LMFDB - Embedded newform 990.2.bg.a.301.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			301.6
Character	$\chi$	$=$	990.301
Dual form			990.2.bg.a.421.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.0126374 + 1.73200i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(-1.72120 - 0.193612i) q^{6} +(2.08037 - 2.31049i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.99968 - 0.0437761i) q^{9} +1.00000 q^{10} +(0.912248 + 3.18870i) q^{11} +(0.372465 - 1.69153i) q^{12} +(-4.07588 + 1.81470i) q^{13} +(2.08037 + 2.31049i) q^{14} +(1.72384 - 0.168476i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-3.50122 + 2.54379i) q^{17} +(0.357088 - 2.97867i) q^{18} +(0.484122 - 1.48997i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(3.97548 + 3.63241i) q^{21} +(-3.26659 + 0.573941i) q^{22} +(-2.36262 + 4.09218i) q^{23} +(1.64333 + 0.547238i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(-1.37871 - 4.24324i) q^{26} +(0.113729 - 5.19491i) q^{27} +(-2.51529 + 1.82746i) q^{28} +(-4.35907 + 4.84123i) q^{29} +(-0.0126374 + 1.73200i) q^{30} +(-9.63646 + 4.29043i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.53437 + 1.53972i) q^{33} +(-2.16387 - 3.74794i) q^{34} +(-2.51529 - 1.82746i) q^{35} +(2.92503 + 0.666488i) q^{36} +(1.85877 + 5.72070i) q^{37} +(1.43121 + 0.637214i) q^{38} +(-3.09156 - 7.08238i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(3.09083 + 3.43271i) q^{41} +(-4.02806 + 3.57401i) q^{42} +(3.01819 + 5.22766i) q^{43} +(-0.229346 - 3.30869i) q^{44} +(0.270016 + 2.98782i) q^{45} +(-3.82280 - 2.77743i) q^{46} +(5.49159 - 1.16727i) q^{47} +(-0.716015 + 1.57712i) q^{48} +(-0.278702 - 2.65167i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-4.36160 - 6.09628i) q^{51} +(4.36411 - 0.927620i) q^{52} +(5.80345 + 4.21645i) q^{53} +(5.15456 + 0.656121i) q^{54} +(3.07588 - 1.24056i) q^{55} +(-1.55453 - 2.69253i) q^{56} +(2.57452 + 0.857331i) q^{57} +(-4.35907 - 4.84123i) q^{58} +(-10.4040 - 2.21143i) q^{59} +(-1.72120 - 0.193612i) q^{60} +(-8.57580 - 3.81819i) q^{61} +(-3.25964 - 10.0321i) q^{62} +(-6.34159 + 6.83965i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.23080 + 3.86386i) q^{65} +(-0.952788 - 5.66500i) q^{66} +(1.11240 - 1.92673i) q^{67} +(3.95359 - 1.76025i) q^{68} +(-7.05782 - 4.14379i) q^{69} +(2.08037 - 2.31049i) q^{70} +(4.31604 - 3.13579i) q^{71} +(-0.968586 + 2.83934i) q^{72} +(-4.11281 - 12.6579i) q^{73} +(-5.88365 + 1.25061i) q^{74} +(-0.347743 - 1.69678i) q^{75} +(-0.783326 + 1.35676i) q^{76} +(9.26526 + 4.52594i) q^{77} +(7.36673 - 2.33431i) q^{78} +(1.55697 - 14.8135i) q^{79} +(0.309017 - 0.951057i) q^{80} +(8.99617 + 0.262629i) q^{81} +(-3.73699 + 2.71508i) q^{82} +(7.12384 + 3.17174i) q^{83} +(-3.13339 - 4.37958i) q^{84} +(2.89583 + 3.21614i) q^{85} +(-5.51451 + 2.45522i) q^{86} +(-8.32995 - 7.61111i) q^{87} +(3.31453 + 0.117762i) q^{88} +8.41468 q^{89} +(-2.99968 - 0.0437761i) q^{90} +(-4.28650 + 13.1925i) q^{91} +(3.16181 - 3.51154i) q^{92} +(-7.30926 - 16.7446i) q^{93} +(0.586851 + 5.58352i) q^{94} +(-1.53242 - 0.325725i) q^{95} +(-1.49364 - 0.876947i) q^{96} +(1.06266 - 10.1105i) q^{97} +2.66628 q^{98} +(-2.59687 - 9.60501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.0126374	+	1.73200i	−0.00729622	+	0.999973i
$3$	−0.0126374	+	1.73200i	−0.00729622	+	0.999973i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$6$	−1.72120	−	0.193612i	−0.702675	−	0.0790418i
$7$	2.08037	−	2.31049i	0.786306	−	0.873281i	−0.208187	−	0.978089i	$-0.566756\pi$
$7$	2.08037	−	2.31049i	0.786306	−	0.873281i	0.994492	+	0.104808i	$0.0334228\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−2.99968	−	0.0437761i	−0.999894	−	0.0145920i
$10$	1.00000			0.316228
$11$	0.912248	+	3.18870i	0.275053	+	0.961429i
$11$	0.912248	+	3.18870i	0.275053	+	0.961429i
$12$	0.372465	−	1.69153i	0.107521	−	0.488302i
$13$	−4.07588	+	1.81470i	−1.13045	+	0.503307i	−0.884762	−	0.466043i	$-0.845679\pi$
$13$	−4.07588	+	1.81470i	−1.13045	+	0.503307i	−0.245684	+	0.969350i	$0.579012\pi$
$14$	2.08037	+	2.31049i	0.556002	+	0.617503i
$15$	1.72384	−	0.168476i	0.445093	−	0.0435002i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−3.50122	+	2.54379i	−0.849171	+	0.616959i	−0.924917	−	0.380168i	$-0.875866\pi$
$17$	−3.50122	+	2.54379i	−0.849171	+	0.616959i	0.0757465	+	0.997127i	$0.475866\pi$
$18$	0.357088	−	2.97867i	0.0841665	−	0.702080i
$19$	0.484122	−	1.48997i	0.111065	−	0.341823i	−0.880041	−	0.474898i	$-0.842485\pi$
$19$	0.484122	−	1.48997i	0.111065	−	0.341823i	0.991106	+	0.133075i	$0.0424850\pi$
$20$	−0.104528	+	0.994522i	−0.0233733	+	0.222382i
$21$	3.97548	+	3.63241i	0.867521	+	0.792657i
$22$	−3.26659	+	0.573941i	−0.696439	+	0.122365i
$23$	−2.36262	+	4.09218i	−0.492641	+	0.853279i	−0.999964	−	0.00847696i	$-0.997302\pi$
$23$	−2.36262	+	4.09218i	−0.492641	+	0.853279i	0.507323	+	0.861756i	$0.330635\pi$
$24$	1.64333	+	0.547238i	0.335443	+	0.111704i
$25$	−0.978148	+	0.207912i	−0.195630	+	0.0415823i
$26$	−1.37871	−	4.24324i	−0.270388	−	0.832168i
$27$	0.113729	−	5.19491i	0.0218871	−	0.999760i
$28$	−2.51529	+	1.82746i	−0.475344	+	0.345358i
$29$	−4.35907	+	4.84123i	−0.809458	+	0.898995i	−0.996520	−	0.0833535i	$-0.973437\pi$
$29$	−4.35907	+	4.84123i	−0.809458	+	0.898995i	0.187062	+	0.982348i	$0.440104\pi$
$30$	−0.0126374	+	1.73200i	−0.00230727	+	0.316219i
$31$	−9.63646	+	4.29043i	−1.73076	+	0.770583i	−0.735053	+	0.678010i	$0.762843\pi$
$31$	−9.63646	+	4.29043i	−1.73076	+	0.770583i	−0.995706	+	0.0925733i	$0.970491\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−5.53437	+	1.53972i	−0.963410	+	0.268031i
$34$	−2.16387	−	3.74794i	−0.371101	−	0.642766i
$35$	−2.51529	−	1.82746i	−0.425161	−	0.308897i
$36$	2.92503	+	0.666488i	0.487505	+	0.111081i
$37$	1.85877	+	5.72070i	0.305579	+	0.940477i	0.979460	+	0.201637i	$0.0646261\pi$
$37$	1.85877	+	5.72070i	0.305579	+	0.940477i	−0.673881	+	0.738840i	$0.735374\pi$
$38$	1.43121	+	0.637214i	0.232172	+	0.103370i
$39$	−3.09156	−	7.08238i	−0.495045	−	1.13409i
$40$	−0.978148	−	0.207912i	−0.154659	−	0.0328737i
$41$	3.09083	+	3.43271i	0.482706	+	0.536100i	0.934472	−	0.356037i	$-0.115872\pi$
$41$	3.09083	+	3.43271i	0.482706	+	0.536100i	−0.451765	+	0.892137i	$0.649206\pi$
$42$	−4.02806	+	3.57401i	−0.621543	+	0.551482i
$43$	3.01819	+	5.22766i	0.460270	+	0.797211i	0.998974	−	0.0452839i	$-0.0144193\pi$
$43$	3.01819	+	5.22766i	0.460270	+	0.797211i	−0.538704	+	0.842495i	$0.681086\pi$
$44$	−0.229346	−	3.30869i	−0.0345752	−	0.498803i
$45$	0.270016	+	2.98782i	0.0402516	+	0.445398i
$46$	−3.82280	−	2.77743i	−0.563642	−	0.409510i
$47$	5.49159	−	1.16727i	0.801030	−	0.170264i	0.210832	−	0.977522i	$-0.432383\pi$
$47$	5.49159	−	1.16727i	0.801030	−	0.170264i	0.590199	+	0.807258i	$0.299049\pi$
$48$	−0.716015	+	1.57712i	−0.103348	+	0.227638i
$49$	−0.278702	−	2.65167i	−0.0398146	−	0.378811i
$50$	−0.104528	−	0.994522i	−0.0147826	−	0.140647i
$51$	−4.36160	−	6.09628i	−0.610747	−	0.853650i
$52$	4.36411	−	0.927620i	0.605193	−	0.128638i
$53$	5.80345	+	4.21645i	0.797165	+	0.579175i	0.910081	−	0.414430i	$-0.136019\pi$
$53$	5.80345	+	4.21645i	0.797165	+	0.579175i	−0.112916	+	0.993605i	$0.536019\pi$
$54$	5.15456	+	0.656121i	0.701447	+	0.0892868i
$55$	3.07588	−	1.24056i	0.414751	−	0.167277i
$56$	−1.55453	−	2.69253i	−0.207733	−	0.359804i
$57$	2.57452	+	0.857331i	0.341004	+	0.113556i
$58$	−4.35907	−	4.84123i	−0.572374	−	0.635685i
$59$	−10.4040	−	2.21143i	−1.35448	−	0.287904i	−0.527224	−	0.849726i	$-0.676767\pi$
$59$	−10.4040	−	2.21143i	−1.35448	−	0.287904i	−0.827258	+	0.561822i	$0.810100\pi$
$60$	−1.72120	−	0.193612i	−0.222205	−	0.0249952i
$61$	−8.57580	−	3.81819i	−1.09802	−	0.488869i	−0.223915	−	0.974609i	$-0.571884\pi$
$61$	−8.57580	−	3.81819i	−1.09802	−	0.488869i	−0.874104	+	0.485739i	$0.838550\pi$
$62$	−3.25964	−	10.0321i	−0.413975	−	1.27408i
$63$	−6.34159	+	6.83965i	−0.798965	+	0.861714i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.23080	+	3.86386i	0.276697	+	0.479253i
$66$	−0.952788	−	5.66500i	−0.117280	−	0.697313i
$67$	1.11240	−	1.92673i	0.135901	−	0.235387i	−0.790040	−	0.613055i	$-0.789940\pi$
$67$	1.11240	−	1.92673i	0.135901	−	0.235387i	0.925941	+	0.377668i	$0.123274\pi$
$68$	3.95359	−	1.76025i	0.479444	−	0.213462i
$69$	−7.05782	−	4.14379i	−0.849662	−	0.498853i
$70$	2.08037	−	2.31049i	0.248652	−	0.276156i
$71$	4.31604	−	3.13579i	0.512220	−	0.372149i	−0.301445	−	0.953483i	$-0.597469\pi$
$71$	4.31604	−	3.13579i	0.512220	−	0.372149i	0.813665	+	0.581334i	$0.197469\pi$
$72$	−0.968586	+	2.83934i	−0.114149	+	0.334619i
$73$	−4.11281	−	12.6579i	−0.481369	−	1.48150i	−0.837172	−	0.546939i	$-0.815793\pi$
$73$	−4.11281	−	12.6579i	−0.481369	−	1.48150i	0.355804	−	0.934561i	$-0.384207\pi$
$74$	−5.88365	+	1.25061i	−0.683961	+	0.145380i
$75$	−0.347743	−	1.69678i	−0.0401539	−	0.195928i
$76$	−0.783326	+	1.35676i	−0.0898536	+	0.155631i
$77$	9.26526	+	4.52594i	1.05587	+	0.515779i
$78$	7.36673	−	2.33431i	0.834118	−	0.264309i
$79$	1.55697	−	14.8135i	0.175172	−	1.66665i	−0.455221	−	0.890378i	$-0.650440\pi$
$79$	1.55697	−	14.8135i	0.175172	−	1.66665i	0.630394	−	0.776276i	$-0.282893\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	8.99617	+	0.262629i	0.999574	+	0.0291810i
$82$	−3.73699	+	2.71508i	−0.412681	+	0.299831i
$83$	7.12384	+	3.17174i	0.781943	+	0.348143i	0.758577	−	0.651584i	$-0.225895\pi$
$83$	7.12384	+	3.17174i	0.781943	+	0.348143i	0.0233659	+	0.999727i	$0.492562\pi$
$84$	−3.13339	−	4.37958i	−0.341880	−	0.477851i
$85$	2.89583	+	3.21614i	0.314097	+	0.348840i
$86$	−5.51451	+	2.45522i	−0.594645	+	0.264753i
$87$	−8.32995	−	7.61111i	−0.893065	−	0.815996i
$88$	3.31453	+	0.117762i	0.353330	+	0.0125535i
$89$	8.41468			0.891955			0.445977	−	0.895044i	$-0.352856\pi$
$89$	8.41468			0.891955			0.445977	+	0.895044i	$0.352856\pi$
$90$	−2.99968	−	0.0437761i	−0.316194	−	0.00461441i
$91$	−4.28650	+	13.1925i	−0.449348	+	1.38295i
$92$	3.16181	−	3.51154i	0.329641	−	0.366103i
$93$	−7.30926	−	16.7446i	−0.757935	−	1.73633i
$94$	0.586851	+	5.58352i	0.0605291	+	0.575896i
$95$	−1.53242	−	0.325725i	−0.157223	−	0.0334187i
$96$	−1.49364	−	0.876947i	−0.152444	−	0.0895030i
$97$	1.06266	−	10.1105i	0.107897	−	1.02657i	−0.797881	−	0.602815i	$-0.794046\pi$
$97$	1.06266	−	10.1105i	0.107897	−	1.02657i	0.905778	−	0.423753i	$-0.139288\pi$
$98$	2.66628			0.269335
$99$	−2.59687	−	9.60501i	−0.260995	−	0.965340i
$100$	1.00000			0.100000
$101$	−0.226806	+	2.15791i	−0.0225680	+	0.214720i	0.977426	+	0.211278i	$0.0677624\pi$
$101$	−0.226806	+	2.15791i	−0.0225680	+	0.214720i	−0.999994	+	0.00344246i	$0.998904\pi$
$102$	6.51879	−	3.70047i	0.645457	−	0.366402i
$103$	11.9156	+	2.53274i	1.17408	+	0.249558i	0.753344	−	0.657627i	$-0.228440\pi$
$103$	11.9156	+	2.53274i	1.17408	+	0.249558i	0.420733	+	0.907184i	$0.361773\pi$
$104$	0.466365	+	4.43716i	0.0457308	+	0.435100i
$105$	3.19696	−	4.33339i	0.311991	−	0.422896i
$106$	−4.79998	+	5.33092i	−0.466216	+	0.517785i
$107$	−1.91868	+	5.90508i	−0.185485	+	0.570865i	−0.999956	−	0.00933896i	$-0.997027\pi$
$107$	−1.91868	+	5.90508i	−0.185485	+	0.570865i	0.814471	+	0.580204i	$0.197027\pi$
$108$	−1.19133	+	5.05774i	−0.114635	+	0.486681i
$109$	7.44945			0.713528			0.356764	−	0.934195i	$-0.383880\pi$
$109$	7.44945			0.713528			0.356764	+	0.934195i	$0.383880\pi$
$110$	0.912248	+	3.18870i	0.0869795	+	0.304031i
$111$	−9.93176	+	3.14710i	−0.942681	+	0.298709i
$112$	2.84027	−	1.26457i	0.268380	−	0.119491i
$113$	2.42324	+	2.69128i	0.227959	+	0.253174i	0.846264	−	0.532764i	$-0.178847\pi$
$113$	2.42324	+	2.69128i	0.227959	+	0.253174i	−0.618305	+	0.785939i	$0.712180\pi$
$114$	−1.12175	+	2.47080i	−0.105061	+	0.231412i
$115$	4.31673	+	1.92193i	0.402537	+	0.179221i
$116$	5.27036	−	3.82914i	0.489341	−	0.355527i
$117$	12.3058	−	5.26509i	1.13767	−	0.486758i
$118$	3.28683	−	10.1158i	0.302577	−	0.931237i
$119$	−1.40646	+	13.3815i	−0.128930	+	1.22668i
$120$	0.372465	−	1.69153i	0.0340013	−	0.154415i
$121$	−9.33561	+	5.81777i	−0.848691	+	0.528888i
$122$	4.69369	−	8.12971i	0.424947	−	0.736029i
$123$	−5.98454	+	5.30995i	−0.539607	+	0.478782i
$124$	10.3179	−	2.19314i	0.926575	−	0.196950i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−6.13930	−	7.02179i	−0.546932	−	0.625551i
$127$	−11.4305	+	8.30473i	−1.01429	+	0.736926i	−0.965105	−	0.261864i	$-0.915663\pi$
$127$	−11.4305	+	8.30473i	−1.01429	+	0.736926i	−0.0491867	+	0.998790i	$0.515663\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−9.09248	+	5.16146i	−0.800548	+	0.454441i
$130$	−4.07588	+	1.81470i	−0.357478	+	0.159160i
$131$	−7.62697	+	13.2103i	−0.666371	+	1.15419i	0.312540	+	0.949905i	$0.398820\pi$
$131$	−7.62697	+	13.2103i	−0.666371	+	1.15419i	−0.978912	+	0.204285i	$0.934513\pi$
$132$	5.73356	−	0.355415i	0.499042	−	0.0309349i
$133$	−2.43541	−	4.21825i	−0.211177	−	0.365769i
$134$	1.79989	+	1.30770i	0.155487	+	0.112968i
$135$	−5.17834	+	0.429910i	−0.445680	+	0.0370008i
$136$	1.33735	+	4.11593i	0.114677	+	0.352938i
$137$	5.50792	+	2.45228i	0.470573	+	0.209513i	0.628302	−	0.777970i	$-0.283750\pi$
$137$	5.50792	+	2.45228i	0.470573	+	0.209513i	−0.157728	+	0.987483i	$0.550417\pi$
$138$	4.85883	−	6.58601i	0.413611	−	0.560639i
$139$	5.37036	+	1.14151i	0.455508	+	0.0968213i	0.429951	−	0.902852i	$-0.358531\pi$
$139$	5.37036	+	1.14151i	0.455508	+	0.0968213i	0.0255570	+	0.999673i	$0.491864\pi$
$140$	2.08037	+	2.31049i	0.175823	+	0.195272i
$141$	1.95232	+	9.52621i	0.164415	+	0.802251i
$142$	2.66746	+	4.62018i	0.223848	+	0.387717i
$143$	−9.50474	−	11.3413i	−0.794827	−	0.948407i
$144$	−2.72254	−	1.26007i	−0.226878	−	0.105006i
$145$	5.27036	+	3.82914i	0.437680	+	0.317993i
$146$	13.0185	−	2.76717i	1.07742	−	0.229013i
$147$	4.59624	−	0.449203i	0.379091	−	0.0370497i
$148$	−0.628749	−	5.98215i	−0.0516828	−	0.491729i
$149$	−0.403159	−	3.83580i	−0.0330281	−	0.314241i	−0.998546	−	0.0539049i	$-0.982833\pi$
$149$	−0.403159	−	3.83580i	−0.0330281	−	0.314241i	0.965518	−	0.260336i	$-0.0838334\pi$
$150$	1.72384	−	0.168476i	0.140751	−	0.0137560i
$151$	−7.07691	+	1.50424i	−0.575911	+	0.122414i	−0.486654	−	0.873595i	$-0.661783\pi$
$151$	−7.07691	+	1.50424i	−0.575911	+	0.122414i	−0.0892571	+	0.996009i	$0.528449\pi$
$152$	−1.26745	−	0.920854i	−0.102804	−	0.0746912i
$153$	10.6139	−	7.47727i	0.858083	−	0.604502i
$154$	−5.46963	+	8.74141i	−0.440755	+	0.704403i
$155$	5.27421	+	9.13519i	0.423634	+	0.733756i
$156$	1.55149	+	7.57038i	0.124219	+	0.606115i
$157$	−10.9667	−	12.1797i	−0.875238	−	0.972050i	0.124559	−	0.992212i	$-0.460248\pi$
$157$	−10.9667	−	12.1797i	−0.875238	−	0.972050i	−0.999797	+	0.0201624i	$0.993582\pi$
$158$	14.5696	+	3.09687i	1.15910	+	0.246374i
$159$	−7.37626	+	9.99832i	−0.584975	+	0.792918i
$160$	0.913545	+	0.406737i	0.0722221	+	0.0321554i
$161$	4.53980	+	13.9721i	0.357786	+	1.10115i
$162$	−1.20155	+	8.91943i	−0.0944023	+	0.700777i
$163$	16.8809	+	12.2647i	1.32221	+	0.960643i	0.999902	+	0.0140090i	$0.00445935\pi$
$163$	16.8809	+	12.2647i	1.32221	+	0.960643i	0.322310	+	0.946634i	$0.395541\pi$
$164$	−2.30959	−	4.00032i	−0.180348	−	0.312373i
$165$	2.10979	+	5.34311i	0.164247	+	0.415960i
$166$	−3.89901	+	6.75327i	−0.302621	+	0.524156i
$167$	0.573314	−	0.255256i	0.0443644	−	0.0197523i	−0.384435	−	0.923152i	$-0.625604\pi$
$167$	0.573314	−	0.255256i	0.0443644	−	0.0197523i	0.428799	+	0.903400i	$0.358937\pi$
$168$	4.68312	−	2.65843i	0.361310	−	0.205102i
$169$	4.62097	−	5.13210i	0.355459	−	0.394777i
$170$	−3.50122	+	2.54379i	−0.268531	+	0.195099i
$171$	−1.51744	+	4.44825i	−0.116041	+	0.340166i
$172$	−1.86535	−	5.74094i	−0.142231	−	0.437743i
$173$	14.0629	−	2.98917i	1.06918	−	0.227262i	0.360480	−	0.932767i	$-0.382613\pi$
$173$	14.0629	−	2.98917i	1.06918	−	0.227262i	0.708705	+	0.705505i	$0.249280\pi$
$174$	8.44013	−	7.48874i	0.639844	−	0.567720i
$175$	−1.55453	+	2.69253i	−0.117512	+	0.203536i
$176$	−0.463580	+	3.28407i	−0.0349437	+	0.247546i
$177$	3.96169	−	17.9918i	0.297779	−	1.35235i
$178$	−0.879574	+	8.36859i	−0.0659269	+	0.627252i
$179$	−1.13401	+	3.49012i	−0.0847598	+	0.260864i	−0.984450	−	0.175665i	$-0.943792\pi$
$179$	−1.13401	+	3.49012i	−0.0847598	+	0.260864i	0.899690	+	0.436529i	$0.143792\pi$
$180$	0.357088	−	2.97867i	0.0266158	−	0.222017i
$181$	−10.9006	+	7.91978i	−0.810238	+	0.588672i	−0.913900	−	0.405940i	$-0.866944\pi$
$181$	−10.9006	+	7.91978i	−0.810238	+	0.588672i	0.103662	+	0.994613i	$0.466944\pi$
$182$	−12.6722	−	5.64201i	−0.939324	−	0.418214i
$183$	6.72150	−	14.8051i	0.496868	−	1.09442i
$184$	3.16181	+	3.51154i	0.233091	+	0.258874i
$185$	5.49506	−	2.44656i	0.404005	−	0.179875i
$186$	17.4169	−	5.51893i	1.27707	−	0.404668i
$187$	−11.3054	−	8.84378i	−0.826729	−	0.646721i
$188$	−5.61427			−0.409463
$189$	−11.7662	−	11.0701i	−0.855862	−	0.805231i
$190$	0.484122	−	1.48997i	0.0351219	−	0.108094i
$191$	−15.7958	+	17.5430i	−1.14295	+	1.26937i	−0.184899	+	0.982758i	$0.559196\pi$
$191$	−15.7958	+	17.5430i	−1.14295	+	1.26937i	−0.958047	+	0.286612i	$0.907471\pi$
$192$	1.02827	−	1.39379i	0.0742090	−	0.100588i
$193$	−0.988286	−	9.40291i	−0.0711384	−	0.676836i	−0.970741	−	0.240128i	$-0.922811\pi$
$193$	−0.988286	−	9.40291i	−0.0711384	−	0.676836i	0.899603	−	0.436709i	$-0.143856\pi$
$194$	9.94406	+	2.11368i	0.713942	+	0.151753i
$195$	−6.72042	+	3.81493i	−0.481259	+	0.273193i
$196$	−0.278702	+	2.65167i	−0.0199073	+	0.189405i
$197$	1.05915			0.0754610			0.0377305	−	0.999288i	$-0.487987\pi$
$197$	1.05915			0.0754610			0.0377305	+	0.999288i	$0.487987\pi$
$198$	9.82384	−	1.57864i	0.698150	−	0.112189i
$199$	−23.8081			−1.68771			−0.843857	−	0.536568i	$-0.819720\pi$
$199$	−23.8081			−1.68771			−0.843857	+	0.536568i	$0.819720\pi$
$200$	−0.104528	+	0.994522i	−0.00739128	+	0.0703233i
$201$	3.32304	+	1.95102i	0.234389	+	0.137615i
$202$	−2.12238	−	0.451126i	−0.149330	−	0.0317411i
$203$	2.11713	+	20.1431i	0.148593	+	1.41377i
$204$	2.99880	+	6.86989i	0.209958	+	0.480988i
$205$	3.09083	−	3.43271i	0.215873	−	0.239751i
$206$	−3.76438	+	11.5856i	−0.262277	+	0.807205i
$207$	7.26625	−	12.1718i	0.505039	−	0.845999i
$208$	−4.46161			−0.309357
$209$	5.19272	+	0.184493i	0.359188	+	0.0127616i
$210$	3.97548	+	3.63241i	0.274334	+	0.250660i
$211$	10.9550	−	4.87749i	0.754174	−	0.335780i	0.00661758	−	0.999978i	$-0.497894\pi$
$211$	10.9550	−	4.87749i	0.754174	−	0.335780i	0.747557	+	0.664198i	$0.231227\pi$
$212$	−4.79998	−	5.33092i	−0.329664	−	0.366129i
$213$	5.37665	+	7.51503i	0.368402	+	0.514921i
$214$	−5.67217	−	2.52541i	−0.387742	−	0.172634i
$215$	4.88354	−	3.54810i	0.333055	−	0.241978i
$216$	−4.90551	−	1.71348i	−0.333777	−	0.116587i
$217$	−10.1344	+	31.1906i	−0.687970	+	2.11735i
$218$	−0.778680	+	7.40864i	−0.0527388	+	0.501777i
$219$	21.9756	−	6.96345i	1.48497	−	0.470546i
$220$	−3.26659	+	0.573941i	−0.220233	+	0.0386951i
$221$	9.65435	−	16.7218i	0.649422	−	1.12483i
$222$	−2.09171	−	10.2063i	−0.140386	−	0.685003i
$223$	−26.6381	+	5.66209i	−1.78382	+	0.379162i	−0.977268	−	0.212007i	$-0.932000\pi$
$223$	−26.6381	+	5.66209i	−1.78382	+	0.379162i	−0.806548	+	0.591169i	$0.798667\pi$
$224$	0.960754	+	2.95690i	0.0641931	+	0.197566i
$225$	2.94323	−	0.580849i	0.196215	−	0.0387233i
$226$	−2.92983	+	2.12865i	−0.194890	+	0.141596i
$227$	9.92471	−	11.0225i	0.658726	−	0.731589i	−0.317521	−	0.948251i	$-0.602850\pi$
$227$	9.92471	−	11.0225i	0.658726	−	0.731589i	0.976247	+	0.216662i	$0.0695169\pi$
$228$	−2.34001	−	1.37387i	−0.154971	−	0.0909867i
$229$	11.0419	−	4.91618i	0.729671	−	0.324871i	−0.00805784	−	0.999968i	$-0.502565\pi$
$229$	11.0419	−	4.91618i	0.729671	−	0.324871i	0.737729	+	0.675097i	$0.235898\pi$
$230$	−2.36262	+	4.09218i	−0.155787	+	0.269830i
$231$	−7.95603	+	15.9903i	−0.523469	+	1.05208i
$232$	3.25726	+	5.64174i	0.213850	+	0.370399i
$233$	11.1124	+	8.07365i	0.728000	+	0.528923i	0.888930	−	0.458043i	$-0.151449\pi$
$233$	11.1124	+	8.07365i	0.728000	+	0.528923i	−0.160930	+	0.986966i	$0.551449\pi$
$234$	3.94994	+	12.7887i	0.258216	+	0.836025i
$235$	−1.73491	−	5.33949i	−0.113173	−	0.348310i
$236$	9.71684	+	4.32622i	0.632512	+	0.281613i
$237$	25.6375	+	2.88388i	1.66533	+	0.187328i
$238$	−13.1612	−	2.79750i	−0.853115	−	0.181335i
$239$	−1.06631	−	1.18426i	−0.0689741	−	0.0766035i	0.707670	−	0.706543i	$-0.249746\pi$
$239$	−1.06631	−	1.18426i	−0.0689741	−	0.0766035i	−0.776644	+	0.629940i	$0.783080\pi$
$240$	1.64333	+	0.547238i	0.106076	+	0.0353240i
$241$	6.21674	+	10.7677i	0.400455	+	0.693609i	0.993781	−	0.111354i	$-0.0355186\pi$
$241$	6.21674	+	10.7677i	0.400455	+	0.693609i	−0.593326	+	0.804963i	$0.702185\pi$
$242$	−4.81007	−	9.89259i	−0.309203	−	0.635920i
$243$	−0.568563	+	15.5781i	−0.0364733	+	0.999335i
$244$	7.59455	+	5.51776i	0.486191	+	0.353239i
$245$	−2.60802	+	0.554351i	−0.166620	+	0.0354162i
$246$	−4.65531	−	6.50679i	−0.296812	−	0.414858i
$247$	0.730631	+	6.95149i	0.0464889	+	0.442313i
$248$	1.10261	+	10.4906i	0.0700158	+	0.666156i
$249$	−5.58349	+	12.2984i	−0.353839	+	0.779382i
$250$	−0.978148	+	0.207912i	−0.0618635	+	0.0131495i
$251$	11.4613	+	8.32709i	0.723428	+	0.525601i	0.887478	−	0.460851i	$-0.152456\pi$
$251$	11.4613	+	8.32709i	0.723428	+	0.525601i	−0.164049	+	0.986452i	$0.552456\pi$
$252$	7.62505	−	5.37169i	0.480333	−	0.338385i
$253$	−15.2040	−	3.80061i	−0.955869	−	0.238942i
$254$	−7.06443	−	12.2359i	−0.443262	−	0.767752i
$255$	−5.60697	+	4.97494i	−0.351122	+	0.311543i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−11.9779	−	2.54598i	−0.747160	−	0.158814i	−0.181429	−	0.983404i	$-0.558072\pi$
$257$	−11.9779	−	2.54598i	−0.747160	−	0.158814i	−0.565730	+	0.824590i	$0.691406\pi$
$258$	−4.18276	−	9.58219i	−0.260407	−	0.596561i
$259$	17.0845	+	7.60651i	1.06158	+	0.472646i
$260$	−1.37871	−	4.24324i	−0.0855041	−	0.263155i
$261$	13.2877	−	14.3313i	0.822490	−	0.887087i
$262$	−12.3407	−	8.96604i	−0.762411	−	0.553924i
$263$	−0.483504	−	0.837454i	−0.0298141	−	0.0516396i	0.850733	−	0.525598i	$-0.176158\pi$
$263$	−0.483504	−	0.837454i	−0.0298141	−	0.0516396i	−0.880547	+	0.473958i	$0.842825\pi$
$264$	−0.245852	+	5.73930i	−0.0151312	+	0.353229i
$265$	3.58673	−	6.21240i	0.220331	−	0.381625i
$266$	4.44971	−	1.98114i	0.272830	−	0.121472i
$267$	−0.106340	+	14.5743i	−0.00650789	+	0.891931i
$268$	−1.48868	+	1.65334i	−0.0909354	+	0.100994i
$269$	9.16420	−	6.65818i	0.558751	−	0.405956i	−0.272251	−	0.962226i	$-0.587768\pi$
$269$	9.16420	−	6.65818i	0.558751	−	0.405956i	0.831002	+	0.556270i	$0.187768\pi$
$270$	0.113729	−	5.19491i	0.00692131	−	0.316152i
$271$	−4.40142	−	13.5462i	−0.267367	−	0.822871i	−0.991139	−	0.132832i	$-0.957593\pi$
$271$	−4.40142	−	13.5462i	−0.267367	−	0.822871i	0.723772	−	0.690040i	$-0.242407\pi$
$272$	−4.23318	+	0.899789i	−0.256674	+	0.0545577i
$273$	−22.7953	−	7.59096i	−1.37963	−	0.459426i
$274$	−3.01458	+	5.22141i	−0.182118	+	0.315437i
$275$	−1.55528	−	2.92935i	−0.0937870	−	0.176647i
$276$	6.04205	+	5.52064i	0.363689	+	0.332303i
$277$	2.89323	−	27.5272i	0.173837	−	1.65395i	−0.465518	−	0.885038i	$-0.654132\pi$
$277$	2.89323	−	27.5272i	0.173837	−	1.65395i	0.639356	−	0.768911i	$-0.279201\pi$
$278$	−1.69661	+	5.22162i	−0.101756	+	0.313172i
$279$	29.0941	−	12.4481i	1.74182	−	0.745246i
$280$	−2.51529	+	1.82746i	−0.150317	+	0.109212i
$281$	−17.7267	−	7.89241i	−1.05748	−	0.470822i	−0.197055	−	0.980393i	$-0.563138\pi$
$281$	−17.7267	−	7.89241i	−1.05748	−	0.470822i	−0.860429	+	0.509571i	$0.829804\pi$
$282$	−9.67809	+	0.945868i	−0.576322	+	0.0563256i
$283$	−3.31651	−	3.68336i	−0.197146	−	0.218953i	0.636464	−	0.771307i	$-0.280396\pi$
$283$	−3.31651	−	3.68336i	−0.197146	−	0.218953i	−0.833610	+	0.552354i	$0.813730\pi$
$284$	−4.87369	+	2.16991i	−0.289200	+	0.128760i
$285$	0.583523	−	2.65004i	0.0345649	−	0.156975i
$286$	12.2727	−	8.26719i	0.725699	−	0.488849i
$287$	14.3613			0.847721
$288$	1.53775	−	2.57591i	0.0906129	−	0.151787i
$289$	0.534412	−	1.64475i	0.0314360	−	0.0967500i
$290$	−4.35907	+	4.84123i	−0.255973	+	0.284287i
$291$	17.4981	+	1.96830i	1.02575	+	0.115384i
$292$	1.39121	+	13.2364i	0.0814141	+	0.774604i
$293$	17.9700	+	3.81965i	1.04982	+	0.223146i	0.700349	−	0.713801i	$-0.253028\pi$
$293$	17.9700	+	3.81965i	1.04982	+	0.223146i	0.349472	+	0.936947i	$0.386361\pi$
$294$	−0.0336949	+	4.61801i	−0.00196513	+	0.269328i
$295$	−1.11181	+	10.5781i	−0.0647319	+	0.615883i
$296$	6.01510			0.349620
$297$	16.6687	−	4.37640i	0.967219	−	0.253944i
$298$	3.85693			0.223426
$299$	2.20369	−	20.9667i	0.127443	−	1.21253i
$300$	−0.0126374	+	1.73200i	−0.000729622	+	0.0999973i
$301$	18.3574	+	3.90198i	1.05810	+	0.224907i
$302$	−0.756265	−	7.19538i	−0.0435181	−	0.414047i
$303$	−3.73465	−	0.420099i	−0.214550	−	0.0241340i
$304$	1.04829	−	1.16425i	0.0601238	−	0.0667742i
$305$	−2.90086	+	8.92793i	−0.166103	+	0.511212i
$306$	6.32686	+	11.3373i	0.361682	+	0.648113i
$307$	23.1991			1.32404			0.662022	−	0.749484i	$-0.269698\pi$
$307$	23.1991			1.32404			0.662022	+	0.749484i	$0.269698\pi$
$308$	−8.12179	−	6.35339i	−0.462782	−	0.362018i
$309$	−4.53729	+	20.6058i	−0.258118	+	1.17223i
$310$	−9.63646	+	4.29043i	−0.547314	+	0.243680i
$311$	−20.6208	−	22.9018i	−1.16930	−	1.29864i	−0.946103	−	0.323866i	$-0.895017\pi$
$311$	−20.6208	−	22.9018i	−1.16930	−	1.29864i	−0.223198	−	0.974773i	$-0.571650\pi$
$312$	−7.69108	+	0.751672i	−0.435422	+	0.0425550i
$313$	19.0276	+	8.47162i	1.07550	+	0.478844i	0.866555	−	0.499082i	$-0.166329\pi$
$313$	19.0276	+	8.47162i	1.07550	+	0.478844i	0.208948	+	0.977927i	$0.432996\pi$
$314$	13.2594	−	9.63349i	0.748269	−	0.543649i
$315$	7.46505	+	5.59191i	0.420608	+	0.315069i
$316$	−4.60285	+	14.1661i	−0.258931	+	0.796907i
$317$	−2.36623	+	22.5132i	−0.132901	+	1.26447i	0.701244	+	0.712922i	$0.252629\pi$
$317$	−2.36623	+	22.5132i	−0.132901	+	1.26447i	−0.834144	+	0.551546i	$0.814038\pi$
$318$	−9.17252	−	8.38096i	−0.514369	−	0.469981i
$319$	−19.4138	−	9.48334i	−1.08696	−	0.530965i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−10.2034	−	3.39778i	−0.569497	−	0.189646i
$322$	−14.3701	+	3.05445i	−0.800812	+	0.170218i
$323$	2.09516	+	6.44823i	0.116578	+	0.358789i
$324$	−8.74498	−	2.12730i	−0.485832	−	0.118183i
$325$	3.60951	−	2.62247i	0.200220	−	0.145468i
$326$	−13.9620	+	15.5064i	−0.773285	+	0.858819i
$327$	−0.0941418	+	12.9025i	−0.00520605	+	0.713509i
$328$	4.21982	−	1.87879i	0.233001	−	0.103739i
$329$	8.72757	−	15.1166i	0.481166	−	0.833405i
$330$	−5.53437	+	1.53972i	−0.304657	+	0.0847589i
$331$	13.9431	+	24.1502i	0.766384	+	1.32742i	0.939512	+	0.342517i	$0.111279\pi$
$331$	13.9431	+	24.1502i	0.766384	+	1.32742i	−0.173128	+	0.984899i	$0.555387\pi$
$332$	−6.30872	−	4.58356i	−0.346236	−	0.251555i
$333$	−5.32528	−	17.2416i	−0.291823	−	0.944836i
$334$	0.193930	+	0.596855i	0.0106114	+	0.0326585i
$335$	−2.03245	−	0.904904i	−0.111045	−	0.0494402i
$336$	2.15435	+	4.93534i	0.117529	+	0.269245i
$337$	9.59217	+	2.03888i	0.522519	+	0.111065i	0.461618	−	0.887079i	$-0.347269\pi$
$337$	9.59217	+	2.03888i	0.522519	+	0.111065i	0.0609013	+	0.998144i	$0.480603\pi$
$338$	4.62097	+	5.13210i	0.251347	+	0.279150i
$339$	−4.69193	+	4.16305i	−0.254831	+	0.226106i
$340$	−2.16387	−	3.74794i	−0.117353	−	0.203261i
$341$	−22.4717	−	26.8138i	−1.21691	−	1.45205i
$342$	−4.26527	−	1.97409i	−0.230639	−	0.106747i
$343$	10.9005	+	7.91971i	0.588574	+	0.427624i
$344$	5.90448	−	1.25504i	0.318348	−	0.0676670i
$345$	−3.38334	+	7.45230i	−0.182153	+	0.401218i
$346$	1.50282	+	14.2983i	0.0807919	+	0.768684i
$347$	−2.42257	−	23.0492i	−0.130050	−	1.23734i	−0.843690	−	0.536831i	$-0.819621\pi$
$347$	−2.42257	−	23.0492i	−0.130050	−	1.23734i	0.713640	−	0.700513i	$-0.247045\pi$
$348$	6.56549	+	9.17668i	0.351947	+	0.491922i
$349$	19.8562	−	4.22057i	1.06288	−	0.225922i	0.356892	−	0.934146i	$-0.383836\pi$
$349$	19.8562	−	4.22057i	1.06288	−	0.225922i	0.705988	+	0.708224i	$0.250503\pi$
$350$	−2.51529	−	1.82746i	−0.134448	−	0.0976820i
$351$	8.96365	+	21.3802i	0.478444	+	1.14119i
$352$	−3.21762	−	0.804319i	−0.171500	−	0.0428704i
$353$	15.9440	+	27.6159i	0.848616	+	1.46985i	0.882444	+	0.470418i	$0.155897\pi$
$353$	15.9440	+	27.6159i	0.848616	+	1.46985i	−0.0338280	+	0.999428i	$0.510770\pi$
$354$	17.4791	+	5.82064i	0.929004	+	0.309364i
$355$	−3.56976	−	3.96462i	−0.189463	−	0.210420i
$356$	−8.23080	−	1.74951i	−0.436232	−	0.0927239i
$357$	−23.1591	−	2.60510i	−1.22571	−	0.137876i
$358$	−3.35247	−	1.49261i	−0.177183	−	0.0788871i
$359$	−11.6169	−	35.7531i	−0.613116	−	1.88698i	−0.426298	−	0.904583i	$-0.640182\pi$
$359$	−11.6169	−	35.7531i	−0.613116	−	1.88698i	−0.186819	−	0.982394i	$-0.559818\pi$
$360$	2.92503	+	0.666488i	0.154163	+	0.0351270i
$361$	13.3857	+	9.72526i	0.704509	+	0.511856i
$362$	−6.73696	−	11.6688i	−0.354087	−	0.613297i
$363$	−9.95843	−	16.2428i	−0.522682	−	0.852528i
$364$	6.93571	−	12.0130i	0.363530	−	0.629652i
$365$	−12.1587	+	5.41340i	−0.636415	+	0.283350i
$366$	14.0214	+	8.23223i	0.732909	+	0.430306i
$367$	−5.26532	+	5.84773i	−0.274848	+	0.305249i	−0.864727	−	0.502242i	$-0.832509\pi$
$367$	−5.26532	+	5.84773i	−0.274848	+	0.305249i	0.589879	+	0.807491i	$0.299175\pi$
$368$	−3.82280	+	2.77743i	−0.199277	+	0.144783i
$369$	−9.12123	−	10.4323i	−0.474832	−	0.543086i
$370$	1.85877	+	5.72070i	0.0966327	+	0.297405i
$371$	21.8154	−	4.63700i	1.13260	−	0.240741i
$372$	3.66813	+	17.8984i	0.190184	+	0.927988i
$373$	6.17423	−	10.6941i	0.319690	−	0.553719i	−0.660733	−	0.750621i	$-0.729755\pi$
$373$	6.17423	−	10.6941i	0.319690	−	0.553719i	0.980423	+	0.196902i	$0.0630880\pi$
$374$	9.97706	−	10.3190i	0.515901	−	0.533582i
$375$	−1.65114	+	0.523200i	−0.0852645	+	0.0270179i
$376$	0.586851	−	5.58352i	0.0302645	−	0.287948i
$377$	8.98165	−	27.6427i	0.462579	−	1.42367i
$378$	12.2394	−	10.5446i	0.629524	−	0.542354i
$379$	−19.6961	+	14.3101i	−1.01172	+	0.735059i	−0.964569	−	0.263829i	$-0.915014\pi$
$379$	−19.6961	+	14.3101i	−1.01172	+	0.735059i	−0.0471518	+	0.998888i	$0.515014\pi$
$380$	1.43121	+	0.637214i	0.0734194	+	0.0326884i
$381$	−14.2394	−	19.9026i	−0.729506	−	1.01964i
$382$	−15.7958	−	17.5430i	−0.808185	−	0.897580i
$383$	10.9874	−	4.89190i	0.561429	−	0.249964i	−0.106344	−	0.994329i	$-0.533914\pi$
$383$	10.9874	−	4.89190i	0.561429	−	0.249964i	0.667773	+	0.744365i	$0.267248\pi$
$384$	1.27867	+	1.16833i	0.0652521	+	0.0596210i
$385$	3.53266	−	9.68759i	0.180041	−	0.493725i
$386$	9.45470			0.481232
$387$	−8.82477	−	15.8134i	−0.448588	−	0.803843i
$388$	−3.14153	+	9.66865i	−0.159487	+	0.490851i
$389$	−21.8286	+	24.2432i	−1.10676	+	1.22918i	−0.135592	+	0.990765i	$0.543294\pi$
$389$	−21.8286	+	24.2432i	−1.10676	+	1.22918i	−0.971164	+	0.238413i	$0.923373\pi$
$390$	−3.09156	−	7.08238i	−0.156547	−	0.358630i
$391$	−2.13757	−	20.3376i	−0.108102	−	1.02852i
$392$	−2.60802	−	0.554351i	−0.131725	−	0.0279990i
$393$	−22.7839	−	13.3769i	−1.14930	−	0.674775i
$394$	−0.110711	+	1.05334i	−0.00557753	+	0.0530667i
$395$	−14.8951			−0.749456
$396$	0.543123	+	9.93504i	0.0272929	+	0.499255i
$397$	13.2793			0.666471			0.333235	−	0.942844i	$-0.391860\pi$
$397$	13.2793			0.666471			0.333235	+	0.942844i	$0.391860\pi$
$398$	2.48863	−	23.6777i	0.124744	−	1.18686i
$399$	7.33681	−	4.16483i	0.367300	−	0.208502i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	−0.719096	−	6.84175i	−0.0359100	−	0.341660i	−0.997695	−	0.0678554i	$-0.978384\pi$
$401$	−0.719096	−	6.84175i	−0.0359100	−	0.341660i	0.961785	−	0.273805i	$-0.0882823\pi$
$402$	−2.28769	+	3.10090i	−0.114100	+	0.154659i
$403$	31.4912	−	34.9745i	1.56869	−	1.74221i
$404$	0.670504	−	2.06360i	0.0333588	−	0.102668i
$405$	−0.679165	−	8.97434i	−0.0337480	−	0.445938i
$406$	−20.2541			−1.00519
$407$	−16.5459	+	11.1457i	−0.820151	+	0.552474i
$408$	−7.14571	+	2.26428i	−0.353766	+	0.112098i
$409$	10.3926	−	4.62708i	0.513881	−	0.228794i	−0.133377	−	0.991065i	$-0.542582\pi$
$409$	10.3926	−	4.62708i	0.513881	−	0.228794i	0.647258	+	0.762271i	$0.275916\pi$
$410$	3.09083	+	3.43271i	0.152645	+	0.169530i
$411$	−4.31697	+	9.50875i	−0.212941	+	0.469032i
$412$	−11.1286	−	4.95478i	−0.548267	−	0.244104i
$413$	−26.7536	+	19.4376i	−1.31646	+	0.956463i
$414$	11.3456	+	8.49875i	0.557606	+	0.417691i
$415$	2.40972	−	7.41635i	0.118288	−	0.364054i
$416$	0.466365	−	4.43716i	0.0228654	−	0.217550i
$417$	−2.04496	+	9.28707i	−0.100142	+	0.454790i
$418$	−0.726269	+	5.14499i	−0.0355230	+	0.251650i
$419$	−10.7533	+	18.6253i	−0.525335	+	0.909908i	0.474229	+	0.880401i	$0.342727\pi$
$419$	−10.7533	+	18.6253i	−0.525335	+	0.909908i	−0.999565	+	0.0295062i	$0.990607\pi$
$420$	−4.02806	+	3.57401i	−0.196549	+	0.174394i
$421$	29.9624	−	6.36870i	1.46028	−	0.310392i	0.591786	−	0.806095i	$-0.298423\pi$
$421$	29.9624	−	6.36870i	1.46028	−	0.310392i	0.868492	+	0.495704i	$0.165090\pi$
$422$	3.70566	+	11.4048i	0.180389	+	0.555179i
$423$	−16.5241	+	3.26105i	−0.803430	+	0.158557i
$424$	5.80345	−	4.21645i	0.281841	−	0.204769i
$425$	2.89583	−	3.21614i	0.140468	−	0.156006i
$426$	−8.03588	+	4.56167i	−0.389339	+	0.221013i
$427$	−26.6627	+	11.8710i	−1.29030	+	0.574478i
$428$	3.10448	−	5.37712i	0.150061	−	0.259913i
$429$	19.7633	−	16.3189i	0.954181	−	0.787886i
$430$	3.01819	+	5.22766i	0.145550	+	0.252100i
$431$	−7.42544	−	5.39490i	−0.357671	−	0.259863i	0.394409	−	0.918935i	$-0.370949\pi$
$431$	−7.42544	−	5.39490i	−0.357671	−	0.259863i	−0.752080	+	0.659072i	$0.770949\pi$
$432$	2.21686	−	4.69953i	0.106659	−	0.226106i
$433$	0.330293	+	1.01654i	0.0158729	+	0.0488517i	0.958679	−	0.284489i	$-0.0918240\pi$
$433$	0.330293	+	1.01654i	0.0158729	+	0.0488517i	−0.942806	+	0.333341i	$0.891824\pi$
$434$	−29.9604	−	13.3392i	−1.43814	−	0.640303i
$435$	−6.69869	+	9.07990i	−0.321178	+	0.435348i
$436$	−7.28666	−	1.54883i	−0.348968	−	0.0741754i
$437$	4.95345	+	5.50136i	0.236955	+	0.263166i
$438$	4.62823	+	22.5831i	0.221145	+	1.07906i
$439$	4.71563	+	8.16771i	0.225065	+	0.389823i	0.956339	−	0.292260i	$-0.0944073\pi$
$439$	4.71563	+	8.16771i	0.225065	+	0.389823i	−0.731274	+	0.682084i	$0.761074\pi$
$440$	−0.229346	−	3.30869i	−0.0109336	−	0.157735i
$441$	0.719938	+	7.96638i	0.0342827	+	0.379351i
$442$	15.6211	+	11.3494i	0.743018	+	0.539834i
$443$	15.0256	−	3.19379i	0.713887	−	0.151741i	0.163369	−	0.986565i	$-0.447764\pi$
$443$	15.0256	−	3.19379i	0.713887	−	0.151741i	0.550517	+	0.834824i	$0.314430\pi$
$444$	10.3690	−	1.01340i	0.492093	−	0.0480937i
$445$	−0.879574	−	8.36859i	−0.0416958	−	0.396709i
$446$	−2.84664	−	27.0840i	−0.134792	−	1.28246i
$447$	6.64872	−	0.649799i	0.314474	−	0.0307344i
$448$	−3.04112	+	0.646411i	−0.143680	+	0.0305400i
$449$	−14.2092	−	10.3236i	−0.670572	−	0.487199i	0.199645	−	0.979868i	$-0.436021\pi$
$449$	−14.2092	−	10.3236i	−0.670572	−	0.487199i	−0.870216	+	0.492670i	$0.836021\pi$
$450$	0.270016	+	2.98782i	0.0127287	+	0.140847i
$451$	−8.12629	+	12.9872i	−0.382652	+	0.611544i
$452$	−1.81074	−	3.13629i	−0.0851699	−	0.147519i
$453$	−2.51592	−	12.2762i	−0.118208	−	0.576789i
$454$	9.92471	+	11.0225i	0.465790	+	0.517312i
$455$	13.5683	+	2.88403i	0.636092	+	0.135205i
$456$	1.61094	−	2.18359i	0.0754392	−	0.102256i
$457$	5.63854	+	2.51044i	0.263760	+	0.117433i	0.534356	−	0.845260i	$-0.320554\pi$
$457$	5.63854	+	2.51044i	0.263760	+	0.117433i	−0.270596	+	0.962693i	$0.587221\pi$
$458$	3.73506	+	11.4953i	0.174528	+	0.537141i
$459$	12.8165	+	18.4778i	0.598225	+	0.862471i
$460$	−3.82280	−	2.77743i	−0.178239	−	0.129498i
$461$	1.49210	+	2.58440i	0.0694942	+	0.120367i	0.898679	−	0.438607i	$-0.144528\pi$
$461$	1.49210	+	2.58440i	0.0694942	+	0.120367i	−0.829185	+	0.558975i	$0.811195\pi$
$462$	−15.0710	−	9.58389i	−0.701168	−	0.445883i
$463$	−6.47344	+	11.2123i	−0.300846	+	0.521081i	−0.976328	−	0.216296i	$-0.930602\pi$
$463$	−6.47344	+	11.2123i	−0.300846	+	0.521081i	0.675481	+	0.737377i	$0.263936\pi$
$464$	−5.95131	+	2.64970i	−0.276283	+	0.123009i
$465$	−15.8889	+	9.01951i	−0.736828	+	0.418270i
$466$	−9.19099	+	10.2076i	−0.425764	+	0.472859i
$467$	−12.3977	+	9.00748i	−0.573698	+	0.416816i	−0.836447	−	0.548048i	$-0.815371\pi$
$467$	−12.3977	+	9.00748i	−0.573698	+	0.416816i	0.262748	+	0.964864i	$0.415371\pi$
$468$	−13.1315	+	2.59152i	−0.607006	+	0.119793i
$469$	−2.13748	−	6.57848i	−0.0986995	−	0.303766i
$470$	5.49159	−	1.16727i	0.253308	−	0.0538423i
$471$	21.2340	−	18.8404i	0.978410	−	0.868122i
$472$	−5.31820	+	9.21140i	−0.244790	+	0.423989i
$473$	−13.9161	+	14.3930i	−0.639863	+	0.661792i
$474$	−5.54792	+	25.1956i	−0.254825	+	1.15727i
$475$	−0.163760	+	1.55807i	−0.00751381	+	0.0714891i
$476$	4.15790	−	12.7967i	0.190577	−	0.586536i
$477$	−17.2239	−	12.9021i	−0.788629	−	0.590745i
$478$	1.28923	−	0.936683i	0.0589682	−	0.0428429i
$479$	12.9707	+	5.77494i	0.592648	+	0.263864i	0.681069	−	0.732219i	$-0.261515\pi$
$479$	12.9707	+	5.77494i	0.592648	+	0.263864i	−0.0884209	+	0.996083i	$0.528182\pi$
$480$	−0.716015	+	1.57712i	−0.0326814	+	0.0719856i
$481$	−17.9575	−	19.9438i	−0.818789	−	0.909358i
$482$	−11.3585	+	5.05715i	−0.517368	+	0.230347i
$483$	−24.2570	+	7.68638i	−1.10373	+	0.349742i
$484$	10.3412	−	3.74966i	0.470054	−	0.170439i
$485$	−10.1662			−0.461624
$486$	−15.4333	−	2.19380i	−0.700069	−	0.0995128i
$487$	−2.34347	+	7.21247i	−0.106193	+	0.326828i	−0.990009	−	0.141007i	$-0.954966\pi$
$487$	−2.34347	+	7.21247i	−0.106193	+	0.326828i	0.883816	+	0.467835i	$0.154966\pi$
$488$	−6.28138	+	6.97618i	−0.284345	+	0.315797i
$489$	−21.4558	+	29.0828i	−0.970265	+	1.31517i
$490$	−0.278702	−	2.65167i	−0.0125905	−	0.119790i
$491$	−19.0103	−	4.04076i	−0.857922	−	0.182357i	−0.242109	−	0.970249i	$-0.577839\pi$
$491$	−19.0103	−	4.04076i	−0.857922	−	0.182357i	−0.615813	+	0.787892i	$0.711172\pi$
$492$	6.95776	−	3.94966i	0.313680	−	0.178064i
$493$	2.94699	−	28.0388i	0.132726	−	1.26280i
$494$	−6.98978			−0.314485
$495$	−9.28095	+	3.58664i	−0.417148	+	0.161207i
$496$	−10.5484			−0.473638
$497$	1.73377	−	16.4957i	0.0777703	−	0.739935i
$498$	−11.6474	−	6.83844i	−0.521934	−	0.306438i
$499$	−18.1664	−	3.86139i	−0.813240	−	0.172859i	−0.217524	−	0.976055i	$-0.569798\pi$
$499$	−18.1664	−	3.86139i	−0.813240	−	0.172859i	−0.595716	+	0.803195i	$0.703131\pi$
$500$	−0.104528	−	0.994522i	−0.00467465	−	0.0444764i
$501$	0.434859	+	0.996209i	0.0194281	+	0.0445073i
$502$	−9.47950	+	10.5281i	−0.423091	+	0.469890i
$503$	−7.54853	+	23.2320i	−0.336572	+	1.03586i	0.629370	+	0.777106i	$0.283313\pi$
$503$	−7.54853	+	23.2320i	−0.336572	+	1.03586i	−0.965942	+	0.258758i	$0.916687\pi$
$504$	4.54523	+	8.14478i	0.202461	+	0.362797i
$505$	2.16980			0.0965547
$506$	5.36904	−	14.7235i	0.238683	−	0.654538i
$507$	8.83043	+	8.06839i	0.392173	+	0.358330i
$508$	12.9074	−	5.74672i	0.572671	−	0.254970i
$509$	3.25539	+	3.61548i	0.144293	+	0.160253i	0.810959	−	0.585103i	$-0.198946\pi$
$509$	3.25539	+	3.61548i	0.144293	+	0.160253i	−0.666666	+	0.745356i	$0.732279\pi$
$510$	−4.36160	−	6.09628i	−0.193135	−	0.269948i
$511$	−37.8022	−	16.8306i	−1.67227	−	0.744542i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−7.68522	−	2.68442i	−0.339311	−	0.118520i
$514$	3.78406	−	11.6461i	0.166908	−	0.513689i
$515$	1.27334	−	12.1151i	0.0561102	−	0.533853i
$516$	9.96691	−	3.15824i	0.438769	−	0.139034i
$517$	8.73177	+	16.4462i	0.384023	+	0.723302i
$518$	−9.35066	+	16.1958i	−0.410844	+	0.711603i
$519$	4.99953	+	24.3948i	0.219455	+	1.07081i
$520$	4.36411	−	0.927620i	0.191379	−	0.0406788i
$521$	2.70061	+	8.31163i	0.118316	+	0.364139i	0.992624	−	0.121232i	$-0.0386845\pi$
$521$	2.70061	+	8.31163i	0.118316	+	0.364139i	−0.874308	+	0.485371i	$0.838684\pi$
$522$	12.8639	+	14.7130i	0.563037	+	0.643970i
$523$	16.9782	−	12.3354i	0.742403	−	0.539387i	−0.151060	−	0.988525i	$-0.548269\pi$
$523$	16.9782	−	12.3354i	0.742403	−	0.539387i	0.893463	+	0.449137i	$0.148269\pi$
$524$	10.2069	−	11.3359i	0.445890	−	0.495211i
$525$	−4.64383	−	2.72648i	−0.202673	−	0.118993i
$526$	0.883406	−	0.393318i	0.0385183	−	0.0171495i
$527$	22.8254	−	39.5348i	0.994291	−	1.72216i
$528$	−5.68216	−	0.844426i	−0.247284	−	0.0367489i
$529$	0.336033	+	0.582027i	0.0146101	+	0.0253055i
$530$	5.80345	+	4.21645i	0.252086	+	0.183151i
$531$	31.1118	+	7.08904i	1.35014	+	0.307638i
$532$	1.50517	+	4.63242i	0.0652572	+	0.200841i
$533$	−18.8272	−	8.38240i	−0.815496	−	0.363082i
$534$	−14.4833	−	1.62918i	−0.626754	−	0.0705017i
$535$	6.07328	+	1.29092i	0.262571	+	0.0558112i
$536$	−1.48868	−	1.65334i	−0.0643010	−	0.0714135i
$537$	−6.03057	−	2.00821i	−0.260238	−	0.0866609i
$538$	5.66378	+	9.80996i	0.244183	+	0.422938i
$539$	8.20115	−	3.30768i	0.353248	−	0.142472i
$540$	5.15456	+	0.656121i	0.221817	+	0.0282350i
$541$	17.2586	+	12.5391i	0.742006	+	0.539099i	0.893339	−	0.449384i	$-0.148357\pi$
$541$	17.2586	+	12.5391i	0.742006	+	0.539099i	−0.151333	+	0.988483i	$0.548357\pi$
$542$	13.9320	−	2.96135i	0.598432	−	0.127201i
$543$	−13.5793	−	18.9800i	−0.582745	−	0.814512i
$544$	−0.452373	−	4.30404i	−0.0193953	−	0.184534i
$545$	−0.778680	−	7.40864i	−0.0333550	−	0.317351i
$546$	9.93214	−	21.8770i	0.425056	−	0.936248i
$547$	25.3941	−	5.39769i	1.08578	−	0.230789i	0.369938	−	0.929056i	$-0.379379\pi$
$547$	25.3941	−	5.39769i	1.08578	−	0.230789i	0.715837	+	0.698268i	$0.246045\pi$
$548$	−4.87770	−	3.54386i	−0.208365	−	0.151386i
$549$	25.5575	+	11.8288i	1.09077	+	0.504840i
$550$	3.07588	−	1.24056i	0.131156	−	0.0528977i
$551$	5.10299	+	8.83864i	0.217395	+	0.376539i
$552$	−6.12196	+	5.43189i	−0.260568	+	0.231196i
$553$	−30.9874	−	34.4150i	−1.31772	−	1.46347i
$554$	27.0740	+	5.75475i	1.15026	+	0.244496i
$555$	4.16801	+	9.54839i	0.176922	+	0.405307i
$556$	−5.01567	−	2.23312i	−0.212712	−	0.0947055i
$557$	8.58454	+	26.4205i	0.363739	+	1.11947i	0.950767	+	0.309906i	$0.100298\pi$
$557$	8.58454	+	26.4205i	0.363739	+	1.11947i	−0.587028	+	0.809566i	$0.699702\pi$
$558$	9.33871	+	30.2359i	0.395339	+	1.27999i
$559$	−21.7884	−	15.8302i	−0.921552	−	0.669547i
$560$	−1.55453	−	2.69253i	−0.0656910	−	0.113780i
$561$	15.4603	−	19.4692i	0.652736	−	0.821989i
$562$	9.70212	−	16.8046i	0.409259	−	0.708858i
$563$	−31.3724	+	13.9679i	−1.32219	+	0.588676i	−0.941807	−	0.336155i	$-0.890874\pi$
$563$	−31.3724	+	13.9679i	−1.32219	+	0.588676i	−0.380380	+	0.924830i	$0.624207\pi$
$564$	0.0709499	−	9.72395i	0.00298753	−	0.409452i
$565$	2.42324	−	2.69128i	0.101946	−	0.113223i
$566$	4.00985	−	2.91333i	0.168547	−	0.122456i
$567$	19.3222	−	20.2391i	0.811454	−	0.849964i
$568$	−1.64858	−	5.07381i	−0.0691729	−	0.212892i
$569$	−17.8121	+	3.78608i	−0.746722	+	0.158721i	−0.565531	−	0.824727i	$-0.691329\pi$
$569$	−17.8121	+	3.78608i	−0.746722	+	0.158721i	−0.181191	+	0.983448i	$0.557995\pi$
$570$	2.57452	+	0.857331i	0.107835	+	0.0359096i
$571$	−14.4229	+	24.9812i	−0.603579	+	1.04543i	0.388695	+	0.921367i	$0.372926\pi$
$571$	−14.4229	+	24.9812i	−0.603579	+	1.04543i	−0.992274	+	0.124064i	$0.960407\pi$
$572$	6.93905	+	13.0696i	0.290136	+	0.546468i
$573$	−30.1850	−	27.5801i	−1.26100	−	1.15218i
$574$	−1.50116	+	14.2826i	−0.0626574	+	0.596145i
$575$	1.46018	−	4.49397i	0.0608937	−	0.187412i
$576$	2.40106	+	1.79858i	0.100044	+	0.0749410i
$577$	−12.4115	+	9.01750i	−0.516699	+	0.375403i	−0.815359	−	0.578956i	$-0.803460\pi$
$577$	−12.4115	+	9.01750i	−0.516699	+	0.375403i	0.298660	+	0.954360i	$0.403460\pi$
$578$	1.57988	+	0.703407i	0.0657143	+	0.0292579i
$579$	16.2984	−	1.59289i	0.677337	−	0.0661981i
$580$	−4.35907	−	4.84123i	−0.181000	−	0.201021i
$581$	22.1485	−	9.86113i	0.918873	−	0.409109i
$582$	−3.78656	+	17.1965i	−0.156958	+	0.712816i
$583$	−8.15082	+	22.3519i	−0.337572	+	0.925722i
$584$	−13.3093			−0.550745
$585$	−6.52255	−	11.6880i	−0.269674	−	0.483240i
$586$	−5.67710	+	17.4723i	−0.234519	+	0.721775i
$587$	−8.74039	+	9.70718i	−0.360754	+	0.400658i	−0.896011	−	0.444031i	$-0.853548\pi$
$587$	−8.74039	+	9.70718i	−0.360754	+	0.400658i	0.535257	+	0.844689i	$0.320215\pi$
$588$	−4.58919	−	0.516224i	−0.189255	−	0.0212887i
$589$	1.72740	+	16.4352i	0.0711765	+	0.677199i
$590$	−10.4040	−	2.21143i	−0.428325	−	0.0910432i
$591$	−0.0133849	+	1.83445i	−0.000550580	+	0.0754590i
$592$	−0.628749	+	5.98215i	−0.0258414	+	0.245865i
$593$	12.2739			0.504030			0.252015	−	0.967723i	$-0.418907\pi$
$593$	12.2739			0.504030			0.252015	+	0.967723i	$0.418907\pi$
$594$	2.61007	+	17.0349i	0.107092	+	0.698950i
$595$	13.4552			0.551611
$596$	−0.403159	+	3.83580i	−0.0165140	+	0.157121i
$597$	0.300873	−	41.2358i	0.0123139	−	1.68767i
$598$	20.6215	+	4.38323i	0.843275	+	0.179244i
$599$	−0.0692980	−	0.659327i	−0.00283144	−	0.0269394i	0.993015	−	0.117989i	$-0.0376446\pi$
$599$	−0.0692980	−	0.659327i	−0.00283144	−	0.0269394i	−0.995846	+	0.0910492i	$0.970978\pi$
$600$	−1.72120	−	0.193612i	−0.0702675	−	0.00790418i
$601$	−13.5245	+	15.0205i	−0.551675	+	0.612698i	−0.952901	−	0.303282i	$-0.901918\pi$
$601$	−13.5245	+	15.0205i	−0.551675	+	0.612698i	0.401226	+	0.915979i	$0.368584\pi$
$602$	−5.79948	+	17.8490i	−0.236369	+	0.727469i
$603$	−3.42118	+	5.73087i	−0.139321	+	0.233379i
$604$	7.23501			0.294388
$605$	6.76174	+	8.67634i	0.274904	+	0.352743i
$606$	0.808174	−	3.67027i	0.0328298	−	0.149095i
$607$	40.4001	−	17.9873i	1.63979	−	0.730081i	0.640506	−	0.767953i	$-0.278725\pi$
$607$	40.4001	−	17.9873i	1.63979	−	0.730081i	0.999283	+	0.0378726i	$0.0120581\pi$
$608$	1.04829	+	1.16425i	0.0425139	+	0.0472165i
$609$	−34.9147	+	3.41232i	−1.41482	+	0.138274i
$610$	−8.57580	−	3.81819i	−0.347224	−	0.154594i
$611$	−20.2648	+	14.7232i	−0.819826	+	0.595638i
$612$	−11.9366	+	5.10712i	−0.482507	+	0.206443i
$613$	8.95604	−	27.5639i	0.361731	−	1.11329i	−0.590272	−	0.807205i	$-0.700979\pi$
$613$	8.95604	−	27.5639i	0.361731	−	1.11329i	0.952003	−	0.306089i	$-0.0990206\pi$
$614$	−2.42497	+	23.0720i	−0.0978638	+	0.931112i
$615$	5.90642	+	5.39671i	0.238170	+	0.217616i
$616$	7.16754	−	7.41319i	0.288789	−	0.298686i
$617$	10.9925	−	19.0396i	0.442541	−	0.766504i	−0.555336	−	0.831626i	$-0.687410\pi$
$617$	10.9925	−	19.0396i	0.442541	−	0.766504i	0.997877	+	0.0651220i	$0.0207437\pi$
$618$	−20.0187	−	6.66633i	−0.805269	−	0.268159i
$619$	−25.5819	+	5.43760i	−1.02822	+	0.218556i	−0.690989	−	0.722865i	$-0.742825\pi$
$619$	−25.5819	+	5.43760i	−1.02822	+	0.218556i	−0.337234	+	0.941421i	$0.609491\pi$
$620$	−3.25964	−	10.0321i	−0.130910	−	0.402900i
$621$	20.9898	+	12.7390i	0.842292	+	0.511199i
$622$	24.9318	−	18.1140i	0.999673	−	0.726305i
$623$	17.5057	−	19.4420i	0.701349	−	0.778927i
$624$	0.0563832	−	7.72752i	0.00225713	−	0.309348i
$625$	0.913545	−	0.406737i	0.0365418	−	0.0162695i
$626$	−10.4141	+	18.0378i	−0.416233	+	0.720936i
$627$	−0.385165	+	8.99148i	−0.0153820	+	0.359085i
$628$	8.19473	+	14.1937i	0.327005	+	0.566390i
$629$	−21.0602	−	15.3011i	−0.839724	−	0.610095i
$630$	−6.34159	+	6.83965i	−0.252655	+	0.272498i
$631$	9.68753	+	29.8151i	0.385654	+	1.18692i	0.936004	+	0.351988i	$0.114494\pi$
$631$	9.68753	+	29.8151i	0.385654	+	1.18692i	−0.550350	+	0.834934i	$0.685506\pi$
$632$	−13.6074	−	6.05840i	−0.541273	−	0.240990i
$633$	8.30939	+	19.0358i	0.330268	+	0.756604i
$634$	−22.1425	−	4.70654i	−0.879393	−	0.186921i
$635$	9.45405	+	10.4998i	0.375173	+	0.416671i
$636$	9.29384	−	8.24622i	0.368525	−	0.326984i
$637$	5.94795	+	10.3021i	0.235666	+	0.408186i
$638$	11.4607	−	18.3162i	0.453733	−	0.725144i
$639$	−13.0840	+	9.21742i	−0.517596	+	0.364635i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−3.08499	+	0.655735i	−0.121850	+	0.0259000i	−0.268433	−	0.963298i	$-0.586506\pi$
$641$	−3.08499	+	0.655735i	−0.121850	+	0.0259000i	0.146583	+	0.989198i	$0.453172\pi$
$642$	4.44571	−	9.79231i	0.175458	−	0.386472i
$643$	−2.62079	−	24.9352i	−0.103354	−	0.983348i	−0.916160	−	0.400813i	$-0.868728\pi$
$643$	−2.62079	−	24.9352i	−0.103354	−	0.983348i	0.812806	−	0.582535i	$-0.197939\pi$
$644$	−1.53564	−	14.6106i	−0.0605126	−	0.575739i
$645$	6.08361	+	8.50315i	0.239542	+	0.334811i
$646$	−6.63191	+	1.40966i	−0.260929	+	0.0554622i
$647$	−5.66619	−	4.11673i	−0.222761	−	0.161845i	0.470808	−	0.882236i	$-0.343963\pi$
$647$	−5.66619	−	4.11673i	−0.222761	−	0.161845i	−0.693569	+	0.720391i	$0.743963\pi$
$648$	3.02974	−	8.47471i	0.119020	−	0.332918i
$649$	−2.43941	−	35.1925i	−0.0957554	−	1.38143i
$650$	2.23080	+	3.86386i	0.0874993	+	0.151553i
$651$	−53.8941	−	17.9470i	−2.11228	−	0.703400i
$652$	−13.9620	−	15.5064i	−0.546795	−	0.607277i
$653$	−42.6267	−	9.06059i	−1.66811	−	0.354568i	−0.725440	−	0.688286i	$-0.758363\pi$
$653$	−42.6267	−	9.06059i	−1.66811	−	0.354568i	−0.942673	+	0.333718i	$0.891697\pi$
$654$	−12.8220	−	1.44230i	−0.501378	−	0.0563985i
$655$	13.9352	+	6.20434i	0.544492	+	0.242423i
$656$	1.42740	+	4.39309i	0.0557307	+	0.171521i
$657$	11.7830	+	38.1498i	0.459699	+	1.48837i
$658$	14.1215	+	10.2599i	0.550513	+	0.399971i
$659$	−13.3765	−	23.1687i	−0.521073	−	0.902525i	−0.999700	−	0.0245068i	$-0.992198\pi$
$659$	−13.3765	−	23.1687i	−0.521073	−	0.902525i	0.478626	−	0.878019i	$-0.341135\pi$
$660$	−0.952788	−	5.66500i	−0.0370872	−	0.220510i
$661$	18.6254	−	32.2601i	0.724443	−	1.25477i	−0.234759	−	0.972054i	$-0.575430\pi$
$661$	18.6254	−	32.2601i	0.724443	−	1.25477i	0.959203	−	0.282719i	$-0.0912365\pi$
$662$	−25.4754	+	11.3424i	−0.990129	+	0.440834i
$663$	28.8403	+	16.9327i	1.12006	+	0.657612i
$664$	5.21789	−	5.79505i	0.202493	−	0.224892i
$665$	−3.94058	+	2.86300i	−0.152809	+	0.111022i
$666$	17.7038	−	3.49386i	0.686009	−	0.135384i
$667$	−9.51238	−	29.2761i	−0.368321	−	1.13358i
$668$	−0.613857	+	0.130479i	−0.0237508	+	0.00504840i
$669$	−9.47014	−	46.2088i	−0.366137	−	1.78654i
$670$	1.11240	−	1.92673i	0.0429756	−	0.0744359i
$671$	4.35181	−	30.8288i	0.168000	−	1.19013i
$672$	−5.13350	+	1.62666i	−0.198029	+	0.0627499i
$673$	−3.74616	+	35.6423i	−0.144404	+	1.37391i	0.646941	+	0.762540i	$0.276048\pi$
$673$	−3.74616	+	35.6423i	−0.144404	+	1.37391i	−0.791345	+	0.611370i	$0.790619\pi$
$674$	−3.03037	+	9.32651i	−0.116725	+	0.359244i
$675$	0.968839	+	5.10503i	0.0372906	+	0.196493i
$676$	−5.58701	+	4.05920i	−0.214885	+	0.156123i
$677$	−31.3048	−	13.9378i	−1.20314	−	0.535673i	−0.295469	−	0.955352i	$-0.595476\pi$
$677$	−31.3048	−	13.9378i	−1.20314	−	0.535673i	−0.907673	+	0.419679i	$0.862143\pi$
$678$	−3.64980	−	5.10139i	−0.140170	−	0.195918i
$679$	−21.1495	−	23.4889i	−0.811643	−	0.901421i
$680$	3.95359	−	1.76025i	0.151613	−	0.0675026i
$681$	18.9656	+	17.3289i	0.726764	+	0.664046i
$682$	29.0159	−	19.5458i	1.11108	−	0.748448i
$683$	16.8617			0.645194			0.322597	−	0.946536i	$-0.395444\pi$
$683$	16.8617			0.645194			0.322597	+	0.946536i	$0.395444\pi$
$684$	2.40912	−	4.03555i	0.0921150	−	0.154303i
$685$	1.86312	−	5.73408i	0.0711860	−	0.219088i
$686$	−9.01574	+	10.0130i	−0.344223	+	0.382298i
$687$	8.37531	+	19.1868i	0.319538	+	0.732022i
$688$	0.630974	+	6.00332i	0.0240557	+	0.228874i
$689$	−31.3058	−	6.65425i	−1.19265	−	0.253507i
$690$	−7.05782	−	4.14379i	−0.268687	−	0.157751i
$691$	0.203536	−	1.93652i	0.00774289	−	0.0736687i	−0.989968	−	0.141291i	$-0.954875\pi$
$691$	0.203536	−	1.93652i	0.00774289	−	0.0736687i	0.997711	+	0.0676224i	$0.0215413\pi$
$692$	−14.3771			−0.546536
$693$	−27.5947	−	13.9820i	−1.04824	−	0.531131i
$694$	23.1761			0.879754
$695$	0.573897	−	5.46026i	0.0217691	−	0.207120i
$696$	−9.81269	+	5.57030i	−0.371949	+	0.211142i
$697$	−19.5538	−	4.15628i	−0.740652	−	0.157430i
$698$	2.12191	+	20.1886i	0.0803155	+	0.764151i
$699$	−14.1240	+	19.1448i	−0.534220	+	0.724121i
$700$	2.08037	−	2.31049i	0.0786306	−	0.0873281i
$701$	3.59157	−	11.0537i	0.135652	−	0.417493i	−0.860039	−	0.510228i	$-0.829561\pi$
$701$	3.59157	−	11.0537i	0.135652	−	0.417493i	0.995691	+	0.0927352i	$0.0295610\pi$
$702$	−22.2000	+	6.67970i	−0.837886	+	0.252109i
$703$	9.42356			0.355416
$704$	1.13625	−	3.11592i	0.0428239	−	0.117436i
$705$	9.26995	−	2.93739i	0.349126	−	0.110628i
$706$	−29.1312	+	12.9701i	−1.09637	+	0.488134i
$707$	4.51398	+	5.01328i	0.169766	+	0.188544i
$708$	−7.61582	+	16.7749i	−0.286220	+	0.630441i
$709$	8.07924	+	3.59711i	0.303422	+	0.135092i	0.552800	−	0.833314i	$-0.313559\pi$
$709$	8.07924	+	3.59711i	0.303422	+	0.135092i	−0.249378	+	0.968406i	$0.580226\pi$
$710$	4.31604	−	3.13579i	0.161978	−	0.117684i
$711$	−5.31888	+	44.3677i	−0.199474	+	1.66392i
$712$	2.60028	−	8.00284i	0.0974496	−	0.299919i
$713$	5.21010	−	49.5708i	0.195120	−	1.85644i
$714$	5.01161	−	22.7599i	0.187555	−	0.851769i
$715$	−10.2857	+	10.6382i	−0.384662	+	0.397845i
$716$	1.83487	−	3.17808i	0.0685721	−	0.118770i
$717$	2.06462	−	1.83189i	0.0771047	−	0.0684133i
$718$	36.7716	−	7.81604i	1.37230	−	0.291692i
$719$	14.8863	+	45.8154i	0.555166	+	1.70863i	0.695503	+	0.718523i	$0.255181\pi$
$719$	14.8863	+	45.8154i	0.555166	+	1.70863i	−0.140337	+	0.990104i	$0.544819\pi$
$720$	−0.968586	+	2.83934i	−0.0360971	+	0.105816i
$721$	30.6407	−	22.2617i	1.14112	−	0.829071i
$722$	−11.0712	+	12.2958i	−0.412026	+	0.457602i
$723$	−18.7283	+	10.6313i	−0.696512	+	0.395384i
$724$	12.3090	−	5.48034i	0.457462	−	0.203675i
$725$	3.25726	−	5.64174i	0.120972	−	0.209529i
$726$	17.1948	−	8.20604i	0.638159	−	0.304555i
$727$	−13.3753	−	23.1667i	−0.496063	−	0.859207i	0.503926	−	0.863747i	$-0.331888\pi$
$727$	−13.3753	−	23.1667i	−0.496063	−	0.859207i	−0.999990	+	0.00453958i	$0.998555\pi$
$728$	11.2222	+	8.15342i	0.415923	+	0.302186i
$729$	−26.9741	−	1.18162i	−0.999042	−	0.0437637i
$730$	−4.11281	−	12.6579i	−0.152222	−	0.468491i
$731$	−23.8654	−	10.6256i	−0.882694	−	0.393001i
$732$	−9.65277	+	13.0841i	−0.356777	+	0.483601i
$733$	−24.1511	−	5.13348i	−0.892041	−	0.189609i	−0.260982	−	0.965344i	$-0.584046\pi$
$733$	−24.1511	−	5.13348i	−0.892041	−	0.189609i	−0.631060	+	0.775734i	$0.717380\pi$
$734$	−5.26532	−	5.84773i	−0.194347	−	0.215844i
$735$	−0.927180	−	4.52410i	−0.0341995	−	0.166874i
$736$	−2.36262	−	4.09218i	−0.0870874	−	0.150840i
$737$	7.15853	+	1.78944i	0.263688	+	0.0659150i
$738$	11.3286	−	7.98078i	0.417013	−	0.293777i
$739$	31.4521	+	22.8513i	1.15698	+	0.840597i	0.989394	−	0.145260i	$-0.0464018\pi$
$739$	31.4521	+	22.8513i	1.15698	+	0.840597i	0.167589	+	0.985857i	$0.446402\pi$
$740$	−5.88365	+	1.25061i	−0.216287	+	0.0459733i
$741$	−12.0492	+	1.17761i	−0.442640	+	0.0432605i
$742$	2.33127	+	22.1806i	0.0855837	+	0.814275i
$743$	4.58407	+	43.6145i	0.168173	+	1.60006i	0.674870	+	0.737936i	$0.264200\pi$
$743$	4.58407	+	43.6145i	0.168173	+	1.60006i	−0.506697	+	0.862124i	$0.669134\pi$
$744$	−18.1838	+	1.77715i	−0.666649	+	0.0651535i
$745$	−3.77265	+	0.801901i	−0.138219	+	0.0293794i
$746$	9.99012	+	7.25825i	0.365764	+	0.265743i
$747$	−21.2304	−	9.82605i	−0.776779	−	0.359516i
$748$	9.21958	+	11.0010i	0.337101	+	0.402238i
$749$	9.65204	+	16.7178i	0.352678	+	0.610856i
$750$	−0.347743	−	1.69678i	−0.0126978	−	0.0619578i
$751$	14.6211	+	16.2384i	0.533531	+	0.592546i	0.948298	−	0.317381i	$-0.102804\pi$
$751$	14.6211	+	16.2384i	0.533531	+	0.592546i	−0.414767	+	0.909928i	$0.636137\pi$
$752$	5.49159	+	1.16727i	0.200258	+	0.0425661i
$753$	−14.5674	+	19.7457i	−0.530866	+	0.719574i
$754$	26.5524	+	11.8219i	0.966982	+	0.430528i
$755$	2.23574	+	6.88090i	0.0813670	+	0.250422i
$756$	9.20744	+	13.2745i	0.334871	+	0.482789i
$757$	10.2670	+	7.45939i	0.373160	+	0.271116i	0.758520	−	0.651650i	$-0.225923\pi$
$757$	10.2670	+	7.45939i	0.373160	+	0.271116i	−0.385360	+	0.922766i	$0.625923\pi$
$758$	−12.1729	−	21.0840i	−0.442138	−	0.765806i
$759$	6.77481	−	26.2854i	0.245910	−	0.954101i
$760$	−0.783326	+	1.35676i	−0.0284142	+	0.0492148i
$761$	23.0654	−	10.2694i	0.836120	−	0.372265i	0.0564120	−	0.998408i	$-0.482034\pi$
$761$	23.0654	−	10.2694i	0.836120	−	0.372265i	0.779708	+	0.626143i	$0.215367\pi$
$762$	21.2820	−	12.0810i	0.770965	−	0.437648i
$763$	15.4976	−	17.2118i	0.561051	−	0.623111i
$764$	19.0980	−	13.8755i	0.690943	−	0.502000i
$765$	−8.54577	−	9.77417i	−0.308973	−	0.353386i
$766$	3.71660	+	11.4385i	0.134286	+	0.413291i
$767$	46.4184	−	9.86654i	1.67607	−	0.356260i
$768$	−1.29559	+	1.14955i	−0.0467504	+	0.0414807i
$769$	−2.89816	+	5.01977i	−0.104510	+	0.181017i	−0.913538	−	0.406753i	$-0.866661\pi$
$769$	−2.89816	+	5.01977i	−0.104510	+	0.181017i	0.809028	+	0.587771i	$0.199994\pi$
$770$	9.26526	+	4.52594i	0.333897	+	0.163103i
$771$	4.56101	−	20.7136i	0.164261	−	0.745981i
$772$	−0.988286	+	9.40291i	−0.0355692	+	0.338418i
$773$	−15.1460	+	46.6147i	−0.544764	+	1.67661i	0.176785	+	0.984250i	$0.443430\pi$
$773$	−15.1460	+	46.6147i	−0.544764	+	1.67661i	−0.721549	+	0.692363i	$0.756570\pi$
$774$	16.6493	−	7.12347i	0.598445	−	0.256048i
$775$	8.53385	−	6.20020i	0.306545	−	0.222718i
$776$	−9.28730	−	4.13497i	−0.333395	−	0.148437i
$777$	−13.3904	+	29.4943i	−0.480379	+	1.05810i
$778$	−21.8286	−	24.2432i	−0.782595	−	0.869160i
$779$	6.61099	−	2.94340i	0.236863	−	0.105458i
$780$	7.36673	−	2.33431i	0.263771	−	0.0835818i
$781$	13.9364	+	10.9019i	0.498683	+	0.390102i
$782$	20.4497			0.731278
$783$	24.6540	+	23.1955i	0.881063	+	0.828941i
$784$	0.823926	−	2.53578i	0.0294259	−	0.0905637i
$785$	−10.9667	+	12.1797i	−0.391418	+	0.434714i
$786$	15.6852	−	21.2608i	0.559472	−	0.758349i
$787$	3.16047	+	30.0699i	0.112659	+	1.07188i	0.894091	+	0.447886i	$0.147823\pi$
$787$	3.16047	+	30.0699i	0.112659	+	1.07188i	−0.781432	+	0.623991i	$0.785510\pi$
$788$	−1.03600	−	0.220209i	−0.0369060	−	0.00784461i
$789$	1.45658	−	0.826848i	0.0518558	−	0.0294366i
$790$	1.55697	−	14.8135i	0.0553944	−	0.527042i
$791$	11.2594			0.400338
$792$	−9.93739	−	0.498347i	−0.353110	−	0.0177080i
$793$	41.8828			1.48730
$794$	−1.38807	+	13.2066i	−0.0492607	+	0.468684i
$795$	10.7146	+	6.29074i	0.380007	+	0.223110i
$796$	23.2879	+	4.94999i	0.825417	+	0.175448i
$797$	5.65702	+	53.8230i	0.200382	+	1.90651i	0.383706	+	0.923455i	$0.374648\pi$
$797$	5.65702	+	53.8230i	0.200382	+	1.90651i	−0.183324	+	0.983053i	$0.558686\pi$
$798$	3.37511	+	7.73196i	0.119478	+	0.273709i
$799$	−16.2580	+	18.0563i	−0.575165	+	0.638786i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	−25.2414	−	0.368362i	−0.891860	−	0.0130154i
$802$	6.87943			0.242921
$803$	36.6105	−	24.6617i	1.29196	−	0.870293i
$804$	−2.84478	−	2.59929i	−0.100328	−	0.0916698i
$805$	13.4210	−	5.97540i	0.473027	−	0.210605i
$806$	31.4912	+	34.9745i	1.10923	+	1.23193i
$807$	11.4162	+	15.9566i	0.401869	+	0.561698i
$808$	1.98221	+	0.882536i	0.0697338	+	0.0310475i
$809$	−17.2202	+	12.5112i	−0.605431	+	0.439872i	−0.847803	−	0.530312i	$-0.822075\pi$
$809$	−17.2202	+	12.5112i	−0.605431	+	0.439872i	0.242371	+	0.970184i	$0.422075\pi$
$810$	8.99617	+	0.262629i	0.316093	+	0.00922784i
$811$	−3.81663	+	11.7464i	−0.134020	+	0.412471i	−0.995436	−	0.0954285i	$-0.969578\pi$
$811$	−3.81663	+	11.7464i	−0.134020	+	0.412471i	0.861416	+	0.507899i	$0.169578\pi$
$812$	2.11713	−	20.1431i	0.0742966	−	0.706885i
$813$	23.5176	−	7.45209i	0.824800	−	0.261356i
$814$	−9.35517	−	17.6203i	−0.327898	−	0.617592i
$815$	10.4330	−	18.0704i	0.365450	−	0.632979i
$816$	−1.50494	−	7.34325i	−0.0526835	−	0.257065i
$817$	9.25025	−	1.96620i	0.323625	−	0.0687887i
$818$	3.51541	+	10.8193i	0.122914	+	0.378289i
$819$	13.4357	−	39.3857i	0.469480	−	1.37625i
$820$	−3.73699	+	2.71508i	−0.130501	+	0.0948147i
$821$	24.5530	−	27.2689i	0.856906	−	0.951690i	−0.142367	−	0.989814i	$-0.545471\pi$
$821$	24.5530	−	27.2689i	0.856906	−	0.951690i	0.999273	+	0.0381237i	$0.0121381\pi$
$822$	−9.00542	−	5.28726i	−0.314100	−	0.184414i
$823$	−26.8516	+	11.9551i	−0.935987	+	0.416728i	−0.817306	−	0.576204i	$-0.804533\pi$
$823$	−26.8516	+	11.9551i	−0.935987	+	0.416728i	−0.118681	+	0.992932i	$0.537867\pi$
$824$	6.09089	−	10.5497i	0.212186	−	0.367517i
$825$	5.09331	−	2.65674i	0.177326	−	0.0924957i
$826$	−16.5346	−	28.6388i	−0.575313	−	0.996472i
$827$	−4.82486	−	3.50546i	−0.167777	−	0.121897i	0.500728	−	0.865604i	$-0.333066\pi$
$827$	−4.82486	−	3.50546i	−0.167777	−	0.121897i	−0.668505	+	0.743708i	$0.733066\pi$
$828$	−9.63813	+	10.3951i	−0.334948	+	0.361254i
$829$	9.36989	+	28.8376i	0.325430	+	1.00157i	0.971246	+	0.238077i	$0.0765171\pi$
$829$	9.36989	+	28.8376i	0.325430	+	1.00157i	−0.645816	+	0.763493i	$0.723483\pi$
$830$	7.12384	+	3.17174i	0.247272	+	0.110093i
$831$	47.6407	+	5.35895i	1.65264	+	0.185900i
$832$	4.36411	+	0.927620i	0.151298	+	0.0321594i
$833$	7.72109	+	8.57514i	0.267520	+	0.297111i
$834$	−9.02244	−	3.00452i	−0.312421	−	0.104038i
$835$	−0.313785	−	0.543492i	−0.0108590	−	0.0188083i
$836$	−5.04089	−	1.26009i	−0.174343	−	0.0435810i
$837$	21.1924	+	50.5484i	0.732517	+	1.74721i
$838$	−17.3993	−	12.6413i	−0.601048	−	0.436687i
$839$	−0.851155	+	0.180919i	−0.0293852	+	0.00624601i	−0.222581	−	0.974914i	$-0.571448\pi$
$839$	−0.851155	+	0.180919i	−0.0293852	+	0.00624601i	0.193196	+	0.981160i	$0.438115\pi$
$840$	−3.13339	−	4.37958i	−0.108112	−	0.151110i
$841$	−1.40476	−	13.3654i	−0.0484400	−	0.460876i
$842$	3.20189	+	30.4640i	0.110344	+	1.04986i
$843$	13.8937	−	30.6029i	0.478525	−	1.05402i
$844$	−11.7297	+	2.49323i	−0.403753	+	0.0858204i
$845$	−5.58701	−	4.05920i	−0.192199	−	0.139641i
$846$	−1.51594	−	16.7745i	−0.0521191	−	0.576718i
$847$	−5.97964	+	33.6729i	−0.205463	+	1.15701i
$848$	3.58673	+	6.21240i	0.123169	+	0.213335i
$849$	6.42151	−	5.69766i	0.220386	−	0.195543i
$850$	2.89583	+	3.21614i	0.0993261	+	0.110313i
$851$	−27.8017	−	5.90943i	−0.953030	−	0.202573i
$852$	−3.69670	−	8.46868i	−0.126647	−	0.290132i
$853$	−1.49893	−	0.667368i	−0.0513225	−	0.0228502i	0.380915	−	0.924610i	$-0.375609\pi$
$853$	−1.49893	−	0.667368i	−0.0513225	−	0.0228502i	−0.432237	+	0.901760i	$0.642276\pi$
$854$	−9.01896	−	27.7575i	−0.308622	−	0.949842i
$855$	4.58250	+	1.04415i	0.156718	+	0.0357093i
$856$	5.02316	+	3.64954i	0.171688	+	0.124739i
$857$	21.3794	+	37.0302i	0.730306	+	1.26493i	0.956752	+	0.290904i	$0.0939560\pi$
$857$	21.3794	+	37.0302i	0.730306	+	1.26493i	−0.226446	+	0.974024i	$0.572711\pi$
$858$	14.1637	+	21.3608i	0.483541	+	0.729247i
$859$	29.1263	−	50.4482i	0.993775	−	1.72127i	0.400411	−	0.916336i	$-0.368867\pi$
$859$	29.1263	−	50.4482i	0.993775	−	1.72127i	0.593364	−	0.804934i	$-0.297799\pi$
$860$	−5.51451	+	2.45522i	−0.188043	+	0.0837223i
$861$	−0.181490	+	24.8738i	−0.00618515	+	0.847698i
$862$	6.14152	−	6.82084i	0.209181	−	0.232319i
$863$	3.69194	−	2.68235i	0.125675	−	0.0913084i	−0.523172	−	0.852227i	$-0.675251\pi$
$863$	3.69194	−	2.68235i	0.125675	−	0.0913084i	0.648847	+	0.760919i	$0.275251\pi$
$864$	4.44206	+	2.69595i	0.151122	+	0.0917179i
$865$	−4.44277	−	13.6734i	−0.151059	−	0.464911i
$866$	−1.04549	+	0.222227i	−0.0355273	+	0.00755156i
$867$	2.84196	+	0.946389i	0.0965181	+	0.0321410i
$868$	16.3978	−	28.4019i	0.556579	−	0.964024i
$869$	48.6563	−	8.54894i	1.65055	−	0.290003i
$870$	−8.32995	−	7.61111i	−0.282412	−	0.258041i
$871$	−1.03756	+	9.87177i	−0.0351565	+	0.334492i
$872$	2.30201	−	7.08485i	0.0779558	−	0.239923i
$873$	−3.63024	+	30.2818i	−0.122865	+	1.02488i
$874$	−5.98900	+	4.35126i	−0.202581	+	0.147184i
$875$	2.84027	+	1.26457i	0.0960187	+	0.0427503i
$876$	−22.9432	+	2.24230i	−0.775177	+	0.0757603i
$877$	10.1444	+	11.2665i	0.342553	+	0.380444i	0.889663	−	0.456617i	$-0.150939\pi$
$877$	10.1444	+	11.2665i	0.342553	+	0.380444i	−0.547111	+	0.837060i	$0.684272\pi$
$878$	−8.61588	+	3.83604i	−0.290772	+	0.129460i
$879$	−6.84274	+	31.0759i	−0.230800	+	1.04816i
$880$	3.31453	+	0.117762i	0.111733	+	0.00396977i
$881$	−28.0475			−0.944946			−0.472473	−	0.881345i	$-0.656639\pi$
$881$	−28.0475			−0.944946			−0.472473	+	0.881345i	$0.656639\pi$
$882$	−7.99799	−	0.116719i	−0.269306	−	0.00393015i
$883$	4.27206	−	13.1480i	0.143766	−	0.442467i	−0.853084	−	0.521773i	$-0.825271\pi$
$883$	4.27206	−	13.1480i	0.143766	−	0.442467i	0.996850	+	0.0793067i	$0.0252706\pi$
$884$	−12.9200	+	14.3492i	−0.434548	+	0.482615i
$885$	−18.3073	−	2.05934i	−0.615394	−	0.0692238i
$886$	1.60569	+	15.2771i	0.0539442	+	0.513244i
$887$	−30.9304	−	6.57446i	−1.03854	−	0.220749i	−0.343075	−	0.939308i	$-0.611469\pi$
$887$	−30.9304	−	6.57446i	−1.03854	−	0.220749i	−0.695466	+	0.718559i	$0.744802\pi$
$888$	−0.0760153	+	10.4182i	−0.00255091	+	0.349611i
$889$	−4.59168	+	43.6869i	−0.154000	+	1.46521i
$890$	8.41468			0.282061
$891$	7.36930	+	28.9257i	0.246881	+	0.969046i
$892$	27.2332			0.911834
$893$	0.919391	−	8.74742i	0.0307663	−	0.292721i
$894$	−0.0487416	+	6.68022i	−0.00163016	+	0.223420i
$895$	3.58954	+	0.762980i	0.119985	+	0.0255036i
$896$	−0.324986	−	3.09203i	−0.0108570	−	0.103298i
$897$	36.2866	+	4.08176i	1.21157	+	0.136286i
$898$	11.7523	−	13.0522i	0.392178	−	0.435558i
$899$	21.2350	−	65.3546i	0.708227	−	2.17970i
$900$	−2.99968	−	0.0437761i	−0.0999894	−	0.00145920i
$901$	−31.0449			−1.03426
$902$	−12.0666	−	9.43930i	−0.401775	−	0.314294i
$903$	−6.99025	+	31.7458i	−0.232621	+	1.05643i
$904$	3.30838	−	1.47299i	0.110035	−	0.0489908i
$905$	9.01582	+	10.0131i	0.299696	+	0.332846i
$906$	12.4720	−	1.21892i	0.414354	−	0.0404960i
$907$	−37.0163	−	16.4807i	−1.22911	−	0.547233i	−0.313606	−	0.949553i	$-0.601537\pi$
$907$	−37.0163	−	16.4807i	−1.22911	−	0.547233i	−0.915499	+	0.402320i	$0.868204\pi$
$908$	−11.9995	+	8.71818i	−0.398219	+	0.289323i
$909$	0.774809	−	6.46311i	0.0256988	−	0.214368i
$910$	−4.28650	+	13.1925i	−0.142096	+	0.437327i
$911$	4.76049	−	45.2931i	0.157722	−	1.50063i	−0.573905	−	0.818922i	$-0.694572\pi$
$911$	4.76049	−	45.2931i	0.157722	−	1.50063i	0.731627	−	0.681705i	$-0.238761\pi$
$912$	2.00324	+	1.83036i	0.0663338	+	0.0606094i
$913$	−3.61500	+	25.6092i	−0.119639	+	0.847540i
$914$	−3.08607	+	5.34523i	−0.102078	+	0.176805i
$915$	−15.4266	−	5.13713i	−0.509986	−	0.169828i
$916$	−11.8228	+	2.51301i	−0.390635	+	0.0830321i
$917$	14.6553	+	45.1043i	0.483960	+	1.48948i
$918$	−19.7163	+	10.8149i	−0.650735	+	0.356944i
$919$	−40.6208	+	29.5127i	−1.33996	+	0.973535i	−0.340510	+	0.940241i	$0.610600\pi$
$919$	−40.6208	+	29.5127i	−1.33996	+	0.973535i	−0.999446	+	0.0332936i	$0.989400\pi$
$920$	3.16181	−	3.51154i	0.104242	−	0.115772i
$921$	−0.293177	+	40.1810i	−0.00966051	+	1.32401i
$922$	−2.72621	+	1.21379i	−0.0897829	+	0.0399739i
$923$	−11.9012	+	20.6134i	−0.391731	+	0.678498i
$924$	11.1067	−	13.9867i	0.365385	−	0.460128i
$925$	−3.00755	−	5.20923i	−0.0988876	−	0.171278i
$926$	−10.4743	−	7.60999i	−0.344205	−	0.250080i
$927$	−35.6321	−	8.11901i	−1.17031	−	0.266663i
$928$	−2.01310	−	6.19568i	−0.0660832	−	0.203383i
$929$	32.9079	+	14.6515i	1.07967	+	0.480701i	0.867962	−	0.496631i	$-0.165430\pi$
$929$	32.9079	+	14.6515i	1.07967	+	0.480701i	0.211711	+	0.977332i	$0.432096\pi$
$930$	−7.30926	−	16.7446i	−0.239680	−	0.549077i
$931$	−4.08585	−	0.868475i	−0.133908	−	0.0284631i
$932$	−9.19099	−	10.2076i	−0.301061	−	0.334362i
$933$	39.9266	−	35.4260i	1.30714	−	1.15979i
$934$	−7.66222	−	13.2713i	−0.250715	−	0.434252i
$935$	−7.61360	+	12.1678i	−0.248991	+	0.397931i
$936$	−1.20470	−	13.3305i	−0.0393770	−	0.435721i
$937$	−25.1040	−	18.2391i	−0.820110	−	0.595845i	0.0966337	−	0.995320i	$-0.469192\pi$
$937$	−25.1040	−	18.2391i	−0.820110	−	0.595845i	−0.916744	+	0.399475i	$0.869192\pi$
$938$	6.76587	−	1.43813i	0.220913	−	0.0469566i
$939$	−14.9134	+	32.8488i	−0.486679	+	1.07198i
$940$	0.586851	+	5.58352i	0.0191410	+	0.182114i
$941$	−6.20071	−	58.9958i	−0.202137	−	1.92321i	−0.354823	−	0.934933i	$-0.615459\pi$
$941$	−6.20071	−	58.9958i	−0.202137	−	1.92321i	0.152686	−	0.988275i	$-0.451208\pi$
$942$	16.5177	+	23.0870i	0.538175	+	0.752216i
$943$	−21.3497	+	4.53803i	−0.695243	+	0.147779i
$944$	−8.60503	−	6.25192i	−0.280070	−	0.203483i
$945$	−9.77956	+	12.8588i	−0.318129	+	0.418298i
$946$	−12.8596	−	15.3444i	−0.418100	−	0.498888i
$947$	−3.19089	−	5.52679i	−0.103690	−	0.179596i	0.809512	−	0.587103i	$-0.199732\pi$
$947$	−3.19089	−	5.52679i	−0.103690	−	0.179596i	−0.913202	+	0.407507i	$0.866398\pi$
$948$	−24.4776	−	8.15118i	−0.794996	−	0.264738i
$949$	39.7337	+	44.1287i	1.28981	+	1.43248i
$950$	−1.53242	−	0.325725i	−0.0497181	−	0.0105679i
$951$	−38.9631	−	4.38284i	−1.26346	−	0.142123i
$952$	12.2920	+	5.47274i	0.398385	+	0.177373i
$953$	10.5898	+	32.5920i	0.343037	+	1.05576i	0.962626	+	0.270834i	$0.0872993\pi$
$953$	10.5898	+	32.5920i	0.343037	+	1.05576i	−0.619589	+	0.784926i	$0.712701\pi$
$954$	14.6318	−	15.7809i	0.473721	−	0.510927i
$955$	19.0980	+	13.8755i	0.617998	+	0.449002i
$956$	0.796790	+	1.38008i	0.0257700	+	0.0446350i
$957$	16.6705	−	33.5049i	0.538882	−	1.08306i
$958$	−7.09912	+	12.2960i	−0.229362	+	0.397267i
$959$	17.1245	−	7.62431i	0.552978	−	0.246202i
$960$	−1.49364	−	0.876947i	−0.0482071	−	0.0283033i
$961$	53.7105	−	59.6515i	1.73260	−	1.92424i
$962$	21.7116	−	15.7744i	0.700009	−	0.508587i
$963$	6.01392	−	17.6294i	0.193796	−	0.568098i
$964$	−3.84216	−	11.8249i	−0.123747	−	0.380856i
$965$	−9.24810	+	1.96574i	−0.297707	+	0.0632795i
$966$	−5.10872	−	24.9276i	−0.164370	−	0.802032i
$967$	−17.8267	+	30.8768i	−0.573269	+	0.992930i	0.422959	+	0.906149i	$0.360991\pi$
$967$	−17.8267	+	30.8768i	−0.573269	+	0.992930i	−0.996227	+	0.0867813i	$0.972342\pi$
$968$	2.64817	+	10.6765i	0.0851154	+	0.343155i
$969$	−11.1948	+	3.54733i	−0.359630	+	0.113957i
$970$	1.06266	−	10.1105i	0.0341199	−	0.324629i
$971$	−10.6529	+	32.7862i	−0.341867	+	1.05216i	0.621372	+	0.783515i	$0.286575\pi$
$971$	−10.6529	+	32.7862i	−0.341867	+	1.05216i	−0.963240	+	0.268644i	$0.913425\pi$
$972$	3.79500	−	15.1195i	0.121725	−	0.484957i
$973$	13.8098	−	10.0334i	0.442721	−	0.321656i
$974$	−6.92800	−	3.08454i	−0.221987	−	0.0988352i
$975$	4.49651	+	6.28484i	0.144004	+	0.201276i
$976$	−6.28138	−	6.97618i	−0.201062	−	0.223302i
$977$	−23.1175	+	10.2926i	−0.739594	+	0.329289i	−0.741720	−	0.670709i	$-0.765990\pi$
$977$	−23.1175	+	10.2926i	−0.739594	+	0.329289i	0.00212620	+	0.999998i	$0.499323\pi$
$978$	−26.6807	−	24.3782i	−0.853155	−	0.779530i
$979$	7.67628	+	26.8319i	0.245335	+	0.857551i
$980$	2.66628			0.0851712
$981$	−22.3460	−	0.326108i	−0.713452	−	0.0104118i
$982$	6.00574	−	18.4838i	0.191651	−	0.589841i
$983$	−8.73585	+	9.70214i	−0.278630	+	0.309450i	−0.866174	−	0.499742i	$-0.833428\pi$
$983$	−8.73585	+	9.70214i	−0.278630	+	0.309450i	0.587544	+	0.809192i	$0.300095\pi$
$984$	3.20074	+	7.33250i	0.102036	+	0.233751i
$985$	−0.110711	−	1.05334i	−0.00352754	−	0.0335623i
$986$	27.5771	+	5.86170i	0.878234	+	0.186674i
$987$	26.0717	+	15.3072i	0.829872	+	0.487234i
$988$	0.730631	−	6.95149i	0.0232445	−	0.221156i
$989$	−28.5234			−0.906991
$990$	−2.59687	−	9.60501i	−0.0825338	−	0.305267i
$991$	7.60421			0.241556			0.120778	−	0.992680i	$-0.461461\pi$
$991$	7.60421			0.241556			0.120778	+	0.992680i	$0.461461\pi$
$992$	1.10261	−	10.4906i	0.0350079	−	0.333078i
$993$	−42.0045	+	23.8444i	−1.33297	+	0.756678i
$994$	16.2242	+	3.44855i	0.514599	+	0.109381i
$995$	2.48863	+	23.6777i	0.0788948	+	0.750634i
$996$	8.01847	−	10.8688i	0.254075	−	0.344392i
$997$	−1.70597	+	1.89467i	−0.0540286	+	0.0600049i	−0.769553	−	0.638583i	$-0.779521\pi$
$997$	−1.70597	+	1.89467i	−0.0540286	+	0.0600049i	0.715525	+	0.698588i	$0.246188\pi$
$998$	5.73914	−	17.6633i	0.181669	−	0.559121i
$999$	29.9299	−	9.00552i	0.946940	−	0.284922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.301.6	✓	88
9.7	even	3	inner	990.2.bg.a.961.4	yes	88
11.3	even	5	inner	990.2.bg.a.751.4	yes	88
99.25	even	15	inner	990.2.bg.a.421.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.301.6	✓	88	1.1	even	1	trivial
990.2.bg.a.421.6	yes	88	99.25	even	15	inner
990.2.bg.a.751.4	yes	88	11.3	even	5	inner
990.2.bg.a.961.4	yes	88	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.0126374 + 1.73200i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(-1.72120 - 0.193612i) q^{6} +(2.08037 - 2.31049i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.99968 - 0.0437761i) q^{9} +1.00000 q^{10} +(0.912248 + 3.18870i) q^{11} +(0.372465 - 1.69153i) q^{12} +(-4.07588 + 1.81470i) q^{13} +(2.08037 + 2.31049i) q^{14} +(1.72384 - 0.168476i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-3.50122 + 2.54379i) q^{17} +(0.357088 - 2.97867i) q^{18} +(0.484122 - 1.48997i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(3.97548 + 3.63241i) q^{21} +(-3.26659 + 0.573941i) q^{22} +(-2.36262 + 4.09218i) q^{23} +(1.64333 + 0.547238i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(-1.37871 - 4.24324i) q^{26} +(0.113729 - 5.19491i) q^{27} +(-2.51529 + 1.82746i) q^{28} +(-4.35907 + 4.84123i) q^{29} +(-0.0126374 + 1.73200i) q^{30} +(-9.63646 + 4.29043i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.53437 + 1.53972i) q^{33} +(-2.16387 - 3.74794i) q^{34} +(-2.51529 - 1.82746i) q^{35} +(2.92503 + 0.666488i) q^{36} +(1.85877 + 5.72070i) q^{37} +(1.43121 + 0.637214i) q^{38} +(-3.09156 - 7.08238i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(3.09083 + 3.43271i) q^{41} +(-4.02806 + 3.57401i) q^{42} +(3.01819 + 5.22766i) q^{43} +(-0.229346 - 3.30869i) q^{44} +(0.270016 + 2.98782i) q^{45} +(-3.82280 - 2.77743i) q^{46} +(5.49159 - 1.16727i) q^{47} +(-0.716015 + 1.57712i) q^{48} +(-0.278702 - 2.65167i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-4.36160 - 6.09628i) q^{51} +(4.36411 - 0.927620i) q^{52} +(5.80345 + 4.21645i) q^{53} +(5.15456 + 0.656121i) q^{54} +(3.07588 - 1.24056i) q^{55} +(-1.55453 - 2.69253i) q^{56} +(2.57452 + 0.857331i) q^{57} +(-4.35907 - 4.84123i) q^{58} +(-10.4040 - 2.21143i) q^{59} +(-1.72120 - 0.193612i) q^{60} +(-8.57580 - 3.81819i) q^{61} +(-3.25964 - 10.0321i) q^{62} +(-6.34159 + 6.83965i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.23080 + 3.86386i) q^{65} +(-0.952788 - 5.66500i) q^{66} +(1.11240 - 1.92673i) q^{67} +(3.95359 - 1.76025i) q^{68} +(-7.05782 - 4.14379i) q^{69} +(2.08037 - 2.31049i) q^{70} +(4.31604 - 3.13579i) q^{71} +(-0.968586 + 2.83934i) q^{72} +(-4.11281 - 12.6579i) q^{73} +(-5.88365 + 1.25061i) q^{74} +(-0.347743 - 1.69678i) q^{75} +(-0.783326 + 1.35676i) q^{76} +(9.26526 + 4.52594i) q^{77} +(7.36673 - 2.33431i) q^{78} +(1.55697 - 14.8135i) q^{79} +(0.309017 - 0.951057i) q^{80} +(8.99617 + 0.262629i) q^{81} +(-3.73699 + 2.71508i) q^{82} +(7.12384 + 3.17174i) q^{83} +(-3.13339 - 4.37958i) q^{84} +(2.89583 + 3.21614i) q^{85} +(-5.51451 + 2.45522i) q^{86} +(-8.32995 - 7.61111i) q^{87} +(3.31453 + 0.117762i) q^{88} +8.41468 q^{89} +(-2.99968 - 0.0437761i) q^{90} +(-4.28650 + 13.1925i) q^{91} +(3.16181 - 3.51154i) q^{92} +(-7.30926 - 16.7446i) q^{93} +(0.586851 + 5.58352i) q^{94} +(-1.53242 - 0.325725i) q^{95} +(-1.49364 - 0.876947i) q^{96} +(1.06266 - 10.1105i) q^{97} +2.66628 q^{98} +(-2.59687 - 9.60501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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