LMFDB - Embedded newform 690.2.m.e.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.2
Root			$-0.877779 - 0.564114i$ of defining polynomial
Character	$\chi$	$=$	690.211
Dual form			690.2.m.e.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.223463 + 1.55422i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.223463 + 1.55422i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(-1.52863 + 3.34723i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.599298 + 4.16821i) q^{13} +(1.32094 - 0.848915i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.64067 + 3.04750i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(-2.25203 + 2.59898i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(0.652285 + 1.42831i) q^{21} +3.67976 q^{22} +(-0.237432 - 4.78995i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(4.04049 - 1.18640i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-1.32094 - 0.848915i) q^{28} +(-1.39640 - 1.61154i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(1.47418 + 0.432859i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.523684 + 3.64230i) q^{33} +(1.67513 - 3.66801i) q^{34} +(-0.652285 + 1.42831i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-4.85371 + 3.11929i) q^{37} +(3.29964 + 0.968863i) q^{38} +(0.599298 + 4.16821i) q^{39} +(0.654861 + 0.755750i) q^{40} +(6.62564 + 4.25804i) q^{41} +(1.02826 - 1.18668i) q^{42} +(-5.85085 + 1.71797i) q^{43} +(-1.52863 - 3.34723i) q^{44} +1.00000 q^{45} +(-4.25846 + 2.20579i) q^{46} +11.5867 q^{47} +(-0.415415 - 0.909632i) q^{48} +(4.35079 - 1.27751i) q^{49} +(0.654861 - 0.755750i) q^{50} +(3.39228 + 2.18009i) q^{51} +(-2.75766 - 3.18251i) q^{52} +(-1.02886 - 7.15585i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(-3.09561 + 1.98943i) q^{55} +(-0.223463 + 1.55422i) q^{56} +(-1.42859 + 3.12818i) q^{57} +(-0.885818 + 1.93967i) q^{58} +(1.86477 - 12.9697i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(7.12736 + 2.09278i) q^{61} +(-0.218655 - 1.52078i) q^{62} +(1.02826 + 1.18668i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.75766 + 3.18251i) q^{65} +(3.53070 - 1.03671i) q^{66} +(-3.14295 - 6.88211i) q^{67} -4.03242 q^{68} +(-1.57730 - 4.52903i) q^{69} +1.57020 q^{70} +(3.98064 + 8.71639i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-3.41607 + 3.94235i) q^{73} +(4.85371 + 3.11929i) q^{74} +(0.654861 + 0.755750i) q^{75} +(-0.489413 - 3.40394i) q^{76} +(-5.54392 - 1.62784i) q^{77} +(3.54258 - 2.27668i) q^{78} +(1.31172 - 9.12322i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.12086 - 7.79574i) q^{82} +(2.22091 - 1.42729i) q^{83} +(-1.50660 - 0.442377i) q^{84} +(0.573873 + 3.99137i) q^{85} +(3.99325 + 4.60846i) q^{86} +(-1.79386 - 1.15285i) q^{87} +(-2.40973 + 2.78098i) q^{88} +(4.50485 - 1.32274i) q^{89} +(-0.415415 - 0.909632i) q^{90} -6.61223 q^{91} +(3.77549 + 2.95731i) q^{92} +1.53642 q^{93} +(-4.81328 - 10.5396i) q^{94} +(-3.29964 + 0.968863i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-9.89035 - 6.35614i) q^{97} +(-2.96944 - 3.42692i) q^{98} +(0.523684 + 3.64230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

Coefficient data

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

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

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

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	0.223463	+	1.55422i	0.0844611	+	0.587440i	0.987469	+	0.157815i	$0.0504450\pi$
$7$	0.223463	+	1.55422i	0.0844611	+	0.587440i	−0.903008	+	0.429625i	$0.858646\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.142315	−	0.989821i	0.0450039	−	0.313009i
$11$	−1.52863	+	3.34723i	−0.460898	+	1.00923i	0.526383	+	0.850247i	$0.323548\pi$
$11$	−1.52863	+	3.34723i	−0.460898	+	1.00923i	−0.987282	+	0.158980i	$0.949180\pi$
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	−0.599298	+	4.16821i	−0.166215	+	1.15605i	0.720405	+	0.693554i	$0.243956\pi$
$13$	−0.599298	+	4.16821i	−0.166215	+	1.15605i	−0.886620	+	0.462499i	$0.846953\pi$
$14$	1.32094	−	0.848915i	0.353036	−	0.226882i
$15$	0.959493	+	0.281733i	0.247740	+	0.0727430i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	2.64067	+	3.04750i	0.640457	+	0.739126i	0.979456	−	0.201660i	$-0.0646337\pi$
$17$	2.64067	+	3.04750i	0.640457	+	0.739126i	−0.338999	+	0.940787i	$0.610088\pi$
$18$	−0.841254	−	0.540641i	−0.198285	−	0.127430i
$19$	−2.25203	+	2.59898i	−0.516651	+	0.596247i	−0.952789	−	0.303632i	$-0.901801\pi$
$19$	−2.25203	+	2.59898i	−0.516651	+	0.596247i	0.436138	+	0.899880i	$0.356346\pi$
$20$	−0.959493	+	0.281733i	−0.214549	+	0.0629973i
$21$	0.652285	+	1.42831i	0.142340	+	0.311682i
$22$	3.67976			0.784527
$23$	−0.237432	−	4.78995i	−0.0495080	−	0.998774i
$23$	−0.237432	−	4.78995i	−0.0495080	−	0.998774i
$24$	1.00000			0.204124
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	4.04049	−	1.18640i	0.792406	−	0.232671i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−1.32094	−	0.848915i	−0.249634	−	0.160430i
$29$	−1.39640	−	1.61154i	−0.259306	−	0.299255i	0.611137	−	0.791525i	$-0.290713\pi$
$29$	−1.39640	−	1.61154i	−0.259306	−	0.299255i	−0.870442	+	0.492270i	$0.836167\pi$
$30$	−0.142315	−	0.989821i	−0.0259830	−	0.180716i
$31$	1.47418	+	0.432859i	0.264771	+	0.0777438i	0.411423	−	0.911444i	$-0.365032\pi$
$31$	1.47418	+	0.432859i	0.264771	+	0.0777438i	−0.146653	+	0.989188i	$0.546850\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	−0.523684	+	3.64230i	−0.0911617	+	0.634044i
$34$	1.67513	−	3.66801i	0.287282	−	0.629059i
$35$	−0.652285	+	1.42831i	−0.110256	+	0.241428i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	−4.85371	+	3.11929i	−0.797945	+	0.512808i	−0.874945	−	0.484223i	$-0.839102\pi$
$37$	−4.85371	+	3.11929i	−0.797945	+	0.512808i	0.0769998	+	0.997031i	$0.475466\pi$
$38$	3.29964	+	0.968863i	0.535273	+	0.157170i
$39$	0.599298	+	4.16821i	0.0959644	+	0.667447i
$40$	0.654861	+	0.755750i	0.103543	+	0.119494i
$41$	6.62564	+	4.25804i	1.03475	+	0.664994i	0.943683	−	0.330851i	$-0.107336\pi$
$41$	6.62564	+	4.25804i	1.03475	+	0.664994i	0.0910675	+	0.995845i	$0.470972\pi$
$42$	1.02826	−	1.18668i	0.158665	−	0.183109i
$43$	−5.85085	+	1.71797i	−0.892247	+	0.261987i	−0.695551	−	0.718477i	$-0.744839\pi$
$43$	−5.85085	+	1.71797i	−0.892247	+	0.261987i	−0.196696	+	0.980464i	$0.563021\pi$
$44$	−1.52863	−	3.34723i	−0.230449	−	0.504613i
$45$	1.00000			0.149071
$46$	−4.25846	+	2.20579i	−0.627876	+	0.325226i
$47$	11.5867			1.69009			0.845046	−	0.534694i	$-0.179573\pi$
$47$	11.5867			1.69009			0.845046	+	0.534694i	$0.179573\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	4.35079	−	1.27751i	0.621541	−	0.182501i
$50$	0.654861	−	0.755750i	0.0926113	−	0.106879i
$51$	3.39228	+	2.18009i	0.475015	+	0.305273i
$52$	−2.75766	−	3.18251i	−0.382419	−	0.441335i
$53$	−1.02886	−	7.15585i	−0.141324	−	0.982932i	−0.929852	−	0.367933i	$-0.880066\pi$
$53$	−1.02886	−	7.15585i	−0.141324	−	0.982932i	0.788528	−	0.614999i	$-0.210843\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	−3.09561	+	1.98943i	−0.417412	+	0.268254i
$56$	−0.223463	+	1.55422i	−0.0298615	+	0.207691i
$57$	−1.42859	+	3.12818i	−0.189221	+	0.414337i
$58$	−0.885818	+	1.93967i	−0.116314	+	0.254691i
$59$	1.86477	−	12.9697i	0.242772	−	1.68852i	−0.395309	−	0.918548i	$-0.629363\pi$
$59$	1.86477	−	12.9697i	0.242772	−	1.68852i	0.638081	−	0.769969i	$-0.279728\pi$
$60$	−0.841254	+	0.540641i	−0.108605	+	0.0697964i
$61$	7.12736	+	2.09278i	0.912565	+	0.267953i	0.704120	−	0.710081i	$-0.251342\pi$
$61$	7.12736	+	2.09278i	0.912565	+	0.267953i	0.208445	+	0.978034i	$0.433160\pi$
$62$	−0.218655	−	1.52078i	−0.0277692	−	0.193139i
$63$	1.02826	+	1.18668i	0.129549	+	0.149508i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−2.75766	+	3.18251i	−0.342046	+	0.394742i
$66$	3.53070	−	1.03671i	0.434600	−	0.127610i
$67$	−3.14295	−	6.88211i	−0.383973	−	0.840784i	−0.998647	−	0.0520024i	$-0.983440\pi$
$67$	−3.14295	−	6.88211i	−0.383973	−	0.840784i	0.614674	−	0.788781i	$-0.289288\pi$
$68$	−4.03242			−0.489002
$69$	−1.57730	−	4.52903i	−0.189885	−	0.545231i
$70$	1.57020			0.187675
$71$	3.98064	+	8.71639i	0.472415	+	1.03444i	0.984480	+	0.175498i	$0.0561535\pi$
$71$	3.98064	+	8.71639i	0.472415	+	1.03444i	−0.512065	+	0.858947i	$0.671119\pi$
$72$	0.959493	−	0.281733i	0.113077	−	0.0332025i
$73$	−3.41607	+	3.94235i	−0.399820	+	0.461417i	−0.919584	−	0.392893i	$-0.871474\pi$
$73$	−3.41607	+	3.94235i	−0.399820	+	0.461417i	0.519764	+	0.854310i	$0.326020\pi$
$74$	4.85371	+	3.11929i	0.564232	+	0.362610i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	−0.489413	−	3.40394i	−0.0561395	−	0.390459i
$77$	−5.54392	−	1.62784i	−0.631788	−	0.185510i
$78$	3.54258	−	2.27668i	0.401118	−	0.257783i
$79$	1.31172	−	9.12322i	0.147580	−	1.02644i	−0.772585	−	0.634912i	$-0.781037\pi$
$79$	1.31172	−	9.12322i	0.147580	−	1.02644i	0.920165	−	0.391531i	$-0.128054\pi$
$80$	0.415415	−	0.909632i	0.0464448	−	0.101700i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	1.12086	−	7.79574i	0.123778	−	0.860896i
$83$	2.22091	−	1.42729i	0.243776	−	0.156666i	−0.413048	−	0.910709i	$-0.635536\pi$
$83$	2.22091	−	1.42729i	0.243776	−	0.156666i	0.656824	+	0.754044i	$0.271899\pi$
$84$	−1.50660	−	0.442377i	−0.164383	−	0.0482673i
$85$	0.573873	+	3.99137i	0.0622452	+	0.432925i
$86$	3.99325	+	4.60846i	0.430603	+	0.496943i
$87$	−1.79386	−	1.15285i	−0.192322	−	0.123598i
$88$	−2.40973	+	2.78098i	−0.256878	+	0.296453i
$89$	4.50485	−	1.32274i	0.477513	−	0.140210i	−0.0341143	−	0.999418i	$-0.510861\pi$
$89$	4.50485	−	1.32274i	0.477513	−	0.140210i	0.511627	+	0.859207i	$0.329043\pi$
$90$	−0.415415	−	0.909632i	−0.0437886	−	0.0958836i
$91$	−6.61223			−0.693150
$92$	3.77549	+	2.95731i	0.393622	+	0.308321i
$93$	1.53642			0.159319
$94$	−4.81328	−	10.5396i	−0.496452	−	1.08708i
$95$	−3.29964	+	0.968863i	−0.338536	+	0.0994033i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	−9.89035	−	6.35614i	−1.00421	−	0.645368i	−0.0683236	−	0.997663i	$-0.521765\pi$
$97$	−9.89035	−	6.35614i	−1.00421	−	0.645368i	−0.935889	+	0.352295i	$0.885401\pi$
$98$	−2.96944	−	3.42692i	−0.299959	−	0.346171i
$99$	0.523684	+	3.64230i	0.0526323	+	0.366065i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	16.6626	−	10.7084i	1.65799	−	1.06552i	0.737034	−	0.675856i	$-0.236226\pi$
$101$	16.6626	−	10.7084i	1.65799	−	1.06552i	0.920955	−	0.389669i	$-0.127411\pi$
$102$	0.573873	−	3.99137i	0.0568219	−	0.395205i
$103$	−1.97212	+	4.31835i	−0.194319	+	0.425499i	−0.981562	−	0.191144i	$-0.938780\pi$
$103$	−1.97212	+	4.31835i	−0.194319	+	0.425499i	0.787243	+	0.616643i	$0.211508\pi$
$104$	−1.74934	+	3.83052i	−0.171537	+	0.375614i
$105$	−0.223463	+	1.55422i	−0.0218078	+	0.151676i
$106$	−6.08179	+	3.90853i	−0.590716	+	0.379630i
$107$	−7.65473	−	2.24763i	−0.740011	−	0.217287i	−0.110063	−	0.993925i	$-0.535105\pi$
$107$	−7.65473	−	2.24763i	−0.740011	−	0.217287i	−0.629947	+	0.776638i	$0.716924\pi$
$108$	0.142315	+	0.989821i	0.0136943	+	0.0952456i
$109$	−1.14117	−	1.31698i	−0.109304	−	0.126144i	0.698461	−	0.715648i	$-0.253869\pi$
$109$	−1.14117	−	1.31698i	−0.109304	−	0.126144i	−0.807765	+	0.589504i	$0.799323\pi$
$110$	3.09561	+	1.98943i	0.295155	+	0.189685i
$111$	−3.77829	+	4.36038i	−0.358620	+	0.413869i
$112$	1.50660	−	0.442377i	0.142360	−	0.0418007i
$113$	0.387376	+	0.848235i	0.0364413	+	0.0797952i	0.926977	−	0.375118i	$-0.122398\pi$
$113$	0.387376	+	0.848235i	0.0364413	+	0.0797952i	−0.890536	+	0.454913i	$0.849670\pi$
$114$	3.43895			0.322087
$115$	2.38990	−	4.15793i	0.222860	−	0.387729i
$116$	2.13237			0.197985
$117$	1.74934	+	3.83052i	0.161727	+	0.354132i
$118$	−12.5723	+	3.69157i	−1.15738	+	0.339837i
$119$	−4.14639	+	4.78518i	−0.380099	+	0.438657i
$120$	0.841254	+	0.540641i	0.0767956	+	0.0493535i
$121$	−1.66376	−	1.92008i	−0.151251	−	0.174553i
$122$	−1.05715	−	7.35265i	−0.0957100	−	0.665678i
$123$	7.55688	+	2.21890i	0.681381	+	0.200071i
$124$	−1.29252	+	0.830650i	−0.116071	+	0.0745946i
$125$	−0.142315	+	0.989821i	−0.0127290	+	0.0885323i
$126$	0.652285	−	1.42831i	0.0581102	−	0.127244i
$127$	−2.84302	+	6.22534i	−0.252277	+	0.552410i	−0.992823	−	0.119597i	$-0.961840\pi$
$127$	−2.84302	+	6.22534i	−0.252277	+	0.552410i	0.740546	+	0.672006i	$0.234567\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	−5.12985	+	3.29675i	−0.451658	+	0.290263i
$130$	4.04049	+	1.18640i	0.354375	+	0.104054i
$131$	1.19669	+	8.32318i	0.104556	+	0.727200i	0.972898	+	0.231235i	$0.0742765\pi$
$131$	1.19669	+	8.32318i	0.104556	+	0.727200i	−0.868342	+	0.495965i	$0.834814\pi$
$132$	−2.40973	−	2.78098i	−0.209740	−	0.242053i
$133$	−4.54263	−	2.91937i	−0.393896	−	0.253142i
$134$	−4.95456	+	5.71786i	−0.428009	+	0.493948i
$135$	0.959493	−	0.281733i	0.0825800	−	0.0242477i
$136$	1.67513	+	3.66801i	0.143641	+	0.314530i
$137$	7.49838			0.640630			0.320315	−	0.947311i	$-0.396211\pi$
$137$	7.49838			0.640630			0.320315	+	0.947311i	$0.396211\pi$
$138$	−3.46452	+	3.31619i	−0.294919	+	0.282293i
$139$	−7.19143			−0.609969			−0.304985	−	0.952357i	$-0.598651\pi$
$139$	−7.19143			−0.609969			−0.304985	+	0.952357i	$0.598651\pi$
$140$	−0.652285	−	1.42831i	−0.0551282	−	0.120714i
$141$	11.1173	−	3.26435i	0.936249	−	0.274908i
$142$	6.27509	−	7.24183i	0.526593	−	0.607721i
$143$	−13.0358	−	8.37762i	−1.09011	−	0.700572i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	−0.303468	−	2.11066i	−0.0252016	−	0.175281i
$146$	5.00517	+	1.46965i	0.414231	+	0.121629i
$147$	3.81464	−	2.45152i	0.314626	−	0.202198i
$148$	0.821102	−	5.71089i	0.0674941	−	0.469432i
$149$	−8.03473	+	17.5936i	−0.658231	+	1.44132i	0.225931	+	0.974143i	$0.427458\pi$
$149$	−8.03473	+	17.5936i	−0.658231	+	1.44132i	−0.884162	+	0.467181i	$0.845270\pi$
$150$	0.415415	−	0.909632i	0.0339185	−	0.0742711i
$151$	−2.34080	+	16.2807i	−0.190492	+	1.32490i	0.640217	+	0.768194i	$0.278844\pi$
$151$	−2.34080	+	16.2807i	−0.190492	+	1.32490i	−0.830709	+	0.556707i	$0.812065\pi$
$152$	−2.89303	+	1.85923i	−0.234655	+	0.150804i
$153$	3.86907	+	1.13606i	0.312796	+	0.0918452i
$154$	0.822290	+	5.71915i	0.0662620	+	0.460863i
$155$	1.00614	+	1.16115i	0.0808151	+	0.0932656i
$156$	−3.54258	−	2.27668i	−0.283633	−	0.182280i
$157$	−4.03424	+	4.65576i	−0.321967	+	0.371570i	−0.893542	−	0.448980i	$-0.851787\pi$
$157$	−4.03424	+	4.65576i	−0.321967	+	0.371570i	0.571574	+	0.820550i	$0.306333\pi$
$158$	−8.84368	+	2.59674i	−0.703565	+	0.206585i
$159$	−3.00322	−	6.57613i	−0.238171	−	0.521521i
$160$	−1.00000			−0.0790569
$161$	7.39158	−	1.43940i	0.582538	−	0.113440i
$162$	−1.00000			−0.0785674
$163$	−9.65699	−	21.1459i	−0.756394	−	1.65627i	−0.754523	−	0.656274i	$-0.772132\pi$
$163$	−9.65699	−	21.1459i	−0.756394	−	1.65627i	−0.00187103	−	0.999998i	$-0.500596\pi$
$164$	−7.55688	+	2.21890i	−0.590093	+	0.173267i
$165$	−2.40973	+	2.78098i	−0.187597	+	0.216499i
$166$	−2.22091	−	1.42729i	−0.172376	−	0.110779i
$167$	−14.6360	−	16.8909i	−1.13257	−	1.30705i	−0.945836	−	0.324644i	$-0.894755\pi$
$167$	−14.6360	−	16.8909i	−1.13257	−	1.30705i	−0.186733	−	0.982411i	$-0.559790\pi$
$168$	0.223463	+	1.55422i	0.0172405	+	0.119911i
$169$	−4.54138	−	1.33347i	−0.349337	−	0.102575i
$170$	3.39228	−	2.18009i	0.260176	−	0.167205i
$171$	−0.489413	+	3.40394i	−0.0374264	+	0.260306i
$172$	2.53314	−	5.54681i	0.193150	−	0.422940i
$173$	3.97926	−	8.71337i	0.302538	−	0.662465i	−0.695912	−	0.718127i	$-0.745000\pi$
$173$	3.97926	−	8.71337i	0.302538	−	0.662465i	0.998450	+	0.0556618i	$0.0177269\pi$
$174$	−0.303468	+	2.11066i	−0.0230058	+	0.160009i
$175$	−1.32094	+	0.848915i	−0.0998535	+	0.0641720i
$176$	3.53070	+	1.03671i	0.266137	+	0.0781448i
$177$	−1.86477	−	12.9697i	−0.140165	−	0.974866i
$178$	−3.07459	−	3.54827i	−0.230450	−	0.265954i
$179$	−16.1010	−	10.3475i	−1.20344	−	0.773405i	−0.223894	−	0.974614i	$-0.571877\pi$
$179$	−16.1010	−	10.3475i	−1.20344	−	0.773405i	−0.979549	+	0.201208i	$0.935513\pi$
$180$	−0.654861	+	0.755750i	−0.0488104	+	0.0563302i
$181$	−2.51625	+	0.738838i	−0.187031	+	0.0549174i	−0.373907	−	0.927466i	$-0.621982\pi$
$181$	−2.51625	+	0.738838i	−0.187031	+	0.0549174i	0.186876	+	0.982384i	$0.440164\pi$
$182$	2.74682	+	6.01470i	0.203608	+	0.445839i
$183$	7.42826			0.549113
$184$	1.12167	−	4.66282i	0.0826906	−	0.343747i
$185$	−5.76961			−0.424190
$186$	−0.638251	−	1.39758i	−0.0467988	−	0.102475i
$187$	−14.2373	+	4.18044i	−1.04113	+	0.305704i
$188$	−7.58766	+	8.75663i	−0.553387	+	0.638643i
$189$	1.32094	+	0.848915i	0.0960841	+	0.0617495i
$190$	2.25203	+	2.59898i	0.163380	+	0.188550i
$191$	−0.601808	−	4.18567i	−0.0435453	−	0.302864i	−0.999942	−	0.0107927i	$-0.996564\pi$
$191$	−0.601808	−	4.18567i	−0.0435453	−	0.302864i	0.956396	−	0.292072i	$-0.0943446\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	1.70213	−	1.09389i	0.122522	−	0.0787402i	−0.477944	−	0.878390i	$-0.658618\pi$
$193$	1.70213	−	1.09389i	0.122522	−	0.0787402i	0.600466	+	0.799650i	$0.294982\pi$
$194$	−1.67315	+	11.6370i	−0.120125	+	0.835489i
$195$	−1.74934	+	3.83052i	−0.125273	+	0.274310i
$196$	−1.88369	+	4.12470i	−0.134549	+	0.294621i
$197$	−1.89357	+	13.1701i	−0.134912	+	0.938330i	0.804112	+	0.594478i	$0.202641\pi$
$197$	−1.89357	+	13.1701i	−0.134912	+	0.938330i	−0.939024	+	0.343853i	$0.888268\pi$
$198$	3.09561	−	1.98943i	0.219995	−	0.141382i
$199$	14.9440	+	4.38795i	1.05935	+	0.311053i	0.764589	−	0.644518i	$-0.222942\pi$
$199$	14.9440	+	4.38795i	1.05935	+	0.311053i	0.294761	+	0.955571i	$0.404760\pi$
$200$	0.142315	+	0.989821i	0.0100632	+	0.0699909i
$201$	−4.95456	−	5.71786i	−0.349468	−	0.403307i
$202$	−16.6626	−	10.7084i	−1.17238	−	0.753440i
$203$	2.19264	−	2.53044i	0.153893	−	0.177602i
$204$	−3.86907	+	1.13606i	−0.270889	+	0.0795403i
$205$	3.27177	+	7.16418i	0.228510	+	0.500368i
$206$	4.74735			0.330764
$207$	−2.78938	−	3.90120i	−0.193876	−	0.271152i
$208$	4.21107			0.291985
$209$	−5.25687	−	11.5109i	−0.363625	−	0.796228i
$210$	1.50660	−	0.442377i	0.103965	−	0.0305269i
$211$	6.14532	−	7.09208i	0.423061	−	0.488239i	−0.503706	−	0.863875i	$-0.668030\pi$
$211$	6.14532	−	7.09208i	0.423061	−	0.488239i	0.926767	+	0.375637i	$0.122576\pi$
$212$	6.08179	+	3.90853i	0.417699	+	0.268439i
$213$	6.27509	+	7.24183i	0.429962	+	0.496202i
$214$	1.13537	+	7.89669i	0.0776125	+	0.539807i
$215$	−5.85085	−	1.71797i	−0.399025	−	0.117164i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−0.343333	+	2.38793i	−0.0233069	+	0.162103i
$218$	−0.723909	+	1.58514i	−0.0490293	+	0.107359i
$219$	−2.16700	+	4.74507i	−0.146432	+	0.320642i
$220$	0.523684	−	3.64230i	0.0353068	−	0.245564i
$221$	−14.2851	+	9.18050i	−0.960923	+	0.617548i
$222$	5.53590	+	1.62549i	0.371546	+	0.109096i
$223$	2.48091	+	17.2551i	0.166134	+	1.15549i	0.886783	+	0.462187i	$0.152935\pi$
$223$	2.48091	+	17.2551i	0.166134	+	1.15549i	−0.720649	+	0.693301i	$0.756156\pi$
$224$	−1.02826	−	1.18668i	−0.0687037	−	0.0792884i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	0.610660	−	0.704739i	0.0406205	−	0.0468785i
$227$	−21.4504	+	6.29842i	−1.42372	+	0.418041i	−0.900759	−	0.434319i	$-0.856989\pi$
$227$	−21.4504	+	6.29842i	−1.42372	+	0.418041i	−0.522956	+	0.852360i	$0.675171\pi$
$228$	−1.42859	−	3.12818i	−0.0946107	−	0.207168i
$229$	15.0836			0.996754			0.498377	−	0.866960i	$-0.333930\pi$
$229$	15.0836			0.996754			0.498377	+	0.866960i	$0.333930\pi$
$230$	−4.77499	−	0.446666i	−0.314853	−	0.0294523i
$231$	−5.77797			−0.380162
$232$	−0.885818	−	1.93967i	−0.0581568	−	0.127346i
$233$	−10.2947	+	3.02280i	−0.674430	+	0.198030i	−0.600975	−	0.799268i	$-0.705221\pi$
$233$	−10.2947	+	3.02280i	−0.674430	+	0.198030i	−0.0734551	+	0.997299i	$0.523403\pi$
$234$	2.75766	−	3.18251i	0.180274	−	0.208047i
$235$	9.74734	+	6.26423i	0.635846	+	0.408634i
$236$	8.58072	+	9.90267i	0.558557	+	0.644609i
$237$	−1.31172	−	9.12322i	−0.0852054	−	0.592617i
$238$	6.07523	+	1.78385i	0.393799	+	0.115630i
$239$	19.7459	−	12.6899i	1.27725	−	0.820842i	0.286708	−	0.958018i	$-0.407439\pi$
$239$	19.7459	−	12.6899i	1.27725	−	0.820842i	0.990547	+	0.137176i	$0.0438027\pi$
$240$	0.142315	−	0.989821i	0.00918638	−	0.0638927i
$241$	−3.20236	+	7.01218i	−0.206282	+	0.451695i	−0.984290	−	0.176560i	$-0.943503\pi$
$241$	−3.20236	+	7.01218i	−0.206282	+	0.451695i	0.778008	+	0.628254i	$0.216230\pi$
$242$	−1.05542	+	2.31104i	−0.0678447	+	0.148559i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−6.24905	+	4.01602i	−0.400054	+	0.257099i
$245$	4.35079	+	1.27751i	0.277962	+	0.0816169i
$246$	−1.12086	−	7.79574i	−0.0714633	−	0.497038i
$247$	−9.48346	−	10.9445i	−0.603418	−	0.696382i
$248$	1.29252	+	0.830650i	0.0820749	+	0.0527464i
$249$	1.72883	−	1.99518i	0.109560	−	0.126439i
$250$	0.959493	−	0.281733i	0.0606837	−	0.0178183i
$251$	2.37616	+	5.20306i	0.149982	+	0.328414i	0.969679	−	0.244383i	$-0.0785854\pi$
$251$	2.37616	+	5.20306i	0.149982	+	0.328414i	−0.819697	+	0.572797i	$0.805858\pi$
$252$	−1.57020			−0.0989134
$253$	16.3960	+	6.52731i	1.03081	+	0.410368i
$254$	6.84380			0.429418
$255$	1.67513	+	3.66801i	0.104900	+	0.229700i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	7.99234	−	9.22365i	0.498548	−	0.575355i	−0.449581	−	0.893239i	$-0.648427\pi$
$257$	7.99234	−	9.22365i	0.498548	−	0.575355i	0.948130	+	0.317884i	$0.102972\pi$
$258$	5.12985	+	3.29675i	0.319370	+	0.205247i
$259$	−5.93268	−	6.84668i	−0.368639	−	0.425432i
$260$	−0.599298	−	4.16821i	−0.0371669	−	0.258501i
$261$	−2.04599	−	0.600758i	−0.126644	−	0.0371860i
$262$	7.07391	−	4.54612i	0.437028	−	0.280861i
$263$	4.38044	−	30.4666i	0.270110	−	1.87865i	−0.177054	−	0.984201i	$-0.556657\pi$
$263$	4.38044	−	30.4666i	0.270110	−	1.87865i	0.447164	−	0.894452i	$-0.352434\pi$
$264$	−1.52863	+	3.34723i	−0.0940805	+	0.206008i
$265$	3.00322	−	6.57613i	0.184486	−	0.403968i
$266$	−0.768477	+	5.34488i	−0.0471184	+	0.327715i
$267$	3.94971	−	2.53833i	0.241718	−	0.155343i
$268$	7.25935	+	2.13154i	0.443435	+	0.130204i
$269$	−1.81402	−	12.6168i	−0.110603	−	0.769260i	−0.967336	−	0.253499i	$-0.918418\pi$
$269$	−1.81402	−	12.6168i	−0.110603	−	0.769260i	0.856733	−	0.515761i	$-0.172491\pi$
$270$	−0.654861	−	0.755750i	−0.0398536	−	0.0459935i
$271$	−2.75578	−	1.77103i	−0.167402	−	0.107583i	0.454257	−	0.890871i	$-0.349905\pi$
$271$	−2.75578	−	1.77103i	−0.167402	−	0.107583i	−0.621659	+	0.783288i	$0.713541\pi$
$272$	2.64067	−	3.04750i	0.160114	−	0.184782i
$273$	−6.34439	+	1.86288i	−0.383980	+	0.112747i
$274$	−3.11494	−	6.82076i	−0.188180	−	0.412057i
$275$	−3.67976			−0.221898
$276$	4.45573	+	1.77384i	0.268203	+	0.106773i
$277$	4.93061			0.296252			0.148126	−	0.988969i	$-0.452676\pi$
$277$	4.93061			0.296252			0.148126	+	0.988969i	$0.452676\pi$
$278$	2.98743	+	6.54156i	0.179174	+	0.392336i
$279$	1.47418	−	0.432859i	0.0882570	−	0.0259146i
$280$	−1.02826	+	1.18668i	−0.0614505	+	0.0709177i
$281$	2.27845	+	1.46427i	0.135921	+	0.0873512i	0.606834	−	0.794828i	$-0.292439\pi$
$281$	2.27845	+	1.46427i	0.135921	+	0.0873512i	−0.470913	+	0.882180i	$0.656076\pi$
$282$	−7.58766	−	8.75663i	−0.451839	−	0.521450i
$283$	−3.15719	−	21.9587i	−0.187675	−	1.30531i	−0.838007	−	0.545660i	$-0.816279\pi$
$283$	−3.15719	−	21.9587i	−0.187675	−	1.30531i	0.650331	−	0.759651i	$-0.274630\pi$
$284$	−9.19417	−	2.69965i	−0.545574	−	0.160195i
$285$	−2.89303	+	1.85923i	−0.171368	+	0.110132i
$286$	−2.20527	+	15.3380i	−0.130400	+	0.906955i
$287$	−5.13734	+	11.2492i	−0.303248	+	0.664020i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	0.105260	−	0.732097i	0.00619174	−	0.0430645i
$290$	−1.79386	+	1.15285i	−0.105339	+	0.0676974i
$291$	−11.2804	−	3.31224i	−0.661272	−	0.194167i
$292$	−0.742382	−	5.16338i	−0.0434446	−	0.302164i
$293$	9.27056	+	10.6988i	0.541592	+	0.625030i	0.958903	−	0.283733i	$-0.0915730\pi$
$293$	9.27056	+	10.6988i	0.541592	+	0.625030i	−0.417311	+	0.908764i	$0.637028\pi$
$294$	−3.81464	−	2.45152i	−0.222474	−	0.142975i
$295$	8.58072	−	9.90267i	0.499589	−	0.576556i
$296$	−5.53590	+	1.62549i	−0.321768	+	0.0944796i
$297$	1.52863	+	3.34723i	0.0886999	+	0.194226i
$298$	19.3415			1.12042
$299$	20.1078	+	1.88094i	1.16286	+	0.108778i
$300$	−1.00000			−0.0577350
$301$	−3.97755	−	8.70961i	−0.229262	−	0.502014i
$302$	15.7818	−	4.63396i	0.908141	−	0.266654i
$303$	12.9707	−	14.9690i	0.745149	−	0.859948i
$304$	2.89303	+	1.85923i	0.165926	+	0.106634i
$305$	4.86448	+	5.61390i	0.278539	+	0.321451i
$306$	−0.573873	−	3.99137i	−0.0328061	−	0.228172i
$307$	17.8866	+	5.25199i	1.02084	+	0.299747i	0.748982	−	0.662590i	$-0.230543\pi$
$307$	17.8866	+	5.25199i	1.02084	+	0.299747i	0.271861	+	0.962337i	$0.412361\pi$
$308$	4.86073	−	3.12380i	0.276966	−	0.177995i
$309$	−0.675619	+	4.69903i	−0.0384346	+	0.267319i
$310$	0.638251	−	1.39758i	0.0362502	−	0.0793769i
$311$	−3.55067	+	7.77489i	−0.201340	+	0.440873i	−0.983188	−	0.182596i	$-0.941550\pi$
$311$	−3.55067	+	7.77489i	−0.201340	+	0.440873i	0.781848	+	0.623469i	$0.214277\pi$
$312$	−0.599298	+	4.16821i	−0.0339286	+	0.235978i
$313$	12.0713	−	7.75778i	0.682313	−	0.438496i	−0.153033	−	0.988221i	$-0.548904\pi$
$313$	12.0713	−	7.75778i	0.682313	−	0.438496i	0.835345	+	0.549725i	$0.185268\pi$
$314$	5.91091	+	1.73560i	0.333572	+	0.0979456i
$315$	0.223463	+	1.55422i	0.0125907	+	0.0875703i
$316$	6.03587	+	6.96577i	0.339544	+	0.391855i
$317$	17.3862	+	11.1734i	0.976504	+	0.627561i	0.928518	−	0.371287i	$-0.121083\pi$
$317$	17.3862	+	11.1734i	0.976504	+	0.627561i	0.0479860	+	0.998848i	$0.484720\pi$
$318$	−4.73427	+	5.46364i	−0.265485	+	0.306386i
$319$	7.52876	−	2.21064i	0.421530	−	0.123772i
$320$	0.415415	+	0.909632i	0.0232224	+	0.0508500i
$321$	−7.97789			−0.445283
$322$	−4.37990	−	6.12567i	−0.244082	−	0.341370i
$323$	−13.8673			−0.771595
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	−4.04049	+	1.18640i	−0.224126	+	0.0658094i
$326$	−15.2233	+	17.5686i	−0.843140	+	0.973036i
$327$	−1.46598	−	0.942130i	−0.0810690	−	0.0520999i
$328$	5.15762	+	5.95222i	0.284782	+	0.328656i
$329$	2.58920	+	18.0083i	0.142747	+	0.992827i
$330$	3.53070	+	1.03671i	0.194359	+	0.0570689i
$331$	15.4096	−	9.90315i	0.846989	−	0.544327i	−0.0436455	−	0.999047i	$-0.513897\pi$
$331$	15.4096	−	9.90315i	0.846989	−	0.544327i	0.890634	+	0.454720i	$0.150261\pi$
$332$	−0.375711	+	2.61313i	−0.0206198	+	0.143414i
$333$	−2.39678	+	5.24823i	−0.131343	+	0.287601i
$334$	−9.28445	+	20.3301i	−0.508023	+	1.11241i
$335$	1.07673	−	7.48881i	0.0588280	−	0.409157i
$336$	1.32094	−	0.848915i	0.0720631	−	0.0463121i
$337$	−5.93444	−	1.74251i	−0.323269	−	0.0949205i	0.116072	−	0.993241i	$-0.462970\pi$
$337$	−5.93444	−	1.74251i	−0.323269	−	0.0949205i	−0.439341	+	0.898320i	$0.644788\pi$
$338$	0.673591	+	4.68493i	0.0366385	+	0.254827i
$339$	0.610660	+	0.704739i	0.0331665	+	0.0382762i
$340$	−3.39228	−	2.18009i	−0.183972	−	0.118232i
$341$	−3.70235	+	4.27274i	−0.200494	+	0.231382i
$342$	3.29964	−	0.968863i	0.178424	−	0.0523901i
$343$	7.52376	+	16.4747i	0.406245	+	0.889553i
$344$	−6.09786			−0.328775
$345$	1.12167	−	4.66282i	0.0603887	−	0.251038i
$346$	−9.57901			−0.514971
$347$	−8.59859	−	18.8283i	−0.461596	−	1.01075i	−0.987121	−	0.159976i	$-0.948858\pi$
$347$	−8.59859	−	18.8283i	−0.461596	−	1.01075i	0.525525	−	0.850778i	$-0.323869\pi$
$348$	2.04599	−	0.600758i	0.109677	−	0.0322040i
$349$	14.9605	−	17.2653i	0.800815	−	0.924190i	−0.197611	−	0.980281i	$-0.563318\pi$
$349$	14.9605	−	17.2653i	0.800815	−	0.924190i	0.998426	+	0.0560907i	$0.0178636\pi$
$350$	1.32094	+	0.848915i	0.0706071	+	0.0453764i
$351$	2.75766	+	3.18251i	0.147193	+	0.169870i
$352$	−0.523684	−	3.64230i	−0.0279125	−	0.194135i
$353$	15.0149	+	4.40876i	0.799161	+	0.234655i	0.655720	−	0.755004i	$-0.272365\pi$
$353$	15.0149	+	4.40876i	0.799161	+	0.234655i	0.143441	+	0.989659i	$0.454183\pi$
$354$	−11.0230	+	7.08408i	−0.585868	+	0.376515i
$355$	−1.36371	+	9.48479i	−0.0723780	+	0.503400i
$356$	−1.95039	+	4.27075i	−0.103370	+	0.226349i
$357$	−2.63029	+	5.75952i	−0.139209	+	0.304826i
$358$	−2.72380	+	18.9444i	−0.143957	+	1.00124i
$359$	3.13152	−	2.01250i	0.165275	−	0.106216i	−0.455389	−	0.890293i	$-0.650500\pi$
$359$	3.13152	−	2.01250i	0.165275	−	0.106216i	0.620664	+	0.784077i	$0.286863\pi$
$360$	0.959493	+	0.281733i	0.0505697	+	0.0148486i
$361$	1.02092	+	7.10063i	0.0537324	+	0.373717i
$362$	1.71736	+	1.98194i	0.0902623	+	0.104168i
$363$	−2.13731	−	1.37357i	−0.112180	−	0.0720936i
$364$	4.33009	−	4.99719i	0.226958	−	0.261924i
$365$	−5.00517	+	1.46965i	−0.261983	+	0.0769251i
$366$	−3.08581	−	6.75698i	−0.161298	−	0.353193i
$367$	31.9910			1.66992			0.834958	−	0.550313i	$-0.185492\pi$
$367$	31.9910			1.66992			0.834958	+	0.550313i	$0.185492\pi$
$368$	−4.70741	+	0.916696i	−0.245390	+	0.0477861i
$369$	7.87591			0.410003
$370$	2.39678	+	5.24823i	0.124603	+	0.272842i
$371$	10.8919	−	3.19814i	0.565477	−	0.166039i
$372$	−1.00614	+	1.16115i	−0.0521659	+	0.0602027i
$373$	30.2239	+	19.4237i	1.56494	+	1.00572i	0.981020	+	0.193908i	$0.0621164\pi$
$373$	30.2239	+	19.4237i	1.56494	+	1.00572i	0.583915	+	0.811815i	$0.301520\pi$
$374$	9.71703	+	11.2141i	0.502456	+	0.579865i
$375$	0.142315	+	0.989821i	0.00734911	+	0.0511142i
$376$	11.1173	+	3.26435i	0.573333	+	0.168346i
$377$	7.55408	−	4.85471i	0.389055	−	0.250030i
$378$	0.223463	−	1.55422i	0.0114937	−	0.0799404i
$379$	−6.28328	+	13.7585i	−0.322751	+	0.706725i	−0.999567	−	0.0294268i	$-0.990632\pi$
$379$	−6.28328	+	13.7585i	−0.322751	+	0.706725i	0.676816	+	0.736152i	$0.263359\pi$
$380$	1.42859	−	3.12818i	0.0732851	−	0.160472i
$381$	−0.973974	+	6.77414i	−0.0498982	+	0.347050i
$382$	−3.55742	+	2.28621i	−0.182013	+	0.116973i
$383$	−27.4813	−	8.06925i	−1.40423	−	0.412319i	−0.510096	−	0.860117i	$-0.670390\pi$
$383$	−27.4813	−	8.06925i	−1.40423	−	0.412319i	−0.894135	+	0.447798i	$0.852208\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−3.78376	−	4.36669i	−0.192838	−	0.222547i
$386$	−1.70213	−	1.09389i	−0.0866362	−	0.0556777i
$387$	−3.99325	+	4.60846i	−0.202988	+	0.234261i
$388$	11.2804	−	3.31224i	0.572678	−	0.168153i
$389$	−1.48611	−	3.25413i	−0.0753488	−	0.164991i	0.868209	−	0.496199i	$-0.165271\pi$
$389$	−1.48611	−	3.25413i	−0.0753488	−	0.164991i	−0.943558	+	0.331208i	$0.892544\pi$
$390$	4.21107			0.213236
$391$	13.9704	−	13.3723i	0.706512	−	0.676264i
$392$	4.53447			0.229025
$393$	3.49313	+	7.64889i	0.176205	+	0.385835i
$394$	12.7666	−	3.74860i	0.643170	−	0.188852i
$395$	6.03587	−	6.96577i	0.303698	−	0.350486i
$396$	−3.09561	−	1.98943i	−0.155560	−	0.0999725i
$397$	6.42502	+	7.41486i	0.322462	+	0.372141i	0.893717	−	0.448632i	$-0.148088\pi$
$397$	6.42502	+	7.41486i	0.322462	+	0.372141i	−0.571254	+	0.820773i	$0.693543\pi$
$398$	−2.21653	−	15.4163i	−0.111105	−	0.772751i
$399$	−5.18111	−	1.52131i	−0.259380	−	0.0761608i
$400$	0.841254	−	0.540641i	0.0420627	−	0.0270320i
$401$	−3.22753	+	22.4480i	−0.161175	+	1.12100i	0.735247	+	0.677799i	$0.237066\pi$
$401$	−3.22753	+	22.4480i	−0.161175	+	1.12100i	−0.896423	+	0.443200i	$0.853843\pi$
$402$	−3.14295	+	6.88211i	−0.156756	+	0.343249i
$403$	−2.68772	+	5.88529i	−0.133885	+	0.293167i
$404$	−2.81881	+	19.6052i	−0.140241	+	0.975397i
$405$	0.841254	−	0.540641i	0.0418022	−	0.0268647i
$406$	−3.21262	−	0.943311i	−0.159440	−	0.0468157i
$407$	−3.02146	−	21.0147i	−0.149768	−	1.04166i
$408$	2.64067	+	3.04750i	0.130733	+	0.150874i
$409$	18.6584	+	11.9910i	0.922599	+	0.592918i	0.913410	−	0.407040i	$-0.133439\pi$
$409$	18.6584	+	11.9910i	0.922599	+	0.592918i	0.00918813	+	0.999958i	$0.497075\pi$
$410$	5.15762	−	5.95222i	0.254717	−	0.293959i
$411$	7.19464	−	2.11254i	0.354885	−	0.104204i
$412$	−1.97212	−	4.31835i	−0.0971595	−	0.212750i
$413$	20.5745			1.01241
$414$	−2.38990	+	4.15793i	−0.117457	+	0.204351i
$415$	2.64000			0.129592
$416$	−1.74934	−	3.83052i	−0.0857685	−	0.187807i
$417$	−6.90013	+	2.02606i	−0.337901	+	0.0992166i
$418$	−8.28693	+	9.56363i	−0.405327	+	0.467772i
$419$	−15.1054	−	9.70768i	−0.737949	−	0.474251i	0.116890	−	0.993145i	$-0.462708\pi$
$419$	−15.1054	−	9.70768i	−0.737949	−	0.474251i	−0.854839	+	0.518894i	$0.826344\pi$
$420$	−1.02826	−	1.18668i	−0.0501741	−	0.0579040i
$421$	−3.89862	−	27.1155i	−0.190007	−	1.32153i	−0.831981	−	0.554804i	$-0.812793\pi$
$421$	−3.89862	−	27.1155i	−0.190007	−	1.32153i	0.641974	−	0.766726i	$-0.278116\pi$
$422$	−9.00404	−	2.64382i	−0.438310	−	0.128699i
$423$	9.74734	−	6.26423i	0.473932	−	0.304578i
$424$	1.02886	−	7.15585i	0.0499657	−	0.347519i
$425$	−1.67513	+	3.66801i	−0.0812555	+	0.177925i
$426$	3.98064	−	8.71639i	0.192863	−	0.422310i
$427$	−1.65994	+	11.5451i	−0.0803302	+	0.558709i
$428$	6.71143	−	4.31317i	0.324409	−	0.208485i
$429$	−14.8680	−	4.36565i	−0.717836	−	0.210776i
$430$	0.867816	+	6.03579i	0.0418498	+	0.291072i
$431$	5.12063	+	5.90952i	0.246652	+	0.284652i	0.865553	−	0.500817i	$-0.166967\pi$
$431$	5.12063	+	5.90952i	0.246652	+	0.284652i	−0.618901	+	0.785469i	$0.712422\pi$
$432$	−0.841254	−	0.540641i	−0.0404748	−	0.0260116i
$433$	−18.4091	+	21.2452i	−0.884684	+	1.02098i	0.114935	+	0.993373i	$0.463334\pi$
$433$	−18.4091	+	21.2452i	−0.884684	+	1.02098i	−0.999619	+	0.0276063i	$0.991212\pi$
$434$	2.31476	−	0.679676i	0.111112	−	0.0326255i
$435$	−0.885818	−	1.93967i	−0.0424717	−	0.0930001i
$436$	1.74262			0.0834562
$437$	12.9837	+	10.1700i	0.621095	+	0.486499i
$438$	5.21648			0.249253
$439$	−8.81047	−	19.2922i	−0.420501	−	0.920768i	−0.994774	−	0.102104i	$-0.967442\pi$
$439$	−8.81047	−	19.2922i	−0.420501	−	0.920768i	0.574273	−	0.818664i	$-0.305285\pi$
$440$	−3.53070	+	1.03671i	−0.168320	+	0.0494231i
$441$	2.96944	−	3.42692i	0.141402	−	0.163187i
$442$	14.2851	+	9.18050i	0.679475	+	0.436672i
$443$	−22.2794	−	25.7119i	−1.05853	−	1.22161i	−0.974322	−	0.225159i	$-0.927710\pi$
$443$	−22.2794	−	25.7119i	−1.05853	−	1.22161i	−0.0842063	−	0.996448i	$-0.526835\pi$
$444$	−0.821102	−	5.71089i	−0.0389678	−	0.271027i
$445$	4.50485	+	1.32274i	0.213550	+	0.0627040i
$446$	14.6652	−	9.42474i	0.694417	−	0.446275i
$447$	−2.75258	+	19.1446i	−0.130192	+	0.905508i
$448$	−0.652285	+	1.42831i	−0.0308176	+	0.0674811i
$449$	3.75432	−	8.22082i	0.177177	−	0.387965i	−0.800119	−	0.599841i	$-0.795230\pi$
$449$	3.75432	−	8.22082i	0.177177	−	0.387965i	0.977296	+	0.211877i	$0.0679576\pi$
$450$	0.142315	−	0.989821i	0.00670879	−	0.0466606i
$451$	−24.3807	+	15.6686i	−1.14804	+	0.737803i
$452$	−0.894730	−	0.262717i	−0.0420846	−	0.0123571i
$453$	2.34080	+	16.2807i	0.109981	+	0.764932i
$454$	14.6401	+	16.8955i	0.687093	+	0.792947i
$455$	−5.56256	−	3.57484i	−0.260777	−	0.167591i
$456$	−2.25203	+	2.59898i	−0.105461	+	0.121708i
$457$	−18.5679	+	5.45203i	−0.868570	+	0.255035i	−0.685507	−	0.728066i	$-0.740419\pi$
$457$	−18.5679	+	5.45203i	−0.868570	+	0.255035i	−0.183063	+	0.983101i	$0.558601\pi$
$458$	−6.26596	−	13.7205i	−0.292789	−	0.641119i
$459$	4.03242			0.188217
$460$	1.57730	+	4.52903i	0.0735420	+	0.211167i
$461$	38.1112			1.77501			0.887507	−	0.460794i	$-0.152435\pi$
$461$	38.1112			1.77501			0.887507	+	0.460794i	$0.152435\pi$
$462$	2.40025	+	5.25582i	0.111670	+	0.244523i
$463$	0.362018	−	0.106298i	0.0168244	−	0.00494009i	−0.273310	−	0.961926i	$-0.588118\pi$
$463$	0.362018	−	0.106298i	0.0168244	−	0.00494009i	0.290134	+	0.956986i	$0.406300\pi$
$464$	−1.39640	+	1.61154i	−0.0648265	+	0.0748137i
$465$	1.29252	+	0.830650i	0.0599390	+	0.0385205i
$466$	7.02622	+	8.10869i	0.325483	+	0.375628i
$467$	1.96853	+	13.6914i	0.0910927	+	0.633564i	0.983307	+	0.181952i	$0.0582417\pi$
$467$	1.96853	+	13.6914i	0.0910927	+	0.633564i	−0.892215	+	0.451612i	$0.850849\pi$
$468$	−4.04049	−	1.18640i	−0.186772	−	0.0548411i
$469$	9.99398	−	6.42274i	0.461479	−	0.296575i
$470$	1.64896	−	11.4687i	0.0760607	−	0.529014i
$471$	−2.55914	+	5.60375i	−0.117919	+	0.258207i
$472$	5.44323	−	11.9190i	0.250545	−	0.548617i
$473$	3.19335	−	22.2103i	0.146831	−	1.02123i
$474$	−7.75386	+	4.98311i	−0.356147	+	0.228882i
$475$	−3.29964	−	0.968863i	−0.151398	−	0.0444545i
$476$	−0.901096	−	6.26726i	−0.0413017	−	0.287259i
$477$	−4.73427	−	5.46364i	−0.216767	−	0.250163i
$478$	−19.7459	−	12.6899i	−0.903155	−	0.580423i
$479$	20.1164	−	23.2155i	0.919141	−	1.06075i	−0.0788182	−	0.996889i	$-0.525115\pi$
$479$	20.1164	−	23.2155i	0.919141	−	1.06075i	0.997959	−	0.0638561i	$-0.0203399\pi$
$480$	−0.959493	+	0.281733i	−0.0437947	+	0.0128593i
$481$	−10.0930	−	22.1006i	−0.460202	−	1.00770i
$482$	7.70881			0.351127
$483$	6.68664	−	3.46354i	0.304253	−	0.157597i
$484$	2.54063			0.115483
$485$	−4.88390	−	10.6943i	−0.221766	−	0.485601i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	−14.3275	+	16.5348i	−0.649240	+	0.749262i	−0.980980	−	0.194108i	$-0.937819\pi$
$487$	−14.3275	+	16.5348i	−0.649240	+	0.749262i	0.331741	+	0.943371i	$0.392364\pi$
$488$	6.24905	+	4.01602i	0.282881	+	0.181797i
$489$	−15.2233	−	17.5686i	−0.688421	−	0.794480i
$490$	−0.645322	−	4.48831i	−0.0291527	−	0.202761i
$491$	−20.5027	−	6.02012i	−0.925272	−	0.271684i	−0.215816	−	0.976434i	$-0.569241\pi$
$491$	−20.5027	−	6.02012i	−0.925272	−	0.271684i	−0.709456	+	0.704750i	$0.751059\pi$
$492$	−6.62564	+	4.25804i	−0.298707	+	0.191967i
$493$	1.22371	−	8.51108i	0.0551130	−	0.383320i
$494$	−6.01589	+	13.1730i	−0.270668	+	0.592680i
$495$	−1.52863	+	3.34723i	−0.0687067	+	0.150447i
$496$	0.218655	−	1.52078i	0.00981790	−	0.0682850i
$497$	−12.6577	+	8.13458i	−0.567773	+	0.364886i
$498$	−2.53306	−	0.743774i	−0.113509	−	0.0333293i
$499$	1.45984	+	10.1534i	0.0653515	+	0.454530i	0.996054	+	0.0887522i	$0.0282879\pi$
$499$	1.45984	+	10.1534i	0.0653515	+	0.454530i	−0.930702	+	0.365778i	$0.880803\pi$
$500$	−0.654861	−	0.755750i	−0.0292863	−	0.0337981i
$501$	−18.8019	−	12.0832i	−0.840006	−	0.539839i
$502$	3.74578	−	4.32286i	0.167182	−	0.192939i
$503$	−27.1290	+	7.96580i	−1.20962	+	0.355178i	−0.823525	−	0.567280i	$-0.807996\pi$
$503$	−27.1290	+	7.96580i	−1.20962	+	0.355178i	−0.386099	+	0.922457i	$0.626178\pi$
$504$	0.652285	+	1.42831i	0.0290551	+	0.0636218i
$505$	19.8068			0.881393
$506$	−0.873693	−	17.6259i	−0.0388404	−	0.783565i
$507$	−4.73311			−0.210205
$508$	−2.84302	−	6.22534i	−0.126139	−	0.276205i
$509$	−3.12518	+	0.917636i	−0.138521	+	0.0406735i	−0.350258	−	0.936653i	$-0.613906\pi$
$509$	−3.12518	+	0.917636i	−0.138521	+	0.0406735i	0.211737	+	0.977327i	$0.432088\pi$
$510$	2.64067	−	3.04750i	0.116931	−	0.134945i
$511$	−6.89064	−	4.42835i	−0.304824	−	0.195898i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	0.489413	+	3.40394i	0.0216081	+	0.150288i
$514$	−11.7103	−	3.43844i	−0.516518	−	0.151663i
$515$	−3.99373	+	2.56661i	−0.175985	+	0.113098i
$516$	0.867816	−	6.03579i	0.0382035	−	0.265711i
$517$	−17.7117	+	38.7833i	−0.778961	+	1.70569i
$518$	−3.76344	+	8.24077i	−0.165356	+	0.362079i
$519$	1.36323	−	9.48151i	0.0598394	−	0.416192i
$520$	−3.54258	+	2.27668i	−0.155352	+	0.0998389i
$521$	−7.36290	−	2.16194i	−0.322575	−	0.0947164i	0.116436	−	0.993198i	$-0.462853\pi$
$521$	−7.36290	−	2.16194i	−0.322575	−	0.0947164i	−0.439011	+	0.898482i	$0.644671\pi$
$522$	0.303468	+	2.11066i	0.0132824	+	0.0923813i
$523$	23.7724	+	27.4348i	1.03950	+	1.19964i	0.979500	+	0.201443i	$0.0645630\pi$
$523$	23.7724	+	27.4348i	1.03950	+	1.19964i	0.0599948	+	0.998199i	$0.480892\pi$
$524$	−7.07391	−	4.54612i	−0.309025	−	0.198598i
$525$	−1.02826	+	1.18668i	−0.0448771	+	0.0517909i
$526$	−29.5331	+	8.67171i	−1.28771	+	0.378104i
$527$	2.57369	+	5.63560i	0.112112	+	0.245491i
$528$	3.67976			0.160141
$529$	−22.8873	+	2.27458i	−0.995098	+	0.0988946i
$530$	−7.22944			−0.314027
$531$	−5.44323	−	11.9190i	−0.236216	−	0.517241i
$532$	5.18111	−	1.52131i	0.224630	−	0.0659572i
$533$	−21.7191	+	25.0652i	−0.940759	+	1.08569i
$534$	−3.94971	−	2.53833i	−0.170921	−	0.109844i
$535$	−5.22441	−	6.02929i	−0.225871	−	0.260669i
$536$	−1.07673	−	7.48881i	−0.0465076	−	0.323467i
$537$	−18.3640	−	5.39215i	−0.792464	−	0.232688i
$538$	−10.7231	+	6.89130i	−0.462304	+	0.297105i
$539$	−2.37463	+	16.5159i	−0.102283	+	0.711390i
$540$	−0.415415	+	0.909632i	−0.0178766	+	0.0391443i
$541$	13.7912	−	30.1986i	0.592932	−	1.29834i	−0.340723	−	0.940164i	$-0.610672\pi$
$541$	13.7912	−	30.1986i	0.592932	−	1.29834i	0.933654	−	0.358175i	$-0.116601\pi$
$542$	−0.466195	+	3.24246i	−0.0200248	+	0.139276i
$543$	−2.20617	+	1.41782i	−0.0946758	+	0.0608444i
$544$	−3.86907	−	1.13606i	−0.165885	−	0.0487083i
$545$	−0.248000	−	1.72488i	−0.0106232	−	0.0738857i
$546$	4.33009	+	4.99719i	0.185311	+	0.213860i
$547$	−1.15335	−	0.741215i	−0.0493138	−	0.0316921i	0.515752	−	0.856738i	$-0.327513\pi$
$547$	−1.15335	−	0.741215i	−0.0493138	−	0.0316921i	−0.565065	+	0.825046i	$0.691149\pi$
$548$	−4.91039	+	5.66690i	−0.209762	+	0.242078i
$549$	7.12736	−	2.09278i	0.304188	−	0.0893178i
$550$	1.52863	+	3.34723i	0.0651809	+	0.142726i
$551$	7.33310			0.312401
$552$	−0.237432	−	4.78995i	−0.0101058	−	0.203874i
$553$	14.4726			0.615438
$554$	−2.04825	−	4.48504i	−0.0870218	−	0.190551i
$555$	−5.53590	+	1.62549i	−0.234986	+	0.0689981i
$556$	4.70939	−	5.43492i	0.199722	−	0.230492i
$557$	−2.53632	−	1.62999i	−0.107467	−	0.0690650i	0.485803	−	0.874068i	$-0.338527\pi$
$557$	−2.53632	−	1.62999i	−0.107467	−	0.0690650i	−0.593270	+	0.805003i	$0.702164\pi$
$558$	−1.00614	−	1.16115i	−0.0425933	−	0.0491553i
$559$	−3.65443	−	25.4171i	−0.154566	−	1.07503i
$560$	1.50660	+	0.442377i	0.0636654	+	0.0186938i
$561$	−12.4828	+	8.02220i	−0.527024	+	0.338698i
$562$	0.385446	−	2.68083i	0.0162590	−	0.113084i
$563$	6.18507	−	13.5434i	0.260670	−	0.570787i	−0.733367	−	0.679833i	$-0.762052\pi$
$563$	6.18507	−	13.5434i	0.260670	−	0.570787i	0.994037	+	0.109046i	$0.0347795\pi$
$564$	−4.81328	+	10.5396i	−0.202676	+	0.443798i
$565$	−0.132709	+	0.923012i	−0.00558311	+	0.0388314i
$566$	−18.6628	+	11.9939i	−0.784457	+	0.504140i
$567$	1.50660	+	0.442377i	0.0632712	+	0.0185781i
$568$	1.36371	+	9.48479i	0.0572199	+	0.397973i
$569$	16.3756	+	18.8984i	0.686499	+	0.792262i	0.986862	−	0.161563i	$-0.0516534\pi$
$569$	16.3756	+	18.8984i	0.686499	+	0.792262i	−0.300363	+	0.953825i	$0.597108\pi$
$570$	2.89303	+	1.85923i	0.121176	+	0.0778748i
$571$	21.1459	−	24.4037i	0.884928	−	1.02126i	−0.114684	−	0.993402i	$-0.536586\pi$
$571$	21.1459	−	24.4037i	0.884928	−	1.02126i	0.999612	−	0.0278592i	$-0.00886899\pi$
$572$	14.8680	−	4.36565i	0.621664	−	0.182537i
$573$	−1.75667	−	3.84657i	−0.0733860	−	0.160693i
$574$	12.3668			0.516179
$575$	4.25846	−	2.20579i	0.177590	−	0.0919879i
$576$	1.00000			0.0416667
$577$	−5.28813	−	11.5794i	−0.220148	−	0.482056i	0.767044	−	0.641594i	$-0.221727\pi$
$577$	−5.28813	−	11.5794i	−0.220148	−	0.482056i	−0.987192	+	0.159538i	$0.948999\pi$
$578$	−0.709665	+	0.208376i	−0.0295182	+	0.00866732i
$579$	1.32500	−	1.52913i	0.0550650	−	0.0635484i
$580$	1.79386	+	1.15285i	0.0744861	+	0.0478693i
$581$	2.71462	+	3.13283i	0.112621	+	0.129972i
$582$	1.67315	+	11.6370i	0.0693543	+	0.482370i
$583$	25.5250	+	7.49481i	1.05714	+	0.310403i
$584$	−4.38838	+	2.82024i	−0.181592	+	0.116702i
$585$	−0.599298	+	4.16821i	−0.0247779	+	0.172334i
$586$	5.88084	−	12.8772i	0.242935	−	0.531954i
$587$	−13.1636	+	28.8242i	−0.543318	+	1.18970i	0.416515	+	0.909129i	$0.363251\pi$
$587$	−13.1636	+	28.8242i	−0.543318	+	1.18970i	−0.959833	+	0.280572i	$0.909476\pi$
$588$	−0.645322	+	4.48831i	−0.0266126	+	0.185095i
$589$	−4.44490	+	2.85656i	−0.183149	+	0.117703i
$590$	−12.5723	−	3.69157i	−0.517595	−	0.151980i
$591$	1.89357	+	13.1701i	0.0778912	+	0.541745i
$592$	3.77829	+	4.36038i	0.155287	+	0.179211i
$593$	−8.38040	−	5.38576i	−0.344142	−	0.221167i	0.357140	−	0.934051i	$-0.383752\pi$
$593$	−8.38040	−	5.38576i	−0.344142	−	0.221167i	−0.701282	+	0.712884i	$0.747388\pi$
$594$	2.40973	−	2.78098i	0.0988724	−	0.114105i
$595$	−6.07523	+	1.78385i	−0.249060	+	0.0731306i
$596$	−8.03473	−	17.5936i	−0.329115	−	0.720662i
$597$	15.5749			0.637437
$598$	−6.64212	−	19.0721i	−0.271616	−	0.779915i
$599$	−23.5164			−0.960856			−0.480428	−	0.877034i	$-0.659519\pi$
$599$	−23.5164			−0.960856			−0.480428	+	0.877034i	$0.659519\pi$
$600$	0.415415	+	0.909632i	0.0169592	+	0.0371356i
$601$	−39.0335	+	11.4613i	−1.59221	+	0.467515i	−0.953365	−	0.301820i	$-0.902406\pi$
$601$	−39.0335	+	11.4613i	−1.59221	+	0.467515i	−0.638845	+	0.769335i	$0.720588\pi$
$602$	−6.27021	+	7.23621i	−0.255555	+	0.294926i
$603$	−6.36477	−	4.09039i	−0.259194	−	0.166574i
$604$	−10.7712	−	12.4306i	−0.438274	−	0.505795i
$605$	−0.361569	−	2.51477i	−0.0146999	−	0.102240i
$606$	−19.0045	−	5.58023i	−0.772006	−	0.226682i
$607$	4.41251	−	2.83575i	0.179098	−	0.115099i	−0.448020	−	0.894024i	$-0.647871\pi$
$607$	4.41251	−	2.83575i	0.179098	−	0.115099i	0.627118	+	0.778924i	$0.284234\pi$
$608$	0.489413	−	3.40394i	0.0198483	−	0.138048i
$609$	1.39091	−	3.04568i	0.0563627	−	0.123417i
$610$	3.08581	−	6.75698i	0.124941	−	0.273582i
$611$	−6.94387	+	48.2957i	−0.280919	+	1.95383i
$612$	−3.39228	+	2.18009i	−0.137125	+	0.0881249i
$613$	−14.2608	−	4.18734i	−0.575987	−	0.169125i	−0.0192512	−	0.999815i	$-0.506128\pi$
$613$	−14.2608	−	4.18734i	−0.575987	−	0.169125i	−0.556736	+	0.830690i	$0.687946\pi$
$614$	−2.65300	−	18.4520i	−0.107066	−	0.744662i
$615$	5.15762	+	5.95222i	0.207975	+	0.240016i
$616$	−4.86073	−	3.12380i	−0.195845	−	0.125862i
$617$	11.3941	−	13.1495i	0.458709	−	0.529379i	−0.478527	−	0.878073i	$-0.658829\pi$
$617$	11.3941	−	13.1495i	0.458709	−	0.529379i	0.937237	+	0.348694i	$0.113375\pi$
$618$	4.55505	−	1.33748i	0.183231	−	0.0538015i
$619$	−2.53063	−	5.54131i	−0.101715	−	0.222724i	0.851932	−	0.523652i	$-0.175431\pi$
$619$	−2.53063	−	5.54131i	−0.101715	−	0.222724i	−0.953647	+	0.300928i	$0.902704\pi$
$620$	−1.53642			−0.0617040
$621$	−3.77549	−	2.95731i	−0.151505	−	0.118673i
$622$	8.54729			0.342715
$623$	3.06250	+	6.70594i	0.122696	+	0.268668i
$624$	4.04049	−	1.18640i	0.161749	−	0.0474938i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−12.0713	−	7.75778i	−0.482468	−	0.310063i
$627$	−8.28693	−	9.56363i	−0.330948	−	0.381935i
$628$	−0.876724	−	6.09775i	−0.0349851	−	0.243327i
$629$	−22.3231	−	6.55464i	−0.890079	−	0.261351i
$630$	1.32094	−	0.848915i	0.0526274	−	0.0338216i
$631$	−0.976840	+	6.79407i	−0.0388874	+	0.270468i	−0.999983	−	0.00574643i	$-0.998171\pi$
$631$	−0.976840	+	6.79407i	−0.0388874	+	0.270468i	0.961096	+	0.276214i	$0.0890799\pi$
$632$	3.82889	−	8.38411i	0.152305	−	0.333502i
$633$	3.89832	−	8.53613i	0.154944	−	0.339281i
$634$	2.94122	−	20.4566i	0.116811	−	0.812436i
$635$	−5.75737	+	3.70004i	−0.228474	+	0.146832i
$636$	6.93659	+	2.03677i	0.275054	+	0.0807631i
$637$	2.71750	+	18.9006i	0.107671	+	0.748869i
$638$	−5.13843	−	5.93007i	−0.203433	−	0.234774i
$639$	8.06116	+	5.18059i	0.318895	+	0.204941i
$640$	0.654861	−	0.755750i	0.0258856	−	0.0298736i
$641$	35.8801	−	10.5353i	1.41718	−	0.416121i	0.518630	−	0.854999i	$-0.326442\pi$
$641$	35.8801	−	10.5353i	1.41718	−	0.416121i	0.898547	+	0.438878i	$0.144624\pi$
$642$	3.31414	+	7.25695i	0.130799	+	0.286409i
$643$	−26.7613			−1.05536			−0.527681	−	0.849443i	$-0.676938\pi$
$643$	−26.7613			−1.05536			−0.527681	+	0.849443i	$0.676938\pi$
$644$	−3.75263	+	6.52879i	−0.147874	+	0.257270i
$645$	−6.09786			−0.240103
$646$	5.76067	+	12.6141i	0.226650	+	0.496295i
$647$	−14.9281	+	4.38329i	−0.586885	+	0.172325i	−0.561676	−	0.827357i	$-0.689843\pi$
$647$	−14.9281	+	4.38329i	−0.586885	+	0.172325i	−0.0252087	+	0.999682i	$0.508025\pi$
$648$	0.654861	−	0.755750i	0.0257254	−	0.0296886i
$649$	40.5621	+	26.0677i	1.59220	+	1.02325i
$650$	2.75766	+	3.18251i	0.108164	+	0.124828i
$651$	0.343333	+	2.38793i	0.0134563	+	0.0935904i
$652$	22.3050	+	6.54933i	0.873530	+	0.256491i
$653$	17.8007	−	11.4398i	0.696594	−	0.447674i	−0.143830	−	0.989602i	$-0.545942\pi$
$653$	17.8007	−	11.4398i	0.696594	−	0.447674i	0.840425	+	0.541928i	$0.182306\pi$
$654$	−0.248000	+	1.72488i	−0.00969757	+	0.0674481i
$655$	−3.49313	+	7.64889i	−0.136488	+	0.298867i
$656$	3.27177	−	7.16418i	0.127741	−	0.279714i
$657$	−0.742382	+	5.16338i	−0.0289631	+	0.201443i
$658$	15.3053	−	9.83611i	0.596662	−	0.383452i
$659$	−7.57503	−	2.22423i	−0.295081	−	0.0866436i	0.130841	−	0.991403i	$-0.458232\pi$
$659$	−7.57503	−	2.22423i	−0.295081	−	0.0866436i	−0.425922	+	0.904760i	$0.640050\pi$
$660$	−0.523684	−	3.64230i	−0.0203844	−	0.141777i
$661$	−27.6553	−	31.9159i	−1.07567	−	1.24138i	−0.968993	−	0.247090i	$-0.920526\pi$
$661$	−27.6553	−	31.9159i	−1.07567	−	1.24138i	−0.106673	−	0.994294i	$-0.534020\pi$
$662$	−15.4096	−	9.90315i	−0.598911	−	0.384897i
$663$	−11.1200	+	12.8332i	−0.431867	+	0.498401i
$664$	2.53306	−	0.743774i	0.0983018	−	0.0288640i
$665$	−2.24317	−	4.91187i	−0.0869866	−	0.190474i
$666$	5.76961			0.223568
$667$	−7.38763	+	7.07134i	−0.286050	+	0.273803i
$668$	22.3498			0.864741
$669$	7.24174	+	15.8572i	0.279982	+	0.613075i
$670$	−7.25935	+	2.13154i	−0.280453	+	0.0823485i
$671$	−17.9001	+	20.6578i	−0.691026	+	0.797486i
$672$	−1.32094	−	0.848915i	−0.0509563	−	0.0327476i
$673$	−15.5259	−	17.9179i	−0.598480	−	0.690683i	0.372993	−	0.927834i	$-0.378332\pi$
$673$	−15.5259	−	17.9179i	−0.598480	−	0.690683i	−0.971473	+	0.237151i	$0.923786\pi$
$674$	0.880213	+	6.12202i	0.0339045	+	0.235811i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	3.98174	−	2.55891i	0.153144	−	0.0984197i
$677$	0.527609	−	3.66960i	0.0202776	−	0.141034i	−0.977168	−	0.212470i	$-0.931849\pi$
$677$	0.527609	−	3.66960i	0.0202776	−	0.141034i	0.997445	+	0.0714362i	$0.0227582\pi$
$678$	0.387376	−	0.848235i	0.0148771	−	0.0325763i
$679$	7.66871	−	16.7921i	0.294298	−	0.644423i
$680$	−0.573873	+	3.99137i	−0.0220070	+	0.153062i
$681$	−18.8071	+	12.0866i	−0.720689	+	0.463158i
$682$	5.42464	+	1.59282i	0.207720	+	0.0609921i
$683$	−1.13061	−	7.86354i	−0.0432615	−	0.300890i	−0.999952	−	0.00978367i	$-0.996886\pi$
$683$	−1.13061	−	7.86354i	−0.0432615	−	0.300890i	0.956691	−	0.291106i	$-0.0940234\pi$
$684$	−2.25203	−	2.59898i	−0.0861086	−	0.0993746i
$685$	6.30804	+	4.05393i	0.241018	+	0.154893i
$686$	11.8605	−	13.6877i	0.452835	−	0.522599i
$687$	14.4726	−	4.24955i	0.552165	−	0.162130i
$688$	2.53314	+	5.54681i	0.0965752	+	0.211470i
$689$	30.4437			1.15981
$690$	−4.70741	+	0.916696i	−0.179208	+	0.0348980i
$691$	−4.62051			−0.175772			−0.0878862	−	0.996131i	$-0.528011\pi$
$691$	−4.62051			−0.175772			−0.0878862	+	0.996131i	$0.528011\pi$
$692$	3.97926	+	8.71337i	0.151269	+	0.331233i
$693$	−5.54392	+	1.62784i	−0.210596	+	0.0618366i
$694$	−13.5548	+	15.6431i	−0.514534	+	0.593804i
$695$	−6.04982	−	3.88798i	−0.229483	−	0.147480i
$696$	−1.39640	−	1.61154i	−0.0529306	−	0.0610852i
$697$	4.51977	+	31.4357i	0.171198	+	1.19071i
$698$	−21.9199	−	6.43625i	−0.829679	−	0.243616i
$699$	−9.02609	+	5.80072i	−0.341398	+	0.219403i
$700$	0.223463	−	1.55422i	0.00844611	−	0.0587440i
$701$	4.01845	−	8.79918i	0.151775	−	0.332340i	−0.818438	−	0.574595i	$-0.805160\pi$
$701$	4.01845	−	8.79918i	0.151775	−	0.332340i	0.970213	+	0.242255i	$0.0778869\pi$
$702$	1.74934	−	3.83052i	0.0660246	−	0.144574i
$703$	2.82372	−	19.6394i	0.106499	−	0.740715i
$704$	−3.09561	+	1.98943i	−0.116670	+	0.0749794i
$705$	11.1173	+	3.26435i	0.418703	+	0.122942i
$706$	−2.22705	−	15.4895i	−0.0838161	−	0.582954i
$707$	20.3667	+	23.5044i	0.765967	+	0.883973i
$708$	11.0230	+	7.08408i	0.414271	+	0.266236i
$709$	13.8221	−	15.9515i	0.519099	−	0.599072i	−0.434306	−	0.900765i	$-0.643006\pi$
$709$	13.8221	−	15.9515i	0.519099	−	0.599072i	0.953405	+	0.301693i	$0.0975518\pi$
$710$	9.19417	−	2.69965i	0.345051	−	0.101316i
$711$	−3.82889	−	8.38411i	−0.143595	−	0.314429i
$712$	4.69503			0.175954
$713$	1.72335	−	7.16404i	0.0645402	−	0.268295i
$714$	6.33171			0.236958
$715$	−6.43716	−	14.0954i	−0.240736	−	0.527138i
$716$	18.3640	−	5.39215i	0.686294	−	0.201514i
$717$	15.3709	−	17.7389i	0.574036	−	0.662473i
$718$	−3.13152	−	2.01250i	−0.116867	−	0.0751060i
$719$	27.5974	+	31.8491i	1.02921	+	1.18777i	0.981999	+	0.188885i	$0.0604874\pi$
$719$	27.5974	+	31.8491i	1.02921	+	1.18777i	0.0472094	+	0.998885i	$0.484967\pi$
$720$	−0.142315	−	0.989821i	−0.00530376	−	0.0368885i
$721$	−7.15235	−	2.10012i	−0.266368	−	0.0782126i
$722$	6.03486	−	3.87837i	0.224594	−	0.144338i
$723$	−1.09708	+	7.63035i	−0.0408008	+	0.283776i
$724$	1.08942	−	2.38549i	0.0404879	−	0.0886560i
$725$	0.885818	−	1.93967i	0.0328985	−	0.0720376i
$726$	−0.361569	+	2.51477i	−0.0134191	+	0.0933318i
$727$	6.66481	−	4.28321i	0.247184	−	0.158856i	−0.411182	−	0.911553i	$-0.634884\pi$
$727$	6.66481	−	4.28321i	0.247184	−	0.158856i	0.658366	+	0.752698i	$0.271248\pi$
$728$	−6.34439	−	1.86288i	−0.235139	−	0.0690429i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	3.41607	+	3.94235i	0.126434	+	0.145913i
$731$	−20.6857	−	13.2939i	−0.765087	−	0.491692i
$732$	−4.86448	+	5.61390i	−0.179796	+	0.207496i
$733$	16.1676	−	4.74724i	0.597165	−	0.175343i	0.0308382	−	0.999524i	$-0.490182\pi$
$733$	16.1676	−	4.74724i	0.597165	−	0.175343i	0.566326	+	0.824181i	$0.308364\pi$
$734$	−13.2895	−	29.1000i	−0.490526	−	1.07410i
$735$	4.53447			0.167256
$736$	2.78938	+	3.90120i	0.102818	+	0.143800i
$737$	27.8404			1.02551
$738$	−3.27177	−	7.16418i	−0.120436	−	0.263717i
$739$	−29.6451	+	8.70458i	−1.09051	+	0.320203i	−0.777076	−	0.629406i	$-0.783298\pi$
$739$	−29.6451	+	8.70458i	−1.09051	+	0.320203i	−0.313435	+	0.949610i	$0.601480\pi$
$740$	3.77829	−	4.36038i	0.138893	−	0.160291i
$741$	−12.1827	−	7.82937i	−0.447544	−	0.287619i
$742$	−7.43377	−	8.57902i	−0.272902	−	0.314946i
$743$	−1.62074	−	11.2725i	−0.0594591	−	0.413547i	−0.997713	−	0.0675987i	$-0.978466\pi$
$743$	−1.62074	−	11.2725i	−0.0594591	−	0.413547i	0.938253	−	0.345949i	$-0.112443\pi$
$744$	1.47418	+	0.432859i	0.0540461	+	0.0158694i
$745$	−16.2711	+	10.4568i	−0.596126	+	0.383107i
$746$	5.11298	−	35.5616i	0.187199	−	1.30200i
$747$	1.09670	−	2.40143i	0.0401260	−	0.0878637i
$748$	6.16406	−	13.4974i	0.225380	−	0.493514i
$749$	1.78276	−	12.3994i	0.0651408	−	0.453064i
$750$	0.841254	−	0.540641i	0.0307182	−	0.0197414i
$751$	52.1674	+	15.3177i	1.90362	+	0.558952i	0.987394	+	0.158284i	$0.0505960\pi$
$751$	52.1674	+	15.3177i	1.90362	+	0.558952i	0.916223	+	0.400669i	$0.131222\pi$
$752$	−1.64896	−	11.4687i	−0.0601313	−	0.418222i
$753$	3.74578	+	4.32286i	0.136504	+	0.157534i
$754$	−7.55408	−	4.85471i	−0.275103	−	0.176798i
$755$	−10.7712	+	12.4306i	−0.392004	+	0.452397i
$756$	−1.50660	+	0.442377i	−0.0547944	+	0.0160891i
$757$	5.05669	+	11.0726i	0.183789	+	0.402441i	0.978991	−	0.203903i	$-0.0653628\pi$
$757$	5.05669	+	11.0726i	0.183789	+	0.402441i	−0.795203	+	0.606344i	$0.792635\pi$
$758$	15.1253			0.549376
$759$	17.5708	+	1.64362i	0.637780	+	0.0596597i
$760$	−3.43895			−0.124744
$761$	−18.4024	−	40.2956i	−0.667085	−	1.46071i	−0.875769	−	0.482730i	$-0.839645\pi$
$761$	−18.4024	−	40.2956i	−0.667085	−	1.46071i	0.208684	−	0.977983i	$-0.433082\pi$
$762$	6.56658	−	1.92812i	0.237882	−	0.0698485i
$763$	1.79187	−	2.06793i	0.0648700	−	0.0748640i
$764$	3.55742	+	2.28621i	0.128703	+	0.0827123i
$765$	2.64067	+	3.04750i	0.0954736	+	0.110182i
$766$	4.07611	+	28.3500i	0.147276	+	1.02433i
$767$	52.9430	+	15.5455i	1.91166	+	0.561315i
$768$	−0.841254	+	0.540641i	−0.0303561	+	0.0195087i
$769$	−7.02741	+	48.8767i	−0.253415	+	1.76254i	0.323970	+	0.946067i	$0.394982\pi$
$769$	−7.02741	+	48.8767i	−0.253415	+	1.76254i	−0.577385	+	0.816472i	$0.695927\pi$
$770$	−2.40025	+	5.25582i	−0.0864991	+	0.189407i
$771$	5.06999	−	11.1017i	0.182591	−	0.399819i
$772$	−0.287950	+	2.00273i	−0.0103635	+	0.0720799i
$773$	−39.3451	+	25.2855i	−1.41514	+	0.909457i	−1.00000		0.000298443i	$-0.999905\pi$
$773$	−39.3451	+	25.2855i	−1.41514	+	0.909457i	−0.415144	+	0.909756i	$0.636269\pi$
$774$	5.85085	+	1.71797i	0.210305	+	0.0617510i
$775$	0.218655	+	1.52078i	0.00785432	+	0.0546280i
$776$	−7.69899	−	8.88510i	−0.276378	−	0.318957i
$777$	−7.62130	−	4.89791i	−0.273413	−	0.175712i
$778$	−2.34271	+	2.70363i	−0.0839901	+	0.0969297i
$779$	−25.9877	+	7.63068i	−0.931106	+	0.273397i
$780$	−1.74934	−	3.83052i	−0.0626365	−	0.137155i
$781$	−35.2606			−1.26172
$782$	−17.9673	−	7.15287i	−0.642511	−	0.255786i
$783$	−2.13237			−0.0762047
$784$	−1.88369	−	4.12470i	−0.0672745	−	0.147311i
$785$	−5.91091	+	1.73560i	−0.210969	+	0.0619462i
$786$	5.50657	−	6.35493i	0.196413	−	0.226673i
$787$	16.1060	+	10.3507i	0.574118	+	0.368963i	0.795251	−	0.606280i	$-0.207339\pi$
$787$	16.1060	+	10.3507i	0.574118	+	0.368963i	−0.221133	+	0.975244i	$0.570975\pi$
$788$	−8.71326	−	10.0556i	−0.310397	−	0.358217i
$789$	−4.38044	−	30.4666i	−0.155948	−	1.08464i
$790$	−8.84368	−	2.59674i	−0.314644	−	0.0923878i
$791$	−1.23178	+	0.791616i	−0.0437970	+	0.0281466i
$792$	−0.523684	+	3.64230i	−0.0186083	+	0.129424i
$793$	−12.9946	+	28.4541i	−0.461451	+	1.01044i
$794$	4.07575	−	8.92465i	0.144643	−	0.316724i
$795$	1.02886	−	7.15585i	0.0364898	−	0.253792i
$796$	−13.1024	+	8.42041i	−0.464403	+	0.298453i
$797$	−34.5615	−	10.1482i	−1.22423	−	0.359467i	−0.395161	−	0.918612i	$-0.629311\pi$
$797$	−34.5615	−	10.1482i	−1.22423	−	0.359467i	−0.829070	+	0.559145i	$0.811129\pi$
$798$	0.768477	+	5.34488i	0.0272038	+	0.189207i
$799$	30.5966	+	35.3104i	1.08243	+	1.24919i
$800$	−0.841254	−	0.540641i	−0.0297428	−	0.0191145i
$801$	3.07459	−	3.54827i	0.108635	−	0.125372i
$802$	21.7602	−	6.38937i	0.768379	−	0.225616i
$803$	−7.97405	−	17.4607i	−0.281398	−	0.616176i
$804$	7.56582			0.266826
$805$	6.99639	+	2.78529i	0.246590	+	0.0981685i
$806$	6.46996			0.227895
$807$	−5.29510	−	11.5947i	−0.186396	−	0.408151i
$808$	19.0045	−	5.58023i	0.668577	−	0.196312i
$809$	−25.8027	+	29.7779i	−0.907173	+	1.04693i	0.0915187	+	0.995803i	$0.470828\pi$
$809$	−25.8027	+	29.7779i	−0.907173	+	1.04693i	−0.998692	+	0.0511304i	$0.983718\pi$
$810$	−0.841254	−	0.540641i	−0.0295586	−	0.0189962i
$811$	−26.9387	−	31.0889i	−0.945946	−	1.09168i	−0.995674	−	0.0929168i	$-0.970381\pi$
$811$	−26.9387	−	31.0889i	−0.945946	−	1.09168i	0.0497282	−	0.998763i	$-0.484165\pi$
$812$	0.476506	+	3.31417i	0.0167221	+	0.116305i
$813$	−3.14311	−	0.922901i	−0.110234	−	0.0323675i
$814$	−17.8605	+	11.4782i	−0.626009	+	0.402312i
$815$	3.30834	−	23.0100i	0.115886	−	0.806005i
$816$	1.67513	−	3.66801i	0.0586411	−	0.128406i
$817$	8.71134	−	19.0752i	0.304771	−	0.667356i
$818$	3.15644	−	21.9535i	0.110362	−	0.767587i
$819$	−5.56256	+	3.57484i	−0.194372	+	0.124915i
$820$	−7.55688	−	2.21890i	−0.263898	−	0.0774874i
$821$	−0.831758	−	5.78501i	−0.0290286	−	0.201898i	0.970146	−	0.242522i	$-0.0779746\pi$
$821$	−0.831758	−	5.78501i	−0.0290286	−	0.201898i	−0.999175	+	0.0406237i	$0.987066\pi$
$822$	−4.91039	−	5.66690i	−0.171270	−	0.197656i
$823$	17.9569	+	11.5402i	0.625938	+	0.402266i	0.814804	−	0.579737i	$-0.196845\pi$
$823$	17.9569	+	11.5402i	0.625938	+	0.402266i	−0.188866	+	0.982003i	$0.560481\pi$
$824$	−3.10886	+	3.58781i	−0.108302	+	0.124987i
$825$	−3.53070	+	1.03671i	−0.122923	+	0.0360935i
$826$	−8.54697	−	18.7153i	−0.297387	−	0.651187i
$827$	−0.250181			−0.00869965			−0.00434983	−	0.999991i	$-0.501385\pi$
$827$	−0.250181			−0.00869965			−0.00434983	+	0.999991i	$0.501385\pi$
$828$	4.77499	+	0.446666i	0.165942	+	0.0155227i
$829$	−45.4669			−1.57913			−0.789566	−	0.613665i	$-0.789694\pi$
$829$	−45.4669			−1.57913			−0.789566	+	0.613665i	$0.789694\pi$
$830$	−1.09670	−	2.40143i	−0.0380669	−	0.0833548i
$831$	4.73089	−	1.38911i	0.164113	−	0.0481878i
$832$	−2.75766	+	3.18251i	−0.0956048	+	0.110334i
$833$	15.3822	+	9.88554i	0.532961	+	0.342514i
$834$	4.70939	+	5.43492i	0.163073	+	0.188196i
$835$	−3.18071	−	22.1223i	−0.110073	−	0.765575i
$836$	12.1419	+	3.56518i	0.419936	+	0.123304i
$837$	1.29252	−	0.830650i	0.0446759	−	0.0287115i
$838$	−2.55539	+	17.7731i	−0.0882744	+	0.613962i
$839$	−11.9357	+	26.1356i	−0.412067	+	0.902301i	0.583836	+	0.811872i	$0.301551\pi$
$839$	−11.9357	+	26.1356i	−0.412067	+	0.902301i	−0.995903	+	0.0904291i	$0.971176\pi$
$840$	−0.652285	+	1.42831i	−0.0225060	+	0.0492812i
$841$	3.48003	−	24.2041i	0.120001	−	0.834624i
$842$	−23.0456	+	14.8105i	−0.794204	+	0.510404i
$843$	2.59869	+	0.763045i	0.0895037	+	0.0262807i
$844$	1.33551	+	9.28864i	0.0459700	+	0.319728i
$845$	−3.09953	−	3.57704i	−0.106627	−	0.123054i
$846$	−9.74734	−	6.26423i	−0.335120	−	0.215369i
$847$	2.61244	−	3.01491i	0.0897644	−	0.103594i
$848$	−6.93659	+	2.03677i	−0.238204	+	0.0699429i
$849$	−9.21579	−	20.1798i	−0.316285	−	0.692568i
$850$	4.03242			0.138311
$851$	16.0937	+	22.5084i	0.551684	+	0.771578i
$852$	−9.58232			−0.328285
$853$	−0.688864	−	1.50840i	−0.0235863	−	0.0516467i	0.897472	−	0.441071i	$-0.145401\pi$
$853$	−0.688864	−	1.50840i	−0.0235863	−	0.0516467i	−0.921059	+	0.389424i	$0.872674\pi$
$854$	11.1914	−	3.28609i	0.382962	−	0.112448i
$855$	−2.25203	+	2.59898i	−0.0770178	+	0.0888833i
$856$	−6.71143	−	4.31317i	−0.229392	−	0.147421i
$857$	33.7952	+	39.0017i	1.15442	+	1.33227i	0.934170	+	0.356829i	$0.116142\pi$
$857$	33.7952	+	39.0017i	1.15442	+	1.33227i	0.220251	+	0.975443i	$0.429313\pi$
$858$	2.20527	+	15.3380i	0.0752867	+	0.523631i
$859$	1.71793	+	0.504429i	0.0586149	+	0.0172109i	0.310909	−	0.950440i	$-0.399367\pi$
$859$	1.71793	+	0.504429i	0.0586149	+	0.0172109i	−0.252294	+	0.967651i	$0.581185\pi$
$860$	5.12985	−	3.29675i	0.174926	−	0.112418i
$861$	−1.75997	+	12.2409i	−0.0599798	+	0.417168i
$862$	3.24830	−	7.11279i	0.110638	−	0.242263i
$863$	11.0704	−	24.2407i	0.376839	−	0.825163i	−0.622263	−	0.782808i	$-0.713787\pi$
$863$	11.0704	−	24.2407i	0.376839	−	0.825163i	0.999103	−	0.0423549i	$-0.0134860\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	8.05837	−	5.17880i	0.273993	−	0.176085i
$866$	26.9727	+	7.91991i	0.916570	+	0.269129i
$867$	−0.105260	−	0.732097i	−0.00357480	−	0.0248633i
$868$	−1.57984	−	1.82324i	−0.0536234	−	0.0618847i
$869$	28.5324	+	18.3366i	0.967894	+	0.622028i
$870$	−1.39640	+	1.61154i	−0.0473426	+	0.0546362i
$871$	30.5696	−	8.97605i	1.03581	−	0.304142i
$872$	−0.723909	−	1.58514i	−0.0245147	−	0.0536796i
$873$	−11.7567			−0.397903
$874$	3.85736	−	16.0352i	0.130477	−	0.542398i
$875$	−1.57020			−0.0530825
$876$	−2.16700	−	4.74507i	−0.0732162	−	0.160321i
$877$	−10.5512	+	3.09812i	−0.356289	+	0.104616i	−0.454979	−	0.890502i	$-0.650353\pi$
$877$	−10.5512	+	3.09812i	−0.356289	+	0.104616i	0.0986895	+	0.995118i	$0.468535\pi$
$878$	−13.8888	+	16.0286i	−0.468726	+	0.540938i
$879$	11.9092	+	7.65360i	0.401689	+	0.258150i
$880$	2.40973	+	2.78098i	0.0812320	+	0.0937467i
$881$	−2.35937	−	16.4098i	−0.0794892	−	0.552860i	−0.990183	−	0.139777i	$-0.955361\pi$
$881$	−2.35937	−	16.4098i	−0.0794892	−	0.552860i	0.910694	−	0.413082i	$-0.135548\pi$
$882$	−4.35079	−	1.27751i	−0.146499	−	0.0430159i
$883$	−14.5047	+	9.32163i	−0.488124	+	0.313698i	−0.761450	−	0.648223i	$-0.775512\pi$
$883$	−14.5047	+	9.32163i	−0.488124	+	0.313698i	0.273327	+	0.961921i	$0.411876\pi$
$884$	2.41662	−	16.8079i	0.0812796	−	0.565312i
$885$	5.44323	−	11.9190i	0.182972	−	0.400653i
$886$	−14.1331	+	30.9472i	−0.474811	+	1.03969i
$887$	−3.47114	+	24.1423i	−0.116549	+	0.810619i	0.844759	+	0.535146i	$0.179743\pi$
$887$	−3.47114	+	24.1423i	−0.116549	+	0.810619i	−0.961309	+	0.275473i	$0.911166\pi$
$888$	−4.85371	+	3.11929i	−0.162880	+	0.104676i
$889$	−10.3109	−	3.02754i	−0.345815	−	0.101540i
$890$	−0.668173	−	4.64724i	−0.0223972	−	0.155776i
$891$	2.40973	+	2.78098i	0.0807290	+	0.0931662i
$892$	−14.6652	−	9.42474i	−0.491027	−	0.315564i
$893$	−26.0936	+	30.1136i	−0.873188	+	1.00771i
$894$	18.5580	−	5.44912i	0.620672	−	0.182246i
$895$	−7.95073	−	17.4097i	−0.265764	−	0.581941i
$896$	1.57020			0.0524568
$897$	19.8232	−	3.86027i	0.661878	−	0.128891i
$898$	−9.03752			−0.301586
$899$	−1.36099	−	2.98015i	−0.0453915	−	0.0993934i
$900$	−0.959493	+	0.281733i	−0.0319831	+	0.00939109i
$901$	19.0906	−	22.0317i	0.635999	−	0.733982i
$902$	24.3807	+	15.6686i	0.811790	+	0.521706i
$903$	−6.27021	−	7.23621i	−0.208659	−	0.240806i
$904$	0.132709	+	0.923012i	0.00441384	+	0.0306989i
$905$	−2.51625	−	0.738838i	−0.0836430	−	0.0245598i
$906$	13.8370	−	8.89250i	0.459703	−	0.295433i
$907$	−4.98422	+	34.6660i	−0.165498	+	1.15107i	0.722551	+	0.691317i	$0.242969\pi$
$907$	−4.98422	+	34.6660i	−0.165498	+	1.15107i	−0.888049	+	0.459748i	$0.847940\pi$
$908$	9.28702	−	20.3357i	0.308201	−	0.674865i
$909$	8.22806	−	18.0169i	0.272908	−	0.597584i
$910$	−0.941018	+	6.54493i	−0.0311945	+	0.216962i
$911$	18.2527	−	11.7303i	0.604738	−	0.388641i	−0.202143	−	0.979356i	$-0.564790\pi$
$911$	18.2527	−	11.7303i	0.604738	−	0.388641i	0.806881	+	0.590715i	$0.201154\pi$
$912$	3.29964	+	0.968863i	0.109262	+	0.0320823i
$913$	1.38253	+	9.61568i	0.0457549	+	0.318233i
$914$	12.6727	+	14.6251i	0.419177	+	0.483756i
$915$	6.24905	+	4.01602i	0.206587	+	0.132766i
$916$	−9.87767	+	11.3994i	−0.326367	+	0.376648i
$917$	−12.6686	+	3.71985i	−0.418355	+	0.122840i
$918$	−1.67513	−	3.66801i	−0.0552874	−	0.121063i
$919$	4.78253			0.157761			0.0788805	−	0.996884i	$-0.474865\pi$
$919$	4.78253			0.157761			0.0788805	+	0.996884i	$0.474865\pi$
$920$	3.46452	−	3.31619i	0.114222	−	0.109332i
$921$	18.6417			0.614266
$922$	−15.8320	−	34.6671i	−0.521398	−	1.14170i
$923$	−38.7173	+	11.3684i	−1.27440	+	0.374196i
$924$	3.78376	−	4.36669i	0.124477	−	0.143654i
$925$	−4.85371	−	3.11929i	−0.159589	−	0.102562i
$926$	−0.247080	−	0.285146i	−0.00811955	−	0.00937047i
$927$	0.675619	+	4.69903i	0.0221902	+	0.154336i
$928$	2.04599	+	0.600758i	0.0671630	+	0.0197208i
$929$	44.8176	−	28.8025i	1.47042	−	0.944979i	0.472442	−	0.881362i	$-0.343373\pi$
$929$	44.8176	−	28.8025i	1.47042	−	0.944979i	0.997974	−	0.0636174i	$-0.0202637\pi$
$930$	0.218655	−	1.52078i	0.00716998	−	0.0498683i
$931$	−6.47789	+	14.1846i	−0.212304	+	0.464882i
$932$	4.45713	−	9.75975i	0.145998	−	0.319691i
$933$	−1.21641	+	8.46029i	−0.0398233	+	0.276977i
$934$	11.6364	−	7.47827i	0.380755	−	0.244696i
$935$	−14.2373	−	4.18044i	−0.465608	−	0.136715i
$936$	0.599298	+	4.16821i	0.0195887	+	0.136242i
$937$	−20.2751	−	23.3987i	−0.662358	−	0.764402i	0.320803	−	0.947146i	$-0.396047\pi$
$937$	−20.2751	−	23.3987i	−0.662358	−	0.764402i	−0.983160	+	0.182744i	$0.941502\pi$
$938$	−9.99398	−	6.42274i	−0.326315	−	0.209710i
$939$	9.39675	−	10.8444i	0.306651	−	0.353895i
$940$	−11.1173	+	3.26435i	−0.362608	+	0.106471i
$941$	12.6525	+	27.7052i	0.412460	+	0.903162i	0.995853	+	0.0909724i	$0.0289975\pi$
$941$	12.6525	+	27.7052i	0.412460	+	0.903162i	−0.583393	+	0.812190i	$0.698275\pi$
$942$	6.16045			0.200718
$943$	18.8227	−	32.7475i	0.612950	−	1.06640i
$944$	−13.1031			−0.426470
$945$	0.652285	+	1.42831i	0.0212188	+	0.0464628i
$946$	−21.5297	+	6.32170i	−0.699992	+	0.205536i
$947$	18.0671	−	20.8505i	0.587101	−	0.677550i	−0.382015	−	0.924156i	$-0.624770\pi$
$947$	18.0671	−	20.8505i	0.587101	−	0.677550i	0.969116	+	0.246606i	$0.0793153\pi$
$948$	7.75386	+	4.98311i	0.251834	+	0.161844i
$949$	−14.3853	−	16.6015i	−0.466966	−	0.538908i
$950$	0.489413	+	3.40394i	0.0158787	+	0.110438i
$951$	19.8298	+	5.82256i	0.643026	+	0.188809i
$952$	−5.32657	+	3.42318i	−0.172635	+	0.110946i
$953$	−6.14495	+	42.7391i	−0.199055	+	1.38446i	0.607981	+	0.793952i	$0.291980\pi$
$953$	−6.14495	+	42.7391i	−0.199055	+	1.38446i	−0.807035	+	0.590503i	$0.798929\pi$
$954$	−3.00322	+	6.57613i	−0.0972327	+	0.212910i
$955$	1.75667	−	3.84657i	0.0568445	−	0.124472i
$956$	−3.34041	+	23.2331i	−0.108037	+	0.751411i
$957$	6.60098	−	4.24219i	0.213380	−	0.137131i
$958$	−29.4742	−	8.65442i	−0.952270	−	0.279612i
$959$	1.67561	+	11.6541i	0.0541083	+	0.376331i
$960$	0.654861	+	0.755750i	0.0211355	+	0.0243917i
$961$	−24.0930	−	15.4836i	−0.777194	−	0.499472i
$962$	−15.9107	+	18.3619i	−0.512980	+	0.592011i
$963$	−7.65473	+	2.24763i	−0.246670	+	0.0724289i
$964$	−3.20236	−	7.01218i	−0.103141	−	0.225847i
$965$	2.02333			0.0651332
$966$	−5.92828	−	4.64358i	−0.190739	−	0.149405i
$967$	20.0919			0.646112			0.323056	−	0.946380i	$-0.395290\pi$
$967$	20.0919			0.646112			0.323056	+	0.946380i	$0.395290\pi$
$968$	−1.05542	−	2.31104i	−0.0339223	−	0.0742795i
$969$	−13.3055	+	3.90686i	−0.427436	+	0.125506i
$970$	−7.69899	+	8.88510i	−0.247200	+	0.285284i
$971$	−7.59884	−	4.88348i	−0.243858	−	0.156718i	0.413003	−	0.910730i	$-0.364480\pi$
$971$	−7.59884	−	4.88348i	−0.243858	−	0.156718i	−0.656861	+	0.754011i	$0.728116\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	−1.60702	−	11.1771i	−0.0515187	−	0.358320i
$974$	20.9924	+	6.16393i	0.672640	+	0.197505i
$975$	−3.54258	+	2.27668i	−0.113453	+	0.0729120i
$976$	1.05715	−	7.35265i	0.0338386	−	0.235353i
$977$	4.51591	−	9.88846i	0.144477	−	0.316360i	−0.823535	−	0.567266i	$-0.808001\pi$
$977$	4.51591	−	9.88846i	0.144477	−	0.316360i	0.968011	+	0.250906i	$0.0807285\pi$
$978$	−9.65699	+	21.1459i	−0.308797	+	0.676170i
$979$	−2.45871	+	17.1007i	−0.0785809	+	0.546542i
$980$	−3.81464	+	2.45152i	−0.121854	+	0.0783109i
$981$	−1.67203	−	0.490952i	−0.0533837	−	0.0156749i
$982$	3.04101	+	21.1507i	0.0970427	+	0.674947i
$983$	27.6080	+	31.8614i	0.880559	+	1.01622i	0.999727	+	0.0233454i	$0.00743174\pi$
$983$	27.6080	+	31.8614i	0.880559	+	1.01622i	−0.119168	+	0.992874i	$0.538023\pi$
$984$	6.62564	+	4.25804i	0.211218	+	0.135741i
$985$	−8.71326	+	10.0556i	−0.277628	+	0.320399i
$986$	−8.25029	+	2.42251i	−0.262743	+	0.0771483i
$987$	7.55783	+	16.5493i	0.240568	+	0.526771i
$988$	14.4816			0.460722
$989$	9.61815	+	27.6174i	0.305839	+	0.878182i
$990$	3.67976			0.116950
$991$	−11.6794	−	25.5743i	−0.371008	−	0.812395i	−0.999405	−	0.0345013i	$-0.989016\pi$
$991$	−11.6794	−	25.5743i	−0.371008	−	0.812395i	0.628396	−	0.777893i	$-0.283712\pi$
$992$	−1.47418	+	0.432859i	−0.0468053	+	0.0137433i
$993$	11.9954	−	13.8434i	0.380662	−	0.439307i
$994$	12.6577	+	8.13458i	0.401476	+	0.258013i
$995$	10.1994	+	11.7707i	0.323342	+	0.373156i
$996$	0.375711	+	2.61313i	0.0119049	+	0.0828001i
$997$	−18.4324	−	5.41223i	−0.583758	−	0.171407i	−0.0234986	−	0.999724i	$-0.507481\pi$
$997$	−18.4324	−	5.41223i	−0.583758	−	0.171407i	−0.560260	+	0.828317i	$0.689299\pi$
$998$	8.62945	−	5.54581i	0.273160	−	0.175549i
$999$	−0.821102	+	5.71089i	−0.0259785	+	0.180685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.211.2	yes	20
23.6	even	11	inner	690.2.m.e.121.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.121.2	✓	20	23.6	even	11	inner
690.2.m.e.211.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.223463 + 1.55422i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.223463 + 1.55422i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.142315 - 0.989821i) q^{10} +(-1.52863 + 3.34723i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.599298 + 4.16821i) q^{13} +(1.32094 - 0.848915i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.64067 + 3.04750i) q^{17} +(-0.841254 - 0.540641i) q^{18} +(-2.25203 + 2.59898i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(0.652285 + 1.42831i) q^{21} +3.67976 q^{22} +(-0.237432 - 4.78995i) q^{23} +1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(4.04049 - 1.18640i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-1.32094 - 0.848915i) q^{28} +(-1.39640 - 1.61154i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(1.47418 + 0.432859i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(-0.523684 + 3.64230i) q^{33} +(1.67513 - 3.66801i) q^{34} +(-0.652285 + 1.42831i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-4.85371 + 3.11929i) q^{37} +(3.29964 + 0.968863i) q^{38} +(0.599298 + 4.16821i) q^{39} +(0.654861 + 0.755750i) q^{40} +(6.62564 + 4.25804i) q^{41} +(1.02826 - 1.18668i) q^{42} +(-5.85085 + 1.71797i) q^{43} +(-1.52863 - 3.34723i) q^{44} +1.00000 q^{45} +(-4.25846 + 2.20579i) q^{46} +11.5867 q^{47} +(-0.415415 - 0.909632i) q^{48} +(4.35079 - 1.27751i) q^{49} +(0.654861 - 0.755750i) q^{50} +(3.39228 + 2.18009i) q^{51} +(-2.75766 - 3.18251i) q^{52} +(-1.02886 - 7.15585i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(-3.09561 + 1.98943i) q^{55} +(-0.223463 + 1.55422i) q^{56} +(-1.42859 + 3.12818i) q^{57} +(-0.885818 + 1.93967i) q^{58} +(1.86477 - 12.9697i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(7.12736 + 2.09278i) q^{61} +(-0.218655 - 1.52078i) q^{62} +(1.02826 + 1.18668i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.75766 + 3.18251i) q^{65} +(3.53070 - 1.03671i) q^{66} +(-3.14295 - 6.88211i) q^{67} -4.03242 q^{68} +(-1.57730 - 4.52903i) q^{69} +1.57020 q^{70} +(3.98064 + 8.71639i) q^{71} +(0.959493 - 0.281733i) q^{72} +(-3.41607 + 3.94235i) q^{73} +(4.85371 + 3.11929i) q^{74} +(0.654861 + 0.755750i) q^{75} +(-0.489413 - 3.40394i) q^{76} +(-5.54392 - 1.62784i) q^{77} +(3.54258 - 2.27668i) q^{78} +(1.31172 - 9.12322i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.12086 - 7.79574i) q^{82} +(2.22091 - 1.42729i) q^{83} +(-1.50660 - 0.442377i) q^{84} +(0.573873 + 3.99137i) q^{85} +(3.99325 + 4.60846i) q^{86} +(-1.79386 - 1.15285i) q^{87} +(-2.40973 + 2.78098i) q^{88} +(4.50485 - 1.32274i) q^{89} +(-0.415415 - 0.909632i) q^{90} -6.61223 q^{91} +(3.77549 + 2.95731i) q^{92} +1.53642 q^{93} +(-4.81328 - 10.5396i) q^{94} +(-3.29964 + 0.968863i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(-9.89035 - 6.35614i) q^{97} +(-2.96944 - 3.42692i) q^{98} +(0.523684 + 3.64230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

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