LMFDB - Embedded newform 690.2.n.b.89.1

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			89.1
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-1.73163 - 0.0381696i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.23565 + 0.0433117i) q^{5} +(-0.208656 - 1.71944i) q^{6} +(1.95813 - 1.25842i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(2.99709 + 0.132191i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-1.73163 - 0.0381696i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.23565 + 0.0433117i) q^{5} +(-0.208656 - 1.71944i) q^{6} +(1.95813 - 1.25842i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(2.99709 + 0.132191i) q^{9} +(-0.361037 - 2.20673i) q^{10} +(0.0412214 - 0.286701i) q^{11} +(1.67224 - 0.451233i) q^{12} +(1.87184 - 2.91263i) q^{13} +(1.52428 + 1.75911i) q^{14} +(3.87297 + 0.0103340i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.45726 + 4.96297i) q^{17} +(0.295684 + 2.98539i) q^{18} +(2.20986 + 7.52609i) q^{19} +(2.13289 - 0.671412i) q^{20} +(-3.43880 + 2.10437i) 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} +(-5.18480 - 0.343304i) q^{27} +(-1.52428 + 1.75911i) q^{28} +(-1.28974 + 4.39246i) q^{29} +(0.540952 + 3.83502i) q^{30} +(-0.269124 - 0.589299i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.0823234 + 0.494887i) q^{33} +(-5.11984 - 0.736122i) q^{34} +(-4.32319 + 2.89819i) q^{35} +(-2.91293 + 0.717540i) q^{36} +(-6.06516 - 6.99957i) q^{37} +(-7.13499 + 3.25844i) q^{38} +(-3.35250 + 4.97215i) q^{39} +(0.968120 + 2.01563i) q^{40} +(6.02707 + 5.22249i) q^{41} +(-2.57234 - 3.10431i) 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} +(-1.47738 + 0.904080i) q^{48} +(-0.657229 + 1.43913i) q^{49} +(0.902728 + 4.91783i) q^{50} +(2.71287 - 8.53840i) q^{51} +(-0.975429 + 3.32201i) q^{52} +(5.71601 + 8.89428i) q^{53} +(-0.398064 - 5.18088i) q^{54} +(-0.0797390 + 0.642748i) q^{55} +(-1.95813 - 1.25842i) q^{56} +(-3.53939 - 13.1168i) q^{57} +(-4.53130 - 0.651502i) q^{58} +(-1.03617 + 1.61231i) q^{59} +(-3.71900 + 1.08123i) q^{60} +(5.15339 - 2.35348i) q^{61} +(0.545000 - 0.350250i) q^{62} +(6.03505 - 3.51273i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-4.05861 + 6.59269i) q^{65} +(-0.501565 - 0.0110558i) q^{66} +(1.48727 + 10.3442i) q^{67} -5.17249i q^{68} +(8.14757 + 1.61775i) q^{69} +(-3.48394 - 3.86674i) q^{70} +(-8.25991 + 1.18760i) q^{71} +(-1.12479 - 2.78116i) q^{72} +(3.93552 + 13.4031i) q^{73} +(6.06516 - 6.99957i) q^{74} +(-8.65905 + 0.144642i) q^{75} +(-4.24069 - 6.59864i) q^{76} +(-0.280072 - 0.613272i) q^{77} +(-5.39866 - 2.61077i) q^{78} +(5.89554 - 9.17364i) q^{79} +(-1.85733 + 1.24512i) q^{80} +(8.96505 + 0.792377i) q^{81} +(-4.31159 + 6.70896i) q^{82} +(-5.21189 + 4.51613i) q^{83} +(2.70663 - 2.98795i) q^{84} +(3.04296 - 11.1586i) q^{85} +(-9.37962 - 2.75411i) q^{86} +(2.40101 - 7.55688i) q^{87} +(-0.277916 + 0.0816036i) q^{88} +(2.75722 - 6.03747i) q^{89} +(-0.790348 - 6.66148i) 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} +(-1.10513 - 1.33367i) q^{96} +(10.7860 - 12.4477i) q^{97} +(-1.51802 - 0.445730i) q^{98} +(0.161443 - 0.853818i) 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
$3$	−1.73163	−	0.0381696i	−0.999757	−	0.0220372i
$3$	−1.73163	−	0.0381696i	−0.999757	−	0.0220372i
$4$	−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
$6$	−0.208656	−	1.71944i	−0.0851833	−	0.701957i
$7$	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
$9$	2.99709	+	0.132191i	0.999029	+	0.0440637i
$10$	−0.361037	−	2.20673i	−0.114170	−	0.697829i
$11$	0.0412214	−	0.286701i	0.0124287	−	0.0864436i	−0.982663	−	0.185401i	$-0.940642\pi$
$11$	0.0412214	−	0.286701i	0.0124287	−	0.0864436i	0.995092	+	0.0989573i	$0.0315507\pi$
$12$	1.67224	−	0.451233i	0.482734	−	0.130260i
$13$	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
$15$	3.87297	+	0.0103340i	0.999996	+	0.00266823i
$16$	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	$0.875087\pi$
$18$	0.295684	+	2.98539i	0.0696934	+	0.703664i
$19$	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
$21$	−3.43880	+	2.10437i	−0.750407	+	0.459211i
$22$	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
$27$	−5.18480	−	0.343304i	−0.997815	−	0.0660689i
$28$	−1.52428	+	1.75911i	−0.288062	+	0.332441i
$29$	−1.28974	+	4.39246i	−0.239499	+	0.815659i	0.748756	+	0.662846i	$0.230651\pi$
$29$	−1.28974	+	4.39246i	−0.239499	+	0.815659i	−0.988255	+	0.152813i	$0.951167\pi$
$30$	0.540952	+	3.83502i	0.0987639	+	0.700175i
$31$	−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
$33$	−0.0823234	+	0.494887i	−0.0143307	+	0.0861487i
$34$	−5.11984	−	0.736122i	−0.878046	−	0.126244i
$35$	−4.32319	+	2.89819i	−0.730753	+	0.489883i
$36$	−2.91293	+	0.717540i	−0.485488	+	0.119590i
$37$	−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
$39$	−3.35250	+	4.97215i	−0.536830	+	0.796182i
$40$	0.968120	+	2.01563i	0.153073	+	0.318698i
$41$	6.02707	+	5.22249i	0.941270	+	0.815615i	0.983017	−	0.183513i	$-0.0587469\pi$
$41$	6.02707	+	5.22249i	0.941270	+	0.815615i	−0.0417470	+	0.999128i	$0.513292\pi$
$42$	−2.57234	−	3.10431i	−0.396921	−	0.479006i
$43$	−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
$45$	−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	$0.132568\pi$
$48$	−1.47738	+	0.904080i	−0.213241	+	0.130493i
$49$	−0.657229	+	1.43913i	−0.0938898	+	0.205590i
$50$	0.902728	+	4.91783i	0.127665	+	0.695487i
$51$	2.71287	−	8.53840i	0.379878	−	1.19562i
$52$	−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	$0.559498\pi$
$54$	−0.398064	−	5.18088i	−0.0541697	−	0.705029i
$55$	−0.0797390	+	0.642748i	−0.0107520	+	0.0866681i
$56$	−1.95813	−	1.25842i	−0.261667	−	0.168163i
$57$	−3.53939	−	13.1168i	−0.468804	−	1.73736i
$58$	−4.53130	−	0.651502i	−0.594988	−	0.0855464i
$59$	−1.03617	+	1.61231i	−0.134898	+	0.209905i	−0.902130	−	0.431465i	$-0.857997\pi$
$59$	−1.03617	+	1.61231i	−0.134898	+	0.209905i	0.767232	+	0.641369i	$0.221633\pi$
$60$	−3.71900	+	1.08123i	−0.480121	+	0.139586i
$61$	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
$63$	6.03505	−	3.51273i	0.760344	−	0.442563i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−4.05861	+	6.59269i	−0.503409	+	0.817723i
$66$	−0.501565	−	0.0110558i	−0.0617384	−	0.00136087i
$67$	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
$69$	8.14757	+	1.61775i	0.980852	+	0.194754i
$70$	−3.48394	−	3.86674i	−0.416411	−	0.462163i
$71$	−8.25991	+	1.18760i	−0.980270	+	0.140942i	−0.613777	−	0.789479i	$-0.710351\pi$
$71$	−8.25991	+	1.18760i	−0.980270	+	0.140942i	−0.366493	+	0.930421i	$0.619442\pi$
$72$	−1.12479	−	2.78116i	−0.132558	−	0.327763i
$73$	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
$75$	−8.65905	+	0.144642i	−0.999861	+	0.0167018i
$76$	−4.24069	−	6.59864i	−0.486440	−	0.756916i
$77$	−0.280072	−	0.613272i	−0.0319172	−	0.0698889i
$78$	−5.39866	−	2.61077i	−0.611277	−	0.295611i
$79$	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
$81$	8.96505	+	0.792377i	0.996117	+	0.0880419i
$82$	−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	$0.396282\pi$
$84$	2.70663	−	2.98795i	0.295318	−	0.326012i
$85$	3.04296	−	11.1586i	0.330056	−	1.21032i
$86$	−9.37962	−	2.75411i	−1.01143	−	0.296983i
$87$	2.40101	−	7.55688i	0.257416	−	0.810183i
$88$	−0.277916	+	0.0816036i	−0.0296260	+	0.00869897i
$89$	2.75722	−	6.03747i	0.292265	−	0.639970i	−0.705360	−	0.708849i	$-0.749215\pi$
$89$	2.75722	−	6.03747i	0.292265	−	0.639970i	0.997625	+	0.0688784i	$0.0219421\pi$
$90$	−0.790348	−	6.66148i	−0.0833100	−	0.702182i
$91$		−	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
$96$	−1.10513	−	1.33367i	−0.112792	−	0.136118i
$97$	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
$99$	0.161443	−	0.853818i	0.0162257	−	0.0858120i
$100$	−4.73930	+	1.59342i	−0.473930	+	0.159342i
$101$	8.44782	−	7.32008i	0.840589	−	0.728375i	−0.123957	−	0.992288i	$-0.539559\pi$
$101$	8.44782	−	7.32008i	0.840589	−	0.728375i	0.964547	+	0.263913i	$0.0850131\pi$
$102$	8.83758	+	1.47011i	0.875050	+	0.145563i
$103$	−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
$105$	7.59680	−	4.85357i	0.741371	−	0.473660i
$106$	−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	$0.537807\pi$
$108$	5.07150	−	1.13133i	0.488005	−	0.108862i
$109$	−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
$111$	10.2354	+	12.3522i	0.971506	+	1.17242i
$112$	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
$115$	10.5959	+	1.65127i	0.988074	+	0.153982i
$116$		−	4.57789i		−	0.425047i
$117$	5.99508	−	8.48197i	0.554245	−	0.784158i
$118$	−1.74336	−	0.796166i	−0.160489	−	0.0732930i
$119$	3.39197	+	11.5520i	0.310941	+	1.05897i
$120$	−1.59949	−	3.52727i	−0.146013	−	0.321994i
$121$	10.4739	+	3.07542i	0.952175	+	0.279584i
$122$	3.06293	+	4.76601i	0.277304	+	0.431494i
$123$	−10.2373	−	9.27347i	−0.923068	−	0.836160i
$124$	0.424247	+	0.489607i	0.0380985	+	0.0439680i
$125$	−11.1615	+	0.649350i	−0.998312	+	0.0580796i
$126$	4.33586	+	5.47370i	0.386269	+	0.487636i
$127$	−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
$129$	7.37144	−	15.2430i	0.649019	−	1.34207i
$130$	−7.10319	−	3.07907i	−0.622991	−	0.270052i
$131$	−4.16913	−	6.48729i	−0.364258	−	0.566797i	0.609952	−	0.792438i	$-0.291189\pi$
$131$	−4.16913	−	6.48729i	−0.364258	−	0.566797i	−0.974210	+	0.225641i	$0.927552\pi$
$132$	−0.0604369	−	0.498033i	−0.00526036	−	0.0433482i
$133$	13.7981	+	11.9562i	1.19645	+	1.03673i
$134$	−10.0272	+	2.94426i	−0.866221	+	0.254345i
$135$	11.6063	+	0.542945i	0.998908	+	0.0467292i
$136$	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	$0.865044\pi$
$138$	−0.441765	+	8.29487i	−0.0376056	+	0.706106i
$139$	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
$141$	−21.7134	−	0.478619i	−1.82860	−	0.0403070i
$142$	−2.35101	−	8.00682i	−0.197293	−	0.671917i
$143$	−0.757895	−	0.656719i	−0.0633783	−	0.0549176i
$144$	2.59278	−	1.50914i	0.216065	−	0.125762i
$145$	2.69316	−	9.87585i	0.223655	−	0.820145i
$146$	−12.7066	+	5.80293i	−1.05161	+	0.480254i
$147$	1.19301	−	2.46696i	0.0983977	−	0.203471i
$148$	7.79149	+	5.00729i	0.640456	+	0.411596i
$149$	−0.0828029	+	0.575907i	−0.00678348	+	0.0471801i	−0.992932	−	0.118684i	$-0.962132\pi$
$149$	−0.0828029	+	0.575907i	−0.00678348	+	0.0471801i	0.986149	+	0.165864i	$0.0530414\pi$
$150$	−1.37548	−	8.55032i	−0.112307	−	0.698131i
$151$	−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
$153$	−5.02359	+	14.6818i	−0.406133	+	1.18695i
$154$	0.567172	−	0.364499i	0.0457040	−	0.0293722i
$155$	0.627190	+	1.30581i	0.0503771	+	0.104885i
$156$	1.81588	−	5.71526i	0.145387	−	0.457587i
$157$	−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
$159$	−9.55852	−	15.6198i	−0.758040	−	1.23873i
$160$	−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
$165$	0.162612	−	1.10996i	0.0126593	−	0.0864101i
$166$	−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	$0.484104\pi$
$168$	3.34273	+	2.25385i	0.257897	+	0.173888i
$169$	0.420735	+	0.921282i	0.0323643	+	0.0708678i
$170$	11.4780	+	1.42396i	0.880326	+	0.109213i
$171$	5.62825	+	22.8485i	0.430403	+	1.74727i
$172$	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	$-0.261298\pi$
$174$	7.82166	+	1.30112i	0.592959	+	0.0986375i
$175$	9.53962	−	6.66657i	0.721127	−	0.503945i
$176$	−0.120325	−	0.263474i	−0.00906981	−	0.0198601i
$177$	1.85580	−	2.75237i	0.139491	−	0.206881i
$178$	6.36841	+	1.86993i	0.477333	+	0.140157i
$179$	−10.9393	−	9.47896i	−0.817642	−	0.708491i	0.141954	−	0.989873i	$-0.454662\pi$
$179$	−10.9393	−	9.47896i	−0.817642	−	0.708491i	−0.959596	+	0.281382i	$0.909207\pi$
$180$	6.48120	−	1.73033i	0.483080	−	0.128971i
$181$	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
$186$	−0.957108	+	0.585702i	−0.0701786	+	0.0429457i
$187$	1.36282	+	0.622378i	0.0996591	+	0.0455128i
$188$	−12.0313	+	3.53272i	−0.877476	+	0.257650i
$189$	−10.5845	+	5.85240i	−0.769913	+	0.425699i
$190$	15.8102	−	7.59375i	1.14699	−	0.550909i
$191$	0.972388	−	0.624916i	0.0703595	−	0.0452173i	−0.504988	−	0.863126i	$-0.668503\pi$
$191$	0.972388	−	0.624916i	0.0703595	−	0.0452173i	0.575348	+	0.817909i	$0.304867\pi$
$192$	1.16282	−	1.28368i	0.0839195	−	0.0926418i
$193$	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
$195$	7.27966	−	11.2612i	0.521307	−	0.806431i
$196$	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	$0.723697\pi$
$198$	0.868103	+	0.0382891i	0.0616934	+	0.00272109i
$199$	−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
$201$	−2.18057	−	17.9691i	−0.153805	−	1.26744i
$202$	8.44782	+	7.32008i	0.594386	+	0.515039i
$203$	3.00205	+	10.2240i	0.210703	+	0.717588i
$204$	−0.197432	+	8.95684i	−0.0138230	+	0.627104i
$205$	−13.7006	−	11.4146i	−0.956892	−	0.797230i
$206$	−5.51624			−0.384334
$207$	−14.0468	−	3.11234i	−0.976322	−	0.216322i
$208$		−	3.46225i		−	0.240064i
$209$	2.24883	−	0.323333i	0.155555	−	0.0223654i
$210$	5.88531	+	6.82874i	0.406125	+	0.471228i
$211$	−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
$213$	14.3484	−	1.74120i	0.983138	−	0.119305i
$214$	−5.81921	−	9.05487i	−0.397793	−	0.618978i
$215$	8.69368	−	20.0557i	0.592904	−	1.36779i
$216$	1.84156	+	4.85887i	0.125303	+	0.330604i
$217$	−1.26856	−	0.815256i	−0.0861157	−	0.0553432i
$218$	−7.38599	−	1.06195i	−0.500242	−	0.0719240i
$219$	−6.30327	−	23.3595i	−0.425935	−	1.57849i
$220$	−0.104574	−	0.639177i	−0.00705038	−	0.0430933i
$221$	11.7276	+	13.5343i	0.788881	+	0.910417i
$222$	−10.7698	+	11.8892i	−0.722821	+	0.797949i
$223$	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
$225$	14.9998	+	0.0800467i	0.999986	+	0.00533645i
$226$	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	$0.630696\pi$
$228$	7.09144	+	11.5883i	0.469642	+	0.767452i
$229$			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	−0.724992	−	0.688757i	$-0.758157\pi$
$233$	4.12602	−	9.03471i	0.270304	−	0.591884i	0.995297	+	0.0968730i	$0.0308841\pi$
$234$	9.24882	+	4.72694i	0.604615	+	0.309010i
$235$	−28.0334	+	0.543097i	−1.82870	+	0.0354277i
$236$	0.539956	−	1.83892i	0.0351481	−	0.119704i
$237$	−10.5591	+	15.6603i	−0.685884	+	1.01725i
$238$	−10.9517	+	5.00147i	−0.709892	+	0.324197i
$239$	−5.12101	+	4.43738i	−0.331250	+	0.287030i	−0.804567	−	0.593863i	$-0.797602\pi$
$239$	−5.12101	+	4.43738i	−0.331250	+	0.287030i	0.473316	+	0.880893i	$0.343057\pi$
$240$	3.26374	−	2.08519i	0.210673	−	0.134599i
$241$	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
$243$	−15.4939	−	1.71430i	−0.993935	−	0.109972i
$244$	−4.28160	+	3.71002i	−0.274101	+	0.237510i
$245$	1.40700	−	3.24586i	0.0898900	−	0.207370i
$246$	7.72215	−	11.4529i	0.492346	−	0.730208i
$247$	26.0572	+	7.65109i	1.65798	+	0.486827i
$248$	−0.424247	+	0.489607i	−0.0269397	+	0.0310901i
$249$	9.19744	−	7.62132i	0.582864	−	0.482982i
$250$	−2.23118	−	10.9554i	−0.141112	−	0.692883i
$251$	−2.29818	−	15.9842i	−0.145060	−	1.00891i	−0.924158	−	0.382011i	$-0.875232\pi$
$251$	−2.29818	−	15.9842i	−0.145060	−	1.00891i	0.779098	−	0.626902i	$-0.215677\pi$
$252$	−4.80093	+	5.07071i	−0.302430	+	0.319425i
$253$	−0.432703	+	1.32000i	−0.0272038	+	0.0829875i
$254$		−	14.4208i		−	0.904841i
$255$	−5.69521	+	19.2064i	−0.356648	+	1.20275i
$256$	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	$0.351997\pi$
$258$	16.1369	+	5.12711i	1.00464	+	0.319200i
$259$	−20.6848	−	6.07360i	−1.28529	−	0.377395i
$260$	2.03684	−	7.46909i	0.126319	−	0.463213i
$261$	−4.44611	+	12.9941i	−0.275207	+	0.804313i
$262$	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	$0.324360\pi$
$264$	0.484363	−	0.130699i	0.0298105	−	0.00804398i
$265$	−13.1642	−	19.6369i	−0.808671	−	1.20629i
$266$	−9.87079	+	15.3592i	−0.605217	+	0.941736i
$267$	−5.00493	+	10.3494i	−0.306297	+	0.633374i
$268$	−4.34132	−	9.50615i	−0.265188	−	0.580681i
$269$	−2.18049	−	3.39291i	−0.132947	−	0.206870i	0.768397	−	0.639974i	$-0.221055\pi$
$269$	−2.18049	−	3.39291i	−0.132947	−	0.206870i	−0.901344	+	0.433104i	$0.857418\pi$
$270$	1.11432	+	11.5654i	0.0678156	+	0.703847i
$271$	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
$273$	−0.307604	+	13.9550i	−0.0186170	+	0.844594i
$274$	−9.53236	+	1.37055i	−0.575871	+	0.0827978i
$275$	0.150430	−	1.44041i	0.00907126	−	0.0868601i
$276$	−8.27331	+	0.743214i	−0.497995	+	0.0447362i
$277$			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
$279$	−0.728687	−	1.80176i	−0.0436253	−	0.107868i
$280$	4.43220	+	2.72857i	0.264875	+	0.163063i
$281$	9.39095	−	10.8377i	0.560217	−	0.646525i	−0.403016	−	0.915193i	$-0.632038\pi$
$281$	9.39095	−	10.8377i	0.560217	−	0.646525i	0.963233	+	0.268668i	$0.0865835\pi$
$282$	−2.61639	−	21.5605i	−0.155804	−	1.28391i
$283$	−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
$285$	8.48094	+	29.1711i	0.502368	+	1.72795i
$286$	0.542175	−	0.843641i	0.0320595	−	0.0498856i
$287$	18.3739	+	2.64176i	1.08458	+	0.155938i
$288$	1.86277	+	2.35161i	0.109765	+	0.138570i
$289$	−8.20614	−	5.27377i	−0.482714	−	0.310222i
$290$	10.1586	+	1.26027i	0.596534	+	0.0740057i
$291$	−19.1524	+	21.1431i	−1.12274	+	1.23943i
$292$	−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	$-0.0515729\pi$
$294$	2.61163	+	0.829781i	0.152313	+	0.0483938i
$295$	2.24668	−	3.64943i	0.130807	−	0.212478i
$296$	−3.84747	+	8.42479i	−0.223630	+	0.489681i
$297$	−0.312150	+	1.47234i	−0.0181128	+	0.0854335i
$298$	−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
$303$	−14.9079	+	12.3532i	−0.856437	+	0.709674i
$304$	5.92796	+	5.13661i	0.339992	+	0.294605i
$305$	−11.4192	+	5.48475i	−0.653864	+	0.314056i
$306$	−15.2473	−	2.88302i	−0.871630	−	0.164811i
$307$	−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
$309$	1.56781	−	9.42489i	0.0891897	−	0.536163i
$310$	−1.20326	+	0.806642i	−0.0683405	+	0.0458142i
$311$	16.8037	+	2.41601i	0.952850	+	0.136999i	0.601170	−	0.799121i	$-0.294701\pi$
$311$	16.8037	+	2.41601i	0.952850	+	0.136999i	0.351680	+	0.936120i	$0.385610\pi$
$312$	5.91551	+	0.984034i	0.334900	+	0.0557099i
$313$	−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
$315$	−13.3401	+	8.11462i	−0.751630	+	0.457207i
$316$	−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	$0.388323\pi$
$318$	14.1005	−	11.6842i	0.790715	−	0.655215i
$319$	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
$324$	−8.82514	+	1.76547i	−0.490286	+	0.0980815i
$325$	8.78809	−	14.9147i	0.487476	−	0.827320i
$326$	0.191256	+	0.651359i	0.0105927	+	0.0360755i
$327$	3.91364	−	12.3177i	0.216425	−	0.681169i
$328$	2.24681	−	7.65192i	0.124059	−	0.422506i
$329$	24.5536	−	15.7796i	1.35368	−	0.869959i
$330$	1.12180	+	0.00299324i	0.0617532	+	0.000164772i
$331$	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
$333$	−17.2525	−	21.7801i	−0.945433	−	1.19354i
$334$	−1.21116	+	8.42381i	−0.0662718	+	0.460930i
$335$	−3.77303	−	23.0615i	−0.206143	−	1.25999i
$336$	−1.75519	+	3.62946i	−0.0957535	+	0.198003i
$337$	−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
$339$	−6.04127	+	0.733115i	−0.328117	+	0.0398173i
$340$	0.224029	+	11.5639i	0.0121497	+	0.627139i
$341$	−0.180046	+	0.0528663i	−0.00975005	+	0.00286287i
$342$	−21.8149	+	8.82264i	−1.17962	+	0.477074i
$343$	2.84288	+	19.7727i	0.153501	+	1.06763i
$344$	9.77560			0.527065
$345$	−18.2852	−	3.26384i	−0.984440	−	0.175719i
$346$	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	$-0.257835\pi$
$348$	−0.174736	+	7.92722i	−0.00936685	+	0.424944i
$349$	−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
$351$	−10.7050	+	14.4588i	−0.571391	+	0.771754i
$352$	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	$0.819526\pi$
$354$	2.98847	+	1.44521i	0.158835	+	0.0768120i
$355$	18.4148	−	3.01280i	0.977357	−	0.159903i
$356$	−0.944581	+	6.56971i	−0.0500627	+	0.348194i
$357$	−5.43270	−	20.1333i	−0.287529	−	1.06556i
$358$	7.82565	−	12.1770i	0.413599	−	0.643572i
$359$	1.01414	+	1.17038i	0.0535243	+	0.0617704i	0.781880	−	0.623428i	$-0.214261\pi$
$359$	1.01414	+	1.17038i	0.0535243	+	0.0617704i	−0.728356	+	0.685199i	$0.759715\pi$
$360$	2.63509	+	6.16898i	0.138881	+	0.325134i
$361$	−35.7747	+	22.9910i	−1.88288	+	1.21005i
$362$	−3.34687	+	11.3984i	−0.175908	+	0.599086i
$363$	−18.0196	−	5.72528i	−0.945782	−	0.300499i
$364$	2.27045	+	7.73243i	0.119004	+	0.405289i
$365$	−9.37895	−	29.7943i	−0.490916	−	1.55950i
$366$	−5.12194	−	8.36987i	−0.267728	−	0.437500i
$367$	−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
$372$	−0.715951	−	0.864012i	−0.0371203	−	0.0447969i
$373$	−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
$375$	19.3523	−	0.698405i	0.999349	−	0.0360655i
$376$	−5.20900	−	11.4061i	−0.268634	−	0.588226i
$377$	10.3794	+	11.9785i	0.534568	+	0.616924i
$378$	−7.29917	−	9.64393i	−0.375429	−	0.496030i
$379$	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
$381$	24.6390	+	4.09865i	1.26229	+	0.209980i
$382$	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	$0.403434\pi$
$384$	1.43610	+	0.968300i	0.0732859	+	0.0494134i
$385$	0.652705	+	1.35893i	0.0332649	+	0.0692575i
$386$	1.48280	+	1.28486i	0.0754727	+	0.0653975i
$387$	−13.3464	+	26.1139i	−0.678437	+	1.32744i
$388$	−6.84215	+	14.9822i	−0.347357	+	0.760607i
$389$	2.14029	+	14.8861i	0.108517	+	0.754754i	0.969318	+	0.245811i	$0.0790543\pi$
$389$	2.14029	+	14.8861i	0.108517	+	0.754754i	−0.860801	+	0.508942i	$0.830037\pi$
$390$	12.1826	+	5.60293i	0.616889	+	0.283715i
$391$	11.0031	−	22.2326i	0.556452	−	1.12435i
$392$	1.58210			0.0799082
$393$	6.97177	+	11.3927i	0.351679	+	0.574687i
$394$	1.52982	−	3.34984i	0.0770712	−	0.168762i
$395$	−12.7830	+	20.7644i	−0.643184	+	1.04477i
$396$	0.0856446	+	0.864716i	0.00430380	+	0.0434536i
$397$	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
$399$	−23.4369	−	21.2303i	−1.17331	−	1.06285i
$400$	4.09841	−	2.86409i	0.204921	−	0.143205i
$401$	−1.78186	−	1.14513i	−0.0889820	−	0.0571852i	0.495393	−	0.868669i	$-0.335024\pi$
$401$	−1.78186	−	1.14513i	−0.0889820	−	0.0571852i	−0.584375	+	0.811484i	$0.698660\pi$
$402$	17.4758	−	4.71563i	0.871615	−	0.235194i
$403$	−2.22017	−	0.319212i	−0.110594	−	0.0159011i
$404$	−6.04332	+	9.40359i	−0.300666	+	0.467846i
$405$	−20.0770	−	1.38319i	−0.997635	−	0.0687310i
$406$	−9.69275	+	4.42653i	−0.481043	+	0.219685i
$407$	−2.25680	+	1.45036i	−0.111865	+	0.0718915i
$408$	−8.89377	+	1.07927i	−0.440307	+	0.0534318i
$409$	−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
$411$	0.367588	−	16.6763i	0.0181318	−	0.822580i
$412$	−0.785042	−	5.46009i	−0.0386763	−	0.268999i
$413$			4.46105i			0.219514i
$414$	1.08159	−	14.3468i	0.0531570	−	0.705106i
$415$	11.4563	−	10.3222i	0.562370	−	0.506697i
$416$	3.42701	−	0.492730i	0.168023	−	0.0241581i
$417$	−2.10279	−	0.0463508i	−0.102974	−	0.00226981i
$418$	0.640084	+	2.17992i	0.0313075	+	0.106624i
$419$	6.35621	−	7.33546i	0.310521	−	0.358361i	−0.578941	−	0.815370i	$-0.696534\pi$
$419$	6.35621	−	7.33546i	0.310521	−	0.358361i	0.889462	+	0.457009i	$0.151079\pi$
$420$	−5.92166	+	6.79723i	−0.288948	+	0.331671i
$421$	−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
$423$	37.5813	+	1.65758i	1.82726	+	0.0805944i
$424$	5.71601	−	8.89428i	0.277594	−	0.431944i
$425$	−6.31970	+	25.0784i	−0.306551	+	1.21648i
$426$	3.76547	+	13.9546i	0.182438	+	0.676102i
$427$	7.12938	−	11.0935i	0.345015	−	0.536854i
$428$	8.13454	−	7.04862i	0.393198	−	0.340708i
$429$	1.28733	+	1.16612i	0.0621527	+	0.0563010i
$430$	21.0888	+	5.75096i	1.01699	+	0.277336i
$431$	24.4936	+	7.19196i	1.17981	+	0.346424i	0.812102	−	0.583516i	$-0.198323\pi$
$431$	24.4936	+	7.19196i	1.17981	+	0.346424i	0.367711	+	0.929940i	$0.380142\pi$
$432$	−4.54733	+	2.51431i	−0.218784	+	0.120970i
$433$	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
$435$	−5.04052	+	16.9985i	−0.241675	+	0.815017i
$436$		−	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
$441$	−2.16001	+	4.22632i	−0.102858	+	0.201253i
$442$	−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	$0.541894\pi$
$444$	−13.3009	−	8.96817i	−0.631230	−	0.425610i
$445$	−5.90268	+	13.6171i	−0.279814	+	0.645511i
$446$	−0.231580	+	0.200666i	−0.0109657	+	0.00950179i
$447$	0.165366	−	0.994097i	0.00782155	−	0.0470192i
$448$	−0.331257	+	2.30395i	−0.0156504	+	0.108851i
$449$	−35.3019	−	5.07565i	−1.66600	−	0.239535i	−0.756128	−	0.654424i	$-0.772911\pi$
$449$	−35.3019	−	5.07565i	−1.66600	−	0.239535i	−0.909872	+	0.414890i	$0.863820\pi$
$450$	2.05546	+	14.8585i	0.0968953	+	0.700437i
$451$	1.74574	−	1.51269i	0.0822035	−	0.0712297i
$452$	−3.19601	+	1.45957i	−0.150327	+	0.0686523i
$453$	21.7771	+	14.6833i	1.02318	+	0.689883i
$454$	−0.151139	+	0.514733i	−0.00709331	+	0.0241576i
$455$	0.349043	+	18.0168i	0.0163634	+	0.844641i
$456$	−10.4611	+	8.66844i	−0.489886	+	0.405937i
$457$	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	$0.0134676\pi$
$461$			1.81631i			0.0845939i	−0.999105	+	0.0422969i	$0.986532\pi$
$462$	−0.996044	+	0.609529i	−0.0463402	+	0.0283579i
$463$	−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
$465$	−1.03622	−	2.28512i	−0.0480535	−	0.105970i
$466$	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	$0.900757\pi$
$468$	−3.36259	+	9.82740i	−0.155436	+	0.454272i
$469$	15.9296	+	18.3837i	0.735558	+	0.848880i
$470$	−4.52714	−	27.6708i	−0.208821	−	1.27636i
$471$	9.67457	−	2.61056i	0.445781	−	0.120288i
$472$	1.89705	+	0.272754i	0.0873187	+	0.0125545i
$473$	2.38200	+	1.53082i	0.109525	+	0.0703872i
$474$	−17.0036	−	8.22288i	−0.781003	−	0.377689i
$475$	12.4985	+	37.1742i	0.573470	+	1.70567i
$476$	−6.50915	−	10.1284i	−0.298346	−	0.464236i
$477$	15.9556	+	27.4125i	0.730558	+	1.25513i
$478$	−5.12101	−	4.43738i	−0.234229	−	0.202961i
$479$	−6.75943	+	1.98475i	−0.308846	+	0.0906855i	−0.432483	−	0.901642i	$-0.642362\pi$
$479$	−6.75943	+	1.98475i	−0.308846	+	0.0906855i	0.123637	+	0.992328i	$0.460544\pi$
$480$	2.52845	+	2.93376i	0.115407	+	0.133907i
$481$	−31.7402	+	4.56355i	−1.44723	+	0.208080i
$482$			20.6763i			0.941780i
$483$	17.9898	−	7.08526i	0.818566	−	0.322390i
$484$	−10.9161			−0.496187
$485$	−23.5745	+	28.2958i	−1.07046	+	1.28485i
$486$	−0.508166	−	15.5802i	−0.0230509	−	0.706731i
$487$	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
$489$	−1.16725	+	0.141648i	−0.0527850	+	0.00640552i
$490$	3.41305	+	0.930747i	0.154186	+	0.0420469i
$491$	30.1714	−	13.7788i	1.36162	−	0.621830i	0.405307	−	0.914181i	$-0.367165\pi$
$491$	30.1714	−	13.7788i	1.36162	−	0.621830i	0.956311	+	0.292350i	$0.0944373\pi$
$492$	12.4353	+	6.01364i	0.560625	+	0.271116i
$493$	−19.9201	−	12.8019i	−0.897158	−	0.576568i
$494$	−3.86488	+	26.8809i	−0.173889	+	1.20943i
$495$	−0.323950	+	1.91583i	−0.0145605	+	0.0861101i
$496$	−0.545000	−	0.350250i	−0.0244712	−	0.0157267i
$497$	−14.6795	+	12.7199i	−0.658466	+	0.570564i
$498$	8.85268	+	8.01920i	0.396698	+	0.359349i
$499$	−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
$501$	−14.0485	−	4.46355i	−0.627639	−	0.199417i
$502$	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	$0.310664\pi$
$504$	−5.70234	−	4.03043i	−0.254003	−	0.179530i
$505$	−18.5693	+	16.7310i	−0.826323	+	0.744520i
$506$	−1.36814	−	0.240443i	−0.0608213	−	0.0106890i
$507$	−0.693393	−	1.61138i	−0.0307947	−	0.0715638i
$508$	14.2740	−	2.05229i	0.633307	−	0.0910558i
$509$	−2.13431	−	0.974707i	−0.0946016	−	0.0432031i	0.367552	−	0.930003i	$-0.380196\pi$
$509$	−2.13431	−	0.974707i	−0.0946016	−	0.0432031i	−0.462154	+	0.886800i	$0.652923\pi$
$510$	−19.8214	−	2.90389i	−0.877706	−	0.128586i
$511$	24.5730	+	21.2926i	1.08705	+	0.941930i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	−8.87394	−	39.7799i	−0.391794	−	1.75633i
$514$	2.37623	+	5.20321i	0.104811	+	0.229504i
$515$	1.51859	−	12.2408i	0.0669172	−	0.539396i
$516$	−2.77840	+	16.7023i	−0.122312	+	0.735279i
$517$	0.516886	−	3.59502i	0.0227326	−	0.158109i
$518$	3.06803	−	21.3386i	0.134801	−	0.937564i
$519$	−6.14056	+	36.9139i	−0.269541	+	1.62034i
$520$	7.68293	+	0.953141i	0.336919	+	0.0417980i
$521$	4.32212	+	9.46411i	0.189355	+	0.414630i	0.980370	−	0.197167i	$-0.0631741\pi$
$521$	4.32212	+	9.46411i	0.189355	+	0.414630i	−0.791015	+	0.611797i	$0.790447\pi$
$522$	−13.4946	−	2.55161i	−0.590641	−	0.111681i
$523$	−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
$525$	−16.7736	+	11.1799i	−0.732058	+	0.487931i
$526$	−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
$531$	−3.31862	+	4.69526i	−0.144016	+	0.203757i
$532$	−16.6077	−	7.58447i	−0.720034	−	0.328828i
$533$	26.4929	−	7.77901i	1.14753	−	0.336946i
$534$	−10.9564	−	3.48111i	−0.474128	−	0.150643i
$535$	21.6953	−	10.4204i	0.937968	−	0.450513i
$536$	8.79156	−	5.64999i	0.379738	−	0.244043i
$537$	18.5810	+	16.8316i	0.801830	+	0.726337i
$538$	3.04806	−	2.64116i	0.131411	−	0.113869i
$539$	0.385508	+	0.247751i	0.0166050	+	0.0106714i
$540$	−11.2891	+	2.74891i	−0.485805	+	0.118294i
$541$	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
$543$	−18.5237	−	8.95799i	−0.794929	−	0.384424i
$544$	−4.70506	+	2.14873i	−0.201728	+	0.0921260i
$545$	4.38984	−	16.0976i	0.188040	−	0.689545i
$546$	−13.8567	+	1.68153i	−0.593013	+	0.0719628i
$547$	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
$549$	15.7563	−	6.37234i	0.672462	−	0.271965i
$550$	1.44716	−	0.0560932i	0.0617071	−	0.00239182i
$551$	−35.9082			−1.52974
$552$	−1.91306	−	8.08333i	−0.0814254	−	0.344049i
$553$		−	25.3823i		−	1.07936i
$554$	−2.52997	+	0.363755i	−0.107488	+	0.0154545i
$555$	−23.4179	−	27.1718i	−0.994033	−	1.15338i
$556$	−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	$0.763869\pi$
$558$	1.67971	−	0.977686i	0.0711079	−	0.0413888i
$559$	18.2983	+	28.4727i	0.773936	+	1.20427i
$560$	−2.07002	+	4.77540i	−0.0874745	+	0.201798i
$561$	−2.33614	−	1.12975i	−0.0986319	−	0.0476979i
$562$	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	$0.203099\pi$
$564$	20.9687	−	5.65814i	0.882941	−	0.238251i
$565$	−7.75338	+	1.26851i	−0.326187	+	0.0533665i
$566$	−6.34803	−	7.32602i	−0.266828	−	0.307936i
$567$	18.5519	−	9.73018i	0.779107	−	0.408629i
$568$	4.51156	+	7.02013i	0.189301	+	0.294558i
$569$	−32.6899	−	9.59861i	−1.37043	−	0.402395i	−0.488002	−	0.872842i	$-0.662274\pi$
$569$	−32.6899	−	9.59861i	−1.37043	−	0.402395i	−0.882428	+	0.470448i	$0.844092\pi$
$570$	−27.6673	+	12.5461i	−1.15885	+	0.525498i
$571$	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
$573$	−1.70767	+	1.04501i	−0.0713389	+	0.0436558i
$574$			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
$579$	−2.61671	+	2.16830i	−0.108747	+	0.0901114i
$580$	0.198276	+	10.2346i	0.00823297	+	0.424967i
$581$	−4.52241	+	15.4019i	−0.187621	+	0.638979i
$582$	−23.6535	−	15.9485i	−0.980471	−	0.661087i
$583$	2.78562	−	1.27215i	0.115369	−	0.0526871i
$584$	10.5571	−	9.14774i	0.436854	−	0.378536i
$585$	−13.0355	+	19.2224i	−0.538952	+	0.794747i
$586$	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	$-0.105048\pi$
$588$	−0.449661	+	2.70314i	−0.0185437	+	0.111475i
$589$	3.84039	−	3.32772i	0.158240	−	0.137116i
$590$	3.93202	+	1.70444i	0.161879	+	0.0701707i
$591$	5.28864	+	3.56589i	0.217545	+	0.146681i
$592$	−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	$0.205281\pi$
$594$	−1.50177	−	0.0994377i	−0.0616185	−	0.00407998i
$595$	−8.08359	−	25.6793i	−0.331395	−	1.05275i
$596$	−0.0828029	−	0.575907i	−0.00339174	−	0.0235901i
$597$	18.7893	−	8.08525i	0.768996	−	0.330907i
$598$	−13.6820	−	9.40795i	−0.559497	−	0.384720i
$599$		−	25.5342i		−	1.04330i	−0.853160	−	0.521649i	$-0.825317\pi$
$599$		−	25.5342i		−	1.04330i	0.853160	−	0.521649i	$-0.174683\pi$
$600$	3.72867	+	7.81646i	0.152222	+	0.319106i
$601$	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
$603$	3.09006	+	31.1990i	0.125837	+	1.27052i
$604$	14.5498	+	4.27220i	0.592022	+	0.173833i
$605$	−23.5492	−	6.42192i	−0.957412	−	0.261088i
$606$	−14.3491	−	12.9981i	−0.582892	−	0.528012i
$607$	−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
$609$	−4.80820	−	17.8189i	−0.194838	−	0.722057i
$610$	−7.05405	−	10.5225i	−0.285610	−	0.426042i
$611$	23.4715	−	36.5223i	0.949554	−	1.47753i
$612$	0.683758	−	15.5024i	0.0276393	−	0.626647i
$613$	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
$615$	23.2887	+	20.2888i	0.939091	+	0.818124i
$616$	−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	$0.969034\pi$
$618$	9.55208	+	0.210552i	0.384241	+	0.00846966i
$619$	−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
$621$	24.2051	+	5.92558i	0.971318	+	0.237785i
$622$			16.9765i			0.680695i
$623$	−2.19864	−	15.2919i	−0.0880868	−	0.612657i
$624$	−0.132153	+	5.99534i	−0.00529035	+	0.240006i
$625$	24.9250	−	1.93514i	0.997000	−	0.0774056i
$626$	14.7100	−	16.9763i	0.587932	−	0.678509i
$627$	−3.90648	+	0.474056i	−0.156010	+	0.0189320i
$628$	4.86698	−	3.12782i	0.194214	−	0.124814i
$629$	43.5772	−	19.9010i	1.73754	−	0.793506i
$630$	−9.93052	−	12.0495i	−0.395642	−	0.480063i
$631$	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
$633$	1.62529	−	0.438565i	0.0645995	−	0.0174314i
$634$	−14.5180	−	9.33018i	−0.576585	−	0.370549i
$635$	32.0006	+	3.96998i	1.26990	+	0.157544i
$636$	13.5719	+	12.2941i	0.538162	+	0.487494i
$637$	2.96143	+	4.60808i	0.117336	+	0.182579i
$638$	−0.373573	+	1.27227i	−0.0147899	+	0.0503697i
$639$	−24.9126	+	2.46744i	−0.985529	+	0.0976103i
$640$	1.90416	+	1.17225i	0.0752687	+	0.0463371i
$641$	0.660736	−	1.44681i	0.0260975	−	0.0571456i	−0.896134	−	0.443783i	$-0.853636\pi$
$641$	0.660736	−	1.44681i	0.0260975	−	0.0571456i	0.922232	+	0.386637i	$0.126363\pi$
$642$	9.73110	+	15.9018i	0.384056	+	0.627594i
$643$	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
$645$	−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	$0.987303\pi$
$648$	−3.00345	−	8.48406i	−0.117986	−	0.333285i
$649$	0.419538	+	0.363532i	0.0164683	+	0.0142699i
$650$	16.0136	+	6.57606i	0.628105	+	0.257934i
$651$	2.16556	+	1.46014i	0.0848752	+	0.0572275i
$652$	−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	$0.794162\pi$
$654$	12.7493	+	2.12082i	0.498536	+	0.0829305i
$655$	9.60168	+	14.3227i	0.375169	+	0.559635i
$656$	7.89378	+	1.13495i	0.308200	+	0.0443125i
$657$	10.0233	+	40.6906i	0.391046	+	1.58749i
$658$	19.1134	+	22.0580i	0.745116	+	0.859910i
$659$	−8.88848	−	19.4631i	−0.346246	−	0.758173i	−0.999999	−	0.00146518i	$-0.999534\pi$
$659$	−8.88848	−	19.4631i	−0.346246	−	0.758173i	0.653753	−	0.756708i	$-0.273194\pi$
$660$	0.156686	+	1.11081i	0.00609901	+	0.0432382i
$661$	−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
$663$	−19.7912	−	23.8841i	−0.768626	−	0.927580i
$664$	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
$669$	−0.277032	−	0.452705i	−0.0107107	−	0.0175026i
$670$	22.2898	−	7.01663i	0.861132	−	0.271076i
$671$	−0.462314	−	1.57450i	−0.0178474	−	0.0607828i
$672$	−3.84231	−	1.22080i	−0.148220	−	0.0470934i
$673$	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
$675$	−25.9710	−	0.711147i	−0.999625	−	0.0273721i
$676$	−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	$0.157100\pi$
$678$	−1.58541	−	5.87544i	−0.0608875	−	0.225645i
$679$	5.45602	−	37.9474i	0.209383	−	1.45629i
$680$	−11.4143	+	1.86746i	−0.437718	+	0.0716138i
$681$	−0.836502	−	0.404528i	−0.0320548	−	0.0155016i
$682$	−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	$0.134938\pi$
$684$	−11.8374	−	20.3373i	−0.452615	−	0.777615i
$685$	−0.417108	−	21.5302i	−0.0159369	−	0.822625i
$686$	−19.1669	+	5.62790i	−0.731794	+	0.214874i
$687$	0.880973	−	39.9669i	0.0336112	−	1.52483i
$688$	1.39121	+	9.67610i	0.0530395	+	0.368898i
$689$	36.6052			1.39455
$690$	0.628367	−	18.5635i	0.0239215	−	0.706702i
$691$	−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
$693$	−0.758331	−	1.87505i	−0.0288066	−	0.0712274i
$694$	22.1201	−	6.49504i	0.839667	−	0.246549i
$695$	−2.71483	+	0.0525950i	−0.102980	+	0.00199504i
$696$	−7.87140	+	0.955203i	−0.298365	+	0.0362069i
$697$	−34.7020	+	22.3016i	−1.31443	+	0.844735i
$698$	−3.17602	−	6.95452i	−0.120214	−	0.263232i
$699$	−7.48958	+	15.4873i	−0.283282	+	0.585783i
$700$	−7.27501	+	9.08415i	−0.274969	+	0.343349i
$701$	2.88505	−	20.0659i	0.108967	−	0.757880i	−0.859930	−	0.510413i	$-0.829493\pi$
$701$	2.88505	−	20.0659i	0.108967	−	0.757880i	0.968896	−	0.247467i	$-0.0795983\pi$
$702$	−15.8351	−	8.53834i	−0.597658	−	0.322259i
$703$	39.2762	−	61.1150i	1.48133	−	2.30500i
$704$	0.189680	+	0.218902i	0.00714883	+	0.00825019i
$705$	48.5642	+	0.129581i	1.82903	+	0.00488031i
$706$	−4.36665	+	2.80628i	−0.164341	+	0.105616i
$707$	7.33026	−	24.9646i	0.275683	−	0.938889i
$708$	−1.00520	+	3.16372i	−0.0377775	+	0.118900i
$709$	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
$711$	18.8821	−	26.7149i	0.708135	−	1.00189i
$712$	−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
$717$	9.03706	−	7.48843i	0.337495	−	0.279661i
$718$	−1.01414	+	1.17038i	−0.0378474	+	0.0436783i
$719$	−13.6120	+	46.3584i	−0.507643	+	1.72887i	0.162561	+	0.986698i	$0.448025\pi$
$719$	−13.6120	+	46.3584i	−0.507643	+	1.72887i	−0.670205	+	0.742176i	$0.733794\pi$
$720$	−5.73118	+	3.48621i	−0.213588	+	0.129923i
$721$	5.33385	+	11.6795i	0.198643	+	0.434967i
$722$	−27.8483	−	32.1386i	−1.03640	−	1.19608i
$723$	−35.3270	−	5.87657i	−1.31382	−	0.218552i
$724$	−11.7587	−	1.69064i	−0.437008	−	0.0628322i
$725$	−5.59323	+	22.1956i	−0.207727	+	0.824323i
$726$	3.10255	−	18.6510i	0.115146	−	0.692202i
$727$	−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
$729$	26.7643	+	3.55992i	0.991270	+	0.131849i
$730$	28.1562	−	13.5236i	1.04211	−	0.500533i
$731$	−38.2139	−	33.1125i	−1.41339	−	1.22471i
$732$	7.55575	−	6.26096i	0.279269	−	0.231412i
$733$	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
$735$	−2.56030	+	5.56692i	−0.0944381	+	0.205339i
$736$	−2.46583	−	4.11335i	−0.0908919	−	0.151620i
$737$	3.02699			0.111501
$738$	−13.8091	+	19.5374i	−0.508319	+	0.719181i
$739$	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
$741$	−44.8294	−	14.2435i	−1.64685	−	0.523246i
$742$	−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	$0.921844\pi$
$744$	0.753327	−	0.831625i	0.0276183	−	0.0304889i
$745$	0.160175	−	1.29111i	0.00586835	−	0.0473027i
$746$	−25.9938	−	16.7052i	−0.951702	−	0.611621i
$747$	−16.2175	+	12.8463i	−0.593366	+	0.470020i
$748$	−1.48296	−	0.213217i	−0.0542223	−	0.00779599i
$749$	−13.5450	+	21.0765i	−0.494924	+	0.770117i
$750$	3.44542	+	19.0559i	0.125809	+	0.695825i
$751$	−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
$753$	3.36949	+	27.7664i	0.122791	+	1.01186i
$754$	−10.3794	+	11.9785i	−0.377996	+	0.436231i
$755$	28.8748	+	17.7760i	1.05086	+	0.646934i
$756$	8.50699	−	8.59735i	0.309396	−	0.312683i
$757$	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
$759$	0.799665	−	2.26923i	0.0290260	−	0.0823678i
$760$	−13.0304	+	11.7404i	−0.472661	+	0.425869i
$761$	3.29333	−	0.473509i	0.119383	−	0.0171647i	−0.0823643	−	0.996602i	$-0.526247\pi$
$761$	3.29333	−	0.473509i	0.119383	−	0.0171647i	0.201747	+	0.979438i	$0.435338\pi$
$762$	−0.550436	+	24.9715i	−0.0199402	+	0.904622i
$763$	4.89333	+	16.6651i	0.177150	+	0.603319i
$764$	−0.756940	+	0.873556i	−0.0273851	+	0.0316041i
$765$	10.5951	−	33.0409i	0.383066	−	1.19460i
$766$	−2.63882	−	4.10608i	−0.0953445	−	0.148359i
$767$	2.75653	+	6.03595i	0.0995324	+	0.217946i
$768$	−0.754065	+	1.55929i	−0.0272100	+	0.0562660i
$769$	−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
$771$	−9.56543	+	2.58111i	−0.344490	+	0.0929564i
$772$	−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	$0.166479\pi$
$774$	−27.7475	−	9.49419i	−0.997362	−	0.341262i
$775$	−1.45873	−	2.89216i	−0.0523992	−	0.103890i
$776$	−15.8035	−	4.64031i	−0.567311	−	0.166578i
$777$	35.5866	+	11.3068i	1.27666	+	0.405628i
$778$	−14.4300	+	4.23702i	−0.517339	+	0.151904i
$779$	−25.9859	+	56.9012i	−0.931042	+	2.03870i
$780$	−3.81214	+	12.8560i	−0.136496	+	0.460317i
$781$			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
$786$	−10.2846	+	8.52216i	−0.366839	+	0.303975i
$787$	−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
$789$	13.5987	−	20.1684i	0.484125	−	0.718015i
$790$	−22.3723	−	9.69784i	−0.795969	−	0.345034i
$791$	6.18066	−	5.35558i	0.219759	−	0.190422i
$792$	−0.843726	+	0.207835i	−0.0299805	+	0.00738509i
$793$	2.79149	−	19.4153i	0.0991288	−	0.689456i
$794$	18.3819	+	2.64292i	0.652350	+	0.0937937i
$795$	22.0460	+	34.5063i	0.781891	+	1.22381i
$796$	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	$0.277192\pi$
$798$	17.6788	−	26.2198i	0.625823	−	0.928170i
$799$	−18.2730	+	62.2320i	−0.646451	+	2.20161i
$800$	3.41820	+	3.64909i	0.120852	+	0.129015i
$801$	9.06173	−	17.7303i	0.320180	−	0.626471i
$802$	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
$807$	3.64630	+	5.95850i	0.128356	+	0.209749i
$808$	−10.1679	−	4.64354i	−0.357706	−	0.163359i
$809$	−6.87263	−	23.4060i	−0.241629	−	0.822912i	−0.987608	−	0.156942i	$-0.949836\pi$
$809$	−6.87263	−	23.4060i	−0.241629	−	0.822912i	0.745979	−	0.665969i	$-0.231982\pi$
$810$	−1.48815	−	20.0695i	−0.0522883	−	0.705171i
$811$	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
$813$	−7.46704	+	8.24314i	−0.261881	+	0.289099i
$814$	−1.75677	−	2.02742i	−0.0615747	−	0.0710610i
$815$	−1.49806	+	0.245093i	−0.0524746	+	0.00858522i
$816$	−2.33400	−	8.64965i	−0.0817063	−	0.302798i
$817$	−75.8976	−	10.9124i	−2.65532	−	0.381777i
$818$	−7.48244	−	4.80867i	−0.261617	−	0.168131i
$819$	1.06531	−	24.1531i	0.0372250	−	0.843979i
$820$	16.3615	+	7.09232i	0.571368	+	0.247675i
$821$	15.6497	+	24.3513i	0.546177	+	0.849868i	0.999132	−	0.0416658i	$-0.0132665\pi$
$821$	15.6497	+	24.3513i	0.546177	+	0.849868i	−0.452955	+	0.891533i	$0.649630\pi$
$822$	16.5588	−	2.00943i	0.577556	−	0.0700871i
$823$	−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
$825$	−0.315469	+	2.48852i	−0.0109832	+	0.0866391i
$826$	−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	$0.913904\pi$
$828$	14.3547	−	0.971183i	0.498860	−	0.0337510i
$829$	−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
$831$	0.0975611	−	4.42603i	0.00338436	−	0.153537i
$832$	0.975429	+	3.32201i	0.0338169	+	0.115170i
$833$	−6.18461	−	5.35899i	−0.214284	−	0.185678i
$834$	−0.253379	−	2.08798i	−0.00877378	−	0.0723008i
$835$	−18.3595	−	5.00667i	−0.635356	−	0.173263i
$836$	−2.06664	+	0.943804i	−0.0714763	+	0.0326421i
$837$	1.19304	+	3.14779i	0.0412376	+	0.108803i
$838$	8.16538	+	5.24757i	0.282068	+	0.181274i
$839$	1.49296	−	10.3838i	0.0515427	−	0.358487i	−0.947686	−	0.319206i	$-0.896584\pi$
$839$	1.49296	−	10.3838i	0.0515427	−	0.358487i	0.999228	−	0.0392816i	$-0.0125069\pi$
$840$	−7.57079	−	4.89404i	−0.261217	−	0.168861i
$841$	6.76611	+	4.34831i	0.233314	+	0.149942i
$842$	19.9768	−	17.3100i	0.688446	−	0.596542i
$843$	−16.6753	+	18.4085i	−0.574329	+	0.634022i
$844$	0.817635	−	0.525462i	0.0281442	−	0.0180871i
$845$	−0.980518	−	2.04144i	−0.0337309	−	0.0702277i
$846$	3.70766	+	37.4347i	0.127472	+	1.28703i
$847$	24.3795	−	7.15847i	0.837690	−	0.245968i
$848$	9.61722	+	4.39204i	0.330257	+	0.150823i
$849$	14.3213	−	8.76389i	0.491504	−	0.300776i
$850$	−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
$855$	−13.5724	−	50.8373i	−0.464166	−	1.73860i
$856$	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	$0.857409\pi$
$858$	−0.971049	+	1.44018i	−0.0331511	+	0.0491669i
$859$	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
$861$	−31.7159	−	5.27588i	−1.08088	−	0.179802i
$862$	−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	$-0.204121\pi$
$864$	−3.13587	−	4.14323i	−0.106684	−	0.140955i
$865$	−5.94779	+	47.9430i	−0.202231	+	1.63011i
$866$	12.7481	+	27.9144i	0.433198	+	0.948572i
$867$	14.0087	+	9.44544i	0.475761	+	0.320784i
$868$	1.44686	+	0.424837i	0.0491097	+	0.0144199i
$869$	−2.38707	−	2.06841i	−0.0809758	−	0.0701659i
$870$	−17.5428	−	2.57007i	−0.594758	−	0.0871337i
$871$	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
$876$	12.6291	+	20.6374i	0.426697	+	0.697275i
$877$	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
$879$	−7.77145	+	24.4596i	−0.262124	+	0.825003i
$880$	0.280415	+	0.583824i	0.00945279	+	0.0196807i
$881$	−39.6360	+	25.4725i	−1.33537	+	0.858190i	−0.996577	−	0.0826710i	$-0.973655\pi$
$881$	−39.6360	+	25.4725i	−1.33537	+	0.858190i	−0.338793	+	0.940861i	$0.610019\pi$
$882$	−4.49070	−	1.53656i	−0.151210	−	0.0517386i
$883$	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
$885$	−4.02971	+	6.23372i	−0.135457	+	0.209544i
$886$	−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	$0.578860\pi$
$888$	6.98397	−	14.4418i	0.234367	−	0.484634i
$889$	−30.5331	+	13.9440i	−1.02405	+	0.467666i
$890$	−14.3185	−	3.90469i	−0.479958	−	0.130885i
$891$	0.596727	−	2.53763i	0.0199911	−	0.0850136i
$892$	−0.231580	−	0.200666i	−0.00775389	−	0.00671878i
$893$	27.7100	+	94.3717i	0.927281	+	3.15803i
$894$	1.00751	+	0.0222082i	0.0336963	+	0.000742752i
$895$	24.8670	+	20.7178i	0.831212	+	0.692521i
$896$	−2.32764			−0.0777609
$897$	19.9628	−	20.7027i	0.666539	−	0.691243i
$898$		−	35.6649i		−	1.19015i
$899$	2.93557	−	0.422071i	0.0979067	−	0.0140769i
$900$	−14.4147	+	4.14912i	−0.480491	+	0.138304i
$901$	−52.4717	+	15.4071i	−1.74809	+	0.513285i
$902$	1.74574	+	1.51269i	0.0581266	+	0.0503670i
$903$	−4.74776	−	39.1242i	−0.157996	−	1.30197i
$904$	−1.89955	−	2.95576i	−0.0631781	−	0.0983070i
$905$	−24.3723	−	10.5648i	−0.810162	−	0.351186i
$906$	−11.4347	+	23.6451i	−0.379891	+	0.785556i
$907$	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
$909$	26.2865	−	20.8222i	0.871868	−	0.690628i
$910$	−17.7837	+	2.90955i	−0.589525	+	0.0964506i
$911$	−12.2432	−	14.1294i	−0.405634	−	0.468126i	0.515773	−	0.856725i	$-0.327505\pi$
$911$	−12.2432	−	14.1294i	−0.405634	−	0.468126i	−0.921407	+	0.388599i	$0.872959\pi$
$912$	−10.0690	−	9.12097i	−0.333417	−	0.302026i
$913$	1.07994	+	1.68041i	0.0357407	+	0.0556136i
$914$	0.161946	+	0.0475518i	0.00535671	+	0.00157287i
$915$	19.9833	−	9.06169i	0.660626	−	0.299570i
$916$	−6.50252	−	22.1456i	−0.214849	−	0.731710i
$917$	−16.3274	−	7.45648i	−0.539179	−	0.246235i
$918$	26.2926	+	5.57431i	0.867786	+	0.183980i
$919$		−	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
$924$	−0.745077	−	0.899161i	−0.0245112	−	0.0295802i
$925$	−31.6586	−	33.7970i	−1.04093	−	1.11124i
$926$	2.63618	−	8.97799i	0.0866301	−	0.295035i
$927$	−3.07461	+	16.2606i	−0.100984	+	0.534067i
$928$	−4.16420	+	1.90173i	−0.136697	+	0.0624272i
$929$	23.9864	−	20.7844i	0.786969	−	0.681913i	−0.165614	−	0.986191i	$-0.552961\pi$
$929$	23.9864	−	20.7844i	0.786969	−	0.681913i	0.952583	+	0.304278i	$0.0984152\pi$
$930$	2.11439	−	1.35088i	0.0693336	−	0.0442970i
$931$	−12.2834	−	1.76609i	−0.402572	−	0.0578812i
$932$	−1.41351	+	9.83118i	−0.0463011	+	0.322031i
$933$	−29.0056	−	4.82502i	−0.949600	−	0.157964i
$934$	8.37879	−	7.26026i	0.274162	−	0.237563i
$935$	−3.07374	−	1.33239i	−0.100522	−	0.0435739i
$936$	−10.2059	−	1.92977i	−0.333591	−	0.0630767i
$937$	−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
$939$	24.8244	+	29.9581i	0.810113	+	0.977647i
$940$	26.7449	−	8.41902i	0.872321	−	0.274598i
$941$	5.20686	+	36.2145i	0.169739	+	1.18056i	0.879424	+	0.476040i	$0.157928\pi$
$941$	5.20686	+	36.2145i	0.169739	+	1.18056i	−0.709685	+	0.704519i	$0.751163\pi$
$942$	3.96082	+	9.20458i	0.129051	+	0.299901i
$943$	−24.1332	−	29.6713i	−0.785886	−	0.966230i
$944$			1.91656i			0.0623786i
$945$	23.4099	−	13.5423i	0.761523	−	0.440532i
$946$	−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	$0.445764\pi$
$948$	5.71931	−	18.0008i	0.185755	−	0.584639i
$949$	46.4051	+	13.6258i	1.50637	+	0.442311i
$950$	−35.0171	+	17.6617i	−1.13611	+	0.573022i
$951$	20.0676	−	22.1533i	0.650735	−	0.718371i
$952$	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	$0.990907\pi$
$954$	−24.8628	+	19.6944i	−0.804963	+	0.637631i
$955$	−2.14685	+	1.43921i	−0.0694705	+	0.0465717i
$956$	3.66342	−	5.70039i	0.118483	−	0.184364i
$957$	−2.06759	−	0.999878i	−0.0668357	−	0.0323215i
$958$	−2.92651	−	6.40817i	−0.0945514	−	0.207039i
$959$	12.1190	+	18.8576i	0.391344	+	0.608943i
$960$	−2.54407	+	2.92023i	−0.0821094	+	0.0942499i
$961$	20.0258	−	23.1110i	0.645995	−	0.745518i
$962$	−9.03419	−	30.7676i	−0.291274	−	0.991988i
$963$	−29.9351	+	12.1067i	−0.964646	+	0.390133i
$964$	−20.4659	+	2.94255i	−0.659161	+	0.0947730i
$965$	−3.25938	+	2.93671i	−0.104923	+	0.0945360i
$966$	9.57336	+	16.7984i	0.308018	+	0.540479i
$967$		−	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
$969$	70.2558	+	1.54862i	2.25694	+	0.0497488i
$970$	−31.3628	−	19.3076i	−1.00700	−	0.619931i
$971$	−27.1776	+	31.3646i	−0.872170	+	1.00654i	0.127721	+	0.991810i	$0.459234\pi$
$971$	−27.1776	+	31.3646i	−0.872170	+	1.00654i	−0.999892	+	0.0147279i	$0.995312\pi$
$972$	15.3493	−	2.72028i	0.492328	−	0.0872531i
$973$	2.37784	−	1.52814i	0.0762300	−	0.0489900i
$974$	−25.1770	+	11.4979i	−0.806722	+	0.368418i
$975$	−15.7870	+	25.4914i	−0.505589	+	0.816377i
$976$	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	$0.416546\pi$
$978$	−0.306323	−	1.13521i	−0.00979514	−	0.0363001i
$979$	−1.61729	−	1.03937i	−0.0516889	−	0.0332184i
$980$	−0.435545	+	3.51077i	−0.0139130	+	0.112148i
$981$	−7.24714	+	21.1803i	−0.231383	+	0.676234i
$982$	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	$0.704932\pi$
$984$	−4.18271	+	13.1645i	−0.133340	+	0.419670i
$985$	7.01233	+	4.31695i	0.223431	+	0.137549i
$986$	9.83666	−	21.5393i	0.313263	−	0.685950i
$987$	−43.1200	+	26.3873i	−1.37253	+	0.839916i
$988$	−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
$993$	−1.74455	−	2.10533i	−0.0553616	−	0.0668105i
$994$	−14.6795	−	12.7199i	−0.465606	−	0.403450i
$995$	23.8040	−	11.4332i	0.754638	−	0.362458i
$996$	−6.67770	+	9.90383i	−0.211591	+	0.313815i
$997$	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
$999$	29.0437	+	38.3736i	0.918901	+	1.21409i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.73163 - 0.0381696i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.23565 + 0.0433117i) q^{5} +(-0.208656 - 1.71944i) q^{6} +(1.95813 - 1.25842i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(2.99709 + 0.132191i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.73163 - 0.0381696i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.23565 + 0.0433117i) q^{5} +(-0.208656 - 1.71944i) q^{6} +(1.95813 - 1.25842i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(2.99709 + 0.132191i) q^{9} +(-0.361037 - 2.20673i) q^{10} +(0.0412214 - 0.286701i) q^{11} +(1.67224 - 0.451233i) q^{12} +(1.87184 - 2.91263i) q^{13} +(1.52428 + 1.75911i) q^{14} +(3.87297 + 0.0103340i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.45726 + 4.96297i) q^{17} +(0.295684 + 2.98539i) q^{18} +(2.20986 + 7.52609i) q^{19} +(2.13289 - 0.671412i) q^{20} +(-3.43880 + 2.10437i) 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} +(-5.18480 - 0.343304i) q^{27} +(-1.52428 + 1.75911i) q^{28} +(-1.28974 + 4.39246i) q^{29} +(0.540952 + 3.83502i) q^{30} +(-0.269124 - 0.589299i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.0823234 + 0.494887i) q^{33} +(-5.11984 - 0.736122i) q^{34} +(-4.32319 + 2.89819i) q^{35} +(-2.91293 + 0.717540i) q^{36} +(-6.06516 - 6.99957i) q^{37} +(-7.13499 + 3.25844i) q^{38} +(-3.35250 + 4.97215i) q^{39} +(0.968120 + 2.01563i) q^{40} +(6.02707 + 5.22249i) q^{41} +(-2.57234 - 3.10431i) 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} +(-1.47738 + 0.904080i) q^{48} +(-0.657229 + 1.43913i) q^{49} +(0.902728 + 4.91783i) q^{50} +(2.71287 - 8.53840i) q^{51} +(-0.975429 + 3.32201i) q^{52} +(5.71601 + 8.89428i) q^{53} +(-0.398064 - 5.18088i) q^{54} +(-0.0797390 + 0.642748i) q^{55} +(-1.95813 - 1.25842i) q^{56} +(-3.53939 - 13.1168i) q^{57} +(-4.53130 - 0.651502i) q^{58} +(-1.03617 + 1.61231i) q^{59} +(-3.71900 + 1.08123i) q^{60} +(5.15339 - 2.35348i) q^{61} +(0.545000 - 0.350250i) q^{62} +(6.03505 - 3.51273i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-4.05861 + 6.59269i) q^{65} +(-0.501565 - 0.0110558i) q^{66} +(1.48727 + 10.3442i) q^{67} -5.17249i q^{68} +(8.14757 + 1.61775i) q^{69} +(-3.48394 - 3.86674i) q^{70} +(-8.25991 + 1.18760i) q^{71} +(-1.12479 - 2.78116i) q^{72} +(3.93552 + 13.4031i) q^{73} +(6.06516 - 6.99957i) q^{74} +(-8.65905 + 0.144642i) q^{75} +(-4.24069 - 6.59864i) q^{76} +(-0.280072 - 0.613272i) q^{77} +(-5.39866 - 2.61077i) q^{78} +(5.89554 - 9.17364i) q^{79} +(-1.85733 + 1.24512i) q^{80} +(8.96505 + 0.792377i) q^{81} +(-4.31159 + 6.70896i) q^{82} +(-5.21189 + 4.51613i) q^{83} +(2.70663 - 2.98795i) q^{84} +(3.04296 - 11.1586i) q^{85} +(-9.37962 - 2.75411i) q^{86} +(2.40101 - 7.55688i) q^{87} +(-0.277916 + 0.0816036i) q^{88} +(2.75722 - 6.03747i) q^{89} +(-0.790348 - 6.66148i) 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} +(-1.10513 - 1.33367i) q^{96} +(10.7860 - 12.4477i) q^{97} +(-1.51802 - 0.445730i) q^{98} +(0.161443 - 0.853818i) 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

L-functions

Modular forms

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