LMFDB - Embedded newform 690.2.n.b.89.18

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			89.18
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(1.16282 + 1.28368i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.275295 - 2.21906i) q^{5} +(-1.10513 + 1.33367i) q^{6} +(-1.95813 + 1.25842i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.295684 + 2.98539i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(1.16282 + 1.28368i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.275295 - 2.21906i) 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} +(2.15729 - 0.588298i) 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} +(2.52845 - 2.93376i) 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} +(0.889324 + 2.05161i) q^{20} +(-3.89237 - 1.05031i) q^{21} -0.289649 q^{22} +(-4.72344 - 0.830119i) q^{23} +(0.684625 - 1.59100i) q^{24} +(-4.84843 + 1.22179i) 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} +(3.26374 + 2.08519i) 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} +(3.33156 + 3.99877i) 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} +(-1.90416 + 1.17225i) 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} +(6.70616 - 0.165724i) q^{45} +(0.149454 - 4.79350i) q^{46} +12.5393 q^{47} +(1.67224 + 0.451233i) q^{48} +(-0.657229 + 1.43913i) q^{49} +(-1.89936 - 4.62520i) 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} +(0.647554 + 0.0125452i) 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} +(-1.59949 + 3.52727i) 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} +(6.97860 + 3.35187i) 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} +(-7.20625 - 4.80311i) 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} +(-1.43131 - 1.71795i) 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} +(11.4143 + 1.86746i) 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} +(1.11842 + 6.61431i) q^{90} -8.05887i q^{91} +(4.76598 - 0.534254i) q^{92} +(0.443530 - 1.03072i) q^{93} +(1.78453 + 12.4116i) q^{94} +(16.0925 - 6.97570i) 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} - 102 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 - 102 * 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
$5$	−0.275295	−	2.21906i	−0.123116	−	0.992392i
$5$	−0.275295	−	2.21906i	−0.123116	−	0.992392i
$6$	−1.10513	+	1.33367i	−0.451167	+	0.544470i
$7$	−1.95813	+	1.25842i	−0.740105	+	0.475637i	−0.855578	−	0.517674i	$-0.826798\pi$
$7$	−1.95813	+	1.25842i	−0.740105	+	0.475637i	0.115473	+	0.993311i	$0.463162\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−0.295684	+	2.98539i	−0.0985614	+	0.995131i
$10$	2.15729	−	0.588298i	0.682195	−	0.186036i
$11$	−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	−0.997523	−	0.0703399i	$-0.977592\pi$
$13$	−1.87184	+	2.91263i	−0.519154	+	0.807819i	0.478369	+	0.878159i	$0.341228\pi$
$14$	−1.52428	−	1.75911i	−0.407381	−	0.470142i
$15$	2.52845	−	2.93376i	0.652842	−	0.757494i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−1.45726	+	4.96297i	−0.353437	+	1.20370i	0.570547	+	0.821265i	$0.306731\pi$
$17$	−1.45726	+	4.96297i	−0.353437	+	1.20370i	−0.923984	+	0.382431i	$0.875087\pi$
$18$	−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	$0.552841\pi$
$20$	0.889324	+	2.05161i	0.198859	+	0.458754i
$21$	−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
$25$	−4.84843	+	1.22179i	−0.969685	+	0.244358i
$26$	−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	$-0.0488333\pi$
$30$	3.26374	+	2.08519i	0.595874	+	0.380702i
$31$	−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
$35$	3.33156	+	3.99877i	0.563137	+	0.675916i
$36$	−0.557376	−	2.94777i	−0.0928959	−	0.491295i
$37$	6.06516	+	6.99957i	0.997107	+	1.15072i	0.988571	+	0.150759i	$0.0481717\pi$
$37$	6.06516	+	6.99957i	0.997107	+	1.15072i	0.00853621	+	0.999964i	$0.497283\pi$
$38$	−7.13499	+	3.25844i	−1.15745	+	0.528589i
$39$	−5.91551	+	0.984034i	−0.947240	+	0.157571i
$40$	−1.90416	+	1.17225i	−0.301075	+	0.185348i
$41$	−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	$-0.595903\pi$
$43$	4.06093	−	8.89220i	0.619286	−	1.35605i	0.916037	−	0.401093i	$-0.131370\pi$
$44$	−0.0412214	−	0.286701i	−0.00621435	−	0.0432218i
$45$	6.70616	−	0.165724i	0.999695	−	0.0247047i
$46$	0.149454	−	4.79350i	0.0220358	−	0.706763i
$47$	12.5393			1.82904			0.914521	−	0.404539i	$-0.132568\pi$
$47$	12.5393			1.82904			0.914521	+	0.404539i	$0.132568\pi$
$48$	1.67224	+	0.451233i	0.241367	+	0.0651299i
$49$	−0.657229	+	1.43913i	−0.0938898	+	0.205590i
$50$	−1.89936	−	4.62520i	−0.268610	−	0.654102i
$51$	−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	$0.0768660\pi$
$53$	5.71601	+	8.89428i	0.785154	+	1.22172i	−0.185831	+	0.982582i	$0.559498\pi$
$54$	−3.65477	−	3.69359i	−0.497352	−	0.502634i
$55$	0.647554	+	0.0125452i	0.0873161	+	0.00169159i
$56$	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	$0.142003\pi$
$60$	−1.59949	+	3.52727i	−0.206493	+	0.455369i
$61$	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
$65$	6.97860	+	3.35187i	0.865589	+	0.415749i
$66$	−0.336811	−	0.371818i	−0.0414585	−	0.0457676i
$67$	−1.48727	−	10.3442i	−0.181699	−	1.26374i	−0.852745	−	0.522327i	$-0.825064\pi$
$67$	−1.48727	−	10.3442i	−0.181699	−	1.26374i	0.671046	−	0.741415i	$-0.265845\pi$
$68$		−	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	$-0.786283\pi$
$73$	−3.93552	−	13.4031i	−0.460617	−	1.56872i	0.322328	−	0.946628i	$-0.395535\pi$
$74$	−6.06516	+	6.99957i	−0.705061	+	0.813684i
$75$	−7.20625	−	4.80311i	−0.832107	−	0.554616i
$76$	−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	$-0.0283962\pi$
$80$	−1.43131	−	1.71795i	−0.160025	−	0.192073i
$81$	−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	$-0.850827\pi$
$83$	−5.21189	+	4.51613i	−0.572079	+	0.495709i	0.320105	+	0.947382i	$0.396282\pi$
$84$	4.03061	−	0.0888450i	0.439775	−	0.00969378i
$85$	11.4143	+	1.86746i	1.23805	+	0.202554i
$86$	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	$0.250785\pi$
$90$	1.11842	+	6.61431i	0.117892	+	0.697210i
$91$		−	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
$95$	16.0925	−	6.97570i	1.65105	−	0.715691i
$96$	−0.208656	+	1.71944i	−0.0212958	+	0.175489i
$97$	−10.7860	+	12.4477i	−1.09515	+	1.26387i	−0.133068	+	0.991107i	$0.542483\pi$
$97$	−10.7860	+	12.4477i	−1.09515	+	1.26387i	−0.962081	+	0.272763i	$0.912063\pi$
$98$	−1.51802	−	0.445730i	−0.153343	−	0.0450255i
$99$	−0.843726	−	0.207835i	−0.0847977	−	0.0208882i
$100$	4.30781	−	2.53826i	0.430781	−	0.253826i
$101$	−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	$-0.866938\pi$
$103$	0.785042	−	5.46009i	0.0773525	−	0.537998i	0.991244	−	0.132041i	$-0.0421529\pi$
$104$	3.42701	+	0.492730i	0.336046	+	0.0483161i
$105$	−1.25914	+	8.92654i	−0.122880	+	0.871141i
$106$	−7.99028	+	6.92361i	−0.776084	+	0.672481i
$107$	−9.79086	+	4.47134i	−0.946518	+	0.432260i	−0.828023	−	0.560694i	$-0.810534\pi$
$107$	−9.79086	+	4.47134i	−0.946518	+	0.432260i	−0.118495	+	0.992955i	$0.537807\pi$
$108$	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	$0.974585\pi$
$110$	0.0797390	+	0.642748i	0.00760281	+	0.0612836i
$111$	−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	$-0.492608\pi$
$113$	3.47775	−	0.500025i	0.327159	−	0.0470384i	0.303938	+	0.952692i	$0.401699\pi$
$114$	−12.4795	−	5.37007i	−1.16882	−	0.502953i
$115$	−0.541741	+	10.7101i	−0.0505176	+	0.998723i
$116$			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
$120$	−3.71900	−	1.08123i	−0.339497	−	0.0987020i
$121$	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
$125$	4.04597	+	10.4226i	0.361883	+	0.932224i
$126$	5.70234	−	4.03043i	0.508005	−	0.359059i
$127$	14.2740	+	2.05229i	1.26661	+	0.182112i	0.742680	−	0.669647i	$-0.233555\pi$
$127$	14.2740	+	2.05229i	1.26661	+	0.182112i	0.523935	+	0.851759i	$0.324464\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	16.1369	−	5.12711i	1.42078	−	0.451417i
$130$	−2.32460	+	7.38459i	−0.203881	+	0.647672i
$131$	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
$135$	8.01081	+	8.41587i	0.689461	+	0.724323i
$136$	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	$0.483600\pi$
$140$	−4.32319	−	2.89819i	−0.365377	−	0.244941i
$141$	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
$145$	−10.1022	−	1.65279i	−0.838940	−	0.137257i
$146$	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	$0.0378677\pi$
$150$	3.72867	−	7.81646i	0.304444	−	0.638211i
$151$	−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
$155$	−1.23360	+	0.759432i	−0.0990851	+	0.0609990i
$156$	5.39866	−	2.61077i	0.432238	−	0.209028i
$157$	5.55105	−	1.62993i	0.443022	−	0.130083i	−0.0526111	−	0.998615i	$-0.516754\pi$
$157$	5.55105	−	1.62993i	0.443022	−	0.130083i	0.495633	+	0.868532i	$0.334936\pi$
$158$	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	$-0.553918\pi$
$163$	−0.671948	+	0.0966116i	−0.0526310	+	0.00756720i	0.115949	+	0.993255i	$0.463009\pi$
$164$	7.25428	+	3.31292i	0.566464	+	0.258695i
$165$	0.736886	+	0.845841i	0.0573665	+	0.0658487i
$166$	−5.21189	−	4.51613i	−0.404521	−	0.350519i
$167$	8.16570	+	2.39767i	0.631881	+	0.185537i	0.581962	−	0.813216i	$-0.302285\pi$
$167$	8.16570	+	2.39767i	0.631881	+	0.185537i	0.0499193	+	0.998753i	$0.484104\pi$
$168$	0.661556	+	3.97694i	0.0510402	+	0.306827i
$169$	0.420735	+	0.921282i	0.0323643	+	0.0708678i
$170$	−0.224029	+	11.5639i	−0.0171823	+	0.886908i
$171$	−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	$-0.647792\pi$
$173$	3.07473	−	21.3852i	0.233767	−	1.62589i	0.681568	−	0.731755i	$-0.261298\pi$
$174$	4.43278	+	6.57433i	0.336048	+	0.498399i
$175$	7.95634	−	8.49377i	0.601443	−	0.642068i
$176$	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	$0.545338\pi$
$180$	−6.38782	+	2.04835i	−0.476120	+	0.152675i
$181$	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
$190$	9.19489	+	14.9359i	0.667067	+	1.08356i
$191$	−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	−0.706593	−	0.707620i	$-0.749769\pi$
$193$	−1.48280	+	1.28486i	−0.106735	+	0.0924860i	0.599859	+	0.800106i	$0.295223\pi$
$194$	−13.8560	−	8.90470i	−0.994801	−	0.639320i
$195$	3.81214	+	12.8560i	0.272993	+	0.920634i
$196$	0.225157	−	1.56600i	0.0160826	−	0.111857i
$197$	−3.09802	−	1.99098i	−0.220725	−	0.141851i	0.425606	−	0.904909i	$-0.360061\pi$
$197$	−3.09802	−	1.99098i	−0.220725	−	0.141851i	−0.646331	+	0.763057i	$0.723697\pi$
$198$	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	$0.501110\pi$
$200$	3.12549	+	3.90273i	0.221005	+	0.275965i
$201$	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
$205$	−9.92977	+	14.8121i	−0.693525	+	1.03452i
$206$	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
$210$	−9.01487	+	0.0240539i	−0.622085	+	0.00165987i
$211$	−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
$215$	−20.8502	−	6.56346i	−1.42198	−	0.447624i
$216$	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
$220$	−0.624857	+	0.170400i	−0.0421279	+	0.0114884i
$221$	−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	$-0.185084\pi$
$223$	−0.165666	−	0.257781i	−0.0110938	−	0.0172623i	−0.846756	+	0.531981i	$0.821448\pi$
$224$	−2.23335	−	0.655771i	−0.149222	−	0.0438156i
$225$	−2.21392	−	14.8357i	−0.147595	−	0.989048i
$226$	0.989872	+	3.37119i	0.0658453	+	0.224248i
$227$	0.487984	+	0.222855i	0.0323886	+	0.0147914i	0.431543	−	0.902092i	$-0.357969\pi$
$227$	0.487984	+	0.222855i	0.0323886	+	0.0147914i	−0.399155	+	0.916884i	$0.630696\pi$
$228$	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	$0.723922\pi$
$230$	−10.6782	+	0.987981i	−0.704099	+	0.0651455i
$231$	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	$-0.758157\pi$
$233$	4.12602	−	9.03471i	0.270304	−	0.591884i	0.995297	+	0.0968730i	$0.0308841\pi$
$234$	5.22503	−	8.97685i	0.341571	−	0.586835i
$235$	−3.45200	−	27.8254i	−0.225184	−	1.81513i
$236$	−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	$0.202398\pi$
$240$	0.540952	−	3.83502i	0.0349183	−	0.247549i
$241$	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
$245$	3.37444	+	1.06224i	0.215585	+	0.0678642i
$246$	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
$250$	−9.74069	+	5.48808i	−0.616055	+	0.347096i
$251$	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
$255$	10.8756	+	16.8238i	0.681055	+	1.05355i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	5.48842	−	1.61155i	0.342358	−	0.100525i	−0.106034	−	0.994363i	$-0.533815\pi$
$257$	5.48842	−	1.61155i	0.342358	−	0.100525i	0.448392	+	0.893837i	$0.351997\pi$
$258$	7.37144	+	15.2430i	0.458926	+	0.948988i
$259$	−20.6848	−	6.07360i	−1.28529	−	0.377395i
$260$	−7.64025	−	1.25000i	−0.473828	−	0.0775217i
$261$	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	$-0.960723\pi$
$263$	−7.59268	+	11.8144i	−0.468185	+	0.728510i	0.524212	+	0.851588i	$0.324360\pi$
$264$	0.427921	+	0.261866i	0.0263367	+	0.0161167i
$265$	18.1633	−	15.1327i	1.11576	−	0.929594i
$266$	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	$0.778945\pi$
$270$	−7.19015	+	9.12698i	−0.437579	+	0.555450i
$271$	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	$-0.975534\pi$
$277$		−	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
$280$	2.25343	−	4.69165i	0.134668	−	0.280379i
$281$	−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	−0.275337	−	0.961348i	$-0.588789\pi$
$283$	8.15487	−	5.24082i	0.484757	−	0.311534i	0.760094	+	0.649814i	$0.225153\pi$
$284$	−7.59074	+	3.46657i	−0.450427	+	0.205703i
$285$	27.6673	+	12.5461i	1.63887	+	0.743167i
$286$	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
$290$	0.198276	−	10.2346i	0.0116432	−	0.600994i
$291$	−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	$-0.766609\pi$
$293$	4.17455	−	14.2172i	0.243880	−	0.830579i	0.986903	−	0.161313i	$-0.0515729\pi$
$294$	−1.19301	−	2.46696i	−0.0695777	−	0.143876i
$295$	−3.86306	−	1.85546i	−0.224916	−	0.108029i
$296$	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
$300$	8.26754	+	2.57832i	0.477327	+	0.148859i
$301$	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
$305$	−6.64120	−	10.7878i	−0.380274	−	0.617706i
$306$	3.71147	−	15.0671i	0.212171	−	0.861328i
$307$	13.6752	−	6.24526i	0.780485	−	0.356436i	0.0149985	−	0.999888i	$-0.495226\pi$
$307$	13.6752	−	6.24526i	0.780485	−	0.356436i	0.765486	+	0.643452i	$0.222498\pi$
$308$	0.441506	+	0.509525i	0.0251571	+	0.0290329i
$309$	7.92189	−	5.34137i	0.450660	−	0.303860i
$310$	−0.927262	−	1.11296i	−0.0526649	−	0.0632121i
$311$	−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	0.999657	−	0.0261966i	$-0.00833958\pi$
$313$	14.7100	+	16.9763i	0.831461	+	0.959557i	−0.168196	+	0.985754i	$0.553794\pi$
$314$	2.40334	+	5.26258i	0.135628	+	0.296985i
$315$	−12.9230	+	8.76365i	−0.728129	+	0.493775i
$316$	−3.07222	+	10.4630i	−0.172826	+	0.588591i
$317$	−11.3013	+	13.0424i	−0.634747	+	0.732537i	−0.978437	−	0.206547i	$-0.933778\pi$
$317$	−11.3013	+	13.0424i	−0.634747	+	0.732537i	0.343690	+	0.939083i	$0.388323\pi$
$318$	−18.1790	−	2.20604i	−1.01943	−	0.123709i
$319$	1.20616	+	0.550833i	0.0675318	+	0.0308407i
$320$	1.85733	+	1.24512i	0.103828	+	0.0696043i
$321$	−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
$325$	5.51682	−	16.4087i	0.306018	−	0.910189i
$326$	−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
$330$	−0.732362	+	0.849762i	−0.0403152	+	0.0467778i
$331$	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
$335$	−22.5449	+	6.14803i	−1.23176	+	0.335903i
$336$	−3.84231	+	1.22080i	−0.209615	+	0.0666001i
$337$	2.09756	+	4.59302i	0.114261	+	0.250198i	0.958119	−	0.286369i	$-0.0924483\pi$
$337$	2.09756	+	4.59302i	0.114261	+	0.250198i	−0.843858	+	0.536567i	$0.819721\pi$
$338$	−0.852028	+	0.547565i	−0.0463442	+	0.0297836i
$339$	4.68589	+	3.88289i	0.254502	+	0.210890i
$340$	−11.4780	+	1.42396i	−0.622485	+	0.0772252i
$341$	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
$345$	−14.3783	+	11.7585i	−0.774104	+	0.633059i
$346$	21.6051			1.16150
$347$	−3.28092	−	22.8193i	−0.176129	−	1.22500i	−0.865617	−	0.500706i	$-0.833074\pi$
$347$	−3.28092	−	22.8193i	−0.176129	−	1.22500i	0.689488	−	0.724297i	$-0.257835\pi$
$348$	−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	$0.474688\pi$
$350$	9.53962	+	6.66657i	0.509914	+	0.356343i
$351$	−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	$-0.0922528\pi$
$353$	2.15627	+	4.72158i	0.114767	+	0.251304i	−0.843528	+	0.537085i	$0.819526\pi$
$354$	1.00520	+	3.16372i	0.0534255	+	0.168150i
$355$	−4.90925	−	18.0023i	−0.260556	−	0.955461i
$356$	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	$0.785739\pi$
$360$	−2.93659	−	6.03129i	−0.154772	−	0.317877i
$361$	−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
$365$	−28.6589	+	12.4230i	−1.50008	+	0.650247i
$366$	−2.55640	+	9.47385i	−0.133625	+	0.495206i
$367$	8.16857			0.426396			0.213198	−	0.977009i	$-0.431612\pi$
$367$	8.16857			0.426396			0.213198	+	0.977009i	$0.431612\pi$
$368$	−4.42241	+	1.85534i	−0.230534	+	0.0967165i
$369$	17.3733	−	16.4490i	0.904417	−	0.856299i
$370$	17.2022	+	11.5320i	0.894298	+	0.599520i
$371$	−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	$-0.477590\pi$
$373$	20.2345	−	23.3518i	1.04770	−	1.20911i	0.977359	−	0.211590i	$-0.0678641\pi$
$374$	0.422094	−	1.43752i	0.0218259	−	0.0743324i
$375$	−8.67454	+	17.3134i	−0.447951	+	0.894058i
$376$	−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	$0.436661\pi$
$380$	−13.4753	+	11.2269i	−0.691269	+	0.575928i
$381$	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	$-0.676161\pi$
$383$	−4.43983	+	2.02760i	−0.226865	+	0.103606i	0.298740	+	0.954335i	$0.403434\pi$
$384$	−0.284218	−	1.70857i	−0.0145039	−	0.0871902i
$385$	−1.28378	+	0.790327i	−0.0654277	+	0.0402788i
$386$	−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	$-0.169963\pi$
$390$	−12.1826	+	5.60293i	−0.616889	+	0.283715i
$391$	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
$395$	−21.9799	−	10.5571i	−1.10593	−	0.531185i
$396$	0.868103	−	0.0382891i	0.0436238	−	0.00192410i
$397$	−5.23204	+	17.8187i	−0.262589	+	0.894294i	0.717638	+	0.696416i	$0.245223\pi$
$397$	−5.23204	+	17.8187i	−0.262589	+	0.894294i	−0.980227	+	0.197878i	$0.936595\pi$
$398$	−6.38483	−	9.93499i	−0.320043	−	0.497996i
$399$	−0.696884	−	31.6154i	−0.0348878	−	1.58275i
$400$	−3.41820	+	3.64909i	−0.170910	+	0.182455i
$401$	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
$405$	−1.48815	+	20.0695i	−0.0739468	+	0.997262i
$406$	−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	$0.297846\pi$
$410$	−16.0745	−	7.72071i	−0.793864	−	0.381299i
$411$	−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	$0.303466\pi$
$420$	−1.30676	−	8.91969i	−0.0637633	−	0.435236i
$421$	−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
$425$	1.00170	−	25.8430i	0.0485896	−	1.25357i
$426$	−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
$430$	3.52935	−	21.5721i	0.170200	−	1.04030i
$431$	−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	−0.897813	−	0.440377i	$-0.854845\pi$
$433$	−29.4446	+	8.64570i	−1.41502	+	0.415486i	−0.517202	+	0.855863i	$0.673027\pi$
$434$	−0.626423	+	1.37167i	−0.0300693	+	0.0658425i
$435$	−9.62538	−	14.8899i	−0.461502	−	0.713915i
$436$		−	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	$-0.177982\pi$
$440$	−0.257592	−	0.594247i	−0.0122802	−	0.0283296i
$441$	−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	$-0.360076\pi$
$443$	6.19490	+	1.81899i	0.294329	+	0.0864227i	−0.131235	+	0.991351i	$0.541894\pi$
$444$	−2.63236	−	15.8244i	−0.124926	−	0.750992i
$445$	14.1565	+	4.45634i	0.671084	+	0.211251i
$446$	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	$0.227089\pi$
$450$	14.3696	−	4.30273i	0.677391	−	0.202833i
$451$	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
$455$	−17.8831	+	2.21857i	−0.838372	+	0.104008i
$456$	13.4869	+	1.63666i	0.631584	+	0.0766435i
$457$	−0.0701152	+	0.153531i	−0.00327985	+	0.00718187i	−0.911265	−	0.411821i	$-0.864893\pi$
$457$	−0.0701152	+	0.153531i	−0.00327985	+	0.00718187i	0.907985	+	0.419003i	$0.137620\pi$
$458$	−22.8456	+	3.28470i	−1.06750	+	0.153484i
$459$	−9.25940	−	25.2317i	−0.432192	−	1.17772i
$460$	−2.49759	−	10.4289i	−0.116451	−	0.486250i
$461$		−	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	0.603257	−	0.797547i	$-0.293869\pi$
$463$	8.51144	+	3.88705i	0.395560	+	0.180646i	−0.207697	+	0.978193i	$0.566597\pi$
$464$	−1.28974	−	4.39246i	−0.0598748	−	0.203915i
$465$	−2.40933	−	0.700465i	−0.111730	−	0.0324833i
$466$	9.52995	+	2.79824i	0.441466	+	0.129626i
$467$	−5.99394	−	9.32675i	−0.277366	−	0.431590i	0.674422	−	0.738346i	$-0.264393\pi$
$467$	−5.99394	−	9.32675i	−0.277366	−	0.431590i	−0.951788	+	0.306756i	$0.900757\pi$
$468$	9.62908	+	3.89430i	0.445104	+	0.180014i
$469$	15.9296	+	18.3837i	0.735558	+	0.848880i
$470$	27.0509	−	7.37683i	1.24776	−	0.340268i
$471$	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
$475$	−19.9096	−	33.7897i	−0.913517	−	1.55038i
$476$	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	$0.357638\pi$
$480$	3.87297	−	0.0103340i	0.176776	−	0.000471681i
$481$	−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
$485$	30.5914	+	20.5079i	1.38908	+	0.931216i
$486$	12.1075	−	9.81880i	0.549207	−	0.445390i
$487$	−7.79785	−	26.5570i	−0.353354	−	1.20341i	−0.924056	−	0.382257i	$-0.875147\pi$
$487$	−7.79785	−	26.5570i	−0.353354	−	1.20341i	0.570702	−	0.821157i	$-0.306671\pi$
$488$	−4.28160	−	3.71002i	−0.193819	−	0.167945i
$489$	−0.905376	−	0.750226i	−0.0409425	−	0.0339264i
$490$	−0.571197	+	3.49127i	−0.0258040	+	0.157719i
$491$	−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
$495$	−0.228924	+	1.92949i	−0.0102894	+	0.0867242i
$496$	−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	$0.349721\pi$
$500$	−6.81846	−	8.86051i	−0.304931	−	0.396254i
$501$	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	$-0.0379372\pi$
$503$	34.8360	+	15.9091i	1.55326	+	0.709351i	0.560356	+	0.828252i	$0.310664\pi$
$504$	−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	$0.619804\pi$
$510$	−15.1049	+	13.1592i	−0.668854	+	0.582697i
$511$	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
$515$	−12.3324	−	0.238917i	−0.543429	−	0.0105280i
$516$	−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
$520$	0.149956	−	7.74038i	0.00657600	−	0.339438i
$521$	−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	0.311289	−	0.950315i	$-0.399239\pi$
$523$	1.35802	+	0.398750i	0.0593819	+	0.0174361i	−0.251907	+	0.967752i	$0.581058\pi$
$524$	−5.82793	−	5.04993i	−0.254594	−	0.220607i
$525$	20.1551	+	0.336673i	0.879642	+	0.0146936i
$526$	−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
$535$	12.6175	+	20.4955i	0.545503	+	0.886099i
$536$	−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
$540$	−10.0573	−	5.81806i	−0.432799	−	0.250370i
$541$	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
$545$	16.4665	+	2.69404i	0.705347	+	0.115400i
$546$	10.7479	+	8.90610i	0.459968	+	0.381146i
$547$	−33.6774	−	29.1816i	−1.43994	−	1.24772i	−0.919078	−	0.394076i	$-0.871065\pi$
$547$	−33.6774	−	29.1816i	−1.43994	−	1.24772i	−0.520863	−	0.853640i	$-0.674390\pi$
$548$	−2.71319	−	9.24029i	−0.115902	−	0.394726i
$549$	5.50228	+	16.0808i	0.234831	+	0.686312i
$550$	1.40434	−	0.353891i	0.0598813	−	0.0150899i
$551$	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
$555$	35.8705	−	0.0957112i	1.52262	−	0.00406272i
$556$	−1.16515	+	0.342119i	−0.0494133	+	0.0145091i
$557$	−4.09228	−	3.54598i	−0.173395	−	0.150248i	0.563840	−	0.825884i	$-0.309324\pi$
$557$	−4.09228	−	3.54598i	−0.173395	−	0.150248i	−0.737235	+	0.675636i	$0.763869\pi$
$558$	0.884487	+	1.73060i	0.0374433	+	0.0732623i
$559$	18.2983	+	28.4727i	0.773936	+	1.20427i
$560$	4.96459	+	1.56280i	0.209792	+	0.0660405i
$561$	−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	$-0.112190\pi$
$563$	41.3284	+	5.94212i	1.74178	+	0.250431i	0.803256	+	0.595634i	$0.203099\pi$
$564$	−18.5252	−	11.3365i	−0.780053	−	0.477353i
$565$	−2.06699	−	7.57968i	−0.0869591	−	0.318879i
$566$	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	$0.337726\pi$
$570$	−8.48094	+	29.1711i	−0.355228	+	1.22184i
$571$	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
$575$	23.9155	−	1.74629i	0.997345	−	0.0728252i
$576$	−2.06258	−	2.17848i	−0.0859407	−	0.0907700i
$577$	−11.4536	+	1.64678i	−0.476821	+	0.0685565i	−0.376536	−	0.926402i	$-0.622885\pi$
$577$	−11.4536	+	1.64678i	−0.476821	+	0.0685565i	−0.100286	+	0.994959i	$0.531976\pi$
$578$	4.05223	−	8.87315i	0.168551	−	0.369074i
$579$	−3.37359	−	0.409389i	−0.140201	−	0.0170136i
$580$	10.1586	−	1.26027i	0.421813	−	0.0523299i
$581$	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
$585$	−12.0701	+	19.8428i	−0.499038	+	0.820398i
$586$	14.6666	+	2.10874i	0.605872	+	0.0871112i
$587$	3.14043	−	21.8422i	0.129619	−	0.901522i	−0.816417	−	0.577462i	$-0.804043\pi$
$587$	3.14043	−	21.8422i	0.129619	−	0.901522i	0.946037	−	0.324060i	$-0.105048\pi$
$588$	2.27206	−	1.53195i	0.0936983	−	0.0631765i
$589$	3.84039	−	3.32772i	0.158240	−	0.137116i
$590$	1.28680	−	4.08780i	0.0529767	−	0.168292i
$591$	−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	$-0.750735\pi$
$593$	2.20177	−	2.54098i	0.0904159	−	0.104345i	0.799155	+	0.601126i	$0.205281\pi$
$594$	1.20961	−	0.895572i	0.0496310	−	0.0367458i
$595$	−24.7007	+	10.7072i	−1.01263	+	0.438952i
$596$	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	$0.825317\pi$
$600$	−1.37548	+	8.55032i	−0.0561537	+	0.349066i
$601$	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
$605$	3.94111	−	24.0889i	0.160229	−	0.979352i
$606$	−0.426662	−	19.3563i	−0.0173320	−	0.786295i
$607$	10.2627	−	8.89265i	0.416549	−	0.360941i	−0.421228	−	0.906955i	$-0.638401\pi$
$607$	10.2627	−	8.89265i	0.416549	−	0.360941i	0.837776	+	0.546014i	$0.183855\pi$
$608$	−4.24069	+	6.59864i	−0.171983	+	0.267610i
$609$	−9.63358	+	15.7424i	−0.390372	+	0.637916i
$610$	9.73283	−	8.10886i	0.394071	−	0.328318i
$611$	−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	$-0.159267\pi$
$613$	−1.47881	−	3.23815i	−0.0597287	−	0.130788i	−0.937143	+	0.348946i	$0.886540\pi$
$614$	8.12787	+	12.6472i	0.328014	+	0.510400i
$615$	−30.5607	+	4.47722i	−1.23232	+	0.180539i
$616$	−0.441506	+	0.509525i	−0.0177888	+	0.0205293i
$617$	−2.62015	−	8.92341i	−0.105483	−	0.359243i	0.889788	−	0.456373i	$-0.150852\pi$
$617$	−2.62015	−	8.92341i	−0.105483	−	0.359243i	−0.995272	+	0.0971303i	$0.969034\pi$
$618$	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
$625$	22.0145	−	11.8475i	0.880578	−	0.473901i
$626$	−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
$630$	−10.5136	−	11.5443i	−0.418871	−	0.459935i
$631$	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
$635$	0.624589	−	32.2398i	0.0247861	−	1.27940i
$636$	−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
$640$	−0.968120	+	2.01563i	−0.0382683	+	0.0796746i
$641$	−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	$-0.527682\pi$
$643$	−4.40482			−0.173709			−0.0868546	+	0.996221i	$0.527682\pi$
$644$	−8.66011	+	7.04373i	−0.341256	+	0.277562i
$645$	−15.8198	−	34.3973i	−0.622902	−	1.35439i
$646$	−5.77401	−	40.1591i	−0.227175	−	1.58004i
$647$	−9.53864	+	20.8867i	−0.375003	+	0.821142i	0.624202	+	0.781263i	$0.285424\pi$
$647$	−9.53864	+	20.8867i	−0.375003	+	0.821142i	−0.999205	+	0.0398784i	$0.987303\pi$
$648$	2.06017	+	8.76103i	0.0809312	+	0.344166i
$649$	0.419538	+	0.363532i	0.0164683	+	0.0142699i
$650$	17.0268	+	3.12547i	0.667845	+	0.122591i
$651$	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	$-0.248708\pi$
$653$	−2.25208	−	2.59904i	−0.0881307	−	0.101708i	−0.798102	+	0.602522i	$0.794162\pi$
$654$	−7.22540	−	10.7161i	−0.282536	−	0.419034i
$655$	13.2479	−	11.0375i	0.517639	−	0.431269i
$656$	−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	$0.726806\pi$
$660$	−0.945338	−	0.603974i	−0.0367972	−	0.0235097i
$661$	−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
$665$	−22.7328	+	33.9103i	−0.881542	+	1.31499i
$666$	−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
$670$	−9.29393	−	21.4404i	−0.359056	−	0.828317i
$671$	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	$0.374375\pi$
$673$	−11.3638	+	38.7016i	−0.438042	+	1.49184i	−0.822539	+	0.568709i	$0.807443\pi$
$674$	−4.24776	+	2.72987i	−0.163617	+	0.105151i
$675$	16.4700	−	20.0933i	0.633929	−	0.773391i
$676$	−0.663248	−	0.765429i	−0.0255095	−	0.0294396i
$677$	2.18258	−	3.39617i	0.0838835	−	0.130525i	−0.796776	−	0.604274i	$-0.793463\pi$
$677$	2.18258	−	3.39617i	0.0838835	−	0.130525i	0.880660	+	0.473749i	$0.157100\pi$
$678$	−3.17650	+	5.19078i	−0.121993	+	0.199351i
$679$	5.45602	−	37.9474i	0.209383	−	1.45629i
$680$	−3.04296	−	11.1586i	−0.116692	−	0.427912i
$681$	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	$-0.498574\pi$
$683$	23.9381	−	15.3841i	0.915964	−	0.588654i	0.911484	+	0.411336i	$0.134938\pi$
$684$	20.9534	−	10.7090i	0.801175	−	0.409469i
$685$	21.3704	−	2.65120i	0.816520	−	0.101297i
$686$	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
$690$	−13.6851	−	12.5586i	−0.520983	−	0.478097i
$691$	−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
$695$	−0.334301	−	2.69469i	−0.0126808	−	0.102215i
$696$	−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
$700$	−5.24108	+	10.3913i	−0.198094	+	0.392753i
$701$	−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
$705$	31.7049	−	36.7873i	1.19407	−	1.38549i
$706$	−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	$0.836825\pi$
$710$	17.1204	−	7.42127i	0.642516	−	0.278515i
$711$	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
$715$	−1.24865	+	1.86260i	−0.0466970	+	0.0696574i
$716$	−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	$-0.266206\pi$
$720$	5.55198	−	3.76504i	0.206910	−	0.140315i
$721$	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
$725$	−0.886552	+	22.8723i	−0.0329257	+	0.849456i
$726$	−15.6767	+	10.5701i	−0.581815	+	0.392292i
$727$	22.3926	+	25.8425i	0.830497	+	0.958445i	0.999631	−	0.0271481i	$-0.00864257\pi$
$727$	22.3926	+	25.8425i	0.830497	+	0.958445i	−0.169134	+	0.985593i	$0.554097\pi$
$728$	−7.33061	+	3.34778i	−0.271690	+	0.124077i
$729$	7.88007	−	25.8245i	0.291854	−	0.956463i
$730$	−16.3751	−	26.5992i	−0.606069	−	0.984481i
$731$	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	$0.282509\pi$
$733$	−9.96858	+	21.8281i	−0.368198	+	0.806241i	−0.999528	+	0.0307263i	$0.990218\pi$
$734$	1.16251	+	8.08542i	0.0429090	+	0.298438i
$735$	2.56030	+	5.56692i	0.0944381	+	0.205339i
$736$	−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	$-0.00518424\pi$
$740$	−8.96649	+	18.6682i	−0.329615	+	0.686258i
$741$	−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	$-0.285480\pi$
$743$	−9.42972	−	14.6729i	−0.345943	−	0.538298i	−0.970007	+	0.243075i	$0.921844\pi$
$744$	−1.12182	+	0.0247279i	−0.0411281	+	0.000906569i
$745$	−1.30076	−	0.0252000i	−0.0476563	−	0.000923256i
$746$	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
$750$	−18.3717	−	6.12229i	−0.670838	−	0.223555i
$751$	−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
$755$	−14.6806	+	30.5650i	−0.534281	+	1.11237i
$756$	−0.926550	+	12.0592i	−0.0336983	+	0.438590i
$757$	−3.69387	−	25.6914i	−0.134256	−	0.933771i	−0.939919	−	0.341397i	$-0.889100\pi$
$757$	−3.69387	−	25.6914i	−0.134256	−	0.933771i	0.805663	−	0.592374i	$-0.201809\pi$
$758$			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
$765$	−8.95012	+	33.5239i	−0.323592	+	1.21206i
$766$	−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	$0.831325\pi$
$770$	−0.964984	−	1.15824i	−0.0347756	−	0.0417401i
$771$	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	$-0.621025\pi$
$773$	13.7681	−	11.9301i	0.495204	−	0.429097i	0.866320	+	0.499490i	$0.166479\pi$
$774$	−10.9955	+	27.1875i	−0.395225	+	0.977235i
$775$	2.02483	+	2.52836i	0.0727339	+	0.0908213i
$776$	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
$780$	−7.27966	−	11.2612i	−0.260654	−	0.403215i
$781$			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
$785$	−5.14509	−	11.8694i	−0.183636	−	0.423636i
$786$	−13.2594	−	1.60904i	−0.472946	−	0.0573925i
$787$	22.0495	−	25.4465i	0.785981	−	0.907070i	−0.211545	−	0.977368i	$-0.567850\pi$
$787$	22.0495	−	25.4465i	0.785981	−	0.907070i	0.997526	+	0.0702981i	$0.0223951\pi$
$788$	3.53346	+	1.03752i	0.125874	+	0.0369600i
$789$	−23.9949	+	3.99151i	−0.854243	+	0.142102i
$790$	7.32157	−	23.2586i	0.260490	−	0.827502i
$791$	−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
$795$	40.5463	+	5.71930i	1.43803	+	0.202843i
$796$	8.92521	−	7.73374i	0.316346	−	0.274115i
$797$	13.7771	−	6.29179i	0.488010	−	0.222867i	−0.156185	−	0.987728i	$-0.549920\pi$
$797$	13.7771	−	6.29179i	0.488010	−	0.222867i	0.644195	+	0.764861i	$0.277192\pi$
$798$	31.1944	−	5.18912i	1.10427	−	0.183693i
$799$	−18.2730	+	62.2320i	−0.646451	+	2.20161i
$800$	−4.09841	−	2.86409i	−0.144901	−	0.101261i
$801$	−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
$805$	−12.4170	−	21.6536i	−0.437641	−	0.763188i
$806$			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	$0.768018\pi$
$810$	−20.0770	+	1.38319i	−0.705435	+	0.0486002i
$811$	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
$815$	0.399371	+	1.46449i	0.0139893	+	0.0512990i
$816$	−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
$820$	5.35448	−	17.0097i	0.186987	−	0.594004i
$821$	−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	0.986262	−	0.165186i	$-0.0528223\pi$
$823$	27.6299	+	23.9414i	0.963118	+	0.834546i	−0.0231445	+	0.999732i	$0.507368\pi$
$824$	−5.29279	+	1.55410i	−0.184383	+	0.0541397i
$825$	1.67411	−	1.86805i	0.0582850	−	0.0650371i
$826$	−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	$0.746591\pi$
$830$	−8.58673	+	12.8087i	−0.298050	+	0.444598i
$831$	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
$835$	3.07258	−	18.7802i	0.106331	−	0.649916i
$836$	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	$0.987493\pi$
$840$	8.64293	−	2.56286i	0.298209	−	0.0884271i
$841$	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
$845$	1.92855	−	1.18726i	0.0663441	−	0.0408430i
$846$	−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	$-0.433368\pi$
$853$	19.9413	−	2.86713i	0.682777	−	0.0981685i	0.474971	+	0.880002i	$0.342459\pi$
$854$	−11.9952	−	5.47804i	−0.410469	−	0.187455i
$855$	16.0669	+	50.1049i	0.549477	+	1.71355i
$856$	8.13454	+	7.04862i	0.278033	+	0.240917i
$857$	−41.7283	−	12.2525i	−1.42541	−	0.418539i	−0.524081	−	0.851669i	$-0.675591\pi$
$857$	−41.7283	−	12.2525i	−1.42541	−	0.418539i	−0.901332	+	0.433130i	$0.857409\pi$
$858$	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	$0.827977\pi$
$860$	21.8548	+	0.423398i	0.745243	+	0.0144377i
$861$	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	$-0.704970\pi$
$863$	5.90459	−	41.0674i	0.200995	−	1.39795i	0.801340	−	0.598209i	$-0.204121\pi$
$864$	−5.07150	−	1.13133i	−0.172536	−	0.0384886i
$865$	−48.3015	−	0.935754i	−1.64230	−	0.0318166i
$866$	−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
$870$	13.3685	−	11.6465i	0.453234	−	0.394852i
$871$	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	$-0.620986\pi$
$877$	−38.9655	−	17.7950i	−1.31577	−	0.600893i	−0.944768	+	0.327739i	$0.893713\pi$
$878$	16.2607	−	4.77458i	0.548773	−	0.161134i
$879$	23.1047	−	11.1733i	0.779301	−	0.376866i
$880$	0.551539	−	0.339540i	0.0185924	−	0.0114459i
$881$	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	−0.834155	−	0.551530i	$-0.814044\pi$
$883$	−12.0927	+	10.4784i	−0.406952	+	0.352626i	0.427203	+	0.904156i	$0.359499\pi$
$884$	15.0656	+	9.68205i	0.506710	+	0.325643i
$885$	−2.11024	−	7.11651i	−0.0709348	−	0.239219i
$886$	−0.918846	+	6.39072i	−0.0308692	+	0.214700i
$887$	15.9268	+	10.2355i	0.534769	+	0.343675i	0.779990	−	0.625792i	$-0.215224\pi$
$887$	15.9268	+	10.2355i	0.534769	+	0.343675i	−0.245221	+	0.969467i	$0.578860\pi$
$888$	15.2887	−	4.85761i	0.513055	−	0.163011i
$889$	−30.5331	+	13.9440i	−1.02405	+	0.467666i
$890$	−2.39630	+	14.6466i	−0.0803241	+	0.490957i
$891$	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
$895$	18.0228	−	26.8844i	0.602436	−	0.898648i
$896$	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
$900$	6.30395	+	13.6110i	0.210132	+	0.453701i
$901$	−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
$905$	7.97610	−	25.3378i	0.265135	−	0.842258i
$906$	25.0318	−	7.95323i	0.831625	−	0.264228i
$907$	−45.4837	−	29.2306i	−1.51026	−	0.970586i	−0.993423	−	0.114502i	$-0.963473\pi$
$907$	−45.4837	−	29.2306i	−1.51026	−	0.970586i	−0.516838	−	0.856083i	$-0.672891\pi$
$908$	−0.531003	−	0.0763467i	−0.0176219	−	0.00253365i
$909$	−19.3554	−	27.3845i	−0.641979	−	0.908286i
$910$	−4.74102	−	17.3853i	−0.157163	−	0.576318i
$911$	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
$915$	6.12554	−	21.0695i	0.202504	−	0.696535i
$916$	−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	$-0.168051\pi$
$920$	9.96731	−	3.95636i	0.328612	−	0.130437i
$921$	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
$925$	−37.9585	−	26.5265i	−1.24807	−	0.872187i
$926$	−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	$0.447039\pi$
$930$	0.350452	−	2.48449i	0.0114918	−	0.0814697i
$931$	−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
$935$	−1.00591	+	3.19551i	−0.0328969	+	0.104504i
$936$	−2.48431	+	10.0853i	−0.0812021	+	0.329648i
$937$	23.1493	+	6.79726i	0.756256	+	0.222057i	0.637060	−	0.770814i	$-0.280150\pi$
$937$	23.1493	+	6.79726i	0.756256	+	0.222057i	0.119196	+	0.992871i	$0.461968\pi$
$938$	−15.9296	+	18.3837i	−0.520118	+	0.600248i
$939$	−4.68700	+	38.6235i	−0.152954	+	1.26043i
$940$	11.1515	+	25.7257i	0.363721	+	0.839080i
$941$	−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
$945$	−26.2769	−	6.39846i	−0.854788	−	0.208142i
$946$	−1.17625	+	2.57562i	−0.0382430	+	0.0837406i
$947$	−6.78864	+	1.99332i	−0.220601	+	0.0647743i	−0.390165	−	0.920745i	$-0.627582\pi$
$947$	−6.78864	+	1.99332i	−0.220601	+	0.0647743i	0.169564	+	0.985519i	$0.445764\pi$
$948$	−17.0036	+	8.22288i	−0.552253	+	0.267067i
$949$	46.4051	+	13.6258i	1.50637	+	0.442311i
$950$	30.6123	−	24.5158i	0.993195	−	0.795396i
$951$	−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	$0.372729\pi$
$953$	−18.8412	+	29.3176i	−0.610328	+	0.949689i	−0.999592	+	0.0285626i	$0.990907\pi$
$954$	−18.3071	−	25.9013i	−0.592715	−	0.838586i
$955$	1.65442	+	1.98575i	0.0535357	+	0.0642573i
$956$	−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
$960$	0.561410	+	3.83208i	0.0181194	+	0.123680i
$961$	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
$970$	−15.9455	+	33.1986i	−0.511980	+	1.06594i
$971$	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
$975$	27.4786	−	11.9985i	0.880020	−	0.384261i
$976$	3.06293	−	4.76601i	0.0980419	−	0.152556i
$977$	24.3797	+	3.50527i	0.779974	+	0.112143i	0.520790	−	0.853685i	$-0.325637\pi$
$977$	24.3797	+	3.50527i	0.779974	+	0.112143i	0.259184	+	0.965828i	$0.416546\pi$
$978$	0.613742	−	1.00293i	0.0196253	−	0.0320701i
$979$	−1.61729	−	1.03937i	−0.0516889	−	0.0332184i
$980$	−3.53702	−	0.0685235i	−0.112986	−	0.00218890i
$981$	−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	$0.476886\pi$
$983$	−16.5449	+	56.3466i	−0.527699	+	1.79718i	−0.600249	+	0.799813i	$0.704932\pi$
$984$	−12.4353	+	6.01364i	−0.396422	+	0.191708i
$985$	−3.56523	+	7.42280i	−0.113598	+	0.236510i
$986$	−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
$990$	−1.94243	+	0.0480019i	−0.0617345	+	0.00152560i
$991$	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
$995$	13.8439	+	22.4877i	0.438882	+	0.712908i
$996$	11.7829	−	1.96006i	0.373354	−	0.0621067i
$997$	−11.8893	+	5.42966i	−0.376537	+	0.171959i	−0.594689	−	0.803956i	$-0.702725\pi$
$997$	−11.8893	+	5.42966i	−0.376537	+	0.171959i	0.218151	+	0.975915i	$0.429997\pi$
$998$	−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.b.89.18	yes	240
3.2	odd	2		690.2.n.a.89.24	yes	240
5.4	even	2		690.2.n.a.89.7	✓	240
15.14	odd	2	inner	690.2.n.b.89.1	yes	240
23.15	odd	22	inner	690.2.n.b.659.1	yes	240
69.38	even	22		690.2.n.a.659.7	yes	240
115.84	odd	22		690.2.n.a.659.24	yes	240
345.314	even	22	inner	690.2.n.b.659.18	yes	240

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

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)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(1.16282 + 1.28368i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.275295 - 2.21906i) q^{5} +(-1.10513 + 1.33367i) q^{6} +(-1.95813 + 1.25842i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.295684 + 2.98539i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(1.16282 + 1.28368i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.275295 - 2.21906i) 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} +(2.15729 - 0.588298i) 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} +(2.52845 - 2.93376i) 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} +(0.889324 + 2.05161i) q^{20} +(-3.89237 - 1.05031i) q^{21} -0.289649 q^{22} +(-4.72344 - 0.830119i) q^{23} +(0.684625 - 1.59100i) q^{24} +(-4.84843 + 1.22179i) 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} +(3.26374 + 2.08519i) 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} +(3.33156 + 3.99877i) 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} +(-1.90416 + 1.17225i) 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} +(6.70616 - 0.165724i) q^{45} +(0.149454 - 4.79350i) q^{46} +12.5393 q^{47} +(1.67224 + 0.451233i) q^{48} +(-0.657229 + 1.43913i) q^{49} +(-1.89936 - 4.62520i) 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} +(0.647554 + 0.0125452i) 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} +(-1.59949 + 3.52727i) 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} +(6.97860 + 3.35187i) 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} +(-7.20625 - 4.80311i) 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} +(-1.43131 - 1.71795i) 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} +(11.4143 + 1.86746i) 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} +(1.11842 + 6.61431i) q^{90} -8.05887i q^{91} +(4.76598 - 0.534254i) q^{92} +(0.443530 - 1.03072i) q^{93} +(1.78453 + 12.4116i) q^{94} +(16.0925 - 6.97570i) 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	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 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 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Introduction

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