LMFDB - Embedded newform 483.2.bc.a.389.51

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(11,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([33, 44, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			389.51
Character	$\chi$	$=$	483.389
Dual form			483.2.bc.a.149.51

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00246 + 0.0953889i) q^{2} +(1.70893 + 0.282086i) q^{3} +(2.00980 + 0.191912i) q^{4} +(-0.959667 - 3.95580i) q^{5} +(3.39514 + 0.727879i) q^{6} +(-2.02230 - 1.70596i) q^{7} +(0.0375805 + 0.00540327i) q^{8} +(2.84085 + 0.964129i) q^{9} +(-1.54435 - 8.01287i) q^{10} +(0.0137743 + 0.289159i) q^{11} +(3.38046 + 0.894900i) q^{12} +(3.86470 + 4.46010i) q^{13} +(-3.88684 - 3.60903i) q^{14} +(-0.524122 - 7.03088i) q^{15} +(-3.89017 - 0.749769i) q^{16} +(1.21182 + 1.70176i) q^{17} +(5.59673 + 2.20161i) q^{18} +(4.51451 + 3.21476i) q^{19} +(-1.16957 - 8.13453i) q^{20} +(-2.97473 - 3.48583i) q^{21} +0.580343i q^{22} +(1.22652 + 4.63634i) q^{23} +(0.0626982 + 0.0198347i) q^{24} +(-10.2832 + 5.30137i) q^{25} +(7.31345 + 9.29981i) q^{26} +(4.58284 + 2.44899i) q^{27} +(-3.73701 - 3.81674i) q^{28} +(-0.623226 - 0.284618i) q^{29} +(-0.378866 - 14.1290i) q^{30} +(-5.63302 - 4.42985i) q^{31} +(-7.79218 - 1.89036i) q^{32} +(-0.0580285 + 0.498037i) q^{33} +(2.26428 + 3.52329i) q^{34} +(-4.80772 + 9.63696i) q^{35} +(5.52451 + 2.48290i) q^{36} +(2.35347 - 2.46825i) q^{37} +(8.73346 + 6.86807i) q^{38} +(5.34635 + 8.71216i) q^{39} +(-0.0146906 - 0.153846i) q^{40} +(0.0413890 - 0.140958i) q^{41} +(-5.62426 - 7.26398i) q^{42} +(-6.90466 + 0.992741i) q^{43} +(-0.0278096 + 0.583794i) q^{44} +(1.08763 - 12.1631i) q^{45} +(2.01379 + 9.40108i) q^{46} +(1.41487 - 0.816878i) q^{47} +(-6.43651 - 2.37866i) q^{48} +(1.17938 + 6.89993i) q^{49} +(-21.0974 + 9.63487i) q^{50} +(1.59086 + 3.25001i) q^{51} +(6.91131 + 9.70558i) q^{52} +(-2.42260 - 6.99966i) q^{53} +(8.94334 + 5.34115i) q^{54} +(1.13064 - 0.331985i) q^{55} +(-0.0667813 - 0.0750380i) q^{56} +(6.80811 + 6.76727i) q^{57} +(-1.22084 - 0.629385i) q^{58} +(0.270532 + 1.40365i) q^{59} +(0.295933 - 14.2312i) q^{60} +(2.22764 + 5.56437i) q^{61} +(-10.8573 - 9.40792i) q^{62} +(-4.10029 - 6.79615i) q^{63} +(-7.82062 - 2.29634i) q^{64} +(13.9344 - 19.5682i) q^{65} +(-0.163707 + 0.991763i) q^{66} +(-4.78500 - 9.28161i) q^{67} +(2.10891 + 3.65275i) q^{68} +(0.788176 + 8.26915i) q^{69} +(-10.5465 + 18.8390i) q^{70} +(5.46332 - 8.50109i) q^{71} +(0.101551 + 0.0515824i) q^{72} +(8.57030 + 0.818364i) q^{73} +(4.94817 - 4.71807i) q^{74} +(-19.0687 + 6.15889i) q^{75} +(8.45629 + 7.32741i) q^{76} +(0.465439 - 0.608264i) q^{77} +(9.87480 + 17.9557i) q^{78} +(-0.670494 - 0.232060i) q^{79} +(0.767331 + 16.1083i) q^{80} +(7.14091 + 5.47790i) q^{81} +(0.0963256 - 0.278315i) q^{82} +(-3.82422 + 1.12289i) q^{83} +(-5.30963 - 7.57669i) q^{84} +(5.56887 - 6.42682i) q^{85} +(-13.9210 + 1.32929i) q^{86} +(-0.984761 - 0.662195i) q^{87} +(-0.00104476 + 0.0109412i) q^{88} +(-2.67881 + 2.10664i) q^{89} +(3.33815 - 24.2523i) q^{90} +(-0.206805 - 15.6127i) q^{91} +(1.57528 + 9.55349i) q^{92} +(-8.37681 - 9.15929i) q^{93} +(2.91115 - 1.50080i) q^{94} +(8.38455 - 20.9436i) q^{95} +(-12.7830 - 5.42855i) q^{96} +(1.17109 - 3.98837i) q^{97} +(1.70348 + 13.9293i) q^{98} +(-0.239656 + 0.834739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00246	+	0.0953889i	1.41595	+	0.0674501i	0.741542	−	0.670907i	$-0.234095\pi$
$2$	2.00246	+	0.0953889i	1.41595	+	0.0674501i	0.674410	+	0.738357i	$0.264398\pi$
$3$	1.70893	+	0.282086i	0.986649	+	0.162863i
$3$	1.70893	+	0.282086i	0.986649	+	0.162863i
$4$	2.00980	+	0.191912i	1.00490	+	0.0959562i
$5$	−0.959667	−	3.95580i	−0.429176	−	1.76909i	−0.617080	−	0.786900i	$-0.711685\pi$
$5$	−0.959667	−	3.95580i	−0.429176	−	1.76909i	0.187904	−	0.982187i	$-0.439831\pi$
$6$	3.39514	+	0.727879i	1.38606	+	0.297155i
$7$	−2.02230	−	1.70596i	−0.764357	−	0.644794i
$7$	−2.02230	−	1.70596i	−0.764357	−	0.644794i
$8$	0.0375805	+	0.00540327i	0.0132867	+	0.00191034i
$9$	2.84085	+	0.964129i	0.946952	+	0.321376i
$10$	−1.54435	−	8.01287i	−0.488368	−	2.53389i
$11$	0.0137743	+	0.289159i	0.00415312	+	0.0871847i	0.999992	−	0.00394422i	$-0.00125549\pi$
$11$	0.0137743	+	0.289159i	0.00415312	+	0.0871847i	−0.995839	+	0.0911289i	$0.970952\pi$
$12$	3.38046	+	0.894900i	0.975854	+	0.258335i
$13$	3.86470	+	4.46010i	1.07187	+	1.23701i	0.970229	+	0.242188i	$0.0778652\pi$
$13$	3.86470	+	4.46010i	1.07187	+	1.23701i	0.101645	+	0.994821i	$0.467589\pi$
$14$	−3.88684	−	3.60903i	−1.03880	−	0.964553i
$15$	−0.524122	−	7.03088i	−0.135328	−	1.81537i
$16$	−3.89017	−	0.749769i	−0.972542	−	0.187442i
$17$	1.21182	+	1.70176i	0.293908	+	0.412737i	0.934956	−	0.354765i	$-0.115439\pi$
$17$	1.21182	+	1.70176i	0.293908	+	0.412737i	−0.641047	+	0.767501i	$0.721500\pi$
$18$	5.59673	+	2.20161i	1.31916	+	0.518925i
$19$	4.51451	+	3.21476i	1.03570	+	0.737518i	0.965603	−	0.260023i	$-0.0837300\pi$
$19$	4.51451	+	3.21476i	1.03570	+	0.737518i	0.0700960	+	0.997540i	$0.477669\pi$
$20$	−1.16957	−	8.13453i	−0.261523	−	1.81894i
$21$	−2.97473	−	3.48583i	−0.649139	−	0.760670i
$22$			0.580343i			0.123730i
$23$	1.22652	+	4.63634i	0.255746	+	0.966744i
$23$	1.22652	+	4.63634i	0.255746	+	0.966744i
$24$	0.0626982	+	0.0198347i	0.0127982	+	0.00404875i
$25$	−10.2832	+	5.30137i	−2.05664	+	1.06027i
$26$	7.31345	+	9.29981i	1.43429	+	1.82384i
$27$	4.58284	+	2.44899i	0.881968	+	0.471309i
$28$	−3.73701	−	3.81674i	−0.706229	−	0.721297i
$29$	−0.623226	−	0.284618i	−0.115730	−	0.0528522i	0.356709	−	0.934216i	$-0.383899\pi$
$29$	−0.623226	−	0.284618i	−0.115730	−	0.0528522i	−0.472439	+	0.881364i	$0.656626\pi$
$30$	−0.378866	−	14.1290i	−0.0691711	−	2.57960i
$31$	−5.63302	−	4.42985i	−1.01172	−	0.795625i	−0.0327153	−	0.999465i	$-0.510415\pi$
$31$	−5.63302	−	4.42985i	−1.01172	−	0.795625i	−0.979004	+	0.203840i	$0.934658\pi$
$32$	−7.79218	−	1.89036i	−1.37748	−	0.334172i
$33$	−0.0580285	+	0.498037i	−0.0101015	+	0.0866971i
$34$	2.26428	+	3.52329i	0.388321	+	0.604239i
$35$	−4.80772	+	9.63696i	−0.812653	+	1.62894i
$36$	5.52451	+	2.48290i	0.920752	+	0.413816i
$37$	2.35347	−	2.46825i	0.386908	−	0.405778i	−0.501260	−	0.865297i	$-0.667130\pi$
$37$	2.35347	−	2.46825i	0.386908	−	0.405778i	0.888168	+	0.459519i	$0.151978\pi$
$38$	8.73346	+	6.86807i	1.41675	+	1.11415i
$39$	5.34635	+	8.71216i	0.856101	+	1.39506i
$40$	−0.0146906	−	0.153846i	−0.00232278	−	0.0243253i
$41$	0.0413890	−	0.140958i	0.00646388	−	0.0220139i	−0.956198	−	0.292721i	$-0.905439\pi$
$41$	0.0413890	−	0.140958i	0.00646388	−	0.0220139i	0.962662	+	0.270707i	$0.0872575\pi$
$42$	−5.62426	−	7.26398i	−0.867842	−	1.12086i
$43$	−6.90466	+	0.992741i	−1.05295	+	0.151392i	−0.646990	−	0.762499i	$-0.723972\pi$
$43$	−6.90466	+	0.992741i	−1.05295	+	0.151392i	−0.405961	+	0.913890i	$0.633063\pi$
$44$	−0.0278096	+	0.583794i	−0.00419245	+	0.0880103i
$45$	1.08763	−	12.1631i	0.162134	−	1.81317i
$46$	2.01379	+	9.40108i	0.296917	+	1.38611i
$47$	1.41487	−	0.816878i	0.206381	−	0.119154i	−0.393248	−	0.919433i	$-0.628648\pi$
$47$	1.41487	−	0.816878i	0.206381	−	0.119154i	0.599628	+	0.800279i	$0.295315\pi$
$48$	−6.43651	−	2.37866i	−0.929030	−	0.343330i
$49$	1.17938	+	6.89993i	0.168483	+	0.985705i
$50$	−21.0974	+	9.63487i	−2.98363	+	1.36258i
$51$	1.59086	+	3.25001i	0.222765	+	0.455093i
$52$	6.91131	+	9.70558i	0.958426	+	1.34592i
$53$	−2.42260	−	6.99966i	−0.332770	−	0.961477i	−0.979968	−	0.199155i	$-0.936180\pi$
$53$	−2.42260	−	6.99966i	−0.332770	−	0.961477i	0.647198	−	0.762322i	$-0.275941\pi$
$54$	8.94334	+	5.34115i	1.21704	+	0.726839i
$55$	1.13064	−	0.331985i	0.152455	−	0.0447648i
$56$	−0.0667813	−	0.0750380i	−0.00892402	−	0.0100274i
$57$	6.80811	+	6.76727i	0.901757	+	0.896347i
$58$	−1.22084	−	0.629385i	−0.160304	−	0.0826422i
$59$	0.270532	+	1.40365i	0.0352203	+	0.182740i	0.995279	−	0.0970600i	$-0.0309439\pi$
$59$	0.270532	+	1.40365i	0.0352203	+	0.182740i	−0.960058	+	0.279800i	$0.909732\pi$
$60$	0.295933	−	14.2312i	0.0382048	−	1.83724i
$61$	2.22764	+	5.56437i	0.285220	+	0.712445i	0.999915	+	0.0130093i	$0.00414109\pi$
$61$	2.22764	+	5.56437i	0.285220	+	0.712445i	−0.714695	+	0.699436i	$0.753435\pi$
$62$	−10.8573	−	9.40792i	−1.37888	−	1.19481i
$63$	−4.10029	−	6.79615i	−0.516587	−	0.856234i
$64$	−7.82062	−	2.29634i	−0.977578	−	0.287043i
$65$	13.9344	−	19.5682i	1.72836	−	2.42714i
$66$	−0.163707	+	0.991763i	−0.0201509	+	0.122078i
$67$	−4.78500	−	9.28161i	−0.584581	−	1.13393i	−0.976819	−	0.214065i	$-0.931329\pi$
$67$	−4.78500	−	9.28161i	−0.584581	−	1.13393i	0.392238	−	0.919864i	$-0.371701\pi$
$68$	2.10891	+	3.65275i	0.255743	+	0.442961i
$69$	0.788176	+	8.26915i	0.0948853	+	0.995488i
$70$	−10.5465	+	18.8390i	−1.26055	+	2.25169i
$71$	5.46332	−	8.50109i	0.648376	−	1.00889i	−0.349044	−	0.937106i	$-0.613494\pi$
$71$	5.46332	−	8.50109i	0.648376	−	1.00889i	0.997420	−	0.0717867i	$-0.0228701\pi$
$72$	0.101551	+	0.0515824i	0.0119679	+	0.00607904i
$73$	8.57030	+	0.818364i	1.00308	+	0.0957823i	0.583649	−	0.812006i	$-0.301624\pi$
$73$	8.57030	+	0.818364i	1.00308	+	0.0957823i	0.419429	+	0.907788i	$0.362230\pi$
$74$	4.94817	−	4.71807i	0.575213	−	0.548465i
$75$	−19.0687	+	6.15889i	−2.20186	+	0.711167i
$76$	8.45629	+	7.32741i	0.970002	+	0.840512i
$77$	0.465439	−	0.608264i	0.0530417	−	0.0693181i
$78$	9.87480	+	17.9557i	1.11810	+	2.03308i
$79$	−0.670494	−	0.232060i	−0.0754365	−	0.0261088i	0.289089	−	0.957302i	$-0.406648\pi$
$79$	−0.670494	−	0.232060i	−0.0754365	−	0.0261088i	−0.364526	+	0.931193i	$0.618769\pi$
$80$	0.767331	+	16.1083i	0.0857902	+	1.80096i
$81$	7.14091	+	5.47790i	0.793434	+	0.608656i
$82$	0.0963256	−	0.278315i	0.0106374	−	0.0307347i
$83$	−3.82422	+	1.12289i	−0.419762	+	0.123253i	−0.484791	−	0.874630i	$-0.661104\pi$
$83$	−3.82422	+	1.12289i	−0.419762	+	0.123253i	0.0650287	+	0.997883i	$0.479286\pi$
$84$	−5.30963	−	7.57669i	−0.579328	−	0.826685i
$85$	5.56887	−	6.42682i	0.604029	−	0.697086i
$86$	−13.9210	+	1.32929i	−1.50114	+	0.143341i
$87$	−0.984761	−	0.662195i	−0.105577	−	0.0709947i
$88$	−0.00104476	+	0.0109412i	−0.000111371	+	0.00116633i
$89$	−2.67881	+	2.10664i	−0.283953	+	0.223303i	−0.749969	−	0.661473i	$-0.769931\pi$
$89$	−2.67881	+	2.10664i	−0.283953	+	0.223303i	0.466016	+	0.884776i	$0.345689\pi$
$90$	3.33815	−	24.2523i	0.351872	−	2.55642i
$91$	−0.206805	−	15.6127i	−0.0216791	−	1.63665i
$92$	1.57528	+	9.55349i	0.164234	+	0.996020i
$93$	−8.37681	−	9.15929i	−0.868634	−	0.949774i
$94$	2.91115	−	1.50080i	0.300262	−	0.154796i
$95$	8.38455	−	20.9436i	0.860236	−	2.14877i
$96$	−12.7830	−	5.42855i	−1.30466	−	0.554049i
$97$	1.17109	−	3.98837i	0.118906	−	0.404957i	−0.878432	−	0.477867i	$-0.841410\pi$
$97$	1.17109	−	3.98837i	0.118906	−	0.404957i	0.997339	+	0.0729094i	$0.0232284\pi$
$98$	1.70348	+	13.9293i	0.172077	+	1.40707i
$99$	−0.239656	+	0.834739i	−0.0240863	+	0.0838944i
$100$	−21.6846	+	8.68120i	−2.16846	+	0.868120i
$101$	−13.7091	−	3.32580i	−1.36411	−	0.330930i	−0.514116	−	0.857721i	$-0.671880\pi$
$101$	−13.7091	−	3.32580i	−1.36411	−	0.330930i	−0.849995	+	0.526791i	$0.823395\pi$
$102$	2.87562	+	6.65976i	0.284728	+	0.659415i
$103$	5.20950	−	10.1050i	0.513308	−	0.995678i	−0.479678	−	0.877444i	$-0.659247\pi$
$103$	5.20950	−	10.1050i	0.513308	−	0.995678i	0.992986	−	0.118233i	$-0.0377231\pi$
$104$	0.121138	+	0.188495i	0.0118786	+	0.0184835i
$105$	−10.9345	+	15.1127i	−1.06710	+	1.47485i
$106$	−4.18348	−	14.2476i	−0.406335	−	1.38385i
$107$	−15.0163	+	6.01162i	−1.45168	+	0.581165i	−0.957561	−	0.288229i	$-0.906933\pi$
$107$	−15.0163	+	6.01162i	−1.45168	+	0.581165i	−0.494119	+	0.869394i	$0.664509\pi$
$108$	8.74059	+	5.80148i	0.841064	+	0.558248i
$109$	−5.93226	+	4.22435i	−0.568208	+	0.404619i	−0.827737	−	0.561116i	$-0.810372\pi$
$109$	−5.93226	+	4.22435i	−0.568208	+	0.404619i	0.259529	+	0.965735i	$0.416433\pi$
$110$	2.29572	−	0.556936i	0.218888	−	0.0531017i
$111$	4.71817	−	3.55417i	0.447828	−	0.337347i
$112$	6.58800	+	8.15274i	0.622508	+	0.770362i
$113$	−2.87874	−	1.85006i	−0.270809	−	0.174039i	0.398187	−	0.917304i	$-0.369639\pi$
$113$	−2.87874	−	1.85006i	−0.270809	−	0.174039i	−0.668996	+	0.743266i	$0.733276\pi$
$114$	12.9874	+	14.2006i	1.21639	+	1.33001i
$115$	17.1634	−	9.30119i	1.60049	−	0.867341i
$116$	−1.19794	−	0.691629i	−0.111226	−	0.0642162i
$117$	6.67894	+	16.3966i	0.617468	+	1.51586i
$118$	0.407836	+	2.83656i	0.0375444	+	0.261127i
$119$	0.452482	−	5.50877i	0.0414790	−	0.504988i
$120$	0.0182929	−	0.267056i	0.00166991	−	0.0243788i
$121$	10.8668	−	1.03765i	0.987888	−	0.0943319i
$122$	3.92998	+	11.3549i	0.355803	+	1.02803i
$123$	0.110493	−	0.229212i	0.00996283	−	0.0206673i
$124$	−10.4711	−	9.98415i	−0.940330	−	0.896603i
$125$	17.5114	+	20.2093i	1.56627	+	1.80757i
$126$	−7.56238	−	14.0001i	−0.673710	−	1.24723i
$127$	−5.03395	+	3.23513i	−0.446691	+	0.287071i	−0.744585	−	0.667528i	$-0.767352\pi$
$127$	−5.03395	+	3.23513i	−0.446691	+	0.287071i	0.297893	+	0.954599i	$0.403716\pi$
$128$	−0.287018	−	0.0993378i	−0.0253690	−	0.00878031i
$129$	−12.0796	−	0.251191i	−1.06355	−	0.0221161i
$130$	29.7697	−	37.8553i	2.61098	−	3.32013i
$131$	−1.36760	+	7.09578i	−0.119488	+	0.619962i	0.871973	+	0.489554i	$0.162841\pi$
$131$	−1.36760	+	7.09578i	−0.119488	+	0.619962i	−0.991461	+	0.130407i	$0.958372\pi$
$132$	−0.212205	+	0.989817i	−0.0184701	+	0.0861525i
$133$	−3.64540	−	14.2028i	−0.316097	−	1.23154i
$134$	−8.69641	−	19.0425i	−0.751255	−	1.64502i
$135$	5.28972	−	20.4790i	0.455267	−	1.76255i
$136$	0.0363456	+	0.0705007i	0.00311661	+	0.00604538i
$137$	−10.8239	+	18.7476i	−0.924750	+	1.60171i	−0.132788	+	0.991144i	$0.542393\pi$
$137$	−10.8239	+	18.7476i	−0.924750	+	1.60171i	−0.791962	+	0.610570i	$0.790940\pi$
$138$	0.789506	+	16.6338i	0.0672072	+	1.41596i
$139$	7.69285			0.652499			0.326250	−	0.945284i	$-0.394215\pi$
$139$	7.69285			0.652499			0.326250	+	0.945284i	$0.394215\pi$
$140$	−11.5120	+	18.4457i	−0.972941	+	1.55894i
$141$	2.64834	−	0.996867i	0.223031	−	0.0839514i
$142$	11.7510	−	16.5019i	0.986120	−	1.38481i
$143$	−1.23644	+	1.17895i	−0.103397	+	0.0985885i
$144$	−10.3285	−	5.88061i	−0.860711	−	0.490051i
$145$	−0.527802	+	2.73850i	−0.0438316	+	0.227420i
$146$	17.0836	+	2.45625i	1.41385	+	0.203281i
$147$	0.0690938	+	12.1242i	0.00569876	+	0.999984i
$148$	5.20368	−	4.50902i	0.427740	−	0.370639i
$149$	13.3543	+	6.88464i	1.09403	+	0.564012i	0.908186	−	0.418568i	$-0.137468\pi$
$149$	13.3543	+	6.88464i	1.09403	+	0.564012i	0.185844	+	0.982579i	$0.440498\pi$
$150$	−38.7718	+	10.5140i	−3.16570	+	0.858463i
$151$	−9.09036	+	1.75202i	−0.739763	+	0.142578i	−0.545192	−	0.838311i	$-0.683543\pi$
$151$	−9.09036	+	1.75202i	−0.739763	+	0.142578i	−0.194570	+	0.980889i	$0.562331\pi$
$152$	0.152287	+	0.145206i	0.0123521	+	0.0117777i
$153$	1.80188	+	6.00279i	0.145673	+	0.485297i
$154$	0.990044	−	1.17363i	0.0797800	−	0.0945735i
$155$	−12.1178	+	26.5343i	−0.973325	+	2.13128i
$156$	9.07311	+	18.5357i	0.726430	+	1.48404i
$157$	−0.320668	+	3.35818i	−0.0255921	+	0.268012i	0.973615	+	0.228197i	$0.0732830\pi$
$157$	−0.320668	+	3.35818i	−0.0255921	+	0.268012i	−0.999207	+	0.0398153i	$0.987323\pi$
$158$	−1.32050	−	0.528649i	−0.105053	−	0.0420570i
$159$	−2.16554	−	12.6453i	−0.171739	−	1.00284i
$160$			32.6384i			2.58029i
$161$	5.42905	−	11.4685i	0.427869	−	0.903841i
$162$	13.7768	+	11.6504i	1.08241	+	0.915344i
$163$	0.0298405	−	0.626429i	0.00233729	−	0.0490657i	−0.997397	−	0.0721004i	$-0.977030\pi$
$163$	0.0298405	−	0.626429i	0.00233729	−	0.0490657i	0.999735	+	0.0230347i	$0.00733282\pi$
$164$	0.110235	−	0.275354i	0.00860791	−	0.0215015i
$165$	2.02582	−	0.248400i	0.157710	−	0.0193379i
$166$	−7.76494	+	1.88375i	−0.602677	+	0.146208i
$167$	5.92157	+	2.70429i	0.458225	+	0.209264i	0.631135	−	0.775673i	$-0.282590\pi$
$167$	5.92157	+	2.70429i	0.458225	+	0.209264i	−0.172910	+	0.984938i	$0.555317\pi$
$168$	−0.0929571	−	0.147073i	−0.00717179	−	0.0113469i
$169$	−3.10650	+	21.6062i	−0.238962	+	1.66202i
$170$	11.7645	−	12.3382i	0.902294	−	0.946299i
$171$	9.72561	+	13.4852i	0.743736	+	1.03124i
$172$	−14.0675	+	0.670117i	−1.07264	+	0.0510959i
$173$	−2.30900	+	4.47884i	−0.175550	+	0.340520i	−0.960151	−	0.279481i	$-0.909838\pi$
$173$	−2.30900	+	4.47884i	−0.175550	+	0.340520i	0.784601	+	0.620001i	$0.212868\pi$
$174$	−1.90878	−	1.41995i	−0.144704	−	0.107646i
$175$	29.8397	+	6.82185i	2.25567	+	0.515683i
$176$	0.163218	−	1.13521i	0.0123030	−	0.0855693i
$177$	0.0663678	+	2.47505i	0.00498851	+	0.186036i
$178$	−5.56515	+	3.96292i	−0.417126	+	0.297034i
$179$	−16.5469	−	17.3538i	−1.23677	−	1.29709i	−0.939605	−	0.342261i	$-0.888807\pi$
$179$	−16.5469	−	17.3538i	−1.23677	−	1.29709i	−0.297165	−	0.954826i	$-0.596041\pi$
$180$	4.52016	−	24.2366i	0.336913	−	1.80649i
$181$	−0.0652991	+	0.00938859i	−0.00485364	+	0.000697849i	−0.144741	−	0.989470i	$-0.546235\pi$
$181$	−0.0652991	+	0.00938859i	−0.00485364	+	0.000697849i	0.139888	+	0.990167i	$0.455326\pi$
$182$	1.07516	−	31.2835i	0.0796959	−	2.31889i
$183$	2.23724	+	10.1375i	0.165381	+	0.749385i
$184$	0.0210417	+	0.180863i	0.00155122	+	0.0133334i
$185$	−12.0224	−	6.94116i	−0.883908	−	0.510325i
$186$	−15.9005	−	19.1401i	−1.16588	−	1.40342i
$187$	−0.475386	+	0.373848i	−0.0347637	+	0.0273385i
$188$	3.00038	−	1.37023i	0.218825	−	0.0999341i
$189$	−5.08998	−	12.7708i	−0.370242	−	0.928935i
$190$	18.7875	−	41.1389i	1.36299	−	2.98453i
$191$	−8.47059	−	1.63257i	−0.612911	−	0.118129i	−0.126657	−	0.991947i	$-0.540425\pi$
$191$	−8.47059	−	1.63257i	−0.612911	−	0.118129i	−0.486254	+	0.873818i	$0.661637\pi$
$192$	−12.7171	−	6.13037i	−0.917777	−	0.442421i
$193$	0.883218	−	3.64068i	0.0635754	−	0.262062i	−0.931150	−	0.364637i	$-0.881193\pi$
$193$	0.883218	−	3.64068i	0.0635754	−	0.262062i	0.994725	+	0.102575i	$0.0327083\pi$
$194$	2.72551	−	7.87483i	0.195680	−	0.565380i
$195$	29.3328	−	29.5099i	2.10057	−	2.11325i
$196$	1.04613	+	14.0938i	0.0747235	+	1.00670i
$197$	−6.61539	+	5.73227i	−0.471327	+	0.408407i	−0.857872	−	0.513863i	$-0.828214\pi$
$197$	−6.61539	+	5.73227i	−0.471327	+	0.408407i	0.386545	+	0.922270i	$0.373668\pi$
$198$	−0.559525	+	1.64867i	−0.0397637	+	0.117166i
$199$	−0.861032	+	1.09489i	−0.0610369	+	0.0776148i	−0.815613	−	0.578598i	$-0.803600\pi$
$199$	−0.861032	+	1.09489i	−0.0610369	+	0.0776148i	0.754576	+	0.656213i	$0.227843\pi$
$200$	−0.415094	+	0.143665i	−0.0293516	+	0.0101587i
$201$	−5.55900	−	17.2114i	−0.392102	−	1.21400i
$202$	−27.1348	−	7.96748i	−1.90919	−	0.560590i
$203$	0.774802	+	1.63878i	0.0543804	+	0.115020i
$204$	2.57359	+	6.83717i	0.180187	+	0.478698i
$205$	−0.597322	−	0.0284539i	−0.0417187	−	0.00198731i
$206$	11.3957	−	19.7380i	0.793977	−	1.37521i
$207$	−0.985678	+	14.3537i	−0.0685094	+	0.997650i
$208$	−11.6903	−	20.2482i	−0.810576	−	1.40396i
$209$	−0.867394	+	1.34969i	−0.0599989	+	0.0933601i
$210$	−23.3374	+	29.2195i	−1.61044	+	2.01633i
$211$	0.959786	+	2.10164i	0.0660744	+	0.144683i	0.939788	−	0.341758i	$-0.111022\pi$
$211$	0.959786	+	2.10164i	0.0660744	+	0.144683i	−0.873714	+	0.486441i	$0.838295\pi$
$212$	−3.52562	−	14.5328i	−0.242141	−	0.998118i
$213$	11.7344	−	12.9866i	0.804031	−	0.889827i
$214$	−30.6429	+	10.6056i	−2.09471	+	0.724986i
$215$	10.5533	+	26.3608i	0.719726	+	1.79779i
$216$	0.158993	+	0.116797i	0.0108181	+	0.00794701i
$217$	3.83447	+	18.5682i	0.260301	+	1.26049i
$218$	−12.2821	+	7.89320i	−0.831846	+	0.534595i
$219$	14.4152	+	3.81609i	0.974086	+	0.257867i
$220$	2.33606	−	0.450239i	0.157497	−	0.0303551i
$221$	−2.90670	+	11.9816i	−0.195526	+	0.805969i
$222$	9.78696	−	6.66702i	0.656858	−	0.447461i
$223$	9.92846	−	11.4581i	0.664859	−	0.767288i	−0.318704	−	0.947854i	$-0.603247\pi$
$223$	9.92846	−	11.4581i	0.664859	−	0.767288i	0.983563	+	0.180566i	$0.0577930\pi$
$224$	12.5332	+	17.1160i	0.837411	+	1.14361i
$225$	−34.3243	+	5.14607i	−2.28829	+	0.343071i
$226$	−5.58809	−	3.97926i	−0.371714	−	0.264696i
$227$	−4.98244	−	1.99467i	−0.330696	−	0.132391i	0.200372	−	0.979720i	$-0.435785\pi$
$227$	−4.98244	−	1.99467i	−0.330696	−	0.132391i	−0.531068	+	0.847329i	$0.678209\pi$
$228$	12.3842	+	14.9074i	0.820164	+	0.987267i
$229$	19.4902	−	11.2527i	1.28795	−	0.743597i	0.309660	−	0.950847i	$-0.399785\pi$
$229$	19.4902	−	11.2527i	1.28795	−	0.743597i	0.978288	+	0.207250i	$0.0664514\pi$
$230$	35.2562	−	16.9881i	2.32473	−	1.12016i
$231$	0.966983	−	0.908185i	0.0636228	−	0.0597542i
$232$	−0.0218833	−	0.0140636i	−0.00143671	−	0.000923318i
$233$	2.64649	+	3.36529i	0.173377	+	0.220467i	0.864974	−	0.501817i	$-0.167335\pi$
$233$	2.64649	+	3.36529i	0.173377	+	0.220467i	−0.691597	+	0.722284i	$0.743092\pi$
$234$	11.8102	+	33.4705i	0.772060	+	2.18804i
$235$	−4.58921	−	4.81303i	−0.299367	−	0.313967i
$236$	0.274336	+	2.87298i	0.0178578	+	0.187015i
$237$	−1.08036	−	0.585711i	−0.0701772	−	0.0380460i
$238$	1.43155	−	10.9879i	0.0927938	−	0.712241i
$239$	−7.25472	−	24.7073i	−0.469269	−	1.59818i	−0.765746	−	0.643143i	$-0.777630\pi$
$239$	−7.25472	−	24.7073i	−0.469269	−	1.59818i	0.296477	−	0.955040i	$-0.404188\pi$
$240$	−3.23261	+	27.7443i	−0.208664	+	1.79089i
$241$	−9.68473	+	0.461341i	−0.623849	+	0.0297176i	−0.357127	−	0.934056i	$-0.616244\pi$
$241$	−9.68473	+	0.461341i	−0.623849	+	0.0297176i	−0.266722	+	0.963774i	$0.585941\pi$
$242$	21.8592	−	1.04128i	1.40516	−	0.0669362i
$243$	10.6580	+	11.3757i	0.683714	+	0.729750i
$244$	3.40923	+	11.6108i	0.218254	+	0.743304i
$245$	26.1629	−	11.2870i	1.67149	−	0.721101i
$246$	0.243122	−	0.448447i	0.0155009	−	0.0285919i
$247$	3.10903	+	32.5592i	0.197823	+	2.07169i
$248$	−0.187756	−	0.196913i	−0.0119225	−	0.0125040i
$249$	−6.85205	+	0.840179i	−0.434231	+	0.0532442i
$250$	33.1382	+	42.1386i	2.09584	+	2.66508i
$251$	−22.2799	−	14.3184i	−1.40629	−	0.903770i	−0.406342	−	0.913721i	$-0.633196\pi$
$251$	−22.2799	−	14.3184i	−1.40629	−	0.903770i	−0.999950	+	0.00995133i	$0.996832\pi$
$252$	−6.93648	−	14.4458i	−0.436957	−	0.909998i
$253$	−1.32375	+	0.418521i	−0.0832232	+	0.0263122i
$254$	−10.3889	+	5.99802i	−0.651856	+	0.376349i
$255$	11.3297	−	9.41205i	0.709494	−	0.589406i
$256$	14.5686	+	5.83238i	0.910537	+	0.364524i
$257$	−9.57456	−	6.81801i	−0.597244	−	0.425296i	0.241051	−	0.970513i	$-0.422508\pi$
$257$	−9.57456	−	6.81801i	−0.597244	−	0.425296i	−0.838295	+	0.545217i	$0.816447\pi$
$258$	−24.1649	−	1.65526i	−1.50444	−	0.103052i
$259$	−8.97016	+	0.976600i	−0.557379	+	0.0606830i
$260$	31.7608	−	36.6539i	1.96972	−	2.27318i
$261$	−1.49609	−	1.40943i	−0.0926055	−	0.0872415i
$262$	−3.41542	+	14.0786i	−0.211005	+	0.869776i
$263$	−28.4522	+	5.48371i	−1.75444	+	0.338140i	−0.962256	−	0.272146i	$-0.912267\pi$
$263$	−28.4522	+	5.48371i	−1.75444	+	0.338140i	−0.792181	+	0.610286i	$0.791054\pi$
$264$	−0.00487177	+	0.0184030i	−0.000299837	+	0.00113262i
$265$	−25.3644	+	16.3007i	−1.55812	+	1.00134i
$266$	−5.94498	−	28.7882i	−0.364510	−	1.76512i
$267$	−5.17214	+	2.84443i	−0.316530	+	0.174076i
$268$	−7.83563	−	19.5724i	−0.478637	−	1.19558i
$269$	25.0389	−	8.66604i	1.52665	−	0.528378i	0.570508	−	0.821292i	$-0.306746\pi$
$269$	25.0389	−	8.66604i	1.52665	−	0.528378i	0.956139	+	0.292915i	$0.0946252\pi$
$270$	12.5459	−	40.5038i	0.763520	−	2.46498i
$271$	2.36626	+	9.75388i	0.143740	+	0.592506i	0.997425	+	0.0717157i	$0.0228474\pi$
$271$	2.36626	+	9.75388i	0.143740	+	0.592506i	−0.853685	+	0.520790i	$0.825637\pi$
$272$	−3.43824	−	7.52870i	−0.208474	−	0.456495i
$273$	4.05071	−	26.7393i	0.245160	−	1.61833i
$274$	−23.4628	+	36.5088i	−1.41744	+	2.20558i
$275$	−1.67458	−	2.90046i	−0.100981	−	0.174905i
$276$	−0.00287723	+	16.7706i	−0.000173189	+	1.00947i
$277$	7.58327	−	13.1346i	0.455634	−	0.789182i	−0.543090	−	0.839674i	$-0.682746\pi$
$277$	7.58327	−	13.1346i	0.455634	−	0.789182i	0.998724	+	0.0504926i	$0.0160791\pi$
$278$	15.4046	+	0.733813i	0.923908	+	0.0440112i
$279$	−11.7316	−	18.0155i	−0.702354	−	1.07856i
$280$	−0.232748	+	0.336185i	−0.0139093	+	0.0200909i
$281$	26.7064	+	7.84170i	1.59317	+	0.467796i	0.953635	−	0.300967i	$-0.0973092\pi$
$281$	26.7064	+	7.84170i	1.59317	+	0.467796i	0.639534	+	0.768763i	$0.279127\pi$
$282$	5.39829	−	1.74356i	0.321464	−	0.103828i
$283$	9.73268	−	3.36851i	0.578548	−	0.200237i	−0.0220937	−	0.999756i	$-0.507033\pi$
$283$	9.73268	−	3.36851i	0.578548	−	0.200237i	0.600641	+	0.799519i	$0.294912\pi$
$284$	12.6116	−	16.0370i	0.748362	−	0.951619i
$285$	20.2365	−	33.4259i	1.19870	−	1.97998i
$286$	−2.58839	+	2.24285i	−0.153055	+	0.132623i
$287$	−0.324170	+	0.214451i	−0.0191352	+	0.0126586i
$288$	−20.3139	−	12.8829i	−1.19701	−	0.759133i
$289$	4.13268	−	11.9406i	0.243099	−	0.702387i
$290$	−1.31812	+	5.43338i	−0.0774029	+	0.319059i
$291$	3.12637	−	6.48547i	0.183271	−	0.380185i
$292$	17.0675	+	3.28949i	0.998800	+	0.192503i
$293$	4.31378	−	9.44586i	0.252014	−	0.551833i	−0.740769	−	0.671760i	$-0.765539\pi$
$293$	4.31378	−	9.44586i	0.252014	−	0.551833i	0.992783	+	0.119927i	$0.0382660\pi$
$294$	−1.01815	+	24.2847i	−0.0593798	+	1.41631i
$295$	5.29295	−	2.41721i	0.308168	−	0.140735i
$296$	0.101781	−	0.0800417i	0.00591592	−	0.00465233i
$297$	−0.645022	+	1.35890i	−0.0374280	+	0.0788516i
$298$	26.0848	+	15.0601i	1.51105	+	0.872406i
$299$	−15.9384	+	23.3884i	−0.921743	+	1.35259i
$300$	−39.5062	+	8.71860i	−2.28089	+	0.503369i
$301$	15.6569	+	9.77148i	0.902447	+	0.563219i
$302$	−18.3702	+	2.64123i	−1.05709	+	0.151986i
$303$	−22.4898	−	9.55071i	−1.29200	−	0.548674i
$304$	−15.1519	−	15.8908i	−0.869019	−	0.911401i
$305$	19.8738	−	14.1520i	1.13797	−	0.810344i
$306$	3.03559	+	12.1922i	0.173533	+	0.696982i
$307$	−0.536794	+	3.73348i	−0.0306364	+	0.213081i	−0.999389	−	0.0349475i	$-0.988874\pi$
$307$	−0.536794	+	3.73348i	−0.0306364	+	0.213081i	0.968753	+	0.248029i	$0.0797827\pi$
$308$	1.05217	−	1.13316i	0.0599530	−	0.0645680i
$309$	11.7531	−	15.7992i	0.668613	−	0.898786i
$310$	−26.7965	+	51.9779i	−1.52194	+	2.95215i
$311$	22.0432	−	1.05005i	1.24996	−	0.0595428i	0.587861	−	0.808962i	$-0.299970\pi$
$311$	22.0432	−	1.05005i	1.24996	−	0.0595428i	0.662096	+	0.749419i	$0.269667\pi$
$312$	0.153845	+	0.356295i	0.00870974	+	0.0201713i
$313$	16.5759	−	17.3843i	0.936924	−	0.982618i	−0.0629572	−	0.998016i	$-0.520053\pi$
$313$	16.5759	−	17.3843i	0.936924	−	0.982618i	0.999881	+	0.0153983i	$0.00490164\pi$
$314$	−0.962457	+	6.69403i	−0.0543146	+	0.377766i
$315$	−22.9493	+	22.7420i	−1.29305	+	1.28136i
$316$	−1.30302	−	0.595070i	−0.0733007	−	0.0334753i
$317$	16.3978	−	3.97806i	0.920991	−	0.223430i	0.252885	−	0.967496i	$-0.418621\pi$
$317$	16.3978	−	3.97806i	0.920991	−	0.223430i	0.668106	+	0.744066i	$0.267105\pi$
$318$	−3.13019	−	25.5282i	−0.175533	−	1.43155i
$319$	0.0737153	−	0.184132i	0.00412727	−	0.0103094i
$320$	−1.57868	+	33.1405i	−0.0882508	+	1.85261i
$321$	−27.3575	+	6.03752i	−1.52695	+	0.336981i
$322$	11.9654	−	22.4472i	0.666806	−	1.25094i
$323$			11.5783i			0.644233i
$324$	13.3005	+	12.3799i	0.738917	+	0.687772i
$325$	−63.3862	−	25.3760i	−3.51603	−	1.40761i
$326$	0.119509	−	1.25155i	0.00661898	−	0.0693171i
$327$	−11.3294	+	5.54568i	−0.626519	+	0.306677i
$328$	0.00231706	−	0.00507364i	0.000127938	−	0.000280145i
$329$	−4.25486	−	0.761753i	−0.234578	−	0.0419968i
$330$	4.08032	−	0.304171i	0.224614	−	0.0167440i
$331$	10.1667	+	9.69389i	0.558810	+	0.532824i	0.915985	−	0.401213i	$-0.131411\pi$
$331$	10.1667	+	9.69389i	0.558810	+	0.532824i	−0.357175	+	0.934038i	$0.616260\pi$
$332$	−7.90139	+	1.52287i	−0.433645	+	0.0835783i
$333$	9.06558	−	4.74289i	0.496791	−	0.259909i
$334$	11.5997	+	5.98008i	0.634710	+	0.327216i
$335$	−32.1242	+	27.8358i	−1.75513	+	1.52083i
$336$	8.95863	+	15.7908i	0.488734	+	0.861460i
$337$	29.2545	+	4.20616i	1.59359	+	0.229124i	0.881230	−	0.472687i	$-0.156716\pi$
$337$	29.2545	+	4.20616i	1.59359	+	0.229124i	0.712363	+	0.701811i	$0.247625\pi$
$338$	−8.28164	+	42.9692i	−0.450462	+	2.33722i
$339$	−4.39768	−	3.97366i	−0.238849	−	0.215820i
$340$	12.4257	−	11.8479i	0.673877	−	0.642541i
$341$	1.20334	−	1.68986i	0.0651646	−	0.0915108i
$342$	18.1888	+	27.9314i	0.983536	+	1.51035i
$343$	9.38598	−	15.9657i	0.506795	−	0.862067i
$344$	−0.264845			−0.0142795
$345$	31.9547	−	11.0535i	1.72038	−	0.595100i
$346$	−5.05091	+	8.74844i	−0.271539	+	0.470319i
$347$	10.7624	+	20.8761i	0.577755	+	1.12069i	0.978836	+	0.204646i	$0.0656045\pi$
$347$	10.7624	+	20.8761i	0.577755	+	1.12069i	−0.401080	+	0.916043i	$0.631365\pi$
$348$	−1.85209	−	1.51986i	−0.0992822	−	0.0814733i
$349$	1.74608	+	3.82338i	0.0934655	+	0.204661i	0.950590	−	0.310448i	$-0.100479\pi$
$349$	1.74608	+	3.82338i	0.0934655	+	0.204661i	−0.857125	+	0.515108i	$0.827752\pi$
$350$	59.1020	+	16.5068i	3.15913	+	0.882328i
$351$	6.78856	+	29.9045i	0.362346	+	1.59619i
$352$	0.439283	−	2.27922i	0.0234139	−	0.121483i
$353$	6.66260	−	8.47218i	0.354614	−	0.450929i	−0.575717	−	0.817649i	$-0.695277\pi$
$353$	6.66260	−	8.47218i	0.354614	−	0.450929i	0.930331	+	0.366720i	$0.119519\pi$
$354$	−0.103194	+	4.96252i	−0.00548469	+	0.263755i
$355$	−38.8716	−	13.4536i	−2.06309	−	0.714042i
$356$	−5.78815	+	3.71982i	−0.306771	+	0.197150i
$357$	2.32721	−	9.28644i	0.123169	−	0.491491i
$358$	−31.4790	−	36.3287i	−1.66372	−	1.92003i
$359$	0.783514	+	0.747079i	0.0413523	+	0.0394293i	0.710473	−	0.703724i	$-0.248481\pi$
$359$	0.783514	+	0.747079i	0.0413523	+	0.0394293i	−0.669121	+	0.743153i	$0.733329\pi$
$360$	0.106594	−	0.451219i	0.00561800	−	0.0237813i
$361$	3.83175	+	11.0711i	0.201671	+	0.582691i
$362$	−0.131654	+	0.0125715i	−0.00691960	+	0.000660741i
$363$	18.8632	+	1.29210i	0.990062	+	0.0678176i
$364$	2.58063	−	31.4180i	0.135262	−	1.64675i
$365$	−4.98735	−	34.6877i	−0.261050	−	1.81564i
$366$	3.51297	+	20.5133i	0.183626	+	1.07225i
$367$	−18.5592	−	10.7152i	−0.968783	−	0.559327i	−0.0699181	−	0.997553i	$-0.522274\pi$
$367$	−18.5592	−	10.7152i	−0.968783	−	0.559327i	−0.898865	+	0.438226i	$0.855607\pi$
$368$	−1.29517	−	18.9558i	−0.0675154	−	0.988137i
$369$	0.253482	−	0.360537i	0.0131957	−	0.0187688i
$370$	−23.4123	−	15.0462i	−1.21715	−	0.782215i
$371$	−7.04193	+	18.2883i	−0.365599	+	0.949479i
$372$	−15.0779	−	20.0159i	−0.781753	−	1.03778i
$373$	3.64354	−	0.883913i	0.188655	−	0.0457673i	−0.140318	−	0.990106i	$-0.544813\pi$
$373$	3.64354	−	0.883913i	0.188655	−	0.0457673i	0.328973	+	0.944339i	$0.393297\pi$
$374$	−0.987602	+	0.703268i	−0.0510677	+	0.0363651i
$375$	24.2250	+	39.4759i	1.25097	+	2.03853i
$376$	0.0575855	−	0.0230538i	0.00296975	−	0.00118891i
$377$	−1.13916	−	3.87962i	−0.0586696	−	0.199810i
$378$	−8.97429	−	26.0584i	−0.461588	−	1.34030i
$379$	2.16959	+	3.37595i	0.111444	+	0.173411i	0.892496	−	0.451056i	$-0.148953\pi$
$379$	2.16959	+	3.37595i	0.111444	+	0.173411i	−0.781051	+	0.624467i	$0.785316\pi$
$380$	20.8706	−	40.4833i	1.07064	−	2.07675i
$381$	−9.51524	+	4.10858i	−0.487480	+	0.210489i
$382$	−16.8063	−	4.07716i	−0.859884	−	0.208606i
$383$	22.9083	−	9.17109i	1.17056	−	0.468621i	0.296780	−	0.954946i	$-0.404087\pi$
$383$	22.9083	−	9.17109i	1.17056	−	0.468621i	0.873778	+	0.486325i	$0.161663\pi$
$384$	−0.462470	−	0.250725i	−0.0236003	−	0.0127947i
$385$	−2.85284	−	1.25745i	−0.145394	−	0.0640857i
$386$	2.11589	−	7.20605i	0.107696	−	0.366778i
$387$	−20.5723	−	3.83675i	−1.04575	−	0.195033i
$388$	3.11907	−	7.79106i	0.158347	−	0.395531i
$389$	1.20215	−	0.619752i	0.0609515	−	0.0314227i	−0.427481	−	0.904024i	$-0.640599\pi$
$389$	1.20215	−	0.619752i	0.0609515	−	0.0314227i	0.488433	+	0.872601i	$0.337569\pi$
$390$	61.5527	−	56.2943i	3.11684	−	2.85057i
$391$	−6.40361	+	7.70562i	−0.323845	+	0.389690i
$392$	0.00703951	+	0.265676i	0.000355549	+	0.0134186i
$393$	−4.33875	+	11.7404i	−0.218861	+	0.592224i
$394$	−13.7938	+	10.8476i	−0.694923	+	0.546494i
$395$	−0.274533	+	2.87504i	−0.0138133	+	0.144659i
$396$	−0.641856	+	1.63166i	−0.0322545	+	0.0819941i
$397$	−16.5731	+	1.58253i	−0.831778	+	0.0794251i	−0.502252	−	0.864721i	$-0.667495\pi$
$397$	−16.5731	+	1.58253i	−0.831778	+	0.0794251i	−0.329526	+	0.944147i	$0.606889\pi$
$398$	−1.82862	+	2.11034i	−0.0916605	+	0.105782i
$399$	−2.22331	−	25.2998i	−0.111305	−	1.26658i
$400$	43.9783	−	12.9132i	2.19891	−	0.645659i
$401$	−1.39362	+	4.02660i	−0.0695941	+	0.201079i	−0.974434	−	0.224672i	$-0.927869\pi$
$401$	−1.39362	+	4.02660i	−0.0695941	+	0.201079i	0.904840	+	0.425751i	$0.139990\pi$
$402$	−9.48989	−	34.9953i	−0.473313	−	1.74541i
$403$	−2.01232	−	42.2439i	−0.100241	−	2.10432i
$404$	−26.9143	−	9.31514i	−1.33904	−	0.463446i
$405$	14.8166	−	33.5050i	0.736242	−	1.66488i
$406$	1.39519	+	3.35550i	0.0692420	+	0.166531i
$407$	0.746134	+	0.646529i	0.0369845	+	0.0320472i
$408$	0.0422247	+	0.130733i	0.00209043	+	0.00647225i
$409$	10.7395	−	10.2401i	0.531035	−	0.506341i	−0.376444	−	0.926440i	$-0.622853\pi$
$409$	10.7395	−	10.2401i	0.531035	−	0.506341i	0.907478	+	0.420099i	$0.138005\pi$
$410$	−1.19340	−	0.113956i	−0.0589377	−	0.00562787i
$411$	−23.7857	+	28.9850i	−1.17326	+	1.42972i
$412$	12.4093	−	19.3093i	0.611363	−	0.951300i
$413$	1.84749	−	3.30012i	0.0909088	−	0.162389i
$414$	−3.34296	+	28.6486i	−0.164298	+	1.40800i
$415$	8.11191	+	14.0502i	0.398198	+	0.689699i
$416$	−21.6832	−	42.0596i	−1.06311	−	2.06214i
$417$	13.1465	+	2.17005i	0.643788	+	0.106268i
$418$	−1.86567	+	2.61996i	−0.0912527	+	0.128146i
$419$	15.4802	+	4.54540i	0.756257	+	0.222057i	0.637061	−	0.770814i	$-0.280150\pi$
$419$	15.4802	+	4.54540i	0.756257	+	0.222057i	0.119196	+	0.992871i	$0.461968\pi$
$420$	−24.8764	+	28.2749i	−1.21384	+	1.37967i
$421$	−8.78003	−	7.60794i	−0.427913	−	0.370788i	0.414113	−	0.910225i	$-0.364092\pi$
$421$	−8.78003	−	7.60794i	−0.427913	−	0.370788i	−0.842026	+	0.539437i	$0.818637\pi$
$422$	1.72146	+	4.30000i	0.0837993	+	0.209321i
$423$	4.80703	−	0.956510i	0.233726	−	0.0465071i
$424$	−0.0532218	−	0.276141i	−0.00258468	−	0.0134106i
$425$	−21.4830	−	11.0753i	−1.04208	−	0.537229i
$426$	24.7365	−	24.8858i	1.19849	−	1.20572i
$427$	4.98767	−	15.0531i	0.241370	−	0.728470i
$428$	−31.3334	+	9.20032i	−1.51456	+	0.444714i
$429$	−2.44556	+	1.66595i	−0.118073	+	0.0804328i
$430$	18.6179	+	53.7930i	0.897837	+	2.59413i
$431$	−7.61116	−	10.6884i	−0.366617	−	0.514841i	0.589523	−	0.807751i	$-0.299316\pi$
$431$	−7.61116	−	10.6884i	−0.366617	−	0.514841i	−0.956140	+	0.292910i	$0.905376\pi$
$432$	−15.9919	−	12.9631i	−0.769409	−	0.623686i
$433$	−24.0704	+	10.9926i	−1.15675	+	0.528270i	−0.899003	−	0.437942i	$-0.855707\pi$
$433$	−24.0704	+	10.9926i	−1.15675	+	0.528270i	−0.257747	+	0.966212i	$0.582980\pi$
$434$	5.90717	+	37.5478i	0.283553	+	1.80235i
$435$	−1.67447	+	4.53100i	−0.0802846	+	0.217245i
$436$	−12.7333	+	7.35160i	−0.609817	+	0.352078i
$437$	−9.36763	+	24.8737i	−0.448115	+	1.18987i
$438$	28.5017	+	9.01660i	1.36187	+	0.430830i
$439$	−1.73616	+	36.4466i	−0.0828626	+	1.73950i	0.449763	+	0.893148i	$0.351509\pi$
$439$	−1.73616	+	36.4466i	−0.0828626	+	1.73950i	−0.532625	+	0.846351i	$0.678794\pi$
$440$	0.0442837	−	0.00636704i	0.00211114	−	0.000303537i
$441$	−3.30198	+	20.7388i	−0.157237	+	0.987561i
$442$	−6.96346	+	23.7154i	−0.331218	+	1.12803i
$443$	0.749959	+	7.85392i	0.0356316	+	0.373151i	0.995647	+	0.0932040i	$0.0297109\pi$
$443$	0.749959	+	7.85392i	0.0356316	+	0.373151i	−0.960015	+	0.279947i	$0.909683\pi$
$444$	10.1646	−	6.23769i	0.482393	−	0.296028i
$445$	10.9042	+	8.57516i	0.516909	+	0.406501i
$446$	20.9743	−	21.9972i	0.993162	−	1.04160i
$447$	20.8795	+	15.5324i	0.987567	+	0.734658i
$448$	11.8982	+	17.9856i	0.562135	+	0.849739i
$449$	11.0228	+	17.1518i	0.520197	+	0.809443i	0.997600	−	0.0692417i	$-0.0220580\pi$
$449$	11.0228	+	17.1518i	0.520197	+	0.809443i	−0.477402	+	0.878685i	$0.658422\pi$
$450$	−69.2239	+	7.03063i	−3.26325	+	0.331427i
$451$	0.0413294	+	0.0100264i	0.00194613	+	0.000472125i
$452$	−5.43064	−	4.27070i	−0.255436	−	0.200877i
$453$	−16.0290	+	0.429812i	−0.753107	+	0.0201943i
$454$	−9.78687	−	4.46951i	−0.459320	−	0.209765i
$455$	−61.5622	+	15.8011i	−2.88608	+	0.740765i
$456$	0.219287	+	0.291104i	0.0102691	+	0.0136322i
$457$	−6.16131	−	7.83474i	−0.288214	−	0.366494i	0.620288	−	0.784374i	$-0.287016\pi$
$457$	−6.16131	−	7.83474i	−0.288214	−	0.366494i	−0.908502	+	0.417880i	$0.862773\pi$
$458$	40.1017	−	20.6738i	1.87383	−	0.966026i
$459$	1.38597	+	10.7666i	0.0646916	+	0.502542i
$460$	36.2800	−	15.3996i	1.69156	−	0.718012i
$461$		−	25.1005i		−	1.16905i	−0.811377	−	0.584524i	$-0.801281\pi$
$461$		−	25.1005i		−	1.16905i	0.811377	−	0.584524i	$-0.198719\pi$
$462$	2.02297	−	1.72636i	0.0941173	−	0.0803176i
$463$	2.50543	+	17.4257i	0.116437	+	0.809839i	0.961428	+	0.275058i	$0.0886969\pi$
$463$	2.50543	+	17.4257i	0.116437	+	0.809839i	−0.844991	+	0.534781i	$0.820394\pi$
$464$	2.21106	+	1.57449i	0.102646	+	0.0730938i
$465$	−28.1934	+	41.9268i	−1.30744	+	1.94431i
$466$	4.97848	+	6.99129i	0.230623	+	0.323865i
$467$	17.6975	+	3.41091i	0.818942	+	0.157838i	0.581482	−	0.813559i	$-0.302473\pi$
$467$	17.6975	+	3.41091i	0.818942	+	0.157838i	0.237460	+	0.971397i	$0.423685\pi$
$468$	10.2766	+	34.2355i	0.475036	+	1.58254i
$469$	−6.15738	+	26.9332i	−0.284322	+	1.24366i
$470$	−8.73060	−	10.0757i	−0.402713	−	0.464755i
$471$	−1.49529	+	5.64843i	−0.0688995	+	0.260266i
$472$	0.00258243	+	0.0542118i	0.000118866	+	0.00249530i
$473$	−0.382167	−	1.98287i	−0.0175721	−	0.0911725i
$474$	−2.10751	−	1.27592i	−0.0968013	−	0.0586048i
$475$	−63.4663	−	9.12508i	−2.91203	−	0.418687i
$476$	1.96660	−	10.9847i	0.0901389	−	0.503482i
$477$	−0.133696	−	22.2207i	−0.00612150	−	1.01742i
$478$	−12.1705	−	50.1674i	−0.556665	−	2.29460i
$479$	12.7694	+	1.21933i	0.583450	+	0.0557127i	0.382608	−	0.923911i	$-0.375026\pi$
$479$	12.7694	+	1.21933i	0.583450	+	0.0557127i	0.200842	+	0.979624i	$0.435632\pi$
$480$	−9.20685	+	55.7766i	−0.420233	+	2.54584i
$481$	20.1041	+	0.957676i	0.916668	+	0.0436663i
$482$	−19.4373			−0.885344
$483$	12.5129	−	18.0673i	0.569358	−	0.822090i
$484$	22.0391			1.00178
$485$	−16.9010	−	0.805096i	−0.767437	−	0.0365575i
$486$	20.2572	+	23.7960i	0.918884	+	1.07941i
$487$	−43.4388	−	4.14790i	−1.96840	−	0.187959i	−0.969935	−	0.243364i	$-0.921749\pi$
$487$	−43.4388	−	4.14790i	−1.96840	−	0.187959i	−0.998464	+	0.0554046i	$0.982355\pi$
$488$	0.0536501	+	0.221149i	0.00242863	+	0.0100109i
$489$	0.227702	−	1.06210i	0.0102971	−	0.0480300i
$490$	53.4669	−	20.1061i	2.41539	−	0.908303i
$491$	−23.3468	−	3.35676i	−1.05363	−	0.151489i	−0.406330	−	0.913727i	$-0.633191\pi$
$491$	−23.3468	−	3.35676i	−1.05363	−	0.151489i	−0.647297	+	0.762238i	$0.724101\pi$
$492$	0.266057	−	0.439464i	0.0119948	−	0.0198126i
$493$	−0.270885	−	1.40548i	−0.0122000	−	0.0632998i
$494$	3.11992	+	65.4951i	0.140372	+	2.94676i
$495$	3.53205	+	0.146959i	0.158754	+	0.00660531i
$496$	18.5920	+	21.4563i	0.834807	+	0.963418i
$497$	−25.5510	+	7.87151i	−1.14612	+	0.353086i
$498$	−13.8011	+	1.02881i	−0.618442	+	0.0461022i
$499$	−7.81322	−	1.50588i	−0.349768	−	0.0674122i	0.0113416	−	0.999936i	$-0.496390\pi$
$499$	−7.81322	−	1.50588i	−0.349768	−	0.0674122i	−0.361109	+	0.932523i	$0.617602\pi$
$500$	31.3160	+	43.9772i	1.40049	+	1.96672i
$501$	9.35668	+	6.29183i	0.418026	+	0.281098i
$502$	−43.2487	−	30.7973i	−1.93028	−	1.37455i
$503$	0.918442	+	6.38790i	0.0409513	+	0.284823i	0.999999	+	0.00157712i	$0.000502012\pi$
$503$	0.918442	+	6.38790i	0.0409513	+	0.284823i	−0.959047	+	0.283245i	$0.908589\pi$
$504$	−0.117370	−	0.277558i	−0.00522806	−	0.0123634i
$505$			57.4223i			2.55526i
$506$	−2.69067	+	0.711800i	−0.119615	+	0.0316434i
$507$	−11.4036	+	36.0471i	−0.506452	+	1.60091i
$508$	−10.7381	+	5.53587i	−0.476425	+	0.245614i
$509$	−8.55708	−	10.8812i	−0.379286	−	0.482301i	0.558505	−	0.829501i	$-0.311375\pi$
$509$	−8.55708	−	10.8812i	−0.379286	−	0.482301i	−0.937791	+	0.347200i	$0.887133\pi$
$510$	23.5851	−	17.7665i	1.04436	−	0.786715i
$511$	−15.9356	−	16.2756i	−0.704949	−	0.719990i
$512$	29.1692	+	13.3211i	1.28911	+	0.588716i
$513$	12.8163	+	25.7887i	0.565855	+	1.13860i
$514$	−18.5223	−	14.5661i	−0.816983	−	0.642483i
$515$	−44.9728	−	10.9103i	−1.98174	−	0.480765i
$516$	−24.2293	−	2.82307i	−1.06664	−	0.124279i
$517$	0.255697	+	0.397872i	0.0112455	+	0.0174984i
$518$	−18.0555	+	1.09995i	−0.793314	+	0.0483290i
$519$	−5.20933	+	7.00267i	−0.228664	+	0.307383i
$520$	0.629396	−	0.660092i	0.0276008	−	0.0289469i
$521$	2.70226	+	2.12508i	0.118388	+	0.0931015i	0.675598	−	0.737270i	$-0.263886\pi$
$521$	2.70226	+	2.12508i	0.118388	+	0.0931015i	−0.557210	+	0.830372i	$0.688128\pi$
$522$	−2.86141	−	2.96503i	−0.125240	−	0.129776i
$523$	0.559484	+	5.85918i	0.0244645	+	0.256204i	0.999427	+	0.0338363i	$0.0107725\pi$
$523$	0.559484	+	5.85918i	0.0244645	+	0.256204i	−0.974963	+	0.222368i	$0.928621\pi$
$524$	−4.11037	+	13.9986i	−0.179562	+	0.611533i
$525$	49.0694	+	20.0754i	2.14157	+	0.876162i
$526$	−57.4974	+	8.26688i	−2.50701	+	0.360453i
$527$	0.712356	−	14.9542i	0.0310307	−	0.651415i
$528$	0.599153	−	1.89394i	0.0260748	−	0.0824232i
$529$	−19.9913	+	11.3731i	−0.869188	+	0.494482i
$530$	−52.3460	+	30.2220i	−2.27376	+	1.31276i
$531$	−0.584761	+	4.24840i	−0.0253765	+	0.184365i
$532$	−4.60083	−	29.2443i	−0.199471	−	1.26790i
$533$	0.788643	−	0.360161i	0.0341599	−	0.0156003i
$534$	−10.6283	+	5.20249i	−0.459932	+	0.225134i
$535$	38.1914	+	53.6323i	1.65116	+	2.31873i
$536$	−0.129672	−	0.374663i	−0.00560098	−	0.0161830i
$537$	−23.3821	−	34.3241i	−1.00901	−	1.48119i
$538$	50.9659	−	14.9649i	2.19730	−	0.645185i
$539$	−1.97893	+	0.436070i	−0.0852387	+	0.0187829i
$540$	14.5614	−	40.1435i	0.626625	−	1.72750i
$541$	21.3402	+	11.0016i	0.917487	+	0.472997i	0.851223	−	0.524805i	$-0.175862\pi$
$541$	21.3402	+	11.0016i	0.917487	+	0.472997i	0.0662641	+	0.997802i	$0.478892\pi$
$542$	3.80794	+	19.7574i	0.163565	+	0.848655i
$543$	−0.114240	−	0.00237557i	−0.00490249	−	0.000101946i
$544$	−6.22574	−	15.5512i	−0.266927	−	0.666750i
$545$	22.4037	+	19.4129i	0.959668	+	0.831557i
$546$	10.6620	−	53.1579i	0.456292	−	2.27495i
$547$	36.9785	+	10.8579i	1.58109	+	0.464249i	0.950204	−	0.311629i	$-0.100875\pi$
$547$	36.9785	+	10.8579i	1.58109	+	0.464249i	0.630883	+	0.775878i	$0.282693\pi$
$548$	−25.3518	+	35.6016i	−1.08297	+	1.52083i
$549$	0.963625	+	17.9553i	0.0411265	+	0.766314i
$550$	−3.07661	−	5.96779i	−0.131187	−	0.254468i
$551$	−1.89858	−	3.28844i	−0.0808822	−	0.140092i
$552$	−0.0150603	+	0.315018i	−0.000641009	+	0.0134080i
$553$	0.960053	+	1.61313i	0.0408256	+	0.0685974i
$554$	16.4381	−	25.5781i	0.698387	−	1.08671i
$555$	−18.5875	−	15.2533i	−0.788994	−	0.647467i
$556$	15.4611	+	1.47635i	0.655696	+	0.0626113i
$557$	−25.4923	+	24.3069i	−1.08014	+	1.02991i	−0.0806935	+	0.996739i	$0.525713\pi$
$557$	−25.4923	+	24.3069i	−1.08014	+	1.02991i	−0.999450	+	0.0331753i	$0.989438\pi$
$558$	−21.7736	−	37.1944i	−0.921751	−	1.57456i
$559$	−31.1122	−	26.9588i	−1.31590	−	1.14024i
$560$	25.9283	−	33.8847i	1.09567	−	1.43189i
$561$	−0.917857	+	0.504778i	−0.0387520	+	0.0213118i
$562$	52.7304	+	18.2502i	2.22430	+	0.769837i
$563$	−0.266735	−	5.59945i	−0.0112415	−	0.235989i	−0.997494	−	0.0707455i	$-0.977462\pi$
$563$	−0.266735	−	5.59945i	−0.0112415	−	0.235989i	0.986253	−	0.165243i	$-0.0528409\pi$
$564$	5.51395	−	1.49525i	0.232179	−	0.0629614i
$565$	−4.55582	+	13.1632i	−0.191665	+	0.553779i
$566$	19.8106	−	5.81692i	0.832702	−	0.244503i
$567$	−5.09595	−	23.2601i	−0.214010	−	0.976832i
$568$	0.251248	−	0.289956i	0.0105421	−	0.0121663i
$569$	−31.6736	+	3.02446i	−1.32783	+	0.126792i	−0.734741	−	0.678347i	$-0.762696\pi$
$569$	−31.6736	+	3.02446i	−1.32783	+	0.126792i	−0.593086	+	0.805139i	$0.702090\pi$
$570$	43.7111	−	65.0036i	1.83086	−	2.72270i
$571$	1.60734	−	16.8328i	0.0672651	−	0.704432i	−0.897446	−	0.441123i	$-0.854580\pi$
$571$	1.60734	−	16.8328i	0.0672651	−	0.704432i	0.964712	−	0.263309i	$-0.0848138\pi$
$572$	−2.71126	+	2.13216i	−0.113363	+	0.0891499i
$573$	−14.0151	−	5.17938i	−0.585489	−	0.216372i
$574$	−0.669594	+	0.398507i	−0.0279483	+	0.0166334i
$575$	−37.1915	−	41.1743i	−1.55099	−	1.71709i
$576$	−20.0033	−	14.0637i	−0.833470	−	0.585986i
$577$	−29.7126	+	15.3179i	−1.23695	+	0.637693i	−0.947578	−	0.319523i	$-0.896477\pi$
$577$	−29.7126	+	15.3179i	−1.23695	+	0.637693i	−0.289374	+	0.957216i	$0.593447\pi$
$578$	9.41451	−	23.5163i	0.391592	−	0.978150i
$579$	2.53634	−	5.97250i	0.105407	−	0.248209i
$580$	−1.58633	+	5.40253i	−0.0658686	+	0.224328i
$581$	9.64931	+	4.25315i	0.400321	+	0.176450i
$582$	6.87907	−	12.6887i	0.285147	−	0.525962i
$583$	1.99064	−	0.796934i	0.0824441	−	0.0330056i
$584$	0.317655	+	0.0770622i	0.0131446	+	0.00318886i
$585$	58.4520	−	42.1558i	2.41669	−	1.74293i
$586$	9.53919	−	18.5034i	0.394060	−	0.764370i
$587$	12.2572	+	19.0725i	0.505908	+	0.787208i	0.996448	−	0.0842106i	$-0.0268369\pi$
$587$	12.2572	+	19.0725i	0.505908	+	0.787208i	−0.490540	+	0.871419i	$0.663201\pi$
$588$	−2.18791	+	24.3804i	−0.0902279	+	1.00543i
$589$	−11.1893	−	38.1074i	−0.461049	−	1.57019i
$590$	10.8295	−	4.33548i	0.445843	−	0.178489i
$591$	−12.9222	+	7.92991i	−0.531548	+	0.326193i
$592$	−11.0060	+	7.83735i	−0.452344	+	0.322113i
$593$	16.8293	−	4.08274i	0.691096	−	0.167658i	0.125196	−	0.992132i	$-0.460044\pi$
$593$	16.8293	−	4.08274i	0.691096	−	0.167658i	0.565900	+	0.824474i	$0.308529\pi$
$594$	−1.42125	+	2.65962i	−0.0583148	+	0.109126i
$595$	−22.2258	+	3.49665i	−0.911170	+	0.143349i
$596$	25.5183	+	16.3996i	1.04527	+	0.671753i
$597$	−1.78029	+	1.62820i	−0.0728626	+	0.0666379i
$598$	−34.1470	+	45.3140i	−1.39638	+	1.85303i
$599$	11.3734	+	6.56643i	0.464704	+	0.268297i	0.714020	−	0.700125i	$-0.246873\pi$
$599$	11.3734	+	6.56643i	0.464704	+	0.268297i	−0.249316	+	0.968422i	$0.580206\pi$
$600$	−0.749890	+	0.128421i	−0.0306141	+	0.00524277i
$601$	−1.21481	−	8.44918i	−0.0495531	−	0.344649i	−0.999482	−	0.0321832i	$-0.989754\pi$
$601$	−1.21481	−	8.44918i	−0.0495531	−	0.344649i	0.949929	−	0.312466i	$-0.101155\pi$
$602$	30.4201	+	21.0605i	1.23983	+	0.858361i
$603$	−4.64483	−	30.9811i	−0.189152	−	1.26165i
$604$	−18.6060	+	1.77666i	−0.757068	+	0.0722912i
$605$	−14.5332	−	41.9910i	−0.590859	−	1.70718i
$606$	−44.1238	−	21.2702i	−1.79241	−	0.864042i
$607$	−4.51514	−	4.30518i	−0.183264	−	0.174742i	0.592894	−	0.805281i	$-0.297985\pi$
$607$	−4.51514	−	4.30518i	−0.183264	−	0.174742i	−0.776158	+	0.630539i	$0.782834\pi$
$608$	−29.1008	−	33.5841i	−1.18019	−	1.36201i
$609$	0.861800	+	3.01912i	0.0349219	+	0.122341i
$610$	41.1463	−	26.4431i	1.66597	−	1.07065i
$611$	9.11142	+	3.15349i	0.368609	+	0.127577i
$612$	2.46940	+	12.4102i	0.0998196	+	0.501652i
$613$	5.44810	−	6.92782i	0.220047	−	0.279812i	−0.663479	−	0.748195i	$-0.730921\pi$
$613$	5.44810	−	6.92782i	0.220047	−	0.279812i	0.883526	+	0.468383i	$0.155163\pi$
$614$	−1.43104	+	7.42494i	−0.0577521	+	0.299646i
$615$	−1.01275	−	0.217122i	−0.0408381	−	0.00875520i
$616$	0.0207781	−	0.0203440i	0.000837172	−	0.000819684i
$617$	13.1685	+	28.8349i	0.530142	+	1.16085i	0.965455	+	0.260570i	$0.0839106\pi$
$617$	13.1685	+	28.8349i	0.530142	+	1.16085i	−0.435313	+	0.900279i	$0.643362\pi$
$618$	25.0422	−	30.5161i	1.00735	−	1.22754i
$619$	6.82042	+	13.2298i	0.274136	+	0.531749i	0.985207	−	0.171371i	$-0.0548198\pi$
$619$	6.82042	+	13.2298i	0.274136	+	0.531749i	−0.711071	+	0.703120i	$0.751789\pi$
$620$	−29.4466	+	51.0029i	−1.18260	+	2.04833i
$621$	−5.73343	+	24.2513i	−0.230075	+	0.973173i
$622$	44.2408			1.77390
$623$	9.01119	+	0.309698i	0.361026	+	0.0124078i
$624$	−14.2661	−	37.9003i	−0.571101	−	1.51723i
$625$	29.5844	−	41.5455i	1.18338	−	1.66182i
$626$	34.8508	−	33.2302i	1.39292	−	1.32814i
$627$	−1.86304	+	2.06184i	−0.0744027	+	0.0823420i
$628$	−1.28895	+	6.68773i	−0.0514348	+	0.266869i
$629$	7.05233	+	1.01397i	0.281195	+	0.0404297i
$630$	−48.1244	+	43.3507i	−1.91732	+	1.72713i
$631$	−9.08534	+	7.87249i	−0.361682	+	0.313399i	−0.816677	−	0.577095i	$-0.804186\pi$
$631$	−9.08534	+	7.87249i	−0.361682	+	0.313399i	0.454995	+	0.890494i	$0.349641\pi$
$632$	−0.0239436	−	0.0123438i	−0.000952427	−	0.000491010i
$633$	1.04736	+	3.86229i	0.0416288	+	0.153512i
$634$	33.2153	−	6.40173i	1.31915	−	0.254245i
$635$	17.6284	+	16.8087i	0.699563	+	0.667032i
$636$	−1.92552	−	25.8300i	−0.0763518	−	1.02423i
$637$	−26.2164	+	31.9263i	−1.03873	+	1.26497i
$638$	0.165176	−	0.361685i	0.00653938	−	0.0143192i
$639$	23.7166	−	18.8830i	0.938215	−	0.747000i
$640$	−0.117519	+	1.23072i	−0.00464535	+	0.0486483i
$641$	25.9643	+	10.3945i	1.02553	+	0.410559i	0.822592	−	0.568633i	$-0.192527\pi$
$641$	25.9643	+	10.3945i	1.02553	+	0.410559i	0.202936	+	0.979192i	$0.434952\pi$
$642$	−55.3582	+	9.48028i	−2.18482	+	0.374157i
$643$		−	28.0339i		−	1.10555i	−0.833330	−	0.552775i	$-0.813569\pi$
$643$		−	28.0339i		−	1.10555i	0.833330	−	0.552775i	$-0.186431\pi$
$644$	13.1122	−	22.0074i	0.516694	−	0.867212i
$645$	10.5987	+	48.0255i	0.417324	+	1.89100i
$646$	−1.10444	+	23.1850i	−0.0434536	+	0.912203i
$647$	1.73225	−	4.32695i	0.0681018	−	0.170110i	−0.890413	−	0.455154i	$-0.849584\pi$
$647$	1.73225	−	4.32695i	0.0681018	−	0.170110i	0.958514	+	0.285044i	$0.0920083\pi$
$648$	0.238761	+	0.244447i	0.00937941	+	0.00960277i
$649$	−0.402153	+	0.0975612i	−0.0157859	+	0.00382961i
$650$	−124.508	−	56.8607i	−4.88359	−	2.23026i
$651$	1.31499	+	32.8133i	0.0515386	+	1.28606i
$652$	0.180193	−	1.25327i	0.00705690	−	0.0490818i
$653$	23.5616	−	24.7107i	0.922035	−	0.967003i	−0.0775148	−	0.996991i	$-0.524698\pi$
$653$	23.5616	−	24.7107i	0.922035	−	0.967003i	0.999550	+	0.0299882i	$0.00954698\pi$
$654$	−23.2157	+	10.0243i	−0.907806	+	0.391981i
$655$	29.3820	−	1.39963i	1.14805	−	0.0546883i
$656$	−0.266696	+	0.517319i	−0.0104127	+	0.0201979i
$657$	23.5580	+	10.5877i	0.919084	+	0.413067i
$658$	−8.44752	−	1.93124i	−0.329319	−	0.0752877i
$659$	−0.214021	+	1.48855i	−0.00833707	+	0.0579856i	−0.993565	−	0.113261i	$-0.963870\pi$
$659$	−0.214021	+	1.48855i	−0.00833707	+	0.0579856i	0.985228	+	0.171247i	$0.0547795\pi$
$660$	4.11916	−	0.110454i	0.160338	−	0.00429942i
$661$	23.3593	−	16.6341i	0.908572	−	0.646991i	−0.0271876	−	0.999630i	$-0.508655\pi$
$661$	23.3593	−	16.6341i	0.908572	−	0.646991i	0.935759	+	0.352639i	$0.114716\pi$
$662$	19.4336	+	20.3814i	0.755309	+	0.792145i
$663$	−8.34718	+	19.6557i	−0.324178	+	0.763365i
$664$	−0.149783	+	0.0215356i	−0.00581272	+	0.000835743i
$665$	−52.6850	+	28.0504i	−2.04304	+	1.08775i
$666$	18.6059	−	8.63268i	0.720962	−	0.334510i
$667$	0.555189	−	3.23858i	0.0214970	−	0.125398i
$668$	11.3822	+	6.57150i	0.440389	+	0.254259i
$669$	20.1992	−	16.7803i	0.780945	−	0.648763i
$670$	−66.9826	+	52.6757i	−2.58776	+	2.03504i
$671$	−1.57830	+	0.720788i	−0.0609298	+	0.0278257i
$672$	16.5901	+	32.7855i	0.639978	+	1.26473i
$673$	11.1555	−	24.4272i	0.430014	−	0.941600i	−0.563310	−	0.826246i	$-0.690472\pi$
$673$	11.1555	−	24.4272i	0.430014	−	0.941600i	0.993324	−	0.115354i	$-0.0368004\pi$
$674$	58.1797	+	11.2132i	2.24100	+	0.431917i
$675$	−60.1094	−	0.888180i	−2.31361	−	0.0341861i
$676$	−10.3899	+	42.8279i	−0.399613	+	1.64723i
$677$	−2.94199	+	8.50033i	−0.113070	+	0.326694i	−0.987311	−	0.158798i	$-0.949238\pi$
$677$	−2.94199	+	8.50033i	−0.113070	+	0.326694i	0.874241	+	0.485492i	$0.161359\pi$
$678$	−8.42713	−	8.37658i	−0.323642	−	0.321701i
$679$	−9.17230	+	6.06783i	−0.352001	+	0.232862i
$680$	0.244007	−	0.211433i	0.00935724	−	0.00810809i
$681$	−7.95196	−	4.81422i	−0.304720	−	0.184481i
$682$	2.57083	−	3.26908i	0.0984423	−	0.125180i
$683$	−20.7544	+	7.18317i	−0.794146	+	0.274857i	−0.693867	−	0.720103i	$-0.744095\pi$
$683$	−20.7544	+	7.18317i	−0.794146	+	0.274857i	−0.100278	+	0.994959i	$0.531973\pi$
$684$	16.9585	+	28.9691i	0.648425	+	1.10766i
$685$	84.5491	+	24.8259i	3.23045	+	0.948547i
$686$	20.3180	−	31.0753i	0.775744	−	1.18646i
$687$	36.4815	−	13.7321i	1.39186	−	0.523911i
$688$	27.6046	+	1.31497i	1.05242	+	0.0501328i
$689$	21.8565	−	37.8566i	0.832668	−	1.44222i
$690$	65.0424	−	19.0860i	2.47612	−	0.726593i
$691$	−21.6951	−	37.5769i	−0.825319	−	1.42949i	−0.901676	−	0.432413i	$-0.857662\pi$
$691$	−21.6951	−	37.5769i	−0.825319	−	1.42949i	0.0763569	−	0.997081i	$-0.475671\pi$
$692$	−5.50017	+	8.55843i	−0.209085	+	0.325343i
$693$	1.90869	−	1.27925i	0.0725051	−	0.0485946i
$694$	19.5599	+	42.8302i	0.742483	+	1.62581i
$695$	−7.38258	−	30.4314i	−0.280037	−	1.15433i
$696$	−0.0334298	−	0.0302066i	−0.00126715	−	0.00114498i
$697$	0.290032	−	0.100381i	0.0109857	−	0.00380220i
$698$	3.13174	+	7.82272i	0.118538	+	0.296094i
$699$	3.57335	+	6.49756i	0.135157	+	0.245760i
$700$	58.6625	+	19.4371i	2.21723	+	0.734655i
$701$	37.0576	−	23.8155i	1.39965	−	0.899499i	0.399794	−	0.916605i	$-0.369082\pi$
$701$	37.0576	−	23.8155i	1.39965	−	0.899499i	0.999854	+	0.0171064i	$0.00544541\pi$
$702$	10.7412	+	60.5302i	0.405402	+	2.28456i
$703$	18.5596	−	3.57707i	0.699988	−	0.134912i
$704$	0.556284	−	2.29303i	0.0209657	−	0.0864220i
$705$	−6.48494	−	9.51966i	−0.244237	−	0.358531i
$706$	14.1497	−	16.3297i	0.532532	−	0.614575i
$707$	22.0503	+	30.1131i	0.829286	+	1.13252i
$708$	−0.341608	+	4.98709i	−0.0128384	+	0.187426i
$709$	−29.0222	−	20.6666i	−1.08995	−	0.776150i	−0.113856	−	0.993497i	$-0.536320\pi$
$709$	−29.0222	−	20.6666i	−1.08995	−	0.776150i	−0.976094	+	0.217347i	$0.930260\pi$
$710$	−76.5554	−	30.6481i	−2.87307	−	1.15020i
$711$	−1.68104	−	1.30569i	−0.0630439	−	0.0489673i
$712$	−0.112054	+	0.0646943i	−0.00419939	+	0.00242452i
$713$	13.6293	−	31.5499i	0.510422	−	1.18155i
$714$	5.54596	−	18.3737i	0.207552	−	0.687619i
$715$	5.85026	+	3.75973i	0.218787	+	0.140606i
$716$	−29.9254	−	38.0532i	−1.11836	−	1.42212i
$717$	−5.42819	−	44.2694i	−0.202719	−	1.65327i
$718$	1.49769	+	1.57073i	0.0558934	+	0.0586193i
$719$	1.14885	+	12.0313i	0.0428450	+	0.448693i	0.991285	+	0.131736i	$0.0420551\pi$
$719$	1.14885	+	12.0313i	0.0428450	+	0.448693i	−0.948440	+	0.316957i	$0.897339\pi$
$720$	−13.3506	+	46.5010i	−0.497546	+	1.73299i
$721$	−27.7740	+	11.5482i	−1.03436	+	0.430076i
$722$	6.61687	+	22.5350i	0.246254	+	0.838665i
$723$	−16.6806	−	1.94353i	−0.620359	−	0.0722808i
$724$	−0.133040	+	0.00633746i	−0.00494438	+	0.000235530i
$725$	7.91764	−	0.377164i	0.294054	−	0.0140075i
$726$	37.6495	+	4.38671i	1.39731	+	0.162806i
$727$	3.99047	+	13.5903i	0.147998	+	0.504036i	0.999804	−	0.0198228i	$-0.00631020\pi$
$727$	3.99047	+	13.5903i	0.147998	+	0.504036i	−0.851805	+	0.523859i	$0.824492\pi$
$728$	0.0765876	−	0.587851i	0.00283853	−	0.0217872i
$729$	15.0049	+	22.4467i	0.555736	+	0.831359i
$730$	−6.67813	−	69.9365i	−0.247169	−	2.58847i
$731$	−10.0566	−	10.5470i	−0.371956	−	0.390096i
$732$	2.55088	+	20.8036i	0.0942833	+	0.768925i
$733$	1.25790	+	1.59955i	0.0464616	+	0.0590807i	0.808729	−	0.588182i	$-0.200156\pi$
$733$	1.25790	+	1.59955i	0.0464616	+	0.0590807i	−0.762267	+	0.647263i	$0.775914\pi$
$734$	−36.1419	−	23.2270i	−1.33402	−	0.857325i
$735$	47.8944	−	11.9085i	1.76661	−	0.439251i
$736$	−0.792866	−	38.4457i	−0.0292254	−	1.41713i
$737$	2.61795	−	1.51147i	0.0964335	−	0.0556759i
$738$	0.541978	−	0.697781i	0.0199505	−	0.0256857i
$739$	0.777682	+	0.311337i	0.0286075	+	0.0114527i	0.385922	−	0.922531i	$-0.373883\pi$
$739$	0.777682	+	0.311337i	0.0286075	+	0.0114527i	−0.357315	+	0.933984i	$0.616308\pi$
$740$	−22.8306	−	16.2576i	−0.839269	−	0.597641i
$741$	−3.87141	+	56.5183i	−0.142220	+	2.07625i
$742$	−15.8457	+	35.9498i	−0.581713	+	1.31976i
$743$	−8.59792	+	9.92253i	−0.315427	+	0.364022i	−0.891218	−	0.453575i	$-0.850149\pi$
$743$	−8.59792	+	9.92253i	−0.315427	+	0.364022i	0.575791	+	0.817597i	$0.304694\pi$
$744$	−0.265315	−	0.389473i	−0.00972691	−	0.0142788i
$745$	14.4185	−	59.4340i	0.528255	−	2.17750i
$746$	7.38035	−	1.42245i	0.270214	−	0.0520795i
$747$	−11.9467	−	0.497067i	−0.437105	−	0.0181867i
$748$	−1.02718	+	0.660126i	−0.0375573	+	0.0241366i
$749$	40.6230	+	13.4600i	1.48433	+	0.491816i
$750$	44.7440	+	81.3596i	1.63382	+	2.97083i
$751$	−5.95656	−	14.8788i	−0.217358	−	0.542934i	0.779112	−	0.626885i	$-0.215670\pi$
$751$	−5.95656	−	14.8788i	−0.217358	−	0.542934i	−0.996470	+	0.0839511i	$0.973246\pi$
$752$	−6.11657	+	2.11697i	−0.223048	+	0.0771978i
$753$	−34.0356	−	30.7539i	−1.24033	−	1.12074i
$754$	−1.91104	−	7.87743i	−0.0695961	−	0.286879i
$755$	15.6544	+	34.2783i	0.569721	+	1.24751i
$756$	−7.77897	−	26.6434i	−0.282918	−	0.969013i
$757$	−5.76106	+	8.96438i	−0.209389	+	0.325816i	−0.930024	−	0.367499i	$-0.880214\pi$
$757$	−5.76106	+	8.96438i	−0.209389	+	0.325816i	0.720635	+	0.693315i	$0.243851\pi$
$758$	4.02249	+	6.96716i	0.146103	+	0.253058i
$759$	−2.38024	+	0.341810i	−0.0863973	+	0.0124069i
$760$	0.428260	−	0.741767i	0.0155346	−	0.0269067i
$761$	−24.3867	−	1.16168i	−0.884017	−	0.0421109i	−0.399339	−	0.916803i	$-0.630760\pi$
$761$	−24.3867	−	1.16168i	−0.884017	−	0.0421109i	−0.484678	+	0.874693i	$0.661063\pi$
$762$	−19.4458	+	7.31961i	−0.704446	+	0.265162i
$763$	19.2034	+	1.57734i	0.695209	+	0.0571035i
$764$	−16.7109	−	4.90675i	−0.604578	−	0.177520i
$765$	22.0166	−	12.8885i	0.796013	−	0.465986i
$766$	46.7477	−	16.1795i	1.68906	−	0.584590i
$767$	−5.21491	+	6.63130i	−0.188300	+	0.239442i
$768$	23.2514	+	14.0767i	0.839013	+	0.507950i
$769$	18.8359	−	16.3214i	0.679241	−	0.588566i	−0.245392	−	0.969424i	$-0.578917\pi$
$769$	18.8359	−	16.3214i	0.679241	−	0.588566i	0.924634	+	0.380858i	$0.124371\pi$
$770$	−5.59274	−	2.79013i	−0.201548	−	0.100549i
$771$	−14.4389	−	14.3523i	−0.520006	−	0.516886i
$772$	2.47378	−	7.14752i	0.0890333	−	0.257245i
$773$	−8.50665	+	35.0649i	−0.305963	+	1.26120i	0.586453	+	0.809983i	$0.300524\pi$
$773$	−8.50665	+	35.0649i	−0.305963	+	1.26120i	−0.892416	+	0.451213i	$0.850991\pi$
$774$	−40.8291	−	9.64531i	−1.46757	−	0.346693i
$775$	81.4098	+	15.6905i	2.92433	+	0.563618i
$776$	0.0655604	−	0.143557i	0.00235348	−	0.00515341i
$777$	−15.6048	−	0.861422i	−0.559820	−	0.0309033i
$778$	2.46638	−	1.12636i	0.0884239	−	0.0403818i
$779$	0.639998	−	0.503300i	0.0229303	−	0.0180326i
$780$	64.6164	−	53.6795i	2.31364	−	1.92203i
$781$	2.53342	+	1.46267i	0.0906529	+	0.0523385i
$782$	−13.5580	+	14.8193i	−0.484833	+	0.529939i
$783$	−2.15912	−	2.83064i	−0.0771607	−	0.101159i
$784$	0.585372	−	27.7262i	0.0209061	−	0.990220i
$785$	13.5920	−	1.95424i	0.485121	−	0.0697498i
$786$	−9.80807	+	23.0958i	−0.349842	+	0.823799i
$787$	9.31252	+	9.76669i	0.331955	+	0.348145i	0.868466	−	0.495749i	$-0.165106\pi$
$787$	9.31252	+	9.76669i	0.331955	+	0.348145i	−0.536511	+	0.843894i	$0.680258\pi$
$788$	−14.3957	+	10.2511i	−0.512825	+	0.365181i
$789$	−50.1696	+	1.34528i	−1.78608	+	0.0478933i
$790$	−0.823988	+	5.73096i	−0.0293162	+	0.203899i
$791$	2.66555	+	8.65239i	0.0947760	+	0.307644i
$792$	−0.0135167	+	0.0300750i	−0.000480295	+	0.00106867i
$793$	−16.2085	+	31.4401i	−0.575581	+	1.11647i
$794$	−33.3378	+	1.58808i	−1.18311	+	0.0563587i
$795$	−47.9440	+	20.7017i	−1.70040	+	0.734214i
$796$	−1.94062	+	2.03527i	−0.0687835	+	0.0721381i
$797$	−4.97328	+	34.5899i	−0.176163	+	1.22524i	0.689379	+	0.724401i	$0.257884\pi$
$797$	−4.97328	+	34.5899i	−0.176163	+	1.22524i	−0.865542	+	0.500837i	$0.833026\pi$
$798$	−2.03877	−	50.8740i	−0.0721716	−	1.80092i
$799$	3.10469	+	1.41787i	0.109836	+	0.0501605i
$800$	90.1502	−	21.8702i	3.18729	−	0.773228i
$801$	−9.64117	+	3.40193i	−0.340654	+	0.120201i
$802$	−3.17476	+	7.93017i	−0.112105	+	0.280024i
$803$	−0.118587	+	2.48945i	−0.00418485	+	0.0878508i
$804$	−7.86939	−	35.6582i	−0.277532	−	1.25757i
$805$	−50.5770	−	10.4703i	−1.78260	−	0.369031i
$806$		−	84.7835i		−	2.98637i
$807$	45.2341	−	7.74649i	1.59232	−	0.272689i
$808$	−0.497227	−	0.199060i	−0.0174924	−	0.00700290i
$809$	−0.538365	+	5.63801i	−0.0189279	+	0.198222i	0.981062	+	0.193695i	$0.0620471\pi$
$809$	−0.538365	+	5.63801i	−0.0189279	+	0.198222i	−0.999990	+	0.00452716i	$0.998559\pi$
$810$	32.8656	−	65.6790i	1.15478	−	2.30772i
$811$	16.7217	−	36.6154i	0.587178	−	1.28574i	−0.349954	−	0.936767i	$-0.613803\pi$
$811$	16.7217	−	36.6154i	0.587178	−	1.28574i	0.937132	−	0.348974i	$-0.113470\pi$
$812$	1.24269	+	3.44232i	0.0436099	+	0.120802i
$813$	1.29234	+	17.3361i	0.0453242	+	0.608005i
$814$	1.43243	+	1.36582i	0.0502067	+	0.0478720i
$815$	−2.50667	+	0.483120i	−0.0878047	+	0.0169230i
$816$	−3.75196	−	13.8359i	−0.131345	−	0.484352i
$817$	−34.3626	−	17.7151i	−1.20219	−	0.619774i
$818$	22.4822	−	19.4810i	0.786072	−	0.681136i
$819$	14.4651	−	44.5528i	0.505453	−	1.55680i
$820$	−1.19503	−	0.171820i	−0.0417324	−	0.00600021i
$821$	9.37333	−	48.6335i	0.327132	−	1.69732i	−0.330357	−	0.943856i	$-0.607169\pi$
$821$	9.37333	−	48.6335i	0.327132	−	1.69732i	0.657489	−	0.753464i	$-0.271619\pi$
$822$	−50.3948	+	55.7723i	−1.75772	+	1.94528i
$823$	−36.3588	+	34.6680i	−1.26739	+	1.20845i	−0.300346	+	0.953830i	$0.597102\pi$
$823$	−36.3588	+	34.6680i	−1.26739	+	1.20845i	−0.967041	+	0.254621i	$0.918049\pi$
$824$	0.250376	−	0.351604i	0.00872226	−	0.0122487i
$825$	−2.04356	−	5.42905i	−0.0711475	−	0.189015i
$826$	4.01431	−	6.43213i	0.139676	−	0.223803i
$827$	8.42773			0.293061			0.146531	−	0.989206i	$-0.453189\pi$
$827$	8.42773			0.293061			0.146531	+	0.989206i	$0.453189\pi$
$828$	−4.73566	+	28.6588i	−0.164576	+	0.995963i
$829$	16.5714	−	28.7025i	0.575549	−	0.996881i	−0.420432	−	0.907324i	$-0.638122\pi$
$829$	16.5714	−	28.7025i	0.575549	−	0.996881i	0.995982	−	0.0895568i	$-0.0285451\pi$
$830$	14.9035	+	28.9088i	0.517309	+	1.00344i
$831$	16.6643	−	20.3069i	0.578079	−	0.704439i
$832$	−19.9824	−	43.7554i	−0.692766	−	1.51695i
$833$	−10.3128	+	10.3685i	−0.357318	+	0.359246i
$834$	26.1184	+	5.59946i	0.904405	+	0.193894i
$835$	5.01490	−	26.0198i	0.173548	−	0.900451i
$836$	−2.00231	+	2.54614i	−0.0692513	+	0.0880601i
$837$	−14.9666	−	34.0965i	−0.517320	−	1.17855i
$838$	30.5649	+	10.5786i	1.05585	+	0.365432i
$839$	−46.6716	+	29.9940i	−1.61128	+	1.03551i	−0.650006	+	0.759929i	$0.725234\pi$
$839$	−46.6716	+	29.9940i	−1.61128	+	1.03551i	−0.961278	+	0.275580i	$0.911130\pi$
$840$	−0.492582	+	0.508860i	−0.0169957	+	0.0175573i
$841$	−18.6836	−	21.5620i	−0.644261	−	0.743516i
$842$	−16.8559	−	16.0721i	−0.580894	−	0.553881i
$843$	43.4272	+	20.9344i	1.49571	+	0.721018i
$844$	1.52564	+	4.40806i	0.0525149	+	0.151732i
$845$	88.4511	−	8.44605i	3.04281	−	0.290553i
$846$	9.71711	−	1.45684i	0.334081	−	0.0500870i
$847$	−23.7460	−	16.4399i	−0.815923	−	0.564881i
$848$	4.17622	+	29.0462i	0.143412	+	0.997452i
$849$	17.5826	−	3.01108i	0.603434	−	0.103340i
$850$	−41.9624	−	24.2270i	−1.43930	−	0.830979i
$851$	14.3302	+	7.88415i	0.491233	+	0.270265i
$852$	26.0761	−	23.8484i	0.893353	−	0.817034i
$853$	−20.3476	−	13.0766i	−0.696687	−	0.447734i	0.143770	−	0.989611i	$-0.454077\pi$
$853$	−20.3476	−	13.0766i	−0.696687	−	0.447734i	−0.840458	+	0.541877i	$0.817714\pi$
$854$	11.4235	−	29.6674i	0.390904	−	1.01520i
$855$	44.0116	−	51.4139i	1.50516	−	1.75832i
$856$	−0.596803	+	0.144783i	−0.0203983	+	0.00494858i
$857$	20.7957	−	14.8085i	0.710367	−	0.505850i	−0.166827	−	0.985986i	$-0.553352\pi$
$857$	20.7957	−	14.8085i	0.710367	−	0.505850i	0.877194	+	0.480136i	$0.159413\pi$
$858$	−5.05604	+	3.10272i	−0.172610	+	0.105925i
$859$	−19.2595	+	7.71035i	−0.657127	+	0.263074i	−0.676171	−	0.736745i	$-0.736362\pi$
$859$	−19.2595	+	7.71035i	−0.657127	+	0.263074i	0.0190441	+	0.999819i	$0.493938\pi$
$860$	16.1510	+	55.0051i	0.550743	+	1.87566i
$861$	−0.614476	+	0.275037i	−0.0209413	+	0.00937323i
$862$	−14.2215	−	22.1291i	−0.484386	−	0.753719i
$863$	−14.6427	+	28.4029i	−0.498444	+	0.966846i	0.496654	+	0.867949i	$0.334562\pi$
$863$	−14.6427	+	28.4029i	−0.498444	+	0.966846i	−0.995098	+	0.0988974i	$0.968468\pi$
$864$	−31.0808	−	27.7462i	−1.05739	−	0.943945i
$865$	19.9333	+	4.83576i	0.677752	+	0.164421i
$866$	−49.2486	+	19.7161i	−1.67353	+	0.669982i
$867$	10.4307	−	19.2398i	0.354246	−	0.653418i
$868$	4.14304	+	38.0542i	0.140624	+	1.29164i
$869$	0.0578667	−	0.197076i	0.00196299	−	0.00668534i
$870$	−3.78526	+	8.91342i	−0.128332	+	0.302193i
$871$	22.9043	−	57.2122i	0.776083	−	1.93856i
$872$	−0.245763	+	0.126700i	−0.00832258	+	0.00429059i
$873$	7.17220	−	10.2013i	0.242742	−	0.345261i
$874$	−21.1310	+	48.9151i	−0.714766	+	1.65458i
$875$	−0.937061	−	70.7430i	−0.0316784	−	2.39155i
$876$	28.2392	+	10.4360i	0.954113	+	0.352600i
$877$	8.07331	−	6.34892i	0.272616	−	0.214388i	−0.472486	−	0.881338i	$-0.656643\pi$
$877$	8.07331	−	6.34892i	0.272616	−	0.214388i	0.745102	+	0.666950i	$0.232401\pi$
$878$	−6.95319	+	72.8171i	−0.234659	+	2.45746i
$879$	10.0365	−	14.9254i	0.338522	−	0.503422i
$880$	−4.64728	+	0.443761i	−0.156660	+	0.0149592i
$881$	−3.45507	+	3.98736i	−0.116404	+	0.134338i	−0.810961	−	0.585100i	$-0.801055\pi$
$881$	−3.45507	+	3.98736i	−0.116404	+	0.134338i	0.694557	+	0.719438i	$0.255601\pi$
$882$	−8.59033	+	41.2136i	−0.289251	+	1.38773i
$883$	−21.5931	+	6.34032i	−0.726667	+	0.213369i	−0.624086	−	0.781356i	$-0.714528\pi$
$883$	−21.5931	+	6.34032i	−0.726667	+	0.213369i	−0.102581	+	0.994725i	$0.532710\pi$
$884$	−8.14130	+	23.5227i	−0.273821	+	0.791155i
$885$	9.72713	−	2.63777i	0.326974	−	0.0886675i
$886$	0.752584	+	15.7987i	0.0252836	+	0.530767i
$887$	−36.3099	−	12.5670i	−1.21917	−	0.421958i	−0.359661	−	0.933083i	$-0.617108\pi$
$887$	−36.3099	−	12.5670i	−1.21917	−	0.421958i	−0.859506	+	0.511125i	$0.829229\pi$
$888$	0.196515	−	0.108074i	0.00659462	−	0.00362673i
$889$	15.6992	+	2.04535i	0.526533	+	0.0685989i
$890$	21.0172	+	18.2115i	0.704499	+	0.610452i
$891$	−1.48562	+	2.14031i	−0.0497702	+	0.0717032i
$892$	22.1531	−	21.1230i	0.741742	−	0.707250i
$893$	9.01353	+	0.860687i	0.301626	+	0.0288018i
$894$	40.3287	+	33.0947i	1.34879	+	1.10685i
$895$	−52.7689	+	82.1100i	−1.76387	+	2.74463i
$896$	0.410969	+	0.690533i	0.0137295	+	0.0230691i
$897$	−33.8352	+	35.4731i	−1.12972	+	1.18441i
$898$	20.4366	+	35.3972i	0.681978	+	1.18122i
$899$	2.24983	+	4.36406i	0.0750360	+	0.145550i
$900$	−69.9725	+	3.75528i	−2.33242	+	0.125176i
$901$	8.97596	−	12.6050i	0.299033	−	0.419933i
$902$	0.0818040	+	0.0240198i	0.00272377	+	0.000799772i
$903$	24.0000	+	21.1153i	0.798671	+	0.702674i
$904$	−0.0981884	−	0.0850807i	−0.00326570	−	0.00282974i
$905$	0.0998048	+	0.249300i	0.00331762	+	0.00828702i
$906$	−32.1383	−	0.668305i	−1.06773	−	0.0222029i
$907$	7.63120	+	39.5944i	0.253390	+	1.31471i	0.856124	+	0.516770i	$0.172866\pi$
$907$	7.63120	+	39.5944i	0.253390	+	1.31471i	−0.602735	+	0.797942i	$0.705922\pi$
$908$	−9.63090	−	4.96507i	−0.319613	−	0.164772i
$909$	−35.7392	−	22.6655i	−1.18539	−	0.751768i
$910$	−124.783	+	25.7686i	−4.13652	+	0.854221i
$911$	13.5049	−	3.96539i	0.447437	−	0.131379i	−0.0502490	−	0.998737i	$-0.516002\pi$
$911$	13.5049	−	3.96539i	0.447437	−	0.131379i	0.497686	+	0.867357i	$0.334183\pi$
$912$	−21.4108	−	31.4304i	−0.708983	−	1.04076i
$913$	−0.377370	−	1.09034i	−0.0124891	−	0.0360850i
$914$	−11.5904	−	16.2765i	−0.383377	−	0.538378i
$915$	37.9549	−	18.5787i	1.25475	−	0.614192i
$916$	41.3308	−	18.8752i	1.36561	−	0.623653i
$917$	14.8708	−	12.0167i	0.491079	−	0.396827i
$918$	1.74834	+	21.6919i	0.0577037	+	0.715939i
$919$	3.75342	−	2.16704i	0.123814	−	0.0714841i	−0.436814	−	0.899552i	$-0.643893\pi$
$919$	3.75342	−	2.16704i	0.123814	−	0.0714841i	0.560628	+	0.828068i	$0.310560\pi$
$920$	0.695267	−	0.256806i	0.0229223	−	0.00846663i
$921$	−1.97050	+	6.22882i	−0.0649303	+	0.205247i
$922$	2.39431	−	50.2627i	0.0788523	−	1.65531i
$923$	59.0298	−	8.48720i	1.94299	−	0.279360i
$924$	2.11773	−	1.63969i	0.0696683	−	0.0539419i
$925$	−11.1162	+	37.8582i	−0.365497	+	1.24477i
$926$	3.35481	+	35.1331i	0.110246	+	1.15455i
$927$	24.5420	−	23.6843i	0.806065	−	0.777894i
$928$	4.31826	+	3.39592i	0.141754	+	0.111476i
$929$	−27.4566	+	28.7956i	−0.900822	+	0.944755i	−0.998727	−	0.0504412i	$-0.983937\pi$
$929$	−27.4566	+	28.7956i	−0.900822	+	0.944755i	0.0979054	+	0.995196i	$0.468786\pi$
$930$	−60.4554	+	81.2674i	−1.98241	+	2.66486i
$931$	−16.8573	+	34.9412i	−0.552477	+	1.14515i
$932$	4.67307	+	7.27143i	0.153071	+	0.238184i
$933$	37.9665	+	4.42364i	1.24297	+	0.144823i
$934$	35.1131	+	8.51835i	1.14894	+	0.278729i
$935$	1.93508	+	1.52176i	0.0632839	+	0.0497670i
$936$	0.162403	+	0.652280i	0.00530831	+	0.0213204i
$937$	4.68394	+	2.13908i	0.153018	+	0.0698809i	0.490452	−	0.871468i	$-0.336832\pi$
$937$	4.68394	+	2.13908i	0.153018	+	0.0698809i	−0.337434	+	0.941349i	$0.609559\pi$
$938$	−14.8990	+	53.3453i	−0.486471	+	1.74179i
$939$	33.2308	−	25.0326i	1.08445	−	0.816909i
$940$	−8.29971	−	10.5539i	−0.270707	−	0.344231i
$941$	−14.1915	+	7.31624i	−0.462631	+	0.238503i	−0.673752	−	0.738957i	$-0.735319\pi$
$941$	−14.1915	+	7.31624i	−0.462631	+	0.238503i	0.211122	+	0.977460i	$0.432288\pi$
$942$	−3.53306	+	11.1681i	−0.115113	+	0.363877i
$943$	0.704294	+	0.0190063i	0.0229350	+	0.000618932i
$944$		−	5.66329i		−	0.184324i
$945$	−45.6339	+	32.3906i	−1.48447	+	1.05367i
$946$	−0.576130	−	4.00707i	−0.0187316	−	0.130281i
$947$	−35.6310	−	25.3727i	−1.15785	−	0.824503i	−0.170864	−	0.985295i	$-0.554656\pi$
$947$	−35.6310	−	25.3727i	−1.15785	−	0.824503i	−0.986988	+	0.160791i	$0.948595\pi$
$948$	−2.05891	−	1.38450i	−0.0668702	−	0.0449663i
$949$	29.4716	+	41.3871i	0.956690	+	1.34348i
$950$	−126.218	−	24.3266i	−4.09506	−	0.789258i
$951$	29.1447	−	2.17262i	0.945083	−	0.0704519i
$952$	0.0467699	−	0.204578i	0.00151582	−	0.00663040i
$953$	−16.2807	−	18.7890i	−0.527385	−	0.608634i	0.428080	−	0.903741i	$-0.359190\pi$
$953$	−16.2807	−	18.7890i	−0.527385	−	0.608634i	−0.955464	+	0.295107i	$0.904645\pi$
$954$	1.85189	−	44.5088i	0.0599571	−	1.44103i
$955$	1.67081	+	35.0747i	0.0540663	+	1.13499i
$956$	−9.83888	−	51.0490i	−0.318212	−	1.65104i
$957$	0.177915	−	0.293874i	0.00575118	−	0.00949959i
$958$	25.4539	+	3.65972i	0.822379	+	0.118240i
$959$	53.8719	−	19.4480i	1.73961	−	0.628008i
$960$	−12.0463	+	56.1894i	−0.388794	+	1.81351i
$961$	4.79875	+	19.7807i	0.154798	+	0.638088i
$962$	40.1663	+	3.83541i	1.29501	+	0.123659i
$963$	−48.4551	+	2.60049i	−1.56144	+	0.0837995i
$964$	−19.5529	−	0.931419i	−0.629756	−	0.0299990i
$965$	−15.2494			−0.490895
$966$	26.7800	−	34.9854i	0.861634	−	1.12564i
$967$	−23.7280			−0.763040			−0.381520	−	0.924361i	$-0.624599\pi$
$967$	−23.7280			−0.763040			−0.381520	+	0.924361i	$0.624599\pi$
$968$	0.413986	+	0.0197206i	0.0133060	+	0.000633843i
$969$	−3.26608	+	19.7864i	−0.104921	+	0.635632i
$970$	−33.7668	−	3.22434i	−1.08419	−	0.103527i
$971$	−7.39707	−	30.4912i	−0.237383	−	0.978508i	−0.958363	−	0.285552i	$-0.907823\pi$
$971$	−7.39707	−	30.4912i	−0.237383	−	0.978508i	0.720980	−	0.692956i	$-0.243692\pi$
$972$	19.2374	+	24.9082i	0.617039	+	0.798931i
$973$	−15.5572	−	13.1237i	−0.498742	−	0.420727i
$974$	−86.5887	−	12.4496i	−2.77448	−	0.398910i
$975$	−101.164	−	61.2461i	−3.23984	−	1.96144i
$976$	−4.49390	−	23.3166i	−0.143846	−	0.746345i
$977$	2.24476	+	47.1232i	0.0718161	+	1.50761i	0.691284	+	0.722583i	$0.257045\pi$
$977$	2.24476	+	47.1232i	0.0718161	+	1.50761i	−0.619468	+	0.785022i	$0.712651\pi$
$978$	0.557277	−	2.10510i	0.0178198	−	0.0673136i
$979$	−0.646052	−	0.745584i	−0.0206479	−	0.0238290i
$980$	54.7483	−	17.6636i	1.74887	−	0.564244i
$981$	−20.9255	+	6.28128i	−0.668100	+	0.200546i
$982$	−46.4308	−	8.94880i	−1.48167	−	0.285568i
$983$	−8.79498	−	12.3508i	−0.280516	−	0.393930i	0.650146	−	0.759809i	$-0.274708\pi$
$983$	−8.79498	−	12.3508i	−0.280516	−	0.393930i	−0.930662	+	0.365879i	$0.880768\pi$
$984$	0.00539088	−	0.00801687i	0.000171855	−	0.000255569i
$985$	29.0243	+	20.6681i	0.924790	+	0.658540i
$986$	−0.408368	−	2.84026i	−0.0130051	−	0.0904524i
$987$	−7.05636	−	2.50202i	−0.224606	−	0.0796401i
$988$			66.0341i			2.10083i
$989$	−13.0714	−	30.7948i	−0.415645	−	0.979216i
$990$	7.05877	+	0.631197i	0.224342	+	0.0200608i
$991$	1.59020	−	0.819804i	0.0505143	−	0.0260419i	−0.432784	−	0.901497i	$-0.642469\pi$
$991$	1.59020	−	0.819804i	0.0505143	−	0.0260419i	0.483299	+	0.875456i	$0.339439\pi$
$992$	35.5194	+	45.1666i	1.12774	+	1.43404i
$993$	14.6396	+	19.4340i	0.464572	+	0.616720i
$994$	−51.9157	+	13.3251i	−1.64666	+	0.422646i
$995$	5.15748	+	2.35534i	0.163503	+	0.0746693i
$996$	−13.9325	+	0.373595i	−0.441467	+	0.0118378i
$997$	13.4924	+	10.6106i	0.427309	+	0.336040i	0.808541	−	0.588440i	$-0.200258\pi$
$997$	13.4924	+	10.6106i	0.427309	+	0.336040i	−0.381232	+	0.924480i	$0.624500\pi$
$998$	−15.5020	−	3.76075i	−0.490707	−	0.119044i
$999$	16.8303	−	5.54797i	0.532487	−	0.175530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bc.a.389.51	yes	1200
3.2	odd	2	inner	483.2.bc.a.389.10	yes	1200
7.2	even	3	inner	483.2.bc.a.44.10	yes	1200
21.2	odd	6	inner	483.2.bc.a.44.51	yes	1200
23.11	odd	22	inner	483.2.bc.a.11.51	yes	1200
69.11	even	22	inner	483.2.bc.a.11.10	✓	1200
161.149	odd	66	inner	483.2.bc.a.149.10	yes	1200
483.149	even	66	inner	483.2.bc.a.149.51	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bc.a.11.10	✓	1200	69.11	even	22	inner
483.2.bc.a.11.51	yes	1200	23.11	odd	22	inner
483.2.bc.a.44.10	yes	1200	7.2	even	3	inner
483.2.bc.a.44.51	yes	1200	21.2	odd	6	inner
483.2.bc.a.149.10	yes	1200	161.149	odd	66	inner
483.2.bc.a.149.51	yes	1200	483.149	even	66	inner
483.2.bc.a.389.10	yes	1200	3.2	odd	2	inner
483.2.bc.a.389.51	yes	1200	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00246 + 0.0953889i) q^{2} +(1.70893 + 0.282086i) q^{3} +(2.00980 + 0.191912i) q^{4} +(-0.959667 - 3.95580i) q^{5} +(3.39514 + 0.727879i) q^{6} +(-2.02230 - 1.70596i) q^{7} +(0.0375805 + 0.00540327i) q^{8} +(2.84085 + 0.964129i) q^{9} +(-1.54435 - 8.01287i) q^{10} +(0.0137743 + 0.289159i) q^{11} +(3.38046 + 0.894900i) q^{12} +(3.86470 + 4.46010i) q^{13} +(-3.88684 - 3.60903i) q^{14} +(-0.524122 - 7.03088i) q^{15} +(-3.89017 - 0.749769i) q^{16} +(1.21182 + 1.70176i) q^{17} +(5.59673 + 2.20161i) q^{18} +(4.51451 + 3.21476i) q^{19} +(-1.16957 - 8.13453i) q^{20} +(-2.97473 - 3.48583i) q^{21} +0.580343i q^{22} +(1.22652 + 4.63634i) q^{23} +(0.0626982 + 0.0198347i) q^{24} +(-10.2832 + 5.30137i) q^{25} +(7.31345 + 9.29981i) q^{26} +(4.58284 + 2.44899i) q^{27} +(-3.73701 - 3.81674i) q^{28} +(-0.623226 - 0.284618i) q^{29} +(-0.378866 - 14.1290i) q^{30} +(-5.63302 - 4.42985i) q^{31} +(-7.79218 - 1.89036i) q^{32} +(-0.0580285 + 0.498037i) q^{33} +(2.26428 + 3.52329i) q^{34} +(-4.80772 + 9.63696i) q^{35} +(5.52451 + 2.48290i) q^{36} +(2.35347 - 2.46825i) q^{37} +(8.73346 + 6.86807i) q^{38} +(5.34635 + 8.71216i) q^{39} +(-0.0146906 - 0.153846i) q^{40} +(0.0413890 - 0.140958i) q^{41} +(-5.62426 - 7.26398i) q^{42} +(-6.90466 + 0.992741i) q^{43} +(-0.0278096 + 0.583794i) q^{44} +(1.08763 - 12.1631i) q^{45} +(2.01379 + 9.40108i) q^{46} +(1.41487 - 0.816878i) q^{47} +(-6.43651 - 2.37866i) q^{48} +(1.17938 + 6.89993i) q^{49} +(-21.0974 + 9.63487i) q^{50} +(1.59086 + 3.25001i) q^{51} +(6.91131 + 9.70558i) q^{52} +(-2.42260 - 6.99966i) q^{53} +(8.94334 + 5.34115i) q^{54} +(1.13064 - 0.331985i) q^{55} +(-0.0667813 - 0.0750380i) q^{56} +(6.80811 + 6.76727i) q^{57} +(-1.22084 - 0.629385i) q^{58} +(0.270532 + 1.40365i) q^{59} +(0.295933 - 14.2312i) q^{60} +(2.22764 + 5.56437i) q^{61} +(-10.8573 - 9.40792i) q^{62} +(-4.10029 - 6.79615i) q^{63} +(-7.82062 - 2.29634i) q^{64} +(13.9344 - 19.5682i) q^{65} +(-0.163707 + 0.991763i) q^{66} +(-4.78500 - 9.28161i) q^{67} +(2.10891 + 3.65275i) q^{68} +(0.788176 + 8.26915i) q^{69} +(-10.5465 + 18.8390i) q^{70} +(5.46332 - 8.50109i) q^{71} +(0.101551 + 0.0515824i) q^{72} +(8.57030 + 0.818364i) q^{73} +(4.94817 - 4.71807i) q^{74} +(-19.0687 + 6.15889i) q^{75} +(8.45629 + 7.32741i) q^{76} +(0.465439 - 0.608264i) q^{77} +(9.87480 + 17.9557i) q^{78} +(-0.670494 - 0.232060i) q^{79} +(0.767331 + 16.1083i) q^{80} +(7.14091 + 5.47790i) q^{81} +(0.0963256 - 0.278315i) q^{82} +(-3.82422 + 1.12289i) q^{83} +(-5.30963 - 7.57669i) q^{84} +(5.56887 - 6.42682i) q^{85} +(-13.9210 + 1.32929i) q^{86} +(-0.984761 - 0.662195i) q^{87} +(-0.00104476 + 0.0109412i) q^{88} +(-2.67881 + 2.10664i) q^{89} +(3.33815 - 24.2523i) q^{90} +(-0.206805 - 15.6127i) q^{91} +(1.57528 + 9.55349i) q^{92} +(-8.37681 - 9.15929i) q^{93} +(2.91115 - 1.50080i) q^{94} +(8.38455 - 20.9436i) q^{95} +(-12.7830 - 5.42855i) q^{96} +(1.17109 - 3.98837i) q^{97} +(1.70348 + 13.9293i) q^{98} +(-0.239656 + 0.834739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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