LMFDB - Embedded newform 690.2.n.a.89.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.16
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.748393 + 1.56202i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.64573 + 1.51379i) q^{5} +(1.43961 - 0.963074i) q^{6} +(1.66558 - 1.07040i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-1.87982 + 2.33801i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.748393 + 1.56202i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.64573 + 1.51379i) q^{5} +(1.43961 - 0.963074i) q^{6} +(1.66558 - 1.07040i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-1.87982 + 2.33801i) q^{9} +(1.73260 + 1.41354i) q^{10} +(0.163968 - 1.14042i) q^{11} +(-1.15815 - 1.28790i) q^{12} +(-3.31360 + 5.15606i) q^{13} +(-1.29654 - 1.49629i) q^{14} +(-3.59623 - 1.43775i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.599806 + 2.04275i) q^{17} +(2.58174 + 1.52795i) q^{18} +(-0.290163 - 0.988203i) q^{19} +(1.15258 - 1.91613i) q^{20} +(2.91849 + 1.80058i) q^{21} -1.15215 q^{22} +(-4.69475 + 0.979447i) q^{23} +(-1.10997 + 1.32965i) q^{24} +(0.416853 - 4.98259i) q^{25} +(5.57516 + 2.54609i) q^{26} +(-5.05886 - 1.18656i) q^{27} +(-1.29654 + 1.49629i) q^{28} +(-0.730713 + 2.48858i) q^{29} +(-0.911320 + 3.76424i) q^{30} +(-2.50579 - 5.48692i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.90408 - 0.597363i) q^{33} +(2.10732 + 0.302987i) q^{34} +(-1.12072 + 4.28293i) q^{35} +(1.14498 - 2.77291i) q^{36} +(5.56307 + 6.42013i) q^{37} +(-0.936850 + 0.427845i) q^{38} +(-10.5337 - 1.31715i) q^{39} +(-2.06066 - 0.868156i) q^{40} +(2.34577 + 2.03262i) q^{41} +(1.36691 - 3.14504i) q^{42} +(-5.08716 + 11.1393i) q^{43} +(0.163968 + 1.14042i) q^{44} +(-0.445595 - 6.69339i) q^{45} +(1.63761 + 4.50757i) q^{46} -4.55049 q^{47} +(1.47408 + 0.909444i) q^{48} +(-1.27952 + 2.80176i) q^{49} +(-4.99120 + 0.296487i) q^{50} +(-3.63971 + 0.591871i) q^{51} +(1.72675 - 5.88075i) q^{52} +(2.42234 + 3.76924i) q^{53} +(-0.454536 + 5.17623i) q^{54} +(1.45652 + 2.12505i) q^{55} +(1.66558 + 1.07040i) q^{56} +(1.32644 - 1.19280i) q^{57} +(2.56724 + 0.369114i) q^{58} +(3.10824 - 4.83651i) q^{59} +(3.85562 + 0.366337i) q^{60} +(-9.92774 + 4.53385i) q^{61} +(-5.07446 + 3.26115i) q^{62} +(-0.628371 + 5.90629i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-2.35193 - 13.5016i) q^{65} +(-0.862262 - 1.79969i) q^{66} +(0.884738 + 6.15349i) q^{67} -2.12899i q^{68} +(-5.04343 - 6.60029i) q^{69} +(4.39883 + 0.499790i) q^{70} +(12.3693 - 1.77844i) q^{71} +(-2.90763 - 0.738698i) q^{72} +(-0.762867 - 2.59809i) q^{73} +(5.56307 - 6.42013i) q^{74} +(8.09488 - 3.07780i) q^{75} +(0.556818 + 0.866426i) q^{76} +(-0.947610 - 2.07498i) q^{77} +(0.195363 + 10.6140i) q^{78} +(6.33604 - 9.85907i) q^{79} +(-0.566057 + 2.16323i) q^{80} +(-1.93258 - 8.79006i) q^{81} +(1.67810 - 2.61117i) q^{82} +(12.6878 - 10.9940i) q^{83} +(-3.30756 - 0.905414i) q^{84} +(-2.10519 - 4.26980i) q^{85} +(11.7499 + 3.45009i) q^{86} +(-4.43407 + 0.721046i) q^{87} +(1.10548 - 0.324599i) q^{88} +(-4.37896 + 9.58859i) q^{89} +(-6.56184 + 1.39363i) q^{90} +12.1347i q^{91} +(4.22864 - 2.26244i) q^{92} +(6.69536 - 8.02046i) q^{93} +(0.647602 + 4.50417i) q^{94} +(1.97347 + 1.18707i) q^{95} +(0.690404 - 1.58850i) q^{96} +(4.00396 - 4.62082i) q^{97} +(2.95533 + 0.867764i) q^{98} +(2.35809 + 2.52715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.748393	+	1.56202i	0.432085	+	0.901833i
$3$	0.748393	+	1.56202i	0.432085	+	0.901833i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−1.64573	+	1.51379i	−0.735993	+	0.676989i
$5$	−1.64573	+	1.51379i	−0.735993	+	0.676989i
$6$	1.43961	−	0.963074i	0.587720	−	0.393173i
$7$	1.66558	−	1.07040i	0.629529	−	0.404574i	−0.186606	−	0.982435i	$-0.559749\pi$
$7$	1.66558	−	1.07040i	0.629529	−	0.404574i	0.816135	+	0.577861i	$0.196113\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−1.87982	+	2.33801i	−0.626606	+	0.779336i
$10$	1.73260	+	1.41354i	0.547896	+	0.447002i
$11$	0.163968	−	1.14042i	0.0494383	−	0.343851i	−0.950057	−	0.312077i	$-0.898975\pi$
$11$	0.163968	−	1.14042i	0.0494383	−	0.343851i	0.999495	−	0.0317739i	$-0.0101156\pi$
$12$	−1.15815	−	1.28790i	−0.334329	−	0.371785i
$13$	−3.31360	+	5.15606i	−0.919027	+	1.43003i	−0.0162778	+	0.999868i	$0.505182\pi$
$13$	−3.31360	+	5.15606i	−0.919027	+	1.43003i	−0.902749	+	0.430167i	$0.858455\pi$
$14$	−1.29654	−	1.49629i	−0.346515	−	0.399900i
$15$	−3.59623	−	1.43775i	−0.928543	−	0.371226i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.599806	+	2.04275i	−0.145474	+	0.495440i	−0.999701	−	0.0244610i	$-0.992213\pi$
$17$	−0.599806	+	2.04275i	−0.145474	+	0.495440i	0.854226	+	0.519901i	$0.174031\pi$
$18$	2.58174	+	1.52795i	0.608521	+	0.360141i
$19$	−0.290163	−	0.988203i	−0.0665679	−	0.226709i	0.919490	−	0.393114i	$-0.128602\pi$
$19$	−0.290163	−	0.988203i	−0.0665679	−	0.226709i	−0.986058	+	0.166405i	$0.946784\pi$
$20$	1.15258	−	1.91613i	0.257725	−	0.428460i
$21$	2.91849	+	1.80058i	0.636867	+	0.392920i
$22$	−1.15215			−0.245640
$23$	−4.69475	+	0.979447i	−0.978923	+	0.204229i
$23$	−4.69475	+	0.979447i	−0.978923	+	0.204229i
$24$	−1.10997	+	1.32965i	−0.226572	+	0.271413i
$25$	0.416853	−	4.98259i	0.0833706	−	0.996519i
$26$	5.57516	+	2.54609i	1.09338	+	0.499329i
$27$	−5.05886	−	1.18656i	−0.973578	−	0.228354i
$28$	−1.29654	+	1.49629i	−0.245023	+	0.282772i
$29$	−0.730713	+	2.48858i	−0.135690	+	0.462118i	−0.999101	−	0.0423827i	$-0.986505\pi$
$29$	−0.730713	+	2.48858i	−0.135690	+	0.462118i	0.863411	+	0.504500i	$0.168323\pi$
$30$	−0.911320	+	3.76424i	−0.166384	+	0.687253i
$31$	−2.50579	−	5.48692i	−0.450053	−	0.985479i	−0.989643	−	0.143551i	$-0.954148\pi$
$31$	−2.50579	−	5.48692i	−0.450053	−	0.985479i	0.539590	−	0.841928i	$-0.318579\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	1.90408	−	0.597363i	0.331458	−	0.103988i
$34$	2.10732	+	0.302987i	0.361403	+	0.0519619i
$35$	−1.12072	+	4.28293i	−0.189437	+	0.723947i
$36$	1.14498	−	2.77291i	0.190830	−	0.462152i
$37$	5.56307	+	6.42013i	0.914563	+	1.05546i	0.998260	+	0.0589712i	$0.0187820\pi$
$37$	5.56307	+	6.42013i	0.914563	+	1.05546i	−0.0836962	+	0.996491i	$0.526673\pi$
$38$	−0.936850	+	0.427845i	−0.151977	+	0.0694057i
$39$	−10.5337	−	1.31715i	−1.68675	−	0.210913i
$40$	−2.06066	−	0.868156i	−0.325818	−	0.137267i
$41$	2.34577	+	2.03262i	0.366348	+	0.317442i	0.818509	−	0.574494i	$-0.194801\pi$
$41$	2.34577	+	2.03262i	0.366348	+	0.317442i	−0.452161	+	0.891936i	$0.649347\pi$
$42$	1.36691	−	3.14504i	0.210919	−	0.485290i
$43$	−5.08716	+	11.1393i	−0.775785	+	1.69873i	−0.0623041	+	0.998057i	$0.519845\pi$
$43$	−5.08716	+	11.1393i	−0.775785	+	1.69873i	−0.713481	+	0.700675i	$0.752882\pi$
$44$	0.163968	+	1.14042i	0.0247192	+	0.171925i
$45$	−0.445595	−	6.69339i	−0.0664253	−	0.997791i
$46$	1.63761	+	4.50757i	0.241453	+	0.664606i
$47$	−4.55049			−0.663757			−0.331879	−	0.943322i	$-0.607682\pi$
$47$	−4.55049			−0.663757			−0.331879	+	0.943322i	$0.607682\pi$
$48$	1.47408	+	0.909444i	0.212765	+	0.131267i
$49$	−1.27952	+	2.80176i	−0.182788	+	0.400251i
$50$	−4.99120	+	0.296487i	−0.705863	+	0.0419296i
$51$	−3.63971	+	0.591871i	−0.509662	+	0.0828785i
$52$	1.72675	−	5.88075i	0.239456	−	0.815514i
$53$	2.42234	+	3.76924i	0.332734	+	0.517745i	0.966800	−	0.255534i	$-0.0822514\pi$
$53$	2.42234	+	3.76924i	0.332734	+	0.517745i	−0.634066	+	0.773279i	$0.718615\pi$
$54$	−0.454536	+	5.17623i	−0.0618545	+	0.704396i
$55$	1.45652	+	2.12505i	0.196397	+	0.286541i
$56$	1.66558	+	1.07040i	0.222572	+	0.143038i
$57$	1.32644	−	1.19280i	0.175691	−	0.157991i
$58$	2.56724	+	0.369114i	0.337095	+	0.0484670i
$59$	3.10824	−	4.83651i	0.404658	−	0.629660i	−0.577793	−	0.816184i	$-0.696086\pi$
$59$	3.10824	−	4.83651i	0.404658	−	0.629660i	0.982450	+	0.186524i	$0.0597221\pi$
$60$	3.85562	+	0.366337i	0.497758	+	0.0472939i
$61$	−9.92774	+	4.53385i	−1.27112	+	0.580499i	−0.932753	−	0.360516i	$-0.882601\pi$
$61$	−9.92774	+	4.53385i	−1.27112	+	0.580499i	−0.338363	+	0.941016i	$0.609873\pi$
$62$	−5.07446	+	3.26115i	−0.644457	+	0.414167i
$63$	−0.628371	+	5.90629i	−0.0791674	+	0.744123i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−2.35193	−	13.5016i	−0.291721	−	1.67467i
$66$	−0.862262	−	1.79969i	−0.106137	−	0.221526i
$67$	0.884738	+	6.15349i	0.108088	+	0.751768i	0.969717	+	0.244230i	$0.0785352\pi$
$67$	0.884738	+	6.15349i	0.108088	+	0.751768i	−0.861629	+	0.507538i	$0.830556\pi$
$68$		−	2.12899i		−	0.258178i
$69$	−5.04343	−	6.60029i	−0.607158	−	0.794581i
$70$	4.39883	+	0.499790i	0.525761	+	0.0597363i
$71$	12.3693	−	1.77844i	1.46797	−	0.211062i	0.638501	−	0.769621i	$-0.279555\pi$
$71$	12.3693	−	1.77844i	1.46797	−	0.211062i	0.829465	+	0.558559i	$0.188646\pi$
$72$	−2.90763	−	0.738698i	−0.342668	−	0.0870563i
$73$	−0.762867	−	2.59809i	−0.0892868	−	0.304083i	0.902727	−	0.430214i	$-0.141562\pi$
$73$	−0.762867	−	2.59809i	−0.0892868	−	0.304083i	−0.992014	+	0.126131i	$0.959744\pi$
$74$	5.56307	−	6.42013i	0.646694	−	0.746325i
$75$	8.09488	−	3.07780i	0.934717	−	0.355394i
$76$	0.556818	+	0.866426i	0.0638714	+	0.0993859i
$77$	−0.947610	−	2.07498i	−0.107990	−	0.236465i
$78$	0.195363	+	10.6140i	0.0221205	+	1.20180i
$79$	6.33604	−	9.85907i	0.712860	−	1.10923i	−0.276111	−	0.961126i	$-0.589046\pi$
$79$	6.33604	−	9.85907i	0.712860	−	1.10923i	0.988971	−	0.148107i	$-0.0473179\pi$
$80$	−0.566057	+	2.16323i	−0.0632871	+	0.241857i
$81$	−1.93258	−	8.79006i	−0.214731	−	0.976673i
$82$	1.67810	−	2.61117i	0.185315	−	0.288355i
$83$	12.6878	−	10.9940i	1.39266	−	1.20675i	0.441809	−	0.897109i	$-0.354337\pi$
$83$	12.6878	−	10.9940i	1.39266	−	1.20675i	0.950854	−	0.309640i	$-0.100208\pi$
$84$	−3.30756	−	0.905414i	−0.360884	−	0.0987887i
$85$	−2.10519	−	4.26980i	−0.228340	−	0.463125i
$86$	11.7499	+	3.45009i	1.26703	+	0.372033i
$87$	−4.43407	+	0.721046i	−0.475383	+	0.0773042i
$88$	1.10548	−	0.324599i	0.117845	−	0.0346023i
$89$	−4.37896	+	9.58859i	−0.464169	+	1.01639i	0.522348	+	0.852732i	$0.325056\pi$
$89$	−4.37896	+	9.58859i	−0.464169	+	1.01639i	−0.986517	+	0.163656i	$0.947671\pi$
$90$	−6.56184	+	1.39363i	−0.691679	+	0.146901i
$91$			12.1347i			1.27206i
$92$	4.22864	−	2.26244i	0.440866	−	0.235875i
$93$	6.69536	−	8.02046i	0.694277	−	0.831683i
$94$	0.647602	+	4.50417i	0.0667951	+	0.464570i
$95$	1.97347	+	1.18707i	0.202473	+	0.121791i
$96$	0.690404	−	1.58850i	0.0704640	−	0.162126i
$97$	4.00396	−	4.62082i	0.406541	−	0.469173i	−0.515149	−	0.857101i	$-0.672263\pi$
$97$	4.00396	−	4.62082i	0.406541	−	0.469173i	0.921690	+	0.387927i	$0.126809\pi$
$98$	2.95533	+	0.867764i	0.298534	+	0.0876574i
$99$	2.35809	+	2.52715i	0.236997	+	0.253988i
$100$	1.00379	+	4.89820i	0.100379	+	0.489820i
$101$	2.19700	−	1.90371i	0.218609	−	0.189426i	−0.538671	−	0.842516i	$-0.681073\pi$
$101$	2.19700	−	1.90371i	0.218609	−	0.189426i	0.757280	+	0.653090i	$0.226528\pi$
$102$	1.10383	+	3.51843i	0.109296	+	0.348377i
$103$	−0.618015	+	4.29839i	−0.0608948	+	0.423533i	0.936456	+	0.350786i	$0.114086\pi$
$103$	−0.618015	+	4.29839i	−0.0608948	+	0.423533i	−0.997350	+	0.0727468i	$0.976824\pi$
$104$	−6.06664	−	0.872251i	−0.594883	−	0.0855312i
$105$	−7.52877	+	1.45472i	−0.734732	+	0.141966i
$106$	3.38614	−	2.93411i	0.328891	−	0.284986i
$107$	0.263932	−	0.120534i	0.0255153	−	0.0116524i	−0.402617	−	0.915369i	$-0.631899\pi$
$107$	0.263932	−	0.120534i	0.0255153	−	0.0116524i	0.428132	+	0.903716i	$0.359172\pi$
$108$	5.18823	−	0.286746i	0.499238	−	0.0275921i
$109$	−1.00167	+	3.41137i	−0.0959424	+	0.326750i	−0.993453	−	0.114243i	$-0.963556\pi$
$109$	−1.00167	+	3.41137i	−0.0959424	+	0.326750i	0.897510	+	0.440993i	$0.145374\pi$
$110$	1.89613	−	1.74412i	0.180789	−	0.166295i
$111$	−5.86501	+	13.4944i	−0.556682	+	1.28083i
$112$	0.822470	−	1.80096i	0.0777161	−	0.170174i
$113$	14.7911	−	2.12664i	1.39143	−	0.200058i	0.594484	−	0.804107i	$-0.297356\pi$
$113$	14.7911	−	2.12664i	1.39143	−	0.200058i	0.796947	+	0.604050i	$0.206447\pi$
$114$	−1.36944	−	1.14318i	−0.128259	−	0.107069i
$115$	6.24361	−	8.71879i	0.582220	−	0.813032i
$116$		−	2.59364i		−	0.240814i
$117$	−5.82596	−	17.4397i	−0.538610	−	1.61230i
$118$	−5.22963	−	2.38829i	−0.481426	−	0.219860i
$119$	1.18754	+	4.04439i	0.108862	+	0.370749i
$120$	−0.186103	−	3.86851i	−0.0169888	−	0.353145i
$121$	9.28074	+	2.72507i	0.843704	+	0.247734i
$122$	5.90056	+	9.18145i	0.534212	+	0.831250i
$123$	−1.41944	+	5.18534i	−0.127987	+	0.467547i
$124$	3.95013	+	4.55869i	0.354732	+	0.409383i
$125$	6.85659	+	8.83103i	0.613272	+	0.789871i
$126$	5.93560	−	0.218577i	0.528785	−	0.0194724i
$127$	−2.97314	−	0.427473i	−0.263824	−	0.0379321i	0.00913362	−	0.999958i	$-0.497093\pi$
$127$	−2.97314	−	0.427473i	−0.263824	−	0.0379321i	−0.272957	+	0.962026i	$0.588002\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−21.2071	+	0.390341i	−1.86718	+	0.0343676i
$130$	−13.0295	+	4.24947i	−1.14276	+	0.372703i
$131$	−6.52880	−	10.1590i	−0.570424	−	0.887597i	0.429456	−	0.903088i	$-0.358705\pi$
$131$	−6.52880	−	10.1590i	−0.570424	−	0.887597i	−0.999880	+	0.0154907i	$0.995069\pi$
$132$	−1.65865	+	1.10961i	−0.144367	+	0.0965789i
$133$	−1.54106	−	1.33534i	−0.133627	−	0.115788i
$134$	5.96494	−	1.75146i	0.515292	−	0.151303i
$135$	10.1217	−	5.70531i	0.871140	−	0.491035i
$136$	−2.10732	+	0.302987i	−0.180701	+	0.0259809i
$137$		−	0.420827i		−	0.0359536i	−0.999838	−	0.0179768i	$-0.994277\pi$
$137$		−	0.420827i		−	0.0359536i	0.999838	−	0.0179768i	$-0.00572251\pi$
$138$	−5.81535	+	5.93142i	−0.495035	+	0.504916i
$139$	18.6589			1.58262			0.791312	−	0.611413i	$-0.209399\pi$
$139$	18.6589			1.58262			0.791312	+	0.611413i	$0.209399\pi$
$140$	−0.131316	−	4.42519i	−0.0110983	−	0.373996i
$141$	−3.40555	−	7.10796i	−0.286799	−	0.598598i
$142$	−3.52067	−	11.9903i	−0.295448	−	1.00620i
$143$	5.33677	+	4.62434i	0.446284	+	0.386707i
$144$	−0.317379	+	2.98316i	−0.0264483	+	0.248597i
$145$	−2.56464	−	5.20168i	−0.212982	−	0.431976i
$146$	−2.46307	+	1.12485i	−0.203846	+	0.0930931i
$147$	−5.33398	+	0.0981781i	−0.439939	+	0.00809760i
$148$	−7.14649	−	4.59277i	−0.587438	−	0.377523i
$149$	1.38027	−	9.59999i	0.113076	−	0.786461i	−0.851821	−	0.523833i	$-0.824502\pi$
$149$	1.38027	−	9.59999i	0.113076	−	0.786461i	0.964897	−	0.262628i	$-0.0845893\pi$
$150$	−4.19850	−	7.57447i	−0.342806	−	0.618453i
$151$	−1.86013	−	1.19543i	−0.151375	−	0.0972829i	0.462761	−	0.886483i	$-0.346859\pi$
$151$	−1.86013	−	1.19543i	−0.151375	−	0.0972829i	−0.614136	+	0.789200i	$0.710495\pi$
$152$	0.778363	−	0.674456i	0.0631336	−	0.0547056i
$153$	−3.64845	−	5.24235i	−0.294960	−	0.423819i
$154$	−1.91900	+	1.23326i	−0.154637	+	0.0993793i
$155$	12.4299	+	5.23673i	0.998395	+	0.420624i
$156$	10.4781	−	1.70390i	0.838923	−	0.136421i
$157$	−9.92259	+	2.91354i	−0.791909	+	0.232526i	−0.652579	−	0.757720i	$-0.726313\pi$
$157$	−9.92259	+	2.91354i	−0.791909	+	0.232526i	−0.139330	+	0.990246i	$0.544495\pi$
$158$	−10.6604	−	4.86846i	−0.848099	−	0.387314i
$159$	−4.07477	+	6.60462i	−0.323150	+	0.523780i
$160$	2.22177	+	0.252435i	0.175647	+	0.0199567i
$161$	−6.77106	+	6.65661i	−0.533635	+	0.524614i
$162$	−8.42556	+	3.16386i	−0.661974	+	0.248576i
$163$	1.35223	−	0.194421i	0.105915	−	0.0152282i	−0.0891537	−	0.996018i	$-0.528416\pi$
$163$	1.35223	−	0.194421i	0.105915	−	0.0152282i	0.195068	+	0.980790i	$0.437507\pi$
$164$	−2.82341	−	1.28941i	−0.220471	−	0.100686i
$165$	−2.22931	+	3.86548i	−0.173552	+	0.300928i
$166$	−12.6878	−	10.9940i	−0.984761	−	0.853300i
$167$	17.7218	+	5.20358i	1.37135	+	0.402665i	0.882751	−	0.469842i	$-0.155689\pi$
$167$	17.7218	+	5.20358i	1.37135	+	0.402665i	0.488602	+	0.872507i	$0.337507\pi$
$168$	−0.425483	+	3.40274i	−0.0328268	+	0.262527i
$169$	−10.2046	−	22.3450i	−0.784972	−	1.71885i
$170$	−3.92674	+	2.69142i	−0.301167	+	0.206422i
$171$	2.85588	+	1.17924i	0.218395	+	0.0901786i
$172$	1.74278	−	12.1213i	0.132886	−	0.924243i
$173$	−2.17092	+	15.0991i	−0.165052	+	1.14796i	0.723882	+	0.689924i	$0.242356\pi$
$173$	−2.17092	+	15.0991i	−0.165052	+	1.14796i	−0.888933	+	0.458036i	$0.848553\pi$
$174$	1.34474	+	4.28633i	0.101945	+	0.324946i
$175$	−4.63907	−	8.74509i	−0.350681	−	0.661067i
$176$	−0.478621	−	1.04803i	−0.0360774	−	0.0789986i
$177$	9.88091	+	1.23552i	0.742694	+	0.0928674i
$178$	10.1142	+	2.96979i	0.758090	+	0.222595i
$179$	6.11494	+	5.29863i	0.457052	+	0.396038i	0.852730	−	0.522351i	$-0.174945\pi$
$179$	6.11494	+	5.29863i	0.457052	+	0.396038i	−0.395678	+	0.918389i	$0.629490\pi$
$180$	2.31329	+	6.29672i	0.172422	+	0.469330i
$181$	−4.11475	−	1.87914i	−0.305847	−	0.139676i	0.256579	−	0.966523i	$-0.417405\pi$
$181$	−4.11475	−	1.87914i	−0.305847	−	0.139676i	−0.562426	+	0.826848i	$0.690132\pi$
$182$	12.0112	−	1.72695i	0.890328	−	0.128010i
$183$	−14.5118	−	12.1142i	−1.07274	−	0.895510i
$184$	−2.84121	−	3.86362i	−0.209457	−	0.284830i
$185$	−18.8741	−	2.14445i	−1.38765	−	0.157663i
$186$	−8.89168	−	5.48578i	−0.651969	−	0.402237i
$187$	2.23126	+	1.01898i	0.163166	+	0.0745152i
$188$	4.36616	−	1.28202i	0.318435	−	0.0935010i
$189$	−9.69602	+	3.43870i	−0.705281	+	0.250128i
$190$	0.894133	−	2.12232i	0.0648672	−	0.153969i
$191$	−11.1897	+	7.19121i	−0.809662	+	0.520338i	−0.878756	−	0.477272i	$-0.841626\pi$
$191$	−11.1897	+	7.19121i	−0.809662	+	0.520338i	0.0690938	+	0.997610i	$0.477989\pi$
$192$	−1.67059	−	0.457309i	−0.120564	−	0.0330034i
$193$	4.29782	−	3.72408i	0.309364	−	0.268065i	−0.486316	−	0.873783i	$-0.661660\pi$
$193$	4.29782	−	3.72408i	0.309364	−	0.268065i	0.795679	+	0.605718i	$0.207114\pi$
$194$	−5.14361	−	3.30560i	−0.369290	−	0.237328i
$195$	19.3296	−	13.7783i	1.38422	−	0.986681i
$196$	0.438344	−	3.04875i	0.0313103	−	0.217768i
$197$	10.4485	+	6.71487i	0.744428	+	0.478415i	0.857056	−	0.515223i	$-0.172291\pi$
$197$	10.4485	+	6.71487i	0.744428	+	0.478415i	−0.112629	+	0.993637i	$0.535927\pi$
$198$	2.16583	−	2.69374i	0.153919	−	0.191436i
$199$	−9.96489	+	4.55081i	−0.706393	+	0.322599i	−0.736018	−	0.676962i	$-0.763296\pi$
$199$	−9.96489	+	4.55081i	−0.706393	+	0.322599i	0.0296250	+	0.999561i	$0.490569\pi$
$200$	4.70549	−	1.69066i	0.332729	−	0.119548i
$201$	−8.94974	+	5.98720i	−0.631266	+	0.422305i
$202$	−2.19700	−	1.90371i	−0.154580	−	0.133944i
$203$	1.44672	+	4.92708i	0.101540	+	0.345813i
$204$	3.32553	−	1.59332i	0.232834	−	0.111555i
$205$	−6.93748	+	0.205868i	−0.484535	+	0.0143785i
$206$	4.34259			0.302563
$207$	6.53532	−	12.8176i	0.454236	−	0.890881i
$208$			6.12902i			0.424971i
$209$	−1.17455	+	0.168875i	−0.0812453	+	0.0116813i
$210$	2.51137	+	7.24511i	0.173301	+	0.499960i
$211$	8.94819	−	2.62743i	0.616019	−	0.180880i	0.0411878	−	0.999151i	$-0.486886\pi$
$211$	8.94819	−	2.62743i	0.616019	−	0.180880i	0.574831	+	0.818272i	$0.305068\pi$
$212$	−3.38614	−	2.93411i	−0.232561	−	0.201515i
$213$	12.0350	+	17.9901i	0.824628	+	1.23266i
$214$	−0.156868	−	0.244092i	−0.0107233	−	0.0166858i
$215$	−8.49056	−	26.0332i	−0.579052	−	1.77545i
$216$	−1.02219	−	5.09462i	−0.0695512	−	0.346645i
$217$	−10.0468	−	6.45668i	−0.682020	−	0.438308i
$218$	3.51920	+	0.505984i	0.238350	+	0.0342696i
$219$	3.48734	−	3.13600i	0.235653	−	0.211911i
$220$	−1.99622	−	1.62862i	−0.134585	−	0.109801i
$221$	−8.54504	−	9.86150i	−0.574802	−	0.663356i
$222$	14.1917	+	3.88486i	0.952487	+	0.260735i
$223$	15.0451	+	23.4106i	1.00749	+	1.56769i	0.809190	+	0.587547i	$0.199906\pi$
$223$	15.0451	+	23.4106i	1.00749	+	1.56769i	0.198302	+	0.980141i	$0.436457\pi$
$224$	−1.89968	−	0.557795i	−0.126927	−	0.0372693i
$225$	10.8657	+	10.3410i	0.724383	+	0.689398i
$226$	−4.20999	−	14.3379i	−0.280044	−	0.953744i
$227$	−16.2449	−	7.41882i	−1.07821	−	0.492404i	−0.204512	−	0.978864i	$-0.565561\pi$
$227$	−16.2449	−	7.41882i	−1.07821	−	0.492404i	−0.873703	+	0.486460i	$0.838288\pi$
$228$	−0.936657	+	1.51819i	−0.0620316	+	0.100544i
$229$		−	16.1774i		−	1.06903i	−0.845159	−	0.534515i	$-0.820494\pi$
$229$		−	16.1774i		−	1.06903i	0.845159	−	0.534515i	$-0.179506\pi$
$230$	−9.51861	−	4.93924i	−0.627638	−	0.325684i
$231$	2.53197	−	3.03308i	0.166591	−	0.199562i
$232$	−2.56724	+	0.369114i	−0.168548	+	0.0242335i
$233$	7.78621	−	17.0494i	0.510092	−	1.11694i	−0.462965	−	0.886377i	$-0.653214\pi$
$233$	7.78621	−	17.0494i	0.510092	−	1.11694i	0.973056	−	0.230568i	$-0.0740584\pi$
$234$	−16.4330	+	8.24858i	−1.07426	+	0.539227i
$235$	7.48888	−	6.88851i	0.488520	−	0.449357i
$236$	−1.61973	+	5.51629i	−0.105435	+	0.359080i
$237$	20.1419	+	2.51857i	1.30836	+	0.163599i
$238$	3.83422	−	1.75103i	0.248536	−	0.113502i
$239$	11.5926	−	10.0450i	0.749861	−	0.649758i	−0.193661	−	0.981068i	$-0.562036\pi$
$239$	11.5926	−	10.0450i	0.749861	−	0.649758i	0.943522	+	0.331311i	$0.107491\pi$
$240$	−3.80265	+	0.734755i	−0.245460	+	0.0474283i
$241$	−18.4645	−	2.65479i	−1.18940	−	0.171010i	−0.480936	−	0.876756i	$-0.659703\pi$
$241$	−18.4645	−	2.65479i	−1.18940	−	0.171010i	−0.708465	+	0.705746i	$0.750612\pi$
$242$	1.37655	−	9.57409i	0.0884878	−	0.615446i
$243$	12.2839	−	9.59714i	0.788014	−	0.615657i
$244$	8.24826	−	7.14716i	0.528041	−	0.457550i
$245$	−2.13554	−	6.54786i	−0.136435	−	0.418327i
$246$	5.33457	+	0.667041i	0.340120	+	0.0425290i
$247$	6.05672	+	1.77841i	0.385380	+	0.113158i
$248$	3.95013	−	4.55869i	0.250834	−	0.289477i
$249$	26.6683	+	11.5907i	1.69003	+	0.734531i
$250$	7.76535	−	8.04359i	0.491124	−	0.508721i
$251$	−0.409367	−	2.84721i	−0.0258390	−	0.179714i	0.972815	−	0.231584i	$-0.0743909\pi$
$251$	−0.409367	−	2.84721i	−0.0258390	−	0.179714i	−0.998654	+	0.0518700i	$0.983482\pi$
$252$	−1.06108	−	5.84408i	−0.0668415	−	0.368142i
$253$	0.347196	+	5.51461i	0.0218280	+	0.346700i
$254$			3.00371i			0.188470i
$255$	5.09401	−	6.48384i	0.318999	−	0.406034i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−7.62412	+	2.23864i	−0.475579	+	0.139643i	−0.510733	−	0.859739i	$-0.670626\pi$
$257$	−7.62412	+	2.23864i	−0.475579	+	0.139643i	0.0351539	+	0.999382i	$0.488808\pi$
$258$	3.40445	+	20.9357i	0.211952	+	1.30340i
$259$	16.1378	+	4.73849i	1.00276	+	0.294436i
$260$	6.06050	+	12.2921i	0.375856	+	0.762322i
$261$	−4.44472	−	6.38649i	−0.275121	−	0.395314i
$262$	−9.12646	+	7.90813i	−0.563835	+	0.488566i
$263$	−9.69651	+	15.0881i	−0.597912	+	0.930370i	0.401979	+	0.915649i	$0.368322\pi$
$263$	−9.69651	+	15.0881i	−0.597912	+	0.930370i	−0.999892	+	0.0147208i	$0.995314\pi$
$264$	1.33436	+	1.48386i	0.0821244	+	0.0913251i
$265$	−9.69238	−	2.53622i	−0.595398	−	0.155799i
$266$	−1.10243	+	1.71541i	−0.0675943	+	0.105179i
$267$	−18.2548	+	0.336000i	−1.11717	+	0.0205629i
$268$	−2.58254	−	5.65497i	−0.157754	−	0.345432i
$269$	14.5143	+	22.5847i	0.884953	+	1.37701i	0.925867	+	0.377851i	$0.123337\pi$
$269$	14.5143	+	22.5847i	0.884953	+	1.37701i	−0.0409139	+	0.999163i	$0.513027\pi$
$270$	−7.08771	−	9.20676i	−0.431344	−	0.560305i
$271$	−21.1673	+	24.4284i	−1.28582	+	1.48392i	−0.499199	+	0.866487i	$0.666372\pi$
$271$	−21.1673	+	24.4284i	−1.28582	+	1.48392i	−0.786624	+	0.617432i	$0.788173\pi$
$272$	0.599806	+	2.04275i	0.0363686	+	0.123860i
$273$	−18.9546	+	9.08152i	−1.14719	+	0.549638i
$274$	−0.416543	+	0.0598899i	−0.0251643	+	0.00361808i
$275$	−5.61392	−	1.29238i	−0.338532	−	0.0779333i
$276$	6.69865	+	4.91203i	0.403212	+	0.295669i
$277$		−	6.65868i		−	0.400081i	−0.979788	−	0.200041i	$-0.935893\pi$
$277$		−	6.65868i		−	0.400081i	0.979788	−	0.200041i	$-0.0641074\pi$
$278$	−2.65543	−	18.4689i	−0.159262	−	1.10769i
$279$	17.5389	+	4.45584i	1.05003	+	0.266764i
$280$	−4.36146	+	0.759749i	−0.260647	+	0.0454037i
$281$	−5.57442	+	6.43323i	−0.332542	+	0.383774i	−0.897255	−	0.441514i	$-0.854442\pi$
$281$	−5.57442	+	6.43323i	−0.332542	+	0.383774i	0.564712	+	0.825288i	$0.308987\pi$
$282$	−6.55095	+	4.38246i	−0.390103	+	0.260972i
$283$	−6.71436	+	4.31506i	−0.399127	+	0.256504i	−0.724772	−	0.688989i	$-0.758055\pi$
$283$	−6.71436	+	4.31506i	−0.399127	+	0.256504i	0.325645	+	0.945492i	$0.394419\pi$
$284$	−11.3672	+	5.19123i	−0.674520	+	0.308043i
$285$	−0.377299	+	3.97099i	−0.0223493	+	0.235221i
$286$	3.81777	−	5.94057i	0.225749	−	0.351273i
$287$	6.08278	+	0.874572i	0.359055	+	0.0516244i
$288$	2.99797	−	0.110400i	0.176657	−	0.00650536i
$289$	10.4882	+	6.74038i	0.616955	+	0.396493i
$290$	−4.78375	+	3.27881i	−0.280911	+	0.192539i
$291$	10.2144	+	2.79609i	0.598776	+	0.163909i
$292$	1.46393	+	2.27792i	0.0856701	+	0.133305i
$293$	−6.14801	+	20.9382i	−0.359171	+	1.22322i	0.559710	+	0.828688i	$0.310912\pi$
$293$	−6.14801	+	20.9382i	−0.359171	+	1.22322i	−0.918881	+	0.394535i	$0.870906\pi$
$294$	0.856284	+	5.26572i	0.0499395	+	0.307103i
$295$	2.20616	+	12.6648i	0.128448	+	0.737374i
$296$	−3.52897	+	7.72737i	−0.205117	+	0.449144i
$297$	−2.18268	+	5.57469i	−0.126652	+	0.323476i
$298$	−9.69870			−0.561831
$299$	10.5064	−	27.4519i	0.607603	−	1.58759i
$300$	−6.89987	+	5.23372i	−0.398364	+	0.302169i
$301$	3.45049	+	23.9987i	0.198883	+	1.38326i
$302$	−0.918541	+	2.01132i	−0.0528561	+	0.115739i
$303$	4.61785	+	2.00703i	0.265289	+	0.115301i
$304$	−0.778363	−	0.674456i	−0.0446422	−	0.0386827i
$305$	9.47506	−	22.4900i	0.542540	−	1.28778i
$306$	−4.66977	+	4.35738i	−0.266953	+	0.249095i
$307$	−1.24426	+	0.568233i	−0.0710135	+	0.0324308i	−0.450605	−	0.892723i	$-0.648792\pi$
$307$	−1.24426	+	0.568233i	−0.0710135	+	0.0324308i	0.379592	+	0.925154i	$0.376064\pi$
$308$	1.49381	+	1.72395i	0.0851179	+	0.0982313i
$309$	−7.17669	+	2.25153i	−0.408268	+	0.128085i
$310$	3.41447	−	13.0487i	0.193929	−	0.741114i
$311$	−29.0889	−	4.18235i	−1.64948	−	0.237159i	−0.746048	−	0.665892i	$-0.768051\pi$
$311$	−29.0889	−	4.18235i	−1.64948	−	0.237159i	−0.903431	+	0.428733i	$0.858960\pi$
$312$	−3.17775	−	10.1290i	−0.179905	−	0.573442i
$313$	−17.6780	−	20.4015i	−0.999221	−	1.15316i	−0.988192	−	0.153224i	$-0.951035\pi$
$313$	−17.6780	−	20.4015i	−0.999221	−	1.15316i	−0.0110296	−	0.999939i	$-0.503511\pi$
$314$	4.29601	+	9.40696i	0.242438	+	0.530865i
$315$	−7.90678	−	10.6714i	−0.445497	−	0.601264i
$316$	−3.30177	+	11.2448i	−0.185739	+	0.632568i
$317$	−20.8969	+	24.1163i	−1.17369	+	1.35451i	−0.251454	+	0.967869i	$0.580909\pi$
$317$	−20.8969	+	24.1163i	−1.17369	+	1.35451i	−0.922232	+	0.386637i	$0.873637\pi$
$318$	7.11729	+	3.09336i	0.399118	+	0.173467i
$319$	2.71822	+	1.24137i	0.152191	+	0.0695035i
$320$	−0.0663257	−	2.23508i	−0.00370772	−	0.124945i
$321$	0.385801	+	0.322061i	0.0215333	+	0.0179757i
$322$	7.55248	+	5.75481i	0.420883	+	0.320703i
$323$	2.19270			0.122005
$324$	4.33074	+	7.88953i	0.240597	+	0.438307i
$325$	24.3093	+	18.6596i	1.34844	+	1.03505i
$326$	−0.384884	−	1.31079i	−0.0213168	−	0.0725982i
$327$	−6.07827	+	0.988417i	−0.336129	+	0.0546596i
$328$	−0.874470	+	2.97817i	−0.0482845	+	0.164442i
$329$	−7.57919	+	4.87085i	−0.417854	+	0.268539i
$330$	4.14340	+	1.65651i	0.228087	+	0.0911878i
$331$	18.5223	+	21.3759i	1.01808	+	1.17492i	0.984481	+	0.175489i	$0.0561505\pi$
$331$	18.5223	+	21.3759i	1.01808	+	1.17492i	0.0335961	+	0.999435i	$0.489304\pi$
$332$	−9.07645	+	14.1232i	−0.498135	+	0.775113i
$333$	−25.4679	+	0.937849i	−1.39563	+	0.0513938i
$334$	2.62855	−	18.2819i	0.143828	−	1.00034i
$335$	−10.7712	−	8.78766i	−0.588491	−	0.480121i
$336$	3.42866	−	0.0631085i	0.187049	−	0.00344285i
$337$	11.0477	+	24.1911i	0.601806	+	1.31777i	0.928039	+	0.372482i	$0.121493\pi$
$337$	11.0477	+	24.1911i	0.601806	+	1.31777i	−0.326233	+	0.945289i	$0.605779\pi$
$338$	−20.6653	+	13.2808i	−1.12405	+	0.722380i
$339$	14.3914	+	21.5125i	0.781634	+	1.16840i
$340$	3.22286	+	3.50374i	0.174784	+	0.190017i
$341$	−6.66828	+	1.95798i	−0.361108	+	0.106031i
$342$	0.760801	−	2.99464i	0.0411394	−	0.161931i
$343$	2.84022	+	19.7542i	0.153358	+	1.06663i
$344$	−12.2460			−0.660259
$345$	18.2916	+	3.22757i	0.984787	+	0.173766i
$346$	15.2543			0.820078
$347$	−0.146080	−	1.01601i	−0.00784198	−	0.0545422i	0.985525	−	0.169532i	$-0.0542256\pi$
$347$	−0.146080	−	1.01601i	−0.00784198	−	0.0545422i	−0.993367	+	0.114990i	$0.963316\pi$
$348$	4.05132	−	1.94106i	0.217174	−	0.104052i
$349$	5.52791	−	1.62314i	0.295902	−	0.0868848i	−0.130412	−	0.991460i	$-0.541630\pi$
$349$	5.52791	−	1.62314i	0.295902	−	0.0868848i	0.426314	+	0.904575i	$0.359812\pi$
$350$	−7.99587	+	5.83641i	−0.427397	+	0.311969i
$351$	22.8810	−	22.1520i	1.22130	−	1.18239i
$352$	−0.969252	+	0.622900i	−0.0516613	+	0.0332007i
$353$	−2.96526	−	6.49302i	−0.157825	−	0.345589i	0.814157	−	0.580645i	$-0.197200\pi$
$353$	−2.96526	−	6.49302i	−0.157825	−	0.345589i	−0.971982	+	0.235057i	$0.924472\pi$
$354$	−0.183255	−	9.95617i	−0.00973988	−	0.529164i
$355$	−17.6643	+	21.6514i	−0.937526	+	1.14914i
$356$	1.50017	−	10.4339i	0.0795086	−	0.552995i
$357$	−5.42868	+	4.88176i	−0.287316	+	0.258370i
$358$	4.37445	−	6.80677i	0.231197	−	0.359749i
$359$	7.81698	+	9.02128i	0.412565	+	0.476125i	0.923557	−	0.383460i	$-0.125268\pi$
$359$	7.81698	+	9.02128i	0.412565	+	0.476125i	−0.510993	+	0.859585i	$0.670722\pi$
$360$	5.90341	−	3.18586i	0.311137	−	0.167910i
$361$	15.0915	−	9.69870i	0.794288	−	0.510458i
$362$	−1.27443	+	4.34030i	−0.0669824	+	0.228121i
$363$	2.68902	+	16.5361i	0.141137	+	0.867922i
$364$	−3.41874	−	11.6432i	−0.179191	−	0.610267i
$365$	5.18844	+	3.12092i	0.271575	+	0.163357i
$366$	−9.92568	+	16.0881i	−0.518824	+	0.840940i
$367$	4.14223			0.216223			0.108111	−	0.994139i	$-0.465520\pi$
$367$	4.14223			0.216223			0.108111	+	0.994139i	$0.465520\pi$
$368$	−3.41995	+	3.36214i	−0.178277	+	0.175264i
$369$	−9.16191	+	1.66348i	−0.476950	+	0.0865972i
$370$	0.563440	+	18.9871i	0.0292918	+	0.987095i
$371$	8.06919	+	3.68508i	0.418932	+	0.191320i
$372$	−4.16453	+	9.58188i	−0.215921	+	0.496797i
$373$	−5.39452	+	6.22560i	−0.279317	+	0.322349i	−0.878022	−	0.478621i	$-0.841137\pi$
$373$	−5.39452	+	6.22560i	−0.279317	+	0.322349i	0.598704	+	0.800970i	$0.295682\pi$
$374$	0.691068	−	2.35356i	0.0357343	−	0.121700i
$375$	−8.66283	+	17.3192i	−0.447347	+	0.894361i
$376$	−1.89034	−	4.13927i	−0.0974869	−	0.213467i
$377$	−10.4100	−	12.0138i	−0.536141	−	0.618740i
$378$	4.78358	+	9.10795i	0.246041	+	0.468462i
$379$	23.4155	+	3.36665i	1.20278	+	0.172933i	0.714423	−	0.699714i	$-0.246689\pi$
$379$	23.4155	+	3.36665i	1.20278	+	0.172933i	0.488352	+	0.872647i	$0.337598\pi$
$380$	−2.22796	−	0.582995i	−0.114292	−	0.0299070i
$381$	−1.55735	−	4.96402i	−0.0797857	−	0.254315i
$382$	8.71049	+	10.0524i	0.445667	+	0.514327i
$383$	15.0234	−	6.86094i	0.767658	−	0.350577i	0.00720760	−	0.999974i	$-0.497706\pi$
$383$	15.0234	−	6.86094i	0.767658	−	0.350577i	0.760450	+	0.649397i	$0.224978\pi$
$384$	−0.214904	+	1.71867i	−0.0109668	+	0.0877054i
$385$	4.70060	+	1.98036i	0.239565	+	0.100929i
$386$	−4.29782	−	3.72408i	−0.218753	−	0.189551i
$387$	−16.4809	−	32.8337i	−0.837773	−	1.66903i
$388$	−2.53994	+	5.56169i	−0.128946	+	0.282352i
$389$	2.99371	+	20.8217i	0.151787	+	1.05570i	0.913222	+	0.407462i	$0.133586\pi$
$389$	2.99371	+	20.8217i	0.151787	+	1.05570i	−0.761435	+	0.648242i	$0.775505\pi$
$390$	−16.3889	−	17.1720i	−0.829884	−	0.869538i
$391$	0.815172	−	10.1777i	0.0412250	−	0.514708i
$392$	−3.08010			−0.155568
$393$	10.9825	−	17.8011i	0.553993	−	0.897944i
$394$	5.15954	−	11.2978i	0.259934	−	0.569176i
$395$	4.49720	+	25.8168i	0.226279	+	1.29899i
$396$	−2.97455	−	1.76043i	−0.149477	−	0.0884650i
$397$	10.5958	−	36.0860i	0.531788	−	1.81110i	−0.0512841	−	0.998684i	$-0.516331\pi$
$397$	10.5958	−	36.0860i	0.531788	−	1.81110i	0.583072	−	0.812420i	$-0.301850\pi$
$398$	5.92265	+	9.21582i	0.296875	+	0.461947i
$399$	0.932506	−	3.40653i	0.0466837	−	0.170540i
$400$	−2.34311	−	4.41699i	−0.117156	−	0.220850i
$401$	−12.7468	−	8.19188i	−0.636545	−	0.409083i	0.182182	−	0.983265i	$-0.441684\pi$
$401$	−12.7468	−	8.19188i	−0.636545	−	0.409083i	−0.818728	+	0.574182i	$0.805320\pi$
$402$	7.19994	+	8.00658i	0.359100	+	0.399332i
$403$	36.5941	+	5.26143i	1.82288	+	0.262091i
$404$	−1.57167	+	2.44556i	−0.0781933	+	0.121671i
$405$	16.4868	+	11.5405i	0.819238	+	0.573454i
$406$	4.67104	−	2.13319i	0.231820	−	0.105868i
$407$	8.23384	−	5.29157i	0.408136	−	0.262293i
$408$	−2.05038	−	3.06493i	−0.101509	−	0.151736i
$409$	13.3214	−	15.3738i	0.658703	−	0.760184i	−0.323862	−	0.946104i	$-0.604981\pi$
$409$	13.3214	−	15.3738i	0.658703	−	0.760184i	0.982565	+	0.185920i	$0.0595266\pi$
$410$	1.19108	+	6.83757i	0.0588232	+	0.337683i
$411$	0.657340	−	0.314943i	0.0324242	−	0.0155350i
$412$	−0.618015	−	4.29839i	−0.0304474	−	0.211766i
$413$		−	11.3826i		−	0.560103i
$414$	−13.6172	−	4.64467i	−0.669247	−	0.228273i
$415$	−4.23796	+	37.2998i	−0.208033	+	1.83098i
$416$	6.06664	−	0.872251i	0.297441	−	0.0427656i
$417$	13.9641	+	29.1455i	0.683827	+	1.42726i
$418$	0.334312	+	1.13856i	0.0163517	+	0.0556888i
$419$	17.2325	−	19.8874i	0.841862	−	0.971561i	−0.158012	−	0.987437i	$-0.550508\pi$
$419$	17.2325	−	19.8874i	0.841862	−	0.971561i	0.999874	+	0.0158763i	$0.00505378\pi$
$420$	6.81396	−	3.51690i	0.332487	−	0.171607i
$421$	6.47964	+	10.0825i	0.315798	+	0.491392i	0.962474	−	0.271373i	$-0.0874778\pi$
$421$	6.47964	+	10.0825i	0.315798	+	0.491392i	−0.646676	+	0.762765i	$0.723841\pi$
$422$	−3.87414	−	8.48319i	−0.188590	−	0.412955i
$423$	8.55409	−	10.6391i	0.415914	−	0.517290i
$424$	−2.42234	+	3.76924i	−0.117639	+	0.183050i
$425$	9.92817	+	3.84012i	0.481587	+	0.186273i
$426$	16.0943	−	14.4728i	0.779769	−	0.701210i
$427$	−11.6824	+	18.1781i	−0.565350	+	0.879701i
$428$	−0.219283	+	0.190010i	−0.0105994	+	0.00918446i
$429$	−3.22931	+	11.7970i	−0.155913	+	0.569563i
$430$	−24.5599	+	12.1091i	−1.18439	+	0.583951i
$431$	−3.32098	−	0.975128i	−0.159966	−	0.0469703i	0.200769	−	0.979639i	$-0.435656\pi$
$431$	−3.32098	−	0.975128i	−0.159966	−	0.0469703i	−0.360735	+	0.932668i	$0.617474\pi$
$432$	−4.89729	+	1.73682i	−0.235621	+	0.0835630i
$433$	−13.1501	+	3.86122i	−0.631954	+	0.185558i	−0.581994	−	0.813193i	$-0.697727\pi$
$433$	−13.1501	+	3.86122i	−0.631954	+	0.185558i	−0.0499597	+	0.998751i	$0.515909\pi$
$434$	−4.96115	+	10.8634i	−0.238143	+	0.521460i
$435$	6.20577	−	7.89892i	0.297544	−	0.378724i
$436$		−	3.55539i		−	0.170272i
$437$	2.33013	+	4.35517i	0.111465	+	0.208336i
$438$	−3.60038	−	3.00555i	−0.172033	−	0.143611i
$439$	−1.33038	−	9.25303i	−0.0634958	−	0.441623i	−0.996626	−	0.0820829i	$-0.973843\pi$
$439$	−1.33038	−	9.25303i	−0.0634958	−	0.441623i	0.933130	−	0.359540i	$-0.117066\pi$
$440$	−1.32795	+	2.20767i	−0.0633075	+	0.105247i
$441$	−4.14527	−	8.25831i	−0.197394	−	0.393253i
$442$	−8.54504	+	9.86150i	−0.406446	+	0.469064i
$443$	3.52398	+	1.03473i	0.167429	+	0.0491616i	0.364373	−	0.931253i	$-0.381283\pi$
$443$	3.52398	+	1.03473i	0.167429	+	0.0491616i	−0.196944	+	0.980415i	$0.563102\pi$
$444$	1.82562	−	14.6002i	0.0866402	−	0.692893i
$445$	−7.30856	−	22.4091i	−0.346459	−	1.06229i
$446$	21.0312	−	18.2236i	0.995854	−	0.862912i
$447$	16.0284	−	5.02855i	0.758115	−	0.237842i
$448$	−0.281766	+	1.95972i	−0.0133122	+	0.0925882i
$449$	−35.6201	−	5.12139i	−1.68101	−	0.241693i	−0.765343	−	0.643622i	$-0.777431\pi$
$449$	−35.6201	−	5.12139i	−1.68101	−	0.241693i	−0.915671	+	0.401929i	$0.868340\pi$
$450$	8.68936	−	12.2268i	0.409620	−	0.576378i
$451$	2.70269	−	2.34189i	0.127264	−	0.110275i
$452$	−13.5928	+	6.20764i	−0.639353	+	0.291983i
$453$	0.475183	−	3.80021i	0.0223261	−	0.178550i
$454$	−5.03141	+	17.1354i	−0.236136	+	0.804204i
$455$	−18.3694	−	19.9704i	−0.861172	−	0.936228i
$456$	1.63604	+	0.711062i	0.0766144	+	0.0332985i
$457$	−2.16833	+	4.74797i	−0.101430	+	0.222101i	−0.953543	−	0.301257i	$-0.902594\pi$
$457$	−2.16833	+	4.74797i	−0.101430	+	0.222101i	0.852113	+	0.523358i	$0.175321\pi$
$458$	−16.0127	+	2.30228i	−0.748224	+	0.107578i
$459$	5.45819	−	9.62229i	0.254767	−	0.449130i
$460$	−3.53433	+	10.1246i	−0.164789	+	0.472064i
$461$			2.28622i			0.106480i	0.998582	+	0.0532399i	$0.0169548\pi$
$461$			2.28622i			0.106480i	−0.998582	+	0.0532399i	$0.983045\pi$
$462$	−3.36255	−	2.07455i	−0.156440	−	0.0965167i
$463$	−19.4958	−	8.90345i	−0.906049	−	0.413778i	−0.0927931	−	0.995685i	$-0.529580\pi$
$463$	−19.4958	−	8.90345i	−0.906049	−	0.413778i	−0.813255	+	0.581907i	$0.802307\pi$
$464$	0.730713	+	2.48858i	0.0339225	+	0.115529i
$465$	1.12258	+	23.3349i	0.0520583	+	1.08213i
$466$	−17.9840	−	5.28057i	−0.833092	−	0.244618i
$467$	−5.61927	−	8.74376i	−0.260029	−	0.404613i	0.686551	−	0.727081i	$-0.259124\pi$
$467$	−5.61927	−	8.74376i	−0.260029	−	0.404613i	−0.946580	+	0.322468i	$0.895487\pi$
$468$	10.5033	+	15.0919i	0.485515	+	0.697623i
$469$	8.06029	+	9.30208i	0.372190	+	0.429530i
$470$	−7.88417	−	6.43231i	−0.363670	−	0.296700i
$471$	−11.9770	−	13.3188i	−0.551871	−	0.613699i
$472$	5.69065	+	0.818192i	0.261933	+	0.0376603i
$473$	11.8694	+	7.62802i	0.545757	+	0.350737i
$474$	−0.373559	−	20.2953i	−0.0171581	−	0.932196i
$475$	−5.04477	+	1.03383i	−0.231470	+	0.0474352i
$476$	−2.27887	−	3.54600i	−0.104452	−	0.162531i
$477$	−13.3661	−	1.42202i	−0.611991	−	0.0651098i
$478$	−11.5926	−	10.0450i	−0.530231	−	0.459448i
$479$	−9.80548	+	2.87915i	−0.448024	+	0.131552i	−0.497959	−	0.867201i	$-0.665917\pi$
$479$	−9.80548	+	2.87915i	−0.448024	+	0.131552i	0.0499347	+	0.998752i	$0.484099\pi$
$480$	1.26845	+	3.65938i	0.0578966	+	0.167027i
$481$	−51.5364	+	7.40981i	−2.34986	+	0.337858i
$482$			18.6543i			0.849682i
$483$	−15.4652	−	5.59478i	−0.703690	−	0.254572i
$484$	−9.67255			−0.439661
$485$	0.405530	+	13.6658i	0.0184142	+	0.620532i
$486$	−11.2476	−	10.7931i	−0.510203	−	0.489584i
$487$	−4.51226	−	15.3673i	−0.204470	−	0.696360i	−0.996325	−	0.0856517i	$-0.972703\pi$
$487$	−4.51226	−	15.3673i	−0.204470	−	0.696360i	0.791855	−	0.610709i	$-0.209115\pi$
$488$	−8.24826	−	7.14716i	−0.373381	−	0.323537i
$489$	1.31569	+	1.96670i	0.0594974	+	0.0889374i
$490$	−6.17729	+	3.04566i	−0.279062	+	0.137589i
$491$	−29.6477	+	13.5396i	−1.33798	+	0.611035i	−0.950466	−	0.310828i	$-0.899394\pi$
$491$	−29.6477	+	13.5396i	−1.33798	+	0.611035i	−0.387515	+	0.921863i	$0.626666\pi$
$492$	−0.0989369	−	5.37520i	−0.00446042	−	0.242333i
$493$	−4.64527	−	2.98533i	−0.209212	−	0.134453i
$494$	0.898351	−	6.24817i	0.0404187	−	0.281118i
$495$	−7.70637	−	0.589337i	−0.346375	−	0.0264887i
$496$	−5.07446	−	3.26115i	−0.227850	−	0.146430i
$497$	18.6984	−	16.2022i	0.838737	−	0.726769i
$498$	7.67744	−	28.0464i	0.344034	−	1.25679i
$499$	25.0161	−	16.0768i	1.11987	−	0.719699i	0.156450	−	0.987686i	$-0.449995\pi$
$499$	25.0161	−	16.0768i	1.11987	−	0.719699i	0.963422	+	0.267987i	$0.0863585\pi$
$500$	−9.06684	−	6.54159i	−0.405482	−	0.292549i
$501$	5.13474	+	31.5761i	0.229403	+	1.41072i
$502$	−2.75997	+	0.810401i	−0.123184	+	0.0361700i
$503$	−17.7920	−	8.12535i	−0.793308	−	0.362291i	−0.0228145	−	0.999740i	$-0.507263\pi$
$503$	−17.7920	−	8.12535i	−0.793308	−	0.362291i	−0.770493	+	0.637448i	$0.779990\pi$
$504$	−5.63359	+	1.88198i	−0.250940	+	0.0838298i
$505$	−0.733840	+	6.45879i	−0.0326554	+	0.287412i
$506$	5.40907	−	1.12847i	0.240462	−	0.0501667i
$507$	27.2663	−	32.6627i	1.21094	−	1.45060i
$508$	2.97314	−	0.427473i	0.131912	−	0.0189660i
$509$	−33.0632	−	15.0995i	−1.46550	−	0.669272i	−0.486604	−	0.873623i	$-0.661765\pi$
$509$	−33.0632	−	15.0995i	−1.46550	−	0.669272i	−0.978898	+	0.204350i	$0.934492\pi$
$510$	−7.14279	−	4.11942i	−0.316288	−	0.182411i
$511$	−4.05161	−	3.51074i	−0.179233	−	0.155306i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	0.295326	+	5.34348i	0.0130389	+	0.235920i
$514$	3.30088	+	7.22792i	0.145596	+	0.318810i
$515$	−5.48979	−	8.00954i	−0.241909	−	0.352942i
$516$	20.2381	−	6.34925i	0.890931	−	0.279510i
$517$	−0.746136	+	5.18949i	−0.0328150	+	0.228234i
$518$	2.39361	−	16.6479i	0.105169	−	0.731468i
$519$	−25.2097	+	7.90901i	−1.10659	+	0.347167i
$520$	11.3045	−	7.74815i	0.495733	−	0.339779i
$521$	16.9256	+	37.0620i	0.741526	+	1.62371i	0.781029	+	0.624495i	$0.214695\pi$
$521$	16.9256	+	37.0620i	0.741526	+	1.62371i	−0.0395030	+	0.999219i	$0.512577\pi$
$522$	−5.68893	+	5.30837i	−0.248998	+	0.232341i
$523$	−2.03180	−	0.596591i	−0.0888445	−	0.0260871i	0.237008	−	0.971508i	$-0.423833\pi$
$523$	−2.03180	−	0.596591i	−0.0888445	−	0.0260871i	−0.325853	+	0.945421i	$0.605651\pi$
$524$	9.12646	+	7.90813i	0.398691	+	0.345468i
$525$	10.1882	−	13.7911i	0.444648	−	0.601892i
$526$	16.3144	+	7.45056i	0.711343	+	0.324860i
$527$	12.7114	−	1.82762i	0.553717	−	0.0796125i
$528$	1.27885	−	1.53196i	0.0556550	−	0.0666699i
$529$	21.0814	−	9.19652i	0.916581	−	0.399849i
$530$	−1.13104	+	9.95466i	−0.0491291	+	0.432403i
$531$	5.46489	+	16.3588i	0.237156	+	0.709913i
$532$	1.85485	+	0.847080i	0.0804178	+	0.0367256i
$533$	−18.2533	+	5.35965i	−0.790637	+	0.232152i
$534$	2.93050	+	18.0211i	0.126815	+	0.779851i
$535$	−0.251898	+	0.597905i	−0.0108905	+	0.0258497i
$536$	−5.22987	+	3.36104i	−0.225896	+	0.145175i
$537$	−3.70019	+	13.5171i	−0.159675	+	0.583307i
$538$	20.2892	−	17.5807i	0.874730	−	0.757958i
$539$	2.98539	+	1.91859i	0.128590	+	0.0826397i
$540$	−8.10436	+	8.32583i	−0.348756	+	0.358287i
$541$	6.16013	−	42.8446i	0.264845	−	1.84204i	−0.230170	−	0.973150i	$-0.573928\pi$
$541$	6.16013	−	42.8446i	0.264845	−	1.84204i	0.495015	−	0.868885i	$-0.335163\pi$
$542$	27.1922	+	17.4753i	1.16800	+	0.750631i
$543$	−0.144188	−	7.83366i	−0.00618769	−	0.336175i
$544$	1.93660	−	0.884415i	0.0830310	−	0.0379190i
$545$	−3.51564	−	7.13051i	−0.150593	−	0.305438i
$546$	11.6866	+	17.4693i	0.500141	+	0.747616i
$547$	−0.847136	−	0.734048i	−0.0362209	−	0.0313856i	0.636562	−	0.771225i	$-0.280356\pi$
$547$	−0.847136	−	0.734048i	−0.0362209	−	0.0313856i	−0.672783	+	0.739840i	$0.734901\pi$
$548$	0.118561	+	0.403780i	0.00506466	+	0.0172486i
$549$	8.06216	−	31.7339i	0.344084	−	1.35437i
$550$	−0.480278	+	5.74070i	−0.0204791	+	0.244784i
$551$	2.67125			0.113799
$552$	3.90871	−	7.32953i	0.166366	−	0.311965i
$553$		−	23.2031i		−	0.986698i
$554$	−6.59091	+	0.947629i	−0.280021	+	0.0402609i
$555$	−10.7755	−	31.0866i	−0.457396	−	1.31955i
$556$	−17.9030	+	5.25681i	−0.759258	+	0.222938i
$557$	20.7887	+	18.0135i	0.880845	+	0.763257i	0.972590	−	0.232526i	$-0.0746991\pi$
$557$	20.7887	+	18.0135i	0.880845	+	0.763257i	−0.0917452	+	0.995783i	$0.529245\pi$
$558$	1.91444	−	17.9945i	0.0810446	−	0.761768i
$559$	−40.5783	−	63.1410i	−1.71628	−	2.67058i
$560$	1.37272	+	4.20894i	0.0580078	+	0.177860i
$561$	0.0781869	+	4.24787i	0.00330105	+	0.179345i
$562$	7.16107	+	4.60214i	0.302072	+	0.194130i
$563$	0.968031	+	0.139182i	0.0407976	+	0.00586582i	0.162683	−	0.986678i	$-0.447985\pi$
$563$	0.968031	+	0.139182i	0.0407976	+	0.00586582i	−0.121886	+	0.992544i	$0.538894\pi$
$564$	5.27015	+	5.86058i	0.221913	+	0.246775i
$565$	−21.1229	+	25.8906i	−0.888646	+	1.08922i
$566$	5.22669	+	6.03192i	0.219694	+	0.253541i
$567$	−12.6277	−	12.5719i	−0.530315	−	0.527970i
$568$	6.75612	+	10.5127i	0.283480	+	0.441104i
$569$	21.2268	+	6.23274i	0.889872	+	0.261290i	0.694546	−	0.719448i	$-0.255605\pi$
$569$	21.2268	+	6.23274i	0.889872	+	0.261290i	0.195326	+	0.980738i	$0.437423\pi$
$570$	3.98426	−	0.191672i	0.166882	−	0.00802826i
$571$	8.83153	+	30.0774i	0.369588	+	1.25870i	0.909048	+	0.416691i	$0.136810\pi$
$571$	8.83153	+	30.0774i	0.369588	+	1.25870i	−0.539460	+	0.842011i	$0.681372\pi$
$572$	−6.42343	−	2.93348i	−0.268577	−	0.122655i
$573$	−19.6071	−	12.0968i	−0.819100	−	0.505350i
$574$		−	6.14533i		−	0.256501i
$575$	2.92317	+	23.8003i	0.121904	+	0.992542i
$576$	−0.535931	−	2.95174i	−0.0223305	−	0.122989i
$577$	−15.0185	+	2.15933i	−0.625227	+	0.0898941i	−0.447644	−	0.894212i	$-0.647737\pi$
$577$	−15.0185	+	2.15933i	−0.625227	+	0.0898941i	−0.177583	+	0.984106i	$0.556828\pi$
$578$	5.17914	−	11.3407i	0.215424	−	0.471713i
$579$	9.03354	+	3.92621i	0.375421	+	0.163168i
$580$	3.92624	+	4.26843i	0.163028	+	0.177237i
$581$	9.36444	−	31.8923i	0.388502	−	1.32312i
$582$	1.31397	−	10.5083i	0.0544659	−	0.435583i
$583$	4.69572	−	2.14446i	0.194477	−	0.0888146i
$584$	2.04640	−	1.77321i	0.0846805	−	0.0733761i
$585$	35.9880	+	19.8817i	1.48792	+	0.822007i
$586$	21.6000	+	3.10562i	0.892289	+	0.128292i
$587$	−1.03759	+	7.21660i	−0.0428259	+	0.297861i	0.957140	+	0.289625i	$0.0935306\pi$
$587$	−1.03759	+	7.21660i	−0.0428259	+	0.297861i	−0.999966	+	0.00823577i	$0.997378\pi$
$588$	5.09026	−	1.59696i	0.209919	−	0.0658574i
$589$	−4.69510	+	4.06833i	−0.193458	+	0.167633i
$590$	12.2219	−	3.98610i	0.503169	−	0.164105i
$591$	−2.66915	+	21.3462i	−0.109794	+	0.878065i
$592$	8.15094	+	2.39333i	0.335001	+	0.0983653i
$593$	8.56362	−	9.88294i	0.351666	−	0.405844i	−0.552165	−	0.833735i	$-0.686198\pi$
$593$	8.56362	−	9.88294i	0.351666	−	0.405844i	0.903830	+	0.427891i	$0.140743\pi$
$594$	5.82858	+	1.36710i	0.239149	+	0.0560929i
$595$	−8.07675	−	4.85829i	−0.331115	−	0.199170i
$596$	1.38027	+	9.59999i	0.0565380	+	0.393231i
$597$	−14.5661	−	12.1596i	−0.596152	−	0.497658i
$598$	−28.6677	−	6.49268i	−1.17231	−	0.265505i
$599$		−	20.7817i		−	0.849116i	−0.905401	−	0.424558i	$-0.860429\pi$
$599$		−	20.7817i		−	0.849116i	0.905401	−	0.424558i	$-0.139571\pi$
$600$	6.16240	+	6.08480i	0.251579	+	0.248411i
$601$	3.38787	−	7.41840i	0.138194	−	0.302603i	−0.827864	−	0.560929i	$-0.810444\pi$
$601$	3.38787	−	7.41840i	0.138194	−	0.302603i	0.966058	+	0.258327i	$0.0831711\pi$
$602$	23.2634	−	6.83074i	0.948145	−	0.278400i
$603$	−16.0501	−	9.49890i	−0.653609	−	0.386825i
$604$	2.12157	+	0.622950i	0.0863256	+	0.0253475i
$605$	−19.3988	+	9.56440i	−0.788673	+	0.388848i
$606$	1.32942	−	4.85648i	0.0540038	−	0.197281i
$607$	−4.70583	+	4.07763i	−0.191004	+	0.165506i	−0.745113	−	0.666938i	$-0.767604\pi$
$607$	−4.70583	+	4.07763i	−0.191004	+	0.165506i	0.554109	+	0.832444i	$0.313059\pi$
$608$	−0.556818	+	0.866426i	−0.0225820	+	0.0351382i
$609$	−6.61348	+	5.94719i	−0.267992	+	0.240992i
$610$	−23.6096	−	6.17795i	−0.955923	−	0.250138i
$611$	15.0785	−	23.4626i	0.610011	−	0.949195i
$612$	4.97760	+	4.00211i	0.201208	+	0.161776i
$613$	−16.7844	−	36.7527i	−0.677916	−	1.48443i	−0.864837	−	0.502053i	$-0.832578\pi$
$613$	−16.7844	−	36.7527i	−0.677916	−	1.48443i	0.186921	−	0.982375i	$-0.440149\pi$
$614$	0.739526	+	1.15072i	0.0298448	+	0.0464395i
$615$	−5.51353	−	10.6824i	−0.222327	−	0.430757i
$616$	1.49381	−	1.72395i	0.0601875	−	0.0694600i
$617$	−10.4759	−	35.6777i	−0.421745	−	1.43633i	−0.847163	−	0.531333i	$-0.821691\pi$
$617$	−10.4759	−	35.6777i	−0.421745	−	1.43633i	0.425418	−	0.904997i	$-0.360127\pi$
$618$	3.24996	+	6.78322i	0.130733	+	0.272861i
$619$	−23.6819	+	3.40494i	−0.951856	+	0.136856i	−0.600712	−	0.799465i	$-0.705116\pi$
$619$	−23.6819	+	3.40494i	−0.951856	+	0.136856i	−0.351144	+	0.936322i	$0.614207\pi$
$620$	−13.4018	−	1.52269i	−0.538228	−	0.0611528i
$621$	24.9123	+	0.615736i	0.999695	+	0.0247086i
$622$			29.3880i			1.17835i
$623$	2.97014	+	20.6578i	0.118996	+	0.827636i
$624$	−9.57366	+	4.58692i	−0.383253	+	0.183624i
$625$	−24.6525	−	4.15402i	−0.986099	−	0.166161i
$626$	−17.6780	+	20.4015i	−0.706556	+	0.815409i
$627$	−1.14281	−	1.70829i	−0.0456394	−	0.0682223i
$628$	8.69982	−	5.59104i	0.347161	−	0.223107i
$629$	−16.4515	+	7.51315i	−0.655964	+	0.299569i
$630$	−9.43751	+	9.34500i	−0.376000	+	0.372314i
$631$	−4.41336	+	6.86732i	−0.175693	+	0.273384i	−0.917921	−	0.396764i	$-0.870133\pi$
$631$	−4.41336	+	6.86732i	−0.175693	+	0.273384i	0.742227	+	0.670148i	$0.233769\pi$
$632$	11.6002	+	1.66786i	0.461432	+	0.0663439i
$633$	10.8009	+	12.0109i	0.429296	+	0.477391i
$634$	26.8448	+	17.2521i	1.06614	+	0.685168i
$635$	5.54009	−	3.79722i	0.219852	−	0.150688i
$636$	2.04897	−	7.48508i	0.0812471	−	0.296803i
$637$	−10.2062	−	15.8812i	−0.404385	−	0.629235i
$638$	0.841892	−	2.86722i	0.0333308	−	0.113514i
$639$	−19.0940	+	32.2627i	−0.755348	+	1.27629i
$640$	−2.20290	+	0.383736i	−0.0870771	+	0.0151685i
$641$	6.95608	−	15.2317i	0.274748	−	0.601615i	−0.721081	−	0.692851i	$-0.756354\pi$
$641$	6.95608	−	15.2317i	0.274748	−	0.601615i	0.995829	+	0.0912357i	$0.0290817\pi$
$642$	0.263878	−	0.427708i	0.0104144	−	0.0168803i
$643$	37.2181			1.46774			0.733869	−	0.679291i	$-0.237713\pi$
$643$	37.2181			1.46774			0.733869	+	0.679291i	$0.237713\pi$
$644$	4.62140	−	8.29460i	0.182109	−	0.326853i
$645$	34.3102	−	32.7455i	1.35096	−	1.28935i
$646$	−0.312053	−	2.17038i	−0.0122776	−	0.0853924i
$647$	−8.96178	+	19.6236i	−0.352324	+	0.771482i	0.647631	+	0.761954i	$0.275760\pi$
$647$	−8.96178	+	19.6236i	−0.352324	+	0.771482i	−0.999955	+	0.00952755i	$0.996967\pi$
$648$	7.19290	−	5.40946i	0.282564	−	0.212503i
$649$	−5.00602	−	4.33774i	−0.196504	−	0.170271i
$650$	15.0101	−	26.7174i	0.588746	−	1.04794i
$651$	2.56652	−	20.5254i	0.100590	−	0.804454i
$652$	−1.24268	+	0.567512i	−0.0486670	+	0.0222255i
$653$	−8.12232	−	9.37366i	−0.317851	−	0.366820i	0.574231	−	0.818693i	$-0.305301\pi$
$653$	−8.12232	−	9.37366i	−0.317851	−	0.366820i	−0.892082	+	0.451874i	$0.850756\pi$
$654$	1.84338	+	5.87574i	0.0720820	+	0.229759i
$655$	26.1233	+	6.83573i	1.02072	+	0.267094i
$656$	3.07231	+	0.441731i	0.119953	+	0.0172467i
$657$	7.50840	+	3.10034i	0.292931	+	0.120956i
$658$	5.89990	+	6.80885i	0.230002	+	0.265437i
$659$	3.05395	+	6.68721i	0.118965	+	0.260497i	0.959741	−	0.280886i	$-0.0906283\pi$
$659$	3.05395	+	6.68721i	0.118965	+	0.260497i	−0.840776	+	0.541383i	$0.817901\pi$
$660$	1.04998	−	4.33698i	0.0408704	−	0.168817i
$661$	−0.711805	+	2.42418i	−0.0276860	+	0.0942899i	−0.972177	−	0.234247i	$-0.924737\pi$
$661$	−0.711805	+	2.42418i	−0.0276860	+	0.0942899i	0.944491	+	0.328537i	$0.106556\pi$
$662$	18.5223	−	21.3759i	0.719890	−	0.830797i
$663$	9.00882	−	20.7278i	0.349874	−	0.805001i
$664$	15.2712	+	6.97412i	0.592637	+	0.270648i
$665$	4.55760	−	0.135246i	0.176736	−	0.00524461i
$666$	4.55276	+	25.0752i	0.176416	+	0.971644i
$667$	0.993082	−	12.3990i	0.0384523	−	0.480090i
$668$	−18.4699			−0.714624
$669$	−25.3082	+	41.0210i	−0.978471	+	1.58596i
$670$	−7.16532	+	11.9121i	−0.276821	+	0.460206i
$671$	3.54267	+	12.0652i	0.136763	+	0.465774i
$672$	−0.550416	−	3.38478i	−0.0212327	−	0.130571i
$673$	9.16093	−	31.1993i	0.353128	−	1.20264i	−0.571125	−	0.820863i	$-0.693493\pi$
$673$	9.16093	−	31.1993i	0.353128	−	1.20264i	0.924253	−	0.381780i	$-0.124689\pi$
$674$	22.3726	−	14.3780i	0.861760	−	0.553820i
$675$	−8.02097	+	24.7116i	−0.308727	+	0.951151i
$676$	16.0866	+	18.5649i	0.618715	+	0.714036i
$677$	3.92374	−	6.10546i	0.150802	−	0.234652i	−0.757631	−	0.652683i	$-0.773643\pi$
$677$	3.92374	−	6.10546i	0.150802	−	0.234652i	0.908433	+	0.418031i	$0.137280\pi$
$678$	19.2454	−	17.3065i	0.739115	−	0.664651i
$679$	1.72278	−	11.9822i	0.0661141	−	0.459834i
$680$	3.00942	−	3.68869i	0.115406	−	0.141455i
$681$	−0.569250	−	30.9271i	−0.0218137	−	1.18513i
$682$	2.88705	+	6.32176i	0.110551	+	0.242073i
$683$	6.66796	−	4.28524i	0.255142	−	0.163970i	−0.406817	−	0.913510i	$-0.633361\pi$
$683$	6.66796	−	4.28524i	0.255142	−	0.163970i	0.661960	+	0.749540i	$0.269725\pi$
$684$	−3.07243	−	0.326876i	−0.117477	−	0.0124984i
$685$	0.637045	+	0.692567i	0.0243402	+	0.0264616i
$686$	19.1489	−	5.62263i	0.731109	−	0.214673i
$687$	25.2694	−	12.1070i	0.964086	−	0.461911i
$688$	1.74278	+	12.1213i	0.0664430	+	0.462121i
$689$	−27.4611			−1.04618
$690$	0.591547	−	18.5648i	0.0225198	−	0.706748i
$691$	−20.3093			−0.772602			−0.386301	−	0.922373i	$-0.626247\pi$
$691$	−20.3093			−0.772602			−0.386301	+	0.922373i	$0.626247\pi$
$692$	−2.17092	−	15.0991i	−0.0825259	−	0.573980i
$693$	6.63265	+	1.68505i	0.251953	+	0.0640099i
$694$	−0.984877	+	0.289186i	−0.0373854	+	0.0109774i
$695$	−30.7074	+	28.2457i	−1.16480	+	1.07142i
$696$	−2.49787	−	3.73384i	−0.0946814	−	0.141531i
$697$	−5.55915	+	3.57265i	−0.210568	+	0.135324i
$698$	−2.39332	−	5.24065i	−0.0905887	−	0.198362i
$699$	32.4587	−	0.597440i	1.22770	−	0.0225972i
$700$	6.91493	+	7.08387i	0.261360	+	0.267745i
$701$	−3.09661	+	21.5374i	−0.116957	+	0.813455i	0.843918	+	0.536472i	$0.180243\pi$
$701$	−3.09661	+	21.5374i	−0.116957	+	0.813455i	−0.960875	+	0.276982i	$0.910666\pi$
$702$	−25.1828	−	19.4956i	−0.950465	−	0.735813i
$703$	4.73020	−	7.36033i	0.178403	−	0.277600i
$704$	0.754499	+	0.870738i	0.0284363	+	0.0328172i
$705$	16.3646	+	6.54247i	0.616327	+	0.246404i
$706$	−6.00493	+	3.85914i	−0.225999	+	0.145240i
$707$	1.62153	−	5.52244i	0.0609841	−	0.207693i
$708$	−9.82875	+	1.59830i	−0.369387	+	0.0600678i
$709$	10.6966	+	36.4292i	0.401719	+	1.36813i	0.873677	+	0.486507i	$0.161729\pi$
$709$	10.6966	+	36.4292i	0.401719	+	1.36813i	−0.471958	+	0.881621i	$0.656453\pi$
$710$	23.9449	+	14.4032i	0.898637	+	0.540543i
$711$	11.1400	+	33.3470i	0.417783	+	1.25061i
$712$	−10.5412			−0.395047
$713$	17.1382	+	23.3054i	0.641831	+	0.872795i
$714$	5.60465	+	4.67868i	0.209749	+	0.175095i
$715$	−15.7832	+	0.468363i	−0.590258	+	0.0175158i
$716$	−7.36004	−	3.36122i	−0.275058	−	0.125615i
$717$	24.3663	+	10.5902i	0.909976	+	0.395499i
$718$	7.81698	−	9.02128i	0.291727	−	0.336671i
$719$	−7.20030	+	24.5220i	−0.268526	+	0.914515i	0.709267	+	0.704940i	$0.249026\pi$
$719$	−7.20030	+	24.5220i	−0.268526	+	0.914515i	−0.977793	+	0.209575i	$0.932792\pi$
$720$	−3.99358	−	5.38993i	−0.148832	−	0.200871i
$721$	3.57165	+	7.82082i	0.133015	+	0.291263i
$722$	−11.7477	−	13.5576i	−0.437205	−	0.504561i
$723$	−9.67184	−	30.8287i	−0.359700	−	1.14653i
$724$	4.47749	+	0.643766i	0.166405	+	0.0239254i
$725$	12.0950	+	4.67822i	0.449196	+	0.173745i
$726$	15.9851	−	5.01499i	0.593264	−	0.186124i
$727$	8.64617	+	9.97821i	0.320669	+	0.370071i	0.893082	−	0.449894i	$-0.148538\pi$
$727$	8.64617	+	9.97821i	0.320669	+	0.370071i	−0.572413	+	0.819965i	$0.693993\pi$
$728$	−11.0381	+	5.04093i	−0.409099	+	0.186829i
$729$	24.1841	+	12.0053i	0.895709	+	0.444642i
$730$	2.35077	−	5.57979i	0.0870058	−	0.206517i
$731$	−19.7036	−	17.0733i	−0.728763	−	0.631477i
$732$	17.3369	+	7.53507i	0.640792	+	0.278504i
$733$	−13.7383	+	30.0827i	−0.507436	+	1.11113i	0.466545	+	0.884497i	$0.345499\pi$
$733$	−13.7383	+	30.0827i	−0.507436	+	1.11113i	−0.973981	+	0.226632i	$0.927229\pi$
$734$	−0.589501	−	4.10007i	−0.0217589	−	0.151336i
$735$	8.62967	−	8.23613i	0.318310	−	0.303794i
$736$	3.81462	+	2.90665i	0.140609	+	0.107141i
$737$	7.16266			0.263840
$738$	2.95042	+	8.83192i	0.108607	+	0.325107i
$739$	7.44755	−	16.3079i	0.273963	−	0.599894i	−0.721775	−	0.692128i	$-0.756673\pi$
$739$	7.44755	−	16.3079i	0.273963	−	0.599894i	0.995737	+	0.0922336i	$0.0294006\pi$
$740$	18.7137	−	3.25986i	0.687929	−	0.119835i
$741$	1.75489	+	10.7917i	0.0644674	+	0.396442i
$742$	2.49920	−	8.51150i	0.0917486	−	0.312467i
$743$	−20.5905	−	32.0395i	−0.755393	−	1.17541i	−0.979617	−	0.200877i	$-0.935621\pi$
$743$	−20.5905	−	32.0395i	−0.755393	−	1.17541i	0.224223	−	0.974538i	$-0.428015\pi$
$744$	10.0770	+	2.75849i	0.369442	+	0.101131i
$745$	12.2609	+	17.8884i	0.449203	+	0.655381i
$746$	6.92995	+	4.45361i	0.253724	+	0.163058i
$747$	1.85342	+	50.3308i	0.0678132	+	1.84151i
$748$	−2.42795	−	0.349087i	−0.0887748	−	0.0127639i
$749$	0.310580	−	0.483272i	0.0113483	−	0.0176584i
$750$	18.3758	+	6.10987i	0.670989	+	0.223101i
$751$	15.5589	−	7.10551i	0.567752	−	0.259284i	−0.110792	−	0.993844i	$-0.535339\pi$
$751$	15.5589	−	7.10551i	0.567752	−	0.259284i	0.678544	+	0.734560i	$0.262611\pi$
$752$	−3.82812	+	2.46018i	−0.139597	+	0.0897135i
$753$	4.14104	−	2.77027i	0.150908	−	0.100954i
$754$	−10.4100	+	12.0138i	−0.379109	+	0.437515i
$755$	4.87091	−	0.848495i	0.177271	−	0.0308799i
$756$	8.33447	−	6.03109i	0.303122	−	0.219349i
$757$	−1.32280	−	9.20027i	−0.0480780	−	0.334389i	−0.999637	−	0.0269249i	$-0.991429\pi$
$757$	−1.32280	−	9.20027i	−0.0480780	−	0.334389i	0.951560	−	0.307465i	$-0.0994806\pi$
$758$		−	23.6563i		−	0.859236i
$759$	−8.35409	+	4.66942i	−0.303234	+	0.169489i
$760$	−0.259989	+	2.28825i	−0.00943078	+	0.0830037i
$761$	29.6915	−	4.26899i	1.07632	−	0.154751i	0.418716	−	0.908117i	$-0.362480\pi$
$761$	29.6915	−	4.26899i	1.07632	−	0.154751i	0.657601	+	0.753366i	$0.271571\pi$
$762$	−4.69186	+	2.24796i	−0.169968	+	0.0814349i
$763$	1.98318	+	6.75408i	0.0717958	+	0.244514i
$764$	8.71049	−	10.0524i	0.315134	−	0.363684i
$765$	13.9402	+	3.10450i	0.504009	+	0.112243i
$766$	−8.92915	−	13.8940i	−0.322623	−	0.502012i
$767$	14.6379	+	32.0525i	0.528544	+	1.15735i
$768$	1.73176	−	0.0318750i	0.0624894	−	0.00115019i
$769$	−22.6676	+	35.2714i	−0.817413	+	1.27192i	0.141986	+	0.989869i	$0.454651\pi$
$769$	−22.6676	+	35.2714i	−0.817413	+	1.27192i	−0.959399	+	0.282051i	$0.908985\pi$
$770$	1.29124	−	4.93459i	0.0465331	−	0.177830i
$771$	−9.20264	−	10.2336i	−0.331425	−	0.368556i
$772$	−3.07453	+	4.78406i	−0.110655	+	0.172182i
$773$	5.07104	−	4.39408i	0.182393	−	0.158044i	−0.558879	−	0.829249i	$-0.688768\pi$
$773$	5.07104	−	4.39408i	0.182393	−	0.158044i	0.741272	+	0.671205i	$0.234223\pi$
$774$	−30.1541	+	20.9859i	−1.08387	+	0.754323i
$775$	−28.3836	+	10.1981i	−1.01957	+	0.366326i
$776$	5.86655	+	1.72258i	0.210597	+	0.0618368i
$777$	4.67581	+	28.7539i	0.167744	+	1.03154i
$778$	20.1838	−	5.92649i	0.723623	−	0.212475i
$779$	1.32799	−	2.90789i	0.0475802	−	0.104186i
$780$	−14.6648	+	18.6659i	−0.525085	+	0.668347i
$781$		−	14.3979i		−	0.515196i
$782$	−10.1901	+	0.641562i	−0.364398	+	0.0229422i
$783$	6.64944	−	11.7223i	0.237631	−	0.418922i
$784$	0.438344	+	3.04875i	0.0156551	+	0.108884i
$785$	11.9194	−	19.8157i	0.425422	−	0.707251i
$786$	−19.1828	−	8.33734i	−0.684229	−	0.297383i
$787$	4.55611	−	5.25803i	0.162408	−	0.187429i	−0.668713	−	0.743521i	$-0.733154\pi$
$787$	4.55611	−	5.25803i	0.162408	−	0.187429i	0.831121	+	0.556092i	$0.187700\pi$
$788$	−11.9171	−	3.49918i	−0.424529	−	0.124653i
$789$	−30.8247	−	3.85435i	−1.09739	−	0.137219i
$790$	24.9140	−	8.12554i	0.886402	−	0.289094i
$791$	22.3594	−	19.3745i	0.795008	−	0.688878i
$792$	−1.31919	+	3.19481i	−0.0468753	+	0.113523i
$793$	9.51976	−	66.2114i	0.338057	−	2.35123i
$794$	−37.2266	−	5.35238i	−1.32112	−	0.189949i
$795$	−3.29207	−	17.0378i	−0.116758	−	0.604268i
$796$	8.27913	−	7.17391i	0.293446	−	0.254273i
$797$	−2.02013	+	0.922561i	−0.0715565	+	0.0326788i	−0.450872	−	0.892589i	$-0.648887\pi$
$797$	−2.02013	+	0.922561i	−0.0715565	+	0.0326788i	0.379315	+	0.925267i	$0.376160\pi$
$798$	−3.50456	−	0.438215i	−0.124060	−	0.0155126i
$799$	2.72941	−	9.29552i	0.0965596	−	0.328852i
$800$	−4.03857	+	2.94787i	−0.142785	+	0.104223i
$801$	−14.1866	−	28.2628i	−0.501258	−	0.998619i
$802$	−6.29444	+	13.7829i	−0.222264	+	0.486691i
$803$	−3.08801	+	0.443989i	−0.108973	+	0.0156680i
$804$	6.90042	−	8.26611i	0.243359	−	0.291523i
$805$	1.06660	−	21.2050i	0.0375928	−	0.747377i
$806$		−	36.9704i		−	1.30223i
$807$	−24.4154	+	39.5739i	−0.859462	+	1.39307i
$808$	2.64434	+	1.20763i	0.0930276	+	0.0424843i
$809$	−4.03083	−	13.7278i	−0.141717	−	0.482642i	0.857792	−	0.513997i	$-0.171836\pi$
$809$	−4.03083	−	13.7278i	−0.141717	−	0.482642i	−0.999508	+	0.0313550i	$0.990018\pi$
$810$	9.07675	−	17.9614i	0.318925	−	0.631100i
$811$	49.0129	+	14.3915i	1.72108	+	0.505353i	0.985148	−	0.171707i	$-0.0549284\pi$
$811$	49.0129	+	14.3915i	1.72108	+	0.505353i	0.735927	+	0.677061i	$0.236747\pi$
$812$	−2.77624	−	4.31991i	−0.0974268	−	0.151599i
$813$	−53.9991	−	14.7818i	−1.89383	−	0.518419i
$814$	−6.40950	−	7.39696i	−0.224653	−	0.259263i
$815$	−1.93109	+	2.36696i	−0.0676430	+	0.0829109i
$816$	−2.74193	+	2.46569i	−0.0959868	+	0.0863164i
$817$	12.4840	+	1.79493i	0.436761	+	0.0627967i
$818$	−17.1131	−	10.9979i	−0.598347	−	0.384534i
$819$	−28.3710	−	22.8110i	−0.991364	−	0.797081i
$820$	6.59846	−	2.15204i	0.230428	−	0.0751526i
$821$	4.13738	+	6.43789i	0.144396	+	0.224684i	0.905916	−	0.423456i	$-0.139183\pi$
$821$	4.13738	+	6.43789i	0.144396	+	0.224684i	−0.761521	+	0.648140i	$0.775547\pi$
$822$	−0.405287	−	0.605828i	−0.0141360	−	0.0211307i
$823$	3.12371	+	2.70671i	0.108886	+	0.0943501i	0.707602	−	0.706611i	$-0.249777\pi$
$823$	3.12371	+	2.70671i	0.108886	+	0.0943501i	−0.598716	+	0.800961i	$0.704322\pi$
$824$	−4.16669	+	1.22345i	−0.145153	+	0.0426209i
$825$	−2.18270	−	9.73627i	−0.0759918	−	0.338973i
$826$	−11.2668	+	1.61992i	−0.392021	+	0.0563641i
$827$			27.3360i			0.950567i	0.879833	+	0.475284i	$0.157655\pi$
$827$			27.3360i			0.950567i	−0.879833	+	0.475284i	$0.842345\pi$
$828$	−2.65947	+	14.1396i	−0.0924229	+	0.491384i
$829$	−20.4731			−0.711061			−0.355530	−	0.934665i	$-0.615700\pi$
$829$	−20.4731			−0.711061			−0.355530	+	0.934665i	$0.615700\pi$
$830$	37.5233	−	1.11350i	1.30245	−	0.0386500i
$831$	10.4010	−	4.98331i	0.360807	−	0.172869i
$832$	−1.72675	−	5.88075i	−0.0598641	−	0.203878i
$833$	−4.95583	−	4.29425i	−0.171709	−	0.148787i
$834$	26.8616	−	17.9699i	0.930139	−	0.622245i
$835$	−37.0424	+	18.2634i	−1.28191	+	0.632032i
$836$	1.07939	−	0.492943i	0.0373316	−	0.0170488i
$837$	6.16587	+	30.7308i	0.213123	+	1.06221i
$838$	−22.1374	−	14.2268i	−0.764723	−	0.491458i
$839$	−5.11611	+	35.5833i	−0.176628	+	1.22847i	0.687869	+	0.725835i	$0.258546\pi$
$839$	−5.11611	+	35.5833i	−0.176628	+	1.22847i	−0.864497	+	0.502638i	$0.832363\pi$
$840$	−4.45083	−	6.24409i	−0.153568	−	0.215442i
$841$	18.7373	+	12.0417i	0.646113	+	0.415231i
$842$	9.05774	−	7.84857i	0.312150	−	0.270480i
$843$	−14.2207	−	3.89279i	−0.489787	−	0.134075i
$844$	−7.84550	+	5.04200i	−0.270053	+	0.173553i
$845$	50.6199	+	21.3262i	1.74138	+	0.733643i
$846$	−11.7482	−	6.95292i	−0.403910	−	0.239046i
$847$	18.3747	−	5.39530i	0.631362	−	0.185385i
$848$	4.07561	+	1.86127i	0.139957	+	0.0639162i
$849$	−11.7652	−	7.25861i	−0.403780	−	0.249115i
$850$	2.38810	−	10.3736i	0.0819113	−	0.355812i
$851$	−32.4054	−	24.6922i	−1.11084	−	0.846436i
$852$	−16.6160	−	13.8707i	−0.569253	−	0.475204i
$853$	44.2725	−	6.36543i	1.51586	−	0.217948i	0.666399	−	0.745595i	$-0.267835\pi$
$853$	44.2725	−	6.36543i	1.51586	−	0.217948i	0.849464	+	0.527647i	$0.176926\pi$
$854$	19.6557	+	8.97644i	0.672603	+	0.307168i
$855$	−6.48513	+	2.38251i	−0.221787	+	0.0814801i
$856$	0.219283	+	0.190010i	0.00749493	+	0.00649440i
$857$	−34.8544	−	10.2342i	−1.19060	−	0.349593i	−0.374350	−	0.927287i	$-0.622134\pi$
$857$	−34.8544	−	10.2342i	−1.19060	−	0.349593i	−0.816253	+	0.577695i	$0.803952\pi$
$858$	12.1365	+	1.51756i	0.414333	+	0.0518086i
$859$	−0.715242	−	1.56616i	−0.0244038	−	0.0534368i	0.897038	−	0.441954i	$-0.145715\pi$
$859$	−0.715242	−	1.56616i	−0.0244038	−	0.0534368i	−0.921441	+	0.388517i	$0.872987\pi$
$860$	15.4810	+	22.5866i	0.527899	+	0.770198i
$861$	3.18621	+	10.1560i	0.108586	+	0.346114i
$862$	−0.492578	+	3.42595i	−0.0167773	+	0.116688i
$863$	−5.00924	+	34.8400i	−0.170516	+	1.18597i	0.707280	+	0.706933i	$0.249922\pi$
$863$	−5.00924	+	34.8400i	−0.170516	+	1.18597i	−0.877796	+	0.479034i	$0.840987\pi$
$864$	2.41610	+	4.60027i	0.0821975	+	0.156504i
$865$	−19.2841	−	28.1353i	−0.655680	−	0.956629i
$866$	5.69338	+	12.4668i	0.193469	+	0.423638i
$867$	−2.67930	+	21.4273i	−0.0909937	+	0.727709i
$868$	11.4589	+	3.36463i	0.388940	+	0.114203i
$869$	−10.2046	−	8.84235i	−0.346168	−	0.299956i
$870$	−8.70170	−	5.01847i	−0.295015	−	0.170142i
$871$	−34.6594	−	15.8284i	−1.17439	−	0.536326i
$872$	−3.51920	+	0.505984i	−0.119175	+	0.0171348i
$873$	3.27680	+	18.0476i	0.110903	+	0.610819i
$874$	3.97923	−	2.92622i	0.134599	−	0.0989810i
$875$	20.8729	+	7.36945i	0.705634	+	0.249133i
$876$	−2.46257	+	3.99147i	−0.0832024	+	0.134859i
$877$	−22.4894	−	10.2706i	−0.759415	−	0.346813i	−0.00221582	−	0.999998i	$-0.500705\pi$
$877$	−22.4894	−	10.2706i	−0.759415	−	0.346813i	−0.757199	+	0.653185i	$0.773433\pi$
$878$	−8.96951	+	2.63369i	−0.302706	+	0.0888826i
$879$	−37.3070	+	6.06668i	−1.25834	+	0.204624i
$880$	2.37419	+	1.00025i	0.0800339	+	0.0337183i
$881$	1.33244	−	0.856307i	0.0448910	−	0.0288497i	−0.518003	−	0.855379i	$-0.673324\pi$
$881$	1.33244	−	0.856307i	0.0448910	−	0.0288497i	0.562894	+	0.826529i	$0.309688\pi$
$882$	−7.58432	+	5.27836i	−0.255377	+	0.177732i
$883$	−15.1254	+	13.1062i	−0.509010	+	0.441060i	−0.871116	−	0.491077i	$-0.836603\pi$
$883$	−15.1254	+	13.1062i	−0.509010	+	0.441060i	0.362106	+	0.932137i	$0.382058\pi$
$884$	10.9772	+	7.05463i	0.369204	+	0.237273i
$885$	−18.1316	+	12.9243i	−0.609488	+	0.434447i
$886$	0.522687	−	3.63536i	0.0175600	−	0.122132i
$887$	−20.6218	−	13.2528i	−0.692412	−	0.444986i	0.146530	−	0.989206i	$-0.453189\pi$
$887$	−20.6218	−	13.2528i	−0.692412	−	0.444986i	−0.838943	+	0.544220i	$0.816826\pi$
$888$	−14.7114	+	0.270780i	−0.493681	+	0.00908677i
$889$	−5.40956	+	2.47046i	−0.181431	+	0.0828567i
$890$	−21.1409	+	10.4233i	−0.708643	+	0.349390i
$891$	−10.3413	+	0.762665i	−0.346446	+	0.0255503i
$892$	−21.0312	−	18.2236i	−0.704175	−	0.610171i
$893$	1.32038	+	4.49681i	0.0441849	+	0.150480i
$894$	−7.25844	−	15.1496i	−0.242758	−	0.506678i
$895$	−18.0846	+	0.536656i	−0.604501	+	0.0179384i
$896$	1.97987			0.0661430
$897$	50.7434	−	4.13355i	1.69427	−	0.138015i
$898$			35.9863i			1.20088i
$899$	15.4856	−	2.22650i	0.516475	−	0.0742579i
$900$	−13.3390	−	6.86085i	−0.444633	−	0.228695i
$901$	−9.15256	+	2.68743i	−0.304916	+	0.0895314i
$902$	−2.70269	−	2.34189i	−0.0899896	−	0.0779764i
$903$	−34.9042	+	23.3502i	−1.16154	+	0.777046i
$904$	8.07891	+	12.5710i	0.268701	+	0.418106i
$905$	9.61641	−	3.13632i	0.319660	−	0.104255i
$906$	−3.82916	+	0.0704801i	−0.127215	+	0.00234155i
$907$	−27.1997	−	17.4802i	−0.903150	−	0.580419i	0.00457305	−	0.999990i	$-0.498544\pi$
$907$	−27.1997	−	17.4802i	−0.903150	−	0.580419i	−0.907723	+	0.419570i	$0.862181\pi$
$908$	17.6770	+	2.54157i	0.586633	+	0.0843451i
$909$	0.320936	+	8.71522i	0.0106448	+	0.289066i
$910$	−17.1529	+	21.0245i	−0.568614	+	0.696957i
$911$	21.6456	+	24.9803i	0.717150	+	0.827635i	0.990961	−	0.134148i	$-0.0428298\pi$
$911$	21.6456	+	24.9803i	0.717150	+	0.827635i	−0.273811	+	0.961783i	$0.588284\pi$
$912$	0.470992	−	1.72058i	0.0155961	−	0.0569740i
$913$	−10.4574	−	16.2721i	−0.346091	−	0.538528i
$914$	5.00823	+	1.47055i	0.165658	+	0.0486414i
$915$	42.2210	−	2.03113i	1.39578	−	0.0671472i
$916$	4.55769	+	15.5221i	0.150590	+	0.512863i
$917$	−21.7484	−	9.93218i	−0.718197	−	0.327989i
$918$	−10.3011	−	4.03324i	−0.339988	−	0.133117i
$919$		−	24.6901i		−	0.814452i	−0.913328	−	0.407226i	$-0.866496\pi$
$919$		−	24.6901i		−	0.814452i	0.913328	−	0.407226i	$-0.133504\pi$
$920$	10.5246	+	2.05747i	0.346985	+	0.0678327i
$921$	−1.81879	−	1.51829i	−0.0599310	−	0.0500295i
$922$	2.26295	−	0.325363i	0.0745262	−	0.0107152i
$923$	−31.8172	+	69.6699i	−1.04728	+	2.29321i
$924$	−1.57489	+	3.62356i	−0.0518101	+	0.119206i
$925$	34.3079	−	25.0423i	1.12804	−	0.823385i
$926$	−6.03828	+	20.5645i	−0.198430	+	0.675791i
$927$	−8.88792	−	9.52511i	−0.291918	−	0.312846i
$928$	2.35926	−	1.07744i	0.0774465	−	0.0353686i
$929$	−3.65462	+	3.16675i	−0.119904	+	0.103898i	−0.712749	−	0.701419i	$-0.752550\pi$
$929$	−3.65462	+	3.16675i	−0.119904	+	0.103898i	0.592845	+	0.805317i	$0.298005\pi$
$930$	22.9376	−	4.43206i	0.752155	−	0.145333i
$931$	3.13997	+	0.451460i	0.102908	+	0.0147960i
$932$	−2.66744	+	18.5524i	−0.0873748	+	0.607705i
$933$	−15.2370	−	48.5675i	−0.498837	−	1.59003i
$934$	−7.85506	+	6.80644i	−0.257025	+	0.222714i
$935$	−5.21457	+	1.70070i	−0.170535	+	0.0556187i
$936$	13.4435	−	12.5442i	0.439415	−	0.410019i
$937$	42.9289	+	12.6051i	1.40243	+	0.411789i	0.893516	−	0.449031i	$-0.148231\pi$
$937$	42.9289	+	12.6051i	1.40243	+	0.411789i	0.508909	+	0.860820i	$0.330049\pi$
$938$	8.06029	−	9.30208i	0.263178	−	0.303724i
$939$	18.6375	−	42.8818i	0.608212	−	1.39939i
$940$	−5.24481	+	8.71933i	−0.171067	+	0.284393i
$941$	3.93962	+	27.4006i	0.128428	+	0.893235i	0.947548	+	0.319613i	$0.103553\pi$
$941$	3.93962	+	27.4006i	0.128428	+	0.893235i	−0.819120	+	0.573622i	$0.805538\pi$
$942$	−11.4788	+	13.7506i	−0.373998	+	0.448017i
$943$	−13.0037	−	7.24510i	−0.423457	−	0.235933i
$944$		−	5.74917i		−	0.187120i
$945$	10.7515	−	20.3369i	0.349748	−	0.661561i
$946$	5.86118	−	12.8342i	0.190564	−	0.417276i
$947$	47.4207	−	13.9240i	1.54096	−	0.452468i	0.602579	−	0.798059i	$-0.294140\pi$
$947$	47.4207	−	13.9240i	1.54096	−	0.452468i	0.938385	+	0.345591i	$0.112321\pi$
$948$	−20.0356	+	3.25808i	−0.650726	+	0.105818i
$949$	15.9237	+	4.67563i	0.516906	+	0.151777i
$950$	1.74125	+	4.84629i	0.0564936	+	0.157235i
$951$	−53.3092	−	14.5929i	−1.72867	−	0.473208i
$952$	−3.18559	+	2.76033i	−0.103245	+	0.0894627i
$953$	19.0934	−	29.7099i	0.618496	−	0.962399i	−0.380791	−	0.924661i	$-0.624348\pi$
$953$	19.0934	−	29.7099i	0.618496	−	0.962399i	0.999288	−	0.0377382i	$-0.0120153\pi$
$954$	0.494646	+	13.4324i	0.0160147	+	0.434890i
$955$	7.52928	−	28.7738i	0.243642	−	0.931097i
$956$	−8.29298	+	12.9041i	−0.268214	+	0.417349i
$957$	0.0952511	+	5.17496i	0.00307903	+	0.167283i
$958$	4.24531	+	9.29593i	0.137160	+	0.300338i
$959$	−0.450453	−	0.700919i	−0.0145459	−	0.0226338i
$960$	3.44161	−	1.77632i	0.111077	−	0.0573306i
$961$	−3.52658	+	4.06989i	−0.113761	+	0.131287i
$962$	14.6688	+	49.9573i	0.472940	+	1.61069i
$963$	−0.214335	+	0.843658i	−0.00690685	+	0.0271865i
$964$	18.4645	−	2.65479i	0.594701	−	0.0855051i
$965$	−1.43555	+	12.6348i	−0.0462121	+	0.406730i
$966$	−3.33691	+	16.1040i	−0.107363	+	0.518137i
$967$			6.05303i			0.194652i	0.995253	+	0.0973261i	$0.0310290\pi$
$967$			6.05303i			0.194652i	−0.995253	+	0.0973261i	$0.968971\pi$
$968$	1.37655	+	9.57409i	0.0442439	+	0.307723i
$969$	1.64100	+	3.42504i	0.0527164	+	0.110028i
$970$	13.4690	−	2.34625i	0.432463	−	0.0753335i
$971$	−0.779866	+	0.900013i	−0.0250271	+	0.0288828i	−0.768125	−	0.640300i	$-0.778810\pi$
$971$	−0.779866	+	0.900013i	−0.0250271	+	0.0288828i	0.743098	+	0.669183i	$0.233356\pi$
$972$	−9.08252	+	12.6692i	−0.291322	+	0.406364i
$973$	31.0777	−	19.9725i	0.996307	−	0.640288i
$974$	−14.5688	+	6.65333i	−0.466813	+	0.213186i
$975$	−10.9539	+	51.9363i	−0.350804	+	1.66329i
$976$	−5.90056	+	9.18145i	−0.188872	+	0.293891i
$977$	−31.1930	−	4.48488i	−0.997953	−	0.143484i	−0.376068	−	0.926592i	$-0.622724\pi$
$977$	−31.1930	−	4.48488i	−0.997953	−	0.143484i	−0.621885	+	0.783108i	$0.713633\pi$
$978$	1.75944	−	1.58219i	0.0562608	−	0.0505927i
$979$	10.2171	+	6.56610i	0.326538	+	0.209853i
$980$	3.89378	+	5.68097i	0.124382	+	0.181472i
$981$	−6.09286	−	8.75466i	−0.194530	−	0.279515i
$982$	17.6211	+	27.4190i	0.562313	+	0.874976i
$983$	13.1080	−	44.6419i	0.418081	−	1.42385i	−0.434222	−	0.900806i	$-0.642977\pi$
$983$	13.1080	−	44.6419i	0.418081	−	1.42385i	0.852303	−	0.523048i	$-0.175205\pi$
$984$	−5.30641	+	0.862901i	−0.169162	+	0.0275083i
$985$	−27.3604	+	4.76608i	−0.871775	+	0.151860i
$986$	−2.29385	+	5.02284i	−0.0730512	+	0.159960i
$987$	−13.2806	−	8.19354i	−0.422725	−	0.260803i
$988$	−6.31242			−0.200825
$989$	12.9726	−	57.2790i	0.412504	−	1.82137i
$990$	0.513393	+	7.71180i	0.0163167	+	0.245097i
$991$	−5.38504	−	37.4538i	−0.171061	−	1.18976i	−0.876647	−	0.481133i	$-0.840225\pi$
$991$	−5.38504	−	37.4538i	−0.171061	−	1.18976i	0.705586	−	0.708624i	$-0.250684\pi$
$992$	−2.50579	+	5.48692i	−0.0795589	+	0.174210i
$993$	−19.5276	+	44.9298i	−0.619690	+	1.42580i
$994$	−18.6984	−	16.2022i	−0.593076	−	0.513904i
$995$	9.51053	−	22.5742i	0.301504	−	0.715651i
$996$	−28.8535	−	3.60788i	−0.914259	−	0.114320i
$997$	−4.98354	+	2.27591i	−0.157830	+	0.0720787i	−0.492764	−	0.870163i	$-0.664013\pi$
$997$	−4.98354	+	2.27591i	−0.157830	+	0.0720787i	0.334934	+	0.942242i	$0.391286\pi$
$998$	−19.4734	−	22.4735i	−0.616419	−	0.711385i
$999$	−20.5249	−	39.0795i	−0.649379	−	1.23642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.89.16	yes	240
3.2	odd	2		690.2.n.b.89.23	yes	240
5.4	even	2		690.2.n.b.89.9	yes	240
15.14	odd	2	inner	690.2.n.a.89.2	✓	240
23.15	odd	22	inner	690.2.n.a.659.2	yes	240
69.38	even	22		690.2.n.b.659.9	yes	240
115.84	odd	22		690.2.n.b.659.23	yes	240
345.314	even	22	inner	690.2.n.a.659.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.2	✓	240	15.14	odd	2	inner
690.2.n.a.89.16	yes	240	1.1	even	1	trivial
690.2.n.a.659.2	yes	240	23.15	odd	22	inner
690.2.n.a.659.16	yes	240	345.314	even	22	inner
690.2.n.b.89.9	yes	240	5.4	even	2
690.2.n.b.89.23	yes	240	3.2	odd	2
690.2.n.b.659.9	yes	240	69.38	even	22
690.2.n.b.659.23	yes	240	115.84	odd	22

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.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.748393 + 1.56202i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.64573 + 1.51379i) q^{5} +(1.43961 - 0.963074i) q^{6} +(1.66558 - 1.07040i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-1.87982 + 2.33801i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.748393 + 1.56202i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.64573 + 1.51379i) q^{5} +(1.43961 - 0.963074i) q^{6} +(1.66558 - 1.07040i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-1.87982 + 2.33801i) q^{9} +(1.73260 + 1.41354i) q^{10} +(0.163968 - 1.14042i) q^{11} +(-1.15815 - 1.28790i) q^{12} +(-3.31360 + 5.15606i) q^{13} +(-1.29654 - 1.49629i) q^{14} +(-3.59623 - 1.43775i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.599806 + 2.04275i) q^{17} +(2.58174 + 1.52795i) q^{18} +(-0.290163 - 0.988203i) q^{19} +(1.15258 - 1.91613i) q^{20} +(2.91849 + 1.80058i) q^{21} -1.15215 q^{22} +(-4.69475 + 0.979447i) q^{23} +(-1.10997 + 1.32965i) q^{24} +(0.416853 - 4.98259i) q^{25} +(5.57516 + 2.54609i) q^{26} +(-5.05886 - 1.18656i) q^{27} +(-1.29654 + 1.49629i) q^{28} +(-0.730713 + 2.48858i) q^{29} +(-0.911320 + 3.76424i) q^{30} +(-2.50579 - 5.48692i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.90408 - 0.597363i) q^{33} +(2.10732 + 0.302987i) q^{34} +(-1.12072 + 4.28293i) q^{35} +(1.14498 - 2.77291i) q^{36} +(5.56307 + 6.42013i) q^{37} +(-0.936850 + 0.427845i) q^{38} +(-10.5337 - 1.31715i) q^{39} +(-2.06066 - 0.868156i) q^{40} +(2.34577 + 2.03262i) q^{41} +(1.36691 - 3.14504i) q^{42} +(-5.08716 + 11.1393i) q^{43} +(0.163968 + 1.14042i) q^{44} +(-0.445595 - 6.69339i) q^{45} +(1.63761 + 4.50757i) q^{46} -4.55049 q^{47} +(1.47408 + 0.909444i) q^{48} +(-1.27952 + 2.80176i) q^{49} +(-4.99120 + 0.296487i) q^{50} +(-3.63971 + 0.591871i) q^{51} +(1.72675 - 5.88075i) q^{52} +(2.42234 + 3.76924i) q^{53} +(-0.454536 + 5.17623i) q^{54} +(1.45652 + 2.12505i) q^{55} +(1.66558 + 1.07040i) q^{56} +(1.32644 - 1.19280i) q^{57} +(2.56724 + 0.369114i) q^{58} +(3.10824 - 4.83651i) q^{59} +(3.85562 + 0.366337i) q^{60} +(-9.92774 + 4.53385i) q^{61} +(-5.07446 + 3.26115i) q^{62} +(-0.628371 + 5.90629i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-2.35193 - 13.5016i) q^{65} +(-0.862262 - 1.79969i) q^{66} +(0.884738 + 6.15349i) q^{67} -2.12899i q^{68} +(-5.04343 - 6.60029i) q^{69} +(4.39883 + 0.499790i) q^{70} +(12.3693 - 1.77844i) q^{71} +(-2.90763 - 0.738698i) q^{72} +(-0.762867 - 2.59809i) q^{73} +(5.56307 - 6.42013i) q^{74} +(8.09488 - 3.07780i) q^{75} +(0.556818 + 0.866426i) q^{76} +(-0.947610 - 2.07498i) q^{77} +(0.195363 + 10.6140i) q^{78} +(6.33604 - 9.85907i) q^{79} +(-0.566057 + 2.16323i) q^{80} +(-1.93258 - 8.79006i) q^{81} +(1.67810 - 2.61117i) q^{82} +(12.6878 - 10.9940i) q^{83} +(-3.30756 - 0.905414i) q^{84} +(-2.10519 - 4.26980i) q^{85} +(11.7499 + 3.45009i) q^{86} +(-4.43407 + 0.721046i) q^{87} +(1.10548 - 0.324599i) q^{88} +(-4.37896 + 9.58859i) q^{89} +(-6.56184 + 1.39363i) q^{90} +12.1347i q^{91} +(4.22864 - 2.26244i) q^{92} +(6.69536 - 8.02046i) q^{93} +(0.647602 + 4.50417i) q^{94} +(1.97347 + 1.18707i) q^{95} +(0.690404 - 1.58850i) q^{96} +(4.00396 - 4.62082i) q^{97} +(2.95533 + 0.867764i) q^{98} +(2.35809 + 2.52715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

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