LMFDB - Embedded newform 507.2.p.b.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.283929 + 0.107680i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.42800 - 1.26510i) q^{4} +(-0.879635 - 0.106807i) q^{5} +(-0.0726712 - 0.294839i) q^{6} +(-0.935242 - 1.78196i) q^{7} +(-0.551463 - 1.05073i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(0.283929 + 0.107680i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.42800 - 1.26510i) q^{4} +(-0.879635 - 0.106807i) q^{5} +(-0.0726712 - 0.294839i) q^{6} +(-0.935242 - 1.78196i) q^{7} +(-0.551463 - 1.05073i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-0.238253 - 0.125045i) q^{10} +(1.28346 - 0.486753i) q^{11} +(-0.229959 + 1.89388i) q^{12} +(-1.51352 + 3.27250i) q^{13} +(-0.0736614 - 0.606657i) q^{14} +(0.411789 + 0.784599i) q^{15} +(0.416483 + 3.43004i) q^{16} +(-1.89179 + 0.992889i) q^{17} +(-0.201365 + 0.227295i) q^{18} +5.96298i q^{19} +(1.12100 + 1.26535i) q^{20} +(-0.935242 + 1.78196i) q^{21} +0.416826 q^{22} -6.76093 q^{23} +(-0.551463 + 1.05073i) q^{24} +(-4.09236 - 1.00868i) q^{25} +(-0.782117 + 0.766182i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.918822 + 3.72781i) q^{28} +(2.38525 - 6.28938i) q^{29} +(0.0324333 + 0.267112i) q^{30} +(-1.20949 - 4.90708i) q^{31} +(-0.819064 + 3.32307i) q^{32} +(-1.12968 - 0.779761i) q^{33} +(-0.644050 + 0.0782018i) q^{34} +(0.632347 + 1.66736i) q^{35} +(1.68926 - 0.886594i) q^{36} +(0.879880 + 3.56981i) q^{37} +(-0.642095 + 1.69307i) q^{38} +(3.55299 - 0.613385i) q^{39} +(0.372862 + 0.983155i) q^{40} +(-6.99800 + 4.83037i) q^{41} +(-0.457424 + 0.405242i) q^{42} +(6.85629 + 1.68992i) q^{43} +(-2.44857 - 0.928622i) q^{44} +(0.411789 - 0.784599i) q^{45} +(-1.91963 - 0.728018i) q^{46} +(-5.18060 - 5.84769i) q^{47} +(2.58628 - 2.29125i) q^{48} +(1.67577 - 2.42777i) q^{49} +(-1.05333 - 0.727059i) q^{50} +(1.89179 + 0.992889i) q^{51} +(6.30134 - 2.75837i) q^{52} +(-6.51757 + 3.42069i) q^{53} +(0.301448 + 0.0366025i) q^{54} +(-1.18097 + 0.291082i) q^{55} +(-1.35659 + 1.96537i) q^{56} +(4.90744 - 3.38736i) q^{57} +(1.35448 - 1.52890i) q^{58} +(4.76639 + 0.578745i) q^{59} +(0.404559 - 1.64136i) q^{60} +(-3.26130 - 1.71166i) q^{61} +(0.184987 - 1.52350i) q^{62} +(1.99780 - 0.242577i) q^{63} +(3.33521 - 4.83189i) q^{64} +(1.68087 - 2.71695i) q^{65} +(-0.236784 - 0.343041i) q^{66} +(0.679073 + 0.766515i) q^{67} +(3.95758 + 0.975456i) q^{68} +(3.84065 + 5.56414i) q^{69} +0.541504i q^{70} +(2.56180 - 1.76828i) q^{71} +(1.17800 - 0.143035i) q^{72} +(-11.2091 + 4.25106i) q^{73} +(-0.134574 + 1.10832i) q^{74} +(1.49460 + 3.94094i) q^{75} +(7.54375 - 8.51514i) q^{76} +(-2.06772 - 1.83184i) q^{77} +(1.07485 + 0.208429i) q^{78} +(4.31523 - 3.82296i) q^{79} -3.06167i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-2.50707 + 0.617938i) q^{82} +(-12.3030 - 8.49214i) q^{83} +(3.58988 - 1.36146i) q^{84} +(1.77013 - 0.671323i) q^{85} +(1.76473 + 1.21811i) q^{86} +(-6.53103 + 1.60976i) q^{87} +(-1.21923 - 1.08014i) q^{88} -7.72878i q^{89} +(0.201405 - 0.178429i) q^{90} +(7.24696 - 0.363548i) q^{91} +(9.65461 + 8.55324i) q^{92} +(-3.35138 + 3.78293i) q^{93} +(-0.841244 - 2.21818i) q^{94} +(0.636888 - 5.24525i) q^{95} +(3.20012 - 1.21364i) q^{96} +(9.07801 - 1.10227i) q^{97} +(0.737222 - 0.508867i) q^{98} +1.37266i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	0.283929	+	0.107680i	0.200768	+	0.0761414i	0.452939	−	0.891541i	$-0.350375\pi$
$2$	0.283929	+	0.107680i	0.200768	+	0.0761414i	−0.252171	+	0.967683i	$0.581145\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	−1.42800	−	1.26510i	−0.714000	−	0.632549i
$5$	−0.879635	−	0.106807i	−0.393385	−	0.0477656i	−0.0785455	−	0.996911i	$-0.525028\pi$
$5$	−0.879635	−	0.106807i	−0.393385	−	0.0477656i	−0.314839	+	0.949145i	$0.601951\pi$
$6$	−0.0726712	−	0.294839i	−0.0296679	−	0.120367i
$7$	−0.935242	−	1.78196i	−0.353488	−	0.673516i	0.642174	−	0.766559i	$-0.278033\pi$
$7$	−0.935242	−	1.78196i	−0.353488	−	0.673516i	−0.995662	+	0.0930434i	$0.970340\pi$
$8$	−0.551463	−	1.05073i	−0.194972	−	0.371488i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−0.238253	−	0.125045i	−0.0753423	−	0.0395427i
$11$	1.28346	−	0.486753i	0.386978	−	0.146762i	−0.153440	−	0.988158i	$-0.549035\pi$
$11$	1.28346	−	0.486753i	0.386978	−	0.146762i	0.540418	+	0.841396i	$0.318266\pi$
$12$	−0.229959	+	1.89388i	−0.0663833	+	0.546716i
$13$	−1.51352	+	3.27250i	−0.419776	+	0.907628i
$13$	−1.51352	+	3.27250i	−0.419776	+	0.907628i
$14$	−0.0736614	−	0.606657i	−0.0196868	−	0.162136i
$15$	0.411789	+	0.784599i	0.106324	+	0.202583i
$16$	0.416483	+	3.43004i	0.104121	+	0.857511i
$17$	−1.89179	+	0.992889i	−0.458827	+	0.240811i	−0.678268	−	0.734815i	$-0.737269\pi$
$17$	−1.89179	+	0.992889i	−0.458827	+	0.240811i	0.219441	+	0.975626i	$0.429577\pi$
$18$	−0.201365	+	0.227295i	−0.0474623	+	0.0535739i
$19$			5.96298i			1.36800i	0.729481	+	0.684001i	$0.239761\pi$
$19$			5.96298i			1.36800i	−0.729481	+	0.684001i	$0.760239\pi$
$20$	1.12100	+	1.26535i	0.250663	+	0.282940i
$21$	−0.935242	+	1.78196i	−0.204087	+	0.388855i
$22$	0.416826			0.0888676
$23$	−6.76093			−1.40975			−0.704876	−	0.709331i	$-0.748997\pi$
$23$	−6.76093			−1.40975			−0.704876	+	0.709331i	$0.748997\pi$
$24$	−0.551463	+	1.05073i	−0.112567	+	0.214478i
$25$	−4.09236	−	1.00868i	−0.818472	−	0.201735i
$26$	−0.782117	+	0.766182i	−0.153386	+	0.150261i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	−0.918822	+	3.72781i	−0.173641	+	0.704489i
$29$	2.38525	−	6.28938i	0.442929	−	1.16791i	−0.508777	−	0.860898i	$-0.669902\pi$
$29$	2.38525	−	6.28938i	0.442929	−	1.16791i	0.951706	−	0.307010i	$-0.0993286\pi$
$30$	0.0324333	+	0.267112i	0.00592148	+	0.0487678i
$31$	−1.20949	−	4.90708i	−0.217230	−	0.881338i	−0.973797	−	0.227421i	$-0.926971\pi$
$31$	−1.20949	−	4.90708i	−0.217230	−	0.881338i	0.756566	−	0.653917i	$-0.226875\pi$
$32$	−0.819064	+	3.32307i	−0.144791	+	0.587442i
$33$	−1.12968	−	0.779761i	−0.196652	−	0.135739i
$34$	−0.644050	+	0.0782018i	−0.110454	+	0.0134115i
$35$	0.632347	+	1.66736i	0.106886	+	0.281835i
$36$	1.68926	−	0.886594i	0.281544	−	0.147766i
$37$	0.879880	+	3.56981i	0.144651	+	0.586874i	0.997865	+	0.0653119i	$0.0208042\pi$
$37$	0.879880	+	3.56981i	0.144651	+	0.586874i	−0.853214	+	0.521562i	$0.825350\pi$
$38$	−0.642095	+	1.69307i	−0.104162	+	0.274651i
$39$	3.55299	−	0.613385i	0.568934	−	0.0982203i
$40$	0.372862	+	0.983155i	0.0589546	+	0.155450i
$41$	−6.99800	+	4.83037i	−1.09290	+	0.754378i	−0.971218	−	0.238191i	$-0.923446\pi$
$41$	−6.99800	+	4.83037i	−1.09290	+	0.754378i	−0.121686	+	0.992569i	$0.538830\pi$
$42$	−0.457424	+	0.405242i	−0.0705821	+	0.0625303i
$43$	6.85629	+	1.68992i	1.04557	+	0.257711i	0.724451	−	0.689327i	$-0.242093\pi$
$43$	6.85629	+	1.68992i	1.04557	+	0.257711i	0.321123	+	0.947037i	$0.395940\pi$
$44$	−2.44857	−	0.928622i	−0.369137	−	0.139995i
$45$	0.411789	−	0.784599i	0.0613859	−	0.116961i
$46$	−1.91963	−	0.728018i	−0.283033	−	0.107340i
$47$	−5.18060	−	5.84769i	−0.755668	−	0.852973i	0.237290	−	0.971439i	$-0.423741\pi$
$47$	−5.18060	−	5.84769i	−0.755668	−	0.852973i	−0.992958	+	0.118466i	$0.962202\pi$
$48$	2.58628	−	2.29125i	0.373298	−	0.330713i
$49$	1.67577	−	2.42777i	0.239395	−	0.346824i
$50$	−1.05333	−	0.727059i	−0.148963	−	0.102822i
$51$	1.89179	+	0.992889i	0.264904	+	0.139032i
$52$	6.30134	−	2.75837i	0.873839	−	0.382518i
$53$	−6.51757	+	3.42069i	−0.895257	+	0.469867i	−0.848595	−	0.529043i	$-0.822551\pi$
$53$	−6.51757	+	3.42069i	−0.895257	+	0.469867i	−0.0466626	+	0.998911i	$0.514859\pi$
$54$	0.301448	+	0.0366025i	0.0410219	+	0.00498096i
$55$	−1.18097	+	0.291082i	−0.159242	+	0.0392495i
$56$	−1.35659	+	1.96537i	−0.181283	+	0.262633i
$57$	4.90744	−	3.38736i	0.650006	−	0.448667i
$58$	1.35448	−	1.52890i	0.177852	−	0.200754i
$59$	4.76639	+	0.578745i	0.620531	+	0.0753462i	0.424764	−	0.905304i	$-0.360357\pi$
$59$	4.76639	+	0.578745i	0.620531	+	0.0753462i	0.195768	+	0.980650i	$0.437280\pi$
$60$	0.404559	−	1.64136i	0.0522284	−	0.211899i
$61$	−3.26130	−	1.71166i	−0.417567	−	0.219156i	0.242836	−	0.970067i	$-0.421922\pi$
$61$	−3.26130	−	1.71166i	−0.417567	−	0.219156i	−0.660403	+	0.750911i	$0.729615\pi$
$62$	0.184987	−	1.52350i	0.0234933	−	0.193485i
$63$	1.99780	−	0.242577i	0.251699	−	0.0305618i
$64$	3.33521	−	4.83189i	0.416901	−	0.603986i
$65$	1.68087	−	2.71695i	0.208487	−	0.336996i
$66$	−0.236784	−	0.343041i	−0.0291461	−	0.0422255i
$67$	0.679073	+	0.766515i	0.0829619	+	0.0936447i	0.788526	−	0.615002i	$-0.210845\pi$
$67$	0.679073	+	0.766515i	0.0829619	+	0.0936447i	−0.705564	+	0.708646i	$0.749306\pi$
$68$	3.95758	+	0.975456i	0.479927	+	0.118291i
$69$	3.84065	+	5.56414i	0.462359	+	0.669843i
$70$			0.541504i			0.0647221i
$71$	2.56180	−	1.76828i	0.304030	−	0.209857i	−0.406275	−	0.913751i	$-0.633172\pi$
$71$	2.56180	−	1.76828i	0.304030	−	0.209857i	0.710305	+	0.703894i	$0.248557\pi$
$72$	1.17800	−	0.143035i	0.138828	−	0.0168568i
$73$	−11.2091	+	4.25106i	−1.31193	+	0.497548i	−0.908661	−	0.417534i	$-0.862894\pi$
$73$	−11.2091	+	4.25106i	−1.31193	+	0.497548i	−0.403266	+	0.915083i	$0.632125\pi$
$74$	−0.134574	+	1.10832i	−0.0156440	+	0.128840i
$75$	1.49460	+	3.94094i	0.172582	+	0.455060i
$76$	7.54375	−	8.51514i	0.865328	−	0.976753i
$77$	−2.06772	−	1.83184i	−0.235639	−	0.208758i
$78$	1.07485	+	0.208429i	0.121703	+	0.0235999i
$79$	4.31523	−	3.82296i	0.485501	−	0.430116i	−0.384531	−	0.923112i	$-0.625637\pi$
$79$	4.31523	−	3.82296i	0.485501	−	0.430116i	0.870032	+	0.492996i	$0.164098\pi$
$80$		−	3.06167i		−	0.342305i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−2.50707	+	0.617938i	−0.276860	+	0.0682399i
$83$	−12.3030	−	8.49214i	−1.35043	−	0.932134i	−0.350439	−	0.936586i	$-0.613968\pi$
$83$	−12.3030	−	8.49214i	−1.35043	−	0.932134i	−0.999990	+	0.00445167i	$0.998583\pi$
$84$	3.58988	−	1.36146i	0.391687	−	0.148547i
$85$	1.77013	−	0.671323i	0.191998	−	0.0728152i
$86$	1.76473	+	1.21811i	0.190296	+	0.131352i
$87$	−6.53103	+	1.60976i	−0.700200	+	0.172584i
$88$	−1.21923	−	1.08014i	−0.129970	−	0.115143i
$89$		−	7.72878i		−	0.819249i	−0.912254	−	0.409624i	$-0.865660\pi$
$89$		−	7.72878i		−	0.819249i	0.912254	−	0.409624i	$-0.134340\pi$
$90$	0.201405	−	0.178429i	0.0212299	−	0.0188081i
$91$	7.24696	−	0.363548i	0.759688	−	0.0381101i
$92$	9.65461	+	8.55324i	1.00656	+	0.891737i
$93$	−3.35138	+	3.78293i	−0.347522	+	0.392271i
$94$	−0.841244	−	2.21818i	−0.0867677	−	0.228788i
$95$	0.636888	−	5.24525i	0.0653434	−	0.538151i
$96$	3.20012	−	1.21364i	0.326610	−	0.123867i
$97$	9.07801	−	1.10227i	0.921733	−	0.111919i	0.354107	−	0.935205i	$-0.384785\pi$
$97$	9.07801	−	1.10227i	0.921733	−	0.111919i	0.567626	+	0.823286i	$0.307862\pi$
$98$	0.737222	−	0.508867i	0.0744706	−	0.0514034i
$99$			1.37266i			0.137958i
$100$	4.56782	+	6.61763i	0.456782	+	0.661763i
$101$	−17.1250	−	4.22092i	−1.70400	−	0.419998i	−0.737227	−	0.675645i	$-0.763865\pi$
$101$	−17.1250	−	4.22092i	−1.70400	−	0.419998i	−0.966770	+	0.255648i	$0.917711\pi$
$102$	0.430221	+	0.485619i	0.0425982	+	0.0480834i
$103$	4.52809	+	6.56007i	0.446166	+	0.646383i	0.979951	−	0.199237i	$-0.0638463\pi$
$103$	4.52809	+	6.56007i	0.446166	+	0.646383i	−0.533785	+	0.845620i	$0.679231\pi$
$104$	4.27315	−	0.214365i	0.419017	−	0.0210202i
$105$	1.01300	−	1.46758i	0.0988584	−	0.143221i
$106$	−2.21887	+	0.269420i	−0.215516	+	0.0261683i
$107$	1.59378	−	13.1259i	0.154076	−	1.26893i	−0.686456	−	0.727172i	$-0.740834\pi$
$107$	1.59378	−	13.1259i	0.154076	−	1.26893i	0.840532	−	0.541762i	$-0.182242\pi$
$108$	−1.68926	−	0.886594i	−0.162549	−	0.0853125i
$109$	3.06801	−	12.4474i	0.293862	−	1.19225i	−0.619467	−	0.785023i	$-0.712651\pi$
$109$	3.06801	−	12.4474i	0.293862	−	1.19225i	0.913329	−	0.407222i	$-0.133503\pi$
$110$	−0.366655	−	0.0445200i	−0.0349592	−	0.00424481i
$111$	2.43807	−	2.75201i	0.231411	−	0.261209i
$112$	5.72267	−	3.95008i	0.540742	−	0.373247i
$113$	−1.15019	+	1.66634i	−0.108201	+	0.156756i	−0.873343	−	0.487105i	$-0.838053\pi$
$113$	−1.15019	+	1.66634i	−0.108201	+	0.156756i	0.765143	+	0.643861i	$0.222668\pi$
$114$	1.75812	−	0.433337i	0.164663	−	0.0405857i
$115$	5.94715	+	0.722115i	0.554575	+	0.0673376i
$116$	−11.3628	+	5.96367i	−1.05501	+	0.553713i
$117$	−2.52314	−	2.57561i	−0.233264	−	0.238116i
$118$	1.29100	+	0.677569i	0.118846	+	0.0623753i
$119$	3.53857	+	2.44250i	0.324380	+	0.223903i
$120$	0.597311	−	0.865355i	0.0545268	−	0.0789957i
$121$	−6.82327	+	6.04489i	−0.620297	+	0.549536i
$122$	−0.741668	−	0.837170i	−0.0671474	−	0.0757938i
$123$	7.95064	+	3.01528i	0.716885	+	0.271879i
$124$	−4.48079	+	8.53744i	−0.402387	+	0.766684i
$125$	7.63462	+	2.89543i	0.682861	+	0.258975i
$126$	0.593354	+	0.146249i	0.0528602	+	0.0130289i
$127$	−11.5138	+	10.2003i	−1.02168	+	0.905130i	−0.995522	−	0.0945281i	$-0.969866\pi$
$127$	−11.5138	+	10.2003i	−1.02168	+	0.905130i	−0.0261581	+	0.999658i	$0.508327\pi$
$128$	7.10063	−	4.90121i	0.627613	−	0.433210i
$129$	−2.50404	−	6.60260i	−0.220468	−	0.581326i
$130$	0.769811	−	0.590425i	0.0675169	−	0.0517837i
$131$	−3.04050	+	8.01715i	−0.265650	+	0.700462i	0.734120	+	0.679020i	$0.237595\pi$
$131$	−3.04050	+	8.01715i	−0.265650	+	0.700462i	−0.999770	+	0.0214419i	$0.993174\pi$
$132$	0.626708	+	2.54266i	0.0545479	+	0.221310i
$133$	10.6258	−	5.57683i	0.921371	−	0.483573i
$134$	0.110270	+	0.290759i	0.00952590	+	0.0251177i
$135$	−0.879635	+	0.106807i	−0.0757069	+	0.00919249i
$136$	2.08651	+	1.44021i	0.178917	+	0.123497i
$137$	−1.02423	+	4.15546i	−0.0875058	+	0.355025i	−0.998330	−	0.0577697i	$-0.981601\pi$
$137$	−1.02423	+	4.15546i	−0.0875058	+	0.355025i	0.910824	+	0.412795i	$0.135447\pi$
$138$	0.491325	+	1.99338i	0.0418243	+	0.169688i
$139$	1.16898	+	9.62741i	0.0991515	+	0.816586i	0.954434	+	0.298423i	$0.0964607\pi$
$139$	1.16898	+	9.62741i	0.0991515	+	0.816586i	−0.855282	+	0.518163i	$0.826616\pi$
$140$	1.20638	−	3.18097i	0.101958	−	0.268841i
$141$	−1.86964	+	7.58541i	−0.157452	+	0.638807i
$142$	0.917780	−	0.226212i	0.0770184	−	0.0189833i
$143$	−0.349652	+	4.93684i	−0.0292394	+	0.412839i
$144$	−3.35483	−	0.826892i	−0.279570	−	0.0689077i
$145$	−2.76990	+	5.27760i	−0.230027	+	0.438281i
$146$	−3.64035			−0.301278
$147$	−2.94996			−0.243308
$148$	3.25969	−	6.21083i	0.267945	−	0.510527i
$149$	−9.44933	−	10.6661i	−0.774119	−	0.873800i	0.220713	−	0.975339i	$-0.429162\pi$
$149$	−9.44933	−	10.6661i	−0.774119	−	0.873800i	−0.994832	+	0.101539i	$0.967623\pi$
$150$			1.27989i			0.104502i
$151$	8.34827	−	9.42325i	0.679373	−	0.766853i	−0.303161	−	0.952939i	$-0.598042\pi$
$151$	8.34827	−	9.42325i	0.679373	−	0.766853i	0.982533	+	0.186086i	$0.0595803\pi$
$152$	6.26545	−	3.28836i	0.508195	−	0.266722i
$153$	−0.257529	−	2.12094i	−0.0208200	−	0.171468i
$154$	−0.389834	−	0.742766i	−0.0314137	−	0.0598538i
$155$	0.539797	+	4.44562i	0.0433575	+	0.357081i
$156$	−5.84967	−	3.61897i	−0.468348	−	0.289749i
$157$	0.821279	−	6.76384i	0.0655452	−	0.539814i	−0.922539	−	0.385903i	$-0.873890\pi$
$157$	0.821279	−	6.76384i	0.0655452	−	0.539814i	0.988085	−	0.153911i	$-0.0491869\pi$
$158$	1.63688	−	0.620785i	0.130223	−	0.0493870i
$159$	6.51757	+	3.42069i	0.516877	+	0.271278i
$160$	1.07540	−	2.83561i	0.0850182	−	0.224175i
$161$	6.32311	+	12.0477i	0.498331	+	0.949490i
$162$	−0.141119	−	0.268880i	−0.0110874	−	0.0211252i
$163$	2.80566	+	11.3830i	0.219756	+	0.891585i	0.972431	+	0.233193i	$0.0749173\pi$
$163$	2.80566	+	11.3830i	0.219756	+	0.891585i	−0.752675	+	0.658393i	$0.771237\pi$
$164$	16.1041	+	1.95539i	1.25752	+	0.152690i
$165$	0.910422	+	0.806563i	0.0708762	+	0.0627909i
$166$	−2.57875	−	3.73596i	−0.200149	−	0.289967i
$167$	11.0567	+	4.19325i	0.855592	+	0.324483i	0.743109	−	0.669170i	$-0.233350\pi$
$167$	11.0567	+	4.19325i	0.855592	+	0.324483i	0.112483	+	0.993654i	$0.464120\pi$
$168$	2.38810			0.184246
$169$	−8.41849	−	9.90601i	−0.647576	−	0.762001i
$170$	0.574881			0.0440914
$171$	−5.57548	−	2.11450i	−0.426368	−	0.161700i
$172$	−7.65286	−	11.0871i	−0.583525	−	0.845382i
$173$	−8.22839	−	7.28972i	−0.625593	−	0.554227i	0.289648	−	0.957133i	$-0.406462\pi$
$173$	−8.22839	−	7.28972i	−0.625593	−	0.554227i	−0.915241	+	0.402906i	$0.868000\pi$
$174$	−2.02769	−	0.246206i	−0.153719	−	0.0186648i
$175$	2.02993	+	8.23576i	0.153448	+	0.622565i
$176$	2.20412	+	4.19961i	0.166142	+	0.316557i
$177$	−2.23132	−	4.25143i	−0.167716	−	0.319557i
$178$	0.832236	−	2.19443i	0.0623787	−	0.164479i
$179$	−18.7549	−	9.84335i	−1.40181	−	0.735726i	−0.416925	−	0.908941i	$-0.636892\pi$
$179$	−18.7549	−	9.84335i	−1.40181	−	0.735726i	−0.984884	+	0.173214i	$0.944585\pi$
$180$	−1.58063	+	0.599454i	−0.117813	+	0.0446807i
$181$	−0.794537	+	6.54360i	−0.0590575	+	0.486382i	0.932931	+	0.360055i	$0.117242\pi$
$181$	−0.794537	+	6.54360i	−0.0590575	+	0.486382i	−0.991989	+	0.126327i	$0.959681\pi$
$182$	2.09677	+	0.677132i	0.155423	+	0.0501924i
$183$	0.443960	+	3.65634i	0.0328185	+	0.270284i
$184$	3.72840	+	7.10388i	0.274862	+	0.523705i
$185$	−0.392692	−	3.23411i	−0.0288713	−	0.237777i
$186$	−1.35890	+	0.713207i	−0.0996396	+	0.0522949i
$187$	−1.94475	+	2.19517i	−0.142214	+	0.160527i
$188$			14.9045i			1.08702i
$189$	−1.33452	−	1.50636i	−0.0970717	−	0.109571i
$190$	0.745641	−	1.42070i	0.0540944	−	0.103068i
$191$	11.6939			0.846143			0.423072	−	0.906096i	$-0.360952\pi$
$191$	11.6939			0.846143			0.423072	+	0.906096i	$0.360952\pi$
$192$	−5.87118			−0.423716
$193$	5.85417	−	11.1542i	0.421393	−	0.802897i	−0.578526	−	0.815664i	$-0.696372\pi$
$193$	5.85417	−	11.1542i	0.421393	−	0.802897i	0.999918	+	0.0127675i	$0.00406413\pi$
$194$	2.69621	+	0.664555i	0.193576	+	0.0477123i
$195$	−3.19085	+	0.160071i	−0.228502	+	0.0114629i
$196$	−5.46436	+	1.34684i	−0.390311	+	0.0962031i
$197$	5.87105	−	23.8198i	0.418295	−	1.69709i	−0.262762	−	0.964861i	$-0.584634\pi$
$197$	5.87105	−	23.8198i	0.418295	−	1.69709i	0.681058	−	0.732230i	$-0.261520\pi$
$198$	−0.147809	+	0.389739i	−0.0105043	+	0.0276976i
$199$	2.91468	+	24.0045i	0.206616	+	1.70164i	0.614756	+	0.788717i	$0.289254\pi$
$199$	2.91468	+	24.0045i	0.206616	+	1.70164i	−0.408140	+	0.912919i	$0.633823\pi$
$200$	1.19694	+	4.85619i	0.0846367	+	0.343385i
$201$	0.245072	−	0.994296i	0.0172860	−	0.0701322i
$202$	−4.40777	−	3.04246i	−0.310129	−	0.214067i
$203$	−13.4382	+	1.63169i	−0.943175	+	0.114522i
$204$	−1.44538	−	3.81115i	−0.101197	−	0.266834i
$205$	6.67161	−	3.50153i	0.465965	−	0.244558i
$206$	0.579268	+	2.35018i	0.0403595	+	0.163745i
$207$	2.39746	−	6.32158i	0.166635	−	0.439380i
$208$	−11.8552	−	3.82851i	−0.822008	−	0.265460i
$209$	2.90250	+	7.65326i	0.200770	+	0.529387i
$210$	0.445649	−	0.307609i	0.0307527	−	0.0212271i
$211$	−1.63355	+	1.44720i	−0.112458	+	0.0996291i	−0.717478	−	0.696581i	$-0.754704\pi$
$211$	−1.63355	+	1.44720i	−0.112458	+	0.0996291i	0.605020	+	0.796210i	$0.293165\pi$
$212$	13.6346	+	3.36063i	0.936428	+	0.230809i
$213$	−2.91054	−	1.10382i	−0.199427	−	0.0756326i
$214$	1.86593	−	3.55522i	0.127552	−	0.243030i
$215$	−5.85054	−	2.21882i	−0.399003	−	0.151322i
$216$	−0.786894	−	0.888219i	−0.0535413	−	0.0604357i
$217$	−7.61304	+	6.74456i	−0.516807	+	0.457851i
$218$	2.21144	−	3.20382i	0.149777	−	0.216990i
$219$	9.86605	+	6.81004i	0.666686	+	0.460180i
$220$	2.05467	+	1.07837i	0.138526	+	0.0727039i
$221$	−0.385956	−	7.69365i	−0.0259622	−	0.517531i
$222$	0.988577	−	0.518845i	0.0663489	−	0.0348226i
$223$	−22.6025	−	2.74444i	−1.51358	−	0.183781i	−0.678780	−	0.734341i	$-0.737491\pi$
$223$	−22.6025	−	2.74444i	−1.51358	−	0.183781i	−0.834796	+	0.550560i	$0.814414\pi$
$224$	6.68759	−	1.64834i	0.446833	−	0.110135i
$225$	2.39430	−	3.46874i	0.159620	−	0.231249i
$226$	−0.506004	+	0.349269i	−0.0336589	+	0.0232330i
$227$	9.61873	−	10.8573i	0.638417	−	0.720624i	−0.336873	−	0.941550i	$-0.609369\pi$
$227$	9.61873	−	10.8573i	0.638417	−	0.720624i	0.975291	+	0.220926i	$0.0709079\pi$
$228$	−11.2932	−	1.37124i	−0.747908	−	0.0908125i
$229$	6.19175	−	25.1209i	0.409162	−	1.66004i	−0.299203	−	0.954190i	$-0.596721\pi$
$229$	6.19175	−	25.1209i	0.409162	−	1.66004i	0.708365	−	0.705846i	$-0.249433\pi$
$230$	1.61081	+	0.845420i	0.106214	+	0.0557454i
$231$	−0.332976	+	2.74230i	−0.0219082	+	0.180430i
$232$	−7.92379	+	0.962122i	−0.520222	+	0.0631664i
$233$	−14.9719	+	21.6906i	−0.980844	+	1.42100i	−0.0750990	+	0.997176i	$0.523927\pi$
$233$	−14.9719	+	21.6906i	−0.980844	+	1.42100i	−0.905745	+	0.423822i	$0.860688\pi$
$234$	−0.439050	−	1.00298i	−0.0287016	−	0.0655671i
$235$	3.93246	+	5.69715i	0.256526	+	0.371641i
$236$	−6.07424	−	6.85640i	−0.395399	−	0.446314i
$237$	−5.59756	−	1.37967i	−0.363601	−	0.0896195i
$238$	0.741695	+	1.07453i	0.0480769	+	0.0696514i
$239$		−	4.98490i		−	0.322446i	−0.986918	−	0.161223i	$-0.948456\pi$
$239$		−	4.98490i		−	0.322446i	0.986918	−	0.161223i	$-0.0515438\pi$
$240$	−2.51971	+	1.73923i	−0.162646	+	0.112267i
$241$	−14.1868	+	1.72259i	−0.913855	+	0.110962i	−0.563937	−	0.825818i	$-0.690714\pi$
$241$	−14.1868	+	1.72259i	−0.913855	+	0.110962i	−0.349918	+	0.936780i	$0.613791\pi$
$242$	−2.58824	+	0.981591i	−0.166379	+	0.0630990i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	2.49172	+	6.57013i	0.159516	+	0.420609i
$245$	−1.73337	+	1.95657i	−0.110741	+	0.125000i
$246$	1.93273	+	1.71225i	0.123227	+	0.109169i
$247$	−19.5138	−	9.02511i	−1.24164	−	0.574254i
$248$	−4.48901	+	3.97691i	−0.285052	+	0.252534i
$249$			14.9493i			0.947370i
$250$	1.85591	+	1.64419i	0.117378	+	0.103988i
$251$	−2.12958	+	0.524895i	−0.134418	+	0.0331311i	−0.305951	−	0.952047i	$-0.598974\pi$
$251$	−2.12958	+	0.524895i	−0.134418	+	0.0331311i	0.171533	+	0.985178i	$0.445128\pi$
$252$	−3.15974	−	2.18101i	−0.199045	−	0.137391i
$253$	−8.67740	+	3.29090i	−0.545543	+	0.206897i
$254$	−4.36746	+	1.65636i	−0.274039	+	0.103929i
$255$	−1.55804	−	1.07544i	−0.0975682	−	0.0673465i
$256$	−8.85731	+	2.18313i	−0.553582	+	0.136446i
$257$	6.01271	+	5.32679i	0.375062	+	0.332276i	0.829505	−	0.558500i	$-0.188623\pi$
$257$	6.01271	+	5.32679i	0.375062	+	0.332276i	−0.454442	+	0.890776i	$0.650161\pi$
$258$		−	2.14431i		−	0.133499i
$259$	5.53835	−	4.90655i	0.344136	−	0.304878i
$260$	−5.83750	+	1.75333i	−0.362026	+	0.108737i
$261$	5.03485	+	4.46049i	0.311650	+	0.276097i
$262$	−1.72658	+	1.94890i	−0.106668	+	0.120404i
$263$	8.58638	+	22.6404i	0.529459	+	1.39607i	0.886825	+	0.462105i	$0.152906\pi$
$263$	8.58638	+	22.6404i	0.529459	+	1.39607i	−0.357366	+	0.933964i	$0.616325\pi$
$264$	−0.196338	+	1.61699i	−0.0120838	+	0.0995190i
$265$	6.09844	−	2.31283i	0.374624	−	0.142076i
$266$	3.61748	−	0.439242i	0.221802	−	0.0269316i
$267$	−6.36066	+	4.39045i	−0.389266	+	0.268691i
$268$		−	1.95368i		−	0.119340i
$269$	11.4940	+	16.6519i	0.700802	+	1.01529i	0.998167	+	0.0605232i	$0.0192769\pi$
$269$	11.4940	+	16.6519i	0.700802	+	1.01529i	−0.297365	+	0.954764i	$0.596108\pi$
$270$	−0.261255	−	0.0643936i	−0.0158995	−	0.00391887i
$271$	15.4211	+	17.4069i	0.936768	+	1.05739i	0.998241	+	0.0592836i	$0.0188816\pi$
$271$	15.4211	+	17.4069i	0.936768	+	1.05739i	−0.0614733	+	0.998109i	$0.519580\pi$
$272$	−4.19355	−	6.07541i	−0.254271	−	0.368376i
$273$	−4.41593	−	5.75761i	−0.267265	−	0.348466i
$274$	−0.738269	+	1.06957i	−0.0446005	+	0.0646150i
$275$	−5.74336	+	0.697371i	−0.346338	+	0.0420530i
$276$	1.55473	−	12.8044i	0.0935840	−	0.770733i
$277$	−6.66347	−	3.49726i	−0.400369	−	0.210130i	0.252506	−	0.967595i	$-0.418745\pi$
$277$	−6.66347	−	3.49726i	−0.400369	−	0.210130i	−0.652875	+	0.757465i	$0.726437\pi$
$278$	−0.704774	+	2.85938i	−0.0422695	+	0.171494i
$279$	5.01709	+	0.609185i	0.300365	+	0.0364710i
$280$	1.40322	−	1.58391i	0.0838586	−	0.0946568i
$281$	4.90368	−	3.38477i	0.292529	−	0.201918i	−0.412757	−	0.910841i	$-0.635434\pi$
$281$	4.90368	−	3.38477i	0.292529	−	0.201918i	0.705286	+	0.708923i	$0.250819\pi$
$282$	−1.34764	+	1.95240i	−0.0802510	+	0.116264i
$283$	−4.21319	+	1.03846i	−0.250448	+	0.0617299i	−0.362541	−	0.931968i	$-0.618091\pi$
$283$	−4.21319	+	1.03846i	−0.250448	+	0.0617299i	0.112093	+	0.993698i	$0.464245\pi$
$284$	−5.89531	−	0.715820i	−0.349822	−	0.0424761i
$285$	−4.67855	+	2.45549i	−0.277133	+	0.145451i
$286$	−0.630876	+	1.36406i	−0.0373045	+	0.0806587i
$287$	15.1523	+	7.95256i	0.894414	+	0.469425i
$288$	−2.81668	−	1.94422i	−0.165975	−	0.114564i
$289$	−7.06405	+	10.2340i	−0.415533	+	0.602003i
$290$	−1.35475	+	1.20020i	−0.0795536	+	0.0704783i
$291$	−6.06405	−	6.84490i	−0.355481	−	0.401255i
$292$	21.3846	+	8.11012i	1.25144	+	0.474609i
$293$	−6.52907	+	12.4401i	−0.381432	+	0.726758i	−0.998174	−	0.0604073i	$-0.980760\pi$
$293$	−6.52907	+	12.4401i	−0.381432	+	0.726758i	0.616742	+	0.787166i	$0.288452\pi$
$294$	−0.837579	−	0.317652i	−0.0488486	−	0.0185258i
$295$	−4.13087	−	1.01817i	−0.240509	−	0.0592801i
$296$	3.26567	−	2.89313i	0.189813	−	0.168160i
$297$	1.12968	−	0.779761i	0.0655506	−	0.0452463i
$298$	−1.53442	−	4.04592i	−0.0888863	−	0.234374i
$299$	10.2328	−	22.1251i	0.591780	−	1.27953i
$300$	2.85138	−	7.51848i	0.164625	−	0.434080i
$301$	−3.40092	−	13.7981i	−0.196026	−	0.795308i
$302$	3.38502	−	1.77659i	0.194786	−	0.102232i
$303$	6.25433	+	16.4913i	0.359302	+	0.947402i
$304$	−20.4533	+	2.48348i	−1.17308	+	0.142437i
$305$	2.68594	+	1.85397i	0.153797	+	0.106158i
$306$	0.155263	−	0.629928i	0.00887581	−	0.0360106i
$307$	3.67928	+	14.9274i	0.209987	+	0.851952i	0.977503	+	0.210922i	$0.0676466\pi$
$307$	3.67928	+	14.9274i	0.209987	+	0.851952i	−0.767516	+	0.641030i	$0.778507\pi$
$308$	0.635248	+	5.23174i	0.0361966	+	0.298106i
$309$	2.82659	−	7.45309i	0.160799	−	0.423992i
$310$	−0.325442	+	1.32037i	−0.0184838	+	0.0749919i
$311$	10.3225	−	2.54426i	0.585333	−	0.144272i	0.0644815	−	0.997919i	$-0.479461\pi$
$311$	10.3225	−	2.54426i	0.585333	−	0.144272i	0.520852	+	0.853647i	$0.325615\pi$
$312$	−2.60384	−	3.39496i	−0.147414	−	0.192202i
$313$	−0.375276	−	0.0924972i	−0.0212119	−	0.00522825i	0.228695	−	0.973498i	$-0.426554\pi$
$313$	−0.375276	−	0.0924972i	−0.0212119	−	0.00522825i	−0.249907	+	0.968270i	$0.580400\pi$
$314$	0.961518	−	1.83202i	0.0542616	−	0.103387i
$315$	−1.78324			−0.100474
$316$	−10.9986			−0.618717
$317$	−0.486988	+	0.927877i	−0.0273519	+	0.0521148i	−0.898749	−	0.438465i	$-0.855522\pi$
$317$	−0.486988	+	0.927877i	−0.0273519	+	0.0521148i	0.871397	+	0.490579i	$0.163215\pi$
$318$	1.48219	+	1.67305i	0.0831171	+	0.0938198i
$319$		−	9.23321i		−	0.516960i
$320$	−3.44985	+	3.89408i	−0.192852	+	0.217685i
$321$	−11.7078	+	6.14473i	−0.653466	+	0.342966i
$322$	0.498020	+	4.10156i	0.0277536	+	0.228571i
$323$	−5.92058	−	11.2807i	−0.329430	−	0.627676i
$324$	0.229959	+	1.89388i	0.0127755	+	0.105216i
$325$	9.49477	−	11.8656i	0.526675	−	0.658184i
$326$	−0.429115	+	3.53408i	−0.0237665	+	0.195735i
$327$	−11.9868	+	4.54601i	−0.662874	+	0.251395i
$328$	8.93454	+	4.68921i	0.493327	+	0.258918i
$329$	−5.57520	+	14.7006i	−0.307371	+	0.810470i
$330$	0.171645	+	0.327041i	0.00944872	+	0.0180030i
$331$	1.64274	+	3.12999i	0.0902934	+	0.172040i	0.926415	−	0.376505i	$-0.122874\pi$
$331$	1.64274	+	3.12999i	0.0902934	+	0.172040i	−0.836121	+	0.548545i	$0.815182\pi$
$332$	6.82529	+	27.6913i	0.374586	+	1.51976i
$333$	−3.64984	−	0.443171i	−0.200010	−	0.0242856i
$334$	2.68779	+	2.38117i	0.147069	+	0.130292i
$335$	−0.515467	−	0.746783i	−0.0281630	−	0.0408011i
$336$	−6.50170	−	2.46577i	−0.354697	−	0.134519i
$337$	4.16877			0.227087			0.113544	−	0.993533i	$-0.463780\pi$
$337$	4.16877			0.227087			0.113544	+	0.993533i	$0.463780\pi$
$338$	−1.32358	−	3.71911i	−0.0719931	−	0.202293i
$339$	2.02475			0.109969
$340$	−3.37704	−	1.28074i	−0.183146	−	0.0694581i
$341$	−3.94087	−	5.70933i	−0.213410	−	0.309178i
$342$	−1.35535	−	1.20074i	−0.0732891	−	0.0649285i
$343$	−19.8780	−	2.41363i	−1.07331	−	0.130324i
$344$	−2.00535	−	8.13601i	−0.108121	−	0.438664i
$345$	−2.78408	−	5.30462i	−0.149890	−	0.285591i
$346$	−1.55132	−	2.95580i	−0.0833996	−	0.158905i
$347$	4.13365	−	10.8995i	0.221906	−	0.585118i	−0.777115	−	0.629359i	$-0.783318\pi$
$347$	4.13365	−	10.8995i	0.221906	−	0.585118i	0.999021	+	0.0442405i	$0.0140868\pi$
$348$	11.3628	+	5.96367i	0.609111	+	0.319686i
$349$	0.216111	−	0.0819602i	0.0115682	−	0.00438723i	−0.348814	−	0.937192i	$-0.613416\pi$
$349$	0.216111	−	0.0819602i	0.0115682	−	0.00438723i	0.360382	+	0.932805i	$0.382646\pi$
$350$	−0.310471	+	2.55696i	−0.0165954	+	0.136675i
$351$	−0.686383	+	3.53962i	−0.0366364	+	0.188931i
$352$	0.566278	+	4.66372i	0.0301827	+	0.248577i
$353$	2.19787	+	4.18769i	0.116981	+	0.222888i	0.936905	−	0.349583i	$-0.113677\pi$
$353$	2.19787	+	4.18769i	0.116981	+	0.222888i	−0.819924	+	0.572472i	$0.805985\pi$
$354$	−0.175743	−	1.44737i	−0.00934064	−	0.0769271i
$355$	−2.44232	+	1.28183i	−0.129625	+	0.0680323i
$356$	−9.77766	+	11.0367i	−0.518215	+	0.584944i
$357$		−	4.29968i		−	0.227563i
$358$	−4.26514	−	4.81435i	−0.225420	−	0.254446i
$359$	13.0208	−	24.8090i	0.687209	−	1.30937i	−0.252568	−	0.967579i	$-0.581275\pi$
$359$	13.0208	−	24.8090i	0.687209	−	1.30937i	0.939777	−	0.341788i	$-0.111033\pi$
$360$	−1.05148			−0.0554181
$361$	−16.5571			−0.871428
$362$	−0.930209	+	1.77236i	−0.0488907	+	0.0931534i
$363$	8.85091	+	2.18155i	0.464552	+	0.114502i
$364$	−10.8086	−	8.64897i	−0.566524	−	0.453329i
$365$	10.3140	−	2.54217i	0.539858	−	0.133063i
$366$	−0.267662	+	1.08595i	−0.0139909	+	0.0567634i
$367$	8.08129	−	21.3086i	0.421840	−	1.11230i	−0.540713	−	0.841207i	$-0.681845\pi$
$367$	8.08129	−	21.3086i	0.421840	−	1.11230i	0.962553	−	0.271094i	$-0.0873853\pi$
$368$	−2.81581	−	23.1903i	−0.146784	−	1.20888i
$369$	−2.03495	−	8.25612i	−0.105935	−	0.429797i
$370$	0.236753	−	0.960544i	0.0123082	−	0.0499363i
$371$	12.1910	+	8.41485i	0.632926	+	0.436877i
$372$	9.57155	−	1.16220i	0.496262	−	0.0602571i
$373$	6.05725	+	15.9717i	0.313633	+	0.826981i	0.995435	+	0.0954446i	$0.0304273\pi$
$373$	6.05725	+	15.9717i	0.313633	+	0.826981i	−0.681802	+	0.731537i	$0.738803\pi$
$374$	−0.788548	+	0.413862i	−0.0407749	+	0.0214003i
$375$	−1.95407	−	7.92796i	−0.100908	−	0.409398i
$376$	−3.28740	+	8.66817i	−0.169535	+	0.447027i
$377$	16.9719	+	17.3248i	0.874095	+	0.892275i
$378$	−0.216703	−	0.571400i	−0.0111460	−	0.0293896i
$379$	−5.96055	+	4.11427i	−0.306173	+	0.211336i	−0.711237	−	0.702953i	$-0.751865\pi$
$379$	−5.96055	+	4.11427i	−0.306173	+	0.211336i	0.405064	+	0.914288i	$0.367249\pi$
$380$	−7.54523	+	6.68449i	−0.387062	+	0.342907i
$381$	14.9352	+	3.68120i	0.765155	+	0.188594i
$382$	3.32025	+	1.25921i	0.169879	+	0.0644265i
$383$	−5.86932	+	11.1831i	−0.299908	+	0.571428i	−0.988047	−	0.154151i	$-0.950736\pi$
$383$	−5.86932	+	11.1831i	−0.299908	+	0.571428i	0.688139	+	0.725579i	$0.258428\pi$
$384$	−8.06723	−	3.05950i	−0.411679	−	0.156129i
$385$	1.62319	+	1.83220i	0.0827252	+	0.0933775i
$386$	2.86326	−	2.53662i	0.145736	−	0.129111i
$387$	−4.01138	+	5.81148i	−0.203910	+	0.295414i
$388$	−14.3579	−	9.91054i	−0.728911	−	0.503131i
$389$	−22.5592	−	11.8400i	−1.14380	−	0.600312i	−0.217112	−	0.976147i	$-0.569664\pi$
$389$	−22.5592	−	11.8400i	−1.14380	−	0.600312i	−0.926687	+	0.375835i	$0.877356\pi$
$390$	−0.923213	−	0.298143i	−0.0467487	−	0.0150970i
$391$	12.7903	−	6.71285i	0.646832	−	0.339484i
$392$	−3.47504	−	0.421946i	−0.175516	−	0.0213115i
$393$	8.32519	−	2.05197i	0.419950	−	0.103508i
$394$	4.23188	−	6.13094i	0.213199	−	0.308872i
$395$	−4.20414	+	2.90191i	−0.211533	+	0.146011i
$396$	1.73655	−	1.96016i	0.0872651	−	0.0985019i
$397$	−21.6976	−	2.63457i	−1.08897	−	0.132225i	−0.443698	−	0.896176i	$-0.646334\pi$
$397$	−21.6976	−	2.63457i	−1.08897	−	0.132225i	−0.645274	+	0.763951i	$0.723257\pi$
$398$	−1.75725	+	7.12945i	−0.0880830	+	0.357367i
$399$	−10.6258	−	5.57683i	−0.531954	−	0.279191i
$400$	1.75541	−	14.4571i	0.0877703	−	0.722854i
$401$	25.0681	−	3.04382i	1.25184	−	0.152001i	0.532364	−	0.846515i	$-0.321304\pi$
$401$	25.0681	−	3.04382i	1.25184	−	0.152001i	0.719479	+	0.694514i	$0.244381\pi$
$402$	0.176649	−	0.255920i	0.00881045	−	0.0127641i
$403$	17.8890	+	3.46894i	0.891115	+	0.172800i
$404$	19.1146	+	27.6922i	0.950985	+	1.37774i
$405$	0.587590	+	0.663252i	0.0291976	+	0.0329573i
$406$	−3.99119	−	0.983741i	−0.198080	−	0.0488223i
$407$	2.86691	+	4.15343i	0.142107	+	0.205878i
$408$		−	2.53530i		−	0.125516i
$409$	23.7539	−	16.3961i	1.17455	−	0.810735i	0.189314	−	0.981917i	$-0.439374\pi$
$409$	23.7539	−	16.3961i	1.17455	−	0.810735i	0.985240	+	0.171181i	$0.0547584\pi$
$410$	2.27131	−	0.275787i	0.112172	−	0.0136202i
$411$	4.00170	−	1.51765i	0.197390	−	0.0748600i
$412$	1.83302	−	15.0963i	0.0903064	−	0.743740i
$413$	−3.42643	−	9.03476i	−0.168604	−	0.444572i
$414$	1.36142	−	1.53672i	0.0669100	−	0.0755258i
$415$	9.91513	+	8.78404i	0.486714	+	0.431191i
$416$	−9.63507	−	7.70993i	−0.472398	−	0.378010i
$417$	7.25914	−	6.43104i	0.355482	−	0.314929i
$418$			2.48553i			0.121571i
$419$	25.2870	+	22.4024i	1.23535	+	1.09443i	0.992228	+	0.124431i	$0.0397106\pi$
$419$	25.2870	+	22.4024i	1.23535	+	1.09443i	0.243124	+	0.969995i	$0.421828\pi$
$420$	−3.30319	+	0.814164i	−0.161179	+	0.0397271i
$421$	−0.0955585	−	0.0659593i	−0.00465724	−	0.00321466i	0.565734	−	0.824588i	$-0.308593\pi$
$421$	−0.0955585	−	0.0659593i	−0.00465724	−	0.00321466i	−0.570391	+	0.821373i	$0.693208\pi$
$422$	−0.619646	+	0.235001i	−0.0301639	+	0.0114397i
$423$	7.30475	−	2.77032i	0.355169	−	0.134698i
$424$	7.18840	+	4.96180i	0.349100	+	0.240966i
$425$	8.74339	−	2.15505i	0.424117	−	0.104535i
$426$	−0.707527	−	0.626815i	−0.0342798	−	0.0303693i
$427$			7.41232i			0.358707i
$428$	−18.8815	+	16.7276i	−0.912673	+	0.808558i
$429$	4.26156	−	2.51669i	0.205750	−	0.121507i
$430$	−1.42222	−	1.25997i	−0.0685854	−	0.0607613i
$431$	7.83151	−	8.83995i	0.377231	−	0.425805i	−0.528978	−	0.848635i	$-0.677425\pi$
$431$	7.83151	−	8.83995i	0.377231	−	0.425805i	0.906209	+	0.422830i	$0.138963\pi$
$432$	1.22524	+	3.23070i	0.0589496	+	0.155437i
$433$	−0.992285	+	8.17221i	−0.0476862	+	0.392731i	0.949251	+	0.314521i	$0.101844\pi$
$433$	−0.992285	+	8.17221i	−0.0476862	+	0.392731i	−0.996937	+	0.0782106i	$0.975079\pi$
$434$	−2.88782	+	1.09521i	−0.138620	+	0.0525716i
$435$	5.91686	−	0.718437i	0.283692	−	0.0344464i
$436$	−20.1283	+	13.8936i	−0.963971	+	0.665381i
$437$		−	40.3153i		−	1.92854i
$438$	2.06795	+	2.99595i	0.0988107	+	0.143152i
$439$	39.5200	+	9.74080i	1.88619	+	0.464903i	0.999999	+	0.00157539i	$0.000501463\pi$
$439$	39.5200	+	9.74080i	1.88619	+	0.464903i	0.886187	+	0.463328i	$0.153345\pi$
$440$	0.957107	+	1.08035i	0.0456283	+	0.0515037i
$441$	1.67577	+	2.42777i	0.0797984	+	0.115608i
$442$	0.718869	−	2.22601i	0.0341931	−	0.105881i
$443$	−7.81302	+	11.3191i	−0.371208	+	0.537787i	−0.963420	−	0.267994i	$-0.913639\pi$
$443$	−7.81302	+	11.3191i	−0.371208	+	0.537787i	0.592213	+	0.805782i	$0.298255\pi$
$444$	−6.96313	+	0.845477i	−0.330456	+	0.0401246i
$445$	−0.825488	+	6.79850i	−0.0391319	+	0.322280i
$446$	−6.12199	−	3.21307i	−0.289885	−	0.152143i
$447$	−3.41019	+	13.8357i	−0.161296	+	0.654405i
$448$	−11.7294	−	1.42421i	−0.554164	−	0.0672877i
$449$	4.07278	−	4.59722i	0.192206	−	0.216956i	−0.644505	−	0.764600i	$-0.722937\pi$
$449$	4.07278	−	4.59722i	0.192206	−	0.216956i	0.836712	+	0.547644i	$0.184475\pi$
$450$	1.05333	−	0.727059i	0.0496543	−	0.0342739i
$451$	−6.63047	+	9.60590i	−0.312217	+	0.452324i
$452$	3.75055	−	0.924427i	0.176411	−	0.0434814i
$453$	−12.4975	−	1.51748i	−0.587186	−	0.0712973i
$454$	3.90015	−	2.04696i	0.183043	−	0.0960685i
$455$	−6.41351	−	0.454237i	−0.300670	−	0.0212950i
$456$	−6.26545	−	3.28836i	−0.293407	−	0.153992i
$457$	−23.4147	−	16.1620i	−1.09529	−	0.756026i	−0.123614	−	0.992330i	$-0.539448\pi$
$457$	−23.4147	−	16.1620i	−1.09529	−	0.756026i	−0.971679	+	0.236304i	$0.924064\pi$
$458$	4.46304	−	6.46583i	0.208544	−	0.302129i
$459$	−1.59921	+	1.41677i	−0.0746445	+	0.0661293i
$460$	−7.57899	−	8.55491i	−0.353372	−	0.398875i
$461$	8.39543	+	3.18397i	0.391014	+	0.148292i	0.542273	−	0.840202i	$-0.317564\pi$
$461$	8.39543	+	3.18397i	0.391014	+	0.148292i	−0.151259	+	0.988494i	$0.548333\pi$
$462$	−0.389834	+	0.742766i	−0.0181367	+	0.0345566i
$463$	19.1082	+	7.24677i	0.888031	+	0.336786i	0.756087	−	0.654471i	$-0.227109\pi$
$463$	19.1082	+	7.24677i	0.888031	+	0.336786i	0.131944	+	0.991257i	$0.457878\pi$
$464$	22.5663	+	5.56209i	1.04761	+	0.258213i
$465$	3.35204	−	2.96965i	0.155447	−	0.137714i
$466$	−6.58662	+	4.54642i	−0.305119	+	0.210609i
$467$	10.6325	+	28.0356i	0.492013	+	1.29733i	0.919421	+	0.393274i	$0.128658\pi$
$467$	10.6325	+	28.0356i	0.492013	+	1.29733i	−0.427408	+	0.904059i	$0.640573\pi$
$468$	0.344637	+	6.86999i	0.0159308	+	0.317566i
$469$	0.730797	−	1.92695i	0.0337451	−	0.0889785i
$470$	0.503071	+	2.04104i	0.0232049	+	0.0941460i
$471$	−6.03308	+	3.16640i	−0.277989	+	0.145900i
$472$	−2.02039	−	5.32733i	−0.0929959	−	0.245210i
$473$	9.62236	−	1.16837i	0.442437	−	0.0537215i
$474$	−1.44075	−	0.994476i	−0.0661757	−	0.0456778i
$475$	6.01471	−	24.4027i	0.275974	−	1.11967i
$476$	−1.96308	−	7.96452i	−0.0899775	−	0.365053i
$477$	−0.887234	−	7.30703i	−0.0406236	−	0.334566i
$478$	0.536775	−	1.41536i	0.0245515	−	0.0647370i
$479$	7.26952	−	29.4936i	0.332153	−	1.34760i	−0.533011	−	0.846108i	$-0.678940\pi$
$479$	7.26952	−	29.4936i	0.332153	−	1.34760i	0.865164	−	0.501489i	$-0.167214\pi$
$480$	−2.94456	+	0.725769i	−0.134400	+	0.0331267i
$481$	−13.0139	−	2.52359i	−0.593384	−	0.115066i
$482$	−4.21355	−	1.03855i	−0.191922	−	0.0473045i
$483$	6.32311	−	12.0477i	0.287711	−	0.548188i
$484$	17.3910			0.790501
$485$	−8.10307			−0.367941
$486$	−0.141119	+	0.268880i	−0.00640129	+	0.0121966i
$487$	5.74445	+	6.48414i	0.260306	+	0.293825i	0.864105	−	0.503312i	$-0.167885\pi$
$487$	5.74445	+	6.48414i	0.260306	+	0.293825i	−0.603799	+	0.797137i	$0.706347\pi$
$488$			4.37066i			0.197850i
$489$	7.77423	−	8.77529i	0.351563	−	0.396832i
$490$	−0.702837	+	0.368877i	−0.0317509	+	0.0166642i
$491$	−2.59787	−	21.3954i	−0.117240	−	0.965560i	−0.926027	−	0.377458i	$-0.876798\pi$
$491$	−2.59787	−	21.3954i	−0.117240	−	0.965560i	0.808787	−	0.588102i	$-0.200125\pi$
$492$	−7.53889	−	14.3642i	−0.339880	−	0.647586i
$493$	1.73226	+	14.2665i	0.0780173	+	0.642530i
$494$	−4.56873	−	4.66375i	−0.205557	−	0.209832i
$495$	0.146610	−	1.20744i	0.00658963	−	0.0542705i
$496$	16.3278	−	6.19231i	0.733139	−	0.278043i
$497$	−5.54691	−	2.91124i	−0.248813	−	0.130587i
$498$	−1.60974	+	4.24453i	−0.0721341	+	0.190202i
$499$	3.32199	+	6.32952i	0.148713	+	0.283348i	0.948405	−	0.317062i	$-0.102696\pi$
$499$	3.32199	+	6.32952i	0.148713	+	0.283348i	−0.799692	+	0.600410i	$0.795004\pi$
$500$	−7.23924	−	13.7932i	−0.323749	−	0.616851i
$501$	−2.82994	−	11.4815i	−0.126432	−	0.512956i
$502$	−0.661172	−	0.0802808i	−0.0295096	−	0.00358311i
$503$	−11.3809	−	10.0826i	−0.507451	−	0.449562i	0.370137	−	0.928977i	$-0.379311\pi$
$503$	−11.3809	−	10.0826i	−0.507451	−	0.449562i	−0.877589	+	0.479415i	$0.840849\pi$
$504$	−1.35659	−	1.96537i	−0.0604275	−	0.0875444i
$505$	14.6129	+	5.54194i	0.650265	+	0.246613i
$506$	−2.81813			−0.125281
$507$	−3.37024	+	12.5555i	−0.149677	+	0.557611i
$508$	29.3460			1.30202
$509$	9.42363	+	3.57391i	0.417695	+	0.158411i	0.554494	−	0.832188i	$-0.312912\pi$
$509$	9.42363	+	3.57391i	0.417695	+	0.158411i	−0.136798	+	0.990599i	$0.543681\pi$
$510$	−0.326570	−	0.473118i	−0.0144608	−	0.0209500i
$511$	18.0584	+	15.9984i	0.798858	+	0.707726i
$512$	−19.8799	−	2.41386i	−0.878577	−	0.106679i
$513$	1.42703	+	5.78971i	0.0630051	+	0.255622i
$514$	1.13359	+	2.15988i	0.0500007	+	0.0952683i
$515$	−3.28241	−	6.25410i	−0.144640	−	0.275589i
$516$	−4.77717	+	12.5964i	−0.210303	+	0.554524i
$517$	−9.49548	−	4.98361i	−0.417611	−	0.219179i
$518$	2.10084	−	0.796742i	0.0923055	−	0.0350068i
$519$	−1.32506	+	10.9129i	−0.0581637	+	0.479021i
$520$	−3.78171	−	0.267840i	−0.165839	−	0.0117455i
$521$	−2.67381	−	22.0208i	−0.117142	−	0.964750i	−0.926203	−	0.377025i	$-0.876947\pi$
$521$	−2.67381	−	22.0208i	−0.117142	−	0.964750i	0.809061	−	0.587725i	$-0.199976\pi$
$522$	0.949236	+	1.80862i	0.0415469	+	0.0791611i
$523$	−4.32466	−	35.6168i	−0.189104	−	1.55741i	−0.710252	−	0.703948i	$-0.751419\pi$
$523$	−4.32466	−	35.6168i	−0.189104	−	1.55741i	0.521147	−	0.853467i	$-0.325504\pi$
$524$	14.4843	−	7.60196i	0.632751	−	0.332093i
$525$	5.62476	−	6.34904i	0.245485	−	0.277095i
$526$			7.35287i			0.320600i
$527$	7.16028	+	8.08229i	0.311907	+	0.352070i
$528$	2.20412	−	4.19961i	0.0959222	−	0.182764i
$529$	22.7102			0.987399
$530$	1.98057			0.0860306
$531$	−2.23132	+	4.25143i	−0.0968311	+	0.184496i
$532$	−22.2288	−	5.47892i	−0.963742	−	0.237541i
$533$	−5.21575	−	30.2118i	−0.225919	−	1.30862i
$534$	−2.27874	+	0.561659i	−0.0986108	+	0.0243054i
$535$	−2.80389	+	11.3758i	−0.121223	+	0.491820i
$536$	0.430913	−	1.13622i	0.0186126	−	0.0490774i
$537$	2.55310	+	21.0267i	0.110174	+	0.907368i
$538$	1.47040	+	5.96565i	0.0633935	+	0.257198i
$539$	0.969060	−	3.93163i	0.0417404	−	0.169347i
$540$	1.39124	+	0.960304i	0.0598695	+	0.0413249i
$541$	−2.21339	+	0.268755i	−0.0951612	+	0.0115547i	−0.167979	−	0.985791i	$-0.553724\pi$
$541$	−2.21339	+	0.268755i	−0.0951612	+	0.0115547i	0.0728175	+	0.997345i	$0.476801\pi$
$542$	2.50414	+	6.60287i	0.107562	+	0.283618i
$543$	5.83663	−	3.06330i	0.250474	−	0.131459i
$544$	−1.74994	−	7.09980i	−0.0750282	−	0.304401i
$545$	−4.02820	+	10.6215i	−0.172549	+	0.454975i
$546$	−0.633833	−	2.11026i	−0.0271255	−	0.0903109i
$547$	−14.2359	−	37.5370i	−0.608684	−	1.60497i	−0.784212	−	0.620493i	$-0.786932\pi$
$547$	−14.2359	−	37.5370i	−0.608684	−	1.60497i	0.175528	−	0.984475i	$-0.443837\pi$
$548$	6.71966	−	4.63825i	0.287050	−	0.198136i
$549$	2.75691	−	2.44241i	0.117662	−	0.104239i
$550$	−1.70580	−	0.420443i	−0.0727357	−	0.0179277i
$551$	37.5035	+	14.2232i	1.59770	+	0.605928i
$552$	3.72840	−	7.10388i	0.158691	−	0.302361i
$553$	−10.8481	−	4.11415i	−0.461309	−	0.174951i
$554$	−1.51537	−	1.71050i	−0.0643818	−	0.0726721i
$555$	−2.43855	+	2.16036i	−0.103511	+	0.0917023i
$556$	10.5103	−	15.2268i	0.445737	−	0.645761i
$557$	20.2474	+	13.9758i	0.857911	+	0.592173i	0.913755	−	0.406266i	$-0.133170\pi$
$557$	20.2474	+	13.9758i	0.857911	+	0.592173i	−0.0558438	+	0.998440i	$0.517785\pi$
$558$	1.35890	+	0.713207i	0.0575269	+	0.0301925i
$559$	−15.9074	+	19.8794i	−0.672812	+	0.840811i
$560$	−5.45576	+	2.86340i	−0.230548	+	0.121001i
$561$	2.91133	+	0.353500i	0.122917	+	0.0149248i
$562$	1.75677	−	0.433005i	0.0741049	−	0.0182652i
$563$	0.116776	−	0.169179i	0.00492153	−	0.00713006i	−0.820515	−	0.571624i	$-0.806313\pi$
$563$	0.116776	−	0.169179i	0.00492153	−	0.00713006i	0.825437	+	0.564494i	$0.190929\pi$
$564$	12.2661	−	8.46670i	0.516497	−	0.356512i
$565$	1.18972	−	1.34292i	0.0500520	−	0.0564970i
$566$	−1.30807	−	0.158828i	−0.0549822	−	0.00667605i
$567$	−0.481616	+	1.95399i	−0.0202260	+	0.0820600i
$568$	−3.27072	−	1.71661i	−0.137236	−	0.0720272i
$569$	−4.88944	+	40.2682i	−0.204976	+	1.68813i	0.420029	+	0.907510i	$0.362020\pi$
$569$	−4.88944	+	40.2682i	−0.204976	+	1.68813i	−0.625006	+	0.780620i	$0.714903\pi$
$570$	−1.59278	+	0.193399i	−0.0667144	+	0.00810060i
$571$	14.4326	−	20.9092i	0.603984	−	0.875022i	−0.395063	−	0.918654i	$-0.629277\pi$
$571$	14.4326	−	20.9092i	0.603984	−	0.875022i	0.999048	+	0.0436317i	$0.0138928\pi$
$572$	6.74489	−	6.60747i	0.282018	−	0.276272i
$573$	−6.64291	−	9.62392i	−0.277512	−	0.402045i
$574$	3.44586	+	3.88957i	0.143827	+	0.162348i
$575$	27.6682	+	6.81959i	1.15384	+	0.284396i
$576$	3.33521	+	4.83189i	0.138967	+	0.201329i
$577$		−	20.9448i		−	0.871942i	−0.899961	−	0.435971i	$-0.856405\pi$
$577$		−	20.9448i		−	0.871942i	0.899961	−	0.435971i	$-0.143595\pi$
$578$	−3.10770	+	2.14509i	−0.129263	+	0.0892239i
$579$	−12.5053	+	1.51841i	−0.519701	+	0.0631032i
$580$	10.6321	−	4.03222i	0.441474	−	0.167429i
$581$	−3.62634	+	29.8656i	−0.150446	+	1.23903i
$582$	−0.984702	−	2.59645i	−0.0408172	−	0.107626i
$583$	−6.70003	+	7.56277i	−0.277487	+	0.313218i
$584$	10.6481	+	9.43340i	0.440622	+	0.390357i
$585$	1.94435	+	2.53509i	0.0803888	+	0.104813i
$586$	−3.19335	+	2.82906i	−0.131916	+	0.116867i
$587$			3.41585i			0.140987i	0.997512	+	0.0704937i	$0.0224575\pi$
$587$			3.41585i			0.140987i	−0.997512	+	0.0704937i	$0.977543\pi$
$588$	4.21254	+	3.73199i	0.173722	+	0.153904i
$589$	29.2608	−	7.21215i	1.20567	−	0.297171i
$590$	−1.06324	−	0.733901i	−0.0437729	−	0.0302142i
$591$	−22.9384	+	8.69941i	−0.943562	+	0.357846i
$592$	−11.8782	+	4.50479i	−0.488189	+	0.185146i
$593$	−35.4329	−	24.4576i	−1.45505	−	1.00435i	−0.993078	−	0.117460i	$-0.962525\pi$
$593$	−35.4329	−	24.4576i	−1.45505	−	1.00435i	−0.461977	−	0.886892i	$-0.652860\pi$
$594$	0.404714	−	0.0997530i	0.0166056	−	0.00409292i
$595$	−2.85177	−	2.52645i	−0.116911	−	0.103574i
$596$			27.1855i			1.11356i
$597$	18.0996	−	16.0349i	0.740768	−	0.656263i
$598$	5.28784	−	5.18010i	0.216236	−	0.211830i
$599$	−19.2857	−	17.0856i	−0.787991	−	0.698099i	0.169828	−	0.985474i	$-0.445679\pi$
$599$	−19.2857	−	17.0856i	−0.787991	−	0.698099i	−0.957818	+	0.287375i	$0.907217\pi$
$600$	3.31663	−	3.74370i	0.135401	−	0.152836i
$601$	7.91137	+	20.8606i	0.322712	+	0.850921i	0.993965	+	0.109693i	$0.0349868\pi$
$601$	7.91137	+	20.8606i	0.322712	+	0.850921i	−0.671254	+	0.741228i	$0.734244\pi$
$602$	0.520159	−	4.28389i	0.0212001	−	0.174598i
$603$	−0.957506	+	0.363134i	−0.0389927	+	0.0147880i
$604$	−23.8427	+	2.89503i	−0.970145	+	0.117797i
$605$	6.64763	−	4.58853i	0.270264	−	0.186550i
$606$			5.35584i			0.217566i
$607$	9.06096	+	13.1271i	0.367773	+	0.532811i	0.962559	−	0.271073i	$-0.0873785\pi$
$607$	9.06096	+	13.1271i	0.367773	+	0.532811i	−0.594786	+	0.803884i	$0.702763\pi$
$608$	−19.8154	−	4.88406i	−0.803621	−	0.198075i
$609$	8.97661	+	10.1325i	0.363751	+	0.410590i
$610$	0.562981	+	0.815619i	0.0227945	+	0.0330235i
$611$	26.9775	−	8.10289i	1.09139	−	0.327808i
$612$	−2.31545	+	3.35450i	−0.0935963	+	0.135598i
$613$	−27.3378	+	3.31941i	−1.10416	+	0.134070i	−0.652259	−	0.757996i	$-0.726178\pi$
$613$	−27.3378	+	3.31941i	−1.10416	+	0.134070i	−0.451905	+	0.892066i	$0.649255\pi$
$614$	−0.562732	+	4.63452i	−0.0227100	+	0.187034i
$615$	−6.67161	−	3.50153i	−0.269025	−	0.141195i
$616$	−0.784489	+	3.18280i	−0.0316080	+	0.128239i
$617$	3.41755	+	0.414966i	0.137585	+	0.0167059i	0.189040	−	0.981969i	$-0.439463\pi$
$617$	3.41755	+	0.414966i	0.137585	+	0.0167059i	−0.0514542	+	0.998675i	$0.516386\pi$
$618$	1.60510	−	1.81178i	0.0645666	−	0.0728807i
$619$	−29.3742	+	20.2756i	−1.18065	+	0.814944i	−0.986133	−	0.165955i	$-0.946929\pi$
$619$	−29.3742	+	20.2756i	−1.18065	+	0.814944i	−0.194517	+	0.980899i	$0.562314\pi$
$620$	4.85332	−	7.03125i	0.194914	−	0.282382i
$621$	−6.56447	+	1.61800i	−0.263423	+	0.0649280i
$622$	3.20482	+	0.389135i	0.128501	+	0.0156029i
$623$	−13.7723	+	7.22828i	−0.551777	+	0.289595i
$624$	3.58370	+	11.9315i	0.143463	+	0.477641i
$625$	12.2538	+	6.43130i	0.490153	+	0.257252i
$626$	−0.0965917	−	0.0666725i	−0.00386058	−	0.00266477i
$627$	4.64970	−	6.73626i	0.185691	−	0.269020i
$628$	−9.72972	+	8.61978i	−0.388258	+	0.343966i
$629$	−5.20898	−	5.87972i	−0.207695	−	0.234440i
$630$	−0.506315	−	0.192020i	−0.0201721	−	0.00765026i
$631$	4.76656	−	9.08191i	0.189754	−	0.361545i	−0.771930	−	0.635708i	$-0.780708\pi$
$631$	4.76656	−	9.08191i	0.189754	−	0.361545i	0.961683	+	0.274163i	$0.0884006\pi$
$632$	−6.39657	−	2.42590i	−0.254442	−	0.0964970i
$633$	2.11898	+	0.522281i	0.0842219	+	0.0207588i
$634$	−0.238184	+	0.211013i	−0.00945950	+	0.00838038i
$635$	11.2174	−	7.74279i	0.445148	−	0.307263i
$636$	−4.97959	−	13.1301i	−0.197454	−	0.520643i
$637$	5.40855	+	9.15843i	0.214295	+	0.362870i
$638$	0.994234	−	2.62158i	0.0393621	−	0.103789i
$639$	0.744947	+	3.02237i	0.0294696	+	0.119563i
$640$	−6.76945	+	3.55288i	−0.267586	+	0.140440i
$641$	−10.6161	−	27.9923i	−0.419309	−	1.10563i	−0.963745	−	0.266825i	$-0.914025\pi$
$641$	−10.6161	−	27.9923i	−0.419309	−	1.10563i	0.544435	−	0.838803i	$-0.316744\pi$
$642$	−3.98586	+	0.483971i	−0.157309	+	0.0191008i
$643$	−1.19348	−	0.823802i	−0.0470664	−	0.0324876i	0.544299	−	0.838891i	$-0.316796\pi$
$643$	−1.19348	−	0.823802i	−0.0470664	−	0.0324876i	−0.591366	+	0.806404i	$0.701411\pi$
$644$	6.21209	−	25.2034i	0.244791	−	0.993155i
$645$	1.49743	+	6.07533i	0.0589614	+	0.239216i
$646$	−0.466316	−	3.84045i	−0.0183469	−	0.151101i
$647$	−4.86438	+	12.8263i	−0.191238	+	0.504254i	−0.996001	−	0.0893427i	$-0.971523\pi$
$647$	−4.86438	+	12.8263i	−0.191238	+	0.504254i	0.804763	+	0.593597i	$0.202293\pi$
$648$	−0.283984	+	1.15217i	−0.0111559	+	0.0452614i
$649$	6.39919	−	1.57726i	0.251190	−	0.0619128i
$650$	3.97353	−	2.34659i	0.155855	−	0.0920408i
$651$	9.87537	+	2.43406i	0.387046	+	0.0953983i
$652$	10.3941	−	19.8044i	0.407066	−	0.775599i
$653$	−18.1193			−0.709064			−0.354532	−	0.935044i	$-0.615360\pi$
$653$	−18.1193			−0.709064			−0.354532	+	0.935044i	$0.615360\pi$
$654$	−3.89293			−0.152226
$655$	3.53082	−	6.72742i	0.137961	−	0.262862i
$656$	−19.4829	−	21.9917i	−0.760681	−	0.858632i
$657$		−	11.9881i		−	0.467702i
$658$	−3.16593	+	3.57359i	−0.123421	+	0.139313i
$659$	−9.28811	+	4.87477i	−0.361813	+	0.189894i	−0.635827	−	0.771831i	$-0.719341\pi$
$659$	−9.28811	+	4.87477i	−0.361813	+	0.189894i	0.274014	+	0.961726i	$0.411649\pi$
$660$	−0.279701	−	2.30355i	−0.0108874	−	0.0896654i
$661$	−10.3936	−	19.8034i	−0.404265	−	0.770262i	0.595180	−	0.803593i	$-0.297081\pi$
$661$	−10.3936	−	19.8034i	−0.404265	−	0.770262i	−0.999444	+	0.0333304i	$0.989389\pi$
$662$	0.129386	+	1.06559i	0.00502872	+	0.0414152i
$663$	−6.11250	+	4.68812i	−0.237390	+	0.182072i
$664$	−2.13826	+	17.6102i	−0.0829807	+	0.683407i
$665$	−9.94244	+	3.77067i	−0.385551	+	0.146220i
$666$	−0.988577	−	0.518845i	−0.0383066	−	0.0201048i
$667$	−16.1265	+	42.5221i	−0.624420	+	1.64646i
$668$	−10.4841	−	19.9758i	−0.405642	−	0.772885i
$669$	10.5811	+	20.1605i	0.409087	+	0.779451i
$670$	−0.0659425	−	0.267539i	−0.00254758	−	0.0103359i
$671$	−5.01892	−	0.609407i	−0.193753	−	0.0235259i
$672$	−5.15554	−	4.56741i	−0.198879	−	0.176192i
$673$	13.7695	+	19.9485i	0.530775	+	0.768960i	0.993039	−	0.117782i	$-0.0375784\pi$
$673$	13.7695	+	19.9485i	0.530775	+	0.768960i	−0.462265	+	0.886742i	$0.652963\pi$
$674$	1.18364	+	0.448894i	0.0455919	+	0.0172907i
$675$	−4.21483			−0.162229
$676$	−0.510459	+	24.7960i	−0.0196331	+	0.953692i
$677$	−2.77963			−0.106830			−0.0534149	−	0.998572i	$-0.517011\pi$
$677$	−2.77963			−0.106830			−0.0534149	+	0.998572i	$0.517011\pi$
$678$	0.574886	+	0.218025i	0.0220783	+	0.00837321i
$679$	−10.4543	−	15.1457i	−0.401201	−	0.581240i
$680$	−1.68154	−	1.48971i	−0.0644841	−	0.0571280i
$681$	−14.3994	−	1.74841i	−0.551788	−	0.0669992i
$682$	−0.504146	−	2.04540i	−0.0193047	−	0.0783224i
$683$	−1.60492	−	3.05792i	−0.0614105	−	0.117008i	0.852816	−	0.522212i	$-0.174893\pi$
$683$	−1.60492	−	3.05792i	−0.0614105	−	0.117008i	−0.914226	+	0.405204i	$0.867201\pi$
$684$	5.28674	+	10.0730i	0.202144	+	0.385152i
$685$	1.34478	−	3.54589i	0.0513814	−	0.135482i
$686$	−5.38405	−	2.82577i	−0.205564	−	0.107888i
$687$	−24.1914	+	9.17459i	−0.922960	+	0.350032i
$688$	−2.94099	+	24.2212i	−0.112124	+	0.923424i
$689$	−1.32969	−	26.5060i	−0.0506571	−	1.00980i
$690$	−0.219279	−	1.80593i	−0.00834782	−	0.0687505i
$691$	19.3004	+	36.7738i	0.734221	+	1.39894i	0.910041	+	0.414518i	$0.136050\pi$
$691$	19.3004	+	36.7738i	0.734221	+	1.39894i	−0.175820	+	0.984422i	$0.556258\pi$
$692$	2.52794	+	20.8194i	0.0960978	+	0.791436i
$693$	2.44602	−	1.28377i	0.0929168	−	0.0487665i
$694$	2.34733	−	2.64959i	0.0891035	−	0.100577i
$695$		−	8.59346i		−	0.325969i
$696$	5.29304	+	5.97460i	0.200632	+	0.226467i
$697$	8.44274	−	16.0863i	0.319792	−	0.609312i
$698$	0.0701858			0.00265657
$699$	26.3560			0.996877
$700$	7.52030	−	14.3287i	0.284241	−	0.541575i
$701$	−38.6146	−	9.51764i	−1.45845	−	0.359476i	−0.571219	−	0.820798i	$-0.693529\pi$
$701$	−38.6146	−	9.51764i	−1.45845	−	0.359476i	−0.887233	+	0.461321i	$0.847375\pi$
$702$	−0.576031	+	0.931091i	−0.0217409	+	0.0351418i
$703$	−21.2867	+	5.24671i	−0.802844	+	0.197883i
$704$	1.92868	−	7.82497i	0.0726899	−	0.294915i
$705$	2.45477	−	6.47270i	0.0924521	−	0.243776i
$706$	0.173108	+	1.42568i	0.00651502	+	0.0536560i
$707$	8.49449	+	34.4635i	0.319468	+	1.29613i
$708$	−2.19215	+	8.89388i	−0.0823859	+	0.334253i
$709$	31.3461	+	21.6366i	1.17723	+	0.812581i	0.985634	−	0.168893i	$-0.0540194\pi$
$709$	31.3461	+	21.6366i	1.17723	+	0.812581i	0.191593	+	0.981475i	$0.438635\pi$
$710$	−0.831472	+	0.100959i	−0.0312046	+	0.00378893i
$711$	2.04433	+	5.39045i	0.0766682	+	0.202157i
$712$	−8.12082	+	4.26214i	−0.304341	+	0.159730i
$713$	8.17726	+	33.1764i	0.306241	+	1.24247i
$714$	0.462990	−	1.22081i	0.0173270	−	0.0456875i
$715$	0.834855	−	4.30527i	0.0312218	−	0.161008i
$716$	14.3293	+	37.7831i	0.535509	+	1.41202i
$717$	−4.10249	+	2.83174i	−0.153210	+	0.105753i
$718$	6.36841	−	5.64192i	0.237667	−	0.210554i
$719$	21.0267	+	5.18261i	0.784163	+	0.193279i	0.611017	−	0.791617i	$-0.290761\pi$
$719$	21.0267	+	5.18261i	0.784163	+	0.193279i	0.173146	+	0.984896i	$0.444607\pi$
$720$	2.86271	+	1.08568i	0.106687	+	0.0404610i
$721$	7.45490	−	14.2041i	0.277635	−	0.528989i
$722$	−4.70105	−	1.78287i	−0.174955	−	0.0663517i
$723$	9.47671	+	10.6970i	0.352443	+	0.397826i
$724$	9.41290	−	8.33910i	0.349828	−	0.309920i
$725$	−16.1052	+	23.3325i	−0.598133	+	0.866546i
$726$	2.27812	+	1.57247i	0.0845491	+	0.0583600i
$727$	−20.2859	−	10.6469i	−0.752362	−	0.394870i	0.0445175	−	0.999009i	$-0.485825\pi$
$727$	−20.2859	−	10.6469i	−0.752362	−	0.394870i	−0.796879	+	0.604139i	$0.793517\pi$
$728$	−4.37842	−	7.41408i	−0.162275	−	0.274784i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	3.20218	+	0.388815i	0.118518	+	0.0143907i
$731$	−14.6486	+	3.61055i	−0.541797	+	0.133541i
$732$	3.99165	−	5.78291i	0.147536	−	0.213742i
$733$	−5.46579	+	3.77276i	−0.201883	+	0.139350i	−0.664717	−	0.747095i	$-0.731448\pi$
$733$	−5.46579	+	3.77276i	−0.201883	+	0.139350i	0.462834	+	0.886445i	$0.346833\pi$
$734$	4.58903	−	5.17995i	0.169384	−	0.191195i
$735$	2.59489	+	0.315076i	0.0957138	+	0.0116218i
$736$	5.53763	−	22.4671i	0.204120	−	0.828147i
$737$	1.24467	+	0.653252i	0.0458479	+	0.0240628i
$738$	0.311238	−	2.56328i	0.0114568	−	0.0943556i
$739$	−24.2606	+	2.94577i	−0.892441	+	0.108362i	−0.553894	−	0.832587i	$-0.686859\pi$
$739$	−24.2606	+	2.94577i	−0.892441	+	0.108362i	−0.338547	+	0.940949i	$0.609936\pi$
$740$	−3.53070	+	5.11511i	−0.129791	+	0.188035i
$741$	3.65761	+	21.1864i	0.134365	+	0.778303i
$742$	2.55527	+	3.70195i	0.0938071	+	0.135903i
$743$	−18.3762	−	20.7425i	−0.674158	−	0.760967i	0.307515	−	0.951543i	$-0.400503\pi$
$743$	−18.3762	−	20.7425i	−0.674158	−	0.760967i	−0.981672	+	0.190577i	$0.938964\pi$
$744$	5.82298	+	1.43524i	0.213481	+	0.0526183i
$745$	7.17275	+	10.3915i	0.262789	+	0.380716i
$746$			5.18707i			0.189912i
$747$	12.3030	−	8.49214i	0.450143	−	0.310711i
$748$	5.55421	−	0.674403i	0.203082	−	0.0246586i
$749$	−24.8804	+	9.43590i	−0.909111	+	0.344780i
$750$	0.298867	−	2.46139i	0.0109131	−	0.0898774i
$751$	−0.861918	−	2.27269i	−0.0314518	−	0.0829317i	0.918370	−	0.395722i	$-0.129506\pi$
$751$	−0.861918	−	2.27269i	−0.0314518	−	0.0829317i	−0.949822	+	0.312790i	$0.898736\pi$
$752$	17.9002	−	20.2051i	0.652753	−	0.736806i
$753$	1.64172	+	1.45444i	0.0598277	+	0.0530027i
$754$	2.95327	+	6.74657i	0.107552	+	0.245695i
$755$	−8.34990	+	7.39737i	−0.303884	+	0.269218i
$756$			3.83937i			0.139637i
$757$	4.06860	+	3.60446i	0.147876	+	0.131006i	0.733817	−	0.679347i	$-0.237737\pi$
$757$	4.06860	+	3.60446i	0.147876	+	0.131006i	−0.585942	+	0.810353i	$0.699275\pi$
$758$	−2.13540	+	0.526329i	−0.0775612	+	0.0191171i
$759$	7.63768	+	5.27191i	0.277230	+	0.191358i
$760$	−5.86254	+	2.22337i	−0.212656	+	0.0806500i
$761$	−41.8490	+	15.8712i	−1.51702	+	0.575331i	−0.965860	−	0.259066i	$-0.916585\pi$
$761$	−41.8490	+	15.8712i	−1.51702	+	0.575331i	−0.551164	+	0.834397i	$0.685816\pi$
$762$	3.84416	+	2.65343i	0.139259	+	0.0961237i
$763$	−25.0501	+	6.17428i	−0.906873	+	0.223524i
$764$	−16.6989	−	14.7940i	−0.604147	−	0.535227i
$765$			1.89316i			0.0684473i
$766$	−2.87067	+	2.54319i	−0.103721	+	0.0918891i
$767$	−9.10799	+	14.7221i	−0.328870	+	0.531583i
$768$	6.82821	+	6.04927i	0.246392	+	0.218284i
$769$	6.48718	−	7.32251i	0.233934	−	0.264056i	−0.619808	−	0.784754i	$-0.712789\pi$
$769$	6.48718	−	7.32251i	0.233934	−	0.264056i	0.853741	+	0.520697i	$0.174328\pi$
$770$	0.263579	+	0.695000i	0.00949872	+	0.0250461i
$771$	0.968258	−	7.97432i	0.0348710	−	0.287188i
$772$	−22.4709	+	8.52209i	−0.808746	+	0.306717i
$773$	−8.47810	+	1.02943i	−0.304936	+	0.0370259i	−0.271574	−	0.962417i	$-0.587544\pi$
$773$	−8.47810	+	1.02943i	−0.304936	+	0.0370259i	−0.0333615	+	0.999443i	$0.510621\pi$
$774$	−1.76473	+	1.21811i	−0.0634319	+	0.0437839i
$775$			21.3015i			0.765173i
$776$	−6.16437	−	8.93064i	−0.221288	−	0.320591i
$777$	−7.18415	−	1.77073i	−0.257730	−	0.0635247i
$778$	−5.13029	−	5.79090i	−0.183930	−	0.207614i
$779$	−28.8034	−	41.7290i	−1.03199	−	1.49510i
$780$	4.75904	+	3.80816i	0.170401	+	0.136354i
$781$	2.42726	−	3.51649i	0.0868541	−	0.125830i
$782$	4.35437	−	0.528717i	0.155712	−	0.0189069i
$783$	0.810789	−	6.67745i	0.0289752	−	0.238633i
$784$	9.02528	+	4.73683i	0.322331	+	0.169173i
$785$	−1.44485	+	5.86200i	−0.0515690	+	0.209224i
$786$	2.58472	+	0.313842i	0.0921940	+	0.0111944i
$787$	−10.0963	+	11.3964i	−0.359896	+	0.406238i	−0.900372	−	0.435121i	$-0.856706\pi$
$787$	−10.0963	+	11.3964i	−0.359896	+	0.406238i	0.540476	+	0.841359i	$0.318244\pi$
$788$	−38.5183	+	26.5872i	−1.37216	+	0.947131i
$789$	13.7551	−	19.9277i	0.489694	−	0.709444i
$790$	−1.50616	+	0.371235i	−0.0535867	+	0.0132079i
$791$	4.04504	+	0.491157i	0.143825	+	0.0174635i
$792$	1.44229	−	0.756973i	0.0512496	−	0.0268979i
$793$	10.5375	−	8.08197i	0.374197	−	0.286999i
$794$	−5.87690	−	3.08444i	−0.208563	−	0.109463i
$795$	−5.36773	−	3.70508i	−0.190374	−	0.131406i
$796$	26.2059	−	37.9658i	0.928845	−	1.34566i
$797$	−27.8905	+	24.7088i	−0.987931	+	0.875230i	−0.992187	−	0.124761i	$-0.960184\pi$
$797$	−27.8905	+	24.7088i	−0.987931	+	0.875230i	0.00425611	+	0.999991i	$0.498645\pi$
$798$	−2.41645	−	2.72761i	−0.0855415	−	0.0965564i
$799$	15.6067	+	5.91884i	0.552126	+	0.209394i
$800$	6.70380	−	12.7730i	0.237015	−	0.451595i
$801$	7.22653	+	2.74066i	0.255337	+	0.0968365i
$802$	7.44534	+	1.83511i	0.262904	+	0.0648001i
$803$	−12.3173	+	10.9121i	−0.434667	+	0.385081i
$804$	−1.60784	+	1.10981i	−0.0567043	+	0.0391402i
$805$	−4.27525	−	11.2729i	−0.150683	−	0.397318i
$806$	4.70568	+	2.91123i	0.165750	+	0.102544i
$807$	7.17494	−	18.9188i	0.252570	−	0.665972i
$808$	5.00875	+	20.3213i	0.176207	+	0.714901i
$809$	−35.2289	+	18.4896i	−1.23858	+	0.650059i	−0.951442	−	0.307829i	$-0.900397\pi$
$809$	−35.2289	+	18.4896i	−1.23858	+	0.650059i	−0.287142	+	0.957888i	$0.592705\pi$
$810$	0.0954150	+	0.251589i	0.00335254	+	0.00883992i
$811$	2.70837	−	0.328856i	0.0951039	−	0.0115477i	−0.0728464	−	0.997343i	$-0.523208\pi$
$811$	2.70837	−	0.328856i	0.0951039	−	0.0115477i	0.167950	+	0.985795i	$0.446285\pi$
$812$	21.2540	+	14.6706i	0.745868	+	0.514836i
$813$	5.56537	−	22.5796i	0.195186	−	0.791901i
$814$	0.366757	+	1.48799i	0.0128548	+	0.0521541i
$815$	−1.25217	−	10.3126i	−0.0438616	−	0.361233i
$816$	−2.61775	+	6.90245i	−0.0916397	+	0.241634i
$817$	−10.0770	+	40.8839i	−0.352549	+	1.43035i
$818$	8.50996	−	2.09752i	0.297544	−	0.0733379i
$819$	−2.22988	+	6.90494i	−0.0779184	+	0.241278i
$820$	−13.9568	−	3.44005i	−0.487394	−	0.120132i
$821$	20.4666	−	38.9959i	0.714290	−	1.36097i	−0.209402	−	0.977830i	$-0.567152\pi$
$821$	20.4666	−	38.9959i	0.714290	−	1.36097i	0.923692	−	0.383136i	$-0.125156\pi$
$822$	1.29962			0.0453295
$823$	−21.0119			−0.732429			−0.366215	−	0.930530i	$-0.619346\pi$
$823$	−21.0119			−0.732429			−0.366215	+	0.930530i	$0.619346\pi$
$824$	4.39576	−	8.37542i	0.153134	−	0.291772i
$825$	3.83653	+	4.33054i	0.133571	+	0.150770i
$826$		−	2.93419i		−	0.102094i
$827$	−28.3905	+	32.0462i	−0.987233	+	1.11436i	0.00620452	+	0.999981i	$0.498025\pi$
$827$	−28.3905	+	32.0462i	−0.987233	+	1.11436i	−0.993438	+	0.114375i	$0.963513\pi$
$828$	−11.4210	+	5.99420i	−0.396907	+	0.208313i
$829$	−3.88347	−	31.9833i	−0.134879	−	1.11082i	−0.890232	−	0.455507i	$-0.849458\pi$
$829$	−3.88347	−	31.9833i	−0.134879	−	1.11082i	0.755354	−	0.655317i	$-0.227465\pi$
$830$	1.86933	+	3.56171i	0.0648853	+	0.123629i
$831$	0.907094	+	7.47059i	0.0314668	+	0.259152i
$832$	10.7644	+	18.2277i	0.373189	+	0.631930i
$833$	−0.759698	+	6.25668i	−0.0263220	+	0.216781i
$834$	2.75358	−	1.04430i	0.0953487	−	0.0361610i
$835$	−9.27799	−	4.86946i	−0.321078	−	0.168515i
$836$	5.53735	−	14.6008i	0.191513	−	0.504979i
$837$	−2.34868	−	4.47504i	−0.0811824	−	0.154680i
$838$	4.76744	+	9.08360i	0.164688	+	0.313788i
$839$	5.11347	+	20.7461i	0.176536	+	0.716237i	0.990753	+	0.135676i	$0.0433205\pi$
$839$	5.11347	+	20.7461i	0.176536	+	0.716237i	−0.814217	+	0.580561i	$0.802833\pi$
$840$	−2.10065	−	0.255066i	−0.0724795	−	0.00880060i
$841$	−12.1601	−	10.7729i	−0.419314	−	0.371479i
$842$	−0.0200294	−	0.0290175i	−0.000690258	−	0.00100001i
$843$	−5.57122	−	2.11288i	−0.191883	−	0.0727716i
$844$	4.16355			0.143315
$845$	6.34717	+	9.61283i	0.218349	+	0.330691i
$846$	2.37234			0.0815628
$847$	17.1531	+	6.50533i	0.589389	+	0.223526i
$848$	−14.4476	−	20.9309i	−0.496131	−	0.718770i
$849$	3.24800	+	2.87747i	0.111471	+	0.0987546i
$850$	2.71456	+	0.329608i	0.0931087	+	0.0113054i
$851$	−5.94881	−	24.1353i	−0.203922	−	0.827346i
$852$	2.75981	+	5.25837i	0.0945495	+	0.180149i
$853$	11.6072	+	22.1156i	0.397422	+	0.757224i	0.999139	−	0.0414854i	$-0.0132090\pi$
$853$	11.6072	+	22.1156i	0.397422	+	0.757224i	−0.601718	+	0.798709i	$0.705517\pi$
$854$	−0.798160	+	2.10458i	−0.0273125	+	0.0720171i
$855$	4.67855	+	2.45549i	0.160003	+	0.0839760i
$856$	−14.6707	+	5.56385i	−0.501433	+	0.190169i
$857$	−4.68204	+	38.5601i	−0.159935	+	1.31719i	0.662814	+	0.748784i	$0.269362\pi$
$857$	−4.68204	+	38.5601i	−0.159935	+	1.31719i	−0.822750	+	0.568404i	$0.807561\pi$
$858$	1.48098	−	0.255675i	0.0505598	−	0.00872861i
$859$	−0.905893	−	7.46070i	−0.0309087	−	0.254556i	−0.999970	−	0.00773608i	$-0.997538\pi$
$859$	−0.905893	−	7.46070i	−0.0309087	−	0.254556i	0.969061	−	0.246820i	$-0.0793856\pi$
$860$	5.54755	+	10.5700i	0.189170	+	0.360433i
$861$	−2.06268	−	16.9877i	−0.0702960	−	0.578939i
$862$	3.17548	−	1.66662i	0.108157	−	0.0567654i
$863$	26.9297	−	30.3974i	0.916698	−	1.03474i	−0.0825742	−	0.996585i	$-0.526314\pi$
$863$	26.9297	−	30.3974i	0.916698	−	1.03474i	0.999272	−	0.0381529i	$-0.0121474\pi$
$864$			3.42252i			0.116437i
$865$	6.45939	+	7.29114i	0.219626	+	0.247906i
$866$	−1.16172	+	2.21348i	−0.0394770	+	0.0752171i
$867$	12.4353			0.422325
$868$	19.4040			0.658613
$869$	3.67759	−	7.00707i	0.124754	−	0.237699i
$870$	1.75733	+	0.433143i	0.0595791	+	0.0146849i
$871$	−3.53621	+	1.06213i	−0.119820	+	0.0359888i
$872$	−14.7707	+	3.64065i	−0.500199	+	0.123288i
$873$	−2.18847	+	8.87896i	−0.0740684	+	0.300507i
$874$	4.34116	−	11.4467i	0.146842	−	0.387190i
$875$	−1.98069	−	16.3125i	−0.0669597	−	0.551462i
$876$	−5.47335	−	22.2063i	−0.184928	−	0.750280i
$877$	3.51979	−	14.2804i	0.118855	−	0.482214i	−0.881102	−	0.472926i	$-0.843198\pi$
$877$	3.51979	−	14.2804i	0.118855	−	0.482214i	0.999957	−	0.00928714i	$-0.00295623\pi$
$878$	10.1720	+	7.02122i	0.343288	+	0.236955i
$879$	13.9469	−	1.69346i	0.470418	−	0.0571191i
$880$	−1.49028	−	3.92954i	−0.0502372	−	0.132465i
$881$	−35.6917	+	18.7325i	−1.20248	+	0.631113i	−0.942405	−	0.334474i	$-0.891441\pi$
$881$	−35.6917	+	18.7325i	−1.20248	+	0.631113i	−0.260080	+	0.965587i	$0.583749\pi$
$882$	0.214377	+	0.869761i	0.00721845	+	0.0292864i
$883$	12.1849	−	32.1290i	0.410056	−	1.08123i	−0.557856	−	0.829938i	$-0.688376\pi$
$883$	12.1849	−	32.1290i	0.410056	−	1.08123i	0.967912	−	0.251290i	$-0.0808549\pi$
$884$	−9.18207	+	11.4748i	−0.308827	+	0.385939i
$885$	1.50867	+	3.97803i	0.0507133	+	0.133720i
$886$	−3.43719	+	2.37252i	−0.115475	+	0.0797064i
$887$	−36.3268	+	32.1828i	−1.21974	+	1.08059i	−0.225405	+	0.974265i	$0.572370\pi$
$887$	−36.3268	+	32.1828i	−1.21974	+	1.08059i	−0.994331	+	0.106326i	$0.966091\pi$
$888$	−4.23611	−	1.04411i	−0.142155	−	0.0350380i
$889$	28.9446	+	10.9772i	0.970771	+	0.368165i
$890$	−0.966445	+	1.84141i	−0.0323953	+	0.0617241i
$891$	−1.28346	−	0.486753i	−0.0429976	−	0.0163068i
$892$	28.8044	+	32.5135i	0.964443	+	1.08863i
$893$	34.8696	−	30.8918i	1.16687	−	1.03375i
$894$	−2.45808	+	3.56114i	−0.0822105	+	0.119102i
$895$	15.4462	+	10.6617i	0.516308	+	0.356382i
$896$	−15.3745	−	8.06918i	−0.513627	−	0.269572i
$897$	−24.0215	+	4.14706i	−0.802056	+	0.138466i
$898$	1.65141	−	0.866727i	0.0551083	−	0.0289231i
$899$	−33.7474	−	4.09768i	−1.12554	−	0.136665i
$900$	−7.80736	+	1.92434i	−0.260245	+	0.0641447i
$901$	8.93353	−	12.9424i	0.297619	−	0.431175i
$902$	−2.91695	+	2.01343i	−0.0971239	+	0.0670398i
$903$	−9.42366	+	10.6371i	−0.313600	+	0.353981i
$904$	2.38515	+	0.289609i	0.0793288	+	0.00963226i
$905$	1.39781	−	5.67112i	0.0464646	−	0.188514i
$906$	−3.38502	−	1.77659i	−0.112460	−	0.0590234i
$907$	3.67110	−	30.2343i	0.121897	−	1.00391i	−0.795504	−	0.605948i	$-0.792794\pi$
$907$	3.67110	−	30.2343i	0.121897	−	1.00391i	0.917401	−	0.397964i	$-0.130283\pi$
$908$	−27.4711	+	3.33559i	−0.911660	+	0.110696i
$909$	10.0192	−	14.5154i	0.332317	−	0.481444i
$910$	−1.77207	−	0.819579i	−0.0587436	−	0.0271688i
$911$	−16.5057	−	23.9126i	−0.546857	−	0.792259i	0.447948	−	0.894060i	$-0.352155\pi$
$911$	−16.5057	−	23.9126i	−0.546857	−	0.792259i	−0.994805	+	0.101801i	$0.967540\pi$
$912$	13.6627	+	15.4219i	0.452416	+	0.510672i
$913$	−19.9240	−	4.91083i	−0.659388	−	0.162525i
$914$	−4.90779	−	7.11016i	−0.162335	−	0.235183i
$915$		−	3.26366i		−	0.107893i
$916$	−40.6222	+	28.0395i	−1.34220	+	0.926451i
$917$	17.1298	−	2.07994i	0.565676	−	0.0686855i
$918$	−0.606620	+	0.230061i	−0.0200214	+	0.00759313i
$919$	3.52923	−	29.0658i	0.116419	−	0.958793i	−0.811072	−	0.584947i	$-0.801115\pi$
$919$	3.52923	−	29.0658i	0.116419	−	0.958793i	0.927490	−	0.373847i	$-0.121961\pi$
$920$	−2.52089	−	6.64704i	−0.0831113	−	0.219147i
$921$	10.1950	−	11.5077i	0.335935	−	0.379192i
$922$	2.04086	+	1.80804i	0.0672121	+	0.0595447i
$923$	1.90936	+	11.0598i	0.0628473	+	0.364039i
$924$	3.94477	−	3.49476i	0.129774	−	0.114969i
$925$		−	15.4965i		−	0.509521i
$926$	4.64503	+	4.11514i	0.152645	+	0.135232i
$927$	−7.73946	+	1.90761i	−0.254197	+	0.0626540i
$928$	18.9464	+	13.0778i	0.621946	+	0.429298i
$929$	−17.1647	+	6.50971i	−0.563156	+	0.213577i	−0.619721	−	0.784822i	$-0.712754\pi$
$929$	−17.1647	+	6.50971i	−0.563156	+	0.213577i	0.0565654	+	0.998399i	$0.481985\pi$
$930$	1.27151	−	0.482222i	0.0416946	−	0.0158127i
$931$	14.4767	+	9.99256i	0.474456	+	0.327493i
$932$	48.8207	−	12.0332i	1.59917	−	0.394161i
$933$	−7.95771	−	7.04991i	−0.260524	−	0.230804i
$934$			9.10504i			0.297926i
$935$	1.94513	−	1.72324i	0.0636126	−	0.0563558i
$936$	−1.31485	+	4.07148i	−0.0429771	+	0.133080i
$937$	11.4318	+	10.1277i	0.373462	+	0.330858i	0.828887	−	0.559416i	$-0.188974\pi$
$937$	11.4318	+	10.1277i	0.373462	+	0.330858i	−0.455426	+	0.890274i	$0.650513\pi$
$938$	0.414990	−	0.468426i	0.0135499	−	0.0152947i
$939$	0.137057	+	0.361390i	0.00447270	+	0.0117935i
$940$	1.59190	−	13.1105i	0.0519221	−	0.427617i
$941$	22.8831	−	8.67840i	0.745967	−	0.282908i	0.0478135	−	0.998856i	$-0.484775\pi$
$941$	22.8831	−	8.67840i	0.745967	−	0.282908i	0.698153	+	0.715948i	$0.254005\pi$
$942$	−2.05393	+	0.249392i	−0.0669205	+	0.00812562i
$943$	47.3130	−	32.6578i	1.54072	−	1.06348i
$944$			16.5900i			0.539958i
$945$	1.01300	+	1.46758i	0.0329528	+	0.0477404i
$946$	2.85788	+	0.704404i	0.0929177	+	0.0229022i
$947$	−20.2164	−	22.8196i	−0.656945	−	0.741538i	0.321757	−	0.946822i	$-0.395727\pi$
$947$	−20.2164	−	22.8196i	−0.656945	−	0.741538i	−0.978702	+	0.205284i	$0.934188\pi$
$948$	6.24789	+	9.05164i	0.202922	+	0.293984i
$949$	3.05368	−	43.1159i	0.0991268	−	1.39960i
$950$	4.33544	−	6.28096i	0.140660	−	0.203781i
$951$	1.04027	−	0.126311i	0.0337330	−	0.00409593i
$952$	0.615004	−	5.06501i	0.0199324	−	0.164158i
$953$	3.10443	+	1.62933i	0.100562	+	0.0527792i	0.514254	−	0.857638i	$-0.328069\pi$
$953$	3.10443	+	1.62933i	0.100562	+	0.0527792i	−0.413692	+	0.910417i	$0.635761\pi$
$954$	0.534910	−	2.17022i	0.0173184	−	0.0702634i
$955$	−10.2864	−	1.24899i	−0.332860	−	0.0404165i
$956$	−6.30638	+	7.11843i	−0.203963	+	0.230227i
$957$	−7.59878	+	5.24506i	−0.245634	+	0.169549i
$958$	5.23991	−	7.59132i	0.169294	−	0.245264i
$959$	8.36275	−	2.06123i	0.270047	−	0.0665606i
$960$	5.16450	+	0.627084i	0.166683	+	0.0202390i
$961$	4.83254	−	2.53631i	0.155888	−	0.0818165i
$962$	−3.42329	−	2.11786i	−0.110371	−	0.0682827i
$963$	11.7078	+	6.14473i	0.377279	+	0.198011i
$964$	22.4381	+	15.4879i	0.722682	+	0.498831i
$965$	−6.34088	+	9.18636i	−0.204120	+	0.295719i
$966$	3.09261	−	2.73982i	0.0995032	−	0.0881521i
$967$	−11.5074	−	12.9892i	−0.370055	−	0.417705i	0.533756	−	0.845639i	$-0.320780\pi$
$967$	−11.5074	−	12.9892i	−0.370055	−	0.417705i	−0.903810	+	0.427934i	$0.859242\pi$
$968$	10.1143	+	3.83585i	0.325086	+	0.123289i
$969$	−5.92058	+	11.2807i	−0.190196	+	0.362389i
$970$	−2.30070	−	0.872540i	−0.0738710	−	0.0280156i
$971$	−8.07908	−	1.99132i	−0.259270	−	0.0639043i	0.107538	−	0.994201i	$-0.465703\pi$
$971$	−8.07908	−	1.99132i	−0.259270	−	0.0639043i	−0.366808	+	0.930297i	$0.619549\pi$
$972$	1.42800	−	1.26510i	0.0458031	−	0.0405780i
$973$	16.0623	−	11.0870i	0.514935	−	0.355434i
$974$	0.932804	+	2.45960i	0.0298890	+	0.0788108i
$975$	−15.1588	−	1.07362i	−0.485471	−	0.0343835i
$976$	4.51281	−	11.8993i	0.144452	−	0.380887i
$977$	1.83792	+	7.45674i	0.0588003	+	0.238562i	0.992987	−	0.118222i	$-0.0377194\pi$
$977$	1.83792	+	7.45674i	0.0588003	+	0.238562i	−0.934187	+	0.356784i	$0.883873\pi$
$978$	3.15226	−	1.65443i	0.100798	−	0.0529029i
$979$	−3.76201	−	9.91959i	−0.120234	−	0.317032i
$980$	4.95050	−	0.601099i	0.158138	−	0.0192014i
$981$	10.5506	+	7.28255i	0.336855	+	0.232514i
$982$	1.56625	−	6.35452i	0.0499810	−	0.202781i
$983$	−9.67298	−	39.2448i	−0.308520	−	1.25172i	−0.896574	−	0.442894i	$-0.853952\pi$
$983$	−9.67298	−	39.2448i	−0.308520	−	1.25172i	0.588054	−	0.808822i	$-0.299894\pi$
$984$	−1.21625	−	10.0168i	−0.0387728	−	0.319322i
$985$	−7.70851	+	20.3257i	−0.245613	+	0.647629i
$986$	−1.04438	+	4.23720i	−0.0332597	+	0.134940i
$987$	15.2654	−	3.76259i	0.485904	−	0.119765i
$988$	16.4481	+	37.5748i	0.523285	+	1.19541i
$989$	−46.3549	−	11.4255i	−1.47400	−	0.363308i
$990$	0.171645	−	0.327041i	0.00545522	−	0.0103941i
$991$	−43.0907			−1.36882			−0.684411	−	0.729097i	$-0.739940\pi$
$991$	−43.0907			−1.36882			−0.684411	+	0.729097i	$0.739940\pi$
$992$	17.2972			0.549188
$993$	1.64274	−	3.12999i	0.0521309	−	0.0993272i
$994$	−1.26145	−	1.42388i	−0.0400107	−	0.0451627i
$995$		−	21.4265i		−	0.679267i
$996$	18.9123	−	21.3475i	0.599258	−	0.676423i
$997$	−36.9891	+	19.4134i	−1.17146	+	0.614828i	−0.934246	−	0.356630i	$-0.883926\pi$
$997$	−36.9891	+	19.4134i	−1.17146	+	0.614828i	−0.237212	+	0.971458i	$0.576234\pi$
$998$	0.261646	+	2.15485i	0.00828225	+	0.0682105i
$999$	1.70862	+	3.25551i	0.0540585	+	0.103000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.9	✓	192
169.142	even	26	inner	507.2.p.b.142.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.9	✓	192	1.1	even	1	trivial
507.2.p.b.142.9	yes	192	169.142	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.283929 + 0.107680i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.42800 - 1.26510i) q^{4} +(-0.879635 - 0.106807i) q^{5} +(-0.0726712 - 0.294839i) q^{6} +(-0.935242 - 1.78196i) q^{7} +(-0.551463 - 1.05073i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(0.283929 + 0.107680i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.42800 - 1.26510i) q^{4} +(-0.879635 - 0.106807i) q^{5} +(-0.0726712 - 0.294839i) q^{6} +(-0.935242 - 1.78196i) q^{7} +(-0.551463 - 1.05073i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-0.238253 - 0.125045i) q^{10} +(1.28346 - 0.486753i) q^{11} +(-0.229959 + 1.89388i) q^{12} +(-1.51352 + 3.27250i) q^{13} +(-0.0736614 - 0.606657i) q^{14} +(0.411789 + 0.784599i) q^{15} +(0.416483 + 3.43004i) q^{16} +(-1.89179 + 0.992889i) q^{17} +(-0.201365 + 0.227295i) q^{18} +5.96298i q^{19} +(1.12100 + 1.26535i) q^{20} +(-0.935242 + 1.78196i) q^{21} +0.416826 q^{22} -6.76093 q^{23} +(-0.551463 + 1.05073i) q^{24} +(-4.09236 - 1.00868i) q^{25} +(-0.782117 + 0.766182i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.918822 + 3.72781i) q^{28} +(2.38525 - 6.28938i) q^{29} +(0.0324333 + 0.267112i) q^{30} +(-1.20949 - 4.90708i) q^{31} +(-0.819064 + 3.32307i) q^{32} +(-1.12968 - 0.779761i) q^{33} +(-0.644050 + 0.0782018i) q^{34} +(0.632347 + 1.66736i) q^{35} +(1.68926 - 0.886594i) q^{36} +(0.879880 + 3.56981i) q^{37} +(-0.642095 + 1.69307i) q^{38} +(3.55299 - 0.613385i) q^{39} +(0.372862 + 0.983155i) q^{40} +(-6.99800 + 4.83037i) q^{41} +(-0.457424 + 0.405242i) q^{42} +(6.85629 + 1.68992i) q^{43} +(-2.44857 - 0.928622i) q^{44} +(0.411789 - 0.784599i) q^{45} +(-1.91963 - 0.728018i) q^{46} +(-5.18060 - 5.84769i) q^{47} +(2.58628 - 2.29125i) q^{48} +(1.67577 - 2.42777i) q^{49} +(-1.05333 - 0.727059i) q^{50} +(1.89179 + 0.992889i) q^{51} +(6.30134 - 2.75837i) q^{52} +(-6.51757 + 3.42069i) q^{53} +(0.301448 + 0.0366025i) q^{54} +(-1.18097 + 0.291082i) q^{55} +(-1.35659 + 1.96537i) q^{56} +(4.90744 - 3.38736i) q^{57} +(1.35448 - 1.52890i) q^{58} +(4.76639 + 0.578745i) q^{59} +(0.404559 - 1.64136i) q^{60} +(-3.26130 - 1.71166i) q^{61} +(0.184987 - 1.52350i) q^{62} +(1.99780 - 0.242577i) q^{63} +(3.33521 - 4.83189i) q^{64} +(1.68087 - 2.71695i) q^{65} +(-0.236784 - 0.343041i) q^{66} +(0.679073 + 0.766515i) q^{67} +(3.95758 + 0.975456i) q^{68} +(3.84065 + 5.56414i) q^{69} +0.541504i q^{70} +(2.56180 - 1.76828i) q^{71} +(1.17800 - 0.143035i) q^{72} +(-11.2091 + 4.25106i) q^{73} +(-0.134574 + 1.10832i) q^{74} +(1.49460 + 3.94094i) q^{75} +(7.54375 - 8.51514i) q^{76} +(-2.06772 - 1.83184i) q^{77} +(1.07485 + 0.208429i) q^{78} +(4.31523 - 3.82296i) q^{79} -3.06167i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-2.50707 + 0.617938i) q^{82} +(-12.3030 - 8.49214i) q^{83} +(3.58988 - 1.36146i) q^{84} +(1.77013 - 0.671323i) q^{85} +(1.76473 + 1.21811i) q^{86} +(-6.53103 + 1.60976i) q^{87} +(-1.21923 - 1.08014i) q^{88} -7.72878i q^{89} +(0.201405 - 0.178429i) q^{90} +(7.24696 - 0.363548i) q^{91} +(9.65461 + 8.55324i) q^{92} +(-3.35138 + 3.78293i) q^{93} +(-0.841244 - 2.21818i) q^{94} +(0.636888 - 5.24525i) q^{95} +(3.20012 - 1.21364i) q^{96} +(9.07801 - 1.10227i) q^{97} +(0.737222 - 0.508867i) q^{98} +1.37266i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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