LMFDB - Embedded newform 75.2.l.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(2,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("75.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	75.8
Dual form			75.2.l.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.888111 + 1.74302i) q^{2} +(1.12908 - 1.31346i) q^{3} +(-1.07379 - 1.47795i) q^{4} +(1.74306 + 1.40062i) q^{5} +(1.28664 + 3.13450i) q^{6} +(-0.551254 + 0.551254i) q^{7} +(-0.334566 + 0.0529901i) q^{8} +(-0.450377 - 2.96600i) q^{9} +O(q^{10})$	\(q+(-0.888111 + 1.74302i) q^{2} +(1.12908 - 1.31346i) q^{3} +(-1.07379 - 1.47795i) q^{4} +(1.74306 + 1.40062i) q^{5} +(1.28664 + 3.13450i) q^{6} +(-0.551254 + 0.551254i) q^{7} +(-0.334566 + 0.0529901i) q^{8} +(-0.450377 - 2.96600i) q^{9} +(-3.98933 + 1.79428i) q^{10} +(0.937544 - 0.304626i) q^{11} +(-3.15362 - 0.258327i) q^{12} +(-4.20319 + 2.14163i) q^{13} +(-0.471270 - 1.45042i) q^{14} +(3.80771 - 0.708044i) q^{15} +(1.33382 - 4.10508i) q^{16} +(-0.535425 - 3.38054i) q^{17} +(5.56977 + 1.84912i) q^{18} +(3.79078 - 5.21756i) q^{19} +(0.198357 - 4.08012i) q^{20} +(0.101645 + 1.34646i) q^{21} +(-0.301674 + 1.90469i) q^{22} +(-0.855694 - 0.435998i) q^{23} +(-0.308150 + 0.499270i) q^{24} +(1.07653 + 4.88273i) q^{25} -9.22822i q^{26} +(-4.40425 - 2.75728i) q^{27} +(1.40666 + 0.222792i) q^{28} +(-8.30669 + 6.03516i) q^{29} +(-2.14754 + 7.26572i) q^{30} +(-2.73448 - 1.98672i) q^{31} +(5.49158 + 5.49158i) q^{32} +(0.658442 - 1.57538i) q^{33} +(6.36785 + 2.06904i) q^{34} +(-1.73297 + 0.188773i) q^{35} +(-3.89998 + 3.85050i) q^{36} +(-1.85119 - 3.63316i) q^{37} +(5.72765 + 11.2411i) q^{38} +(-1.93276 + 7.93880i) q^{39} +(-0.657388 - 0.376235i) q^{40} +(3.89453 + 1.26541i) q^{41} +(-2.43717 - 1.01864i) q^{42} +(4.93949 + 4.93949i) q^{43} +(-1.45695 - 1.05853i) q^{44} +(3.36920 - 5.80073i) q^{45} +(1.51990 - 1.10427i) q^{46} +(4.62454 + 0.732455i) q^{47} +(-3.88589 - 6.38686i) q^{48} +6.39224i q^{49} +(-9.46676 - 2.46000i) q^{50} +(-5.04475 - 3.11362i) q^{51} +(7.67856 + 3.91242i) q^{52} +(0.542970 - 3.42818i) q^{53} +(8.71745 - 5.22789i) q^{54} +(2.06086 + 0.782159i) q^{55} +(0.155220 - 0.213642i) q^{56} +(-2.57300 - 10.8701i) q^{57} +(-3.14212 - 19.8386i) q^{58} +(-0.172592 + 0.531183i) q^{59} +(-5.13514 - 4.86730i) q^{60} +(2.95410 + 9.09178i) q^{61} +(5.89140 - 3.00182i) q^{62} +(1.88329 + 1.38675i) q^{63} +(-6.23890 + 2.02714i) q^{64} +(-10.3260 - 2.15407i) q^{65} +(2.16114 + 2.54678i) q^{66} +(6.82141 - 1.08040i) q^{67} +(-4.42132 + 4.42132i) q^{68} +(-1.53881 + 0.631649i) q^{69} +(1.21003 - 3.18824i) q^{70} +(5.08421 + 6.99781i) q^{71} +(0.307850 + 0.968458i) q^{72} +(-4.09480 + 8.03649i) q^{73} +7.97671 q^{74} +(7.62878 + 4.09899i) q^{75} -11.7818 q^{76} +(-0.348898 + 0.684752i) q^{77} +(-12.1209 - 10.4194i) q^{78} +(-3.84334 - 5.28990i) q^{79} +(8.07458 - 5.28723i) q^{80} +(-8.59432 + 2.67164i) q^{81} +(-5.66440 + 5.66440i) q^{82} +(1.41101 - 0.223482i) q^{83} +(1.88085 - 1.59604i) q^{84} +(3.80157 - 6.64241i) q^{85} +(-12.9964 + 4.22279i) q^{86} +(-1.45191 + 17.7247i) q^{87} +(-0.297528 + 0.151598i) q^{88} +(-3.04398 - 9.36841i) q^{89} +(7.11853 + 11.0243i) q^{90} +(1.13644 - 3.49761i) q^{91} +(0.274455 + 1.73284i) q^{92} +(-5.69692 + 1.34849i) q^{93} +(-5.38378 + 7.41014i) q^{94} +(13.9154 - 3.78509i) q^{95} +(13.4134 - 1.01259i) q^{96} +(0.873583 - 5.51558i) q^{97} +(-11.1418 - 5.67701i) q^{98} +(-1.32577 - 2.64356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.888111	+	1.74302i	−0.627989	+	1.23250i	0.329535	+	0.944143i	$0.393108\pi$
$2$	−0.888111	+	1.74302i	−0.627989	+	1.23250i	−0.957524	+	0.288354i	$0.906892\pi$
$3$	1.12908	−	1.31346i	0.651872	−	0.758329i
$3$	1.12908	−	1.31346i	0.651872	−	0.758329i
$4$	−1.07379	−	1.47795i	−0.536895	−	0.738973i
$5$	1.74306	+	1.40062i	0.779521	+	0.626376i
$5$	1.74306	+	1.40062i	0.779521	+	0.626376i
$6$	1.28664	+	3.13450i	0.525270	+	1.27965i
$7$	−0.551254	+	0.551254i	−0.208355	+	0.208355i	−0.803568	−	0.595213i	$-0.797068\pi$
$7$	−0.551254	+	0.551254i	−0.208355	+	0.208355i	0.595213	+	0.803568i	$0.297068\pi$
$8$	−0.334566	+	0.0529901i	−0.118287	+	0.0187348i
$9$	−0.450377	−	2.96600i	−0.150126	−	0.988667i
$10$	−3.98933	+	1.79428i	−1.26154	+	0.567400i
$11$	0.937544	−	0.304626i	0.282680	−	0.0918483i	−0.164245	−	0.986420i	$-0.552519\pi$
$11$	0.937544	−	0.304626i	0.282680	−	0.0918483i	0.446925	+	0.894571i	$0.352519\pi$
$12$	−3.15362	−	0.258327i	−0.910372	−	0.0745726i
$13$	−4.20319	+	2.14163i	−1.16575	+	0.593981i	−0.926248	−	0.376914i	$-0.876985\pi$
$13$	−4.20319	+	2.14163i	−1.16575	+	0.593981i	−0.239505	+	0.970895i	$0.576985\pi$
$14$	−0.471270	−	1.45042i	−0.125952	−	0.387641i
$15$	3.80771	−	0.708044i	0.983147	−	0.182816i
$16$	1.33382	−	4.10508i	0.333455	−	1.02627i
$17$	−0.535425	−	3.38054i	−0.129860	−	0.819901i	−0.963522	−	0.267627i	$-0.913760\pi$
$17$	−0.535425	−	3.38054i	−0.129860	−	0.819901i	0.833663	−	0.552274i	$-0.186240\pi$
$18$	5.56977	+	1.84912i	1.31281	+	0.435842i
$19$	3.79078	−	5.21756i	0.869664	−	1.19699i	−0.109514	−	0.993985i	$-0.534930\pi$
$19$	3.79078	−	5.21756i	0.869664	−	1.19699i	0.979178	−	0.203004i	$-0.0650705\pi$
$20$	0.198357	−	4.08012i	0.0443540	−	0.912344i
$21$	0.101645	+	1.34646i	0.0221808	+	0.293822i
$22$	−0.301674	+	1.90469i	−0.0643171	+	0.406082i
$23$	−0.855694	−	0.435998i	−0.178424	−	0.0909118i	0.362497	−	0.931985i	$-0.381924\pi$
$23$	−0.855694	−	0.435998i	−0.178424	−	0.0909118i	−0.540921	+	0.841073i	$0.681924\pi$
$24$	−0.308150	+	0.499270i	−0.0629008	+	0.101913i
$25$	1.07653	+	4.88273i	0.215306	+	0.976547i
$26$		−	9.22822i		−	1.80980i
$27$	−4.40425	−	2.75728i	−0.847598	−	0.530640i
$28$	1.40666	+	0.222792i	0.265833	+	0.0421038i
$29$	−8.30669	+	6.03516i	−1.54251	+	1.12070i	−0.593778	+	0.804629i	$0.702364\pi$
$29$	−8.30669	+	6.03516i	−1.54251	+	1.12070i	−0.948735	+	0.316073i	$0.897636\pi$
$30$	−2.14754	+	7.26572i	−0.392085	+	1.32653i
$31$	−2.73448	−	1.98672i	−0.491128	−	0.356825i	0.314490	−	0.949261i	$-0.398166\pi$
$31$	−2.73448	−	1.98672i	−0.491128	−	0.356825i	−0.805618	+	0.592436i	$0.798166\pi$
$32$	5.49158	+	5.49158i	0.970784	+	0.970784i
$33$	0.658442	−	1.57538i	0.114620	−	0.274238i
$34$	6.36785	+	2.06904i	1.09208	+	0.354837i
$35$	−1.73297	+	0.188773i	−0.292925	+	0.0319084i
$36$	−3.89998	+	3.85050i	−0.649997	+	0.641750i
$37$	−1.85119	−	3.63316i	−0.304333	−	0.597288i	0.687300	−	0.726374i	$-0.258796\pi$
$37$	−1.85119	−	3.63316i	−0.304333	−	0.597288i	−0.991633	+	0.129086i	$0.958796\pi$
$38$	5.72765	+	11.2411i	0.929148	+	1.82355i
$39$	−1.93276	+	7.93880i	−0.309489	+	1.27122i
$40$	−0.657388	−	0.376235i	−0.103942	−	0.0594880i
$41$	3.89453	+	1.26541i	0.608223	+	0.197624i	0.596905	−	0.802312i	$-0.296397\pi$
$41$	3.89453	+	1.26541i	0.608223	+	0.197624i	0.0113186	+	0.999936i	$0.496397\pi$
$42$	−2.43717	−	1.01864i	−0.376064	−	0.157179i
$43$	4.93949	+	4.93949i	0.753265	+	0.753265i	0.975087	−	0.221822i	$-0.0712005\pi$
$43$	4.93949	+	4.93949i	0.753265	+	0.753265i	−0.221822	+	0.975087i	$0.571201\pi$
$44$	−1.45695	−	1.05853i	−0.219643	−	0.159580i
$45$	3.36920	−	5.80073i	0.502251	−	0.864722i
$46$	1.51990	−	1.10427i	0.224097	−	0.162816i
$47$	4.62454	+	0.732455i	0.674558	+	0.106840i	0.484310	−	0.874897i	$-0.339071\pi$
$47$	4.62454	+	0.732455i	0.674558	+	0.106840i	0.190248	+	0.981736i	$0.439071\pi$
$48$	−3.88589	−	6.38686i	−0.560879	−	0.921865i
$49$			6.39224i			0.913177i
$50$	−9.46676	−	2.46000i	−1.33880	−	0.347897i
$51$	−5.04475	−	3.11362i	−0.706407	−	0.435994i
$52$	7.67856	+	3.91242i	1.06482	+	0.542555i
$53$	0.542970	−	3.42818i	0.0745826	−	0.470896i	−0.921923	−	0.387373i	$-0.873383\pi$
$53$	0.542970	−	3.42818i	0.0745826	−	0.470896i	0.996506	−	0.0835235i	$-0.0266174\pi$
$54$	8.71745	−	5.22789i	1.18629	−	0.711426i
$55$	2.06086	+	0.782159i	0.277887	+	0.105466i
$56$	0.155220	−	0.213642i	0.0207421	−	0.0285491i
$57$	−2.57300	−	10.8701i	−0.340802	−	1.43978i
$58$	−3.14212	−	19.8386i	−0.412581	−	2.60493i
$59$	−0.172592	+	0.531183i	−0.0224696	+	0.0691542i	−0.961663	−	0.274236i	$-0.911575\pi$
$59$	−0.172592	+	0.531183i	−0.0224696	+	0.0691542i	0.939193	+	0.343390i	$0.111575\pi$
$60$	−5.13514	−	4.86730i	−0.662944	−	0.628366i
$61$	2.95410	+	9.09178i	0.378233	+	1.16408i	0.941271	+	0.337652i	$0.109633\pi$
$61$	2.95410	+	9.09178i	0.378233	+	1.16408i	−0.563038	+	0.826431i	$0.690367\pi$
$62$	5.89140	−	3.00182i	0.748209	−	0.381231i
$63$	1.88329	+	1.38675i	0.237273	+	0.174714i
$64$	−6.23890	+	2.02714i	−0.779862	+	0.253393i
$65$	−10.3260	−	2.15407i	−1.28079	−	0.267180i
$66$	2.16114	+	2.54678i	0.266017	+	0.313487i
$67$	6.82141	−	1.08040i	0.833367	−	0.131992i	0.274852	−	0.961487i	$-0.411371\pi$
$67$	6.82141	−	1.08040i	0.833367	−	0.131992i	0.558515	+	0.829494i	$0.311371\pi$
$68$	−4.42132	+	4.42132i	−0.536164	+	0.536164i
$69$	−1.53881	+	0.631649i	−0.185251	+	0.0760416i
$70$	1.21003	−	3.18824i	0.144627	−	0.381068i
$71$	5.08421	+	6.99781i	0.603385	+	0.830488i	0.996013	−	0.0892096i	$-0.0284341\pi$
$71$	5.08421	+	6.99781i	0.603385	+	0.830488i	−0.392628	+	0.919697i	$0.628434\pi$
$72$	0.307850	+	0.968458i	0.0362804	+	0.114134i
$73$	−4.09480	+	8.03649i	−0.479260	+	0.940600i	0.517147	+	0.855897i	$0.326994\pi$
$73$	−4.09480	+	8.03649i	−0.479260	+	0.940600i	−0.996406	+	0.0847030i	$0.973006\pi$
$74$	7.97671			0.927274
$75$	7.62878	+	4.09899i	0.880895	+	0.473311i
$76$	−11.7818			−1.35146
$77$	−0.348898	+	0.684752i	−0.0397607	+	0.0780347i
$78$	−12.1209	−	10.4194i	−1.37243	−	1.17976i
$79$	−3.84334	−	5.28990i	−0.432410	−	0.595161i	0.536095	−	0.844158i	$-0.319899\pi$
$79$	−3.84334	−	5.28990i	−0.432410	−	0.595161i	−0.968504	+	0.248997i	$0.919899\pi$
$80$	8.07458	−	5.28723i	0.902766	−	0.591130i
$81$	−8.59432	+	2.67164i	−0.954925	+	0.296849i
$82$	−5.66440	+	5.66440i	−0.625528	+	0.625528i
$83$	1.41101	−	0.223482i	0.154878	−	0.0245303i	−0.0785138	−	0.996913i	$-0.525017\pi$
$83$	1.41101	−	0.223482i	0.154878	−	0.0245303i	0.233392	+	0.972383i	$0.425017\pi$
$84$	1.88085	−	1.59604i	0.205218	−	0.174143i
$85$	3.80157	−	6.64241i	0.412338	−	0.720471i
$86$	−12.9964	+	4.22279i	−1.40144	+	0.455355i
$87$	−1.45191	+	17.7247i	−0.155661	+	1.90029i
$88$	−0.297528	+	0.151598i	−0.0317166	+	0.0161604i
$89$	−3.04398	−	9.36841i	−0.322661	−	0.993049i	−0.972485	−	0.232964i	$-0.925157\pi$
$89$	−3.04398	−	9.36841i	−0.322661	−	0.993049i	0.649824	−	0.760085i	$-0.274843\pi$
$90$	7.11853	+	11.0243i	0.750359	+	1.16206i
$91$	1.13644	−	3.49761i	0.119131	−	0.366649i
$92$	0.274455	+	1.73284i	0.0286139	+	0.180661i
$93$	−5.69692	+	1.34849i	−0.590743	+	0.139832i
$94$	−5.38378	+	7.41014i	−0.555295	+	0.764297i
$95$	13.9154	−	3.78509i	1.42769	−	0.388342i
$96$	13.4134	−	1.01259i	1.36900	−	0.103347i
$97$	0.873583	−	5.51558i	0.0886989	−	0.560023i	−0.902816	−	0.430028i	$-0.858504\pi$
$97$	0.873583	−	5.51558i	0.0886989	−	0.560023i	0.991515	−	0.129995i	$-0.0414962\pi$
$98$	−11.1418	−	5.67701i	−1.12549	−	0.573465i
$99$	−1.32577	−	2.64356i	−0.133245	−	0.265688i
$100$	6.06045	−	6.83409i	0.606045	−	0.683409i
$101$		−	3.43356i		−	0.341652i	−0.985301	−	0.170826i	$-0.945356\pi$
$101$		−	3.43356i		−	0.341652i	0.985301	−	0.170826i	$-0.0546437\pi$
$102$	9.90739	−	6.02784i	0.980978	−	0.596845i
$103$	4.88052	+	0.772999i	0.480892	+	0.0761658i	0.392174	−	0.919891i	$-0.371723\pi$
$103$	4.88052	+	0.772999i	0.480892	+	0.0761658i	0.0887178	+	0.996057i	$0.471723\pi$
$104$	1.29276	−	0.939244i	0.126765	−	0.0921004i
$105$	−1.70871	+	2.48933i	−0.166753	+	0.242934i
$106$	5.49315	+	3.99100i	0.533542	+	0.387641i
$107$	−2.44736	−	2.44736i	−0.236595	−	0.236595i	0.578844	−	0.815439i	$-0.303504\pi$
$107$	−2.44736	−	2.44736i	−0.236595	−	0.236595i	−0.815439	+	0.578844i	$0.803504\pi$
$108$	0.654121	+	9.46999i	0.0629429	+	0.911250i
$109$	−2.20399	−	0.716119i	−0.211104	−	0.0685918i	0.201556	−	0.979477i	$-0.435400\pi$
$109$	−2.20399	−	0.716119i	−0.211104	−	0.0685918i	−0.412660	+	0.910885i	$0.635400\pi$
$110$	−3.19359	+	2.89747i	−0.304497	+	0.276263i
$111$	−6.86216	−	1.67064i	−0.651327	−	0.158570i
$112$	1.52767	+	2.99821i	0.144351	+	0.283305i
$113$	−1.48114	−	2.90689i	−0.139334	−	0.273457i	0.810786	−	0.585342i	$-0.199040\pi$
$113$	−1.48114	−	2.90689i	−0.139334	−	0.273457i	−0.950120	+	0.311885i	$0.899040\pi$
$114$	21.2318	+	5.16904i	1.98854	+	0.484125i
$115$	−0.880860	−	1.95847i	−0.0821406	−	0.182629i
$116$	17.8393	+	5.79634i	1.65634	+	0.538176i
$117$	8.24509	+	11.5021i	0.762259	+	1.06337i
$118$	−0.772580	−	0.772580i	−0.0711217	−	0.0711217i
$119$	2.15869	+	1.56838i	0.197887	+	0.143773i
$120$	−1.23641	+	0.438659i	−0.112868	+	0.0400439i
$121$	−8.11300	+	5.89444i	−0.737545	+	0.535858i
$122$	−18.4707	−	2.92547i	−1.67226	−	0.264859i
$123$	6.05929	−	3.68658i	0.546347	−	0.332408i
$124$			6.17474i			0.554508i
$125$	−4.96240	+	10.0187i	−0.443850	+	0.896101i
$126$	−4.08970	+	2.05102i	−0.364339	+	0.182720i
$127$	−13.5468	−	6.90244i	−1.20208	−	0.612493i	−0.265900	−	0.964001i	$-0.585669\pi$
$127$	−13.5468	−	6.90244i	−1.20208	−	0.612493i	−0.936185	+	0.351508i	$0.885669\pi$
$128$	−0.422332	+	2.66650i	−0.0373292	+	0.235687i
$129$	12.0649	−	0.910786i	1.06225	−	0.0801903i
$130$	12.9252	−	16.0854i	1.13362	−	1.41078i
$131$	0.850285	−	1.17032i	0.0742897	−	0.102251i	−0.770255	−	0.637736i	$-0.779871\pi$
$131$	0.850285	−	1.17032i	0.0742897	−	0.102251i	0.844545	+	0.535485i	$0.179871\pi$
$132$	−3.03535	+	0.718483i	−0.264193	+	0.0625360i
$133$	0.786518	+	4.96588i	0.0681998	+	0.430597i
$134$	−4.17500	+	12.8493i	−0.360665	+	1.11001i
$135$	−3.81497	−	10.9748i	−0.328340	−	0.944560i
$136$	0.358270	+	1.10264i	0.0307214	+	0.0945507i
$137$	8.44422	−	4.30255i	0.721438	−	0.367591i	−0.0544031	−	0.998519i	$-0.517326\pi$
$137$	8.44422	−	4.30255i	0.721438	−	0.367591i	0.775842	+	0.630928i	$0.217326\pi$
$138$	0.265660	−	3.24314i	0.0226145	−	0.276075i
$139$	−6.29917	+	2.04672i	−0.534288	+	0.173601i	−0.563720	−	0.825966i	$-0.690630\pi$
$139$	−6.29917	+	2.04672i	−0.534288	+	0.173601i	0.0294316	+	0.999567i	$0.490630\pi$
$140$	2.13984	+	2.35853i	0.180850	+	0.199332i
$141$	6.18350	−	5.24717i	0.520745	−	0.441891i
$142$	−16.7126	+	2.64702i	−1.40249	+	0.222133i
$143$	−3.28827	+	3.28827i	−0.274979	+	0.274979i
$144$	−12.7764	−	2.10728i	−1.06470	−	0.175607i
$145$	−22.9320	−	1.11485i	−1.90440	−	0.0925833i
$146$	−10.3711	−	14.2746i	−0.858318	−	1.18137i
$147$	8.39598	+	7.21732i	0.692488	+	0.595274i
$148$	−3.38183	+	6.63721i	−0.277985	+	0.545575i
$149$	10.3466			0.847626			0.423813	−	0.905750i	$-0.360691\pi$
$149$	10.3466			0.847626			0.423813	+	0.905750i	$0.360691\pi$
$150$	−13.9198	+	9.65672i	−1.13655	+	0.788468i
$151$	5.60298			0.455964			0.227982	−	0.973665i	$-0.426787\pi$
$151$	5.60298			0.455964			0.227982	+	0.973665i	$0.426787\pi$
$152$	−0.991787	+	1.94649i	−0.0804445	+	0.157881i
$153$	−9.78554	+	3.11059i	−0.791114	+	0.251476i
$154$	−0.883672	−	1.21627i	−0.0712083	−	0.0980098i
$155$	−1.98374	−	7.29294i	−0.159338	−	0.585783i
$156$	13.8085	−	5.66809i	1.10556	−	0.453811i
$157$	7.18526	−	7.18526i	0.573446	−	0.573446i	−0.359644	−	0.933090i	$-0.617102\pi$
$157$	7.18526	−	7.18526i	0.573446	−	0.573446i	0.933090	+	0.359644i	$0.117102\pi$
$158$	12.6337	−	2.00098i	1.00508	−	0.159189i
$159$	−3.88973	−	4.58384i	−0.308476	−	0.363522i
$160$	1.88055	+	17.2638i	0.148670	+	1.36482i
$161$	0.712050	−	0.231359i	0.0561174	−	0.0182337i
$162$	2.97600	−	17.3527i	0.233817	−	1.36336i
$163$	17.3725	−	8.85172i	1.36072	−	0.693320i	0.387214	−	0.921990i	$-0.373438\pi$
$163$	17.3725	−	8.85172i	1.36072	−	0.693320i	0.973504	+	0.228670i	$0.0734376\pi$
$164$	−2.31170	−	7.11469i	−0.180514	−	0.555564i
$165$	3.35421	−	1.82375i	0.261125	−	0.141979i
$166$	−0.863599	+	2.65788i	−0.0670283	+	0.206292i
$167$	0.0839087	+	0.529779i	0.00649305	+	0.0409955i	0.990722	−	0.135903i	$-0.0433936\pi$
$167$	0.0839087	+	0.529779i	0.00649305	+	0.0409955i	−0.984229	+	0.176899i	$0.943394\pi$
$168$	−0.105356	−	0.445094i	−0.00812840	−	0.0343397i
$169$	5.43898	−	7.48611i	0.418383	−	0.575855i
$170$	8.20161	+	12.5254i	0.629035	+	0.960654i
$171$	−17.1826	−	8.89358i	−1.31398	−	0.680109i
$172$	1.99632	−	12.6043i	0.152218	−	0.961067i
$173$	14.1938	+	7.23210i	1.07913	+	0.549846i	0.900849	−	0.434132i	$-0.142945\pi$
$173$	14.1938	+	7.23210i	1.07913	+	0.549846i	0.178285	+	0.983979i	$0.442945\pi$
$174$	−29.6050	−	18.2722i	−2.24435	−	1.38521i
$175$	−3.28507	−	2.09819i	−0.248328	−	0.158608i
$176$		−	4.25500i		−	0.320733i
$177$	0.502821	+	0.826439i	0.0377943	+	0.0621190i
$178$	19.0327	+	3.01448i	1.42656	+	0.225945i
$179$	−14.7628	+	10.7258i	−1.10342	+	0.801684i	−0.981615	−	0.190870i	$-0.938869\pi$
$179$	−14.7628	+	10.7258i	−1.10342	+	0.801684i	−0.121808	+	0.992554i	$0.538869\pi$
$180$	−12.1910	+	1.24927i	−0.908663	+	0.0931150i
$181$	8.42806	+	6.12334i	0.626453	+	0.455145i	0.855170	−	0.518348i	$-0.173453\pi$
$181$	8.42806	+	6.12334i	0.626453	+	0.455145i	−0.228717	+	0.973493i	$0.573453\pi$
$182$	5.08710	+	5.08710i	0.377081	+	0.377081i
$183$	15.2771	+	6.38520i	1.12932	+	0.472008i
$184$	0.309390	+	0.100527i	0.0228085	+	0.00741093i
$185$	1.86194	−	8.92563i	0.136893	−	0.656226i
$186$	2.70906	−	11.1274i	0.198638	−	0.815903i
$187$	−1.53179	−	3.00630i	−0.112015	−	0.219842i
$188$	−3.88326	−	7.62132i	−0.283216	−	0.555842i
$189$	3.94782	−	0.907895i	0.287162	−	0.0660396i
$190$	−5.76092	+	27.6163i	−0.417941	+	2.00350i
$191$	−16.3919	−	5.32604i	−1.18607	−	0.385379i	−0.351454	−	0.936205i	$-0.614313\pi$
$191$	−16.3919	−	5.32604i	−1.18607	−	0.385379i	−0.834620	+	0.550826i	$0.814313\pi$
$192$	−4.38161	+	10.4834i	−0.316215	+	0.756571i
$193$	−13.5906	−	13.5906i	−0.978276	−	0.978276i	0.0214931	−	0.999769i	$-0.493158\pi$
$193$	−13.5906	−	13.5906i	−0.978276	−	0.978276i	−0.999769	+	0.0214931i	$0.993158\pi$
$194$	8.83791	+	6.42112i	0.634525	+	0.461009i
$195$	−14.4882	+	11.1308i	−1.03752	+	0.797090i
$196$	9.44738	−	6.86393i	0.674813	−	0.490280i
$197$	−2.11254	−	0.334594i	−0.150512	−	0.0238388i	0.0807236	−	0.996737i	$-0.474277\pi$
$197$	−2.11254	−	0.334594i	−0.150512	−	0.0238388i	−0.231236	+	0.972898i	$0.574277\pi$
$198$	5.78519	+	0.0369342i	0.411136	+	0.00262480i
$199$		−	18.8648i		−	1.33729i	−0.743582	−	0.668644i	$-0.766875\pi$
$199$		−	18.8648i		−	1.33729i	0.743582	−	0.668644i	$-0.233125\pi$
$200$	−0.618906	−	1.57655i	−0.0437633	−	0.111479i
$201$	6.28281	−	10.1795i	0.443155	−	0.718009i
$202$	5.98476	+	3.04939i	0.421086	+	0.214554i
$203$	1.25219	−	7.90601i	0.0878864	−	0.554893i
$204$	0.815242	+	10.7993i	0.0570784	+	0.756099i
$205$	5.01605	+	7.66044i	0.350336	+	0.535028i
$206$	−5.68179	+	7.82031i	−0.395869	+	0.544867i
$207$	−0.907785	+	2.73435i	−0.0630954	+	0.190051i
$208$	3.18526	+	20.1109i	0.220858	+	1.39444i
$209$	1.96461	−	6.04646i	0.135895	−	0.418242i
$210$	−2.82142	−	5.18910i	−0.194697	−	0.358082i
$211$	−1.54603	−	4.75818i	−0.106433	−	0.327567i	0.883631	−	0.468184i	$-0.155091\pi$
$211$	−1.54603	−	4.75818i	−0.106433	−	0.327567i	−0.990064	+	0.140617i	$0.955091\pi$
$212$	−5.64970	+	2.87866i	−0.388023	+	0.197708i
$213$	14.9318	+	1.22313i	1.02311	+	0.0838076i
$214$	6.43931	−	2.09226i	0.440182	−	0.143024i
$215$	1.69149	+	15.5282i	0.115359	+	1.05901i
$216$	1.61962	+	0.689113i	0.110201	+	0.0468882i
$217$	2.60258	−	0.412209i	0.176675	−	0.0279825i
$218$	3.20559	−	3.20559i	0.217110	−	0.217110i
$219$	5.93231	+	14.4522i	0.400868	+	0.976587i
$220$	−1.05695	−	3.88572i	−0.0712592	−	0.261975i
$221$	9.49035	+	13.0623i	0.638390	+	0.878669i
$222$	9.00631	−	10.4771i	0.604464	−	0.703179i
$223$	−5.52678	+	10.8469i	−0.370101	+	0.726363i	−0.998679	−	0.0513829i	$-0.983637\pi$
$223$	−5.52678	+	10.8469i	−0.370101	+	0.726363i	0.628578	+	0.777746i	$0.283637\pi$
$224$	−6.05452			−0.404534
$225$	13.9973	−	5.39206i	0.933156	−	0.359470i
$226$	6.38217			0.424536
$227$	−6.80520	+	13.3560i	−0.451677	+	0.886466i	0.547102	+	0.837066i	$0.315731\pi$
$227$	−6.80520	+	13.3560i	−0.451677	+	0.886466i	−0.998779	+	0.0494003i	$0.984269\pi$
$228$	−13.3025	+	15.4749i	−0.880980	+	1.02485i
$229$	9.00455	+	12.3937i	0.595037	+	0.818999i	0.995243	−	0.0974268i	$-0.0310612\pi$
$229$	9.00455	+	12.3937i	0.595037	+	0.818999i	−0.400205	+	0.916426i	$0.631061\pi$
$230$	4.19595	+	0.203988i	0.276673	+	0.0134506i
$231$	0.505464	+	1.23140i	0.0332571	+	0.0810203i
$232$	2.45933	−	2.45933i	0.161463	−	0.161463i
$233$	−2.13821	+	0.338659i	−0.140079	+	0.0221863i	−0.226080	−	0.974109i	$-0.572591\pi$
$233$	−2.13821	+	0.338659i	−0.140079	+	0.0221863i	0.0860013	+	0.996295i	$0.472591\pi$
$234$	−27.3709	+	4.15618i	−1.78929	+	0.271698i
$235$	7.03496	+	7.75393i	0.458910	+	0.505811i
$236$	0.970388	−	0.315298i	0.0631669	−	0.0205242i
$237$	−11.2875	−	0.924610i	−0.733203	−	0.0600599i
$238$	−4.65087	+	2.36974i	−0.301471	+	0.153607i
$239$	−7.04340	−	21.6774i	−0.455600	−	1.40219i	−0.870430	−	0.492293i	$-0.836159\pi$
$239$	−7.04340	−	21.6774i	−0.455600	−	1.40219i	0.414830	−	0.909899i	$-0.363841\pi$
$240$	2.17223	−	16.5754i	0.140217	−	1.06993i
$241$	−0.706155	+	2.17332i	−0.0454874	+	0.139996i	−0.971221	−	0.238181i	$-0.923449\pi$
$241$	−0.706155	+	2.17332i	−0.0454874	+	0.139996i	0.925733	+	0.378177i	$0.123449\pi$
$242$	−3.06885	−	19.3760i	−0.197273	−	1.24554i
$243$	−6.19453	+	14.3048i	−0.397380	+	0.917654i
$244$	10.2651	−	14.1287i	0.657154	−	0.904495i
$245$	−8.95309	+	11.1421i	−0.571992	+	0.711840i
$246$	1.04445	+	13.8355i	0.0665918	+	0.882120i
$247$	−4.75926	+	30.0488i	−0.302825	+	1.91196i
$248$	1.02014	+	0.519788i	0.0647791	+	0.0330066i
$249$	1.29960	−	2.10564i	0.0823587	−	0.133439i
$250$	−13.0556	−	17.5473i	−0.825709	−	1.10979i
$251$			14.3226i			0.904036i	0.892009	+	0.452018i	$0.149296\pi$
$251$			14.3226i			0.904036i	−0.892009	+	0.452018i	$0.850704\pi$
$252$	0.0272766	−	4.27248i	0.00171827	−	0.269141i
$253$	−0.935067	−	0.148100i	−0.0587871	−	0.00931097i
$254$	24.0621	−	17.4822i	1.50979	−	1.09693i
$255$	−4.43231	−	12.4930i	−0.277562	−	0.782343i
$256$	−14.8869	−	10.8160i	−0.930432	−	0.675998i
$257$	−4.31188	−	4.31188i	−0.268968	−	0.268968i	0.559716	−	0.828684i	$-0.310910\pi$
$257$	−4.31188	−	4.31188i	−0.268968	−	0.268968i	−0.828684	+	0.559716i	$0.810910\pi$
$258$	−9.12744	+	21.8382i	−0.568250	+	1.35959i
$259$	3.02327	+	0.982320i	0.187857	+	0.0610384i
$260$	7.90439	+	17.5743i	0.490209	+	1.08991i
$261$	21.6414	+	21.9195i	1.33957	+	1.35679i
$262$	1.28473	+	2.52143i	0.0793711	+	0.155774i
$263$	−14.1510	−	27.7729i	−0.872587	−	1.71255i	−0.682642	−	0.730753i	$-0.739169\pi$
$263$	−14.1510	−	27.7729i	−0.872587	−	1.71255i	−0.189945	−	0.981795i	$-0.560831\pi$
$264$	−0.136813	+	0.561958i	−0.00842026	+	0.0345861i
$265$	5.74800	−	5.21503i	0.353097	−	0.320357i
$266$	−9.35412	−	3.03934i	−0.573538	−	0.186354i
$267$	−15.7420	−	6.57948i	−0.963392	−	0.402658i
$268$	−8.92154	−	8.92154i	−0.544970	−	0.544970i
$269$	11.9339	+	8.67050i	0.727624	+	0.528649i	0.888811	−	0.458274i	$-0.151532\pi$
$269$	11.9339	+	8.67050i	0.727624	+	0.528649i	−0.161187	+	0.986924i	$0.551532\pi$
$270$	22.5173	+	3.09728i	1.37036	+	0.188495i
$271$	19.8939	−	14.4538i	1.20847	−	0.878004i	0.213378	−	0.976970i	$-0.431553\pi$
$271$	19.8939	−	14.4538i	1.20847	−	0.878004i	0.995091	+	0.0989656i	$0.0315534\pi$
$272$	−14.5915	−	2.31107i	−0.884741	−	0.140129i
$273$	−3.31085	−	5.44174i	−0.200382	−	0.329349i
$274$			18.5395i			1.12001i
$275$	2.49670	+	4.24984i	0.150557	+	0.256275i
$276$	2.58590	+	1.59602i	0.155653	+	0.0960691i
$277$	−2.98592	−	1.52140i	−0.179406	−	0.0914121i	0.361981	−	0.932186i	$-0.382101\pi$
$277$	−2.98592	−	1.52140i	−0.179406	−	0.0914121i	−0.541387	+	0.840773i	$0.682101\pi$
$278$	2.02689	−	12.7973i	0.121565	−	0.767529i
$279$	−4.66106	+	9.00525i	−0.279050	+	0.539130i
$280$	0.569789	−	0.154987i	0.0340514	−	0.00926225i
$281$	0.291342	−	0.400997i	0.0173800	−	0.0239215i	−0.800239	−	0.599682i	$-0.795294\pi$
$281$	0.291342	−	0.400997i	0.0173800	−	0.0239215i	0.817619	+	0.575760i	$0.195294\pi$
$282$	3.65426	+	15.4380i	0.217608	+	0.919320i
$283$	−3.58300	−	22.6222i	−0.212987	−	1.34475i	−0.829986	−	0.557784i	$-0.811652\pi$
$283$	−3.58300	−	22.6222i	−0.212987	−	1.34475i	0.616999	−	0.786964i	$-0.288348\pi$
$284$	4.88302	−	15.0284i	0.289754	−	0.891770i
$285$	10.7399	−	22.5510i	0.636178	−	1.33581i
$286$	−2.81116	−	8.65186i	−0.166227	−	0.511595i
$287$	−2.84444	+	1.44931i	−0.167902	+	0.0855502i
$288$	13.8148	−	18.7613i	0.814042	−	1.10552i
$289$	5.02660	−	1.63324i	0.295682	−	0.0960730i
$290$	22.3094	−	38.9808i	1.31005	−	2.28903i
$291$	−6.25818	−	7.37493i	−0.366861	−	0.432326i
$292$	16.2745	−	2.57762i	0.952390	−	0.150844i
$293$	7.39973	−	7.39973i	0.432297	−	0.432297i	−0.457112	−	0.889409i	$-0.651116\pi$
$293$	7.39973	−	7.39973i	0.432297	−	0.432297i	0.889409	+	0.457112i	$0.151116\pi$
$294$	−20.0365	+	8.22454i	−1.16855	+	0.479665i
$295$	−1.04482	+	0.684150i	−0.0608320	+	0.0398327i
$296$	0.811866	+	1.11744i	0.0471888	+	0.0649498i
$297$	−4.96911	−	1.24342i	−0.288337	−	0.0721508i
$298$	−9.18892	+	18.0343i	−0.532300	+	1.04470i
$299$	4.53039			0.261999
$300$	−2.13362	−	15.6764i	−0.123185	−	0.905077i
$301$	−5.44583			−0.313892
$302$	−4.97607	+	9.76609i	−0.286341	+	0.561975i
$303$	−4.50987	−	3.87675i	−0.259085	−	0.222714i
$304$	−16.3622	−	22.5207i	−0.938439	−	1.29165i
$305$	−7.58495	+	19.9851i	−0.434313	+	1.14434i
$306$	3.26884	−	19.8189i	0.186867	−	1.13297i
$307$	−6.95771	+	6.95771i	−0.397097	+	0.397097i	−0.877208	−	0.480111i	$-0.840596\pi$
$307$	−6.95771	+	6.95771i	−0.397097	+	0.397097i	0.480111	+	0.877208i	$0.340596\pi$
$308$	1.38667	−	0.219627i	0.0790129	−	0.0125144i
$309$	6.52578	−	5.53762i	0.371239	−	0.315024i
$310$	14.4735	+	3.01926i	0.822039	+	0.171482i
$311$	−2.10692	+	0.684580i	−0.119473	+	0.0388190i	−0.368143	−	0.929769i	$-0.620006\pi$
$311$	−2.10692	+	0.684580i	−0.119473	+	0.0388190i	0.248671	+	0.968588i	$0.420006\pi$
$312$	0.225958	−	2.75847i	0.0127924	−	0.156168i
$313$	−21.3996	+	10.9036i	−1.20958	+	0.616309i	−0.938176	−	0.346158i	$-0.887486\pi$
$313$	−21.3996	+	10.9036i	−1.20958	+	0.616309i	−0.271399	+	0.962467i	$0.587486\pi$
$314$	6.14271	+	18.9053i	0.346653	+	1.06689i
$315$	1.34039	+	5.05497i	0.0755224	+	0.284815i
$316$	−3.69125	+	11.3605i	−0.207649	+	0.639078i
$317$	−0.121880	−	0.769521i	−0.00684547	−	0.0432206i	0.984029	−	0.178007i	$-0.0569651\pi$
$317$	−0.121880	−	0.769521i	−0.00684547	−	0.0432206i	−0.990875	+	0.134787i	$0.956965\pi$
$318$	11.4442	−	2.70891i	0.641760	−	0.151908i
$319$	−5.94941	+	8.18866i	−0.333103	+	0.458477i
$320$	−13.7140	−	5.20489i	−0.766638	−	0.290962i
$321$	−5.97777	+	0.451266i	−0.333647	+	0.0251872i
$322$	−0.229117	+	1.44659i	−0.0127682	+	0.0806152i
$323$	−19.6678	−	10.0213i	−1.09435	−	0.557598i
$324$	13.1770	+	9.83316i	0.732058	+	0.546287i
$325$	−14.9819	−	18.2175i	−0.831044	−	1.01053i
$326$			38.1418i			2.11248i
$327$	−3.42907	+	2.08631i	−0.189628	+	0.115373i
$328$	−1.37003	−	0.216992i	−0.0756473	−	0.0119814i
$329$	−2.95306	+	2.14553i	−0.162808	+	0.118287i
$330$	0.199920	+	7.46613i	0.0110052	+	0.410997i
$331$	−12.1264	−	8.81032i	−0.666525	−	0.484259i	0.202335	−	0.979316i	$-0.435147\pi$
$331$	−12.1264	−	8.81032i	−0.666525	−	0.484259i	−0.868860	+	0.495057i	$0.835147\pi$
$332$	−1.84542	−	1.84542i	−0.101281	−	0.101281i
$333$	−9.94222	+	7.12692i	−0.544830	+	0.390553i
$334$	−0.997933	−	0.324248i	−0.0546044	−	0.0177421i
$335$	13.4034	+	7.67098i	0.732304	+	0.419111i
$336$	5.66290	+	1.37867i	0.308936	+	0.0752129i
$337$	10.9434	+	21.4776i	0.596124	+	1.16996i	0.970142	+	0.242537i	$0.0779796\pi$
$337$	10.9434	+	21.4776i	0.596124	+	1.16996i	−0.374019	+	0.927421i	$0.622020\pi$
$338$	8.21799	+	16.1287i	0.447000	+	0.877287i
$339$	−5.49041	−	1.33668i	−0.298198	−	0.0725986i
$340$	−13.8992	+	1.51405i	−0.753791	+	0.0821107i
$341$	−3.16890	−	1.02964i	−0.171606	−	0.0557581i
$342$	30.7616	−	22.0510i	1.66340	−	1.19238i
$343$	−7.38253	−	7.38253i	−0.398619	−	0.398619i
$344$	−1.91433	−	1.39084i	−0.103214	−	0.0749891i
$345$	−3.56694	−	1.05429i	−0.192038	−	0.0567608i
$346$	−25.2113	+	18.3171i	−1.35537	+	0.984733i
$347$	31.9302	+	5.05725i	1.71410	+	0.271487i	0.934804	−	0.355164i	$-0.115575\pi$
$347$	31.9302	+	5.05725i	1.71410	+	0.271487i	0.779299	+	0.626652i	$0.215575\pi$
$348$	27.7552	−	16.8868i	1.48783	−	0.905226i
$349$			8.46821i			0.453293i	0.973977	+	0.226646i	$0.0727762\pi$
$349$			8.46821i			0.453293i	−0.973977	+	0.226646i	$0.927224\pi$
$350$	6.57468	−	3.86250i	0.351431	−	0.206459i
$351$	24.4169	+	2.15711i	1.30328	+	0.115138i
$352$	6.82148	+	3.47572i	0.363586	+	0.185256i
$353$	−5.26415	+	33.2366i	−0.280183	+	1.76900i	0.299437	+	0.954116i	$0.403201\pi$
$353$	−5.26415	+	33.2366i	−0.280183	+	1.76900i	−0.579619	+	0.814887i	$0.696799\pi$
$354$	−1.88706	+	0.142455i	−0.100296	+	0.00757141i
$355$	−0.939185	+	19.3187i	−0.0498468	+	1.02533i
$356$	−10.5774	+	14.5586i	−0.560601	+	0.771602i
$357$	4.49734	−	1.06454i	0.238024	−	0.0563416i
$358$	−5.58424	−	35.2575i	−0.295136	−	1.86342i
$359$	−2.38803	+	7.34959i	−0.126035	+	0.387897i	−0.994088	−	0.108575i	$-0.965371\pi$
$359$	−2.38803	+	7.34959i	−0.126035	+	0.387897i	0.868053	+	0.496471i	$0.165371\pi$
$360$	−0.819840	+	2.11926i	−0.0432094	+	0.111695i
$361$	−6.98158	−	21.4871i	−0.367452	−	1.13090i
$362$	−18.1581	+	9.25203i	−0.954370	+	0.486276i
$363$	−1.41805	+	17.3114i	−0.0744284	+	0.908613i
$364$	−6.38958	+	2.07610i	−0.334905	+	0.108817i
$365$	−18.3935	+	8.27284i	−0.962762	+	0.433020i
$366$	−24.6973	+	20.9575i	−1.29095	+	1.09547i
$367$	11.7708	−	1.86431i	0.614431	−	0.0973164i	0.158541	−	0.987352i	$-0.449321\pi$
$367$	11.7708	−	1.86431i	0.614431	−	0.0973164i	0.455890	+	0.890036i	$0.349321\pi$
$368$	−2.93115	+	2.93115i	−0.152796	+	0.152796i
$369$	1.99920	−	12.1211i	0.104074	−	0.630998i
$370$	13.9039	+	11.1723i	0.722830	+	0.580822i
$371$	1.59048	+	2.18911i	0.0825737	+	0.113653i
$372$	8.11030	+	6.97175i	0.420499	+	0.361468i
$373$	11.4767	−	22.5244i	0.594243	−	1.16627i	−0.376560	−	0.926392i	$-0.622893\pi$
$373$	11.4767	−	22.5244i	0.594243	−	1.16627i	0.970804	−	0.239876i	$-0.0771067\pi$
$374$	6.60042			0.341299
$375$	7.55630	+	17.8298i	0.390206	+	0.920728i
$376$	−1.58603			−0.0817931
$377$	21.9895	−	43.1568i	1.13251	−	2.22269i
$378$	−1.92363	+	7.68743i	−0.0989409	+	0.395399i
$379$	11.2506	+	15.4851i	0.577904	+	0.795416i	0.993464	−	0.114150i	$-0.0364143\pi$
$379$	11.2506	+	15.4851i	0.577904	+	0.795416i	−0.415560	+	0.909566i	$0.636414\pi$
$380$	−20.5364	−	16.5018i	−1.05349	−	0.846523i
$381$	−24.3615	+	9.99987i	−1.24808	+	0.512309i
$382$	23.8412	−	23.8412i	1.21982	−	1.21982i
$383$	−20.9309	+	3.31513i	−1.06952	+	0.169395i	−0.666282	−	0.745700i	$-0.732115\pi$
$383$	−20.9309	+	3.31513i	−1.06952	+	0.169395i	−0.403238	+	0.915095i	$0.632115\pi$
$384$	3.02551	+	3.56539i	0.154395	+	0.181946i
$385$	−1.56723	+	0.704890i	−0.0798733	+	0.0359245i
$386$	35.7587	−	11.6187i	1.82007	−	0.591376i
$387$	12.4259	−	16.8752i	0.631643	−	0.857812i
$388$	−9.08978	+	4.63148i	−0.461464	+	0.235128i
$389$	3.35765	+	10.3338i	0.170240	+	0.523944i	0.999384	−	0.0350902i	$-0.0111719\pi$
$389$	3.35765	+	10.3338i	0.170240	+	0.523944i	−0.829144	+	0.559035i	$0.811172\pi$
$390$	−6.53399	−	35.1384i	−0.330861	−	1.77930i
$391$	−1.01575	+	3.12615i	−0.0513686	+	0.158096i
$392$	−0.338725	−	2.13863i	−0.0171082	−	0.108017i
$393$	−0.577134	−	2.43819i	−0.0291125	−	0.122991i
$394$	2.45937	−	3.38503i	0.123901	−	0.170536i
$395$	0.709964	−	14.6037i	0.0357222	−	0.734791i
$396$	−2.48344	+	4.79805i	−0.124797	+	0.241111i
$397$	1.19893	−	7.56976i	0.0601727	−	0.379915i	−0.939163	−	0.343472i	$-0.888397\pi$
$397$	1.19893	−	7.56976i	0.0601727	−	0.379915i	0.999336	−	0.0364437i	$-0.0116029\pi$
$398$	32.8816	+	16.7540i	1.64821	+	0.839802i
$399$	7.41055	+	4.57379i	0.370991	+	0.228976i
$400$	21.4799	+	2.09346i	1.07399	+	0.104673i
$401$		−	20.7216i		−	1.03479i	−0.855747	−	0.517395i	$-0.826902\pi$
$401$		−	20.7216i		−	1.03479i	0.855747	−	0.517395i	$-0.173098\pi$
$402$	12.1632	+	19.9916i	0.606648	+	0.997089i
$403$	15.7484	+	2.49429i	0.784481	+	0.124250i
$404$	−5.07463	+	3.68693i	−0.252472	+	0.183432i
$405$	−18.7224	−	7.38054i	−0.930323	−	0.366742i
$406$	12.6682	+	9.20399i	0.628713	+	0.456786i
$407$	−2.84233	−	2.84233i	−0.140889	−	0.140889i
$408$	1.85279	+	0.774391i	0.0917270	+	0.0383380i
$409$	30.3286	+	9.85436i	1.49965	+	0.487267i	0.939917	−	0.341404i	$-0.110902\pi$
$409$	30.3286	+	9.85436i	1.49965	+	0.487267i	0.559736	+	0.828671i	$0.310902\pi$
$410$	−17.8071	+	1.93973i	−0.879428	+	0.0957963i
$411$	3.88292	−	15.9491i	0.191530	−	0.786710i
$412$	−4.09821	−	8.04319i	−0.201904	−	0.396259i
$413$	−0.197675	−	0.387959i	−0.00972695	−	0.0190902i
$414$	−3.95980	−	4.01069i	−0.194614	−	0.197115i
$415$	2.77249	+	1.58674i	0.136096	+	0.0778901i
$416$	−34.8431	−	11.3212i	−1.70832	−	0.555068i
$417$	−4.42394	+	10.5846i	−0.216641	+	0.518332i
$418$	8.79427	+	8.79427i	0.430142	+	0.430142i
$419$	−10.4586	−	7.59860i	−0.510935	−	0.371216i	0.302243	−	0.953231i	$-0.402264\pi$
$419$	−10.4586	−	7.59860i	−0.510935	−	0.371216i	−0.813178	+	0.582015i	$0.802264\pi$
$420$	5.51389	−	0.147645i	0.269050	−	0.00720434i
$421$	−9.92844	+	7.21344i	−0.483883	+	0.351561i	−0.802827	−	0.596212i	$-0.796672\pi$
$421$	−9.92844	+	7.21344i	−0.483883	+	0.351561i	0.318944	+	0.947773i	$0.396672\pi$
$422$	9.66663	+	1.53104i	0.470564	+	0.0745300i
$423$	0.0896750	−	14.0463i	0.00436015	−	0.682953i
$424$			1.17572i			0.0570982i
$425$	15.9299	−	6.25358i	0.772712	−	0.303343i
$426$	−15.3931	+	24.9401i	−0.745796	+	1.20835i
$427$	−6.64034	−	3.38342i	−0.321349	−	0.163735i
$428$	−0.989114	+	6.24502i	−0.0478106	+	0.301864i
$429$	0.606321	+	8.03174i	0.0292735	+	0.387776i
$430$	−28.5681	−	10.8424i	−1.37767	−	0.522869i
$431$	23.6623	−	32.5684i	1.13977	−	1.56876i	0.371760	−	0.928329i	$-0.378754\pi$
$431$	23.6623	−	32.5684i	1.13977	−	1.56876i	0.768013	−	0.640434i	$-0.221246\pi$
$432$	−17.1933	+	14.4020i	−0.827215	+	0.692919i
$433$	0.109046	+	0.688486i	0.00524039	+	0.0330865i	0.990170	−	0.139869i	$-0.0446682\pi$
$433$	0.109046	+	0.688486i	0.00524039	+	0.0330865i	−0.984930	+	0.172956i	$0.944668\pi$
$434$	−1.59290	+	4.90243i	−0.0764614	+	0.235324i
$435$	−27.3563	+	28.8617i	−1.31163	+	1.38381i
$436$	1.30824	+	4.02634i	0.0626532	+	0.192827i
$437$	−5.51859	+	2.81186i	−0.263990	+	0.134510i
$438$	−30.4589	−	2.49502i	−1.45538	−	0.119217i
$439$	−32.6150	+	10.5973i	−1.55663	+	0.505780i	−0.955905	−	0.293677i	$-0.905121\pi$
$439$	−32.6150	+	10.5973i	−1.55663	+	0.505780i	−0.600724	+	0.799456i	$0.705121\pi$
$440$	−0.730941	−	0.152479i	−0.0348463	−	0.00726914i
$441$	18.9594	−	2.87892i	0.902828	−	0.137091i
$442$	−31.1964	+	4.94102i	−1.48386	+	0.235020i
$443$	20.2627	−	20.2627i	0.962712	−	0.962712i	−0.0366177	−	0.999329i	$-0.511658\pi$
$443$	20.2627	−	20.2627i	0.962712	−	0.962712i	0.999329	+	0.0366177i	$0.0116584\pi$
$444$	4.89940	+	11.9358i	0.232515	+	0.566449i
$445$	7.81573	−	20.5932i	0.370501	−	0.976210i
$446$	−13.9979	−	19.2665i	−0.662822	−	0.912296i
$447$	11.6821	−	13.5899i	0.552544	−	0.642780i
$448$	2.32175	−	4.55669i	0.109692	−	0.215283i
$449$	−18.2524			−0.861386			−0.430693	−	0.902499i	$-0.641731\pi$
$449$	−18.2524			−0.861386			−0.430693	+	0.902499i	$0.641731\pi$
$450$	−3.03275	+	29.1863i	−0.142965	+	1.37586i
$451$	4.03677			0.190084
$452$	−2.70580	+	5.31043i	−0.127270	+	0.249782i
$453$	6.32619	−	7.35932i	0.297230	−	0.345771i
$454$	−17.2359	−	23.7231i	−0.808919	−	1.11338i
$455$	6.87970	−	4.50482i	0.322525	−	0.211189i
$456$	1.43684	+	3.50041i	0.0672864	+	0.163922i
$457$	−15.1979	+	15.1979i	−0.710929	+	0.710929i	−0.966730	−	0.255800i	$-0.917661\pi$
$457$	−15.1979	+	15.1979i	−0.710929	+	0.710929i	0.255800	+	0.966730i	$0.417661\pi$
$458$	−29.5994	+	4.68809i	−1.38309	+	0.219060i
$459$	−6.96296	+	16.3650i	−0.325003	+	0.763855i
$460$	−1.94866	+	3.40485i	−0.0908567	+	0.158752i
$461$	17.1732	−	5.57990i	0.799835	−	0.259882i	0.119548	−	0.992828i	$-0.461855\pi$
$461$	17.1732	−	5.57990i	0.799835	−	0.259882i	0.680286	+	0.732946i	$0.261855\pi$
$462$	−2.59526	−	0.212589i	−0.120742	−	0.00989054i
$463$	−9.06411	+	4.61839i	−0.421245	+	0.214635i	−0.651746	−	0.758437i	$-0.725963\pi$
$463$	−9.06411	+	4.61839i	−0.421245	+	0.214635i	0.230502	+	0.973072i	$0.425963\pi$
$464$	13.6952	+	42.1494i	0.635782	+	1.95674i
$465$	−11.8188	−	5.62872i	−0.548084	−	0.261025i
$466$	1.30868	−	4.02770i	0.0606233	−	0.186579i
$467$	1.76013	+	11.1130i	0.0814493	+	0.514250i	0.994357	+	0.106085i	$0.0338315\pi$
$467$	1.76013	+	11.1130i	0.0814493	+	0.514250i	−0.912908	+	0.408166i	$0.866169\pi$
$468$	8.14599	−	24.5367i	0.376549	−	1.13421i
$469$	−3.16475	+	4.35591i	−0.146135	+	0.201137i
$470$	−19.7630	+	5.37570i	−0.911601	+	0.247963i
$471$	−1.32488	−	17.5503i	−0.0610473	−	0.808674i
$472$	0.0295960	−	0.186862i	0.00136226	−	0.00860100i
$473$	6.13568	+	3.12629i	0.282119	+	0.143747i
$474$	11.6362	−	18.8532i	0.534467	−	0.865954i
$475$	29.5568	+	12.8925i	1.35616	+	0.591548i
$476$		−	4.87454i		−	0.223424i
$477$	−10.4125	−	0.0664762i	−0.476756	−	0.00304374i
$478$	44.0393	+	6.97514i	2.01431	+	0.319035i
$479$	14.0049	−	10.1752i	0.639901	−	0.464915i	−0.219915	−	0.975519i	$-0.570578\pi$
$479$	14.0049	−	10.1752i	0.639901	−	0.464915i	0.859816	+	0.510604i	$0.170578\pi$
$480$	24.7987	+	17.0221i	1.13190	+	0.776948i
$481$	15.5618	+	11.3063i	0.709556	+	0.515522i
$482$	−3.16099	−	3.16099i	−0.143979	−	0.143979i
$483$	0.500077	−	1.19647i	0.0227543	−	0.0544415i
$484$	17.4233	+	5.66118i	0.791969	+	0.257326i
$485$	9.24794	−	8.39045i	0.419927	−	0.380991i
$486$	−19.4321	−	23.5014i	−0.881457	−	1.06605i
$487$	−4.82316	−	9.46599i	−0.218558	−	0.428945i	0.755530	−	0.655115i	$-0.227380\pi$
$487$	−4.82316	−	9.46599i	−0.218558	−	0.428945i	−0.974088	+	0.226170i	$0.927380\pi$
$488$	−1.47011	−	2.88526i	−0.0665490	−	0.130610i
$489$	7.98842	−	32.8124i	0.361249	−	1.48383i
$490$	−11.4695	−	25.5008i	−0.518137	−	1.15201i
$491$	7.07290	+	2.29812i	0.319195	+	0.103713i	0.464233	−	0.885713i	$-0.346330\pi$
$491$	7.07290	+	2.29812i	0.319195	+	0.103713i	−0.145037	+	0.989426i	$0.546330\pi$
$492$	−11.9550	−	4.99668i	−0.538972	−	0.225268i
$493$	24.8497	+	24.8497i	1.11917	+	1.11917i
$494$	−48.1487	−	34.9821i	−2.16631	−	1.57392i
$495$	1.39172	−	6.46479i	0.0625532	−	0.290570i
$496$	−11.8029	+	8.57533i	−0.529967	+	0.385044i
$497$	−6.66027	−	1.05488i	−0.298754	−	0.0473179i
$498$	2.51597	+	4.13526i	0.112743	+	0.185305i
$499$			22.9184i			1.02597i	0.858398	+	0.512985i	$0.171460\pi$
$499$			22.9184i			1.02597i	−0.858398	+	0.512985i	$0.828540\pi$
$500$	20.1357	−	3.42385i	0.900496	−	0.153119i
$501$	0.790585	+	0.487949i	0.0353207	+	0.0218000i
$502$	−24.9646	−	12.7201i	−1.11422	−	0.567725i
$503$	1.32865	−	8.38878i	0.0592416	−	0.374037i	−0.940200	−	0.340623i	$-0.889362\pi$
$503$	1.32865	−	8.38878i	0.0592416	−	0.374037i	0.999442	−	0.0334140i	$-0.0106380\pi$
$504$	−0.703570	−	0.364163i	−0.0313395	−	0.0162211i
$505$	4.80912	−	5.98492i	0.214003	−	0.266325i
$506$	1.08858	−	1.49831i	0.0483934	−	0.0666078i
$507$	−3.69172	−	15.5963i	−0.163955	−	0.692655i
$508$	4.34500	+	27.4332i	0.192778	+	1.21715i
$509$	0.901786	−	2.77541i	0.0399710	−	0.123018i	−0.929080	−	0.369879i	$-0.879399\pi$
$509$	0.901786	−	2.77541i	0.0399710	−	0.123018i	0.969051	+	0.246861i	$0.0793991\pi$
$510$	25.7119	+	3.36959i	1.13854	+	0.149208i
$511$	−2.17288	−	6.68742i	−0.0961223	−	0.295834i
$512$	27.2627	−	13.8910i	1.20485	−	0.613902i
$513$	−31.0818	+	12.5272i	−1.37229	+	0.553087i
$514$	11.3451	−	3.68625i	0.500411	−	0.162594i
$515$	7.42437	+	8.18314i	0.327157	+	0.360592i
$516$	−14.3013	−	16.8533i	−0.629578	−	0.741924i
$517$	4.55883	−	0.722048i	0.200497	−	0.0317556i
$518$	−4.39720	+	4.39720i	−0.193202	+	0.193202i
$519$	25.5250	−	10.4775i	1.12042	−	0.459909i
$520$	3.56888	+	0.173503i	0.156506	+	0.00760859i
$521$	−4.48976	−	6.17962i	−0.196700	−	0.270734i	0.699262	−	0.714866i	$-0.253512\pi$
$521$	−4.48976	−	6.17962i	−0.196700	−	0.270734i	−0.895962	+	0.444132i	$0.853512\pi$
$522$	−57.4261	+	18.2544i	−2.51347	+	0.798972i
$523$	3.05143	−	5.98876i	0.133430	−	0.261870i	−0.814619	−	0.579997i	$-0.803054\pi$
$523$	3.05143	−	5.98876i	0.133430	−	0.261870i	0.948048	+	0.318127i	$0.103054\pi$
$524$	−2.64269			−0.115447
$525$	−6.46498	+	1.94581i	−0.282155	+	0.0849221i
$526$	60.9762			2.65869
$527$	−5.25207	+	10.3078i	−0.228784	+	0.449013i
$528$	−5.58880	−	4.80422i	−0.243221	−	0.209077i
$529$	−12.9769	−	17.8612i	−0.564215	−	0.776575i
$530$	3.98501	+	14.6504i	0.173098	+	0.636372i
$531$	1.65322	+	0.272675i	0.0717437	+	0.0118331i
$532$	6.49475	−	6.49475i	0.281583	−	0.281583i
$533$	−19.0795	+	3.02189i	−0.826423	+	0.130893i
$534$	25.4487	−	21.5952i	1.10127	−	0.934514i
$535$	−0.838079	−	7.69372i	−0.0362333	−	0.332628i
$536$	−2.22496	+	0.722933i	−0.0961037	+	0.0312260i
$537$	−2.58036	+	31.5007i	−0.111351	+	1.35935i
$538$	−25.7114	+	13.1006i	−1.10850	+	0.564808i
$539$	1.94724	+	5.99300i	0.0838737	+	0.258137i
$540$	−12.1237	+	17.4229i	−0.521720	+	0.749764i
$541$	−4.34775	+	13.3810i	−0.186924	+	0.575294i	−0.999976	−	0.00689744i	$-0.997804\pi$
$541$	−4.34775	+	13.3810i	−0.186924	+	0.575294i	0.813052	+	0.582191i	$0.197804\pi$
$542$	7.52515	+	47.5119i	0.323233	+	2.04081i
$543$	17.5587	−	4.15624i	0.753516	−	0.178361i
$544$	15.6242	−	21.5048i	0.669881	−	0.922012i
$545$	−2.83868	−	4.33519i	−0.121596	−	0.185699i
$546$	12.4254	−	0.938004i	0.531759	−	0.0401429i
$547$	2.93480	−	18.5296i	0.125483	−	0.792269i	−0.842027	−	0.539436i	$-0.818638\pi$
$547$	2.93480	−	18.5296i	0.125483	−	0.792269i	0.967510	−	0.252833i	$-0.0813623\pi$
$548$	−15.4263	−	7.86007i	−0.658977	−	0.335766i
$549$	25.6358	−	12.8566i	1.09411	−	0.548706i
$550$	−9.62488	+	0.577465i	−0.410406	+	0.0246232i
$551$			66.2186i			2.82101i
$552$	0.481363	−	0.292870i	0.0204882	−	0.0124654i
$553$	5.03474	+	0.797424i	0.214099	+	0.0339099i
$554$	5.30365	−	3.85333i	0.225331	−	0.163712i
$555$	−9.62123	−	12.5233i	−0.408398	−	0.531585i
$556$	9.78894	+	7.11208i	0.415143	+	0.301619i
$557$	−4.41902	−	4.41902i	−0.187240	−	0.187240i	0.607262	−	0.794502i	$-0.292268\pi$
$557$	−4.41902	−	4.41902i	−0.187240	−	0.187240i	−0.794502	+	0.607262i	$0.792268\pi$
$558$	−11.5568	−	16.1220i	−0.489236	−	0.682497i
$559$	−31.3401	−	10.1830i	−1.32555	−	0.430696i
$560$	−1.53654	+	7.36575i	−0.0649307	+	0.311260i
$561$	−5.67817	−	1.38239i	−0.239732	−	0.0583646i
$562$	0.440201	+	0.863943i	0.0185688	+	0.0364432i
$563$	20.0350	+	39.3209i	0.844375	+	1.65718i	0.749802	+	0.661662i	$0.230149\pi$
$563$	20.0350	+	39.3209i	0.844375	+	1.65718i	0.0945733	+	0.995518i	$0.469851\pi$
$564$	−14.3948	−	3.50453i	−0.606132	−	0.147567i
$565$	1.48974	−	7.14140i	0.0626738	−	0.300441i
$566$	42.6129	+	13.8458i	1.79115	+	0.581981i
$567$	3.26490	−	6.21041i	0.137113	−	0.260813i
$568$	−2.07182	−	2.07182i	−0.0869316	−	0.0869316i
$569$	7.36407	+	5.35031i	0.308718	+	0.224297i	0.731346	−	0.682006i	$-0.238892\pi$
$569$	7.36407	+	5.35031i	0.308718	+	0.224297i	−0.422628	+	0.906303i	$0.638892\pi$
$570$	29.7685	+	38.7476i	1.24686	+	1.62296i
$571$	14.7509	−	10.7172i	0.617307	−	0.448500i	−0.234673	−	0.972074i	$-0.575402\pi$
$571$	14.7509	−	10.7172i	0.617307	−	0.448500i	0.851980	+	0.523575i	$0.175402\pi$
$572$	8.39081	+	1.32897i	0.350837	+	0.0555672i
$573$	−25.5032	+	15.5166i	−1.06541	+	0.648217i
$574$		−	6.24505i		−	0.260663i
$575$	1.20768	−	4.64749i	0.0503638	−	0.193814i
$576$	8.82236	+	17.5916i	0.367598	+	0.732983i
$577$	29.5375	+	15.0501i	1.22966	+	0.626544i	0.943416	−	0.331613i	$-0.107593\pi$
$577$	29.5375	+	15.0501i	1.22966	+	0.626544i	0.286245	+	0.958156i	$0.407593\pi$
$578$	−1.61741	+	10.2119i	−0.0672755	+	0.424761i
$579$	−33.1957	+	2.50596i	−1.37957	+	0.104144i
$580$	22.9765	+	35.0894i	0.954048	+	1.45701i
$581$	−0.654629	+	0.901019i	−0.0271586	+	0.0373806i
$582$	18.4126	−	4.35835i	0.763226	−	0.180660i
$583$	−0.535255	−	3.37947i	−0.0221680	−	0.139963i
$584$	0.944126	−	2.90572i	0.0390682	−	0.120240i
$585$	−1.73837	+	31.5971i	−0.0718728	+	1.30638i
$586$	6.32606	+	19.4696i	0.261327	+	0.804282i
$587$	−26.4642	+	13.4842i	−1.09229	+	0.556551i	−0.904853	−	0.425725i	$-0.860019\pi$
$587$	−26.4642	+	13.4842i	−1.09229	+	0.556551i	−0.187440	+	0.982276i	$0.560019\pi$
$588$	1.65129	−	20.1587i	0.0680979	−	0.831331i
$589$	−20.7316	+	6.73611i	−0.854232	+	0.277557i
$590$	−0.264564	−	2.42875i	−0.0108919	−	0.0999899i
$591$	−2.82469	+	2.39697i	−0.116192	+	0.0985980i
$592$	−17.3835	+	2.75328i	−0.714459	+	0.113159i
$593$	15.2390	−	15.2390i	0.625792	−	0.625792i	−0.321215	−	0.947006i	$-0.604091\pi$
$593$	15.2390	−	15.2390i	0.625792	−	0.625792i	0.947006	+	0.321215i	$0.104091\pi$
$594$	6.58043	−	7.55694i	0.269998	−	0.310065i
$595$	1.56603	+	5.75729i	0.0642008	+	0.236026i
$596$	−11.1101	−	15.2917i	−0.455087	−	0.626373i
$597$	−24.7782	−	21.2998i	−1.01410	−	0.871741i
$598$	−4.02348	+	7.89653i	−0.164532	+	0.322913i
$599$	−29.5824			−1.20870			−0.604351	−	0.796718i	$-0.706568\pi$
$599$	−29.5824			−1.20870			−0.604351	+	0.796718i	$0.706568\pi$
$600$	−2.76954	−	0.967135i	−0.113066	−	0.0394831i
$601$	−27.6332			−1.12718			−0.563591	−	0.826054i	$-0.690581\pi$
$601$	−27.6332			−1.12718			−0.563591	+	0.826054i	$0.690581\pi$
$602$	4.83650	−	9.49216i	0.197121	−	0.386871i
$603$	−6.27669	−	19.7457i	−0.255606	−	0.804107i
$604$	−6.01643	−	8.28091i	−0.244805	−	0.336945i
$605$	−22.3973	−	1.08886i	−0.910580	−	0.0442683i
$606$	10.7625	−	4.41778i	0.437197	−	0.179460i
$607$	−20.2336	+	20.2336i	−0.821256	+	0.821256i	−0.986288	−	0.165032i	$-0.947227\pi$
$607$	−20.2336	+	20.2336i	−0.821256	+	0.821256i	0.165032	+	0.986288i	$0.447227\pi$
$608$	49.4700	−	7.83528i	2.00627	−	0.317763i
$609$	−8.97044	−	10.5712i	−0.363501	−	0.428366i
$610$	−28.0981	−	30.9697i	−1.13766	−	1.25392i
$611$	−21.0064	+	6.82540i	−0.849829	+	0.276126i
$612$	15.1049	+	11.1224i	0.610579	+	0.449595i
$613$	12.0999	−	6.16521i	0.488711	−	0.249011i	−0.192229	−	0.981350i	$-0.561572\pi$
$613$	12.0999	−	6.16521i	0.488711	−	0.249011i	0.680940	+	0.732340i	$0.261572\pi$
$614$	−5.94817	−	18.3066i	−0.240049	−	0.738794i
$615$	15.7252	+	2.06081i	0.634102	+	0.0831001i
$616$	0.0804445	−	0.247583i	0.00324120	−	0.00997540i
$617$	5.28301	+	33.3556i	0.212686	+	1.34285i	0.830718	+	0.556694i	$0.187930\pi$
$617$	5.28301	+	33.3556i	0.212686	+	1.34285i	−0.618032	+	0.786153i	$0.712070\pi$
$618$	3.85653	+	16.2926i	0.155133	+	0.655383i
$619$	12.4660	−	17.1580i	0.501052	−	0.689638i	−0.481327	−	0.876541i	$-0.659845\pi$
$619$	12.4660	−	17.1580i	0.501052	−	0.689638i	0.982378	+	0.186903i	$0.0598450\pi$
$620$	−8.64846	+	10.7630i	−0.347331	+	0.432251i
$621$	2.56652	+	4.27963i	0.102991	+	0.171736i
$622$	0.677945	−	4.28038i	0.0271831	−	0.171628i
$623$	6.84238	+	3.48637i	0.274134	+	0.139678i
$624$	30.0114	+	18.5230i	1.20142	+	0.741515i
$625$	−22.6822	+	10.5128i	−0.907287	+	0.420512i
$626$		−	46.9834i		−	1.87783i
$627$	−5.72361	−	9.40735i	−0.228579	−	0.375694i
$628$	−18.3349	−	2.90396i	−0.731642	−	0.115881i
$629$	−11.2909	+	8.20329i	−0.450196	+	0.327087i
$630$	−10.0013	−	2.15305i	−0.398461	−	0.0857795i
$631$	−6.46706	−	4.69860i	−0.257450	−	0.187048i	0.451572	−	0.892235i	$-0.350863\pi$
$631$	−6.46706	−	4.69860i	−0.257450	−	0.187048i	−0.709022	+	0.705186i	$0.750863\pi$
$632$	1.56616	+	1.56616i	0.0622986	+	0.0622986i
$633$	−7.99528	−	3.34170i	−0.317784	−	0.132820i
$634$	1.44953	+	0.470981i	0.0575682	+	0.0187050i
$635$	−13.9452	−	31.0053i	−0.553399	−	1.23041i
$636$	−2.59791	+	10.6709i	−0.103014	+	0.423129i
$637$	−13.6898	−	26.8678i	−0.542410	−	1.06454i
$638$	−8.98923	−	17.6424i	−0.355887	−	0.698468i
$639$	18.4657	−	18.2314i	0.730492	−	0.721224i
$640$	−4.47090	+	4.05634i	−0.176728	+	0.160341i
$641$	−39.9287	−	12.9736i	−1.57709	−	0.512427i	−0.615784	−	0.787915i	$-0.711160\pi$
$641$	−39.9287	−	12.9736i	−1.57709	−	0.512427i	−0.961304	+	0.275488i	$0.911160\pi$
$642$	4.52236	−	10.8201i	0.178483	−	0.427036i
$643$	10.8134	+	10.8134i	0.426437	+	0.426437i	0.887413	−	0.460975i	$-0.152500\pi$
$643$	10.8134	+	10.8134i	0.426437	+	0.426437i	−0.460975	+	0.887413i	$0.652500\pi$
$644$	−1.10653	−	0.803941i	−0.0436034	−	0.0316797i
$645$	22.3055	+	15.3108i	0.878279	+	0.602861i
$646$	34.9344	−	25.3813i	1.37448	−	0.998615i
$647$	0.421374	+	0.0667390i	0.0165659	+	0.00262378i	0.164712	−	0.986342i	$-0.447331\pi$
$647$	0.421374	+	0.0667390i	0.0165659	+	0.00262378i	−0.148146	+	0.988965i	$0.547331\pi$
$648$	2.73380	−	1.34925i	0.107394	−	0.0530037i
$649$			0.550584i			0.0216123i
$650$	45.0589	−	9.93444i	1.76736	−	0.389661i
$651$	2.39709	−	3.88381i	0.0939494	−	0.152219i
$652$	−31.7368	−	16.1707i	−1.24291	−	0.633293i
$653$	−1.32998	+	8.39719i	−0.0520463	+	0.328608i	0.947903	+	0.318559i	$0.103199\pi$
$653$	−1.32998	+	8.39719i	−0.0520463	+	0.328608i	−0.999950	+	0.0100490i	$0.996801\pi$
$654$	−0.591075	−	7.82978i	−0.0231129	−	0.306169i
$655$	3.12127	−	0.849009i	0.121958	−	0.0331735i
$656$	10.3892	−	14.2995i	0.405630	−	0.558302i
$657$	25.6804	+	8.52571i	1.00189	+	0.332620i
$658$	−1.11704	−	7.05270i	−0.0435467	−	0.274943i
$659$	11.7433	−	36.1421i	0.457453	−	1.40790i	−0.410778	−	0.911735i	$-0.634743\pi$
$659$	11.7433	−	36.1421i	0.457453	−	1.40790i	0.868231	−	0.496160i	$-0.165257\pi$
$660$	−6.29713	−	2.99901i	−0.245115	−	0.116736i
$661$	5.76600	+	17.7459i	0.224271	+	0.690236i	0.998365	+	0.0571648i	$0.0182061\pi$
$661$	5.76600	+	17.7459i	0.224271	+	0.690236i	−0.774093	+	0.633071i	$0.781794\pi$
$662$	26.1261	−	13.3119i	1.01542	−	0.517382i
$663$	27.8722	+	2.28314i	1.08247	+	0.0886697i
$664$	−0.460233	+	0.149539i	−0.0178605	+	0.00580323i
$665$	−5.58436	+	9.75745i	−0.216552	+	0.378378i
$666$	−3.59253	−	23.6589i	−0.139208	−	0.916765i
$667$	9.73930	−	1.54255i	0.377107	−	0.0597279i
$668$	0.692884	−	0.692884i	0.0268085	−	0.0268085i
$669$	8.00689	+	19.5062i	0.309564	+	0.754154i
$670$	−25.2743	+	16.5496i	−0.976432	+	0.639366i
$671$	5.53919	+	7.62404i	0.213838	+	0.294323i
$672$	−6.83601	+	7.95239i	−0.263705	+	0.306770i
$673$	6.90421	−	13.5503i	0.266138	−	0.522325i	−0.718804	−	0.695213i	$-0.755310\pi$
$673$	6.90421	−	13.5503i	0.266138	−	0.522325i	0.984941	+	0.172888i	$0.0553100\pi$
$674$	−47.1547			−1.81633
$675$	8.72179	−	24.4731i	0.335702	−	0.941968i
$676$	−16.9044			−0.650169
$677$	3.54092	−	6.94944i	0.136089	−	0.267089i	−0.812898	−	0.582407i	$-0.802111\pi$
$677$	3.54092	−	6.94944i	0.136089	−	0.267089i	0.948986	+	0.315318i	$0.102111\pi$
$678$	7.20595	−	8.38275i	0.276743	−	0.321938i
$679$	2.55892	+	3.52205i	0.0982024	+	0.135164i
$680$	−0.919895	+	2.42377i	−0.0352764	+	0.0929474i
$681$	9.85899	+	24.0183i	0.377797	+	0.920382i
$682$	4.60901	−	4.60901i	0.176488	−	0.176488i
$683$	12.9039	−	2.04378i	0.493754	−	0.0782029i	0.0954080	−	0.995438i	$-0.469584\pi$
$683$	12.9039	−	2.04378i	0.493754	−	0.0782029i	0.398346	+	0.917235i	$0.369584\pi$
$684$	5.30624	+	34.9447i	0.202889	+	1.33615i
$685$	20.7450	+	4.32754i	0.792627	+	0.165347i
$686$	19.4244	−	6.31136i	0.741626	−	0.240969i
$687$	26.4455	+	2.16627i	1.00896	+	0.0826482i
$688$	26.8653	−	13.6886i	1.02423	−	0.521872i
$689$	5.05968	+	15.5721i	0.192759	+	0.593250i
$690$	5.00547	−	5.28091i	0.190555	−	0.201041i
$691$	−13.0283	+	40.0970i	−0.495620	+	1.52536i	0.320368	+	0.947293i	$0.396193\pi$
$691$	−13.0283	+	40.0970i	−0.495620	+	1.52536i	−0.815988	+	0.578068i	$0.803807\pi$
$692$	−4.55251	−	28.7434i	−0.173061	−	1.09266i
$693$	2.18811	+	0.726436i	0.0831194	+	0.0275950i
$694$	−37.1724	+	51.1634i	−1.41105	+	1.94214i
$695$	−13.8465	−	5.25517i	−0.525228	−	0.199340i
$696$	−0.453474	−	6.00702i	−0.0171889	−	0.227695i
$697$	2.19254	−	13.8431i	0.0830482	−	0.524346i
$698$	−14.7602	−	7.52071i	−0.558682	−	0.284663i
$699$	−1.96938	+	3.19083i	−0.0744889	+	0.120688i
$700$	0.426470	+	7.10817i	0.0161190	+	0.268664i
$701$		−	42.0365i		−	1.58770i	−0.608116	−	0.793848i	$-0.708075\pi$
$701$		−	42.0365i		−	1.58770i	0.608116	−	0.793848i	$-0.291925\pi$
$702$	−25.4448	+	40.6433i	−0.960353	+	1.53398i
$703$	−25.9737	−	4.11382i	−0.979615	−	0.155156i
$704$	−5.23172	+	3.80106i	−0.197178	+	0.143258i
$705$	18.1275	−	0.485400i	0.682722	−	0.0182812i
$706$	−53.2567	−	38.6932i	−2.00434	−	1.45624i
$707$	1.89277	+	1.89277i	0.0711848	+	0.0711848i
$708$	0.681508	−	1.63057i	0.0256127	−	0.0612804i
$709$	−28.0166	−	9.10314i	−1.05219	−	0.341876i	−0.268660	−	0.963235i	$-0.586581\pi$
$709$	−28.0166	−	9.10314i	−1.05219	−	0.341876i	−0.783526	+	0.621359i	$0.786581\pi$
$710$	−32.8386	−	18.7941i	−1.23241	−	0.705331i
$711$	−13.9589	+	13.7818i	−0.523500	+	0.516858i
$712$	1.51485	+	2.97305i	0.0567712	+	0.111420i
$713$	1.47368	+	2.89225i	0.0551896	+	0.108316i
$714$	−2.13862	+	8.78436i	−0.0800358	+	0.328746i
$715$	−10.3373	+	1.12604i	−0.386592	+	0.0421116i
$716$	31.7043	+	10.3014i	1.18485	+	0.384980i
$717$	−36.4250	−	15.2241i	−1.36032	−	0.568555i
$718$	−10.6896	−	10.6896i	−0.398933	−	0.398933i
$719$	25.9550	+	18.8574i	0.967957	+	0.703262i	0.954985	−	0.296654i	$-0.0958708\pi$
$719$	25.9550	+	18.8574i	0.967957	+	0.703262i	0.0129720	+	0.999916i	$0.495871\pi$
$720$	−19.3185	−	21.5680i	−0.719959	−	0.803791i
$721$	−3.11653	+	2.26429i	−0.116066	+	0.0843265i
$722$	43.6527	+	6.91392i	1.62459	+	0.257309i
$723$	2.05728	+	3.38135i	0.0765110	+	0.125754i
$724$		−	19.0314i		−	0.707297i
$725$	−38.4105	−	34.0623i	−1.42653	−	1.26504i
$726$	−28.9146	−	17.8461i	−1.07312	−	0.662332i
$727$	42.0031	+	21.4016i	1.55781	+	0.793742i	0.999359	−	0.0357969i	$-0.0113970\pi$
$727$	42.0031	+	21.4016i	1.55781	+	0.793742i	0.558448	+	0.829539i	$0.311397\pi$
$728$	−0.194876	+	1.23040i	−0.00722260	+	0.0456017i
$729$	11.7948	+	24.2875i	0.436843	+	0.899538i
$730$	1.91581	−	39.4074i	0.0709073	−	1.45853i
$731$	14.0534	−	19.3428i	0.519784	−	0.715421i
$732$	−6.96745	−	29.4351i	−0.257524	−	1.08795i
$733$	0.582209	+	3.67592i	0.0215044	+	0.135773i	0.996105	−	0.0881779i	$-0.0281044\pi$
$733$	0.582209	+	3.67592i	0.0215044	+	0.135773i	−0.974600	+	0.223951i	$0.928104\pi$
$734$	−7.20426	+	22.1724i	−0.265914	+	0.818399i
$735$	4.52599	+	24.3398i	0.166944	+	0.897787i
$736$	−2.30480	−	7.09343i	−0.0849559	−	0.261467i
$737$	6.06625	−	3.09091i	0.223453	−	0.113855i
$738$	19.3517	+	14.2495i	0.712347	+	0.524531i
$739$	45.0233	−	14.6289i	1.65621	−	0.538134i	0.676136	−	0.736777i	$-0.263653\pi$
$739$	45.0233	−	14.6289i	1.65621	−	0.538134i	0.980072	+	0.198643i	$0.0636533\pi$
$740$	−15.1909	+	6.83241i	−0.558430	+	0.251165i
$741$	34.0945	+	40.1785i	1.25249	+	1.47599i
$742$	−5.22818	+	0.828062i	−0.191932	+	0.0303991i
$743$	−37.4947	+	37.4947i	−1.37555	+	1.37555i	−0.523556	+	0.851991i	$0.675395\pi$
$743$	−37.4947	+	37.4947i	−1.37555	+	1.37555i	−0.851991	+	0.523556i	$0.824605\pi$
$744$	1.83454	−	0.753040i	0.0672575	−	0.0276078i
$745$	18.0348	+	14.4916i	0.660742	+	0.530933i
$746$	29.0677	+	40.0083i	1.06424	+	1.46481i
$747$	−1.29833	−	4.08440i	−0.0475035	−	0.149440i
$748$	−2.79833	+	5.49203i	−0.102317	+	0.200809i
$749$	2.69823			0.0985913
$750$	−37.7885	−	2.66410i	−1.37984	−	0.0972791i
$751$	−21.2697			−0.776142			−0.388071	−	0.921629i	$-0.626858\pi$
$751$	−21.2697			−0.776142			−0.388071	+	0.921629i	$0.626858\pi$
$752$	9.17508	−	18.0071i	0.334581	−	0.656652i
$753$	18.8123	+	16.1713i	0.685557	+	0.589316i
$754$	55.6938	+	76.6559i	2.02825	+	2.79164i
$755$	9.76635	+	7.84765i	0.355434	+	0.285605i
$756$	−5.58096	−	4.85978i	−0.202977	−	0.176749i
$757$	−22.1455	+	22.1455i	−0.804891	+	0.804891i	−0.983856	−	0.178964i	$-0.942725\pi$
$757$	−22.1455	+	22.1455i	−0.804891	+	0.804891i	0.178964	+	0.983856i	$0.442725\pi$
$758$	−36.9825	+	5.85746i	−1.34327	+	0.212752i
$759$	−1.25028	+	1.06096i	−0.0453825	+	0.0385104i
$760$	−4.45504	+	2.00374i	−0.161601	+	0.0726832i
$761$	−33.4555	+	10.8703i	−1.21276	+	0.394050i	−0.844440	−	0.535649i	$-0.820067\pi$
$761$	−33.4555	+	10.8703i	−1.21276	+	0.394050i	−0.368320	+	0.929699i	$0.620067\pi$
$762$	4.20576	−	51.3434i	0.152359	−	1.85998i
$763$	1.60972	−	0.820194i	0.0582758	−	0.0296930i
$764$	9.72984	+	29.9454i	0.352013	+	1.08339i
$765$	−21.4135	−	8.28387i	−0.774208	−	0.299504i
$766$	12.8106	−	39.4271i	0.462867	−	1.42456i
$767$	−0.412162	−	2.60229i	−0.0148823	−	0.0939632i
$768$	−31.0148	+	7.34138i	−1.11915	+	0.264909i
$769$	17.0696	−	23.4943i	0.615545	−	0.847225i	−0.381474	−	0.924380i	$-0.624583\pi$
$769$	17.0696	−	23.4943i	0.615545	−	0.847225i	0.997019	+	0.0771542i	$0.0245834\pi$
$770$	0.163237	−	3.35772i	0.00588266	−	0.121004i
$771$	−10.5319	+	0.795064i	−0.379299	+	0.0286335i
$772$	−5.49273	+	34.6798i	−0.197688	+	1.24815i
$773$	35.2461	+	17.9588i	1.26771	+	0.645933i	0.952918	−	0.303227i	$-0.0980639\pi$
$773$	35.2461	+	17.9588i	1.26771	+	0.645933i	0.314796	+	0.949159i	$0.398064\pi$
$774$	18.3781	+	36.6455i	0.660587	+	1.31720i
$775$	6.75687	−	15.4905i	0.242714	−	0.556436i
$776$			1.89162i			0.0679051i
$777$	4.70374	−	2.86184i	0.168746	−	0.102668i
$778$	−20.9939	−	3.32511i	−0.752669	−	0.119211i
$779$	21.3656	−	15.5230i	0.765503	−	0.556170i
$780$	32.0079	+	9.46061i	1.14607	+	0.338744i
$781$	6.89839	+	5.01197i	0.246844	+	0.179342i
$782$	−4.54683	−	4.54683i	−0.162594	−	0.162594i
$783$	53.2254	−	3.67644i	1.90212	−	0.131385i
$784$	26.2406	+	8.52609i	0.937165	+	0.304503i
$785$	22.5882	−	2.46053i	0.806206	−	0.0878202i
$786$	4.76237	+	1.15943i	0.169868	+	0.0413556i
$787$	−6.02216	−	11.8192i	−0.214667	−	0.421307i	0.758413	−	0.651774i	$-0.225975\pi$
$787$	−6.02216	−	11.8192i	−0.214667	−	0.421307i	−0.973080	+	0.230466i	$0.925975\pi$
$788$	1.77392	+	3.48151i	0.0631931	+	0.124024i
$789$	−52.4562	−	12.7708i	−1.86749	−	0.454654i
$790$	24.8239	+	14.2072i	0.883195	+	0.505468i
$791$	2.41892	+	0.785955i	0.0860069	+	0.0279453i
$792$	0.583640	+	0.814192i	0.0207388	+	0.0289311i
$793$	−31.8878	−	31.8878i	−1.13237	−	1.13237i
$794$	12.1294	+	8.81254i	0.430457	+	0.312745i
$795$	−0.359828	−	13.4380i	−0.0127618	−	0.476595i
$796$	−27.8811	+	20.2568i	−0.988220	+	0.717984i
$797$	−22.9393	−	3.63324i	−0.812553	−	0.128696i	−0.263690	−	0.964608i	$-0.584939\pi$
$797$	−22.9393	−	3.63324i	−0.812553	−	0.128696i	−0.548864	+	0.835912i	$0.684939\pi$
$798$	−14.5536	+	8.85466i	−0.515191	+	0.313452i
$799$		−	16.0256i		−	0.566945i
$800$	−20.9021	+	32.7258i	−0.739001	+	1.15703i
$801$	−26.4158	+	13.2478i	−0.933355	+	0.468087i
$802$	36.1181	+	18.4031i	1.27538	+	0.649836i
$803$	−1.39092	+	8.78194i	−0.0490846	+	0.309908i
$804$	−21.7912	+	1.64503i	−0.768517	+	0.0580159i
$805$	1.56519	+	0.594039i	0.0551658	+	0.0209371i
$806$	−18.3339	+	25.2344i	−0.645783	+	0.888844i
$807$	24.8627	−	5.88513i	0.875208	−	0.207166i
$808$	0.181945	+	1.14875i	0.00640080	+	0.0404130i
$809$	−7.57984	+	23.3283i	−0.266493	+	0.820181i	0.724853	+	0.688904i	$0.241908\pi$
$809$	−7.57984	+	23.3283i	−0.266493	+	0.820181i	−0.991346	+	0.131277i	$0.958092\pi$
$810$	29.4919	−	26.0787i	1.03624	−	0.916311i
$811$	−7.17737	−	22.0897i	−0.252032	−	0.775674i	−0.994400	−	0.105682i	$-0.966298\pi$
$811$	−7.17737	−	22.0897i	−0.252032	−	0.775674i	0.742368	−	0.669992i	$-0.233702\pi$
$812$	−13.0292	+	6.63873i	−0.457237	+	0.232974i
$813$	3.47721	−	42.4493i	0.121951	−	1.48876i
$814$	7.47852	−	2.42992i	0.262122	−	0.0851686i
$815$	42.6792	+	8.90314i	1.49499	+	0.311863i
$816$	−19.5104	+	16.5561i	−0.683002	+	0.579579i
$817$	44.4965	−	7.04756i	1.55674	−	0.246563i
$818$	−44.1115	+	44.1115i	−1.54232	+	1.54232i
$819$	−10.8857	−	1.79544i	−0.380378	−	0.0627379i
$820$	5.93553	−	15.6392i	0.207278	−	0.546143i
$821$	−14.1182	−	19.4320i	−0.492729	−	0.678183i	0.488160	−	0.872754i	$-0.337668\pi$
$821$	−14.1182	−	19.4320i	−0.492729	−	0.678183i	−0.980888	+	0.194572i	$0.937668\pi$
$822$	24.3510	+	20.9325i	0.849340	+	0.730106i
$823$	−13.6197	+	26.7301i	−0.474751	+	0.931752i	0.522132	+	0.852865i	$0.325137\pi$
$823$	−13.6197	+	26.7301i	−0.474751	+	0.931752i	−0.996884	+	0.0788873i	$0.974863\pi$
$824$	−1.67382			−0.0583102
$825$	8.40097	+	1.51906i	0.292484	+	0.0528868i
$826$	0.851776			0.0296371
$827$	3.17364	−	6.22861i	0.110358	−	0.216590i	−0.829222	−	0.558920i	$-0.811216\pi$
$827$	3.17364	−	6.22861i	0.110358	−	0.216590i	0.939580	+	0.342330i	$0.111216\pi$
$828$	5.01600	−	1.59447i	0.174318	−	0.0554115i
$829$	4.72836	+	6.50802i	0.164223	+	0.226033i	0.883195	−	0.469005i	$-0.155387\pi$
$829$	4.72836	+	6.50802i	0.164223	+	0.226033i	−0.718973	+	0.695038i	$0.755387\pi$
$830$	−5.22799	+	3.42328i	−0.181466	+	0.118824i
$831$	−5.36963	+	2.20412i	−0.186270	+	0.0764601i
$832$	21.8818	−	21.8818i	0.758617	−	0.758617i
$833$	21.6092	−	3.42256i	0.748715	−	0.118585i
$834$	−14.5202	−	17.1113i	−0.502795	−	0.592516i
$835$	−0.595760	+	1.04096i	−0.0206171	+	0.0360239i
$836$	−11.0459	+	3.58904i	−0.382031	+	0.124129i
$837$	6.56539	+	16.2897i	0.226933	+	0.563056i
$838$	22.5328	−	11.4811i	0.778384	−	0.396606i
$839$	3.47947	+	10.7087i	0.120125	+	0.369706i	0.992981	−	0.118271i	$-0.0377351\pi$
$839$	3.47947	+	10.7087i	0.120125	+	0.369706i	−0.872857	+	0.487977i	$0.837735\pi$
$840$	0.439765	−	0.923390i	0.0151733	−	0.0318600i
$841$	23.6164	−	72.6838i	0.814358	−	2.50634i
$842$	−3.75557	−	23.7118i	−0.129426	−	0.817161i
$843$	−0.197749	−	0.835423i	−0.00681084	−	0.0287735i
$844$	−5.37223	+	7.39424i	−0.184920	+	0.254520i
$845$	19.9657	−	5.43081i	0.686840	−	0.186826i
$846$	24.4032	+	12.6309i	0.839000	+	0.434261i
$847$	1.22299	−	7.72166i	0.0420224	−	0.265319i
$848$	−13.3487	−	6.80150i	−0.458396	−	0.233565i
$849$	−33.7589	−	20.8360i	−1.15860	−	0.715089i
$850$	−3.24739	+	33.3199i	−0.111385	+	1.14286i
$851$			3.91599i			0.134238i
$852$	−14.2259	−	23.3818i	−0.487373	−	0.801049i
$853$	−15.1469	−	2.39903i	−0.518619	−	0.0821411i	−0.108362	−	0.994111i	$-0.534561\pi$
$853$	−15.1469	−	2.39903i	−0.518619	−	0.0821411i	−0.410256	+	0.911970i	$0.634561\pi$
$854$	11.7947	−	8.56936i	0.403607	−	0.293237i
$855$	−17.4937	−	39.5683i	−0.598273	−	1.35321i
$856$	0.948489	+	0.689118i	0.0324187	+	0.0235536i
$857$	−2.97404	−	2.97404i	−0.101591	−	0.101591i	0.654484	−	0.756076i	$-0.272886\pi$
$857$	−2.97404	−	2.97404i	−0.101591	−	0.101591i	−0.756076	+	0.654484i	$0.772886\pi$
$858$	−14.5379	−	6.07624i	−0.496316	−	0.207440i
$859$	−24.1552	−	7.84850i	−0.824165	−	0.267787i	−0.133579	−	0.991038i	$-0.542647\pi$
$859$	−24.1552	−	7.84850i	−0.824165	−	0.267787i	−0.690585	+	0.723251i	$0.742647\pi$
$860$	21.1335	−	19.1739i	0.720646	−	0.653826i
$861$	−1.30796	+	5.37245i	−0.0445753	+	0.183093i
$862$	35.7524	+	70.1681i	1.21773	+	2.38993i
$863$	−6.12466	−	12.0203i	−0.208486	−	0.409177i	0.762957	−	0.646449i	$-0.223747\pi$
$863$	−6.12466	−	12.0203i	−0.208486	−	0.409177i	−0.971443	+	0.237272i	$0.923747\pi$
$864$	−9.04443	−	39.3281i	−0.307698	−	1.33797i
$865$	14.6112	+	32.4861i	0.496797	+	1.10456i
$866$	−1.29689	−	0.421384i	−0.0440700	−	0.0143192i
$867$	3.53021	−	8.44631i	0.119892	−	0.286852i
$868$	−3.40385	−	3.40385i	−0.115534	−	0.115534i
$869$	−5.21474	−	3.78873i	−0.176898	−	0.128524i
$870$	−26.0109	−	73.3148i	−0.881851	−	2.48561i
$871$	−26.3578	+	19.1501i	−0.893100	+	0.648875i
$872$	0.775327	+	0.122800i	0.0262559	+	0.00415852i
$873$	−16.7527	−	0.106953i	−0.566992	−	0.00361982i
$874$		−	12.1162i		−	0.409837i
$875$	−2.78732	−	8.25840i	−0.0942285	−	0.279185i
$876$	14.9895	−	24.2862i	0.506447	−	0.820556i
$877$	−13.4225	−	6.83909i	−0.453245	−	0.230940i	0.212438	−	0.977175i	$-0.431860\pi$
$877$	−13.4225	−	6.83909i	−0.453245	−	0.230940i	−0.665683	+	0.746235i	$0.731860\pi$
$878$	10.4946	−	66.2600i	0.354174	−	2.23617i
$879$	−1.36443	−	18.0741i	−0.0460210	−	0.609625i
$880$	5.95964	−	7.41673i	0.200900	−	0.250018i
$881$	−26.2832	+	36.1757i	−0.885504	+	1.21879i	0.0893619	+	0.995999i	$0.471517\pi$
$881$	−26.2832	+	36.1757i	−0.885504	+	1.21879i	−0.974866	+	0.222792i	$0.928483\pi$
$882$	−11.8200	+	35.6033i	−0.398001	+	1.19883i
$883$	2.73187	+	17.2484i	0.0919349	+	0.580454i	0.990052	+	0.140699i	$0.0449349\pi$
$883$	2.73187	+	17.2484i	0.0919349	+	0.580454i	−0.898118	+	0.439755i	$0.855065\pi$
$884$	9.11480	−	28.0525i	0.306564	−	0.943506i
$885$	−0.281079	+	2.14480i	−0.00944837	+	0.0720965i
$886$	17.3227	+	53.3138i	0.581968	+	1.79111i
$887$	−37.3069	+	19.0088i	−1.25264	+	0.638253i	−0.949223	−	0.314604i	$-0.898128\pi$
$887$	−37.3069	+	19.0088i	−1.25264	+	0.638253i	−0.303420	+	0.952857i	$0.598128\pi$
$888$	2.38437	+	0.195314i	0.0800143	+	0.00655432i
$889$	11.2727	−	3.66273i	0.378075	−	0.122844i
$890$	28.9530	+	31.9119i	0.970506	+	1.06969i
$891$	−7.24370	+	5.12283i	−0.242673	+	0.171621i
$892$	21.9658	−	3.47904i	0.735468	−	0.116487i
$893$	21.3522	−	21.3522i	0.714524	−	0.714524i
$894$	13.3124	+	32.4314i	0.445233	+	1.08467i
$895$	−40.7552	−	1.98133i	−1.36230	−	0.0662287i
$896$	−1.23711	−	1.70273i	−0.0413288	−	0.0568842i
$897$	5.11515	−	5.95050i	0.170790	−	0.198681i
$898$	16.2102	−	31.8143i	0.540941	−	1.06166i
$899$	34.7047			1.15747
$900$	−22.9994	−	14.8974i	−0.766647	−	0.496580i
$901$	−11.8798			−0.395774
$902$	−3.58510	+	7.03615i	−0.119371	+	0.234278i
$903$	−6.14875	+	7.15290i	−0.204618	+	0.238034i
$904$	0.649574	+	0.894062i	0.0216045	+	0.0297361i
$905$	6.11415	+	22.4779i	0.203241	+	0.747190i
$906$	7.20905	+	17.5625i	0.239505	+	0.583476i
$907$	3.29748	−	3.29748i	0.109491	−	0.109491i	−0.650239	−	0.759730i	$-0.725331\pi$
$907$	3.29748	−	3.29748i	0.109491	−	0.109491i	0.759730	+	0.650239i	$0.225331\pi$
$908$	27.0468	−	4.28379i	0.897578	−	0.142162i
$909$	−10.1840	+	1.54640i	−0.337780	+	0.0512908i
$910$	1.74204	+	15.9922i	0.0577479	+	0.530137i
$911$	32.2491	−	10.4784i	1.06846	−	0.347164i	0.278573	−	0.960415i	$-0.410139\pi$
$911$	32.2491	−	10.4784i	1.06846	−	0.347164i	0.789888	+	0.613251i	$0.210139\pi$
$912$	−48.0543	−	3.93634i	−1.59124	−	0.130345i
$913$	1.25480	−	0.639354i	0.0415279	−	0.0211595i
$914$	−12.9928	−	39.9877i	−0.429763	−	1.32267i
$915$	17.6857	+	32.5272i	0.584672	+	1.07532i
$916$	8.64822	−	26.6165i	0.285745	−	0.879433i
$917$	0.176419	+	1.11387i	0.00582587	+	0.0367831i
$918$	−22.3406	−	26.6705i	−0.737351	−	0.880258i
$919$	−26.7422	+	36.8075i	−0.882144	+	1.21417i	0.0936779	+	0.995603i	$0.470138\pi$
$919$	−26.7422	+	36.8075i	−0.882144	+	1.21417i	−0.975822	+	0.218565i	$0.929862\pi$
$920$	0.398486	+	0.608562i	0.0131377	+	0.0200637i
$921$	1.28292	+	16.9945i	0.0422738	+	0.559987i
$922$	−5.52582	+	34.8887i	−0.181983	+	1.14900i
$923$	−36.3566	−	18.5246i	−1.19669	−	0.609745i
$924$	1.27718	−	2.06932i	0.0420162	−	0.0680755i
$925$	15.7469	−	12.9501i	0.517755	−	0.425795i
$926$		−	19.9005i		−	0.653972i
$927$	0.0946388	−	14.8238i	0.00310835	−	0.486876i
$928$	−78.7595	−	12.4743i	−2.58541	−	0.409488i
$929$	28.1643	−	20.4626i	0.924041	−	0.671355i	−0.0204855	−	0.999790i	$-0.506521\pi$
$929$	28.1643	−	20.4626i	0.924041	−	0.671355i	0.944527	+	0.328435i	$0.106521\pi$
$930$	20.3073	−	15.6014i	0.665904	−	0.511591i
$931$	33.3519	+	24.2315i	1.09306	+	0.794157i
$932$	2.79651	+	2.79651i	0.0916027	+	0.0916027i
$933$	−1.47970	+	3.54031i	−0.0484432	+	0.115905i
$934$	−20.9334	−	6.80167i	−0.684962	−	0.222558i
$935$	1.54068	−	7.38561i	0.0503857	−	0.241535i
$936$	−3.36803	−	3.41131i	−0.110087	−	0.111502i
$937$	−13.0305	−	25.5737i	−0.425687	−	0.835458i	−0.999860	−	0.0167239i	$-0.994676\pi$
$937$	−13.0305	−	25.5737i	−0.425687	−	0.835458i	0.574173	−	0.818734i	$-0.305324\pi$
$938$	−4.78176	−	9.38474i	−0.156130	−	0.306422i
$939$	−9.84021	+	40.4186i	−0.321123	+	1.31901i
$940$	3.90582	−	18.7234i	0.127394	−	0.610690i
$941$	48.7206	+	15.8303i	1.58825	+	0.516053i	0.964164	−	0.265305i	$-0.0854727\pi$
$941$	48.7206	+	15.8303i	1.58825	+	0.516053i	0.624083	+	0.781358i	$0.285473\pi$
$942$	31.7670	+	13.2773i	1.03503	+	0.432598i
$943$	−2.78081	−	2.78081i	−0.0905556	−	0.0905556i
$944$	1.95034	+	1.41701i	0.0634782	+	0.0461196i
$945$	8.15292	+	3.94688i	0.265214	+	0.128392i
$946$	−10.8983	+	7.91810i	−0.354335	+	0.257440i
$947$	−27.7042	−	4.38792i	−0.900267	−	0.142588i	−0.310890	−	0.950446i	$-0.600627\pi$
$947$	−27.7042	−	4.38792i	−0.900267	−	0.142588i	−0.589377	+	0.807858i	$0.700627\pi$
$948$	10.7539	+	17.6752i	0.349271	+	0.574063i
$949$		−	42.5484i		−	1.38118i
$950$	−48.7215	+	40.0680i	−1.58074	+	1.29998i
$951$	−1.14835	−	0.708762i	−0.0372378	−	0.0229832i
$952$	−0.805334	−	0.410338i	−0.0261010	−	0.0132991i
$953$	−0.526345	+	3.32321i	−0.0170500	+	0.107649i	−0.994746	−	0.102377i	$-0.967355\pi$
$953$	−0.526345	+	3.32321i	−0.0170500	+	0.107649i	0.977696	+	0.210027i	$0.0673551\pi$
$954$	9.36333	−	18.0901i	0.303149	−	0.585690i
$955$	−21.1123	−	32.2424i	−0.683178	−	1.04334i
$956$	−24.4748	+	33.6867i	−0.791573	+	1.08951i
$957$	4.03818	+	17.0600i	0.130536	+	0.551470i
$958$	5.29756	+	33.4475i	0.171156	+	1.08064i
$959$	−2.28312	+	7.02671i	−0.0737257	+	0.226904i
$960$	−22.3206	+	12.1362i	−0.720395	+	0.391694i
$961$	−6.04918	−	18.6175i	−0.195135	−	0.600563i
$962$	−33.5276	+	17.0832i	−1.08097	+	0.550783i
$963$	−6.15663	+	8.36110i	−0.198395	+	0.269433i
$964$	3.97032	−	1.29003i	0.127875	−	0.0415492i
$965$	−4.65401	−	42.7247i	−0.149818	−	1.37536i
$966$	1.64135	+	1.93424i	0.0528096	+	0.0622333i
$967$	−28.2117	+	4.46829i	−0.907226	+	0.143690i	−0.592573	−	0.805516i	$-0.701888\pi$
$967$	−28.2117	+	4.46829i	−0.907226	+	0.143690i	−0.314653	+	0.949207i	$0.601888\pi$
$968$	2.40199	−	2.40199i	0.0772028	−	0.0772028i
$969$	−35.3690	+	14.5182i	−1.13622	+	0.466393i
$970$	6.41148	+	23.5709i	0.205860	+	0.756818i
$971$	18.4852	+	25.4427i	0.593218	+	0.816495i	0.995066	−	0.0992113i	$-0.0316320\pi$
$971$	18.4852	+	25.4427i	0.593218	+	0.816495i	−0.401848	+	0.915706i	$0.631632\pi$
$972$	27.7934	−	6.20519i	0.891473	−	0.199032i
$973$	2.34418	−	4.60071i	0.0751509	−	0.147492i
$974$	20.7829			0.665926
$975$	−40.8437	−	0.890804i	−1.30804	−	0.0285286i
$976$	41.2627			1.32079
$977$	−2.09071	+	4.10325i	−0.0668877	+	0.131275i	−0.922029	−	0.387120i	$-0.873470\pi$
$977$	−2.09071	+	4.10325i	−0.0668877	+	0.131275i	0.855142	+	0.518394i	$0.173470\pi$
$978$	50.0979	+	43.0650i	1.60195	+	1.37707i
$979$	−5.70773	−	7.85601i	−0.182420	−	0.251079i
$980$	26.0811	+	1.26795i	0.833131	+	0.0405030i
$981$	−1.13138	+	6.85955i	−0.0361223	+	0.219009i
$982$	−10.2872	+	10.2872i	−0.328277	+	0.328277i
$983$	12.6446	−	2.00270i	0.403299	−	0.0638763i	0.0485102	−	0.998823i	$-0.484553\pi$
$983$	12.6446	−	2.00270i	0.403299	−	0.0638763i	0.354789	+	0.934946i	$0.384553\pi$
$984$	−1.83188	+	1.55449i	−0.0583982	+	0.0495552i
$985$	−3.21365	−	3.54208i	−0.102395	−	0.112860i
$986$	−65.3827	+	21.2441i	−2.08221	+	0.676551i
$987$	−0.516160	+	6.30121i	−0.0164295	+	0.200570i
$988$	49.5210	−	25.2322i	1.57547	−	0.802743i
$989$	−2.07308	−	6.38029i	−0.0659202	−	0.202882i
$990$	10.0322	+	8.16723i	0.318845	+	0.259572i
$991$	−14.7045	+	45.2557i	−0.467103	+	1.43759i	0.389216	+	0.921147i	$0.372746\pi$
$991$	−14.7045	+	45.2557i	−0.467103	+	1.43759i	−0.856319	+	0.516448i	$0.827254\pi$
$992$	−4.10641	−	25.9269i	−0.130379	−	0.823179i
$993$	−25.2636	+	5.98003i	−0.801717	+	0.189771i
$994$	7.75373	−	10.6721i	0.245933	−	0.338498i
$995$	26.4224	−	32.8825i	0.837646	−	1.04244i
$996$	−4.50752	+	0.340275i	−0.142826	+	0.0107820i
$997$	3.19474	−	20.1708i	0.101179	−	0.638816i	−0.884027	−	0.467437i	$-0.845178\pi$
$997$	3.19474	−	20.1708i	0.101179	−	0.638816i	0.985205	−	0.171379i	$-0.0548224\pi$
$998$	−39.9472	−	20.3541i	−1.26451	−	0.644297i
$999$	−1.86457	+	21.1056i	−0.0589924	+	0.667751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.8.2	✓	64
3.2	odd	2	inner	75.2.l.a.8.7	yes	64
5.2	odd	4		375.2.l.a.107.2		64
5.3	odd	4		375.2.l.b.107.7		64
5.4	even	2		375.2.l.c.143.7		64
15.2	even	4		375.2.l.a.107.7		64
15.8	even	4		375.2.l.b.107.2		64
15.14	odd	2		375.2.l.c.143.2		64
25.3	odd	20		375.2.l.c.257.2		64
25.4	even	10		375.2.l.b.368.2		64
25.21	even	5		375.2.l.a.368.7		64
25.22	odd	20	inner	75.2.l.a.47.7	yes	64
75.29	odd	10		375.2.l.b.368.7		64
75.47	even	20	inner	75.2.l.a.47.2	yes	64
75.53	even	20		375.2.l.c.257.7		64
75.71	odd	10		375.2.l.a.368.2		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.2	✓	64	1.1	even	1	trivial
75.2.l.a.8.7	yes	64	3.2	odd	2	inner
75.2.l.a.47.2	yes	64	75.47	even	20	inner
75.2.l.a.47.7	yes	64	25.22	odd	20	inner
375.2.l.a.107.2		64	5.2	odd	4
375.2.l.a.107.7		64	15.2	even	4
375.2.l.a.368.2		64	75.71	odd	10
375.2.l.a.368.7		64	25.21	even	5
375.2.l.b.107.2		64	15.8	even	4
375.2.l.b.107.7		64	5.3	odd	4
375.2.l.b.368.2		64	25.4	even	10
375.2.l.b.368.7		64	75.29	odd	10
375.2.l.c.143.2		64	15.14	odd	2
375.2.l.c.143.7		64	5.4	even	2
375.2.l.c.257.2		64	25.3	odd	20
375.2.l.c.257.7		64	75.53	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.888111 + 1.74302i) q^{2} +(1.12908 - 1.31346i) q^{3} +(-1.07379 - 1.47795i) q^{4} +(1.74306 + 1.40062i) q^{5} +(1.28664 + 3.13450i) q^{6} +(-0.551254 + 0.551254i) q^{7} +(-0.334566 + 0.0529901i) q^{8} +(-0.450377 - 2.96600i) q^{9} +O(q^{10})\)	\(q+(-0.888111 + 1.74302i) q^{2} +(1.12908 - 1.31346i) q^{3} +(-1.07379 - 1.47795i) q^{4} +(1.74306 + 1.40062i) q^{5} +(1.28664 + 3.13450i) q^{6} +(-0.551254 + 0.551254i) q^{7} +(-0.334566 + 0.0529901i) q^{8} +(-0.450377 - 2.96600i) q^{9} +(-3.98933 + 1.79428i) q^{10} +(0.937544 - 0.304626i) q^{11} +(-3.15362 - 0.258327i) q^{12} +(-4.20319 + 2.14163i) q^{13} +(-0.471270 - 1.45042i) q^{14} +(3.80771 - 0.708044i) q^{15} +(1.33382 - 4.10508i) q^{16} +(-0.535425 - 3.38054i) q^{17} +(5.56977 + 1.84912i) q^{18} +(3.79078 - 5.21756i) q^{19} +(0.198357 - 4.08012i) q^{20} +(0.101645 + 1.34646i) q^{21} +(-0.301674 + 1.90469i) q^{22} +(-0.855694 - 0.435998i) q^{23} +(-0.308150 + 0.499270i) q^{24} +(1.07653 + 4.88273i) q^{25} -9.22822i q^{26} +(-4.40425 - 2.75728i) q^{27} +(1.40666 + 0.222792i) q^{28} +(-8.30669 + 6.03516i) q^{29} +(-2.14754 + 7.26572i) q^{30} +(-2.73448 - 1.98672i) q^{31} +(5.49158 + 5.49158i) q^{32} +(0.658442 - 1.57538i) q^{33} +(6.36785 + 2.06904i) q^{34} +(-1.73297 + 0.188773i) q^{35} +(-3.89998 + 3.85050i) q^{36} +(-1.85119 - 3.63316i) q^{37} +(5.72765 + 11.2411i) q^{38} +(-1.93276 + 7.93880i) q^{39} +(-0.657388 - 0.376235i) q^{40} +(3.89453 + 1.26541i) q^{41} +(-2.43717 - 1.01864i) q^{42} +(4.93949 + 4.93949i) q^{43} +(-1.45695 - 1.05853i) q^{44} +(3.36920 - 5.80073i) q^{45} +(1.51990 - 1.10427i) q^{46} +(4.62454 + 0.732455i) q^{47} +(-3.88589 - 6.38686i) q^{48} +6.39224i q^{49} +(-9.46676 - 2.46000i) q^{50} +(-5.04475 - 3.11362i) q^{51} +(7.67856 + 3.91242i) q^{52} +(0.542970 - 3.42818i) q^{53} +(8.71745 - 5.22789i) q^{54} +(2.06086 + 0.782159i) q^{55} +(0.155220 - 0.213642i) q^{56} +(-2.57300 - 10.8701i) q^{57} +(-3.14212 - 19.8386i) q^{58} +(-0.172592 + 0.531183i) q^{59} +(-5.13514 - 4.86730i) q^{60} +(2.95410 + 9.09178i) q^{61} +(5.89140 - 3.00182i) q^{62} +(1.88329 + 1.38675i) q^{63} +(-6.23890 + 2.02714i) q^{64} +(-10.3260 - 2.15407i) q^{65} +(2.16114 + 2.54678i) q^{66} +(6.82141 - 1.08040i) q^{67} +(-4.42132 + 4.42132i) q^{68} +(-1.53881 + 0.631649i) q^{69} +(1.21003 - 3.18824i) q^{70} +(5.08421 + 6.99781i) q^{71} +(0.307850 + 0.968458i) q^{72} +(-4.09480 + 8.03649i) q^{73} +7.97671 q^{74} +(7.62878 + 4.09899i) q^{75} -11.7818 q^{76} +(-0.348898 + 0.684752i) q^{77} +(-12.1209 - 10.4194i) q^{78} +(-3.84334 - 5.28990i) q^{79} +(8.07458 - 5.28723i) q^{80} +(-8.59432 + 2.67164i) q^{81} +(-5.66440 + 5.66440i) q^{82} +(1.41101 - 0.223482i) q^{83} +(1.88085 - 1.59604i) q^{84} +(3.80157 - 6.64241i) q^{85} +(-12.9964 + 4.22279i) q^{86} +(-1.45191 + 17.7247i) q^{87} +(-0.297528 + 0.151598i) q^{88} +(-3.04398 - 9.36841i) q^{89} +(7.11853 + 11.0243i) q^{90} +(1.13644 - 3.49761i) q^{91} +(0.274455 + 1.73284i) q^{92} +(-5.69692 + 1.34849i) q^{93} +(-5.38378 + 7.41014i) q^{94} +(13.9154 - 3.78509i) q^{95} +(13.4134 - 1.01259i) q^{96} +(0.873583 - 5.51558i) q^{97} +(-11.1418 - 5.67701i) q^{98} +(-1.32577 - 2.64356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more