LMFDB - Embedded newform 570.2.v.a.83.1

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			83.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	570.83
Dual form			570.2.v.a.467.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.158919 + 1.72474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.67303 - 1.48356i) q^{5} +(-1.62484 - 0.599900i) q^{6} +(2.12132 - 2.12132i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.158919 + 1.72474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.67303 - 1.48356i) q^{5} +(-1.62484 - 0.599900i) q^{6} +(2.12132 - 2.12132i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94949 - 0.548188i) q^{9} +(1.86603 - 1.23205i) q^{10} -0.171573i q^{11} +(1.00000 - 1.41421i) q^{12} +(2.73205 - 0.732051i) q^{13} +(1.50000 + 2.59808i) q^{14} +(2.82465 - 2.64979i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.580438 - 2.16622i) q^{17} +(1.29289 - 2.70711i) q^{18} +(4.33013 - 0.500000i) q^{19} +(0.707107 + 2.12132i) q^{20} +(3.32162 + 3.99585i) q^{21} +(0.165727 + 0.0444063i) q^{22} +(-0.776457 - 2.89778i) q^{23} +(1.10721 + 1.33195i) q^{24} +(0.598076 + 4.96410i) q^{25} +2.82843i q^{26} +(1.41421 - 5.00000i) q^{27} +(-2.89778 + 0.776457i) q^{28} +(1.58579 - 2.74666i) q^{29} +(1.82843 + 3.41421i) q^{30} +6.24264 q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.295919 + 0.0272661i) q^{33} +(1.94218 + 1.12132i) q^{34} +(-6.69615 + 0.401924i) q^{35} +(2.28024 + 1.94949i) q^{36} +(-2.12132 + 2.12132i) q^{37} +(-0.637756 + 4.31199i) q^{38} +(0.828427 + 4.82843i) q^{39} +(-2.23205 + 0.133975i) q^{40} +(2.59808 - 1.50000i) q^{41} +(-4.71940 + 2.17423i) q^{42} +(1.09808 - 4.09808i) q^{43} +(-0.0857864 + 0.148586i) q^{44} +(4.12132 + 5.29289i) q^{45} +3.00000 q^{46} +(-6.26430 + 1.67851i) q^{47} +(-1.57313 + 0.724745i) q^{48} -2.00000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(3.64394 + 1.34536i) q^{51} +(-2.73205 - 0.732051i) q^{52} +(2.45497 + 9.16208i) q^{53} +(4.46360 + 2.66012i) q^{54} +(-0.254539 + 0.287047i) q^{55} -3.00000i q^{56} +(0.174235 + 7.54782i) q^{57} +(2.24264 + 2.24264i) q^{58} +(-2.82843 - 4.89898i) q^{59} +(-3.77111 + 0.882461i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(-1.61571 + 6.02993i) q^{62} +(-7.41970 + 5.09393i) q^{63} -1.00000i q^{64} +(-5.65685 - 2.82843i) q^{65} +(-0.102927 + 0.278779i) q^{66} +(-1.46410 - 5.46410i) q^{67} +(-1.58579 + 1.58579i) q^{68} +(5.12132 - 0.878680i) q^{69} +(1.34486 - 6.57201i) q^{70} +(9.16756 - 5.29289i) q^{71} +(-2.47323 + 1.69798i) q^{72} +(4.20390 - 15.6892i) 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} +(-4.87832 - 0.449490i) q^{78} +(-5.61642 + 3.24264i) q^{79} +(0.448288 - 2.19067i) q^{80} +(8.39898 + 3.23375i) q^{81} +(0.776457 + 2.89778i) q^{82} +(-3.00000 + 3.00000i) q^{83} +(-0.878680 - 5.12132i) q^{84} +(-4.18482 + 2.76305i) 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} +(-6.17922 + 2.61099i) q^{90} +(4.24264 - 7.34847i) q^{91} +(-0.776457 + 2.89778i) q^{92} +(-0.992072 + 10.7670i) q^{93} -6.48528i q^{94} +(-7.98623 - 5.58750i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(-13.9917 - 3.74907i) q^{97} +(1.93185 + 0.517638i) q^{98} +(-0.0940542 + 0.506052i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.158919	+	1.72474i	−0.0917517	+	0.995782i
$3$	−0.158919	+	1.72474i	−0.0917517	+	0.995782i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.67303	−	1.48356i	−0.748203	−	0.663470i
$5$	−1.67303	−	1.48356i	−0.748203	−	0.663470i
$6$	−1.62484	−	0.599900i	−0.663340	−	0.244908i
$7$	2.12132	−	2.12132i	0.801784	−	0.801784i	−0.181591	−	0.983374i	$-0.558125\pi$
$7$	2.12132	−	2.12132i	0.801784	−	0.801784i	0.983374	+	0.181591i	$0.0581245\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.94949	−	0.548188i	−0.983163	−	0.182729i
$10$	1.86603	−	1.23205i	0.590089	−	0.389609i
$11$		−	0.171573i		−	0.0517312i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$		−	0.171573i		−	0.0517312i	0.999665	−	0.0258656i	$-0.00823419\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$	2.73205	−	0.732051i	0.757735	−	0.203034i	0.140788	−	0.990040i	$-0.455036\pi$
$13$	2.73205	−	0.732051i	0.757735	−	0.203034i	0.616946	+	0.787005i	$0.288370\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$	2.82465	−	2.64979i	0.729320	−	0.684172i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.580438	−	2.16622i	0.140777	−	0.525387i	−0.859130	−	0.511757i	$-0.828995\pi$
$17$	0.580438	−	2.16622i	0.140777	−	0.525387i	0.999907	−	0.0136295i	$-0.00433855\pi$
$18$	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
$21$	3.32162	+	3.99585i	0.724837	+	0.871967i
$22$	0.165727	+	0.0444063i	0.0353330	+	0.00946746i
$23$	−0.776457	−	2.89778i	−0.161903	−	0.604228i	−0.998415	−	0.0562805i	$-0.982076\pi$
$23$	−0.776457	−	2.89778i	−0.161903	−	0.604228i	0.836512	−	0.547948i	$-0.184591\pi$
$24$	1.10721	+	1.33195i	0.226008	+	0.271883i
$25$	0.598076	+	4.96410i	0.119615	+	0.992820i
$26$			2.82843i			0.554700i
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$	−2.89778	+	0.776457i	−0.547628	+	0.146737i
$29$	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	$0.310568\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.295919	+	0.0272661i	0.0515130	+	0.00474642i
$34$	1.94218	+	1.12132i	0.333082	+	0.192305i
$35$	−6.69615	+	0.401924i	−1.13186	+	0.0679375i
$36$	2.28024	+	1.94949i	0.380040	+	0.324915i
$37$	−2.12132	+	2.12132i	−0.348743	+	0.348743i	−0.859641	−	0.510898i	$-0.829313\pi$
$37$	−2.12132	+	2.12132i	−0.348743	+	0.348743i	0.510898	+	0.859641i	$0.329313\pi$
$38$	−0.637756	+	4.31199i	−0.103458	+	0.699497i
$39$	0.828427	+	4.82843i	0.132655	+	0.773167i
$40$	−2.23205	+	0.133975i	−0.352918	+	0.0211832i
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	−4.71940	+	2.17423i	−0.728219	+	0.335492i
$43$	1.09808	−	4.09808i	0.167455	−	0.624951i	−0.830259	−	0.557377i	$-0.811808\pi$
$43$	1.09808	−	4.09808i	0.167455	−	0.624951i	0.997714	−	0.0675734i	$-0.0215257\pi$
$44$	−0.0857864	+	0.148586i	−0.0129328	+	0.0224003i
$45$	4.12132	+	5.29289i	0.614370	+	0.789018i
$46$	3.00000			0.442326
$47$	−6.26430	+	1.67851i	−0.913742	+	0.244836i	−0.684909	−	0.728629i	$-0.740158\pi$
$47$	−6.26430	+	1.67851i	−0.913742	+	0.244836i	−0.228834	+	0.973466i	$0.573491\pi$
$48$	−1.57313	+	0.724745i	−0.227062	+	0.104608i
$49$		−	2.00000i		−	0.285714i
$50$	−4.94975	−	0.707107i	−0.700000	−	0.100000i
$51$	3.64394	+	1.34536i	0.510254	+	0.188388i
$52$	−2.73205	−	0.732051i	−0.378867	−	0.101517i
$53$	2.45497	+	9.16208i	0.337216	+	1.25851i	0.901446	+	0.432891i	$0.142506\pi$
$53$	2.45497	+	9.16208i	0.337216	+	1.25851i	−0.564230	+	0.825618i	$0.690827\pi$
$54$	4.46360	+	2.66012i	0.607420	+	0.361997i
$55$	−0.254539	+	0.287047i	−0.0343221	+	0.0387054i
$56$		−	3.00000i		−	0.400892i
$57$	0.174235	+	7.54782i	0.0230779	+	0.999734i
$58$	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	$0.953369\pi$
$60$	−3.77111	+	0.882461i	−0.486848	+	0.113925i
$61$	−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	$0.212525\pi$
$62$	−1.61571	+	6.02993i	−0.205196	+	0.765802i
$63$	−7.41970	+	5.09393i	−0.934794	+	0.641775i
$64$		−	1.00000i		−	0.125000i
$65$	−5.65685	−	2.82843i	−0.701646	−	0.350823i
$66$	−0.102927	+	0.278779i	−0.0126694	+	0.0343154i
$67$	−1.46410	−	5.46410i	−0.178868	−	0.667546i	−0.995860	−	0.0908970i	$-0.971027\pi$
$67$	−1.46410	−	5.46410i	−0.178868	−	0.667546i	0.816992	−	0.576649i	$-0.195640\pi$
$68$	−1.58579	+	1.58579i	−0.192305	+	0.192305i
$69$	5.12132	−	0.878680i	0.616535	−	0.105781i
$70$	1.34486	−	6.57201i	0.160742	−	0.785506i
$71$	9.16756	−	5.29289i	1.08799	−	0.628151i	0.154949	−	0.987922i	$-0.450479\pi$
$71$	9.16756	−	5.29289i	1.08799	−	0.628151i	0.933040	+	0.359772i	$0.117145\pi$
$72$	−2.47323	+	1.69798i	−0.291473	+	0.200108i
$73$	4.20390	−	15.6892i	0.492030	−	1.83628i	−0.0540373	−	0.998539i	$-0.517209\pi$
$73$	4.20390	−	15.6892i	0.492030	−	1.83628i	0.546067	−	0.837741i	$-0.316124\pi$
$74$	−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
$78$	−4.87832	−	0.449490i	−0.552360	−	0.0508947i
$79$	−5.61642	+	3.24264i	−0.631896	+	0.364826i	−0.781486	−	0.623923i	$-0.785538\pi$
$79$	−5.61642	+	3.24264i	−0.631896	+	0.364826i	0.149590	+	0.988748i	$0.452205\pi$
$80$	0.448288	−	2.19067i	0.0501201	−	0.244924i
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$	0.776457	+	2.89778i	0.0857453	+	0.320006i
$83$	−3.00000	+	3.00000i	−0.329293	+	0.329293i	−0.852318	−	0.523025i	$-0.824804\pi$
$83$	−3.00000	+	3.00000i	−0.329293	+	0.329293i	0.523025	+	0.852318i	$0.324804\pi$
$84$	−0.878680	−	5.12132i	−0.0958718	−	0.558782i
$85$	−4.18482	+	2.76305i	−0.453908	+	0.299695i
$86$	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	$-0.0490121\pi$
$90$	−6.17922	+	2.61099i	−0.651347	+	0.275222i
$91$	4.24264	−	7.34847i	0.444750	−	0.770329i
$92$	−0.776457	+	2.89778i	−0.0809513	+	0.302114i
$93$	−0.992072	+	10.7670i	−0.102873	+	1.11648i
$94$		−	6.48528i		−	0.668906i
$95$	−7.98623	−	5.58750i	−0.819369	−	0.573266i
$96$	−0.292893	−	1.70711i	−0.0298933	−	0.174231i
$97$	−13.9917	−	3.74907i	−1.42064	−	0.380660i	−0.534931	−	0.844896i	$-0.679662\pi$
$97$	−13.9917	−	3.74907i	−1.42064	−	0.380660i	−0.885712	+	0.464236i	$0.846329\pi$
$98$	1.93185	+	0.517638i	0.195146	+	0.0522893i
$99$	−0.0940542	+	0.506052i	−0.00945280	+	0.0508602i
$100$	1.96410	−	4.59808i	0.196410	−	0.459808i
$101$	14.9941	+	8.65685i	1.49197	+	0.861389i	0.999958	−	0.00919913i	$-0.00292822\pi$
$101$	14.9941	+	8.65685i	1.49197	+	0.861389i	0.492012	+	0.870588i	$0.336262\pi$
$102$	−2.24264	+	3.17157i	−0.222055	+	0.314033i
$103$	−2.12132	−	2.12132i	−0.209020	−	0.209020i	0.594831	−	0.803851i	$-0.297219\pi$
$103$	−2.12132	−	2.12132i	−0.209020	−	0.209020i	−0.803851	+	0.594831i	$0.797219\pi$
$104$	1.41421	−	2.44949i	0.138675	−	0.240192i
$105$	0.370927	−	11.6130i	0.0361988	−	1.13332i
$106$	−9.48528			−0.921292
$107$	6.00000	+	6.00000i	0.580042	+	0.580042i	0.934915	−	0.354873i	$-0.115476\pi$
$107$	6.00000	+	6.00000i	0.580042	+	0.580042i	−0.354873	+	0.934915i	$0.615476\pi$
$108$	−3.72474	+	3.62302i	−0.358414	+	0.348625i
$109$	1.94218	−	1.12132i	0.186027	−	0.107403i	−0.404094	−	0.914717i	$-0.632413\pi$
$109$	1.94218	−	1.12132i	0.186027	−	0.107403i	0.590122	+	0.807314i	$0.299080\pi$
$110$	−0.211386	−	0.320159i	−0.0201549	−	0.0305260i
$111$	−3.32162	−	3.99585i	−0.315274	−	0.379270i
$112$	2.89778	+	0.776457i	0.273814	+	0.0733683i
$113$	14.1421	−	14.1421i	1.33038	−	1.33038i	0.425352	−	0.905028i	$-0.360150\pi$
$113$	14.1421	−	14.1421i	1.33038	−	1.33038i	0.905028	−	0.425352i	$-0.139850\pi$
$114$	−7.33573	−	1.78522i	−0.687054	−	0.167201i
$115$	−3.00000	+	6.00000i	−0.279751	+	0.559503i
$116$	−2.74666	+	1.58579i	−0.255021	+	0.147237i
$117$	−8.45946	+	0.661498i	−0.782077	+	0.0611556i
$118$	5.46410	−	1.46410i	0.503011	−	0.134781i
$119$	−3.36396	−	5.82655i	−0.308374	−	0.534119i
$120$	0.123642	−	3.87101i	0.0112870	−	0.353373i
$121$	10.9706			0.997324
$122$	−1.58579	−	1.58579i	−0.143570	−	0.143570i
$123$	2.17423	+	4.71940i	0.196044	+	0.425534i
$124$	−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
$127$	−0.687644	−	2.56632i	−0.0610186	−	0.227724i	0.928682	−	0.370877i	$-0.120943\pi$
$127$	−0.687644	−	2.56632i	−0.0610186	−	0.227724i	−0.989701	+	0.143152i	$0.954276\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	6.89363	+	2.54516i	0.606950	+	0.224089i
$130$	4.19615	−	4.73205i	0.368027	−	0.415028i
$131$	−12.9904	+	7.50000i	−1.13497	+	0.655278i	−0.945181	−	0.326546i	$-0.894115\pi$
$131$	−12.9904	+	7.50000i	−1.13497	+	0.655278i	−0.189794	+	0.981824i	$0.560782\pi$
$132$	−0.242641	−	0.171573i	−0.0211192	−	0.0149335i
$133$	8.12493	−	10.2462i	0.704520	−	0.888462i
$134$	5.65685			0.488678
$135$	−9.78384	+	6.26709i	−0.842059	+	0.539385i
$136$	−1.12132	−	1.94218i	−0.0961524	−	0.166541i
$137$	−19.7873	+	5.30198i	−1.69054	+	0.452979i	−0.970529	−	0.240984i	$-0.922530\pi$
$137$	−19.7873	+	5.30198i	−1.69054	+	0.452979i	−0.720011	+	0.693963i	$0.755863\pi$
$138$	−0.476756	+	5.17423i	−0.0405842	+	0.440460i
$139$	12.1244	+	7.00000i	1.02837	+	0.593732i	0.916519	−	0.399992i	$-0.130987\pi$
$139$	12.1244	+	7.00000i	1.02837	+	0.593732i	0.111856	+	0.993724i	$0.464321\pi$
$140$	6.00000	+	3.00000i	0.507093	+	0.253546i
$141$	−1.89949	−	11.0711i	−0.159966	−	0.932352i
$142$	2.73980	+	10.2251i	0.229919	+	0.858070i
$143$	−0.125600	−	0.468746i	−0.0105032	−	0.0391985i
$144$	−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
$147$	3.44949	+	0.317837i	0.284509	+	0.0262148i
$148$	2.89778	−	0.776457i	0.238196	−	0.0638244i
$149$	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	$0.679953\pi$
$150$	2.00619	−	8.42468i	0.163804	−	0.687872i
$151$	−10.7279			−0.873026			−0.436513	−	0.899698i	$-0.643787\pi$
$151$	−10.7279			−0.873026			−0.436513	+	0.899698i	$0.643787\pi$
$152$	2.70831	−	3.41542i	0.219673	−	0.277027i
$153$	−2.89949	+	6.07107i	−0.234410	+	0.490817i
$154$	0.445759	−	0.257359i	0.0359203	−	0.0207386i
$155$	−10.4441	−	9.26136i	−0.838894	−	0.743890i
$156$	1.69677	−	4.59575i	0.135851	−	0.367955i
$157$	−11.4254	−	3.06142i	−0.911845	−	0.244328i	−0.227749	−	0.973720i	$-0.573136\pi$
$157$	−11.4254	−	3.06142i	−0.911845	−	0.244328i	−0.684096	+	0.729392i	$0.739803\pi$
$158$	−1.67851	−	6.26430i	−0.133535	−	0.498361i
$159$	−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
$162$	−5.29738	+	7.27583i	−0.416201	+	0.571644i
$163$	−14.2426	−	14.2426i	−1.11557	−	1.11557i	−0.992384	−	0.123186i	$-0.960689\pi$
$163$	−14.2426	−	14.2426i	−1.11557	−	1.11557i	−0.123186	−	0.992384i	$-0.539311\pi$
$164$	−3.00000			−0.234261
$165$	−0.454632	−	0.484633i	−0.0353930	−	0.0377286i
$166$	−2.12132	−	3.67423i	−0.164646	−	0.285176i
$167$	−22.6850	+	6.07844i	−1.75542	+	0.470364i	−0.985770	−	0.168101i	$-0.946237\pi$
$167$	−22.6850	+	6.07844i	−1.75542	+	0.470364i	−0.769651	+	0.638464i	$0.779570\pi$
$168$	5.17423	+	0.476756i	0.399201	+	0.0367825i
$169$	−4.33013	+	2.50000i	−0.333087	+	0.192308i
$170$	−1.58579	−	4.75736i	−0.121624	−	0.364873i
$171$	−13.0458	−	0.898979i	−0.997634	−	0.0687467i
$172$	−3.00000	+	3.00000i	−0.228748	+	0.228748i
$173$	19.2901	+	5.16876i	1.46660	+	0.392974i	0.901763	−	0.432230i	$-0.142273\pi$
$173$	19.2901	+	5.16876i	1.46660	+	0.392974i	0.564835	+	0.825204i	$0.308940\pi$
$174$	−4.22438	+	3.51159i	−0.320249	+	0.266213i
$175$	11.7992	+	9.26174i	0.891933	+	0.700122i
$176$	0.148586	−	0.0857864i	0.0112001	−	0.00646640i
$177$	8.89898	−	4.09978i	0.668888	−	0.308158i
$178$	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	$0.613536\pi$
$180$	−0.922722	−	6.64444i	−0.0687756	−	0.495247i
$181$	−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
$185$	6.69615	−	0.401924i	0.492311	−	0.0295500i
$186$	−10.1433	−	3.74496i	−0.743744	−	0.274594i
$187$	−0.371665	−	0.0995874i	−0.0271789	−	0.00728255i
$188$	6.26430	+	1.67851i	0.456871	+	0.122418i
$189$	−7.60660	−	13.6066i	−0.553299	−	0.989735i
$190$	7.46410	−	6.26795i	0.541503	−	0.454725i
$191$			10.5858i			0.765961i	0.923757	+	0.382980i	$0.125102\pi$
$191$			10.5858i			0.765961i	−0.923757	+	0.382980i	$0.874898\pi$
$192$	1.72474	+	0.158919i	0.124473	+	0.0114690i
$193$	−3.10583	+	11.5911i	−0.223562	+	0.834346i	0.759413	+	0.650609i	$0.225486\pi$
$193$	−3.10583	+	11.5911i	−0.223562	+	0.834346i	−0.982975	+	0.183737i	$0.941180\pi$
$194$	7.24264	−	12.5446i	0.519991	−	0.900651i
$195$	5.77729	−	9.30714i	0.413721	−	0.666498i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	6.02082	+	6.02082i	0.428965	+	0.428965i	0.888276	−	0.459310i	$-0.151903\pi$
$197$	6.02082	+	6.02082i	0.428965	+	0.428965i	−0.459310	+	0.888276i	$0.651903\pi$
$198$	−0.464466	−	0.221825i	−0.0330082	−	0.0157644i
$199$	−12.3345	−	7.12132i	−0.874369	−	0.504817i	−0.00557117	−	0.999984i	$-0.501773\pi$
$199$	−12.3345	−	7.12132i	−0.874369	−	0.504817i	−0.868798	+	0.495167i	$0.835107\pi$
$200$	3.93305	+	3.08725i	0.278109	+	0.218301i
$201$	9.65685	−	1.65685i	0.681142	−	0.116865i
$202$	−12.2426	+	12.2426i	−0.861389	+	0.861389i
$203$	−2.46259	−	9.19051i	−0.172840	−	0.645048i
$204$	−2.48307	−	2.98709i	−0.173849	−	0.209138i
$205$	−6.57201	−	1.34486i	−0.459009	−	0.0939293i
$206$	2.59808	−	1.50000i	0.181017	−	0.104510i
$207$	0.701625	+	8.97261i	0.0487663	+	0.623639i
$208$	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	$0.871613\pi$
$212$	2.45497	−	9.16208i	0.168608	−	0.629254i
$213$	7.67199	+	16.6528i	0.525676	+	1.14103i
$214$	−7.34847	+	4.24264i	−0.502331	+	0.290021i
$215$	−7.91688	+	5.22715i	−0.539926	+	0.356489i
$216$	−2.53553	−	4.53553i	−0.172521	−	0.308604i
$217$	13.2426	−	13.2426i	0.898969	−	0.898969i
$218$	0.580438	+	2.16622i	0.0393122	+	0.146715i
$219$	26.3918	+	9.74397i	1.78339	+	0.658436i
$220$	0.363961	−	0.121320i	0.0245382	−	0.00817942i
$221$		−	6.34315i		−	0.426686i
$222$	4.71940	−	2.17423i	0.316745	−	0.145925i
$223$	−4.52552	+	16.8895i	−0.303051	+	1.13100i	0.631558	+	0.775328i	$0.282416\pi$
$223$	−4.52552	+	16.8895i	−0.303051	+	1.13100i	−0.934610	+	0.355675i	$0.884251\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$	0.957242	−	14.9694i	0.0638161	−	0.997962i
$226$	10.0000	+	17.3205i	0.665190	+	1.15214i
$227$	16.2426	+	16.2426i	1.07806	+	1.07806i	0.996683	+	0.0813787i	$0.0259323\pi$
$227$	16.2426	+	16.2426i	1.07806	+	1.07806i	0.0813787	+	0.996683i	$0.474068\pi$
$228$	3.62302	−	6.62372i	0.239940	−	0.438667i
$229$			15.7574i			1.04128i	0.853778	+	0.520638i	$0.174306\pi$
$229$			15.7574i			1.04128i	−0.853778	+	0.520638i	$0.825694\pi$
$230$	−5.01910	−	4.45069i	−0.330950	−	0.293470i
$231$	0.685580	−	0.569900i	0.0451079	−	0.0374966i
$232$	−0.820863	−	3.06350i	−0.0538923	−	0.201129i
$233$	−10.1280	−	2.71379i	−0.663508	−	0.177786i	−0.0886791	−	0.996060i	$-0.528265\pi$
$233$	−10.1280	−	2.71379i	−0.663508	−	0.177786i	−0.574828	+	0.818274i	$0.694931\pi$
$234$	1.55051	−	8.34242i	0.101360	−	0.545361i
$235$	12.9706	+	6.48528i	0.846106	+	0.423053i
$236$			5.65685i			0.368230i
$237$	−4.70017	−	10.2022i	−0.305309	−	0.662704i
$238$	6.49867	−	1.74131i	0.421246	−	0.112873i
$239$	−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	$0.161691\pi$
$242$	−2.83939	+	10.5967i	−0.182523	+	0.681185i
$243$	−6.91215	+	13.9722i	−0.443415	+	0.896317i
$244$	1.94218	−	1.12132i	0.124336	−	0.0717852i
$245$	−2.96713	+	3.34607i	−0.189563	+	0.213772i
$246$	−5.12132	+	0.878680i	−0.326523	+	0.0560226i
$247$	11.4641	−	4.53590i	0.729443	−	0.288612i
$248$	4.41421	−	4.41421i	0.280303	−	0.280303i
$249$	−4.69748	−	5.65099i	−0.297691	−	0.358117i
$250$	7.23205	+	8.52628i	0.457395	+	0.539249i
$251$	14.9941	+	8.65685i	0.946420	+	0.546416i	0.891967	−	0.452101i	$-0.149325\pi$
$251$	14.9941	+	8.65685i	0.946420	+	0.546416i	0.0544529	+	0.998516i	$0.482659\pi$
$252$	8.97261	−	0.701625i	0.565221	−	0.0441982i
$253$	−0.497180	+	0.133219i	−0.0312574	+	0.00837541i
$254$	2.65685			0.166706
$255$	−4.10051	−	7.65685i	−0.256784	−	0.479491i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.96178	+	2.13335i	−0.496642	+	0.133075i	−0.498441	−	0.866924i	$-0.666094\pi$
$257$	−7.96178	+	2.13335i	−0.496642	+	0.133075i	0.00179903	+	0.999998i	$0.499427\pi$
$258$	−4.24264	+	6.00000i	−0.264135	+	0.373544i
$259$			9.00000i			0.559233i
$260$	3.48477	+	5.27792i	0.216116	+	0.327323i
$261$	−6.18295	+	7.23194i	−0.382715	+	0.447646i
$262$	−3.88229	−	14.4889i	−0.239848	−	0.895126i
$263$	1.43467	+	0.384419i	0.0884656	+	0.0237043i	0.302780	−	0.953060i	$-0.402085\pi$
$263$	1.43467	+	0.384419i	0.0884656	+	0.0237043i	−0.214315	+	0.976765i	$0.568752\pi$
$264$	0.228527	−	0.189967i	0.0140648	−	0.0116916i
$265$	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
$268$	−1.46410	+	5.46410i	−0.0894342	+	0.333773i
$269$	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	$0.725214\pi$
$270$	−3.52130	−	11.0725i	−0.214299	−	0.673851i
$271$	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	$0.813985\pi$
$272$	2.16622	−	0.580438i	0.131347	−	0.0351942i
$273$	12.0000	+	8.48528i	0.726273	+	0.513553i
$274$		−	20.4853i		−	1.23756i
$275$	0.851705	−	0.102614i	0.0513598	−	0.00618784i
$276$	−4.87453	−	1.79970i	−0.293412	−	0.108329i
$277$	20.4853	−	20.4853i	1.23084	−	1.23084i	0.267200	−	0.963641i	$-0.413901\pi$
$277$	20.4853	−	20.4853i	1.23084	−	1.23084i	0.963641	−	0.267200i	$-0.0860985\pi$
$278$	−9.89949	+	9.89949i	−0.593732	+	0.593732i
$279$	−18.4126	−	3.42214i	−1.10233	−	0.204878i
$280$	−4.45069	+	5.01910i	−0.265980	+	0.299948i
$281$	−5.34474	−	3.08579i	−0.318840	−	0.184083i	0.332035	−	0.943267i	$-0.392265\pi$
$281$	−5.34474	−	3.08579i	−0.318840	−	0.184083i	−0.650876	+	0.759184i	$0.725598\pi$
$282$	11.1855	+	1.03063i	0.666084	+	0.0613732i
$283$	−3.01702	+	11.2597i	−0.179343	+	0.669317i	0.816428	+	0.577447i	$0.195951\pi$
$283$	−3.01702	+	11.2597i	−0.179343	+	0.669317i	−0.995771	+	0.0918699i	$0.970716\pi$
$284$	−10.5858			−0.628151
$285$	10.9062	−	12.8862i	0.646026	−	0.763315i
$286$	0.485281			0.0286953
$287$	2.32937	−	8.69333i	0.137498	−	0.513151i
$288$	2.99087	−	0.233875i	0.176239	−	0.0137812i
$289$	10.3668	+	5.98528i	0.609812	+	0.352075i
$290$	−0.424910	−	7.07911i	−0.0249516	−	0.415700i
$291$	8.68973	−	23.5363i	0.509401	−	1.37972i
$292$	−11.4853	+	11.4853i	−0.672125	+	0.672125i
$293$	18.3640	−	18.3640i	1.07283	−	1.07283i	0.0757037	−	0.997130i	$-0.475880\pi$
$293$	18.3640	−	18.3640i	1.07283	−	1.07283i	0.997130	−	0.0757037i	$-0.0241203\pi$
$294$	−1.19980	+	3.24969i	−0.0699738	+	0.189526i
$295$	−2.53590	+	12.3923i	−0.147646	+	0.721508i
$296$			3.00000i			0.174371i
$297$	−0.857864	−	0.242641i	−0.0497783	−	0.0140794i
$298$	−10.9282	+	2.92820i	−0.633054	+	0.169626i
$299$	−4.24264	−	7.34847i	−0.245358	−	0.424973i
$300$	7.61838	+	4.11829i	0.439847	+	0.237770i
$301$	−6.36396	−	11.0227i	−0.366813	−	0.635338i
$302$	2.77659	−	10.3624i	0.159775	−	0.596288i
$303$	−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
$306$	−5.11376	−	4.37201i	−0.292334	−	0.249931i
$307$	19.4558	+	5.21317i	1.11040	+	0.297531i	0.766993	−	0.641655i	$-0.221752\pi$
$307$	19.4558	+	5.21317i	1.11040	+	0.297531i	0.343408	+	0.939186i	$0.388419\pi$
$308$	0.133219	+	0.497180i	0.00759086	+	0.0283295i
$309$	3.99585	−	3.32162i	0.227316	−	0.188960i
$310$	11.6489	−	7.69125i	0.661615	−	0.436834i
$311$			8.48528i			0.481156i	0.970630	+	0.240578i	$0.0773370\pi$
$311$			8.48528i			0.481156i	−0.970630	+	0.240578i	$0.922663\pi$
$312$	4.00000	+	2.82843i	0.226455	+	0.160128i
$313$	−20.8218	+	5.57919i	−1.17692	+	0.315355i	−0.793704	−	0.608304i	$-0.791850\pi$
$313$	−20.8218	+	5.57919i	−1.17692	+	0.315355i	−0.383216	+	0.923659i	$0.625183\pi$
$314$	5.91421	−	10.2437i	0.333758	−	0.578086i
$315$	19.9706	+	2.48528i	1.12521	+	0.140030i
$316$	6.48528			0.364826
$317$	−27.4862	+	7.36491i	−1.54378	+	0.413655i	−0.927485	−	0.373860i	$-0.878034\pi$
$317$	−27.4862	+	7.36491i	−1.54378	+	0.413655i	−0.616296	+	0.787515i	$0.711367\pi$
$318$	1.50739	−	16.3597i	0.0845301	−	0.917406i
$319$	−0.471253	−	0.272078i	−0.0263851	−	0.0152334i
$320$	−1.48356	+	1.67303i	−0.0829337	+	0.0935254i
$321$	−11.3020	+	9.39496i	−0.630815	+	0.524375i
$322$	6.36396	−	6.36396i	0.354650	−	0.354650i
$323$	1.43026	−	9.67025i	0.0795817	−	0.538067i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	5.26795	+	13.1244i	0.292213	+	0.728008i
$326$	17.4436	−	10.0711i	0.966112	−	0.557785i
$327$	1.62534	+	3.52797i	0.0898816	+	0.195097i
$328$	0.776457	−	2.89778i	0.0428727	−	0.160003i
$329$	−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	$0.611760\pi$
$332$	4.09808	−	1.09808i	0.224911	−	0.0602648i
$333$	7.41970	−	5.09393i	0.406597	−	0.279146i
$334$		−	23.4853i		−	1.28506i
$335$	−5.65685	+	11.3137i	−0.309067	+	0.618134i
$336$	−1.79970	+	4.87453i	−0.0981818	+	0.265928i
$337$	−2.40060	−	0.643238i	−0.130769	−	0.0350394i	0.192841	−	0.981230i	$-0.438230\pi$
$337$	−2.40060	−	0.643238i	−0.130769	−	0.0350394i	−0.323610	+	0.946191i	$0.604897\pi$
$338$	−1.29410	−	4.82963i	−0.0703895	−	0.262697i
$339$	22.1441	+	26.6390i	1.20270	+	1.44683i
$340$	5.00569	−	0.300457i	0.271472	−	0.0162946i
$341$		−	1.07107i		−	0.0580016i
$342$	4.24484	−	12.3686i	0.229535	−	0.668815i
$343$	10.6066	+	10.6066i	0.572703	+	0.572703i
$344$	−2.12132	−	3.67423i	−0.114374	−	0.198101i
$345$	−9.87171	−	6.12775i	−0.531475	−	0.329907i
$346$	−9.98528	+	17.2950i	−0.536812	+	0.929786i
$347$	2.83939	−	10.5967i	0.152426	−	0.568863i	−0.846886	−	0.531775i	$-0.821525\pi$
$347$	2.83939	−	10.5967i	0.152426	−	0.568863i	0.999312	−	0.0370881i	$-0.0118082\pi$
$348$	−2.29858	−	4.98930i	−0.123217	−	0.267455i
$349$			22.2426i			1.19062i	0.803496	+	0.595311i	$0.202971\pi$
$349$			22.2426i			1.19062i	−0.803496	+	0.595311i	$0.797029\pi$
$350$	−12.0000	+	9.00000i	−0.641427	+	0.481070i
$351$	0.203449	−	14.6955i	0.0108593	−	0.784389i
$352$	0.0444063	+	0.165727i	0.00236687	+	0.00883326i
$353$	−3.51472	+	3.51472i	−0.187070	+	0.187070i	−0.794428	−	0.607358i	$-0.792229\pi$
$353$	−3.51472	+	3.51472i	−0.187070	+	0.187070i	0.607358	+	0.794428i	$0.292229\pi$
$354$	1.65685	+	9.65685i	0.0880608	+	0.513256i
$355$	−23.1900	−	4.74548i	−1.23080	−	0.251864i
$356$	−10.2437	+	5.91421i	−0.542916	+	0.313453i
$357$	10.5839	−	4.87603i	0.560160	−	0.258067i
$358$	2.41818	−	9.02479i	0.127805	−	0.476975i
$359$	−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
$363$	−1.74343	+	18.9214i	−0.0915062	+	0.993117i
$364$	−7.34847	+	4.24264i	−0.385164	+	0.222375i
$365$	−30.3092	+	20.0118i	−1.58645	+	1.04746i
$366$	2.98709	−	2.48307i	0.156138	−	0.129792i
$367$	1.55291	+	5.79555i	0.0810615	+	0.302526i	0.994539	−	0.104363i	$-0.0332804\pi$
$367$	1.55291	+	5.79555i	0.0810615	+	0.302526i	−0.913478	+	0.406889i	$0.866614\pi$
$368$	2.12132	−	2.12132i	0.110581	−	0.110581i
$369$	−8.48528	+	3.00000i	−0.441726	+	0.156174i
$370$	−1.34486	+	6.57201i	−0.0699161	+	0.341663i
$371$	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	0.950600	−	0.310418i	$-0.100469\pi$
$373$	12.3640	+	12.3640i	0.640182	+	0.640182i	−0.310418	+	0.950600i	$0.600469\pi$
$374$	0.192388	−	0.333226i	0.00994815	−	0.0172307i
$375$	14.8432	+	12.4371i	0.766498	+	0.642247i
$376$	−3.24264	+	5.61642i	−0.167226	+	0.289645i
$377$	2.32175	−	8.66490i	0.119576	−	0.446265i
$378$	15.1117	−	3.82577i	0.777262	−	0.196776i
$379$		−	22.4853i		−	1.15499i	−0.816394	−	0.577496i	$-0.804030\pi$
$379$		−	22.4853i		−	1.15499i	0.816394	−	0.577496i	$-0.195970\pi$
$380$	4.12252	+	8.83203i	0.211481	+	0.453074i
$381$	4.53553	−	0.778175i	0.232362	−	0.0398671i
$382$	−10.2251	−	2.73980i	−0.523161	−	0.140181i
$383$	−29.4465	−	7.89017i	−1.50465	−	0.403169i	−0.589994	−	0.807408i	$-0.700870\pi$
$383$	−29.4465	−	7.89017i	−1.50465	−	0.403169i	−0.914653	+	0.404239i	$0.867536\pi$
$384$	−0.599900	+	1.62484i	−0.0306135	+	0.0829175i
$385$	0.0689592	+	1.14888i	0.00351449	+	0.0585523i
$386$	−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	$0.206545\pi$
$390$	7.49473	+	7.98930i	0.379511	+	0.404554i
$391$	−6.72792			−0.340246
$392$	−1.41421	−	1.41421i	−0.0714286	−	0.0714286i
$393$	−10.8712	−	23.5970i	−0.548378	−	1.19031i
$394$	−7.37396	+	4.25736i	−0.371495	+	0.214483i
$395$	14.2071	+	2.90727i	0.714838	+	0.146281i
$396$	0.334480	−	0.391227i	0.0168082	−	0.0196599i
$397$	7.69897	+	2.06293i	0.386400	+	0.103536i	0.446789	−	0.894639i	$-0.352567\pi$
$397$	7.69897	+	2.06293i	0.386400	+	0.103536i	−0.0603888	+	0.998175i	$0.519234\pi$
$398$	10.0711	−	10.0711i	0.504817	−	0.504817i
$399$	16.3810	+	15.6417i	0.820074	+	0.783067i
$400$	−4.00000	+	3.00000i	−0.200000	+	0.150000i
$401$	29.9882	−	17.3137i	1.49754	−	0.864605i	0.497544	−	0.867439i	$-0.334235\pi$
$401$	29.9882	−	17.3137i	1.49754	−	0.864605i	0.999996	+	0.00283317i	$0.000901827\pi$
$402$	−0.898979	+	9.75663i	−0.0448370	+	0.486616i
$403$	17.0552	−	4.56993i	0.849581	−	0.227644i
$404$	−8.65685	−	14.9941i	−0.430695	−	0.745985i
$405$	−9.25429	−	17.8706i	−0.459849	−	0.887997i
$406$	9.51472			0.472208
$407$	0.363961	+	0.363961i	0.0180409	+	0.0180409i
$408$	3.52797	−	1.62534i	0.174661	−	0.0804664i
$409$	21.1794	+	12.2279i	1.04725	+	0.604632i	0.921879	−	0.387478i	$-0.126654\pi$
$409$	21.1794	+	12.2279i	1.04725	+	0.604632i	0.125374	+	0.992110i	$0.459987\pi$
$410$	3.00000	−	6.00000i	0.148159	−	0.296319i
$411$	−6.00000	−	34.9706i	−0.295958	−	1.72497i
$412$	0.776457	+	2.89778i	0.0382533	+	0.142763i
$413$	−16.3923	−	4.39230i	−0.806613	−	0.216131i
$414$	−8.84847	−	1.64456i	−0.434879	−	0.0808259i
$415$	9.46979	−	0.568406i	0.464854	−	0.0279020i
$416$	−2.44949	+	1.41421i	−0.120096	+	0.0693375i
$417$	−14.0000	+	19.7990i	−0.685583	+	0.969561i
$418$	0.739821	+	0.109422i	0.0361858	+	0.00535199i
$419$	29.8284			1.45721			0.728607	−	0.684932i	$-0.240168\pi$
$419$	29.8284			1.45721			0.728607	+	0.684932i	$0.240168\pi$
$420$	−6.12775	+	9.87171i	−0.299003	+	0.481690i
$421$	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	$0.662601\pi$
$422$	3.36652	−	0.902057i	0.163880	−	0.0439115i
$423$	19.3966	−	1.51675i	0.943097	−	0.0737467i
$424$	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
$427$	1.74131	+	6.49867i	0.0842681	+	0.314493i
$428$	−2.19615	−	8.19615i	−0.106155	−	0.396176i
$429$	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	0.245105	−	0.969497i	$-0.421178\pi$
$431$	−9.79796	−	5.65685i	−0.471951	−	0.272481i	−0.717056	+	0.697015i	$0.754511\pi$
$432$	5.03723	−	1.27526i	0.242354	−	0.0613557i
$433$	−9.19051	+	2.46259i	−0.441668	+	0.118345i	−0.472798	−	0.881171i	$-0.656756\pi$
$433$	−9.19051	+	2.46259i	−0.441668	+	0.118345i	0.0311302	+	0.999515i	$0.490089\pi$
$434$	9.36396	+	16.2189i	0.449485	+	0.778530i
$435$	−2.79879	−	11.9603i	−0.134192	−	0.573455i
$436$	−2.24264			−0.107403
$437$	−4.81105	−	12.1595i	−0.230144	−	0.581669i
$438$	−16.2426	+	22.9706i	−0.776103	+	1.09758i
$439$	−25.5095	+	14.7279i	−1.21750	+	0.702925i	−0.964383	−	0.264510i	$-0.914790\pi$
$439$	−25.5095	+	14.7279i	−1.21750	+	0.702925i	−0.253119	+	0.967435i	$0.581457\pi$
$440$	0.0229864	+	0.382959i	0.00109583	+	0.0182569i
$441$	−1.09638	+	5.89898i	−0.0522084	+	0.280904i
$442$	6.12701	+	1.64173i	0.291432	+	0.0780890i
$443$	−8.86265	−	33.0759i	−0.421077	−	1.57148i	−0.772343	−	0.635205i	$-0.780915\pi$
$443$	−8.86265	−	33.0759i	−0.421077	−	1.57148i	0.351266	−	0.936276i	$-0.385751\pi$
$444$	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
$447$	−17.7980	+	8.19955i	−0.841815	+	0.387826i
$448$	−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	$0.361789\pi$
$450$	14.2116	+	4.79900i	0.669941	+	0.226227i
$451$	−0.257359	−	0.445759i	−0.0121186	−	0.0209900i
$452$	−19.3185	+	5.17638i	−0.908667	+	0.243476i
$453$	1.70487	−	18.5029i	0.0801016	−	0.869343i
$454$	−19.8931	+	11.4853i	−0.933629	+	0.539031i
$455$	−18.0000	+	6.00000i	−0.843853	+	0.281284i
$456$	5.46032	+	5.21391i	0.255703	+	0.244164i
$457$	−24.9706	+	24.9706i	−1.16807	+	1.16807i	−0.185413	+	0.982661i	$0.559362\pi$
$457$	−24.9706	+	24.9706i	−1.16807	+	1.16807i	−0.982661	+	0.185413i	$0.940638\pi$
$458$	−15.2204	−	4.07830i	−0.711204	−	0.190567i
$459$	−10.0103	−	5.96569i	−0.467239	−	0.278455i
$460$	5.59808	−	3.69615i	0.261012	−	0.172334i
$461$	−21.7482	+	12.5563i	−1.01292	+	0.584807i	−0.912044	−	0.410092i	$-0.865497\pi$
$461$	−21.7482	+	12.5563i	−1.01292	+	0.584807i	−0.100872	+	0.994899i	$0.532163\pi$
$462$	0.373040	+	0.809720i	0.0173554	+	0.0376716i
$463$	−29.3345	−	29.3345i	−1.36329	−	1.36329i	−0.869687	−	0.493604i	$-0.835679\pi$
$463$	−29.3345	−	29.3345i	−1.36329	−	1.36329i	−0.493604	−	0.869687i	$-0.664321\pi$
$464$	3.17157			0.147237
$465$	17.6332	−	16.5417i	0.817722	−	0.767102i
$466$	5.24264	−	9.08052i	0.242861	−	0.420647i
$467$	−1.75736	−	1.75736i	−0.0813209	−	0.0813209i	0.665276	−	0.746597i	$-0.268314\pi$
$467$	−1.75736	−	1.75736i	−0.0813209	−	0.0813209i	−0.746597	+	0.665276i	$0.768314\pi$
$468$	7.65685	+	3.65685i	0.353938	+	0.169038i
$469$	−14.6969	−	8.48528i	−0.678642	−	0.391814i
$470$	−9.62133	+	10.8501i	−0.443799	+	0.500477i
$471$	7.09588	−	19.2194i	0.326961	−	0.885581i
$472$	−5.46410	−	1.46410i	−0.251506	−	0.0673907i
$473$	−0.703119	−	0.188400i	−0.0323294	−	0.00866265i
$474$	11.0711	−	1.89949i	0.508511	−	0.0872467i
$475$	5.07180	+	21.1962i	0.232710	+	0.972546i
$476$			6.72792i			0.308374i
$477$	−2.21837	−	28.3692i	−0.101572	−	1.29894i
$478$	0.177625	−	0.662907i	0.00812439	−	0.0303206i
$479$	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	$-0.0775564\pi$
$480$	−2.04258	+	3.29057i	−0.0932307	+	0.150193i
$481$	−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
$485$	17.8466	+	27.0299i	0.810372	+	1.22736i
$486$	−11.7071	−	10.2929i	−0.531045	−	0.466895i
$487$	24.6066	−	24.6066i	1.11503	−	1.11503i	0.122572	−	0.992460i	$-0.460886\pi$
$487$	24.6066	−	24.6066i	1.11503	−	1.11503i	0.992460	−	0.122572i	$-0.0391142\pi$
$488$	0.580438	+	2.16622i	0.0262752	+	0.0980604i
$489$	26.8283	−	22.3015i	1.21322	−	1.00851i
$490$	−2.46410	−	3.73205i	−0.111317	−	0.168597i
$491$	−5.93908	+	3.42893i	−0.268027	+	0.154746i	−0.627991	−	0.778221i	$-0.716122\pi$
$491$	−5.93908	+	3.42893i	−0.268027	+	0.154746i	0.359964	+	0.932966i	$0.382789\pi$
$492$	0.476756	−	5.17423i	0.0214938	−	0.233273i
$493$	−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
$497$	8.21941	−	30.6753i	0.368691	−	1.37597i
$498$	6.67423	−	3.07483i	0.299080	−	0.137787i
$499$	−32.8835	+	18.9853i	−1.47207	+	0.849898i	−0.999507	−	0.0314008i	$-0.990003\pi$
$499$	−32.8835	+	18.9853i	−1.47207	+	0.849898i	−0.472560	+	0.881299i	$0.656670\pi$
$500$	−10.1075	+	4.77886i	−0.452023	+	0.213717i
$501$	−6.87868	−	40.0919i	−0.307317	−	1.79117i
$502$	−12.2426	+	12.2426i	−0.546416	+	0.546416i
$503$	4.65112	+	17.3582i	0.207383	+	0.773965i	0.988710	+	0.149843i	$0.0478767\pi$
$503$	4.65112	+	17.3582i	0.207383	+	0.773965i	−0.781326	+	0.624123i	$0.785457\pi$
$504$	−1.64456	+	8.84847i	−0.0732547	+	0.394142i
$505$	−12.2426	−	36.7279i	−0.544790	−	1.63437i
$506$		−	0.514719i		−	0.0228820i
$507$	−3.62372	−	7.86566i	−0.160935	−	0.349326i
$508$	−0.687644	+	2.56632i	−0.0305093	+	0.113862i
$509$	−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	$0.257690\pi$
$510$	8.45724	−	1.97904i	0.374493	−	0.0876335i
$511$	−24.3640	−	42.1996i	−1.07780	−	1.86680i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.62372	−	22.3577i	0.159991	−	0.987118i
$514$		−	8.24264i		−	0.363567i
$515$	0.401924	+	6.69615i	0.0177109	+	0.295068i
$516$	−4.69748	−	5.65099i	−0.206795	−	0.248771i
$517$	0.287988	+	1.07478i	0.0126657	+	0.0472690i
$518$	−8.69333	−	2.32937i	−0.381963	−	0.102347i
$519$	−11.9803	+	32.4491i	−0.525879	+	1.42436i
$520$	−6.00000	+	2.00000i	−0.263117	+	0.0877058i
$521$			35.3137i			1.54712i	0.633722	+	0.773561i	$0.281526\pi$
$521$			35.3137i			1.54712i	−0.633722	+	0.773561i	$0.718474\pi$
$522$	−5.38526	−	7.84403i	−0.235706	−	0.343324i
$523$	22.8508	−	6.12284i	0.999194	−	0.267733i	0.278086	−	0.960556i	$-0.410300\pi$
$523$	22.8508	−	6.12284i	0.999194	−	0.267733i	0.721108	+	0.692823i	$0.243633\pi$
$524$	15.0000			0.655278
$525$	−17.8492	+	18.8787i	−0.779005	+	0.823933i
$526$	−0.742641	+	1.28629i	−0.0323807	+	0.0560850i
$527$	3.62347	−	13.5230i	0.157841	−	0.589069i
$528$	0.124347	+	0.269907i	0.00541149	+	0.0117462i
$529$	12.1244	−	7.00000i	0.527146	−	0.304348i
$530$	15.8692	+	14.0720i	0.689313	+	0.611250i
$531$	5.65685	+	16.0000i	0.245487	+	0.694341i
$532$	−12.1595	+	4.81105i	−0.527182	+	0.208585i
$533$	6.00000	−	6.00000i	0.259889	−	0.259889i
$534$	−15.7549	+	13.0965i	−0.681781	+	0.566741i
$535$	−1.13681	−	18.9396i	−0.0491487	−	0.818829i
$536$	−4.89898	−	2.82843i	−0.211604	−	0.122169i
$537$	1.48480	−	16.1145i	0.0640738	−	0.695394i
$538$	−10.5565	+	2.82862i	−0.455125	+	0.121950i
$539$	−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	$0.175372\pi$
$542$	−1.93185	+	0.517638i	−0.0829801	+	0.0222345i
$543$	−20.4853	−	14.4853i	−0.879108	−	0.621623i
$544$			2.24264i			0.0961524i
$545$	−4.91289	−	1.00535i	−0.210445	−	0.0430644i
$546$	−11.3020	+	9.39496i	−0.483680	+	0.402067i
$547$	5.03554	+	18.7929i	0.215304	+	0.803526i	0.986059	+	0.166395i	$0.0532126\pi$
$547$	5.03554	+	18.7929i	0.215304	+	0.803526i	−0.770755	+	0.637132i	$0.780121\pi$
$548$	19.7873	+	5.30198i	0.845270	+	0.226489i
$549$	4.37201	−	5.11376i	0.186593	−	0.218250i
$550$	−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
$553$	−5.03554	+	18.7929i	−0.214133	+	0.799155i
$554$	14.4853	+	25.0892i	0.615421	+	1.06594i
$555$	−0.370927	+	11.6130i	−0.0157450	+	0.492946i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	13.4945	−	3.61585i	0.571781	−	0.153208i	0.0386680	−	0.999252i	$-0.487689\pi$
$557$	13.4945	−	3.61585i	0.571781	−	0.153208i	0.533114	+	0.846044i	$0.321022\pi$
$558$	8.07107	−	16.8995i	0.341676	−	0.715413i
$559$		−	12.0000i		−	0.507546i
$560$	−3.69615	−	5.59808i	−0.156191	−	0.236562i
$561$	0.230827	−	0.625202i	0.00974554	−	0.0263960i
$562$	4.36396	−	4.36396i	0.184083	−	0.184083i
$563$	−27.1716	+	27.1716i	−1.14515	+	1.14515i	−0.157650	+	0.987495i	$0.550392\pi$
$563$	−27.1716	+	27.1716i	−1.14515	+	1.14515i	−0.987495	+	0.157650i	$0.949608\pi$
$564$	−3.89052	+	10.5376i	−0.163821	+	0.443712i
$565$	−44.6410	+	2.67949i	−1.87806	+	0.112727i
$566$	−10.0951	−	5.82843i	−0.424330	−	0.244987i
$567$	24.6767	−	10.9571i	1.03633	−	0.460155i
$568$	2.73980	−	10.2251i	0.114960	−	0.429035i
$569$	10.7990			0.452717			0.226359	−	0.974044i	$-0.427318\pi$
$569$	10.7990			0.452717			0.226359	+	0.974044i	$0.427318\pi$
$570$	9.62443	+	13.8698i	0.403123	+	0.580941i
$571$	−10.4853			−0.438795			−0.219398	−	0.975636i	$-0.570409\pi$
$571$	−10.4853			−0.438795			−0.219398	+	0.975636i	$0.570409\pi$
$572$	−0.125600	+	0.468746i	−0.00525160	+	0.0195992i
$573$	−18.2578	−	1.68228i	−0.762730	−	0.0702782i
$574$	7.79423	+	4.50000i	0.325325	+	0.187826i
$575$	13.9205	−	5.58750i	0.580524	−	0.233015i
$576$	−0.548188	+	2.94949i	−0.0228412	+	0.122895i
$577$	−2.48528	+	2.48528i	−0.103464	+	0.103464i	−0.756944	−	0.653480i	$-0.773308\pi$
$577$	−2.48528	+	2.48528i	−0.103464	+	0.103464i	0.653480	+	0.756944i	$0.273308\pi$
$578$	−8.46447	+	8.46447i	−0.352075	+	0.352075i
$579$	−19.4981	−	7.19881i	−0.810315	−	0.299172i
$580$	6.94787	+	1.42178i	0.288495	+	0.0590361i
$581$			12.7279i			0.528043i
$582$	20.4853	+	14.4853i	0.849142	+	0.600434i
$583$	1.57196	−	0.421207i	0.0651041	−	0.0174446i
$584$	−8.12132	−	14.0665i	−0.336063	−	0.582078i
$585$	15.1343	+	11.4434i	0.625727	+	0.473128i
$586$	12.9853	+	22.4912i	0.536417	+	0.929102i
$587$	10.6040	−	39.5745i	0.437672	−	1.63342i	−0.296917	−	0.954903i	$-0.595958\pi$
$587$	10.6040	−	39.5745i	0.437672	−	1.63342i	0.734589	−	0.678512i	$-0.237375\pi$
$588$	−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
$591$	−11.3412	+	9.42755i	−0.466514	+	0.387798i
$592$	−2.89778	−	0.776457i	−0.119098	−	0.0319122i
$593$	9.96072	+	37.1739i	0.409038	+	1.52655i	0.796485	+	0.604658i	$0.206690\pi$
$593$	9.96072	+	37.1739i	0.409038	+	1.52655i	−0.387447	+	0.921892i	$0.626643\pi$
$594$	0.456405	−	0.765833i	0.0187265	−	0.0314225i
$595$	−3.01604	+	14.7387i	−0.123646	+	0.604226i
$596$		−	11.3137i		−	0.463428i
$597$	14.2426	−	20.1421i	0.582912	−	0.824363i
$598$	8.19615	−	2.19615i	0.335166	−	0.0898074i
$599$	−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	$0.344580\pi$
$602$	12.2942	−	3.29423i	0.501075	−	0.134263i
$603$	1.32300	+	16.9189i	0.0538766	+	0.688991i
$604$	9.29065	+	5.36396i	0.378031	+	0.218256i
$605$	−18.3541	−	16.2755i	−0.746201	−	0.661694i
$606$	−19.1698	−	23.0610i	−0.778722	−	0.936790i
$607$	−4.36396	+	4.36396i	−0.177128	+	0.177128i	−0.790102	−	0.612975i	$-0.789973\pi$
$607$	−4.36396	+	4.36396i	−0.177128	+	0.177128i	0.612975	+	0.790102i	$0.289973\pi$
$608$	−4.05317	+	1.60368i	−0.164378	+	0.0650379i
$609$	16.2426	−	2.78680i	0.658185	−	0.112927i
$610$	0.300457	+	5.00569i	0.0121651	+	0.202674i
$611$	−15.8856	+	9.17157i	−0.642664	+	0.371042i
$612$	5.54657	−	3.80795i	0.224207	−	0.153927i
$613$	2.79498	−	10.4310i	0.112888	−	0.421305i	−0.886232	−	0.463242i	$-0.846686\pi$
$613$	2.79498	−	10.4310i	0.112888	−	0.421305i	0.999120	+	0.0419368i	$0.0133528\pi$
$614$	−10.0711	+	17.4436i	−0.406435	+	0.703966i
$615$	3.36396	−	11.1213i	0.135648	−	0.448455i
$616$	−0.514719			−0.0207386
$617$	31.0871	−	8.32977i	1.25152	−	0.335344i	0.428597	−	0.903496i	$-0.359008\pi$
$617$	31.0871	−	8.32977i	1.25152	−	0.335344i	0.822924	+	0.568152i	$0.192341\pi$
$618$	2.17423	+	4.71940i	0.0874605	+	0.189842i
$619$		−	24.9411i		−	1.00247i	−0.865312	−	0.501234i	$-0.832879\pi$
$619$		−	24.9411i		−	1.00247i	0.865312	−	0.501234i	$-0.167121\pi$
$620$	4.41421	+	13.2426i	0.177279	+	0.531837i
$621$	−15.5870	−	0.215791i	−0.625483	−	0.00865938i
$622$	−8.19615	−	2.19615i	−0.328636	−	0.0880577i
$623$	−9.18427	−	34.2761i	−0.367960	−	1.37324i
$624$	−3.76733	+	3.13165i	−0.150814	+	0.125366i
$625$	−24.2846	+	5.93782i	−0.971384	+	0.237513i
$626$		−	21.5563i		−	0.861565i
$627$	1.29500	−	0.0298939i	0.0517174	−	0.00119385i
$628$	8.36396	+	8.36396i	0.333758	+	0.333758i
$629$	3.36396	+	5.82655i	0.134130	+	0.232320i
$630$	−7.56936	+	18.6468i	−0.301570	+	0.742908i
$631$	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	$0.165129\pi$
$632$	−1.67851	+	6.26430i	−0.0667677	+	0.249181i
$633$	5.48281	−	2.52594i	0.217922	−	0.100397i
$634$		−	28.4558i		−	1.13013i
$635$	−2.65685	+	5.31371i	−0.105434	+	0.210868i
$636$	15.4121	+	5.69022i	0.611130	+	0.225632i
$637$	−1.46410	−	5.46410i	−0.0580098	−	0.216496i
$638$	0.384776	−	0.384776i	0.0152334	−	0.0152334i
$639$	−29.9411	+	10.5858i	−1.18445	+	0.418767i
$640$	−1.23205	−	1.86603i	−0.0487011	−	0.0737611i
$641$	15.2913	−	8.82843i	0.603969	−	0.348702i	−0.166632	−	0.986019i	$-0.553289\pi$
$641$	15.2913	−	8.82843i	0.603969	−	0.348702i	0.770602	+	0.637317i	$0.219956\pi$
$642$	−6.14966	−	13.3485i	−0.242708	−	0.526822i
$643$	−4.29272	+	16.0206i	−0.169288	+	0.631792i	0.828166	+	0.560483i	$0.189384\pi$
$643$	−4.29272	+	16.0206i	−0.169288	+	0.631792i	−0.997454	+	0.0713094i	$0.977282\pi$
$644$	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	0.411735	−	0.911303i	$-0.364923\pi$
$647$	−12.7071	−	12.7071i	−0.499568	−	0.499568i	−0.911303	+	0.411735i	$0.864923\pi$
$648$	8.22558	−	3.65237i	0.323131	−	0.143479i
$649$	−0.840532	+	0.485281i	−0.0329938	+	0.0190490i
$650$	−14.0406	+	1.69161i	−0.550718	+	0.0663506i
$651$	20.7357	+	24.9447i	0.812695	+	0.977659i
$652$	5.21317	+	19.4558i	0.204163	+	0.761948i
$653$	−14.8492	+	14.8492i	−0.581096	+	0.581096i	−0.935204	−	0.354109i	$-0.884784\pi$
$653$	−14.8492	+	14.8492i	−0.581096	+	0.581096i	0.354109	+	0.935204i	$0.384784\pi$
$654$	−3.82843	+	0.656854i	−0.149703	+	0.0256850i
$655$	32.8601	+	6.72432i	1.28395	+	0.262741i
$656$	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	$-0.112040\pi$
$660$	0.151406	+	0.647020i	0.00589349	+	0.0251852i
$661$	−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	$0.202382\pi$
$662$	3.23905	−	12.0883i	0.125889	−	0.469825i
$663$	10.9403	+	1.00804i	0.424886	+	0.0391492i
$664$			4.24264i			0.164646i
$665$	−28.7942	+	5.08846i	−1.11659	+	0.197322i
$666$	3.00000	+	8.48528i	0.116248	+	0.328798i
$667$	−9.19051	−	2.46259i	−0.355858	−	0.0953519i
$668$	22.6850	+	6.07844i	0.877711	+	0.235182i
$669$	−28.4109	−	10.4894i	−1.09843	−	0.405545i
$670$	−9.46410	−	8.39230i	−0.365630	−	0.324223i
$671$	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	−0.992218	−	0.124515i	$-0.960262\pi$
$673$	−28.9706	−	28.9706i	−1.11673	−	1.11673i	−0.124515	−	0.992218i	$-0.539738\pi$
$674$	1.24264	−	2.15232i	0.0478647	−	0.0829041i
$675$	25.6663	+	4.02992i	0.987897	+	0.155112i
$676$	5.00000			0.192308
$677$	34.6066	+	34.6066i	1.33004	+	1.33004i	0.905329	+	0.424711i	$0.139624\pi$
$677$	34.6066	+	34.6066i	1.33004	+	1.33004i	0.424711	+	0.905329i	$0.360376\pi$
$678$	−31.4626	+	14.4949i	−1.20832	+	0.556673i
$679$	−37.6339	+	21.7279i	−1.44426	+	0.833841i
$680$	−1.00535	+	4.91289i	−0.0385533	+	0.188401i
$681$	−30.5957	+	25.4332i	−1.17243	+	0.974601i
$682$	1.03457	+	0.277213i	0.0396158	+	0.0106150i
$683$	−0.899495	+	0.899495i	−0.0344182	+	0.0344182i	−0.724106	−	0.689688i	$-0.757748\pi$
$683$	−0.899495	+	0.899495i	−0.0344182	+	0.0344182i	0.689688	+	0.724106i	$0.257748\pi$
$684$	10.8485	+	7.30142i	0.414802	+	0.279177i
$685$	40.9706	+	20.4853i	1.56540	+	0.782702i
$686$	−12.9904	+	7.50000i	−0.495975	+	0.286351i
$687$	−27.1774	−	2.50414i	−1.03688	−	0.0955388i
$688$	4.09808	−	1.09808i	0.156238	−	0.0418638i
$689$	13.4142	+	23.2341i	0.511041	+	0.885149i
$690$	8.47394	−	7.94937i	0.322597	−	0.302627i
$691$	−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
$693$	0.873980	+	1.27302i	0.0331998	+	0.0483580i
$694$	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
$697$	−1.74131	−	6.49867i	−0.0659570	−	0.246155i
$698$	−21.4847	−	5.75682i	−0.813209	−	0.217899i
$699$	6.29012	−	17.0370i	0.237914	−	0.644397i
$700$	−5.58750	−	13.9205i	−0.211188	−	0.526145i
$701$	−28.7635	+	16.6066i	−1.08638	+	0.627223i	−0.932611	−	0.360884i	$-0.882475\pi$
$701$	−28.7635	+	16.6066i	−1.08638	+	0.627223i	−0.153771	+	0.988107i	$0.549142\pi$
$702$	14.1421	+	4.00000i	0.533761	+	0.150970i
$703$	−8.12493	+	10.2462i	−0.306437	+	0.386445i
$704$	−0.171573			−0.00646640
$705$	−13.2467	+	21.3403i	−0.498900	+	0.803721i
$706$	−2.48528	−	4.30463i	−0.0935348	−	0.162007i
$707$	50.1713	−	13.4434i	1.88688	−	0.505589i
$708$	−9.75663	−	0.898979i	−0.366677	−	0.0337857i
$709$	37.8440	+	21.8492i	1.42126	+	0.820566i	0.996407	−	0.0846962i	$-0.0269920\pi$
$709$	37.8440	+	21.8492i	1.42126	+	0.820566i	0.424854	+	0.905262i	$0.360325\pi$
$710$	10.5858	−	21.1716i	0.397277	−	0.794555i
$711$	18.3431	−	6.48528i	0.687922	−	0.243217i
$712$	−3.06142	−	11.4254i	−0.114732	−	0.428184i
$713$	−4.84714	−	18.0898i	−0.181527	−	0.677468i
$714$	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
$717$	0.109065	−	1.18368i	0.00407309	−	0.0442053i
$718$	8.89927	−	2.38455i	0.332118	−	0.0889907i
$719$	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	$0.789185\pi$
$720$	−2.52312	+	6.21561i	−0.0940311	+	0.231642i
$721$	−9.00000			−0.335178
$722$	−0.605571	+	18.9903i	−0.0225370	+	0.706748i
$723$	0.686292	+	0.485281i	0.0255235	+	0.0180478i
$724$	12.5446	−	7.24264i	0.466217	−	0.269171i
$725$	14.5831	+	6.22929i	0.541604	+	0.231350i
$726$	−17.8255	−	6.58125i	−0.661565	−	0.244253i
$727$	14.6546	+	3.92669i	0.543510	+	0.145633i	0.520120	−	0.854093i	$-0.325887\pi$
$727$	14.6546	+	3.92669i	0.543510	+	0.145633i	0.0233900	+	0.999726i	$0.492554\pi$
$728$	−2.19615	−	8.19615i	−0.0813948	−	0.303770i
$729$	−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
$732$	1.62534	+	3.52797i	0.0600744	+	0.130398i
$733$	−8.12132	−	8.12132i	−0.299968	−	0.299968i	0.541033	−	0.841001i	$-0.318033\pi$
$733$	−8.12132	−	8.12132i	−0.299968	−	0.299968i	−0.841001	+	0.541033i	$0.818033\pi$
$734$	−6.00000			−0.221464
$735$	−5.29958	−	5.64929i	−0.195478	−	0.208377i
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	−0.937492	+	0.251200i	−0.0345329	+	0.00925308i
$738$	−0.701625	−	8.97261i	−0.0258272	−	0.330286i
$739$	29.4194	−	16.9853i	1.08221	−	0.624814i	0.150718	−	0.988577i	$-0.451842\pi$
$739$	29.4194	−	16.9853i	1.08221	−	0.624814i	0.931491	+	0.363763i	$0.118508\pi$
$740$	−6.00000	−	3.00000i	−0.220564	−	0.110282i
$741$	6.00141	+	20.4935i	0.220467	+	0.752847i
$742$	−20.1213	+	20.1213i	−0.738677	+	0.738677i
$743$	25.0856	+	6.72168i	0.920303	+	0.246594i	0.687715	−	0.725981i	$-0.258614\pi$
$743$	25.0856	+	6.72168i	0.920303	+	0.246594i	0.232588	+	0.972575i	$0.425281\pi$
$744$	6.91189	+	8.31489i	0.253402	+	0.304839i
$745$	5.07180	−	24.7846i	0.185816	−	0.908038i
$746$	−15.1427	+	8.74264i	−0.554414	+	0.320091i
$747$	10.4930	−	7.20390i	0.383920	−	0.263577i
$748$	0.272078	+	0.272078i	0.00994815	+	0.00994815i
$749$	25.4558			0.930136
$750$	−15.8550	+	11.1185i	−0.578941	+	0.405989i
$751$	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
$755$	17.9482	+	15.9156i	0.653201	+	0.579226i
$756$	−0.215791	+	15.5870i	−0.00784823	+	0.566892i
$757$	44.2100	+	11.8460i	1.60684	+	0.430551i	0.947099	−	0.320942i	$-0.103999\pi$
$757$	44.2100	+	11.8460i	1.60684	+	0.430551i	0.659741	+	0.751493i	$0.270666\pi$
$758$	21.7191	+	5.81962i	0.788874	+	0.211378i
$759$	−0.150758	−	0.878680i	−0.00547215	−	0.0318941i
$760$	−9.59808	+	1.69615i	−0.348159	+	0.0615259i
$761$		−	6.51472i		−	0.236158i	−0.993004	−	0.118079i	$-0.962326\pi$
$761$		−	6.51472i		−	0.236158i	0.993004	−	0.118079i	$-0.0376737\pi$
$762$	−0.422224	+	4.58240i	−0.0152955	+	0.166003i
$763$	1.74131	−	6.49867i	0.0630398	−	0.235268i
$764$	5.29289	−	9.16756i	0.191490	−	0.331671i
$765$	13.8578	−	5.85551i	0.501029	−	0.211706i
$766$	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	0.964283	−	0.264873i	$-0.0853301\pi$
$769$	33.7495	+	19.4853i	1.21704	+	0.702657i	0.252755	+	0.967530i	$0.418663\pi$
$770$	−1.12758	−	0.230742i	−0.0406351	−	0.00831537i
$771$	−2.41421	−	14.0711i	−0.0869458	−	0.506757i
$772$	8.48528	−	8.48528i	0.305392	−	0.305392i
$773$	−2.18853	−	8.16772i	−0.0787161	−	0.293772i	0.915334	−	0.402695i	$-0.131927\pi$
$773$	−2.18853	−	8.16772i	−0.0787161	−	0.293772i	−0.994050	+	0.108923i	$0.965260\pi$
$774$	−9.67423	−	8.27098i	−0.347733	−	0.297294i
$775$	3.73357	+	30.9891i	0.134114	+	1.11316i
$776$	−12.5446	+	7.24264i	−0.450326	+	0.259996i
$777$	−15.5227	−	1.43027i	−0.556874	−	0.0513106i
$778$	−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
$782$	1.74131	−	6.49867i	0.0622693	−	0.232392i
$783$	−11.4907	−	11.8133i	−0.410643	−	0.422173i
$784$	1.73205	−	1.00000i	0.0618590	−	0.0357143i
$785$	14.5732	+	22.0721i	0.520141	+	0.787789i
$786$	25.6066	−	4.39340i	0.913357	−	0.156707i
$787$	2.72792	−	2.72792i	0.0972399	−	0.0972399i	−0.656813	−	0.754053i	$-0.728096\pi$
$787$	2.72792	−	2.72792i	0.0972399	−	0.0972399i	0.754053	+	0.656813i	$0.228096\pi$
$788$	−2.20377	−	8.22459i	−0.0785061	−	0.292989i
$789$	−0.891021	+	2.41335i	−0.0317212	+	0.0859176i
$790$	−6.48528	+	12.9706i	−0.230736	+	0.461472i
$791$		−	60.0000i		−	2.13335i
$792$	0.291327	+	0.424339i	0.0103518	+	0.0150782i
$793$	−1.64173	+	6.12701i	−0.0582994	+	0.217576i
$794$	−3.98528	+	6.90271i	−0.141432	+	0.244968i
$795$	31.2120	+	19.3745i	1.10698	+	0.687142i
$796$	7.12132	+	12.3345i	0.252409	+	0.437184i
$797$	−1.77817	−	1.77817i	−0.0629862	−	0.0629862i	0.674912	−	0.737898i	$-0.264182\pi$
$797$	−1.77817	−	1.77817i	−0.0629862	−	0.0629862i	−0.737898	+	0.674912i	$0.764182\pi$
$798$	−19.3485	+	11.7744i	−0.684928	+	0.416810i
$799$			14.5442i			0.514535i
$800$	−1.86250	−	4.64016i	−0.0658494	−	0.164054i
$801$	−23.0594	+	26.9716i	−0.814764	+	0.952996i
$802$	8.96224	+	33.4475i	0.316468	+	1.18107i
$803$	−2.69184	−	0.721276i	−0.0949929	−	0.0254533i
$804$	−9.19151	−	3.39355i	−0.324160	−	0.119681i
$805$	6.36396	+	19.0919i	0.224300	+	0.672900i
$806$			17.6569i			0.621936i
$807$	−17.1927	+	7.92069i	−0.605210	+	0.278821i
$808$	16.7238	−	4.48112i	0.588340	−	0.157645i
$809$	−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	$0.283600\pi$
$812$	−2.46259	+	9.19051i	−0.0864200	+	0.322524i
$813$	−3.14626	+	1.44949i	−0.110344	+	0.0508358i
$814$	−0.445759	+	0.257359i	−0.0156239	+	0.00902044i
$815$	2.69853	+	44.9583i	0.0945255	+	1.57482i
$816$	0.656854	+	3.82843i	0.0229945	+	0.134022i
$817$	2.70577	−	18.2942i	0.0946630	−	0.640034i
$818$	−17.2929	+	17.2929i	−0.604632	+	0.604632i
$819$	−16.5420	+	19.3485i	−0.578023	+	0.676090i
$820$	5.01910	+	4.45069i	0.175274	+	0.155425i
$821$	5.79050	+	3.34315i	0.202090	+	0.116677i	0.597630	−	0.801772i	$-0.296109\pi$
$821$	5.79050	+	3.34315i	0.202090	+	0.116677i	−0.395540	+	0.918449i	$0.629443\pi$
$822$	35.3319	+	3.25549i	1.23234	+	0.113548i
$823$	38.0026	−	10.1828i	1.32469	−	0.354949i	0.473955	−	0.880549i	$-0.342826\pi$
$823$	38.0026	−	10.1828i	1.32469	−	0.354949i	0.850731	+	0.525601i	$0.176159\pi$
$824$	−3.00000			−0.104510
$825$	0.0416306	+	1.48528i	0.00144939	+	0.0517109i
$826$	8.48528	−	14.6969i	0.295241	−	0.511372i
$827$	6.73305	−	1.80411i	0.234131	−	0.0627352i	−0.139846	−	0.990173i	$-0.544661\pi$
$827$	6.73305	−	1.80411i	0.234131	−	0.0627352i	0.373977	+	0.927438i	$0.377994\pi$
$828$	3.87868	−	8.12132i	0.134793	−	0.282235i
$829$		−	28.9706i		−	1.00619i	−0.864231	−	0.503095i	$-0.832195\pi$
$829$		−	28.9706i		−	1.00619i	0.864231	−	0.503095i	$-0.167805\pi$
$830$	−1.90192	+	9.29423i	−0.0660167	+	0.322607i
$831$	32.0764	+	38.5874i	1.11272	+	1.33858i
$832$	−0.732051	−	2.73205i	−0.0253793	−	0.0947168i
$833$	−4.33245	−	1.16088i	−0.150110	−	0.0402220i
$834$	−15.5009	−	18.6473i	−0.536752	−	0.645704i
$835$	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
$838$	−7.72017	+	28.8120i	−0.266689	+	0.995296i
$839$	−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	$0.995432\pi$
$840$	−7.94937	−	8.47394i	−0.274279	−	0.292379i
$841$	9.47056	+	16.4035i	0.326571	+	0.565638i
$842$	−20.2560	+	5.42758i	−0.698068	+	0.187047i
$843$	6.17157	−	8.72792i	0.212560	−	0.300606i
$844$			3.48528i			0.119968i
$845$	10.9534	+	2.24144i	0.376807	+	0.0771078i
$846$	−3.55515	+	19.1283i	−0.122229	+	0.657644i
$847$	23.2721	−	23.2721i	0.799638	−	0.799638i
$848$	−6.70711	+	6.70711i	−0.230323	+	0.230323i
$849$	−18.9406	−	6.99295i	−0.650039	−	0.239997i
$850$	−4.40477	+	10.3118i	−0.151083	+	0.353693i
$851$	7.79423	+	4.50000i	0.267183	+	0.154258i
$852$	1.68228	−	18.2578i	0.0576339	−	0.625501i
$853$	5.47961	−	20.4502i	0.187618	−	0.700200i	−0.806437	−	0.591320i	$-0.798607\pi$
$853$	5.47961	−	20.4502i	0.187618	−	0.700200i	0.994055	−	0.108880i	$-0.0347265\pi$
$854$	−6.72792			−0.230225
$855$	20.4923	+	20.8582i	0.700821	+	0.713337i
$856$	8.48528			0.290021
$857$	−2.19615	+	8.19615i	−0.0750191	+	0.279975i	−0.993238	−	0.116099i	$-0.962961\pi$
$857$	−2.19615	+	8.19615i	−0.0750191	+	0.279975i	0.918219	+	0.396074i	$0.129628\pi$
$858$	−0.0771202	+	0.836987i	−0.00263284	+	0.0285743i
$859$	−12.5191	−	7.22792i	−0.427147	−	0.246614i	0.270983	−	0.962584i	$-0.412651\pi$
$859$	−12.5191	−	7.22792i	−0.427147	−	0.246614i	−0.698131	+	0.715971i	$0.745984\pi$
$860$	9.46979	−	0.568406i	0.322917	−	0.0193825i
$861$	14.6236	+	5.39910i	0.498371	+	0.184001i
$862$	8.00000	−	8.00000i	0.272481	−	0.272481i
$863$	39.2340	−	39.2340i	1.33554	−	1.33554i	0.435215	−	0.900327i	$-0.356672\pi$
$863$	39.2340	−	39.2340i	1.33554	−	1.33554i	0.900327	−	0.435215i	$-0.143328\pi$
$864$	−0.0719302	+	5.19565i	−0.00244711	+	0.176760i
$865$	−24.6047	−	37.2656i	−0.836587	−	1.26707i
$866$		−	9.51472i		−	0.323323i
$867$	−11.9706	+	16.9289i	−0.406542	+	0.574937i
$868$	−18.0898	+	4.84714i	−0.614007	+	0.164523i
$869$	0.556349	+	0.963625i	0.0188729	+	0.0326887i
$870$	12.2772	+	0.392141i	0.416236	+	0.0132948i
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	0.580438	−	2.16622i	0.0196561	−	0.0733576i
$873$	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
$876$	−17.9840	−	21.6344i	−0.607622	−	0.730959i
$877$	−27.4862	−	7.36491i	−0.928144	−	0.248695i	−0.237081	−	0.971490i	$-0.576191\pi$
$877$	−27.4862	−	7.36491i	−0.928144	−	0.248695i	−0.691063	+	0.722794i	$0.742857\pi$
$878$	−7.62373	−	28.4522i	−0.257289	−	0.960214i
$879$	28.7548	+	34.5915i	0.969874	+	1.16674i
$880$	−0.375860	−	0.0769140i	−0.0126702	−	0.00259277i
$881$			49.2843i			1.66043i	0.557444	+	0.830215i	$0.311782\pi$
$881$			49.2843i			1.66043i	−0.557444	+	0.830215i	$0.688218\pi$
$882$	−5.41421	−	2.58579i	−0.182306	−	0.0870680i
$883$	−3.39496	+	0.909676i	−0.114249	+	0.0306130i	−0.315491	−	0.948929i	$-0.602169\pi$
$883$	−3.39496	+	0.909676i	−0.114249	+	0.0306130i	0.201241	+	0.979542i	$0.435502\pi$
$884$	−3.17157	+	5.49333i	−0.106672	+	0.184761i
$885$	−20.9706	−	6.34315i	−0.704918	−	0.213223i
$886$	34.2426			1.15040
$887$	−18.7929	+	5.03554i	−0.631004	+	0.169077i	−0.560125	−	0.828408i	$-0.689247\pi$
$887$	−18.7929	+	5.03554i	−0.631004	+	0.169077i	−0.0708787	+	0.997485i	$0.522580\pi$
$888$	−5.17423	−	0.476756i	−0.173636	−	0.0159989i
$889$	−6.90271	−	3.98528i	−0.231509	−	0.133662i
$890$	−1.58471	−	26.4017i	−0.0531196	−	0.884985i
$891$	0.554824	−	1.44104i	0.0185873	−	0.0482766i
$892$	12.3640	−	12.3640i	0.413976	−	0.413976i
$893$	−26.2860	+	10.4003i	−0.879626	+	0.348034i
$894$	−3.31371	−	19.3137i	−0.110827	−	0.645947i
$895$	15.6314	+	13.8612i	0.522500	+	0.463327i
$896$	2.59808	−	1.50000i	0.0867956	−	0.0501115i
$897$	13.3485	−	6.14966i	0.445692	−	0.205331i
$898$	−4.61434	+	17.2209i	−0.153982	+	0.574670i
$899$	9.89949	−	17.1464i	0.330167	−	0.571865i
$900$	−8.31371	+	12.4853i	−0.277124	+	0.416176i
$901$	21.2721			0.708676
$902$	0.497180	−	0.133219i	0.0165543	−	0.00443571i
$903$	20.0227	−	9.22450i	0.666314	−	0.306972i
$904$		−	20.0000i		−	0.665190i
$905$	30.7279	−	10.2426i	1.02143	−	0.340477i
$906$	17.4312	+	6.43568i	0.579113	+	0.213811i
$907$	−30.6753	−	8.21941i	−1.01856	−	0.272921i	−0.289355	−	0.957222i	$-0.593441\pi$
$907$	−30.6753	−	8.21941i	−1.01856	−	0.272921i	−0.729200	+	0.684301i	$0.760108\pi$
$908$	−5.94522	−	22.1879i	−0.197299	−	0.736330i
$909$	−39.4794	−	33.7529i	−1.30945	−	1.11951i
$910$	−1.13681	−	18.9396i	−0.0376850	−	0.627841i
$911$			29.3137i			0.971206i	0.874179	+	0.485603i	$0.161400\pi$
$911$			29.3137i			0.971206i	−0.874179	+	0.485603i	$0.838600\pi$
$912$	−6.44949	+	3.92480i	−0.213564	+	0.129963i
$913$	0.514719	+	0.514719i	0.0170347	+	0.0170347i
$914$	−17.6569	−	30.5826i	−0.584037	−	1.01158i
$915$	1.97904	+	8.45724i	0.0654252	+	0.279588i
$916$	7.87868	−	13.6463i	0.260319	−	0.450886i
$917$	−11.6469	+	43.4667i	−0.384613	+	1.43540i
$918$	8.35326	−	8.12513i	0.275699	−	0.268169i
$919$		−	23.2721i		−	0.767675i	−0.923401	−	0.383838i	$-0.874602\pi$
$919$		−	23.2721i		−	0.767675i	0.923401	−	0.383838i	$-0.125398\pi$
$920$	2.12132	+	6.36396i	0.0699379	+	0.209814i
$921$	−12.0833	+	32.7278i	−0.398157	+	1.07842i
$922$	−6.49964	−	24.2570i	−0.214054	−	0.798862i
$923$	21.1716	−	21.1716i	0.696871	−	0.696871i
$924$	−0.878680	+	0.150758i	−0.0289064	+	0.00495956i
$925$	−11.7992	−	9.26174i	−0.387954	−	0.304524i
$926$	35.9273	−	20.7426i	1.18064	−	0.681645i
$927$	5.09393	+	7.41970i	0.167307	+	0.243695i
$928$	−0.820863	+	3.06350i	−0.0269462	+	0.100564i
$929$	−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
$933$	−14.6349	−	1.34847i	−0.479127	−	0.0441469i
$934$	2.15232	−	1.24264i	0.0704260	−	0.0406604i
$935$	0.474064	+	0.718002i	0.0155035	+	0.0234812i
$936$	−5.51399	+	6.44949i	−0.180230	+	0.210808i
$937$	−1.45333	−	5.42389i	−0.0474781	−	0.177191i	0.938115	−	0.346323i	$-0.112570\pi$
$937$	−1.45333	−	5.42389i	−0.0474781	−	0.177191i	−0.985593	+	0.169133i	$0.945903\pi$
$938$	12.0000	−	12.0000i	0.391814	−	0.391814i
$939$	−6.31371	−	36.7990i	−0.206040	−	1.20089i
$940$	−7.99020	−	12.1017i	−0.260611	−	0.394714i
$941$	22.3426	+	12.8995i	0.728347	+	0.420512i	0.817817	−	0.575478i	$-0.195184\pi$
$941$	22.3426	+	12.8995i	0.728347	+	0.420512i	−0.0894699	+	0.995990i	$0.528517\pi$
$942$	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
$945$	−7.46017	+	34.0492i	−0.242679	+	1.10762i
$946$	0.363961	−	0.630399i	0.0118334	−	0.0204960i
$947$	−14.2902	+	53.3319i	−0.464370	+	1.73305i	0.194599	+	0.980883i	$0.437659\pi$
$947$	−14.2902	+	53.3319i	−0.464370	+	1.73305i	−0.658969	+	0.752170i	$0.729007\pi$
$948$	−1.03063	+	11.1855i	−0.0334734	+	0.363287i
$949$		−	45.9411i		−	1.49131i
$950$	−21.7866	−	0.586988i	−0.706850	−	0.0190444i
$951$	−8.33452	−	48.5772i	−0.270265	−	1.57522i
$952$	−6.49867	−	1.74131i	−0.210623	−	0.0564363i
$953$	−4.80119	−	1.28648i	−0.155526	−	0.0416731i	0.180216	−	0.983627i	$-0.442320\pi$
$953$	−4.80119	−	1.28648i	−0.155526	−	0.0416731i	−0.335742	+	0.941954i	$0.608987\pi$
$954$	27.9767	+	5.19972i	0.905780	+	0.168347i
$955$	15.7047	−	17.7104i	0.508192	−	0.573094i
$956$	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
$960$	−2.64979	−	2.82465i	−0.0855216	−	0.0911650i
$961$	7.97056			0.257115
$962$	−6.00000	−	6.00000i	−0.193448	−	0.193448i
$963$	−14.4078	−	20.9861i	−0.464285	−	0.676267i
$964$	−0.420266	+	0.242641i	−0.0135359	+	0.00781493i
$965$	22.3923	−	14.7846i	0.720834	−	0.475933i
$966$	9.96486	+	11.9876i	0.320614	+	0.385693i
$967$	41.9751	+	11.2472i	1.34983	+	0.361686i	0.860072	−	0.510173i	$-0.170419\pi$
$967$	41.9751	+	11.2472i	1.34983	+	0.361686i	0.489757	+	0.871859i	$0.337085\pi$
$968$	7.75736	−	7.75736i	0.249331	−	0.249331i
$969$	16.4514	+	4.00361i	0.528496	+	0.128615i
$970$	−30.7279	+	10.2426i	−0.986614	+	0.328871i
$971$	−16.8493	+	9.72792i	−0.540718	+	0.312184i	−0.745370	−	0.666651i	$-0.767727\pi$
$971$	−16.8493	+	9.72792i	−0.540718	+	0.312184i	0.204652	+	0.978835i	$0.434394\pi$
$972$	12.9722	−	8.64420i	0.416083	−	0.277263i
$973$	40.5689	−	10.8704i	1.30058	−	0.348489i
$974$	17.3995	+	30.1368i	0.557516	+	0.965646i
$975$	−23.4733	+	7.00016i	−0.751749	+	0.224185i
$976$	−2.24264			−0.0717852
$977$	−7.75736	−	7.75736i	−0.248180	−	0.248180i	0.572043	−	0.820223i	$-0.306151\pi$
$977$	−7.75736	−	7.75736i	−0.248180	−	0.248180i	−0.820223	+	0.572043i	$0.806151\pi$
$978$	14.5979	+	31.6862i	0.466790	+	1.01321i
$979$	−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
$982$	−1.77495	−	6.62419i	−0.0566408	−	0.211386i
$983$	15.8951	+	4.25909i	0.506976	+	0.135844i	0.503236	−	0.864149i	$-0.332143\pi$
$983$	15.8951	+	4.25909i	0.506976	+	0.135844i	0.00374017	+	0.999993i	$0.498809\pi$
$984$	4.87453	+	1.79970i	0.155394	+	0.0573724i
$985$	−1.14076	−	19.0053i	−0.0363475	−	0.605559i
$986$	6.15978	−	3.55635i	0.196167	−	0.113257i
$987$	−27.5147	−	19.4558i	−0.875803	−	0.619286i
$988$	−12.1962	−	1.80385i	−0.388011	−	0.0573880i
$989$	−12.7279			−0.404724
$990$	0.447975	+	1.06019i	0.0142376	+	0.0336949i
$991$	−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	$0.863714\pi$
$992$	−6.02993	+	1.61571i	−0.191450	+	0.0512990i
$993$	1.98882	−	21.5847i	0.0631134	−	0.684970i
$994$	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
$997$	−4.05991	−	15.1518i	−0.128579	−	0.479862i	0.871363	−	0.490638i	$-0.163236\pi$
$997$	−4.05991	−	15.1518i	−0.128579	−	0.479862i	−0.999942	+	0.0107763i	$0.996570\pi$
$998$	−9.82750	−	36.6767i	−0.311084	−	1.16098i
$999$	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.83.1	✓	8
3.2	odd	2		570.2.v.b.83.2	yes	8
5.2	odd	4		570.2.v.b.197.1	yes	8
15.2	even	4	inner	570.2.v.a.197.2	yes	8
19.11	even	3	inner	570.2.v.a.353.2	yes	8
57.11	odd	6		570.2.v.b.353.1	yes	8
95.87	odd	12		570.2.v.b.467.2	yes	8
285.182	even	12	inner	570.2.v.a.467.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.a.83.1	✓	8	1.1	even	1	trivial
570.2.v.a.197.2	yes	8	15.2	even	4	inner
570.2.v.a.353.2	yes	8	19.11	even	3	inner
570.2.v.a.467.1	yes	8	285.182	even	12	inner
570.2.v.b.83.2	yes	8	3.2	odd	2
570.2.v.b.197.1	yes	8	5.2	odd	4
570.2.v.b.353.1	yes	8	57.11	odd	6
570.2.v.b.467.2	yes	8	95.87	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.158919 + 1.72474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.67303 - 1.48356i) q^{5} +(-1.62484 - 0.599900i) q^{6} +(2.12132 - 2.12132i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.158919 + 1.72474i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.67303 - 1.48356i) q^{5} +(-1.62484 - 0.599900i) q^{6} +(2.12132 - 2.12132i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94949 - 0.548188i) q^{9} +(1.86603 - 1.23205i) q^{10} -0.171573i q^{11} +(1.00000 - 1.41421i) q^{12} +(2.73205 - 0.732051i) q^{13} +(1.50000 + 2.59808i) q^{14} +(2.82465 - 2.64979i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.580438 - 2.16622i) q^{17} +(1.29289 - 2.70711i) q^{18} +(4.33013 - 0.500000i) q^{19} +(0.707107 + 2.12132i) q^{20} +(3.32162 + 3.99585i) q^{21} +(0.165727 + 0.0444063i) q^{22} +(-0.776457 - 2.89778i) q^{23} +(1.10721 + 1.33195i) q^{24} +(0.598076 + 4.96410i) q^{25} +2.82843i q^{26} +(1.41421 - 5.00000i) q^{27} +(-2.89778 + 0.776457i) q^{28} +(1.58579 - 2.74666i) q^{29} +(1.82843 + 3.41421i) q^{30} +6.24264 q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.295919 + 0.0272661i) q^{33} +(1.94218 + 1.12132i) q^{34} +(-6.69615 + 0.401924i) q^{35} +(2.28024 + 1.94949i) q^{36} +(-2.12132 + 2.12132i) q^{37} +(-0.637756 + 4.31199i) q^{38} +(0.828427 + 4.82843i) q^{39} +(-2.23205 + 0.133975i) q^{40} +(2.59808 - 1.50000i) q^{41} +(-4.71940 + 2.17423i) q^{42} +(1.09808 - 4.09808i) q^{43} +(-0.0857864 + 0.148586i) q^{44} +(4.12132 + 5.29289i) q^{45} +3.00000 q^{46} +(-6.26430 + 1.67851i) q^{47} +(-1.57313 + 0.724745i) q^{48} -2.00000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(3.64394 + 1.34536i) q^{51} +(-2.73205 - 0.732051i) q^{52} +(2.45497 + 9.16208i) q^{53} +(4.46360 + 2.66012i) q^{54} +(-0.254539 + 0.287047i) q^{55} -3.00000i q^{56} +(0.174235 + 7.54782i) q^{57} +(2.24264 + 2.24264i) q^{58} +(-2.82843 - 4.89898i) q^{59} +(-3.77111 + 0.882461i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(-1.61571 + 6.02993i) q^{62} +(-7.41970 + 5.09393i) q^{63} -1.00000i q^{64} +(-5.65685 - 2.82843i) q^{65} +(-0.102927 + 0.278779i) q^{66} +(-1.46410 - 5.46410i) q^{67} +(-1.58579 + 1.58579i) q^{68} +(5.12132 - 0.878680i) q^{69} +(1.34486 - 6.57201i) q^{70} +(9.16756 - 5.29289i) q^{71} +(-2.47323 + 1.69798i) q^{72} +(4.20390 - 15.6892i) 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} +(-4.87832 - 0.449490i) q^{78} +(-5.61642 + 3.24264i) q^{79} +(0.448288 - 2.19067i) q^{80} +(8.39898 + 3.23375i) q^{81} +(0.776457 + 2.89778i) q^{82} +(-3.00000 + 3.00000i) q^{83} +(-0.878680 - 5.12132i) q^{84} +(-4.18482 + 2.76305i) 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} +(-6.17922 + 2.61099i) q^{90} +(4.24264 - 7.34847i) q^{91} +(-0.776457 + 2.89778i) q^{92} +(-0.992072 + 10.7670i) q^{93} -6.48528i q^{94} +(-7.98623 - 5.58750i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(-13.9917 - 3.74907i) q^{97} +(1.93185 + 0.517638i) q^{98} +(-0.0940542 + 0.506052i) 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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