LMFDB - Embedded newform 690.2.n.a.659.7

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			659.7
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-1.16282 + 1.28368i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.23565 + 0.0433117i) q^{5} +(-1.10513 - 1.33367i) q^{6} +(1.95813 + 1.25842i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.295684 - 2.98539i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-1.16282 + 1.28368i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.23565 + 0.0433117i) q^{5} +(-1.10513 - 1.33367i) q^{6} +(1.95813 + 1.25842i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.295684 - 2.98539i) q^{9} +(-0.361037 + 2.20673i) q^{10} +(-0.0412214 - 0.286701i) q^{11} +(1.47738 - 0.904080i) q^{12} +(1.87184 + 2.91263i) q^{13} +(-1.52428 + 1.75911i) q^{14} +(-2.65526 + 2.81950i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.45726 + 4.96297i) q^{17} +(2.99709 + 0.132191i) q^{18} +(2.20986 - 7.52609i) q^{19} +(-2.13289 - 0.671412i) q^{20} +(-3.89237 + 1.05031i) q^{21} +0.289649 q^{22} +(4.72344 - 0.830119i) q^{23} +(0.684625 + 1.59100i) q^{24} +(4.99625 + 0.193659i) q^{25} +(-3.14938 + 1.43827i) q^{26} +(4.17613 + 3.09192i) q^{27} +(-1.52428 - 1.75911i) q^{28} +(1.28974 + 4.39246i) q^{29} +(-2.41292 - 3.02949i) q^{30} +(-0.269124 + 0.589299i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.415966 + 0.280467i) q^{33} +(-5.11984 + 0.736122i) q^{34} +(4.32319 + 2.89819i) q^{35} +(-0.557376 + 2.94777i) q^{36} +(-6.06516 + 6.99957i) q^{37} +(7.13499 + 3.25844i) q^{38} +(-5.91551 - 0.984034i) q^{39} +(0.968120 - 2.01563i) q^{40} +(-6.02707 + 5.22249i) q^{41} +(-0.485675 - 4.00223i) q^{42} +(-4.06093 - 8.89220i) q^{43} +(-0.0412214 + 0.286701i) q^{44} +(-0.531743 - 6.68710i) q^{45} +(0.149454 + 4.79350i) q^{46} -12.5393 q^{47} +(-1.67224 + 0.451233i) q^{48} +(-0.657229 - 1.43913i) q^{49} +(-0.902728 + 4.91783i) q^{50} +(-8.06541 - 3.90040i) q^{51} +(-0.975429 - 3.32201i) q^{52} +(-5.71601 + 8.89428i) q^{53} +(-3.65477 + 3.69359i) q^{54} +(-0.0797390 - 0.642748i) q^{55} +(1.95813 - 1.25842i) q^{56} +(7.09144 + 11.5883i) q^{57} +(-4.53130 + 0.651502i) q^{58} +(1.03617 + 1.61231i) q^{59} +(3.34205 - 1.95722i) q^{60} +(5.15339 + 2.35348i) q^{61} +(-0.545000 - 0.350250i) q^{62} +(3.17788 - 6.21789i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(4.05861 + 6.59269i) q^{65} +(-0.336811 + 0.371818i) q^{66} +(1.48727 - 10.3442i) q^{67} -5.17249i q^{68} +(-4.42692 + 7.02868i) q^{69} +(-3.48394 + 3.86674i) q^{70} +(8.25991 + 1.18760i) q^{71} +(-2.83844 - 0.971213i) q^{72} +(3.93552 - 13.4031i) q^{73} +(-6.06516 - 6.99957i) q^{74} +(-6.05835 + 6.18841i) q^{75} +(-4.24069 + 6.59864i) q^{76} +(0.280072 - 0.613272i) q^{77} +(1.81588 - 5.71526i) q^{78} +(5.89554 + 9.17364i) q^{79} +(1.85733 + 1.24512i) q^{80} +(-8.82514 + 1.76547i) q^{81} +(-4.31159 - 6.70896i) q^{82} +(5.21189 + 4.51613i) q^{83} +(4.03061 + 0.0888450i) q^{84} +(3.04296 + 11.1586i) q^{85} +(9.37962 - 2.75411i) q^{86} +(-7.13826 - 3.45203i) q^{87} +(-0.277916 - 0.0816036i) q^{88} +(-2.75722 - 6.03747i) q^{89} +(6.69471 + 0.425342i) q^{90} +8.05887i q^{91} +(-4.76598 - 0.534254i) q^{92} +(-0.443530 - 1.03072i) q^{93} +(1.78453 - 12.4116i) q^{94} +(5.26643 - 16.7300i) q^{95} +(-0.208656 - 1.71944i) q^{96} +(10.7860 + 12.4477i) q^{97} +(1.51802 - 0.445730i) q^{98} +(-0.843726 + 0.207835i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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
$3$	−1.16282	+	1.28368i	−0.671356	+	0.741135i
$3$	−1.16282	+	1.28368i	−0.671356	+	0.741135i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	2.23565	+	0.0433117i	0.999812	+	0.0193696i
$5$	2.23565	+	0.0433117i	0.999812	+	0.0193696i
$6$	−1.10513	−	1.33367i	−0.451167	−	0.544470i
$7$	1.95813	+	1.25842i	0.740105	+	0.475637i	0.855578	−	0.517674i	$-0.173202\pi$
$7$	1.95813	+	1.25842i	0.740105	+	0.475637i	−0.115473	+	0.993311i	$0.536838\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.295684	−	2.98539i	−0.0985614	−	0.995131i
$10$	−0.361037	+	2.20673i	−0.114170	+	0.697829i
$11$	−0.0412214	−	0.286701i	−0.0124287	−	0.0864436i	0.982663	−	0.185401i	$-0.0593584\pi$
$11$	−0.0412214	−	0.286701i	−0.0124287	−	0.0864436i	−0.995092	+	0.0989573i	$0.968449\pi$
$12$	1.47738	−	0.904080i	0.426482	−	0.260985i
$13$	1.87184	+	2.91263i	0.519154	+	0.807819i	0.997523	−	0.0703399i	$-0.0224084\pi$
$13$	1.87184	+	2.91263i	0.519154	+	0.807819i	−0.478369	+	0.878159i	$0.658772\pi$
$14$	−1.52428	+	1.75911i	−0.407381	+	0.470142i
$15$	−2.65526	+	2.81950i	−0.685586	+	0.727992i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	1.45726	+	4.96297i	0.353437	+	1.20370i	0.923984	+	0.382431i	$0.124913\pi$
$17$	1.45726	+	4.96297i	0.353437	+	1.20370i	−0.570547	+	0.821265i	$0.693269\pi$
$18$	2.99709	+	0.132191i	0.706420	+	0.0311578i
$19$	2.20986	−	7.52609i	0.506976	−	1.72660i	−0.165245	−	0.986253i	$-0.552841\pi$
$19$	2.20986	−	7.52609i	0.506976	−	1.72660i	0.672221	−	0.740350i	$-0.265340\pi$
$20$	−2.13289	−	0.671412i	−0.476928	−	0.150132i
$21$	−3.89237	+	1.05031i	−0.849385	+	0.229196i
$22$	0.289649			0.0617534
$23$	4.72344	−	0.830119i	0.984906	−	0.173092i
$23$	4.72344	−	0.830119i	0.984906	−	0.173092i
$24$	0.684625	+	1.59100i	0.139748	+	0.324762i
$25$	4.99625	+	0.193659i	0.999250	+	0.0387319i
$26$	−3.14938	+	1.43827i	−0.617643	+	0.282068i
$27$	4.17613	+	3.09192i	0.803696	+	0.595040i
$28$	−1.52428	−	1.75911i	−0.288062	−	0.332441i
$29$	1.28974	+	4.39246i	0.239499	+	0.815659i	0.988255	+	0.152813i	$0.0488333\pi$
$29$	1.28974	+	4.39246i	0.239499	+	0.815659i	−0.748756	+	0.662846i	$0.769349\pi$
$30$	−2.41292	−	3.02949i	−0.440537	−	0.553107i
$31$	−0.269124	+	0.589299i	−0.0483361	+	0.105841i	−0.932259	−	0.361791i	$-0.882165\pi$
$31$	−0.269124	+	0.589299i	−0.0483361	+	0.105841i	0.883923	+	0.467632i	$0.154893\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	0.415966	+	0.280467i	0.0724104	+	0.0488231i
$34$	−5.11984	+	0.736122i	−0.878046	+	0.126244i
$35$	4.32319	+	2.89819i	0.730753	+	0.489883i
$36$	−0.557376	+	2.94777i	−0.0928959	+	0.491295i
$37$	−6.06516	+	6.99957i	−0.997107	+	1.15072i	−0.00853621	+	0.999964i	$0.502717\pi$
$37$	−6.06516	+	6.99957i	−0.997107	+	1.15072i	−0.988571	+	0.150759i	$0.951828\pi$
$38$	7.13499	+	3.25844i	1.15745	+	0.528589i
$39$	−5.91551	−	0.984034i	−0.947240	−	0.157571i
$40$	0.968120	−	2.01563i	0.153073	−	0.318698i
$41$	−6.02707	+	5.22249i	−0.941270	+	0.815615i	−0.983017	−	0.183513i	$-0.941253\pi$
$41$	−6.02707	+	5.22249i	−0.941270	+	0.815615i	0.0417470	+	0.999128i	$0.486708\pi$
$42$	−0.485675	−	4.00223i	−0.0749412	−	0.617557i
$43$	−4.06093	−	8.89220i	−0.619286	−	1.35605i	−0.916037	−	0.401093i	$-0.868630\pi$
$43$	−4.06093	−	8.89220i	−0.619286	−	1.35605i	0.296751	−	0.954955i	$-0.404097\pi$
$44$	−0.0412214	+	0.286701i	−0.00621435	+	0.0432218i
$45$	−0.531743	−	6.68710i	−0.0792676	−	0.996853i
$46$	0.149454	+	4.79350i	0.0220358	+	0.706763i
$47$	−12.5393			−1.82904			−0.914521	−	0.404539i	$-0.867432\pi$
$47$	−12.5393			−1.82904			−0.914521	+	0.404539i	$0.867432\pi$
$48$	−1.67224	+	0.451233i	−0.241367	+	0.0651299i
$49$	−0.657229	−	1.43913i	−0.0938898	−	0.205590i
$50$	−0.902728	+	4.91783i	−0.127665	+	0.695487i
$51$	−8.06541	−	3.90040i	−1.12938	−	0.546165i
$52$	−0.975429	−	3.32201i	−0.135268	−	0.460679i
$53$	−5.71601	+	8.89428i	−0.785154	+	1.22172i	0.185831	+	0.982582i	$0.440502\pi$
$53$	−5.71601	+	8.89428i	−0.785154	+	1.22172i	−0.970985	+	0.239142i	$0.923134\pi$
$54$	−3.65477	+	3.69359i	−0.497352	+	0.502634i
$55$	−0.0797390	−	0.642748i	−0.0107520	−	0.0866681i
$56$	1.95813	−	1.25842i	0.261667	−	0.168163i
$57$	7.09144	+	11.5883i	0.939284	+	1.53490i
$58$	−4.53130	+	0.651502i	−0.594988	+	0.0855464i
$59$	1.03617	+	1.61231i	0.134898	+	0.209905i	0.902130	−	0.431465i	$-0.142003\pi$
$59$	1.03617	+	1.61231i	0.134898	+	0.209905i	−0.767232	+	0.641369i	$0.778367\pi$
$60$	3.34205	−	1.95722i	0.431457	−	0.252676i
$61$	5.15339	+	2.35348i	0.659825	+	0.301332i	0.717042	−	0.697030i	$-0.245496\pi$
$61$	5.15339	+	2.35348i	0.659825	+	0.301332i	−0.0572174	+	0.998362i	$0.518223\pi$
$62$	−0.545000	−	0.350250i	−0.0692151	−	0.0444819i
$63$	3.17788	−	6.21789i	0.400375	−	0.783381i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	4.05861	+	6.59269i	0.503409	+	0.817723i
$66$	−0.336811	+	0.371818i	−0.0414585	+	0.0457676i
$67$	1.48727	−	10.3442i	0.181699	−	1.26374i	−0.671046	−	0.741415i	$-0.734155\pi$
$67$	1.48727	−	10.3442i	0.181699	−	1.26374i	0.852745	−	0.522327i	$-0.174936\pi$
$68$		−	5.17249i		−	0.627257i
$69$	−4.42692	+	7.02868i	−0.532938	+	0.846154i
$70$	−3.48394	+	3.86674i	−0.416411	+	0.462163i
$71$	8.25991	+	1.18760i	0.980270	+	0.140942i	0.613777	−	0.789479i	$-0.289649\pi$
$71$	8.25991	+	1.18760i	0.980270	+	0.140942i	0.366493	+	0.930421i	$0.380558\pi$
$72$	−2.83844	−	0.971213i	−0.334513	−	0.114459i
$73$	3.93552	−	13.4031i	0.460617	−	1.56872i	−0.322328	−	0.946628i	$-0.604465\pi$
$73$	3.93552	−	13.4031i	0.460617	−	1.56872i	0.782945	−	0.622091i	$-0.213717\pi$
$74$	−6.06516	−	6.99957i	−0.705061	−	0.813684i
$75$	−6.05835	+	6.18841i	−0.699558	+	0.714576i
$76$	−4.24069	+	6.59864i	−0.486440	+	0.756916i
$77$	0.280072	−	0.613272i	0.0319172	−	0.0698889i
$78$	1.81588	−	5.71526i	0.205608	−	0.647125i
$79$	5.89554	+	9.17364i	0.663300	+	1.03212i	0.996023	+	0.0890910i	$0.0283962\pi$
$79$	5.89554	+	9.17364i	0.663300	+	1.03212i	−0.332723	+	0.943025i	$0.607967\pi$
$80$	1.85733	+	1.24512i	0.207656	+	0.139209i
$81$	−8.82514	+	1.76547i	−0.980571	+	0.196163i
$82$	−4.31159	−	6.70896i	−0.476135	−	0.740881i
$83$	5.21189	+	4.51613i	0.572079	+	0.495709i	0.892184	−	0.451673i	$-0.149173\pi$
$83$	5.21189	+	4.51613i	0.572079	+	0.495709i	−0.320105	+	0.947382i	$0.603718\pi$
$84$	4.03061	+	0.0888450i	0.439775	+	0.00969378i
$85$	3.04296	+	11.1586i	0.330056	+	1.21032i
$86$	9.37962	−	2.75411i	1.01143	−	0.296983i
$87$	−7.13826	−	3.45203i	−0.765302	−	0.370097i
$88$	−0.277916	−	0.0816036i	−0.0296260	−	0.00869897i
$89$	−2.75722	−	6.03747i	−0.292265	−	0.639970i	0.705360	−	0.708849i	$-0.250785\pi$
$89$	−2.75722	−	6.03747i	−0.292265	−	0.639970i	−0.997625	+	0.0688784i	$0.978058\pi$
$90$	6.69471	+	0.425342i	0.705684	+	0.0448350i
$91$			8.05887i			0.844799i
$92$	−4.76598	−	0.534254i	−0.496888	−	0.0556998i
$93$	−0.443530	−	1.03072i	−0.0459919	−	0.106881i
$94$	1.78453	−	12.4116i	0.184060	−	1.28016i
$95$	5.26643	−	16.7300i	0.540325	−	1.71646i
$96$	−0.208656	−	1.71944i	−0.0212958	−	0.175489i
$97$	10.7860	+	12.4477i	1.09515	+	1.26387i	0.962081	+	0.272763i	$0.0879374\pi$
$97$	10.7860	+	12.4477i	1.09515	+	1.26387i	0.133068	+	0.991107i	$0.457517\pi$
$98$	1.51802	−	0.445730i	0.153343	−	0.0450255i
$99$	−0.843726	+	0.207835i	−0.0847977	+	0.0208882i
$100$	−4.73930	−	1.59342i	−0.473930	−	0.159342i
$101$	−8.44782	−	7.32008i	−0.840589	−	0.728375i	0.123957	−	0.992288i	$-0.460441\pi$
$101$	−8.44782	−	7.32008i	−0.840589	−	0.728375i	−0.964547	+	0.263913i	$0.914987\pi$
$102$	5.00852	−	7.42823i	0.495918	−	0.735505i
$103$	−0.785042	−	5.46009i	−0.0773525	−	0.537998i	−0.991244	−	0.132041i	$-0.957847\pi$
$103$	−0.785042	−	5.46009i	−0.0773525	−	0.537998i	0.913892	−	0.405958i	$-0.133062\pi$
$104$	3.42701	−	0.492730i	0.336046	−	0.0483161i
$105$	−8.74746	+	2.17953i	−0.853665	+	0.212701i
$106$	−7.99028	−	6.92361i	−0.776084	−	0.672481i
$107$	9.79086	+	4.47134i	0.946518	+	0.432260i	0.828023	−	0.560694i	$-0.189466\pi$
$107$	9.79086	+	4.47134i	0.946518	+	0.432260i	0.118495	+	0.992955i	$0.462193\pi$
$108$	−3.13587	−	4.14323i	−0.301749	−	0.398682i
$109$	−2.10227	−	7.15968i	−0.201361	−	0.685773i	−0.996814	−	0.0797579i	$-0.974585\pi$
$109$	−2.10227	−	7.15968i	−0.201361	−	0.685773i	0.795453	−	0.606015i	$-0.207233\pi$
$110$	0.647554	+	0.0125452i	0.0617418	+	0.00119614i
$111$	−1.93252	−	15.9250i	−0.183427	−	1.51154i
$112$	0.966936	+	2.11729i	0.0913668	+	0.200065i
$113$	−3.47775	−	0.500025i	−0.327159	−	0.0470384i	−0.0232218	−	0.999730i	$-0.507392\pi$
$113$	−3.47775	−	0.500025i	−0.327159	−	0.0470384i	−0.303938	+	0.952692i	$0.598301\pi$
$114$	−12.4795	+	5.37007i	−1.16882	+	0.502953i
$115$	10.5959	−	1.65127i	0.988074	−	0.153982i
$116$		−	4.57789i		−	0.425047i
$117$	8.14188	−	6.44938i	0.752717	−	0.596246i
$118$	−1.74336	+	0.796166i	−0.160489	+	0.0732930i
$119$	−3.39197	+	11.5520i	−0.310941	+	1.05897i
$120$	1.46167	+	3.58657i	0.133432	+	0.327408i
$121$	10.4739	−	3.07542i	0.952175	−	0.279584i
$122$	−3.06293	+	4.76601i	−0.277304	+	0.431494i
$123$	0.304401	−	13.8097i	0.0274469	−	1.24518i
$124$	0.424247	−	0.489607i	0.0380985	−	0.0439680i
$125$	11.1615	+	0.649350i	0.998312	+	0.0580796i
$126$	5.70234	+	4.03043i	0.508005	+	0.359059i
$127$	−14.2740	+	2.05229i	−1.26661	+	0.182112i	−0.742680	−	0.669647i	$-0.766445\pi$
$127$	−14.2740	+	2.05229i	−1.26661	+	0.182112i	−0.523935	+	0.851759i	$0.675536\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	16.1369	+	5.12711i	1.42078	+	0.451417i
$130$	−7.10319	+	3.07907i	−0.622991	+	0.270052i
$131$	4.16913	−	6.48729i	0.364258	−	0.566797i	−0.609952	−	0.792438i	$-0.708811\pi$
$131$	4.16913	−	6.48729i	0.364258	−	0.566797i	0.974210	+	0.225641i	$0.0724477\pi$
$132$	−0.320100	−	0.386298i	−0.0278611	−	0.0336229i
$133$	13.7981	−	11.9562i	1.19645	−	1.03673i
$134$	10.0272	+	2.94426i	0.866221	+	0.254345i
$135$	9.20243	+	7.09332i	0.792019	+	0.610496i
$136$	5.11984	+	0.736122i	0.439023	+	0.0631220i
$137$			9.63039i			0.822779i	0.911460	+	0.411390i	$0.134956\pi$
$137$			9.63039i			0.822779i	−0.911460	+	0.411390i	$0.865044\pi$
$138$	−6.32713	−	5.38214i	−0.538601	−	0.458159i
$139$	1.21434			0.102999			0.0514994	−	0.998673i	$-0.483600\pi$
$139$	1.21434			0.102999			0.0514994	+	0.998673i	$0.483600\pi$
$140$	−3.33156	−	3.99877i	−0.281568	−	0.337958i
$141$	14.5810	−	16.0965i	1.22794	−	1.35557i
$142$	−2.35101	+	8.00682i	−0.197293	+	0.671917i
$143$	0.757895	−	0.656719i	0.0633783	−	0.0549176i
$144$	1.36528	−	2.67133i	0.113773	−	0.222611i
$145$	2.69316	+	9.87585i	0.223655	+	0.820145i
$146$	12.7066	+	5.80293i	1.05161	+	0.480254i
$147$	2.61163	+	0.829781i	0.215403	+	0.0684392i
$148$	7.79149	−	5.00729i	0.640456	−	0.411596i
$149$	0.0828029	+	0.575907i	0.00678348	+	0.0471801i	0.992932	−	0.118684i	$-0.0378677\pi$
$149$	0.0828029	+	0.575907i	0.00678348	+	0.0471801i	−0.986149	+	0.165864i	$0.946959\pi$
$150$	−5.26323	−	6.87739i	−0.429741	−	0.561536i
$151$	−12.7568	+	8.19829i	−1.03813	+	0.667168i	−0.944524	−	0.328442i	$-0.893477\pi$
$151$	−12.7568	+	8.19829i	−1.03813	+	0.667168i	−0.0936087	+	0.995609i	$0.529840\pi$
$152$	−5.92796	−	5.13661i	−0.480821	−	0.416634i
$153$	14.3855	−	5.81796i	1.16300	−	0.470354i
$154$	0.567172	+	0.364499i	0.0457040	+	0.0293722i
$155$	−0.627190	+	1.30581i	−0.0503771	+	0.104885i
$156$	5.39866	+	2.61077i	0.432238	+	0.209028i
$157$	−5.55105	−	1.62993i	−0.443022	−	0.130083i	0.0526111	−	0.998615i	$-0.483246\pi$
$157$	−5.55105	−	1.62993i	−0.443022	−	0.130083i	−0.495633	+	0.868532i	$0.665064\pi$
$158$	−9.91929	+	4.52999i	−0.789137	+	0.360387i
$159$	−4.77073	−	17.6800i	−0.378344	−	1.40212i
$160$	−1.49677	+	1.66123i	−0.118330	+	0.131332i
$161$	10.2938	+	4.31857i	0.811262	+	0.340351i
$162$	−0.491548	−	8.98657i	−0.0386197	−	0.706051i
$163$	0.671948	+	0.0966116i	0.0526310	+	0.00756720i	0.168580	−	0.985688i	$-0.446082\pi$
$163$	0.671948	+	0.0966116i	0.0526310	+	0.00756720i	−0.115949	+	0.993255i	$0.536991\pi$
$164$	7.25428	−	3.31292i	0.566464	−	0.258695i
$165$	0.917807	+	0.645042i	0.0714512	+	0.0502165i
$166$	−5.21189	+	4.51613i	−0.404521	+	0.350519i
$167$	−8.16570	+	2.39767i	−0.631881	+	0.185537i	−0.581962	−	0.813216i	$-0.697715\pi$
$167$	−8.16570	+	2.39767i	−0.631881	+	0.185537i	−0.0499193	+	0.998753i	$0.515896\pi$
$168$	−0.661556	+	3.97694i	−0.0510402	+	0.306827i
$169$	0.420735	−	0.921282i	0.0323643	−	0.0708678i
$170$	−11.4780	+	1.42396i	−0.880326	+	0.109213i
$171$	−23.1217	−	4.37195i	−1.76816	−	0.334332i
$172$	1.39121	+	9.67610i	0.106079	+	0.737796i
$173$	−3.07473	−	21.3852i	−0.233767	−	1.62589i	−0.681568	−	0.731755i	$-0.738702\pi$
$173$	−3.07473	−	21.3852i	−0.233767	−	1.62589i	0.447800	−	0.894134i	$-0.352208\pi$
$174$	4.43278	−	6.57433i	0.336048	−	0.498399i
$175$	9.53962	+	6.66657i	0.721127	+	0.503945i
$176$	0.120325	−	0.263474i	0.00906981	−	0.0198601i
$177$	−3.27457	−	0.544719i	−0.246132	−	0.0409436i
$178$	6.36841	−	1.86993i	0.477333	−	0.140157i
$179$	10.9393	−	9.47896i	0.817642	−	0.708491i	−0.141954	−	0.989873i	$-0.545338\pi$
$179$	10.9393	−	9.47896i	0.817642	−	0.708491i	0.959596	+	0.281382i	$0.0907929\pi$
$180$	−1.37377	+	6.56603i	−0.102395	+	0.489403i
$181$	10.8061	−	4.93496i	0.803208	−	0.366813i	0.0288686	−	0.999583i	$-0.490810\pi$
$181$	10.8061	−	4.93496i	0.803208	−	0.366813i	0.774339	+	0.632770i	$0.218082\pi$
$182$	−7.97684	−	1.14690i	−0.591283	−	0.0850136i
$183$	−9.01361	+	3.87865i	−0.666305	+	0.286718i
$184$	1.20709	−	4.64144i	0.0889875	−	0.342171i
$185$	−13.8627	+	15.3859i	−1.01921	+	1.13119i
$186$	1.08335	−	0.292328i	0.0794350	−	0.0214346i
$187$	1.36282	−	0.622378i	0.0996591	−	0.0455128i
$188$	12.0313	+	3.53272i	0.877476	+	0.257650i
$189$	4.28649	+	11.3097i	0.311796	+	0.822659i
$190$	15.8102	+	7.59375i	1.14699	+	0.550909i
$191$	−0.972388	−	0.624916i	−0.0703595	−	0.0452173i	0.504988	−	0.863126i	$-0.331497\pi$
$191$	−0.972388	−	0.624916i	−0.0703595	−	0.0452173i	−0.575348	+	0.817909i	$0.695133\pi$
$192$	1.73163	+	0.0381696i	0.124970	+	0.00275465i
$193$	1.48280	+	1.28486i	0.106735	+	0.0924860i	0.706593	−	0.707620i	$-0.250231\pi$
$193$	1.48280	+	1.28486i	0.106735	+	0.0924860i	−0.599859	+	0.800106i	$0.704777\pi$
$194$	−13.8560	+	8.90470i	−0.994801	+	0.639320i
$195$	−13.1824	−	2.45616i	−0.944010	−	0.175890i
$196$	0.225157	+	1.56600i	0.0160826	+	0.111857i
$197$	3.09802	−	1.99098i	0.220725	−	0.141851i	−0.425606	−	0.904909i	$-0.639939\pi$
$197$	3.09802	−	1.99098i	0.220725	−	0.141851i	0.646331	+	0.763057i	$0.276303\pi$
$198$	−0.0856446	−	0.864716i	−0.00608650	−	0.0614527i
$199$	−10.7425	−	4.90595i	−0.761517	−	0.347773i	−0.00348810	−	0.999994i	$-0.501110\pi$
$199$	−10.7425	−	4.90595i	−0.761517	−	0.347773i	−0.758029	+	0.652221i	$0.773838\pi$
$200$	2.25168	−	4.46430i	0.159217	−	0.315674i
$201$	11.5492	+	13.9376i	0.814619	+	0.983085i
$202$	8.44782	−	7.32008i	0.594386	−	0.515039i
$203$	−3.00205	+	10.2240i	−0.210703	+	0.717588i
$204$	6.63984	+	6.01469i	0.464882	+	0.421113i
$205$	−13.7006	+	11.4146i	−0.956892	+	0.797230i
$206$	5.51624			0.384334
$207$	−3.87488	−	13.8559i	−0.269323	−	0.963050i
$208$			3.46225i			0.240064i
$209$	−2.24883	−	0.323333i	−0.155555	−	0.0223654i
$210$	−0.912455	−	8.96861i	−0.0629654	−	0.618893i
$211$	−0.932555	−	0.273823i	−0.0641997	−	0.0188507i	0.249475	−	0.968381i	$-0.419742\pi$
$211$	−0.932555	−	0.273823i	−0.0641997	−	0.0188507i	−0.313675	+	0.949531i	$0.601560\pi$
$212$	7.99028	−	6.92361i	0.548774	−	0.475516i
$213$	−11.1293	+	9.22214i	−0.762567	+	0.631890i
$214$	−5.81921	+	9.05487i	−0.397793	+	0.618978i
$215$	−8.69368	−	20.0557i	−0.592904	−	1.36779i
$216$	4.54733	−	2.51431i	0.309407	−	0.171077i
$217$	−1.26856	+	0.815256i	−0.0861157	+	0.0553432i
$218$	7.38599	−	1.06195i	0.500242	−	0.0719240i
$219$	12.6291	+	20.6374i	0.853394	+	1.39455i
$220$	−0.104574	+	0.639177i	−0.00705038	+	0.0430933i
$221$	−11.7276	+	13.5343i	−0.788881	+	0.910417i
$222$	16.0379	+	0.353518i	1.07640	+	0.0237266i
$223$	0.165666	−	0.257781i	0.0110938	−	0.0172623i	−0.835662	−	0.549244i	$-0.814916\pi$
$223$	0.165666	−	0.257781i	0.0110938	−	0.0172623i	0.846756	+	0.531981i	$0.178552\pi$
$224$	−2.23335	+	0.655771i	−0.149222	+	0.0438156i
$225$	−0.899162	−	14.9730i	−0.0599441	−	0.998202i
$226$	0.989872	−	3.37119i	0.0658453	−	0.224248i
$227$	−0.487984	+	0.222855i	−0.0323886	+	0.0147914i	−0.431543	−	0.902092i	$-0.642031\pi$
$227$	−0.487984	+	0.222855i	−0.0323886	+	0.0147914i	0.399155	+	0.916884i	$0.369304\pi$
$228$	−3.53939	−	13.1168i	−0.234402	−	0.868678i
$229$		−	23.0805i		−	1.52520i	−0.646870	−	0.762601i	$-0.723922\pi$
$229$		−	23.0805i		−	1.52520i	0.646870	−	0.762601i	$-0.276078\pi$
$230$	0.126512	+	10.7231i	0.00834197	+	0.707058i
$231$	0.461573	+	1.07265i	0.0303693	+	0.0705753i
$232$	4.53130	+	0.651502i	0.297494	+	0.0427732i
$233$	−4.12602	−	9.03471i	−0.270304	−	0.591884i	0.724992	−	0.688757i	$-0.241843\pi$
$233$	−4.12602	−	9.03471i	−0.270304	−	0.591884i	−0.995297	+	0.0968730i	$0.969116\pi$
$234$	5.22503	+	8.97685i	0.341571	+	0.586835i
$235$	−28.0334	−	0.543097i	−1.82870	−	0.0354277i
$236$	−0.539956	−	1.83892i	−0.0351481	−	0.119704i
$237$	−18.6315	−	3.09932i	−1.21025	−	0.201322i
$238$	−10.9517	−	5.00147i	−0.709892	−	0.324197i
$239$	5.12101	+	4.43738i	0.331250	+	0.287030i	0.804567	−	0.593863i	$-0.202398\pi$
$239$	5.12101	+	4.43738i	0.331250	+	0.287030i	−0.473316	+	0.880893i	$0.656943\pi$
$240$	−3.75809	+	0.936371i	−0.242583	+	0.0604425i
$241$	20.4659	−	2.94255i	1.31832	−	0.189546i	0.552993	−	0.833186i	$-0.313486\pi$
$241$	20.4659	−	2.94255i	1.31832	−	0.189546i	0.765329	+	0.643640i	$0.222576\pi$
$242$	1.55352	+	10.8050i	0.0998643	+	0.694571i
$243$	7.99578	−	13.3816i	0.512930	−	0.858431i
$244$	−4.28160	−	3.71002i	−0.274101	−	0.237510i
$245$	−1.40700	−	3.24586i	−0.0898900	−	0.207370i
$246$	13.6258	+	2.26662i	0.868749	+	0.144515i
$247$	26.0572	−	7.65109i	1.65798	−	0.486827i
$248$	0.424247	+	0.489607i	0.0269397	+	0.0310901i
$249$	−11.8578	+	1.43895i	−0.751456	+	0.0911901i
$250$	−2.23118	+	10.9554i	−0.141112	+	0.692883i
$251$	2.29818	−	15.9842i	0.145060	−	1.00891i	−0.779098	−	0.626902i	$-0.784323\pi$
$251$	2.29818	−	15.9842i	0.145060	−	1.00891i	0.924158	−	0.382011i	$-0.124768\pi$
$252$	−4.80093	+	5.07071i	−0.302430	+	0.319425i
$253$	−0.432703	−	1.32000i	−0.0272038	−	0.0829875i
$254$		−	14.4208i		−	0.904841i
$255$	−17.8625	−	9.06924i	−1.11859	−	0.567938i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−5.48842	−	1.61155i	−0.342358	−	0.100525i	0.106034	−	0.994363i	$-0.466185\pi$
$257$	−5.48842	−	1.61155i	−0.342358	−	0.100525i	−0.448392	+	0.893837i	$0.648003\pi$
$258$	−7.37144	+	15.2430i	−0.458926	+	0.948988i
$259$	−20.6848	+	6.07360i	−1.28529	+	0.377395i
$260$	−2.03684	−	7.46909i	−0.126319	−	0.463213i
$261$	12.7319	−	5.14917i	0.788082	−	0.318725i
$262$	5.82793	+	5.04993i	0.360051	+	0.311986i
$263$	7.59268	+	11.8144i	0.468185	+	0.728510i	0.992397	−	0.123078i	$-0.0392765\pi$
$263$	7.59268	+	11.8144i	0.468185	+	0.728510i	−0.524212	+	0.851588i	$0.675640\pi$
$264$	0.427921	−	0.261866i	0.0263367	−	0.0161167i
$265$	−13.1642	+	19.6369i	−0.808671	+	1.20629i
$266$	9.87079	+	15.3592i	0.605217	+	0.941736i
$267$	10.9564	+	3.48111i	0.670518	+	0.213041i
$268$	−4.34132	+	9.50615i	−0.265188	+	0.580681i
$269$	2.18049	−	3.39291i	0.132947	−	0.206870i	−0.768397	−	0.639974i	$-0.778945\pi$
$269$	2.18049	−	3.39291i	0.132947	−	0.206870i	0.901344	+	0.433104i	$0.142582\pi$
$270$	−8.33076	+	8.09928i	−0.506994	+	0.492907i
$271$	4.20517	+	4.85303i	0.255446	+	0.294800i	0.868959	−	0.494884i	$-0.164790\pi$
$271$	4.20517	+	4.85303i	0.255446	+	0.294800i	−0.613513	+	0.789685i	$0.710244\pi$
$272$	−1.45726	+	4.96297i	−0.0883593	+	0.300924i
$273$	−10.3450	−	9.37104i	−0.626110	−	0.567161i
$274$	−9.53236	−	1.37055i	−0.575871	−	0.0827978i
$275$	−0.150430	−	1.44041i	−0.00907126	−	0.0868601i
$276$	6.22781	−	5.49677i	0.374870	−	0.330866i
$277$		−	2.55599i		−	0.153575i	−0.997048	−	0.0767873i	$-0.975534\pi$
$277$		−	2.55599i		−	0.153575i	0.997048	−	0.0767873i	$-0.0244662\pi$
$278$	−0.172818	+	1.20198i	−0.0103650	+	0.0720899i
$279$	1.83886	+	0.629194i	0.110090	+	0.0376689i
$280$	4.43220	−	2.72857i	0.264875	−	0.163063i
$281$	−9.39095	−	10.8377i	−0.560217	−	0.646525i	0.403016	−	0.915193i	$-0.367962\pi$
$281$	−9.39095	−	10.8377i	−0.560217	−	0.646525i	−0.963233	+	0.268668i	$0.913417\pi$
$282$	13.8575	+	16.7233i	0.825204	+	0.995859i
$283$	−8.15487	−	5.24082i	−0.484757	−	0.311534i	0.275337	−	0.961348i	$-0.411211\pi$
$283$	−8.15487	−	5.24082i	−0.484757	−	0.311534i	−0.760094	+	0.649814i	$0.774847\pi$
$284$	−7.59074	−	3.46657i	−0.450427	−	0.205703i
$285$	15.3521	+	26.2144i	0.909377	+	1.55281i
$286$	0.542175	+	0.843641i	0.0320595	+	0.0498856i
$287$	−18.3739	+	2.64176i	−1.08458	+	0.155938i
$288$	2.44984	+	1.73155i	0.144358	+	0.102033i
$289$	−8.20614	+	5.27377i	−0.482714	+	0.310222i
$290$	−10.1586	+	1.26027i	−0.596534	+	0.0740057i
$291$	−28.5210	−	0.628677i	−1.67193	−	0.0368537i
$292$	−7.55220	+	11.7515i	−0.441959	+	0.687702i
$293$	−4.17455	−	14.2172i	−0.243880	−	0.830579i	−0.986903	−	0.161313i	$-0.948427\pi$
$293$	−4.17455	−	14.2172i	−0.243880	−	0.830579i	0.743023	−	0.669266i	$-0.233391\pi$
$294$	−1.19301	+	2.46696i	−0.0695777	+	0.143876i
$295$	2.24668	+	3.64943i	0.130807	+	0.212478i
$296$	3.84747	+	8.42479i	0.223630	+	0.489681i
$297$	0.714310	−	1.32475i	0.0414485	−	0.0768699i
$298$	−0.581829			−0.0337044
$299$	11.2593	+	12.2038i	0.651144	+	0.705764i
$300$	7.55642	−	4.23090i	0.436270	−	0.244271i
$301$	3.23824	−	22.5225i	0.186649	−	1.29817i
$302$	−6.29936	−	13.7937i	−0.362488	−	0.793737i
$303$	19.2200	−	2.33237i	1.10416	−	0.133991i
$304$	5.92796	−	5.13661i	0.339992	−	0.294605i
$305$	11.4192	+	5.48475i	0.653864	+	0.314056i
$306$	3.71147	+	15.0671i	0.212171	+	0.861328i
$307$	−13.6752	−	6.24526i	−0.780485	−	0.356436i	−0.0149985	−	0.999888i	$-0.504774\pi$
$307$	−13.6752	−	6.24526i	−0.780485	−	0.356436i	−0.765486	+	0.643452i	$0.777502\pi$
$308$	−0.441506	+	0.509525i	−0.0251571	+	0.0290329i
$309$	7.92189	+	5.34137i	0.450660	+	0.303860i
$310$	−1.20326	−	0.806642i	−0.0683405	−	0.0458142i
$311$	−16.8037	+	2.41601i	−0.952850	+	0.136999i	−0.601170	−	0.799121i	$-0.705299\pi$
$311$	−16.8037	+	2.41601i	−0.952850	+	0.136999i	−0.351680	+	0.936120i	$0.614390\pi$
$312$	−3.35250	+	4.97215i	−0.189798	+	0.281493i
$313$	−14.7100	+	16.9763i	−0.831461	+	0.959557i	−0.999657	−	0.0261966i	$-0.991660\pi$
$313$	−14.7100	+	16.9763i	−0.831461	+	0.959557i	0.168196	+	0.985754i	$0.446206\pi$
$314$	2.40334	−	5.26258i	0.135628	−	0.296985i
$315$	7.37392	−	13.7634i	0.415474	−	0.775479i
$316$	−3.07222	−	10.4630i	−0.172826	−	0.588591i
$317$	11.3013	+	13.0424i	0.634747	+	0.732537i	0.978437	−	0.206547i	$-0.0662225\pi$
$317$	11.3013	+	13.0424i	0.634747	+	0.732537i	−0.343690	+	0.939083i	$0.611677\pi$
$318$	18.1790	−	2.20604i	1.01943	−	0.123709i
$319$	1.20616	−	0.550833i	0.0675318	−	0.0308407i
$320$	−1.43131	−	1.71795i	−0.0800124	−	0.0960365i
$321$	−17.1248	+	7.36899i	−0.955814	+	0.411297i
$322$	−5.73957	+	9.57439i	−0.319854	+	0.533560i
$323$	40.5721			2.25749
$324$	8.96505	+	0.792377i	0.498058	+	0.0440210i
$325$	8.78809	+	14.9147i	0.487476	+	0.827320i
$326$	−0.191256	+	0.651359i	−0.0105927	+	0.0360755i
$327$	11.6353	+	5.62679i	0.643435	+	0.311162i
$328$	2.24681	+	7.65192i	0.124059	+	0.422506i
$329$	−24.5536	−	15.7796i	−1.35368	−	0.869959i
$330$	−0.769094	+	0.816666i	−0.0423373	+	0.0449560i
$331$	1.03376	−	1.19302i	0.0568204	−	0.0655743i	−0.726628	−	0.687031i	$-0.758914\pi$
$331$	1.03376	−	1.19302i	0.0568204	−	0.0655743i	0.783448	+	0.621457i	$0.213459\pi$
$332$	−3.72843	−	5.80155i	−0.204624	−	0.318401i
$333$	22.6898	+	16.0372i	1.24340	+	0.878835i
$334$	−1.21116	−	8.42381i	−0.0662718	−	0.460930i
$335$	3.77303	−	23.0615i	0.206143	−	1.25999i
$336$	−3.84231	−	1.22080i	−0.209615	−	0.0666001i
$337$	−2.09756	+	4.59302i	−0.114261	+	0.250198i	−0.958119	−	0.286369i	$-0.907552\pi$
$337$	−2.09756	+	4.59302i	−0.114261	+	0.250198i	0.843858	+	0.536567i	$0.180279\pi$
$338$	0.852028	+	0.547565i	0.0463442	+	0.0297836i
$339$	4.68589	−	3.88289i	0.254502	−	0.210890i
$340$	0.224029	−	11.5639i	0.0121497	−	0.627139i
$341$	0.180046	+	0.0528663i	0.00975005	+	0.00286287i
$342$	7.61802	−	22.2642i	0.411935	−	1.20391i
$343$	2.84288	−	19.7727i	0.153501	−	1.06763i
$344$	−9.77560			−0.527065
$345$	−10.2015	+	15.5219i	−0.549228	+	0.835673i
$346$	21.6051			1.16150
$347$	3.28092	−	22.8193i	0.176129	−	1.22500i	−0.689488	−	0.724297i	$-0.742165\pi$
$347$	3.28092	−	22.8193i	0.176129	−	1.22500i	0.865617	−	0.500706i	$-0.166926\pi$
$348$	5.87656	+	5.32328i	0.315017	+	0.285358i
$349$	−7.33573	−	2.15396i	−0.392673	−	0.115299i	0.0794349	−	0.996840i	$-0.474688\pi$
$349$	−7.33573	−	2.15396i	−0.392673	−	0.115299i	−0.472107	+	0.881541i	$0.656507\pi$
$350$	−7.95634	+	8.49377i	−0.425284	+	0.454011i
$351$	−1.18860	+	17.9511i	−0.0634430	+	0.958158i
$352$	0.243668	+	0.156596i	0.0129876	+	0.00834660i
$353$	−2.15627	+	4.72158i	−0.114767	+	0.251304i	−0.958295	−	0.285780i	$-0.907747\pi$
$353$	−2.15627	+	4.72158i	−0.114767	+	0.251304i	0.843528	+	0.537085i	$0.180474\pi$
$354$	1.00520	−	3.16372i	0.0534255	−	0.168150i
$355$	18.4148	+	3.01280i	0.977357	+	0.159903i
$356$	0.944581	+	6.56971i	0.0500627	+	0.348194i
$357$	−10.8848	−	17.7871i	−0.576087	−	0.941395i
$358$	7.82565	+	12.1770i	0.413599	+	0.643572i
$359$	−1.01414	+	1.17038i	−0.0535243	+	0.0617704i	−0.781880	−	0.623428i	$-0.785739\pi$
$359$	−1.01414	+	1.17038i	−0.0535243	+	0.0617704i	0.728356	+	0.685199i	$0.240285\pi$
$360$	−6.30369	−	2.29423i	−0.332234	−	0.120916i
$361$	−35.7747	−	22.9910i	−1.88288	−	1.21005i
$362$	3.34687	+	11.3984i	0.175908	+	0.599086i
$363$	−8.23146	+	17.0214i	−0.432039	+	0.893390i
$364$	2.27045	−	7.73243i	0.119004	−	0.405289i
$365$	9.37895	−	29.7943i	0.490916	−	1.55950i
$366$	−2.55640	−	9.47385i	−0.133625	−	0.495206i
$367$	−8.16857			−0.426396			−0.213198	−	0.977009i	$-0.568388\pi$
$367$	−8.16857			−0.426396			−0.213198	+	0.977009i	$0.568388\pi$
$368$	4.42241	+	1.85534i	0.230534	+	0.0967165i
$369$	17.3733	+	16.4490i	0.904417	+	0.856299i
$370$	−13.2564	−	15.9113i	−0.689168	−	0.827188i
$371$	−22.3854	+	10.2231i	−1.16219	+	0.530756i
$372$	0.135176	+	1.11393i	0.00700855	+	0.0577543i
$373$	−20.2345	−	23.3518i	−1.04770	−	1.20911i	−0.977359	−	0.211590i	$-0.932136\pi$
$373$	−20.2345	−	23.3518i	−1.04770	−	1.20911i	−0.0703436	−	0.997523i	$-0.522410\pi$
$374$	0.422094	+	1.43752i	0.0218259	+	0.0743324i
$375$	−13.8124	+	13.5727i	−0.713268	+	0.700892i
$376$	−5.20900	+	11.4061i	−0.268634	+	0.588226i
$377$	−10.3794	+	11.9785i	−0.534568	+	0.616924i
$378$	−11.8046	+	2.63332i	−0.607164	+	0.135444i
$379$	12.9173	−	1.85723i	0.663518	−	0.0953995i	0.197676	−	0.980267i	$-0.436661\pi$
$379$	12.9173	−	1.85723i	0.663518	−	0.0953995i	0.465842	+	0.884868i	$0.345752\pi$
$380$	−9.76649	+	14.5686i	−0.501010	+	0.747352i
$381$	13.9637	−	20.7098i	0.715380	−	1.06099i
$382$	0.756940	−	0.873556i	0.0387284	−	0.0446950i
$383$	4.43983	+	2.02760i	0.226865	+	0.103606i	0.525605	−	0.850729i	$-0.323839\pi$
$383$	4.43983	+	2.02760i	0.226865	+	0.103606i	−0.298740	+	0.954335i	$0.596566\pi$
$384$	−0.284218	+	1.70857i	−0.0145039	+	0.0871902i
$385$	0.652705	−	1.35893i	0.0332649	−	0.0692575i
$386$	−1.48280	+	1.28486i	−0.0754727	+	0.0653975i
$387$	−25.3460	+	14.7528i	−1.28841	+	0.749925i
$388$	−6.84215	−	14.9822i	−0.347357	−	0.760607i
$389$	−2.14029	+	14.8861i	−0.108517	+	0.754754i	0.860801	+	0.508942i	$0.169963\pi$
$389$	−2.14029	+	14.8861i	−0.108517	+	0.754754i	−0.969318	+	0.245811i	$0.920946\pi$
$390$	4.30721	−	12.6987i	0.218104	−	0.643021i
$391$	11.0031	+	22.2326i	0.556452	+	1.12435i
$392$	−1.58210			−0.0799082
$393$	3.47967	+	12.8954i	0.175526	+	0.650487i
$394$	1.52982	+	3.34984i	0.0770712	+	0.168762i
$395$	12.7830	+	20.7644i	0.643184	+	1.04477i
$396$	0.868103	+	0.0382891i	0.0436238	+	0.00192410i
$397$	5.23204	+	17.8187i	0.262589	+	0.894294i	0.980227	+	0.197878i	$0.0634050\pi$
$397$	5.23204	+	17.8187i	0.262589	+	0.894294i	−0.717638	+	0.696416i	$0.754777\pi$
$398$	6.38483	−	9.93499i	0.320043	−	0.497996i
$399$	−0.696884	+	31.6154i	−0.0348878	+	1.58275i
$400$	4.09841	+	2.86409i	0.204921	+	0.143205i
$401$	1.78186	−	1.14513i	0.0889820	−	0.0571852i	−0.495393	−	0.868669i	$-0.664976\pi$
$401$	1.78186	−	1.14513i	0.0889820	−	0.0571852i	0.584375	+	0.811484i	$0.301340\pi$
$402$	−15.4394	+	9.44813i	−0.770047	+	0.471230i
$403$	−2.22017	+	0.319212i	−0.110594	+	0.0159011i
$404$	6.04332	+	9.40359i	0.300666	+	0.467846i
$405$	−19.8064	+	3.56473i	−0.984187	+	0.177133i
$406$	−9.69275	−	4.42653i	−0.481043	−	0.219685i
$407$	2.25680	+	1.45036i	0.111865	+	0.0718915i
$408$	−6.89842	+	5.71627i	−0.341523	+	0.282998i
$409$	−5.82459	−	6.72194i	−0.288008	−	0.332378i	0.593247	−	0.805021i	$-0.297846\pi$
$409$	−5.82459	−	6.72194i	−0.288008	−	0.332378i	−0.881254	+	0.472642i	$0.843300\pi$
$410$	−9.34862	−	15.1856i	−0.461695	−	0.749964i
$411$	−12.3624	−	11.1984i	−0.609790	−	0.552378i
$412$	−0.785042	+	5.46009i	−0.0386763	+	0.268999i
$413$			4.46105i			0.219514i
$414$	14.2663	−	1.86354i	0.701150	−	0.0915881i
$415$	11.4563	+	10.3222i	0.562370	+	0.506697i
$416$	−3.42701	−	0.492730i	−0.168023	−	0.0241581i
$417$	−1.41206	+	1.55883i	−0.0691489	+	0.0763360i
$418$	0.640084	−	2.17992i	0.0313075	−	0.106624i
$419$	−6.35621	−	7.33546i	−0.310521	−	0.358361i	0.578941	−	0.815370i	$-0.303466\pi$
$419$	−6.35621	−	7.33546i	−0.310521	−	0.358361i	−0.889462	+	0.457009i	$0.848921\pi$
$420$	9.00717	+	0.373199i	0.439505	+	0.0182102i
$421$	−14.2908	+	22.2369i	−0.696491	+	1.08376i	0.295239	+	0.955423i	$0.404601\pi$
$421$	−14.2908	+	22.2369i	−0.696491	+	1.08376i	−0.991730	+	0.128338i	$0.959036\pi$
$422$	0.403752	−	0.884094i	0.0196543	−	0.0430370i
$423$	3.70766	+	37.4347i	0.180273	+	1.82014i
$424$	5.71601	+	8.89428i	0.277594	+	0.431944i
$425$	6.31970	+	25.0784i	0.306551	+	1.21648i
$426$	−7.54440	−	12.3285i	−0.365528	−	0.597316i
$427$	7.12938	+	11.0935i	0.345015	+	0.536854i
$428$	−8.13454	−	7.04862i	−0.393198	−	0.340708i
$429$	−0.0382779	+	1.73655i	−0.00184808	+	0.0838412i
$430$	21.0888	−	5.75096i	1.01699	−	0.277336i
$431$	−24.4936	+	7.19196i	−1.17981	+	0.346424i	−0.812102	−	0.583516i	$-0.801677\pi$
$431$	−24.4936	+	7.19196i	−1.17981	+	0.346424i	−0.367711	+	0.929940i	$0.619858\pi$
$432$	1.84156	+	4.85887i	0.0886023	+	0.233773i
$433$	29.4446	+	8.64570i	1.41502	+	0.415486i	0.897813	−	0.440377i	$-0.145155\pi$
$433$	29.4446	+	8.64570i	1.41502	+	0.415486i	0.517202	+	0.855863i	$0.326973\pi$
$434$	−0.626423	−	1.37167i	−0.0300693	−	0.0658425i
$435$	−15.8091	−	8.02670i	−0.757990	−	0.384851i
$436$			7.46194i			0.357362i
$437$	4.19059	−	37.3835i	0.200463	−	1.78829i
$438$	−22.2247	+	9.56351i	−1.06194	+	0.456962i
$439$	−2.41184	+	16.7747i	−0.115111	+	0.800613i	0.847708	+	0.530464i	$0.177982\pi$
$439$	−2.41184	+	16.7747i	−0.115111	+	0.800613i	−0.962818	+	0.270149i	$0.912927\pi$
$440$	−0.617789	−	0.194474i	−0.0294519	−	0.00927118i
$441$	−4.10204	+	2.38761i	−0.195335	+	0.113696i
$442$	−11.7276	−	13.5343i	−0.557823	−	0.643762i
$443$	−6.19490	+	1.81899i	−0.294329	+	0.0864227i	−0.425563	−	0.904929i	$-0.639924\pi$
$443$	−6.19490	+	1.81899i	−0.294329	+	0.0864227i	0.131235	+	0.991351i	$0.458106\pi$
$444$	−2.63236	+	15.8244i	−0.124926	+	0.750992i
$445$	−5.90268	−	13.6171i	−0.279814	−	0.645511i
$446$	0.231580	+	0.200666i	0.0109657	+	0.00950179i
$447$	−0.835567	−	0.563385i	−0.0395210	−	0.0266472i
$448$	−0.331257	−	2.30395i	−0.0156504	−	0.108851i
$449$	35.3019	−	5.07565i	1.66600	−	0.239535i	0.756128	−	0.654424i	$-0.227089\pi$
$449$	35.3019	−	5.07565i	1.66600	−	0.239535i	0.909872	+	0.414890i	$0.136180\pi$
$450$	14.9486	+	1.24087i	0.704683	+	0.0584954i
$451$	1.74574	+	1.51269i	0.0822035	+	0.0712297i
$452$	3.19601	+	1.45957i	0.150327	+	0.0686523i
$453$	4.30989	−	25.9088i	0.202496	−	1.21730i
$454$	−0.151139	−	0.514733i	−0.00709331	−	0.0241576i
$455$	−0.349043	+	18.0168i	−0.0163634	+	0.844641i
$456$	13.4869	−	1.63666i	0.631584	−	0.0766435i
$457$	0.0701152	+	0.153531i	0.00327985	+	0.00718187i	0.911265	−	0.411821i	$-0.135107\pi$
$457$	0.0701152	+	0.153531i	0.00327985	+	0.00718187i	−0.907985	+	0.419003i	$0.862380\pi$
$458$	22.8456	+	3.28470i	1.06750	+	0.153484i
$459$	−9.25940	+	25.2317i	−0.432192	+	1.17772i
$460$	−10.6319	−	1.40083i	−0.495716	−	0.0653138i
$461$			1.81631i			0.0845939i	0.999105	+	0.0422969i	$0.0134676\pi$
$461$			1.81631i			0.0845939i	−0.999105	+	0.0422969i	$0.986532\pi$
$462$	−1.12742	+	0.304221i	−0.0524524	+	0.0141536i
$463$	−8.51144	+	3.88705i	−0.395560	+	0.180646i	−0.603257	−	0.797547i	$-0.706131\pi$
$463$	−8.51144	+	3.88705i	−0.395560	+	0.180646i	0.207697	+	0.978193i	$0.433403\pi$
$464$	−1.28974	+	4.39246i	−0.0598748	+	0.203915i
$465$	−0.946934	−	2.32354i	−0.0439130	−	0.107751i
$466$	9.52995	−	2.79824i	0.441466	−	0.129626i
$467$	5.99394	−	9.32675i	0.277366	−	0.431590i	−0.674422	−	0.738346i	$-0.735607\pi$
$467$	5.99394	−	9.32675i	0.277366	−	0.431590i	0.951788	+	0.306756i	$0.0992435\pi$
$468$	−9.62908	+	3.89430i	−0.445104	+	0.180014i
$469$	15.9296	−	18.3837i	0.735558	−	0.848880i
$470$	4.52714	−	27.6708i	0.208821	−	1.27636i
$471$	8.54720	−	5.23046i	0.393834	−	0.241007i
$472$	1.89705	−	0.272754i	0.0873187	−	0.0125545i
$473$	−2.38200	+	1.53082i	−0.109525	+	0.0703872i
$474$	5.71931	−	18.0008i	0.262697	−	0.826804i
$475$	12.4985	−	37.1742i	0.573470	−	1.70567i
$476$	6.50915	−	10.1284i	0.298346	−	0.464236i
$477$	28.2431	+	14.4346i	1.29316	+	0.660916i
$478$	−5.12101	+	4.43738i	−0.234229	+	0.202961i
$479$	6.75943	+	1.98475i	0.308846	+	0.0906855i	0.432483	−	0.901642i	$-0.357638\pi$
$479$	6.75943	+	1.98475i	0.308846	+	0.0906855i	−0.123637	+	0.992328i	$0.539456\pi$
$480$	−0.392009	−	3.85309i	−0.0178927	−	0.175869i
$481$	−31.7402	−	4.56355i	−1.44723	−	0.208080i
$482$			20.6763i			0.941780i
$483$	−17.5135	+	8.19220i	−0.796892	+	0.372758i
$484$	−10.9161			−0.496187
$485$	23.5745	+	28.2958i	1.07046	+	1.28485i
$486$	12.1075	+	9.81880i	0.549207	+	0.445390i
$487$	7.79785	−	26.5570i	0.353354	−	1.20341i	−0.570702	−	0.821157i	$-0.693329\pi$
$487$	7.79785	−	26.5570i	0.353354	−	1.20341i	0.924056	−	0.382257i	$-0.124853\pi$
$488$	4.28160	−	3.71002i	0.193819	−	0.167945i
$489$	−0.905376	+	0.750226i	−0.0409425	+	0.0339264i
$490$	3.41305	−	0.930747i	0.154186	−	0.0420469i
$491$	−30.1714	−	13.7788i	−1.36162	−	0.621830i	−0.405307	−	0.914181i	$-0.632835\pi$
$491$	−30.1714	−	13.7788i	−1.36162	−	0.621830i	−0.956311	+	0.292350i	$0.905563\pi$
$492$	−4.18271	+	13.1645i	−0.188571	+	0.593503i
$493$	−19.9201	+	12.8019i	−0.897158	+	0.576568i
$494$	3.86488	+	26.8809i	0.173889	+	1.20943i
$495$	−1.89528	+	0.428103i	−0.0851864	+	0.0192418i
$496$	−0.545000	+	0.350250i	−0.0244712	+	0.0157267i
$497$	14.6795	+	12.7199i	0.658466	+	0.570564i
$498$	0.263230	−	11.9419i	0.0117956	−	0.535128i
$499$	−3.71790	−	2.38935i	−0.166436	−	0.106962i	0.454771	−	0.890608i	$-0.349721\pi$
$499$	−3.71790	−	2.38935i	−0.166436	−	0.106962i	−0.621207	+	0.783646i	$0.713357\pi$
$500$	−10.5264	−	3.76760i	−0.470755	−	0.168492i
$501$	6.41742	−	13.2702i	0.286709	−	0.592870i
$502$	15.4944	+	4.54957i	0.691550	+	0.203057i
$503$	−34.8360	+	15.9091i	−1.55326	+	0.709351i	−0.992906	−	0.118901i	$-0.962063\pi$
$503$	−34.8360	+	15.9091i	−1.55326	+	0.709351i	−0.560356	+	0.828252i	$0.689336\pi$
$504$	−4.33586	−	5.47370i	−0.193134	−	0.243818i
$505$	−18.5693	−	16.7310i	−0.826323	−	0.744520i
$506$	1.36814	−	0.240443i	0.0608213	−	0.0106890i
$507$	0.693393	+	1.61138i	0.0307947	+	0.0715638i
$508$	14.2740	+	2.05229i	0.633307	+	0.0910558i
$509$	2.13431	−	0.974707i	0.0946016	−	0.0432031i	−0.367552	−	0.930003i	$-0.619804\pi$
$509$	2.13431	−	0.974707i	0.0946016	−	0.0432031i	0.462154	+	0.886800i	$0.347077\pi$
$510$	11.5190	−	16.3900i	0.510071	−	0.725761i
$511$	24.5730	−	21.2926i	1.08705	−	0.941930i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	32.4987	−	24.5972i	1.43485	−	1.08599i
$514$	2.37623	−	5.20321i	0.104811	−	0.229504i
$515$	−1.51859	−	12.2408i	−0.0669172	−	0.539396i
$516$	−14.0388	−	9.46572i	−0.618023	−	0.416705i
$517$	0.516886	+	3.59502i	0.0227326	+	0.158109i
$518$	−3.06803	−	21.3386i	−0.134801	−	0.937564i
$519$	31.0272	+	20.9203i	1.36194	+	0.918297i
$520$	7.68293	−	0.953141i	0.336919	−	0.0417980i
$521$	−4.32212	+	9.46411i	−0.189355	+	0.414630i	−0.980370	−	0.197167i	$-0.936826\pi$
$521$	−4.32212	+	9.46411i	−0.189355	+	0.414630i	0.791015	+	0.611797i	$0.209553\pi$
$522$	3.28482	+	13.3351i	0.143773	+	0.583660i
$523$	−1.35802	+	0.398750i	−0.0593819	+	0.0174361i	−0.311289	−	0.950315i	$-0.600761\pi$
$523$	−1.35802	+	0.398750i	−0.0593819	+	0.0174361i	0.251907	+	0.967752i	$0.418942\pi$
$524$	−5.82793	+	5.04993i	−0.254594	+	0.220607i
$525$	−19.6507	+	4.49380i	−0.857625	+	0.196126i
$526$	−12.7747	+	5.83403i	−0.557005	+	0.254376i
$527$	−3.31685	−	0.476892i	−0.144484	−	0.0207737i
$528$	0.198301	+	0.460832i	0.00862994	+	0.0200552i
$529$	21.6218	−	7.84204i	0.940078	−	0.340958i
$530$	−17.5636	−	15.8248i	−0.762913	−	0.687387i
$531$	4.50700	−	3.57010i	0.195587	−	0.154929i
$532$	−16.6077	+	7.58447i	−0.720034	+	0.328828i
$533$	−26.4929	−	7.77901i	−1.14753	−	0.336946i
$534$	−5.00493	+	10.3494i	−0.216585	+	0.447863i
$535$	21.6953	+	10.4204i	0.937968	+	0.450513i
$536$	−8.79156	−	5.64999i	−0.379738	−	0.244043i
$537$	−0.552496	+	25.0650i	−0.0238420	+	1.08163i
$538$	3.04806	+	2.64116i	0.131411	+	0.113869i
$539$	−0.385508	+	0.247751i	−0.0166050	+	0.0106714i
$540$	−6.83125	−	9.39862i	−0.293970	−	0.404452i
$541$	6.44354	+	44.8158i	0.277029	+	1.92678i	0.365726	+	0.930722i	$0.380821\pi$
$541$	6.44354	+	44.8158i	0.277029	+	1.92678i	−0.0886969	+	0.996059i	$0.528270\pi$
$542$	−5.40209	+	3.47171i	−0.232040	+	0.149123i
$543$	−6.23061	+	19.6100i	−0.267381	+	0.841547i
$544$	−4.70506	−	2.14873i	−0.201728	−	0.0921260i
$545$	−4.38984	−	16.0976i	−0.188040	−	0.689545i
$546$	10.7479	−	8.90610i	0.459968	−	0.381146i
$547$	33.6774	−	29.1816i	1.43994	−	1.24772i	0.520863	−	0.853640i	$-0.325610\pi$
$547$	33.6774	−	29.1816i	1.43994	−	1.24772i	0.919078	−	0.394076i	$-0.128935\pi$
$548$	2.71319	−	9.24029i	0.115902	−	0.394726i
$549$	5.50228	−	16.0808i	0.234831	−	0.686312i
$550$	1.44716	+	0.0560932i	0.0617071	+	0.00239182i
$551$	35.9082			1.52974
$552$	4.55451	+	6.94669i	0.193853	+	0.295671i
$553$			25.3823i			1.07936i
$554$	2.52997	+	0.363755i	0.107488	+	0.0154545i
$555$	−3.63069	−	35.6864i	−0.154114	−	1.51480i
$556$	−1.16515	−	0.342119i	−0.0494133	−	0.0145091i
$557$	4.09228	−	3.54598i	0.173395	−	0.150248i	−0.563840	−	0.825884i	$-0.690676\pi$
$557$	4.09228	−	3.54598i	0.173395	−	0.150248i	0.737235	+	0.675636i	$0.236131\pi$
$558$	−0.884487	+	1.73060i	−0.0374433	+	0.0732623i
$559$	18.2983	−	28.4727i	0.773936	−	1.20427i
$560$	2.07002	+	4.77540i	0.0874745	+	0.201798i
$561$	−0.785780	+	2.47314i	−0.0331756	+	0.104416i
$562$	12.0639	−	7.75299i	0.508885	−	0.327040i
$563$	−41.3284	+	5.94212i	−1.74178	+	0.250431i	−0.938528	−	0.345203i	$-0.887810\pi$
$563$	−41.3284	+	5.94212i	−1.74178	+	0.250431i	−0.803256	+	0.595634i	$0.796901\pi$
$564$	−18.5252	+	11.3365i	−0.780053	+	0.477353i
$565$	−7.75338	−	1.26851i	−0.326187	−	0.0533665i
$566$	6.34803	−	7.32602i	0.266828	−	0.307936i
$567$	−19.5025	−	7.64868i	−0.819028	−	0.321214i
$568$	4.51156	−	7.02013i	0.189301	−	0.294558i
$569$	32.6899	−	9.59861i	1.37043	−	0.402395i	0.488002	−	0.872842i	$-0.337726\pi$
$569$	32.6899	−	9.59861i	1.37043	−	0.402395i	0.882428	+	0.470448i	$0.155908\pi$
$570$	−28.1324	+	11.4651i	−1.17834	+	0.480220i
$571$	4.26062	−	14.5103i	0.178301	−	0.607239i	−0.821037	−	0.570875i	$-0.806604\pi$
$571$	4.26062	−	14.5103i	0.178301	−	0.607239i	0.999339	−	0.0363642i	$-0.0115776\pi$
$572$	−0.912214	+	0.416594i	−0.0381416	+	0.0174187i
$573$	1.93291	−	0.521571i	0.0807484	−	0.0217889i
$574$		−	18.5628i		−	0.774797i
$575$	23.7602	−	3.23274i	0.990871	−	0.134815i
$576$	−2.06258	+	2.17848i	−0.0859407	+	0.0907700i
$577$	11.4536	+	1.64678i	0.476821	+	0.0685565i	0.376536	−	0.926402i	$-0.377115\pi$
$577$	11.4536	+	1.64678i	0.476821	+	0.0685565i	0.100286	+	0.994959i	$0.468024\pi$
$578$	−4.05223	−	8.87315i	−0.168551	−	0.369074i
$579$	−3.37359	+	0.409389i	−0.140201	+	0.0170136i
$580$	0.198276	−	10.2346i	0.00823297	−	0.424967i
$581$	4.52241	+	15.4019i	0.187621	+	0.638979i
$582$	4.68125	−	28.1413i	0.194044	−	1.16649i
$583$	2.78562	+	1.27215i	0.115369	+	0.0526871i
$584$	−10.5571	−	9.14774i	−0.436854	−	0.378536i
$585$	18.4817	−	14.0659i	0.764125	−	0.581554i
$586$	14.6666	−	2.10874i	0.605872	−	0.0871112i
$587$	−3.14043	−	21.8422i	−0.129619	−	0.901522i	−0.946037	−	0.324060i	$-0.894952\pi$
$587$	−3.14043	−	21.8422i	−0.129619	−	0.901522i	0.816417	−	0.577462i	$-0.195957\pi$
$588$	−2.27206	−	1.53195i	−0.0936983	−	0.0631765i
$589$	3.84039	+	3.32772i	0.158240	+	0.137116i
$590$	−3.93202	+	1.70444i	−0.161879	+	0.0701707i
$591$	−1.04667	+	6.29204i	−0.0430542	+	0.258820i
$592$	−8.88659	+	2.60934i	−0.365237	+	0.107243i
$593$	−2.20177	−	2.54098i	−0.0904159	−	0.104345i	0.708739	−	0.705471i	$-0.249265\pi$
$593$	−2.20177	−	2.54098i	−0.0904159	−	0.104345i	−0.799155	+	0.601126i	$0.794719\pi$
$594$	1.20961	+	0.895572i	0.0496310	+	0.0367458i
$595$	−8.08359	+	25.6793i	−0.331395	+	1.05275i
$596$	0.0828029	−	0.575907i	0.00339174	−	0.0235901i
$597$	18.7893	−	8.08525i	0.768996	−	0.330907i
$598$	−13.6820	+	9.40795i	−0.559497	+	0.384720i
$599$		−	25.5342i		−	1.04330i	−0.853160	−	0.521649i	$-0.825317\pi$
$599$		−	25.5342i		−	1.04330i	0.853160	−	0.521649i	$-0.174683\pi$
$600$	3.11244	+	8.08163i	0.127065	+	0.329931i
$601$	3.97349	+	8.70074i	0.162082	+	0.354911i	0.973196	−	0.229978i	$-0.0738655\pi$
$601$	3.97349	+	8.70074i	0.162082	+	0.354911i	−0.811114	+	0.584889i	$0.801138\pi$
$602$	21.8324	+	6.41056i	0.889821	+	0.261275i
$603$	−31.3212	−	1.38147i	−1.27550	−	0.0562579i
$604$	14.5498	−	4.27220i	0.592022	−	0.173833i
$605$	23.5492	−	6.42192i	0.957412	−	0.261088i
$606$	−0.426662	+	19.3563i	−0.0173320	+	0.786295i
$607$	−10.2627	−	8.89265i	−0.416549	−	0.360941i	0.421228	−	0.906955i	$-0.361599\pi$
$607$	−10.2627	−	8.89265i	−0.416549	−	0.360941i	−0.837776	+	0.546014i	$0.816145\pi$
$608$	4.24069	+	6.59864i	0.171983	+	0.267610i
$609$	−9.63358	−	15.7424i	−0.390372	−	0.637916i
$610$	−7.05405	+	10.5225i	−0.285610	+	0.426042i
$611$	−23.4715	−	36.5223i	−0.949554	−	1.47753i
$612$	−15.4419	+	1.52942i	−0.624202	+	0.0618233i
$613$	1.47881	−	3.23815i	0.0597287	−	0.130788i	−0.877414	−	0.479734i	$-0.840733\pi$
$613$	1.47881	−	3.23815i	0.0597287	−	0.130788i	0.937143	+	0.348946i	$0.113460\pi$
$614$	8.12787	−	12.6472i	0.328014	−	0.510400i
$615$	1.27865	−	30.8604i	0.0515603	−	1.24441i
$616$	−0.441506	−	0.509525i	−0.0177888	−	0.0205293i
$617$	2.62015	−	8.92341i	0.105483	−	0.359243i	−0.889788	−	0.456373i	$-0.849148\pi$
$617$	2.62015	−	8.92341i	0.105483	−	0.359243i	0.995272	+	0.0971303i	$0.0309664\pi$
$618$	−6.41441	+	7.08110i	−0.258025	+	0.284844i
$619$	−36.3861	−	5.23154i	−1.46248	−	0.210273i	−0.635326	−	0.772244i	$-0.719134\pi$
$619$	−36.3861	−	5.23154i	−1.46248	−	0.210273i	−0.827157	+	0.561971i	$0.810043\pi$
$620$	0.969673	−	1.07621i	0.0389430	−	0.0432218i
$621$	22.2924	+	11.1378i	0.894561	+	0.446945i
$622$		−	16.9765i		−	0.680695i
$623$	2.19864	−	15.2919i	0.0880868	−	0.612657i
$624$	−4.44443	−	4.02599i	−0.177920	−	0.161168i
$625$	24.9250	+	1.93514i	0.997000	+	0.0774056i
$626$	−14.7100	−	16.9763i	−0.587932	−	0.678509i
$627$	3.03005	−	2.51081i	0.121008	−	0.100272i
$628$	4.86698	+	3.12782i	0.194214	+	0.124814i
$629$	−43.5772	−	19.9010i	−1.73754	−	0.793506i
$630$	12.5739	+	9.25760i	0.500955	+	0.368832i
$631$	9.49427	+	14.7734i	0.377961	+	0.588118i	0.977166	−	0.212477i	$-0.0681531\pi$
$631$	9.49427	+	14.7734i	0.377961	+	0.588118i	−0.599205	+	0.800595i	$0.704517\pi$
$632$	10.7937	−	1.55191i	0.429352	−	0.0617315i
$633$	1.43590	−	0.878697i	0.0570718	−	0.0349251i
$634$	−14.5180	+	9.33018i	−0.576585	+	0.370549i
$635$	−32.0006	+	3.96998i	−1.26990	+	0.157544i
$636$	−0.403554	+	18.3079i	−0.0160019	+	0.725956i
$637$	2.96143	−	4.60808i	0.117336	−	0.182579i
$638$	0.373573	+	1.27227i	0.0147899	+	0.0503697i
$639$	1.10312	−	25.0102i	0.0436386	−	0.989389i
$640$	1.90416	−	1.17225i	0.0752687	−	0.0463371i
$641$	−0.660736	−	1.44681i	−0.0260975	−	0.0571456i	0.896134	−	0.443783i	$-0.146364\pi$
$641$	−0.660736	−	1.44681i	−0.0260975	−	0.0571456i	−0.922232	+	0.386637i	$0.873637\pi$
$642$	−4.85687	−	17.9992i	−0.191685	−	0.710373i
$643$	4.40482			0.173709			0.0868546	−	0.996221i	$-0.472318\pi$
$643$	4.40482			0.173709			0.0868546	+	0.996221i	$0.472318\pi$
$644$	−8.66011	−	7.04373i	−0.341256	−	0.277562i
$645$	35.8544	+	12.1613i	1.41177	+	0.478852i
$646$	−5.77401	+	40.1591i	−0.227175	+	1.58004i
$647$	9.53864	+	20.8867i	0.375003	+	0.821142i	0.999205	+	0.0398784i	$0.0126970\pi$
$647$	9.53864	+	20.8867i	0.375003	+	0.821142i	−0.624202	+	0.781263i	$0.714576\pi$
$648$	−2.06017	+	8.76103i	−0.0809312	+	0.344166i
$649$	0.419538	−	0.363532i	0.0164683	−	0.0142699i
$650$	−16.0136	+	6.57606i	−0.628105	+	0.257934i
$651$	0.428585	−	2.57643i	0.0167976	−	0.100978i
$652$	−0.617511	−	0.282008i	−0.0241836	−	0.0110443i
$653$	2.25208	−	2.59904i	0.0881307	−	0.101708i	−0.709971	−	0.704231i	$-0.751292\pi$
$653$	2.25208	−	2.59904i	0.0881307	−	0.101708i	0.798102	+	0.602522i	$0.205838\pi$
$654$	−7.22540	+	10.7161i	−0.282536	+	0.419034i
$655$	9.60168	−	14.3227i	0.375169	−	0.559635i
$656$	−7.89378	+	1.13495i	−0.308200	+	0.0443125i
$657$	−41.1773	−	7.78597i	−1.60648	−	0.303760i
$658$	19.1134	−	22.0580i	0.745116	−	0.859910i
$659$	8.88848	−	19.4631i	0.346246	−	0.758173i	−0.653753	−	0.756708i	$-0.726806\pi$
$659$	8.88848	−	19.4631i	0.346246	−	0.758173i	0.999999	−	0.00146518i	$-0.000466381\pi$
$660$	−0.698900	−	0.877490i	−0.0272046	−	0.0341562i
$661$	−1.46242	−	4.98055i	−0.0568816	−	0.193721i	0.926151	−	0.377154i	$-0.123097\pi$
$661$	−1.46242	−	4.98055i	−0.0568816	−	0.193721i	−0.983032	+	0.183433i	$0.941279\pi$
$662$	1.03376	+	1.19302i	0.0401781	+	0.0463680i
$663$	−3.73670	−	30.7925i	−0.145121	−	1.19588i
$664$	6.27311	−	2.86483i	0.243444	−	0.111177i
$665$	31.3657	−	26.1322i	1.21631	−	1.01336i
$666$	−19.1031	+	20.1766i	−0.740230	+	0.781826i
$667$	9.73828	+	19.6769i	0.377068	+	0.761892i
$668$	8.51043			0.329279
$669$	0.138269	+	0.512416i	0.00534579	+	0.0198111i
$670$	22.2898	+	7.01663i	0.861132	+	0.271076i
$671$	0.462314	−	1.57450i	0.0178474	−	0.0607828i
$672$	1.75519	−	3.62946i	0.0677080	−	0.140010i
$673$	11.3638	+	38.7016i	0.438042	+	1.49184i	0.822539	+	0.568709i	$0.192557\pi$
$673$	11.3638	+	38.7016i	0.438042	+	1.49184i	−0.384496	+	0.923127i	$0.625625\pi$
$674$	−4.24776	−	2.72987i	−0.163617	−	0.105151i
$675$	20.2662	+	16.2567i	0.780046	+	0.625722i
$676$	−0.663248	+	0.765429i	−0.0255095	+	0.0294396i
$677$	−2.18258	−	3.39617i	−0.0838835	−	0.130525i	0.796776	−	0.604274i	$-0.206537\pi$
$677$	−2.18258	−	3.39617i	−0.0838835	−	0.130525i	−0.880660	+	0.473749i	$0.842900\pi$
$678$	3.17650	+	5.19078i	0.121993	+	0.199351i
$679$	5.45602	+	37.9474i	0.209383	+	1.45629i
$680$	11.4143	+	1.86746i	0.437718	+	0.0716138i
$681$	0.281364	−	0.885558i	0.0107819	−	0.0339346i
$682$	−0.0779515	+	0.170690i	−0.00298492	+	0.00653605i
$683$	−23.9381	−	15.3841i	−0.915964	−	0.588654i	−0.00448020	−	0.999990i	$-0.501426\pi$
$683$	−23.9381	−	15.3841i	−0.915964	−	0.588654i	−0.911484	+	0.411336i	$0.865062\pi$
$684$	20.9534	+	10.7090i	0.801175	+	0.409469i
$685$	−0.417108	+	21.5302i	−0.0159369	+	0.822625i
$686$	19.1669	+	5.62790i	0.731794	+	0.214874i
$687$	29.6280	+	26.8385i	1.13038	+	1.02395i
$688$	1.39121	−	9.67610i	0.0530395	−	0.368898i
$689$	−36.6052			−1.39455
$690$	−13.9121	−	12.3066i	−0.529625	−	0.468505i
$691$	−3.78308			−0.143915			−0.0719576	−	0.997408i	$-0.522925\pi$
$691$	−3.78308			−0.143915			−0.0719576	+	0.997408i	$0.522925\pi$
$692$	−3.07473	+	21.3852i	−0.116884	+	0.812944i
$693$	−1.91367	−	0.654790i	−0.0726944	−	0.0248734i
$694$	22.1201	+	6.49504i	0.839667	+	0.246549i
$695$	2.71483	+	0.0525950i	0.102980	+	0.00199504i
$696$	−6.10542	+	5.05917i	−0.231425	+	0.191767i
$697$	−34.7020	−	22.3016i	−1.31443	−	0.844735i
$698$	3.17602	−	6.95452i	0.120214	−	0.263232i
$699$	16.3955	+	5.20928i	0.620136	+	0.197033i
$700$	−7.27501	−	9.08415i	−0.274969	−	0.343349i
$701$	−2.88505	−	20.0659i	−0.108967	−	0.757880i	−0.968896	−	0.247467i	$-0.920402\pi$
$701$	−2.88505	−	20.0659i	−0.108967	−	0.757880i	0.859930	−	0.510413i	$-0.170507\pi$
$702$	−17.5992	−	3.73121i	−0.664239	−	0.140826i
$703$	39.2762	+	61.1150i	1.48133	+	2.30500i
$704$	−0.189680	+	0.218902i	−0.00714883	+	0.00825019i
$705$	33.2951	−	35.3545i	1.25396	−	1.33153i
$706$	−4.36665	−	2.80628i	−0.164341	−	0.105616i
$707$	−7.33026	−	24.9646i	−0.275683	−	0.938889i
$708$	2.98847	+	1.44521i	0.112313	+	0.0543143i
$709$	3.37706	−	11.5012i	0.126828	−	0.431937i	−0.871457	−	0.490471i	$-0.836825\pi$
$709$	3.37706	−	11.5012i	0.126828	−	0.431937i	0.998285	+	0.0585346i	$0.0186428\pi$
$710$	−5.60283	+	17.7986i	−0.210270	+	0.667970i
$711$	25.6437	−	20.3130i	0.961714	−	0.761798i
$712$	−6.63727			−0.248742
$713$	−0.782002	+	3.00692i	−0.0292862	+	0.112610i
$714$	19.1552	−	8.24267i	0.716864	−	0.308474i
$715$	1.72283	−	1.43537i	0.0644302	−	0.0536797i
$716$	−13.1667	+	6.01304i	−0.492063	+	0.224718i
$717$	−11.6510	+	1.41386i	−0.435115	+	0.0528017i
$718$	−1.01414	−	1.17038i	−0.0378474	−	0.0436783i
$719$	13.6120	+	46.3584i	0.507643	+	1.72887i	0.670205	+	0.742176i	$0.266206\pi$
$719$	13.6120	+	46.3584i	0.507643	+	1.72887i	−0.162561	+	0.986698i	$0.551975\pi$
$720$	3.16799	−	5.91303i	0.118064	−	0.220365i
$721$	5.33385	−	11.6795i	0.198643	−	0.434967i
$722$	27.8483	−	32.1386i	1.03640	−	1.19608i
$723$	−20.0209	+	29.6933i	−0.744584	+	1.10431i
$724$	−11.7587	+	1.69064i	−0.437008	+	0.0628322i
$725$	5.59323	+	22.1956i	0.207727	+	0.824323i
$726$	−15.6767	−	10.5701i	−0.581815	−	0.392292i
$727$	−22.3926	+	25.8425i	−0.830497	+	0.958445i	−0.999631	−	0.0271481i	$-0.991357\pi$
$727$	−22.3926	+	25.8425i	−0.830497	+	0.958445i	0.169134	+	0.985593i	$0.445903\pi$
$728$	7.33061	+	3.34778i	0.271690	+	0.124077i
$729$	7.88007	+	25.8245i	0.291854	+	0.956463i
$730$	28.1562	+	13.5236i	1.04211	+	0.500533i
$731$	38.2139	−	33.1125i	1.41339	−	1.22471i
$732$	9.74123	−	1.18211i	0.360046	−	0.0436920i
$733$	9.96858	+	21.8281i	0.368198	+	0.806241i	0.999528	+	0.0307263i	$0.00978204\pi$
$733$	9.96858	+	21.8281i	0.368198	+	0.806241i	−0.631330	+	0.775514i	$0.717491\pi$
$734$	1.16251	−	8.08542i	0.0429090	−	0.298438i
$735$	5.80274	+	1.96821i	0.214037	+	0.0725986i
$736$	−2.46583	+	4.11335i	−0.0908919	+	0.151620i
$737$	−3.02699			−0.111501
$738$	−18.7540	+	14.8555i	−0.690345	+	0.546839i
$739$	9.71581	+	21.2746i	0.357402	+	0.782600i	0.999867	+	0.0162861i	$0.00518424\pi$
$739$	9.71581	+	21.2746i	0.357402	+	0.782600i	−0.642466	+	0.766314i	$0.722088\pi$
$740$	17.6359	−	10.8571i	0.648309	−	0.399114i
$741$	−20.4784	+	42.3461i	−0.752292	+	1.55562i
$742$	−6.93324	−	23.6125i	−0.254527	−	0.866840i
$743$	9.42972	−	14.6729i	0.345943	−	0.538298i	−0.624064	−	0.781373i	$-0.714520\pi$
$743$	9.42972	−	14.6729i	0.345943	−	0.538298i	0.970007	+	0.243075i	$0.0781561\pi$
$744$	−1.12182	−	0.0247279i	−0.0411281	−	0.000906569i
$745$	0.160175	+	1.29111i	0.00586835	+	0.0473027i
$746$	25.9938	−	16.7052i	0.951702	−	0.611621i
$747$	11.9413	−	16.8949i	0.436911	−	0.618151i
$748$	−1.48296	+	0.213217i	−0.0542223	+	0.00779599i
$749$	13.5450	+	21.0765i	0.494924	+	0.770117i
$750$	−11.4689	−	15.6034i	−0.418783	−	0.569755i
$751$	−21.6229	−	9.87483i	−0.789029	−	0.360337i	−0.0202033	−	0.999796i	$-0.506431\pi$
$751$	−21.6229	−	9.87483i	−0.789029	−	0.360337i	−0.768826	+	0.639458i	$0.779159\pi$
$752$	−10.5487	−	6.77924i	−0.384672	−	0.247214i
$753$	17.8462	+	21.5369i	0.650353	+	0.784849i
$754$	−10.3794	−	11.9785i	−0.377996	−	0.436231i
$755$	−28.8748	+	17.7760i	−1.05086	+	0.646934i
$756$	−0.926550	−	12.0592i	−0.0336983	−	0.438590i
$757$	3.69387	−	25.6914i	0.134256	−	0.933771i	−0.805663	−	0.592374i	$-0.798191\pi$
$757$	3.69387	−	25.6914i	0.134256	−	0.933771i	0.939919	−	0.341397i	$-0.110900\pi$
$758$			13.0501i			0.474003i
$759$	2.19761	+	0.979469i	0.0797683	+	0.0355525i
$760$	−13.0304	−	11.7404i	−0.472661	−	0.425869i
$761$	−3.29333	−	0.473509i	−0.119383	−	0.0171647i	0.0823643	−	0.996602i	$-0.473753\pi$
$761$	−3.29333	−	0.473509i	−0.119383	−	0.0171647i	−0.201747	+	0.979438i	$0.564662\pi$
$762$	18.5117	+	16.7688i	0.670609	+	0.607471i
$763$	4.89333	−	16.6651i	0.177150	−	0.603319i
$764$	0.756940	+	0.873556i	0.0273851	+	0.0316041i
$765$	32.4130	−	12.3839i	1.17189	−	0.447739i
$766$	−2.63882	+	4.10608i	−0.0953445	+	0.148359i
$767$	−2.75653	+	6.03595i	−0.0995324	+	0.217946i
$768$	−1.65073	−	0.524480i	−0.0595657	−	0.0189255i
$769$	−26.7378	−	41.6048i	−0.964189	−	1.50031i	−0.862853	−	0.505455i	$-0.831325\pi$
$769$	−26.7378	−	41.6048i	−0.964189	−	1.50031i	−0.101336	−	0.994852i	$-0.532312\pi$
$770$	1.25221	+	0.839457i	0.0451265	+	0.0302519i
$771$	8.45078	−	5.17145i	0.304347	−	0.186245i
$772$	−1.06075	−	1.65056i	−0.0381774	−	0.0594051i
$773$	−13.7681	−	11.9301i	−0.495204	−	0.429097i	0.371115	−	0.928587i	$-0.378975\pi$
$773$	−13.7681	−	11.9301i	−0.495204	−	0.429097i	−0.866320	+	0.499490i	$0.833521\pi$
$774$	−10.9955	−	27.1875i	−0.395225	−	0.977235i
$775$	−1.45873	+	2.89216i	−0.0523992	+	0.103890i
$776$	15.8035	−	4.64031i	0.567311	−	0.166578i
$777$	16.2562	−	33.6152i	0.583187	−	1.20594i
$778$	−14.4300	−	4.23702i	−0.517339	−	0.151904i
$779$	25.9859	+	56.9012i	0.931042	+	2.03870i
$780$	11.9564	+	6.07058i	0.428109	+	0.217362i
$781$		−	2.41708i		−	0.0864898i
$782$	−23.5722	+	7.72711i	−0.842940	+	0.276321i
$783$	−8.19500	+	22.3312i	−0.292865	+	0.798053i
$784$	0.225157	−	1.56600i	0.00804131	−	0.0559285i
$785$	−12.3396	−	3.88438i	−0.440419	−	0.138640i
$786$	−13.2594	+	1.60904i	−0.472946	+	0.0573925i
$787$	−22.0495	−	25.4465i	−0.785981	−	0.907070i	0.211545	−	0.977368i	$-0.432150\pi$
$787$	−22.0495	−	25.4465i	−0.785981	−	0.907070i	−0.997526	+	0.0702981i	$0.977605\pi$
$788$	−3.53346	+	1.03752i	−0.125874	+	0.0369600i
$789$	−23.9949	−	3.99151i	−0.854243	−	0.142102i
$790$	−22.3723	+	9.69784i	−0.795969	+	0.345034i
$791$	−6.18066	−	5.35558i	−0.219759	−	0.190422i
$792$	−0.161443	+	0.853818i	−0.00573664	+	0.0303391i
$793$	2.79149	+	19.4153i	0.0991288	+	0.689456i
$794$	−18.3819	+	2.64292i	−0.652350	+	0.0937937i
$795$	−9.89993	−	39.7329i	−0.351114	−	1.40918i
$796$	8.92521	+	7.73374i	0.316346	+	0.274115i
$797$	−13.7771	−	6.29179i	−0.488010	−	0.222867i	0.156185	−	0.987728i	$-0.450080\pi$
$797$	−13.7771	−	6.29179i	−0.488010	−	0.222867i	−0.644195	+	0.764861i	$0.722808\pi$
$798$	−31.1944	−	5.18912i	−1.10427	−	0.183693i
$799$	−18.2730	−	62.2320i	−0.646451	−	2.20161i
$800$	−3.41820	+	3.64909i	−0.120852	+	0.129015i
$801$	−17.2090	+	10.0166i	−0.608048	+	0.353918i
$802$	0.879892	+	1.92670i	0.0310701	+	0.0680340i
$803$	−4.00492	−	0.575821i	−0.141331	−	0.0203203i
$804$	−7.15471	−	16.6269i	−0.252327	−	0.586384i
$805$	22.8262	+	10.1006i	0.804518	+	0.356001i
$806$		−	2.24300i		−	0.0790062i
$807$	1.81990	+	6.74442i	0.0640634	+	0.237415i
$808$	−10.1679	+	4.64354i	−0.357706	+	0.163359i
$809$	6.87263	−	23.4060i	0.241629	−	0.822912i	−0.745979	−	0.665969i	$-0.768018\pi$
$809$	6.87263	−	23.4060i	0.241629	−	0.822912i	0.987608	−	0.156942i	$-0.0501637\pi$
$810$	−0.709705	−	20.1121i	−0.0249365	−	0.706667i
$811$	17.8624	−	5.24486i	0.627232	−	0.184172i	0.0473579	−	0.998878i	$-0.484920\pi$
$811$	17.8624	−	5.24486i	0.627232	−	0.184172i	0.579874	+	0.814706i	$0.303102\pi$
$812$	5.76089	−	8.96413i	0.202168	−	0.314579i
$813$	−11.1196	−	0.245105i	−0.389982	−	0.00859621i
$814$	−1.75677	+	2.02742i	−0.0615747	+	0.0710610i
$815$	1.49806	+	0.245093i	0.0524746	+	0.00858522i
$816$	−4.67634	−	7.64171i	−0.163705	−	0.267513i
$817$	−75.8976	+	10.9124i	−2.65532	+	0.381777i
$818$	7.48244	−	4.80867i	0.261617	−	0.168131i
$819$	24.0589	−	2.38288i	0.840686	−	0.0832646i
$820$	16.3615	−	7.09232i	0.571368	−	0.247675i
$821$	−15.6497	+	24.3513i	−0.546177	+	0.849868i	−0.999132	−	0.0416658i	$-0.986734\pi$
$821$	−15.6497	+	24.3513i	−0.546177	+	0.849868i	0.452955	+	0.891533i	$0.350370\pi$
$822$	12.8438	−	10.6428i	0.447979	−	0.371211i
$823$	−27.6299	+	23.9414i	−0.963118	+	0.834546i	−0.986262	−	0.165186i	$-0.947178\pi$
$823$	−27.6299	+	23.9414i	−0.963118	+	0.834546i	0.0231445	+	0.999732i	$0.492632\pi$
$824$	−5.29279	−	1.55410i	−0.184383	−	0.0541397i
$825$	2.02396	+	1.48184i	0.0704651	+	0.0515910i
$826$	−4.41564	−	0.634873i	−0.153640	−	0.0220901i
$827$			15.3676i			0.534384i	0.963643	+	0.267192i	$0.0860959\pi$
$827$			15.3676i			0.534384i	−0.963643	+	0.267192i	$0.913904\pi$
$828$	−0.185732	+	14.3863i	−0.00645464	+	0.499958i
$829$	−40.2801			−1.39899			−0.699493	−	0.714640i	$-0.746591\pi$
$829$	−40.2801			−1.39899			−0.699493	+	0.714640i	$0.746591\pi$
$830$	−11.8475	+	9.87074i	−0.411234	+	0.342618i
$831$	3.28108	+	2.97216i	0.113819	+	0.103103i
$832$	0.975429	−	3.32201i	0.0338169	−	0.115170i
$833$	6.18461	−	5.35899i	0.214284	−	0.185678i
$834$	−1.34200	−	1.61953i	−0.0464697	−	0.0560798i
$835$	−18.3595	+	5.00667i	−0.635356	+	0.173263i
$836$	2.06664	+	0.943804i	0.0714763	+	0.0326421i
$837$	−2.94596	+	1.62888i	−0.101827	+	0.0563022i
$838$	8.16538	−	5.24757i	0.282068	−	0.181274i
$839$	−1.49296	−	10.3838i	−0.0515427	−	0.358487i	−0.999228	−	0.0392816i	$-0.987493\pi$
$839$	−1.49296	−	10.3838i	−0.0515427	−	0.358487i	0.947686	−	0.319206i	$-0.103416\pi$
$840$	−1.65125	+	8.86238i	−0.0569737	+	0.305781i
$841$	6.76611	−	4.34831i	0.233314	−	0.149942i
$842$	−19.9768	−	17.3100i	−0.688446	−	0.596542i
$843$	24.8322	+	0.547366i	0.855267	+	0.0188523i
$844$	0.817635	+	0.525462i	0.0281442	+	0.0180871i
$845$	0.980518	−	2.04144i	0.0337309	−	0.0702277i
$846$	−37.5813	−	1.65758i	−1.29207	−	0.0569889i
$847$	24.3795	+	7.15847i	0.837690	+	0.245968i
$848$	−9.61722	+	4.39204i	−0.330257	+	0.150823i
$849$	16.2102	−	4.37412i	0.556333	−	0.150120i
$850$	−25.7226	+	2.68634i	−0.882276	+	0.0921408i
$851$	−22.8380	+	38.0969i	−0.782875	+	1.30594i
$852$	13.2767	−	5.71309i	0.454851	−	0.195727i
$853$	−19.9413	−	2.86713i	−0.682777	−	0.0981685i	−0.207806	−	0.978170i	$-0.566632\pi$
$853$	−19.9413	−	2.86713i	−0.682777	−	0.0981685i	−0.474971	+	0.880002i	$0.657541\pi$
$854$	−11.9952	+	5.47804i	−0.410469	+	0.187455i
$855$	−51.5027	−	10.7756i	−1.76136	−	0.368517i
$856$	8.13454	−	7.04862i	0.278033	−	0.240917i
$857$	41.7283	−	12.2525i	1.42541	−	0.418539i	0.524081	−	0.851669i	$-0.324409\pi$
$857$	41.7283	−	12.2525i	1.42541	−	0.418539i	0.901332	+	0.433130i	$0.142591\pi$
$858$	−1.71342	−	0.285024i	−0.0584953	−	0.00973057i
$859$	2.72218	−	5.96075i	0.0928798	−	0.203378i	−0.857490	−	0.514500i	$-0.827977\pi$
$859$	2.72218	−	5.96075i	0.0928798	−	0.203378i	0.950370	+	0.311122i	$0.100705\pi$
$860$	2.69118	+	21.6926i	0.0917683	+	0.739712i
$861$	17.9744	−	26.6581i	0.612565	−	0.908507i
$862$	−3.63296	−	25.2678i	−0.123739	−	0.860624i
$863$	−5.90459	−	41.0674i	−0.200995	−	1.39795i	−0.801340	−	0.598209i	$-0.795879\pi$
$863$	−5.90459	−	41.0674i	−0.200995	−	1.39795i	0.600346	−	0.799741i	$-0.295030\pi$
$864$	−5.07150	+	1.13133i	−0.172536	+	0.0384886i
$865$	−5.94779	−	47.9430i	−0.202231	−	1.63011i
$866$	−12.7481	+	27.9144i	−0.433198	+	0.948572i
$867$	2.77245	−	16.6665i	0.0941572	−	0.566025i
$868$	1.44686	−	0.424837i	0.0491097	−	0.0144199i
$869$	2.38707	−	2.06841i	0.0809758	−	0.0701659i
$870$	10.1949	−	14.5059i	0.345639	−	0.491796i
$871$	32.9127	−	15.0307i	1.11520	−	0.509297i
$872$	−7.38599	−	1.06195i	−0.250121	−	0.0359620i
$873$	33.9720	−	35.8809i	1.14978	−	1.21439i
$874$	36.4066	+	9.46816i	1.23147	+	0.320265i
$875$	21.0385	+	15.3173i	0.711231	+	0.517819i
$876$	−6.30327	−	23.3595i	−0.212968	−	0.789244i
$877$	38.9655	−	17.7950i	1.31577	−	0.600893i	0.371003	−	0.928631i	$-0.379014\pi$
$877$	38.9655	−	17.7950i	1.31577	−	0.600893i	0.944768	+	0.327739i	$0.106287\pi$
$878$	−16.2607	−	4.77458i	−0.548773	−	0.161134i
$879$	23.1047	+	11.1733i	0.779301	+	0.376866i
$880$	0.280415	−	0.583824i	0.00945279	−	0.0196807i
$881$	39.6360	+	25.4725i	1.33537	+	0.858190i	0.996577	−	0.0826710i	$-0.0263451\pi$
$881$	39.6360	+	25.4725i	1.33537	+	0.858190i	0.338793	+	0.940861i	$0.389981\pi$
$882$	−1.77953	−	4.40008i	−0.0599199	−	0.148158i
$883$	12.0927	+	10.4784i	0.406952	+	0.352626i	0.834155	−	0.551530i	$-0.185956\pi$
$883$	12.0927	+	10.4784i	0.406952	+	0.352626i	−0.427203	+	0.904156i	$0.640501\pi$
$884$	15.0656	−	9.68205i	0.506710	−	0.325643i
$885$	−7.29720	−	1.35963i	−0.245293	−	0.0457034i
$886$	−0.918846	−	6.39072i	−0.0308692	−	0.214700i
$887$	−15.9268	+	10.2355i	−0.534769	+	0.343675i	−0.779990	−	0.625792i	$-0.784776\pi$
$887$	−15.9268	+	10.2355i	−0.534769	+	0.343675i	0.245221	+	0.969467i	$0.421140\pi$
$888$	−15.2887	−	4.85761i	−0.513055	−	0.163011i
$889$	−30.5331	−	13.9440i	−1.02405	−	0.467666i
$890$	14.3185	−	3.90469i	0.479958	−	0.130885i
$891$	0.869945	+	2.45740i	0.0291443	+	0.0823260i
$892$	−0.231580	+	0.200666i	−0.00775389	+	0.00671878i
$893$	−27.7100	+	94.3717i	−0.927281	+	3.15803i
$894$	0.676564	−	0.746884i	0.0226277	−	0.0249795i
$895$	24.8670	−	20.7178i	0.831212	−	0.692521i
$896$	2.32764			0.0777609
$897$	−28.7584	+	0.262553i	−0.960216	+	0.00876640i
$898$			35.6649i			1.19015i
$899$	−2.93557	−	0.422071i	−0.0979067	−	0.0140769i
$900$	−3.35565	+	14.6198i	−0.111855	+	0.487328i
$901$	−52.4717	−	15.4071i	−1.74809	−	0.513285i
$902$	−1.74574	+	1.51269i	−0.0581266	+	0.0503670i
$903$	25.1462	+	30.3465i	0.836813	+	1.00987i
$904$	−1.89955	+	2.95576i	−0.0631781	+	0.0983070i
$905$	24.3723	−	10.5648i	0.810162	−	0.351186i
$906$	25.0318	+	7.95323i	0.831625	+	0.264228i
$907$	45.4837	−	29.2306i	1.51026	−	0.970586i	0.516838	−	0.856083i	$-0.327109\pi$
$907$	45.4837	−	29.2306i	1.51026	−	0.970586i	0.993423	−	0.114502i	$-0.0365273\pi$
$908$	0.531003	−	0.0763467i	0.0176219	−	0.00253365i
$909$	−19.3554	+	27.3845i	−0.641979	+	0.908286i
$910$	−17.7837	−	2.90955i	−0.589525	−	0.0964506i
$911$	12.2432	−	14.1294i	0.405634	−	0.468126i	−0.515773	−	0.856725i	$-0.672495\pi$
$911$	12.2432	−	14.1294i	0.405634	−	0.468126i	0.921407	+	0.388599i	$0.127041\pi$
$912$	−0.299395	+	13.5826i	−0.00991397	+	0.449765i
$913$	1.07994	−	1.68041i	0.0357407	−	0.0556136i
$914$	−0.161946	+	0.0475518i	−0.00535671	+	0.00157287i
$915$	−20.3192	+	8.28090i	−0.671733	+	0.273758i
$916$	−6.50252	+	22.1456i	−0.214849	+	0.731710i
$917$	16.3274	−	7.45648i	0.539179	−	0.246235i
$918$	−23.6571	−	12.7560i	−0.780802	−	0.421011i
$919$			30.5431i			1.00752i	0.863842	+	0.503762i	$0.168051\pi$
$919$			30.5431i			1.00752i	−0.863842	+	0.503762i	$0.831949\pi$
$920$	2.89965	−	10.3243i	0.0955985	−	0.340383i
$921$	23.9188	−	10.2925i	0.788150	−	0.339149i
$922$	−1.79782	−	0.258488i	−0.0592081	−	0.00851283i
$923$	12.0022	+	26.2810i	0.395056	+	0.865051i
$924$	−0.140675	−	1.15924i	−0.00462788	−	0.0381362i
$925$	−31.6586	+	33.7970i	−1.04093	+	1.11124i
$926$	−2.63618	−	8.97799i	−0.0866301	−	0.295035i
$927$	−16.0684	+	3.95812i	−0.527755	+	0.130002i
$928$	−4.16420	−	1.90173i	−0.136697	−	0.0624272i
$929$	−23.9864	−	20.7844i	−0.786969	−	0.681913i	0.165614	−	0.986191i	$-0.447039\pi$
$929$	−23.9864	−	20.7844i	−0.786969	−	0.681913i	−0.952583	+	0.304278i	$0.901585\pi$
$930$	2.43465	−	0.606622i	0.0798353	−	0.0198919i
$931$	−12.2834	+	1.76609i	−0.402572	+	0.0578812i
$932$	1.41351	+	9.83118i	0.0463011	+	0.322031i
$933$	16.4383	−	24.3800i	0.538167	−	0.798166i
$934$	8.37879	+	7.26026i	0.274162	+	0.237563i
$935$	3.07374	−	1.33239i	0.100522	−	0.0435739i
$936$	−2.48431	−	10.0853i	−0.0812021	−	0.329648i
$937$	−23.1493	+	6.79726i	−0.756256	+	0.222057i	−0.637060	−	0.770814i	$-0.719850\pi$
$937$	−23.1493	+	6.79726i	−0.756256	+	0.222057i	−0.119196	+	0.992871i	$0.538032\pi$
$938$	15.9296	+	18.3837i	0.520118	+	0.600248i
$939$	−4.68700	−	38.6235i	−0.152954	−	1.26043i
$940$	26.7449	+	8.41902i	0.872321	+	0.274598i
$941$	−5.20686	+	36.2145i	−0.169739	+	1.18056i	0.709685	+	0.704519i	$0.248837\pi$
$941$	−5.20686	+	36.2145i	−0.169739	+	1.18056i	−0.879424	+	0.476040i	$0.842072\pi$
$942$	3.96082	+	9.20458i	0.129051	+	0.299901i
$943$	−24.1332	+	29.6713i	−0.785886	+	0.966230i
$944$			1.91656i			0.0623786i
$945$	9.09325	+	25.4702i	0.295803	+	0.828544i
$946$	−1.17625	−	2.57562i	−0.0382430	−	0.0837406i
$947$	6.78864	+	1.99332i	0.220601	+	0.0647743i	0.390165	−	0.920745i	$-0.372418\pi$
$947$	6.78864	+	1.99332i	0.220601	+	0.0647743i	−0.169564	+	0.985519i	$0.554236\pi$
$948$	17.0036	+	8.22288i	0.552253	+	0.267067i
$949$	46.4051	−	13.6258i	1.50637	−	0.442311i
$950$	35.0171	+	17.6617i	1.13611	+	0.573022i
$951$	−29.8838	−	0.658717i	−0.969049	−	0.0213603i
$952$	9.09899	+	7.88432i	0.294900	+	0.255532i
$953$	18.8412	+	29.3176i	0.610328	+	0.949689i	0.999592	+	0.0285626i	$0.00909300\pi$
$953$	18.8412	+	29.3176i	0.610328	+	0.949689i	−0.389264	+	0.921126i	$0.627271\pi$
$954$	−18.3071	+	25.9013i	−0.592715	+	0.838586i
$955$	−2.14685	−	1.43921i	−0.0694705	−	0.0465717i
$956$	−3.66342	−	5.70039i	−0.118483	−	0.184364i
$957$	−0.695451	+	2.18884i	−0.0224808	+	0.0707553i
$958$	−2.92651	+	6.40817i	−0.0945514	+	0.207039i
$959$	−12.1190	+	18.8576i	−0.391344	+	0.608943i
$960$	3.86966	+	0.160334i	0.124893	+	0.00517474i
$961$	20.0258	+	23.1110i	0.645995	+	0.745518i
$962$	9.03419	−	30.7676i	0.291274	−	0.991988i
$963$	10.4537	−	30.5517i	0.336866	−	0.984514i
$964$	−20.4659	−	2.94255i	−0.659161	−	0.0947730i
$965$	3.25938	+	2.93671i	0.104923	+	0.0945360i
$966$	−5.61638	−	18.5011i	−0.180704	−	0.595264i
$967$			46.1090i			1.48277i	0.671082	+	0.741383i	$0.265830\pi$
$967$			46.1090i			1.48277i	−0.671082	+	0.741383i	$0.734170\pi$
$968$	1.55352	−	10.8050i	0.0499321	−	0.347286i
$969$	−47.1781	+	52.0817i	−1.51558	+	1.67310i
$970$	−31.3628	+	19.3076i	−1.00700	+	0.619931i
$971$	27.1776	+	31.3646i	0.872170	+	1.00654i	0.999892	+	0.0147279i	$0.00468821\pi$
$971$	27.1776	+	31.3646i	0.872170	+	1.00654i	−0.127721	+	0.991810i	$0.540766\pi$
$972$	−11.4419	+	10.5869i	−0.367000	+	0.339575i
$973$	2.37784	+	1.52814i	0.0762300	+	0.0489900i
$974$	25.1770	+	11.4979i	0.806722	+	0.368418i
$975$	−29.3648	−	6.06207i	−0.940426	−	0.194142i
$976$	3.06293	+	4.76601i	0.0980419	+	0.152556i
$977$	−24.3797	+	3.50527i	−0.779974	+	0.112143i	−0.520790	−	0.853685i	$-0.674363\pi$
$977$	−24.3797	+	3.50527i	−0.779974	+	0.112143i	−0.259184	+	0.965828i	$0.583454\pi$
$978$	−0.613742	−	1.00293i	−0.0196253	−	0.0320701i
$979$	−1.61729	+	1.03937i	−0.0516889	+	0.0332184i
$980$	0.435545	+	3.51077i	0.0139130	+	0.112148i
$981$	−20.7529	+	8.39311i	−0.662588	+	0.267971i
$982$	17.9324	−	27.9034i	0.572247	−	0.890434i
$983$	16.5449	+	56.3466i	0.527699	+	1.79718i	0.600249	+	0.799813i	$0.295068\pi$
$983$	16.5449	+	56.3466i	0.527699	+	1.79718i	−0.0725496	+	0.997365i	$0.523114\pi$
$984$	−12.4353	−	6.01364i	−0.396422	−	0.191708i
$985$	7.01233	−	4.31695i	0.223431	−	0.137549i
$986$	−9.83666	−	21.5393i	−0.313263	−	0.685950i
$987$	48.8075	−	13.1701i	1.55356	−	0.419209i
$988$	−27.1573			−0.863988
$989$	−26.5632	−	38.6307i	−0.844659	−	1.22839i
$990$	−0.154019	−	1.93691i	−0.00489504	−	0.0615591i
$991$	3.14592	−	21.8803i	0.0999334	−	0.695052i	−0.876841	−	0.480781i	$-0.840353\pi$
$991$	3.14592	−	21.8803i	0.0999334	−	0.695052i	0.976774	−	0.214271i	$-0.0687376\pi$
$992$	−0.269124	−	0.589299i	−0.00854469	−	0.0187103i
$993$	0.329382	+	2.71429i	0.0104526	+	0.0861353i
$994$	−14.6795	+	12.7199i	−0.465606	+	0.403450i
$995$	−23.8040	−	11.4332i	−0.754638	−	0.362458i
$996$	11.7829	+	1.96006i	0.373354	+	0.0621067i
$997$	11.8893	+	5.42966i	0.376537	+	0.171959i	0.594689	−	0.803956i	$-0.297275\pi$
$997$	11.8893	+	5.42966i	0.376537	+	0.171959i	−0.218151	+	0.975915i	$0.570003\pi$
$998$	2.89414	−	3.34002i	0.0916125	−	0.105726i
$999$	−46.9710	+	10.4781i	−1.48610	+	0.331512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.659.7	yes	240
3.2	odd	2		690.2.n.b.659.1	yes	240
5.4	even	2		690.2.n.b.659.18	yes	240
15.14	odd	2	inner	690.2.n.a.659.24	yes	240
23.20	odd	22	inner	690.2.n.a.89.24	yes	240
69.20	even	22		690.2.n.b.89.18	yes	240
115.89	odd	22		690.2.n.b.89.1	yes	240
345.89	even	22	inner	690.2.n.a.89.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.7	✓	240	345.89	even	22	inner
690.2.n.a.89.24	yes	240	23.20	odd	22	inner
690.2.n.a.659.7	yes	240	1.1	even	1	trivial
690.2.n.a.659.24	yes	240	15.14	odd	2	inner
690.2.n.b.89.1	yes	240	115.89	odd	22
690.2.n.b.89.18	yes	240	69.20	even	22
690.2.n.b.659.1	yes	240	3.2	odd	2
690.2.n.b.659.18	yes	240	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-1.16282 + 1.28368i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.23565 + 0.0433117i) q^{5} +(-1.10513 - 1.33367i) q^{6} +(1.95813 + 1.25842i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.295684 - 2.98539i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-1.16282 + 1.28368i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.23565 + 0.0433117i) q^{5} +(-1.10513 - 1.33367i) q^{6} +(1.95813 + 1.25842i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.295684 - 2.98539i) q^{9} +(-0.361037 + 2.20673i) q^{10} +(-0.0412214 - 0.286701i) q^{11} +(1.47738 - 0.904080i) q^{12} +(1.87184 + 2.91263i) q^{13} +(-1.52428 + 1.75911i) q^{14} +(-2.65526 + 2.81950i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.45726 + 4.96297i) q^{17} +(2.99709 + 0.132191i) q^{18} +(2.20986 - 7.52609i) q^{19} +(-2.13289 - 0.671412i) q^{20} +(-3.89237 + 1.05031i) q^{21} +0.289649 q^{22} +(4.72344 - 0.830119i) q^{23} +(0.684625 + 1.59100i) q^{24} +(4.99625 + 0.193659i) q^{25} +(-3.14938 + 1.43827i) q^{26} +(4.17613 + 3.09192i) q^{27} +(-1.52428 - 1.75911i) q^{28} +(1.28974 + 4.39246i) q^{29} +(-2.41292 - 3.02949i) q^{30} +(-0.269124 + 0.589299i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.415966 + 0.280467i) q^{33} +(-5.11984 + 0.736122i) q^{34} +(4.32319 + 2.89819i) q^{35} +(-0.557376 + 2.94777i) q^{36} +(-6.06516 + 6.99957i) q^{37} +(7.13499 + 3.25844i) q^{38} +(-5.91551 - 0.984034i) q^{39} +(0.968120 - 2.01563i) q^{40} +(-6.02707 + 5.22249i) q^{41} +(-0.485675 - 4.00223i) q^{42} +(-4.06093 - 8.89220i) q^{43} +(-0.0412214 + 0.286701i) q^{44} +(-0.531743 - 6.68710i) q^{45} +(0.149454 + 4.79350i) q^{46} -12.5393 q^{47} +(-1.67224 + 0.451233i) q^{48} +(-0.657229 - 1.43913i) q^{49} +(-0.902728 + 4.91783i) q^{50} +(-8.06541 - 3.90040i) q^{51} +(-0.975429 - 3.32201i) q^{52} +(-5.71601 + 8.89428i) q^{53} +(-3.65477 + 3.69359i) q^{54} +(-0.0797390 - 0.642748i) q^{55} +(1.95813 - 1.25842i) q^{56} +(7.09144 + 11.5883i) q^{57} +(-4.53130 + 0.651502i) q^{58} +(1.03617 + 1.61231i) q^{59} +(3.34205 - 1.95722i) q^{60} +(5.15339 + 2.35348i) q^{61} +(-0.545000 - 0.350250i) q^{62} +(3.17788 - 6.21789i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(4.05861 + 6.59269i) q^{65} +(-0.336811 + 0.371818i) q^{66} +(1.48727 - 10.3442i) q^{67} -5.17249i q^{68} +(-4.42692 + 7.02868i) q^{69} +(-3.48394 + 3.86674i) q^{70} +(8.25991 + 1.18760i) q^{71} +(-2.83844 - 0.971213i) q^{72} +(3.93552 - 13.4031i) q^{73} +(-6.06516 - 6.99957i) q^{74} +(-6.05835 + 6.18841i) q^{75} +(-4.24069 + 6.59864i) q^{76} +(0.280072 - 0.613272i) q^{77} +(1.81588 - 5.71526i) q^{78} +(5.89554 + 9.17364i) q^{79} +(1.85733 + 1.24512i) q^{80} +(-8.82514 + 1.76547i) q^{81} +(-4.31159 - 6.70896i) q^{82} +(5.21189 + 4.51613i) q^{83} +(4.03061 + 0.0888450i) q^{84} +(3.04296 + 11.1586i) q^{85} +(9.37962 - 2.75411i) q^{86} +(-7.13826 - 3.45203i) q^{87} +(-0.277916 - 0.0816036i) q^{88} +(-2.75722 - 6.03747i) q^{89} +(6.69471 + 0.425342i) q^{90} +8.05887i q^{91} +(-4.76598 - 0.534254i) q^{92} +(-0.443530 - 1.03072i) q^{93} +(1.78453 - 12.4116i) q^{94} +(5.26643 - 16.7300i) q^{95} +(-0.208656 - 1.71944i) q^{96} +(10.7860 + 12.4477i) q^{97} +(1.51802 - 0.445730i) q^{98} +(-0.843726 + 0.207835i) 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

L-functions

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