LMFDB - Embedded newform 690.2.n.a.89.7

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			89.7
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.7

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$3$	−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	−0.115473	−	0.993311i	$-0.536838\pi$
$7$	1.95813	−	1.25842i	0.740105	−	0.475637i	0.855578	+	0.517674i	$0.173202\pi$
$8$	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	−0.995092	−	0.0989573i	$-0.968449\pi$
$11$	−0.0412214	+	0.286701i	−0.0124287	+	0.0864436i	0.982663	+	0.185401i	$0.0593584\pi$
$12$	1.47738	+	0.904080i	0.426482	+	0.260985i
$13$	1.87184	−	2.91263i	0.519154	−	0.807819i	−0.478369	−	0.878159i	$-0.658772\pi$
$13$	1.87184	−	2.91263i	0.519154	−	0.807819i	0.997523	+	0.0703399i	$0.0224084\pi$
$14$	−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	−0.570547	−	0.821265i	$-0.693269\pi$
$17$	1.45726	−	4.96297i	0.353437	−	1.20370i	0.923984	−	0.382431i	$-0.124913\pi$
$18$	2.99709	−	0.132191i	0.706420	−	0.0311578i
$19$	2.20986	+	7.52609i	0.506976	+	1.72660i	0.672221	+	0.740350i	$0.265340\pi$
$19$	2.20986	+	7.52609i	0.506976	+	1.72660i	−0.165245	+	0.986253i	$0.552841\pi$
$20$	−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	−0.748756	−	0.662846i	$-0.769349\pi$
$29$	1.28974	−	4.39246i	0.239499	−	0.815659i	0.988255	−	0.152813i	$-0.0488333\pi$
$30$	−2.41292	+	3.02949i	−0.440537	+	0.553107i
$31$	−0.269124	−	0.589299i	−0.0483361	−	0.105841i	0.883923	−	0.467632i	$-0.154893\pi$
$31$	−0.269124	−	0.589299i	−0.0483361	−	0.105841i	−0.932259	+	0.361791i	$0.882165\pi$
$32$	−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	−0.988571	−	0.150759i	$-0.951828\pi$
$37$	−6.06516	−	6.99957i	−0.997107	−	1.15072i	−0.00853621	−	0.999964i	$-0.502717\pi$
$38$	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	0.0417470	−	0.999128i	$-0.486708\pi$
$41$	−6.02707	−	5.22249i	−0.941270	−	0.815615i	−0.983017	+	0.183513i	$0.941253\pi$
$42$	−0.485675	+	4.00223i	−0.0749412	+	0.617557i
$43$	−4.06093	+	8.89220i	−0.619286	+	1.35605i	0.296751	+	0.954955i	$0.404097\pi$
$43$	−4.06093	+	8.89220i	−0.619286	+	1.35605i	−0.916037	+	0.401093i	$0.868630\pi$
$44$	−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	−0.970985	−	0.239142i	$-0.923134\pi$
$53$	−5.71601	−	8.89428i	−0.785154	−	1.22172i	0.185831	−	0.982582i	$-0.440502\pi$
$54$	−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	−0.767232	−	0.641369i	$-0.778367\pi$
$59$	1.03617	−	1.61231i	0.134898	−	0.209905i	0.902130	+	0.431465i	$0.142003\pi$
$60$	3.34205	+	1.95722i	0.431457	+	0.252676i
$61$	5.15339	−	2.35348i	0.659825	−	0.301332i	−0.0572174	−	0.998362i	$-0.518223\pi$
$61$	5.15339	−	2.35348i	0.659825	−	0.301332i	0.717042	+	0.697030i	$0.245496\pi$
$62$	−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	0.852745	+	0.522327i	$0.174936\pi$
$67$	1.48727	+	10.3442i	0.181699	+	1.26374i	−0.671046	+	0.741415i	$0.734155\pi$
$68$			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	0.366493	−	0.930421i	$-0.380558\pi$
$71$	8.25991	−	1.18760i	0.980270	−	0.140942i	0.613777	+	0.789479i	$0.289649\pi$
$72$	−2.83844	+	0.971213i	−0.334513	+	0.114459i
$73$	3.93552	+	13.4031i	0.460617	+	1.56872i	0.782945	+	0.622091i	$0.213717\pi$
$73$	3.93552	+	13.4031i	0.460617	+	1.56872i	−0.322328	+	0.946628i	$0.604465\pi$
$74$	−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	−0.332723	−	0.943025i	$-0.607967\pi$
$79$	5.89554	−	9.17364i	0.663300	−	1.03212i	0.996023	−	0.0890910i	$-0.0283962\pi$
$80$	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	−0.320105	−	0.947382i	$-0.603718\pi$
$83$	5.21189	−	4.51613i	0.572079	−	0.495709i	0.892184	+	0.451673i	$0.149173\pi$
$84$	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	−0.997625	−	0.0688784i	$-0.978058\pi$
$89$	−2.75722	+	6.03747i	−0.292265	+	0.639970i	0.705360	+	0.708849i	$0.250785\pi$
$90$	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	0.133068	−	0.991107i	$-0.457517\pi$
$97$	10.7860	−	12.4477i	1.09515	−	1.26387i	0.962081	−	0.272763i	$-0.0879374\pi$
$98$	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	−0.964547	−	0.263913i	$-0.914987\pi$
$101$	−8.44782	+	7.32008i	−0.840589	+	0.728375i	0.123957	+	0.992288i	$0.460441\pi$
$102$	5.00852	+	7.42823i	0.495918	+	0.735505i
$103$	−0.785042	+	5.46009i	−0.0773525	+	0.537998i	0.913892	+	0.405958i	$0.133062\pi$
$103$	−0.785042	+	5.46009i	−0.0773525	+	0.537998i	−0.991244	+	0.132041i	$0.957847\pi$
$104$	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	0.118495	−	0.992955i	$-0.462193\pi$
$107$	9.79086	−	4.47134i	0.946518	−	0.432260i	0.828023	+	0.560694i	$0.189466\pi$
$108$	−3.13587	+	4.14323i	−0.301749	+	0.398682i
$109$	−2.10227	+	7.15968i	−0.201361	+	0.685773i	0.795453	+	0.606015i	$0.207233\pi$
$109$	−2.10227	+	7.15968i	−0.201361	+	0.685773i	−0.996814	+	0.0797579i	$0.974585\pi$
$110$	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	−0.303938	−	0.952692i	$-0.598301\pi$
$113$	−3.47775	+	0.500025i	−0.327159	+	0.0470384i	−0.0232218	+	0.999730i	$0.507392\pi$
$114$	−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	−0.523935	−	0.851759i	$-0.675536\pi$
$127$	−14.2740	−	2.05229i	−1.26661	−	0.182112i	−0.742680	+	0.669647i	$0.766445\pi$
$128$	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	0.974210	−	0.225641i	$-0.0724477\pi$
$131$	4.16913	+	6.48729i	0.364258	+	0.566797i	−0.609952	+	0.792438i	$0.708811\pi$
$132$	−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	$-0.865044\pi$
$137$		−	9.63039i		−	0.822779i	0.911460	−	0.411390i	$-0.134956\pi$
$138$	−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	−0.986149	−	0.165864i	$-0.946959\pi$
$149$	0.0828029	−	0.575907i	0.00678348	−	0.0471801i	0.992932	+	0.118684i	$0.0378677\pi$
$150$	−5.26323	+	6.87739i	−0.429741	+	0.561536i
$151$	−12.7568	−	8.19829i	−1.03813	−	0.667168i	−0.0936087	−	0.995609i	$-0.529840\pi$
$151$	−12.7568	−	8.19829i	−1.03813	−	0.667168i	−0.944524	+	0.328442i	$0.893477\pi$
$152$	−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	−0.495633	−	0.868532i	$-0.665064\pi$
$157$	−5.55105	+	1.62993i	−0.443022	+	0.130083i	0.0526111	+	0.998615i	$0.483246\pi$
$158$	−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	−0.115949	−	0.993255i	$-0.536991\pi$
$163$	0.671948	−	0.0966116i	0.0526310	−	0.00756720i	0.168580	+	0.985688i	$0.446082\pi$
$164$	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	−0.0499193	−	0.998753i	$-0.515896\pi$
$167$	−8.16570	−	2.39767i	−0.631881	−	0.185537i	−0.581962	+	0.813216i	$0.697715\pi$
$168$	−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	0.447800	+	0.894134i	$0.352208\pi$
$173$	−3.07473	+	21.3852i	−0.233767	+	1.62589i	−0.681568	+	0.731755i	$0.738702\pi$
$174$	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	0.959596	−	0.281382i	$-0.0907929\pi$
$179$	10.9393	+	9.47896i	0.817642	+	0.708491i	−0.141954	+	0.989873i	$0.545338\pi$
$180$	−1.37377	−	6.56603i	−0.102395	−	0.489403i
$181$	10.8061	+	4.93496i	0.803208	+	0.366813i	0.774339	−	0.632770i	$-0.218082\pi$
$181$	10.8061	+	4.93496i	0.803208	+	0.366813i	0.0288686	+	0.999583i	$0.490810\pi$
$182$	−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	−0.575348	−	0.817909i	$-0.695133\pi$
$191$	−0.972388	+	0.624916i	−0.0703595	+	0.0452173i	0.504988	+	0.863126i	$0.331497\pi$
$192$	1.73163	−	0.0381696i	0.124970	−	0.00275465i
$193$	1.48280	−	1.28486i	0.106735	−	0.0924860i	−0.599859	−	0.800106i	$-0.704777\pi$
$193$	1.48280	−	1.28486i	0.106735	−	0.0924860i	0.706593	+	0.707620i	$0.250231\pi$
$194$	−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	0.646331	−	0.763057i	$-0.276303\pi$
$197$	3.09802	+	1.99098i	0.220725	+	0.141851i	−0.425606	+	0.904909i	$0.639939\pi$
$198$	−0.0856446	+	0.864716i	−0.00608650	+	0.0614527i
$199$	−10.7425	+	4.90595i	−0.761517	+	0.347773i	−0.758029	−	0.652221i	$-0.773838\pi$
$199$	−10.7425	+	4.90595i	−0.761517	+	0.347773i	−0.00348810	+	0.999994i	$0.501110\pi$
$200$	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	−0.313675	−	0.949531i	$-0.601560\pi$
$211$	−0.932555	+	0.273823i	−0.0641997	+	0.0188507i	0.249475	+	0.968381i	$0.419742\pi$
$212$	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	0.846756	−	0.531981i	$-0.178552\pi$
$223$	0.165666	+	0.257781i	0.0110938	+	0.0172623i	−0.835662	+	0.549244i	$0.814916\pi$
$224$	−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	0.399155	−	0.916884i	$-0.369304\pi$
$227$	−0.487984	−	0.222855i	−0.0323886	−	0.0147914i	−0.431543	+	0.902092i	$0.642031\pi$
$228$	−3.53939	+	13.1168i	−0.234402	+	0.868678i
$229$			23.0805i			1.52520i	0.646870	+	0.762601i	$0.276078\pi$
$229$			23.0805i			1.52520i	−0.646870	+	0.762601i	$0.723922\pi$
$230$	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	−0.995297	−	0.0968730i	$-0.969116\pi$
$233$	−4.12602	+	9.03471i	−0.270304	+	0.591884i	0.724992	+	0.688757i	$0.241843\pi$
$234$	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	−0.473316	−	0.880893i	$-0.656943\pi$
$239$	5.12101	−	4.43738i	0.331250	−	0.287030i	0.804567	+	0.593863i	$0.202398\pi$
$240$	−3.75809	−	0.936371i	−0.242583	−	0.0604425i
$241$	20.4659	+	2.94255i	1.31832	+	0.189546i	0.765329	−	0.643640i	$-0.222576\pi$
$241$	20.4659	+	2.94255i	1.31832	+	0.189546i	0.552993	+	0.833186i	$0.313486\pi$
$242$	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	0.924158	+	0.382011i	$0.124768\pi$
$251$	2.29818	+	15.9842i	0.145060	+	1.00891i	−0.779098	+	0.626902i	$0.784323\pi$
$252$	−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	−0.448392	−	0.893837i	$-0.648003\pi$
$257$	−5.48842	+	1.61155i	−0.342358	+	0.100525i	0.106034	+	0.994363i	$0.466185\pi$
$258$	−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	−0.524212	−	0.851588i	$-0.675640\pi$
$263$	7.59268	−	11.8144i	0.468185	−	0.728510i	0.992397	+	0.123078i	$0.0392765\pi$
$264$	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	0.901344	−	0.433104i	$-0.142582\pi$
$269$	2.18049	+	3.39291i	0.132947	+	0.206870i	−0.768397	+	0.639974i	$0.778945\pi$
$270$	−8.33076	−	8.09928i	−0.506994	−	0.492907i
$271$	4.20517	−	4.85303i	0.255446	−	0.294800i	−0.613513	−	0.789685i	$-0.710244\pi$
$271$	4.20517	−	4.85303i	0.255446	−	0.294800i	0.868959	+	0.494884i	$0.164790\pi$
$272$	−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	$0.0244662\pi$
$277$			2.55599i			0.153575i	−0.997048	+	0.0767873i	$0.975534\pi$
$278$	−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	−0.963233	−	0.268668i	$-0.913417\pi$
$281$	−9.39095	+	10.8377i	−0.560217	+	0.646525i	0.403016	+	0.915193i	$0.367962\pi$
$282$	13.8575	−	16.7233i	0.825204	−	0.995859i
$283$	−8.15487	+	5.24082i	−0.484757	+	0.311534i	−0.760094	−	0.649814i	$-0.774847\pi$
$283$	−8.15487	+	5.24082i	−0.484757	+	0.311534i	0.275337	+	0.961348i	$0.411211\pi$
$284$	−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	0.743023	+	0.669266i	$0.233391\pi$
$293$	−4.17455	+	14.2172i	−0.243880	+	0.830579i	−0.986903	+	0.161313i	$0.948427\pi$
$294$	−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	−0.765486	−	0.643452i	$-0.777502\pi$
$307$	−13.6752	+	6.24526i	−0.780485	+	0.356436i	−0.0149985	+	0.999888i	$0.504774\pi$
$308$	−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	−0.351680	−	0.936120i	$-0.614390\pi$
$311$	−16.8037	−	2.41601i	−0.952850	−	0.136999i	−0.601170	+	0.799121i	$0.705299\pi$
$312$	−3.35250	−	4.97215i	−0.189798	−	0.281493i
$313$	−14.7100	−	16.9763i	−0.831461	−	0.959557i	0.168196	−	0.985754i	$-0.446206\pi$
$313$	−14.7100	−	16.9763i	−0.831461	−	0.959557i	−0.999657	+	0.0261966i	$0.991660\pi$
$314$	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	−0.343690	−	0.939083i	$-0.611677\pi$
$317$	11.3013	−	13.0424i	0.634747	−	0.732537i	0.978437	+	0.206547i	$0.0662225\pi$
$318$	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	0.783448	−	0.621457i	$-0.213459\pi$
$331$	1.03376	+	1.19302i	0.0568204	+	0.0655743i	−0.726628	+	0.687031i	$0.758914\pi$
$332$	−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	0.843858	−	0.536567i	$-0.180279\pi$
$337$	−2.09756	−	4.59302i	−0.114261	−	0.250198i	−0.958119	+	0.286369i	$0.907552\pi$
$338$	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	0.865617	+	0.500706i	$0.166926\pi$
$347$	3.28092	+	22.8193i	0.176129	+	1.22500i	−0.689488	+	0.724297i	$0.742165\pi$
$348$	5.87656	−	5.32328i	0.315017	−	0.285358i
$349$	−7.33573	+	2.15396i	−0.392673	+	0.115299i	−0.472107	−	0.881541i	$-0.656507\pi$
$349$	−7.33573	+	2.15396i	−0.392673	+	0.115299i	0.0794349	+	0.996840i	$0.474688\pi$
$350$	−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	0.843528	−	0.537085i	$-0.180474\pi$
$353$	−2.15627	−	4.72158i	−0.114767	−	0.251304i	−0.958295	+	0.285780i	$0.907747\pi$
$354$	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	0.728356	−	0.685199i	$-0.240285\pi$
$359$	−1.01414	−	1.17038i	−0.0535243	−	0.0617704i	−0.781880	+	0.623428i	$0.785739\pi$
$360$	−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	−0.0703436	+	0.997523i	$0.522410\pi$
$373$	−20.2345	+	23.3518i	−1.04770	+	1.20911i	−0.977359	+	0.211590i	$0.932136\pi$
$374$	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	0.465842	−	0.884868i	$-0.345752\pi$
$379$	12.9173	+	1.85723i	0.663518	+	0.0953995i	0.197676	+	0.980267i	$0.436661\pi$
$380$	−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	−0.298740	−	0.954335i	$-0.596566\pi$
$383$	4.43983	−	2.02760i	0.226865	−	0.103606i	0.525605	+	0.850729i	$0.323839\pi$
$384$	−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	−0.969318	−	0.245811i	$-0.920946\pi$
$389$	−2.14029	−	14.8861i	−0.108517	−	0.754754i	0.860801	−	0.508942i	$-0.169963\pi$
$390$	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	−0.717638	−	0.696416i	$-0.754777\pi$
$397$	5.23204	−	17.8187i	0.262589	−	0.894294i	0.980227	−	0.197878i	$-0.0634050\pi$
$398$	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	0.584375	−	0.811484i	$-0.301340\pi$
$401$	1.78186	+	1.14513i	0.0889820	+	0.0571852i	−0.495393	+	0.868669i	$0.664976\pi$
$402$	−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	−0.881254	−	0.472642i	$-0.843300\pi$
$409$	−5.82459	+	6.72194i	−0.288008	+	0.332378i	0.593247	+	0.805021i	$0.297846\pi$
$410$	−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	−0.889462	−	0.457009i	$-0.848921\pi$
$419$	−6.35621	+	7.33546i	−0.310521	+	0.358361i	0.578941	+	0.815370i	$0.303466\pi$
$420$	9.00717	−	0.373199i	0.439505	−	0.0182102i
$421$	−14.2908	−	22.2369i	−0.696491	−	1.08376i	−0.991730	−	0.128338i	$-0.959036\pi$
$421$	−14.2908	−	22.2369i	−0.696491	−	1.08376i	0.295239	−	0.955423i	$-0.404601\pi$
$422$	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	−0.367711	−	0.929940i	$-0.619858\pi$
$431$	−24.4936	−	7.19196i	−1.17981	−	0.346424i	−0.812102	+	0.583516i	$0.801677\pi$
$432$	1.84156	−	4.85887i	0.0886023	−	0.233773i
$433$	29.4446	−	8.64570i	1.41502	−	0.415486i	0.517202	−	0.855863i	$-0.326973\pi$
$433$	29.4446	−	8.64570i	1.41502	−	0.415486i	0.897813	+	0.440377i	$0.145155\pi$
$434$	−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	−0.962818	−	0.270149i	$-0.912927\pi$
$439$	−2.41184	−	16.7747i	−0.115111	−	0.800613i	0.847708	−	0.530464i	$-0.177982\pi$
$440$	−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	0.131235	−	0.991351i	$-0.458106\pi$
$443$	−6.19490	−	1.81899i	−0.294329	−	0.0864227i	−0.425563	+	0.904929i	$0.639924\pi$
$444$	−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	0.909872	−	0.414890i	$-0.136180\pi$
$449$	35.3019	+	5.07565i	1.66600	+	0.239535i	0.756128	+	0.654424i	$0.227089\pi$
$450$	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	−0.907985	−	0.419003i	$-0.862380\pi$
$457$	0.0701152	−	0.153531i	0.00327985	−	0.00718187i	0.911265	+	0.411821i	$0.135107\pi$
$458$	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	$-0.986532\pi$
$461$		−	1.81631i		−	0.0845939i	0.999105	−	0.0422969i	$-0.0134676\pi$
$462$	−1.12742	−	0.304221i	−0.0524524	−	0.0141536i
$463$	−8.51144	−	3.88705i	−0.395560	−	0.180646i	0.207697	−	0.978193i	$-0.433403\pi$
$463$	−8.51144	−	3.88705i	−0.395560	−	0.180646i	−0.603257	+	0.797547i	$0.706131\pi$
$464$	−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	0.951788	−	0.306756i	$-0.0992435\pi$
$467$	5.99394	+	9.32675i	0.277366	+	0.431590i	−0.674422	+	0.738346i	$0.735607\pi$
$468$	−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	−0.123637	−	0.992328i	$-0.539456\pi$
$479$	6.75943	−	1.98475i	0.308846	−	0.0906855i	0.432483	+	0.901642i	$0.357638\pi$
$480$	−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	0.924056	+	0.382257i	$0.124853\pi$
$487$	7.79785	+	26.5570i	0.353354	+	1.20341i	−0.570702	+	0.821157i	$0.693329\pi$
$488$	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	−0.956311	−	0.292350i	$-0.905563\pi$
$491$	−30.1714	+	13.7788i	−1.36162	+	0.621830i	−0.405307	+	0.914181i	$0.632835\pi$
$492$	−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	−0.621207	−	0.783646i	$-0.713357\pi$
$499$	−3.71790	+	2.38935i	−0.166436	+	0.106962i	0.454771	+	0.890608i	$0.349721\pi$
$500$	−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	−0.560356	−	0.828252i	$-0.689336\pi$
$503$	−34.8360	−	15.9091i	−1.55326	−	0.709351i	−0.992906	+	0.118901i	$0.962063\pi$
$504$	−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	0.462154	−	0.886800i	$-0.347077\pi$
$509$	2.13431	+	0.974707i	0.0946016	+	0.0432031i	−0.367552	+	0.930003i	$0.619804\pi$
$510$	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	0.791015	−	0.611797i	$-0.209553\pi$
$521$	−4.32212	−	9.46411i	−0.189355	−	0.414630i	−0.980370	+	0.197167i	$0.936826\pi$
$522$	3.28482	−	13.3351i	0.143773	−	0.583660i
$523$	−1.35802	−	0.398750i	−0.0593819	−	0.0174361i	0.251907	−	0.967752i	$-0.418942\pi$
$523$	−1.35802	−	0.398750i	−0.0593819	−	0.0174361i	−0.311289	+	0.950315i	$0.600761\pi$
$524$	−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	−0.0886969	−	0.996059i	$-0.528270\pi$
$541$	6.44354	−	44.8158i	0.277029	−	1.92678i	0.365726	−	0.930722i	$-0.380821\pi$
$542$	−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	0.919078	+	0.394076i	$0.128935\pi$
$547$	33.6774	+	29.1816i	1.43994	+	1.24772i	0.520863	+	0.853640i	$0.325610\pi$
$548$	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	0.737235	−	0.675636i	$-0.236131\pi$
$557$	4.09228	+	3.54598i	0.173395	+	0.150248i	−0.563840	+	0.825884i	$0.690676\pi$
$558$	−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	−0.803256	−	0.595634i	$-0.796901\pi$
$563$	−41.3284	−	5.94212i	−1.74178	−	0.250431i	−0.938528	+	0.345203i	$0.887810\pi$
$564$	−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	0.882428	−	0.470448i	$-0.155908\pi$
$569$	32.6899	+	9.59861i	1.37043	+	0.402395i	0.488002	+	0.872842i	$0.337726\pi$
$570$	−28.1324	−	11.4651i	−1.17834	−	0.480220i
$571$	4.26062	+	14.5103i	0.178301	+	0.607239i	0.999339	+	0.0363642i	$0.0115776\pi$
$571$	4.26062	+	14.5103i	0.178301	+	0.607239i	−0.821037	+	0.570875i	$0.806604\pi$
$572$	−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	0.100286	−	0.994959i	$-0.468024\pi$
$577$	11.4536	−	1.64678i	0.476821	−	0.0685565i	0.376536	+	0.926402i	$0.377115\pi$
$578$	−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	0.816417	+	0.577462i	$0.195957\pi$
$587$	−3.14043	+	21.8422i	−0.129619	+	0.901522i	−0.946037	+	0.324060i	$0.894952\pi$
$588$	−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	−0.799155	−	0.601126i	$-0.794719\pi$
$593$	−2.20177	+	2.54098i	−0.0904159	+	0.104345i	0.708739	+	0.705471i	$0.249265\pi$
$594$	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	$0.174683\pi$
$599$			25.5342i			1.04330i	−0.853160	+	0.521649i	$0.825317\pi$
$600$	3.11244	−	8.08163i	0.127065	−	0.329931i
$601$	3.97349	−	8.70074i	0.162082	−	0.354911i	−0.811114	−	0.584889i	$-0.801138\pi$
$601$	3.97349	−	8.70074i	0.162082	−	0.354911i	0.973196	+	0.229978i	$0.0738655\pi$
$602$	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	−0.837776	−	0.546014i	$-0.816145\pi$
$607$	−10.2627	+	8.89265i	−0.416549	+	0.360941i	0.421228	+	0.906955i	$0.361599\pi$
$608$	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	0.937143	−	0.348946i	$-0.113460\pi$
$613$	1.47881	+	3.23815i	0.0597287	+	0.130788i	−0.877414	+	0.479734i	$0.840733\pi$
$614$	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	0.995272	−	0.0971303i	$-0.0309664\pi$
$617$	2.62015	+	8.92341i	0.105483	+	0.359243i	−0.889788	+	0.456373i	$0.849148\pi$
$618$	−6.41441	−	7.08110i	−0.258025	−	0.284844i
$619$	−36.3861	+	5.23154i	−1.46248	+	0.210273i	−0.827157	−	0.561971i	$-0.810043\pi$
$619$	−36.3861	+	5.23154i	−1.46248	+	0.210273i	−0.635326	+	0.772244i	$0.719134\pi$
$620$	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	−0.599205	−	0.800595i	$-0.704517\pi$
$631$	9.49427	−	14.7734i	0.377961	−	0.588118i	0.977166	+	0.212477i	$0.0681531\pi$
$632$	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	−0.922232	−	0.386637i	$-0.873637\pi$
$641$	−0.660736	+	1.44681i	−0.0260975	+	0.0571456i	0.896134	+	0.443783i	$0.146364\pi$
$642$	−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	−0.624202	−	0.781263i	$-0.714576\pi$
$647$	9.53864	−	20.8867i	0.375003	−	0.821142i	0.999205	−	0.0398784i	$-0.0126970\pi$
$648$	−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	0.798102	−	0.602522i	$-0.205838\pi$
$653$	2.25208	+	2.59904i	0.0881307	+	0.101708i	−0.709971	+	0.704231i	$0.751292\pi$
$654$	−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	0.999999	+	0.00146518i	$0.000466381\pi$
$659$	8.88848	+	19.4631i	0.346246	+	0.758173i	−0.653753	+	0.756708i	$0.726806\pi$
$660$	−0.698900	+	0.877490i	−0.0272046	+	0.0341562i
$661$	−1.46242	+	4.98055i	−0.0568816	+	0.193721i	−0.983032	−	0.183433i	$-0.941279\pi$
$661$	−1.46242	+	4.98055i	−0.0568816	+	0.193721i	0.926151	+	0.377154i	$0.123097\pi$
$662$	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	−0.384496	−	0.923127i	$-0.625625\pi$
$673$	11.3638	−	38.7016i	0.438042	−	1.49184i	0.822539	−	0.568709i	$-0.192557\pi$
$674$	−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	−0.880660	−	0.473749i	$-0.842900\pi$
$677$	−2.18258	+	3.39617i	−0.0838835	+	0.130525i	0.796776	+	0.604274i	$0.206537\pi$
$678$	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	−0.911484	−	0.411336i	$-0.865062\pi$
$683$	−23.9381	+	15.3841i	−0.915964	+	0.588654i	−0.00448020	+	0.999990i	$0.501426\pi$
$684$	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	0.859930	+	0.510413i	$0.170507\pi$
$701$	−2.88505	+	20.0659i	−0.108967	+	0.757880i	−0.968896	+	0.247467i	$0.920402\pi$
$702$	−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	0.998285	−	0.0585346i	$-0.0186428\pi$
$709$	3.37706	+	11.5012i	0.126828	+	0.431937i	−0.871457	+	0.490471i	$0.836825\pi$
$710$	−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	−0.162561	−	0.986698i	$-0.551975\pi$
$719$	13.6120	−	46.3584i	0.507643	−	1.72887i	0.670205	−	0.742176i	$-0.266206\pi$
$720$	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	0.169134	−	0.985593i	$-0.445903\pi$
$727$	−22.3926	−	25.8425i	−0.830497	−	0.958445i	−0.999631	+	0.0271481i	$0.991357\pi$
$728$	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	−0.631330	−	0.775514i	$-0.717491\pi$
$733$	9.96858	−	21.8281i	0.368198	−	0.806241i	0.999528	−	0.0307263i	$-0.00978204\pi$
$734$	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	−0.642466	−	0.766314i	$-0.722088\pi$
$739$	9.71581	−	21.2746i	0.357402	−	0.782600i	0.999867	−	0.0162861i	$-0.00518424\pi$
$740$	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	0.970007	−	0.243075i	$-0.0781561\pi$
$743$	9.42972	+	14.6729i	0.345943	+	0.538298i	−0.624064	+	0.781373i	$0.714520\pi$
$744$	−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	−0.768826	−	0.639458i	$-0.779159\pi$
$751$	−21.6229	+	9.87483i	−0.789029	+	0.360337i	−0.0202033	+	0.999796i	$0.506431\pi$
$752$	−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	0.939919	+	0.341397i	$0.110900\pi$
$757$	3.69387	+	25.6914i	0.134256	+	0.933771i	−0.805663	+	0.592374i	$0.798191\pi$
$758$		−	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	−0.201747	−	0.979438i	$-0.564662\pi$
$761$	−3.29333	+	0.473509i	−0.119383	+	0.0171647i	0.0823643	+	0.996602i	$0.473753\pi$
$762$	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	−0.101336	+	0.994852i	$0.532312\pi$
$769$	−26.7378	+	41.6048i	−0.964189	+	1.50031i	−0.862853	+	0.505455i	$0.831325\pi$
$770$	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	−0.866320	−	0.499490i	$-0.833521\pi$
$773$	−13.7681	+	11.9301i	−0.495204	+	0.429097i	0.371115	+	0.928587i	$0.378975\pi$
$774$	−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	−0.997526	−	0.0702981i	$-0.977605\pi$
$787$	−22.0495	+	25.4465i	−0.785981	+	0.907070i	0.211545	+	0.977368i	$0.432150\pi$
$788$	−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	−0.644195	−	0.764861i	$-0.722808\pi$
$797$	−13.7771	+	6.29179i	−0.488010	+	0.222867i	0.156185	+	0.987728i	$0.450080\pi$
$798$	−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	0.987608	+	0.156942i	$0.0501637\pi$
$809$	6.87263	+	23.4060i	0.241629	+	0.822912i	−0.745979	+	0.665969i	$0.768018\pi$
$810$	−0.709705	+	20.1121i	−0.0249365	+	0.706667i
$811$	17.8624	+	5.24486i	0.627232	+	0.184172i	0.579874	−	0.814706i	$-0.303102\pi$
$811$	17.8624	+	5.24486i	0.627232	+	0.184172i	0.0473579	+	0.998878i	$0.484920\pi$
$812$	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	0.452955	−	0.891533i	$-0.350370\pi$
$821$	−15.6497	−	24.3513i	−0.546177	−	0.849868i	−0.999132	+	0.0416658i	$0.986734\pi$
$822$	12.8438	+	10.6428i	0.447979	+	0.371211i
$823$	−27.6299	−	23.9414i	−0.963118	−	0.834546i	0.0231445	−	0.999732i	$-0.492632\pi$
$823$	−27.6299	−	23.9414i	−0.963118	−	0.834546i	−0.986262	+	0.165186i	$0.947178\pi$
$824$	−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	$-0.913904\pi$
$827$		−	15.3676i		−	0.534384i	0.963643	−	0.267192i	$-0.0860959\pi$
$828$	−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	0.947686	+	0.319206i	$0.103416\pi$
$839$	−1.49296	+	10.3838i	−0.0515427	+	0.358487i	−0.999228	+	0.0392816i	$0.987493\pi$
$840$	−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	−0.474971	−	0.880002i	$-0.657541\pi$
$853$	−19.9413	+	2.86713i	−0.682777	+	0.0981685i	−0.207806	+	0.978170i	$0.566632\pi$
$854$	−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	0.901332	−	0.433130i	$-0.142591\pi$
$857$	41.7283	+	12.2525i	1.42541	+	0.418539i	0.524081	+	0.851669i	$0.324409\pi$
$858$	−1.71342	+	0.285024i	−0.0584953	+	0.00973057i
$859$	2.72218	+	5.96075i	0.0928798	+	0.203378i	0.950370	−	0.311122i	$-0.100705\pi$
$859$	2.72218	+	5.96075i	0.0928798	+	0.203378i	−0.857490	+	0.514500i	$0.827977\pi$
$860$	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	0.600346	+	0.799741i	$0.295030\pi$
$863$	−5.90459	+	41.0674i	−0.200995	+	1.39795i	−0.801340	+	0.598209i	$0.795879\pi$
$864$	−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	0.944768	−	0.327739i	$-0.106287\pi$
$877$	38.9655	+	17.7950i	1.31577	+	0.600893i	0.371003	+	0.928631i	$0.379014\pi$
$878$	−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	0.338793	−	0.940861i	$-0.389981\pi$
$881$	39.6360	−	25.4725i	1.33537	−	0.858190i	0.996577	+	0.0826710i	$0.0263451\pi$
$882$	−1.77953	+	4.40008i	−0.0599199	+	0.148158i
$883$	12.0927	−	10.4784i	0.406952	−	0.352626i	−0.427203	−	0.904156i	$-0.640501\pi$
$883$	12.0927	−	10.4784i	0.406952	−	0.352626i	0.834155	+	0.551530i	$0.185956\pi$
$884$	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	0.245221	−	0.969467i	$-0.421140\pi$
$887$	−15.9268	−	10.2355i	−0.534769	−	0.343675i	−0.779990	+	0.625792i	$0.784776\pi$
$888$	−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	0.993423	+	0.114502i	$0.0365273\pi$
$907$	45.4837	+	29.2306i	1.51026	+	0.970586i	0.516838	+	0.856083i	$0.327109\pi$
$908$	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	0.921407	−	0.388599i	$-0.127041\pi$
$911$	12.2432	+	14.1294i	0.405634	+	0.468126i	−0.515773	+	0.856725i	$0.672495\pi$
$912$	−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	$-0.831949\pi$
$919$		−	30.5431i		−	1.00752i	0.863842	−	0.503762i	$-0.168051\pi$
$920$	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	−0.952583	−	0.304278i	$-0.901585\pi$
$929$	−23.9864	+	20.7844i	−0.786969	+	0.681913i	0.165614	+	0.986191i	$0.447039\pi$
$930$	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	−0.119196	−	0.992871i	$-0.538032\pi$
$937$	−23.1493	−	6.79726i	−0.756256	−	0.222057i	−0.637060	+	0.770814i	$0.719850\pi$
$938$	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	−0.879424	−	0.476040i	$-0.842072\pi$
$941$	−5.20686	−	36.2145i	−0.169739	−	1.18056i	0.709685	−	0.704519i	$-0.248837\pi$
$942$	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	−0.169564	−	0.985519i	$-0.554236\pi$
$947$	6.78864	−	1.99332i	0.220601	−	0.0647743i	0.390165	+	0.920745i	$0.372418\pi$
$948$	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	−0.389264	−	0.921126i	$-0.627271\pi$
$953$	18.8412	−	29.3176i	0.610328	−	0.949689i	0.999592	−	0.0285626i	$-0.00909300\pi$
$954$	−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	$-0.734170\pi$
$967$		−	46.1090i		−	1.48277i	0.671082	−	0.741383i	$-0.265830\pi$
$968$	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	−0.127721	−	0.991810i	$-0.540766\pi$
$971$	27.1776	−	31.3646i	0.872170	−	1.00654i	0.999892	−	0.0147279i	$-0.00468821\pi$
$972$	−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	−0.259184	−	0.965828i	$-0.583454\pi$
$977$	−24.3797	−	3.50527i	−0.779974	−	0.112143i	−0.520790	+	0.853685i	$0.674363\pi$
$978$	−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	−0.0725496	−	0.997365i	$-0.523114\pi$
$983$	16.5449	−	56.3466i	0.527699	−	1.79718i	0.600249	−	0.799813i	$-0.295068\pi$
$984$	−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	0.976774	+	0.214271i	$0.0687376\pi$
$991$	3.14592	+	21.8803i	0.0999334	+	0.695052i	−0.876841	+	0.480781i	$0.840353\pi$
$992$	−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	−0.218151	−	0.975915i	$-0.570003\pi$
$997$	11.8893	−	5.42966i	0.376537	−	0.171959i	0.594689	+	0.803956i	$0.297275\pi$
$998$	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.89.7	✓	240
3.2	odd	2		690.2.n.b.89.1	yes	240
5.4	even	2		690.2.n.b.89.18	yes	240
15.14	odd	2	inner	690.2.n.a.89.24	yes	240
23.15	odd	22	inner	690.2.n.a.659.24	yes	240
69.38	even	22		690.2.n.b.659.18	yes	240
115.84	odd	22		690.2.n.b.659.1	yes	240
345.314	even	22	inner	690.2.n.a.659.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.7	✓	240	1.1	even	1	trivial
690.2.n.a.89.24	yes	240	15.14	odd	2	inner
690.2.n.a.659.7	yes	240	345.314	even	22	inner
690.2.n.a.659.24	yes	240	23.15	odd	22	inner
690.2.n.b.89.1	yes	240	3.2	odd	2
690.2.n.b.89.18	yes	240	5.4	even	2
690.2.n.b.659.1	yes	240	115.84	odd	22
690.2.n.b.659.18	yes	240	69.38	even	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.16282 - 1.28368i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.23565 - 0.0433117i) q^{5} +(-1.10513 + 1.33367i) q^{6} +(1.95813 - 1.25842i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.295684 + 2.98539i) q^{9} +O(q^{10})\)	\(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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