LMFDB - Embedded newform 570.2.v.a.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	570.197
Dual form			570.2.v.a.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(1.57313 + 0.724745i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.448288 - 2.19067i) q^{5} +(1.33195 + 1.10721i) q^{6} +(2.12132 + 2.12132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.94949 + 2.28024i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(1.57313 + 0.724745i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.448288 - 2.19067i) q^{5} +(1.33195 + 1.10721i) q^{6} +(2.12132 + 2.12132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.94949 + 2.28024i) q^{9} +(0.133975 - 2.23205i) q^{10} +0.171573i q^{11} +(1.00000 + 1.41421i) q^{12} +(-0.732051 - 2.73205i) q^{13} +(1.50000 + 2.59808i) q^{14} +(0.882461 - 3.77111i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.16622 - 0.580438i) q^{17} +(1.29289 + 2.70711i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(0.707107 - 2.12132i) q^{20} +(1.79970 + 4.87453i) q^{21} +(-0.0444063 + 0.165727i) q^{22} +(2.89778 - 0.776457i) q^{23} +(0.599900 + 1.62484i) q^{24} +(-4.59808 + 1.96410i) q^{25} -2.82843i q^{26} +(1.41421 + 5.00000i) q^{27} +(0.776457 + 2.89778i) q^{28} +(1.58579 - 2.74666i) q^{29} +(1.82843 - 3.41421i) q^{30} +6.24264 q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.124347 + 0.269907i) q^{33} +(-1.94218 - 1.12132i) q^{34} +(3.69615 - 5.59808i) q^{35} +(0.548188 + 2.94949i) q^{36} +(-2.12132 - 2.12132i) q^{37} +(-4.31199 - 0.637756i) q^{38} +(0.828427 - 4.82843i) q^{39} +(1.23205 - 1.86603i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(0.476756 + 5.17423i) q^{42} +(-4.09808 - 1.09808i) q^{43} +(-0.0857864 + 0.148586i) q^{44} +(4.12132 - 5.29289i) q^{45} +3.00000 q^{46} +(1.67851 + 6.26430i) q^{47} +(0.158919 + 1.72474i) q^{48} +2.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-2.98709 - 2.48307i) q^{51} +(0.732051 - 2.73205i) q^{52} +(-9.16208 + 2.45497i) q^{53} +(0.0719302 + 5.19565i) q^{54} +(0.375860 - 0.0769140i) q^{55} +3.00000i q^{56} +(-7.17423 - 2.35167i) q^{57} +(2.24264 - 2.24264i) q^{58} +(-2.82843 - 4.89898i) q^{59} +(2.64979 - 2.82465i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(6.02993 + 1.61571i) q^{62} +(-0.701625 + 8.97261i) q^{63} +1.00000i q^{64} +(-5.65685 + 2.82843i) q^{65} +(-0.189967 + 0.228527i) q^{66} +(5.46410 - 1.46410i) q^{67} +(-1.58579 - 1.58579i) q^{68} +(5.12132 + 0.878680i) q^{69} +(5.01910 - 4.45069i) q^{70} +(-9.16756 + 5.29289i) q^{71} +(-0.233875 + 2.99087i) q^{72} +(-15.6892 - 4.20390i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(-8.65685 - 0.242641i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(-0.363961 + 0.363961i) q^{77} +(2.04989 - 4.44949i) q^{78} +(5.61642 - 3.24264i) q^{79} +(1.67303 - 1.48356i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(-2.89778 + 0.776457i) q^{82} +(-3.00000 - 3.00000i) q^{83} +(-0.878680 + 5.12132i) q^{84} +(-0.300457 + 5.00569i) q^{85} +(-3.67423 - 2.12132i) q^{86} +(4.48528 - 3.17157i) q^{87} +(-0.121320 + 0.121320i) q^{88} +(5.91421 - 10.2437i) q^{89} +(5.35079 - 4.04587i) q^{90} +(4.24264 - 7.34847i) q^{91} +(2.89778 + 0.776457i) q^{92} +(9.82050 + 4.52432i) q^{93} +6.48528i q^{94} +(3.03648 + 9.26174i) q^{95} +(-0.292893 + 1.70711i) q^{96} +(3.74907 - 13.9917i) q^{97} +(-0.517638 + 1.93185i) q^{98} +(-0.391227 + 0.334480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^6 - 4 * q^9	$ 8 q - 4 q^{6} - 4 q^{9} + 8 q^{10} + 8 q^{12} + 8 q^{13} + 12 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} + 16 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{24} - 16 q^{25} + 24 q^{29} - 8 q^{30} + 16 q^{31} + 12 q^{33} - 12 q^{35} - 16 q^{39} - 4 q^{40} - 12 q^{43} - 12 q^{44} + 16 q^{45} + 24 q^{46} - 24 q^{47} - 20 q^{51} - 8 q^{52} - 24 q^{53} + 4 q^{54} - 8 q^{55} - 28 q^{57} - 16 q^{58} + 4 q^{60} + 8 q^{61} + 12 q^{62} - 24 q^{63} - 4 q^{66} + 16 q^{67} - 24 q^{68} + 24 q^{69} - 8 q^{72} - 12 q^{73} - 12 q^{74} - 24 q^{75} - 32 q^{76} + 48 q^{77} + 28 q^{81} - 24 q^{83} - 24 q^{84} + 16 q^{85} - 32 q^{87} + 16 q^{88} + 36 q^{89} + 8 q^{90} + 24 q^{93} - 8 q^{96} - 24 q^{97} + 32 q^{99}+O(q^{100}) $ 8 * q - 4 * q^6 - 4 * q^9 + 8 * q^10 + 8 * q^12 + 8 * q^13 + 12 * q^14 + 12 * q^15 + 4 * q^16 - 12 * q^17 + 16 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^24 - 16 * q^25 + 24 * q^29 - 8 * q^30 + 16 * q^31 + 12 * q^33 - 12 * q^35 - 16 * q^39 - 4 * q^40 - 12 * q^43 - 12 * q^44 + 16 * q^45 + 24 * q^46 - 24 * q^47 - 20 * q^51 - 8 * q^52 - 24 * q^53 + 4 * q^54 - 8 * q^55 - 28 * q^57 - 16 * q^58 + 4 * q^60 + 8 * q^61 + 12 * q^62 - 24 * q^63 - 4 * q^66 + 16 * q^67 - 24 * q^68 + 24 * q^69 - 8 * q^72 - 12 * q^73 - 12 * q^74 - 24 * q^75 - 32 * q^76 + 48 * q^77 + 28 * q^81 - 24 * q^83 - 24 * q^84 + 16 * q^85 - 32 * q^87 + 16 * q^88 + 36 * q^89 + 8 * q^90 + 24 * q^93 - 8 * q^96 - 24 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	1.57313	+	0.724745i	0.908248	+	0.418432i
$3$	1.57313	+	0.724745i	0.908248	+	0.418432i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.448288	−	2.19067i	−0.200480	−	0.979698i
$5$	−0.448288	−	2.19067i	−0.200480	−	0.979698i
$6$	1.33195	+	1.10721i	0.543767	+	0.452015i
$7$	2.12132	+	2.12132i	0.801784	+	0.801784i	0.983374	−	0.181591i	$-0.0581245\pi$
$7$	2.12132	+	2.12132i	0.801784	+	0.801784i	−0.181591	+	0.983374i	$0.558125\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.94949	+	2.28024i	0.649830	+	0.760080i
$10$	0.133975	−	2.23205i	0.0423665	−	0.705836i
$11$			0.171573i			0.0517312i	0.999665	+	0.0258656i	$0.00823419\pi$
$11$			0.171573i			0.0517312i	−0.999665	+	0.0258656i	$0.991766\pi$
$12$	1.00000	+	1.41421i	0.288675	+	0.408248i
$13$	−0.732051	−	2.73205i	−0.203034	−	0.757735i	−0.990040	−	0.140788i	$-0.955036\pi$
$13$	−0.732051	−	2.73205i	−0.203034	−	0.757735i	0.787005	−	0.616946i	$-0.211630\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$	0.882461	−	3.77111i	0.227851	−	0.973696i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.16622	−	0.580438i	−0.525387	−	0.140777i	−0.0136295	−	0.999907i	$-0.504339\pi$
$17$	−2.16622	−	0.580438i	−0.525387	−	0.140777i	−0.511757	+	0.859130i	$0.671005\pi$
$18$	1.29289	+	2.70711i	0.304738	+	0.638071i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$20$	0.707107	−	2.12132i	0.158114	−	0.474342i
$21$	1.79970	+	4.87453i	0.392727	+	1.06371i
$22$	−0.0444063	+	0.165727i	−0.00946746	+	0.0353330i
$23$	2.89778	−	0.776457i	0.604228	−	0.161903i	0.0562805	−	0.998415i	$-0.482076\pi$
$23$	2.89778	−	0.776457i	0.604228	−	0.161903i	0.547948	+	0.836512i	$0.315409\pi$
$24$	0.599900	+	1.62484i	0.122454	+	0.331670i
$25$	−4.59808	+	1.96410i	−0.919615	+	0.392820i
$26$		−	2.82843i		−	0.554700i
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$	0.776457	+	2.89778i	0.146737	+	0.547628i
$29$	1.58579	−	2.74666i	0.294473	−	0.510042i	−0.680389	−	0.732851i	$-0.738189\pi$
$29$	1.58579	−	2.74666i	0.294473	−	0.510042i	0.974862	+	0.222809i	$0.0715225\pi$
$30$	1.82843	−	3.41421i	0.333824	−	0.623347i
$31$	6.24264			1.12121			0.560606	−	0.828083i	$-0.310568\pi$
$31$	6.24264			1.12121			0.560606	+	0.828083i	$0.310568\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−0.124347	+	0.269907i	−0.0216460	+	0.0469847i
$34$	−1.94218	−	1.12132i	−0.333082	−	0.192305i
$35$	3.69615	−	5.59808i	0.624764	−	0.946248i
$36$	0.548188	+	2.94949i	0.0913647	+	0.491582i
$37$	−2.12132	−	2.12132i	−0.348743	−	0.348743i	0.510898	−	0.859641i	$-0.329313\pi$
$37$	−2.12132	−	2.12132i	−0.348743	−	0.348743i	−0.859641	+	0.510898i	$0.829313\pi$
$38$	−4.31199	−	0.637756i	−0.699497	−	0.103458i
$39$	0.828427	−	4.82843i	0.132655	−	0.773167i
$40$	1.23205	−	1.86603i	0.194804	−	0.295045i
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$	0.476756	+	5.17423i	0.0735650	+	0.798402i
$43$	−4.09808	−	1.09808i	−0.624951	−	0.167455i	−0.0675734	−	0.997714i	$-0.521526\pi$
$43$	−4.09808	−	1.09808i	−0.624951	−	0.167455i	−0.557377	+	0.830259i	$0.688192\pi$
$44$	−0.0857864	+	0.148586i	−0.0129328	+	0.0224003i
$45$	4.12132	−	5.29289i	0.614370	−	0.789018i
$46$	3.00000			0.442326
$47$	1.67851	+	6.26430i	0.244836	+	0.913742i	0.973466	+	0.228834i	$0.0734912\pi$
$47$	1.67851	+	6.26430i	0.244836	+	0.913742i	−0.728629	+	0.684909i	$0.759842\pi$
$48$	0.158919	+	1.72474i	0.0229379	+	0.248945i
$49$			2.00000i			0.285714i
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$	−2.98709	−	2.48307i	−0.418276	−	0.347699i
$52$	0.732051	−	2.73205i	0.101517	−	0.378867i
$53$	−9.16208	+	2.45497i	−1.25851	+	0.337216i	−0.825618	−	0.564230i	$-0.809173\pi$
$53$	−9.16208	+	2.45497i	−1.25851	+	0.337216i	−0.432891	+	0.901446i	$0.642506\pi$
$54$	0.0719302	+	5.19565i	0.00978846	+	0.707039i
$55$	0.375860	−	0.0769140i	0.0506809	−	0.0103711i
$56$			3.00000i			0.400892i
$57$	−7.17423	−	2.35167i	−0.950251	−	0.311486i
$58$	2.24264	−	2.24264i	0.294473	−	0.294473i
$59$	−2.82843	−	4.89898i	−0.368230	−	0.637793i	0.621059	−	0.783764i	$-0.286703\pi$
$59$	−2.82843	−	4.89898i	−0.368230	−	0.637793i	−0.989289	+	0.145971i	$0.953369\pi$
$60$	2.64979	−	2.82465i	0.342086	−	0.364660i
$61$	−1.12132	+	1.94218i	−0.143570	+	0.248671i	−0.928839	−	0.370484i	$-0.879192\pi$
$61$	−1.12132	+	1.94218i	−0.143570	+	0.248671i	0.785268	+	0.619156i	$0.212525\pi$
$62$	6.02993	+	1.61571i	0.765802	+	0.205196i
$63$	−0.701625	+	8.97261i	−0.0883964	+	1.13044i
$64$			1.00000i			0.125000i
$65$	−5.65685	+	2.82843i	−0.701646	+	0.350823i
$66$	−0.189967	+	0.228527i	−0.0233833	+	0.0281297i
$67$	5.46410	−	1.46410i	0.667546	−	0.178868i	0.0908970	−	0.995860i	$-0.471027\pi$
$67$	5.46410	−	1.46410i	0.667546	−	0.178868i	0.576649	+	0.816992i	$0.304360\pi$
$68$	−1.58579	−	1.58579i	−0.192305	−	0.192305i
$69$	5.12132	+	0.878680i	0.616535	+	0.105781i
$70$	5.01910	−	4.45069i	0.599897	−	0.531959i
$71$	−9.16756	+	5.29289i	−1.08799	+	0.628151i	−0.933040	−	0.359772i	$-0.882855\pi$
$71$	−9.16756	+	5.29289i	−1.08799	+	0.628151i	−0.154949	+	0.987922i	$0.549521\pi$
$72$	−0.233875	+	2.99087i	−0.0275624	+	0.352477i
$73$	−15.6892	−	4.20390i	−1.83628	−	0.492030i	−0.837741	−	0.546067i	$-0.816124\pi$
$73$	−15.6892	−	4.20390i	−1.83628	−	0.492030i	−0.998539	+	0.0540373i	$0.982791\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$	−8.65685	−	0.242641i	−0.999607	−	0.0280177i
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$	−0.363961	+	0.363961i	−0.0414772	+	0.0414772i
$78$	2.04989	−	4.44949i	0.232104	−	0.503806i
$79$	5.61642	−	3.24264i	0.631896	−	0.364826i	−0.149590	−	0.988748i	$-0.547795\pi$
$79$	5.61642	−	3.24264i	0.631896	−	0.364826i	0.781486	+	0.623923i	$0.214462\pi$
$80$	1.67303	−	1.48356i	0.187051	−	0.165867i
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	−2.89778	+	0.776457i	−0.320006	+	0.0857453i
$83$	−3.00000	−	3.00000i	−0.329293	−	0.329293i	0.523025	−	0.852318i	$-0.324804\pi$
$83$	−3.00000	−	3.00000i	−0.329293	−	0.329293i	−0.852318	+	0.523025i	$0.824804\pi$
$84$	−0.878680	+	5.12132i	−0.0958718	+	0.558782i
$85$	−0.300457	+	5.00569i	−0.0325891	+	0.542943i
$86$	−3.67423	−	2.12132i	−0.396203	−	0.228748i
$87$	4.48528	−	3.17157i	0.480873	−	0.340028i
$88$	−0.121320	+	0.121320i	−0.0129328	+	0.0129328i
$89$	5.91421	−	10.2437i	0.626905	−	1.08583i	−0.361264	−	0.932464i	$-0.617655\pi$
$89$	5.91421	−	10.2437i	0.626905	−	1.08583i	0.988169	−	0.153368i	$-0.0490121\pi$
$90$	5.35079	−	4.04587i	0.564023	−	0.426472i
$91$	4.24264	−	7.34847i	0.444750	−	0.770329i
$92$	2.89778	+	0.776457i	0.302114	+	0.0809513i
$93$	9.82050	+	4.52432i	1.01834	+	0.469150i
$94$			6.48528i			0.668906i
$95$	3.03648	+	9.26174i	0.311536	+	0.950234i
$96$	−0.292893	+	1.70711i	−0.0298933	+	0.174231i
$97$	3.74907	−	13.9917i	0.380660	−	1.42064i	−0.464236	−	0.885712i	$-0.653671\pi$
$97$	3.74907	−	13.9917i	0.380660	−	1.42064i	0.844896	−	0.534931i	$-0.179662\pi$
$98$	−0.517638	+	1.93185i	−0.0522893	+	0.195146i
$99$	−0.391227	+	0.334480i	−0.0393198	+	0.0336165i
$100$	−4.96410	−	0.598076i	−0.496410	−	0.0598076i
$101$	−14.9941	−	8.65685i	−1.49197	−	0.861389i	−0.492012	−	0.870588i	$-0.663738\pi$
$101$	−14.9941	−	8.65685i	−1.49197	−	0.861389i	−0.999958	+	0.00919913i	$0.997072\pi$
$102$	−2.24264	−	3.17157i	−0.222055	−	0.314033i
$103$	−2.12132	+	2.12132i	−0.209020	+	0.209020i	−0.803851	−	0.594831i	$-0.797219\pi$
$103$	−2.12132	+	2.12132i	−0.209020	+	0.209020i	0.594831	+	0.803851i	$0.297219\pi$
$104$	1.41421	−	2.44949i	0.138675	−	0.240192i
$105$	9.87171	−	6.12775i	0.963381	−	0.598007i
$106$	−9.48528			−0.921292
$107$	6.00000	−	6.00000i	0.580042	−	0.580042i	−0.354873	−	0.934915i	$-0.615476\pi$
$107$	6.00000	−	6.00000i	0.580042	−	0.580042i	0.934915	+	0.354873i	$0.115476\pi$
$108$	−1.27526	+	5.03723i	−0.122711	+	0.484708i
$109$	−1.94218	+	1.12132i	−0.186027	+	0.107403i	−0.590122	−	0.807314i	$-0.700920\pi$
$109$	−1.94218	+	1.12132i	−0.186027	+	0.107403i	0.404094	+	0.914717i	$0.367587\pi$
$110$	0.382959	+	0.0229864i	0.0365137	+	0.00219167i
$111$	−1.79970	−	4.87453i	−0.170820	−	0.462670i
$112$	−0.776457	+	2.89778i	−0.0733683	+	0.273814i
$113$	14.1421	+	14.1421i	1.33038	+	1.33038i	0.905028	+	0.425352i	$0.139850\pi$
$113$	14.1421	+	14.1421i	1.33038	+	1.33038i	0.425352	+	0.905028i	$0.360150\pi$
$114$	−6.32112	−	4.12837i	−0.592027	−	0.386657i
$115$	−3.00000	−	6.00000i	−0.279751	−	0.559503i
$116$	2.74666	−	1.58579i	0.255021	−	0.147237i
$117$	4.80260	−	6.99536i	0.444001	−	0.646721i
$118$	−1.46410	−	5.46410i	−0.134781	−	0.503011i
$119$	−3.36396	−	5.82655i	−0.308374	−	0.534119i
$120$	3.29057	−	2.04258i	0.300387	−	0.186461i
$121$	10.9706			0.997324
$122$	−1.58579	+	1.58579i	−0.143570	+	0.143570i
$123$	−5.17423	+	0.476756i	−0.466545	+	0.0429876i
$124$	5.40629	+	3.12132i	0.485499	+	0.280303i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$	−3.00000	+	8.48528i	−0.267261	+	0.755929i
$127$	2.56632	−	0.687644i	0.227724	−	0.0610186i	−0.143152	−	0.989701i	$-0.545724\pi$
$127$	2.56632	−	0.687644i	0.227724	−	0.0610186i	0.370877	+	0.928682i	$0.379057\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−5.65099	−	4.69748i	−0.497542	−	0.413590i
$130$	−6.19615	+	1.26795i	−0.543439	+	0.111207i
$131$	12.9904	−	7.50000i	1.13497	−	0.655278i	0.189794	−	0.981824i	$-0.439218\pi$
$131$	12.9904	−	7.50000i	1.13497	−	0.655278i	0.945181	+	0.326546i	$0.105885\pi$
$132$	−0.242641	+	0.171573i	−0.0211192	+	0.0149335i
$133$	−10.2462	−	8.12493i	−0.888462	−	0.704520i
$134$	5.65685			0.488678
$135$	10.3194	−	5.33951i	0.888151	−	0.459552i
$136$	−1.12132	−	1.94218i	−0.0961524	−	0.166541i
$137$	5.30198	+	19.7873i	0.452979	+	1.69054i	0.693963	+	0.720011i	$0.255863\pi$
$137$	5.30198	+	19.7873i	0.452979	+	1.69054i	−0.240984	+	0.970529i	$0.577470\pi$
$138$	4.71940	+	2.17423i	0.401742	+	0.185083i
$139$	−12.1244	−	7.00000i	−1.02837	−	0.593732i	−0.111856	−	0.993724i	$-0.535679\pi$
$139$	−12.1244	−	7.00000i	−1.02837	−	0.593732i	−0.916519	+	0.399992i	$0.869013\pi$
$140$	6.00000	−	3.00000i	0.507093	−	0.253546i
$141$	−1.89949	+	11.0711i	−0.159966	+	0.932352i
$142$	−10.2251	+	2.73980i	−0.858070	+	0.229919i
$143$	0.468746	−	0.125600i	0.0391985	−	0.0105032i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	−6.72792	−	2.24264i	−0.558724	−	0.186241i
$146$	−14.0665	−	8.12132i	−1.16416	−	0.672125i
$147$	−1.44949	+	3.14626i	−0.119552	+	0.259500i
$148$	−0.776457	−	2.89778i	−0.0638244	−	0.238196i
$149$	5.65685	+	9.79796i	0.463428	+	0.802680i	0.999129	−	0.0417274i	$-0.0132861\pi$
$149$	5.65685	+	9.79796i	0.463428	+	0.802680i	−0.535701	+	0.844407i	$0.679953\pi$
$150$	−8.29908	−	2.47493i	−0.677617	−	0.202077i
$151$	−10.7279			−0.873026			−0.436513	−	0.899698i	$-0.643787\pi$
$151$	−10.7279			−0.873026			−0.436513	+	0.899698i	$0.643787\pi$
$152$	−3.41542	−	2.70831i	−0.277027	−	0.219673i
$153$	−2.89949	−	6.07107i	−0.234410	−	0.490817i
$154$	−0.445759	+	0.257359i	−0.0359203	+	0.0207386i
$155$	−2.79850	−	13.6756i	−0.224781	−	1.09845i
$156$	3.13165	−	3.76733i	0.250733	−	0.301628i
$157$	3.06142	−	11.4254i	0.244328	−	0.911845i	−0.729392	−	0.684096i	$-0.760197\pi$
$157$	3.06142	−	11.4254i	0.244328	−	0.911845i	0.973720	−	0.227749i	$-0.0731365\pi$
$158$	6.26430	−	1.67851i	0.498361	−	0.133535i
$159$	−16.1924	−	2.77817i	−1.28414	−	0.220324i
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$	7.79423	+	4.50000i	0.614271	+	0.354650i
$162$	−3.65237	+	8.22558i	−0.286957	+	0.646263i
$163$	−14.2426	+	14.2426i	−1.11557	+	1.11557i	−0.123186	+	0.992384i	$0.539311\pi$
$163$	−14.2426	+	14.2426i	−1.11557	+	1.11557i	−0.992384	+	0.123186i	$0.960689\pi$
$164$	−3.00000			−0.234261
$165$	0.647020	+	0.151406i	0.0503704	+	0.0117870i
$166$	−2.12132	−	3.67423i	−0.164646	−	0.285176i
$167$	6.07844	+	22.6850i	0.470364	+	1.75542i	0.638464	+	0.769651i	$0.279570\pi$
$167$	6.07844	+	22.6850i	0.470364	+	1.75542i	−0.168101	+	0.985770i	$0.553763\pi$
$168$	−2.17423	+	4.71940i	−0.167746	+	0.364109i
$169$	4.33013	−	2.50000i	0.333087	−	0.192308i
$170$	−1.58579	+	4.75736i	−0.121624	+	0.364873i
$171$	−9.58166	−	8.89898i	−0.732728	−	0.680522i
$172$	−3.00000	−	3.00000i	−0.228748	−	0.228748i
$173$	−5.16876	+	19.2901i	−0.392974	+	1.46660i	0.432230	+	0.901763i	$0.357727\pi$
$173$	−5.16876	+	19.2901i	−0.392974	+	1.46660i	−0.825204	+	0.564835i	$0.808940\pi$
$174$	5.15331	−	1.90263i	0.390672	−	0.144238i
$175$	−13.9205	−	5.58750i	−1.05229	−	0.422376i
$176$	−0.148586	+	0.0857864i	−0.0112001	+	0.00646640i
$177$	−0.898979	−	9.75663i	−0.0675714	−	0.733353i
$178$	8.36396	−	8.36396i	0.626905	−	0.626905i
$179$	−9.34315			−0.698340			−0.349170	−	0.937059i	$-0.613536\pi$
$179$	−9.34315			−0.698340			−0.349170	+	0.937059i	$0.613536\pi$
$180$	6.21561	−	2.52312i	0.463285	−	0.188062i
$181$	−7.24264	+	12.5446i	−0.538341	+	0.932434i	0.460652	+	0.887581i	$0.347616\pi$
$181$	−7.24264	+	12.5446i	−0.538341	+	0.932434i	−0.998994	+	0.0448537i	$0.985718\pi$
$182$	6.00000	−	6.00000i	0.444750	−	0.444750i
$183$	−3.17157	+	2.24264i	−0.234449	+	0.165781i
$184$	2.59808	+	1.50000i	0.191533	+	0.110581i
$185$	−3.69615	+	5.59808i	−0.271747	+	0.411579i
$186$	8.31489	+	6.91189i	0.609678	+	0.506804i
$187$	0.0995874	−	0.371665i	0.00728255	−	0.0271789i
$188$	−1.67851	+	6.26430i	−0.122418	+	0.456871i
$189$	−7.60660	+	13.6066i	−0.553299	+	0.989735i
$190$	0.535898	+	9.73205i	0.0388782	+	0.706037i
$191$		−	10.5858i		−	0.765961i	−0.923757	−	0.382980i	$-0.874898\pi$
$191$		−	10.5858i		−	0.765961i	0.923757	−	0.382980i	$-0.125102\pi$
$192$	−0.724745	+	1.57313i	−0.0523040	+	0.113531i
$193$	11.5911	+	3.10583i	0.834346	+	0.223562i	0.650609	−	0.759413i	$-0.274514\pi$
$193$	11.5911	+	3.10583i	0.834346	+	0.223562i	0.183737	+	0.982975i	$0.441180\pi$
$194$	7.24264	−	12.5446i	0.519991	−	0.900651i
$195$	−10.9489	+	0.349714i	−0.784065	+	0.0250435i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	6.02082	−	6.02082i	0.428965	−	0.428965i	−0.459310	−	0.888276i	$-0.651903\pi$
$197$	6.02082	−	6.02082i	0.428965	−	0.428965i	0.888276	+	0.459310i	$0.151903\pi$
$198$	−0.464466	+	0.221825i	−0.0330082	+	0.0157644i
$199$	12.3345	+	7.12132i	0.874369	+	0.504817i	0.868798	−	0.495167i	$-0.164893\pi$
$199$	12.3345	+	7.12132i	0.874369	+	0.504817i	0.00557117	+	0.999984i	$0.498227\pi$
$200$	−4.64016	−	1.86250i	−0.328109	−	0.131699i
$201$	9.65685	+	1.65685i	0.681142	+	0.116865i
$202$	−12.2426	−	12.2426i	−0.861389	−	0.861389i
$203$	9.19051	−	2.46259i	0.645048	−	0.172840i
$204$	−1.34536	−	3.64394i	−0.0941941	−	0.255127i
$205$	4.45069	+	5.01910i	0.310850	+	0.350549i
$206$	−2.59808	+	1.50000i	−0.181017	+	0.104510i
$207$	7.41970	+	5.09393i	0.515704	+	0.354053i
$208$	2.00000	−	2.00000i	0.138675	−	0.138675i
$209$	−0.0857864	−	0.742932i	−0.00593397	−	0.0513897i
$210$	11.1213	−	3.36396i	0.767444	−	0.232135i
$211$	−1.74264	−	3.01834i	−0.119968	−	0.207791i	0.799787	−	0.600284i	$-0.204946\pi$
$211$	−1.74264	−	3.01834i	−0.119968	−	0.207791i	−0.919755	+	0.392493i	$0.871613\pi$
$212$	−9.16208	−	2.45497i	−0.629254	−	0.168608i
$213$	−18.2578	+	1.68228i	−1.25100	+	0.115268i
$214$	7.34847	−	4.24264i	0.502331	−	0.290021i
$215$	−0.568406	+	9.46979i	−0.0387650	+	0.645834i
$216$	−2.53553	+	4.53553i	−0.172521	+	0.308604i
$217$	13.2426	+	13.2426i	0.898969	+	0.898969i
$218$	−2.16622	+	0.580438i	−0.146715	+	0.0393122i
$219$	−21.6344	−	17.9840i	−1.46192	−	1.21524i
$220$	0.363961	+	0.121320i	0.0245382	+	0.00817942i
$221$			6.34315i			0.426686i
$222$	−0.476756	−	5.17423i	−0.0319978	−	0.347272i
$223$	16.8895	+	4.52552i	1.13100	+	0.303051i	0.775328	−	0.631558i	$-0.217584\pi$
$223$	16.8895	+	4.52552i	1.13100	+	0.303051i	0.355675	+	0.934610i	$0.384251\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$	−13.4425	−	6.65572i	−0.896168	−	0.443714i
$226$	10.0000	+	17.3205i	0.665190	+	1.15214i
$227$	16.2426	−	16.2426i	1.07806	−	1.07806i	0.0813787	−	0.996683i	$-0.474068\pi$
$227$	16.2426	−	16.2426i	1.07806	−	1.07806i	0.996683	−	0.0813787i	$-0.0259323\pi$
$228$	−5.03723	−	5.62372i	−0.333599	−	0.372440i
$229$		−	15.7574i		−	1.04128i	−0.853778	−	0.520638i	$-0.825694\pi$
$229$		−	15.7574i		−	1.04128i	0.853778	−	0.520638i	$-0.174306\pi$
$230$	−1.34486	−	6.57201i	−0.0886777	−	0.433346i
$231$	−0.836338	+	0.308780i	−0.0550270	+	0.0203162i
$232$	3.06350	−	0.820863i	0.201129	−	0.0538923i
$233$	2.71379	−	10.1280i	0.177786	−	0.663508i	−0.818274	−	0.574828i	$-0.805069\pi$
$233$	2.71379	−	10.1280i	0.177786	−	0.663508i	0.996060	−	0.0886791i	$-0.0282646\pi$
$234$	6.44949	−	5.51399i	0.421616	−	0.360461i
$235$	12.9706	−	6.48528i	0.846106	−	0.423053i
$236$		−	5.65685i		−	0.368230i
$237$	11.1855	−	1.03063i	0.726573	−	0.0669467i
$238$	−1.74131	−	6.49867i	−0.112873	−	0.421246i
$239$	−0.686292			−0.0443925			−0.0221963	−	0.999754i	$-0.507066\pi$
$239$	−0.686292			−0.0443925			−0.0221963	+	0.999754i	$0.507066\pi$
$240$	3.70711	−	1.12132i	0.239293	−	0.0723809i
$241$	0.242641	−	0.420266i	0.0156299	−	0.0270717i	−0.858105	−	0.513475i	$-0.828358\pi$
$241$	0.242641	−	0.420266i	0.0156299	−	0.0270717i	0.873735	+	0.486403i	$0.161691\pi$
$242$	10.5967	+	2.83939i	0.681185	+	0.182523i
$243$	−8.64420	+	12.9722i	−0.554526	+	0.832167i
$244$	−1.94218	+	1.12132i	−0.124336	+	0.0717852i
$245$	4.38134	−	0.896575i	0.279914	−	0.0572801i
$246$	−5.12132	−	0.878680i	−0.326523	−	0.0560226i
$247$	4.53590	+	11.4641i	0.288612	+	0.729443i
$248$	4.41421	+	4.41421i	0.280303	+	0.280303i
$249$	−2.54516	−	6.89363i	−0.161293	−	0.436866i
$250$	3.76795	+	10.5263i	0.238306	+	0.665740i
$251$	−14.9941	−	8.65685i	−0.946420	−	0.546416i	−0.0544529	−	0.998516i	$-0.517341\pi$
$251$	−14.9941	−	8.65685i	−0.946420	−	0.546416i	−0.891967	+	0.452101i	$0.850675\pi$
$252$	−5.09393	+	7.41970i	−0.320887	+	0.467397i
$253$	0.133219	+	0.497180i	0.00837541	+	0.0312574i
$254$	2.65685			0.166706
$255$	−4.10051	+	7.65685i	−0.256784	+	0.479491i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.13335	+	7.96178i	0.133075	+	0.496642i	0.999998	−	0.00179903i	$-0.000572648\pi$
$257$	2.13335	+	7.96178i	0.133075	+	0.496642i	−0.866924	+	0.498441i	$0.833906\pi$
$258$	−4.24264	−	6.00000i	−0.264135	−	0.373544i
$259$		−	9.00000i		−	0.559233i
$260$	−6.31319	−	0.378937i	−0.391528	−	0.0235007i
$261$	9.35452	−	1.73862i	0.579030	−	0.107618i
$262$	14.4889	−	3.88229i	0.895126	−	0.239848i
$263$	−0.384419	+	1.43467i	−0.0237043	+	0.0884656i	−0.976765	−	0.214315i	$-0.931248\pi$
$263$	−0.384419	+	1.43467i	−0.0237043	+	0.0884656i	0.953060	+	0.302780i	$0.0979149\pi$
$264$	−0.278779	+	0.102927i	−0.0171577	+	0.00633470i
$265$	9.48528	+	18.9706i	0.582676	+	1.16535i
$266$	−7.79423	−	10.5000i	−0.477895	−	0.643796i
$267$	16.7279	−	11.8284i	1.02373	−	0.723888i
$268$	5.46410	+	1.46410i	0.333773	+	0.0894342i
$269$	5.46447	+	9.46473i	0.333174	+	0.577075i	0.983132	−	0.182895i	$-0.0585469\pi$
$269$	5.46447	+	9.46473i	0.333174	+	0.577075i	−0.649958	+	0.759970i	$0.725214\pi$
$270$	11.3497	−	2.48672i	0.690722	−	0.151337i
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$	−0.580438	−	2.16622i	−0.0351942	−	0.131347i
$273$	12.0000	−	8.48528i	0.726273	−	0.513553i
$274$			20.4853i			1.23756i
$275$	−0.336987	−	0.788905i	−0.0203211	−	0.0475728i
$276$	3.99585	+	3.32162i	0.240522	+	0.199938i
$277$	20.4853	+	20.4853i	1.23084	+	1.23084i	0.963641	+	0.267200i	$0.0860985\pi$
$277$	20.4853	+	20.4853i	1.23084	+	1.23084i	0.267200	+	0.963641i	$0.413901\pi$
$278$	−9.89949	−	9.89949i	−0.593732	−	0.593732i
$279$	12.1700	+	14.2347i	0.728597	+	0.852210i
$280$	6.57201	−	1.34486i	0.392753	−	0.0803709i
$281$	5.34474	+	3.08579i	0.318840	+	0.184083i	0.650876	−	0.759184i	$-0.274402\pi$
$281$	5.34474	+	3.08579i	0.318840	+	0.184083i	−0.332035	+	0.943267i	$0.607735\pi$
$282$	−4.70017	+	10.2022i	−0.279891	+	0.607532i
$283$	11.2597	+	3.01702i	0.669317	+	0.179343i	0.577447	−	0.816428i	$-0.304049\pi$
$283$	11.2597	+	3.01702i	0.669317	+	0.179343i	0.0918699	+	0.995771i	$0.470716\pi$
$284$	−10.5858			−0.628151
$285$	−1.93562	+	16.7706i	−0.114656	+	0.993405i
$286$	0.485281			0.0286953
$287$	−8.69333	−	2.32937i	−0.513151	−	0.137498i
$288$	−1.69798	+	2.47323i	−0.100054	+	0.145737i
$289$	−10.3668	−	5.98528i	−0.609812	−	0.352075i
$290$	−5.91824	−	3.90754i	−0.347531	−	0.229459i
$291$	16.0382	−	19.2937i	0.940176	−	1.13102i
$292$	−11.4853	−	11.4853i	−0.672125	−	0.672125i
$293$	18.3640	+	18.3640i	1.07283	+	1.07283i	0.997130	+	0.0757037i	$0.0241203\pi$
$293$	18.3640	+	18.3640i	1.07283	+	1.07283i	0.0757037	+	0.997130i	$0.475880\pi$
$294$	−2.21441	+	2.66390i	−0.129147	+	0.155362i
$295$	−9.46410	+	8.39230i	−0.551021	+	0.488619i
$296$		−	3.00000i		−	0.174371i
$297$	−0.857864	+	0.242641i	−0.0497783	+	0.0140794i
$298$	2.92820	+	10.9282i	0.169626	+	0.633054i
$299$	−4.24264	−	7.34847i	−0.245358	−	0.424973i
$300$	−7.37574	−	4.53856i	−0.425838	−	0.262034i
$301$	−6.36396	−	11.0227i	−0.366813	−	0.635338i
$302$	−10.3624	−	2.77659i	−0.596288	−	0.159775i
$303$	−17.3137	−	24.4853i	−0.994647	−	1.40664i
$304$	−2.59808	−	3.50000i	−0.149010	−	0.200739i
$305$	4.75736	+	1.58579i	0.272406	+	0.0908019i
$306$	−1.22939	−	6.61465i	−0.0702795	−	0.378134i
$307$	−5.21317	+	19.4558i	−0.297531	+	1.11040i	0.641655	+	0.766993i	$0.278248\pi$
$307$	−5.21317	+	19.4558i	−0.297531	+	1.11040i	−0.939186	+	0.343408i	$0.888419\pi$
$308$	−0.497180	+	0.133219i	−0.0283295	+	0.00759086i
$309$	−4.87453	+	1.79970i	−0.277303	+	0.102381i
$310$	0.836355	−	13.9339i	0.0475018	−	0.791392i
$311$		−	8.48528i		−	0.481156i	−0.970630	−	0.240578i	$-0.922663\pi$
$311$		−	8.48528i		−	0.481156i	0.970630	−	0.240578i	$-0.0773370\pi$
$312$	4.00000	−	2.82843i	0.226455	−	0.160128i
$313$	5.57919	+	20.8218i	0.315355	+	1.17692i	0.923659	+	0.383216i	$0.125183\pi$
$313$	5.57919	+	20.8218i	0.315355	+	1.17692i	−0.608304	+	0.793704i	$0.708150\pi$
$314$	5.91421	−	10.2437i	0.333758	−	0.578086i
$315$	19.9706	−	2.48528i	1.12521	−	0.140030i
$316$	6.48528			0.364826
$317$	7.36491	+	27.4862i	0.413655	+	1.54378i	0.787515	+	0.616296i	$0.211367\pi$
$317$	7.36491	+	27.4862i	0.413655	+	1.54378i	−0.373860	+	0.927485i	$0.621966\pi$
$318$	−14.9216	−	6.87441i	−0.836762	−	0.385498i
$319$	0.471253	+	0.272078i	0.0263851	+	0.0152334i
$320$	2.19067	−	0.448288i	0.122462	−	0.0250600i
$321$	13.7873	−	5.09032i	0.769530	−	0.284114i
$322$	6.36396	+	6.36396i	0.354650	+	0.354650i
$323$	9.67025	+	1.43026i	0.538067	+	0.0795817i
$324$	−5.65685	+	7.00000i	−0.314270	+	0.388889i
$325$	8.73205	+	11.1244i	0.484367	+	0.617068i
$326$	−17.4436	+	10.0711i	−0.966112	+	0.557785i
$327$	−3.86798	+	0.356397i	−0.213900	+	0.0197088i
$328$	−2.89778	−	0.776457i	−0.160003	−	0.0428727i
$329$	−9.72792	+	16.8493i	−0.536318	+	0.928930i
$330$	0.585786	+	0.313708i	0.0322465	+	0.0172691i
$331$	−12.5147			−0.687871			−0.343936	−	0.938993i	$-0.611760\pi$
$331$	−12.5147			−0.687871			−0.343936	+	0.938993i	$0.611760\pi$
$332$	−1.09808	−	4.09808i	−0.0602648	−	0.224911i
$333$	0.701625	−	8.97261i	0.0384488	−	0.491696i
$334$			23.4853i			1.28506i
$335$	−5.65685	−	11.3137i	−0.309067	−	0.618134i
$336$	−3.32162	+	3.99585i	−0.181209	+	0.217992i
$337$	0.643238	−	2.40060i	0.0350394	−	0.130769i	−0.946191	−	0.323610i	$-0.895103\pi$
$337$	0.643238	−	2.40060i	0.0350394	−	0.130769i	0.981230	+	0.192841i	$0.0617701\pi$
$338$	4.82963	−	1.29410i	0.262697	−	0.0703895i
$339$	11.9980	+	32.4969i	0.651642	+	1.76499i
$340$	−2.76305	+	4.18482i	−0.149847	+	0.226954i
$341$			1.07107i			0.0580016i
$342$	−6.95195	−	11.0757i	−0.375918	−	0.598904i
$343$	10.6066	−	10.6066i	0.572703	−	0.572703i
$344$	−2.12132	−	3.67423i	−0.114374	−	0.198101i
$345$	−0.370927	−	11.6130i	−0.0199701	−	0.625224i
$346$	−9.98528	+	17.2950i	−0.536812	+	0.929786i
$347$	−10.5967	−	2.83939i	−0.568863	−	0.152426i	−0.0370881	−	0.999312i	$-0.511808\pi$
$347$	−10.5967	−	2.83939i	−0.568863	−	0.152426i	−0.531775	+	0.846886i	$0.678475\pi$
$348$	5.47015	−	0.504022i	0.293231	−	0.0270184i
$349$		−	22.2426i		−	1.19062i	−0.803496	−	0.595311i	$-0.797029\pi$
$349$		−	22.2426i		−	1.19062i	0.803496	−	0.595311i	$-0.202971\pi$
$350$	−12.0000	−	9.00000i	−0.641427	−	0.481070i
$351$	12.6250	−	7.52396i	0.673871	−	0.401599i
$352$	−0.165727	+	0.0444063i	−0.00883326	+	0.00236687i
$353$	−3.51472	−	3.51472i	−0.187070	−	0.187070i	0.607358	−	0.794428i	$-0.292229\pi$
$353$	−3.51472	−	3.51472i	−0.187070	−	0.187070i	−0.794428	+	0.607358i	$0.792229\pi$
$354$	1.65685	−	9.65685i	0.0880608	−	0.513256i
$355$	15.7047	+	17.7104i	0.833518	+	0.939969i
$356$	10.2437	−	5.91421i	0.542916	−	0.313453i
$357$	−1.06919	−	11.6039i	−0.0565876	−	0.614146i
$358$	−9.02479	−	2.41818i	−0.476975	−	0.127805i
$359$	−4.60660	−	7.97887i	−0.243127	−	0.421109i	0.718476	−	0.695551i	$-0.244840\pi$
$359$	−4.60660	−	7.97887i	−0.243127	−	0.421109i	−0.961603	+	0.274443i	$0.911507\pi$
$360$	6.65685	−	0.828427i	0.350847	−	0.0436619i
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	−10.2426	+	10.2426i	−0.538341	+	0.538341i
$363$	17.2581	+	7.95086i	0.905818	+	0.417312i
$364$	7.34847	−	4.24264i	0.385164	−	0.222375i
$365$	−2.17610	+	36.2544i	−0.113902	+	1.89764i
$366$	−3.64394	+	1.34536i	−0.190472	+	0.0703232i
$367$	−5.79555	+	1.55291i	−0.302526	+	0.0810615i	−0.406889	−	0.913478i	$-0.633386\pi$
$367$	−5.79555	+	1.55291i	−0.302526	+	0.0810615i	0.104363	+	0.994539i	$0.466720\pi$
$368$	2.12132	+	2.12132i	0.110581	+	0.110581i
$369$	−8.48528	−	3.00000i	−0.441726	−	0.156174i
$370$	−5.01910	+	4.45069i	−0.260930	+	0.231380i
$371$	−24.6435	−	14.2279i	−1.27943	−	0.738677i
$372$	6.24264	+	8.82843i	0.323666	+	0.457733i
$373$	12.3640	−	12.3640i	0.640182	−	0.640182i	−0.310418	−	0.950600i	$-0.600469\pi$
$373$	12.3640	−	12.3640i	0.640182	−	0.640182i	0.950600	+	0.310418i	$0.100469\pi$
$374$	0.192388	−	0.333226i	0.00994815	−	0.0172307i
$375$	3.34922	+	19.0731i	0.172953	+	0.984930i
$376$	−3.24264	+	5.61642i	−0.167226	+	0.289645i
$377$	−8.66490	−	2.32175i	−0.446265	−	0.119576i
$378$	−10.8691	+	11.1742i	−0.559044	+	0.574741i
$379$			22.4853i			1.15499i	0.816394	+	0.577496i	$0.195970\pi$
$379$			22.4853i			1.15499i	−0.816394	+	0.577496i	$0.804030\pi$
$380$	−2.00120	+	9.53914i	−0.102659	+	0.489348i
$381$	4.53553	+	0.778175i	0.232362	+	0.0398671i
$382$	2.73980	−	10.2251i	0.140181	−	0.523161i
$383$	7.89017	−	29.4465i	0.403169	−	1.50465i	−0.404239	−	0.914653i	$-0.632464\pi$
$383$	7.89017	−	29.4465i	0.403169	−	1.50465i	0.807408	−	0.589994i	$-0.200870\pi$
$384$	−1.10721	+	1.33195i	−0.0565019	+	0.0679709i
$385$	0.960478	+	0.634159i	0.0489505	+	0.0323198i
$386$	10.3923	+	6.00000i	0.528954	+	0.305392i
$387$	−5.48528	−	11.4853i	−0.278833	−	0.583830i
$388$	10.2426	−	10.2426i	0.519991	−	0.519991i
$389$	−2.46447	+	4.26858i	−0.124953	+	0.216426i	−0.921715	−	0.387868i	$-0.873211\pi$
$389$	−2.46447	+	4.26858i	−0.124953	+	0.216426i	0.796761	+	0.604294i	$0.206545\pi$
$390$	−10.6663	−	2.49598i	−0.540109	−	0.126389i
$391$	−6.72792			−0.340246
$392$	−1.41421	+	1.41421i	−0.0714286	+	0.0714286i
$393$	25.8712	−	2.38378i	1.30503	−	0.120246i
$394$	7.37396	−	4.25736i	0.371495	−	0.214483i
$395$	−9.62133	−	10.8501i	−0.484102	−	0.545927i
$396$	−0.506052	+	0.0940542i	−0.0254301	+	0.00472640i
$397$	−2.06293	+	7.69897i	−0.103536	+	0.386400i	−0.998175	−	0.0603888i	$-0.980766\pi$
$397$	−2.06293	+	7.69897i	−0.103536	+	0.386400i	0.894639	+	0.446789i	$0.147433\pi$
$398$	10.0711	+	10.0711i	0.504817	+	0.504817i
$399$	−10.2302	−	20.2075i	−0.512151	−	1.01164i
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$	−29.9882	+	17.3137i	−1.49754	+	0.864605i	−0.999996	−	0.00283317i	$-0.999098\pi$
$401$	−29.9882	+	17.3137i	−1.49754	+	0.864605i	−0.497544	+	0.867439i	$0.665765\pi$
$402$	8.89898	+	4.09978i	0.443841	+	0.204478i
$403$	−4.56993	−	17.0552i	−0.227644	−	0.849581i
$404$	−8.65685	−	14.9941i	−0.430695	−	0.745985i
$405$	20.1035	−	0.920846i	0.998953	−	0.0457572i
$406$	9.51472			0.472208
$407$	0.363961	−	0.363961i	0.0180409	−	0.0180409i
$408$	−0.356397	−	3.86798i	−0.0176443	−	0.191494i
$409$	−21.1794	−	12.2279i	−1.04725	−	0.604632i	−0.125374	−	0.992110i	$-0.540013\pi$
$409$	−21.1794	−	12.2279i	−1.04725	−	0.604632i	−0.921879	+	0.387478i	$0.873346\pi$
$410$	3.00000	+	6.00000i	0.148159	+	0.296319i
$411$	−6.00000	+	34.9706i	−0.295958	+	1.72497i
$412$	−2.89778	+	0.776457i	−0.142763	+	0.0382533i
$413$	4.39230	−	16.3923i	0.216131	−	0.806613i
$414$	5.84847	+	6.84072i	0.287437	+	0.336203i
$415$	−5.22715	+	7.91688i	−0.256591	+	0.388624i
$416$	2.44949	−	1.41421i	0.120096	−	0.0693375i
$417$	−14.0000	−	19.7990i	−0.685583	−	0.969561i
$418$	0.109422	−	0.739821i	0.00535199	−	0.0361858i
$419$	29.8284			1.45721			0.728607	−	0.684932i	$-0.240168\pi$
$419$	29.8284			1.45721			0.728607	+	0.684932i	$0.240168\pi$
$420$	11.6130	−	0.370927i	0.566658	−	0.0180994i
$421$	10.4853	+	18.1610i	0.511021	+	0.885115i	0.999918	+	0.0127735i	$0.00406603\pi$
$421$	10.4853	+	18.1610i	0.511021	+	0.885115i	−0.488897	+	0.872341i	$0.662601\pi$
$422$	−0.902057	−	3.36652i	−0.0439115	−	0.163880i
$423$	−11.0119	+	16.0396i	−0.535415	+	0.779872i
$424$	−8.21449	−	4.74264i	−0.398931	−	0.230323i
$425$	11.1005	−	1.58579i	0.538454	−	0.0769219i
$426$	−18.0711	−	3.10051i	−0.875546	−	0.150220i
$427$	−6.49867	+	1.74131i	−0.314493	+	0.0842681i
$428$	8.19615	−	2.19615i	0.396176	−	0.106155i
$429$	0.828427	+	0.142136i	0.0399968	+	0.00686237i
$430$	−3.00000	+	9.00000i	−0.144673	+	0.434019i
$431$	9.79796	+	5.65685i	0.471951	+	0.272481i	0.717056	−	0.697015i	$-0.245489\pi$
$431$	9.79796	+	5.65685i	0.471951	+	0.272481i	−0.245105	+	0.969497i	$0.578822\pi$
$432$	−3.62302	+	3.72474i	−0.174313	+	0.179207i
$433$	2.46259	+	9.19051i	0.118345	+	0.441668i	0.999515	−	0.0311302i	$-0.00991067\pi$
$433$	2.46259	+	9.19051i	0.118345	+	0.441668i	−0.881171	+	0.472798i	$0.843244\pi$
$434$	9.36396	+	16.2189i	0.449485	+	0.778530i
$435$	−8.95857	−	8.40400i	−0.429530	−	0.402941i
$436$	−2.24264			−0.107403
$437$	−12.1595	+	4.81105i	−0.581669	+	0.230144i
$438$	−16.2426	−	22.9706i	−0.776103	−	1.09758i
$439$	25.5095	−	14.7279i	1.21750	−	0.702925i	0.253119	−	0.967435i	$-0.418543\pi$
$439$	25.5095	−	14.7279i	1.21750	−	0.702925i	0.964383	+	0.264510i	$0.0852101\pi$
$440$	0.320159	+	0.211386i	0.0152630	+	0.0100775i
$441$	−4.56048	+	3.89898i	−0.217166	+	0.185666i
$442$	−1.64173	+	6.12701i	−0.0780890	+	0.291432i
$443$	33.0759	−	8.86265i	1.57148	−	0.421077i	0.635205	−	0.772343i	$-0.280915\pi$
$443$	33.0759	−	8.86265i	1.57148	−	0.421077i	0.936276	+	0.351266i	$0.114249\pi$
$444$	0.878680	−	5.12132i	0.0417003	−	0.243047i
$445$	−25.0919	−	8.36396i	−1.18947	−	0.396490i
$446$	15.1427	+	8.74264i	0.717028	+	0.413976i
$447$	1.79796	+	19.5133i	0.0850405	+	0.922946i
$448$	−2.12132	+	2.12132i	−0.100223	+	0.100223i
$449$	17.8284			0.841375			0.420688	−	0.907205i	$-0.361789\pi$
$449$	17.8284			0.841375			0.420688	+	0.907205i	$0.361789\pi$
$450$	−11.2619	−	9.90811i	−0.530889	−	0.467073i
$451$	−0.257359	−	0.445759i	−0.0121186	−	0.0209900i
$452$	5.17638	+	19.3185i	0.243476	+	0.908667i
$453$	−16.8764	−	7.77501i	−0.792924	−	0.365302i
$454$	19.8931	−	11.4853i	0.933629	−	0.539031i
$455$	−18.0000	−	6.00000i	−0.843853	−	0.281284i
$456$	−3.41007	−	6.73583i	−0.159691	−	0.315434i
$457$	−24.9706	−	24.9706i	−1.16807	−	1.16807i	−0.982661	−	0.185413i	$-0.940638\pi$
$457$	−24.9706	−	24.9706i	−1.16807	−	1.16807i	−0.185413	−	0.982661i	$-0.559362\pi$
$458$	4.07830	−	15.2204i	0.190567	−	0.711204i
$459$	−0.161314	−	11.6520i	−0.00752947	−	0.543868i
$460$	0.401924	−	6.69615i	0.0187398	−	0.312210i
$461$	21.7482	−	12.5563i	1.01292	−	0.584807i	0.100872	−	0.994899i	$-0.467837\pi$
$461$	21.7482	−	12.5563i	1.01292	−	0.584807i	0.912044	+	0.410092i	$0.134503\pi$
$462$	−0.887758	+	0.0817984i	−0.0413023	+	0.00380560i
$463$	−29.3345	+	29.3345i	−1.36329	+	1.36329i	−0.493604	+	0.869687i	$0.664321\pi$
$463$	−29.3345	+	29.3345i	−1.36329	+	1.36329i	−0.869687	+	0.493604i	$0.835679\pi$
$464$	3.17157			0.147237
$465$	5.50889	−	23.5417i	0.255469	−	1.09172i
$466$	5.24264	−	9.08052i	0.242861	−	0.420647i
$467$	−1.75736	+	1.75736i	−0.0813209	+	0.0813209i	−0.746597	−	0.665276i	$-0.768314\pi$
$467$	−1.75736	+	1.75736i	−0.0813209	+	0.0813209i	0.665276	+	0.746597i	$0.268314\pi$
$468$	7.65685	−	3.65685i	0.353938	−	0.169038i
$469$	14.6969	+	8.48528i	0.678642	+	0.391814i
$470$	14.2071	−	2.90727i	0.655325	−	0.134102i
$471$	13.0965	−	15.7549i	0.603455	−	0.725947i
$472$	1.46410	−	5.46410i	0.0673907	−	0.251506i
$473$	0.188400	−	0.703119i	0.00866265	−	0.0323294i
$474$	11.0711	+	1.89949i	0.508511	+	0.0872467i
$475$	18.9282	−	10.8038i	0.868486	−	0.495715i
$476$		−	6.72792i		−	0.308374i
$477$	−23.4593	−	16.1058i	−1.07413	−	0.737433i
$478$	−0.662907	−	0.177625i	−0.0303206	−	0.00812439i
$479$	15.1924	−	26.3140i	0.694158	−	1.20232i	−0.276306	−	0.961070i	$-0.589110\pi$
$479$	15.1924	−	26.3140i	0.694158	−	1.20232i	0.970464	−	0.241247i	$-0.0775564\pi$
$480$	3.87101	−	0.123642i	0.176687	−	0.00564348i
$481$	−4.24264	+	7.34847i	−0.193448	+	0.335061i
$482$	0.343146	−	0.343146i	0.0156299	−	0.0156299i
$483$	9.00000	+	12.7279i	0.409514	+	0.579141i
$484$	9.50079	+	5.48528i	0.431854	+	0.249331i
$485$	−32.3319	−	1.94066i	−1.46812	−	0.0881208i
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	24.6066	+	24.6066i	1.11503	+	1.11503i	0.992460	+	0.122572i	$0.0391142\pi$
$487$	24.6066	+	24.6066i	1.11503	+	1.11503i	0.122572	+	0.992460i	$0.460886\pi$
$488$	−2.16622	+	0.580438i	−0.0980604	+	0.0262752i
$489$	−32.7278	+	12.0833i	−1.48000	+	0.546425i
$490$	4.46410	+	0.267949i	0.201668	+	0.0121047i
$491$	5.93908	−	3.42893i	0.268027	−	0.154746i	−0.359964	−	0.932966i	$-0.617211\pi$
$491$	5.93908	−	3.42893i	0.268027	−	0.154746i	0.627991	+	0.778221i	$0.283878\pi$
$492$	−4.71940	−	2.17423i	−0.212767	−	0.0980221i
$493$	−5.02944	+	5.02944i	−0.226514	+	0.226514i
$494$	1.41421	+	12.2474i	0.0636285	+	0.551039i
$495$	0.908117	+	0.707107i	0.0408168	+	0.0317821i
$496$	3.12132	+	5.40629i	0.140151	+	0.242749i
$497$	−30.6753	−	8.21941i	−1.37597	−	0.368691i
$498$	−0.674235	−	7.31747i	−0.0302132	−	0.327904i
$499$	32.8835	−	18.9853i	1.47207	−	0.849898i	0.472560	−	0.881299i	$-0.343330\pi$
$499$	32.8835	−	18.9853i	1.47207	−	0.849898i	0.999507	+	0.0314008i	$0.00999684\pi$
$500$	0.915158	+	11.1428i	0.0409271	+	0.498322i
$501$	−6.87868	+	40.0919i	−0.307317	+	1.79117i
$502$	−12.2426	−	12.2426i	−0.546416	−	0.546416i
$503$	−17.3582	+	4.65112i	−0.773965	+	0.207383i	−0.624123	−	0.781326i	$-0.714543\pi$
$503$	−17.3582	+	4.65112i	−0.773965	+	0.207383i	−0.149843	+	0.988710i	$0.547877\pi$
$504$	−6.84072	+	5.84847i	−0.304710	+	0.260512i
$505$	−12.2426	+	36.7279i	−0.544790	+	1.63437i
$506$			0.514719i			0.0228820i
$507$	8.62372	−	0.794593i	0.382993	−	0.0352891i
$508$	2.56632	+	0.687644i	0.113862	+	0.0305093i
$509$	−6.36396	+	11.0227i	−0.282078	+	0.488573i	−0.971896	−	0.235409i	$-0.924357\pi$
$509$	−6.36396	+	11.0227i	−0.282078	+	0.488573i	0.689819	+	0.723982i	$0.257690\pi$
$510$	−5.94252	+	6.33466i	−0.263139	+	0.280504i
$511$	−24.3640	−	42.1996i	−1.07780	−	1.86680i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−8.62372	−	20.9435i	−0.380747	−	0.924679i
$514$			8.24264i			0.363567i
$515$	5.59808	+	3.69615i	0.246681	+	0.162872i
$516$	−2.54516	−	6.89363i	−0.112045	−	0.303475i
$517$	−1.07478	+	0.287988i	−0.0472690	+	0.0126657i
$518$	2.32937	−	8.69333i	0.102347	−	0.381963i
$519$	−22.1115	+	26.5998i	−0.970589	+	1.16760i
$520$	−6.00000	−	2.00000i	−0.263117	−	0.0877058i
$521$		−	35.3137i		−	1.54712i	−0.633722	−	0.773561i	$-0.718474\pi$
$521$		−	35.3137i		−	1.54712i	0.633722	−	0.773561i	$-0.281526\pi$
$522$	9.48576	+	0.741752i	0.415181	+	0.0324656i
$523$	−6.12284	−	22.8508i	−0.267733	−	0.999194i	−0.960556	−	0.278086i	$-0.910300\pi$
$523$	−6.12284	−	22.8508i	−0.267733	−	0.999194i	0.692823	−	0.721108i	$-0.256367\pi$
$524$	15.0000			0.655278
$525$	−17.8492	−	18.8787i	−0.779005	−	0.823933i
$526$	−0.742641	+	1.28629i	−0.0323807	+	0.0560850i
$527$	−13.5230	−	3.62347i	−0.589069	−	0.157841i
$528$	−0.295919	+	0.0272661i	−0.0128782	+	0.00118661i
$529$	−12.1244	+	7.00000i	−0.527146	+	0.304348i
$530$	4.25214	+	20.7791i	0.184701	+	0.902588i
$531$	5.65685	−	16.0000i	0.245487	−	0.694341i
$532$	−4.81105	−	12.1595i	−0.208585	−	0.527182i
$533$	6.00000	+	6.00000i	0.259889	+	0.259889i
$534$	19.2194	−	7.09588i	0.831703	−	0.307069i
$535$	−15.8338	−	10.4543i	−0.684553	−	0.451979i
$536$	4.89898	+	2.82843i	0.211604	+	0.122169i
$537$	−14.6980	−	6.77140i	−0.634266	−	0.292207i
$538$	2.82862	+	10.5565i	0.121950	+	0.455125i
$539$	−0.343146			−0.0147803
$540$	11.6066	+	0.535534i	0.499469	+	0.0230457i
$541$	−0.636039	+	1.10165i	−0.0273455	+	0.0473637i	−0.879374	−	0.476131i	$-0.842039\pi$
$541$	−0.636039	+	1.10165i	−0.0273455	+	0.0473637i	0.852029	+	0.523495i	$0.175372\pi$
$542$	0.517638	+	1.93185i	0.0222345	+	0.0829801i
$543$	−20.4853	+	14.4853i	−0.879108	+	0.621623i
$544$		−	2.24264i		−	0.0961524i
$545$	3.32710	+	3.75201i	0.142517	+	0.160718i
$546$	13.7873	−	5.09032i	0.590040	−	0.217846i
$547$	−18.7929	+	5.03554i	−0.803526	+	0.215304i	−0.637132	−	0.770755i	$-0.719879\pi$
$547$	−18.7929	+	5.03554i	−0.803526	+	0.215304i	−0.166395	+	0.986059i	$0.553213\pi$
$548$	−5.30198	+	19.7873i	−0.226489	+	0.845270i
$549$	−6.61465	+	1.22939i	−0.282306	+	0.0524690i
$550$	−0.121320	−	0.849242i	−0.00517312	−	0.0362118i
$551$	−5.49333	+	12.6863i	−0.234024	+	0.540454i
$552$	3.00000	+	4.24264i	0.127688	+	0.180579i
$553$	18.7929	+	5.03554i	0.799155	+	0.214133i
$554$	14.4853	+	25.0892i	0.615421	+	1.06594i
$555$	−9.87171	+	6.12775i	−0.419031	+	0.260108i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	−3.61585	−	13.4945i	−0.153208	−	0.571781i	−0.999252	−	0.0386680i	$-0.987689\pi$
$557$	−3.61585	−	13.4945i	−0.153208	−	0.571781i	0.846044	−	0.533114i	$-0.178978\pi$
$558$	8.07107	+	16.8995i	0.341676	+	0.715413i
$559$			12.0000i			0.507546i
$560$	6.69615	+	0.401924i	0.282964	+	0.0169844i
$561$	0.426027	−	0.512503i	0.0179869	−	0.0216379i
$562$	4.36396	+	4.36396i	0.184083	+	0.184083i
$563$	−27.1716	−	27.1716i	−1.14515	−	1.14515i	−0.987495	−	0.157650i	$-0.949608\pi$
$563$	−27.1716	−	27.1716i	−1.14515	−	1.14515i	−0.157650	−	0.987495i	$-0.550392\pi$
$564$	−7.18054	+	8.63808i	−0.302355	+	0.363729i
$565$	24.6410	−	37.3205i	1.03666	−	1.57009i
$566$	10.0951	+	5.82843i	0.424330	+	0.244987i
$567$	−21.8275	+	15.8921i	−0.916669	+	0.667407i
$568$	−10.2251	−	2.73980i	−0.429035	−	0.114960i
$569$	10.7990			0.452717			0.226359	−	0.974044i	$-0.427318\pi$
$569$	10.7990			0.452717			0.226359	+	0.974044i	$0.427318\pi$
$570$	−6.21021	+	15.6982i	−0.260117	+	0.657525i
$571$	−10.4853			−0.438795			−0.219398	−	0.975636i	$-0.570409\pi$
$571$	−10.4853			−0.438795			−0.219398	+	0.975636i	$0.570409\pi$
$572$	0.468746	+	0.125600i	0.0195992	+	0.00525160i
$573$	7.67199	−	16.6528i	0.320502	−	0.695682i
$574$	−7.79423	−	4.50000i	−0.325325	−	0.187826i
$575$	−11.7992	+	9.26174i	−0.492059	+	0.386241i
$576$	−2.28024	+	1.94949i	−0.0950100	+	0.0812287i
$577$	−2.48528	−	2.48528i	−0.103464	−	0.103464i	0.653480	−	0.756944i	$-0.273308\pi$
$577$	−2.48528	−	2.48528i	−0.103464	−	0.103464i	−0.756944	+	0.653480i	$0.773308\pi$
$578$	−8.46447	−	8.46447i	−0.352075	−	0.352075i
$579$	15.9834	+	13.2865i	0.664248	+	0.552167i
$580$	−4.70523	−	5.30614i	−0.195374	−	0.220326i
$581$		−	12.7279i		−	0.528043i
$582$	20.4853	−	14.4853i	0.849142	−	0.600434i
$583$	−0.421207	−	1.57196i	−0.0174446	−	0.0651041i
$584$	−8.12132	−	14.0665i	−0.336063	−	0.582078i
$585$	−17.4775	−	7.38499i	−0.722604	−	0.305332i
$586$	12.9853	+	22.4912i	0.536417	+	0.929102i
$587$	−39.5745	−	10.6040i	−1.63342	−	0.437672i	−0.678512	−	0.734589i	$-0.737375\pi$
$587$	−39.5745	−	10.6040i	−1.63342	−	0.437672i	−0.954903	+	0.296917i	$0.904042\pi$
$588$	−2.82843	+	2.00000i	−0.116642	+	0.0824786i
$589$	−27.0314	+	3.12132i	−1.11381	+	0.128612i
$590$	−11.3137	+	5.65685i	−0.465778	+	0.232889i
$591$	13.8351	−	5.10798i	0.569100	−	0.210114i
$592$	0.776457	−	2.89778i	0.0319122	−	0.119098i
$593$	−37.1739	+	9.96072i	−1.52655	+	0.409038i	−0.921892	−	0.387447i	$-0.873357\pi$
$593$	−37.1739	+	9.96072i	−1.52655	+	0.409038i	−0.604658	+	0.796485i	$0.706690\pi$
$594$	−0.891433	+	0.0123413i	−0.0365760	+	0.000506368i
$595$	−11.2560	+	9.98130i	−0.461452	+	0.409194i
$596$			11.3137i			0.463428i
$597$	14.2426	+	20.1421i	0.582912	+	0.824363i
$598$	−2.19615	−	8.19615i	−0.0898074	−	0.335166i
$599$	−11.8492	+	20.5235i	−0.484147	+	0.838567i	−0.999834	−	0.0182098i	$-0.994203\pi$
$599$	−11.8492	+	20.5235i	−0.484147	+	0.838567i	0.515687	+	0.856777i	$0.327537\pi$
$600$	−5.94975	−	6.29289i	−0.242897	−	0.256906i
$601$	23.0000			0.938190			0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000			0.938190			0.469095	+	0.883148i	$0.344580\pi$
$602$	−3.29423	−	12.2942i	−0.134263	−	0.501075i
$603$	13.9907	+	9.60521i	0.569746	+	0.391154i
$604$	−9.29065	−	5.36396i	−0.378031	−	0.218256i
$605$	−4.91797	−	24.0329i	−0.199944	−	0.977076i
$606$	−10.3865	−	28.1321i	−0.421923	−	1.14279i
$607$	−4.36396	−	4.36396i	−0.177128	−	0.177128i	0.612975	−	0.790102i	$-0.289973\pi$
$607$	−4.36396	−	4.36396i	−0.177128	−	0.177128i	−0.790102	+	0.612975i	$0.789973\pi$
$608$	−1.60368	−	4.05317i	−0.0650379	−	0.164378i
$609$	16.2426	+	2.78680i	0.658185	+	0.112927i
$610$	4.18482	+	2.76305i	0.169439	+	0.111873i
$611$	15.8856	−	9.17157i	0.642664	−	0.371042i
$612$	0.524498	−	6.70745i	0.0212016	−	0.271132i
$613$	−10.4310	−	2.79498i	−0.421305	−	0.112888i	0.0419368	−	0.999120i	$-0.486647\pi$
$613$	−10.4310	−	2.79498i	−0.421305	−	0.112888i	−0.463242	+	0.886232i	$0.653314\pi$
$614$	−10.0711	+	17.4436i	−0.406435	+	0.703966i
$615$	3.36396	+	11.1213i	0.135648	+	0.448455i
$616$	−0.514719			−0.0207386
$617$	−8.32977	−	31.0871i	−0.335344	−	1.25152i	−0.903496	−	0.428597i	$-0.859008\pi$
$617$	−8.32977	−	31.0871i	−0.335344	−	1.25152i	0.568152	−	0.822924i	$-0.307659\pi$
$618$	−5.17423	+	0.476756i	−0.208138	+	0.0191779i
$619$			24.9411i			1.00247i	0.865312	+	0.501234i	$0.167121\pi$
$619$			24.9411i			1.00247i	−0.865312	+	0.501234i	$0.832879\pi$
$620$	4.41421	−	13.2426i	0.177279	−	0.531837i
$621$	7.98036	+	13.3908i	0.320241	+	0.537355i
$622$	2.19615	−	8.19615i	0.0880577	−	0.328636i
$623$	34.2761	−	9.18427i	1.37324	−	0.367960i
$624$	4.59575	−	1.69677i	0.183977	−	0.0679253i
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$			21.5563i			0.861565i
$627$	0.403483	−	1.23090i	0.0161136	−	0.0491576i
$628$	8.36396	−	8.36396i	0.333758	−	0.333758i
$629$	3.36396	+	5.82655i	0.134130	+	0.232320i
$630$	19.9333	+	2.76816i	0.794162	+	0.110286i
$631$	0.121320	−	0.210133i	0.00482969	−	0.00836526i	−0.863600	−	0.504177i	$-0.831796\pi$
$631$	0.121320	−	0.210133i	0.00482969	−	0.00836526i	0.868430	+	0.495812i	$0.165129\pi$
$632$	6.26430	+	1.67851i	0.249181	+	0.0667677i
$633$	−0.553876	−	6.01122i	−0.0220146	−	0.238925i
$634$			28.4558i			1.13013i
$635$	−2.65685	−	5.31371i	−0.105434	−	0.210868i
$636$	−12.6339	−	10.5022i	−0.500968	−	0.416438i
$637$	5.46410	−	1.46410i	0.216496	−	0.0580098i
$638$	0.384776	+	0.384776i	0.0152334	+	0.0152334i
$639$	−29.9411	−	10.5858i	−1.18445	−	0.418767i
$640$	2.23205	+	0.133975i	0.0882296	+	0.00529581i
$641$	−15.2913	+	8.82843i	−0.603969	+	0.348702i	−0.770602	−	0.637317i	$-0.780044\pi$
$641$	−15.2913	+	8.82843i	−0.603969	+	0.348702i	0.166632	+	0.986019i	$0.446711\pi$
$642$	14.6349	−	1.34847i	0.577595	−	0.0532198i
$643$	16.0206	+	4.29272i	0.631792	+	0.169288i	0.560483	−	0.828166i	$-0.310616\pi$
$643$	16.0206	+	4.29272i	0.631792	+	0.169288i	0.0713094	+	0.997454i	$0.477282\pi$
$644$	4.50000	+	7.79423i	0.177325	+	0.307136i
$645$	−7.75736	+	14.4853i	−0.305446	+	0.570357i
$646$	8.97056	+	3.88437i	0.352942	+	0.152828i
$647$	−12.7071	+	12.7071i	−0.499568	+	0.499568i	−0.911303	−	0.411735i	$-0.864923\pi$
$647$	−12.7071	+	12.7071i	−0.499568	+	0.499568i	0.411735	+	0.911303i	$0.364923\pi$
$648$	−7.27583	+	5.29738i	−0.285822	+	0.208101i
$649$	0.840532	−	0.485281i	0.0329938	−	0.0190490i
$650$	5.55532	+	13.0053i	0.217898	+	0.510111i
$651$	11.2349	+	30.4300i	0.440330	+	1.19264i
$652$	−19.4558	+	5.21317i	−0.761948	+	0.204163i
$653$	−14.8492	−	14.8492i	−0.581096	−	0.581096i	0.354109	−	0.935204i	$-0.384784\pi$
$653$	−14.8492	−	14.8492i	−0.581096	−	0.581096i	−0.935204	+	0.354109i	$0.884784\pi$
$654$	−3.82843	−	0.656854i	−0.149703	−	0.0256850i
$655$	−22.2535	−	25.0955i	−0.869515	−	0.980562i
$656$	−2.59808	−	1.50000i	−0.101438	−	0.0585652i
$657$	−21.0000	−	43.9706i	−0.819288	−	1.71546i
$658$	−13.7574	+	13.7574i	−0.536318	+	0.536318i
$659$	19.7132	−	34.1443i	0.767917	−	1.33007i	−0.170773	−	0.985310i	$-0.554626\pi$
$659$	19.7132	−	34.1443i	0.767917	−	1.33007i	0.938690	−	0.344762i	$-0.112040\pi$
$660$	0.484633	+	0.454632i	0.0188643	+	0.0176965i
$661$	−2.87868	+	4.98602i	−0.111968	+	0.193934i	−0.916564	−	0.399889i	$-0.869049\pi$
$661$	−2.87868	+	4.98602i	−0.111968	+	0.193934i	0.804596	+	0.593823i	$0.202382\pi$
$662$	−12.0883	−	3.23905i	−0.469825	−	0.125889i
$663$	−4.59716	+	9.97861i	−0.178539	+	0.387537i
$664$		−	4.24264i		−	0.164646i
$665$	−13.2058	+	26.0885i	−0.512098	+	1.01167i
$666$	3.00000	−	8.48528i	0.116248	−	0.328798i
$667$	2.46259	−	9.19051i	0.0953519	−	0.355858i
$668$	−6.07844	+	22.6850i	−0.235182	+	0.877711i
$669$	23.2895	+	19.3598i	0.900426	+	0.748494i
$670$	−2.53590	−	12.3923i	−0.0979703	−	0.478757i
$671$	−0.333226	−	0.192388i	−0.0128640	−	0.00742706i
$672$	−4.24264	+	3.00000i	−0.163663	+	0.115728i
$673$	−28.9706	+	28.9706i	−1.11673	+	1.11673i	−0.124515	+	0.992218i	$0.539738\pi$
$673$	−28.9706	+	28.9706i	−1.11673	+	1.11673i	−0.992218	+	0.124515i	$0.960262\pi$
$674$	1.24264	−	2.15232i	0.0478647	−	0.0829041i
$675$	−16.3232	−	20.2127i	−0.628279	−	0.777988i
$676$	5.00000			0.192308
$677$	34.6066	−	34.6066i	1.33004	−	1.33004i	0.424711	−	0.905329i	$-0.360376\pi$
$677$	34.6066	−	34.6066i	1.33004	−	1.33004i	0.905329	−	0.424711i	$-0.139624\pi$
$678$	3.17837	+	34.4949i	0.122065	+	1.32477i
$679$	37.6339	−	21.7279i	1.44426	−	0.833841i
$680$	−3.75201	+	3.32710i	−0.143883	+	0.127588i
$681$	37.3236	−	13.7801i	1.43024	−	0.528053i
$682$	−0.277213	+	1.03457i	−0.0106150	+	0.0396158i
$683$	−0.899495	−	0.899495i	−0.0344182	−	0.0344182i	0.689688	−	0.724106i	$-0.257748\pi$
$683$	−0.899495	−	0.899495i	−0.0344182	−	0.0344182i	−0.724106	+	0.689688i	$0.757748\pi$
$684$	−3.84847	−	12.4976i	−0.147150	−	0.477857i
$685$	40.9706	−	20.4853i	1.56540	−	0.782702i
$686$	12.9904	−	7.50000i	0.495975	−	0.286351i
$687$	11.4201	−	24.7884i	0.435703	−	0.945737i
$688$	−1.09808	−	4.09808i	−0.0418638	−	0.156238i
$689$	13.4142	+	23.2341i	0.511041	+	0.885149i
$690$	2.64738	−	11.3133i	0.100784	−	0.430691i
$691$	−27.9706			−1.06405			−0.532025	−	0.846729i	$-0.678569\pi$
$691$	−27.9706			−1.06405			−0.532025	+	0.846729i	$0.678569\pi$
$692$	−14.1213	+	14.1213i	−0.536812	+	0.536812i
$693$	−1.53946	−	0.120380i	−0.0584791	−	0.00457285i
$694$	−9.50079	−	5.48528i	−0.360645	−	0.208218i
$695$	−9.89949	+	29.6985i	−0.375509	+	1.12653i
$696$	5.41421	+	0.928932i	0.205225	+	0.0352111i
$697$	6.49867	−	1.74131i	0.246155	−	0.0659570i
$698$	5.75682	−	21.4847i	0.217899	−	0.813209i
$699$	11.6094	−	13.9659i	0.439107	−	0.528238i
$700$	−9.26174	−	11.7992i	−0.350061	−	0.445966i
$701$	28.7635	−	16.6066i	1.08638	−	0.627223i	0.153771	−	0.988107i	$-0.450858\pi$
$701$	28.7635	−	16.6066i	1.08638	−	0.627223i	0.932611	+	0.360884i	$0.117525\pi$
$702$	14.1421	−	4.00000i	0.533761	−	0.150970i
$703$	10.2462	+	8.12493i	0.386445	+	0.306437i
$704$	−0.171573			−0.00646640
$705$	25.1046	−	0.801856i	0.945493	−	0.0301996i
$706$	−2.48528	−	4.30463i	−0.0935348	−	0.162007i
$707$	−13.4434	−	50.1713i	−0.505589	−	1.88688i
$708$	4.09978	−	8.89898i	0.154079	−	0.334444i
$709$	−37.8440	−	21.8492i	−1.42126	−	0.820566i	−0.424854	−	0.905262i	$-0.639675\pi$
$709$	−37.8440	−	21.8492i	−1.42126	−	0.820566i	−0.996407	+	0.0846962i	$0.973008\pi$
$710$	10.5858	+	21.1716i	0.397277	+	0.794555i
$711$	18.3431	+	6.48528i	0.687922	+	0.243217i
$712$	11.4254	−	3.06142i	0.428184	−	0.114732i
$713$	18.0898	−	4.84714i	0.677468	−	0.181527i
$714$	1.97056	−	11.4853i	0.0737465	−	0.429826i
$715$	−0.485281	−	0.970563i	−0.0181485	−	0.0362970i
$716$	−8.09140	−	4.67157i	−0.302390	−	0.174585i
$717$	−1.07963	−	0.497386i	−0.0403194	−	0.0185752i
$718$	−2.38455	−	8.89927i	−0.0889907	−	0.332118i
$719$	3.70711	+	6.42090i	0.138252	+	0.239459i	0.926835	−	0.375469i	$-0.122518\pi$
$719$	3.70711	+	6.42090i	0.138252	+	0.239459i	−0.788583	+	0.614928i	$0.789185\pi$
$720$	6.64444	+	0.922722i	0.247624	+	0.0343878i
$721$	−9.00000			−0.335178
$722$	18.9903	+	0.605571i	0.706748	+	0.0225370i
$723$	0.686292	−	0.485281i	0.0255235	−	0.0180478i
$724$	−12.5446	+	7.24264i	−0.466217	+	0.269171i
$725$	−1.89684	+	15.7440i	−0.0704470	+	0.584718i
$726$	14.6123	+	12.1467i	0.542312	+	0.450805i
$727$	−3.92669	+	14.6546i	−0.145633	+	0.543510i	0.854093	+	0.520120i	$0.174113\pi$
$727$	−3.92669	+	14.6546i	−0.145633	+	0.543510i	−0.999726	+	0.0233900i	$0.992554\pi$
$728$	8.19615	−	2.19615i	0.303770	−	0.0813948i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$	−11.4853	+	34.4558i	−0.425089	+	1.27527i
$731$	8.23999	+	4.75736i	0.304767	+	0.175957i
$732$	−3.86798	+	0.356397i	−0.142965	+	0.0131728i
$733$	−8.12132	+	8.12132i	−0.299968	+	0.299968i	−0.841001	−	0.541033i	$-0.818033\pi$
$733$	−8.12132	+	8.12132i	−0.299968	+	0.299968i	0.541033	+	0.841001i	$0.318033\pi$
$734$	−6.00000			−0.221464
$735$	7.54222	+	1.76492i	0.278199	+	0.0651002i
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	0.251200	+	0.937492i	0.00925308	+	0.0345329i
$738$	−7.41970	−	5.09393i	−0.273123	−	0.187510i
$739$	−29.4194	+	16.9853i	−1.08221	+	0.624814i	−0.931491	−	0.363763i	$-0.881492\pi$
$739$	−29.4194	+	16.9853i	−1.08221	+	0.624814i	−0.150718	+	0.988577i	$0.548158\pi$
$740$	−6.00000	+	3.00000i	−0.220564	+	0.110282i
$741$	−1.17298	+	21.3219i	−0.0430905	+	0.783280i
$742$	−20.1213	−	20.1213i	−0.738677	−	0.738677i
$743$	−6.72168	+	25.0856i	−0.246594	+	0.920303i	0.725981	+	0.687715i	$0.241386\pi$
$743$	−6.72168	+	25.0856i	−0.246594	+	0.920303i	−0.972575	+	0.232588i	$0.925281\pi$
$744$	3.74496	+	10.1433i	0.137297	+	0.371872i
$745$	18.9282	−	16.7846i	0.693476	−	0.614941i
$746$	15.1427	−	8.74264i	0.554414	−	0.320091i
$747$	0.992248	−	12.6892i	0.0363044	−	0.464273i
$748$	0.272078	−	0.272078i	0.00994815	−	0.00994815i
$749$	25.4558			0.930136
$750$	−1.70138	+	19.2900i	−0.0621258	+	0.704372i
$751$	21.6066	−	37.4237i	0.788436	−	1.36561i	−0.138489	−	0.990364i	$-0.544224\pi$
$751$	21.6066	−	37.4237i	0.788436	−	1.36561i	0.926925	−	0.375247i	$-0.122442\pi$
$752$	−4.58579	+	4.58579i	−0.167226	+	0.167226i
$753$	−17.3137	−	24.4853i	−0.630947	−	0.892293i
$754$	−7.76874	−	4.48528i	−0.282921	−	0.163344i
$755$	4.80920	+	23.5013i	0.175025	+	0.855301i
$756$	−13.3908	+	7.98036i	−0.487019	+	0.290243i
$757$	−11.8460	+	44.2100i	−0.430551	+	1.60684i	0.320942	+	0.947099i	$0.396001\pi$
$757$	−11.8460	+	44.2100i	−0.430551	+	1.60684i	−0.751493	+	0.659741i	$0.770666\pi$
$758$	−5.81962	+	21.7191i	−0.211378	+	0.788874i
$759$	−0.150758	+	0.878680i	−0.00547215	+	0.0318941i
$760$	−4.40192	+	8.69615i	−0.159675	+	0.315443i
$761$			6.51472i			0.236158i	0.993004	+	0.118079i	$0.0376737\pi$
$761$			6.51472i			0.236158i	−0.993004	+	0.118079i	$0.962326\pi$
$762$	4.17958	+	1.92554i	0.151410	+	0.0697550i
$763$	−6.49867	−	1.74131i	−0.235268	−	0.0630398i
$764$	5.29289	−	9.16756i	0.191490	−	0.331671i
$765$	−11.9999	+	9.07342i	−0.433857	+	0.328050i
$766$	15.2426	−	26.4010i	0.550739	−	0.953908i
$767$	−11.3137	+	11.3137i	−0.408514	+	0.408514i
$768$	−1.41421	+	1.00000i	−0.0510310	+	0.0360844i
$769$	−33.7495	−	19.4853i	−1.21704	−	0.702657i	−0.252755	−	0.967530i	$-0.581337\pi$
$769$	−33.7495	−	19.4853i	−1.21704	−	0.702657i	−0.964283	+	0.264873i	$0.914670\pi$
$770$	0.763618	+	0.861141i	0.0275189	+	0.0310334i
$771$	−2.41421	+	14.0711i	−0.0869458	+	0.506757i
$772$	8.48528	+	8.48528i	0.305392	+	0.305392i
$773$	8.16772	−	2.18853i	0.293772	−	0.0787161i	−0.108923	−	0.994050i	$-0.534740\pi$
$773$	8.16772	−	2.18853i	0.293772	−	0.0787161i	0.402695	+	0.915334i	$0.368073\pi$
$774$	−2.32577	−	12.5136i	−0.0835979	−	0.449793i
$775$	−28.7041	+	12.2612i	−1.03108	+	0.440435i
$776$	12.5446	−	7.24264i	0.450326	−	0.259996i
$777$	6.52270	−	14.1582i	0.234001	−	0.507922i
$778$	−3.48528	+	3.48528i	−0.124953	+	0.124953i
$779$	10.5000	−	7.79423i	0.376202	−	0.279257i
$780$	−9.65685	−	5.17157i	−0.345771	−	0.185172i
$781$	−0.908117	−	1.57290i	−0.0324950	−	0.0562830i
$782$	−6.49867	−	1.74131i	−0.232392	−	0.0622693i
$783$	15.9760	+	4.04456i	0.570934	+	0.144541i
$784$	−1.73205	+	1.00000i	−0.0618590	+	0.0357143i
$785$	−26.4017	−	1.58471i	−0.942315	−	0.0565607i
$786$	25.6066	+	4.39340i	0.913357	+	0.156707i
$787$	2.72792	+	2.72792i	0.0972399	+	0.0972399i	0.754053	−	0.656813i	$-0.228096\pi$
$787$	2.72792	+	2.72792i	0.0972399	+	0.0972399i	−0.656813	+	0.754053i	$0.728096\pi$
$788$	8.22459	−	2.20377i	0.292989	−	0.0785061i
$789$	−1.64451	+	1.97832i	−0.0585462	+	0.0704301i
$790$	−6.48528	−	12.9706i	−0.230736	−	0.461472i
$791$			60.0000i			2.13335i
$792$	−0.513152	−	0.0401266i	−0.0182341	−	0.00142584i
$793$	6.12701	+	1.64173i	0.217576	+	0.0582994i
$794$	−3.98528	+	6.90271i	−0.141432	+	0.244968i
$795$	1.17278	+	36.7176i	0.0415943	+	1.30224i
$796$	7.12132	+	12.3345i	0.252409	+	0.437184i
$797$	−1.77817	+	1.77817i	−0.0629862	+	0.0629862i	−0.737898	−	0.674912i	$-0.764182\pi$
$797$	−1.77817	+	1.77817i	−0.0629862	+	0.0629862i	0.674912	+	0.737898i	$0.264182\pi$
$798$	−4.65153	−	22.1667i	−0.164662	−	0.784693i
$799$		−	14.5442i		−	0.514535i
$800$	−3.08725	−	3.93305i	−0.109151	−	0.139054i
$801$	34.8878	−	6.48420i	1.23270	−	0.229108i
$802$	−33.4475	+	8.96224i	−1.18107	+	0.316468i
$803$	0.721276	−	2.69184i	0.0254533	−	0.0949929i
$804$	7.53465	+	6.26330i	0.265727	+	0.220890i
$805$	6.36396	−	19.0919i	0.224300	−	0.672900i
$806$		−	17.6569i		−	0.621936i
$807$	1.73681	+	18.8496i	0.0611386	+	0.663538i
$808$	−4.48112	−	16.7238i	−0.157645	−	0.588340i
$809$	−24.6863			−0.867924			−0.433962	−	0.900931i	$-0.642885\pi$
$809$	−24.6863			−0.867924			−0.433962	+	0.900931i	$0.642885\pi$
$810$	19.6569	+	4.31371i	0.690671	+	0.151568i
$811$	−10.2279	+	17.7153i	−0.359151	+	0.622068i	−0.987819	−	0.155606i	$-0.950267\pi$
$811$	−10.2279	+	17.7153i	−0.359151	+	0.622068i	0.628668	+	0.777674i	$0.283600\pi$
$812$	9.19051	+	2.46259i	0.322524	+	0.0864200i
$813$	0.317837	+	3.44949i	0.0111470	+	0.120979i
$814$	0.445759	−	0.257359i	0.0156239	−	0.00902044i
$815$	37.5857	+	24.8161i	1.31657	+	0.869271i
$816$	0.656854	−	3.82843i	0.0229945	−	0.134022i
$817$	18.2942	+	2.70577i	0.640034	+	0.0946630i
$818$	−17.2929	−	17.2929i	−0.604632	−	0.604632i
$819$	25.0273	−	4.65153i	0.874523	−	0.162538i
$820$	1.34486	+	6.57201i	0.0469647	+	0.229505i
$821$	−5.79050	−	3.34315i	−0.202090	−	0.116677i	0.395540	−	0.918449i	$-0.370557\pi$
$821$	−5.79050	−	3.34315i	−0.202090	−	0.116677i	−0.597630	+	0.801772i	$0.703891\pi$
$822$	−14.8466	+	32.2261i	−0.517835	+	1.12401i
$823$	−10.1828	−	38.0026i	−0.354949	−	1.32469i	−0.880549	−	0.473955i	$-0.842826\pi$
$823$	−10.1828	−	38.0026i	−0.354949	−	1.32469i	0.525601	−	0.850731i	$-0.323841\pi$
$824$	−3.00000			−0.104510
$825$	0.0416306	−	1.48528i	0.00144939	−	0.0517109i
$826$	8.48528	−	14.6969i	0.295241	−	0.511372i
$827$	−1.80411	−	6.73305i	−0.0627352	−	0.234131i	0.927438	−	0.373977i	$-0.122006\pi$
$827$	−1.80411	−	6.73305i	−0.0627352	−	0.234131i	−0.990173	+	0.139846i	$0.955339\pi$
$828$	3.87868	+	8.12132i	0.134793	+	0.282235i
$829$			28.9706i			1.00619i	0.864231	+	0.503095i	$0.167805\pi$
$829$			28.9706i			1.00619i	−0.864231	+	0.503095i	$0.832195\pi$
$830$	−7.09808	+	6.29423i	−0.246378	+	0.218476i
$831$	17.3795	+	47.0727i	0.602887	+	1.63293i
$832$	2.73205	−	0.732051i	0.0947168	−	0.0253793i
$833$	1.16088	−	4.33245i	0.0402220	−	0.150110i
$834$	−8.39861	−	22.7478i	−0.290820	−	0.787693i
$835$	46.9706	−	23.4853i	1.62548	−	0.812742i
$836$	0.297173	−	0.686292i	0.0102779	−	0.0237359i
$837$	8.82843	+	31.2132i	0.305155	+	1.07889i
$838$	28.8120	+	7.72017i	0.995296	+	0.266689i
$839$	−14.1213	−	24.4588i	−0.487522	−	0.844413i	0.512375	−	0.858762i	$-0.328766\pi$
$839$	−14.1213	−	24.4588i	−0.487522	−	0.844413i	−0.999897	+	0.0143488i	$0.995432\pi$
$840$	11.3133	+	2.64738i	0.390347	+	0.0913434i
$841$	9.47056	+	16.4035i	0.326571	+	0.565638i
$842$	5.42758	+	20.2560i	0.187047	+	0.698068i
$843$	6.17157	+	8.72792i	0.212560	+	0.300606i
$844$		−	3.48528i		−	0.119968i
$845$	−7.41782	−	8.36516i	−0.255181	−	0.287770i
$846$	−14.7880	+	12.6430i	−0.508422	+	0.434675i
$847$	23.2721	+	23.2721i	0.799638	+	0.799638i
$848$	−6.70711	−	6.70711i	−0.230323	−	0.230323i
$849$	15.5264	+	12.9065i	0.532863	+	0.442951i
$850$	11.1327	+	1.34127i	0.381848	+	0.0460052i
$851$	−7.79423	−	4.50000i	−0.267183	−	0.154258i
$852$	−16.6528	−	7.67199i	−0.570517	−	0.262838i
$853$	−20.4502	−	5.47961i	−0.700200	−	0.187618i	−0.108880	−	0.994055i	$-0.534726\pi$
$853$	−20.4502	−	5.47961i	−0.700200	−	0.187618i	−0.591320	+	0.806437i	$0.701393\pi$
$854$	−6.72792			−0.230225
$855$	−15.1994	+	24.9796i	−0.519808	+	0.854283i
$856$	8.48528			0.290021
$857$	8.19615	+	2.19615i	0.279975	+	0.0750191i	0.396074	−	0.918219i	$-0.370372\pi$
$857$	8.19615	+	2.19615i	0.279975	+	0.0750191i	−0.116099	+	0.993238i	$0.537039\pi$
$858$	0.763412	+	0.351705i	0.0260624	+	0.0120070i
$859$	12.5191	+	7.22792i	0.427147	+	0.246614i	0.698131	−	0.715971i	$-0.254016\pi$
$859$	12.5191	+	7.22792i	0.427147	+	0.246614i	−0.270983	+	0.962584i	$0.587349\pi$
$860$	−5.22715	+	7.91688i	−0.178244	+	0.269963i
$861$	−11.9876	−	9.96486i	−0.408535	−	0.339601i
$862$	8.00000	+	8.00000i	0.272481	+	0.272481i
$863$	39.2340	+	39.2340i	1.33554	+	1.33554i	0.900327	+	0.435215i	$0.143328\pi$
$863$	39.2340	+	39.2340i	1.33554	+	1.33554i	0.435215	+	0.900327i	$0.356672\pi$
$864$	−4.46360	+	2.66012i	−0.151855	+	0.0904991i
$865$	44.5753	+	2.67555i	1.51561	+	0.0909714i
$866$			9.51472i			0.323323i
$867$	−11.9706	−	16.9289i	−0.406542	−	0.574937i
$868$	4.84714	+	18.0898i	0.164523	+	0.614007i
$869$	0.556349	+	0.963625i	0.0188729	+	0.0326887i
$870$	−6.47820	−	10.4363i	−0.219631	−	0.353823i
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	−2.16622	−	0.580438i	−0.0733576	−	0.0196561i
$873$	39.2132	−	18.7279i	1.32717	−	0.633844i
$874$	−12.9904	+	1.50000i	−0.439406	+	0.0507383i
$875$	−6.00000	+	33.0000i	−0.202837	+	1.11560i
$876$	−9.74397	−	26.3918i	−0.329218	−	0.891695i
$877$	7.36491	−	27.4862i	0.248695	−	0.928144i	−0.722794	−	0.691063i	$-0.757143\pi$
$877$	7.36491	−	27.4862i	0.248695	−	0.928144i	0.971490	−	0.237081i	$-0.0761907\pi$
$878$	28.4522	−	7.62373i	0.960214	−	0.257289i
$879$	15.5798	+	42.1981i	0.525492	+	1.42331i
$880$	0.254539	+	0.287047i	0.00858052	+	0.00967635i
$881$		−	49.2843i		−	1.66043i	−0.557444	−	0.830215i	$-0.688218\pi$
$881$		−	49.2843i		−	1.66043i	0.557444	−	0.830215i	$-0.311782\pi$
$882$	−5.41421	+	2.58579i	−0.182306	+	0.0870680i
$883$	0.909676	+	3.39496i	0.0306130	+	0.114249i	0.979542	−	0.201241i	$-0.0644975\pi$
$883$	0.909676	+	3.39496i	0.0306130	+	0.114249i	−0.948929	+	0.315491i	$0.897831\pi$
$884$	−3.17157	+	5.49333i	−0.106672	+	0.184761i
$885$	−20.9706	+	6.34315i	−0.704918	+	0.213223i
$886$	34.2426			1.15040
$887$	5.03554	+	18.7929i	0.169077	+	0.631004i	0.997485	+	0.0708787i	$0.0225803\pi$
$887$	5.03554	+	18.7929i	0.169077	+	0.631004i	−0.828408	+	0.560125i	$0.810753\pi$
$888$	2.17423	−	4.71940i	0.0729625	−	0.158373i
$889$	6.90271	+	3.98528i	0.231509	+	0.133662i
$890$	−22.0721	−	14.5732i	−0.739860	−	0.488496i
$891$	−1.52539	−	0.240027i	−0.0511024	−	0.00804120i
$892$	12.3640	+	12.3640i	0.413976	+	0.413976i
$893$	−10.4003	−	26.2860i	−0.348034	−	0.879626i
$894$	−3.31371	+	19.3137i	−0.110827	+	0.645947i
$895$	4.18842	+	20.4678i	0.140003	+	0.684162i
$896$	−2.59808	+	1.50000i	−0.0867956	+	0.0501115i
$897$	−1.34847	−	14.6349i	−0.0450241	−	0.488647i
$898$	17.2209	+	4.61434i	0.574670	+	0.153982i
$899$	9.89949	−	17.1464i	0.330167	−	0.571865i
$900$	−8.31371	−	12.4853i	−0.277124	−	0.416176i
$901$	21.2721			0.708676
$902$	−0.133219	−	0.497180i	−0.00443571	−	0.0165543i
$903$	−2.02270	−	21.9524i	−0.0673114	−	0.730531i
$904$			20.0000i			0.665190i
$905$	30.7279	+	10.2426i	1.02143	+	0.340477i
$906$	−14.2891	−	11.8780i	−0.474723	−	0.394621i
$907$	8.21941	−	30.6753i	0.272921	−	1.01856i	−0.684301	−	0.729200i	$-0.739892\pi$
$907$	8.21941	−	30.6753i	0.272921	−	1.01856i	0.957222	−	0.289355i	$-0.0934409\pi$
$908$	22.1879	−	5.94522i	0.736330	−	0.197299i
$909$	−9.49117	−	51.0666i	−0.314802	−	1.69377i
$910$	−15.8338	−	10.4543i	−0.524884	−	0.346557i
$911$		−	29.3137i		−	0.971206i	−0.874179	−	0.485603i	$-0.838600\pi$
$911$		−	29.3137i		−	0.971206i	0.874179	−	0.485603i	$-0.161400\pi$
$912$	−1.55051	−	7.38891i	−0.0513425	−	0.244671i
$913$	0.514719	−	0.514719i	0.0170347	−	0.0170347i
$914$	−17.6569	−	30.5826i	−0.584037	−	1.01158i
$915$	6.33466	+	5.94252i	0.209418	+	0.196454i
$916$	7.87868	−	13.6463i	0.260319	−	0.450886i
$917$	43.4667	+	11.6469i	1.43540	+	0.384613i
$918$	2.85994	−	11.2967i	0.0943921	−	0.372847i
$919$			23.2721i			0.767675i	0.923401	+	0.383838i	$0.125398\pi$
$919$			23.2721i			0.767675i	−0.923401	+	0.383838i	$0.874602\pi$
$920$	2.12132	−	6.36396i	0.0699379	−	0.209814i
$921$	−22.3015	+	26.8283i	−0.734859	+	0.884024i
$922$	24.2570	−	6.49964i	0.798862	−	0.214054i
$923$	21.1716	+	21.1716i	0.696871	+	0.696871i
$924$	−0.878680	−	0.150758i	−0.0289064	−	0.00495956i
$925$	13.9205	+	5.58750i	0.457703	+	0.183716i
$926$	−35.9273	+	20.7426i	−1.18064	+	0.681645i
$927$	−8.97261	−	0.701625i	−0.294699	−	0.0230444i
$928$	3.06350	+	0.820863i	0.100564	+	0.0269462i
$929$	−24.2990	−	42.0871i	−0.797224	−	1.38083i	−0.921417	−	0.388574i	$-0.872968\pi$
$929$	−24.2990	−	42.0871i	−0.797224	−	1.38083i	0.124193	−	0.992258i	$-0.460366\pi$
$930$	11.4142	−	21.3137i	0.374287	−	0.698904i
$931$	−1.00000	−	8.66025i	−0.0327737	−	0.283828i
$932$	7.41421	−	7.41421i	0.242861	−	0.242861i
$933$	6.14966	−	13.3485i	0.201331	−	0.437009i
$934$	−2.15232	+	1.24264i	−0.0704260	+	0.0406604i
$935$	−0.858840	−	0.0515503i	−0.0280871	−	0.00168587i
$936$	8.34242	−	1.55051i	0.272680	−	0.0506800i
$937$	5.42389	−	1.45333i	0.177191	−	0.0474781i	−0.169133	−	0.985593i	$-0.554097\pi$
$937$	5.42389	−	1.45333i	0.177191	−	0.0474781i	0.346323	+	0.938115i	$0.387430\pi$
$938$	12.0000	+	12.0000i	0.391814	+	0.391814i
$939$	−6.31371	+	36.7990i	−0.206040	+	1.20089i
$940$	14.4755	+	0.868863i	0.472138	+	0.0283392i
$941$	−22.3426	−	12.8995i	−0.728347	−	0.420512i	0.0894699	−	0.995990i	$-0.471483\pi$
$941$	−22.3426	−	12.8995i	−0.728347	−	0.420512i	−0.817817	+	0.575478i	$0.804816\pi$
$942$	16.7279	−	11.8284i	0.545025	−	0.385391i
$943$	−6.36396	+	6.36396i	−0.207239	+	0.207239i
$944$	2.82843	−	4.89898i	0.0920575	−	0.159448i
$945$	33.2175	+	10.5639i	1.08057	+	0.343643i
$946$	0.363961	−	0.630399i	0.0118334	−	0.0204960i
$947$	53.3319	+	14.2902i	1.73305	+	0.464370i	0.980883	−	0.194599i	$-0.0623407\pi$
$947$	53.3319	+	14.2902i	1.73305	+	0.464370i	0.752170	+	0.658969i	$0.229007\pi$
$948$	10.2022	+	4.70017i	0.331352	+	0.152655i
$949$			45.9411i			1.49131i
$950$	21.0795	−	5.53674i	0.683909	−	0.179635i
$951$	−8.33452	+	48.5772i	−0.270265	+	1.57522i
$952$	1.74131	−	6.49867i	0.0564363	−	0.210623i
$953$	1.28648	−	4.80119i	0.0416731	−	0.155526i	−0.941954	−	0.335742i	$-0.891013\pi$
$953$	1.28648	−	4.80119i	0.0416731	−	0.155526i	0.983627	+	0.180216i	$0.0576797\pi$
$954$	−18.4915	−	21.6287i	−0.598683	−	0.700255i
$955$	−23.1900	+	4.74548i	−0.750410	+	0.153560i
$956$	−0.594346	−	0.343146i	−0.0192225	−	0.0110981i
$957$	0.544156	+	0.769553i	0.0175901	+	0.0248761i
$958$	21.4853	−	21.4853i	0.694158	−	0.694158i
$959$	−30.7279	+	53.2223i	−0.992256	+	1.71864i
$960$	3.77111	+	0.882461i	0.121712	+	0.0284813i
$961$	7.97056			0.257115
$962$	−6.00000	+	6.00000i	−0.193448	+	0.193448i
$963$	25.3784	+	1.98450i	0.817807	+	0.0639495i
$964$	0.420266	−	0.242641i	0.0135359	−	0.00781493i
$965$	1.60770	−	26.7846i	0.0517535	−	0.862227i
$966$	5.39910	+	14.6236i	0.173713	+	0.470507i
$967$	−11.2472	+	41.9751i	−0.361686	+	1.34983i	0.510173	+	0.860072i	$0.329581\pi$
$967$	−11.2472	+	41.9751i	−0.361686	+	1.34983i	−0.871859	+	0.489757i	$0.837085\pi$
$968$	7.75736	+	7.75736i	0.249331	+	0.249331i
$969$	14.1760	+	9.25845i	0.455399	+	0.297424i
$970$	−30.7279	−	10.2426i	−0.986614	−	0.328871i
$971$	16.8493	−	9.72792i	0.540718	−	0.312184i	−0.204652	−	0.978835i	$-0.565606\pi$
$971$	16.8493	−	9.72792i	0.540718	−	0.312184i	0.745370	+	0.666651i	$0.232273\pi$
$972$	−13.9722	+	6.91215i	−0.448158	+	0.221707i
$973$	−10.8704	−	40.5689i	−0.348489	−	1.30058i
$974$	17.3995	+	30.1368i	0.557516	+	0.965646i
$975$	5.67435	+	23.8286i	0.181725	+	0.763126i
$976$	−2.24264			−0.0717852
$977$	−7.75736	+	7.75736i	−0.248180	+	0.248180i	−0.820223	−	0.572043i	$-0.806151\pi$
$977$	−7.75736	+	7.75736i	−0.248180	+	0.248180i	0.572043	+	0.820223i	$0.306151\pi$
$978$	−34.7400	+	3.20096i	−1.11086	+	0.102355i
$979$	1.75754	+	1.01472i	0.0561714	+	0.0324305i
$980$	4.24264	+	1.41421i	0.135526	+	0.0451754i
$981$	−6.34315	−	2.24264i	−0.202521	−	0.0716020i
$982$	6.62419	−	1.77495i	0.211386	−	0.0566408i
$983$	−4.25909	+	15.8951i	−0.135844	+	0.506976i	0.864149	+	0.503236i	$0.167857\pi$
$983$	−4.25909	+	15.8951i	−0.135844	+	0.506976i	−0.999993	+	0.00374017i	$0.998809\pi$
$984$	−3.99585	−	3.32162i	−0.127383	−	0.105889i
$985$	−15.8887	−	10.4906i	−0.506255	−	0.334257i
$986$	−6.15978	+	3.55635i	−0.196167	+	0.113257i
$987$	−27.5147	+	19.4558i	−0.875803	+	0.619286i
$988$	−1.80385	+	12.1962i	−0.0573880	+	0.388011i
$989$	−12.7279			−0.404724
$990$	0.694161	+	0.918051i	0.0220619	+	0.0291776i
$991$	−3.00000	−	5.19615i	−0.0952981	−	0.165061i	0.814435	−	0.580255i	$-0.197047\pi$
$991$	−3.00000	−	5.19615i	−0.0952981	−	0.165061i	−0.909733	+	0.415194i	$0.863714\pi$
$992$	1.61571	+	6.02993i	0.0512990	+	0.191450i
$993$	−19.6873	−	9.06998i	−0.624758	−	0.287827i
$994$	−27.5027	−	15.8787i	−0.872332	−	0.503641i
$995$	10.0711	−	30.2132i	0.319274	−	0.957823i
$996$	1.24264	−	7.24264i	0.0393746	−	0.229492i
$997$	15.1518	−	4.05991i	0.479862	−	0.128579i	−0.0107763	−	0.999942i	$-0.503430\pi$
$997$	15.1518	−	4.05991i	0.479862	−	0.128579i	0.490638	+	0.871363i	$0.336764\pi$
$998$	36.6767	−	9.82750i	1.16098	−	0.311084i
$999$	7.60660	−	13.6066i	0.240662	−	0.430494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.a.197.2	yes	8
3.2	odd	2		570.2.v.b.197.1	yes	8
5.3	odd	4		570.2.v.b.83.2	yes	8
15.8	even	4	inner	570.2.v.a.83.1	✓	8
19.11	even	3	inner	570.2.v.a.467.1	yes	8
57.11	odd	6		570.2.v.b.467.2	yes	8
95.68	odd	12		570.2.v.b.353.1	yes	8
285.68	even	12	inner	570.2.v.a.353.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.a.83.1	✓	8	15.8	even	4	inner
570.2.v.a.197.2	yes	8	1.1	even	1	trivial
570.2.v.a.353.2	yes	8	285.68	even	12	inner
570.2.v.a.467.1	yes	8	19.11	even	3	inner
570.2.v.b.83.2	yes	8	5.3	odd	4
570.2.v.b.197.1	yes	8	3.2	odd	2
570.2.v.b.353.1	yes	8	95.68	odd	12
570.2.v.b.467.2	yes	8	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.57313 + 0.724745i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.448288 - 2.19067i) q^{5} +(1.33195 + 1.10721i) q^{6} +(2.12132 + 2.12132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.94949 + 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.57313 + 0.724745i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.448288 - 2.19067i) q^{5} +(1.33195 + 1.10721i) q^{6} +(2.12132 + 2.12132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.94949 + 2.28024i) q^{9} +(0.133975 - 2.23205i) q^{10} +0.171573i q^{11} +(1.00000 + 1.41421i) q^{12} +(-0.732051 - 2.73205i) q^{13} +(1.50000 + 2.59808i) q^{14} +(0.882461 - 3.77111i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.16622 - 0.580438i) q^{17} +(1.29289 + 2.70711i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(0.707107 - 2.12132i) q^{20} +(1.79970 + 4.87453i) q^{21} +(-0.0444063 + 0.165727i) q^{22} +(2.89778 - 0.776457i) q^{23} +(0.599900 + 1.62484i) q^{24} +(-4.59808 + 1.96410i) q^{25} -2.82843i q^{26} +(1.41421 + 5.00000i) q^{27} +(0.776457 + 2.89778i) q^{28} +(1.58579 - 2.74666i) q^{29} +(1.82843 - 3.41421i) q^{30} +6.24264 q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.124347 + 0.269907i) q^{33} +(-1.94218 - 1.12132i) q^{34} +(3.69615 - 5.59808i) q^{35} +(0.548188 + 2.94949i) q^{36} +(-2.12132 - 2.12132i) q^{37} +(-4.31199 - 0.637756i) q^{38} +(0.828427 - 4.82843i) q^{39} +(1.23205 - 1.86603i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(0.476756 + 5.17423i) q^{42} +(-4.09808 - 1.09808i) q^{43} +(-0.0857864 + 0.148586i) q^{44} +(4.12132 - 5.29289i) q^{45} +3.00000 q^{46} +(1.67851 + 6.26430i) q^{47} +(0.158919 + 1.72474i) q^{48} +2.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-2.98709 - 2.48307i) q^{51} +(0.732051 - 2.73205i) q^{52} +(-9.16208 + 2.45497i) q^{53} +(0.0719302 + 5.19565i) q^{54} +(0.375860 - 0.0769140i) q^{55} +3.00000i q^{56} +(-7.17423 - 2.35167i) q^{57} +(2.24264 - 2.24264i) q^{58} +(-2.82843 - 4.89898i) q^{59} +(2.64979 - 2.82465i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(6.02993 + 1.61571i) q^{62} +(-0.701625 + 8.97261i) q^{63} +1.00000i q^{64} +(-5.65685 + 2.82843i) q^{65} +(-0.189967 + 0.228527i) q^{66} +(5.46410 - 1.46410i) q^{67} +(-1.58579 - 1.58579i) q^{68} +(5.12132 + 0.878680i) q^{69} +(5.01910 - 4.45069i) q^{70} +(-9.16756 + 5.29289i) q^{71} +(-0.233875 + 2.99087i) q^{72} +(-15.6892 - 4.20390i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(-8.65685 - 0.242641i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(-0.363961 + 0.363961i) q^{77} +(2.04989 - 4.44949i) q^{78} +(5.61642 - 3.24264i) q^{79} +(1.67303 - 1.48356i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(-2.89778 + 0.776457i) q^{82} +(-3.00000 - 3.00000i) q^{83} +(-0.878680 + 5.12132i) q^{84} +(-0.300457 + 5.00569i) q^{85} +(-3.67423 - 2.12132i) q^{86} +(4.48528 - 3.17157i) q^{87} +(-0.121320 + 0.121320i) q^{88} +(5.91421 - 10.2437i) q^{89} +(5.35079 - 4.04587i) q^{90} +(4.24264 - 7.34847i) q^{91} +(2.89778 + 0.776457i) q^{92} +(9.82050 + 4.52432i) q^{93} +6.48528i q^{94} +(3.03648 + 9.26174i) q^{95} +(-0.292893 + 1.70711i) q^{96} +(3.74907 - 13.9917i) q^{97} +(-0.517638 + 1.93185i) q^{98} +(-0.391227 + 0.334480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^6 - 4 * q^9	\( 8 q - 4 q^{6} - 4 q^{9} + 8 q^{10} + 8 q^{12} + 8 q^{13} + 12 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} + 16 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{24} - 16 q^{25} + 24 q^{29} - 8 q^{30} + 16 q^{31} + 12 q^{33} - 12 q^{35} - 16 q^{39} - 4 q^{40} - 12 q^{43} - 12 q^{44} + 16 q^{45} + 24 q^{46} - 24 q^{47} - 20 q^{51} - 8 q^{52} - 24 q^{53} + 4 q^{54} - 8 q^{55} - 28 q^{57} - 16 q^{58} + 4 q^{60} + 8 q^{61} + 12 q^{62} - 24 q^{63} - 4 q^{66} + 16 q^{67} - 24 q^{68} + 24 q^{69} - 8 q^{72} - 12 q^{73} - 12 q^{74} - 24 q^{75} - 32 q^{76} + 48 q^{77} + 28 q^{81} - 24 q^{83} - 24 q^{84} + 16 q^{85} - 32 q^{87} + 16 q^{88} + 36 q^{89} + 8 q^{90} + 24 q^{93} - 8 q^{96} - 24 q^{97} + 32 q^{99}+O(q^{100}) \) 8 * q - 4 * q^6 - 4 * q^9 + 8 * q^10 + 8 * q^12 + 8 * q^13 + 12 * q^14 + 12 * q^15 + 4 * q^16 - 12 * q^17 + 16 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^24 - 16 * q^25 + 24 * q^29 - 8 * q^30 + 16 * q^31 + 12 * q^33 - 12 * q^35 - 16 * q^39 - 4 * q^40 - 12 * q^43 - 12 * q^44 + 16 * q^45 + 24 * q^46 - 24 * q^47 - 20 * q^51 - 8 * q^52 - 24 * q^53 + 4 * q^54 - 8 * q^55 - 28 * q^57 - 16 * q^58 + 4 * q^60 + 8 * q^61 + 12 * q^62 - 24 * q^63 - 4 * q^66 + 16 * q^67 - 24 * q^68 + 24 * q^69 - 8 * q^72 - 12 * q^73 - 12 * q^74 - 24 * q^75 - 32 * q^76 + 48 * q^77 + 28 * q^81 - 24 * q^83 - 24 * q^84 + 16 * q^85 - 32 * q^87 + 16 * q^88 + 36 * q^89 + 8 * q^90 + 24 * q^93 - 8 * q^96 - 24 * q^97 + 32 * q^99

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