LMFDB - Embedded newform 150.2.l.a.113.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.9
Character	$\chi$	$=$	150.113
Dual form			150.2.l.a.77.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(1.00892 - 1.40787i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.66221 + 1.49568i) q^{5} +(1.54836 + 0.776257i) q^{6} +(-0.00784794 + 0.00784794i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.964173 - 2.84084i) q^{9} +O(q^{10})$	\(q+(0.156434 + 0.987688i) q^{2} +(1.00892 - 1.40787i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.66221 + 1.49568i) q^{5} +(1.54836 + 0.776257i) q^{6} +(-0.00784794 + 0.00784794i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.964173 - 2.84084i) q^{9} +(-1.21724 + 1.87572i) q^{10} +(-0.297822 + 0.409916i) q^{11} +(-0.524483 + 1.65073i) q^{12} +(3.89992 + 0.617686i) q^{13} +(-0.00897901 - 0.00652363i) q^{14} +(3.78275 - 0.831157i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.99929 + 1.01869i) q^{17} +(2.65503 - 1.39671i) q^{18} +(-4.68585 - 1.52252i) q^{19} +(-2.04305 - 0.908822i) q^{20} +(0.00313093 + 0.0189668i) q^{21} +(-0.451459 - 0.230030i) q^{22} +(-8.33555 + 1.32022i) q^{23} +(-1.71246 - 0.259794i) q^{24} +(0.525896 + 4.97227i) q^{25} +3.94853i q^{26} +(-4.97229 - 1.50875i) q^{27} +(0.00503869 - 0.00988898i) q^{28} +(-0.391550 - 1.20507i) q^{29} +(1.41268 + 3.60615i) q^{30} +(2.76166 - 8.49952i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.276630 + 0.832864i) q^{33} +(-1.31890 - 1.81531i) q^{34} +(-0.0247829 + 0.00130695i) q^{35} +(1.79485 + 2.40385i) q^{36} +(-0.561423 + 3.54469i) q^{37} +(0.770751 - 4.86633i) q^{38} +(4.80431 - 4.86737i) q^{39} +(0.578030 - 2.16007i) q^{40} +(-6.80489 - 9.36613i) q^{41} +(-0.0182435 + 0.00605944i) q^{42} +(4.42647 + 4.42647i) q^{43} +(0.156574 - 0.481886i) q^{44} +(2.64632 - 6.16417i) q^{45} +(-2.60793 - 8.02639i) q^{46} +(-0.996101 + 1.95496i) q^{47} +(-0.0112919 - 1.73201i) q^{48} +6.99988i q^{49} +(-4.82878 + 1.29726i) q^{50} +(-0.582939 + 3.84250i) q^{51} +(-3.89992 + 0.617686i) q^{52} +(7.25397 + 3.69608i) q^{53} +(0.712332 - 5.14709i) q^{54} +(-1.10815 + 0.235923i) q^{55} +(0.0105555 + 0.00342968i) q^{56} +(-6.87114 + 5.06094i) q^{57} +(1.12898 - 0.575243i) q^{58} +(2.70425 - 1.96475i) q^{59} +(-3.34077 + 1.95941i) q^{60} +(-4.82361 - 3.50456i) q^{61} +(8.82690 + 1.39804i) q^{62} +(0.0298615 + 0.0147280i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(5.55863 + 6.85975i) q^{65} +(-0.779336 + 0.403513i) q^{66} +(-2.12122 - 4.16313i) q^{67} +(1.58664 - 1.58664i) q^{68} +(-6.55118 + 13.0673i) q^{69} +(-0.00516776 - 0.0242734i) q^{70} +(11.1129 - 3.61079i) q^{71} +(-2.09348 + 2.14880i) q^{72} +(1.49152 + 9.41706i) q^{73} -3.58887 q^{74} +(7.53087 + 4.27621i) q^{75} +4.92699 q^{76} +(-0.000879712 - 0.00555428i) q^{77} +(5.55900 + 3.98374i) q^{78} +(0.373190 - 0.121257i) q^{79} +(2.22389 + 0.233005i) q^{80} +(-7.14074 + 5.47812i) q^{81} +(8.18630 - 8.18630i) q^{82} +(4.76829 + 9.35829i) q^{83} +(-0.00883874 - 0.0170710i) q^{84} +(-4.84687 - 1.29701i) q^{85} +(-3.67952 + 5.06443i) q^{86} +(-2.09161 - 0.664562i) q^{87} +(0.500446 + 0.0792629i) q^{88} +(12.1475 + 8.82566i) q^{89} +(6.50225 + 1.64945i) q^{90} +(-0.0354539 + 0.0257588i) q^{91} +(7.51960 - 3.83143i) q^{92} +(-9.17990 - 12.4634i) q^{93} +(-2.08671 - 0.678015i) q^{94} +(-5.51167 - 9.53928i) q^{95} +(1.70892 - 0.282100i) q^{96} +(7.85809 + 4.00390i) q^{97} +(-6.91370 + 1.09502i) q^{98} +(1.45166 + 0.450833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	1.00892	−	1.40787i	0.582498	−	0.812832i
$3$	1.00892	−	1.40787i	0.582498	−	0.812832i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	1.66221	+	1.49568i	0.743364	+	0.668887i
$5$	1.66221	+	1.49568i	0.743364	+	0.668887i
$6$	1.54836	+	0.776257i	0.632116	+	0.316906i
$7$	−0.00784794	+	0.00784794i	−0.00296624	+	0.00296624i	−0.708588	−	0.705622i	$-0.750668\pi$
$7$	−0.00784794	+	0.00784794i	−0.00296624	+	0.00296624i	0.705622	+	0.708588i	$0.250668\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−0.964173	−	2.84084i	−0.321391	−	0.946947i
$10$	−1.21724	+	1.87572i	−0.384924	+	0.593156i
$11$	−0.297822	+	0.409916i	−0.0897966	+	0.123594i	−0.851552	−	0.524271i	$-0.824338\pi$
$11$	−0.297822	+	0.409916i	−0.0897966	+	0.123594i	0.761755	+	0.647865i	$0.224338\pi$
$12$	−0.524483	+	1.65073i	−0.151405	+	0.476525i
$13$	3.89992	+	0.617686i	1.08164	+	0.171315i	0.671720	−	0.740805i	$-0.265556\pi$
$13$	3.89992	+	0.617686i	1.08164	+	0.171315i	0.409923	+	0.912120i	$0.365556\pi$
$14$	−0.00897901	−	0.00652363i	−0.00239974	−	0.00174351i
$15$	3.78275	−	0.831157i	0.976701	−	0.214604i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−1.99929	+	1.01869i	−0.484898	+	0.247068i	−0.679309	−	0.733852i	$-0.737720\pi$
$17$	−1.99929	+	1.01869i	−0.484898	+	0.247068i	0.194411	+	0.980920i	$0.437720\pi$
$18$	2.65503	−	1.39671i	0.625798	−	0.329207i
$19$	−4.68585	−	1.52252i	−1.07501	−	0.349291i	−0.282571	−	0.959246i	$-0.591187\pi$
$19$	−4.68585	−	1.52252i	−1.07501	−	0.349291i	−0.792436	+	0.609955i	$0.791187\pi$
$20$	−2.04305	−	0.908822i	−0.456839	−	0.203219i
$21$	0.00313093	+	0.0189668i	0.000683224	+	0.00413889i
$22$	−0.451459	−	0.230030i	−0.0962514	−	0.0490425i
$23$	−8.33555	+	1.32022i	−1.73808	+	0.275285i	−0.943380	−	0.331715i	$-0.892373\pi$
$23$	−8.33555	+	1.32022i	−1.73808	+	0.275285i	−0.794702	+	0.607000i	$0.792373\pi$
$24$	−1.71246	−	0.259794i	−0.349554	−	0.0530302i
$25$	0.525896	+	4.97227i	0.105179	+	0.994453i
$26$			3.94853i			0.774371i
$27$	−4.97229	−	1.50875i	−0.956918	−	0.290358i
$28$	0.00503869	−	0.00988898i	0.000952222	−	0.00186884i
$29$	−0.391550	−	1.20507i	−0.0727090	−	0.223775i	0.908098	−	0.418759i	$-0.137535\pi$
$29$	−0.391550	−	1.20507i	−0.0727090	−	0.223775i	−0.980807	+	0.194983i	$0.937535\pi$
$30$	1.41268	+	3.60615i	0.257918	+	0.658391i
$31$	2.76166	−	8.49952i	0.496009	−	1.52656i	−0.319369	−	0.947630i	$-0.603471\pi$
$31$	2.76166	−	8.49952i	0.496009	−	1.52656i	0.815378	−	0.578929i	$-0.196529\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.276630	+	0.832864i	0.0481551	+	0.144983i
$34$	−1.31890	−	1.81531i	−0.226190	−	0.311324i
$35$	−0.0247829	+	0.00130695i	−0.00418908	+	0.000220915i
$36$	1.79485	+	2.40385i	0.299142	+	0.400642i
$37$	−0.561423	+	3.54469i	−0.0922974	+	0.582743i	0.897584	+	0.440844i	$0.145321\pi$
$37$	−0.561423	+	3.54469i	−0.0922974	+	0.582743i	−0.989881	+	0.141899i	$0.954679\pi$
$38$	0.770751	−	4.86633i	0.125032	−	0.789423i
$39$	4.80431	−	4.86737i	0.769306	−	0.779403i
$40$	0.578030	−	2.16007i	0.0913946	−	0.341536i
$41$	−6.80489	−	9.36613i	−1.06275	−	1.46274i	−0.877211	−	0.480106i	$-0.840598\pi$
$41$	−6.80489	−	9.36613i	−1.06275	−	1.46274i	−0.185535	−	0.982638i	$-0.559402\pi$
$42$	−0.0182435	+	0.00605944i	−0.00281503	+	0.000934991i
$43$	4.42647	+	4.42647i	0.675031	+	0.675031i	0.958872	−	0.283840i	$-0.0916086\pi$
$43$	4.42647	+	4.42647i	0.675031	+	0.675031i	−0.283840	+	0.958872i	$0.591609\pi$
$44$	0.156574	−	0.481886i	0.0236044	−	0.0726470i
$45$	2.64632	−	6.16417i	0.394490	−	0.918900i
$46$	−2.60793	−	8.02639i	−0.384519	−	1.18343i
$47$	−0.996101	+	1.95496i	−0.145296	+	0.285160i	−0.952173	−	0.305560i	$-0.901156\pi$
$47$	−0.996101	+	1.95496i	−0.145296	+	0.285160i	0.806876	+	0.590720i	$0.201156\pi$
$48$	−0.0112919	−	1.73201i	−0.00162984	−	0.249995i
$49$			6.99988i			0.999982i
$50$	−4.82878	+	1.29726i	−0.682893	+	0.183460i
$51$	−0.582939	+	3.84250i	−0.0816278	+	0.538057i
$52$	−3.89992	+	0.617686i	−0.540821	+	0.0856577i
$53$	7.25397	+	3.69608i	0.996410	+	0.507696i	0.874594	−	0.484857i	$-0.161128\pi$
$53$	7.25397	+	3.69608i	0.996410	+	0.507696i	0.121816	+	0.992553i	$0.461128\pi$
$54$	0.712332	−	5.14709i	0.0969361	−	0.700431i
$55$	−1.10815	+	0.235923i	−0.149422	+	0.0318118i
$56$	0.0105555	+	0.00342968i	0.00141053	+	0.000458310i
$57$	−6.87114	+	5.06094i	−0.910105	+	0.670338i
$58$	1.12898	−	0.575243i	0.148242	−	0.0755331i
$59$	2.70425	−	1.96475i	0.352063	−	0.255789i	−0.397671	−	0.917528i	$-0.630181\pi$
$59$	2.70425	−	1.96475i	0.352063	−	0.255789i	0.749734	+	0.661739i	$0.230181\pi$
$60$	−3.34077	+	1.95941i	−0.431291	+	0.252959i
$61$	−4.82361	−	3.50456i	−0.617600	−	0.448712i	0.234483	−	0.972120i	$-0.424660\pi$
$61$	−4.82361	−	3.50456i	−0.617600	−	0.448712i	−0.852082	+	0.523408i	$0.824660\pi$
$62$	8.82690	+	1.39804i	1.12102	+	0.177552i
$63$	0.0298615	+	0.0147280i	0.00376220	+	0.00185555i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	5.55863	+	6.85975i	0.689463	+	0.850847i
$66$	−0.779336	+	0.403513i	−0.0959296	+	0.0496690i
$67$	−2.12122	−	4.16313i	−0.259149	−	0.508608i	0.724371	−	0.689411i	$-0.242130\pi$
$67$	−2.12122	−	4.16313i	−0.259149	−	0.508608i	−0.983519	+	0.180803i	$0.942130\pi$
$68$	1.58664	−	1.58664i	0.192409	−	0.192409i
$69$	−6.55118	+	13.0673i	−0.788669	+	1.57312i
$70$	−0.00516776	−	0.0242734i	−0.000617666	−	0.00290122i
$71$	11.1129	−	3.61079i	1.31885	−	0.428522i	0.436753	−	0.899582i	$-0.356129\pi$
$71$	11.1129	−	3.61079i	1.31885	−	0.428522i	0.882101	+	0.471060i	$0.156129\pi$
$72$	−2.09348	+	2.14880i	−0.246719	+	0.253238i
$73$	1.49152	+	9.41706i	0.174569	+	1.10218i	0.906934	+	0.421272i	$0.138416\pi$
$73$	1.49152	+	9.41706i	0.174569	+	1.10218i	−0.732366	+	0.680912i	$0.761584\pi$
$74$	−3.58887			−0.417198
$75$	7.53087	+	4.27621i	0.869590	+	0.493775i
$76$	4.92699			0.565165
$77$	−0.000879712	−	0.00555428i	−0.000100253	−	0.000632969i
$78$	5.55900	+	3.98374i	0.629433	+	0.451070i
$79$	0.373190	−	0.121257i	0.0419872	−	0.0136425i	−0.287948	−	0.957646i	$-0.592973\pi$
$79$	0.373190	−	0.121257i	0.0419872	−	0.0136425i	0.329935	+	0.944004i	$0.392973\pi$
$80$	2.22389	+	0.233005i	0.248639	+	0.0260508i
$81$	−7.14074	+	5.47812i	−0.793416	+	0.608680i
$82$	8.18630	−	8.18630i	0.904025	−	0.904025i
$83$	4.76829	+	9.35829i	0.523388	+	1.02721i	0.989777	+	0.142626i	$0.0455547\pi$
$83$	4.76829	+	9.35829i	0.523388	+	1.02721i	−0.466389	+	0.884580i	$0.654445\pi$
$84$	−0.00883874	−	0.0170710i	−0.000964386	−	0.00186259i
$85$	−4.84687	−	1.29701i	−0.525716	−	0.140681i
$86$	−3.67952	+	5.06443i	−0.396773	+	0.546112i
$87$	−2.09161	−	0.664562i	−0.224245	−	0.0712486i
$88$	0.500446	+	0.0792629i	0.0533478	+	0.00844945i
$89$	12.1475	+	8.82566i	1.28763	+	0.935518i	0.999755	−	0.0221500i	$-0.00705114\pi$
$89$	12.1475	+	8.82566i	1.28763	+	0.935518i	0.287875	+	0.957668i	$0.407051\pi$
$90$	6.50225	+	1.64945i	0.685398	+	0.173867i
$91$	−0.0354539	+	0.0257588i	−0.00371658	+	0.00270025i
$92$	7.51960	−	3.83143i	0.783973	−	0.399454i
$93$	−9.17990	−	12.4634i	−0.951911	−	1.29239i
$94$	−2.08671	−	0.678015i	−0.215228	−	0.0699319i
$95$	−5.51167	−	9.53928i	−0.565485	−	0.978709i
$96$	1.70892	−	0.282100i	0.174416	−	0.0287917i
$97$	7.85809	+	4.00390i	0.797868	+	0.406534i	0.804877	−	0.593441i	$-0.202231\pi$
$97$	7.85809	+	4.00390i	0.797868	+	0.406534i	−0.00700895	+	0.999975i	$0.502231\pi$
$98$	−6.91370	+	1.09502i	−0.698389	+	0.110614i
$99$	1.45166	+	0.450833i	0.145897	+	0.0453104i
$100$	−2.03667	−	4.56640i	−0.203667	−	0.456640i
$101$		−	8.84627i		−	0.880237i	−0.897940	−	0.440118i	$-0.854936\pi$
$101$		−	8.84627i		−	0.880237i	0.897940	−	0.440118i	$-0.145064\pi$
$102$	−3.88638	+	0.0253373i	−0.384809	+	0.00250876i
$103$	2.94517	−	5.78022i	0.290196	−	0.569542i	−0.699176	−	0.714950i	$-0.746450\pi$
$103$	2.94517	−	5.78022i	0.290196	−	0.569542i	0.989372	+	0.145408i	$0.0464495\pi$
$104$	−1.22016	−	3.75528i	−0.119647	−	0.368235i
$105$	−0.0231639	+	0.0362096i	−0.00226057	+	0.00353370i
$106$	−2.51581	+	7.74286i	−0.244357	+	0.752053i
$107$	−5.18111	−	5.18111i	−0.500877	−	0.500877i	0.410834	−	0.911710i	$-0.365238\pi$
$107$	−5.18111	−	5.18111i	−0.500877	−	0.500877i	−0.911710	+	0.410834i	$0.865238\pi$
$108$	5.19516	−	0.101621i	0.499904	−	0.00977848i
$109$	2.16720	+	2.98290i	0.207581	+	0.285710i	0.900095	−	0.435694i	$-0.143497\pi$
$109$	2.16720	+	2.98290i	0.207581	+	0.285710i	−0.692514	+	0.721404i	$0.743497\pi$
$110$	−0.406370	−	1.05760i	−0.0387459	−	0.100838i
$111$	4.42401	+	4.36670i	0.419909	+	0.414469i
$112$	−0.00173621	+	0.0109620i	−0.000164057	+	0.00103581i
$113$	2.04761	−	12.9281i	0.192623	−	1.21617i	−0.681994	−	0.731358i	$-0.738887\pi$
$113$	2.04761	−	12.9281i	0.192623	−	1.21617i	0.874617	−	0.484815i	$-0.161113\pi$
$114$	−6.07352	−	5.99484i	−0.568837	−	0.561468i
$115$	−15.8301	−	10.2728i	−1.47616	−	0.957944i
$116$	0.744772	+	1.02509i	0.0691504	+	0.0951773i
$117$	−2.00545	−	11.6746i	−0.185404	−	1.07932i
$118$	2.36360	+	2.36360i	0.217587	+	0.217587i
$119$	0.00769568	−	0.0236849i	0.000705462	−	0.00217119i
$120$	−2.45790	−	2.99312i	−0.224374	−	0.273233i
$121$	3.31985	+	10.2175i	0.301805	+	0.928860i
$122$	2.70683	−	5.31245i	0.245065	−	0.480967i
$123$	−20.0518	+	0.130728i	−1.80801	+	0.0117873i
$124$			8.93692i			0.802560i
$125$	−6.56276	+	9.05153i	−0.586991	+	0.809594i
$126$	−0.00987527	+	0.0317978i	−0.000879759	+	0.00283278i
$127$	13.0085	−	2.06035i	1.15432	−	0.182826i	0.450214	−	0.892921i	$-0.351348\pi$
$127$	13.0085	−	2.06035i	1.15432	−	0.182826i	0.704106	+	0.710095i	$0.251348\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	10.6978	−	1.76594i	0.941891	−	0.155482i
$130$	−5.90573	+	6.56330i	−0.517967	+	0.575639i
$131$	5.41574	+	1.75968i	0.473176	+	0.153744i	0.535891	−	0.844287i	$-0.319976\pi$
$131$	5.41574	+	1.75968i	0.473176	+	0.153744i	−0.0627151	+	0.998031i	$0.519976\pi$
$132$	−0.520460	−	0.706618i	−0.0453002	−	0.0615032i
$133$	0.0487229	−	0.0248256i	0.00422481	−	0.00215265i
$134$	3.78005	−	2.74636i	0.326546	−	0.237250i
$135$	−6.00841	−	9.94480i	−0.517121	−	0.855912i
$136$	1.81531	+	1.31890i	0.155662	+	0.113095i
$137$	−2.30141	−	0.364508i	−0.196623	−	0.0311420i	0.0573462	−	0.998354i	$-0.481736\pi$
$137$	−2.30141	−	0.364508i	−0.196623	−	0.0311420i	−0.253969	+	0.967212i	$0.581736\pi$
$138$	−13.9313	−	4.42634i	−1.18591	−	0.376795i
$139$	−2.06601	+	2.84362i	−0.175237	+	0.241193i	−0.887597	−	0.460622i	$-0.847626\pi$
$139$	−2.06601	+	2.84362i	−0.175237	+	0.241193i	0.712360	+	0.701814i	$0.247626\pi$
$140$	0.0231661	−	0.00890133i	0.00195789	−	0.000752299i
$141$	1.74734	+	3.37477i	0.147152	+	0.284207i
$142$	5.30477	+	10.4112i	0.445166	+	0.873688i
$143$	−1.41468	+	1.41468i	−0.118301	+	0.118301i
$144$	−2.44984	−	1.73156i	−0.204153	−	0.144297i
$145$	1.15155	−	2.58871i	0.0956312	−	0.214981i
$146$	−9.06780	+	2.94631i	−0.750456	+	0.243838i
$147$	9.85489	+	7.06229i	0.812817	+	0.582488i
$148$	−0.561423	−	3.54469i	−0.0461487	−	0.291371i
$149$	−19.1766			−1.57101			−0.785503	−	0.618857i	$-0.787596\pi$
$149$	−19.1766			−1.57101			−0.785503	+	0.618857i	$0.787596\pi$
$150$	−3.04548	+	8.10710i	−0.248662	+	0.661942i
$151$	−11.3802			−0.926104			−0.463052	−	0.886331i	$-0.653246\pi$
$151$	−11.3802			−0.926104			−0.463052	+	0.886331i	$0.653246\pi$
$152$	0.770751	+	4.86633i	0.0625162	+	0.394712i
$153$	4.82159	+	4.69746i	0.389802	+	0.379767i
$154$	0.00534828	−	0.00173776i	0.000430977	−	0.000140033i
$155$	17.3030	−	9.99745i	1.38981	−	0.803014i
$156$	−3.06507	+	6.11376i	−0.245402	+	0.489492i
$157$	13.7792	−	13.7792i	1.09970	−	1.09970i	0.105252	−	0.994446i	$-0.466435\pi$
$157$	13.7792	−	13.7792i	1.09970	−	1.09970i	0.994446	−	0.105252i	$-0.0335650\pi$
$158$	0.178144	+	0.349627i	0.0141724	+	0.0278148i
$159$	12.5222	−	6.48358i	0.993079	−	0.514181i
$160$	0.117757	+	2.23297i	0.00930953	+	0.176531i
$161$	0.0550558	−	0.0757779i	0.00433901	−	0.00597213i
$162$	−6.52774	−	6.19586i	−0.512867	−	0.486793i
$163$	−12.6122	−	1.99758i	−0.987867	−	0.156463i	−0.358465	−	0.933543i	$-0.616700\pi$
$163$	−12.6122	−	1.99758i	−0.987867	−	0.156463i	−0.629401	+	0.777080i	$0.716700\pi$
$164$	9.36613	+	6.80489i	0.731372	+	0.531373i
$165$	−0.785879	+	1.79815i	−0.0611806	+	0.139986i
$166$	−8.49715	+	6.17354i	−0.659507	+	0.479160i
$167$	−18.8890	+	9.62444i	−1.46168	+	0.744762i	−0.990530	−	0.137293i	$-0.956160\pi$
$167$	−18.8890	+	9.62444i	−1.46168	+	0.744762i	−0.471147	+	0.882055i	$0.656160\pi$
$168$	0.0154781	−	0.0114004i	0.00119416	−	0.000879561i
$169$	2.46410	+	0.800633i	0.189546	+	0.0615872i
$170$	0.522829	−	4.99009i	0.0400992	−	0.382722i
$171$	0.192721	+	14.7797i	0.0147377	+	1.13023i
$172$	−5.57768	−	2.84197i	−0.425294	−	0.216698i
$173$	−2.86992	+	0.454550i	−0.218196	+	0.0345588i	−0.264575	−	0.964365i	$-0.585232\pi$
$173$	−2.86992	+	0.454550i	−0.218196	+	0.0345588i	0.0463793	+	0.998924i	$0.485232\pi$
$174$	0.329180	−	2.16982i	0.0249551	−	0.164494i
$175$	−0.0431492	−	0.0348948i	−0.00326178	−	0.00263780i
$176$			0.506684i			0.0381928i
$177$	−0.0377446	−	5.78949i	−0.00283706	−	0.435165i
$178$	−6.81672	+	13.3786i	−0.510934	+	1.00277i
$179$	−6.51405	−	20.0482i	−0.486883	−	1.49847i	−0.829235	−	0.558901i	$-0.811223\pi$
$179$	−6.51405	−	20.0482i	−0.486883	−	1.49847i	0.342351	−	0.939572i	$-0.388777\pi$
$180$	−0.611968	+	6.68023i	−0.0456134	+	0.497915i
$181$	2.74046	−	8.43428i	0.203697	−	0.626915i	−0.796067	−	0.605208i	$-0.793090\pi$
$181$	2.74046	−	8.43428i	0.203697	−	0.626915i	0.999764	−	0.0217071i	$-0.00691012\pi$
$182$	−0.0309878	−	0.0309878i	−0.00229697	−	0.00229697i
$183$	−9.80056	+	3.25519i	−0.724478	+	0.240630i
$184$	4.96058	+	6.82766i	0.365699	+	0.503342i
$185$	−6.23491	+	5.05231i	−0.458400	+	0.371453i
$186$	10.8739	−	11.0166i	0.797310	−	0.807775i
$187$	0.177854	−	1.12293i	0.0130060	−	0.0821166i
$188$	0.343233	−	2.16709i	0.0250328	−	0.158051i
$189$	0.0508628	−	0.0271817i	0.00369972	−	0.00197718i
$190$	8.55962	−	6.93608i	0.620980	−	0.503196i
$191$	10.6498	+	14.6581i	0.770589	+	1.06062i	0.996259	+	0.0864210i	$0.0275430\pi$
$191$	10.6498	+	14.6581i	0.770589	+	1.06062i	−0.225670	+	0.974204i	$0.572457\pi$
$192$	0.545961	+	1.64375i	0.0394013	+	0.118628i
$193$	−9.56326	−	9.56326i	−0.688379	−	0.688379i	0.273495	−	0.961873i	$-0.411820\pi$
$193$	−9.56326	−	9.56326i	−0.688379	−	0.688379i	−0.961873	+	0.273495i	$0.911820\pi$
$194$	−2.72533	+	8.38769i	−0.195667	+	0.602201i
$195$	15.2658	−	0.904892i	1.09321	−	0.0648006i
$196$	−2.16308	−	6.65728i	−0.154506	−	0.475520i
$197$	7.59735	−	14.9106i	0.541289	−	1.06234i	−0.444723	−	0.895668i	$-0.646698\pi$
$197$	7.59735	−	14.9106i	0.541289	−	1.06234i	0.986012	−	0.166672i	$-0.0533020\pi$
$198$	−0.218193	+	1.50431i	−0.0155063	+	0.106907i
$199$			5.31518i			0.376783i	0.982094	+	0.188392i	$0.0603274\pi$
$199$			5.31518i			0.376783i	−0.982094	+	0.188392i	$0.939673\pi$
$200$	4.19157	−	2.72594i	0.296389	−	0.192753i
$201$	−8.00127	−	1.21386i	−0.564366	−	0.0856190i
$202$	8.73736	−	1.38386i	0.614758	−	0.0973682i
$203$	0.0125301	+	0.00638443i	0.000879444	+	0.000448099i
$204$	−0.632989	−	3.83457i	−0.0443181	−	0.268474i
$205$	2.69754	−	25.7464i	0.188404	−	1.79821i
$206$	6.16978	+	2.00468i	0.429869	+	0.139673i
$207$	11.7874	+	22.4070i	0.819284	+	1.55740i
$208$	3.51817	−	1.79260i	0.243941	−	0.124294i
$209$	2.01965	−	1.46736i	0.139702	−	0.101500i
$210$	−0.0393875	−	0.0172143i	−0.00271799	−	0.00118790i
$211$	−7.45392	−	5.41559i	−0.513149	−	0.372825i	0.300868	−	0.953666i	$-0.402724\pi$
$211$	−7.45392	−	5.41559i	−0.513149	−	0.372825i	−0.814017	+	0.580841i	$0.802724\pi$
$212$	−8.04109	−	1.27358i	−0.552264	−	0.0874701i
$213$	6.12845	−	19.2884i	0.419914	−	1.32162i
$214$	4.30682	−	5.92782i	0.294408	−	0.405218i
$215$	0.737159	+	13.9783i	0.0502738	+	0.953313i
$216$	0.913072	+	5.11530i	0.0621267	+	0.348052i
$217$	0.0450304	+	0.0883771i	0.00305686	+	0.00599943i
$218$	−2.60715	+	2.60715i	−0.176579	+	0.176579i
$219$	14.7628	+	7.40118i	0.997576	+	0.500125i
$220$	0.981005	−	0.566811i	0.0661393	−	0.0382144i
$221$	−8.42628	+	2.73787i	−0.566813	+	0.184169i
$222$	−3.62087	+	5.05265i	−0.243017	+	0.339112i
$223$	2.34331	+	14.7951i	0.156920	+	0.990753i	0.932937	+	0.360041i	$0.117237\pi$
$223$	2.34331	+	14.7951i	0.156920	+	0.990753i	−0.776017	+	0.630712i	$0.782763\pi$
$224$	−0.0110987			−0.000741561
$225$	13.6184	−	6.28811i	0.907890	−	0.419207i
$226$	13.0892			0.870683
$227$	2.48346	+	15.6799i	0.164833	+	1.04071i	0.921915	+	0.387393i	$0.126624\pi$
$227$	2.48346	+	15.6799i	0.164833	+	1.04071i	−0.757082	+	0.653320i	$0.773376\pi$
$228$	4.97093	−	6.93654i	0.329208	−	0.459384i
$229$	5.34094	−	1.73538i	0.352939	−	0.114677i	−0.127181	−	0.991879i	$-0.540593\pi$
$229$	5.34094	−	1.73538i	0.352939	−	0.114677i	0.480120	+	0.877203i	$0.340593\pi$
$230$	7.66996	−	17.2422i	0.505742	−	1.13692i
$231$	−0.00870724	−	0.00436529i	−0.000572895	−	0.000287215i
$232$	−0.895962	+	0.895962i	−0.0588228	+	0.0588228i
$233$	13.2643	+	26.0327i	0.868974	+	1.70546i	0.692841	+	0.721090i	$0.256359\pi$
$233$	13.2643	+	26.0327i	0.868974	+	1.70546i	0.176132	+	0.984367i	$0.443641\pi$
$234$	11.2171	−	3.80707i	0.733288	−	0.248876i
$235$	−4.57972	+	1.75971i	−0.298748	+	0.114791i
$236$	−1.96475	+	2.70425i	−0.127894	+	0.176032i
$237$	0.205805	−	0.647740i	0.0133685	−	0.0420753i
$238$	0.0245971	+	0.00389581i	0.00159440	+	0.000252528i
$239$	3.00438	+	2.18281i	0.194337	+	0.141194i	0.680699	−	0.732563i	$-0.261676\pi$
$239$	3.00438	+	2.18281i	0.194337	+	0.141194i	−0.486362	+	0.873758i	$0.661676\pi$
$240$	2.57177	−	2.89586i	0.166007	−	0.186927i
$241$	3.40480	−	2.47374i	0.219323	−	0.159347i	−0.472699	−	0.881224i	$-0.656720\pi$
$241$	3.40480	−	2.47374i	0.219323	−	0.159347i	0.692022	+	0.721877i	$0.256720\pi$
$242$	−9.57232	+	4.87734i	−0.615332	+	0.313527i
$243$	0.508047	+	15.5802i	0.0325912	+	0.999469i
$244$	5.67049	+	1.84245i	0.363016	+	0.117951i
$245$	−10.4696	+	11.6353i	−0.668876	+	0.743351i
$246$	−3.26591	−	19.7845i	−0.208227	−	1.26141i
$247$	−17.3340	−	8.83211i	−1.10293	−	0.561973i
$248$	−8.82690	+	1.39804i	−0.560508	+	0.0887758i
$249$	17.9860	+	2.72863i	1.13982	+	0.172920i
$250$	−9.96673	−	5.06599i	−0.630352	−	0.320401i
$251$			15.3633i			0.969724i	0.874591	+	0.484862i	$0.161130\pi$
$251$			15.3633i			0.969724i	−0.874591	+	0.484862i	$0.838870\pi$
$252$	−0.0329512	−	0.00477941i	−0.00207573	−	0.000301075i
$253$	1.94133	−	3.81007i	0.122050	−	0.239537i
$254$	4.06996	+	12.5261i	0.255372	+	0.785955i
$255$	−6.71611	+	5.51516i	−0.420579	+	0.345373i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.38421	−	4.38421i	−0.273479	−	0.273479i	0.557020	−	0.830499i	$-0.311945\pi$
$257$	−4.38421	−	4.38421i	−0.273479	−	0.273479i	−0.830499	+	0.557020i	$0.811945\pi$
$258$	3.41770	+	10.2899i	0.212777	+	0.640619i
$259$	−0.0234125	−	0.0322245i	−0.00145478	−	0.00200233i
$260$	−7.40635	−	4.80630i	−0.459322	−	0.298074i
$261$	−3.04588	+	2.27422i	−0.188535	+	0.140771i
$262$	−0.890808	+	5.62434i	−0.0550343	+	0.347473i
$263$	3.43441	−	21.6840i	0.211775	−	1.33709i	−0.621144	−	0.783697i	$-0.713332\pi$
$263$	3.43441	−	21.6840i	0.211775	−	1.33709i	0.832918	−	0.553396i	$-0.186668\pi$
$264$	0.616500	−	0.624592i	0.0379430	−	0.0384410i
$265$	6.52949	+	16.9933i	0.401103	+	1.04389i
$266$	0.0321419	+	0.0442395i	0.00197074	+	0.00271250i
$267$	24.6811	−	8.19766i	1.51046	−	0.501689i
$268$	3.30388	+	3.30388i	0.201817	+	0.201817i
$269$	4.19451	−	12.9094i	0.255744	−	0.787098i	−0.737939	−	0.674868i	$-0.764201\pi$
$269$	4.19451	−	12.9094i	0.255744	−	0.787098i	0.993682	−	0.112230i	$-0.0357994\pi$
$270$	8.88244	−	7.49014i	0.540568	−	0.455836i
$271$	6.18361	+	19.0312i	0.375627	+	1.15606i	0.943054	+	0.332639i	$0.107939\pi$
$271$	6.18361	+	19.0312i	0.375627	+	1.15606i	−0.567427	+	0.823424i	$0.692061\pi$
$272$	−1.01869	+	1.99929i	−0.0617670	+	0.121225i
$273$	0.000494848		0.0759028i	2.99496e−5		0.00459385i
$274$		−	2.33010i		−	0.140766i
$275$	−2.19484	−	1.26528i	−0.132354	−	0.0762990i
$276$	2.19252	−	14.4522i	0.131974	−	0.869920i
$277$	−16.1926	+	2.56465i	−0.972917	+	0.154095i	−0.622603	−	0.782538i	$-0.713925\pi$
$277$	−16.1926	+	2.56465i	−0.972917	+	0.154095i	−0.350313	+	0.936633i	$0.613925\pi$
$278$	−3.13181	−	1.59573i	−0.187833	−	0.0957058i
$279$	−26.8085	+	0.349571i	−1.60498	+	0.0209282i
$280$	0.0124157	+	0.0214884i	0.000741981	+	0.00128418i
$281$	−14.3418	−	4.65995i	−0.855563	−	0.277989i	−0.151789	−	0.988413i	$-0.548503\pi$
$281$	−14.3418	−	4.65995i	−0.855563	−	0.277989i	−0.703774	+	0.710424i	$0.748503\pi$
$282$	−3.05988	+	2.25375i	−0.182213	+	0.134209i
$283$	−8.64154	+	4.40308i	−0.513686	+	0.261736i	−0.691562	−	0.722317i	$-0.743077\pi$
$283$	−8.64154	+	4.40308i	−0.513686	+	0.261736i	0.177876	+	0.984053i	$0.443077\pi$
$284$	−9.45316	+	6.86812i	−0.560942	+	0.407548i
$285$	−18.9908	−	1.86465i	−1.12492	−	0.110452i
$286$	−1.61857	−	1.17596i	−0.0957079	−	0.0695359i
$287$	0.126909	+	0.0201004i	0.00749121	+	0.00118649i
$288$	1.32700	−	2.69055i	0.0781944	−	0.158542i
$289$	−7.03293	+	9.67999i	−0.413702	+	0.569411i
$290$	2.73698	+	0.732412i	0.160721	+	0.0430087i
$291$	13.5651	−	7.02354i	0.795201	−	0.411727i
$292$	−4.32855	−	8.49525i	−0.253309	−	0.497147i
$293$	3.63591	−	3.63591i	0.212412	−	0.212412i	−0.592879	−	0.805291i	$-0.702009\pi$
$293$	3.63591	−	3.63591i	0.212412	−	0.212412i	0.805291	+	0.592879i	$0.202009\pi$
$294$	−5.43370	+	10.8383i	−0.316900	+	0.632105i
$295$	7.43367	+	0.778852i	0.432805	+	0.0453465i
$296$	3.41322	−	1.10902i	0.198389	−	0.0644606i
$297$	2.09932	−	1.58889i	0.121815	−	0.0921966i
$298$	−2.99988	−	18.9405i	−0.173778	−	1.09719i
$299$	−33.3234			−1.92714
$300$	−8.48371	−	1.73975i	−0.489807	−	0.100445i
$301$	−0.0694774			−0.00400461
$302$	−1.78025	−	11.2400i	−0.102442	−	0.646792i
$303$	−12.4544	−	8.92515i	−0.715485	−	0.512737i
$304$	−4.68585	+	1.52252i	−0.268752	+	0.0873227i
$305$	−2.77617	−	13.0399i	−0.158963	−	0.746661i
$306$	−3.88537	+	5.49707i	−0.222112	+	0.314247i
$307$	−8.16612	+	8.16612i	−0.466065	+	0.466065i	−0.900637	−	0.434572i	$-0.856900\pi$
$307$	−8.16612	+	8.16612i	−0.466065	+	0.466065i	0.434572	+	0.900637i	$0.356900\pi$
$308$	0.00255302	+	0.00501059i	0.000145472	+	0.000285505i
$309$	−5.16634	−	9.97816i	−0.293903	−	0.567638i
$310$	12.5811	+	15.5260i	0.714561	+	0.881820i
$311$	6.84018	−	9.41470i	0.387871	−	0.533859i	−0.569777	−	0.821799i	$-0.692971\pi$
$311$	6.84018	−	9.41470i	0.387871	−	0.533859i	0.957648	+	0.287940i	$0.0929705\pi$
$312$	−6.51797	−	2.07094i	−0.369007	−	0.117244i
$313$	17.0326	+	2.69771i	0.962742	+	0.152483i	0.617969	−	0.786203i	$-0.287956\pi$
$313$	17.0326	+	2.69771i	0.962742	+	0.152483i	0.344773	+	0.938686i	$0.387956\pi$
$314$	15.7651	+	11.4540i	0.889674	+	0.646386i
$315$	0.0276079	+	0.0691442i	0.00155553	+	0.00389583i
$316$	−0.317455	+	0.230644i	−0.0178582	+	0.0129748i
$317$	13.9658	−	7.11591i	0.784396	−	0.399670i	−0.0154460	−	0.999881i	$-0.504917\pi$
$317$	13.9658	−	7.11591i	0.784396	−	0.399670i	0.799842	+	0.600211i	$0.204917\pi$
$318$	8.36267	+	11.3538i	0.468955	+	0.636691i
$319$	0.610589	+	0.198392i	0.0341864	+	0.0111078i
$320$	−2.18705	+	0.465620i	−0.122260	+	0.0260290i
$321$	−12.5216	+	2.06700i	−0.698888	+	0.115369i
$322$	0.0834575	+	0.0425237i	0.00465091	+	0.00236976i
$323$	10.9193	−	1.72945i	0.607568	−	0.0962293i
$324$	5.09842	−	7.41661i	0.283245	−	0.412034i
$325$	−1.02035	+	19.7163i	−0.0565988	+	1.09366i
$326$		−	12.7694i		−	0.707234i
$327$	6.38605	−	0.0416339i	0.353150	−	0.00230236i
$328$	−5.25593	+	10.3153i	−0.290210	+	0.569569i
$329$	−0.00752506	−	0.0231597i	−0.000414870	−	0.00127684i
$330$	−1.89895	−	0.494912i	−0.104534	−	0.0272440i
$331$	2.11085	−	6.49653i	0.116023	−	0.357081i	−0.876136	−	0.482064i	$-0.839887\pi$
$331$	2.11085	−	6.49653i	0.116023	−	0.357081i	0.992159	+	0.124982i	$0.0398874\pi$
$332$	−7.42678	−	7.42678i	−0.407598	−	0.407598i
$333$	10.6112	−	1.82278i	0.581490	−	0.0998876i
$334$	−12.4608	−	17.1509i	−0.681827	−	0.938455i
$335$	2.70079	−	10.0927i	0.147560	−	0.551422i
$336$	0.0136814	+	0.0135041i	0.000746379	+	0.000736710i
$337$	−0.243159	+	1.53525i	−0.0132457	+	0.0836303i	−0.993426	−	0.114479i	$-0.963480\pi$
$337$	−0.243159	+	1.53525i	−0.0132457	+	0.0836303i	0.980180	+	0.198109i	$0.0634801\pi$
$338$	−0.405307	+	2.55901i	−0.0220458	+	0.139192i
$339$	−16.1351	−	15.9261i	−0.876341	−	0.864988i
$340$	5.01044	−	0.264230i	0.271729	−	0.0143299i
$341$	2.66161	+	3.66339i	0.144134	+	0.198384i
$342$	−14.5676	+	2.50241i	−0.787726	+	0.135315i
$343$	−0.109870	−	0.109870i	−0.00593243	−	0.00593243i
$344$	1.93444	−	5.95360i	0.104298	−	0.320996i
$345$	−30.4340	+	11.9222i	−1.63851	+	0.641870i
$346$	−0.897908	−	2.76348i	−0.0482718	−	0.148565i
$347$	−2.48795	+	4.88287i	−0.133560	+	0.262126i	−0.948094	−	0.317989i	$-0.896993\pi$
$347$	−2.48795	+	4.88287i	−0.133560	+	0.262126i	0.814534	+	0.580115i	$0.196993\pi$
$348$	2.19460	−	0.0143077i	0.117643	−	0.000766974i
$349$		−	33.2146i		−	1.77794i	−0.457970	−	0.888968i	$-0.651423\pi$
$349$		−	33.2146i		−	1.77794i	0.457970	−	0.888968i	$-0.348577\pi$
$350$	0.0277152	−	0.0480768i	0.00148144	−	0.00256981i
$351$	−18.4596	−	8.95530i	−0.985301	−	0.477999i
$352$	−0.500446	+	0.0792629i	−0.0266739	+	0.00422473i
$353$	13.6950	+	6.97794i	0.728910	+	0.371398i	0.778729	−	0.627360i	$-0.215864\pi$
$353$	13.6950	+	6.97794i	0.728910	+	0.371398i	−0.0498191	+	0.998758i	$0.515864\pi$
$354$	5.71231	−	0.942956i	0.303606	−	0.0501175i
$355$	23.8725	+	10.6194i	1.26702	+	0.563617i
$356$	−14.2802	−	4.63992i	−0.756850	−	0.245915i
$357$	−0.0255808	−	0.0347306i	−0.00135388	−	0.00183814i
$358$	18.7824	−	9.57009i	0.992678	−	0.505795i
$359$	−12.4175	+	9.02184i	−0.655370	+	0.476154i	−0.865096	−	0.501606i	$-0.832743\pi$
$359$	−12.4175	+	9.02184i	−0.655370	+	0.476154i	0.209726	+	0.977760i	$0.432743\pi$
$360$	−6.69372	+	0.440585i	−0.352790	+	0.0232209i
$361$	4.26776	+	3.10071i	0.224619	+	0.163195i
$362$	8.75914	+	1.38731i	0.460370	+	0.0729155i
$363$	17.7343	+	5.63466i	0.930808	+	0.295743i
$364$	0.0257588	−	0.0354539i	0.00135013	−	0.00185829i
$365$	−11.6057	+	17.8840i	−0.607469	+	0.936090i
$366$	−4.74826	−	9.17068i	−0.248195	−	0.479359i
$367$	12.8267	+	25.1739i	0.669549	+	1.31406i	0.936606	+	0.350384i	$0.113949\pi$
$367$	12.8267	+	25.1739i	0.669549	+	1.31406i	−0.267057	+	0.963681i	$0.586051\pi$
$368$	−5.96759	+	5.96759i	−0.311082	+	0.311082i
$369$	−20.0466	+	28.3622i	−1.04358	+	1.47648i
$370$	−5.96546	−	5.36779i	−0.310130	−	0.279058i
$371$	−0.0859354	+	0.0279221i	−0.00446154	+	0.00144964i
$372$	12.5820	+	9.01662i	0.652346	+	0.467490i
$373$	−1.85635	−	11.7205i	−0.0961181	−	0.606866i	−0.987983	−	0.154564i	$-0.950603\pi$
$373$	−1.85635	−	11.7205i	−0.0961181	−	0.606866i	0.891865	−	0.452302i	$-0.149397\pi$
$374$	1.13692			0.0587890
$375$	6.12206	+	18.3717i	0.316142	+	0.948712i
$376$	2.19410			0.113152
$377$	−0.782659	−	4.94152i	−0.0403090	−	0.254501i
$378$	0.0348037	+	0.0459844i	0.00179011	+	0.00236518i
$379$	−25.1222	+	8.16269i	−1.29044	+	0.419289i	−0.872245	−	0.489069i	$-0.837337\pi$
$379$	−25.1222	+	8.16269i	−1.29044	+	0.419289i	−0.418194	+	0.908358i	$0.637337\pi$
$380$	8.18970	+	7.36919i	0.420123	+	0.378032i
$381$	10.2238	−	20.3930i	0.523782	−	1.04476i
$382$	−12.8117	+	12.8117i	−0.655502	+	0.655502i
$383$	−5.53391	−	10.8609i	−0.282769	−	0.554966i	0.705312	−	0.708897i	$-0.250807\pi$
$383$	−5.53391	−	10.8609i	−0.282769	−	0.554966i	−0.988082	+	0.153931i	$0.950807\pi$
$384$	−1.53811	+	0.796379i	−0.0784913	+	0.0406400i
$385$	0.00684515	−	0.0105482i	0.000348861	−	0.000537584i
$386$	7.94950	−	10.9415i	0.404619	−	0.556910i
$387$	8.30702	−	16.8428i	0.422269	−	0.856167i
$388$	−8.71076	−	1.37965i	−0.442222	−	0.0700411i
$389$	10.3541	+	7.52272i	0.524975	+	0.381417i	0.818475	−	0.574542i	$-0.194820\pi$
$389$	10.3541	+	7.52272i	0.524975	+	0.381417i	−0.293500	+	0.955959i	$0.594820\pi$
$390$	3.28185	+	14.9363i	0.166183	+	0.756329i
$391$	15.3203	−	11.1308i	0.774778	−	0.562909i
$392$	6.23694	−	3.17788i	0.315013	−	0.160507i
$393$	7.94143	−	5.84927i	0.400592	−	0.295056i
$394$	15.9156	+	5.17128i	0.801814	+	0.260525i
$395$	0.801683	+	0.356618i	0.0403370	+	0.0179434i
$396$	−1.51992	+	0.0198191i	−0.0763791	+	0.000995948i
$397$	−16.2895	−	8.29993i	−0.817548	−	0.416562i	−0.00538038	−	0.999986i	$-0.501713\pi$
$397$	−16.2895	−	8.29993i	−0.817548	−	0.416562i	−0.812168	+	0.583424i	$0.801713\pi$
$398$	−5.24974	+	0.831477i	−0.263146	+	0.0416782i
$399$	0.0142063	−	0.0936423i	0.000711205	−	0.00468798i
$400$	3.34808	+	3.71353i	0.167404	+	0.185677i
$401$		−	10.8625i		−	0.542447i	−0.962516	−	0.271223i	$-0.912572\pi$
$401$		−	10.8625i		−	0.542447i	0.962516	−	0.271223i	$-0.0874282\pi$
$402$	−0.0527600	−	8.09265i	−0.00263143	−	0.403625i
$403$	16.0203	−	31.4416i	0.798028	−	1.56622i
$404$	2.73365	+	8.41330i	0.136004	+	0.418578i
$405$	−20.0629	−	1.57445i	−0.996935	−	0.0782349i
$406$	−0.00434568	+	0.0133746i	−0.000215672	+	0.000663772i
$407$	−1.28582	−	1.28582i	−0.0637358	−	0.0637358i
$408$	3.68834	−	1.22506i	0.182600	−	0.0606493i
$409$	−6.04678	−	8.32268i	−0.298994	−	0.411530i	0.632915	−	0.774221i	$-0.281858\pi$
$409$	−6.04678	−	8.32268i	−0.298994	−	0.411530i	−0.931909	+	0.362691i	$0.881858\pi$
$410$	25.8514	−	1.36330i	1.27671	−	0.0673284i
$411$	−2.83511	+	2.87232i	−0.139846	+	0.141681i
$412$	−1.01484	+	6.40742i	−0.0499974	+	0.315671i
$413$	−0.00580353	+	0.0366420i	−0.000285573	+	0.00180304i
$414$	−20.2872	+	15.1476i	−0.997061	+	0.744462i
$415$	−6.07109	+	22.6873i	−0.298018	+	1.11368i
$416$	2.32089	+	3.19443i	0.113791	+	0.156620i
$417$	1.91900	+	5.77764i	0.0939740	+	0.282932i
$418$	1.76524	+	1.76524i	0.0863408	+	0.0863408i
$419$	6.92665	−	21.3180i	0.338389	−	1.04145i	−0.626640	−	0.779309i	$-0.715570\pi$
$419$	6.92665	−	21.3180i	0.338389	−	1.04145i	0.965029	−	0.262145i	$-0.0844298\pi$
$420$	0.0108408	−	0.0415955i	0.000528976	−	0.00202965i
$421$	1.65219	+	5.08491i	0.0805228	+	0.247824i	0.983211	−	0.182471i	$-0.0584096\pi$
$421$	1.65219	+	5.08491i	0.0805228	+	0.247824i	−0.902688	+	0.430295i	$0.858410\pi$
$422$	4.18287	−	8.20934i	0.203619	−	0.399624i
$423$	6.51414	+	0.944845i	0.316728	+	0.0459400i
$424$		−	8.14132i		−	0.395378i
$425$	−6.11660	−	9.40526i	−0.296699	−	0.456222i
$426$	20.0096	+	3.03563i	0.969470	+	0.147077i
$427$	0.0653589	−	0.0103518i	0.00316294	−	0.000500960i
$428$	6.52858	+	3.32648i	0.315571	+	0.160791i
$429$	0.564385	+	3.41897i	0.0272488	+	0.165070i
$430$	−13.6909	+	2.91477i	−0.660234	+	0.140563i
$431$	20.9740	+	6.81487i	1.01028	+	0.328261i	0.766967	−	0.641687i	$-0.221765\pi$
$431$	20.9740	+	6.81487i	1.01028	+	0.328261i	0.243315	+	0.969947i	$0.421765\pi$
$432$	−4.90949	+	1.70204i	−0.236208	+	0.0818894i
$433$	−0.678763	+	0.345847i	−0.0326193	+	0.0166204i	−0.470224	−	0.882547i	$-0.655827\pi$
$433$	−0.678763	+	0.345847i	−0.0326193	+	0.0166204i	0.437605	+	0.899167i	$0.355827\pi$
$434$	−0.0802447	+	0.0583012i	−0.00385187	+	0.00279855i
$435$	−2.48273	−	4.23302i	−0.119038	−	0.202958i
$436$	−2.98290	−	2.16720i	−0.142855	−	0.103790i
$437$	41.0692	+	6.50472i	1.96460	+	0.311163i
$438$	−5.00065	+	15.7388i	−0.238940	+	0.752030i
$439$	19.3109	−	26.5792i	0.921658	−	1.26855i	−0.0413674	−	0.999144i	$-0.513171\pi$
$439$	19.3109	−	26.5792i	0.921658	−	1.26855i	0.963026	−	0.269410i	$-0.0868286\pi$
$440$	0.713296	+	0.880258i	0.0340051	+	0.0419647i
$441$	19.8855	−	6.74909i	0.946930	−	0.321385i
$442$	−4.02232	−	7.89425i	−0.191322	−	0.375491i
$443$	12.6732	−	12.6732i	0.602124	−	0.602124i	−0.338752	−	0.940876i	$-0.610005\pi$
$443$	12.6732	−	12.6732i	0.602124	−	0.602124i	0.940876	+	0.338752i	$0.110005\pi$
$444$	−5.55687	−	2.78589i	−0.263717	−	0.132212i
$445$	6.99134	+	32.8388i	0.331421	+	1.55671i
$446$	−14.2464	+	4.62893i	−0.674585	+	0.219186i
$447$	−19.3476	+	26.9981i	−0.915109	+	1.27696i
$448$	−0.00173621	−	0.0109620i	−8.20284e−5	−	0.000517907i
$449$	13.7692			0.649809			0.324904	−	0.945747i	$-0.394668\pi$
$449$	13.7692			0.649809			0.324904	+	0.945747i	$0.394668\pi$
$450$	8.34107	+	12.4670i	0.393202	+	0.587701i
$451$	5.86597			0.276218
$452$	2.04761	+	12.9281i	0.0963114	+	0.608086i
$453$	−11.4816	+	16.0217i	−0.539454	+	0.752766i
$454$	−15.0984	+	4.90576i	−0.708602	+	0.230239i
$455$	−0.0974587	−	0.0102111i	−0.00456893	−	0.000478703i
$456$	7.62877	+	3.82461i	0.357250	+	0.179104i
$457$	−14.4895	+	14.4895i	−0.677791	+	0.677791i	−0.959500	−	0.281709i	$-0.909099\pi$
$457$	−14.4895	+	14.4895i	−0.677791	+	0.677791i	0.281709	+	0.959500i	$0.409099\pi$
$458$	2.54952	+	5.00371i	0.119131	+	0.233808i
$459$	11.4780	−	2.04880i	0.535746	−	0.0956297i
$460$	18.2298	+	4.87826i	0.849967	+	0.227450i
$461$	−2.28454	+	3.14440i	−0.106402	+	0.146449i	−0.858897	−	0.512148i	$-0.828850\pi$
$461$	−2.28454	+	3.14440i	−0.106402	+	0.146449i	0.752496	+	0.658597i	$0.228850\pi$
$462$	0.00294944	−	0.00928293i	0.000137220	−	0.000431881i
$463$	−10.8474	−	1.71806i	−0.504123	−	0.0798452i	−0.100807	−	0.994906i	$-0.532142\pi$
$463$	−10.8474	−	1.71806i	−0.504123	−	0.0798452i	−0.403316	+	0.915061i	$0.632142\pi$
$464$	−1.02509	−	0.744772i	−0.0475887	−	0.0345752i
$465$	3.38224	−	34.4469i	0.156847	−	1.59744i
$466$	−23.6372	+	17.1734i	−1.09497	+	0.795543i
$467$	−15.3981	+	7.84574i	−0.712541	+	0.363058i	−0.772389	−	0.635150i	$-0.780938\pi$
$467$	−15.3981	+	7.84574i	−0.712541	+	0.363058i	0.0598482	+	0.998207i	$0.480938\pi$
$468$	5.51495	+	10.4835i	0.254928	+	0.484599i
$469$	0.0493192	+	0.0160248i	0.00227735	+	0.000739956i
$470$	−2.45447	−	4.24806i	−0.113216	−	0.195948i
$471$	−5.49719	−	33.3013i	−0.253297	−	1.53444i
$472$	−2.97831	−	1.51753i	−0.137088	−	0.0698498i
$473$	−3.13278	+	0.496184i	−0.144046	+	0.0228146i
$474$	0.671961	+	0.101942i	0.0308642	+	0.00468235i
$475$	5.10613	−	24.1000i	0.234285	−	1.10578i
$476$			0.0249038i			0.00114146i
$477$	3.50590	−	24.1710i	0.160524	−	1.10672i
$478$	−1.68595	+	3.30886i	−0.0771134	+	0.151344i
$479$	7.02419	+	21.6182i	0.320943	+	0.987762i	0.973239	+	0.229797i	$0.0738062\pi$
$479$	7.02419	+	21.6182i	0.320943	+	0.987762i	−0.652295	+	0.757965i	$0.726194\pi$
$480$	3.26252	+	2.08709i	0.148913	+	0.0952622i
$481$	−4.37901	+	13.4772i	−0.199666	+	0.614508i
$482$	2.97591	+	2.97591i	0.135549	+	0.135549i
$483$	−0.0511383	−	0.153965i	−0.00232687	−	0.00700564i
$484$	−6.31474	−	8.69149i	−0.287033	−	0.395068i
$485$	7.07327	+	18.4085i	0.321181	+	0.835887i
$486$	−15.3089	+	2.93907i	−0.694425	+	0.133319i
$487$	−0.936123	+	5.91045i	−0.0424198	+	0.267828i	−0.999778	−	0.0210760i	$-0.993291\pi$
$487$	−0.936123	+	5.91045i	−0.0424198	+	0.267828i	0.957358	+	0.288904i	$0.0932908\pi$
$488$	−0.932710	+	5.88890i	−0.0422218	+	0.266578i
$489$	−15.5370	+	15.7409i	−0.702609	+	0.711830i
$490$	−13.1298	−	8.52050i	−0.593145	−	0.384917i
$491$	−2.93875	−	4.04485i	−0.132624	−	0.182541i	0.737540	−	0.675303i	$-0.235987\pi$
$491$	−2.93875	−	4.04485i	−0.132624	−	0.182541i	−0.870164	+	0.492762i	$0.835987\pi$
$492$	19.0300	−	6.32068i	0.857940	−	0.284958i
$493$	2.01041	+	2.01041i	0.0905442	+	0.0905442i
$494$	6.01174	−	18.5022i	0.270481	−	0.832454i
$495$	1.73866	+	2.92059i	0.0781470	+	0.131271i
$496$	−2.76166	−	8.49952i	−0.124002	−	0.381640i
$497$	−0.0588758	+	0.115550i	−0.00264094	+	0.00518314i
$498$	0.118599	+	18.1914i	0.00531455	+	0.815178i
$499$		−	18.3771i		−	0.822674i	−0.911483	−	0.411337i	$-0.865062\pi$
$499$		−	18.3771i		−	0.822674i	0.911483	−	0.411337i	$-0.134938\pi$
$500$	3.44448	−	10.6365i	0.154042	−	0.475680i
$501$	−5.50754	+	36.3035i	−0.246059	+	1.62192i
$502$	−15.1742	+	2.40335i	−0.677256	+	0.107267i
$503$	−7.33312	−	3.73641i	−0.326968	−	0.166598i	0.282799	−	0.959179i	$-0.408737\pi$
$503$	−7.33312	−	3.73641i	−0.326968	−	0.166598i	−0.609767	+	0.792581i	$0.708737\pi$
$504$	−0.000434128	−	0.0332932i	−1.93376e−5	−	0.00148300i
$505$	13.2312	−	14.7044i	0.588779	−	0.654336i
$506$	4.06685	+	1.32140i	0.180793	+	0.0587434i
$507$	3.61325	−	2.66134i	0.160470	−	0.118194i
$508$	−11.7352	+	5.97936i	−0.520663	+	0.265291i
$509$	−1.11703	+	0.811566i	−0.0495113	+	0.0359720i	−0.612266	−	0.790652i	$-0.709742\pi$
$509$	−1.11703	+	0.811566i	−0.0495113	+	0.0359720i	0.562754	+	0.826624i	$0.309742\pi$
$510$	−6.49789	−	5.77066i	−0.287731	−	0.255529i
$511$	−0.0856099	−	0.0621992i	−0.00378716	−	0.00275153i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	21.0023	+	14.6402i	0.927274	+	0.646380i
$514$	3.64439	−	5.01607i	0.160747	−	0.221249i
$515$	13.5408	−	5.20292i	0.596680	−	0.229268i
$516$	−9.62853	+	4.98532i	−0.423873	+	0.219466i
$517$	−0.504709	−	0.990547i	−0.0221971	−	0.0435642i
$518$	0.0281652	−	0.0281652i	0.00123751	−	0.00123751i
$519$	−2.25556	+	4.49906i	−0.0990082	+	0.197487i
$520$	3.58851	−	8.06704i	0.157367	−	0.353763i
$521$	3.46443	−	1.12566i	0.151779	−	0.0493161i	−0.232142	−	0.972682i	$-0.574573\pi$
$521$	3.46443	−	1.12566i	0.151779	−	0.0493161i	0.383921	+	0.923366i	$0.374573\pi$
$522$	−2.72270	−	2.65261i	−0.119170	−	0.116102i
$523$	3.42302	+	21.6121i	0.149678	+	0.945031i	0.942167	+	0.335145i	$0.108785\pi$
$523$	3.42302	+	21.6121i	0.149678	+	0.945031i	−0.792488	+	0.609887i	$0.791215\pi$
$524$	−5.69445			−0.248763
$525$	−0.0926613	+	0.0255423i	−0.00404407	+	0.00111476i
$526$	21.9543			0.957252
$527$	3.13700	+	19.8062i	0.136650	+	0.862774i
$528$	0.713344	+	0.511203i	0.0310443	+	0.0222472i
$529$	45.8640	−	14.9021i	1.99409	−	0.647919i
$530$	−15.7626	+	9.10743i	−0.684685	+	0.395602i
$531$	−8.18891	−	5.78798i	−0.355368	−	0.251177i
$532$	−0.0386667	+	0.0386667i	−0.00167642	+	0.00167642i
$533$	−20.7532	−	40.7304i	−0.898920	−	1.76423i
$534$	11.9577	+	23.0949i	0.517461	+	0.999413i
$535$	−0.862831	−	16.3614i	−0.0373034	−	0.707364i
$536$	−2.74636	+	3.78005i	−0.118625	+	0.163273i
$537$	−34.7973	−	11.0561i	−1.50162	−	0.477104i
$538$	13.4066	+	2.12340i	0.578000	+	0.0915461i
$539$	−2.86936	−	2.08471i	−0.123592	−	0.0897950i
$540$	8.78745	+	7.60137i	0.378151	+	0.327111i
$541$	1.72373	−	1.25236i	0.0741089	−	0.0538433i	−0.550114	−	0.835090i	$-0.685416\pi$
$541$	1.72373	−	1.25236i	0.0741089	−	0.0538433i	0.624223	+	0.781246i	$0.285416\pi$
$542$	−17.8296	+	9.08461i	−0.765845	+	0.390218i
$543$	−9.10944	−	12.3677i	−0.390923	−	0.530749i
$544$	−2.13403	−	0.693388i	−0.0914958	−	0.0297288i
$545$	−0.859106	+	8.19965i	−0.0368001	+	0.351235i
$546$	−0.0748909	+	0.0123626i	−0.00320503	+	0.000529069i
$547$	−19.1762	−	9.77077i	−0.819915	−	0.417768i	−0.00687601	−	0.999976i	$-0.502189\pi$
$547$	−19.1762	−	9.77077i	−0.819915	−	0.417768i	−0.813039	+	0.582209i	$0.802189\pi$
$548$	2.30141	−	0.364508i	0.0983114	−	0.0155710i
$549$	−5.30509	+	17.0821i	−0.226416	+	0.729046i
$550$	0.906350	−	2.36575i	0.0386469	−	0.100876i
$551$			6.24290i			0.265957i
$552$	14.6172	−	0.0952971i	0.622151	−	0.00405611i
$553$	−0.00197716	+	0.00388039i	−8.40774e−5	+	0.000165011i
$554$	−5.06615	−	15.5920i	−0.215240	−	0.662441i
$555$	0.822467	+	13.8753i	0.0349118	+	0.588973i
$556$	1.08617	−	3.34288i	0.0460637	−	0.141770i
$557$	−12.1500	−	12.1500i	−0.514813	−	0.514813i	0.401184	−	0.915997i	$-0.368599\pi$
$557$	−12.1500	−	12.1500i	−0.514813	−	0.514813i	−0.915997	+	0.401184i	$0.868599\pi$
$558$	−4.53904	−	26.4238i	−0.192153	−	1.11861i
$559$	14.5287	+	19.9971i	0.614499	+	0.845786i
$560$	−0.0192816	+	0.0156244i	−0.000814796	+	0.000660251i
$561$	−1.40149	−	1.38334i	−0.0591710	−	0.0584045i
$562$	2.35902	−	14.8943i	0.0995092	−	0.628276i
$563$	−3.95356	+	24.9618i	−0.166623	+	1.05201i	0.752658	+	0.658412i	$0.228771\pi$
$563$	−3.95356	+	24.9618i	−0.166623	+	1.05201i	−0.919281	+	0.393603i	$0.871229\pi$
$564$	−2.70468	−	2.66964i	−0.113887	−	0.112412i
$565$	22.7398	−	18.4267i	0.956671	−	0.775215i
$566$	−5.70071	−	7.84635i	−0.239619	−	0.329807i
$567$	0.0130481	−	0.0990321i	0.000547970	−	0.00415896i
$568$	−8.26237	−	8.26237i	−0.346681	−	0.346681i
$569$	9.76589	−	30.0563i	0.409407	−	1.26003i	−0.507751	−	0.861504i	$-0.669523\pi$
$569$	9.76589	−	30.0563i	0.409407	−	1.26003i	0.917158	−	0.398523i	$-0.130477\pi$
$570$	−1.12913	−	19.0487i	−0.0472939	−	0.797863i
$571$	4.89957	+	15.0793i	0.205041	+	0.631050i	0.999712	+	0.0240101i	$0.00764337\pi$
$571$	4.89957	+	15.0793i	0.205041	+	0.631050i	−0.794671	+	0.607040i	$0.792357\pi$
$572$	0.908280	−	1.78260i	0.0379771	−	0.0745343i
$573$	31.3814	−	0.204591i	1.31098	−	0.00854691i
$574$			0.128491i			0.00536312i
$575$	−10.9481	−	40.7523i	−0.456568	−	1.69949i
$576$	2.86501	+	0.889771i	0.119376	+	0.0370738i
$577$	−12.1944	+	1.93140i	−0.507658	+	0.0804052i	−0.405009	−	0.914312i	$-0.632732\pi$
$577$	−12.1944	+	1.93140i	−0.507658	+	0.0804052i	−0.102649	+	0.994718i	$0.532732\pi$
$578$	−10.6610	−	5.43206i	−0.443439	−	0.225944i
$579$	−23.1123	+	3.81525i	−0.960516	+	0.158557i
$580$	−0.295237	+	2.81786i	−0.0122590	+	0.117005i
$581$	−0.110865	−	0.0360221i	−0.00459944	−	0.00149445i
$582$	9.05912	+	12.2994i	0.375513	+	0.509826i
$583$	−3.67548	+	1.87275i	−0.152223	+	0.0775613i
$584$	7.71353	−	5.60421i	0.319188	−	0.231904i
$585$	14.1280	−	22.4052i	0.584119	−	0.926340i
$586$	4.15993	+	3.02236i	0.171845	+	0.124853i
$587$	−15.5817	−	2.46790i	−0.643126	−	0.101861i	−0.173652	−	0.984807i	$-0.555557\pi$
$587$	−15.5817	−	2.46790i	−0.643126	−	0.101861i	−0.469475	+	0.882946i	$0.655557\pi$
$588$	−11.5549	−	3.67131i	−0.476517	−	0.151402i
$589$	−25.8814	+	35.6228i	−1.06643	+	1.46781i
$590$	0.393620	+	7.46399i	0.0162051	+	0.307288i
$591$	−13.3271	−	25.7397i	−0.548203	−	1.05879i
$592$	1.62931	+	3.19771i	0.0669644	+	0.131425i
$593$	−25.4841	+	25.4841i	−1.04651	+	1.04651i	−0.0476423	+	0.998864i	$0.515171\pi$
$593$	−25.4841	+	25.4841i	−1.04651	+	1.04651i	−0.998864	+	0.0476423i	$0.984829\pi$
$594$	1.89773	+	1.82491i	0.0778648	+	0.0748771i
$595$	0.0482168	−	0.0278590i	0.00197670	−	0.00114211i
$596$	18.2380	−	5.92589i	0.747058	−	0.242734i
$597$	7.48306	+	5.36257i	0.306261	+	0.219476i
$598$	−5.21293	−	32.9132i	−0.213173	−	1.34592i
$599$	16.2566			0.664228			0.332114	−	0.943239i	$-0.392238\pi$
$599$	16.2566			0.664228			0.332114	+	0.943239i	$0.392238\pi$
$600$	0.391190	−	8.65141i	0.0159703	−	0.353193i
$601$	−39.0305			−1.59209			−0.796044	−	0.605239i	$-0.793077\pi$
$601$	−39.0305			−1.59209			−0.796044	+	0.605239i	$0.793077\pi$
$602$	−0.0108687	−	0.0686220i	−0.000442974	−	0.00279682i
$603$	−9.78157	+	10.0400i	−0.398336	+	0.408862i
$604$	10.8232	−	3.51666i	0.440388	−	0.143091i
$605$	−9.76373	+	21.9490i	−0.396952	+	0.892354i
$606$	6.86698	−	13.6972i	0.278952	−	0.556412i
$607$	12.9928	−	12.9928i	0.527363	−	0.527363i	−0.392422	−	0.919785i	$-0.628363\pi$
$607$	12.9928	−	12.9928i	0.527363	−	0.527363i	0.919785	+	0.392422i	$0.128363\pi$
$608$	−2.23681	−	4.38998i	−0.0907145	−	0.178037i
$609$	0.0216303	−	0.0111994i	0.000876504	−	0.000453823i
$610$	12.4450	−	4.78188i	0.503885	−	0.193613i
$611$	−5.09227	+	7.00890i	−0.206011	+	0.283550i
$612$	−6.03720	−	2.97760i	−0.244039	−	0.120362i
$613$	−31.2308	−	4.94647i	−1.26140	−	0.199786i	−0.510313	−	0.859989i	$-0.670470\pi$
$613$	−31.2308	−	4.94647i	−1.26140	−	0.199786i	−0.751088	+	0.660203i	$0.770470\pi$
$614$	−9.34304	−	6.78812i	−0.377054	−	0.273946i
$615$	−33.5259	−	29.7738i	−1.35189	−	1.20059i
$616$	−0.00454952	+	0.00330542i	−0.000183305	+	0.000133179i
$617$	−9.14457	+	4.65939i	−0.368147	+	0.187580i	−0.628270	−	0.777995i	$-0.716237\pi$
$617$	−9.14457	+	4.65939i	−0.368147	+	0.187580i	0.260124	+	0.965575i	$0.416237\pi$
$618$	9.04712	−	6.66366i	0.363928	−	0.268052i
$619$	12.6211	+	4.10083i	0.507283	+	0.164826i	0.551466	−	0.834197i	$-0.314068\pi$
$619$	12.6211	+	4.10083i	0.507283	+	0.164826i	−0.0441830	+	0.999023i	$0.514068\pi$
$620$	−13.3668	+	14.8551i	−0.536822	+	0.596594i
$621$	43.4386	+	6.01169i	1.74313	+	0.241241i
$622$	10.3688	+	5.28318i	0.415752	+	0.211836i
$623$	−0.164596	+	0.0260694i	−0.00659439	+	0.00104445i
$624$	1.02580	−	6.76169i	0.0410650	−	0.270684i
$625$	−24.4469	+	5.22979i	−0.977875	+	0.209192i
$626$			17.2450i			0.689247i
$627$	−0.0281893	−	4.32385i	−0.00112577	−	0.172678i
$628$	−8.84677	+	17.3628i	−0.353025	+	0.692850i
$629$	−2.48848	−	7.65876i	−0.0992222	−	0.305375i
$630$	−0.0639741	+	0.0380845i	−0.00254879	+	0.00151732i
$631$	−5.37850	+	16.5533i	−0.214115	+	0.658977i	0.785101	+	0.619368i	$0.212611\pi$
$631$	−5.37850	+	16.5533i	−0.214115	+	0.658977i	−0.999215	+	0.0396089i	$0.987389\pi$
$632$	−0.277466	−	0.277466i	−0.0110370	−	0.0110370i
$633$	−15.1448	+	5.03024i	−0.601952	+	0.199934i
$634$	9.21303	+	12.6807i	0.365896	+	0.503613i
$635$	24.7045	+	16.0318i	0.980370	+	0.636204i
$636$	−9.90583	+	10.0358i	−0.392792	+	0.397947i
$637$	−4.32373	+	27.2990i	−0.171312	+	1.08162i
$638$	−0.100433	+	0.634107i	−0.00397617	+	0.0251045i
$639$	−20.9724	−	28.0884i	−0.829655	−	1.11116i
$640$	−0.802018	−	2.08729i	−0.0317025	−	0.0825073i
$641$	−26.2268	−	36.0981i	−1.03590	−	1.42579i	−0.900426	−	0.435009i	$-0.856745\pi$
$641$	−26.2268	−	36.0981i	−1.03590	−	1.42579i	−0.135472	−	0.990781i	$-0.543255\pi$
$642$	−4.00036	−	12.0441i	−0.157882	−	0.475343i
$643$	−15.2783	−	15.2783i	−0.602518	−	0.602518i	0.338462	−	0.940980i	$-0.390093\pi$
$643$	−15.2783	−	15.2783i	−0.602518	−	0.602518i	−0.940980	+	0.338462i	$0.890093\pi$
$644$	−0.0289446	+	0.0890822i	−0.00114058	+	0.00351033i
$645$	20.4233	+	13.0651i	0.804168	+	0.514439i
$646$	3.41632	+	10.5143i	0.134413	+	0.413681i
$647$	2.92135	−	5.73348i	0.114850	−	0.225406i	−0.826425	−	0.563047i	$-0.809629\pi$
$647$	2.92135	−	5.73348i	0.114850	−	0.225406i	0.941275	+	0.337641i	$0.109629\pi$
$648$	8.12287	+	3.87543i	0.319097	+	0.152241i
$649$			1.69366i			0.0664820i
$650$	−19.6332	+	2.07652i	−0.770076	+	0.0814477i
$651$	0.169855	+	0.0257684i	0.00665714	+	0.00100994i
$652$	12.6122	−	1.99758i	0.493933	−	0.0782313i
$653$	−20.6139	−	10.5033i	−0.806684	−	0.411026i	0.00146890	−	0.999999i	$-0.499532\pi$
$653$	−20.6139	−	10.5033i	−0.806684	−	0.411026i	−0.808153	+	0.588973i	$0.799532\pi$
$654$	1.04012	+	6.30092i	0.0406719	+	0.246385i
$655$	6.37019	+	11.0252i	0.248904	+	0.430789i
$656$	−11.0105	−	3.57754i	−0.429890	−	0.139680i
$657$	25.3143	−	13.3168i	0.987604	−	0.519539i
$658$	0.0216974	−	0.0110554i	0.000845854	−	0.000430984i
$659$	−30.0141	+	21.8065i	−1.16918	+	0.849461i	−0.990911	−	0.134520i	$-0.957051\pi$
$659$	−30.0141	+	21.8065i	−1.16918	+	0.849461i	−0.178272	+	0.983981i	$0.557051\pi$
$660$	0.191758	−	1.95299i	0.00746417	−	0.0760200i
$661$	27.7173	+	20.1378i	1.07808	+	0.783268i	0.977346	−	0.211646i	$-0.0678823\pi$
$661$	27.7173	+	20.1378i	1.07808	+	0.783268i	0.100730	+	0.994914i	$0.467882\pi$
$662$	6.74675	+	1.06858i	0.262220	+	0.0415316i
$663$	−4.64687	+	14.6254i	−0.180470	+	0.568002i
$664$	6.17354	−	8.49715i	0.239580	−	0.329753i
$665$	0.118119	+	0.0316084i	0.00458045	+	0.00122572i
$666$	3.46029	+	10.1954i	0.134084	+	0.395064i
$667$	4.85474	+	9.52796i	0.187976	+	0.368924i
$668$	14.9904	−	14.9904i	0.579997	−	0.579997i
$669$	23.1937	+	11.6280i	0.896721	+	0.449563i
$670$	10.3909	+	1.08869i	0.401436	+	0.0420598i
$671$	2.87315	−	0.933543i	0.110917	−	0.0360390i
$672$	−0.0111976	+	0.0156254i	−0.000431958	+	0.000602764i
$673$	2.09957	+	13.2562i	0.0809325	+	0.510988i	0.994537	+	0.104384i	$0.0332871\pi$
$673$	2.09957	+	13.2562i	0.0809325	+	0.510988i	−0.913605	+	0.406604i	$0.866713\pi$
$674$	−1.55439			−0.0598727
$675$	4.88697	−	25.5170i	0.188100	−	0.982150i
$676$	−2.59090			−0.0996502
$677$	1.92134	+	12.1309i	0.0738432	+	0.466227i	0.996706	+	0.0810988i	$0.0258429\pi$
$677$	1.92134	+	12.1309i	0.0738432	+	0.466227i	−0.922863	+	0.385129i	$0.874157\pi$
$678$	13.2060	−	18.4279i	0.507172	−	0.707719i
$679$	−0.0930922	+	0.0302475i	−0.00357255	+	0.00116079i
$680$	1.04478	+	4.90742i	0.0400656	+	0.188191i
$681$	24.5808	+	12.3234i	0.941940	+	0.472233i
$682$	−3.20192	+	3.20192i	−0.122608	+	0.122608i
$683$	−2.14496	−	4.20973i	−0.0820748	−	0.161081i	0.846322	−	0.532672i	$-0.178812\pi$
$683$	−2.14496	−	4.20973i	−0.0820748	−	0.161081i	−0.928396	+	0.371592i	$0.878812\pi$
$684$	−4.75047	−	13.9968i	−0.181639	−	0.535181i
$685$	−3.28024	−	4.04806i	−0.125332	−	0.154668i
$686$	0.0913300	−	0.125705i	0.00348700	−	0.00479944i
$687$	2.94539	−	9.27017i	0.112373	−	0.353679i
$688$	6.18291	+	0.979277i	0.235721	+	0.0373346i
$689$	26.0069	+	18.8951i	0.990783	+	0.719846i
$690$	−16.5363	−	28.1942i	−0.629528	−	1.07334i
$691$	−38.0936	+	27.6766i	−1.44915	+	1.05287i	−0.463120	+	0.886295i	$0.653270\pi$
$691$	−38.0936	+	27.6766i	−1.44915	+	1.05287i	−0.986029	+	0.166573i	$0.946730\pi$
$692$	2.58899	−	1.31916i	0.0984186	−	0.0501468i
$693$	−0.0149306	+	0.00785441i	−0.000567168	+	0.000298364i
$694$	−5.21196	−	1.69347i	−0.197843	−	0.0642831i
$695$	−7.68729	+	1.63661i	−0.291595	+	0.0620802i
$696$	0.357443	+	2.16535i	0.0135489	+	0.0820772i
$697$	23.1461	+	11.7935i	0.876720	+	0.446711i
$698$	32.8057	−	5.19591i	1.24171	−	0.196668i
$699$	50.0331	+	7.59043i	1.89243	+	0.287097i
$700$	0.0518205	+	0.0198531i	0.00195863	+	0.000750377i
$701$			21.1946i			0.800509i	0.916404	+	0.400254i	$0.131078\pi$
$701$			21.1946i			0.800509i	−0.916404	+	0.400254i	$0.868922\pi$
$702$	5.95733	−	19.6333i	0.224845	−	0.741009i
$703$	8.02761	−	15.7551i	0.302767	−	0.594214i
$704$	−0.156574	−	0.481886i	−0.00590111	−	0.0181617i
$705$	−2.14312	+	8.22303i	−0.0807147	+	0.309697i
$706$	−4.74967	+	14.6180i	−0.178756	+	0.550154i
$707$	0.0694250	+	0.0694250i	0.00261100	+	0.00261100i
$708$	1.82495	+	5.49447i	0.0685858	+	0.206495i
$709$	3.51205	+	4.83393i	0.131898	+	0.181542i	0.869858	−	0.493303i	$-0.164211\pi$
$709$	3.51205	+	4.83393i	0.131898	+	0.181542i	−0.737960	+	0.674845i	$0.764211\pi$
$710$	−6.75414	+	25.2398i	−0.253478	+	0.947234i
$711$	−0.704292	−	0.943262i	−0.0264130	−	0.0353751i
$712$	2.34888	−	14.8302i	0.0880280	−	0.555787i
$713$	−11.7987	+	74.4941i	−0.441865	+	2.78983i
$714$	0.0303012	−	0.0306989i	0.00113400	−	0.00114888i
$715$	−4.46740	+	0.235592i	−0.167071	+	0.00881065i
$716$	12.3905	+	17.0540i	0.463054	+	0.637339i
$717$	6.10427	−	2.02749i	0.227968	−	0.0757180i
$718$	−10.8533	−	10.8533i	−0.405041	−	0.405041i
$719$	5.15491	−	15.8652i	0.192246	−	0.591671i	−0.807752	−	0.589522i	$-0.799316\pi$
$719$	5.15491	−	15.8652i	0.192246	−	0.591671i	0.999998	−	0.00214885i	$-0.000684002\pi$
$720$	−1.48229	−	6.54239i	−0.0552417	−	0.243820i
$721$	0.0222493	+	0.0684763i	0.000828607	+	0.00255019i
$722$	−2.39491	+	4.70028i	−0.0891294	+	0.174926i
$723$	−0.0475226	−	7.28930i	−0.00176738	−	0.271092i
$724$			8.86833i			0.329589i
$725$	5.78600	−	2.58063i	0.214887	−	0.0958422i
$726$	−2.79104	+	18.3974i	−0.103585	+	0.682791i
$727$	29.9306	−	4.74054i	1.11006	−	0.175817i	0.425634	−	0.904895i	$-0.360051\pi$
$727$	29.9306	−	4.74054i	1.11006	−	0.175817i	0.684430	+	0.729079i	$0.260051\pi$
$728$	0.0390470	+	0.0198954i	0.00144718	+	0.000737373i
$729$	22.4474	+	15.0038i	0.831384	+	0.555698i
$730$	−19.4793	−	8.66512i	−0.720962	−	0.320710i
$731$	−13.3590	−	4.34060i	−0.494100	−	0.160543i
$732$	8.31498	−	6.12441i	0.307331	−	0.226365i
$733$	−12.5178	+	6.37815i	−0.462356	+	0.235582i	−0.669622	−	0.742702i	$-0.733544\pi$
$733$	−12.5178	+	6.37815i	−0.462356	+	0.235582i	0.207265	+	0.978285i	$0.433544\pi$
$734$	−22.8574	+	16.6069i	−0.843681	+	0.612970i
$735$	5.81799	+	26.4788i	0.214600	+	0.976684i
$736$	−6.82766	−	4.96058i	−0.251671	−	0.182850i
$737$	2.33828	+	0.370348i	0.0861317	+	0.0136419i
$738$	−31.1490	−	15.3629i	−1.14661	−	0.565518i
$739$	7.81299	−	10.7537i	0.287405	−	0.395580i	−0.640764	−	0.767738i	$-0.721382\pi$
$739$	7.81299	−	10.7537i	0.287405	−	0.395580i	0.928169	+	0.372158i	$0.121382\pi$
$740$	4.36850	−	6.73173i	0.160589	−	0.247463i
$741$	−29.9230	+	15.4931i	−1.09925	+	0.569152i
$742$	−0.0410216	−	0.0805094i	−0.00150595	−	0.00295559i
$743$	4.79366	−	4.79366i	0.175862	−	0.175862i	−0.613687	−	0.789549i	$-0.710314\pi$
$743$	4.79366	−	4.79366i	0.175862	−	0.175862i	0.789549	+	0.613687i	$0.210314\pi$
$744$	−6.93735	+	13.8376i	−0.254336	+	0.507311i
$745$	−31.8755	−	28.6820i	−1.16783	−	1.05083i
$746$	11.2858	−	3.66699i	0.413204	−	0.134258i
$747$	21.9880	−	22.5690i	0.804497	−	0.825755i
$748$	0.177854	+	1.12293i	0.00650299	+	0.0410583i
$749$	0.0813220			0.00297144
$750$	−17.1878	+	8.92066i	−0.627611	+	0.325737i
$751$	16.9834			0.619735			0.309867	−	0.950780i	$-0.399715\pi$
$751$	16.9834			0.619735			0.309867	+	0.950780i	$0.399715\pi$
$752$	0.343233	+	2.16709i	0.0125164	+	0.0790256i
$753$	21.6295	+	15.5003i	0.788223	+	0.564863i
$754$	4.75824	−	1.54605i	0.173285	−	0.0563037i
$755$	−18.9162	−	17.0210i	−0.688432	−	0.619459i
$756$	−0.0399738	+	0.0415688i	−0.00145383	+	0.00151184i
$757$	32.0188	−	32.0188i	1.16374	−	1.16374i	0.180094	−	0.983649i	$-0.442360\pi$
$757$	32.0188	−	32.0188i	1.16374	−	1.16374i	0.983649	−	0.180094i	$-0.0576401\pi$
$758$	−11.9922	−	23.5359i	−0.435575	−	0.854864i
$759$	−3.40543	−	6.57717i	−0.123609	−	0.238736i
$760$	−5.99731	+	9.24167i	−0.217545	+	0.335231i
$761$	7.23738	−	9.96139i	0.262355	−	0.361100i	−0.657435	−	0.753511i	$-0.728359\pi$
$761$	7.23738	−	9.96139i	0.262355	−	0.361100i	0.919790	+	0.392411i	$0.128359\pi$
$762$	21.7413	+	6.90779i	0.787603	+	0.250243i
$763$	−0.0404177	−	0.00640154i	−0.00146322	−	0.000231751i
$764$	−14.6581	−	10.6498i	−0.530312	−	0.385295i
$765$	0.988607	+	15.0197i	0.0357432	+	0.543039i
$766$	9.86149	−	7.16479i	0.356310	−	0.258875i
$767$	11.7600	−	5.99200i	0.424627	−	0.216358i
$768$	−1.02719	−	1.39459i	−0.0370654	−	0.0503230i
$769$	−32.2540	−	10.4800i	−1.16311	−	0.377917i	−0.337043	−	0.941489i	$-0.609427\pi$
$769$	−32.2540	−	10.4800i	−1.16311	−	0.377917i	−0.826067	+	0.563572i	$0.809427\pi$
$770$	0.0114891	+	0.00511078i	0.000414039	+	0.000184180i
$771$	−10.5957	+	1.74908i	−0.381594	+	0.0629914i
$772$	12.0504	+	6.13999i	0.433704	+	0.220983i
$773$	5.86246	−	0.928522i	0.210858	−	0.0333966i	−0.0501118	−	0.998744i	$-0.515958\pi$
$773$	5.86246	−	0.928522i	0.210858	−	0.0333966i	0.260970	+	0.965347i	$0.415958\pi$
$774$	17.9349	+	5.56995i	0.644658	+	0.200208i
$775$	43.7142	+	9.26185i	1.57026	+	0.332696i
$776$		−	8.81934i		−	0.316596i
$777$	−0.0689890		0.000449774i	−0.00247497		1.61355e-5i
$778$	−5.81036	+	11.4035i	−0.208311	+	0.408834i
$779$	17.6265	+	54.2489i	0.631536	+	1.94367i
$780$	−14.2390	+	5.57800i	−0.509838	+	0.199724i
$781$	−1.82953	+	5.63071i	−0.0654657	+	0.201483i
$782$	13.3904	+	13.3904i	0.478839	+	0.478839i
$783$	0.128762	+	6.58269i	0.00460158	+	0.235246i
$784$	4.11442	+	5.66302i	0.146944	+	0.202251i
$785$	43.5131	−	2.29470i	1.55305	−	0.0819014i
$786$	7.01956	+	6.92863i	0.250380	+	0.247136i
$787$	6.09887	−	38.5068i	0.217401	−	1.37262i	−0.601587	−	0.798807i	$-0.705465\pi$
$787$	6.09887	−	38.5068i	0.217401	−	1.37262i	0.818988	−	0.573811i	$-0.194535\pi$
$788$	−2.61787	+	16.5286i	−0.0932578	+	0.588806i
$789$	−27.0631	−	26.7125i	−0.963473	−	0.950991i
$790$	−0.226817	+	0.847600i	−0.00806977	+	0.0301563i
$791$	0.0853893	+	0.117528i	0.00303610	+	0.00417883i
$792$	−0.257344	−	1.49811i	−0.00914431	−	0.0532331i
$793$	−16.6470	−	16.6470i	−0.591151	−	0.591151i
$794$	5.64950	−	17.3874i	0.200493	−	0.617055i
$795$	30.5120	+	7.95216i	1.08215	+	0.282034i
$796$	−1.64248	−	5.05504i	−0.0582162	−	0.179171i
$797$	13.6280	−	26.7464i	0.482728	−	0.947407i	−0.513287	−	0.858217i	$-0.671572\pi$
$797$	13.6280	−	26.7464i	0.482728	−	0.947407i	0.996015	−	0.0891898i	$-0.0284278\pi$
$798$	0.0947117		0.000617473i	0.00335276		2.18583e-5i
$799$		−	4.92324i		−	0.174172i
$800$	−3.14406	+	3.88779i	−0.111159	+	0.137454i
$801$	13.3600	−	43.0185i	0.472053	−	1.51998i
$802$	10.7288	−	1.69927i	0.378845	−	0.0600032i
$803$	−4.30441	−	2.19321i	−0.151899	−	0.0773966i
$804$	7.98477	−	1.31808i	0.281601	−	0.0464851i
$805$	0.204854	−	0.0436131i	0.00722015	−	0.00153716i
$806$	33.5606	+	10.9045i	1.18212	+	0.384095i
$807$	−13.9428	−	18.9298i	−0.490808	−	0.666360i
$808$	−7.88209	+	4.01612i	−0.277291	+	0.141287i
$809$	−3.66835	+	2.66521i	−0.128972	+	0.0937040i	−0.650401	−	0.759591i	$-0.725399\pi$
$809$	−3.66835	+	2.66521i	−0.128972	+	0.0937040i	0.521429	+	0.853295i	$0.325399\pi$
$810$	−1.58347	−	20.0622i	−0.0556375	−	0.704915i
$811$	2.33181	+	1.69416i	0.0818808	+	0.0594899i	0.627973	−	0.778235i	$-0.283885\pi$
$811$	2.33181	+	1.69416i	0.0818808	+	0.0594899i	−0.546092	+	0.837725i	$0.683885\pi$
$812$	−0.0138898	−	0.00219992i	−0.000487436	−	7.72022e-5i
$813$	33.0321	+	10.4952i	1.15849	+	0.368083i
$814$	1.06884	−	1.47114i	0.0374629	−	0.0515633i
$815$	−17.9765	−	22.1842i	−0.629688	−	0.777080i
$816$	1.78696	+	3.45129i	0.0625560	+	0.120819i
$817$	−14.0024	−	27.4812i	−0.489881	−	0.961445i
$818$	7.27429	−	7.27429i	0.254339	−	0.254339i
$819$	0.107360	+	0.0758829i	0.00375147	+	0.00265156i
$820$	5.39057	+	25.3199i	0.188247	+	0.884209i
$821$	−7.12613	+	2.31542i	−0.248704	+	0.0808088i	−0.430716	−	0.902488i	$-0.641739\pi$
$821$	−7.12613	+	2.31542i	−0.248704	+	0.0808088i	0.182012	+	0.983296i	$0.441739\pi$
$822$	−3.28046	−	2.35087i	−0.114419	−	0.0819962i
$823$	−4.90027	−	30.9391i	−0.170813	−	1.07847i	−0.912905	−	0.408171i	$-0.866167\pi$
$823$	−4.90027	−	30.9391i	−0.170813	−	1.07847i	0.742093	−	0.670297i	$-0.233833\pi$
$824$	−6.48729			−0.225995
$825$	−3.99575	+	1.81348i	−0.139114	+	0.0631372i
$826$	−0.0370988			−0.00129083
$827$	−5.31436	−	33.5536i	−0.184799	−	1.16677i	−0.889387	−	0.457156i	$-0.848868\pi$
$827$	−5.31436	−	33.5536i	−0.184799	−	1.16677i	0.704588	−	0.709616i	$-0.251132\pi$
$828$	−18.1347	−	17.6678i	−0.630224	−	0.613999i
$829$	16.4858	−	5.35656i	0.572575	−	0.186041i	−0.00839647	−	0.999965i	$-0.502673\pi$
$829$	16.4858	−	5.35656i	0.572575	−	0.186041i	0.580972	+	0.813924i	$0.302673\pi$
$830$	−23.3577	−	2.44727i	−0.810758	−	0.0849459i
$831$	−12.7263	+	25.3845i	−0.441469	+	0.880578i
$832$	−2.79203	+	2.79203i	−0.0967964	+	0.0967964i
$833$	−7.13069	−	13.9948i	−0.247064	−	0.484890i
$834$	−5.40631	+	2.79920i	−0.187205	+	0.0969283i
$835$	−45.7926	−	12.2540i	−1.58472	−	0.424069i
$836$	−1.46736	+	2.01965i	−0.0507499	+	0.0698512i
$837$	−26.5554	+	38.0955i	−0.917889	+	1.31677i
$838$	22.1391	+	3.50649i	0.764784	+	0.121130i
$839$	27.1876	+	19.7529i	0.938619	+	0.681947i	0.948088	−	0.318009i	$-0.103014\pi$
$839$	27.1876	+	19.7529i	0.938619	+	0.681947i	−0.00946893	+	0.999955i	$0.503014\pi$
$840$	0.0427792	+	0.00420036i	0.00147602	+	0.000144926i
$841$	22.1626	−	16.1021i	0.764228	−	0.555244i
$842$	−4.76385	+	2.42730i	−0.164173	+	0.0836504i
$843$	−21.0303	+	15.4899i	−0.724323	+	0.533500i
$844$	8.76261	+	2.84714i	0.301621	+	0.0980028i
$845$	2.89836	+	5.01632i	0.0997066	+	0.172567i
$846$	0.0858230	+	6.58175i	0.00295065	+	0.226285i
$847$	−0.106240	−	0.0541320i	−0.00365045	−	0.00186000i
$848$	8.04109	−	1.27358i	0.276132	−	0.0437350i
$849$	−2.51964	+	16.6085i	−0.0864739	+	0.570001i
$850$	8.33262	−	7.51260i	0.285807	−	0.257680i
$851$		−	30.2881i		−	1.03826i
$852$	0.131943	+	20.2382i	0.00452028	+	0.693348i
$853$	−4.37029	+	8.57717i	−0.149636	+	0.293677i	−0.953642	−	0.300945i	$-0.902698\pi$
$853$	−4.37029	+	8.57717i	−0.149636	+	0.293677i	0.804006	+	0.594621i	$0.202698\pi$
$854$	0.0204488	+	0.0629349i	0.000699743	+	0.00215359i
$855$	−21.7854	+	24.8553i	−0.745043	+	0.850032i
$856$	−2.26423	+	6.96857i	−0.0773897	+	0.238181i
$857$	−1.51254	−	1.51254i	−0.0516674	−	0.0516674i	0.680801	−	0.732468i	$-0.261632\pi$
$857$	−1.51254	−	1.51254i	−0.0516674	−	0.0516674i	−0.732468	+	0.680801i	$0.761632\pi$
$858$	−3.28859	+	1.09228i	−0.112271	+	0.0372899i
$859$	16.4497	+	22.6411i	0.561257	+	0.772504i	0.991486	−	0.130216i	$-0.0415671\pi$
$859$	16.4497	+	22.6411i	0.561257	+	0.772504i	−0.430229	+	0.902720i	$0.641567\pi$
$860$	−5.02062	−	13.0664i	−0.171202	−	0.445560i
$861$	0.156340	−	0.158391i	0.00532804	−	0.00539797i
$862$	−3.44991	+	21.7819i	−0.117504	+	0.741893i
$863$	−4.58709	+	28.9617i	−0.156146	+	0.985869i	0.777815	+	0.628494i	$0.216328\pi$
$863$	−4.58709	+	28.9617i	−0.156146	+	0.985869i	−0.933961	+	0.357375i	$0.883672\pi$
$864$	−2.44910	−	4.58279i	−0.0833200	−	0.155910i
$865$	−5.45027	−	3.53691i	−0.185315	−	0.120259i
$866$	−0.447771	−	0.616304i	−0.0152159	−	0.0209429i
$867$	6.53249	+	19.6677i	0.221855	+	0.667951i
$868$	−0.0701364	−	0.0701364i	−0.00238059	−	0.00238059i
$869$	−0.0614390	+	0.189090i	−0.00208418	+	0.00641443i
$870$	3.79252	−	3.11436i	0.128579	−	0.105587i
$871$	−5.70108	−	17.5461i	−0.193174	−	0.594528i
$872$	1.67389	−	3.28520i	0.0566852	−	0.111251i
$873$	3.79787	−	26.1840i	0.128538	−	0.886195i
$874$			41.5811i			1.40650i
$875$	−0.0195317	−	0.122540i	−0.000660293	−	0.00414261i
$876$	−16.3273	−	2.47699i	−0.551649	−	0.0836898i
$877$	−42.1581	+	6.67719i	−1.42358	+	0.225473i	−0.820243	−	0.572015i	$-0.806162\pi$
$877$	−42.1581	+	6.67719i	−1.42358	+	0.225473i	−0.603335	+	0.797488i	$0.706162\pi$
$878$	29.2728	+	14.9152i	0.987909	+	0.503365i
$879$	−1.45054	−	8.78720i	−0.0489256	−	0.296385i
$880$	−0.757837	+	0.842217i	−0.0255467	+	0.0283911i
$881$	−49.4925	−	16.0811i	−1.66745	−	0.541786i	−0.685034	−	0.728511i	$-0.740213\pi$
$881$	−49.4925	−	16.0811i	−1.66745	−	0.541786i	−0.982412	+	0.186725i	$0.940213\pi$
$882$	9.77678	+	18.5849i	0.329201	+	0.625787i
$883$	−13.3998	+	6.82753i	−0.450938	+	0.229765i	−0.664684	−	0.747125i	$-0.731434\pi$
$883$	−13.3998	+	6.82753i	−0.450938	+	0.229765i	0.213745	+	0.976889i	$0.431434\pi$
$884$	7.16783	−	5.20773i	0.241080	−	0.175155i
$885$	8.59648	−	9.67982i	0.288967	−	0.325383i
$886$	14.4997	+	10.5347i	0.487128	+	0.353919i
$887$	5.44762	+	0.862818i	0.182913	+	0.0289706i	0.247219	−	0.968960i	$-0.420483\pi$
$887$	5.44762	+	0.862818i	0.182913	+	0.0289706i	−0.0643058	+	0.997930i	$0.520483\pi$
$888$	1.88230	−	5.92427i	0.0631659	−	0.198805i
$889$	−0.0859206	+	0.118260i	−0.00288168	+	0.00396630i
$890$	−31.3408	+	12.0424i	−1.05055	+	0.403662i
$891$	−0.118905	−	4.55861i	−0.00398345	−	0.152719i
$892$	−6.80056	−	13.3469i	−0.227700	−	0.446886i
$893$	7.64405	−	7.64405i	0.255798	−	0.255798i
$894$	−29.6923	−	14.8860i	−0.993059	−	0.497861i
$895$	19.1579	−	43.0673i	0.640378	−	1.43958i
$896$	0.0105555	−	0.00342968i	0.000352633	−	0.000114577i
$897$	−33.6206	+	46.9149i	−1.12256	+	1.56644i
$898$	2.15398	+	13.5997i	0.0718791	+	0.453827i
$899$	−11.3238			−0.377670
$900$	−11.0087	+	10.1887i	−0.366956	+	0.339622i
$901$	−18.2679			−0.608593
$902$	0.917640	+	5.79375i	0.0305541	+	0.192911i
$903$	−0.0700969	+	0.0978149i	−0.00233268	+	0.00325508i
$904$	−12.4486	+	4.04480i	−0.414034	+	0.134528i
$905$	17.1702	−	9.92071i	0.570757	−	0.329776i
$906$	−17.6206	−	8.83392i	−0.585405	−	0.293487i
$907$	−33.8062	+	33.8062i	−1.12252	+	1.12252i	−0.131153	+	0.991362i	$0.541868\pi$
$907$	−33.8062	+	33.8062i	−1.12252	+	1.12252i	−0.991362	+	0.131153i	$0.958132\pi$
$908$	−7.20727	−	14.1451i	−0.239182	−	0.469421i
$909$	−25.1308	+	8.52934i	−0.833537	+	0.282900i
$910$	−0.00516053	−	0.0978562i	−0.000171070	−	0.00324390i
$911$	−7.28561	+	10.0278i	−0.241383	+	0.332235i	−0.912470	−	0.409143i	$-0.865828\pi$
$911$	−7.28561	+	10.0278i	−0.241383	+	0.332235i	0.671087	+	0.741378i	$0.265828\pi$
$912$	−2.58412	+	8.13315i	−0.0855688	+	0.269315i
$913$	−5.25622	−	0.832503i	−0.173955	−	0.0275518i
$914$	−16.5778	−	12.0445i	−0.548345	−	0.398396i
$915$	−21.1593	−	9.24768i	−0.699506	−	0.305719i
$916$	−4.54327	+	3.30088i	−0.150114	+	0.109064i
$917$	−0.0563123	+	0.0286925i	−0.00185960	+	0.000947511i
$918$	3.81912	+	11.0162i	0.126050	+	0.363587i
$919$	−4.10646	−	1.33427i	−0.135460	−	0.0440135i	0.240503	−	0.970648i	$-0.422688\pi$
$919$	−4.10646	−	1.33427i	−0.135460	−	0.0440135i	−0.375962	+	0.926635i	$0.622688\pi$
$920$	−1.96644	+	18.7684i	−0.0648315	+	0.618777i
$921$	3.25786	+	19.7357i	0.107350	+	0.650314i
$922$	−3.46307	−	1.76452i	−0.114050	−	0.0581114i
$923$	45.5696	−	7.21751i	1.49994	−	0.237567i
$924$	0.00963003	+	0.00146096i	0.000316805	+	4.80619e-5i
$925$	−17.9204	−	0.927409i	−0.589218	−	0.0304930i
$926$		−	10.9826i		−	0.360912i
$927$	−19.2603	−	2.79362i	−0.632592	−	0.0917545i
$928$	0.575243	−	1.12898i	0.0188833	−	0.0370605i
$929$	−2.03518	−	6.26364i	−0.0667721	−	0.205503i	0.912104	−	0.409960i	$-0.134457\pi$
$929$	−2.03518	−	6.26364i	−0.0667721	−	0.205503i	−0.978876	+	0.204457i	$0.934457\pi$
$930$	34.5519	−	2.04809i	1.13300	−	0.0671595i
$931$	10.6575	−	32.8004i	0.349285	−	1.07499i
$932$	−20.6596	−	20.6596i	−0.676729	−	0.676729i
$933$	−6.35346	−	19.1287i	−0.208003	−	0.626246i
$934$	−10.1579	−	13.9812i	−0.332378	−	0.457479i
$935$	1.97517	−	1.60053i	0.0645949	−	0.0523429i
$936$	−9.49169	+	7.08703i	−0.310246	+	0.231647i
$937$	3.77782	−	23.8522i	0.123416	−	0.779218i	−0.845889	−	0.533358i	$-0.820930\pi$
$937$	3.77782	−	23.8522i	0.123416	−	0.779218i	0.969305	−	0.245860i	$-0.0790702\pi$
$938$	−0.00811227	+	0.0512189i	−0.000264875	+	0.00167236i
$939$	20.9825	−	21.2579i	0.684739	−	0.693726i
$940$	3.81179	−	3.08879i	0.124327	−	0.100745i
$941$	27.0506	+	37.2319i	0.881823	+	1.21372i	0.975913	+	0.218161i	$0.0700059\pi$
$941$	27.0506	+	37.2319i	0.881823	+	1.21372i	−0.0940900	+	0.995564i	$0.529994\pi$
$942$	32.0313	−	10.6390i	1.04364	−	0.346636i
$943$	69.0878	+	69.0878i	2.24981	+	2.24981i
$944$	1.03293	−	3.17904i	0.0336191	−	0.103469i
$945$	0.125200	+	0.0308926i	0.00407275	+	0.00100494i
$946$	−0.980151	−	3.01659i	−0.0318675	−	0.0980779i
$947$	2.89853	−	5.68868i	0.0941895	−	0.184857i	−0.839105	−	0.543970i	$-0.816921\pi$
$947$	2.89853	−	5.68868i	0.0941895	−	0.184857i	0.933294	+	0.359113i	$0.116921\pi$
$948$	0.00443088	+	0.679635i	0.000143908	+	0.0220735i
$949$			37.6471i			1.22208i
$950$	24.6020	+	1.27320i	0.798195	+	0.0413079i
$951$	4.07205	−	26.8413i	0.132045	−	0.870389i
$952$	−0.0245971	+	0.00389581i	−0.000797198	+	0.000126264i
$953$	−39.7752	−	20.2665i	−1.28844	−	0.656495i	−0.330597	−	0.943772i	$-0.607250\pi$
$953$	−39.7752	−	20.2665i	−1.28844	−	0.656495i	−0.957848	+	0.287277i	$0.907250\pi$
$954$	24.4219	−	0.318450i	0.790688	−	0.0103102i
$955$	−4.22169	+	40.2935i	−0.136611	+	1.30387i
$956$	−3.53186	−	1.14757i	−0.114228	−	0.0371151i
$957$	0.895343	−	0.659466i	0.0289423	−	0.0213175i
$958$	−20.2532	+	10.3195i	−0.654353	+	0.333409i
$959$	0.0209220	−	0.0152007i	0.000675605	−	0.000490856i
$960$	−1.55102	+	3.54885i	−0.0500591	+	0.114539i
$961$	−39.5355	−	28.7243i	−1.27534	−	0.926589i
$962$	−13.9963	−	2.21680i	−0.451259	−	0.0714724i
$963$	−9.72321	+	19.7142i	−0.313326	+	0.635281i
$964$	−2.47374	+	3.40480i	−0.0796737	+	0.109661i
$965$	−1.59261	−	30.1997i	−0.0512679	−	0.972164i
$966$	0.144069	−	0.0745941i	0.00463536	−	0.00240003i
$967$	−10.8927	−	21.3781i	−0.350286	−	0.687475i	0.646889	−	0.762584i	$-0.276070\pi$
$967$	−10.8927	−	21.3781i	−0.350286	−	0.687475i	−0.997175	+	0.0751090i	$0.976070\pi$
$968$	7.59664	−	7.59664i	0.244165	−	0.244165i
$969$	8.58186	−	17.1178i	0.275689	−	0.549904i
$970$	−17.0754	+	9.86591i	−0.548257	+	0.316775i
$971$	20.8604	−	6.77794i	0.669441	−	0.217515i	0.0454742	−	0.998966i	$-0.485520\pi$
$971$	20.8604	−	6.77794i	0.669441	−	0.217515i	0.623967	+	0.781451i	$0.285520\pi$
$972$	−5.29772	−	14.6606i	−0.169924	−	0.470240i
$973$	−0.00610263	−	0.0385305i	−0.000195641	−	0.00123523i
$974$	−5.98412			−0.191744
$975$	26.7284	+	21.3286i	0.855995	+	0.683062i
$976$	−5.96231			−0.190849
$977$	9.37414	+	59.1860i	0.299905	+	1.89353i	0.431317	+	0.902200i	$0.358049\pi$
$977$	9.37414	+	59.1860i	0.299905	+	1.89353i	−0.131412	+	0.991328i	$0.541951\pi$
$978$	−17.9777	−	12.8833i	−0.574863	−	0.411963i
$979$	−7.23556	+	2.35098i	−0.231250	+	0.0751375i
$980$	6.36164	−	14.3011i	0.203215	−	0.456831i
$981$	6.38438	−	9.03271i	0.203838	−	0.288392i
$982$	3.53533	−	3.53533i	0.112817	−	0.112817i
$983$	−1.60535	−	3.15067i	−0.0512026	−	0.100491i	0.863987	−	0.503513i	$-0.167960\pi$
$983$	−1.60535	−	3.15067i	−0.0512026	−	0.100491i	−0.915190	+	0.403023i	$0.867960\pi$
$984$	9.21982	+	17.8070i	0.293917	+	0.567665i
$985$	34.9299	−	13.4215i	1.11296	−	0.427643i
$986$	−1.67116	+	2.30015i	−0.0532205	+	0.0732518i
$987$	−0.0401980	−	0.0127720i	−0.00127952	−	0.000406537i
$988$	19.2149	+	3.04334i	0.611306	+	0.0968214i
$989$	−42.7410	−	31.0532i	−1.35908	−	0.987433i
$990$	−2.61265	+	2.17414i	−0.0830354	+	0.0690986i
$991$	28.2381	−	20.5162i	0.897013	−	0.651718i	−0.0406840	−	0.999172i	$-0.512954\pi$
$991$	28.2381	−	20.5162i	0.897013	−	0.651718i	0.937697	+	0.347454i	$0.112954\pi$
$992$	7.96286	−	4.05728i	0.252821	−	0.128819i
$993$	−7.01657	−	9.52625i	−0.222664	−	0.302306i
$994$	−0.123338	−	0.0400749i	−0.00391204	−	0.00127110i
$995$	−7.94980	+	8.83495i	−0.252025	+	0.280087i
$996$	−17.9489	+	2.96291i	−0.568733	+	0.0938833i
$997$	48.5536	+	24.7393i	1.53771	+	0.783501i	0.998285	−	0.0585356i	$-0.0186431\pi$
$997$	48.5536	+	24.7393i	1.53771	+	0.783501i	0.539421	+	0.842036i	$0.318643\pi$
$998$	18.1509	−	2.87482i	0.574556	−	0.0910008i
$999$	8.13959	−	16.7782i	0.257525	−	0.530838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.113.9	yes	80
3.2	odd	2	inner	150.2.l.a.113.4	yes	80
5.2	odd	4		750.2.l.c.707.1		80
5.3	odd	4		750.2.l.a.707.10		80
5.4	even	2		750.2.l.b.293.2		80
15.2	even	4		750.2.l.c.707.6		80
15.8	even	4		750.2.l.a.707.5		80
15.14	odd	2		750.2.l.b.293.7		80
25.2	odd	20	inner	150.2.l.a.77.4	✓	80
25.11	even	5		750.2.l.c.593.6		80
25.14	even	10		750.2.l.a.593.5		80
25.23	odd	20		750.2.l.b.407.7		80
75.2	even	20	inner	150.2.l.a.77.9	yes	80
75.11	odd	10		750.2.l.c.593.1		80
75.14	odd	10		750.2.l.a.593.10		80
75.23	even	20		750.2.l.b.407.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.4	✓	80	25.2	odd	20	inner
150.2.l.a.77.9	yes	80	75.2	even	20	inner
150.2.l.a.113.4	yes	80	3.2	odd	2	inner
150.2.l.a.113.9	yes	80	1.1	even	1	trivial
750.2.l.a.593.5		80	25.14	even	10
750.2.l.a.593.10		80	75.14	odd	10
750.2.l.a.707.5		80	15.8	even	4
750.2.l.a.707.10		80	5.3	odd	4
750.2.l.b.293.2		80	5.4	even	2
750.2.l.b.293.7		80	15.14	odd	2
750.2.l.b.407.2		80	75.23	even	20
750.2.l.b.407.7		80	25.23	odd	20
750.2.l.c.593.1		80	75.11	odd	10
750.2.l.c.593.6		80	25.11	even	5
750.2.l.c.707.1		80	5.2	odd	4
750.2.l.c.707.6		80	15.2	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(1.00892 - 1.40787i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.66221 + 1.49568i) q^{5} +(1.54836 + 0.776257i) q^{6} +(-0.00784794 + 0.00784794i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.964173 - 2.84084i) q^{9} +O(q^{10})\)	\(q+(0.156434 + 0.987688i) q^{2} +(1.00892 - 1.40787i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.66221 + 1.49568i) q^{5} +(1.54836 + 0.776257i) q^{6} +(-0.00784794 + 0.00784794i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.964173 - 2.84084i) q^{9} +(-1.21724 + 1.87572i) q^{10} +(-0.297822 + 0.409916i) q^{11} +(-0.524483 + 1.65073i) q^{12} +(3.89992 + 0.617686i) q^{13} +(-0.00897901 - 0.00652363i) q^{14} +(3.78275 - 0.831157i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.99929 + 1.01869i) q^{17} +(2.65503 - 1.39671i) q^{18} +(-4.68585 - 1.52252i) q^{19} +(-2.04305 - 0.908822i) q^{20} +(0.00313093 + 0.0189668i) q^{21} +(-0.451459 - 0.230030i) q^{22} +(-8.33555 + 1.32022i) q^{23} +(-1.71246 - 0.259794i) q^{24} +(0.525896 + 4.97227i) q^{25} +3.94853i q^{26} +(-4.97229 - 1.50875i) q^{27} +(0.00503869 - 0.00988898i) q^{28} +(-0.391550 - 1.20507i) q^{29} +(1.41268 + 3.60615i) q^{30} +(2.76166 - 8.49952i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.276630 + 0.832864i) q^{33} +(-1.31890 - 1.81531i) q^{34} +(-0.0247829 + 0.00130695i) q^{35} +(1.79485 + 2.40385i) q^{36} +(-0.561423 + 3.54469i) q^{37} +(0.770751 - 4.86633i) q^{38} +(4.80431 - 4.86737i) q^{39} +(0.578030 - 2.16007i) q^{40} +(-6.80489 - 9.36613i) q^{41} +(-0.0182435 + 0.00605944i) q^{42} +(4.42647 + 4.42647i) q^{43} +(0.156574 - 0.481886i) q^{44} +(2.64632 - 6.16417i) q^{45} +(-2.60793 - 8.02639i) q^{46} +(-0.996101 + 1.95496i) q^{47} +(-0.0112919 - 1.73201i) q^{48} +6.99988i q^{49} +(-4.82878 + 1.29726i) q^{50} +(-0.582939 + 3.84250i) q^{51} +(-3.89992 + 0.617686i) q^{52} +(7.25397 + 3.69608i) q^{53} +(0.712332 - 5.14709i) q^{54} +(-1.10815 + 0.235923i) q^{55} +(0.0105555 + 0.00342968i) q^{56} +(-6.87114 + 5.06094i) q^{57} +(1.12898 - 0.575243i) q^{58} +(2.70425 - 1.96475i) q^{59} +(-3.34077 + 1.95941i) q^{60} +(-4.82361 - 3.50456i) q^{61} +(8.82690 + 1.39804i) q^{62} +(0.0298615 + 0.0147280i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(5.55863 + 6.85975i) q^{65} +(-0.779336 + 0.403513i) q^{66} +(-2.12122 - 4.16313i) q^{67} +(1.58664 - 1.58664i) q^{68} +(-6.55118 + 13.0673i) q^{69} +(-0.00516776 - 0.0242734i) q^{70} +(11.1129 - 3.61079i) q^{71} +(-2.09348 + 2.14880i) q^{72} +(1.49152 + 9.41706i) q^{73} -3.58887 q^{74} +(7.53087 + 4.27621i) q^{75} +4.92699 q^{76} +(-0.000879712 - 0.00555428i) q^{77} +(5.55900 + 3.98374i) q^{78} +(0.373190 - 0.121257i) q^{79} +(2.22389 + 0.233005i) q^{80} +(-7.14074 + 5.47812i) q^{81} +(8.18630 - 8.18630i) q^{82} +(4.76829 + 9.35829i) q^{83} +(-0.00883874 - 0.0170710i) q^{84} +(-4.84687 - 1.29701i) q^{85} +(-3.67952 + 5.06443i) q^{86} +(-2.09161 - 0.664562i) q^{87} +(0.500446 + 0.0792629i) q^{88} +(12.1475 + 8.82566i) q^{89} +(6.50225 + 1.64945i) q^{90} +(-0.0354539 + 0.0257588i) q^{91} +(7.51960 - 3.83143i) q^{92} +(-9.17990 - 12.4634i) q^{93} +(-2.08671 - 0.678015i) q^{94} +(-5.51167 - 9.53928i) q^{95} +(1.70892 - 0.282100i) q^{96} +(7.85809 + 4.00390i) q^{97} +(-6.91370 + 1.09502i) q^{98} +(1.45166 + 0.450833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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