LMFDB - Embedded newform 570.2.v.b.197.1

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			197.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	570.197
Dual form			570.2.v.b.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.72474 + 0.158919i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.448288 + 2.19067i) q^{5} +(-1.62484 - 0.599900i) q^{6} +(2.12132 + 2.12132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.72474 + 0.158919i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.448288 + 2.19067i) 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} +(0.133975 - 2.23205i) q^{10} -0.171573i q^{11} +(1.41421 + 1.00000i) q^{12} +(-0.732051 - 2.73205i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.425044 + 3.84959i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.16622 + 0.580438i) q^{17} +(-2.70711 - 1.29289i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-0.707107 + 2.12132i) q^{20} +(3.32162 + 3.99585i) q^{21} +(-0.0444063 + 0.165727i) q^{22} +(-2.89778 + 0.776457i) q^{23} +(-1.10721 - 1.33195i) q^{24} +(-4.59808 + 1.96410i) q^{25} +2.82843i q^{26} +(5.00000 + 1.41421i) q^{27} +(0.776457 + 2.89778i) q^{28} +(-1.58579 + 2.74666i) q^{29} +(0.585786 - 3.82843i) q^{30} +6.24264 q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.0272661 - 0.295919i) q^{33} +(-1.94218 - 1.12132i) q^{34} +(-3.69615 + 5.59808i) q^{35} +(2.28024 + 1.94949i) 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} +(-2.17423 - 4.71940i) q^{42} +(-4.09808 - 1.09808i) q^{43} +(0.0857864 - 0.148586i) q^{44} +(0.121320 + 6.70711i) q^{45} +3.00000 q^{46} +(-1.67851 - 6.26430i) q^{47} +(0.724745 + 1.57313i) q^{48} +2.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(3.64394 + 1.34536i) q^{51} +(0.732051 - 2.73205i) q^{52} +(9.16208 - 2.45497i) q^{53} +(-4.46360 - 2.66012i) q^{54} +(0.375860 - 0.0769140i) q^{55} -3.00000i q^{56} +(-7.54782 + 0.174235i) q^{57} +(2.24264 - 2.24264i) q^{58} +(2.82843 + 4.89898i) q^{59} +(-1.55670 + 3.54636i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(-6.02993 - 1.61571i) q^{62} +(5.09393 + 7.41970i) q^{63} +1.00000i q^{64} +(5.65685 - 2.82843i) q^{65} +(-0.102927 + 0.278779i) 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} +(-1.69798 - 2.47323i) q^{72} +(-15.6892 - 4.20390i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-8.24264 + 2.65685i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(0.363961 - 0.363961i) q^{77} +(-0.449490 + 4.87832i) q^{78} +(5.61642 - 3.24264i) q^{79} +(-1.67303 + 1.48356i) q^{80} +(8.39898 + 3.23375i) 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} +(-3.17157 + 4.48528i) q^{87} +(-0.121320 + 0.121320i) q^{88} +(-5.91421 + 10.2437i) q^{89} +(1.61874 - 6.50997i) q^{90} +(4.24264 - 7.34847i) q^{91} +(-2.89778 - 0.776457i) q^{92} +(10.7670 + 0.992072i) 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} +(0.0940542 - 0.506052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{6} + 4 q^{9} + 8 q^{10} + 8 q^{13} - 12 q^{14} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 16 q^{18} + 12 q^{21} - 8 q^{22} - 4 q^{24} - 16 q^{25} + 40 q^{27} - 24 q^{29} + 16 q^{30} + 16 q^{31} + 16 q^{33} + 12 q^{35} + 16 q^{39} - 4 q^{40} + 12 q^{42} - 12 q^{43} + 12 q^{44} - 16 q^{45} + 24 q^{46} + 24 q^{47} - 4 q^{48} - 20 q^{51} - 8 q^{52} + 24 q^{53} - 4 q^{54} - 8 q^{55} - 16 q^{58} + 12 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} - 32 q^{75} - 32 q^{76} - 48 q^{77} + 16 q^{78} + 28 q^{81} + 24 q^{83} + 24 q^{84} + 16 q^{85} - 48 q^{87} + 16 q^{88} - 36 q^{89} - 8 q^{90} + 8 q^{93} - 8 q^{96} - 24 q^{97} - 32 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^9 + 8 * q^10 + 8 * q^13 - 12 * q^14 - 4 * q^15 + 4 * q^16 + 12 * q^17 - 16 * q^18 + 12 * q^21 - 8 * q^22 - 4 * q^24 - 16 * q^25 + 40 * q^27 - 24 * q^29 + 16 * q^30 + 16 * q^31 + 16 * q^33 + 12 * q^35 + 16 * q^39 - 4 * q^40 + 12 * q^42 - 12 * q^43 + 12 * q^44 - 16 * q^45 + 24 * q^46 + 24 * q^47 - 4 * q^48 - 20 * q^51 - 8 * q^52 + 24 * q^53 - 4 * q^54 - 8 * q^55 - 16 * q^58 + 12 * 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 - 32 * q^75 - 32 * q^76 - 48 * q^77 + 16 * q^78 + 28 * q^81 + 24 * q^83 + 24 * q^84 + 16 * q^85 - 48 * q^87 + 16 * q^88 - 36 * q^89 - 8 * q^90 + 8 * 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
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$4$	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
$6$	−1.62484	−	0.599900i	−0.663340	−	0.244908i
$7$	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
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$	0.133975	−	2.23205i	0.0423665	−	0.705836i
$11$		−	0.171573i		−	0.0517312i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$		−	0.171573i		−	0.0517312i	0.999665	−	0.0258656i	$-0.00823419\pi$
$12$	1.41421	+	1.00000i	0.408248	+	0.288675i
$13$	−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
$15$	0.425044	+	3.84959i	0.109746	+	0.993960i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.16622	+	0.580438i	0.525387	+	0.140777i	0.511757	−	0.859130i	$-0.328995\pi$
$17$	2.16622	+	0.580438i	0.525387	+	0.140777i	0.0136295	+	0.999907i	$0.495661\pi$
$18$	−2.70711	−	1.29289i	−0.638071	−	0.304738i
$19$	−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
$22$	−0.0444063	+	0.165727i	−0.00946746	+	0.0353330i
$23$	−2.89778	+	0.776457i	−0.604228	+	0.161903i	−0.547948	−	0.836512i	$-0.684591\pi$
$23$	−2.89778	+	0.776457i	−0.604228	+	0.161903i	−0.0562805	+	0.998415i	$0.517924\pi$
$24$	−1.10721	−	1.33195i	−0.226008	−	0.271883i
$25$	−4.59808	+	1.96410i	−0.919615	+	0.392820i
$26$			2.82843i			0.554700i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	0.776457	+	2.89778i	0.146737	+	0.547628i
$29$	−1.58579	+	2.74666i	−0.294473	+	0.510042i	−0.974862	−	0.222809i	$-0.928477\pi$
$29$	−1.58579	+	2.74666i	−0.294473	+	0.510042i	0.680389	+	0.732851i	$0.261811\pi$
$30$	0.585786	−	3.82843i	0.106949	−	0.698972i
$31$	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
$33$	0.0272661	−	0.295919i	0.00474642	−	0.0515130i
$34$	−1.94218	−	1.12132i	−0.333082	−	0.192305i
$35$	−3.69615	+	5.59808i	−0.624764	+	0.946248i
$36$	2.28024	+	1.94949i	0.380040	+	0.324915i
$37$	−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	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	−2.17423	−	4.71940i	−0.335492	−	0.728219i
$43$	−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
$45$	0.121320	+	6.70711i	0.0180854	+	0.999836i
$46$	3.00000			0.442326
$47$	−1.67851	−	6.26430i	−0.244836	−	0.913742i	−0.973466	−	0.228834i	$-0.926509\pi$
$47$	−1.67851	−	6.26430i	−0.244836	−	0.913742i	0.728629	−	0.684909i	$-0.240158\pi$
$48$	0.724745	+	1.57313i	0.104608	+	0.227062i
$49$			2.00000i			0.285714i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$	3.64394	+	1.34536i	0.510254	+	0.188388i
$52$	0.732051	−	2.73205i	0.101517	−	0.378867i
$53$	9.16208	−	2.45497i	1.25851	−	0.337216i	0.432891	−	0.901446i	$-0.357494\pi$
$53$	9.16208	−	2.45497i	1.25851	−	0.337216i	0.825618	+	0.564230i	$0.190827\pi$
$54$	−4.46360	−	2.66012i	−0.607420	−	0.361997i
$55$	0.375860	−	0.0769140i	0.0506809	−	0.0103711i
$56$		−	3.00000i		−	0.400892i
$57$	−7.54782	+	0.174235i	−0.999734	+	0.0230779i
$58$	2.24264	−	2.24264i	0.294473	−	0.294473i
$59$	2.82843	+	4.89898i	0.368230	+	0.637793i	0.989289	−	0.145971i	$-0.0466306\pi$
$59$	2.82843	+	4.89898i	0.368230	+	0.637793i	−0.621059	+	0.783764i	$0.713297\pi$
$60$	−1.55670	+	3.54636i	−0.200969	+	0.457834i
$61$	−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
$63$	5.09393	+	7.41970i	0.641775	+	0.934794i
$64$			1.00000i			0.125000i
$65$	5.65685	−	2.82843i	0.701646	−	0.350823i
$66$	−0.102927	+	0.278779i	−0.0126694	+	0.0343154i
$67$	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	0.154949	−	0.987922i	$-0.450479\pi$
$71$	9.16756	−	5.29289i	1.08799	−	0.628151i	0.933040	+	0.359772i	$0.117145\pi$
$72$	−1.69798	−	2.47323i	−0.200108	−	0.291473i
$73$	−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
$75$	−8.24264	+	2.65685i	−0.951778	+	0.306787i
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$	0.363961	−	0.363961i	0.0414772	−	0.0414772i
$78$	−0.449490	+	4.87832i	−0.0508947	+	0.552360i
$79$	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
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$	−2.89778	+	0.776457i	−0.320006	+	0.0857453i
$83$	3.00000	+	3.00000i	0.329293	+	0.329293i	0.852318	−	0.523025i	$-0.175196\pi$
$83$	3.00000	+	3.00000i	0.329293	+	0.329293i	−0.523025	+	0.852318i	$0.675196\pi$
$84$	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
$87$	−3.17157	+	4.48528i	−0.340028	+	0.480873i
$88$	−0.121320	+	0.121320i	−0.0129328	+	0.0129328i
$89$	−5.91421	+	10.2437i	−0.626905	+	1.08583i	0.361264	+	0.932464i	$0.382345\pi$
$89$	−5.91421	+	10.2437i	−0.626905	+	1.08583i	−0.988169	+	0.153368i	$0.950988\pi$
$90$	1.61874	−	6.50997i	0.170630	−	0.686211i
$91$	4.24264	−	7.34847i	0.444750	−	0.770329i
$92$	−2.89778	−	0.776457i	−0.302114	−	0.0809513i
$93$	10.7670	+	0.992072i	1.11648	+	0.102873i
$94$			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
$99$	0.0940542	−	0.506052i	0.00945280	−	0.0508602i
$100$	−4.96410	−	0.598076i	−0.496410	−	0.0598076i
$101$	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	$0.336262\pi$
$102$	−3.17157	−	2.24264i	−0.314033	−	0.222055i
$103$	−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
$105$	−7.26456	+	9.06787i	−0.708948	+	0.884933i
$106$	−9.48528			−0.921292
$107$	−6.00000	+	6.00000i	−0.580042	+	0.580042i	−0.934915	−	0.354873i	$-0.884524\pi$
$107$	−6.00000	+	6.00000i	−0.580042	+	0.580042i	0.354873	+	0.934915i	$0.384524\pi$
$108$	3.62302	+	3.72474i	0.348625	+	0.358414i
$109$	−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
$111$	−3.32162	−	3.99585i	−0.315274	−	0.379270i
$112$	−0.776457	+	2.89778i	−0.0733683	+	0.273814i
$113$	−14.1421	−	14.1421i	−1.33038	−	1.33038i	−0.905028	−	0.425352i	$-0.860150\pi$
$113$	−14.1421	−	14.1421i	−1.33038	−	1.33038i	−0.425352	−	0.905028i	$-0.639850\pi$
$114$	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
$117$	−0.661498	−	8.45946i	−0.0611556	−	0.782077i
$118$	−1.46410	−	5.46410i	−0.134781	−	0.503011i
$119$	3.36396	+	5.82655i	0.308374	+	0.534119i
$120$	2.42152	−	3.02262i	0.221053	−	0.275926i
$121$	10.9706			0.997324
$122$	1.58579	−	1.58579i	0.143570	−	0.143570i
$123$	4.71940	−	2.17423i	0.425534	−	0.196044i
$124$	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
$129$	−6.89363	−	2.54516i	−0.606950	−	0.224089i
$130$	−6.19615	+	1.26795i	−0.543439	+	0.111207i
$131$	−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	$0.560782\pi$
$132$	0.171573	−	0.242641i	0.0149335	−	0.0211192i
$133$	−10.2462	−	8.12493i	−0.888462	−	0.704520i
$134$	−5.65685			−0.488678
$135$	−0.856638	+	11.5873i	−0.0737276	+	0.997278i
$136$	−1.12132	−	1.94218i	−0.0961524	−	0.166541i
$137$	−5.30198	−	19.7873i	−0.452979	−	1.69054i	−0.693963	−	0.720011i	$-0.744137\pi$
$137$	−5.30198	−	19.7873i	−0.452979	−	1.69054i	0.240984	−	0.970529i	$-0.422530\pi$
$138$	5.17423	+	0.476756i	0.440460	+	0.0405842i
$139$	−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
$147$	−0.317837	+	3.44949i	−0.0262148	+	0.284509i
$148$	−0.776457	−	2.89778i	−0.0638244	−	0.238196i
$149$	−5.65685	−	9.79796i	−0.463428	−	0.802680i	0.535701	−	0.844407i	$-0.320047\pi$
$149$	−5.65685	−	9.79796i	−0.463428	−	0.802680i	−0.999129	+	0.0417274i	$0.986714\pi$
$150$	8.64942	−	0.432972i	0.706223	−	0.0353520i
$151$	−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
$153$	6.07107	+	2.89949i	0.490817	+	0.234410i
$154$	−0.445759	+	0.257359i	−0.0359203	+	0.0207386i
$155$	2.79850	+	13.6756i	0.224781	+	1.09845i
$156$	1.69677	−	4.59575i	0.135851	−	0.367955i
$157$	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
$162$	−7.27583	−	5.29738i	−0.571644	−	0.416201i
$163$	−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
$165$	0.660485	−	0.0729260i	0.0514187	−	0.00567728i
$166$	−2.12132	−	3.67423i	−0.164646	−	0.285176i
$167$	−6.07844	−	22.6850i	−0.470364	−	1.75542i	−0.638464	−	0.769651i	$-0.720430\pi$
$167$	−6.07844	−	22.6850i	−0.470364	−	1.75542i	0.168101	−	0.985770i	$-0.446237\pi$
$168$	0.476756	−	5.17423i	0.0367825	−	0.399201i
$169$	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
$173$	5.16876	−	19.2901i	0.392974	−	1.46660i	−0.432230	−	0.901763i	$-0.642273\pi$
$173$	5.16876	−	19.2901i	0.392974	−	1.46660i	0.825204	−	0.564835i	$-0.191060\pi$
$174$	4.22438	−	3.51159i	0.320249	−	0.266213i
$175$	−13.9205	−	5.58750i	−1.05229	−	0.422376i
$176$	0.148586	−	0.0857864i	0.0112001	−	0.00646640i
$177$	4.09978	+	8.89898i	0.308158	+	0.668888i
$178$	8.36396	−	8.36396i	0.626905	−	0.626905i
$179$	9.34315			0.698340			0.349170	−	0.937059i	$-0.386464\pi$
$179$	9.34315			0.698340			0.349170	+	0.937059i	$0.386464\pi$
$180$	−3.24849	+	5.86919i	−0.242128	+	0.437463i
$181$	−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
$183$	−2.24264	+	3.17157i	−0.165781	+	0.234449i
$184$	2.59808	+	1.50000i	0.191533	+	0.110581i
$185$	3.69615	−	5.59808i	0.271747	−	0.411579i
$186$	−10.1433	−	3.74496i	−0.743744	−	0.274594i
$187$	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	$0.125102\pi$
$191$			10.5858i			0.765961i	−0.923757	+	0.382980i	$0.874898\pi$
$192$	−0.158919	+	1.72474i	−0.0114690	+	0.124473i
$193$	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
$195$	10.2061	−	3.97934i	0.730875	−	0.284966i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	−6.02082	+	6.02082i	−0.428965	+	0.428965i	−0.888276	−	0.459310i	$-0.848097\pi$
$197$	−6.02082	+	6.02082i	−0.428965	+	0.428965i	0.459310	+	0.888276i	$0.348097\pi$
$198$	−0.221825	+	0.464466i	−0.0157644	+	0.0330082i
$199$	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
$204$	2.48307	+	2.98709i	0.173849	+	0.209138i
$205$	4.45069	+	5.01910i	0.310850	+	0.350549i
$206$	2.59808	−	1.50000i	0.181017	−	0.104510i
$207$	−8.97261	+	0.701625i	−0.623639	+	0.0487663i
$208$	2.00000	−	2.00000i	0.138675	−	0.138675i
$209$	0.0857864	+	0.742932i	0.00593397	+	0.0513897i
$210$	9.36396	−	6.87868i	0.646175	−	0.474674i
$211$	−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
$213$	16.6528	−	7.67199i	1.14103	−	0.525676i
$214$	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
$219$	−26.3918	−	9.74397i	−1.78339	−	0.658436i
$220$	0.363961	+	0.121320i	0.0245382	+	0.00817942i
$221$		−	6.34315i		−	0.426686i
$222$	2.17423	+	4.71940i	0.145925	+	0.316745i
$223$	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
$225$	−14.6387	+	3.27249i	−0.975912	+	0.218166i
$226$	10.0000	+	17.3205i	0.665190	+	1.15214i
$227$	−16.2426	+	16.2426i	−1.07806	+	1.07806i	−0.0813787	+	0.996683i	$0.525932\pi$
$227$	−16.2426	+	16.2426i	−1.07806	+	1.07806i	−0.996683	+	0.0813787i	$0.974068\pi$
$228$	−6.62372	−	3.62302i	−0.438667	−	0.239940i
$229$		−	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
$231$	0.685580	−	0.569900i	0.0451079	−	0.0374966i
$232$	3.06350	−	0.820863i	0.201129	−	0.0538923i
$233$	−2.71379	+	10.1280i	−0.177786	+	0.663508i	0.818274	+	0.574828i	$0.194931\pi$
$233$	−2.71379	+	10.1280i	−0.177786	+	0.663508i	−0.996060	+	0.0886791i	$0.971735\pi$
$234$	−1.55051	+	8.34242i	−0.101360	+	0.545361i
$235$	12.9706	−	6.48528i	0.846106	−	0.423053i
$236$			5.65685i			0.368230i
$237$	10.2022	−	4.70017i	0.662704	−	0.305309i
$238$	−1.74131	−	6.49867i	−0.112873	−	0.421246i
$239$	0.686292			0.0443925			0.0221963	−	0.999754i	$-0.492934\pi$
$239$	0.686292			0.0443925			0.0221963	+	0.999754i	$0.492934\pi$
$240$	−3.12132	+	2.29289i	−0.201480	+	0.148006i
$241$	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
$243$	13.9722	+	6.91215i	0.896317	+	0.443415i
$244$	−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
$249$	4.69748	+	5.65099i	0.297691	+	0.358117i
$250$	3.76795	+	10.5263i	0.238306	+	0.665740i
$251$	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	$0.482659\pi$
$252$	0.701625	+	8.97261i	0.0441982	+	0.565221i
$253$	0.133219	+	0.497180i	0.00837541	+	0.0312574i
$254$	−2.65685			−0.166706
$255$	−1.31371	+	8.58579i	−0.0822676	+	0.537663i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.13335	−	7.96178i	−0.133075	−	0.496642i	0.866924	−	0.498441i	$-0.166094\pi$
$257$	−2.13335	−	7.96178i	−0.133075	−	0.496642i	−0.999998	+	0.00179903i	$0.999427\pi$
$258$	6.00000	+	4.24264i	0.373544	+	0.264135i
$259$		−	9.00000i		−	0.559233i
$260$	6.31319	+	0.378937i	0.391528	+	0.0235007i
$261$	−6.18295	+	7.23194i	−0.382715	+	0.447646i
$262$	14.4889	−	3.88229i	0.895126	−	0.239848i
$263$	0.384419	−	1.43467i	0.0237043	−	0.0884656i	−0.953060	−	0.302780i	$-0.902085\pi$
$263$	0.384419	−	1.43467i	0.0237043	−	0.0884656i	0.976765	+	0.214315i	$0.0687518\pi$
$264$	−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
$267$	−11.8284	+	16.7279i	−0.723888	+	1.02373i
$268$	5.46410	+	1.46410i	0.333773	+	0.0894342i
$269$	−5.46447	−	9.46473i	−0.333174	−	0.577075i	0.649958	−	0.759970i	$-0.274786\pi$
$269$	−5.46447	−	9.46473i	−0.333174	−	0.577075i	−0.983132	+	0.182895i	$0.941453\pi$
$270$	3.82647	−	10.9708i	0.232872	−	0.667661i
$271$	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
$273$	8.48528	−	12.0000i	0.513553	−	0.726273i
$274$			20.4853i			1.23756i
$275$	0.336987	+	0.788905i	0.0203211	+	0.0475728i
$276$	−4.87453	−	1.79970i	−0.293412	−	0.108329i
$277$	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
$279$	18.4126	+	3.42214i	1.10233	+	0.204878i
$280$	6.57201	−	1.34486i	0.392753	−	0.0803709i
$281$	−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	$0.725598\pi$
$282$	−1.03063	+	11.1855i	−0.0613732	+	0.666084i
$283$	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
$285$	−3.76529	−	16.4567i	−0.223036	−	0.974810i
$286$	0.485281			0.0286953
$287$	8.69333	+	2.32937i	0.513151	+	0.137498i
$288$	−0.233875	−	2.99087i	−0.0137812	−	0.176239i
$289$	−10.3668	−	5.98528i	−0.609812	−	0.352075i
$290$	5.91824	+	3.90754i	0.347531	+	0.229459i
$291$	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	−0.997130	−	0.0757037i	$-0.975880\pi$
$293$	−18.3640	−	18.3640i	−1.07283	−	1.07283i	−0.0757037	−	0.997130i	$-0.524120\pi$
$294$	1.19980	−	3.24969i	0.0699738	−	0.189526i
$295$	−9.46410	+	8.39230i	−0.551021	+	0.488619i
$296$			3.00000i			0.174371i
$297$	0.242641	−	0.857864i	0.0140794	−	0.0497783i
$298$	2.92820	+	10.9282i	0.169626	+	0.633054i
$299$	4.24264	+	7.34847i	0.245358	+	0.424973i
$300$	−8.46676	−	1.82042i	−0.488829	−	0.105102i
$301$	−6.36396	−	11.0227i	−0.366813	−	0.635338i
$302$	10.3624	+	2.77659i	0.596288	+	0.159775i
$303$	24.4853	+	17.3137i	1.40664	+	0.994647i
$304$	−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
$307$	−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
$309$	−3.99585	+	3.32162i	−0.227316	+	0.188960i
$310$	0.836355	−	13.9339i	0.0475018	−	0.791392i
$311$			8.48528i			0.481156i	0.970630	+	0.240578i	$0.0773370\pi$
$311$			8.48528i			0.481156i	−0.970630	+	0.240578i	$0.922663\pi$
$312$	−2.82843	+	4.00000i	−0.160128	+	0.226455i
$313$	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
$315$	−13.9706	+	14.4853i	−0.787152	+	0.816153i
$316$	6.48528			0.364826
$317$	−7.36491	−	27.4862i	−0.413655	−	1.54378i	−0.787515	−	0.616296i	$-0.788633\pi$
$317$	−7.36491	−	27.4862i	−0.413655	−	1.54378i	0.373860	−	0.927485i	$-0.378034\pi$
$318$	−16.3597	−	1.50739i	−0.917406	−	0.0845301i
$319$	0.471253	+	0.272078i	0.0263851	+	0.0152334i
$320$	−2.19067	+	0.448288i	−0.122462	+	0.0250600i
$321$	−11.3020	+	9.39496i	−0.630815	+	0.524375i
$322$	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
$327$	−3.52797	+	1.62534i	−0.195097	+	0.0898816i
$328$	−2.89778	−	0.776457i	−0.160003	−	0.0428727i
$329$	9.72792	−	16.8493i	0.536318	−	0.928930i
$330$	−0.656854	−	0.100505i	−0.0361586	−	0.00553262i
$331$	−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
$333$	−5.09393	−	7.41970i	−0.279146	−	0.406597i
$334$			23.4853i			1.28506i
$335$	5.65685	+	11.3137i	0.309067	+	0.618134i
$336$	−1.79970	+	4.87453i	−0.0981818	+	0.265928i
$337$	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
$339$	−22.1441	−	26.6390i	−1.20270	−	1.44683i
$340$	−2.76305	+	4.18482i	−0.149847	+	0.226954i
$341$		−	1.07107i		−	0.0580016i
$342$	12.3686	+	4.24484i	0.668815	+	0.229535i
$343$	10.6066	−	10.6066i	0.572703	−	0.572703i
$344$	2.12132	+	3.67423i	0.114374	+	0.198101i
$345$	−4.22072	−	10.8252i	−0.227236	−	0.582811i
$346$	−9.98528	+	17.2950i	−0.536812	+	0.929786i
$347$	10.5967	+	2.83939i	0.568863	+	0.152426i	0.531775	−	0.846886i	$-0.321525\pi$
$347$	10.5967	+	2.83939i	0.568863	+	0.152426i	0.0370881	+	0.999312i	$0.488192\pi$
$348$	−4.98930	+	2.29858i	−0.267455	+	0.123217i
$349$		−	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
$351$	0.203449	−	14.6955i	0.0108593	−	0.784389i
$352$	−0.165727	+	0.0444063i	−0.00883326	+	0.00236687i
$353$	3.51472	+	3.51472i	0.187070	+	0.187070i	0.794428	−	0.607358i	$-0.207771\pi$
$353$	3.51472	+	3.51472i	0.187070	+	0.187070i	−0.607358	+	0.794428i	$0.707771\pi$
$354$	−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
$357$	4.87603	+	10.5839i	0.258067	+	0.560160i
$358$	−9.02479	−	2.41818i	−0.476975	−	0.127805i
$359$	4.60660	+	7.97887i	0.243127	+	0.421109i	0.961603	−	0.274443i	$-0.0884934\pi$
$359$	4.60660	+	7.97887i	0.243127	+	0.421109i	−0.718476	+	0.695551i	$0.755160\pi$
$360$	4.65685	−	4.82843i	0.245438	−	0.254480i
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	10.2426	−	10.2426i	0.538341	−	0.538341i
$363$	18.9214	+	1.74343i	0.993117	+	0.0915062i
$364$	7.34847	−	4.24264i	0.385164	−	0.222375i
$365$	2.17610	−	36.2544i	0.113902	−	1.89764i
$366$	2.98709	−	2.48307i	0.156138	−	0.129792i
$367$	−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
$372$	8.82843	+	6.24264i	0.457733	+	0.323666i
$373$	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
$375$	−9.51537	−	16.8659i	−0.491371	−	0.870950i
$376$	−3.24264	+	5.61642i	−0.167226	+	0.289645i
$377$	8.66490	+	2.32175i	0.446265	+	0.119576i
$378$	−3.82577	−	15.1117i	−0.196776	−	0.777262i
$379$			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	$0.367536\pi$
$383$	−7.89017	+	29.4465i	−0.403169	+	1.50465i	−0.807408	+	0.589994i	$0.799130\pi$
$384$	0.599900	−	1.62484i	0.0306135	−	0.0829175i
$385$	0.960478	+	0.634159i	0.0489505	+	0.0323198i
$386$	−10.3923	−	6.00000i	−0.528954	−	0.305392i
$387$	−11.4853	−	5.48528i	−0.583830	−	0.278833i
$388$	10.2426	−	10.2426i	0.519991	−	0.519991i
$389$	2.46447	−	4.26858i	0.124953	−	0.216426i	−0.796761	−	0.604294i	$-0.793455\pi$
$389$	2.46447	−	4.26858i	0.124953	−	0.216426i	0.921715	+	0.387868i	$0.126789\pi$
$390$	−10.8883	+	1.20220i	−0.551350	+	0.0608760i
$391$	−6.72792			−0.340246
$392$	1.41421	−	1.41421i	0.0714286	−	0.0714286i
$393$	−23.5970	+	10.8712i	−1.19031	+	0.548378i
$394$	7.37396	−	4.25736i	0.371495	−	0.214483i
$395$	9.62133	+	10.8501i	0.484102	+	0.545927i
$396$	0.334480	−	0.391227i	0.0168082	−	0.0196599i
$397$	−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
$399$	−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	$0.000901827\pi$
$402$	−9.75663	−	0.898979i	−0.486616	−	0.0448370i
$403$	−4.56993	−	17.0552i	−0.227644	−	0.849581i
$404$	8.65685	+	14.9941i	0.430695	+	0.745985i
$405$	−3.31892	+	19.8490i	−0.164919	+	0.986307i
$406$	9.51472			0.472208
$407$	−0.363961	+	0.363961i	−0.0180409	+	0.0180409i
$408$	−1.62534	−	3.52797i	−0.0804664	−	0.174661i
$409$	−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
$414$	8.84847	+	1.64456i	0.434879	+	0.0808259i
$415$	−5.22715	+	7.91688i	−0.256591	+	0.388624i
$416$	−2.44949	+	1.41421i	−0.120096	+	0.0693375i
$417$	−19.7990	−	14.0000i	−0.969561	−	0.685583i
$418$	0.109422	−	0.739821i	0.00535199	−	0.0361858i
$419$	−29.8284			−1.45721			−0.728607	−	0.684932i	$-0.759832\pi$
$419$	−29.8284			−1.45721			−0.728607	+	0.684932i	$0.759832\pi$
$420$	−10.8252	+	4.22072i	−0.528217	+	0.205950i
$421$	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
$423$	−1.51675	−	19.3966i	−0.0737467	−	0.943097i
$424$	−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	0.245105	−	0.969497i	$-0.421178\pi$
$431$	−9.79796	−	5.65685i	−0.471951	−	0.272481i	−0.717056	+	0.697015i	$0.754511\pi$
$432$	1.27526	+	5.03723i	0.0613557	+	0.242354i
$433$	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
$435$	−11.2476	−	4.93718i	−0.539279	−	0.236719i
$436$	−2.24264			−0.107403
$437$	12.1595	−	4.81105i	0.581669	−	0.230144i
$438$	22.9706	+	16.2426i	1.09758	+	0.776103i
$439$	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
$441$	−1.09638	+	5.89898i	−0.0522084	+	0.280904i
$442$	−1.64173	+	6.12701i	−0.0780890	+	0.291432i
$443$	−33.0759	+	8.86265i	−1.57148	+	0.421077i	−0.936276	−	0.351266i	$-0.885751\pi$
$443$	−33.0759	+	8.86265i	−1.57148	+	0.421077i	−0.635205	+	0.772343i	$0.719085\pi$
$444$	−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
$447$	−8.19955	−	17.7980i	−0.387826	−	0.841815i
$448$	−2.12132	+	2.12132i	−0.100223	+	0.100223i
$449$	−17.8284			−0.841375			−0.420688	−	0.907205i	$-0.638211\pi$
$449$	−17.8284			−0.841375			−0.420688	+	0.907205i	$0.638211\pi$
$450$	14.9869	+	0.627789i	0.706487	+	0.0295942i
$451$	−0.257359	−	0.445759i	−0.0121186	−	0.0209900i
$452$	−5.17638	−	19.3185i	−0.243476	−	0.908667i
$453$	−18.5029	−	1.70487i	−0.869343	−	0.0801016i
$454$	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	−0.982661	−	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
$459$	10.0103	+	5.96569i	0.467239	+	0.278455i
$460$	0.401924	−	6.69615i	0.0187398	−	0.312210i
$461$	−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	$0.532163\pi$
$462$	−0.809720	+	0.373040i	−0.0376716	+	0.0173554i
$463$	−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
$465$	2.65339	+	24.0316i	0.123048	+	1.11444i
$466$	5.24264	−	9.08052i	0.242861	−	0.420647i
$467$	1.75736	−	1.75736i	0.0813209	−	0.0813209i	−0.665276	−	0.746597i	$-0.731686\pi$
$467$	1.75736	−	1.75736i	0.0813209	−	0.0813209i	0.746597	+	0.665276i	$0.231686\pi$
$468$	3.65685	−	7.65685i	0.169038	−	0.353938i
$469$	14.6969	+	8.48528i	0.678642	+	0.391814i
$470$	−14.2071	+	2.90727i	−0.655325	+	0.134102i
$471$	7.09588	−	19.2194i	0.326961	−	0.885581i
$472$	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
$477$	28.3692	−	2.21837i	1.29894	−	0.101572i
$478$	−0.662907	−	0.177625i	−0.0303206	−	0.00812439i
$479$	−15.1924	+	26.3140i	−0.694158	+	1.20232i	0.276306	+	0.961070i	$0.410890\pi$
$479$	−15.1924	+	26.3140i	−0.694158	+	1.20232i	−0.970464	+	0.241247i	$0.922444\pi$
$480$	3.60841	−	1.40691i	0.164701	−	0.0642163i
$481$	−4.24264	+	7.34847i	−0.193448	+	0.335061i
$482$	−0.343146	+	0.343146i	−0.0156299	+	0.0156299i
$483$	−12.7279	−	9.00000i	−0.579141	−	0.409514i
$484$	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
$489$	−26.8283	+	22.3015i	−1.21322	+	1.00851i
$490$	4.46410	+	0.267949i	0.201668	+	0.0121047i
$491$	−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	$0.382789\pi$
$492$	5.17423	+	0.476756i	0.233273	+	0.0214938i
$493$	−5.02944	+	5.02944i	−0.226514	+	0.226514i
$494$	−1.41421	−	12.2474i	−0.0636285	−	0.551039i
$495$	1.15076	−	0.0208153i	0.0517227	−	0.000935577i
$496$	3.12132	+	5.40629i	0.140151	+	0.242749i
$497$	30.6753	+	8.21941i	1.37597	+	0.368691i
$498$	−3.07483	−	6.67423i	−0.137787	−	0.299080i
$499$	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	0.149843	−	0.988710i	$-0.452123\pi$
$503$	17.3582	−	4.65112i	0.773965	−	0.207383i	0.624123	+	0.781326i	$0.285457\pi$
$504$	1.64456	−	8.84847i	0.0732547	−	0.394142i
$505$	−12.2426	+	36.7279i	−0.544790	+	1.63437i
$506$		−	0.514719i		−	0.0228820i
$507$	7.86566	−	3.62372i	0.349326	−	0.160935i
$508$	2.56632	+	0.687644i	0.113862	+	0.0305093i
$509$	6.36396	−	11.0227i	0.282078	−	0.488573i	−0.689819	−	0.723982i	$-0.742310\pi$
$509$	6.36396	−	11.0227i	0.282078	−	0.488573i	0.971896	+	0.235409i	$0.0756431\pi$
$510$	3.49111	−	7.95322i	0.154589	−	0.352175i
$511$	−24.3640	−	42.1996i	−1.07780	−	1.86680i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−22.3577	−	3.62372i	−0.987118	−	0.159991i
$514$			8.24264i			0.363567i
$515$	−5.59808	−	3.69615i	−0.246681	−	0.162872i
$516$	−4.69748	−	5.65099i	−0.206795	−	0.248771i
$517$	−1.07478	+	0.287988i	−0.0472690	+	0.0126657i
$518$	−2.32937	+	8.69333i	−0.102347	+	0.381963i
$519$	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	$0.718474\pi$
$522$	7.84403	−	5.38526i	0.343324	−	0.235706i
$523$	−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
$525$	−23.1213	−	11.8492i	−1.00910	−	0.517143i
$526$	−0.742641	+	1.28629i	−0.0323807	+	0.0560850i
$527$	13.5230	+	3.62347i	0.589069	+	0.157841i
$528$	0.269907	−	0.124347i	0.0117462	−	0.00541149i
$529$	−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
$534$	15.7549	−	13.0965i	0.681781	−	0.566741i
$535$	−15.8338	−	10.4543i	−0.684553	−	0.451979i
$536$	−4.89898	−	2.82843i	−0.211604	−	0.122169i
$537$	16.1145	+	1.48480i	0.695394	+	0.0640738i
$538$	2.82862	+	10.5565i	0.121950	+	0.455125i
$539$	0.343146			0.0147803
$540$	−6.53553	+	9.60660i	−0.281245	+	0.413402i
$541$	−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
$543$	−14.4853	+	20.4853i	−0.621623	+	0.879108i
$544$		−	2.24264i		−	0.0961524i
$545$	−3.32710	−	3.75201i	−0.142517	−	0.160718i
$546$	−11.3020	+	9.39496i	−0.483680	+	0.402067i
$547$	−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
$549$	−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
$552$	4.24264	+	3.00000i	0.180579	+	0.127688i
$553$	18.7929	+	5.03554i	0.799155	+	0.214133i
$554$	−14.4853	−	25.0892i	−0.615421	−	1.06594i
$555$	7.26456	−	9.06787i	0.308363	−	0.384909i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	3.61585	+	13.4945i	0.153208	+	0.571781i	0.999252	+	0.0386680i	$0.0123115\pi$
$557$	3.61585	+	13.4945i	0.153208	+	0.571781i	−0.846044	+	0.533114i	$0.821022\pi$
$558$	−16.8995	−	8.07107i	−0.715413	−	0.341676i
$559$			12.0000i			0.507546i
$560$	−6.69615	−	0.401924i	−0.282964	−	0.0169844i
$561$	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	0.987495	+	0.157650i	$0.0503919\pi$
$563$	27.1716	+	27.1716i	1.14515	+	1.14515i	0.157650	+	0.987495i	$0.449608\pi$
$564$	3.89052	−	10.5376i	0.163821	−	0.443712i
$565$	24.6410	−	37.3205i	1.03666	−	1.57009i
$566$	−10.0951	−	5.82843i	−0.424330	−	0.244987i
$567$	10.9571	+	24.6767i	0.460155	+	1.03633i
$568$	−10.2251	−	2.73980i	−0.429035	−	0.114960i
$569$	−10.7990			−0.452717			−0.226359	−	0.974044i	$-0.572682\pi$
$569$	−10.7990			−0.452717			−0.226359	+	0.974044i	$0.572682\pi$
$570$	−0.622316	+	16.8705i	−0.0260660	+	0.706626i
$571$	−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
$573$	−1.68228	+	18.2578i	−0.0702782	+	0.762730i
$574$	−7.79423	−	4.50000i	−0.325325	−	0.187826i
$575$	11.7992	−	9.26174i	0.492059	−	0.386241i
$576$	−0.548188	+	2.94949i	−0.0228412	+	0.122895i
$577$	−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
$579$	19.4981	+	7.19881i	0.810315	+	0.299172i
$580$	−4.70523	−	5.30614i	−0.195374	−	0.220326i
$581$			12.7279i			0.528043i
$582$	−14.4853	+	20.4853i	−0.600434	+	0.849142i
$583$	−0.421207	−	1.57196i	−0.0174446	−	0.0651041i
$584$	8.12132	+	14.0665i	0.336063	+	0.582078i
$585$	18.2353	−	5.24140i	0.753939	−	0.216705i
$586$	12.9853	+	22.4912i	0.536417	+	0.929102i
$587$	39.5745	+	10.6040i	1.63342	+	0.437672i	0.954903	−	0.296917i	$-0.0959584\pi$
$587$	39.5745	+	10.6040i	1.63342	+	0.437672i	0.678512	+	0.734589i	$0.262625\pi$
$588$	−2.00000	+	2.82843i	−0.0824786	+	0.116642i
$589$	−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
$592$	0.776457	−	2.89778i	0.0319122	−	0.119098i
$593$	37.1739	−	9.96072i	1.52655	−	0.409038i	0.604658	−	0.796485i	$-0.293310\pi$
$593$	37.1739	−	9.96072i	1.52655	−	0.409038i	0.921892	+	0.387447i	$0.126643\pi$
$594$	−0.456405	+	0.765833i	−0.0187265	+	0.0314225i
$595$	−11.2560	+	9.98130i	−0.461452	+	0.409194i
$596$		−	11.3137i		−	0.463428i
$597$	20.1421	+	14.2426i	0.824363	+	0.582912i
$598$	−2.19615	−	8.19615i	−0.0898074	−	0.335166i
$599$	11.8492	−	20.5235i	0.484147	−	0.838567i	−0.515687	−	0.856777i	$-0.672463\pi$
$599$	11.8492	−	20.5235i	0.484147	−	0.838567i	0.999834	+	0.0182098i	$0.00579669\pi$
$600$	7.70711	+	3.94975i	0.314641	+	0.161248i
$601$	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
$603$	16.9189	−	1.32300i	0.688991	−	0.0538766i
$604$	−9.29065	−	5.36396i	−0.378031	−	0.218256i
$605$	4.91797	+	24.0329i	0.199944	+	0.977076i
$606$	−19.1698	−	23.0610i	−0.778722	−	0.936790i
$607$	−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
$612$	3.80795	+	5.54657i	0.153927	+	0.224207i
$613$	−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
$615$	6.87868	+	9.36396i	0.277375	+	0.377591i
$616$	−0.514719			−0.0207386
$617$	8.32977	+	31.0871i	0.335344	+	1.25152i	0.903496	+	0.428597i	$0.140992\pi$
$617$	8.32977	+	31.0871i	0.335344	+	1.25152i	−0.568152	+	0.822924i	$0.692341\pi$
$618$	4.71940	−	2.17423i	0.189842	−	0.0874605i
$619$			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
$621$	−15.5870	−	0.215791i	−0.625483	−	0.00865938i
$622$	2.19615	−	8.19615i	0.0880577	−	0.328636i
$623$	−34.2761	+	9.18427i	−1.37324	+	0.367960i
$624$	3.76733	−	3.13165i	0.150814	−	0.125366i
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$		−	21.5563i		−	0.861565i
$627$	0.0298939	+	1.29500i	0.00119385	+	0.0517174i
$628$	8.36396	−	8.36396i	0.333758	−	0.333758i
$629$	−3.36396	−	5.82655i	−0.134130	−	0.232320i
$630$	17.2436	−	10.3759i	0.687001	−	0.413384i
$631$	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
$633$	−2.52594	−	5.48281i	−0.100397	−	0.217922i
$634$			28.4558i			1.13013i
$635$	2.65685	+	5.31371i	0.105434	+	0.210868i
$636$	15.4121	+	5.69022i	0.611130	+	0.225632i
$637$	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	−0.166632	−	0.986019i	$-0.553289\pi$
$641$	15.2913	−	8.82843i	0.603969	−	0.348702i	0.770602	+	0.637317i	$0.219956\pi$
$642$	13.3485	−	6.14966i	0.526822	−	0.242708i
$643$	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
$645$	2.48528	−	16.2426i	0.0978579	−	0.639553i
$646$	8.97056	+	3.88437i	0.352942	+	0.152828i
$647$	12.7071	−	12.7071i	0.499568	−	0.499568i	−0.411735	−	0.911303i	$-0.635077\pi$
$647$	12.7071	−	12.7071i	0.499568	−	0.499568i	0.911303	+	0.411735i	$0.135077\pi$
$648$	−3.65237	−	8.22558i	−0.143479	−	0.323131i
$649$	0.840532	−	0.485281i	0.0329938	−	0.0190490i
$650$	−5.55532	−	13.0053i	−0.217898	−	0.510111i
$651$	20.7357	+	24.9447i	0.812695	+	0.977659i
$652$	−19.4558	+	5.21317i	−0.761948	+	0.204163i
$653$	14.8492	+	14.8492i	0.581096	+	0.581096i	0.935204	−	0.354109i	$-0.115216\pi$
$653$	14.8492	+	14.8492i	0.581096	+	0.581096i	−0.354109	+	0.935204i	$0.615216\pi$
$654$	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
$657$	−43.9706	−	21.0000i	−1.71546	−	0.819288i
$658$	−13.7574	+	13.7574i	−0.536318	+	0.536318i
$659$	−19.7132	+	34.1443i	−0.767917	+	1.33007i	0.170773	+	0.985310i	$0.445374\pi$
$659$	−19.7132	+	34.1443i	−0.767917	+	1.33007i	−0.938690	+	0.344762i	$0.887960\pi$
$660$	0.608460	+	0.267087i	0.0236843	+	0.0103963i
$661$	−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
$663$	1.00804	−	10.9403i	0.0391492	−	0.424886i
$664$		−	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
$669$	28.4109	+	10.4894i	1.09843	+	0.405545i
$670$	−2.53590	−	12.3923i	−0.0979703	−	0.478757i
$671$	0.333226	+	0.192388i	0.0128640	+	0.00742706i
$672$	3.00000	−	4.24264i	0.115728	−	0.163663i
$673$	−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
$675$	−25.7680	+	3.31785i	−0.991812	+	0.127704i
$676$	5.00000			0.192308
$677$	−34.6066	+	34.6066i	−1.33004	+	1.33004i	−0.424711	+	0.905329i	$0.639624\pi$
$677$	−34.6066	+	34.6066i	−1.33004	+	1.33004i	−0.905329	+	0.424711i	$0.860376\pi$
$678$	14.4949	+	31.4626i	0.556673	+	1.20832i
$679$	37.6339	−	21.7279i	1.44426	−	0.833841i
$680$	3.75201	−	3.32710i	0.143883	−	0.127588i
$681$	−30.5957	+	25.4332i	−1.17243	+	0.974601i
$682$	−0.277213	+	1.03457i	−0.0106150	+	0.0396158i
$683$	0.899495	+	0.899495i	0.0344182	+	0.0344182i	0.724106	−	0.689688i	$-0.242252\pi$
$683$	0.899495	+	0.899495i	0.0344182	+	0.0344182i	−0.689688	+	0.724106i	$0.742252\pi$
$684$	−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
$687$	2.50414	−	27.1774i	0.0955388	−	1.03688i
$688$	−1.09808	−	4.09808i	−0.0418638	−	0.156238i
$689$	−13.4142	−	23.2341i	−0.511041	−	0.885149i
$690$	1.27513	+	11.5488i	0.0485434	+	0.439654i
$691$	−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
$693$	1.27302	−	0.873980i	0.0483580	−	0.0331998i
$694$	−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
$699$	−6.29012	+	17.0370i	−0.237914	+	0.644397i
$700$	−9.26174	−	11.7992i	−0.350061	−	0.445966i
$701$	−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	$0.549142\pi$
$702$	−4.00000	+	14.1421i	−0.150970	+	0.533761i
$703$	10.2462	+	8.12493i	0.386445	+	0.306437i
$704$	0.171573			0.00646640
$705$	23.4015	−	9.12419i	0.881353	−	0.343637i
$706$	−2.48528	−	4.30463i	−0.0935348	−	0.162007i
$707$	13.4434	+	50.1713i	0.505589	+	1.88688i
$708$	−0.898979	+	9.75663i	−0.0337857	+	0.366677i
$709$	−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
$717$	1.18368	+	0.109065i	0.0442053	+	0.00407309i
$718$	−2.38455	−	8.89927i	−0.0889907	−	0.332118i
$719$	−3.70711	−	6.42090i	−0.138252	−	0.239459i	0.788583	−	0.614928i	$-0.210815\pi$
$719$	−3.70711	−	6.42090i	−0.138252	−	0.239459i	−0.926835	+	0.375469i	$0.877482\pi$
$720$	−5.74786	+	3.45862i	−0.214210	+	0.128895i
$721$	−9.00000			−0.335178
$722$	−18.9903	−	0.605571i	−0.706748	−	0.0225370i
$723$	0.485281	−	0.686292i	0.0180478	−	0.0255235i
$724$	−12.5446	+	7.24264i	−0.466217	+	0.269171i
$725$	1.89684	−	15.7440i	0.0704470	−	0.584718i
$726$	−17.8255	−	6.58125i	−0.661565	−	0.244253i
$727$	−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
$732$	−3.52797	+	1.62534i	−0.130398	+	0.0600744i
$733$	−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
$735$	−7.69918	+	0.850087i	−0.283988	+	0.0313559i
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$	−0.251200	−	0.937492i	−0.00925308	−	0.0345329i
$738$	−8.97261	+	0.701625i	−0.330286	+	0.0258272i
$739$	−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
$741$	6.00141	+	20.4935i	0.220467	+	0.752847i
$742$	−20.1213	−	20.1213i	−0.738677	−	0.738677i
$743$	6.72168	−	25.0856i	0.246594	−	0.920303i	−0.725981	−	0.687715i	$-0.758614\pi$
$743$	6.72168	−	25.0856i	0.246594	−	0.920303i	0.972575	−	0.232588i	$-0.0747194\pi$
$744$	−6.91189	−	8.31489i	−0.253402	−	0.304839i
$745$	18.9282	−	16.7846i	0.693476	−	0.614941i
$746$	−15.1427	+	8.74264i	−0.554414	+	0.320091i
$747$	7.20390	+	10.4930i	0.263577	+	0.383920i
$748$	0.272078	−	0.272078i	0.00994815	−	0.00994815i
$749$	−25.4558			−0.930136
$750$	4.82593	+	18.7539i	0.176218	+	0.684797i
$751$	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
$753$	24.4853	+	17.3137i	0.892293	+	0.630947i
$754$	−7.76874	−	4.48528i	−0.282921	−	0.163344i
$755$	−4.80920	−	23.5013i	−0.175025	−	0.855301i
$756$	−0.215791	+	15.5870i	−0.00784823	+	0.566892i
$757$	−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	$-0.962326\pi$
$761$		−	6.51472i		−	0.236158i	0.993004	−	0.118079i	$-0.0376737\pi$
$762$	−4.58240	−	0.422224i	−0.166003	−	0.0152955i
$763$	−6.49867	−	1.74131i	−0.235268	−	0.0630398i
$764$	−5.29289	+	9.16756i	−0.191490	+	0.331671i
$765$	−3.63025	+	14.5995i	−0.131252	+	0.527847i
$766$	15.2426	−	26.4010i	0.550739	−	0.953908i
$767$	11.3137	−	11.3137i	0.408514	−	0.408514i
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$	−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	−0.402695	−	0.915334i	$-0.631927\pi$
$773$	−8.16772	+	2.18853i	−0.293772	+	0.0787161i	0.108923	+	0.994050i	$0.465260\pi$
$774$	9.67423	+	8.27098i	0.347733	+	0.297294i
$775$	−28.7041	+	12.2612i	−1.03108	+	0.440435i
$776$	−12.5446	+	7.24264i	−0.450326	+	0.259996i
$777$	1.43027	−	15.5227i	0.0513106	−	0.556874i
$778$	−3.48528	+	3.48528i	−0.124953	+	0.124953i
$779$	−10.5000	+	7.79423i	−0.376202	+	0.279257i
$780$	10.8284	+	1.65685i	0.387720	+	0.0593249i
$781$	−0.908117	−	1.57290i	−0.0324950	−	0.0562830i
$782$	6.49867	+	1.74131i	0.232392	+	0.0622693i
$783$	−11.8133	+	11.4907i	−0.422173	+	0.410643i
$784$	−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
$789$	0.891021	−	2.41335i	0.0317212	−	0.0859176i
$790$	−6.48528	−	12.9706i	−0.230736	−	0.461472i
$791$		−	60.0000i		−	2.13335i
$792$	−0.424339	+	0.291327i	−0.0150782	+	0.0103518i
$793$	6.12701	+	1.64173i	0.217576	+	0.0582994i
$794$	3.98528	−	6.90271i	0.141432	−	0.244968i
$795$	13.3449	+	34.2268i	0.473295	+	1.21390i
$796$	7.12132	+	12.3345i	0.252409	+	0.437184i
$797$	1.77817	−	1.77817i	0.0629862	−	0.0629862i	−0.674912	−	0.737898i	$-0.735818\pi$
$797$	1.77817	−	1.77817i	0.0629862	−	0.0629862i	0.737898	+	0.674912i	$0.235818\pi$
$798$	11.7744	+	19.3485i	0.416810	+	0.684928i
$799$		−	14.5442i		−	0.514535i
$800$	3.08725	+	3.93305i	0.109151	+	0.139054i
$801$	−23.0594	+	26.9716i	−0.814764	+	0.952996i
$802$	−33.4475	+	8.96224i	−1.18107	+	0.316468i
$803$	−0.721276	+	2.69184i	−0.0254533	+	0.0949929i
$804$	9.19151	+	3.39355i	0.324160	+	0.119681i
$805$	6.36396	−	19.0919i	0.224300	−	0.672900i
$806$			17.6569i			0.621936i
$807$	−7.92069	−	17.1927i	−0.278821	−	0.605210i
$808$	−4.48112	−	16.7238i	−0.157645	−	0.588340i
$809$	24.6863			0.867924			0.433962	−	0.900931i	$-0.357115\pi$
$809$	24.6863			0.867924			0.433962	+	0.900931i	$0.357115\pi$
$810$	8.34315	−	18.3137i	0.293148	−	0.643478i
$811$	−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
$813$	1.44949	+	3.14626i	0.0508358	+	0.110344i
$814$	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
$819$	16.5420	−	19.3485i	0.578023	−	0.676090i
$820$	1.34486	+	6.57201i	0.0469647	+	0.229505i
$821$	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	$0.629443\pi$
$822$	−3.25549	+	35.3319i	−0.113548	+	1.23234i
$823$	−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
$825$	0.455844	+	1.41421i	0.0158705	+	0.0492366i
$826$	8.48528	−	14.6969i	0.295241	−	0.511372i
$827$	1.80411	+	6.73305i	0.0627352	+	0.234131i	0.990173	−	0.139846i	$-0.0446607\pi$
$827$	1.80411	+	6.73305i	0.0627352	+	0.234131i	−0.927438	+	0.373977i	$0.877994\pi$
$828$	−8.12132	−	3.87868i	−0.282235	−	0.134793i
$829$			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
$831$	32.0764	+	38.5874i	1.11272	+	1.33858i
$832$	2.73205	−	0.732051i	0.0947168	−	0.0253793i
$833$	−1.16088	+	4.33245i	−0.0402220	+	0.150110i
$834$	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
$837$	31.2132	+	8.82843i	1.07889	+	0.305155i
$838$	28.8120	+	7.72017i	0.995296	+	0.266689i
$839$	14.1213	+	24.4588i	0.487522	+	0.844413i	0.999897	−	0.0143488i	$-0.00456751\pi$
$839$	14.1213	+	24.4588i	0.487522	+	0.844413i	−0.512375	+	0.858762i	$0.671234\pi$
$840$	11.5488	−	1.27513i	0.398470	−	0.0439962i
$841$	9.47056	+	16.4035i	0.326571	+	0.565638i
$842$	−5.42758	−	20.2560i	−0.187047	−	0.698068i
$843$	−8.72792	−	6.17157i	−0.300606	−	0.212560i
$844$		−	3.48528i		−	0.119968i
$845$	7.41782	+	8.36516i	0.255181	+	0.287770i
$846$	−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
$850$	11.1327	+	1.34127i	0.381848	+	0.0460052i
$851$	7.79423	+	4.50000i	0.267183	+	0.154258i
$852$	18.2578	+	1.68228i	0.625501	+	0.0576339i
$853$	−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
$855$	−3.87889	−	28.9820i	−0.132655	−	0.991162i
$856$	8.48528			0.290021
$857$	−8.19615	−	2.19615i	−0.279975	−	0.0750191i	0.116099	−	0.993238i	$-0.462961\pi$
$857$	−8.19615	−	2.19615i	−0.279975	−	0.0750191i	−0.396074	+	0.918219i	$0.629628\pi$
$858$	0.836987	+	0.0771202i	0.0285743	+	0.00263284i
$859$	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
$861$	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	−0.900327	−	0.435215i	$-0.856672\pi$
$863$	−39.2340	−	39.2340i	−1.33554	−	1.33554i	−0.435215	−	0.900327i	$-0.643328\pi$
$864$	0.0719302	−	5.19565i	0.00244711	−	0.176760i
$865$	44.5753	+	2.67555i	1.51561	+	0.0909714i
$866$		−	9.51472i		−	0.323323i
$867$	−16.9289	−	11.9706i	−0.574937	−	0.406542i
$868$	4.84714	+	18.0898i	0.164523	+	0.614007i
$869$	−0.556349	−	0.963625i	−0.0188729	−	0.0326887i
$870$	9.58647	+	7.68003i	0.325012	+	0.260377i
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	2.16622	+	0.580438i	0.0733576	+	0.0196561i
$873$	18.7279	−	39.2132i	0.633844	−	1.32717i
$874$	−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
$877$	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
$879$	−28.7548	−	34.5915i	−0.969874	−	1.16674i
$880$	0.254539	+	0.287047i	0.00858052	+	0.00967635i
$881$			49.2843i			1.66043i	0.557444	+	0.830215i	$0.311782\pi$
$881$			49.2843i			1.66043i	−0.557444	+	0.830215i	$0.688218\pi$
$882$	2.58579	−	5.41421i	0.0870680	−	0.182306i
$883$	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
$885$	−17.6569	+	12.9706i	−0.593529	+	0.436001i
$886$	34.2426			1.15040
$887$	−5.03554	−	18.7929i	−0.169077	−	0.631004i	−0.997485	−	0.0708787i	$-0.977420\pi$
$887$	−5.03554	−	18.7929i	−0.169077	−	0.631004i	0.828408	−	0.560125i	$-0.189247\pi$
$888$	−0.476756	+	5.17423i	−0.0159989	+	0.173636i
$889$	6.90271	+	3.98528i	0.231509	+	0.133662i
$890$	22.0721	+	14.5732i	0.739860	+	0.488496i
$891$	0.554824	−	1.44104i	0.0185873	−	0.0482766i
$892$	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
$897$	6.14966	+	13.3485i	0.205331	+	0.445692i
$898$	17.2209	+	4.61434i	0.574670	+	0.153982i
$899$	−9.89949	+	17.1464i	−0.330167	+	0.571865i
$900$	−14.3137	−	4.48528i	−0.477124	−	0.149509i
$901$	21.2721			0.708676
$902$	0.133219	+	0.497180i	0.00443571	+	0.0165543i
$903$	−9.22450	−	20.0227i	−0.306972	−	0.666314i
$904$			20.0000i			0.665190i
$905$	−30.7279	−	10.2426i	−1.02143	−	0.340477i
$906$	17.4312	+	6.43568i	0.579113	+	0.213811i
$907$	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
$909$	39.4794	+	33.7529i	1.30945	+	1.11951i
$910$	−15.8338	−	10.4543i	−0.524884	−	0.346557i
$911$			29.3137i			0.971206i	0.874179	+	0.485603i	$0.161400\pi$
$911$			29.3137i			0.971206i	−0.874179	+	0.485603i	$0.838600\pi$
$912$	−3.92480	−	6.44949i	−0.129963	−	0.213564i
$913$	0.514719	−	0.514719i	0.0170347	−	0.0170347i
$914$	17.6569	+	30.5826i	0.584037	+	1.01158i
$915$	−7.95322	−	3.49111i	−0.262925	−	0.115413i
$916$	7.87868	−	13.6463i	0.260319	−	0.450886i
$917$	−43.4667	−	11.6469i	−1.43540	−	0.384613i
$918$	−8.12513	−	8.35326i	−0.268169	−	0.275699i
$919$			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
$921$	−12.0833	+	32.7278i	−0.398157	+	1.07842i
$922$	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
$927$	−7.41970	+	5.09393i	−0.243695	+	0.167307i
$928$	3.06350	+	0.820863i	0.100564	+	0.0269462i
$929$	24.2990	+	42.0871i	0.797224	+	1.38083i	0.921417	+	0.388574i	$0.127032\pi$
$929$	24.2990	+	42.0871i	0.797224	+	1.38083i	−0.124193	+	0.992258i	$0.539634\pi$
$930$	3.65685	−	23.8995i	0.119913	−	0.783695i
$931$	−1.00000	−	8.66025i	−0.0327737	−	0.283828i
$932$	−7.41421	+	7.41421i	−0.242861	+	0.242861i
$933$	−1.34847	+	14.6349i	−0.0441469	+	0.479127i
$934$	−2.15232	+	1.24264i	−0.0704260	+	0.0406604i
$935$	0.858840	+	0.0515503i	0.0280871	+	0.00168587i
$936$	−5.51399	+	6.44949i	−0.180230	+	0.210808i
$937$	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	0.817817	−	0.575478i	$-0.195184\pi$
$941$	22.3426	+	12.8995i	0.728347	+	0.420512i	−0.0894699	+	0.995990i	$0.528517\pi$
$942$	−11.8284	+	16.7279i	−0.385391	+	0.545025i
$943$	−6.36396	+	6.36396i	−0.207239	+	0.207239i
$944$	−2.82843	+	4.89898i	−0.0920575	+	0.159448i
$945$	−26.3976	+	22.7632i	−0.858715	+	0.740488i
$946$	0.363961	−	0.630399i	0.0118334	−	0.0204960i
$947$	−53.3319	−	14.2902i	−1.73305	−	0.464370i	−0.752170	−	0.658969i	$-0.770993\pi$
$947$	−53.3319	−	14.2902i	−1.73305	−	0.464370i	−0.980883	+	0.194599i	$0.937659\pi$
$948$	11.1855	+	1.03063i	0.363287	+	0.0334734i
$949$			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	−0.983627	−	0.180216i	$-0.942320\pi$
$953$	−1.28648	+	4.80119i	−0.0416731	+	0.155526i	0.941954	+	0.335742i	$0.108987\pi$
$954$	−27.9767	−	5.19972i	−0.905780	−	0.168347i
$955$	−23.1900	+	4.74548i	−0.750410	+	0.153560i
$956$	0.594346	+	0.343146i	0.0192225	+	0.0110981i
$957$	0.769553	+	0.544156i	0.0248761	+	0.0175901i
$958$	21.4853	−	21.4853i	0.694158	−	0.694158i
$959$	30.7279	−	53.2223i	0.992256	−	1.71864i
$960$	−3.84959	+	0.425044i	−0.124245	+	0.0137182i
$961$	7.97056			0.257115
$962$	6.00000	−	6.00000i	0.193448	−	0.193448i
$963$	−20.9861	+	14.4078i	−0.676267	+	0.464285i
$964$	0.420266	−	0.242641i	0.0135359	−	0.00781493i
$965$	−1.60770	+	26.7846i	−0.0517535	+	0.862227i
$966$	9.96486	+	11.9876i	0.320614	+	0.385693i
$967$	−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
$969$	−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	$0.434394\pi$
$972$	8.64420	+	12.9722i	0.277263	+	0.416083i
$973$	−10.8704	−	40.5689i	−0.348489	−	1.30058i
$974$	−17.3995	−	30.1368i	−0.557516	−	0.965646i
$975$	13.2927	+	20.5744i	0.425707	+	0.658907i
$976$	−2.24264			−0.0717852
$977$	7.75736	−	7.75736i	0.248180	−	0.248180i	−0.572043	−	0.820223i	$-0.693849\pi$
$977$	7.75736	−	7.75736i	0.248180	−	0.248180i	0.820223	+	0.572043i	$0.193849\pi$
$978$	31.6862	−	14.5979i	1.01321	−	0.466790i
$979$	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	$-0.832143\pi$
$983$	4.25909	−	15.8951i	0.135844	−	0.506976i	0.999993	−	0.00374017i	$-0.00119053\pi$
$984$	−4.87453	−	1.79970i	−0.155394	−	0.0573724i
$985$	−15.8887	−	10.4906i	−0.506255	−	0.334257i
$986$	6.15978	−	3.55635i	0.196167	−	0.113257i
$987$	19.4558	−	27.5147i	0.619286	−	0.875803i
$988$	−1.80385	+	12.1962i	−0.0573880	+	0.388011i
$989$	12.7279			0.404724
$990$	−1.11693	−	0.277732i	−0.0354985	−	0.00882690i
$991$	−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
$993$	−21.5847	−	1.98882i	−0.684970	−	0.0631134i
$994$	−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.b.197.1	yes	8
3.2	odd	2		570.2.v.a.197.2	yes	8
5.3	odd	4		570.2.v.a.83.1	✓	8
15.8	even	4	inner	570.2.v.b.83.2	yes	8
19.11	even	3	inner	570.2.v.b.467.2	yes	8
57.11	odd	6		570.2.v.a.467.1	yes	8
95.68	odd	12		570.2.v.a.353.2	yes	8
285.68	even	12	inner	570.2.v.b.353.1	yes	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.72474 + 0.158919i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.448288 + 2.19067i) q^{5} +(-1.62484 - 0.599900i) q^{6} +(2.12132 + 2.12132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.72474 + 0.158919i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.448288 + 2.19067i) 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} +(0.133975 - 2.23205i) q^{10} -0.171573i q^{11} +(1.41421 + 1.00000i) q^{12} +(-0.732051 - 2.73205i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.425044 + 3.84959i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.16622 + 0.580438i) q^{17} +(-2.70711 - 1.29289i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-0.707107 + 2.12132i) q^{20} +(3.32162 + 3.99585i) q^{21} +(-0.0444063 + 0.165727i) q^{22} +(-2.89778 + 0.776457i) q^{23} +(-1.10721 - 1.33195i) q^{24} +(-4.59808 + 1.96410i) q^{25} +2.82843i q^{26} +(5.00000 + 1.41421i) q^{27} +(0.776457 + 2.89778i) q^{28} +(-1.58579 + 2.74666i) q^{29} +(0.585786 - 3.82843i) q^{30} +6.24264 q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.0272661 - 0.295919i) q^{33} +(-1.94218 - 1.12132i) q^{34} +(-3.69615 + 5.59808i) q^{35} +(2.28024 + 1.94949i) 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} +(-2.17423 - 4.71940i) q^{42} +(-4.09808 - 1.09808i) q^{43} +(0.0857864 - 0.148586i) q^{44} +(0.121320 + 6.70711i) q^{45} +3.00000 q^{46} +(-1.67851 - 6.26430i) q^{47} +(0.724745 + 1.57313i) q^{48} +2.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(3.64394 + 1.34536i) q^{51} +(0.732051 - 2.73205i) q^{52} +(9.16208 - 2.45497i) q^{53} +(-4.46360 - 2.66012i) q^{54} +(0.375860 - 0.0769140i) q^{55} -3.00000i q^{56} +(-7.54782 + 0.174235i) q^{57} +(2.24264 - 2.24264i) q^{58} +(2.82843 + 4.89898i) q^{59} +(-1.55670 + 3.54636i) q^{60} +(-1.12132 + 1.94218i) q^{61} +(-6.02993 - 1.61571i) q^{62} +(5.09393 + 7.41970i) q^{63} +1.00000i q^{64} +(5.65685 - 2.82843i) q^{65} +(-0.102927 + 0.278779i) 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} +(-1.69798 - 2.47323i) q^{72} +(-15.6892 - 4.20390i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-8.24264 + 2.65685i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(0.363961 - 0.363961i) q^{77} +(-0.449490 + 4.87832i) q^{78} +(5.61642 - 3.24264i) q^{79} +(-1.67303 + 1.48356i) q^{80} +(8.39898 + 3.23375i) 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} +(-3.17157 + 4.48528i) q^{87} +(-0.121320 + 0.121320i) q^{88} +(-5.91421 + 10.2437i) q^{89} +(1.61874 - 6.50997i) q^{90} +(4.24264 - 7.34847i) q^{91} +(-2.89778 - 0.776457i) q^{92} +(10.7670 + 0.992072i) 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} +(0.0940542 - 0.506052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{9} + 8 q^{10} + 8 q^{13} - 12 q^{14} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 16 q^{18} + 12 q^{21} - 8 q^{22} - 4 q^{24} - 16 q^{25} + 40 q^{27} - 24 q^{29} + 16 q^{30} + 16 q^{31} + 16 q^{33} + 12 q^{35} + 16 q^{39} - 4 q^{40} + 12 q^{42} - 12 q^{43} + 12 q^{44} - 16 q^{45} + 24 q^{46} + 24 q^{47} - 4 q^{48} - 20 q^{51} - 8 q^{52} + 24 q^{53} - 4 q^{54} - 8 q^{55} - 16 q^{58} + 12 q^{60} + 8 q^{61} - 12 q^{62} - 24 q^{63} - 4 q^{66} + 16 q^{67} + 24 q^{68} - 24 q^{69} + 8 q^{72} - 12 q^{73} + 12 q^{74} - 32 q^{75} - 32 q^{76} - 48 q^{77} + 16 q^{78} + 28 q^{81} + 24 q^{83} + 24 q^{84} + 16 q^{85} - 48 q^{87} + 16 q^{88} - 36 q^{89} - 8 q^{90} + 8 q^{93} - 8 q^{96} - 24 q^{97} - 32 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^9 + 8 * q^10 + 8 * q^13 - 12 * q^14 - 4 * q^15 + 4 * q^16 + 12 * q^17 - 16 * q^18 + 12 * q^21 - 8 * q^22 - 4 * q^24 - 16 * q^25 + 40 * q^27 - 24 * q^29 + 16 * q^30 + 16 * q^31 + 16 * q^33 + 12 * q^35 + 16 * q^39 - 4 * q^40 + 12 * q^42 - 12 * q^43 + 12 * q^44 - 16 * q^45 + 24 * q^46 + 24 * q^47 - 4 * q^48 - 20 * q^51 - 8 * q^52 + 24 * q^53 - 4 * q^54 - 8 * q^55 - 16 * q^58 + 12 * 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 - 32 * q^75 - 32 * q^76 - 48 * q^77 + 16 * q^78 + 28 * q^81 + 24 * q^83 + 24 * q^84 + 16 * q^85 - 48 * q^87 + 16 * q^88 - 36 * q^89 - 8 * q^90 + 8 * q^93 - 8 * q^96 - 24 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more