488957	−	0.872308i	$-0.337378\pi$
$827$	−0.632823	−	0.365361i	−0.0220054	−	0.0127048i	−0.510962	+	0.859603i	$0.670711\pi$
$828$	−0.419435	−	16.0898i	−0.0145764	−	0.559159i
$829$	−27.6353	+	15.9553i	−0.959814	+	0.554149i	−0.896116	−	0.443820i	$-0.853623\pi$
$829$	−27.6353	+	15.9553i	−0.959814	+	0.554149i	−0.0636982	+	0.997969i	$0.520289\pi$
$830$	30.8825	−	8.34064i	1.07195	−	0.289508i
$831$	−10.0885	−	5.67695i	−0.349968	−	0.196931i
$832$	−7.86677	+	47.9447i	−0.272731	+	1.66218i
$833$	5.70851	−	2.07773i	0.197788	−	0.0719891i
$834$	9.18884	+	6.25725i	0.318183	+	0.216671i
$835$	−47.1220	+	8.30888i	−1.63073	+	0.287541i
$836$	1.81595	−	5.05154i	0.0628059	−	0.174711i
$837$	−5.09631	+	35.8038i	−0.176154	+	1.23756i
$838$	−4.43895	−	6.31279i	−0.153341	−	0.218072i
$839$	−0.846322	−	4.79973i	−0.0292183	−	0.165705i	0.966707	−	0.255885i	$-0.0823669\pi$
$839$	−0.846322	−	4.79973i	−0.0292183	−	0.165705i	−0.995925	+	0.0901800i	$0.971256\pi$
$840$	−57.8318	−	25.7799i	−1.99539	−	0.889491i
$841$	−23.1604	+	8.42970i	−0.798635	+	0.290679i
$842$	−3.28025	+	38.3700i	−0.113045	+	1.32232i
$843$	4.30201	+	7.26476i	0.148169	+	0.250212i
$844$	−30.3499	−	25.2621i	−1.04469	−	0.869556i
$845$	66.5886	−	38.4450i	2.29072	−	1.32255i
$846$	−2.75799	−	24.6673i	−0.0948217	−	0.848079i
$847$	4.52353	−	7.83498i	0.155430	−	0.269213i
$848$	0.0703001	+	8.85959i	0.00241412	+	0.304240i
$849$	−4.36751	+	12.4250i	−0.149893	+	0.426426i
$850$	−2.14491	−	4.57605i	−0.0735697	−	0.156957i
$851$	15.0952	+	2.66169i	0.517456	+	0.0912415i
$852$	−0.236804	+	0.290975i	−0.00811276	+	0.00996863i
$853$	15.8114	+	18.8433i	0.541372	+	0.645182i	0.965495	−	0.260422i	$-0.0838618\pi$
$853$	15.8114	+	18.8433i	0.541372	+	0.645182i	−0.424122	+	0.905605i	$0.639417\pi$
$854$	−24.3534	+	2.17933i	−0.833355	+	0.0745752i
$855$	−4.21369	+	7.68562i	−0.144105	+	0.262843i
$856$	−10.6248	−	10.4991i	−0.363148	−	0.358852i
$857$	−2.03225	−	0.739678i	−0.0694202	−	0.0252669i	0.307077	−	0.951685i	$-0.400649\pi$
$857$	−2.03225	−	0.739678i	−0.0694202	−	0.0252669i	−0.376497	+	0.926418i	$0.622871\pi$
$858$	−40.1129	−	18.0724i	−1.36943	−	0.616980i
$859$	−2.15971	+	2.57385i	−0.0736885	+	0.0878186i	−0.801629	−	0.597822i	$-0.796033\pi$
$859$	−2.15971	+	2.57385i	−0.0736885	+	0.0878186i	0.727941	+	0.685640i	$0.240478\pi$
$860$	0.0761649	+	19.1977i	0.00259720	+	0.654636i
$861$	30.9406	+	25.3851i	1.05445	+	0.865121i
$862$	14.9834	+	14.9241i	0.510336	+	0.508315i
$863$	10.6438			0.362319			0.181159	−	0.983454i	$-0.442015\pi$
$863$	10.6438			0.362319			0.181159	+	0.983454i	$0.442015\pi$
$864$	−28.0385	+	8.82287i	−0.953889	+	0.300160i
$865$	7.60223			0.258484
$866$	−5.14539	−	5.12501i	−0.174847	−	0.174155i
$867$	−26.8367	+	10.1049i	−0.911422	+	0.343180i
$868$	−0.221714	−	55.8840i	−0.00752547	−	1.89683i
$869$	31.2453	−	37.2366i	1.05992	−	1.26317i
$870$	1.64742	+	16.3702i	0.0558527	+	0.555000i
$871$	31.4378	+	11.4424i	1.06523	+	0.387712i
$872$	−24.7252	−	24.4326i	−0.837300	−	0.827393i
$873$	20.3016	−	7.90136i	0.687104	−	0.267420i
$874$	3.42923	−	0.306875i	0.115995	−	0.0103802i
$875$	−3.02273	−	3.60235i	−0.102187	−	0.121782i
$876$	15.8752	+	41.6598i	0.536375	+	1.40755i
$877$	23.2865	+	4.10603i	0.786328	+	0.138651i	0.552374	−	0.833597i	$-0.313722\pi$
$877$	23.2865	+	4.10603i	0.786328	+	0.138651i	0.233955	+	0.972248i	$0.424833\pi$
$878$	2.75494	+	5.87751i	0.0929746	+	0.198356i
$879$	5.29635	−	0.994340i	0.178641	−	0.0335382i
$880$	38.0825	−	0.302181i	1.28376	−	0.0101865i
$881$	−25.7770	+	44.6471i	−0.868450	+	1.50420i	−0.00487041	+	0.999988i	$0.501550\pi$
$881$	−25.7770	+	44.6471i	−0.868450	+	1.50420i	−0.863580	+	0.504212i	$0.831783\pi$
$882$	9.10994	−	37.5974i	0.306748	−	1.26597i
$883$	−15.6743	+	9.04958i	−0.527483	+	0.304543i	−0.739991	−	0.672617i	$-0.765170\pi$
$883$	−15.6743	+	9.04958i	−0.527483	+	0.304543i	0.212508	+	0.977159i	$0.431837\pi$
$884$	−6.21971	−	5.17705i	−0.209192	−	0.174123i
$885$	−47.7998	+	0.528093i	−1.60677	+	0.0177516i
$886$	4.74369	−	55.4881i	0.159367	−	1.86416i
$887$	54.2033	−	19.7284i	1.81997	−	0.662414i	0.824662	−	0.565626i	$-0.191365\pi$
$887$	54.2033	−	19.7284i	1.81997	−	0.662414i	0.995305	−	0.0967883i	$-0.0308570\pi$
$888$	−2.91338	−	27.8407i	−0.0977667	−	0.934274i
$889$	−3.18245	−	18.0486i	−0.106736	−	0.605330i
$890$	−33.7699	−	48.0254i	−1.13197	−	1.60982i
$891$	−1.17583	−	26.5911i	−0.0393919	−	0.890836i
$892$	12.6000	−	35.0504i	0.421881	−	1.17357i
$893$	5.22879	−	0.921977i	0.174975	−	0.0308528i
$894$	−15.3784	+	7.41652i	−0.514329	+	0.248046i
$895$	−67.7625	+	24.6636i	−2.26505	+	0.824412i
$896$	40.8956	−	19.7658i	1.36622	−	0.660329i
$897$	−0.311734	−	28.2163i	−0.0104085	−	0.942116i
$898$	50.9288	−	13.7547i	1.69952	−	0.458999i
$899$	−12.5759	+	7.26068i	−0.419429	+	0.242157i
$900$	−31.8290	−	4.76070i	−1.06097	−	0.158690i
$901$	−1.27798	−	0.737843i	−0.0425757	−	0.0245811i
$902$	−23.2638	−	6.18409i	−0.774601	−	0.205908i
$903$	−20.3779	+	3.82576i	−0.678134	+	0.127313i
$904$	47.8073	−	4.46943i	1.59005	−	0.148651i
$905$	2.90697	−	16.4863i	0.0966310	−	0.548022i
$906$	2.06385	−	8.12441i	0.0685667	−	0.269916i
$907$	29.7089	+	35.4057i	0.986468	+	1.17563i	0.984456	+	0.175629i	$0.0561959\pi$
$907$	29.7089	+	35.4057i	0.986468	+	1.17563i	0.00201160	+	0.999998i	$0.499360\pi$
$908$	22.0198	−	18.6261i	0.730751	−	0.618130i
$909$	1.62762	−	2.02913i	0.0539847	−	0.0673019i
$910$	−100.700	−	46.7143i	−3.33818	−	1.54856i
$911$	−6.32605	−	2.30249i	−0.209591	−	0.0762850i	0.235091	−	0.971973i	$-0.424461\pi$
$911$	−6.32605	−	2.30249i	−0.209591	−	0.0762850i	−0.444682	+	0.895688i	$0.646683\pi$
$912$	−2.26226	−	5.86656i	−0.0749109	−	0.194261i
$913$	−15.9183	−	13.3571i	−0.526820	−	0.442054i
$914$	−11.0110	+	15.7920i	−0.364213	+	0.522352i
$915$	−22.4723	+	8.46155i	−0.742912	+	0.279730i
$916$	−7.99315	+	46.4073i	−0.264101	+	1.53334i
$917$			43.7582i			1.44502i
$918$	1.10027	−	4.77056i	0.0363142	−	0.157452i
$919$	−43.0453			−1.41993			−0.709966	−	0.704236i	$-0.751290\pi$
$919$	−43.0453			−1.41993			−0.709966	+	0.704236i	$0.751290\pi$
$920$	10.4544	+	22.0756i	0.344672	+	0.727812i
$921$	−21.0080	+	25.6056i	−0.692238	+	0.843734i
$922$	33.6298	+	23.4486i	1.10754	+	0.772238i
$923$	−0.422774	+	0.503843i	−0.0139158	+	0.0165842i
$924$	7.74966	+	40.3942i	0.254945	+	1.32887i
$925$	10.4826	−	28.8006i	0.344665	−	0.946958i
$926$	7.04053	+	3.26606i	0.231366	+	0.107330i
$927$	−14.1713	−	23.3389i	−0.465446	−	0.766550i
$928$	−9.73484	−	6.67351i	−0.319562	−	0.219069i
$929$	3.96708	−	3.32878i	0.130156	−	0.109214i	−0.575386	−	0.817882i	$-0.695148\pi$
$929$	3.96708	−	3.32878i	0.130156	−	0.109214i	0.705542	+	0.708668i	$0.250704\pi$
$930$	−14.8944	−	52.8234i	−0.488406	−	1.73215i
$931$	8.14946	+	1.43697i	0.267088	+	0.0470948i
$932$	−33.9914	−	19.4456i	−1.11343	−	0.636961i
$933$	−1.85902	−	0.653463i	−0.0608617	−	0.0213934i
$934$	37.0637	+	9.85244i	1.21276	+	0.322382i
$935$	−3.17158	+	5.49333i	−0.103722	+	0.179651i
$936$	−49.3835	+	14.7284i	−1.61415	+	0.481412i
$937$	−16.2869	−	28.2097i	−0.532069	−	0.921571i	−0.999299	−	0.0374348i	$-0.988081\pi$
$937$	−16.2869	−	28.2097i	−0.532069	−	0.921571i	0.467230	−	0.884136i	$-0.345252\pi$
$938$	−8.15491	−	30.1948i	−0.266267	−	0.985896i
$939$	15.0029	+	25.3352i	0.489601	+	0.826784i
$940$	18.9633	+	32.5465i	0.618515	+	1.06155i
$941$	2.75720	+	7.57533i	0.0898820	+	0.246949i	0.976486	−	0.215580i	$-0.0691643\pi$
$941$	2.75720	+	7.57533i	0.0898820	+	0.246949i	−0.886604	+	0.462529i	$0.846942\pi$
$942$	−3.32164	+	44.6625i	−0.108225	+	1.45518i
$943$	−2.68097	−	15.2045i	−0.0873043	−	0.495127i
$944$	21.8333	−	26.4432i	0.710613	−	0.860653i
$945$	−2.22540	−	67.1216i	−0.0723924	−	2.18347i
$946$	10.2013	−	7.17322i	0.331673	−	0.233222i
$947$	3.75554	−	0.662203i	0.122039	−	0.0215187i	−0.112295	−	0.993675i	$-0.535820\pi$
$947$	3.75554	−	0.662203i	0.122039	−	0.0215187i	0.234334	+	0.972156i	$0.424709\pi$
$948$	−0.854862	−	56.9298i	−0.0277646	−	1.84900i
$949$	26.7326	+	73.4471i	0.867776	+	2.38420i
$950$	0.586398	−	6.85925i	0.0190253	−	0.222543i
$951$	−30.6217	−	17.2312i	−0.992977	−	0.558761i
$952$	−0.614504	+	7.54038i	−0.0199162	+	0.244385i
$953$	22.6701	+	39.2657i	0.734356	+	1.27194i	0.955005	+	0.296588i	$0.0958489\pi$
$953$	22.6701	+	39.2657i	0.734356	+	1.27194i	−0.220650	+	0.975353i	$0.570818\pi$
$954$	−8.41877	+	4.17538i	−0.272568	+	0.135183i
$955$	7.46399	+	4.30934i	0.241529	+	0.139447i
$956$	9.03944	+	24.5324i	0.292356	+	0.793434i
$957$	8.11085	−	6.95994i	0.262187	−	0.224983i
$958$	22.1738	+	47.3066i	0.716402	+	1.52841i
$959$	−9.15997	+	51.9488i	−0.295791	+	1.67751i
$960$	33.5046	−	29.4500i	1.08136	−	0.950493i
$961$	13.3599	−	11.2103i	0.430964	−	0.361622i
$962$	−4.37428	−	48.8813i	−0.141033	−	1.57600i
$963$	5.08845	−	15.0038i	0.163973	−	0.483491i
$964$	11.4495	−	2.06572i	0.368763	−	0.0665324i
$965$	26.1633	−	71.8831i	0.842227	−	2.31400i
$966$	−21.4105	+	15.4115i	−0.688873	+	0.495856i
$967$	20.5095	+	17.2095i	0.659540	+	0.553420i	0.909949	−	0.414721i	$-0.136121\pi$
$967$	20.5095	+	17.2095i	0.659540	+	0.553420i	−0.250409	+	0.968140i	$0.580565\pi$
$968$	3.68683	+	5.19921i	0.118499	+	0.167109i
$969$	1.03329	+	0.170450i	0.0331942	+	0.00547564i
$970$	−23.3310	+	23.4237i	−0.749113	+	0.752091i
$971$		−	43.2082i		−	1.38662i	−0.720640	−	0.693309i	$-0.756152\pi$
$971$		−	43.2082i		−	1.38662i	0.720640	−	0.693309i	$-0.243848\pi$
$972$	−21.4182	−	22.6553i	−0.686989	−	0.726668i
$973$		−	18.2210i		−	0.584137i
$974$	41.6632	+	41.4982i	1.33497	+	1.32969i
$975$	−55.6707	−	9.18330i	−1.78289	−	0.294101i
$976$	5.76292	−	16.2331i	0.184467	−	0.519609i
$977$	16.3016	+	13.6787i	0.521534	+	0.437619i	0.865166	−	0.501485i	$-0.167213\pi$
$977$	16.3016	+	13.6787i	0.521534	+	0.437619i	−0.343632	+	0.939104i	$0.611657\pi$
$978$	−9.76995	−	13.5730i	−0.312409	−	0.434017i
$979$	−13.0438	+	35.8377i	−0.416883	+	1.14538i
$980$	10.4239	+	57.7757i	0.332980	+	1.84558i
$981$	11.8414	−	34.9157i	0.378068	−	1.11477i
$982$	37.2077	−	3.32964i	1.18735	−	0.106253i
$983$	−40.4159	+	33.9129i	−1.28907	+	1.08165i	−0.297140	+	0.954834i	$0.596033\pi$
$983$	−40.4159	+	33.9129i	−1.28907	+	1.08165i	−0.991926	+	0.126820i	$0.959523\pi$
$984$	−25.3476	+	12.3486i	−0.808051	+	0.393658i
$985$	−10.1669	+	57.6593i	−0.323944	+	1.83718i
$986$	1.78000	−	0.834330i	0.0566867	−	0.0265705i
$987$	−30.8734	+	26.4926i	−0.982712	+	0.843267i
$988$	−3.81130	−	10.3436i	−0.121254	−	0.329073i
$989$	6.92691	+	3.99925i	0.220263	+	0.127169i
$990$	17.9476	+	36.1876i	0.570413	+	1.15012i
$991$	3.39955	+	5.88820i	0.107990	+	0.187045i	0.914956	−	0.403554i	$-0.132225\pi$
$991$	3.39955	+	5.88820i	0.107990	+	0.187045i	−0.806966	+	0.590598i	$0.798892\pi$
$992$	35.8456	+	16.2842i	1.13810	+	0.517024i
$993$	−5.69542	−	3.20489i	−0.180739	−	0.101704i
$994$	0.612652	+	0.0523757i	0.0194321	+	0.00166126i
$995$	−7.56558	−	20.7863i	−0.239845	−	0.658969i
$996$	−24.3370	+	0.365446i	−0.771147	+	0.0115796i
$997$	33.4728	−	5.90216i	1.06009	−	0.186923i	0.383696	−	0.923459i	$-0.374651\pi$
$997$	33.4728	−	5.90216i	1.06009	−	0.186923i	0.676398	+	0.736536i	$0.263540\pi$
$998$	−0.238804	−	0.339611i	−0.00755919	−	0.0107502i
$999$	25.2069	−	15.6893i	0.797512	−	0.496387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.26	yes	204
3.2	odd	2		648.2.t.a.253.9		204
4.3	odd	2		864.2.bf.a.337.19		204
8.3	odd	2		864.2.bf.a.337.16		204
8.5	even	2	inner	216.2.t.a.13.12	✓	204
24.5	odd	2		648.2.t.a.253.23		204
27.2	odd	18		648.2.t.a.397.23		204
27.25	even	9	inner	216.2.t.a.133.12	yes	204
108.79	odd	18		864.2.bf.a.241.16		204
216.29	odd	18		648.2.t.a.397.9		204
216.133	even	18	inner	216.2.t.a.133.26	yes	204
216.187	odd	18		864.2.bf.a.241.19		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.12	✓	204	8.5	even	2	inner
216.2.t.a.13.26	yes	204	1.1	even	1	trivial
216.2.t.a.133.12	yes	204	27.25	even	9	inner
216.2.t.a.133.26	yes	204	216.133	even	18	inner
648.2.t.a.253.9		204	3.2	odd	2
648.2.t.a.253.23		204	24.5	odd	2
648.2.t.a.397.9		204	216.29	odd	18
648.2.t.a.397.23		204	27.2	odd	18
864.2.bf.a.241.16		204	108.79	odd	18
864.2.bf.a.241.19		204	216.187	odd	18
864.2.bf.a.337.16		204	8.3	odd	2
864.2.bf.a.337.19		204	4.3	odd	2

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.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00198 + 0.998014i) q^{2} +(-0.281905 + 1.70896i) q^{3} +(0.00793474 + 1.99998i) q^{4} +(2.06932 - 2.46612i) q^{5} +(-1.98803 + 1.43100i) q^{6} +(3.77263 + 1.37313i) q^{7} +(-1.98806 + 2.01187i) q^{8} +(-2.84106 - 0.963527i) q^{9} +O(q^{10})\)	\(q+(1.00198 + 0.998014i) q^{2} +(-0.281905 + 1.70896i) q^{3} +(0.00793474 + 1.99998i) q^{4} +(2.06932 - 2.46612i) q^{5} +(-1.98803 + 1.43100i) q^{6} +(3.77263 + 1.37313i) q^{7} +(-1.98806 + 2.01187i) q^{8} +(-2.84106 - 0.963527i) q^{9} +(4.53465 - 0.405796i) q^{10} +(-1.90102 - 2.26554i) q^{11} +(-3.42012 - 0.550246i) q^{12} +(-5.98096 - 1.05461i) q^{13} +(2.40971 + 5.14099i) q^{14} +(3.63114 + 4.23159i) q^{15} +(-3.99987 + 0.0317387i) q^{16} +(0.333117 - 0.576975i) q^{17} +(-1.88507 - 3.80085i) q^{18} +(0.785955 - 0.453771i) q^{19} +(4.94862 + 4.11904i) q^{20} +(-3.41014 + 6.06017i) q^{21} +(0.356261 - 4.16727i) q^{22} +(2.52077 - 0.917484i) q^{23} +(-2.87775 - 3.96467i) q^{24} +(-0.931421 - 5.28235i) q^{25} +(-4.94030 - 7.02578i) q^{26} +(2.44753 - 4.58362i) q^{27} +(-2.71630 + 7.55610i) q^{28} +(2.05474 - 0.362306i) q^{29} +(-0.584853 + 7.86390i) q^{30} +(-6.54016 + 2.38042i) q^{31} +(-4.03948 - 3.96013i) q^{32} +(4.40762 - 2.61008i) q^{33} +(0.909607 - 0.245663i) q^{34} +(11.1931 - 6.46233i) q^{35} +(1.90450 - 5.68972i) q^{36} +(4.94847 + 2.85700i) q^{37} +(1.24038 + 0.329724i) q^{38} +(3.48834 - 9.92390i) q^{39} +(0.847567 + 9.06600i) q^{40} +(0.999412 - 5.66795i) q^{41} +(-9.46503 + 2.66881i) q^{42} +(1.91659 + 2.28410i) q^{43} +(4.51597 - 3.81998i) q^{44} +(-8.25524 + 5.01255i) q^{45} +(3.44142 + 1.59646i) q^{46} +(5.49754 + 2.00094i) q^{47} +(1.07335 - 6.84455i) q^{48} +(6.98497 + 5.86109i) q^{49} +(4.33860 - 6.22239i) q^{50} +(0.892118 + 0.731934i) q^{51} +(2.06174 - 11.9702i) q^{52} -2.21497i q^{53} +(7.02690 - 2.15003i) q^{54} -9.52091 q^{55} +(-10.2628 + 4.86017i) q^{56} +(0.553910 + 1.47108i) q^{57} +(2.42040 + 1.68763i) q^{58} +(-5.51061 + 6.56729i) q^{59} +(-8.43430 + 7.29580i) q^{60} +(-1.47289 + 4.04672i) q^{61} +(-8.92882 - 4.14203i) q^{62} +(-9.39523 - 7.53617i) q^{63} +(-0.0952148 - 7.99943i) q^{64} +(-14.9773 + 12.5675i) q^{65} +(7.02125 + 1.78361i) q^{66} +(-5.42498 - 0.956570i) q^{67} +(1.15658 + 0.661650i) q^{68} +(0.857322 + 4.56652i) q^{69} +(17.6648 + 4.69572i) q^{70} +(0.0541491 - 0.0937891i) q^{71} +(7.58669 - 3.80028i) q^{72} +(-6.43487 - 11.1455i) q^{73} +(2.10695 + 7.80130i) q^{74} +(9.28988 - 0.102635i) q^{75} +(0.913771 + 1.56830i) q^{76} +(-4.06096 - 11.1574i) q^{77} +(13.3994 - 6.46216i) q^{78} +(2.85410 + 16.1864i) q^{79} +(-8.19875 + 9.92985i) q^{80} +(7.14323 + 5.47488i) q^{81} +(6.65808 - 4.68175i) q^{82} +(6.91953 - 1.22010i) q^{83} +(-12.1473 - 6.77213i) q^{84} +(-0.733565 - 2.01545i) q^{85} +(-0.359180 + 4.20142i) q^{86} +(0.0399230 + 3.61359i) q^{87} +(8.33731 + 0.679450i) q^{88} +(-6.44771 - 11.1678i) q^{89} +(-13.2742 - 3.21636i) q^{90} +(-21.1159 - 12.1913i) q^{91} +(1.85496 + 5.03421i) q^{92} +(-2.22433 - 11.8479i) q^{93} +(3.51147 + 7.49153i) q^{94} +(0.507338 - 2.87726i) q^{95} +(7.90644 - 5.78690i) q^{96} +(-5.56275 + 4.66770i) q^{97} +(1.14936 + 12.8438i) q^{98} +(3.21799 + 8.26822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 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

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