LMFDB - Embedded newform 538.2.e.a.9.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(9,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([109]))

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

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

chi := DirichletCharacter("538.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.e (of order $134$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$1452$
Relative dimension:	$22$ over $\Q(\zeta_{134})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{134}]$

Embedding invariants

Embedding label			9.12
Character	$\chi$	$=$	538.9
Dual form			538.2.e.a.299.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.833094 - 0.553131i) q^{2} +(-1.66856 + 2.94291i) q^{3} +(0.388092 - 0.921621i) q^{4} +(-0.524262 - 0.366075i) q^{5} +(0.237745 + 3.37465i) q^{6} +(-0.443772 - 3.13391i) q^{7} +(-0.186460 - 0.982463i) q^{8} +(-4.33618 - 7.24652i) q^{9} +(-0.639247 - 0.0149897i) q^{10} +(-1.09436 - 0.316273i) q^{11} +(2.06469 + 2.67990i) q^{12} +(0.0167715 - 0.715234i) q^{13} +(-2.10316 - 2.36537i) q^{14} +(1.95209 - 0.932034i) q^{15} +(-0.698769 - 0.715347i) q^{16} +(-0.925623 - 3.20282i) q^{17} +(-7.62073 - 3.63856i) q^{18} +(1.16589 + 3.42361i) q^{19} +(-0.540844 + 0.341099i) q^{20} +(9.96325 + 3.92313i) q^{21} +(-1.08665 + 0.341841i) q^{22} +(-1.91231 - 1.08423i) q^{23} +(3.20242 + 1.09056i) q^{24} +(-1.58150 - 4.31015i) q^{25} +(-0.381646 - 0.605134i) q^{26} +(18.4148 - 0.431808i) q^{27} +(-3.06050 - 0.807253i) q^{28} +(0.225686 + 0.0828093i) q^{29} +(1.11074 - 1.85623i) q^{30} +(3.32311 - 5.26910i) q^{31} +(-0.977821 - 0.209440i) q^{32} +(2.75678 - 2.69289i) q^{33} +(-2.54271 - 2.15626i) q^{34} +(-0.914592 + 1.80544i) q^{35} +(-8.36138 + 1.18400i) q^{36} +(1.45706 - 8.79852i) q^{37} +(2.86501 + 2.20730i) q^{38} +(2.07688 + 1.24277i) q^{39} +(-0.261901 + 0.583326i) q^{40} +(-3.99002 + 6.00954i) q^{41} +(10.4703 - 2.24265i) q^{42} +(-2.88697 + 7.86806i) q^{43} +(-0.716198 + 0.885845i) q^{44} +(-0.379477 + 5.38644i) q^{45} +(-2.19286 + 0.154488i) q^{46} +(0.225556 + 0.0212146i) q^{47} +(3.27114 - 0.862814i) q^{48} +(-2.89963 + 0.837999i) q^{49} +(-3.70161 - 2.71599i) q^{50} +(10.9701 + 2.62008i) q^{51} +(-0.652666 - 0.293034i) q^{52} +(-1.96812 - 9.18863i) q^{53} +(15.1024 - 10.5455i) q^{54} +(0.457953 + 0.566429i) q^{55} +(-2.99620 + 1.02034i) q^{56} +(-12.0207 - 2.28140i) q^{57} +(0.233822 - 0.0558458i) q^{58} +(-7.78112 - 3.27661i) q^{59} +(-0.101393 - 2.16080i) q^{60} +(-5.22842 + 4.87304i) q^{61} +(-0.146035 - 6.22777i) q^{62} +(-20.7856 + 16.8050i) q^{63} +(-0.930465 + 0.366380i) q^{64} +(-0.270622 + 0.368830i) q^{65} +(0.807133 - 3.76829i) q^{66} +(1.75791 + 4.17459i) q^{67} +(-3.31102 - 0.389917i) q^{68} +(6.38160 - 3.81863i) q^{69} +(0.236704 + 2.00999i) q^{70} +(-3.75510 - 3.33883i) q^{71} +(-6.31091 + 5.61133i) q^{72} +(-0.638678 + 5.42340i) q^{73} +(-3.65287 - 8.13594i) q^{74} +(15.3232 + 2.53756i) q^{75} +(3.60775 + 0.254167i) q^{76} +(-0.505523 + 3.56999i) q^{77} +(2.41765 - 0.113446i) q^{78} +(-3.57107 - 11.3518i) q^{79} +(0.104467 + 0.630831i) q^{80} +(-17.4801 + 32.5880i) q^{81} +7.21352i q^{82} +(11.2343 + 6.02603i) q^{83} +(7.48229 - 7.65980i) q^{84} +(-0.687206 + 2.01797i) q^{85} +(1.94695 + 8.15171i) q^{86} +(-0.620270 + 0.526000i) q^{87} +(-0.106672 + 1.13414i) q^{88} +(-13.4970 - 6.83724i) q^{89} +(2.66327 + 4.69731i) q^{90} +(-2.24892 + 0.264841i) q^{91} +(-1.74140 + 1.34164i) q^{92} +(9.96165 + 18.5714i) q^{93} +(0.199644 - 0.107088i) q^{94} +(0.642068 - 2.22167i) q^{95} +(2.24792 - 2.52817i) q^{96} +(8.49922 + 7.92151i) q^{97} +(-1.95214 + 2.30201i) q^{98} +(2.45348 + 9.30175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{109}{134}\right)$

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 $

$2$	0.833094	−	0.553131i	0.589087	−	0.391123i
$2$	0.833094	−	0.553131i	0.589087	−	0.391123i
$3$	−1.66856	+	2.94291i	−0.963344	+	1.69909i	−0.294557	+	0.955634i	$0.595172\pi$
$3$	−1.66856	+	2.94291i	−0.963344	+	1.69909i	−0.668787	+	0.743454i	$0.733186\pi$
$4$	0.388092	−	0.921621i	0.194046	−	0.460810i
$5$	−0.524262	−	0.366075i	−0.234457	−	0.163714i	0.449398	−	0.893331i	$-0.351638\pi$
$5$	−0.524262	−	0.366075i	−0.234457	−	0.163714i	−0.683855	+	0.729618i	$0.739698\pi$
$6$	0.237745	+	3.37465i	0.0970592	+	1.37770i
$7$	−0.443772	−	3.13391i	−0.167730	−	1.18450i	−0.877326	−	0.479896i	$-0.840675\pi$
$7$	−0.443772	−	3.13391i	−0.167730	−	1.18450i	0.709596	−	0.704609i	$-0.248878\pi$
$8$	−0.186460	−	0.982463i	−0.0659236	−	0.347353i
$9$	−4.33618	−	7.24652i	−1.44539	−	2.41551i
$10$	−0.639247	−	0.0149897i	−0.202148	−	0.00474016i
$11$	−1.09436	−	0.316273i	−0.329963	−	0.0953600i	0.108534	−	0.994093i	$-0.465384\pi$
$11$	−1.09436	−	0.316273i	−0.329963	−	0.0953600i	−0.438497	+	0.898733i	$0.644489\pi$
$12$	2.06469	+	2.67990i	0.596024	+	0.773620i
$13$	0.0167715	−	0.715234i	0.00465159	−	0.198370i	−0.992467	−	0.122512i	$-0.960905\pi$
$13$	0.0167715	−	0.715234i	0.00465159	−	0.198370i	0.997119	−	0.0758582i	$-0.0241696\pi$
$14$	−2.10316	−	2.36537i	−0.562094	−	0.632173i
$15$	1.95209	−	0.932034i	0.504027	−	0.240650i
$16$	−0.698769	−	0.715347i	−0.174692	−	0.178837i
$17$	−0.925623	−	3.20282i	−0.224497	−	0.776799i	−0.990919	−	0.134462i	$-0.957069\pi$
$17$	−0.925623	−	3.20282i	−0.224497	−	0.776799i	0.766422	−	0.642337i	$-0.222035\pi$
$18$	−7.62073	−	3.63856i	−1.79622	−	0.857616i
$19$	1.16589	+	3.42361i	0.267474	+	0.785431i	0.995047	+	0.0994013i	$0.0316928\pi$
$19$	1.16589	+	3.42361i	0.267474	+	0.785431i	−0.727574	+	0.686030i	$0.759352\pi$
$20$	−0.540844	+	0.341099i	−0.120936	+	0.0762722i
$21$	9.96325	+	3.92313i	2.17416	+	0.856097i
$22$	−1.08665	+	0.341841i	−0.231674	+	0.0728808i
$23$	−1.91231	−	1.08423i	−0.398744	−	0.226079i	0.280717	−	0.959791i	$-0.409428\pi$
$23$	−1.91231	−	1.08423i	−0.398744	−	0.226079i	−0.679460	+	0.733712i	$0.737786\pi$
$24$	3.20242	+	1.09056i	0.653690	+	0.222610i
$25$	−1.58150	−	4.31015i	−0.316299	−	0.862031i
$26$	−0.381646	−	0.605134i	−0.0748470	−	0.118677i
$27$	18.4148	−	0.431808i	3.54392	−	0.0831015i
$28$	−3.06050	−	0.807253i	−0.578379	−	0.152557i
$29$	0.225686	+	0.0828093i	0.0419088	+	0.0153773i	0.365335	−	0.930876i	$-0.380954\pi$
$29$	0.225686	+	0.0828093i	0.0419088	+	0.0153773i	−0.323427	+	0.946253i	$0.604835\pi$
$30$	1.11074	−	1.85623i	0.202792	−	0.338900i
$31$	3.32311	−	5.26910i	0.596849	−	0.946358i	−0.402670	−	0.915345i	$-0.631918\pi$
$31$	3.32311	−	5.26910i	0.596849	−	0.946358i	0.999519	−	0.0310126i	$-0.00987321\pi$
$32$	−0.977821	−	0.209440i	−0.172856	−	0.0370242i
$33$	2.75678	−	2.69289i	0.479893	−	0.468772i
$34$	−2.54271	−	2.15626i	−0.436072	−	0.369796i
$35$	−0.914592	+	1.80544i	−0.154594	+	0.305175i
$36$	−8.36138	+	1.18400i	−1.39356	+	0.197334i
$37$	1.45706	−	8.79852i	0.239539	−	1.44647i	−0.551230	−	0.834353i	$-0.685841\pi$
$37$	1.45706	−	8.79852i	0.239539	−	1.44647i	0.790769	−	0.612115i	$-0.209681\pi$
$38$	2.86501	+	2.20730i	0.464765	+	0.358072i
$39$	2.07688	+	1.24277i	0.332568	+	0.199002i
$40$	−0.261901	+	0.583326i	−0.0414102	+	0.0922319i
$41$	−3.99002	+	6.00954i	−0.623137	+	0.938533i	0.376788	+	0.926299i	$0.377028\pi$
$41$	−3.99002	+	6.00954i	−0.623137	+	0.938533i	−0.999925	+	0.0122335i	$0.996106\pi$
$42$	10.4703	−	2.24265i	1.61561	−	0.346048i
$43$	−2.88697	+	7.86806i	−0.440259	+	1.19987i	0.501966	+	0.864888i	$0.332610\pi$
$43$	−2.88697	+	7.86806i	−0.440259	+	1.19987i	−0.942225	+	0.334981i	$0.891270\pi$
$44$	−0.716198	+	0.885845i	−0.107971	+	0.133546i
$45$	−0.379477	+	5.38644i	−0.0565691	+	0.802963i
$46$	−2.19286	+	0.154488i	−0.323319	+	0.0227779i
$47$	0.225556	+	0.0212146i	0.0329008	+	0.00309447i	0.110079	−	0.993923i	$-0.464890\pi$
$47$	0.225556	+	0.0212146i	0.0329008	+	0.00309447i	−0.0771783	+	0.997017i	$0.524591\pi$
$48$	3.27114	−	0.862814i	0.472148	−	0.124536i
$49$	−2.89963	+	0.837999i	−0.414233	+	0.119714i
$50$	−3.70161	−	2.71599i	−0.523487	−	0.384099i
$51$	10.9701	+	2.62008i	1.53612	+	0.366885i
$52$	−0.652666	−	0.293034i	−0.0905085	−	0.0406365i
$53$	−1.96812	−	9.18863i	−0.270342	−	1.26216i	−0.882082	−	0.471096i	$-0.843858\pi$
$53$	−1.96812	−	9.18863i	−0.270342	−	1.26216i	0.611740	−	0.791059i	$-0.290470\pi$
$54$	15.1024	−	10.5455i	2.05517	−	1.43506i
$55$	0.457953	+	0.566429i	0.0617504	+	0.0763773i
$56$	−2.99620	+	1.02034i	−0.400384	+	0.136348i
$57$	−12.0207	−	2.28140i	−1.59219	−	0.302178i
$58$	0.233822	−	0.0558458i	0.0307023	−	0.00733292i
$59$	−7.78112	−	3.27661i	−1.01302	−	0.426578i	−0.182281	−	0.983247i	$-0.558348\pi$
$59$	−7.78112	−	3.27661i	−1.01302	−	0.426578i	−0.830735	+	0.556669i	$0.812079\pi$
$60$	−0.101393	−	2.16080i	−0.0130898	−	0.278958i
$61$	−5.22842	+	4.87304i	−0.669431	+	0.623929i	−0.940966	−	0.338500i	$-0.890081\pi$
$61$	−5.22842	+	4.87304i	−0.669431	+	0.623929i	0.271535	+	0.962428i	$0.412469\pi$
$62$	−0.146035	−	6.22777i	−0.0185465	−	0.790928i
$63$	−20.7856	+	16.8050i	−2.61874	+	2.11723i
$64$	−0.930465	+	0.366380i	−0.116308	+	0.0457975i
$65$	−0.270622	+	0.368830i	−0.0335666	+	0.0457478i
$66$	0.807133	−	3.76829i	0.0993511	−	0.463844i
$67$	1.75791	+	4.17459i	0.214763	+	0.510008i	0.993021	−	0.117937i	$-0.0376280\pi$
$67$	1.75791	+	4.17459i	0.214763	+	0.510008i	−0.778258	+	0.627944i	$0.783897\pi$
$68$	−3.31102	−	0.389917i	−0.401520	−	0.0472844i
$69$	6.38160	−	3.81863i	0.768255	−	0.459709i
$70$	0.236704	+	2.00999i	0.0282915	+	0.240240i
$71$	−3.75510	−	3.33883i	−0.445648	−	0.396246i	0.411423	−	0.911444i	$-0.365032\pi$
$71$	−3.75510	−	3.33883i	−0.445648	−	0.396246i	−0.857071	+	0.515198i	$0.827718\pi$
$72$	−6.31091	+	5.61133i	−0.743748	+	0.661301i
$73$	−0.638678	+	5.42340i	−0.0747516	+	0.634761i	0.903683	+	0.428203i	$0.140853\pi$
$73$	−0.638678	+	5.42340i	−0.0747516	+	0.634761i	−0.978434	+	0.206558i	$0.933774\pi$
$74$	−3.65287	−	8.13594i	−0.424638	−	0.945784i
$75$	15.3232	+	2.53756i	1.76937	+	0.293012i
$76$	3.60775	+	0.254167i	0.413837	+	0.0291550i
$77$	−0.505523	+	3.56999i	−0.0576097	+	0.406838i
$78$	2.41765	−	0.113446i	0.273745	−	0.0128452i
$79$	−3.57107	−	11.3518i	−0.401777	−	1.27717i	−0.909518	−	0.415664i	$-0.863549\pi$
$79$	−3.57107	−	11.3518i	−0.401777	−	1.27717i	0.507742	−	0.861509i	$-0.330480\pi$
$80$	0.104467	+	0.630831i	0.0116798	+	0.0705291i
$81$	−17.4801	+	32.5880i	−1.94223	+	3.62089i
$82$			7.21352i			0.796600i
$83$	11.2343	+	6.02603i	1.23312	+	0.661442i	0.954286	−	0.298896i	$-0.0966185\pi$
$83$	11.2343	+	6.02603i	1.23312	+	0.661442i	0.278836	+	0.960339i	$0.410051\pi$
$84$	7.48229	−	7.65980i	0.816385	−	0.835753i
$85$	−0.687206	+	2.01797i	−0.0745380	+	0.218879i
$86$	1.94695	+	8.15171i	0.209945	+	0.879022i
$87$	−0.620270	+	0.526000i	−0.0665000	+	0.0563931i
$88$	−0.106672	+	1.13414i	−0.0113712	+	0.120900i
$89$	−13.4970	−	6.83724i	−1.43068	−	0.724746i	−0.445339	−	0.895362i	$-0.646917\pi$
$89$	−13.4970	−	6.83724i	−1.43068	−	0.724746i	−0.985338	+	0.170615i	$0.945424\pi$
$90$	2.66327	+	4.69731i	0.280733	+	0.495140i
$91$	−2.24892	+	0.264841i	−0.235751	+	0.0277628i
$92$	−1.74140	+	1.34164i	−0.181554	+	0.139876i
$93$	9.96165	+	18.5714i	1.03297	+	1.92577i
$94$	0.199644	−	0.107088i	0.0205917	−	0.0110453i
$95$	0.642068	−	2.22167i	0.0658748	−	0.227939i
$96$	2.24792	−	2.52817i	0.229427	−	0.258031i
$97$	8.49922	+	7.92151i	0.862965	+	0.804307i	0.982059	−	0.188576i	$-0.0603870\pi$
$97$	8.49922	+	7.92151i	0.862965	+	0.804307i	−0.119094	+	0.992883i	$0.537999\pi$
$98$	−1.95214	+	2.30201i	−0.197196	+	0.232538i
$99$	2.45348	+	9.30175i	0.246584	+	0.934861i
$100$	−4.58609	−	0.215197i	−0.458609	−	0.0215197i
$101$	1.03903	−	5.47469i	0.103388	−	0.544752i	−0.892257	−	0.451527i	$-0.850879\pi$
$101$	1.03903	−	5.47469i	0.103388	−	0.544752i	0.995645	−	0.0932249i	$-0.0297176\pi$
$102$	10.5884	−	3.88511i	1.04840	−	0.384683i
$103$	13.3385	−	1.25455i	1.31428	−	0.123615i	0.586796	−	0.809735i	$-0.300389\pi$
$103$	13.3385	−	1.25455i	1.31428	−	0.123615i	0.727489	+	0.686120i	$0.240687\pi$
$104$	−0.705818	+	0.116885i	−0.0692112	+	0.0114615i
$105$	−3.78719	−	5.70405i	−0.369592	−	0.556658i
$106$	−6.72214	−	6.56636i	−0.652912	−	0.637782i
$107$	1.90005	+	20.2016i	0.183685	+	1.95296i	0.286058	+	0.958212i	$0.407655\pi$
$107$	1.90005	+	20.2016i	0.183685	+	1.95296i	−0.102373	+	0.994746i	$0.532643\pi$
$108$	6.74866	−	17.1390i	0.649390	−	1.64920i
$109$	−14.1241	−	15.1542i	−1.35284	−	1.45150i	−0.768190	−	0.640222i	$-0.778843\pi$
$109$	−14.1241	−	15.1542i	−1.35284	−	1.45150i	−0.584653	−	0.811283i	$-0.698769\pi$
$110$	0.694828	+	0.218581i	0.0662492	+	0.0208409i
$111$	23.4620	+	18.9689i	2.22692	+	1.80044i
$112$	−1.93174	+	2.50733i	−0.182532	+	0.236920i
$113$	0.232773	−	0.170793i	0.0218975	−	0.0160669i	−0.580569	−	0.814211i	$-0.697170\pi$
$113$	0.232773	−	0.170793i	0.0218975	−	0.0160669i	0.602466	+	0.798144i	$0.294185\pi$
$114$	−11.2763	+	4.74843i	−1.05612	+	0.444731i
$115$	0.605638	+	1.26847i	0.0564760	+	0.118286i
$116$	0.163906	−	0.175859i	0.0152182	−	0.0163281i
$117$	−5.25569	+	2.97985i	−0.485888	+	0.275487i
$118$	−8.29480	+	1.57426i	−0.763598	+	0.144922i
$119$	−9.62658	+	4.32214i	−0.882467	+	0.396210i
$120$	−1.27968	−	1.74407i	−0.116818	−	0.159211i
$121$	−8.20655	−	5.17571i	−0.746050	−	0.470519i
$122$	−1.66034	+	6.95170i	−0.150320	+	0.629378i
$123$	−11.0279	−	21.7696i	−0.994355	−	1.96289i
$124$	−3.56644	−	5.10754i	−0.320275	−	0.458671i
$125$	−1.56412	+	5.92998i	−0.139899	+	0.530393i
$126$	−8.02102	+	25.4973i	−0.714570	+	2.27148i
$127$	6.77945	+	0.959995i	0.601579	+	0.0851858i	0.434368	−	0.900735i	$-0.356972\pi$
$127$	6.77945	+	0.959995i	0.601579	+	0.0851858i	0.167211	+	0.985921i	$0.446524\pi$
$128$	−0.572509	+	0.819898i	−0.0506031	+	0.0724695i
$129$	−18.3379	−	21.6244i	−1.61456	−	1.90393i
$130$	−0.0214423	+	0.456960i	−0.00188061	+	0.0400780i
$131$	3.10243	−	6.49785i	0.271061	−	0.567720i	−0.721079	−	0.692853i	$-0.756354\pi$
$131$	3.10243	−	6.49785i	0.271061	−	0.567720i	0.992140	+	0.125133i	$0.0399357\pi$
$132$	−1.41194	−	3.58579i	−0.122894	−	0.312103i
$133$	10.2119	−	5.17310i	0.885483	−	0.448564i
$134$	3.77360	+	2.50547i	0.325989	+	0.216440i
$135$	−9.81223	−	6.51481i	−0.844502	−	0.560705i
$136$	−2.97406	+	1.50659i	−0.255024	+	0.129189i
$137$	0.442849	+	1.12467i	0.0378351	+	0.0960868i	0.948142	−	0.317848i	$-0.102960\pi$
$137$	0.442849	+	1.12467i	0.0378351	+	0.0960868i	−0.910307	+	0.413935i	$0.864154\pi$
$138$	3.20427	−	6.71114i	0.272766	−	0.571291i
$139$	0.948232	−	20.2079i	0.0804280	−	1.71401i	−0.472957	−	0.881086i	$-0.656813\pi$
$139$	0.948232	−	20.2079i	0.0804280	−	1.71401i	0.553385	−	0.832926i	$-0.313336\pi$
$140$	1.30898	+	1.54358i	0.110629	+	0.130457i
$141$	−0.438787	+	0.628393i	−0.0369525	+	0.0529203i
$142$	−4.97516	−	0.704500i	−0.417506	−	0.0591204i
$143$	−0.244564	+	0.777422i	−0.0204515	+	0.0650113i
$144$	−2.15378	+	8.16552i	−0.179482	+	0.680460i
$145$	−0.0880039	−	0.126032i	−0.00730833	−	0.0104664i
$146$	2.46777	+	4.87147i	0.204234	+	0.403166i
$147$	2.37206	−	9.93160i	0.195644	−	0.819144i
$148$	−7.54343	−	4.75749i	−0.620066	−	0.391063i
$149$	9.94245	+	13.5505i	0.814517	+	1.11010i	0.992032	+	0.125985i	$0.0402092\pi$
$149$	9.94245	+	13.5505i	0.814517	+	1.11010i	−0.177515	+	0.984118i	$0.556806\pi$
$150$	14.1693	−	6.36171i	1.15692	−	0.519432i
$151$	−1.37479	+	0.260918i	−0.111878	+	0.0212332i	−0.242097	−	0.970252i	$-0.577835\pi$
$151$	−1.37479	+	0.260918i	−0.111878	+	0.0212332i	0.130218	+	0.991485i	$0.458432\pi$
$152$	3.14618	−	1.78381i	0.255189	−	0.144686i
$153$	−19.1957	+	20.5956i	−1.55188	+	1.66505i
$154$	1.55352	+	3.25375i	0.125186	+	0.262195i
$155$	−3.67107	+	1.54588i	−0.294867	+	0.124168i
$156$	1.95138	−	1.43179i	0.156236	−	0.114635i
$157$	10.5120	−	13.6443i	0.838952	−	1.08893i	−0.155918	−	0.987770i	$-0.549834\pi$
$157$	10.5120	−	13.6443i	0.838952	−	1.08893i	0.994870	−	0.101162i	$-0.0322560\pi$
$158$	−9.25405	−	7.48182i	−0.736213	−	0.595221i
$159$	30.3252	+	9.53979i	2.40495	+	0.756555i
$160$	0.435963	+	0.467758i	0.0344659	+	0.0369795i
$161$	−2.54926	+	6.47414i	−0.200910	+	0.510234i
$162$	3.46288	+	36.8177i	0.272069	+	2.89267i
$163$	7.47929	+	7.30596i	0.585823	+	0.572247i	0.930416	−	0.366505i	$-0.119446\pi$
$163$	7.47929	+	7.30596i	0.585823	+	0.572247i	−0.344593	+	0.938752i	$0.611983\pi$
$164$	3.99002	+	6.00954i	0.311569	+	0.469267i
$165$	−2.43107	+	0.402591i	−0.189259	+	0.0313417i
$166$	12.6924	−	1.19378i	0.985121	−	0.0926553i
$167$	5.37135	−	1.97087i	0.415648	−	0.152511i	−0.128097	−	0.991762i	$-0.540887\pi$
$167$	5.37135	−	1.97087i	0.415648	−	0.152511i	0.543744	+	0.839251i	$0.317006\pi$
$168$	1.99658	−	10.5200i	0.154039	−	0.811638i
$169$	12.4744	+	0.585348i	0.959572	+	0.0450268i
$170$	0.543692	+	2.06127i	0.0416993	+	0.158092i
$171$	19.7538	−	23.2941i	1.51061	−	1.78134i
$172$	6.13096	+	5.71423i	0.467481	+	0.435706i
$173$	5.22228	−	5.87336i	0.397043	−	0.446543i	−0.514660	−	0.857394i	$-0.672082\pi$
$173$	5.22228	−	5.87336i	0.397043	−	0.446543i	0.911703	+	0.410851i	$0.134768\pi$
$174$	−0.225797	+	0.781298i	−0.0171176	+	0.0592301i
$175$	−12.8058	+	6.86898i	−0.968027	+	0.519246i
$176$	0.538463	+	1.00385i	0.0405882	+	0.0756682i
$177$	22.6260	−	17.4319i	1.70068	−	1.31026i
$178$	−15.0261	+	1.76953i	−1.12626	+	0.132632i
$179$	3.17501	+	5.59990i	0.237312	+	0.418556i	0.963013	−	0.269453i	$-0.0868430\pi$
$179$	3.17501	+	5.59990i	0.237312	+	0.418556i	−0.725702	+	0.688009i	$0.758485\pi$
$180$	4.81698	+	2.44017i	0.359037	+	0.181879i
$181$	−0.241232	+	2.56480i	−0.0179306	+	0.190640i	0.982067	+	0.188531i	$0.0603727\pi$
$181$	−0.241232	+	2.56480i	−0.0179306	+	0.190640i	−0.999998	+	0.00210871i	$0.999329\pi$
$182$	−1.72707	+	1.46458i	−0.128019	+	0.108562i
$183$	−5.61696	−	23.5177i	−0.415217	−	1.73848i
$184$	−0.708651	+	2.08094i	−0.0522424	+	0.153409i
$185$	−3.98480	+	4.07934i	−0.292968	+	0.299919i
$186$	18.5714	+	9.96165i	1.36172	+	0.730423i
$187$			3.79781i			0.277723i
$188$	0.107088	−	0.199644i	0.00781023	−	0.0145605i
$189$	−9.52521	−	57.5185i	−0.692857	−	4.18386i
$190$	−0.693973	−	2.20601i	−0.0503461	−	0.160041i
$191$	11.9310	−	0.559850i	0.863299	−	0.0405093i	0.389380	−	0.921077i	$-0.372689\pi$
$191$	11.9310	−	0.559850i	0.863299	−	0.0405093i	0.473920	+	0.880568i	$0.342839\pi$
$192$	0.474315	−	3.34960i	0.0342308	−	0.241737i
$193$	27.0126	+	1.90304i	1.94441	+	0.136984i	0.987938	−	0.154851i	$-0.0494896\pi$
$193$	27.0126	+	1.90304i	1.94441	+	0.136984i	0.956469	+	0.291835i	$0.0942657\pi$
$194$	11.4623	+	1.89818i	0.822944	+	0.136282i
$195$	−0.633883	−	1.41183i	−0.0453933	−	0.101103i
$196$	−0.353006	+	2.99758i	−0.0252147	+	0.214113i
$197$	−19.4721	+	17.3136i	−1.38733	+	1.23354i	−0.446447	+	0.894810i	$0.647311\pi$
$197$	−19.4721	+	17.3136i	−1.38733	+	1.23354i	−0.940883	+	0.338730i	$0.890003\pi$
$198$	7.18907	+	6.39214i	0.510905	+	0.454269i
$199$	1.21012	+	10.2759i	0.0857834	+	0.728438i	0.966832	+	0.255413i	$0.0822113\pi$
$199$	1.21012	+	10.2759i	0.0857834	+	0.728438i	−0.881049	+	0.473026i	$0.843162\pi$
$200$	−3.93968	+	2.35743i	−0.278577	+	0.166696i
$201$	−15.2186	−	1.79220i	−1.07344	−	0.126412i
$202$	−2.16261	−	5.13565i	−0.152161	−	0.361343i
$203$	0.159363	−	0.744026i	0.0111851	−	0.0522204i
$204$	6.67212	−	9.09341i	0.467142	−	0.636666i
$205$	4.29176	−	1.68992i	0.299750	−	0.118029i
$206$	10.4183	−	8.42312i	0.725879	−	0.586867i
$207$	0.435191	+	18.5590i	0.0302479	+	1.28994i
$208$	−0.523360	+	0.487786i	−0.0362885	+	0.0338219i
$209$	−0.193111	−	4.11542i	−0.0133578	−	0.284670i
$210$	−6.31017	−	2.65719i	−0.435443	−	0.183364i
$211$	−4.28956	+	1.02452i	−0.295305	+	0.0705305i	−0.377266	−	0.926105i	$-0.623136\pi$
$211$	−4.28956	+	1.02452i	−0.295305	+	0.0705305i	0.0819603	+	0.996636i	$0.473882\pi$
$212$	−9.23224	−	1.75217i	−0.634073	−	0.120340i
$213$	16.0915	−	5.47986i	1.10257	−	0.375474i
$214$	12.7570	+	15.7788i	0.872053	+	1.07862i
$215$	4.39383	−	3.06807i	0.299657	−	0.209241i
$216$	−3.85785	−	18.0113i	−0.262494	−	1.22551i
$217$	−17.9876	−	8.07604i	−1.22107	−	0.548238i
$218$	−20.1489	−	4.81236i	−1.36466	−	0.325934i
$219$	−14.8949	−	10.9288i	−1.00650	−	0.738502i
$220$	0.699761	−	0.202232i	0.0471779	−	0.0136345i
$221$	−2.30629	+	0.608321i	−0.155138	+	0.0409201i
$222$	30.0384	+	2.82525i	2.01604	+	0.189618i
$223$	−11.0556	+	0.778873i	−0.740339	+	0.0521572i	−0.435428	−	0.900224i	$-0.643403\pi$
$223$	−11.0556	+	0.778873i	−0.740339	+	0.0521572i	−0.304911	+	0.952381i	$0.598627\pi$
$224$	−0.222436	+	3.15734i	−0.0148621	+	0.210959i
$225$	−24.3760	+	30.1500i	−1.62506	+	2.01000i
$226$	0.0994511	−	0.271041i	0.00661539	−	0.0180294i
$227$	−3.73338	+	0.799656i	−0.247793	+	0.0530750i	−0.331649	−	0.943403i	$-0.607605\pi$
$227$	−3.73338	+	0.799656i	−0.247793	+	0.0530750i	0.0838556	+	0.996478i	$0.473277\pi$
$228$	−6.76773	+	10.1932i	−0.448204	+	0.675059i
$229$	10.2197	−	22.7621i	0.675339	−	1.50416i	−0.178672	−	0.983909i	$-0.557180\pi$
$229$	10.2197	−	22.7621i	0.675339	−	1.50416i	0.854011	−	0.520256i	$-0.174163\pi$
$230$	1.20618	+	0.721758i	0.0795334	+	0.0475913i
$231$	−9.66264	−	7.44444i	−0.635755	−	0.489808i
$232$	0.0392757	−	0.237168i	0.00257857	−	0.0155709i
$233$	4.10929	−	0.581890i	0.269209	−	0.0381209i	−0.00429887	−	0.999991i	$-0.501368\pi$
$233$	4.10929	−	0.581890i	0.269209	−	0.0381209i	0.273508	+	0.961870i	$0.411816\pi$
$234$	−2.73023	+	5.38958i	−0.178481	+	0.352328i
$235$	−0.110484	−	0.0936926i	−0.00720720	−	0.00611183i
$236$	−6.03958	+	5.89962i	−0.393143	+	0.384032i
$237$	39.3657	+	8.43177i	2.55708	+	0.547702i
$238$	−5.62914	+	8.92551i	−0.364883	+	0.578555i
$239$	−6.56148	+	10.9654i	−0.424427	+	0.709292i	−0.993604	−	0.112924i	$-0.963978\pi$
$239$	−6.56148	+	10.9654i	−0.424427	+	0.709292i	0.569177	+	0.822215i	$0.307262\pi$
$240$	−2.03079	−	0.745143i	−0.131087	−	0.0480987i
$241$	14.0366	+	3.70238i	0.904178	+	0.238491i	0.677538	−	0.735487i	$-0.263047\pi$
$241$	14.0366	+	3.70238i	0.904178	+	0.238491i	0.226640	+	0.973979i	$0.427226\pi$
$242$	−9.69967	+	0.227448i	−0.623519	+	0.0146209i
$243$	−37.2588	−	59.0772i	−2.39015	−	3.78980i
$244$	2.46198	+	6.70981i	0.157612	+	0.429551i
$245$	1.82694	+	0.622152i	0.116719	+	0.0397478i
$246$	−21.2287	−	12.0362i	−1.35349	−	0.767400i
$247$	2.46824	−	0.776466i	0.157050	−	0.0494054i
$248$	−5.79632	−	2.28236i	−0.368067	−	0.144930i
$249$	−36.4791	+	23.0066i	−2.31177	+	1.45799i
$250$	1.97699	+	5.80540i	0.125036	+	0.367165i
$251$	3.55145	+	1.69566i	0.224166	+	0.107029i	0.539610	−	0.841915i	$-0.318572\pi$
$251$	3.55145	+	1.69566i	0.224166	+	0.107029i	−0.315445	+	0.948944i	$0.602154\pi$
$252$	7.42110	+	25.6783i	0.467485	+	1.61758i
$253$	1.74985	+	1.79136i	0.110012	+	0.112622i
$254$	6.17893	−	2.95016i	0.387700	−	0.185110i
$255$	−4.79204	−	5.38948i	−0.300089	−	0.337502i
$256$	−0.0234426	+	0.999725i	−0.00146516	+	0.0624828i
$257$	−12.6617	−	16.4344i	−0.789814	−	1.02515i	−0.998883	−	0.0472512i	$-0.984954\pi$
$257$	−12.6617	−	16.4344i	−0.789814	−	1.02515i	0.209069	−	0.977901i	$-0.432957\pi$
$258$	−27.2383	−	7.87193i	−1.69578	−	0.490085i
$259$	−28.2203	−	0.661739i	−1.75353	−	0.0411185i
$260$	0.234895	+	0.392551i	0.0145676	+	0.0243450i
$261$	−0.378535	−	1.99451i	−0.0234308	−	0.123457i
$262$	−1.00954	−	7.12937i	−0.0623699	−	0.440454i
$263$	1.35087	+	19.1748i	0.0832985	+	1.18237i	0.845117	+	0.534581i	$0.179530\pi$
$263$	1.35087	+	19.1748i	0.0832985	+	1.18237i	−0.761819	+	0.647790i	$0.775693\pi$
$264$	−3.15969	−	2.20631i	−0.194466	−	0.135789i
$265$	−2.33192	+	5.53772i	−0.143249	+	0.340180i
$266$	5.64607	−	9.95819i	0.346183	−	0.610576i
$267$	42.6419	−	28.3120i	2.60964	−	1.73267i
$268$	4.52962			0.276691
$269$	−1.37412	+	16.3436i	−0.0837818	+	0.996484i
$269$	−1.37412	+	16.3436i	−0.0837818	+	0.996484i
$270$	−11.7781			−0.716789
$271$	−4.32290	+	2.87018i	−0.262597	+	0.174351i	−0.677517	−	0.735507i	$-0.736944\pi$
$271$	−4.32290	+	2.87018i	−0.262597	+	0.174351i	0.414920	+	0.909858i	$0.363810\pi$
$272$	−1.64433	+	2.90018i	−0.0997024	+	0.175849i
$273$	2.97306	−	7.06026i	0.179938	−	0.427307i
$274$	0.991023	+	0.692000i	0.0598699	+	0.0418052i
$275$	0.367544	+	5.21706i	0.0221637	+	0.314601i
$276$	−1.04268	−	7.36340i	−0.0627622	−	0.443224i
$277$	0.126091	+	0.664376i	0.00757606	+	0.0399185i	0.986048	−	0.166462i	$-0.0532344\pi$
$277$	0.126091	+	0.664376i	0.00757606	+	0.0399185i	−0.978472	+	0.206381i	$0.933831\pi$
$278$	−10.3876	−	17.3596i	−0.623010	−	1.04116i
$279$	−52.5923	−	1.23324i	−3.14862	−	0.0738320i
$280$	1.94431	+	0.561910i	0.116195	+	0.0335806i
$281$	−0.975522	−	1.26619i	−0.0581947	−	0.0755348i	0.762164	−	0.647384i	$-0.224137\pi$
$281$	−0.975522	−	1.26619i	−0.0581947	−	0.0755348i	−0.820359	+	0.571849i	$0.806226\pi$
$282$	−0.0179671	+	0.766218i	−0.00106992	+	0.0456276i
$283$	−15.5367	−	17.4737i	−0.923562	−	1.03871i	−0.999136	−	0.0415656i	$-0.986765\pi$
$283$	−15.5367	−	17.4737i	−0.923562	−	1.03871i	0.0755739	−	0.997140i	$-0.475921\pi$
$284$	−4.53446	+	2.16500i	−0.269071	+	0.128469i
$285$	5.46685	+	5.59654i	0.323828	+	0.331511i
$286$	0.226272	+	0.782942i	0.0133797	+	0.0462963i
$287$	20.6040	+	9.83749i	1.21622	+	0.580689i
$288$	2.72230	+	7.99398i	0.160413	+	0.471050i
$289$	4.97784	−	3.13942i	0.292814	−	0.184672i
$290$	−0.143028	−	0.0563185i	−0.00839887	−	0.00330714i
$291$	−37.4937	+	11.7949i	−2.19792	+	0.691428i
$292$	4.75045	+	2.69340i	0.277999	+	0.157619i
$293$	14.2664	+	4.85833i	0.833451	+	0.283827i	0.706172	−	0.708040i	$-0.250420\pi$
$293$	14.2664	+	4.85833i	0.833451	+	0.283827i	0.127279	+	0.991867i	$0.459376\pi$
$294$	−3.51733	−	9.58601i	−0.205135	−	0.559068i
$295$	2.87986	+	4.56627i	0.167672	+	0.265859i
$296$	−8.91590	+	0.209069i	−0.518226	+	0.0121519i
$297$	−20.2890	−	5.35155i	−1.17729	−	0.310528i
$298$	15.7782	+	5.78939i	0.914008	+	0.335371i
$299$	−0.807554	+	1.34956i	−0.0467021	+	0.0780473i
$300$	8.28548	−	13.1374i	0.478362	−	0.758487i
$301$	25.9389	+	5.55588i	1.49509	+	0.320235i
$302$	−1.00100	+	0.977806i	−0.0576013	+	0.0562664i
$303$	14.3778	+	12.1926i	0.825984	+	0.700448i
$304$	1.63438	−	3.22633i	0.0937383	−	0.185043i
$305$	4.52496	−	0.640750i	0.259098	−	0.0366893i
$306$	−4.59974	+	27.7758i	−0.262949	+	1.58784i
$307$	16.6849	+	12.8546i	0.952255	+	0.733651i	0.963895	−	0.266281i	$-0.0857950\pi$
$307$	16.6849	+	12.8546i	0.952255	+	0.733651i	−0.0116407	+	0.999932i	$0.503705\pi$
$308$	3.09398	+	1.85138i	0.176296	+	0.105492i
$309$	−18.5641	+	41.3474i	−1.05608	+	2.35217i
$310$	−2.20327	+	3.31844i	−0.125137	+	0.188475i
$311$	7.81236	−	1.67334i	0.442998	−	0.0948861i	0.0175032	−	0.999847i	$-0.494428\pi$
$311$	7.81236	−	1.67334i	0.442998	−	0.0948861i	0.425495	+	0.904961i	$0.360100\pi$
$312$	0.833718	−	2.27219i	0.0472000	−	0.128637i
$313$	1.11449	−	1.37848i	0.0629945	−	0.0779162i	−0.745164	−	0.666881i	$-0.767629\pi$
$313$	1.11449	−	1.37848i	0.0629945	−	0.0779162i	0.808158	+	0.588965i	$0.200465\pi$
$314$	1.21044	−	17.1815i	0.0683093	−	0.969608i
$315$	17.0490	−	1.20111i	0.960602	−	0.0676748i
$316$	−11.8479	−	1.11435i	−0.666498	−	0.0626873i
$317$	−2.73638	+	0.721762i	−0.153690	+	0.0405382i	−0.331081	−	0.943602i	$-0.607413\pi$
$317$	−2.73638	+	0.721762i	−0.153690	+	0.0405382i	0.177391	+	0.984140i	$0.443234\pi$
$318$	30.5405	−	8.82627i	1.71263	−	0.494953i
$319$	−0.220792	−	0.162002i	−0.0123620	−	0.00907036i
$320$	0.621930	+	0.148541i	0.0347669	+	0.00830371i
$321$	−62.6217	−	28.1158i	−3.49520	−	1.56927i
$322$	1.45728	+	6.80365i	0.0812109	+	0.379152i
$323$	9.88606	−	6.90312i	0.550075	−	0.384100i
$324$	23.2499	+	28.7572i	1.29166	+	1.59762i
$325$	−3.10929	+	1.05885i	−0.172473	+	0.0587345i
$326$	10.2721	+	1.94953i	0.568919	+	0.107974i
$327$	68.1642	−	16.2803i	3.76949	−	0.900302i
$328$	6.64813	+	2.79951i	0.367082	+	0.154577i
$329$	−0.0336109	−	0.716287i	−0.00185303	−	0.0394902i
$330$	−1.80263	+	1.68010i	−0.0992313	+	0.0924863i
$331$	−0.389244	−	16.5996i	−0.0213948	−	0.912395i	−0.900267	−	0.435338i	$-0.856629\pi$
$331$	−0.389244	−	16.5996i	−0.0213948	−	0.912395i	0.878872	−	0.477057i	$-0.158296\pi$
$332$	9.91364	−	8.01509i	0.544082	−	0.439885i
$333$	−70.0768	+	27.5934i	−3.84018	+	1.51211i
$334$	3.38469	−	4.61298i	0.185202	−	0.252411i
$335$	0.606611	−	2.83210i	0.0331427	−	0.154734i
$336$	−4.15562	−	9.86855i	−0.226707	−	0.538373i
$337$	4.73806	+	0.557971i	0.258099	+	0.0303946i	0.245013	−	0.969520i	$-0.421208\pi$
$337$	4.73806	+	0.557971i	0.258099	+	0.0303946i	0.0130857	+	0.999914i	$0.495835\pi$
$338$	10.7162	−	6.41235i	0.582882	−	0.348786i
$339$	0.114232	+	0.970008i	0.00620421	+	0.0526836i
$340$	1.59310	+	1.41650i	0.0863979	+	0.0768205i
$341$	−5.30317	+	4.71530i	−0.287183	+	0.255348i
$342$	3.57207	−	30.3326i	0.193156	−	1.64020i
$343$	−5.16197	−	11.4971i	−0.278720	−	0.620786i
$344$	8.26838	+	1.36926i	0.445801	+	0.0738258i
$345$	−4.74354	−	0.334184i	−0.255383	−	0.0179919i
$346$	1.10191	−	7.78167i	0.0592392	−	0.418345i
$347$	−25.2825	+	1.18635i	−1.35724	+	0.0636868i	−0.713014	−	0.701150i	$-0.752670\pi$
$347$	−25.2825	+	1.18635i	−1.35724	+	0.0636868i	−0.644224	+	0.764837i	$0.722820\pi$
$348$	0.244050	+	0.775790i	0.0130825	+	0.0415867i
$349$	0.870910	+	5.25904i	0.0466187	+	0.281510i	0.999781	−	0.0209511i	$-0.00666943\pi$
$349$	0.870910	+	5.25904i	0.0466187	+	0.281510i	−0.953162	+	0.302461i	$0.902192\pi$
$350$	−6.86898	+	12.8058i	−0.367163	+	0.684498i
$351$		−	13.1781i		−	0.703396i
$352$	1.00385	+	0.538463i	0.0535055	+	0.0287002i
$353$	17.9511	−	18.3769i	0.955439	−	0.978106i	−0.0443425	−	0.999016i	$-0.514119\pi$
$353$	17.9511	−	18.3769i	0.955439	−	0.978106i	0.999781	+	0.0209108i	$0.00665660\pi$
$354$	9.20748	−	27.0376i	0.489372	−	1.43703i
$355$	0.746389	+	3.12507i	0.0396142	+	0.165861i
$356$	−11.5394	+	9.78562i	−0.611588	+	0.518637i
$357$	3.34288	−	35.5419i	0.176924	−	1.88108i
$358$	5.74256	+	2.90904i	0.303504	+	0.153748i
$359$	−10.1388	−	17.8821i	−0.535103	−	0.943783i	−0.998343	−	0.0575500i	$-0.981671\pi$
$359$	−10.1388	−	17.8821i	−0.535103	−	0.943783i	0.463239	−	0.886233i	$-0.346687\pi$
$360$	5.36273	−	0.631534i	0.282641	−	0.0332848i
$361$	4.68926	−	3.61277i	0.246803	−	0.190146i
$362$	1.21770	+	2.27015i	0.0640010	+	0.119317i
$363$	28.9247	−	15.5151i	1.51816	−	0.814333i
$364$	−0.628705	+	2.17543i	−0.0329531	+	0.114024i
$365$	2.32021	−	2.60947i	0.121445	−	0.136586i
$366$	−17.6878	−	16.4856i	−0.924558	−	0.861714i
$367$	11.8448	−	13.9677i	0.618296	−	0.729108i	−0.360769	−	0.932655i	$-0.617486\pi$
$367$	11.8448	−	13.9677i	0.618296	−	0.729108i	0.979065	+	0.203547i	$0.0652470\pi$
$368$	0.560658	+	2.12559i	0.0292263	+	0.110804i
$369$	60.8498	+	2.85530i	3.16771	+	0.148641i
$370$	−1.06331	+	5.60259i	−0.0552787	+	0.291265i
$371$	−27.9229	+	10.2456i	−1.44968	+	0.531923i
$372$	20.9818	−	1.97344i	1.08786	−	0.102318i
$373$	32.1322	−	5.32117i	1.66374	−	0.275520i	0.744040	−	0.668135i	$-0.232907\pi$
$373$	32.1322	−	5.32117i	1.66374	−	0.275520i	0.919703	+	0.392616i	$0.128430\pi$
$374$	2.10068	+	3.16393i	0.108624	+	0.163603i
$375$	−14.8415	−	14.4976i	−0.766414	−	0.748653i
$376$	−0.0212146	−	0.225556i	−0.00109406	−	0.0116322i
$377$	0.0630131	−	0.160029i	0.00324534	−	0.00824193i
$378$	−39.7507	−	42.6496i	−2.04455	−	2.19366i
$379$	−25.3153	−	7.96375i	−1.30036	−	0.409070i	−0.430597	−	0.902544i	$-0.641697\pi$
$379$	−25.3153	−	7.96375i	−1.30036	−	0.409070i	−0.869761	+	0.493474i	$0.835727\pi$
$380$	−1.79836	−	1.45396i	−0.0922538	−	0.0745864i
$381$	−14.1371	+	18.3495i	−0.724266	+	0.940073i
$382$	9.63000	−	7.06583i	0.492714	−	0.361520i
$383$	−11.8022	+	4.96989i	−0.603067	+	0.253950i	−0.668266	−	0.743923i	$-0.732963\pi$
$383$	−11.8022	+	4.96989i	−0.603067	+	0.253950i	0.0651991	+	0.997872i	$0.479232\pi$
$384$	−1.45762	−	3.05289i	−0.0743838	−	0.155792i
$385$	1.57191	−	1.68655i	0.0801119	−	0.0859544i
$386$	23.5566	−	13.3561i	1.19900	−	0.679806i
$387$	69.5345	−	13.1969i	3.53464	−	0.670834i
$388$	10.5991	−	4.75878i	0.538088	−	0.241590i
$389$	20.8193	+	28.3746i	1.05558	+	1.43865i	0.891955	+	0.452125i	$0.149334\pi$
$389$	20.8193	+	28.3746i	1.05558	+	1.43865i	0.163626	+	0.986522i	$0.447681\pi$
$390$	−1.30901	−	0.825568i	−0.0662844	−	0.0418043i
$391$	−1.70254	+	7.12838i	−0.0861010	+	0.360498i
$392$	1.36397	+	2.69253i	0.0688908	+	0.135993i
$393$	13.9460	+	19.9722i	0.703481	+	1.00747i
$394$	−6.64543	+	25.1945i	−0.334792	+	1.26928i
$395$	−2.28342	+	7.25857i	−0.114891	+	0.365218i
$396$	9.52486	+	1.34875i	0.478642	+	0.0677775i
$397$	−7.52490	+	10.7765i	−0.377664	+	0.540858i	−0.962848	−	0.270042i	$-0.912962\pi$
$397$	−7.52490	+	10.7765i	−0.377664	+	0.540858i	0.585185	+	0.810900i	$0.301022\pi$
$398$	6.69206	+	7.89142i	0.335443	+	0.395561i
$399$	−1.81521	+	38.6843i	−0.0908744	+	1.93664i
$400$	−1.97816	+	4.14312i	−0.0989078	+	0.207156i
$401$	−9.50989	−	24.1515i	−0.474901	−	1.20607i	−0.946052	−	0.324015i	$-0.894967\pi$
$401$	−9.50989	−	24.1515i	−0.474901	−	1.20607i	0.471151	−	0.882053i	$-0.343839\pi$
$402$	−13.6699	+	6.92482i	−0.681791	+	0.345379i
$403$	−3.71291	−	2.46518i	−0.184953	−	0.122799i
$404$	−4.64235	−	3.08228i	−0.230965	−	0.153349i
$405$	21.0938	−	10.6856i	1.04816	−	0.530973i
$406$	−0.278779	−	0.707993i	−0.0138356	−	0.0351371i
$407$	−4.37729	+	9.16796i	−0.216974	+	0.454439i
$408$	0.528655	−	11.2662i	0.0261723	−	0.557761i
$409$	14.9619	+	17.6434i	0.739818	+	0.872410i	0.995540	−	0.0943407i	$-0.0300743\pi$
$409$	14.9619	+	17.6434i	0.739818	+	0.872410i	−0.255722	+	0.966750i	$0.582313\pi$
$410$	2.64069	−	3.78177i	0.130414	−	0.186768i
$411$	−4.04871	−	0.573312i	−0.199708	−	0.0282794i
$412$	4.02036	−	12.7800i	0.198069	−	0.629623i
$413$	−6.81553	+	25.8394i	−0.335370	+	1.27147i
$414$	10.6281	+	15.2207i	0.522344	+	0.748056i
$415$	−3.68372	−	7.27180i	−0.180827	−	0.356959i
$416$	−0.166198	+	0.695859i	−0.00814855	+	0.0341173i
$417$	57.8878	+	36.5087i	2.83478	+	1.78784i
$418$	−2.43725	−	3.32172i	−0.119210	−	0.162470i
$419$	−17.4277	+	7.82468i	−0.851399	+	0.382261i	−0.787961	−	0.615725i	$-0.788863\pi$
$419$	−17.4277	+	7.82468i	−0.851399	+	0.382261i	−0.0634381	+	0.997986i	$0.520207\pi$
$420$	−6.72674	+	1.27666i	−0.328231	+	0.0622945i
$421$	24.8986	−	14.1169i	1.21348	−	0.688017i	0.253300	−	0.967388i	$-0.418484\pi$
$421$	24.8986	−	14.1169i	1.21348	−	0.688017i	0.960183	+	0.279371i	$0.0901259\pi$
$422$	−3.00692	+	3.22621i	−0.146374	+	0.157049i
$423$	−0.824321	−	1.72649i	−0.0400799	−	0.0839448i
$424$	−8.66051	+	3.64692i	−0.420591	+	0.177110i
$425$	−12.3408	+	9.05483i	−0.598617	+	0.439224i
$426$	10.3746	−	13.4659i	0.502653	−	0.652427i
$427$	17.5919	+	14.2229i	0.851330	+	0.688293i
$428$	19.3556	+	6.08893i	0.935587	+	0.294320i
$429$	−1.87981	−	2.01690i	−0.0907582	−	0.0973771i
$430$	1.96343	−	4.98636i	0.0946849	−	0.240464i
$431$	−1.85576	−	19.7307i	−0.0893890	−	0.950393i	−0.919577	−	0.392910i	$-0.871469\pi$
$431$	−1.85576	−	19.7307i	−0.0893890	−	0.950393i	0.830188	−	0.557483i	$-0.188233\pi$
$432$	−13.1766	−	12.8712i	−0.633958	−	0.619267i
$433$	−7.67967	−	11.5667i	−0.369062	−	0.555859i	0.600836	−	0.799372i	$-0.294834\pi$
$433$	−7.67967	−	11.5667i	−0.369062	−	0.555859i	−0.969898	+	0.243513i	$0.921700\pi$
$434$	−19.4524	+	3.22137i	−0.933747	+	0.154631i
$435$	0.517739	−	0.0486958i	0.0248237	−	0.00233479i
$436$	−19.4478	+	7.13586i	−0.931382	+	0.341746i
$437$	1.48246	−	7.81110i	0.0709156	−	0.373656i
$438$	−18.4539	−	0.865929i	−0.881762	−	0.0413757i
$439$	1.75890	+	6.66842i	0.0839477	+	0.318266i	0.995719	−	0.0924320i	$-0.0294641\pi$
$439$	1.75890	+	6.66842i	0.0839477	+	0.318266i	−0.911771	+	0.410698i	$0.865285\pi$
$440$	0.471106	−	0.555538i	0.0224591	−	0.0264842i
$441$	18.6459	+	17.3785i	0.887901	+	0.827548i
$442$	−1.58488	+	1.78247i	−0.0753850	+	0.0847835i
$443$	5.46736	−	18.9181i	0.259762	−	0.898824i	−0.719204	−	0.694799i	$-0.755493\pi$
$443$	5.46736	−	18.9181i	0.259762	−	0.898824i	0.978966	−	0.204025i	$-0.0654023\pi$
$444$	26.5875	−	14.2615i	1.26179	−	0.676819i
$445$	4.57300	+	8.52541i	0.216781	+	0.404143i
$446$	−8.77956	+	6.76408i	−0.415724	+	0.320289i
$447$	−56.4676	+	6.64982i	−2.67082	+	0.314526i
$448$	1.56111	+	2.75340i	0.0737557	+	0.130086i
$449$	−16.3639	−	8.28955i	−0.772260	−	0.391208i	0.0212435	−	0.999774i	$-0.493237\pi$
$449$	−16.3639	−	8.28955i	−0.772260	−	0.391208i	−0.793503	+	0.608566i	$0.791745\pi$
$450$	−3.63060	+	38.6009i	−0.171148	+	1.81966i
$451$	6.26720	−	5.31469i	0.295111	−	0.250259i
$452$	−0.0670689	−	0.280812i	−0.00315466	−	0.0132083i
$453$	1.52605	−	4.48122i	0.0717003	−	0.210546i
$454$	−2.66794	+	2.73124i	−0.125213	+	0.128183i
$455$	1.27597	+	0.684428i	0.0598186	+	0.0320865i
$456$			12.2353i			0.572971i
$457$	−0.243639	+	0.454215i	−0.0113970	+	0.0212473i	−0.886864	−	0.462031i	$-0.847121\pi$
$457$	−0.243639	+	0.454215i	−0.0113970	+	0.0212473i	0.875467	+	0.483278i	$0.160554\pi$
$458$	−4.07645	−	24.6159i	−0.190480	−	1.15022i
$459$	−18.4281	−	58.5796i	−0.860152	−	2.73426i
$460$	1.40409	−	0.0658854i	0.0654661	−	0.00307192i
$461$	4.21687	−	29.7794i	0.196399	−	1.38697i	−0.608500	−	0.793554i	$-0.708228\pi$
$461$	4.21687	−	29.7794i	0.196399	−	1.38697i	0.804899	−	0.593412i	$-0.202219\pi$
$462$	−12.1676	−	0.857215i	−0.566090	−	0.0398813i
$463$	8.52470	+	1.41171i	0.396176	+	0.0656078i	0.358138	−	0.933669i	$-0.383412\pi$
$463$	8.52470	+	1.41171i	0.396176	+	0.0656078i	0.0380380	+	0.999276i	$0.487889\pi$
$464$	−0.0984649	−	0.219308i	−0.00457112	−	0.0101811i
$465$	1.57603	−	13.3830i	0.0730866	−	0.620621i
$466$	3.10157	−	2.75775i	0.143677	−	0.127750i
$467$	−3.15132	−	2.80199i	−0.145826	−	0.129661i	0.588388	−	0.808579i	$-0.299763\pi$
$467$	−3.15132	−	2.80199i	−0.145826	−	0.129661i	−0.734214	+	0.678918i	$0.762449\pi$
$468$	0.706605	+	6.00020i	0.0326628	+	0.277360i
$469$	12.3027	−	7.36169i	0.568084	−	0.339931i
$470$	−0.143868	−	0.0169424i	−0.00663614	−	0.000781496i
$471$	22.6139	+	53.7022i	1.04199	+	2.47447i
$472$	−1.76828	+	8.25562i	−0.0813915	+	0.379996i
$473$	5.64786	−	7.69745i	0.259689	−	0.353929i
$474$	37.4592	−	14.7499i	1.72056	−	0.677488i
$475$	12.9125	−	10.4396i	0.592464	−	0.479002i
$476$	0.247374	+	10.5494i	0.0113384	+	0.483533i
$477$	−58.0515	+	54.1056i	−2.65799	+	2.47733i
$478$	0.598962	+	12.7646i	0.0273959	+	0.583837i
$479$	13.1964	+	5.55696i	0.602958	+	0.253904i	0.668219	−	0.743964i	$-0.267057\pi$
$479$	13.1964	+	5.55696i	0.602958	+	0.253904i	−0.0652615	+	0.997868i	$0.520788\pi$
$480$	−2.10400	+	0.502517i	−0.0960339	+	0.0229367i
$481$	−6.26857	−	1.18970i	−0.285822	−	0.0542457i
$482$	13.7417	−	4.67966i	0.625919	−	0.213153i
$483$	−14.7992	−	18.3047i	−0.673387	−	0.832894i
$484$	−7.95493	+	5.55468i	−0.361588	+	0.252485i
$485$	−1.55594	−	7.26430i	−0.0706518	−	0.329855i
$486$	−63.7175	−	28.6079i	−2.89029	−	1.29768i
$487$	−27.0190	−	6.45321i	−1.22435	−	0.292423i	−0.431653	−	0.902040i	$-0.642070\pi$
$487$	−27.0190	−	6.45321i	−1.22435	−	0.292423i	−0.792696	+	0.609617i	$0.791323\pi$
$488$	5.76247	+	4.22810i	0.260855	+	0.191397i
$489$	−33.9804	+	9.82041i	−1.53665	+	0.444094i
$490$	1.86614	−	0.492224i	0.0843037	−	0.0222364i
$491$	10.7355	+	1.00972i	0.484484	+	0.0455680i	0.333069	−	0.942902i	$-0.391916\pi$
$491$	10.7355	+	1.00972i	0.484484	+	0.0455680i	0.151415	+	0.988470i	$0.451617\pi$
$492$	−24.3431	+	1.71498i	−1.09747	+	0.0773174i
$493$	0.0563238	−	0.799482i	0.00253670	−	0.0360068i
$494$	1.62679	−	2.01213i	0.0731927	−	0.0905300i
$495$	2.11887	−	5.77471i	0.0952363	−	0.259554i
$496$	−6.09132	+	1.30470i	−0.273508	+	0.0585830i
$497$	−8.79717	+	13.2498i	−0.394607	+	0.594335i
$498$	−17.6648	+	39.3444i	−0.791580	+	1.76307i
$499$	−7.32392	−	4.38250i	−0.327863	−	0.196187i	0.340085	−	0.940395i	$-0.389544\pi$
$499$	−7.32392	−	4.38250i	−0.327863	−	0.196187i	−0.667949	+	0.744207i	$0.732828\pi$
$500$	4.85817	+	3.74290i	0.217264	+	0.167388i
$501$	−3.16233	+	19.0959i	−0.141282	+	0.853142i
$502$	3.89662	−	0.551775i	0.173915	−	0.0246269i
$503$	−19.6205	+	38.7317i	−0.874836	+	1.72696i	−0.213389	+	0.976967i	$0.568450\pi$
$503$	−19.6205	+	38.7317i	−0.874836	+	1.72696i	−0.661447	+	0.749992i	$0.730057\pi$
$504$	20.3860	+	17.2876i	0.908063	+	0.770053i
$505$	−2.54887	+	2.48980i	−0.113423	+	0.110795i
$506$	2.44864	+	0.524477i	0.108855	+	0.0233158i
$507$	−22.5370	+	35.7344i	−1.00090	+	1.58702i
$508$	3.51580	−	5.87552i	0.155988	−	0.260684i
$509$	−4.38435	−	1.60872i	−0.194333	−	0.0713053i	0.245450	−	0.969409i	$-0.421064\pi$
$509$	−4.38435	−	1.60872i	−0.194333	−	0.0713053i	−0.439783	+	0.898104i	$0.644945\pi$
$510$	−6.97331	−	1.83932i	−0.308783	−	0.0814464i
$511$	17.2798	−	0.405195i	0.764415	−	0.0179248i
$512$	0.533449	+	0.845832i	0.0235753	+	0.0373808i
$513$	22.9480	+	62.5416i	1.01318	+	2.76128i
$514$	−19.6388	−	6.68787i	−0.866229	−	0.294989i
$515$	−7.45214	−	4.22519i	−0.328381	−	0.186184i
$516$	−27.0463	+	8.50831i	−1.19065	+	0.374557i
$517$	−0.240131	−	0.0945540i	−0.0105610	−	0.00415848i
$518$	−23.8762	+	15.0583i	−1.04906	+	0.661622i
$519$	8.57107	+	25.1687i	0.376228	+	1.10479i
$520$	0.412822	+	0.197104i	0.0181034	+	0.00864359i
$521$	9.32292	+	32.2590i	0.408444	+	1.41329i	0.855043	+	0.518558i	$0.173531\pi$
$521$	9.32292	+	32.2590i	0.408444	+	1.41329i	−0.446598	+	0.894735i	$0.647365\pi$
$522$	−1.41858	−	1.45224i	−0.0620897	−	0.0635627i
$523$	28.1917	−	13.4603i	1.23274	−	0.588577i	0.301666	−	0.953414i	$-0.402457\pi$
$523$	28.1917	−	13.4603i	1.23274	−	0.588577i	0.931072	+	0.364836i	$0.118875\pi$
$524$	−4.78452	−	5.38103i	−0.209013	−	0.235071i
$525$	1.15246	−	49.1476i	0.0502976	−	2.14498i
$526$	11.7316	+	15.2272i	0.511522	+	0.663939i
$527$	−19.9519	−	5.76615i	−0.869120	−	0.251178i
$528$	−3.85270	−	0.0903421i	−0.167667	−	0.00393163i
$529$	−9.32855	−	15.5896i	−0.405589	−	0.677810i
$530$	1.12038	+	5.90330i	0.0486661	+	0.256423i
$531$	9.99637	+	70.5940i	0.433805	+	3.06352i
$532$	−0.804482	−	11.4191i	−0.0348787	−	0.495082i
$533$	4.23131	+	2.95459i	0.183279	+	0.127978i
$534$	19.8645	−	47.1731i	0.859620	−	2.04138i
$535$	6.39916	−	11.2865i	0.276660	−	0.487956i
$536$	3.77360	−	2.50547i	0.162995	−	0.108220i
$537$	−21.7777			−0.939777
$538$	7.89536	+	14.3758i	0.340393	+	0.619784i
$539$	3.43829			0.148098
$540$	−9.81223	+	6.51481i	−0.422251	+	0.280353i
$541$	18.5155	−	32.6566i	0.796044	−	1.40402i	−0.115711	−	0.993283i	$-0.536915\pi$
$541$	18.5155	−	32.6566i	0.796044	−	1.40402i	0.911756	−	0.410733i	$-0.134727\pi$
$542$	−2.01380	+	4.78226i	−0.0865000	+	0.205416i
$543$	−7.14546	−	4.98945i	−0.306641	−	0.214118i
$544$	0.234293	+	3.32565i	0.0100453	+	0.142586i
$545$	1.85716	+	13.1152i	0.0795521	+	0.561794i
$546$	−1.42842	−	7.52635i	−0.0611305	−	0.322098i
$547$	−2.17834	−	3.64039i	−0.0931391	−	0.155652i	0.807999	−	0.589184i	$-0.200551\pi$
$547$	−2.17834	−	3.64039i	−0.0931391	−	0.155652i	−0.901138	+	0.433532i	$0.857267\pi$
$548$	1.20838	+	0.0283354i	0.0516195	+	0.00121043i
$549$	57.9840	+	16.7575i	2.47470	+	0.715192i
$550$	3.19192	+	4.14300i	0.136104	+	0.176658i
$551$	−0.0203821	+	0.869207i	−0.000868305	+	0.0370295i
$552$	−4.94158	−	5.55766i	−0.210328	−	0.236550i
$553$	−33.9906	+	16.2290i	−1.44543	+	0.690127i
$554$	0.472532	+	0.483743i	0.0200760	+	0.0205523i
$555$	−5.35622	−	18.5335i	−0.227359	−	0.786704i
$556$	−18.2560	−	8.71643i	−0.774227	−	0.369659i
$557$	−10.5420	−	30.9563i	−0.446679	−	1.31166i	−0.905957	−	0.423370i	$-0.860847\pi$
$557$	−10.5420	−	30.9563i	−0.446679	−	1.31166i	0.459278	−	0.888292i	$-0.348108\pi$
$558$	−44.4964	+	28.0630i	−1.88368	+	1.18800i
$559$	5.57909	+	2.19682i	0.235970	+	0.0929157i
$560$	1.93060	−	0.607335i	0.0815829	−	0.0256646i
$561$	−11.1766	−	6.33687i	−0.471876	−	0.267543i
$562$	−1.51307	−	0.515268i	−0.0638251	−	0.0217353i
$563$	2.85707	+	7.78655i	0.120411	+	0.328164i	0.984554	−	0.175083i	$-0.0560193\pi$
$563$	2.85707	+	7.78655i	0.120411	+	0.328164i	−0.864143	+	0.503247i	$0.832139\pi$
$564$	0.408851	+	0.648270i	0.0172157	+	0.0272971i
$565$	−0.184557	+	0.00432768i	−0.00776438	+	0.000182067i
$566$	−22.6088	−	5.96343i	−0.950319	−	0.250662i
$567$	109.885	+	40.3193i	4.61474	+	1.69325i
$568$	−2.58010	+	4.31180i	−0.108259	+	0.180919i
$569$	1.58075	−	2.50642i	0.0662684	−	0.105075i	−0.811065	−	0.584957i	$-0.801112\pi$
$569$	1.58075	−	2.50642i	0.0662684	−	0.105075i	0.877333	+	0.479882i	$0.159321\pi$
$570$	7.65002	+	1.63856i	0.320424	+	0.0686319i
$571$	−26.9407	+	26.3163i	−1.12743	+	1.10130i	−0.133528	+	0.991045i	$0.542631\pi$
$571$	−26.9407	+	26.3163i	−1.12743	+	1.10130i	−0.993903	+	0.110259i	$0.964832\pi$
$572$	0.621575	+	0.527106i	0.0259894	+	0.0220394i
$573$	−18.2601	+	36.0461i	−0.762825	+	1.50585i
$574$	22.6065	−	3.20116i	0.943577	−	0.133614i
$575$	−1.64891	+	9.95705i	−0.0687644	+	0.415238i
$576$	6.68965	+	5.15395i	0.278735	+	0.214748i
$577$	26.3635	+	15.7754i	1.09752	+	0.656739i	0.943515	−	0.331331i	$-0.107498\pi$
$577$	26.3635	+	15.7754i	1.09752	+	0.656739i	0.154010	+	0.988069i	$0.450781\pi$
$578$	2.41050	−	5.36883i	0.100263	−	0.223314i
$579$	−50.6726	+	76.3201i	−2.10588	+	3.17176i
$580$	−0.150307	+	0.0321944i	−0.00624116	+	0.00133680i
$581$	13.8995	−	37.8813i	0.576650	−	1.57158i
$582$	−24.7117	+	30.5652i	−1.02433	+	1.26697i
$583$	−0.752281	+	10.6782i	−0.0311563	+	0.442244i
$584$	5.44737	−	0.383769i	0.225414	−	0.0158805i
$585$	3.84620	+	0.361754i	0.159021	+	0.0149567i
$586$	14.5725	−	3.84373i	0.601986	−	0.158783i
$587$	18.2886	−	5.28544i	0.754851	−	0.218154i	0.122110	−	0.992517i	$-0.461034\pi$
$587$	18.2886	−	5.28544i	0.754851	−	0.218154i	0.632742	+	0.774363i	$0.281930\pi$
$588$	−8.23259	−	6.04051i	−0.339506	−	0.249106i
$589$	21.9137	+	5.23386i	0.902940	+	0.215658i
$590$	4.92494	+	2.21120i	0.202757	+	0.0910336i
$591$	−18.4618	−	86.1933i	−0.759418	−	3.54552i
$592$	−7.31214	+	5.10584i	−0.300527	+	0.209849i
$593$	−11.4156	−	14.1197i	−0.468784	−	0.579826i	0.487183	−	0.873300i	$-0.338025\pi$
$593$	−11.4156	−	14.1197i	−0.468784	−	0.579826i	−0.955967	+	0.293474i	$0.905189\pi$
$594$	−19.8628	+	6.76415i	−0.814980	+	0.277536i
$595$	6.62907	+	1.25812i	0.271766	+	0.0515780i
$596$	16.3470	−	3.90432i	0.669601	−	0.159927i
$597$	−32.2601	−	13.5847i	−1.32032	−	0.555983i
$598$	0.0737172	+	1.57100i	0.00301452	+	0.0642429i
$599$	21.9929	−	20.4980i	0.898606	−	0.837526i	−0.0887485	−	0.996054i	$-0.528287\pi$
$599$	21.9929	−	20.4980i	0.898606	−	0.837526i	0.987354	+	0.158528i	$0.0506748\pi$
$600$	−0.364108	−	15.5276i	−0.0148646	−	0.633913i
$601$	−0.310072	+	0.250690i	−0.0126481	+	0.0102259i	−0.635016	−	0.772499i	$-0.719007\pi$
$601$	−0.310072	+	0.250690i	−0.0126481	+	0.0102259i	0.622368	+	0.782725i	$0.286171\pi$
$602$	24.6827	−	9.71906i	1.00599	−	0.396119i
$603$	22.6287	−	30.8405i	0.921510	−	1.25592i
$604$	−0.293075	+	1.36829i	−0.0119251	+	0.0556750i
$605$	2.40768	+	5.71764i	0.0978861	+	0.232455i
$606$	18.7222	+	2.20479i	0.760537	+	0.0895635i
$607$	−23.9305	+	14.3196i	−0.971308	+	0.581213i	−0.908979	−	0.416843i	$-0.863137\pi$
$607$	−23.9305	+	14.3196i	−0.971308	+	0.581213i	−0.0623295	+	0.998056i	$0.519853\pi$
$608$	−0.422991	−	3.59187i	−0.0171546	−	0.145669i
$609$	1.92369	+	1.71044i	0.0779519	+	0.0693107i
$610$	3.41530	−	3.03670i	0.138281	−	0.122952i
$611$	0.0189564	−	0.160970i	0.000766893	−	0.00651214i
$612$	11.5316	+	25.6841i	0.466139	+	1.03822i
$613$	−7.06487	−	1.16996i	−0.285347	−	0.0472542i	0.0189862	−	0.999820i	$-0.493956\pi$
$613$	−7.06487	−	1.16996i	−0.285347	−	0.0472542i	−0.304334	+	0.952566i	$0.598434\pi$
$614$	21.0103	+	1.48019i	0.847908	+	0.0597354i
$615$	−2.18777	+	15.4500i	−0.0882196	+	0.623004i
$616$	3.60164	−	0.169003i	0.145114	−	0.00680931i
$617$	−13.4190	−	42.6565i	−0.540228	−	1.71728i	−0.685666	−	0.727917i	$-0.740489\pi$
$617$	−13.4190	−	42.6565i	−0.540228	−	1.71728i	0.145437	−	0.989367i	$-0.453541\pi$
$618$	7.40485	+	44.7146i	0.297867	+	1.79869i
$619$	−3.53669	+	6.59343i	−0.142152	+	0.265012i	−0.942286	−	0.334808i	$-0.891328\pi$
$619$	−3.53669	+	6.59343i	−0.142152	+	0.265012i	0.800135	+	0.599820i	$0.204761\pi$
$620$			3.98327i			0.159972i
$621$	−35.6829	−	19.1402i	−1.43190	−	0.768069i
$622$	5.58286	−	5.71531i	0.223852	−	0.229163i
$623$	−15.4377	+	45.3324i	−0.618498	+	1.81621i
$624$	−0.562252	−	2.35410i	−0.0225081	−	0.0942395i
$625$	−14.5171	+	12.3108i	−0.580686	+	0.492431i
$626$	0.165993	−	1.76486i	0.00663443	−	0.0705380i
$627$	12.4335	+	6.29852i	0.496547	+	0.251539i
$628$	−8.49521	−	14.9833i	−0.338996	−	0.597901i
$629$	−29.5288	+	3.47742i	−1.17739	+	0.138654i
$630$	13.5391	−	10.4310i	0.539409	−	0.415580i
$631$	−4.21508	−	7.85814i	−0.167800	−	0.312828i	0.783337	−	0.621597i	$-0.213516\pi$
$631$	−4.21508	−	7.85814i	−0.167800	−	0.312828i	−0.951137	+	0.308769i	$0.900083\pi$
$632$	−10.4868	+	5.62509i	−0.417143	+	0.223754i
$633$	4.14234	−	14.3332i	0.164643	−	0.569695i
$634$	−1.88043	+	2.11487i	−0.0746815	+	0.0839923i
$635$	−3.20278	−	2.98508i	−0.127098	−	0.118459i
$636$	20.5610	−	24.2460i	0.815298	−	0.961417i
$637$	0.550735	+	2.08797i	0.0218209	+	0.0827284i
$638$	−0.273549	−	0.0128360i	−0.0108299	−	0.000508180i
$639$	−7.91212	+	41.6892i	−0.312999	+	1.64920i
$640$	0.600289	−	0.220260i	0.0237285	−	0.00870654i
$641$	−43.8863	+	4.12772i	−1.73341	+	0.163035i	−0.912786	−	0.408439i	$-0.866073\pi$
$641$	−43.8863	+	4.12772i	−1.73341	+	0.163035i	−0.820620	+	0.571474i	$0.806372\pi$
$642$	−67.7215	+	11.2148i	−2.67275	+	0.442615i
$643$	7.24619	+	10.9138i	0.285762	+	0.430398i	0.947701	−	0.319160i	$-0.103401\pi$
$643$	7.24619	+	10.9138i	0.285762	+	0.430398i	−0.661939	+	0.749558i	$0.730266\pi$
$644$	4.97736	+	4.86201i	0.196135	+	0.191590i
$645$	1.69768	+	18.0499i	0.0668461	+	0.710714i
$646$	4.41769	−	11.2192i	0.173812	−	0.441415i
$647$	20.6501	+	22.1561i	0.811840	+	0.871047i	0.993676	−	0.112282i	$-0.0358160\pi$
$647$	20.6501	+	22.1561i	0.811840	+	0.871047i	−0.181836	+	0.983329i	$0.558204\pi$
$648$	35.2759	+	11.0972i	1.38577	+	0.435939i
$649$	7.47907	+	6.04676i	0.293579	+	0.237356i
$650$	−2.00465	+	2.60197i	−0.0786289	+	0.102058i
$651$	53.7804	−	39.4603i	2.10782	−	1.54657i
$652$	9.63597	−	4.05768i	0.377374	−	0.158911i
$653$	−18.1522	−	38.0187i	−0.710352	−	1.48779i	−0.866037	−	0.499980i	$-0.833341\pi$
$653$	−18.1522	−	38.0187i	−0.710352	−	1.48779i	0.155685	−	0.987807i	$-0.450241\pi$
$654$	47.7821	−	51.2667i	1.86843	−	2.00469i
$655$	−4.00519	+	2.27085i	−0.156496	+	0.0887294i
$656$	7.08702	−	1.34503i	0.276701	−	0.0525147i
$657$	42.0702	−	18.8887i	1.64131	−	0.736917i
$658$	−0.424201	−	0.578143i	−0.0165371	−	0.0225384i
$659$	−0.159303	−	0.100469i	−0.00620555	−	0.00391372i	0.530343	−	0.847783i	$-0.322063\pi$
$659$	−0.159303	−	0.100469i	−0.00620555	−	0.00391372i	−0.536548	+	0.843870i	$0.680272\pi$
$660$	−0.572442	+	2.39677i	−0.0222823	+	0.0932941i
$661$	3.15307	+	6.22429i	0.122640	+	0.242097i	0.945138	−	0.326672i	$-0.105927\pi$
$661$	3.15307	+	6.22429i	0.122640	+	0.242097i	−0.822497	+	0.568769i	$0.807420\pi$
$662$	−9.50602	−	13.6137i	−0.369462	−	0.529112i
$663$	2.05796	−	7.80223i	0.0799245	−	0.303013i
$664$	3.82560	−	12.1609i	0.148462	−	0.471933i
$665$	−7.24744	−	1.02626i	−0.281044	−	0.0397968i
$666$	−43.1178	+	61.7496i	−1.67078	+	2.39275i
$667$	−0.341796	−	0.403053i	−0.0132344	−	0.0156063i
$668$	0.268180	−	5.71523i	0.0103762	−	0.221129i
$669$	16.1548	−	33.8353i	0.624582	−	1.30815i
$670$	−1.06116	−	2.69495i	−0.0409963	−	0.104115i
$671$	7.26301	−	3.67927i	0.280385	−	0.142036i
$672$	−8.92062	−	5.92283i	−0.344120	−	0.228478i
$673$	−6.80805	−	4.52019i	−0.262431	−	0.174241i	0.415012	−	0.909816i	$-0.363777\pi$
$673$	−6.80805	−	4.52019i	−0.262431	−	0.174241i	−0.677443	+	0.735576i	$0.736912\pi$
$674$	4.25589	−	2.15593i	0.163931	−	0.0830433i
$675$	−30.9840	−	78.6876i	−1.19258	−	3.02869i
$676$	5.38069	−	11.2695i	0.206950	−	0.433443i
$677$	0.570516	−	12.1583i	0.0219267	−	0.467283i	−0.960229	−	0.279214i	$-0.909926\pi$
$677$	0.570516	−	12.1583i	0.0219267	−	0.467283i	0.982156	−	0.188070i	$-0.0602230\pi$
$678$	0.631708	+	0.744923i	0.0242606	+	0.0286086i
$679$	21.0535	−	30.1511i	0.807961	−	1.15709i
$680$	2.11071	+	0.298884i	0.0809421	+	0.0114617i
$681$	3.87606	−	12.3213i	0.148531	−	0.472152i
$682$	−1.80986	+	6.86164i	−0.0693032	+	0.262746i
$683$	23.7081	+	33.9527i	0.907165	+	1.29916i	0.953859	+	0.300255i	$0.0970719\pi$
$683$	23.7081	+	33.9527i	0.907165	+	1.29916i	−0.0466936	+	0.998909i	$0.514868\pi$
$684$	−13.8020	−	27.2457i	−0.527734	−	1.04177i
$685$	0.179544	−	0.751736i	0.00686002	−	0.0287223i
$686$	−10.6598	−	6.72294i	−0.406994	−	0.256683i
$687$	49.9346	+	68.0557i	1.90512	+	2.59649i
$688$	7.64572	−	3.43277i	0.291490	−	0.130873i
$689$	−6.60503	+	1.25356i	−0.251632	+	0.0477568i
$690$	−4.13666	+	2.34539i	−0.157480	+	0.0892875i
$691$	2.80378	−	3.00826i	0.106661	−	0.114440i	−0.675960	−	0.736939i	$-0.736271\pi$
$691$	2.80378	−	3.00826i	0.106661	−	0.114440i	0.782620	+	0.622499i	$0.213883\pi$
$692$	−3.38629	−	7.09237i	−0.128727	−	0.269611i
$693$	28.0620	−	11.8168i	1.06599	−	0.448884i
$694$	−20.4065	+	14.9729i	−0.774621	+	0.568364i
$695$	−7.89473	+	10.2471i	−0.299464	+	0.388695i
$696$	0.632431	+	0.511314i	0.0239722	+	0.0193813i
$697$	22.9408	+	7.21678i	0.868944	+	0.273355i
$698$	3.63449	+	3.89955i	0.137567	+	0.147600i
$699$	−5.14415	+	13.0642i	−0.194570	+	0.494133i
$700$	1.36077	+	14.4679i	0.0514324	+	0.546834i
$701$	11.7935	+	11.5202i	0.445434	+	0.435112i	0.886756	−	0.462237i	$-0.152953\pi$
$701$	11.7935	+	11.5202i	0.445434	+	0.435112i	−0.441322	+	0.897349i	$0.645490\pi$
$702$	−7.28923	−	10.9786i	−0.275114	−	0.414361i
$703$	31.8215	−	5.26972i	1.20017	−	0.198751i
$704$	1.13414	−	0.106672i	0.0427447	−	0.00402034i
$705$	0.460078	−	0.168813i	0.0173276	−	0.00635788i
$706$	4.79007	−	25.2390i	0.180277	−	0.949883i
$707$	−17.6182	−	0.826716i	−0.662602	−	0.0310918i
$708$	−7.28462	−	27.6178i	−0.273773	−	1.03794i
$709$	−0.663480	+	0.782390i	−0.0249175	+	0.0293833i	−0.775002	−	0.631958i	$-0.782251\pi$
$709$	−0.663480	+	0.782390i	−0.0249175	+	0.0293833i	0.750085	+	0.661342i	$0.230013\pi$
$710$	2.35039	+	2.19063i	0.0882084	+	0.0822127i
$711$	−66.7760	+	75.1012i	−2.50429	+	2.81651i
$712$	−4.20069	+	14.5352i	−0.157427	+	0.544728i
$713$	−12.0678	+	6.47310i	−0.451941	+	0.242420i
$714$	−16.8744	−	31.4588i	−0.631508	−	1.17732i
$715$	0.412810	−	0.318044i	0.0154382	−	0.0118942i
$716$	6.39318	−	0.752883i	0.238924	−	0.0281366i
$717$	−21.3219	−	37.6062i	−0.796280	−	1.40443i
$718$	−18.3377	−	9.28944i	−0.684357	−	0.346679i
$719$	−1.48080	+	15.7440i	−0.0552245	+	0.587153i	0.923726	+	0.383054i	$0.125128\pi$
$719$	−1.48080	+	15.7440i	−0.0552245	+	0.587153i	−0.978950	+	0.204099i	$0.934574\pi$
$720$	4.11834	−	3.49242i	0.153482	−	0.130155i
$721$	−9.85092	−	41.2450i	−0.366867	−	1.53604i
$722$	1.90826	−	5.60355i	0.0710179	−	0.208543i
$723$	−34.3167	+	35.1308i	−1.27625	+	1.30653i
$724$	2.27015	+	1.21770i	0.0843696	+	0.0452555i
$725$		−	1.10370i		−	0.0409905i
$726$	15.5151	−	28.9247i	0.575821	−	1.07350i
$727$	−2.64787	−	15.9893i	−0.0982041	−	0.593011i	−0.990055	−	0.140681i	$-0.955071\pi$
$727$	−2.64787	−	15.9893i	−0.0982041	−	0.593011i	0.891851	−	0.452330i	$-0.149407\pi$
$728$	0.679530	+	2.16010i	0.0251850	+	0.0800585i
$729$	125.209	−	5.87527i	4.63736	−	0.217602i
$730$	0.489568	−	3.45732i	0.0181197	−	0.127961i
$731$	27.8723	+	1.96361i	1.03089	+	0.0726268i
$732$	−23.8543	−	3.95033i	−0.881681	−	0.146008i
$733$	−15.6492	−	34.8551i	−0.578017	−	1.28740i	−0.935449	−	0.353463i	$-0.885004\pi$
$733$	−15.6492	−	34.8551i	−0.578017	−	1.28740i	0.357431	−	0.933939i	$-0.383653\pi$
$734$	2.14190	−	18.1882i	0.0790590	−	0.671337i
$735$	−4.87929	+	4.33840i	−0.179975	+	0.160024i
$736$	1.64281	+	1.46070i	0.0605549	+	0.0538422i
$737$	−0.603479	−	5.12450i	−0.0222295	−	0.188763i
$738$	52.2729	−	31.2792i	1.92419	−	1.15140i
$739$	−38.3658	−	4.51809i	−1.41131	−	0.166201i	−0.623357	−	0.781937i	$-0.714232\pi$
$739$	−38.3658	−	4.51809i	−1.41131	−	0.166201i	−0.787952	+	0.615736i	$0.788859\pi$
$740$	2.21313	+	5.25563i	0.0813563	+	0.193201i
$741$	−1.83334	+	8.55938i	−0.0673494	+	0.314437i
$742$	−17.5953	+	23.9805i	−0.645942	+	0.880353i
$743$	5.19911	−	2.04720i	0.190737	−	0.0751046i	−0.269082	−	0.963117i	$-0.586720\pi$
$743$	5.19911	−	2.04720i	0.190737	−	0.0751046i	0.459819	+	0.888013i	$0.347914\pi$
$744$	16.3883	−	13.2498i	0.600823	−	0.485760i
$745$	−0.251929	−	10.7437i	−0.00922998	−	0.393619i
$746$	23.8258	−	22.2064i	0.872326	−	0.813033i
$747$	−5.04616	−	107.539i	−0.184629	−	3.93466i
$748$	3.50014	+	1.47390i	0.127978	+	0.0538910i
$749$	62.4666	−	14.9195i	2.28248	−	0.545146i
$750$	−20.3835	−	3.86855i	−0.744299	−	0.141259i
$751$	−31.8262	+	10.8382i	−1.16135	+	0.395492i	−0.835265	−	0.549847i	$-0.814686\pi$
$751$	−31.8262	+	10.8382i	−1.16135	+	0.395492i	−0.326088	+	0.945339i	$0.605731\pi$
$752$	−0.142436	−	0.176175i	−0.00519411	−	0.00642445i
$753$	−10.9160	+	7.62229i	−0.397801	+	0.277772i
$754$	−0.0360213	−	0.168174i	−0.00131182	−	0.00612454i
$755$	0.816263	+	0.366485i	0.0297068	+	0.0133378i
$756$	−56.7069	−	13.5438i	−2.06241	−	0.492585i
$757$	3.15549	+	2.31528i	0.114688	+	0.0841502i	0.647418	−	0.762135i	$-0.275849\pi$
$757$	3.15549	+	2.31528i	0.114688	+	0.0841502i	−0.532730	+	0.846285i	$0.678834\pi$
$758$	−25.4950	+	7.36811i	−0.926020	+	0.267622i
$759$	−8.19153	+	2.16064i	−0.297334	+	0.0784264i
$760$	−2.30243	−	0.216555i	−0.0835179	−	0.00785526i
$761$	5.34558	−	0.376598i	0.193777	−	0.0136517i	0.0269447	−	0.999637i	$-0.491422\pi$
$761$	5.34558	−	0.376598i	0.193777	−	0.0136517i	0.166832	+	0.985985i	$0.446646\pi$
$762$	−1.62786	+	23.1065i	−0.0589713	+	0.837061i
$763$	−41.2238	+	50.9886i	−1.49240	+	1.84591i
$764$	4.11437	−	11.2132i	0.148853	−	0.405678i
$765$	17.6031	−	3.77042i	0.636441	−	0.136320i
$766$	−7.08338	+	10.6686i	−0.255933	+	0.385471i
$767$	−2.47404	+	5.51037i	−0.0893325	+	0.198968i
$768$	−2.90298	−	1.73709i	−0.104752	−	0.0626819i
$769$	20.3597	+	15.6859i	0.734191	+	0.565647i	0.907918	−	0.419147i	$-0.137671\pi$
$769$	20.3597	+	15.6859i	0.734191	+	0.565647i	−0.173728	+	0.984794i	$0.555581\pi$
$770$	0.376667	−	2.27452i	0.0135741	−	0.0819682i
$771$	69.4918	−	9.84029i	2.50269	−	0.354389i
$772$	12.2372	−	24.1568i	0.440428	−	0.869422i
$773$	15.4424	+	13.0955i	0.555426	+	0.471011i	0.880082	−	0.474821i	$-0.157487\pi$
$773$	15.4424	+	13.0955i	0.555426	+	0.471011i	−0.324656	+	0.945832i	$0.605249\pi$
$774$	50.6292	−	49.4559i	1.81983	−	1.77766i
$775$	−27.9661	−	5.99008i	−1.00457	−	0.215170i
$776$	6.19782	−	9.82721i	0.222489	−	0.352776i
$777$	49.0348	−	81.9457i	1.75911	−	2.93979i
$778$	33.0393	+	12.1229i	1.18452	+	0.434626i
$779$	−25.2263	−	6.65383i	−0.903826	−	0.238398i
$780$	−1.54718	+	0.0362798i	−0.0553979	+	0.00129903i
$781$	3.05346	+	4.84153i	0.109261	+	0.173244i
$782$	2.52455	+	6.88034i	0.0902779	+	0.246040i
$783$	4.19171	+	1.42746i	0.149799	+	0.0510133i
$784$	2.62563	+	1.48867i	0.0937726	+	0.0531669i
$785$	−10.5059	+	3.30497i	−0.374971	+	0.117960i
$786$	22.6656	+	8.92479i	0.808454	+	0.318337i
$787$	32.6664	−	20.6020i	1.16443	−	0.734383i	0.195254	−	0.980753i	$-0.437447\pi$
$787$	32.6664	−	20.6020i	1.16443	−	0.734383i	0.969176	+	0.246370i	$0.0792379\pi$
$788$	8.39957	+	24.6652i	0.299222	+	0.878660i
$789$	−58.6838	−	28.0189i	−2.08920	−	0.997498i
$790$	2.11264	+	7.31011i	0.0751642	+	0.260082i
$791$	−0.638547	−	0.653696i	−0.0227041	−	0.0232428i
$792$	8.68115	−	4.14486i	0.308471	−	0.147281i
$793$	3.39767	+	3.82128i	0.120655	+	0.135697i
$794$	−0.308123	+	13.1401i	−0.0109349	+	0.466325i
$795$	−12.4061	−	16.1026i	−0.439997	−	0.571102i
$796$	9.94011	+	2.87271i	0.352318	+	0.101821i
$797$	−28.0640	−	0.658072i	−0.994077	−	0.0233101i	−0.476698	−	0.879067i	$-0.658167\pi$
$797$	−28.0640	−	0.658072i	−0.994077	−	0.0233101i	−0.517378	+	0.855757i	$0.673092\pi$
$798$	19.8852	+	33.2317i	0.703930	+	1.17639i
$799$	−0.140833	−	0.742054i	−0.00498232	−	0.0262520i
$800$	0.643700	+	4.54579i	0.0227582	+	0.160718i
$801$	8.97916	+	127.454i	0.317263	+	4.50336i
$802$	−21.2816	−	14.8602i	−0.751478	−	0.524733i
$803$	2.41422	−	5.73317i	0.0851961	−	0.202319i
$804$	−7.55795	+	13.3303i	−0.266548	+	0.470122i
$805$	3.70650	−	2.46092i	0.130637	−	0.0867362i
$806$	−4.45677			−0.156983
$807$	−45.8048	−	31.3141i	−1.61240	−	1.10231i
$808$	−5.57242			−0.196037
$809$	21.3998	−	14.2083i	0.752376	−	0.499538i	−0.117340	−	0.993092i	$-0.537437\pi$
$809$	21.3998	−	14.2083i	0.752376	−	0.499538i	0.869715	+	0.493553i	$0.164302\pi$
$810$	11.6626	−	20.5698i	0.409782	−	0.722748i
$811$	−12.1441	+	28.8393i	−0.426439	+	1.01268i	0.556847	+	0.830615i	$0.312011\pi$
$811$	−12.1441	+	28.8393i	−0.426439	+	1.01268i	−0.983286	+	0.182070i	$0.941720\pi$
$812$	−0.623862	−	0.435623i	−0.0218933	−	0.0152874i
$813$	−1.23365	−	17.5110i	−0.0432661	−	0.614136i
$814$	1.42439	+	10.0590i	0.0499248	+	0.352567i
$815$	−1.24657	−	6.56821i	−0.0436655	−	0.230075i
$816$	−5.79128	−	9.67824i	−0.202735	−	0.338806i
$817$	−30.3031	−	0.710578i	−1.06017	−	0.0248600i
$818$	22.2238	+	6.42272i	0.777036	+	0.224565i
$819$	11.6709	+	15.1484i	0.407814	+	0.529329i
$820$	0.108129	−	4.61122i	0.00377601	−	0.161031i
$821$	21.6269	+	24.3232i	0.754782	+	0.848884i	0.992474	−	0.122457i	$-0.0390773\pi$
$821$	21.6269	+	24.3232i	0.754782	+	0.848884i	−0.237691	+	0.971341i	$0.576391\pi$
$822$	−3.69007	+	1.76185i	−0.128706	+	0.0614514i
$823$	20.6750	+	21.1654i	0.720684	+	0.737781i	0.973237	−	0.229802i	$-0.0738078\pi$
$823$	20.6750	+	21.1654i	0.720684	+	0.737781i	−0.252554	+	0.967583i	$0.581270\pi$
$824$	−3.71966	−	12.8707i	−0.129580	−	0.448372i
$825$	−15.9666	−	7.62334i	−0.555886	−	0.265410i
$826$	8.61457	+	25.2965i	0.299739	+	0.880178i
$827$	−23.9676	+	15.1159i	−0.833434	+	0.525630i	−0.880933	−	0.473241i	$-0.843084\pi$
$827$	−23.9676	+	15.1159i	−0.833434	+	0.525630i	0.0474989	+	0.998871i	$0.484875\pi$
$828$	17.2733	+	6.80152i	0.600288	+	0.236369i
$829$	−49.3662	+	15.5298i	−1.71456	+	0.539371i	−0.988887	−	0.148672i	$-0.952500\pi$
$829$	−49.3662	+	15.5298i	−1.71456	+	0.539371i	−0.725671	+	0.688042i	$0.758470\pi$
$830$	−7.09115	−	4.02052i	−0.246137	−	0.139554i
$831$	−2.16559	−	0.737477i	−0.0751233	−	0.0255828i
$832$	0.246442	+	0.671645i	0.00854385	+	0.0232851i
$833$	5.36793	+	8.51134i	0.185988	+	0.294900i
$834$	68.4200	−	1.60438i	2.36919	−	0.0555552i
$835$	−3.53748	−	0.933065i	−0.122420	−	0.0322901i
$836$	−3.86780	−	1.41919i	−0.133771	−	0.0490836i
$837$	58.9191	−	98.4641i	2.03654	−	3.40342i
$838$	−10.1908	+	16.1585i	−0.352037	+	0.558186i
$839$	−1.38061	−	0.295715i	−0.0476641	−	0.0102092i	0.185546	−	0.982636i	$-0.440595\pi$
$839$	−1.38061	−	0.295715i	−0.0476641	−	0.0102092i	−0.233210	+	0.972426i	$0.574923\pi$
$840$	−4.89785	+	4.78435i	−0.168992	+	0.165076i
$841$	−22.0738	−	18.7189i	−0.761165	−	0.645481i
$842$	12.9344	−	25.5329i	0.445747	−	0.879922i
$843$	5.35401	−	0.758147i	0.184402	−	0.0261120i
$844$	−0.720528	+	4.35095i	−0.0248016	+	0.149766i
$845$	−6.32558	−	4.87346i	−0.217607	−	0.167652i
$846$	−1.64171	−	0.982370i	−0.0564432	−	0.0337746i
$847$	−12.5783	+	28.0154i	−0.432197	+	0.962620i
$848$	−5.19780	+	7.82862i	−0.178493	+	0.268836i
$849$	77.3475	−	16.5671i	2.65456	−	0.568582i
$850$	−5.27254	+	14.3696i	−0.180847	+	0.492873i
$851$	−12.3260	+	15.2457i	−0.422530	+	0.522616i
$852$	1.19462	−	16.9569i	0.0409271	−	0.580935i
$853$	37.8527	−	2.66673i	1.29605	−	0.0913072i	0.594598	−	0.804023i	$-0.297311\pi$
$853$	37.8527	−	2.66673i	1.29605	−	0.0913072i	0.701453	+	0.712716i	$0.252535\pi$
$854$	22.5228	+	2.11838i	0.770714	+	0.0724893i
$855$	−18.8835	+	4.98082i	−0.645803	+	0.170341i
$856$	19.4930	−	5.63351i	0.666257	−	0.192550i
$857$	23.2208	+	17.0378i	0.793208	+	0.582002i	0.911654	−	0.410959i	$-0.134806\pi$
$857$	23.2208	+	17.0378i	0.793208	+	0.582002i	−0.118446	+	0.992961i	$0.537791\pi$
$858$	−2.68167	−	0.640489i	−0.0915508	−	0.0218659i
$859$	11.1233	+	4.99414i	0.379522	+	0.170398i	0.590392	−	0.807116i	$-0.298973\pi$
$859$	11.1233	+	4.99414i	0.379522	+	0.170398i	−0.210870	+	0.977514i	$0.567630\pi$
$860$	−1.12239	−	5.24014i	−0.0382732	−	0.178687i
$861$	−63.3298	+	44.2212i	−2.15827	+	1.50705i
$862$	−12.4597	−	15.4110i	−0.424378	−	0.524902i
$863$	−12.2520	+	4.17236i	−0.417064	+	0.142029i	−0.522977	−	0.852347i	$-0.675179\pi$
$863$	−12.2520	+	4.17236i	−0.417064	+	0.142029i	0.105913	+	0.994375i	$0.466224\pi$
$864$	−18.0968	−	3.43456i	−0.615665	−	0.116846i
$865$	−4.88793	+	1.16743i	−0.166195	+	0.0396938i
$866$	−12.7958	−	5.38827i	−0.434818	−	0.183101i
$867$	0.933204	+	19.8876i	0.0316933	+	0.675419i
$868$	−14.4239	+	13.4435i	−0.489578	+	0.456301i
$869$	0.317790	+	13.5524i	0.0107803	+	0.459733i
$870$	0.404390	−	0.326946i	0.0137101	−	0.0110845i
$871$	3.01529	−	1.18730i	0.102169	−	0.0402302i
$872$	−12.2548	+	16.7020i	−0.415000	+	0.565603i
$873$	20.5492	−	95.9389i	0.695486	−	3.24704i
$874$	−3.08554	−	7.32738i	−0.104370	−	0.247852i
$875$	19.2781	+	2.27026i	0.651719	+	0.0767487i
$876$	−15.8528	+	9.48604i	−0.535617	+	0.320503i
$877$	1.64245	+	13.9470i	0.0554617	+	0.470958i	0.992547	+	0.121859i	$0.0388856\pi$
$877$	1.64245	+	13.9470i	0.0554617	+	0.470958i	−0.937086	+	0.349099i	$0.886488\pi$
$878$	5.15384	+	4.58252i	0.173934	+	0.154652i
$879$	−38.1020	+	33.8782i	−1.28515	+	1.14268i
$880$	0.0851900	−	0.723399i	0.00287175	−	0.0243858i
$881$	−17.6085	−	39.2189i	−0.593245	−	1.32132i	−0.925721	−	0.378206i	$-0.876541\pi$
$881$	−17.6085	−	39.2189i	−0.593245	−	1.32132i	0.332477	−	0.943112i	$-0.392116\pi$
$882$	25.1464	+	4.16431i	0.846723	+	0.140219i
$883$	−48.6400	−	3.42671i	−1.63687	−	0.115318i	−0.778257	−	0.627946i	$-0.783896\pi$
$883$	−48.6400	−	3.42671i	−1.63687	−	0.115318i	−0.858610	+	0.512629i	$0.828672\pi$
$884$	−0.334413	+	2.36161i	−0.0112475	+	0.0794296i
$885$	−18.2433	+	0.856047i	−0.613243	+	0.0287757i
$886$	−5.90934	−	18.7847i	−0.198528	−	0.631084i
$887$	−2.28813	−	13.8170i	−0.0768280	−	0.463930i	−0.997320	−	0.0731681i	$-0.976689\pi$
$887$	−2.28813	−	13.8170i	−0.0768280	−	0.463930i	0.920492	−	0.390762i	$-0.127789\pi$
$888$	14.2615	−	26.5875i	0.478583	−	0.892219i
$889$		−	21.6722i		−	0.726862i
$890$	8.52541	+	4.57300i	0.285773	+	0.153287i
$891$	29.4363	−	30.1347i	0.986154	−	1.00955i
$892$	−3.57277	+	10.4914i	−0.119625	+	0.351277i
$893$	0.190343	+	0.796952i	0.00636960	+	0.0266690i
$894$	−43.3646	+	36.7739i	−1.45033	+	1.22990i
$895$	0.385446	−	4.09811i	0.0128841	−	0.136985i
$896$	2.82355	+	1.43034i	0.0943281	+	0.0477843i
$897$	−2.62419	−	4.62839i	−0.0876191	−	0.154537i
$898$	−18.2179	+	2.14540i	−0.607938	+	0.0715929i
$899$	1.18631	−	0.913975i	0.0395656	−	0.0304828i
$900$	18.3267	+	34.1664i	0.610890	+	1.13888i
$901$	−27.6078	+	14.8087i	−0.919750	+	0.493351i
$902$	2.28145	−	7.89422i	0.0759638	−	0.262849i
$903$	−59.6311	+	67.0655i	−1.98440	+	2.23180i
$904$	−0.211201	−	0.196845i	−0.00702443	−	0.00654696i
$905$	1.06538	−	1.25632i	0.0354144	−	0.0417614i
$906$	−1.20736	−	4.57739i	−0.0401118	−	0.152074i
$907$	28.8402	+	1.35329i	0.957624	+	0.0449354i	0.519948	−	0.854198i	$-0.325951\pi$
$907$	28.8402	+	1.35329i	0.957624	+	0.0449354i	0.437675	+	0.899133i	$0.355802\pi$
$908$	−0.711916	+	3.75110i	−0.0236258	+	0.124485i
$909$	−44.1779	+	16.2099i	−1.46529	+	0.537648i
$910$	1.44158	−	0.135588i	0.0477881	−	0.00449469i
$911$	−5.53238	+	0.916176i	−0.183296	+	0.0303543i	−0.254319	−	0.967120i	$-0.581851\pi$
$911$	−5.53238	+	0.916176i	−0.183296	+	0.0303543i	0.0710229	+	0.997475i	$0.477374\pi$
$912$	6.76773	+	10.1932i	0.224102	+	0.337530i
$913$	−10.3885	−	10.1478i	−0.343810	−	0.335842i
$914$	0.0482660	+	0.513169i	0.00159650	+	0.0169741i
$915$	−5.66450	+	14.3857i	−0.187263	+	0.475575i
$916$	−17.0119	−	18.2525i	−0.562088	−	0.603080i
$917$	−21.7404	−	6.83916i	−0.717932	−	0.225849i
$918$	−47.7546	−	38.6091i	−1.57614	−	1.27429i
$919$	14.1332	−	18.3445i	0.466212	−	0.605128i	−0.498998	−	0.866603i	$-0.666299\pi$
$919$	14.1332	−	18.3445i	0.466212	−	0.605128i	0.965210	+	0.261475i	$0.0842090\pi$
$920$	1.13330	−	0.831536i	0.0373637	−	0.0274149i
$921$	−65.6696	+	27.6533i	−2.16389	+	0.911206i
$922$	−12.9589	−	27.1416i	−0.426778	−	0.893859i
$923$	−2.45103	+	2.62978i	−0.0806765	+	0.0865601i
$924$	−10.6109	+	6.01616i	−0.349074	+	0.197917i
$925$	−40.2273	+	7.63468i	−1.32267	+	0.251027i
$926$	7.88274	−	3.53919i	0.259043	−	0.116305i
$927$	−66.9295	−	91.2180i	−2.19825	−	2.99599i
$928$	−0.203337	−	0.128240i	−0.00667485	−	0.00420970i
$929$	2.23334	−	9.35079i	0.0732734	−	0.306789i	−0.923834	−	0.382793i	$-0.874962\pi$
$929$	2.23334	−	9.35079i	0.0732734	−	0.306789i	0.997108	+	0.0760035i	$0.0242160\pi$
$930$	−6.08957	−	12.0210i	−0.199685	−	0.394186i
$931$	−6.24964	−	8.95020i	−0.204824	−	0.293331i
$932$	1.05850	−	4.01304i	0.0346723	−	0.131451i
$933$	−8.11093	+	25.7831i	−0.265540	+	0.844101i
$934$	−4.17522	−	0.591226i	−0.136617	−	0.0193455i
$935$	1.39028	−	1.99104i	0.0454671	−	0.0651141i
$936$	3.90757	+	4.60789i	0.127723	+	0.150614i
$937$	−2.36505	+	50.4019i	−0.0772629	+	1.64656i	0.527066	+	0.849824i	$0.323292\pi$
$937$	−2.36505	+	50.4019i	−0.0772629	+	1.64656i	−0.604329	+	0.796735i	$0.706559\pi$
$938$	6.17730	−	12.9380i	0.201696	−	0.422440i
$939$	2.19714	+	5.57991i	0.0717011	+	0.182093i
$940$	−0.129227	+	0.0654633i	−0.00421492	+	0.00213518i
$941$	15.1299	+	10.0455i	0.493221	+	0.327473i	0.774952	−	0.632021i	$-0.217774\pi$
$941$	15.1299	+	10.0455i	0.493221	+	0.327473i	−0.281731	+	0.959493i	$0.590909\pi$
$942$	48.5439	+	32.2306i	1.58164	+	1.05013i
$943$	14.1459	−	7.16598i	0.460654	−	0.233356i
$944$	3.09330	+	7.85579i	0.100678	+	0.255684i
$945$	−16.0624	+	33.6417i	−0.522510	+	1.09436i
$946$	0.447499	−	9.53671i	0.0145494	−	0.310065i
$947$	−9.01341	−	10.6288i	−0.292897	−	0.345390i	0.596428	−	0.802667i	$-0.296586\pi$
$947$	−9.01341	−	10.6288i	−0.292897	−	0.345390i	−0.889325	+	0.457277i	$0.848825\pi$
$948$	23.0484	−	33.0080i	0.748578	−	1.07205i
$949$	3.86829	+	0.547763i	0.125570	+	0.0177812i
$950$	4.98282	−	15.8395i	0.161664	−	0.513900i
$951$	2.44173	−	9.25721i	0.0791786	−	0.300186i
$952$	6.04131	+	8.65185i	0.195800	+	0.280408i
$953$	−19.9339	−	39.3502i	−0.645721	−	1.27468i	−0.947028	−	0.321151i	$-0.895930\pi$
$953$	−19.9339	−	39.3502i	−0.645721	−	1.27468i	0.301307	−	0.953527i	$-0.402577\pi$
$954$	−18.4348	+	77.1851i	−0.596850	+	2.49896i
$955$	−6.45993	−	4.07415i	−0.209038	−	0.131836i
$956$	7.55947	+	10.3028i	0.244491	+	0.333216i
$957$	0.845161	−	0.379460i	0.0273202	−	0.0122662i
$958$	14.0675	−	2.66986i	0.454502	−	0.0862592i
$959$	3.32808	−	1.88694i	0.107469	−	0.0609325i
$960$	−1.47487	+	1.58243i	−0.0476012	+	0.0510728i
$961$	−3.36352	−	7.04469i	−0.108501	−	0.227248i
$962$	−5.88037	+	2.47621i	−0.189591	+	0.0798361i
$963$	138.152	−	101.366i	4.45189	−	3.26649i
$964$	8.85969	−	11.4996i	0.285351	−	0.370377i
$965$	−13.4650	−	10.8863i	−0.433453	−	0.350443i
$966$	−22.4541	−	7.06366i	−0.722447	−	0.227270i
$967$	−13.8634	−	14.8745i	−0.445817	−	0.478330i	0.468422	−	0.883505i	$-0.344823\pi$
$967$	−13.8634	−	14.8745i	−0.445817	−	0.478330i	−0.914239	+	0.405175i	$0.867211\pi$
$968$	−3.55474	+	9.02769i	−0.114254	+	0.290161i
$969$	3.81975	+	40.6120i	0.122708	+	1.30465i
$970$	−5.31436	−	5.19120i	−0.170634	−	0.166679i
$971$	−21.2978	−	32.0775i	−0.683480	−	1.02942i	−0.996813	−	0.0797743i	$-0.974580\pi$
$971$	−21.2978	−	32.0775i	−0.683480	−	1.02942i	0.313333	−	0.949643i	$-0.398554\pi$
$972$	−68.9066	+	11.4111i	−2.21018	+	0.366011i
$973$	−63.7504	+	5.99603i	−2.04374	+	0.192224i
$974$	−26.0789	+	9.56894i	−0.835621	+	0.306609i
$975$	2.07194	−	10.9171i	0.0663553	−	0.349628i
$976$	7.13937	+	0.335007i	0.228526	+	0.0107233i
$977$	−8.89573	−	33.7259i	−0.284600	−	1.07899i	−0.944734	−	0.327839i	$-0.893680\pi$
$977$	−8.89573	−	33.7259i	−0.284600	−	1.07899i	0.660134	−	0.751148i	$-0.270500\pi$
$978$	−22.8769	+	26.9769i	−0.731523	+	0.862628i
$979$	12.6082	+	11.7512i	0.402959	+	0.375569i
$980$	1.28241	−	1.44229i	0.0409650	−	0.0460722i
$981$	−48.5702	+	168.062i	−1.55073	+	5.36580i
$982$	9.50215	−	5.09692i	0.303226	−	0.162649i
$983$	−22.4216	−	41.8004i	−0.715138	−	1.33323i	−0.933930	−	0.357455i	$-0.883645\pi$
$983$	−22.4216	−	41.8004i	−0.715138	−	1.33323i	0.218793	−	0.975771i	$-0.429788\pi$
$984$	−19.3315	+	14.8937i	−0.616266	+	0.474793i
$985$	16.5465	−	1.94858i	0.527217	−	0.0620869i
$986$	−0.395295	−	0.697198i	−0.0125888	−	0.0222033i
$987$	2.16405	+	1.09625i	0.0688824	+	0.0348941i
$988$	0.242297	−	2.57612i	0.00770848	−	0.0819573i
$989$	14.0516	−	11.9160i	0.446815	−	0.378907i
$990$	−1.42895	−	5.98289i	−0.0454150	−	0.190149i
$991$	2.77038	−	8.13516i	0.0880040	−	0.258422i	−0.893754	−	0.448558i	$-0.851938\pi$
$991$	2.77038	−	8.13516i	0.0880040	−	0.258422i	0.981758	+	0.190136i	$0.0608930\pi$
$992$	−4.35297	+	4.45624i	−0.138207	+	0.141486i
$993$	49.5005	+	26.5519i	1.57085	+	0.842599i
$994$			15.9043i			0.504454i
$995$	3.12732	−	5.83025i	0.0991428	−	0.184831i
$996$	7.04615	+	42.5486i	0.223266	+	1.34820i
$997$	−4.17909	−	13.2845i	−0.132353	−	0.420726i	0.864252	−	0.503060i	$-0.167792\pi$
$997$	−4.17909	−	13.2845i	−0.132353	−	0.420726i	−0.996605	+	0.0823341i	$0.973763\pi$
$998$	−8.52561	+	0.400054i	−0.269873	+	0.0126635i
$999$	23.0321	−	162.652i	0.728703	−	5.14608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.e.a.9.12	✓	1452
269.30	even	134	inner	538.2.e.a.299.12	yes	1452

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.e.a.9.12	✓	1452	1.1	even	1	trivial
538.2.e.a.299.12	yes	1452	269.30	even	134	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(0.833094 - 0.553131i) q^{2} +(-1.66856 + 2.94291i) q^{3} +(0.388092 - 0.921621i) q^{4} +(-0.524262 - 0.366075i) q^{5} +(0.237745 + 3.37465i) q^{6} +(-0.443772 - 3.13391i) q^{7} +(-0.186460 - 0.982463i) q^{8} +(-4.33618 - 7.24652i) q^{9} +(-0.639247 - 0.0149897i) q^{10} +(-1.09436 - 0.316273i) q^{11} +(2.06469 + 2.67990i) q^{12} +(0.0167715 - 0.715234i) q^{13} +(-2.10316 - 2.36537i) q^{14} +(1.95209 - 0.932034i) q^{15} +(-0.698769 - 0.715347i) q^{16} +(-0.925623 - 3.20282i) q^{17} +(-7.62073 - 3.63856i) q^{18} +(1.16589 + 3.42361i) q^{19} +(-0.540844 + 0.341099i) q^{20} +(9.96325 + 3.92313i) q^{21} +(-1.08665 + 0.341841i) q^{22} +(-1.91231 - 1.08423i) q^{23} +(3.20242 + 1.09056i) q^{24} +(-1.58150 - 4.31015i) q^{25} +(-0.381646 - 0.605134i) q^{26} +(18.4148 - 0.431808i) q^{27} +(-3.06050 - 0.807253i) q^{28} +(0.225686 + 0.0828093i) q^{29} +(1.11074 - 1.85623i) q^{30} +(3.32311 - 5.26910i) q^{31} +(-0.977821 - 0.209440i) q^{32} +(2.75678 - 2.69289i) q^{33} +(-2.54271 - 2.15626i) q^{34} +(-0.914592 + 1.80544i) q^{35} +(-8.36138 + 1.18400i) q^{36} +(1.45706 - 8.79852i) q^{37} +(2.86501 + 2.20730i) q^{38} +(2.07688 + 1.24277i) q^{39} +(-0.261901 + 0.583326i) q^{40} +(-3.99002 + 6.00954i) q^{41} +(10.4703 - 2.24265i) q^{42} +(-2.88697 + 7.86806i) q^{43} +(-0.716198 + 0.885845i) q^{44} +(-0.379477 + 5.38644i) q^{45} +(-2.19286 + 0.154488i) q^{46} +(0.225556 + 0.0212146i) q^{47} +(3.27114 - 0.862814i) q^{48} +(-2.89963 + 0.837999i) q^{49} +(-3.70161 - 2.71599i) q^{50} +(10.9701 + 2.62008i) q^{51} +(-0.652666 - 0.293034i) q^{52} +(-1.96812 - 9.18863i) q^{53} +(15.1024 - 10.5455i) q^{54} +(0.457953 + 0.566429i) q^{55} +(-2.99620 + 1.02034i) q^{56} +(-12.0207 - 2.28140i) q^{57} +(0.233822 - 0.0558458i) q^{58} +(-7.78112 - 3.27661i) q^{59} +(-0.101393 - 2.16080i) q^{60} +(-5.22842 + 4.87304i) q^{61} +(-0.146035 - 6.22777i) q^{62} +(-20.7856 + 16.8050i) q^{63} +(-0.930465 + 0.366380i) q^{64} +(-0.270622 + 0.368830i) q^{65} +(0.807133 - 3.76829i) q^{66} +(1.75791 + 4.17459i) q^{67} +(-3.31102 - 0.389917i) q^{68} +(6.38160 - 3.81863i) q^{69} +(0.236704 + 2.00999i) q^{70} +(-3.75510 - 3.33883i) q^{71} +(-6.31091 + 5.61133i) q^{72} +(-0.638678 + 5.42340i) q^{73} +(-3.65287 - 8.13594i) q^{74} +(15.3232 + 2.53756i) q^{75} +(3.60775 + 0.254167i) q^{76} +(-0.505523 + 3.56999i) q^{77} +(2.41765 - 0.113446i) q^{78} +(-3.57107 - 11.3518i) q^{79} +(0.104467 + 0.630831i) q^{80} +(-17.4801 + 32.5880i) q^{81} +7.21352i q^{82} +(11.2343 + 6.02603i) q^{83} +(7.48229 - 7.65980i) q^{84} +(-0.687206 + 2.01797i) q^{85} +(1.94695 + 8.15171i) q^{86} +(-0.620270 + 0.526000i) q^{87} +(-0.106672 + 1.13414i) q^{88} +(-13.4970 - 6.83724i) q^{89} +(2.66327 + 4.69731i) q^{90} +(-2.24892 + 0.264841i) q^{91} +(-1.74140 + 1.34164i) q^{92} +(9.96165 + 18.5714i) q^{93} +(0.199644 - 0.107088i) q^{94} +(0.642068 - 2.22167i) q^{95} +(2.24792 - 2.52817i) q^{96} +(8.49922 + 7.92151i) q^{97} +(-1.95214 + 2.30201i) q^{98} +(2.45348 + 9.30175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38}+ \cdots + 18 q^{99}+O(q^{100}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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