LMFDB - Embedded newform 216.2.t.a.13.2

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			13.2
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39072 + 0.256713i) q^{2} +(-1.23413 + 1.21529i) q^{3} +(1.86820 - 0.714031i) q^{4} +(1.46572 - 1.74677i) q^{5} +(1.40435 - 2.00694i) q^{6} +(-1.21500 - 0.442225i) q^{7} +(-2.41483 + 1.47261i) q^{8} +(0.0461478 - 2.99965i) q^{9} +O(q^{10})$	\(q+(-1.39072 + 0.256713i) q^{2} +(-1.23413 + 1.21529i) q^{3} +(1.86820 - 0.714031i) q^{4} +(1.46572 - 1.74677i) q^{5} +(1.40435 - 2.00694i) q^{6} +(-1.21500 - 0.442225i) q^{7} +(-2.41483 + 1.47261i) q^{8} +(0.0461478 - 2.99965i) q^{9} +(-1.58998 + 2.80554i) q^{10} +(-2.93828 - 3.50170i) q^{11} +(-1.43784 + 3.15160i) q^{12} +(4.95227 + 0.873219i) q^{13} +(1.80325 + 0.303103i) q^{14} +(0.313950 + 3.93701i) q^{15} +(2.98032 - 2.66790i) q^{16} +(0.909480 - 1.57526i) q^{17} +(0.705870 + 4.18351i) q^{18} +(6.49748 - 3.75132i) q^{19} +(1.49100 - 4.30988i) q^{20} +(2.03690 - 0.930816i) q^{21} +(4.98525 + 4.11559i) q^{22} +(0.835352 - 0.304043i) q^{23} +(1.19057 - 4.75211i) q^{24} +(-0.0346491 - 0.196505i) q^{25} +(-7.11138 + 0.0569110i) q^{26} +(3.58848 + 3.75803i) q^{27} +(-2.58563 + 0.0413872i) q^{28} +(1.50546 - 0.265453i) q^{29} +(-1.44730 - 5.39468i) q^{30} +(-1.86625 + 0.679258i) q^{31} +(-3.45990 + 4.47539i) q^{32} +(7.88180 + 0.750698i) q^{33} +(-0.860439 + 2.42423i) q^{34} +(-2.55331 + 1.47416i) q^{35} +(-2.05563 - 5.63688i) q^{36} +(-8.19426 - 4.73096i) q^{37} +(-8.07315 + 6.88502i) q^{38} +(-7.17295 + 4.94077i) q^{39} +(-0.967152 + 6.37659i) q^{40} +(0.859892 - 4.87669i) q^{41} +(-2.59380 + 1.81740i) q^{42} +(-1.62715 - 1.93916i) q^{43} +(-7.98961 - 4.44385i) q^{44} +(-5.17206 - 4.47724i) q^{45} +(-1.08369 + 0.637285i) q^{46} +(7.64813 + 2.78369i) q^{47} +(-0.435825 + 6.91448i) q^{48} +(-4.08164 - 3.42490i) q^{49} +(0.0986326 + 0.264388i) q^{50} +(0.791986 + 3.04936i) q^{51} +(9.87532 - 1.90473i) q^{52} +3.70167i q^{53} +(-5.95530 - 4.30515i) q^{54} -10.4234 q^{55} +(3.58525 - 0.721322i) q^{56} +(-3.45979 + 12.5259i) q^{57} +(-2.02553 + 0.755642i) q^{58} +(3.63062 - 4.32680i) q^{59} +(3.39767 + 7.13094i) q^{60} +(-4.89674 + 13.4537i) q^{61} +(2.42105 - 1.42375i) q^{62} +(-1.38259 + 3.62417i) q^{63} +(3.66285 - 7.11221i) q^{64} +(8.78393 - 7.37060i) q^{65} +(-11.1541 + 0.979351i) q^{66} +(8.09804 + 1.42790i) q^{67} +(0.574298 - 3.59230i) q^{68} +(-0.661432 + 1.39042i) q^{69} +(3.17251 - 2.70561i) q^{70} +(-4.59959 + 7.96673i) q^{71} +(4.30586 + 7.31160i) q^{72} +(-5.72007 - 9.90745i) q^{73} +(12.6104 + 4.47586i) q^{74} +(0.281572 + 0.200404i) q^{75} +(9.46001 - 11.6476i) q^{76} +(2.02148 + 5.55396i) q^{77} +(8.70720 - 8.71261i) q^{78} +(-1.39403 - 7.90593i) q^{79} +(-0.291918 - 9.11632i) q^{80} +(-8.99574 - 0.276854i) q^{81} +(0.0560425 + 7.00285i) q^{82} +(-13.3270 + 2.34991i) q^{83} +(3.14070 - 3.19336i) q^{84} +(-1.41859 - 3.89754i) q^{85} +(2.76072 + 2.27912i) q^{86} +(-1.53533 + 2.15717i) q^{87} +(12.2521 + 4.12911i) q^{88} +(3.65721 + 6.33447i) q^{89} +(8.34224 + 4.89884i) q^{90} +(-5.63086 - 3.25098i) q^{91} +(1.34351 - 1.16448i) q^{92} +(1.47769 - 3.10632i) q^{93} +(-11.3510 - 1.90796i) q^{94} +(2.97075 - 16.8480i) q^{95} +(-1.16893 - 9.72798i) q^{96} +(2.14122 - 1.79669i) q^{97} +(6.55563 + 3.71527i) q^{98} +(-10.6395 + 8.65220i) 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 $

$2$	−1.39072	+	0.256713i	−0.983387	+	0.181524i
$2$	−1.39072	+	0.256713i	−0.983387	+	0.181524i
$3$	−1.23413	+	1.21529i	−0.712525	+	0.701647i
$3$	−1.23413	+	1.21529i	−0.712525	+	0.701647i
$4$	1.86820	−	0.714031i	0.934098	−	0.357016i
$5$	1.46572	−	1.74677i	0.655488	−	0.781180i	−0.331243	−	0.943546i	$-0.607468\pi$
$5$	1.46572	−	1.74677i	0.655488	−	0.781180i	0.986731	+	0.162365i	$0.0519123\pi$
$6$	1.40435	−	2.00694i	0.573322	−	0.819330i
$7$	−1.21500	−	0.442225i	−0.459228	−	0.167145i	0.102039	−	0.994780i	$-0.467463\pi$
$7$	−1.21500	−	0.442225i	−0.459228	−	0.167145i	−0.561266	+	0.827635i	$0.689686\pi$
$8$	−2.41483	+	1.47261i	−0.853773	+	0.520645i
$9$	0.0461478	−	2.99965i	0.0153826	−	0.999882i
$10$	−1.58998	+	2.80554i	−0.502796	+	0.887189i
$11$	−2.93828	−	3.50170i	−0.885924	−	1.05580i	−0.998069	−	0.0621118i	$-0.980216\pi$
$11$	−2.93828	−	3.50170i	−0.885924	−	1.05580i	0.112145	−	0.993692i	$-0.464228\pi$
$12$	−1.43784	+	3.15160i	−0.415069	+	0.909790i
$13$	4.95227	+	0.873219i	1.37351	+	0.242187i	0.811215	−	0.584748i	$-0.198807\pi$
$13$	4.95227	+	0.873219i	1.37351	+	0.242187i	0.562297	+	0.826935i	$0.309918\pi$
$14$	1.80325	+	0.303103i	0.481939	+	0.0810077i
$15$	0.313950	+	3.93701i	0.0810615	+	1.01653i
$16$	2.98032	−	2.66790i	0.745080	−	0.666976i
$17$	0.909480	−	1.57526i	0.220581	−	0.382058i	−0.734403	−	0.678713i	$-0.762538\pi$
$17$	0.909480	−	1.57526i	0.220581	−	0.382058i	0.954985	+	0.296655i	$0.0958713\pi$
$18$	0.705870	+	4.18351i	0.166375	+	0.986063i
$19$	6.49748	−	3.75132i	1.49062	−	0.860612i	0.490681	−	0.871339i	$-0.336748\pi$
$19$	6.49748	−	3.75132i	1.49062	−	0.860612i	0.999942	+	0.0107271i	$0.00341459\pi$
$20$	1.49100	−	4.30988i	0.333397	−	0.963719i
$21$	2.03690	−	0.930816i	0.444488	−	0.203121i
$22$	4.98525	+	4.11559i	1.06286	+	0.877447i
$23$	0.835352	−	0.304043i	0.174183	−	0.0633974i	−0.253457	−	0.967347i	$-0.581567\pi$
$23$	0.835352	−	0.304043i	0.174183	−	0.0633974i	0.427640	+	0.903949i	$0.359345\pi$
$24$	1.19057	−	4.75211i	0.243025	−	0.970020i
$25$	−0.0346491	−	0.196505i	−0.00692983	−	0.0393010i
$26$	−7.11138	+	0.0569110i	−1.39466	+	0.0111612i
$27$	3.58848	+	3.75803i	0.690604	+	0.723233i
$28$	−2.58563	+	0.0413872i	−0.488637	+	0.00782145i
$29$	1.50546	−	0.265453i	0.279557	−	0.0492934i	−0.0321117	−	0.999484i	$-0.510223\pi$
$29$	1.50546	−	0.265453i	0.279557	−	0.0492934i	0.311669	+	0.950191i	$0.399112\pi$
$30$	−1.44730	−	5.39468i	−0.264239	−	0.984929i
$31$	−1.86625	+	0.679258i	−0.335188	+	0.121998i	−0.504130	−	0.863628i	$-0.668187\pi$
$31$	−1.86625	+	0.679258i	−0.335188	+	0.121998i	0.168943	+	0.985626i	$0.445965\pi$
$32$	−3.45990	+	4.47539i	−0.611629	+	0.791144i
$33$	7.88180	+	0.750698i	1.37204	+	0.130680i
$34$	−0.860439	+	2.42423i	−0.147564	+	0.415751i
$35$	−2.55331	+	1.47416i	−0.431589	+	0.249178i
$36$	−2.05563	−	5.63688i	−0.342605	−	0.939480i
$37$	−8.19426	−	4.73096i	−1.34713	−	0.777765i	−0.359286	−	0.933227i	$-0.616980\pi$
$37$	−8.19426	−	4.73096i	−1.34713	−	0.777765i	−0.987842	+	0.155463i	$0.950313\pi$
$38$	−8.07315	+	6.88502i	−1.30964	+	1.11690i
$39$	−7.17295	+	4.94077i	−1.14859	+	0.791157i
$40$	−0.967152	+	6.37659i	−0.152920	+	1.00823i
$41$	0.859892	−	4.87669i	0.134293	−	0.761611i	−0.841057	−	0.540946i	$-0.818066\pi$
$41$	0.859892	−	4.87669i	0.134293	−	0.761611i	0.975350	−	0.220665i	$-0.0708227\pi$
$42$	−2.59380	+	1.81740i	−0.400232	+	0.280431i
$43$	−1.62715	−	1.93916i	−0.248138	−	0.295720i	0.627570	−	0.778560i	$-0.284050\pi$
$43$	−1.62715	−	1.93916i	−0.248138	−	0.295720i	−0.875708	+	0.482840i	$0.839605\pi$
$44$	−7.98961	−	4.44385i	−1.20448	−	0.669936i
$45$	−5.17206	−	4.47724i	−0.771005	−	0.667427i
$46$	−1.08369	+	0.637285i	−0.159781	+	0.0939625i
$47$	7.64813	+	2.78369i	1.11560	+	0.406043i	0.833043	−	0.553208i	$-0.186597\pi$
$47$	7.64813	+	2.78369i	1.11560	+	0.406043i	0.282552	+	0.959252i	$0.408819\pi$
$48$	−0.435825	+	6.91448i	−0.0629059	+	0.998019i
$49$	−4.08164	−	3.42490i	−0.583092	−	0.489272i
$50$	0.0986326	+	0.264388i	0.0139488	+	0.0373902i
$51$	0.791986	+	3.04936i	0.110900	+	0.426996i
$52$	9.87532	−	1.90473i	1.36946	−	0.264139i
$53$			3.70167i			0.508464i	0.967143	+	0.254232i	$0.0818227\pi$
$53$			3.70167i			0.508464i	−0.967143	+	0.254232i	$0.918177\pi$
$54$	−5.95530	−	4.30515i	−0.810414	−	0.585857i
$55$	−10.4234			−1.40549
$56$	3.58525	−	0.721322i	0.479100	−	0.0963907i
$57$	−3.45979	+	12.5259i	−0.458260	+	1.65910i
$58$	−2.02553	+	0.755642i	−0.265965	+	0.0992207i
$59$	3.63062	−	4.32680i	0.472666	−	0.563302i	−0.476055	−	0.879415i	$-0.657934\pi$
$59$	3.63062	−	4.32680i	0.472666	−	0.563302i	0.948721	+	0.316114i	$0.102378\pi$
$60$	3.39767	+	7.13094i	0.438637	+	0.920600i
$61$	−4.89674	+	13.4537i	−0.626963	+	1.72257i	0.0623005	+	0.998057i	$0.480156\pi$
$61$	−4.89674	+	13.4537i	−0.626963	+	1.72257i	−0.689264	+	0.724510i	$0.742066\pi$
$62$	2.42105	−	1.42375i	0.307473	−	0.180816i
$63$	−1.38259	+	3.62417i	−0.174190	+	0.456602i
$64$	3.66285	−	7.11221i	0.457857	−	0.889026i
$65$	8.78393	−	7.37060i	1.08951	−	0.914210i
$66$	−11.1541	+	0.979351i	−1.37297	+	0.120550i
$67$	8.09804	+	1.42790i	0.989333	+	0.174446i	0.644819	−	0.764335i	$-0.276933\pi$
$67$	8.09804	+	1.42790i	0.989333	+	0.174446i	0.344514	+	0.938781i	$0.388044\pi$
$68$	0.574298	−	3.59230i	0.0696439	−	0.435631i
$69$	−0.661432	+	1.39042i	−0.0796270	+	0.167387i
$70$	3.17251	−	2.70561i	0.379187	−	0.323382i
$71$	−4.59959	+	7.96673i	−0.545871	+	0.945477i	0.452680	+	0.891673i	$0.350468\pi$
$71$	−4.59959	+	7.96673i	−0.545871	+	0.945477i	−0.998552	+	0.0538037i	$0.982865\pi$
$72$	4.30586	+	7.31160i	0.507451	+	0.861681i
$73$	−5.72007	−	9.90745i	−0.669484	−	1.15958i	−0.978049	−	0.208377i	$-0.933182\pi$
$73$	−5.72007	−	9.90745i	−0.669484	−	1.15958i	0.308565	−	0.951203i	$-0.400151\pi$
$74$	12.6104	+	4.47586i	1.46593	+	0.520308i
$75$	0.281572	+	0.200404i	0.0325131	+	0.0231406i
$76$	9.46001	−	11.6476i	1.08514	−	1.33607i
$77$	2.02148	+	5.55396i	0.230369	+	0.632932i
$78$	8.70720	−	8.71261i	0.985896	−	0.986509i
$79$	−1.39403	−	7.90593i	−0.156841	−	0.889487i	−0.957084	−	0.289811i	$-0.906407\pi$
$79$	−1.39403	−	7.90593i	−0.156841	−	0.889487i	0.800243	−	0.599676i	$-0.204704\pi$
$80$	−0.291918	−	9.11632i	−0.0326375	−	1.01924i
$81$	−8.99574	−	0.276854i	−0.999527	−	0.0307615i
$82$	0.0560425	+	7.00285i	0.00618886	+	0.773336i
$83$	−13.3270	+	2.34991i	−1.46283	+	0.257936i	−0.847693	−	0.530488i	$-0.822009\pi$
$83$	−13.3270	+	2.34991i	−1.46283	+	0.257936i	−0.615133	+	0.788423i	$0.710898\pi$
$84$	3.14070	−	3.19336i	0.342678	−	0.348424i
$85$	−1.41859	−	3.89754i	−0.153868	−	0.422748i
$86$	2.76072	+	2.27912i	0.297696	+	0.245764i
$87$	−1.53533	+	2.15717i	−0.164605	+	0.231273i
$88$	12.2521	+	4.12911i	1.30608	+	0.440164i
$89$	3.65721	+	6.33447i	0.387663	+	0.671452i	0.992135	−	0.125174i	$-0.0399490\pi$
$89$	3.65721	+	6.33447i	0.387663	+	0.671452i	−0.604472	+	0.796627i	$0.706616\pi$
$90$	8.34224	+	4.89884i	0.879350	+	0.516383i
$91$	−5.63086	−	3.25098i	−0.590275	−	0.340795i
$92$	1.34351	−	1.16448i	0.140070	−	0.121405i
$93$	1.47769	−	3.10632i	0.153230	−	0.322110i
$94$	−11.3510	−	1.90796i	−1.17077	−	0.196791i
$95$	2.97075	−	16.8480i	0.304793	−	1.72857i
$96$	−1.16893	−	9.72798i	−0.119303	−	0.992858i
$97$	2.14122	−	1.79669i	0.217408	−	0.182427i	−0.527579	−	0.849506i	$-0.676900\pi$
$97$	2.14122	−	1.79669i	0.217408	−	0.182427i	0.744987	+	0.667079i	$0.232456\pi$
$98$	6.55563	+	3.71527i	0.662219	+	0.375299i
$99$	−10.6395	+	8.65220i	−1.06931	+	0.869579i
$100$	−0.205042	−	0.342369i	−0.0205042	−	0.0342369i
$101$	0.520014	−	1.42873i	0.0517434	−	0.142164i	−0.911129	−	0.412122i	$-0.864788\pi$
$101$	0.520014	−	1.42873i	0.0517434	−	0.142164i	0.962872	+	0.269958i	$0.0870099\pi$
$102$	−1.88424	−	4.03749i	−0.186568	−	0.399771i
$103$	8.67365	+	7.27806i	0.854640	+	0.717128i	0.960806	−	0.277220i	$-0.0894132\pi$
$103$	8.67365	+	7.27806i	0.854640	+	0.717128i	−0.106166	+	0.994348i	$0.533858\pi$
$104$	−13.2448	+	5.18407i	−1.29876	+	0.508340i
$105$	1.35959	−	4.92231i	0.132683	−	0.480369i
$106$	−0.950268	−	5.14799i	−0.0922982	−	0.500017i
$107$			8.87714i			0.858186i	0.903260	+	0.429093i	$0.141167\pi$
$107$			8.87714i			0.858186i	−0.903260	+	0.429093i	$0.858833\pi$
$108$	9.38734	+	4.45845i	0.903297	+	0.429015i
$109$			3.79557i			0.363550i	0.983340	+	0.181775i	$0.0581842\pi$
$109$			3.79557i			0.363550i	−0.983340	+	0.181775i	$0.941816\pi$
$110$	14.4960	−	2.67581i	1.38214	−	0.255129i
$111$	15.8622	−	4.11978i	1.50558	−	0.391032i
$112$	−4.80091	+	1.92354i	−0.453643	+	0.181757i
$113$	3.60533	+	3.02523i	0.339161	+	0.284590i	0.796420	−	0.604744i	$-0.206724\pi$
$113$	3.60533	+	3.02523i	0.339161	+	0.284590i	−0.457259	+	0.889333i	$0.651169\pi$
$114$	1.59602	−	18.3082i	0.149481	−	1.71472i
$115$	0.693295	−	1.90481i	0.0646501	−	0.177625i
$116$	2.62295	−	1.57087i	0.243535	−	0.145851i
$117$	2.84788	−	14.8148i	0.263287	−	1.36962i
$118$	−3.93842	+	6.94939i	−0.362561	+	0.639743i
$119$	−1.80164	+	1.51176i	−0.165156	+	0.138582i
$120$	−6.55581	−	9.04490i	−0.598461	−	0.825683i
$121$	−1.71832	+	9.74509i	−0.156211	+	0.885917i
$122$	3.35625	−	19.9673i	0.303861	−	1.80776i
$123$	4.86537	+	7.06348i	0.438696	+	0.636893i
$124$	−3.00150	+	2.60154i	−0.269543	+	0.233626i
$125$	9.47973	+	5.47313i	0.847893	+	0.489531i
$126$	0.992418	−	5.39513i	0.0884116	−	0.480636i
$127$	2.25950	+	3.91357i	0.200498	+	0.347273i	0.948689	−	0.316210i	$-0.102411\pi$
$127$	2.25950	+	3.91357i	0.200498	+	0.347273i	−0.748191	+	0.663484i	$0.769077\pi$
$128$	−3.26820	+	10.8314i	−0.288871	+	0.957368i
$129$	4.36476	+	0.415719i	0.384296	+	0.0366020i
$130$	−10.3239	+	12.5054i	−0.905462	+	1.09679i
$131$	−5.52132	−	15.1697i	−0.482400	−	1.32538i	−0.907430	−	0.420203i	$-0.861959\pi$
$131$	−5.52132	−	15.1697i	−0.482400	−	1.32538i	0.425030	−	0.905179i	$-0.360263\pi$
$132$	15.2608	−	4.22540i	1.32828	−	0.367774i
$133$	−9.55338	+	1.68452i	−0.828383	+	0.146066i
$134$	−11.6287	+	0.0930620i	−1.00456	+	0.00803933i
$135$	11.8241	−	0.760054i	1.01766	−	0.0654151i
$136$	0.123504	+	5.14331i	0.0105904	+	0.441035i
$137$	1.74704	+	9.90795i	0.149260	+	0.846493i	0.963848	+	0.266454i	$0.0858519\pi$
$137$	1.74704	+	9.90795i	0.149260	+	0.846493i	−0.814588	+	0.580040i	$0.803037\pi$
$138$	0.562926	−	2.10348i	0.0479194	−	0.179061i
$139$	2.76868	+	7.60688i	0.234836	+	0.645207i	0.999999	+	0.00137051i	$0.000436247\pi$
$139$	2.76868	+	7.60688i	0.234836	+	0.645207i	−0.765163	+	0.643837i	$0.777342\pi$
$140$	−3.71750	+	4.57716i	−0.314186	+	0.386841i
$141$	−12.8218	+	5.85925i	−1.07979	+	0.493438i
$142$	4.35158	−	12.2603i	0.365176	−	1.02886i
$143$	−11.4934	−	19.9071i	−0.961126	−	1.66472i
$144$	−7.86523	−	9.06301i	−0.655435	−	0.755251i
$145$	1.74289	−	3.01878i	0.144739	−	0.250696i
$146$	10.4984	+	12.3101i	0.868852	+	1.01879i
$147$	9.19952	−	0.733600i	0.758764	−	0.0605063i
$148$	−18.6865	−	2.98740i	−1.53602	−	0.245563i
$149$	15.8906	+	2.80194i	1.30181	+	0.229544i	0.781216	−	0.624260i	$-0.214600\pi$
$149$	15.8906	+	2.80194i	1.30181	+	0.229544i	0.520594	+	0.853805i	$0.325711\pi$
$150$	−0.443033	−	0.206422i	−0.0361735	−	0.0168543i
$151$	7.90059	−	6.62938i	0.642941	−	0.539491i	−0.261979	−	0.965074i	$-0.584375\pi$
$151$	7.90059	−	6.62938i	0.642941	−	0.539491i	0.904920	+	0.425582i	$0.139931\pi$
$152$	−10.1661	+	18.6271i	−0.824581	+	1.51085i
$153$	−4.68327	−	2.80081i	−0.378620	−	0.226432i
$154$	−4.23708	−	7.20506i	−0.341434	−	0.580600i
$155$	−1.54888	+	4.25550i	−0.124409	+	0.341810i
$156$	−9.87262	+	14.3520i	−0.790442	+	1.14908i
$157$	−13.4195	+	15.9928i	−1.07099	+	1.27636i	−0.111763	+	0.993735i	$0.535650\pi$
$157$	−13.4195	+	15.9928i	−1.07099	+	1.27636i	−0.959230	+	0.282626i	$0.908795\pi$
$158$	3.96826	+	10.6371i	0.315698	+	0.846239i
$159$	−4.49860	−	4.56834i	−0.356762	−	0.362293i
$160$	2.74626	+	12.6033i	0.217111	+	0.996379i
$161$	−1.14941			−0.0905862
$162$	12.5816	−	1.92430i	0.988505	−	0.151187i
$163$		−	7.57305i		−	0.593167i	−0.955007	−	0.296584i	$-0.904153\pi$
$163$		−	7.57305i		−	0.593167i	0.955007	−	0.296584i	$-0.0958473\pi$
$164$	−1.87566	−	9.72461i	−0.146465	−	0.759365i
$165$	12.8638	−	12.6674i	1.00144	−	0.986155i
$166$	17.9308	−	6.68927i	1.39170	−	0.519188i
$167$	8.24570	+	6.91897i	0.638072	+	0.535406i	0.903425	−	0.428745i	$-0.141044\pi$
$167$	8.24570	+	6.91897i	0.638072	+	0.535406i	−0.265354	+	0.964151i	$0.585489\pi$
$168$	−3.54805	+	5.24732i	−0.273738	+	0.404840i
$169$	11.5465	+	4.20257i	0.888189	+	0.323274i
$170$	2.97341	+	5.05622i	0.228050	+	0.387794i
$171$	−10.9528	−	19.6632i	−0.837581	−	1.50369i
$172$	−4.42446	−	2.46090i	−0.337362	−	0.187642i
$173$	1.94847	+	2.32210i	0.148139	+	0.176546i	0.835011	−	0.550233i	$-0.185461\pi$
$173$	1.94847	+	2.32210i	0.148139	+	0.176546i	−0.686872	+	0.726779i	$0.741017\pi$
$174$	1.58144	−	3.39416i	0.119888	−	0.257311i
$175$	−0.0448006	+	0.254077i	−0.00338661	+	0.0192064i
$176$	−18.0992	−	2.59715i	−1.36428	−	0.195768i
$177$	0.777663	+	9.75208i	0.0584527	+	0.733011i
$178$	−6.71229	−	7.87061i	−0.503107	−	0.589927i
$179$	6.05490	+	3.49580i	0.452565	+	0.261288i	0.708913	−	0.705296i	$-0.249186\pi$
$179$	6.05490	+	3.49580i	0.452565	+	0.261288i	−0.256348	+	0.966585i	$0.582519\pi$
$180$	−12.8593	−	4.67135i	−0.958476	−	0.348182i
$181$	6.40756	−	3.69941i	0.476271	−	0.274975i	−0.242590	−	0.970129i	$-0.577997\pi$
$181$	6.40756	−	3.69941i	0.476271	−	0.274975i	0.718861	+	0.695154i	$0.244664\pi$
$182$	8.66551	+	3.07568i	0.642331	+	0.227985i
$183$	−10.3069	−	22.5545i	−0.761908	−	1.66728i
$184$	−1.56950	+	1.96436i	−0.115705	+	0.144815i
$185$	−20.2744	+	7.37926i	−1.49060	+	0.542534i
$186$	−1.25762	+	4.69936i	−0.0922133	+	0.344574i
$187$	−8.18842	+	1.44384i	−0.598796	+	0.105584i
$188$	16.2759	−	0.260522i	1.18704	−	0.0190005i
$189$	−2.69812	−	6.15293i	−0.196259	−	0.447560i
$190$	0.193616	+	24.1934i	0.0140463	+	1.75518i
$191$	4.49698	+	25.5037i	0.325390	+	1.84538i	0.506918	+	0.861994i	$0.330785\pi$
$191$	4.49698	+	25.5037i	0.325390	+	1.84538i	−0.181528	+	0.983386i	$0.558104\pi$
$192$	4.12295	+	13.2288i	0.297548	+	0.954707i
$193$	−16.9847	+	6.18192i	−1.22258	+	0.444984i	−0.871051	−	0.491192i	$-0.836561\pi$
$193$	−16.9847	+	6.18192i	−1.22258	+	0.444984i	−0.351532	+	0.936176i	$0.614339\pi$
$194$	−2.51659	+	3.04837i	−0.180681	+	0.218860i
$195$	−1.88311	+	19.7713i	−0.134852	+	1.41585i
$196$	−10.0708	−	3.48397i	−0.719343	−	0.248855i
$197$	3.88751	−	2.24446i	0.276974	−	0.159911i	−0.355079	−	0.934836i	$-0.615546\pi$
$197$	3.88751	−	2.24446i	0.276974	−	0.159911i	0.632053	+	0.774926i	$0.282213\pi$
$198$	12.5754	−	14.7641i	0.893693	−	1.04924i
$199$	−5.96011	+	10.3232i	−0.422501	+	0.731793i	−0.996183	−	0.0872848i	$-0.972181\pi$
$199$	−5.96011	+	10.3232i	−0.422501	+	0.731793i	0.573683	+	0.819078i	$0.305514\pi$
$200$	0.373047	+	0.423503i	0.0263784	+	0.0299462i
$201$	−11.7293	+	8.07924i	−0.827324	+	0.569866i
$202$	−0.356420	+	2.12045i	−0.0250777	+	0.149195i
$203$	−1.94653	−	0.343225i	−0.136619	−	0.0240897i
$204$	3.65693	+	5.13130i	0.256036	+	0.359263i
$205$	−7.25811	−	8.64988i	−0.506929	−	0.604134i
$206$	−13.9310	−	7.89509i	−0.970617	−	0.550077i
$207$	−0.873472	−	2.51979i	−0.0607105	−	0.175138i
$208$	17.0890	−	10.6097i	1.18491	−	0.735651i
$209$	−32.2274	−	11.7298i	−2.22922	−	0.811369i
$210$	−0.627189	+	7.19458i	−0.0432802	+	0.496473i
$211$	11.4128	−	13.6012i	0.785686	−	0.936344i	−0.213489	−	0.976945i	$-0.568483\pi$
$211$	11.4128	−	13.6012i	0.785686	−	0.936344i	0.999175	+	0.0406011i	$0.0129273\pi$
$212$	2.64311	+	6.91546i	0.181530	+	0.474955i
$213$	−4.00538	−	15.4218i	−0.274444	−	1.05668i
$214$	−2.27888	−	12.3456i	−0.155781	−	0.843928i
$215$	−5.77222			−0.393662
$216$	−14.1997	−	3.79060i	−0.966167	−	0.257918i
$217$	2.56788			0.174319
$218$	−0.974373	−	5.27857i	−0.0659929	−	0.357510i
$219$	19.0997	+	5.27554i	1.29064	+	0.356488i
$220$	−19.4729	+	7.44261i	−1.31286	+	0.501781i
$221$	5.87954	−	7.00696i	0.395501	−	0.471339i
$222$	−21.0023	+	9.80150i	−1.40958	+	0.657834i
$223$	−11.2910	−	4.10960i	−0.756104	−	0.275199i	−0.0649319	−	0.997890i	$-0.520683\pi$
$223$	−11.2910	−	4.10960i	−0.756104	−	0.275199i	−0.691172	+	0.722690i	$0.742905\pi$
$224$	6.18291	−	3.90756i	0.413113	−	0.261085i
$225$	−0.591044	+	0.0948668i	−0.0394030	+	0.00632446i
$226$	−5.79061	−	3.28171i	−0.385186	−	0.218296i
$227$	−6.05029	−	7.21045i	−0.401572	−	0.478575i	0.526927	−	0.849911i	$-0.323344\pi$
$227$	−6.05029	−	7.21045i	−0.401572	−	0.478575i	−0.928499	+	0.371336i	$0.878900\pi$
$228$	2.48034	+	25.8713i	0.164264	+	1.71337i
$229$	16.1662	+	2.85054i	1.06829	+	0.188369i	0.680033	−	0.733182i	$-0.261965\pi$
$229$	16.1662	+	2.85054i	1.06829	+	0.188369i	0.388259	+	0.921550i	$0.373077\pi$
$230$	−0.475188	+	2.82703i	−0.0313329	+	0.186409i
$231$	−9.24442	−	4.39762i	−0.608239	−	0.289342i
$232$	−3.24453	+	2.85798i	−0.213014	+	0.187635i
$233$	4.13470	−	7.16150i	0.270873	−	0.469166i	−0.698213	−	0.715890i	$-0.746021\pi$
$233$	4.13470	−	7.16150i	0.270873	−	0.469166i	0.969086	+	0.246725i	$0.0793544\pi$
$234$	−0.157461	+	21.3342i	−0.0102936	+	1.39466i
$235$	16.0725	−	9.27945i	1.04845	−	0.605324i
$236$	3.69324	−	10.6757i	0.240409	−	0.694928i
$237$	11.3284	+	8.06279i	0.735859	+	0.523735i
$238$	2.11749	−	2.56493i	0.137256	−	0.166260i
$239$	14.8870	−	5.41844i	0.962963	−	0.350490i	0.187769	−	0.982213i	$-0.439874\pi$
$239$	14.8870	−	5.41844i	0.962963	−	0.350490i	0.775194	+	0.631724i	$0.217652\pi$
$240$	11.4392	+	10.8960i	0.738399	+	0.703331i
$241$	3.79086	+	21.4990i	0.244191	+	1.38488i	0.822364	+	0.568961i	$0.192655\pi$
$241$	3.79086	+	21.4990i	0.244191	+	1.38488i	−0.578174	+	0.815914i	$0.696234\pi$
$242$	−0.111990	−	13.9938i	−0.00719897	−	0.899555i
$243$	11.4384	−	10.5907i	0.733771	−	0.679397i
$244$	0.458279	+	28.6306i	0.0293383	+	1.83288i
$245$	−11.9651	+	2.10976i	−0.764419	+	0.134788i
$246$	−8.57965	−	8.57431i	−0.547019	−	0.546678i
$247$	35.4530	−	12.9038i	2.25582	−	0.821051i
$248$	3.50639	−	4.38854i	0.222656	−	0.278673i
$249$	13.5914	−	19.0962i	0.861320	−	1.21017i
$250$	−14.5887	−	5.17801i	−0.922668	−	0.327486i
$251$	3.84480	−	2.21980i	0.242682	−	0.140112i	−0.373727	−	0.927539i	$-0.621920\pi$
$251$	3.84480	−	2.21980i	0.242682	−	0.140112i	0.616409	+	0.787426i	$0.288587\pi$
$252$	0.00482610	+	7.75787i	0.000304015	+	0.488700i
$253$	−3.51917	−	2.03179i	−0.221248	−	0.127738i
$254$	−4.14700	−	4.86263i	−0.260206	−	0.305109i
$255$	6.48736	+	3.08608i	0.406255	+	0.193258i
$256$	1.76459	−	15.9024i	0.110287	−	0.993900i
$257$	−3.91461	+	22.2008i	−0.244187	+	1.38485i	0.578188	+	0.815904i	$0.303760\pi$
$257$	−3.91461	+	22.2008i	−0.244187	+	1.38485i	−0.822374	+	0.568947i	$0.807351\pi$
$258$	−6.17687	+	0.542342i	−0.384555	+	0.0337648i
$259$	7.86390	+	9.37183i	0.488639	+	0.582337i
$260$	11.1473	−	20.0417i	0.691325	−	1.24294i
$261$	−0.726792	−	4.52810i	−0.0449873	−	0.280282i
$262$	11.5729	+	19.6794i	0.714974	+	1.21580i
$263$	−21.0056	−	7.64543i	−1.29526	−	0.471437i	−0.399812	−	0.916597i	$-0.630925\pi$
$263$	−21.0056	−	7.64543i	−1.29526	−	0.471437i	−0.895451	+	0.445160i	$0.853147\pi$
$264$	−20.1387	+	9.79398i	−1.23945	+	0.602778i
$265$	6.46598	+	5.42560i	0.397202	+	0.333292i
$266$	12.8536	−	4.79517i	0.788106	−	0.294011i
$267$	−12.2117	−	3.37299i	−0.747342	−	0.206424i
$268$	16.1483	−	3.11465i	0.986415	−	0.190258i
$269$			12.5171i			0.763184i	0.924331	+	0.381592i	$0.124624\pi$
$269$			12.5171i			0.763184i	−0.924331	+	0.381592i	$0.875376\pi$
$270$	−16.2489	+	4.09243i	−0.988877	+	0.249057i
$271$	9.28509			0.564029			0.282015	−	0.959410i	$-0.408997\pi$
$271$	9.28509			0.564029			0.282015	+	0.959410i	$0.408997\pi$
$272$	−1.49211	−	7.12119i	−0.0904727	−	0.431786i
$273$	10.9001	−	2.83099i	0.659703	−	0.171340i
$274$	−4.97314	−	13.3307i	−0.300438	−	0.805336i
$275$	−0.586294	+	0.698718i	−0.0353548	+	0.0421343i
$276$	−0.242879	+	3.06987i	−0.0146196	+	0.184784i
$277$	3.85712	−	10.5974i	0.231752	−	0.636734i	−0.768242	−	0.640160i	$-0.778868\pi$
$277$	3.85712	−	10.5974i	0.231752	−	0.636734i	0.999994	+	0.00342581i	$0.00109047\pi$
$278$	−5.80324	−	9.86828i	−0.348055	−	0.591860i
$279$	1.95141	+	5.62942i	0.116828	+	0.337024i
$280$	3.99498	−	7.31988i	0.238746	−	0.437446i
$281$	12.0912	−	10.1457i	0.721299	−	0.605241i	−0.206446	−	0.978458i	$-0.566190\pi$
$281$	12.0912	−	10.1457i	0.721299	−	0.605241i	0.927744	+	0.373217i	$0.121745\pi$
$282$	16.3273	−	11.4401i	0.972279	−	0.681248i
$283$	−11.1062	−	1.95832i	−0.660194	−	0.116410i	−0.166494	−	0.986042i	$-0.553245\pi$
$283$	−11.1062	−	1.95832i	−0.660194	−	0.116410i	−0.493700	+	0.869632i	$0.664356\pi$
$284$	−2.90445	+	18.1677i	−0.172347	+	1.07805i
$285$	16.8089	+	24.4029i	0.995672	+	1.44550i
$286$	21.0945	+	24.7347i	1.24734	+	1.46260i
$287$	−3.20137	+	5.54493i	−0.188971	+	0.327307i
$288$	13.2649	+	10.5850i	0.781642	+	0.623727i
$289$	6.84569	+	11.8571i	0.402688	+	0.697476i
$290$	−1.64891	+	4.64569i	−0.0968274	+	0.272804i
$291$	−0.459035	+	4.81955i	−0.0269091	+	0.282527i
$292$	−17.7605	−	14.4248i	−1.03935	−	0.844145i
$293$	−11.3855	−	31.2814i	−0.665148	−	1.82748i	−0.551896	−	0.833913i	$-0.686095\pi$
$293$	−11.3855	−	31.2814i	−0.665148	−	1.82748i	−0.113252	−	0.993566i	$-0.536127\pi$
$294$	−12.6056	+	3.38187i	−0.735175	+	0.197235i
$295$	−2.23648	−	12.6837i	−0.130213	−	0.738475i
$296$	26.7546	−	0.642446i	1.55508	−	0.0373414i
$297$	2.61555	−	23.6079i	0.151770	−	1.36987i
$298$	−22.8187	+	0.182614i	−1.32185	+	0.0105785i
$299$	4.40239	−	0.776259i	0.254597	−	0.0448922i
$300$	0.669126	+	0.173343i	0.0386320	+	0.0100079i
$301$	1.11945	+	3.07566i	0.0645239	+	0.177278i
$302$	−9.28564	+	11.2478i	−0.534329	+	0.647237i
$303$	1.09455	+	2.39520i	0.0628803	+	0.137601i
$304$	9.35639	−	28.5148i	0.536626	−	1.63543i
$305$	16.3233	+	28.2728i	0.934669	+	1.61889i
$306$	7.23211	+	2.69288i	0.413432	+	0.153942i
$307$	−9.81977	−	5.66945i	−0.560444	−	0.323573i	0.192880	−	0.981222i	$-0.438217\pi$
$307$	−9.81977	−	5.66945i	−0.560444	−	0.323573i	−0.753324	+	0.657650i	$0.771551\pi$
$308$	7.74222	+	8.93249i	0.441154	+	0.508976i
$309$	−19.5493	+	1.55893i	−1.11212	+	0.0886843i
$310$	1.06161	−	6.31583i	0.0602953	−	0.358715i
$311$	−0.869735	+	4.93251i	−0.0493181	+	0.279697i	−0.999487	−	0.0320399i	$-0.989800\pi$
$311$	−0.869735	+	4.93251i	−0.0493181	+	0.279697i	0.950168	+	0.311737i	$0.100911\pi$
$312$	10.0457	−	22.4941i	0.568724	−	1.27348i
$313$	−4.75687	+	3.99148i	−0.268874	+	0.225612i	−0.767249	−	0.641350i	$-0.778375\pi$
$313$	−4.75687	+	3.99148i	−0.268874	+	0.225612i	0.498375	+	0.866962i	$0.333930\pi$
$314$	14.5572	−	25.6864i	0.821511	−	1.44957i
$315$	4.30412	+	7.72707i	0.242510	+	0.435371i
$316$	−8.24941	−	13.7745i	−0.464065	−	0.774874i
$317$	−5.47491	+	15.0422i	−0.307501	+	0.844853i	0.685641	+	0.727940i	$0.259522\pi$
$317$	−5.47491	+	15.0422i	−0.307501	+	0.844853i	−0.993142	+	0.116913i	$0.962700\pi$
$318$	7.42904	+	5.19843i	0.416600	+	0.291513i
$319$	−5.35300	−	4.49170i	−0.299711	−	0.251487i
$320$	−7.05470	−	16.8226i	−0.394370	−	0.940415i
$321$	−10.7883	−	10.9555i	−0.602143	−	0.611478i
$322$	1.59851	−	0.295069i	0.0890813	−	0.0164435i
$323$		−	13.6470i		−	0.759339i
$324$	−17.0035	+	5.90602i	−0.944639	+	0.328112i
$325$		−	1.00340i		−	0.0556587i
$326$	1.94410	+	10.5320i	0.107674	+	0.583313i
$327$	−4.61272	−	4.68423i	−0.255084	−	0.259038i
$328$	5.10496	+	13.0427i	0.281874	+	0.720162i
$329$	−8.06148	−	6.76439i	−0.444444	−	0.372933i
$330$	−14.6380	+	20.9191i	−0.805795	+	1.15156i
$331$	−0.933712	+	2.56535i	−0.0513214	+	0.141005i	−0.962705	−	0.270554i	$-0.912793\pi$
$331$	−0.933712	+	2.56535i	−0.0513214	+	0.141005i	0.911383	+	0.411558i	$0.135015\pi$
$332$	−23.2195	+	13.9060i	−1.27434	+	0.763189i
$333$	−14.5693	+	24.3615i	−0.798395	+	1.33500i
$334$	−13.2436	−	7.50555i	−0.724660	−	0.410686i
$335$	14.3636	−	12.0525i	0.784770	−	0.658500i
$336$	3.58728	−	8.20838i	0.195702	−	0.447804i
$337$	3.64020	−	20.6446i	0.198294	−	1.12458i	−0.709355	−	0.704852i	$-0.751014\pi$
$337$	3.64020	−	20.6446i	0.198294	−	1.12458i	0.907649	−	0.419730i	$-0.137875\pi$
$338$	−17.1367	−	2.88046i	−0.932115	−	0.156676i
$339$	−8.12597	+	0.647991i	−0.441342	+	0.0351940i
$340$	−5.43318	−	6.26846i	−0.294655	−	0.339955i
$341$	7.86211	+	4.53919i	0.425757	+	0.245811i
$342$	20.2801	+	24.5343i	1.09662	+	1.32666i
$343$	7.97005	+	13.8045i	0.430342	+	0.745375i
$344$	6.78493	+	2.28660i	0.365819	+	0.123285i
$345$	1.45928	+	3.19334i	0.0785650	+	0.171923i
$346$	−3.30589	−	2.72919i	−0.177726	−	0.146722i
$347$	8.56303	+	23.5267i	0.459687	+	1.26298i	0.925719	+	0.378212i	$0.123461\pi$
$347$	8.56303	+	23.5267i	0.459687	+	1.26298i	−0.466031	+	0.884768i	$0.654317\pi$
$348$	−1.32801	+	5.12630i	−0.0711888	+	0.274798i
$349$	−1.68825	+	0.297684i	−0.0903700	+	0.0159347i	−0.218650	−	0.975803i	$-0.570165\pi$
$349$	−1.68825	+	0.297684i	−0.0903700	+	0.0159347i	0.128280	+	0.991738i	$0.459054\pi$
$350$	−0.00291983	−	0.364850i	−0.000156071	−	0.0195021i
$351$	14.4895	+	21.7443i	0.773395	+	1.16063i
$352$	25.8376	−	1.03440i	1.37715	−	0.0551336i
$353$	−4.10027	−	23.2538i	−0.218235	−	1.23767i	−0.875203	−	0.483756i	$-0.839272\pi$
$353$	−4.10027	−	23.2538i	−0.218235	−	1.23767i	0.656967	−	0.753919i	$-0.271839\pi$
$354$	−3.58500	−	13.3628i	−0.190540	−	0.710223i
$355$	7.17436	+	19.7114i	0.380776	+	1.04617i
$356$	11.3554	+	9.22267i	0.601835	+	0.488801i
$357$	0.386237	−	4.05522i	0.0204418	−	0.214625i
$358$	−9.31808	−	3.30730i	−0.492476	−	0.174796i
$359$	0.0166089	+	0.0287675i	0.000876586	+	0.00151829i	0.866463	−	0.499241i	$-0.166388\pi$
$359$	0.0166089	+	0.0287675i	0.000876586	+	0.00151829i	−0.865587	+	0.500759i	$0.833054\pi$
$360$	19.0829	+	3.19538i	1.00576	+	0.168411i
$361$	18.6448	−	32.2938i	0.981306	−	1.69967i
$362$	−7.96143	+	6.78974i	−0.418444	+	0.356861i
$363$	−9.72246	−	14.1149i	−0.510297	−	0.740843i
$364$	−12.8409	−	2.05286i	−0.673044	−	0.107599i
$365$	−25.6901	−	4.52985i	−1.34468	−	0.237103i
$366$	20.1240	+	28.7211i	1.05190	+	1.50128i
$367$	−19.6835	+	16.5164i	−1.02747	+	0.862150i	−0.990548	−	0.137168i	$-0.956200\pi$
$367$	−19.6835	+	16.5164i	−1.02747	+	0.862150i	−0.0369225	+	0.999318i	$0.511755\pi$
$368$	1.67846	−	3.13478i	0.0874956	−	0.163412i
$369$	−14.5887	−	2.80442i	−0.759456	−	0.145992i
$370$	26.3016	−	15.4672i	1.36735	−	0.804100i
$371$	1.63697	−	4.49754i	0.0849874	−	0.233501i
$372$	0.542612	−	6.85833i	0.0281331	−	0.355588i
$373$	4.20427	−	5.01046i	0.217689	−	0.259432i	−0.646138	−	0.763221i	$-0.723617\pi$
$373$	4.20427	−	5.01046i	0.217689	−	0.259432i	0.863827	+	0.503789i	$0.168061\pi$
$374$	11.0171	−	4.11005i	0.569682	−	0.212526i
$375$	−18.3506	+	4.76607i	−0.947623	+	0.246119i
$376$	−22.5683	+	4.54054i	−1.16387	+	0.234161i
$377$	7.68724			0.395913
$378$	5.33186	+	7.86436i	0.274242	+	0.404499i
$379$			22.9600i			1.17938i	0.807631	+	0.589688i	$0.200749\pi$
$379$			22.9600i			1.17938i	−0.807631	+	0.589688i	$0.799251\pi$
$380$	−6.48004	−	33.5966i	−0.332419	−	1.72347i
$381$	−7.54463	−	2.08390i	−0.386523	−	0.106762i
$382$	−12.8012	−	34.3140i	−0.654965	−	1.75566i
$383$	−9.59765	−	8.05339i	−0.490417	−	0.411509i	0.363759	−	0.931493i	$-0.381493\pi$
$383$	−9.59765	−	8.05339i	−0.490417	−	0.411509i	−0.854176	+	0.519984i	$0.825938\pi$
$384$	−9.12987	−	17.3391i	−0.465907	−	0.884834i
$385$	12.6644	+	4.60947i	0.645438	+	0.234920i
$386$	22.0339	−	12.9575i	1.12150	−	0.659519i
$387$	−5.89189	+	4.79139i	−0.299502	+	0.243560i
$388$	2.71732	−	4.88547i	0.137951	−	0.248022i
$389$	−16.8629	−	20.0964i	−0.854983	−	1.01893i	−0.999567	−	0.0294361i	$-0.990629\pi$
$389$	−16.8629	−	20.0964i	−0.854983	−	1.01893i	0.144584	−	0.989493i	$-0.453816\pi$
$390$	−2.45668	−	27.9797i	−0.124399	−	1.41681i
$391$	0.280787	−	1.59242i	0.0142000	−	0.0805323i
$392$	14.9000	+	2.25992i	0.752565	+	0.114143i
$393$	25.2496	+	12.0114i	1.27367	+	0.605893i
$394$	−4.83025	+	4.11938i	−0.243345	+	0.207531i
$395$	−15.8531	−	9.15280i	−0.797657	−	0.460527i
$396$	−13.6987	+	23.7609i	−0.688384	+	1.19403i
$397$	23.2006	−	13.3949i	1.16440	−	0.672269i	0.212049	−	0.977259i	$-0.431986\pi$
$397$	23.2006	−	13.3949i	1.16440	−	0.672269i	0.952356	+	0.304990i	$0.0986531\pi$
$398$	5.63873	−	15.8867i	0.282644	−	0.796329i
$399$	9.74292	−	13.6890i	0.487756	−	0.685308i
$400$	−0.627522	−	0.493207i	−0.0313761	−	0.0246603i
$401$	−16.3873	+	5.96448i	−0.818342	+	0.297852i	−0.717065	−	0.697006i	$-0.754515\pi$
$401$	−16.3873	+	5.96448i	−0.818342	+	0.297852i	−0.101277	+	0.994858i	$0.532293\pi$
$402$	14.2382	−	14.2470i	0.710135	−	0.710577i
$403$	−9.83529	+	1.73423i	−0.489931	+	0.0863880i
$404$	−0.0486674	−	3.04045i	−0.00242130	−	0.151268i
$405$	−13.6688	+	15.3077i	−0.679208	+	0.760647i
$406$	2.79518	−	0.0223693i	0.138723	−	0.00111017i
$407$	7.51060	+	42.5948i	0.372287	+	2.11134i
$408$	−6.40303	−	6.19742i	−0.316997	−	0.306818i
$409$	−12.2946	+	4.47486i	−0.607928	+	0.221268i	−0.627596	−	0.778539i	$-0.715961\pi$
$409$	−12.2946	+	4.47486i	−0.607928	+	0.221268i	0.0196684	+	0.999807i	$0.493739\pi$
$410$	12.3145	+	10.1663i	0.608171	+	0.502078i
$411$	−14.1971	−	10.1045i	−0.700291	−	0.498420i
$412$	21.4008	+	7.40358i	1.05434	+	0.364748i
$413$	−6.32463	+	3.65153i	−0.311215	+	0.179680i
$414$	1.86162	+	3.28009i	0.0914935	+	0.161208i
$415$	−15.4288	+	26.7235i	−0.757371	+	1.31180i
$416$	−21.0423	+	19.1421i	−1.03169	+	0.938518i
$417$	−12.6615	−	6.02313i	−0.620035	−	0.294954i
$418$	47.8305	+	8.03968i	2.33947	+	0.393234i
$419$	7.40741	+	1.30613i	0.361876	+	0.0638084i	0.351630	−	0.936139i	$-0.385628\pi$
$419$	7.40741	+	1.30613i	0.361876	+	0.0638084i	0.0102456	+	0.999948i	$0.496739\pi$
$420$	−0.974699	−	10.1666i	−0.0475604	−	0.496081i
$421$	14.2717	+	17.0084i	0.695561	+	0.828938i	0.992016	−	0.126109i	$-0.0402490\pi$
$421$	14.2717	+	17.0084i	0.695561	+	0.828938i	−0.296455	+	0.955047i	$0.595805\pi$
$422$	−12.3803	+	21.8452i	−0.602665	+	1.06341i
$423$	8.70304	−	22.8132i	0.423156	−	1.10922i
$424$	−5.45111	−	8.93893i	−0.264729	−	0.434113i
$425$	−0.341060	−	0.124136i	−0.0165438	−	0.00602147i
$426$	9.52934	+	20.4191i	0.461698	+	0.989311i
$427$	11.8991	−	14.1808i	0.575838	−	0.686257i
$428$	6.33856	+	16.5842i	0.306386	+	0.801630i
$429$	38.3773	+	10.6002i	1.85287	+	0.511782i
$430$	8.02753	−	1.48180i	0.387122	−	0.0714590i
$431$	−14.5079			−0.698819			−0.349409	−	0.936970i	$-0.613618\pi$
$431$	−14.5079			−0.698819			−0.349409	+	0.936970i	$0.613618\pi$
$432$	20.7209	+	1.62641i	0.996934	+	0.0782506i
$433$	23.2737			1.11846			0.559232	−	0.829011i	$-0.311096\pi$
$433$	23.2737			1.11846			0.559232	+	0.829011i	$0.311096\pi$
$434$	−3.57119	+	0.659208i	−0.171423	+	0.0316430i
$435$	1.51773	+	5.84367i	0.0727697	+	0.280183i
$436$	2.71016	+	7.09088i	0.129793	+	0.339591i
$437$	4.28712	−	5.10919i	0.205081	−	0.244406i
$438$	−27.9166	−	2.43364i	−1.33391	−	0.116284i
$439$	−2.54109	−	0.924881i	−0.121280	−	0.0441421i	0.280667	−	0.959805i	$-0.409444\pi$
$439$	−2.54109	−	0.924881i	−0.121280	−	0.0441421i	−0.401947	+	0.915663i	$0.631666\pi$
$440$	25.1707	−	15.3495i	1.19997	−	0.731760i
$441$	−10.4619	+	12.0854i	−0.498184	+	0.575497i
$442$	−6.37801	+	11.2541i	−0.303371	+	0.535301i
$443$	9.93953	+	11.8455i	0.472241	+	0.562795i	0.948609	−	0.316451i	$-0.102491\pi$
$443$	9.93953	+	11.8455i	0.472241	+	0.562795i	−0.476368	+	0.879246i	$0.658047\pi$
$444$	26.6922	−	19.0227i	1.26675	−	0.902777i
$445$	16.4253	+	2.89622i	0.778634	+	0.137294i
$446$	16.7576	+	2.81674i	0.793497	+	0.133377i
$447$	−23.0162	+	15.8537i	−1.08863	+	0.749855i
$448$	−7.59557	+	7.02155i	−0.358857	+	0.331737i
$449$	12.9786	−	22.4796i	0.612498	−	1.06088i	−0.378320	−	0.925675i	$-0.623498\pi$
$449$	12.9786	−	22.4796i	0.612498	−	1.06088i	0.990818	−	0.135203i	$-0.0431687\pi$
$450$	0.797623	−	0.283662i	0.0376003	−	0.0133720i
$451$	−19.6033	+	11.3180i	−0.923085	+	0.532944i
$452$	8.89557	+	3.07741i	0.418413	+	0.144749i
$453$	−1.69373	+	17.7830i	−0.0795785	+	0.835518i
$454$	10.2653	+	8.47452i	0.481773	+	0.397729i
$455$	−13.9320	+	5.07082i	−0.653140	+	0.237724i
$456$	−10.0910	−	35.3429i	−0.472552	−	1.65509i
$457$	1.67588	+	9.50439i	0.0783944	+	0.444597i	0.998588	+	0.0531319i	$0.0169204\pi$
$457$	1.67588	+	9.50439i	0.0783944	+	0.444597i	−0.920193	+	0.391465i	$0.871969\pi$
$458$	−23.2144	+	0.185780i	−1.08474	+	0.00868095i
$459$	9.18355	−	2.23496i	0.428651	−	0.104319i
$460$	−0.0648845	−	4.05360i	−0.00302526	−	0.189000i
$461$	−8.54169	+	1.50613i	−0.397826	+	0.0701475i	−0.368982	−	0.929436i	$-0.620294\pi$
$461$	−8.54169	+	1.50613i	−0.397826	+	0.0701475i	−0.0288440	+	0.999584i	$0.509183\pi$
$462$	13.9853	+	3.74269i	0.650656	+	0.174126i
$463$	−18.1001	+	6.58791i	−0.841184	+	0.306166i	−0.726441	−	0.687229i	$-0.758827\pi$
$463$	−18.1001	+	6.58791i	−0.841184	+	0.306166i	−0.114743	+	0.993395i	$0.536605\pi$
$464$	3.77855	−	4.80756i	0.175415	−	0.223185i
$465$	−3.26015	−	7.13417i	−0.151186	−	0.330839i
$466$	−3.91175	+	11.0211i	−0.181208	+	0.510541i
$467$	−13.0762	+	7.54953i	−0.605093	+	0.349350i	−0.771042	−	0.636784i	$-0.780264\pi$
$467$	−13.0762	+	7.54953i	−0.605093	+	0.349350i	0.165950	+	0.986134i	$0.446931\pi$
$468$	−5.25780	−	29.7104i	−0.243042	−	1.37336i
$469$	−9.20769	−	5.31606i	−0.425171	−	0.245473i
$470$	−19.9701	+	17.0311i	−0.921153	+	0.785587i
$471$	−2.87440	−	36.0457i	−0.132445	−	1.66090i
$472$	−2.39566	+	15.7950i	−0.110269	+	0.727023i
$473$	−2.00935	+	11.3956i	−0.0923902	+	0.523971i
$474$	−17.8244	−	8.30492i	−0.818704	−	0.381458i
$475$	−0.962285	−	1.14681i	−0.0441527	−	0.0526191i
$476$	−2.28638	+	4.11069i	−0.104796	+	0.188413i
$477$	11.1037	+	0.170824i	0.508404	+	0.00782149i
$478$	−19.3127	+	11.3572i	−0.883342	+	0.519467i
$479$	−27.5254	−	10.0184i	−1.25767	−	0.457754i	−0.374682	−	0.927153i	$-0.622248\pi$
$479$	−27.5254	−	10.0184i	−1.25767	−	0.457754i	−0.882986	+	0.469400i	$0.844470\pi$
$480$	−18.7059	−	12.2166i	−0.853803	−	0.557609i
$481$	−36.4490	−	30.5844i	−1.66193	−	1.39453i
$482$	−10.7911	−	28.9260i	−0.491521	−	1.31754i
$483$	1.41852	−	1.39687i	0.0645449	−	0.0635596i
$484$	3.74814	+	19.4327i	0.170370	+	0.883303i
$485$		−	6.37366i		−	0.289413i
$486$	−13.1888	+	17.6651i	−0.598254	+	0.801306i
$487$	20.4526			0.926797			0.463398	−	0.886150i	$-0.346630\pi$
$487$	20.4526			0.926797			0.463398	+	0.886150i	$0.346630\pi$
$488$	−7.98718	−	39.6994i	−0.361563	−	1.79711i
$489$	9.20344	+	9.34612i	0.416194	+	0.422646i
$490$	16.0984	−	6.00567i	0.727253	−	0.271309i
$491$	2.04697	−	2.43948i	0.0923784	−	0.110092i	−0.717875	−	0.696172i	$-0.754885\pi$
$491$	2.04697	−	2.43948i	0.0923784	−	0.110092i	0.810253	+	0.586080i	$0.199330\pi$
$492$	14.1330	+	9.72195i	0.637166	+	0.438299i
$493$	0.951026	−	2.61292i	0.0428321	−	0.117680i
$494$	−45.9925	+	27.0468i	−2.06930	+	1.21690i
$495$	−0.481015	+	31.2664i	−0.0216200	+	1.40532i
$496$	−3.74981	+	7.00336i	−0.168371	+	0.314460i
$497$	9.11160	−	7.64554i	0.408711	−	0.342949i
$498$	−13.9996	+	30.0465i	−0.627335	+	1.34642i
$499$	−36.7668	−	6.48298i	−1.64591	−	0.290218i	−0.727575	−	0.686028i	$-0.759353\pi$
$499$	−36.7668	−	6.48298i	−1.64591	−	0.290218i	−0.918332	+	0.395810i	$0.870464\pi$
$500$	21.6180	+	3.45605i	0.966786	+	0.154559i
$501$	−18.5848	+	1.48201i	−0.830308	+	0.0662114i
$502$	−4.77719	+	4.07412i	−0.213216	+	0.181837i
$503$	−0.252106	+	0.436661i	−0.0112409	+	0.0194697i	−0.871591	−	0.490234i	$-0.836911\pi$
$503$	−0.252106	+	0.436661i	−0.0112409	+	0.0194697i	0.860350	+	0.509703i	$0.170245\pi$
$504$	−1.99826	−	10.7878i	−0.0890095	−	0.480526i
$505$	−1.73347	−	3.00246i	−0.0771383	−	0.133608i
$506$	5.41576	+	1.92224i	0.240760	+	0.0854538i
$507$	−19.3571	+	8.84577i	−0.859681	+	0.392854i
$508$	7.01561	+	5.69797i	0.311267	+	0.252806i
$509$	13.3918	+	36.7936i	0.593580	+	1.63085i	0.763809	+	0.645442i	$0.223327\pi$
$509$	13.3918	+	36.7936i	0.593580	+	1.63085i	−0.170229	+	0.985404i	$0.554451\pi$
$510$	−9.81433	−	2.62647i	−0.434586	−	0.116302i
$511$	2.56858	+	14.5671i	0.113627	+	0.644412i
$512$	1.62830	+	22.5688i	0.0719615	+	0.997407i
$513$	37.4137	+	10.9562i	1.65185	+	0.483727i
$514$	−0.255130	−	31.8801i	−0.0112533	−	1.40617i
$515$	25.4262	−	4.48333i	1.12041	−	0.197559i
$516$	8.45106	−	2.33993i	0.372037	−	0.103010i
$517$	−12.7247	−	34.9608i	−0.559631	−	1.53757i
$518$	−13.3423	−	11.0148i	−0.586229	−	0.483963i
$519$	−5.22668	−	0.497813i	−0.229426	−	0.0218515i
$520$	−10.3578	+	30.7341i	−0.454218	+	1.34778i
$521$	−1.86826	−	3.23593i	−0.0818501	−	0.141768i	0.822195	−	0.569207i	$-0.192750\pi$
$521$	−1.86826	−	3.23593i	−0.0818501	−	0.141768i	−0.904045	+	0.427438i	$0.859416\pi$
$522$	2.17319	+	6.11073i	0.0951177	+	0.267459i
$523$	−24.2166	−	13.9814i	−1.05892	−	0.611365i	−0.133784	−	0.991011i	$-0.542713\pi$
$523$	−24.2166	−	13.9814i	−1.05892	−	0.611365i	−0.925132	+	0.379645i	$0.876046\pi$
$524$	−21.1465	−	24.3976i	−0.923791	−	1.06581i
$525$	−0.253487	−	0.368009i	−0.0110631	−	0.0160612i
$526$	31.1756	+	5.24022i	1.35932	+	0.228484i
$527$	−0.627301	+	3.55760i	−0.0273257	+	0.154972i
$528$	25.4930	−	18.7905i	1.10944	−	0.817754i
$529$	−17.0137	+	14.2761i	−0.739724	+	0.620702i
$530$	−10.3852	−	5.88559i	−0.451104	−	0.255653i
$531$	−12.8113	−	11.0902i	−0.555964	−	0.481275i
$532$	−16.6448	+	9.96843i	−0.721643	+	0.432186i
$533$	8.51684	−	23.3998i	0.368905	−	1.01356i
$534$	17.8489	+	1.55598i	0.772397	+	0.0673339i
$535$	15.5063	+	13.0114i	0.670398	+	0.562530i
$536$	−21.6582	+	8.47709i	−0.935491	+	0.366154i
$537$	−11.7209	+	3.04419i	−0.505796	+	0.131366i
$538$	−3.21332	−	17.4078i	−0.138536	−	0.750505i
$539$			24.3560i			1.04909i
$540$	21.5471	−	9.86272i	0.927239	−	0.424424i
$541$			11.3487i			0.487917i	0.969786	+	0.243959i	$0.0784461\pi$
$541$			11.3487i			0.487917i	−0.969786	+	0.243959i	$0.921554\pi$
$542$	−12.9130	+	2.38361i	−0.554659	+	0.102385i
$543$	−3.41191	+	12.3526i	−0.146419	+	0.530100i
$544$	3.90322	+	9.52053i	0.167349	+	0.408189i
$545$	6.63000	+	5.56323i	0.283998	+	0.238303i
$546$	−14.4322	+	6.73531i	−0.617641	+	0.288245i
$547$	−7.08764	+	19.4731i	−0.303046	+	0.832611i	0.690921	+	0.722930i	$0.257205\pi$
$547$	−7.08764	+	19.4731i	−0.303046	+	0.832611i	−0.993967	+	0.109681i	$0.965017\pi$
$548$	10.3384	+	17.2626i	0.441635	+	0.737420i
$549$	40.1303	+	15.3093i	1.71272	+	0.653387i
$550$	0.636000	−	1.12223i	0.0271191	−	0.0478520i
$551$	8.78590	−	7.37224i	0.374292	−	0.314068i
$552$	−0.450298	−	4.33167i	−0.0191660	−	0.184368i
$553$	−1.80245	+	10.2222i	−0.0766480	+	0.434692i
$554$	−2.64369	+	15.7281i	−0.112320	+	0.668224i
$555$	16.0532	−	33.7462i	0.681422	−	1.43244i
$556$	10.6040	+	12.2342i	0.449709	+	0.518847i
$557$	−32.7009	−	18.8798i	−1.38558	−	0.799965i	−0.392766	−	0.919638i	$-0.628482\pi$
$557$	−32.7009	−	18.8798i	−1.38558	−	0.799965i	−0.992813	+	0.119673i	$0.961815\pi$
$558$	−4.15901	−	7.32799i	−0.176065	−	0.310218i
$559$	−6.36478	−	11.0241i	−0.269201	−	0.466271i
$560$	−3.67678	+	11.2055i	−0.155372	+	0.473517i
$561$	8.35088	−	11.7332i	0.352574	−	0.495375i
$562$	−14.2109	+	17.2138i	−0.599450	+	0.726119i
$563$	4.41394	+	12.1272i	0.186025	+	0.511100i	0.997289	−	0.0735797i	$-0.0234423\pi$
$563$	4.41394	+	12.1272i	0.186025	+	0.511100i	−0.811264	+	0.584680i	$0.801220\pi$
$564$	−19.7699	+	20.1014i	−0.832463	+	0.846421i
$565$	10.5688	−	1.86356i	0.444632	−	0.0784006i
$566$	15.9483	−	0.127631i	0.670357	−	0.00536474i
$567$	10.8074	+	4.31452i	0.453869	+	0.181193i
$568$	−0.624608	−	26.0117i	−0.0262079	−	1.09143i
$569$	−1.87797	−	10.6505i	−0.0787286	−	0.446492i	−0.998535	−	0.0541184i	$-0.982765\pi$
$569$	−1.87797	−	10.6505i	−0.0787286	−	0.446492i	0.919806	−	0.392374i	$-0.128346\pi$
$570$	−29.6410	−	29.6225i	−1.24152	−	1.24075i
$571$	10.2558	+	28.1775i	0.429190	+	1.17919i	0.946305	+	0.323274i	$0.104784\pi$
$571$	10.2558	+	28.1775i	0.429190	+	1.17919i	−0.517115	+	0.855916i	$0.672994\pi$
$572$	−35.6863	−	28.9838i	−1.49212	−	1.21187i
$573$	−36.5442	−	26.0097i	−1.52665	−	1.08657i
$574$	3.02874	−	8.53327i	0.126417	−	0.356172i
$575$	−0.0886903	−	0.153616i	−0.00369864	−	0.00640623i
$576$	−21.1651	−	11.3155i	−0.881878	−	0.471478i
$577$	8.40915	−	14.5651i	0.350078	−	0.606352i	−0.636185	−	0.771536i	$-0.719489\pi$
$577$	8.40915	−	14.5651i	0.350078	−	0.606352i	0.986263	+	0.165184i	$0.0528219\pi$
$578$	−12.5643	−	14.7325i	−0.522606	−	0.612791i
$579$	13.4485	−	28.2706i	0.558899	−	1.17488i
$580$	1.10056	−	6.88415i	0.0456984	−	0.285849i
$581$	17.2315	+	3.03838i	0.714883	+	0.126053i
$582$	−0.598852	−	6.82047i	−0.0248232	−	0.282718i
$583$	12.9622	−	10.8766i	0.536838	−	0.450461i
$584$	28.4028	+	15.5014i	1.17532	+	0.641454i
$585$	−21.7038	−	26.6888i	−0.897342	−	1.10345i
$586$	23.8644	+	40.5808i	0.985828	+	1.67638i
$587$	7.82140	−	21.4891i	0.322824	−	0.886951i	−0.667052	−	0.745012i	$-0.732444\pi$
$587$	7.82140	−	21.4891i	0.322824	−	0.886951i	0.989875	−	0.141939i	$-0.0453338\pi$
$588$	16.6627	−	7.93926i	0.687158	−	0.327409i
$589$	−9.57777	+	11.4143i	−0.394645	+	0.470320i
$590$	6.36640	+	17.0654i	0.262100	+	0.702570i
$591$	−2.07003	+	7.49439i	−0.0851496	+	0.308278i
$592$	−37.0432	+	7.76173i	−1.52247	+	0.319005i
$593$	44.2631			1.81767			0.908833	−	0.417160i	$-0.136974\pi$
$593$	44.2631			1.81767			0.908833	+	0.417160i	$0.136974\pi$
$594$	2.42297	+	33.5035i	0.0994157	+	1.37466i
$595$			5.36286i			0.219856i
$596$	31.6875	−	6.11182i	1.29797	−	0.250350i
$597$	−5.19014	−	19.9834i	−0.212418	−	0.817867i
$598$	−5.92320	+	2.20971i	−0.242218	+	0.0903617i
$599$	6.46594	+	5.42556i	0.264191	+	0.221683i	0.765254	−	0.643728i	$-0.222613\pi$
$599$	6.46594	+	5.42556i	0.264191	+	0.221683i	−0.501063	+	0.865411i	$0.667058\pi$
$600$	−0.975065	−	0.0692973i	−0.0398069	−	0.00282905i
$601$	−10.2943	−	3.74683i	−0.419915	−	0.152836i	0.123416	−	0.992355i	$-0.460615\pi$
$601$	−10.2943	−	3.74683i	−0.419915	−	0.152836i	−0.543331	+	0.839519i	$0.682837\pi$
$602$	−2.34640	−	3.98999i	−0.0956320	−	0.162620i
$603$	4.65691	−	24.2254i	0.189644	−	0.986533i
$604$	10.0263	−	18.0263i	0.407963	−	0.733478i
$605$	14.5039	+	17.2850i	0.589666	+	0.702737i
$606$	−2.13709	−	3.05007i	−0.0868135	−	0.123900i
$607$	5.08144	−	28.8183i	0.206249	−	1.16970i	−0.689212	−	0.724559i	$-0.742043\pi$
$607$	5.08144	−	28.8183i	0.206249	−	1.16970i	0.895462	−	0.445138i	$-0.146846\pi$
$608$	−5.69200	+	42.0579i	−0.230841	+	1.70567i
$609$	2.81938	−	1.94201i	0.114247	−	0.0786942i
$610$	−29.9591	−	35.1291i	−1.21301	−	1.42233i
$611$	35.4449	+	20.4641i	1.43395	+	0.827889i
$612$	−10.7491	−	1.88847i	−0.434508	−	0.0763368i
$613$	−4.66918	+	2.69575i	−0.188586	+	0.108880i	−0.591321	−	0.806437i	$-0.701393\pi$
$613$	−4.66918	+	2.69575i	−0.188586	+	0.108880i	0.402734	+	0.915317i	$0.368060\pi$
$614$	15.1120	+	5.36374i	0.609869	+	0.216463i
$615$	19.4695	+	1.85437i	0.785088	+	0.0747753i
$616$	−13.0603	−	10.4351i	−0.526216	−	0.420440i
$617$	38.2253	−	13.9129i	1.53889	−	0.560111i	0.573113	−	0.819477i	$-0.305736\pi$
$617$	38.2253	−	13.9129i	1.53889	−	0.560111i	0.965779	+	0.259366i	$0.0835135\pi$
$618$	26.7874	−	7.18660i	1.07755	−	0.289088i
$619$	15.6107	−	2.75259i	0.627447	−	0.110636i	0.149122	−	0.988819i	$-0.452355\pi$
$619$	15.6107	−	2.75259i	0.627447	−	0.110636i	0.478325	+	0.878183i	$0.341244\pi$
$620$	0.144957	+	9.05607i	0.00582162	+	0.363700i
$621$	4.14025	+	2.04823i	0.166143	+	0.0821925i
$622$	−0.0566840	−	7.08301i	−0.00227282	−	0.284003i
$623$	−1.64226	−	9.31370i	−0.0657956	−	0.373146i
$624$	−8.19618	+	33.8618i	−0.328110	+	1.35556i
$625$	24.3924	−	8.87811i	0.975697	−	0.355125i
$626$	5.59080	−	6.77218i	0.223453	−	0.270671i
$627$	54.0279	−	24.6895i	2.15767	−	0.986004i
$628$	−13.6510	+	39.4596i	−0.544733	+	1.57461i
$629$	−14.9050	+	8.60542i	−0.594302	+	0.343121i
$630$	−7.96946	−	9.64125i	−0.317511	−	0.384117i
$631$	5.53855	−	9.59305i	0.220486	−	0.381893i	−0.734470	−	0.678642i	$-0.762569\pi$
$631$	5.53855	−	9.59305i	0.220486	−	0.381893i	0.954956	+	0.296748i	$0.0959023\pi$
$632$	15.0087	+	17.0387i	0.597013	+	0.677762i
$633$	2.44456	+	30.6554i	0.0971626	+	1.21844i
$634$	3.75253	−	22.3249i	0.149032	−	0.886636i
$635$	10.1479	+	1.78935i	0.402707	+	0.0710082i
$636$	−11.6662	−	5.32242i	−0.462596	−	0.211048i
$637$	−17.2227	−	20.5252i	−0.682388	−	0.813239i
$638$	8.59760	+	4.87251i	0.340382	+	0.192904i
$639$	23.6851	+	14.1648i	0.936968	+	0.560350i
$640$	14.1297	+	21.5845i	0.558526	+	0.853204i
$641$	−14.4922	−	5.27474i	−0.572408	−	0.208340i	0.0395664	−	0.999217i	$-0.487402\pi$
$641$	−14.4922	−	5.27474i	−0.572408	−	0.208340i	−0.611975	+	0.790877i	$0.709625\pi$
$642$	17.8159	+	12.4666i	0.703138	+	0.492016i
$643$	10.7001	−	12.7519i	0.421970	−	0.502884i	−0.512618	−	0.858617i	$-0.671324\pi$
$643$	10.7001	−	12.7519i	0.421970	−	0.502884i	0.934588	+	0.355733i	$0.115769\pi$
$644$	−2.14733	+	0.820715i	−0.0846165	+	0.0323407i
$645$	7.12366	−	7.01491i	0.280494	−	0.276212i
$646$	3.50336	+	18.9791i	0.137838	+	0.746724i
$647$	9.34488			0.367385			0.183693	−	0.982984i	$-0.441195\pi$
$647$	9.34488			0.367385			0.183693	+	0.982984i	$0.441195\pi$
$648$	22.1309	−	12.5786i	0.869385	−	0.494136i
$649$	−25.8190			−1.01348
$650$	0.257586	+	1.39545i	0.0101034	+	0.0547341i
$651$	−3.16909	+	3.12071i	−0.124206	+	0.122310i
$652$	−5.40740	−	14.1479i	−0.211770	−	0.554076i
$653$	−19.5285	+	23.2732i	−0.764211	+	0.910751i	−0.998106	−	0.0615108i	$-0.980408\pi$
$653$	−19.5285	+	23.2732i	−0.764211	+	0.910751i	0.233896	+	0.972262i	$0.424853\pi$
$654$	7.61749	+	5.33030i	0.297868	+	0.208431i
$655$	−34.5907	−	12.5900i	−1.35157	−	0.491931i
$656$	−10.4478	−	16.8282i	−0.407918	−	0.657031i
$657$	−29.9828	+	16.7010i	−1.16974	+	0.651567i
$658$	12.9478	+	7.33787i	0.504756	+	0.286060i
$659$	18.3717	+	21.8946i	0.715661	+	0.852892i	0.994202	−	0.107533i	$-0.0342951\pi$
$659$	18.3717	+	21.8946i	0.715661	+	0.852892i	−0.278541	+	0.960424i	$0.589851\pi$
$660$	14.9871	−	32.8503i	0.583374	−	1.27870i
$661$	1.85841	+	0.327688i	0.0722838	+	0.0127456i	0.209673	−	0.977772i	$-0.432760\pi$
$661$	1.85841	+	0.327688i	0.0722838	+	0.0127456i	−0.137389	+	0.990517i	$0.543871\pi$
$662$	0.639971	−	3.80738i	0.0248732	−	0.147978i
$663$	1.25937	+	15.7928i	0.0489099	+	0.613343i
$664$	28.7220	−	25.3000i	1.11463	−	0.981832i
$665$	−11.0601	+	19.1566i	−0.428891	+	0.742861i
$666$	14.0079	−	37.6202i	0.542796	−	1.45775i
$667$	1.17688	−	0.679472i	0.0455690	−	0.0263093i
$668$	20.3450	+	7.03830i	0.787170	+	0.272320i
$669$	18.9289	−	8.65009i	0.731835	−	0.334432i
$670$	−16.8818	+	20.4490i	−0.652199	+	0.790015i
$671$	61.4988	−	22.3837i	2.37414	−	0.864115i
$672$	−2.88170	+	12.3364i	−0.111164	+	0.475889i
$673$	−0.709316	−	4.02273i	−0.0273421	−	0.155065i	0.968080	−	0.250642i	$-0.0806416\pi$
$673$	−0.709316	−	4.02273i	−0.0273421	−	0.155065i	−0.995422	+	0.0955768i	$0.969530\pi$
$674$	0.237246	+	29.6453i	0.00913836	+	1.14189i
$675$	0.614134	−	0.835367i	0.0236380	−	0.0321533i
$676$	24.5718	−	0.393313i	0.945070	−	0.0151274i
$677$	10.8614	−	1.91516i	0.417438	−	0.0736057i	0.0390158	−	0.999239i	$-0.487578\pi$
$677$	10.8614	−	1.91516i	0.417438	−	0.0736057i	0.378423	+	0.925633i	$0.376467\pi$
$678$	11.1346	−	2.98722i	0.427621	−	0.114723i
$679$	−3.39613	+	1.23609i	−0.130331	+	0.0474367i
$680$	9.16521	+	7.32290i	0.351470	+	0.280820i
$681$	16.2296	+	1.54578i	0.621920	+	0.0592345i
$682$	−12.0993	−	4.29443i	−0.463304	−	0.164442i
$683$	32.8628	−	18.9733i	1.25746	−	0.725994i	0.284879	−	0.958563i	$-0.408047\pi$
$683$	32.8628	−	18.9733i	1.25746	−	0.725994i	0.972580	+	0.232569i	$0.0747132\pi$
$684$	−34.5021	−	28.9142i	−1.31922	−	1.10556i
$685$	19.8676	+	11.4706i	0.759102	+	0.438268i
$686$	−14.6279	−	17.1522i	−0.558496	−	0.654874i
$687$	−23.4154	+	16.1287i	−0.893353	+	0.615347i
$688$	−10.0229	−	1.43824i	−0.382121	−	0.0548325i
$689$	−3.23237	+	18.3317i	−0.123144	+	0.698382i
$690$	−2.84922	−	4.06641i	−0.108468	−	0.154806i
$691$	−13.3549	−	15.9157i	−0.508043	−	0.605462i	0.449667	−	0.893196i	$-0.351543\pi$
$691$	−13.3549	−	15.9157i	−0.508043	−	0.605462i	−0.957710	+	0.287734i	$0.907098\pi$
$692$	5.29818	+	2.94686i	0.201406	+	0.112023i
$693$	16.7532	−	5.80741i	0.636401	−	0.220605i
$694$	−17.9484	−	30.5208i	−0.681311	−	1.15855i
$695$	17.3456	+	6.31328i	0.657956	+	0.239476i
$696$	0.530899	−	7.47015i	0.0201237	−	0.283155i
$697$	−6.90003	−	5.78981i	−0.261357	−	0.219305i
$698$	2.27146	−	0.847391i	0.0859761	−	0.0320742i
$699$	3.60054	+	13.8631i	0.136185	+	0.524349i
$700$	0.0977225	+	0.506654i	0.00369356	+	0.0191497i
$701$		−	42.7784i		−	1.61572i	−0.589375	−	0.807860i	$-0.700626\pi$
$701$		−	42.7784i		−	1.61572i	0.589375	−	0.807860i	$-0.299374\pi$
$702$	−25.7329	−	26.5206i	−0.971227	−	1.00095i
$703$	−70.9894			−2.67741
$704$	−35.6673	+	8.07142i	−1.34426	+	0.304203i
$705$	−8.55830	+	30.9847i	−0.322324	+	1.16695i
$706$	11.6719	+	31.2869i	0.439277	+	1.17750i
$707$	−1.26364	+	1.50594i	−0.0475240	+	0.0566369i
$708$	8.41612	+	17.6635i	0.316297	+	0.663836i
$709$	9.51434	−	26.1404i	0.357318	−	0.981724i	−0.622638	−	0.782510i	$-0.713939\pi$
$709$	9.51434	−	26.1404i	0.357318	−	0.981724i	0.979956	−	0.199214i	$-0.0638388\pi$
$710$	−15.0377	−	25.5713i	−0.564355	−	0.959672i
$711$	−23.7793	+	3.81675i	−0.891794	+	0.143139i
$712$	−18.1597	−	9.91106i	−0.680565	−	0.371433i
$713$	−1.35245	+	1.13484i	−0.0506496	+	0.0425000i
$714$	0.503880	+	5.73882i	0.0188572	+	0.214770i
$715$	−51.6193	−	9.10188i	−1.93045	−	0.340391i
$716$	13.8079	+	2.20745i	0.516024	+	0.0824963i
$717$	−11.7876	+	24.7791i	−0.440214	+	0.925392i
$718$	−0.0304833	−	0.0357438i	−0.00113763	−	0.00133395i
$719$	17.1489	−	29.7028i	0.639546	−	1.10773i	−0.345986	−	0.938240i	$-0.612456\pi$
$719$	17.1489	−	29.7028i	0.639546	−	1.10773i	0.985532	−	0.169487i	$-0.0542112\pi$
$720$	−27.3592	+	0.454954i	−1.01962	+	0.0169551i
$721$	−7.31997	−	12.6786i	−0.272610	−	0.472174i
$722$	−17.6395	+	49.6979i	−0.656473	+	1.84957i
$723$	−30.8059	−	21.9256i	−1.14569	−	0.815422i
$724$	9.32910	−	11.4864i	0.346713	−	0.426890i
$725$	−0.104326	−	0.286633i	−0.00387456	−	0.0106453i
$726$	17.1447	+	17.1340i	0.636299	+	0.635904i
$727$	−7.66167	−	43.4515i	−0.284156	−	1.61153i	−0.708285	−	0.705926i	$-0.750531\pi$
$727$	−7.66167	−	43.4515i	−0.284156	−	1.61153i	0.424130	−	0.905601i	$-0.360580\pi$
$728$	18.3850	−	0.441471i	0.681394	−	0.0163620i
$729$	−1.24560	+	26.9713i	−0.0461332	+	0.998935i
$730$	36.8905	−	0.295228i	1.36538	−	0.0109269i
$731$	−4.53456	+	0.799565i	−0.167717	+	0.0295730i
$732$	−35.3600	−	34.7769i	−1.30694	−	1.28539i
$733$	−6.41336	−	17.6206i	−0.236883	−	0.650831i	−0.999990	−	0.00455803i	$-0.998549\pi$
$733$	−6.41336	−	17.6206i	−0.236883	−	0.650831i	0.763107	−	0.646273i	$-0.223673\pi$
$734$	23.1342	−	28.0227i	0.853900	−	1.03434i
$735$	12.2025	−	17.1447i	0.450094	−	0.632392i
$736$	−1.52952	+	4.79049i	−0.0563789	+	0.176580i
$737$	−18.7942	−	32.5525i	−0.692294	−	1.19909i
$738$	21.0087	+	0.155058i	0.773339	+	0.00570778i
$739$	31.6248	+	18.2586i	1.16334	+	0.671652i	0.952101	−	0.305783i	$-0.0989183\pi$
$739$	31.6248	+	18.2586i	1.16334	+	0.671652i	0.211235	+	0.977435i	$0.432252\pi$
$740$	−32.6075	+	28.2625i	−1.19867	+	1.03895i
$741$	−28.0717	+	59.0106i	−1.03124	+	2.16781i
$742$	−1.12199	+	6.67505i	−0.0411895	+	0.245049i
$743$	0.0717778	−	0.407072i	0.00263327	−	0.0149340i	−0.983463	−	0.181110i	$-0.942031\pi$
$743$	0.0717778	−	0.407072i	0.00263327	−	0.0149340i	0.986096	+	0.166176i	$0.0531420\pi$
$744$	1.00600	+	9.67731i	0.0368819	+	0.354787i
$745$	28.1855	−	23.6504i	1.03264	−	0.866485i
$746$	−4.56071	+	8.04743i	−0.166979	+	0.294637i
$747$	6.43387	+	40.0846i	0.235403	+	1.46662i
$748$	−14.2666	+	8.54416i	−0.521640	+	0.312406i
$749$	3.92569	−	10.7857i	0.143442	−	0.394103i
$750$	24.2971	−	11.3391i	0.887203	−	0.414046i
$751$	10.6301	+	8.91971i	0.387898	+	0.325485i	0.815794	−	0.578343i	$-0.196301\pi$
$751$	10.6301	+	8.91971i	0.387898	+	0.325485i	−0.427896	+	0.903828i	$0.640745\pi$
$752$	30.2205	−	12.1082i	1.10203	−	0.441540i
$753$	−2.04729	+	7.41206i	−0.0746073	+	0.270110i
$754$	−10.6908	+	1.97342i	−0.389336	+	0.0718676i
$755$		−	23.5173i		−	0.855883i
$756$	−9.43401	−	9.56835i	−0.343112	−	0.347997i
$757$			5.96005i			0.216622i	0.994117	+	0.108311i	$0.0345442\pi$
$757$			5.96005i			0.216622i	−0.994117	+	0.108311i	$0.965456\pi$
$758$	−5.89413	−	31.9309i	−0.214084	−	1.15978i
$759$	6.81232	−	1.76931i	0.247272	−	0.0642219i
$760$	17.6366	+	45.0599i	0.639746	+	1.63449i
$761$	−16.9390	−	14.2135i	−0.614037	−	0.515238i	0.281886	−	0.959448i	$-0.409040\pi$
$761$	−16.9390	−	14.2135i	−0.614037	−	0.515238i	−0.895923	+	0.444210i	$0.853484\pi$
$762$	11.0274	+	0.961319i	0.399482	+	0.0348249i
$763$	1.67850	−	4.61163i	0.0607656	−	0.166952i
$764$	26.6117	+	44.4349i	0.962776	+	1.60760i
$765$	−11.7567	+	4.07540i	−0.425065	+	0.147347i
$766$	15.4150	+	8.73615i	0.556968	+	0.315650i
$767$	21.7580	−	18.2572i	0.785637	−	0.659228i
$768$	17.1483	+	21.7701i	0.618785	+	0.785561i
$769$	−4.94612	+	28.0509i	−0.178362	+	1.01154i	0.755830	+	0.654768i	$0.227234\pi$
$769$	−4.94612	+	28.0509i	−0.178362	+	1.01154i	−0.934192	+	0.356772i	$0.883877\pi$
$770$	−18.7959	−	3.15935i	−0.677359	−	0.113855i
$771$	−22.1493	−	32.1561i	−0.797688	−	1.15807i
$772$	−27.3166	+	23.6766i	−0.983147	+	0.852140i
$773$	−17.4609	−	10.0810i	−0.628024	−	0.362590i	0.151962	−	0.988386i	$-0.451441\pi$
$773$	−17.4609	−	10.0810i	−0.628024	−	0.362590i	−0.779986	+	0.625796i	$0.784774\pi$
$774$	6.96395	−	8.17600i	0.250314	−	0.293880i
$775$	0.198141	+	0.343191i	0.00711745	+	0.0123278i
$776$	−2.52486	+	7.49189i	−0.0906371	+	0.268943i
$777$	−21.0945	−	2.00914i	−0.756762	−	0.0720775i
$778$	28.6106	+	23.6195i	1.02574	+	0.846801i
$779$	−12.7069	−	34.9119i	−0.455272	−	1.25085i
$780$	10.5993	+	38.2812i	0.379516	+	1.37069i
$781$	41.4120	−	7.30205i	1.48184	−	0.261288i
$782$	0.0183000	+	2.28669i	0.000654406	+	0.0817720i
$783$	6.39990	+	4.70499i	0.228714	+	0.168143i
$784$	−21.3019	+	0.682119i	−0.760782	+	0.0243614i
$785$	8.26650	+	46.8817i	0.295044	+	1.67328i
$786$	−38.1985	−	10.2225i	−1.36250	−	0.364626i
$787$	5.28733	+	14.5268i	0.188473	+	0.517826i	0.997556	−	0.0698687i	$-0.0222580\pi$
$787$	5.28733	+	14.5268i	0.188473	+	0.517826i	−0.809083	+	0.587694i	$0.800036\pi$
$788$	5.66002	−	6.96889i	0.201630	−	0.248256i
$789$	35.2151	−	16.0925i	1.25369	−	0.572907i
$790$	24.3969	+	8.65927i	0.868001	+	0.308083i
$791$	−3.04265	−	5.27003i	−0.108184	−	0.187381i
$792$	12.9513	−	36.5614i	0.460203	−	1.29915i
$793$	−35.9980	+	62.3503i	−1.27833	+	2.21413i
$794$	−28.8269	+	24.5844i	−1.02303	+	0.872467i
$795$	−14.5735	+	1.16214i	−0.516870	+	0.0412169i
$796$	−3.76356	+	23.5415i	−0.133396	+	0.834406i
$797$	−42.6976	−	7.52875i	−1.51243	−	0.266682i	−0.644976	−	0.764203i	$-0.723133\pi$
$797$	−42.6976	−	7.52875i	−1.51243	−	0.266682i	−0.867452	+	0.497521i	$0.834244\pi$
$798$	−10.0355	+	21.5387i	−0.355253	+	0.762462i
$799$	11.3409	−	9.51613i	0.401211	−	0.336656i
$800$	0.999319	+	0.524819i	0.0353313	+	0.0185552i
$801$	19.1699	−	10.6780i	0.677336	−	0.377289i
$802$	21.2589	−	12.5017i	0.750679	−	0.441452i
$803$	−17.8858	+	49.1409i	−0.631177	+	1.73414i
$804$	−16.1439	+	23.4687i	−0.569351	+	0.827678i
$805$	−1.68471	+	2.00776i	−0.0593782	+	0.0707642i
$806$	13.2329	−	4.93667i	0.466110	−	0.173887i
$807$	−15.2119	−	15.4478i	−0.535486	−	0.543787i
$808$	0.848206	+	4.21592i	0.0298398	+	0.148315i
$809$	−18.8726			−0.663527			−0.331763	−	0.943363i	$-0.607644\pi$
$809$	−18.8726			−0.663527			−0.331763	+	0.943363i	$0.607644\pi$
$810$	15.0798	−	24.7977i	0.529849	−	0.871302i
$811$			26.5177i			0.931161i	0.885005	+	0.465581i	$0.154154\pi$
$811$			26.5177i			0.931161i	−0.885005	+	0.465581i	$0.845846\pi$
$812$	−3.88157	+	0.748670i	−0.136216	+	0.0262732i
$813$	−11.4590	+	11.2841i	−0.401885	+	0.395750i
$814$	−21.3798	−	57.3092i	−0.749360	−	2.00869i
$815$	−13.2284	−	11.0999i	−0.463370	−	0.388814i
$816$	10.4958	+	6.97512i	0.367425	+	0.244178i
$817$	−17.8468	−	6.49571i	−0.624381	−	0.227256i
$818$	15.9496	−	9.37946i	0.557663	−	0.327945i
$819$	−10.0116	+	16.7406i	−0.349835	+	0.584962i
$820$	−19.7359	−	10.9772i	−0.689207	−	0.383339i
$821$	3.82534	+	4.55887i	0.133505	+	0.159106i	0.828655	−	0.559759i	$-0.189106\pi$
$821$	3.82534	+	4.55887i	0.133505	+	0.159106i	−0.695150	+	0.718865i	$0.744662\pi$
$822$	22.3381	+	10.4080i	0.779131	+	0.363020i
$823$	−1.21437	+	6.88704i	−0.0423303	+	0.240067i	−0.998630	−	0.0523200i	$-0.983338\pi$
$823$	−1.21437	+	6.88704i	−0.0423303	+	0.240067i	0.956300	+	0.292387i	$0.0944495\pi$
$824$	−31.6631	−	4.80242i	−1.10304	−	0.167300i
$825$	−0.125582	−	1.57482i	−0.00437219	−	0.0548283i
$826$	7.85838	−	6.70186i	0.273428	−	0.233188i
$827$	−20.7782	−	11.9963i	−0.722529	−	0.417152i	0.0931541	−	0.995652i	$-0.470305\pi$
$827$	−20.7782	−	11.9963i	−0.722529	−	0.417152i	−0.815683	+	0.578500i	$0.803638\pi$
$828$	−3.43103	−	4.08378i	−0.119236	−	0.141921i
$829$	−13.2292	+	7.63790i	−0.459470	+	0.265275i	−0.711822	−	0.702360i	$-0.752130\pi$
$829$	−13.2292	+	7.63790i	−0.459470	+	0.265275i	0.252351	+	0.967636i	$0.418796\pi$
$830$	14.5969	−	41.1256i	0.506665	−	1.42749i
$831$	8.11866	+	17.7660i	0.281633	+	0.616297i
$832$	24.3500	−	32.0231i	0.844183	−	1.11020i
$833$	−9.10730	+	3.31479i	−0.315549	+	0.114851i
$834$	19.1548	+	5.12611i	0.663275	+	0.177503i
$835$	24.1717	−	4.26213i	0.836497	−	0.147497i
$836$	−68.5826	+	1.09778i	−2.37198	+	0.0379675i
$837$	−9.24966	−	4.57590i	−0.319715	−	0.158166i
$838$	−10.6369	+	0.0851253i	−0.367446	+	0.00294060i
$839$	5.29503	+	30.0296i	0.182805	+	1.03674i	0.928744	+	0.370722i	$0.120890\pi$
$839$	5.29503	+	30.0296i	0.182805	+	1.03674i	−0.745939	+	0.666014i	$0.767999\pi$
$840$	3.96544	+	13.8887i	0.136821	+	0.479206i
$841$	−25.0551	+	9.11933i	−0.863970	+	0.314459i
$842$	−24.2142	−	19.9901i	−0.834477	−	0.688905i
$843$	−2.59211	+	27.2154i	−0.0892771	+	0.937347i
$844$	11.6096	−	33.5588i	0.399619	−	1.15514i
$845$	24.2648	−	14.0093i	0.834733	−	0.481933i
$846$	−6.24702	+	33.9610i	−0.214777	+	1.16760i
$847$	6.39728	−	11.0804i	0.219813	−	0.380728i
$848$	9.87571	+	11.0322i	0.339133	+	0.378846i
$849$	16.0864	−	11.0804i	0.552083	−	0.380278i
$850$	0.506186	+	0.0850833i	0.0173620	+	0.00291833i
$851$	−8.28351	−	1.46061i	−0.283955	−	0.0500689i
$852$	−18.4945	−	25.9510i	−0.633611	−	0.889066i
$853$	33.1306	+	39.4836i	1.13437	+	1.35189i	0.927632	+	0.373496i	$0.121841\pi$
$853$	33.1306	+	39.4836i	1.13437	+	1.35189i	0.206740	+	0.978396i	$0.433715\pi$
$854$	−12.9079	+	22.7762i	−0.441700	+	0.779384i
$855$	−50.4009	−	9.68871i	−1.72367	−	0.331347i
$856$	−13.0725	−	21.4368i	−0.446810	−	0.732696i
$857$	−5.66779	−	2.06291i	−0.193608	−	0.0704676i	0.243396	−	0.969927i	$-0.421738\pi$
$857$	−5.66779	−	2.06291i	−0.193608	−	0.0704676i	−0.437004	+	0.899459i	$0.643961\pi$
$858$	−56.0932	−	4.88994i	−1.91499	−	0.166940i
$859$	−1.74563	+	2.08036i	−0.0595602	+	0.0709810i	−0.795002	−	0.606607i	$-0.792530\pi$
$859$	−1.74563	+	2.08036i	−0.0595602	+	0.0709810i	0.735442	+	0.677588i	$0.236975\pi$
$860$	−10.7836	+	4.12155i	−0.367719	+	0.140544i
$861$	−2.78779	−	10.7337i	−0.0950076	−	0.365805i
$862$	20.1764	−	3.72436i	0.687209	−	0.126852i
$863$	−0.498885			−0.0169822			−0.00849112	−	0.999964i	$-0.502703\pi$
$863$	−0.498885			−0.0169822			−0.00849112	+	0.999964i	$0.502703\pi$
$864$	−29.2344	+	3.05745i	−0.994576	+	0.104016i
$865$	6.91208			0.235018
$866$	−32.3672	+	5.97467i	−1.09988	+	0.203028i
$867$	−22.8583	−	6.31368i	−0.776307	−	0.214424i
$868$	4.79730	−	1.83354i	0.162831	−	0.0622346i
$869$	−23.5882	+	28.1113i	−0.800175	+	0.953611i
$870$	−3.61089	−	7.73728i	−0.122420	−	0.262318i
$871$	38.8568	+	14.1427i	1.31661	+	0.479208i
$872$	−5.58939	−	9.16568i	−0.189281	−	0.310389i
$873$	−5.29063	−	6.50580i	−0.179061	−	0.220188i
$874$	−4.65058	+	8.20600i	−0.157308	+	0.277572i
$875$	−9.09755	−	10.8420i	−0.307553	−	0.366528i
$876$	39.4489	−	3.78206i	1.33286	−	0.127784i
$877$	11.0278	+	1.94450i	0.372383	+	0.0656612i	0.356708	−	0.934216i	$-0.383899\pi$
$877$	11.0278	+	1.94450i	0.372383	+	0.0656612i	0.0156751	+	0.999877i	$0.495010\pi$
$878$	3.77137	+	0.633918i	0.127278	+	0.0213937i
$879$	52.0671	+	24.7686i	1.75618	+	0.835425i
$880$	−31.0649	+	27.8085i	−1.04720	+	0.937425i
$881$	−12.4891	+	21.6317i	−0.420768	+	0.728792i	−0.996015	−	0.0891883i	$-0.971573\pi$
$881$	−12.4891	+	21.6317i	−0.420768	+	0.728792i	0.575247	+	0.817980i	$0.304906\pi$
$882$	11.4470	−	19.4931i	0.385441	−	0.656368i
$883$	−27.0133	+	15.5962i	−0.909071	+	0.524852i	−0.880132	−	0.474729i	$-0.842546\pi$
$883$	−27.0133	+	15.5962i	−0.909071	+	0.524852i	−0.0289389	+	0.999581i	$0.509213\pi$
$884$	5.98094	−	17.2886i	0.201161	−	0.581477i
$885$	18.1745	+	12.9354i	0.610929	+	0.434818i
$886$	−16.8640	−	13.9221i	−0.566556	−	0.467722i
$887$	−11.7648	+	4.28205i	−0.395025	+	0.143777i	−0.531892	−	0.846812i	$-0.678519\pi$
$887$	−11.7648	+	4.28205i	−0.395025	+	0.143777i	0.136867	+	0.990589i	$0.456297\pi$
$888$	−32.2379	+	33.3075i	−1.08183	+	1.11772i
$889$	−1.01462	−	5.75421i	−0.0340293	−	0.192990i
$890$	−23.5865	+	0.188758i	−0.790620	+	0.00632719i
$891$	25.4625	+	32.3139i	0.853027	+	1.08256i
$892$	−24.0283	+	0.384612i	−0.804526	+	0.0128778i
$893$	60.1361	−	10.6036i	2.01238	−	0.354837i
$894$	27.9393	−	27.9566i	0.934428	−	0.935010i
$895$	14.9811	−	5.45269i	0.500764	−	0.182263i
$896$	8.76078	−	11.7149i	0.292677	−	0.391367i
$897$	−4.48973	+	6.30817i	−0.149908	+	0.210624i
$898$	−12.2788	+	34.5946i	−0.409748	+	1.15444i
$899$	−2.62925	+	1.51800i	−0.0876903	+	0.0506280i
$900$	−1.03645	+	0.599254i	−0.0345483	+	0.0199751i
$901$	5.83112	+	3.36660i	0.194263	+	0.112158i
$902$	24.3573	−	20.7726i	0.811008	−	0.691651i
$903$	−5.11935	−	2.43530i	−0.170361	−	0.0810418i
$904$	−13.1612	−	1.99620i	−0.437737	−	0.0663925i
$905$	2.92964	−	16.6148i	0.0973847	−	0.552296i
$906$	−2.20962	−	25.1660i	−0.0734098	−	0.836083i
$907$	−12.8068	−	15.2625i	−0.425242	−	0.506784i	0.510301	−	0.859996i	$-0.329534\pi$
$907$	−12.8068	−	15.2625i	−0.425242	−	0.506784i	−0.935543	+	0.353212i	$0.885090\pi$
$908$	−16.4516	−	9.15045i	−0.545966	−	0.303668i
$909$	−4.26168	−	1.62579i	−0.141351	−	0.0539241i
$910$	18.0737	−	10.6286i	0.599137	−	0.352335i
$911$	4.64046	+	1.68899i	0.153745	+	0.0559587i	0.417746	−	0.908564i	$-0.362820\pi$
$911$	4.64046	+	1.68899i	0.153745	+	0.0559587i	−0.264001	+	0.964522i	$0.585042\pi$
$912$	23.1067	+	46.5616i	0.765138	+	1.54181i
$913$	47.3871	+	39.7625i	1.56828	+	1.31595i
$914$	−4.77058	−	12.7877i	−0.157797	−	0.422980i
$915$	−54.5046	−	15.0547i	−1.80187	−	0.497694i
$916$	32.2370	−	6.21781i	1.06514	−	0.205442i
$917$			20.8729i			0.689283i
$918$	−12.1980	+	5.46573i	−0.402594	+	0.180396i
$919$	41.0836			1.35522			0.677612	−	0.735420i	$-0.263015\pi$
$919$	41.0836			1.35522			0.677612	+	0.735420i	$0.263015\pi$
$920$	1.13085	+	5.62076i	0.0372829	+	0.185311i
$921$	19.0089	−	4.93703i	0.626364	−	0.162681i
$922$	11.4924	−	4.28737i	0.378484	−	0.141197i
$923$	−29.7351	+	35.4369i	−0.978743	+	1.16642i
$924$	−20.4104	−	1.61482i	−0.671454	−	0.0531236i
$925$	−0.645733	+	1.77414i	−0.0212316	+	0.0583333i
$926$	23.4810	−	13.8085i	0.771633	−	0.453774i
$927$	22.2319	−	25.6820i	0.730190	−	0.843508i
$928$	−4.02073	+	7.65596i	−0.131987	+	0.251319i
$929$	22.2060	−	18.6330i	0.728555	−	0.611330i	−0.201183	−	0.979554i	$-0.564478\pi$
$929$	22.2060	−	18.6330i	0.728555	−	0.611330i	0.929737	+	0.368224i	$0.120034\pi$
$930$	6.36539	+	9.08470i	0.208729	+	0.297899i
$931$	−39.3683	−	6.94169i	−1.29024	−	0.227505i
$932$	2.61089	−	16.3314i	0.0855224	−	0.534953i
$933$	−4.92106	−	7.14433i	−0.161108	−	0.233895i
$934$	16.2472	−	13.8561i	0.531625	−	0.453385i
$935$	−9.47984	+	16.4196i	−0.310024	+	0.536977i
$936$	14.9392	+	39.9690i	0.488301	+	1.30643i
$937$	−12.6728	−	21.9500i	−0.414004	−	0.717075i	0.581320	−	0.813675i	$-0.302537\pi$
$937$	−12.6728	−	21.9500i	−0.414004	−	0.717075i	−0.995323	+	0.0966000i	$0.969203\pi$
$938$	14.1700	+	5.02941i	0.462667	+	0.164216i
$939$	1.01978	−	10.7070i	0.0332793	−	0.349409i
$940$	23.4007	−	28.8121i	0.763247	−	0.939746i
$941$	−10.2032	−	28.0332i	−0.332616	−	0.913856i	−0.987429	−	0.158064i	$-0.949475\pi$
$941$	−10.2032	−	28.0332i	−0.332616	−	0.913856i	0.654813	−	0.755791i	$-0.272748\pi$
$942$	13.2509	+	49.3915i	0.431737	+	1.60926i
$943$	−0.764413	−	4.33520i	−0.0248927	−	0.141174i
$944$	−0.723090	−	22.5814i	−0.0235346	−	0.734961i
$945$	−14.7024	−	4.30545i	−0.478271	−	0.140056i
$946$	−0.130957	−	16.3639i	−0.00425779	−	0.532037i
$947$	1.18920	−	0.209688i	0.0386438	−	0.00681395i	−0.154293	−	0.988025i	$-0.549310\pi$
$947$	1.18920	−	0.209688i	0.0386438	−	0.00681395i	0.192937	+	0.981211i	$0.438199\pi$
$948$	26.9208	+	6.97405i	0.874346	+	0.226506i
$949$	−19.6760	−	54.0593i	−0.638709	−	1.75484i
$950$	1.63267	+	1.34785i	0.0529708	+	0.0437302i
$951$	−11.5238	−	25.2176i	−0.373686	−	0.817736i
$952$	2.12444	−	6.30375i	0.0688536	−	0.204306i
$953$	−0.148926	−	0.257948i	−0.00482419	−	0.00835575i	0.863603	−	0.504172i	$-0.168202\pi$
$953$	−0.148926	−	0.257948i	−0.00482419	−	0.00835575i	−0.868427	+	0.495816i	$0.834869\pi$
$954$	−15.4860	+	2.61290i	−0.501377	+	0.0845958i
$955$	51.1404	+	29.5259i	1.65486	+	0.955436i
$956$	23.9430	−	20.7525i	0.774371	−	0.671185i
$957$	12.0650	−	0.962103i	0.390006	−	0.0311004i
$958$	40.8520	+	6.86668i	1.31987	+	0.221852i
$959$	2.25888	−	12.8108i	0.0729432	−	0.413681i
$960$	29.1508	+	12.1878i	0.940837	+	0.393360i
$961$	−20.7259	+	17.3911i	−0.668577	+	0.561003i
$962$	58.5417	+	33.1773i	1.88746	+	1.06968i
$963$	26.6283	+	0.409660i	0.858084	+	0.0132011i
$964$	22.4331	+	37.4576i	0.722520	+	1.20643i
$965$	−14.0963	+	38.7293i	−0.453776	+	1.24674i
$966$	−1.61417	+	2.30680i	−0.0519351	+	0.0742201i
$967$	−25.2691	−	21.2033i	−0.812601	−	0.681853i	0.138626	−	0.990345i	$-0.455731\pi$
$967$	−25.2691	−	21.2033i	−0.812601	−	0.681853i	−0.951227	+	0.308492i	$0.900176\pi$
$968$	−10.2012	−	26.0632i	−0.327880	−	0.837702i
$969$	16.5850	+	16.8422i	0.532788	+	0.541048i
$970$	1.63620	+	8.86397i	0.0525353	+	0.284605i
$971$		−	36.2843i		−	1.16442i	−0.813039	−	0.582210i	$-0.802188\pi$
$971$		−	36.2843i		−	1.16442i	0.813039	−	0.582210i	$-0.197812\pi$
$972$	13.8070	−	27.9529i	0.442859	−	0.896591i
$973$		−	10.4668i		−	0.335549i
$974$	−28.4438	+	5.25046i	−0.911399	+	0.168235i
$975$	1.21942	+	1.23833i	0.0390528	+	0.0396582i
$976$	21.2993	+	53.1603i	0.681773	+	1.70162i
$977$	−6.97592	−	5.85349i	−0.223179	−	0.187270i	0.524341	−	0.851508i	$-0.324312\pi$
$977$	−6.97592	−	5.85349i	−0.223179	−	0.187270i	−0.747521	+	0.664238i	$0.768756\pi$
$978$	−15.1987	−	10.6352i	−0.486000	−	0.340076i
$979$	11.4355	−	31.4189i	0.365482	−	1.00415i
$980$	−20.8466	+	12.4849i	−0.665922	+	0.398815i
$981$	11.3854	+	0.175157i	0.363507	+	0.00559234i
$982$	−2.22051	+	3.91812i	−0.0708593	+	0.125032i
$983$	−24.3687	+	20.4478i	−0.777241	+	0.652183i	−0.942552	−	0.334059i	$-0.891582\pi$
$983$	−24.3687	+	20.4478i	−0.777241	+	0.652183i	0.165311	+	0.986241i	$0.447137\pi$
$984$	−22.1508	−	9.89237i	−0.706142	−	0.315357i
$985$	1.77743	−	10.0803i	0.0566338	−	0.321186i
$986$	−0.651838	+	3.87798i	−0.0207588	+	0.123500i
$987$	18.1696	−	1.44890i	0.578345	−	0.0461191i
$988$	57.0194	−	49.4214i	1.81403	−	1.57231i
$989$	−1.94883	−	1.12516i	−0.0619693	−	0.0357780i
$990$	−7.35754	−	43.6062i	−0.233838	−	1.38590i
$991$	1.91613	+	3.31884i	0.0608679	+	0.105426i	0.894854	−	0.446360i	$-0.147280\pi$
$991$	1.91613	+	3.31884i	0.0608679	+	0.105426i	−0.833986	+	0.551786i	$0.813946\pi$
$992$	3.41708	−	10.7023i	0.108492	−	0.339799i
$993$	−1.96532	−	4.30070i	−0.0623676	−	0.136479i
$994$	−10.7090	+	12.9719i	−0.339668	+	0.411442i
$995$	9.29647	+	25.5418i	0.294718	+	0.809731i
$996$	11.7561	−	45.3802i	0.372506	−	1.43793i
$997$	−9.12312	+	1.60865i	−0.288932	+	0.0509465i	−0.316236	−	0.948681i	$-0.602419\pi$
$997$	−9.12312	+	1.60865i	−0.288932	+	0.0509465i	0.0273036	+	0.999627i	$0.491308\pi$
$998$	52.7965	−	0.422521i	1.67124	−	0.0133747i
$999$	−11.6259	−	47.7712i	−0.367826	−	1.51142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.2	✓	204
3.2	odd	2		648.2.t.a.253.33		204
4.3	odd	2		864.2.bf.a.337.25		204
8.3	odd	2		864.2.bf.a.337.10		204
8.5	even	2	inner	216.2.t.a.13.32	yes	204
24.5	odd	2		648.2.t.a.253.3		204
27.2	odd	18		648.2.t.a.397.3		204
27.25	even	9	inner	216.2.t.a.133.32	yes	204
108.79	odd	18		864.2.bf.a.241.10		204
216.29	odd	18		648.2.t.a.397.33		204
216.133	even	18	inner	216.2.t.a.133.2	yes	204
216.187	odd	18		864.2.bf.a.241.25		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.2	✓	204	1.1	even	1	trivial
216.2.t.a.13.32	yes	204	8.5	even	2	inner
216.2.t.a.133.2	yes	204	216.133	even	18	inner
216.2.t.a.133.32	yes	204	27.25	even	9	inner
648.2.t.a.253.3		204	24.5	odd	2
648.2.t.a.253.33		204	3.2	odd	2
648.2.t.a.397.3		204	27.2	odd	18
648.2.t.a.397.33		204	216.29	odd	18
864.2.bf.a.241.10		204	108.79	odd	18
864.2.bf.a.241.25		204	216.187	odd	18
864.2.bf.a.337.10		204	8.3	odd	2
864.2.bf.a.337.25		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)

\(f(q)\)	\(=\)	\(q+(-1.39072 + 0.256713i) q^{2} +(-1.23413 + 1.21529i) q^{3} +(1.86820 - 0.714031i) q^{4} +(1.46572 - 1.74677i) q^{5} +(1.40435 - 2.00694i) q^{6} +(-1.21500 - 0.442225i) q^{7} +(-2.41483 + 1.47261i) q^{8} +(0.0461478 - 2.99965i) q^{9} +O(q^{10})\)	\(q+(-1.39072 + 0.256713i) q^{2} +(-1.23413 + 1.21529i) q^{3} +(1.86820 - 0.714031i) q^{4} +(1.46572 - 1.74677i) q^{5} +(1.40435 - 2.00694i) q^{6} +(-1.21500 - 0.442225i) q^{7} +(-2.41483 + 1.47261i) q^{8} +(0.0461478 - 2.99965i) q^{9} +(-1.58998 + 2.80554i) q^{10} +(-2.93828 - 3.50170i) q^{11} +(-1.43784 + 3.15160i) q^{12} +(4.95227 + 0.873219i) q^{13} +(1.80325 + 0.303103i) q^{14} +(0.313950 + 3.93701i) q^{15} +(2.98032 - 2.66790i) q^{16} +(0.909480 - 1.57526i) q^{17} +(0.705870 + 4.18351i) q^{18} +(6.49748 - 3.75132i) q^{19} +(1.49100 - 4.30988i) q^{20} +(2.03690 - 0.930816i) q^{21} +(4.98525 + 4.11559i) q^{22} +(0.835352 - 0.304043i) q^{23} +(1.19057 - 4.75211i) q^{24} +(-0.0346491 - 0.196505i) q^{25} +(-7.11138 + 0.0569110i) q^{26} +(3.58848 + 3.75803i) q^{27} +(-2.58563 + 0.0413872i) q^{28} +(1.50546 - 0.265453i) q^{29} +(-1.44730 - 5.39468i) q^{30} +(-1.86625 + 0.679258i) q^{31} +(-3.45990 + 4.47539i) q^{32} +(7.88180 + 0.750698i) q^{33} +(-0.860439 + 2.42423i) q^{34} +(-2.55331 + 1.47416i) q^{35} +(-2.05563 - 5.63688i) q^{36} +(-8.19426 - 4.73096i) q^{37} +(-8.07315 + 6.88502i) q^{38} +(-7.17295 + 4.94077i) q^{39} +(-0.967152 + 6.37659i) q^{40} +(0.859892 - 4.87669i) q^{41} +(-2.59380 + 1.81740i) q^{42} +(-1.62715 - 1.93916i) q^{43} +(-7.98961 - 4.44385i) q^{44} +(-5.17206 - 4.47724i) q^{45} +(-1.08369 + 0.637285i) q^{46} +(7.64813 + 2.78369i) q^{47} +(-0.435825 + 6.91448i) q^{48} +(-4.08164 - 3.42490i) q^{49} +(0.0986326 + 0.264388i) q^{50} +(0.791986 + 3.04936i) q^{51} +(9.87532 - 1.90473i) q^{52} +3.70167i q^{53} +(-5.95530 - 4.30515i) q^{54} -10.4234 q^{55} +(3.58525 - 0.721322i) q^{56} +(-3.45979 + 12.5259i) q^{57} +(-2.02553 + 0.755642i) q^{58} +(3.63062 - 4.32680i) q^{59} +(3.39767 + 7.13094i) q^{60} +(-4.89674 + 13.4537i) q^{61} +(2.42105 - 1.42375i) q^{62} +(-1.38259 + 3.62417i) q^{63} +(3.66285 - 7.11221i) q^{64} +(8.78393 - 7.37060i) q^{65} +(-11.1541 + 0.979351i) q^{66} +(8.09804 + 1.42790i) q^{67} +(0.574298 - 3.59230i) q^{68} +(-0.661432 + 1.39042i) q^{69} +(3.17251 - 2.70561i) q^{70} +(-4.59959 + 7.96673i) q^{71} +(4.30586 + 7.31160i) q^{72} +(-5.72007 - 9.90745i) q^{73} +(12.6104 + 4.47586i) q^{74} +(0.281572 + 0.200404i) q^{75} +(9.46001 - 11.6476i) q^{76} +(2.02148 + 5.55396i) q^{77} +(8.70720 - 8.71261i) q^{78} +(-1.39403 - 7.90593i) q^{79} +(-0.291918 - 9.11632i) q^{80} +(-8.99574 - 0.276854i) q^{81} +(0.0560425 + 7.00285i) q^{82} +(-13.3270 + 2.34991i) q^{83} +(3.14070 - 3.19336i) q^{84} +(-1.41859 - 3.89754i) q^{85} +(2.76072 + 2.27912i) q^{86} +(-1.53533 + 2.15717i) q^{87} +(12.2521 + 4.12911i) q^{88} +(3.65721 + 6.33447i) q^{89} +(8.34224 + 4.89884i) q^{90} +(-5.63086 - 3.25098i) q^{91} +(1.34351 - 1.16448i) q^{92} +(1.47769 - 3.10632i) q^{93} +(-11.3510 - 1.90796i) q^{94} +(2.97075 - 16.8480i) q^{95} +(-1.16893 - 9.72798i) q^{96} +(2.14122 - 1.79669i) q^{97} +(6.55563 + 3.71527i) q^{98} +(-10.6395 + 8.65220i) 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

Modular forms

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