LMFDB - Embedded newform 507.2.s.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, 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:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.259021 + 1.41343i) q^{2} +(0.863683 + 1.50135i) q^{3} +(-0.0606581 - 0.0230046i) q^{4} +(-2.17786 - 0.131736i) q^{5} +(-2.34576 + 0.831874i) q^{6} +(-1.46195 - 0.883779i) q^{7} +(-1.43857 + 2.37968i) q^{8} +(-1.50810 + 2.59338i) q^{9} +(0.750309 - 3.04412i) q^{10} +(-0.572827 - 3.12581i) q^{11} +(-0.0178514 - 0.110938i) q^{12} +(-2.57136 + 2.52747i) q^{13} +(1.62783 - 1.83744i) q^{14} +(-1.68319 - 3.38350i) q^{15} +(-3.08801 - 2.73574i) q^{16} +(0.0868613 - 0.0214094i) q^{17} +(-3.27493 - 2.80334i) q^{18} +(-2.68160 + 2.68160i) q^{19} +(0.129074 + 0.0580915i) q^{20} +(0.0642017 - 2.95820i) q^{21} +4.56649 q^{22} +8.51685 q^{23} +(-4.81520 - 0.104504i) q^{24} +(-0.237842 - 0.0288792i) q^{25} +(-2.90637 - 4.28910i) q^{26} +(-5.19610 - 0.0243356i) q^{27} +(0.0683481 + 0.0872399i) q^{28} +(-5.37469 + 3.70988i) q^{29} +(5.21832 - 1.50268i) q^{30} +(0.135605 + 0.106239i) q^{31} +(0.288769 - 0.226236i) q^{32} +(4.19820 - 3.55973i) q^{33} +(0.00776180 + 0.128318i) q^{34} +(3.06749 + 2.11734i) q^{35} +(0.151138 - 0.122616i) q^{36} +(-4.08038 + 5.20822i) q^{37} +(-3.09566 - 4.48484i) q^{38} +(-6.01546 - 1.67758i) q^{39} +(3.44648 - 4.99309i) q^{40} +(1.55831 + 5.00078i) q^{41} +(4.16458 + 0.856980i) q^{42} +(11.6872 + 1.41908i) q^{43} +(-0.0371615 + 0.202784i) q^{44} +(3.62608 - 5.44934i) q^{45} +(-2.20604 + 12.0380i) q^{46} +(10.8898 + 4.90110i) q^{47} +(1.44024 - 6.99899i) q^{48} +(-1.89683 - 3.61411i) q^{49} +(0.102425 - 0.328692i) q^{50} +(0.107164 + 0.111918i) q^{51} +(0.214117 - 0.0941585i) q^{52} +(0.277411 + 1.12550i) q^{53} +(1.38029 - 7.33801i) q^{54} +(0.835752 + 6.88304i) q^{55} +(4.20623 - 2.20760i) q^{56} +(-6.34207 - 1.70997i) q^{57} +(-3.85150 - 8.55767i) q^{58} +(-0.195524 + 3.23240i) q^{59} +(0.0242633 + 0.243958i) q^{60} +(6.43464 + 1.58600i) q^{61} +(-0.185286 + 0.164149i) q^{62} +(4.49675 - 2.45856i) q^{63} +(-3.58950 - 6.83921i) q^{64} +(5.93301 - 5.16573i) q^{65} +(3.94400 + 6.85590i) q^{66} +(-14.7671 - 6.64611i) q^{67} +(-0.00576136 - 0.000699555i) q^{68} +(7.35585 + 12.7868i) q^{69} +(-3.78725 + 3.78725i) q^{70} +(-2.90014 - 9.30689i) q^{71} +(-4.00191 - 7.31956i) q^{72} +(-1.94409 + 0.356268i) q^{73} +(-6.30455 - 7.11636i) q^{74} +(-0.162062 - 0.382026i) q^{75} +(0.224350 - 0.100972i) q^{76} +(-1.92509 + 5.07603i) q^{77} +(3.92926 - 8.06790i) q^{78} +(4.99006 + 13.1577i) q^{79} +(6.36485 + 6.36485i) q^{80} +(-4.45124 - 7.82218i) q^{81} +(-7.47189 + 0.907251i) q^{82} +(-4.70562 - 1.46633i) q^{83} +(-0.0719466 + 0.177962i) q^{84} +(-0.191992 + 0.0351838i) q^{85} +(-5.03299 + 16.1514i) q^{86} +(-10.2118 - 4.86513i) q^{87} +(8.26249 + 3.13355i) q^{88} +(-1.07963 + 1.07963i) q^{89} +(6.76302 + 6.53669i) q^{90} +(5.99292 - 1.42252i) q^{91} +(-0.516616 - 0.195926i) q^{92} +(-0.0423833 + 0.295347i) q^{93} +(-9.74805 + 14.1225i) q^{94} +(6.19340 - 5.48688i) q^{95} +(0.589065 + 0.238147i) q^{96} +(13.1814 - 0.797325i) q^{97} +(5.59961 - 1.74491i) q^{98} +(8.97031 + 3.22850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.259021	+	1.41343i	−0.183155	+	0.999445i	0.755645	+	0.654982i	$0.227324\pi$
$2$	−0.259021	+	1.41343i	−0.183155	+	0.999445i	−0.938800	+	0.344463i	$0.888061\pi$
$3$	0.863683	+	1.50135i	0.498647	+	0.866805i
$3$	0.863683	+	1.50135i	0.498647	+	0.866805i
$4$	−0.0606581	−	0.0230046i	−0.0303290	−	0.0115023i
$5$	−2.17786	−	0.131736i	−0.973967	−	0.0589141i	−0.434278	−	0.900779i	$-0.642997\pi$
$5$	−2.17786	−	0.131736i	−0.973967	−	0.0589141i	−0.539689	+	0.841865i	$0.681458\pi$
$6$	−2.34576	+	0.831874i	−0.957654	+	0.339611i
$7$	−1.46195	−	0.883779i	−0.552565	−	0.334037i	0.213353	−	0.976975i	$-0.431561\pi$
$7$	−1.46195	−	0.883779i	−0.552565	−	0.334037i	−0.765918	+	0.642938i	$0.777715\pi$
$8$	−1.43857	+	2.37968i	−0.508610	+	0.841344i
$9$	−1.50810	+	2.59338i	−0.502702	+	0.864460i
$10$	0.750309	−	3.04412i	0.237269	−	0.962636i
$11$	−0.572827	−	3.12581i	−0.172714	−	0.942469i	−0.949749	−	0.313012i	$-0.898662\pi$
$11$	−0.572827	−	3.12581i	−0.172714	−	0.942469i	0.777035	−	0.629457i	$-0.216723\pi$
$12$	−0.0178514	−	0.110938i	−0.00515326	−	0.0320250i
$13$	−2.57136	+	2.52747i	−0.713167	+	0.700994i
$13$	−2.57136	+	2.52747i	−0.713167	+	0.700994i
$14$	1.62783	−	1.83744i	0.435057	−	0.491078i
$15$	−1.68319	−	3.38350i	−0.434599	−	0.873617i
$16$	−3.08801	−	2.73574i	−0.772003	−	0.683935i
$17$	0.0868613	−	0.0214094i	0.0210670	−	0.00519254i	−0.228768	−	0.973481i	$-0.573470\pi$
$17$	0.0868613	−	0.0214094i	0.0210670	−	0.00519254i	0.249835	+	0.968288i	$0.419624\pi$
$18$	−3.27493	−	2.80334i	−0.771908	−	0.660753i
$19$	−2.68160	+	2.68160i	−0.615201	+	0.615201i	−0.944297	−	0.329095i	$-0.893256\pi$
$19$	−2.68160	+	2.68160i	−0.615201	+	0.615201i	0.329095	+	0.944297i	$0.393256\pi$
$20$	0.129074	+	0.0580915i	0.0288618	+	0.0129897i
$21$	0.0642017	−	2.95820i	0.0140100	−	0.645533i
$22$	4.56649			0.973579
$23$	8.51685			1.77589			0.887943	−	0.459954i	$-0.152134\pi$
$23$	8.51685			1.77589			0.887943	+	0.459954i	$0.152134\pi$
$24$	−4.81520	−	0.104504i	−0.982899	−	0.0213318i
$25$	−0.237842	−	0.0288792i	−0.0475684	−	0.00577585i
$26$	−2.90637	−	4.28910i	−0.569985	−	0.841162i
$27$	−5.19610	−	0.0243356i	−0.999989	−	0.00468339i
$28$	0.0683481	+	0.0872399i	0.0129166	+	0.0164868i
$29$	−5.37469	+	3.70988i	−0.998054	+	0.688907i	−0.950745	−	0.309973i	$-0.899680\pi$
$29$	−5.37469	+	3.70988i	−0.998054	+	0.688907i	−0.0473088	+	0.998880i	$0.515064\pi$
$30$	5.21832	−	1.50268i	0.952731	−	0.274351i
$31$	0.135605	+	0.106239i	0.0243553	+	0.0190812i	0.628823	−	0.777549i	$-0.283537\pi$
$31$	0.135605	+	0.106239i	0.0243553	+	0.0190812i	−0.604467	+	0.796630i	$0.706614\pi$
$32$	0.288769	−	0.226236i	0.0510477	−	0.0399933i
$33$	4.19820	−	3.55973i	0.730813	−	0.619669i
$34$	0.00776180	+	0.128318i	0.00133114	+	0.0220063i
$35$	3.06749	+	2.11734i	0.518500	+	0.357895i
$36$	0.151138	−	0.122616i	0.0251897	−	0.0204360i
$37$	−4.08038	+	5.20822i	−0.670810	+	0.856226i	−0.995994	−	0.0894252i	$-0.971497\pi$
$37$	−4.08038	+	5.20822i	−0.670810	+	0.856226i	0.325184	+	0.945651i	$0.394574\pi$
$38$	−3.09566	−	4.48484i	−0.502183	−	0.727538i
$39$	−6.01546	−	1.67758i	−0.963244	−	0.268627i
$40$	3.44648	−	4.99309i	0.544937	−	0.789477i
$41$	1.55831	+	5.00078i	0.243367	+	0.780991i	0.992892	+	0.119016i	$0.0379739\pi$
$41$	1.55831	+	5.00078i	0.243367	+	0.780991i	−0.749526	+	0.661975i	$0.769718\pi$
$42$	4.16458	+	0.856980i	0.642609	+	0.132235i
$43$	11.6872	+	1.41908i	1.78228	+	0.216408i	0.944253	−	0.329221i	$-0.106786\pi$
$43$	11.6872	+	1.41908i	1.78228	+	0.216408i	0.838027	+	0.545629i	$0.183709\pi$
$44$	−0.0371615	+	0.202784i	−0.00560230	+	0.0305708i
$45$	3.62608	−	5.44934i	0.540544	−	0.812339i
$46$	−2.20604	+	12.0380i	−0.325263	+	1.77490i
$47$	10.8898	+	4.90110i	1.58844	+	0.714900i	0.995885	−	0.0906291i	$-0.0288878\pi$
$47$	10.8898	+	4.90110i	1.58844	+	0.714900i	0.592557	+	0.805529i	$0.298119\pi$
$48$	1.44024	−	6.99899i	0.207881	−	1.01022i
$49$	−1.89683	−	3.61411i	−0.270976	−	0.516302i
$50$	0.102425	−	0.328692i	0.0144850	−	0.0464841i
$51$	0.107164	+	0.111918i	0.0150059	+	0.0156717i
$52$	0.214117	−	0.0941585i	0.0296927	−	0.0130574i
$53$	0.277411	+	1.12550i	0.0381053	+	0.154599i	0.986913	−	0.161256i	$-0.0515546\pi$
$53$	0.277411	+	1.12550i	0.0381053	+	0.154599i	−0.948807	+	0.315856i	$0.897708\pi$
$54$	1.38029	−	7.33801i	0.187834	−	0.998577i
$55$	0.835752	+	6.88304i	0.112693	+	0.928108i
$56$	4.20623	−	2.20760i	0.562081	−	0.295003i
$57$	−6.34207	−	1.70997i	−0.840028	−	0.226491i
$58$	−3.85150	−	8.55767i	−0.505726	−	1.12368i
$59$	−0.195524	+	3.23240i	−0.0254551	+	0.420823i	0.963019	+	0.269433i	$0.0868363\pi$
$59$	−0.195524	+	3.23240i	−0.0254551	+	0.420823i	−0.988474	+	0.151390i	$0.951625\pi$
$60$	0.0242633	+	0.243958i	0.00313238	+	0.0314948i
$61$	6.43464	+	1.58600i	0.823872	+	0.203066i	0.628645	−	0.777692i	$-0.283610\pi$
$61$	6.43464	+	1.58600i	0.823872	+	0.203066i	0.195226	+	0.980758i	$0.437456\pi$
$62$	−0.185286	+	0.164149i	−0.0235314	+	0.0208470i
$63$	4.49675	−	2.45856i	0.566537	−	0.309749i
$64$	−3.58950	−	6.83921i	−0.448687	−	0.854902i
$65$	5.93301	−	5.16573i	0.735899	−	0.640730i
$66$	3.94400	+	6.85590i	0.485473	+	0.843903i
$67$	−14.7671	−	6.64611i	−1.80408	−	0.811952i	−0.962226	−	0.272252i	$-0.912232\pi$
$67$	−14.7671	−	6.64611i	−1.80408	−	0.811952i	−0.841857	−	0.539700i	$-0.818538\pi$
$68$	−0.00576136		0.000699555i	−0.000698667		8.48336e-5i
$69$	7.35585	+	12.7868i	0.885540	+	1.53935i
$70$	−3.78725	+	3.78725i	−0.452663	+	0.452663i
$71$	−2.90014	−	9.30689i	−0.344184	−	1.10452i	−0.950872	−	0.309585i	$-0.899810\pi$
$71$	−2.90014	−	9.30689i	−0.344184	−	1.10452i	0.606688	−	0.794940i	$-0.292498\pi$
$72$	−4.00191	−	7.31956i	−0.471629	−	0.862619i
$73$	−1.94409	+	0.356268i	−0.227539	+	0.0416980i	−0.292814	−	0.956169i	$-0.594592\pi$
$73$	−1.94409	+	0.356268i	−0.227539	+	0.0416980i	0.0652760	+	0.997867i	$0.479207\pi$
$74$	−6.30455	−	7.11636i	−0.732889	−	0.827260i
$75$	−0.162062	−	0.382026i	−0.0187133	−	0.0441126i
$76$	0.224350	−	0.100972i	0.0257347	−	0.0115822i
$77$	−1.92509	+	5.07603i	−0.219384	+	0.578468i
$78$	3.92926	−	8.06790i	0.444902	−	0.913509i
$79$	4.99006	+	13.1577i	0.561425	+	1.48036i	0.852019	+	0.523510i	$0.175378\pi$
$79$	4.99006	+	13.1577i	0.561425	+	1.48036i	−0.290594	+	0.956846i	$0.593853\pi$
$80$	6.36485	+	6.36485i	0.711611	+	0.711611i
$81$	−4.45124	−	7.82218i	−0.494582	−	0.869131i
$82$	−7.47189	+	0.907251i	−0.825132	+	0.100189i
$83$	−4.70562	−	1.46633i	−0.516509	−	0.160951i	0.0281575	−	0.999603i	$-0.491036\pi$
$83$	−4.70562	−	1.46633i	−0.516509	−	0.160951i	−0.544666	+	0.838653i	$0.683344\pi$
$84$	−0.0719466	+	0.177962i	−0.00785001	+	0.0194172i
$85$	−0.191992	+	0.0351838i	−0.0208244	+	0.00381622i
$86$	−5.03299	+	16.1514i	−0.542722	+	1.74165i
$87$	−10.2118	−	4.86513i	−1.09482	−	0.521596i
$88$	8.26249	+	3.13355i	0.880785	+	0.334038i
$89$	−1.07963	+	1.07963i	−0.114441	+	0.114441i	−0.762008	−	0.647567i	$-0.775786\pi$
$89$	−1.07963	+	1.07963i	−0.114441	+	0.114441i	0.647567	+	0.762008i	$0.275786\pi$
$90$	6.76302	+	6.53669i	0.712885	+	0.689028i
$91$	5.99292	−	1.42252i	0.628229	−	0.149121i
$92$	−0.516616	−	0.195926i	−0.0538609	−	0.0204267i
$93$	−0.0423833	+	0.295347i	−0.00439494	+	0.0306261i
$94$	−9.74805	+	14.1225i	−1.00543	+	1.45662i
$95$	6.19340	−	5.48688i	0.635430	−	0.562942i
$96$	0.589065	+	0.238147i	0.0601212	+	0.0243058i
$97$	13.1814	−	0.797325i	1.33836	−	0.0809561i	0.624381	−	0.781120i	$-0.285351\pi$
$97$	13.1814	−	0.797325i	1.33836	−	0.0809561i	0.713983	+	0.700163i	$0.246890\pi$
$98$	5.59961	−	1.74491i	0.565646	−	0.176262i
$99$	8.97031	+	3.22850i	0.901550	+	0.324476i
$100$	0.0137627	+	0.00722321i	0.00137627	+	0.000722321i
$101$	−1.24291	+	10.2363i	−0.123674	+	1.01855i	0.790285	+	0.612739i	$0.209932\pi$
$101$	−1.24291	+	10.2363i	−0.123674	+	1.01855i	−0.913959	+	0.405807i	$0.866991\pi$
$102$	−0.185946	+	0.122479i	−0.0184114	+	0.0121272i
$103$	−8.34279	+	15.8959i	−0.822039	+	1.56627i	0.00218214	+	0.999998i	$0.499305\pi$
$103$	−8.34279	+	15.8959i	−0.822039	+	1.56627i	−0.824222	+	0.566268i	$0.808387\pi$
$104$	−2.31550	−	9.75495i	−0.227054	−	0.956552i
$105$	−0.529524	+	6.43408i	−0.0516762	+	0.627902i
$106$	−1.66267	+	0.100573i	−0.161493	+	0.00976851i
$107$	1.56932	+	1.77139i	0.151712	+	0.171247i	0.819453	−	0.573146i	$-0.194277\pi$
$107$	1.56932	+	1.77139i	0.151712	+	0.171247i	−0.667741	+	0.744393i	$0.732739\pi$
$108$	0.314625	+	0.121010i	0.0302748	+	0.0116442i
$109$	5.48713	+	7.00381i	0.525572	+	0.670843i	0.974931	−	0.222508i	$-0.0714244\pi$
$109$	5.48713	+	7.00381i	0.525572	+	0.670843i	−0.449359	+	0.893351i	$0.648348\pi$
$110$	−9.94516	−	0.601571i	−0.948234	−	0.0573576i
$111$	−11.3435	−	1.62783i	−1.07668	−	0.154507i
$112$	2.09673	+	6.72863i	0.198122	+	0.635796i
$113$	−5.67281	−	10.8086i	−0.533653	−	1.01679i	−0.991786	−	0.127908i	$-0.959174\pi$
$113$	−5.67281	−	10.8086i	−0.533653	−	1.01679i	0.458133	−	0.888884i	$-0.348518\pi$
$114$	4.05965	−	8.52116i	0.380221	−	0.798079i
$115$	−18.5485	−	1.12198i	−1.72965	−	0.104625i
$116$	0.411362	−	0.101392i	0.0381940	−	0.00941398i
$117$	−2.67681	−	10.4802i	−0.247472	−	0.968895i
$118$	−4.51812	−	1.11362i	−0.415927	−	0.102517i
$119$	−0.145908	−	0.0454668i	−0.0133754	−	0.00416793i
$120$	10.4730	+	0.861930i	0.956054	+	0.0786831i
$121$	0.842592	−	0.319553i	0.0765993	−	0.0290503i
$122$	−3.90840	+	8.68411i	−0.353850	+	0.786222i
$123$	−6.16204	+	6.65865i	−0.555613	+	0.600391i
$124$	−0.00578153	−	0.00956381i	−0.000519196	−	0.000858856i
$125$	11.2447	+	2.06066i	1.00575	+	0.184311i
$126$	2.31025	+	6.99265i	0.205813	+	0.622955i
$127$	6.33419	−	2.40224i	0.562068	−	0.213164i	−0.0571743	−	0.998364i	$-0.518209\pi$
$127$	6.33419	−	2.40224i	0.562068	−	0.213164i	0.619242	+	0.785200i	$0.287440\pi$
$128$	11.2970	−	3.52027i	0.998519	−	0.311151i
$129$	7.96348	+	18.7722i	0.701146	+	1.65280i
$130$	5.76462	+	9.72392i	0.505591	+	0.852844i
$131$	−15.2316	+	10.5136i	−1.33079	+	0.918581i	−0.999687	−	0.0250115i	$-0.992038\pi$
$131$	−15.2316	+	10.5136i	−1.33079	+	0.918581i	−0.331108	+	0.943593i	$0.607422\pi$
$132$	−0.336545	+	0.119348i	−0.0292925	+	0.0103879i
$133$	6.29031	−	1.55042i	0.545439	−	0.134439i
$134$	13.2188	−	19.1507i	1.14193	−	1.65437i
$135$	11.3131	+	0.737512i	0.973680	+	0.0634750i
$136$	−0.0740084	+	0.237501i	−0.00634616	+	0.0203656i
$137$	1.05303	+	1.34409i	0.0899660	+	0.114833i	0.830070	−	0.557660i	$-0.188301\pi$
$137$	1.05303	+	1.34409i	0.0899660	+	0.114833i	−0.740104	+	0.672493i	$0.765224\pi$
$138$	−19.9785	+	7.08494i	−1.70068	+	0.603110i
$139$	6.75877	+	5.98775i	0.573272	+	0.507874i	0.899210	−	0.437516i	$-0.144142\pi$
$139$	6.75877	+	5.98775i	0.573272	+	0.507874i	−0.325939	+	0.945391i	$0.605680\pi$
$140$	−0.137360	−	0.199000i	−0.0116090	−	0.0168186i
$141$	2.04706	+	20.5824i	0.172394	+	1.73335i
$142$	13.9058	−	1.68847i	1.16695	−	0.141694i
$143$	9.37335	+	6.58979i	0.783839	+	0.551066i
$144$	11.7519	−	3.88261i	0.979321	−	0.323550i
$145$	12.1940	−	7.37154i	1.01266	−	0.612173i
$146$		−	2.84011i		−	0.235050i
$147$	3.78779	−	5.96925i	0.312411	−	0.492336i
$148$	0.367321	−	0.222053i	0.0301936	−	0.0182527i
$149$	−0.835763	+	1.85699i	−0.0684684	+	0.152131i	−0.942956	−	0.332917i	$-0.891967\pi$
$149$	−0.835763	+	1.85699i	−0.0684684	+	0.152131i	0.874488	+	0.485048i	$0.161198\pi$
$150$	0.581945	−	0.130111i	0.0475156	−	0.0106235i
$151$	1.68960	−	0.760428i	0.137498	−	0.0618827i	−0.340496	−	0.940246i	$-0.610595\pi$
$151$	1.68960	−	0.760428i	0.137498	−	0.0618827i	0.477994	+	0.878363i	$0.341364\pi$
$152$	−2.52369	−	10.2390i	−0.204698	−	0.830494i
$153$	−0.0754733	+	0.257552i	−0.00610165	+	0.0208219i
$154$	−6.67598	−	4.03577i	−0.537966	−	0.325212i
$155$	−0.281332	−	0.249238i	−0.0225971	−	0.0200193i
$156$	0.326294	+	0.240142i	0.0261244	+	0.0192267i
$157$	6.35055	−	5.62610i	0.506829	−	0.449012i	−0.370548	−	0.928813i	$-0.620830\pi$
$157$	6.35055	−	5.62610i	0.506829	−	0.449012i	0.877377	+	0.479802i	$0.159291\pi$
$158$	−19.8900	+	3.64498i	−1.58236	+	0.289979i
$159$	−1.45017	+	1.38857i	−0.115006	+	0.110120i
$160$	−0.658701	+	0.454669i	−0.0520749	+	0.0359447i
$161$	−12.4512	−	7.52701i	−0.981292	−	0.593212i
$162$	12.2091	−	4.26541i	0.959234	−	0.335122i
$163$	−6.94566	+	8.86549i	−0.544026	+	0.694398i	−0.978491	−	0.206291i	$-0.933861\pi$
$163$	−6.94566	+	8.86549i	−0.544026	+	0.694398i	0.434464	+	0.900689i	$0.356938\pi$
$164$	0.0205170	−	0.339186i	0.00160211	−	0.0264860i
$165$	−9.61202	+	7.19952i	−0.748295	+	0.560481i
$166$	3.29141	−	6.27125i	0.255463	−	0.486743i
$167$	−0.350989	−	0.0643211i	−0.0271603	−	0.00497731i	0.166658	−	0.986015i	$-0.446703\pi$
$167$	−0.350989	−	0.0643211i	−0.0271603	−	0.00497731i	−0.193818	+	0.981037i	$0.562087\pi$
$168$	6.94722	+	4.40835i	0.535990	+	0.340112i
$169$	0.223778	−	12.9981i	0.0172137	−	0.999852i
$170$		−	0.280480i		−	0.0215119i
$171$	−2.91028	−	10.9985i	−0.222554	−	0.841080i
$172$	−0.676277	−	0.354938i	−0.0515657	−	0.0270637i
$173$	2.76289	−	7.28514i	0.210058	−	0.553879i	−0.788033	−	0.615633i	$-0.788900\pi$
$173$	2.76289	−	7.28514i	0.210058	−	0.553879i	0.998091	+	0.0617545i	$0.0196696\pi$
$174$	9.52159	−	13.1736i	0.721830	−	0.998685i
$175$	0.322190	+	0.252420i	0.0243553	+	0.0190811i
$176$	−6.78252	+	11.2197i	−0.511251	+	0.845713i
$177$	−5.02184	+	2.49822i	−0.377464	+	0.187778i
$178$	−1.24634	−	1.80563i	−0.0934168	−	0.135338i
$179$	−18.5525	−	4.57277i	−1.38668	−	0.341785i	−0.525803	−	0.850606i	$-0.676235\pi$
$179$	−18.5525	−	4.57277i	−1.38668	−	0.341785i	−0.860872	+	0.508821i	$0.830081\pi$
$180$	−0.345311	+	0.247130i	−0.0257379	+	0.0184200i
$181$	−7.54247	−	8.51369i	−0.560628	−	0.632818i	0.398032	−	0.917371i	$-0.369693\pi$
$181$	−7.54247	−	8.51369i	−0.560628	−	0.632818i	−0.958660	+	0.284553i	$0.908155\pi$
$182$	0.458343	+	8.83904i	0.0339746	+	0.655193i
$183$	3.17635	+	11.0305i	0.234803	+	0.815394i
$184$	−12.2521	+	20.2674i	−0.903234	+	1.49413i
$185$	9.57259	−	10.8052i	0.703791	−	0.794415i
$186$	−0.406474	−	0.136407i	−0.0298042	−	0.0100018i
$187$	−0.116678	−	0.259249i	−0.00853236	−	0.0189581i
$188$	−0.547807	−	0.547807i	−0.0399529	−	0.0399529i
$189$	7.57492	+	4.62778i	0.550994	+	0.336621i
$190$	6.15109	+	10.1752i	0.446247	+	0.738183i
$191$			7.46461i			0.540120i	0.962843	+	0.270060i	$0.0870436\pi$
$191$			7.46461i			0.540120i	−0.962843	+	0.270060i	$0.912956\pi$
$192$	7.16787	−	11.2960i	0.517296	−	0.815218i
$193$	3.49942	+	5.78874i	0.251893	+	0.416683i	0.955980	−	0.293431i	$-0.0947972\pi$
$193$	3.49942	+	5.78874i	0.251893	+	0.416683i	−0.704087	+	0.710114i	$0.748643\pi$
$194$	−2.28728	+	18.8374i	−0.164217	+	1.35245i
$195$	12.8798	+	4.44598i	0.922342	+	0.318383i
$196$	0.0319171	+	0.262861i	0.00227979	+	0.0187758i
$197$	8.75595	−	6.85985i	0.623836	−	0.488744i	−0.254319	−	0.967120i	$-0.581851\pi$
$197$	8.75595	−	6.85985i	0.623836	−	0.488744i	0.878155	+	0.478376i	$0.158774\pi$
$198$	−6.88675	+	11.8426i	−0.489420	+	0.841620i
$199$	−11.8885	+	13.4194i	−0.842755	+	0.951274i	−0.999338	−	0.0363910i	$-0.988414\pi$
$199$	−11.8885	+	13.4194i	−0.842755	+	0.951274i	0.156582	+	0.987665i	$0.449952\pi$
$200$	0.410875	−	0.524443i	0.0290532	−	0.0370837i
$201$	−2.77591	−	27.9107i	−0.195797	−	1.96867i
$202$	−14.1463	−	4.40816i	−0.995330	−	0.310157i
$203$	11.1362	−	0.673618i	0.781610	−	0.0472787i
$204$	−0.00392571	−	0.00925401i	−0.000274854	−	0.000647910i
$205$	−2.73499	−	11.0963i	−0.191020	−	0.774997i
$206$	−20.3067	−	15.9093i	−1.41484	−	1.10845i
$207$	−12.8443	+	22.0874i	−0.892740	+	1.53518i
$208$	14.8549	−	0.770291i	1.03000	−	0.0534100i
$209$	9.91828	+	6.84609i	0.686062	+	0.473554i
$210$	−8.95696	−	2.41500i	−0.618089	−	0.166651i
$211$	−6.65919	−	17.5588i	−0.458438	−	1.20880i	−0.942630	−	0.333839i	$-0.891656\pi$
$211$	−6.65919	−	17.5588i	−0.458438	−	1.20880i	0.484192	−	0.874962i	$-0.339114\pi$
$212$	0.00906444	−	0.0746524i	0.000622549	−	0.00512715i
$213$	11.4681	−	12.3923i	0.785781	−	0.849109i
$214$	−2.91023	+	1.75929i	−0.198939	+	0.120263i
$215$	−25.2661	−	4.63018i	−1.72313	−	0.315776i
$216$	7.53285	−	12.3300i	0.512545	−	0.838953i
$217$	−0.104355	−	0.275161i	−0.00708408	−	0.0186792i
$218$	−11.3207	+	5.94154i	−0.766732	+	0.402412i
$219$	−2.21396	−	2.61106i	−0.149606	−	0.176439i
$220$	0.107646	−	0.436738i	0.00725751	−	0.0294449i
$221$	−0.169240	+	0.274591i	−0.0113843	+	0.0184710i
$222$	5.23902	−	15.6116i	0.351620	−	1.04778i
$223$	0.639410	−	10.5707i	0.0428181	−	0.707867i	−0.911911	−	0.410389i	$-0.865393\pi$
$223$	0.639410	−	10.5707i	0.0428181	−	0.707867i	0.954729	−	0.297478i	$-0.0961455\pi$
$224$	−0.622109	+	0.0755377i	−0.0415664	+	0.00504708i
$225$	0.433585	−	0.573261i	0.0289057	−	0.0382174i
$226$	16.7466	−	5.21846i	1.11397	−	0.347127i
$227$	14.2629	−	6.41922i	0.946663	−	0.426059i	0.122537	−	0.992464i	$-0.460897\pi$
$227$	14.2629	−	6.41922i	0.946663	−	0.426059i	0.824127	+	0.566405i	$0.191666\pi$
$228$	0.345361	+	0.249620i	0.0228721	+	0.0165315i
$229$	11.7808	−	9.22969i	0.778499	−	0.609915i	−0.146794	−	0.989167i	$-0.546896\pi$
$229$	11.7808	−	9.22969i	0.778499	−	0.609915i	0.925293	+	0.379252i	$0.123819\pi$
$230$	6.39027	−	25.9263i	0.421362	−	1.70953i
$231$	−9.28357	+	1.49385i	−0.610814	+	0.0982884i
$232$	−1.09648	−	18.1269i	−0.0719873	−	1.19009i
$233$	0.615212	−	0.322888i	0.0403039	−	0.0211531i	−0.444451	−	0.895803i	$-0.646601\pi$
$233$	0.615212	−	0.322888i	0.0403039	−	0.0211531i	0.484755	+	0.874650i	$0.338909\pi$
$234$	15.5064	−	1.06890i	1.01368	−	0.0698762i
$235$	−23.0708	−	12.1085i	−1.50497	−	0.789870i
$236$	0.0862201	−	0.191573i	0.00561245	−	0.0124704i
$237$	−15.4445	+	18.8559i	−1.00323	+	1.22482i
$238$	0.102057	−	0.194454i	0.00661539	−	0.0126046i
$239$	−3.94143	−	3.94143i	−0.254950	−	0.254950i	0.568046	−	0.822997i	$-0.307699\pi$
$239$	−3.94143	−	3.94143i	−0.254950	−	0.254950i	−0.822997	+	0.568046i	$0.807699\pi$
$240$	−4.05866	+	15.0531i	−0.261985	+	0.971672i
$241$	0.469738	+	7.76570i	0.0302585	+	0.500233i	0.981461	+	0.191664i	$0.0613884\pi$
$241$	0.469738	+	7.76570i	0.0302585	+	0.500233i	−0.951202	+	0.308569i	$0.900150\pi$
$242$	0.233417	+	1.27372i	0.0150046	+	0.0818775i
$243$	7.89937	−	13.4388i	0.506745	−	0.862096i
$244$	−0.353828	−	0.244230i	−0.0226515	−	0.0156352i
$245$	3.65492	+	8.12090i	0.233504	+	0.518825i
$246$	−7.81544	−	10.4343i	−0.498294	−	0.665269i
$247$	0.117690	−	13.6730i	0.00748846	−	0.869994i
$248$	−0.447893	+	0.169863i	−0.0284412	+	0.0107863i
$249$	−1.86269	−	8.33123i	−0.118043	−	0.527970i
$250$	−5.82520	+	15.3598i	−0.368418	+	0.971439i
$251$	0.638366	+	5.25742i	0.0402933	+	0.331845i	0.998891	+	0.0470815i	$0.0149920\pi$
$251$	0.638366	+	5.25742i	0.0402933	+	0.331845i	−0.958598	+	0.284764i	$0.908085\pi$
$252$	−0.329322	+	0.0456857i	−0.0207454	+	0.00287793i
$253$	−4.87868	−	26.6221i	−0.306720	−	1.67372i
$254$	1.75471	+	9.57515i	0.110100	+	0.600799i
$255$	−0.218643	−	0.257859i	−0.0136920	−	0.0161478i
$256$	0.187477	+	1.54401i	0.0117173	+	0.0965007i
$257$	2.57776	−	6.79699i	0.160796	−	0.423984i	−0.830269	−	0.557363i	$-0.811813\pi$
$257$	2.57776	−	6.79699i	0.160796	−	0.423984i	0.991065	+	0.133378i	$0.0425825\pi$
$258$	−28.5959	+	6.39344i	−1.78030	+	0.398038i
$259$	10.5682	−	4.00800i	0.656677	−	0.249045i
$260$	−0.478720	+	0.176857i	−0.0296890	+	0.0109682i
$261$	−1.51553	−	19.5335i	−0.0938093	−	1.20909i
$262$	−10.9150	−	24.2521i	−0.674330	−	1.49830i
$263$	14.3456	+	9.90204i	0.884586	+	0.610586i	0.921348	−	0.388738i	$-0.127089\pi$
$263$	14.3456	+	9.90204i	0.884586	+	0.610586i	−0.0367620	+	0.999324i	$0.511704\pi$
$264$	2.43162	+	15.1113i	0.149656	+	0.930035i
$265$	−0.455892	−	2.48772i	−0.0280052	−	0.152820i
$266$	0.562092	+	9.29250i	0.0344641	+	0.569759i
$267$	−2.55336	−	0.688446i	−0.156263	−	0.0421322i
$268$	0.742851	+	0.742851i	0.0453768	+	0.0453768i
$269$	−3.70674	+	7.06261i	−0.226004	+	0.430615i	−0.971882	−	0.235468i	$-0.924338\pi$
$269$	−3.70674	+	7.06261i	−0.226004	+	0.430615i	0.745878	+	0.666083i	$0.232030\pi$
$270$	−3.97276	+	15.7993i	−0.241774	+	0.961514i
$271$	5.67815	−	12.6163i	0.344923	−	0.766387i	−0.655019	−	0.755612i	$-0.727339\pi$
$271$	5.67815	−	12.6163i	0.344923	−	0.766387i	0.999942	−	0.0107747i	$-0.00342977\pi$
$272$	−0.326799	−	0.171517i	−0.0198151	−	0.0103998i
$273$	7.31169	+	7.76887i	0.442523	+	0.470193i
$274$	−2.17253	+	1.14023i	−0.131247	+	0.0688839i
$275$	0.0459711	+	0.759992i	0.00277216	+	0.0458293i
$276$	−0.152038	−	0.944839i	−0.00915160	−	0.0568726i
$277$	1.44064	−	5.84491i	0.0865597	−	0.351187i	−0.911652	−	0.410963i	$-0.865193\pi$
$277$	1.44064	−	5.84491i	0.0865597	−	0.351187i	0.998212	+	0.0597763i	$0.0190387\pi$
$278$	−10.2139	+	8.00210i	−0.612590	+	0.479934i
$279$	−0.480025	+	0.191454i	−0.0287384	+	0.0114621i
$280$	−9.45137	+	4.25372i	−0.564828	+	0.254208i
$281$	12.1504	−	3.78621i	0.724830	−	0.225866i	0.0871803	−	0.996193i	$-0.472214\pi$
$281$	12.1504	−	3.78621i	0.724830	−	0.225866i	0.637650	+	0.770326i	$0.279907\pi$
$282$	−29.6220	−	2.43789i	−1.76397	−	0.145174i
$283$	13.5664	−	1.64726i	0.806438	−	0.0979193i	0.293073	−	0.956090i	$-0.405322\pi$
$283$	13.5664	−	1.64726i	0.806438	−	0.0979193i	0.513364	+	0.858171i	$0.328399\pi$
$284$	−0.0381839	+	0.631255i	−0.00226580	+	0.0374581i
$285$	13.5869	+	4.55955i	0.804816	+	0.270084i
$286$	−11.7421	+	11.5417i	−0.694324	+	0.682474i
$287$	2.14142	−	8.68809i	0.126404	−	0.512842i
$288$	0.151222	+	1.09008i	0.00891087	+	0.0642334i
$289$	−15.0457	+	7.89657i	−0.885039	+	0.464504i
$290$	7.26065	+	19.1448i	0.426360	+	1.12422i
$291$	12.5816	+	19.1012i	0.737545	+	1.11973i
$292$	0.126121	+	0.0231125i	0.00738065	+	0.00135255i
$293$	−5.87156	+	3.54948i	−0.343020	+	0.207363i	−0.678352	−	0.734737i	$-0.737305\pi$
$293$	−5.87156	+	3.54948i	−0.343020	+	0.207363i	0.335332	+	0.942100i	$0.391152\pi$
$294$	7.45600	+	6.89993i	0.434843	+	0.402412i
$295$	0.851647	−	7.01395i	0.0495848	−	0.408368i
$296$	−6.52400	−	17.2024i	−0.379200	−	0.999868i
$297$	2.90039	+	16.2560i	0.168298	+	0.943267i
$298$	−2.40824	−	1.66229i	−0.139506	−	0.0962939i
$299$	−21.8999	+	21.5261i	−1.26650	+	1.24489i
$300$	0.00104202	+	0.0269012i	6.01609e−5	+	0.00155314i
$301$	−15.8319	−	12.4035i	−0.912537	−	0.714927i
$302$	0.637169	+	2.58510i	0.0366650	+	0.148756i
$303$	−16.4417	+	6.97484i	−0.944550	+	0.400694i
$304$	15.6170	−	0.944653i	0.895695	−	0.0541795i
$305$	−13.8048	−	4.30175i	−0.790460	−	0.246317i
$306$	−0.344483	−	0.173387i	−0.0196928	−	0.00991190i
$307$	2.57490	−	3.28662i	0.146958	−	0.187577i	−0.708098	−	0.706115i	$-0.750446\pi$
$307$	2.57490	−	3.28662i	0.146958	−	0.187577i	0.855055	+	0.518537i	$0.173523\pi$
$308$	0.233544	−	0.263617i	0.0133074	−	0.0150210i
$309$	−31.0708	+	1.20353i	−1.76755	+	0.0684663i
$310$	0.425152	−	0.333085i	0.0241470	−	0.0189180i
$311$	0.512222	+	4.21853i	0.0290455	+	0.239211i	1.00000		5.31935e-5i	$-1.69320e-5\pi$
$311$	0.512222	+	4.21853i	0.0290455	+	0.239211i	−0.970955	+	0.239264i	$0.923094\pi$
$312$	12.6457	−	11.9016i	0.715924	−	0.673793i
$313$	3.64260	−	29.9995i	0.205892	−	1.69567i	−0.413430	−	0.910536i	$-0.635669\pi$
$313$	3.64260	−	29.9995i	0.205892	−	1.69567i	0.619322	−	0.785137i	$-0.287407\pi$
$314$	6.30717	+	10.4333i	0.355934	+	0.588787i
$315$	−10.1172	+	4.76200i	−0.570037	+	0.268309i
$316$		−	0.912915i		−	0.0513555i
$317$	6.72919	+	11.1314i	0.377949	+	0.625204i	0.985618	−	0.168986i	$-0.0540492\pi$
$317$	6.72919	+	11.1314i	0.377949	+	0.625204i	−0.607669	+	0.794190i	$0.707895\pi$
$318$	−1.58701	−	2.40939i	−0.0889953	−	0.135112i
$319$	14.6752	+	14.6752i	0.821651	+	0.821651i
$320$	6.91643	+	15.3677i	0.386640	+	0.859080i
$321$	−1.30409	+	3.88602i	−0.0727872	+	0.216896i
$322$	13.8640	−	15.6492i	0.772611	−	0.872098i
$323$	−0.175516	+	0.290339i	−0.00976597	+	0.0161549i
$324$	0.0900579	+	0.576877i	0.00500322	+	0.0320487i
$325$	0.684568	−	0.526880i	0.0379730	−	0.0292260i
$326$	−10.7317	−	12.1135i	−0.594372	−	0.670907i
$327$	−5.77603	+	14.2872i	−0.319415	+	0.790083i
$328$	−14.1420	−	3.48569i	−0.780861	−	0.192465i
$329$	−11.5889	−	16.7894i	−0.638914	−	0.925627i
$330$	−7.68629	−	15.4507i	−0.423117	−	0.850535i
$331$	7.96069	−	13.1686i	0.437559	−	0.723811i	−0.556711	−	0.830706i	$-0.687937\pi$
$331$	7.96069	−	13.1686i	0.437559	−	0.723811i	0.994270	+	0.106895i	$0.0340909\pi$
$332$	0.251702	+	0.197196i	0.0138139	+	0.0108225i
$333$	−7.35325	−	18.4365i	−0.402956	−	1.01031i
$334$	0.181827	−	0.479437i	0.00994911	−	0.0262336i
$335$	31.2850	+	16.4196i	1.70928	+	0.897100i
$336$	−8.29112	+	8.95932i	−0.452318	+	0.488771i
$337$		−	8.57762i		−	0.467253i	−0.972326	−	0.233626i	$-0.924941\pi$
$337$		−	8.57762i		−	0.467253i	0.972326	−	0.233626i	$-0.0750592\pi$
$338$	18.3139	+	3.68306i	0.996145	+	0.200332i
$339$	11.3280	−	17.8521i	0.615255	−	0.969594i
$340$	0.0124553	+	0.00228251i	0.000675481	+	0.000123786i
$341$	0.254407	−	0.484732i	0.0137769	−	0.0262497i
$342$	16.2995	−	1.26462i	0.881375	−	0.0683828i
$343$	−1.14303	+	18.8965i	−0.0617176	+	1.02031i
$344$	−20.1898	+	25.7703i	−1.08856	+	1.38944i
$345$	−14.3355	−	28.8168i	−0.771798	−	1.55144i
$346$	9.58138	+	5.79215i	0.515098	+	0.311388i
$347$	22.8631	−	15.7813i	1.22736	−	0.847183i	0.235171	−	0.971954i	$-0.424435\pi$
$347$	22.8631	−	15.7813i	1.22736	−	0.847183i	0.992186	+	0.124771i	$0.0398195\pi$
$348$	0.507511	+	0.530029i	0.0272054	+	0.0284125i
$349$	18.8234	−	3.44952i	1.00760	−	0.184649i	0.348981	−	0.937130i	$-0.386528\pi$
$349$	18.8234	−	3.44952i	1.00760	−	0.184649i	0.658614	+	0.752481i	$0.271143\pi$
$350$	−0.440231	+	0.390011i	−0.0235313	+	0.0208470i
$351$	13.4225	−	13.0704i	0.716442	−	0.697647i
$352$	−0.872587	−	0.773045i	−0.0465091	−	0.0412034i
$353$	4.17749	+	2.52538i	0.222346	+	0.134413i	0.624127	−	0.781323i	$-0.285455\pi$
$353$	4.17749	+	2.52538i	0.222346	+	0.134413i	−0.401781	+	0.915736i	$0.631609\pi$
$354$	−2.23030	−	7.74510i	−0.118539	−	0.411647i
$355$	5.09004	+	20.6511i	0.270152	+	1.09605i
$356$	0.0903248	−	0.0406519i	0.00478721	−	0.00215455i
$357$	−0.0577567	−	0.258328i	−0.00305681	−	0.0136722i
$358$	11.2688	−	25.0381i	0.595572	−	1.32331i
$359$	30.1867	−	18.2485i	1.59319	−	0.963117i	0.607546	−	0.794284i	$-0.292154\pi$
$359$	30.1867	−	18.2485i	1.59319	−	0.963117i	0.985645	−	0.168833i	$-0.0539999\pi$
$360$	7.75133	+	16.4681i	0.408531	+	0.867947i
$361$			4.61803i			0.243054i
$362$	13.9872	−	8.45553i	0.735149	−	0.444413i
$363$	1.20749	+	0.989034i	0.0633770	+	0.0519108i
$364$	−0.396244	−	0.0515773i	−0.0207688	−	0.00270338i
$365$	4.28088	−	0.519793i	0.224072	−	0.0272072i
$366$	−16.4135	+	1.63244i	−0.857948	+	0.0853288i
$367$	10.9995	+	15.9355i	0.574169	+	0.831828i	0.997238	−	0.0742696i	$-0.0236625\pi$
$367$	10.9995	+	15.9355i	0.574169	+	0.831828i	−0.423069	+	0.906098i	$0.639047\pi$
$368$	−26.3001	−	23.2999i	−1.37099	−	1.21459i
$369$	−15.3190	−	3.50042i	−0.797476	−	0.182225i
$370$	12.7929	+	16.3289i	0.665072	+	0.848901i
$371$	0.589133	−	1.89059i	0.0305863	−	0.0981548i
$372$	0.00936523	−	0.0169402i	0.000485565	−	0.000878308i
$373$	−0.626079	+	0.907032i	−0.0324171	+	0.0469643i	−0.838857	−	0.544351i	$-0.816776\pi$
$373$	−0.626079	+	0.907032i	−0.0324171	+	0.0469643i	0.806440	+	0.591316i	$0.201391\pi$
$374$	0.396652	−	0.0977658i	0.0205104	−	0.00505535i
$375$	6.61805	+	18.6619i	0.341755	+	0.963699i
$376$	−27.3288	+	18.8637i	−1.40937	+	0.972821i
$377$	4.44364	−	23.1238i	0.228859	−	1.19094i
$378$	−8.50310	+	9.50793i	−0.437352	+	0.489035i
$379$	5.22536	−	1.62829i	0.268409	−	0.0836395i	−0.160345	−	0.987061i	$-0.551261\pi$
$379$	5.22536	−	1.62829i	0.268409	−	0.0836395i	0.428753	+	0.903422i	$0.358953\pi$
$380$	−0.501903	+	0.190347i	−0.0257471	+	0.00976459i
$381$	9.07733	+	7.43506i	0.465046	+	0.380910i
$382$	−10.5507	−	1.93349i	−0.539821	−	0.0989258i
$383$	4.76427	+	7.88107i	0.243443	+	0.402704i	0.953478	−	0.301462i	$-0.0974748\pi$
$383$	4.76427	+	7.88107i	0.243443	+	0.402704i	−0.710035	+	0.704166i	$0.751321\pi$
$384$	15.0421	+	13.9203i	0.767616	+	0.710366i
$385$	4.86126	−	10.8013i	0.247753	−	0.550484i
$386$	−9.08840	+	3.44677i	−0.462587	+	0.175436i
$387$	−21.3057	+	28.1692i	−1.08303	+	1.43192i
$388$	−0.817898	−	0.254867i	−0.0415225	−	0.0129389i
$389$	−30.4317	−	7.50074i	−1.54295	−	0.380303i	−0.626166	−	0.779690i	$-0.715377\pi$
$389$	−30.4317	−	7.50074i	−1.54295	−	0.380303i	−0.916782	+	0.399387i	$0.869223\pi$
$390$	−9.62020	+	17.0531i	−0.487138	+	0.863517i
$391$	0.739785	−	0.182341i	0.0374125	−	0.00922136i
$392$	11.3292	+	0.685288i	0.572209	+	0.0346123i
$393$	−28.9400	−	13.7876i	−1.45983	−	0.695491i
$394$	7.42794	+	14.1528i	0.374214	+	0.713006i
$395$	−9.13428	−	29.3129i	−0.459596	−	1.47489i
$396$	−0.469852	−	0.402193i	−0.0236109	−	0.0202109i
$397$	−1.57534	−	0.0952903i	−0.0790639	−	0.00478248i	0.0207992	−	0.999784i	$-0.493379\pi$
$397$	−1.57534	−	0.0952903i	−0.0790639	−	0.00478248i	−0.0998631	+	0.995001i	$0.531840\pi$
$398$	−15.8880	−	20.2795i	−0.796391	−	1.01652i
$399$	7.76056	+	8.10488i	0.388514	+	0.405752i
$400$	0.655452	+	0.739852i	0.0327726	+	0.0369926i
$401$	−21.8858	+	1.32385i	−1.09292	+	0.0661097i	−0.596989	−	0.802250i	$-0.703636\pi$
$401$	−21.8858	+	1.32385i	−1.09292	+	0.0661097i	−0.495935	+	0.868359i	$0.665175\pi$
$402$	40.1688	+	3.30588i	2.00344	+	0.164882i
$403$	−0.617206	+	0.0695571i	−0.0307452	+	0.00346488i
$404$	0.310873	−	0.592319i	0.0154665	−	0.0294690i
$405$	8.66370	+	17.6220i	0.430503	+	0.875642i
$406$	−1.93240	+	15.9148i	−0.0959035	+	0.789836i
$407$	18.6173	+	9.77110i	0.922824	+	0.484335i
$408$	−0.420492	+	0.0940132i	−0.0208175	+	0.00465435i
$409$	−1.71312	+	0.533830i	−0.0847084	+	0.0263962i	−0.339564	−	0.940583i	$-0.610280\pi$
$409$	−1.71312	+	0.533830i	−0.0847084	+	0.0263962i	0.254856	+	0.966979i	$0.417972\pi$
$410$	16.3922	−	0.991546i	0.809554	−	0.0489690i
$411$	−1.10847	+	2.74183i	−0.0546766	+	0.135244i
$412$	0.871735	−	0.772290i	0.0429473	−	0.0380480i
$413$	3.14257	−	4.55281i	0.154636	−	0.224029i
$414$	−27.8921	−	23.8756i	−1.37082	−	1.17342i
$415$	10.0550	+	3.81336i	0.493580	+	0.187190i
$416$	−0.170724	+	1.31159i	−0.00837043	+	0.0643060i
$417$	−3.15228	+	15.3188i	−0.154368	+	0.750165i
$418$	−12.2455	+	12.2455i	−0.598947	+	0.598947i
$419$	15.1667	+	5.75196i	0.740940	+	0.281002i	0.696053	−	0.717991i	$-0.254938\pi$
$419$	15.1667	+	5.75196i	0.740940	+	0.281002i	0.0448873	+	0.998992i	$0.485707\pi$
$420$	0.180133	−	0.378098i	0.00878960	−	0.0184493i
$421$	0.588374	−	1.88816i	0.0286756	−	0.0920232i	−0.939274	−	0.343169i	$-0.888500\pi$
$421$	0.588374	−	1.88816i	0.0286756	−	0.0920232i	0.967949	+	0.251146i	$0.0808073\pi$
$422$	26.5431	−	4.86420i	1.29210	−	0.236785i
$423$	−29.1334	+	20.8500i	−1.41651	+	1.01376i
$424$	−3.07741	−	0.958958i	−0.149452	−	0.0465711i
$425$	−0.0212775	+	0.00258356i	−0.00103211	+	0.000125321i
$426$	14.5452	+	19.4192i	0.704718	+	0.940864i
$427$	−8.00545	−	8.00545i	−0.387411	−	0.387411i
$428$	−0.0544417	−	0.143551i	−0.00263154	−	0.00693879i
$429$	−1.79798	+	19.7642i	−0.0868074	+	0.954223i
$430$	13.0889	−	34.5125i	0.631201	−	1.66434i
$431$	−22.2707	+	10.0232i	−1.07274	+	0.482802i	−0.868281	−	0.496072i	$-0.834775\pi$
$431$	−22.2707	+	10.0232i	−1.07274	+	0.482802i	−0.204462	+	0.978875i	$0.565544\pi$
$432$	15.9790	+	14.2903i	0.768791	+	0.687543i
$433$	13.1975	+	14.8969i	0.634229	+	0.715897i	0.974489	−	0.224434i	$-0.0720535\pi$
$433$	13.1975	+	14.8969i	0.634229	+	0.715897i	−0.340260	+	0.940331i	$0.610515\pi$
$434$	0.415951	−	0.0762259i	0.0199663	−	0.00365896i
$435$	21.5990	+	11.9408i	1.03559	+	0.572518i
$436$	−0.171719	−	0.551067i	−0.00822387	−	0.0263913i
$437$	−22.8388	+	22.8388i	−1.09253	+	1.09253i
$438$	4.26401	−	2.45296i	0.203742	−	0.117207i
$439$	−29.9114	−	3.63190i	−1.42759	−	0.173341i	−0.630027	−	0.776573i	$-0.716956\pi$
$439$	−29.9114	−	3.63190i	−1.42759	−	0.173341i	−0.797566	+	0.603232i	$0.793879\pi$
$440$	−17.5817	−	7.91289i	−0.838176	−	0.377232i
$441$	12.2334	+	0.531252i	0.582542	+	0.0252977i
$442$	−0.344278	−	0.310334i	−0.0163756	−	0.0147611i
$443$	−5.06624	−	9.65292i	−0.240704	−	0.458624i	0.734895	−	0.678181i	$-0.237231\pi$
$443$	−5.06624	−	9.65292i	−0.240704	−	0.458624i	−0.975600	+	0.219557i	$0.929539\pi$
$444$	0.650628	+	0.359694i	0.0308774	+	0.0170703i
$445$	2.49351	−	2.20905i	0.118204	−	0.104719i
$446$	14.7753	+	3.64179i	0.699632	+	0.172444i
$447$	−3.50983	+	0.349077i	−0.166009	+	0.0165108i
$448$	−0.796693	+	13.1709i	−0.0376402	+	0.622267i
$449$	9.71284	+	21.5810i	0.458377	+	1.01847i	0.985654	+	0.168779i	$0.0539824\pi$
$449$	9.71284	+	21.5810i	0.458377	+	1.01847i	−0.527277	+	0.849694i	$0.676787\pi$
$450$	0.697957	+	0.761328i	0.0329020	+	0.0358894i
$451$	14.7389	−	7.73556i	0.694027	−	0.364253i
$452$	0.0954537	+	0.786132i	0.00448977	+	0.0369765i
$453$	2.60095	+	1.87991i	0.122203	+	0.0883261i
$454$	5.37872	+	21.8223i	0.252436	+	1.02417i
$455$	−13.2391	+	2.30856i	−0.620660	+	0.108227i
$456$	13.1927	−	12.6322i	0.617804	−	0.591557i
$457$	0.107204	−	0.344029i	0.00501478	−	0.0160930i	−0.952180	−	0.305539i	$-0.901163\pi$
$457$	0.107204	−	0.344029i	0.00501478	−	0.0160930i	0.957194	+	0.289446i	$0.0934711\pi$
$458$	9.99404	+	19.0421i	0.466991	+	0.889777i
$459$	−0.451861	+	0.109131i	−0.0210911	+	0.00509382i
$460$	1.09930	+	0.494756i	0.0512553	+	0.0230681i
$461$	−4.79213	+	26.1498i	−0.223192	+	1.21792i	0.660853	+	0.750515i	$0.270195\pi$
$461$	−4.79213	+	26.1498i	−0.223192	+	1.21792i	−0.884045	+	0.467402i	$0.845190\pi$
$462$	0.293177	−	13.5086i	0.0136398	−	0.628477i
$463$	−6.09115	+	33.2383i	−0.283080	+	1.54472i	0.467534	+	0.883975i	$0.345142\pi$
$463$	−6.09115	+	33.2383i	−0.283080	+	1.54472i	−0.750614	+	0.660741i	$0.770242\pi$
$464$	26.7463	+	3.24759i	1.24167	+	0.150766i
$465$	0.131213	−	0.637641i	0.00608483	−	0.0295699i
$466$	0.297027	+	0.953194i	0.0137595	+	0.0441558i
$467$	1.32593	−	1.92094i	0.0613566	−	0.0888904i	−0.791105	−	0.611681i	$-0.790494\pi$
$467$	1.32593	−	1.92094i	0.0613566	−	0.0888904i	0.852461	+	0.522791i	$0.175109\pi$
$468$	−0.0787222	+	0.697288i	−0.00363893	+	0.0322322i
$469$	15.7150	+	22.7671i	0.725651	+	1.05129i
$470$	23.0903	−	29.4726i	1.06508	−	1.35947i
$471$	13.9316	+	4.67524i	0.641935	+	0.215424i
$472$	−7.41081	−	5.11531i	−0.341110	−	0.235451i
$473$	−2.25895	−	37.3449i	−0.103867	−	1.71712i
$474$	−22.6510	−	26.7138i	−1.04040	−	1.22700i
$475$	0.715239	−	0.560354i	0.0328174	−	0.0257108i
$476$	0.00780456	+	0.00611448i	0.000357721	+	0.000280257i
$477$	−3.33721	−	0.977940i	−0.152801	−	0.0447768i
$478$	6.59185	−	4.55003i	0.301504	−	0.208113i
$479$	17.6016	+	22.4668i	0.804238	+	1.02653i	0.998956	+	0.0456748i	$0.0145438\pi$
$479$	17.6016	+	22.4668i	0.804238	+	1.02653i	−0.194718	+	0.980859i	$0.562379\pi$
$480$	−1.25153	−	0.596252i	−0.0571241	−	0.0272151i
$481$	−2.67150	−	23.7052i	−0.121810	−	1.08087i
$482$	−11.0979	−	1.34753i	−0.505497	−	0.0613785i
$483$	0.546796	−	25.1946i	0.0248801	−	1.14639i
$484$	−0.0584612			−0.00265733
$485$	−28.8121			−1.30829
$486$	16.9486	+	14.6461i	0.768805	+	0.664361i
$487$	−32.7764	−	14.7514i	−1.48524	−	0.668451i	−0.504435	−	0.863450i	$-0.668299\pi$
$487$	−32.7764	−	14.7514i	−1.48524	−	0.668451i	−0.980804	+	0.194998i	$0.937530\pi$
$488$	−13.0308	+	13.0308i	−0.589878	+	0.589878i
$489$	−19.3090	−	2.77091i	−0.873185	−	0.125305i
$490$	−12.4250	+	3.06249i	−0.561305	+	0.138349i
$491$	−15.3007	−	13.5553i	−0.690513	−	0.611741i	0.243110	−	0.969999i	$-0.421832\pi$
$491$	−15.3007	−	13.5553i	−0.690513	−	0.611741i	−0.933623	+	0.358258i	$0.883371\pi$
$492$	0.526957	−	0.262146i	0.0237571	−	0.0118185i
$493$	−0.387426	+	0.437314i	−0.0174488	+	0.0196956i
$494$	19.2954	+	3.70794i	0.868140	+	0.166828i
$495$	−19.1107	−	8.21292i	−0.858963	−	0.369143i
$496$	−0.128105	−	0.699048i	−0.00575209	−	0.0313882i
$497$	−3.98537	+	16.1693i	−0.178768	+	0.725292i
$498$	12.2581	−	0.474817i	0.549297	−	0.0212771i
$499$	−16.9146	+	27.9802i	−0.757203	+	1.25257i	0.204605	+	0.978845i	$0.434409\pi$
$499$	−16.9146	+	27.9802i	−0.757203	+	1.25257i	−0.961809	+	0.273723i	$0.911745\pi$
$500$	−0.634676	−	0.383675i	−0.0283836	−	0.0171585i
$501$	−0.206574	−	0.582510i	−0.00922906	−	0.0260246i
$502$	−7.59633	−	0.459494i	−0.339041	−	0.0205082i
$503$	26.1335	+	9.91111i	1.16523	+	0.441915i	0.859966	−	0.510352i	$-0.170485\pi$
$503$	26.1335	+	9.91111i	1.16523	+	0.441915i	0.305267	+	0.952267i	$0.401254\pi$
$504$	−0.618289	+	14.2376i	−0.0275408	+	0.634194i
$505$	4.05536	−	22.1294i	0.180461	−	0.984744i
$506$	38.8921			1.72896
$507$	19.7079	−	10.8902i	0.875260	−	0.483653i
$508$	−0.439482			−0.0194989
$509$	1.21703	−	6.64110i	0.0539437	−	0.294361i	−0.945574	−	0.325406i	$-0.894499\pi$
$509$	1.21703	−	6.64110i	0.0539437	−	0.294361i	0.999518	+	0.0310450i	$0.00988352\pi$
$510$	0.421099	−	0.242246i	0.0186466	−	0.0107268i
$511$	3.15702	+	1.19730i	0.139658	+	0.0529655i
$512$	21.3914	+	1.29394i	0.945374	+	0.0571846i
$513$	13.9991	−	13.8686i	0.618076	−	0.612313i
$514$	8.93937	+	5.40404i	0.394299	+	0.238362i
$515$	20.2634	−	33.5198i	0.892914	−	1.47706i
$516$	−0.0512032	−	1.32188i	−0.00225409	−	0.0581926i
$517$	9.08197	−	36.8470i	0.399425	−	1.62053i
$518$	2.92763	+	15.9756i	0.128633	+	0.701927i
$519$	13.3238	−	2.14398i	0.584850	−	0.0941104i
$520$	3.75775	+	21.5499i	0.164788	+	0.945027i
$521$	−11.9254	+	13.4609i	−0.522459	+	0.589735i	−0.949213	−	0.314633i	$-0.898119\pi$
$521$	−11.9254	+	13.4609i	−0.522459	+	0.589735i	0.426754	+	0.904368i	$0.359657\pi$
$522$	28.0018	+	2.91747i	1.22560	+	0.127694i
$523$	−27.1712	−	24.0716i	−1.18811	−	1.05258i	−0.997482	−	0.0709152i	$-0.977408\pi$
$523$	−27.1712	−	24.0716i	−1.18811	−	1.05258i	−0.190631	−	0.981662i	$-0.561054\pi$
$524$	1.16578	−	0.287340i	0.0509275	−	0.0125525i
$525$	−0.100700	+	0.701730i	−0.00439493	+	0.0306260i
$526$	−17.7116	+	17.7116i	−0.772264	+	0.772264i
$527$	0.0140533	+	0.00632489i	0.000612173	+	0.000275517i
$528$	−22.7026	−	0.492713i	−0.988002	−	0.0214426i
$529$	49.5367			2.15377
$530$	3.63430			0.157864
$531$	−8.08797	−	5.38187i	−0.350988	−	0.233553i
$532$	−0.417225	−	0.0506603i	−0.0180890	−	0.00219640i
$533$	−16.6463	−	8.92024i	−0.721031	−	0.386378i
$534$	1.63444	−	3.43068i	0.0707293	−	0.148460i
$535$	−3.18439	−	4.06458i	−0.137673	−	0.175727i
$536$	37.0590	−	25.5800i	1.60071	−	1.10489i
$537$	−9.15810	−	31.8031i	−0.395201	−	1.37241i
$538$	−9.02238	−	7.06858i	−0.388982	−	0.304748i
$539$	−10.2105	+	7.99940i	−0.439797	+	0.344559i
$540$	−0.669267	−	0.304990i	−0.0288007	−	0.0131247i
$541$	1.87158	+	30.9409i	0.0804656	+	1.33025i	0.784518	+	0.620106i	$0.212911\pi$
$541$	1.87158	+	30.9409i	0.0804656	+	1.33025i	−0.704052	+	0.710148i	$0.748628\pi$
$542$	16.3615	+	11.2935i	0.702788	+	0.485099i
$543$	6.26773	−	18.6770i	0.268974	−	0.801508i
$544$	0.0202393	−	0.0258336i	0.000867753	−	0.00110760i
$545$	−11.0275	−	15.9761i	−0.472368	−	0.684343i
$546$	−12.8746	+	8.32225i	−0.550983	+	0.356160i
$547$	−3.81535	+	5.52749i	−0.163133	+	0.236338i	−0.896022	−	0.444009i	$-0.853556\pi$
$547$	−3.81535	+	5.52749i	−0.163133	+	0.236338i	0.732890	+	0.680347i	$0.238171\pi$
$548$	−0.0329543	−	0.105754i	−0.00140774	−	0.00451760i
$549$	−13.8172	+	14.2956i	−0.589704	+	0.610123i
$550$	−1.08610	−	0.131877i	−0.0463116	−	0.00562324i
$551$	4.46435	−	24.3612i	0.190188	−	1.03782i
$552$	−41.0103	−	0.890045i	−1.74552	−	0.0378828i
$553$	4.33329	−	23.6460i	0.184270	−	1.00553i
$554$	7.88821	+	3.55020i	0.335138	+	0.150833i
$555$	24.4901	+	5.03953i	1.03955	+	0.213916i
$556$	−0.272229	−	0.518688i	−0.0115451	−	0.0219973i
$557$	1.96032	−	6.29089i	0.0830614	−	0.266554i	−0.903842	−	0.427867i	$-0.859265\pi$
$557$	1.96032	−	6.29089i	0.0830614	−	0.266554i	0.986903	+	0.161313i	$0.0515729\pi$
$558$	−0.146271	−	0.728073i	−0.00619213	−	0.0308218i
$559$	−33.6386	+	25.8901i	−1.42276	+	1.09503i
$560$	−3.67996	−	14.9302i	−0.155507	−	0.630916i
$561$	0.288450	−	0.399083i	0.0121784	−	0.0168493i
$562$	2.20434	+	18.1544i	0.0929846	+	0.765797i
$563$	−26.8509	+	14.0925i	−1.13163	+	0.593926i	−0.923280	−	0.384127i	$-0.874502\pi$
$563$	−26.8509	+	14.0925i	−1.13163	+	0.593926i	−0.208352	+	0.978054i	$0.566810\pi$
$564$	0.349319	−	1.29558i	0.0147090	−	0.0545538i
$565$	10.9307	+	24.2870i	0.459857	+	1.02176i
$566$	−1.18569	+	19.6018i	−0.0498383	+	0.823925i
$567$	−0.405588	+	15.3695i	−0.0170331	+	0.645460i
$568$	26.3195	+	6.48717i	1.10434	+	0.272196i
$569$	9.35924	−	8.29156i	0.392360	−	0.347600i	−0.443762	−	0.896145i	$-0.646356\pi$
$569$	9.35924	−	8.29156i	0.392360	−	0.347600i	0.836121	+	0.548545i	$0.184818\pi$
$570$	−9.96387	+	18.0230i	−0.417341	+	0.754902i
$571$	2.84836	+	5.42710i	0.119200	+	0.227117i	0.937744	−	0.347327i	$-0.112911\pi$
$571$	2.84836	+	5.42710i	0.119200	+	0.227117i	−0.818544	+	0.574444i	$0.805218\pi$
$572$	−0.416974	−	0.615354i	−0.0174346	−	0.0257292i
$573$	−11.2070	+	6.44705i	−0.468179	+	0.269329i
$574$	11.7253	+	5.27714i	0.489406	+	0.220264i
$575$	−2.02566	−	0.245960i	−0.0844760	−	0.0102572i
$576$	23.1500	+	1.00532i	0.964584	+	0.0418884i
$577$	27.7952	−	27.7952i	1.15713	−	1.15713i	0.172040	−	0.985090i	$-0.444964\pi$
$577$	27.7952	−	27.7952i	1.15713	−	1.15713i	0.985090	−	0.172040i	$-0.0550359\pi$
$578$	−7.26411	−	23.3114i	−0.302147	−	0.969625i
$579$	−5.66854	+	10.2535i	−0.235577	+	0.426120i
$580$	−0.909245	+	0.166625i	−0.0377543	+	0.00691874i
$581$	5.58347	+	6.30243i	0.231641	+	0.261469i
$582$	−30.2571	+	12.8356i	−1.25420	+	0.532051i
$583$	3.35920	−	1.51185i	0.139124	−	0.0626145i
$584$	1.94890	−	5.13883i	0.0806461	−	0.212646i
$585$	4.44910	+	23.1770i	0.183948	+	0.958251i
$586$	−3.49609	−	9.21842i	−0.144422	−	0.380809i
$587$	1.73228	+	1.73228i	0.0714990	+	0.0714990i	0.741952	−	0.670453i	$-0.233900\pi$
$587$	1.73228	+	1.73228i	0.0714990	+	0.0714990i	−0.670453	+	0.741952i	$0.733900\pi$
$588$	−0.367080	+	0.274947i	−0.0151381	+	0.0113386i
$589$	−0.648530	+	0.0787458i	−0.0267222	+	0.00324466i
$590$	9.69312	+	3.02050i	0.399060	+	0.124352i
$591$	17.8614	+	7.22102i	0.734720	+	0.297033i
$592$	26.8486	−	4.92018i	1.10347	−	0.202218i
$593$	−3.93537	+	12.6290i	−0.161606	+	0.518612i	−0.999635	−	0.0270134i	$-0.991400\pi$
$593$	−3.93537	+	12.6290i	−0.161606	+	0.518612i	0.838029	+	0.545626i	$0.183708\pi$
$594$	−23.7279	−	0.111128i	−0.973569	−	0.00455965i
$595$	0.311777	+	0.118241i	0.0127816	+	0.00484743i
$596$	0.0934151	−	0.0934151i	0.00382643	−	0.00382643i
$597$	−30.4151	−	6.25876i	−1.24481	−	0.256154i
$598$	−24.7531	−	36.5296i	−1.01223	−	1.49381i
$599$	34.9504	+	13.2549i	1.42803	+	0.541582i	0.942964	−	0.332894i	$-0.108025\pi$
$599$	34.9504	+	13.2549i	1.42803	+	0.541582i	0.485069	+	0.874476i	$0.338794\pi$
$600$	1.14224	+	0.163915i	0.0466317	+	0.00669179i
$601$	9.71182	−	14.0700i	0.396153	−	0.573927i	−0.573256	−	0.819376i	$-0.694320\pi$
$601$	9.71182	−	14.0700i	0.396153	−	0.573927i	0.969410	+	0.245449i	$0.0789353\pi$
$602$	21.6323	−	19.1645i	0.881666	−	0.781088i
$603$	39.5062	−	28.2736i	1.60882	−	1.15139i
$604$	−0.119981	+	0.00725753i	−0.00488197	+	0.000295305i
$605$	−1.87714	+	0.584941i	−0.0763167	+	0.0237812i
$606$	−5.59971	−	25.0458i	−0.227473	−	1.01742i
$607$	26.8622	+	14.0984i	1.09030	+	0.572236i	0.911355	−	0.411622i	$-0.135038\pi$
$607$	26.8622	+	14.0984i	1.09030	+	0.572236i	0.178950	+	0.983858i	$0.442730\pi$
$608$	−0.167689	+	1.38104i	−0.00680067	+	0.0560085i
$609$	10.6295	+	16.1376i	0.430729	+	0.653928i
$610$	9.65594	−	18.3979i	0.390958	−	0.744908i
$611$	−40.3890	+	14.9212i	−1.63396	+	0.603646i
$612$	0.0105029	−	0.0138864i	0.000424556	−	0.000561324i
$613$	−12.7019	+	0.768322i	−0.513024	+	0.0310322i	−0.314863	−	0.949137i	$-0.601958\pi$
$613$	−12.7019	+	0.768322i	−0.513024	+	0.0310322i	−0.198161	+	0.980169i	$0.563497\pi$
$614$	3.97845	+	4.49075i	0.160557	+	0.181232i
$615$	14.2972	−	13.6898i	0.576520	−	0.552027i
$616$	−9.30998	−	11.8833i	−0.375110	−	0.478792i
$617$	−44.4054	−	2.68603i	−1.78770	−	0.108136i	−0.866973	−	0.498355i	$-0.833938\pi$
$617$	−44.4054	−	2.68603i	−1.78770	−	0.108136i	−0.920722	+	0.390219i	$0.872399\pi$
$618$	6.34686	−	44.2281i	0.255308	−	1.77911i
$619$	12.7633	+	40.9587i	0.512999	+	1.64627i	0.740173	+	0.672416i	$0.234743\pi$
$619$	12.7633	+	40.9587i	0.512999	+	1.64627i	−0.227175	+	0.973854i	$0.572949\pi$
$620$	0.0113314	+	0.0215902i	0.000455081	+	0.000867085i
$621$	−44.2543	−	0.207263i	−1.77587	−	0.00831716i
$622$	−6.09527	−	0.368696i	−0.244398	−	0.0147834i
$623$	2.53252	−	0.624210i	0.101463	−	0.0250085i
$624$	13.9864	+	21.6371i	0.559903	+	0.866177i
$625$	−23.0547	−	5.68247i	−0.922187	−	0.227299i
$626$	41.4587	+	12.9190i	1.65702	+	0.516349i
$627$	−1.71214	+	20.8037i	−0.0683762	+	0.830818i
$628$	−0.514638	+	0.195177i	−0.0205363	+	0.00778840i
$629$	−0.242922	+	0.539751i	−0.00968595	+	0.0215213i
$630$	−4.11021	−	15.5333i	−0.163755	−	0.618863i
$631$	−6.52306	−	10.7905i	−0.259679	−	0.429562i	0.698551	−	0.715560i	$-0.253829\pi$
$631$	−6.52306	−	10.7905i	−0.259679	−	0.429562i	−0.958230	+	0.285999i	$0.907675\pi$
$632$	−38.4897	−	7.05349i	−1.53104	−	0.280573i
$633$	20.6106	−	25.1631i	0.819196	−	1.00014i
$634$	−17.4765	+	6.62797i	−0.694081	+	0.263230i
$635$	−14.1114	+	4.39729i	−0.559994	+	0.174501i
$636$	0.119908	−	0.0508671i	0.00475467	−	0.00201701i
$637$	14.0120	+	4.49899i	0.555176	+	0.178257i
$638$	−24.5435	+	16.9411i	−0.971685	+	0.670706i
$639$	28.5100	+	6.51459i	1.12784	+	0.257713i
$640$	−25.0669	+	6.17843i	−0.990856	+	0.244224i
$641$	−4.11276	+	5.95836i	−0.162444	+	0.235341i	−0.895750	−	0.444558i	$-0.853361\pi$
$641$	−4.11276	+	5.95836i	−0.162444	+	0.235341i	0.733306	+	0.679899i	$0.237976\pi$
$642$	−5.15483	−	2.84980i	−0.203445	−	0.112473i
$643$	−7.83755	+	25.1516i	−0.309083	+	0.991881i	0.661262	+	0.750155i	$0.270021\pi$
$643$	−7.83755	+	25.1516i	−0.309083	+	0.991881i	−0.970344	+	0.241726i	$0.922286\pi$
$644$	0.582110	+	0.743009i	0.0229384	+	0.0292786i
$645$	−14.8703	−	41.9322i	−0.585519	−	1.65108i
$646$	−0.364911	−	0.323283i	−0.0143572	−	0.0127194i
$647$	−19.1349	−	27.7217i	−0.752270	−	1.08985i	−0.992867	−	0.119226i	$-0.961959\pi$
$647$	−19.1349	−	27.7217i	−0.752270	−	1.08985i	0.240597	−	0.970625i	$-0.422657\pi$
$648$	25.0177	+	0.660194i	0.982788	+	0.0259349i
$649$	10.2159	−	1.24043i	0.401009	−	0.0486913i
$650$	0.567390	+	1.10406i	0.0222549	+	0.0433049i
$651$	0.322984	−	0.394325i	0.0126587	−	0.0154548i
$652$	0.625258	−	0.377981i	0.0244870	−	0.0148029i
$653$		−	16.8978i		−	0.661263i	−0.943760	−	0.330632i	$-0.892738\pi$
$653$		−	16.8978i		−	0.661263i	0.943760	−	0.330632i	$-0.107262\pi$
$654$	−18.6978	−	11.8647i	−0.731142	−	0.463946i
$655$	34.5574	−	20.8906i	1.35027	−	0.816265i
$656$	8.86877	−	19.7056i	0.346267	−	0.769374i
$657$	2.00795	−	5.57905i	0.0783377	−	0.217660i
$658$	26.7323	−	12.0312i	1.04213	−	0.469026i
$659$	−3.21196	−	13.0314i	−0.125120	−	0.507633i	−0.999740	−	0.0228225i	$-0.992735\pi$
$659$	−3.21196	−	13.0314i	−0.125120	−	0.507633i	0.874619	−	0.484810i	$-0.161111\pi$
$660$	0.748669	−	0.215588i	0.0291419	−	0.00839176i
$661$	2.16319	+	1.30769i	0.0841382	+	0.0508633i	0.558781	−	0.829315i	$-0.311269\pi$
$661$	2.16319	+	1.30769i	0.0841382	+	0.0508633i	−0.474643	+	0.880178i	$0.657423\pi$
$662$	16.5509	+	14.6628i	0.643268	+	0.569886i
$663$	−0.558427	−	0.0169293i	−0.0216875	−	0.000657480i
$664$	10.2588	−	9.08846i	0.398117	−	0.352701i
$665$	−13.9036	+	2.54793i	−0.539160	+	0.0988047i
$666$	27.9633	−	5.61787i	1.08356	−	0.217688i
$667$	−45.7754	+	31.5965i	−1.77243	+	1.22342i
$668$	0.0198106	+	0.0119759i	0.000766496	+	0.000463363i
$669$	16.4226	−	8.16976i	0.634934	−	0.315861i
$670$	−31.3114	+	39.9661i	−1.20967	+	1.54403i
$671$	1.27160	−	21.0220i	0.0490895	−	0.811546i
$672$	−0.650713	−	0.868763i	−0.0251018	−	0.0335133i
$673$	7.94982	−	15.1471i	0.306443	−	0.583878i	−0.682723	−	0.730677i	$-0.739205\pi$
$673$	7.94982	−	15.1471i	0.306443	−	0.583878i	0.989166	+	0.146799i	$0.0468969\pi$
$674$	12.1239	+	2.22178i	0.466994	+	0.0855797i
$675$	1.23515	+	0.155847i	0.0475408	+	0.00599856i
$676$	−0.312589	+	0.783290i	−0.0120227	+	0.0301266i
$677$			41.7690i			1.60531i	0.596441	+	0.802657i	$0.296581\pi$
$677$			41.7690i			1.60531i	−0.596441	+	0.802657i	$0.703419\pi$
$678$	22.2985	+	20.6355i	0.856369	+	0.792500i
$679$	−19.9751	−	10.4838i	−0.766575	−	0.402330i
$680$	0.192467	−	0.507494i	0.00738077	−	0.0194615i
$681$	21.9561	+	15.8695i	0.841361	+	0.608120i
$682$	0.619238	+	0.485142i	0.0237118	+	0.0185770i
$683$	−19.7723	+	32.7075i	−0.756568	+	1.25152i	0.205487	+	0.978660i	$0.434122\pi$
$683$	−19.7723	+	32.7075i	−0.756568	+	1.25152i	−0.962055	+	0.272856i	$0.912032\pi$
$684$	−0.0764851	+	0.734100i	−0.00292448	+	0.0280690i
$685$	−2.11627	−	3.06595i	−0.0808586	−	0.117144i
$686$	−26.4127	−	6.51016i	−1.00844	−	0.248559i
$687$	24.0319	+	9.71563i	0.916874	+	0.370674i
$688$	−32.2079	−	36.3552i	−1.22792	−	1.38603i
$689$	−3.55799	−	2.19292i	−0.135549	−	0.0835435i
$690$	44.4437	−	12.7981i	1.69194	−	0.487215i
$691$	−23.3202	+	38.5764i	−0.887143	+	1.46751i	−0.00316067	+	0.999995i	$0.501006\pi$
$691$	−23.3202	+	38.5764i	−0.887143	+	1.46751i	−0.883983	+	0.467519i	$0.845148\pi$
$692$	−0.335183	+	0.378343i	−0.0127417	+	0.0143825i
$693$	−10.2609	−	12.6477i	−0.389778	−	0.480445i
$694$	16.3837	+	36.4031i	0.621917	+	1.38184i
$695$	−13.9308	−	13.9308i	−0.528427	−	0.528427i
$696$	26.2679	−	17.3021i	0.995682	−	0.655835i
$697$	0.242420	+	0.401012i	0.00918233	+	0.0151894i
$698$			27.4991i			1.04086i
$699$	1.01612	+	0.644776i	0.0384331	+	0.0243877i
$700$	−0.0137366	−	0.0227231i	−0.000519195	−	0.000858854i
$701$	3.90590	−	32.1680i	0.147524	−	1.21497i	−0.711371	−	0.702816i	$-0.751926\pi$
$701$	3.90590	−	32.1680i	0.147524	−	1.21497i	0.858895	−	0.512151i	$-0.171151\pi$
$702$	14.9974	+	22.3573i	0.566040	+	0.843822i
$703$	−3.02442	−	24.9083i	−0.114068	−	0.939435i
$704$	−19.3219	+	15.1378i	−0.728223	+	0.570527i
$705$	−1.74676	−	45.0952i	−0.0657870	−	1.69838i
$706$	−4.65151	+	5.25047i	−0.175062	+	0.197604i
$707$	10.8637	−	13.8664i	0.408570	−	0.521501i
$708$	0.362085	−	0.0360119i	0.0136080	−	0.00135341i
$709$	1.71036	+	0.532971i	0.0642341	+	0.0200161i	0.329452	−	0.944172i	$-0.393136\pi$
$709$	1.71036	+	0.532971i	0.0642341	+	0.0200161i	−0.265218	+	0.964189i	$0.585444\pi$
$710$	−30.5073	+	1.84535i	−1.14492	+	0.0692549i
$711$	−41.6484	−	6.90207i	−1.56194	−	0.258848i
$712$	−1.01606	−	4.12230i	−0.0380783	−	0.154490i
$713$	1.15492	+	0.904825i	0.0432523	+	0.0338860i
$714$	0.380088	−	0.0147227i	0.0142245	−	0.000550985i
$715$	−19.5457	−	15.5864i	−0.730968	−	0.582899i
$716$	1.02016	+	0.704167i	0.0381252	+	0.0263159i
$717$	2.51332	−	9.32162i	0.0938618	−	0.348122i
$718$	17.9740	+	47.3934i	0.670782	+	1.76871i
$719$	2.55491	−	21.0415i	0.0952819	−	0.784717i	−0.864239	−	0.503081i	$-0.832200\pi$
$719$	2.55491	−	21.0415i	0.0952819	−	0.784717i	0.959521	−	0.281636i	$-0.0908772\pi$
$720$	−26.1053	+	6.90761i	−0.972888	+	0.257432i
$721$	26.2452	−	15.8658i	0.977421	−	0.590871i
$722$	−6.52726	−	1.19617i	−0.242920	−	0.0445167i
$723$	−11.2533	+	7.41234i	−0.418516	+	0.275668i
$724$	0.261658	+	0.689936i	0.00972445	+	0.0256413i
$725$	1.38546	−	0.727147i	0.0514548	−	0.0270056i
$726$	−1.71069	+	1.45053i	−0.0634898	+	0.0538341i
$727$	3.18105	−	12.9060i	0.117979	−	0.478658i	−0.881994	−	0.471261i	$-0.843799\pi$
$727$	3.18105	−	12.9060i	0.117979	−	0.478658i	0.999973	−	0.00739737i	$-0.00235468\pi$
$728$	−5.23608	+	16.3076i	−0.194062	+	0.604401i
$729$	26.9988	+	0.252900i	0.999956	+	0.00936668i
$730$	−0.374145	+	6.18536i	−0.0138477	+	0.228930i
$731$	1.04555	−	0.126952i	0.0386709	−	0.00469550i
$732$	0.0610794	−	0.742157i	0.00225756	−	0.0274309i
$733$	−27.9003	+	8.69408i	−1.03052	+	0.321123i	−0.765716	−	0.643179i	$-0.777615\pi$
$733$	−27.9003	+	8.69408i	−1.03052	+	0.321123i	−0.264804	+	0.964302i	$0.585307\pi$
$734$	−25.3728	+	11.4194i	−0.936529	+	0.421497i
$735$	−9.03562	+	12.5012i	−0.333284	+	0.461113i
$736$	2.45940	−	1.92682i	0.0906548	−	0.0710235i
$737$	−12.3156	+	49.9662i	−0.453649	+	1.84053i
$738$	8.91554	−	20.7457i	0.328186	−	0.763659i
$739$	0.270082	+	4.46499i	0.00993512	+	0.164247i	0.999759	+	0.0219498i	$0.00698739\pi$
$739$	0.270082	+	4.46499i	0.00993512	+	0.164247i	−0.989824	+	0.142297i	$0.954551\pi$
$740$	−0.829224	+	0.435210i	−0.0304829	+	0.0159987i
$741$	20.6297	−	11.6325i	0.757849	−	0.427329i
$742$	2.51962	+	1.32240i	0.0924983	+	0.0485468i
$743$	−19.7237	+	43.8243i	−0.723594	+	1.60776i	0.0687130	+	0.997636i	$0.478111\pi$
$743$	−19.7237	+	43.8243i	−0.723594	+	1.60776i	−0.792307	+	0.610123i	$0.791120\pi$
$744$	−0.641861	−	0.525736i	−0.0235318	−	0.0192744i
$745$	2.06481	−	3.93416i	0.0756486	−	0.144136i
$746$	−1.11986	−	1.11986i	−0.0410009	−	0.0410009i
$747$	10.8993	−	9.99208i	0.398785	−	0.365591i
$748$	0.00111358	+	0.0184097i	4.07165e−5	+	0.000673124i
$749$	−0.728742	−	3.97662i	−0.0266277	−	0.145302i
$750$	−28.0916	+	4.52032i	−1.02576	+	0.165059i
$751$	−22.7536	−	15.7057i	−0.830292	−	0.573109i	0.0753475	−	0.997157i	$-0.475993\pi$
$751$	−22.7536	−	15.7057i	−0.830292	−	0.573109i	−0.905640	+	0.424048i	$0.860609\pi$
$752$	−20.2197	−	44.9263i	−0.737336	−	1.63829i
$753$	−7.34188	+	5.49915i	−0.267553	+	0.200400i
$754$	31.5328	+	12.2703i	1.14836	+	0.446858i
$755$	−3.77988	+	1.43352i	−0.137564	+	0.0521712i
$756$	−0.353020	−	0.454970i	−0.0128392	−	0.0165471i
$757$	12.6224	−	33.2826i	0.458769	−	1.20968i	−0.483656	−	0.875258i	$-0.660691\pi$
$757$	12.6224	−	33.2826i	0.458769	−	1.20968i	0.942425	−	0.334417i	$-0.108539\pi$
$758$	0.947994	+	7.80744i	0.0344327	+	0.283579i
$759$	35.7554	−	30.3176i	1.29784	−	1.10046i
$760$	4.14739	+	22.6316i	0.150442	+	0.820933i
$761$	−3.83844	−	20.9457i	−0.139143	−	0.759281i	−0.976975	−	0.213352i	$-0.931562\pi$
$761$	−3.83844	−	20.9457i	−0.139143	−	0.759281i	0.837832	−	0.545928i	$-0.183823\pi$
$762$	−12.8601	+	10.9043i	−0.465874	+	0.395022i
$763$	−1.83209	−	15.0886i	−0.0663261	−	0.546245i
$764$	0.171720	−	0.452789i	0.00621262	−	0.0163813i
$765$	0.198299	−	0.550969i	0.00716951	−	0.0199203i
$766$	−12.3734	+	4.69261i	−0.447069	+	0.169551i
$767$	−7.66704	−	8.80585i	−0.276841	−	0.317961i
$768$	−2.15618	+	1.61500i	−0.0778045	+	0.0582765i
$769$	−5.17088	−

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.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.259021 + 1.41343i) q^{2} +(0.863683 + 1.50135i) q^{3} +(-0.0606581 - 0.0230046i) q^{4} +(-2.17786 - 0.131736i) q^{5} +(-2.34576 + 0.831874i) q^{6} +(-1.46195 - 0.883779i) q^{7} +(-1.43857 + 2.37968i) q^{8} +(-1.50810 + 2.59338i) q^{9} +(0.750309 - 3.04412i) q^{10} +(-0.572827 - 3.12581i) q^{11} +(-0.0178514 - 0.110938i) q^{12} +(-2.57136 + 2.52747i) q^{13} +(1.62783 - 1.83744i) q^{14} +(-1.68319 - 3.38350i) q^{15} +(-3.08801 - 2.73574i) q^{16} +(0.0868613 - 0.0214094i) q^{17} +(-3.27493 - 2.80334i) q^{18} +(-2.68160 + 2.68160i) q^{19} +(0.129074 + 0.0580915i) q^{20} +(0.0642017 - 2.95820i) q^{21} +4.56649 q^{22} +8.51685 q^{23} +(-4.81520 - 0.104504i) q^{24} +(-0.237842 - 0.0288792i) q^{25} +(-2.90637 - 4.28910i) q^{26} +(-5.19610 - 0.0243356i) q^{27} +(0.0683481 + 0.0872399i) q^{28} +(-5.37469 + 3.70988i) q^{29} +(5.21832 - 1.50268i) q^{30} +(0.135605 + 0.106239i) q^{31} +(0.288769 - 0.226236i) q^{32} +(4.19820 - 3.55973i) q^{33} +(0.00776180 + 0.128318i) q^{34} +(3.06749 + 2.11734i) q^{35} +(0.151138 - 0.122616i) q^{36} +(-4.08038 + 5.20822i) q^{37} +(-3.09566 - 4.48484i) q^{38} +(-6.01546 - 1.67758i) q^{39} +(3.44648 - 4.99309i) q^{40} +(1.55831 + 5.00078i) q^{41} +(4.16458 + 0.856980i) q^{42} +(11.6872 + 1.41908i) q^{43} +(-0.0371615 + 0.202784i) q^{44} +(3.62608 - 5.44934i) q^{45} +(-2.20604 + 12.0380i) q^{46} +(10.8898 + 4.90110i) q^{47} +(1.44024 - 6.99899i) q^{48} +(-1.89683 - 3.61411i) q^{49} +(0.102425 - 0.328692i) q^{50} +(0.107164 + 0.111918i) q^{51} +(0.214117 - 0.0941585i) q^{52} +(0.277411 + 1.12550i) q^{53} +(1.38029 - 7.33801i) q^{54} +(0.835752 + 6.88304i) q^{55} +(4.20623 - 2.20760i) q^{56} +(-6.34207 - 1.70997i) q^{57} +(-3.85150 - 8.55767i) q^{58} +(-0.195524 + 3.23240i) q^{59} +(0.0242633 + 0.243958i) q^{60} +(6.43464 + 1.58600i) q^{61} +(-0.185286 + 0.164149i) q^{62} +(4.49675 - 2.45856i) q^{63} +(-3.58950 - 6.83921i) q^{64} +(5.93301 - 5.16573i) q^{65} +(3.94400 + 6.85590i) q^{66} +(-14.7671 - 6.64611i) q^{67} +(-0.00576136 - 0.000699555i) q^{68} +(7.35585 + 12.7868i) q^{69} +(-3.78725 + 3.78725i) q^{70} +(-2.90014 - 9.30689i) q^{71} +(-4.00191 - 7.31956i) q^{72} +(-1.94409 + 0.356268i) q^{73} +(-6.30455 - 7.11636i) q^{74} +(-0.162062 - 0.382026i) q^{75} +(0.224350 - 0.100972i) q^{76} +(-1.92509 + 5.07603i) q^{77} +(3.92926 - 8.06790i) q^{78} +(4.99006 + 13.1577i) q^{79} +(6.36485 + 6.36485i) q^{80} +(-4.45124 - 7.82218i) q^{81} +(-7.47189 + 0.907251i) q^{82} +(-4.70562 - 1.46633i) q^{83} +(-0.0719466 + 0.177962i) q^{84} +(-0.191992 + 0.0351838i) q^{85} +(-5.03299 + 16.1514i) q^{86} +(-10.2118 - 4.86513i) q^{87} +(8.26249 + 3.13355i) q^{88} +(-1.07963 + 1.07963i) q^{89} +(6.76302 + 6.53669i) q^{90} +(5.99292 - 1.42252i) q^{91} +(-0.516616 - 0.195926i) q^{92} +(-0.0423833 + 0.295347i) q^{93} +(-9.74805 + 14.1225i) q^{94} +(6.19340 - 5.48688i) q^{95} +(0.589065 + 0.238147i) q^{96} +(13.1814 - 0.797325i) q^{97} +(5.59961 - 1.74491i) q^{98} +(8.97031 + 3.22850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

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