LMFDB - Embedded newform 507.2.s.a.5.15

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			5.15
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.289269 + 1.57849i) q^{2} +(-1.18129 + 1.26671i) q^{3} +(-0.537915 - 0.204004i) q^{4} +(-1.19167 - 0.0720827i) q^{5} +(-1.65777 - 2.23107i) q^{6} +(-3.74112 - 2.26159i) q^{7} +(-1.18280 + 1.95659i) q^{8} +(-0.209095 - 2.99270i) q^{9} +(0.458494 - 1.86018i) q^{10} +(-0.185051 - 1.00979i) q^{11} +(0.893848 - 0.440392i) q^{12} +(2.51344 + 2.58508i) q^{13} +(4.65208 - 5.25111i) q^{14} +(1.49902 - 1.42435i) q^{15} +(-3.60754 - 3.19601i) q^{16} +(4.73822 - 1.16787i) q^{17} +(4.78443 + 0.535641i) q^{18} +(4.07170 - 4.07170i) q^{19} +(0.626311 + 0.281880i) q^{20} +(7.28413 - 2.06731i) q^{21} +1.64747 q^{22} -7.42034 q^{23} +(-1.08119 - 3.80957i) q^{24} +(-3.54867 - 0.430886i) q^{25} +(-4.80757 + 3.21965i) q^{26} +(4.03788 + 3.27040i) q^{27} +(1.55103 + 1.97975i) q^{28} +(-1.05171 + 0.725946i) q^{29} +(1.81469 + 2.77820i) q^{30} +(-4.89889 - 3.83804i) q^{31} +(2.48890 - 1.94993i) q^{32} +(1.49771 + 0.958455i) q^{33} +(0.472845 + 7.81706i) q^{34} +(4.29516 + 2.96473i) q^{35} +(-0.498049 + 1.65248i) q^{36} +(2.33279 - 2.97758i) q^{37} +(5.24931 + 7.60494i) q^{38} +(-6.24364 + 0.130058i) q^{39} +(1.55054 - 2.24635i) q^{40} +(-1.70650 - 5.47636i) q^{41} +(1.15615 + 12.0959i) q^{42} +(8.88768 + 1.07916i) q^{43} +(-0.106460 + 0.580934i) q^{44} +(0.0334502 + 3.58138i) q^{45} +(2.14647 - 11.7129i) q^{46} +(-8.55029 - 3.84817i) q^{47} +(8.30997 - 0.794285i) q^{48} +(5.62816 + 10.7236i) q^{49} +(1.70667 - 5.47688i) q^{50} +(-4.11788 + 7.38154i) q^{51} +(-0.824649 - 1.90330i) q^{52} +(0.334521 + 1.35721i) q^{53} +(-6.33031 + 5.42773i) q^{54} +(0.147731 + 1.21668i) q^{55} +(8.85000 - 4.64484i) q^{56} +(0.347783 + 9.96751i) q^{57} +(-0.841669 - 1.87011i) q^{58} +(0.0449835 - 0.743666i) q^{59} +(-1.09692 + 0.460370i) q^{60} +(-11.5386 - 2.84400i) q^{61} +(7.47539 - 6.62262i) q^{62} +(-5.98601 + 11.6690i) q^{63} +(-2.12161 - 4.04240i) q^{64} +(-2.80885 - 3.26173i) q^{65} +(-1.94615 + 2.08687i) q^{66} +(-1.66267 - 0.748308i) q^{67} +(-2.78701 - 0.338404i) q^{68} +(8.76559 - 9.39940i) q^{69} +(-5.92225 + 5.92225i) q^{70} +(-2.72139 - 8.73324i) q^{71} +(6.10282 + 3.13066i) q^{72} +(9.76789 - 1.79003i) q^{73} +(4.02528 + 4.54360i) q^{74} +(4.73782 - 3.98612i) q^{75} +(-3.02087 + 1.35958i) q^{76} +(-1.59143 + 4.19627i) q^{77} +(1.60079 - 9.89314i) q^{78} +(-0.380575 - 1.00349i) q^{79} +(4.06862 + 4.06862i) q^{80} +(-8.91256 + 1.25152i) q^{81} +(9.13800 - 1.10955i) q^{82} +(-11.9846 - 3.73456i) q^{83} +(-4.33998 - 0.373956i) q^{84} +(-5.73058 + 1.05017i) q^{85} +(-4.27437 + 13.7169i) q^{86} +(0.322821 - 2.18977i) q^{87} +(2.19463 + 0.832313i) q^{88} +(-10.1460 + 10.1460i) q^{89} +(-5.66285 - 0.983182i) q^{90} +(-3.55670 - 15.3555i) q^{91} +(3.99151 + 1.51378i) q^{92} +(10.6487 - 1.67162i) q^{93} +(8.54762 - 12.3834i) q^{94} +(-5.14561 + 4.55862i) q^{95} +(-0.470130 + 5.45614i) q^{96} +(-7.39354 + 0.447227i) q^{97} +(-18.5551 + 5.78199i) q^{98} +(-2.98332 + 0.764947i) 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 $

$2$	−0.289269	+	1.57849i	−0.204544	+	1.11616i	0.707700	+	0.706513i	$0.249733\pi$
$2$	−0.289269	+	1.57849i	−0.204544	+	1.11616i	−0.912244	+	0.409647i	$0.865652\pi$
$3$	−1.18129	+	1.26671i	−0.682020	+	0.731334i
$3$	−1.18129	+	1.26671i	−0.682020	+	0.731334i
$4$	−0.537915	−	0.204004i	−0.268957	−	0.102002i
$5$	−1.19167	−	0.0720827i	−0.532931	−	0.0322364i	−0.208278	−	0.978070i	$-0.566786\pi$
$5$	−1.19167	−	0.0720827i	−0.532931	−	0.0322364i	−0.324653	+	0.945833i	$0.605247\pi$
$6$	−1.65777	−	2.23107i	−0.676782	−	0.910832i
$7$	−3.74112	−	2.26159i	−1.41401	−	0.854800i	−0.415513	−	0.909587i	$-0.636398\pi$
$7$	−3.74112	−	2.26159i	−1.41401	−	0.854800i	−0.998498	+	0.0547875i	$0.982552\pi$
$8$	−1.18280	+	1.95659i	−0.418183	+	0.691759i
$9$	−0.209095	−	2.99270i	−0.0696984	−	0.997568i
$10$	0.458494	−	1.86018i	0.144989	−	0.588242i
$11$	−0.185051	−	1.00979i	−0.0557951	−	0.304464i	0.943871	−	0.330315i	$-0.107155\pi$
$11$	−0.185051	−	1.00979i	−0.0557951	−	0.304464i	−0.999666	+	0.0258512i	$0.991770\pi$
$12$	0.893848	−	0.440392i	0.258032	−	0.127130i
$13$	2.51344	+	2.58508i	0.697102	+	0.716972i
$13$	2.51344	+	2.58508i	0.697102	+	0.716972i
$14$	4.65208	−	5.25111i	1.24332	−	1.40342i
$15$	1.49902	−	1.42435i	0.387045	−	0.367764i
$16$	−3.60754	−	3.19601i	−0.901886	−	0.799001i
$17$	4.73822	−	1.16787i	1.14919	−	0.283249i	0.381684	−	0.924293i	$-0.375344\pi$
$17$	4.73822	−	1.16787i	1.14919	−	0.283249i	0.767505	+	0.641043i	$0.221498\pi$
$18$	4.78443	+	0.535641i	1.12770	+	0.126252i
$19$	4.07170	−	4.07170i	0.934111	−	0.934111i	−0.0638484	−	0.997960i	$-0.520337\pi$
$19$	4.07170	−	4.07170i	0.934111	−	0.934111i	0.997960	+	0.0638484i	$0.0203374\pi$
$20$	0.626311	+	0.281880i	0.140047	+	0.0630302i
$21$	7.28413	−	2.06731i	1.58953	−	0.451124i
$22$	1.64747			0.351243
$23$	−7.42034			−1.54725			−0.773624	−	0.633645i	$-0.781558\pi$
$23$	−7.42034			−1.54725			−0.773624	+	0.633645i	$0.781558\pi$
$24$	−1.08119	−	3.80957i	−0.220698	−	0.777625i
$25$	−3.54867	−	0.430886i	−0.709733	−	0.0861772i
$26$	−4.80757	+	3.21965i	−0.942842	+	0.631425i
$27$	4.03788	+	3.27040i	0.777091	+	0.629388i
$28$	1.55103	+	1.97975i	0.293117	+	0.374137i
$29$	−1.05171	+	0.725946i	−0.195298	+	0.134805i	−0.661701	−	0.749768i	$-0.730165\pi$
$29$	−1.05171	+	0.725946i	−0.195298	+	0.134805i	0.466403	+	0.884573i	$0.345550\pi$
$30$	1.81469	+	2.77820i	0.331316	+	0.507227i
$31$	−4.89889	−	3.83804i	−0.879867	−	0.689332i	0.0714834	−	0.997442i	$-0.477227\pi$
$31$	−4.89889	−	3.83804i	−0.879867	−	0.689332i	−0.951351	+	0.308110i	$0.900304\pi$
$32$	2.48890	−	1.94993i	0.439979	−	0.344701i
$33$	1.49771	+	0.958455i	0.260718	+	0.166846i
$34$	0.472845	+	7.81706i	0.0810922	+	1.34061i
$35$	4.29516	+	2.96473i	0.726014	+	0.501131i
$36$	−0.498049	+	1.65248i	−0.0830081	+	0.275413i
$37$	2.33279	−	2.97758i	0.383508	−	0.489512i	−0.556412	−	0.830906i	$-0.687822\pi$
$37$	2.33279	−	2.97758i	0.383508	−	0.489512i	0.939920	+	0.341395i	$0.110899\pi$
$38$	5.24931	+	7.60494i	0.851550	+	1.23368i
$39$	−6.24364	+	0.130058i	−0.999783	+	0.0208260i
$40$	1.55054	−	2.24635i	0.245162	−	0.355179i
$41$	−1.70650	−	5.47636i	−0.266511	−	0.855263i	−0.986850	−	0.161641i	$-0.948321\pi$
$41$	−1.70650	−	5.47636i	−0.266511	−	0.855263i	0.720339	−	0.693622i	$-0.243986\pi$
$42$	1.15615	+	12.0959i	0.178399	+	1.86644i
$43$	8.88768	+	1.07916i	1.35536	+	0.164570i	0.765760	−	0.643126i	$-0.222363\pi$
$43$	8.88768	+	1.07916i	1.35536	+	0.164570i	0.589598	+	0.807697i	$0.299286\pi$
$44$	−0.106460	+	0.580934i	−0.0160495	+	0.0875790i
$45$	0.0334502	+	3.58138i	0.00498646	+	0.533881i
$46$	2.14647	−	11.7129i	0.316480	−	1.72697i
$47$	−8.55029	−	3.84817i	−1.24719	−	0.561314i	−0.324144	−	0.946008i	$-0.605076\pi$
$47$	−8.55029	−	3.84817i	−1.24719	−	0.561314i	−0.923044	+	0.384694i	$0.874307\pi$
$48$	8.30997	−	0.794285i	1.19944	−	0.114645i
$49$	5.62816	+	10.7236i	0.804022	+	1.53194i
$50$	1.70667	−	5.47688i	0.241359	−	0.774548i
$51$	−4.11788	+	7.38154i	−0.576619	+	1.03362i
$52$	−0.824649	−	1.90330i	−0.114358	−	0.263941i
$53$	0.334521	+	1.35721i	0.0459500	+	0.186427i	0.989432	−	0.144997i	$-0.0463172\pi$
$53$	0.334521	+	1.35721i	0.0459500	+	0.186427i	−0.943482	+	0.331424i	$0.892471\pi$
$54$	−6.33031	+	5.42773i	−0.861447	+	0.738620i
$55$	0.147731	+	1.21668i	0.0199201	+	0.164057i
$56$	8.85000	−	4.64484i	1.18263	−	0.620693i
$57$	0.347783	+	9.96751i	0.0460650	+	1.32023i
$58$	−0.841669	−	1.87011i	−0.110517	−	0.245558i
$59$	0.0449835	−	0.743666i	0.00585635	−	0.0968171i	−0.994073	−	0.108716i	$-0.965326\pi$
$59$	0.0449835	−	0.743666i	0.00585635	−	0.0968171i	0.999929	+	0.0118989i	$0.00378763\pi$
$60$	−1.09692	+	0.460370i	−0.141611	+	0.0594336i
$61$	−11.5386	−	2.84400i	−1.47736	−	0.364137i	−0.583366	−	0.812210i	$-0.698265\pi$
$61$	−11.5386	−	2.84400i	−1.47736	−	0.364137i	−0.893997	+	0.448072i	$0.852111\pi$
$62$	7.47539	−	6.62262i	0.949376	−	0.841074i
$63$	−5.98601	+	11.6690i	−0.754166	+	1.47015i
$64$	−2.12161	−	4.04240i	−0.265202	−	0.505300i
$65$	−2.80885	−	3.26173i	−0.348395	−	0.404568i
$66$	−1.94615	+	2.08687i	−0.239554	+	0.256876i
$67$	−1.66267	−	0.748308i	−0.203128	−	0.0914203i	0.306296	−	0.951936i	$-0.400910\pi$
$67$	−1.66267	−	0.748308i	−0.203128	−	0.0914203i	−0.509423	+	0.860516i	$0.670141\pi$
$68$	−2.78701	−	0.338404i	−0.337975	−	0.0410376i
$69$	8.76559	−	9.39940i	1.05525	−	1.13155i
$70$	−5.92225	+	5.92225i	−0.707844	+	0.707844i
$71$	−2.72139	−	8.73324i	−0.322969	−	1.03644i	−0.963318	−	0.268361i	$-0.913518\pi$
$71$	−2.72139	−	8.73324i	−0.322969	−	1.03644i	0.640349	−	0.768084i	$-0.278790\pi$
$72$	6.10282	+	3.13066i	0.719224	+	0.368952i
$73$	9.76789	−	1.79003i	1.14325	−	0.209507i	0.424931	−	0.905226i	$-0.360299\pi$
$73$	9.76789	−	1.79003i	1.14325	−	0.209507i	0.718315	+	0.695719i	$0.244914\pi$
$74$	4.02528	+	4.54360i	0.467929	+	0.528182i
$75$	4.73782	−	3.98612i	0.547076	−	0.460277i
$76$	−3.02087	+	1.35958i	−0.346517	+	0.155955i
$77$	−1.59143	+	4.19627i	−0.181361	+	0.478209i
$78$	1.60079	−	9.89314i	0.181254	−	1.12018i
$79$	−0.380575	−	1.00349i	−0.0428180	−	0.112902i	0.911902	−	0.410409i	$-0.134614\pi$
$79$	−0.380575	−	1.00349i	−0.0428180	−	0.112902i	−0.954720	+	0.297507i	$0.903845\pi$
$80$	4.06862	+	4.06862i	0.454886	+	0.454886i
$81$	−8.91256	+	1.25152i	−0.990284	+	0.139058i
$82$	9.13800	−	1.10955i	1.00912	−	0.122530i
$83$	−11.9846	−	3.73456i	−1.31548	−	0.409921i	−0.442105	−	0.896963i	$-0.645768\pi$
$83$	−11.9846	−	3.73456i	−1.31548	−	0.409921i	−0.873379	+	0.487042i	$0.838076\pi$
$84$	−4.33998	−	0.373956i	−0.473531	−	0.0408019i
$85$	−5.73058	+	1.05017i	−0.621569	+	0.113907i
$86$	−4.27437	+	13.7169i	−0.460917	+	1.47913i
$87$	0.322821	−	2.18977i	0.0346101	−	0.234768i
$88$	2.19463	+	0.832313i	0.233948	+	0.0887249i
$89$	−10.1460	+	10.1460i	−1.07548	+	1.07548i	−0.0785673	+	0.996909i	$0.525035\pi$
$89$	−10.1460	+	10.1460i	−1.07548	+	1.07548i	−0.996909	+	0.0785673i	$0.974965\pi$
$90$	−5.66285	−	0.983182i	−0.596917	−	0.103636i
$91$	−3.55670	−	15.3555i	−0.372844	−	1.60969i
$92$	3.99151	+	1.51378i	0.416144	+	0.157822i
$93$	10.6487	−	1.67162i	1.10422	−	0.173339i
$94$	8.54762	−	12.3834i	0.881620	−	1.27725i
$95$	−5.14561	+	4.55862i	−0.527929	+	0.467704i
$96$	−0.470130	+	5.45614i	−0.0479824	+	0.556865i
$97$	−7.39354	+	0.447227i	−0.750700	+	0.0454090i	−0.431297	−	0.902210i	$-0.641944\pi$
$97$	−7.39354	+	0.447227i	−0.750700	+	0.0454090i	−0.319403	+	0.947619i	$0.603482\pi$
$98$	−18.5551	+	5.78199i	−1.87434	+	0.584069i
$99$	−2.98332	+	0.764947i	−0.299835	+	0.0768800i
$100$	1.82098	+	0.955723i	0.182098	+	0.0955723i
$101$	−0.729193	+	6.00545i	−0.0725574	+	0.597564i	0.910400	+	0.413730i	$0.135774\pi$
$101$	−0.729193	+	6.00545i	−0.0725574	+	0.597564i	−0.982957	+	0.183835i	$0.941149\pi$
$102$	−10.4605	−	8.63528i	−1.03574	−	0.855020i
$103$	−0.394929	+	0.752474i	−0.0389135	+	0.0741435i	−0.904136	−	0.427244i	$-0.859485\pi$
$103$	−0.394929	+	0.752474i	−0.0389135	+	0.0741435i	0.865223	+	0.501387i	$0.167177\pi$
$104$	−8.03084	+	1.86014i	−0.787488	+	0.182402i
$105$	−8.82929	+	1.93849i	−0.861650	+	0.189177i
$106$	−2.23910	+	0.135441i	−0.217481	+	0.0131552i
$107$	0.0586319	+	0.0661817i	0.00566816	+	0.00639803i	0.751338	−	0.659918i	$-0.229409\pi$
$107$	0.0586319	+	0.0661817i	0.00566816	+	0.00639803i	−0.745670	+	0.666316i	$0.767870\pi$
$108$	−1.50486	−	2.58294i	−0.144805	−	0.248544i
$109$	−5.01949	−	6.40690i	−0.480780	−	0.613670i	0.484531	−	0.874774i	$-0.338990\pi$
$109$	−5.01949	−	6.40690i	−0.480780	−	0.613670i	−0.965311	+	0.261104i	$0.915913\pi$
$110$	−1.96324	−	0.118754i	−0.187188	−	0.0113228i
$111$	1.01602	+	6.47236i	0.0964365	+	0.614329i
$112$	6.26822	+	20.1154i	0.592291	+	1.90073i
$113$	3.61910	+	6.89561i	0.340456	+	0.648684i	0.994142	−	0.108081i	$-0.0344707\pi$
$113$	3.61910	+	6.89561i	0.340456	+	0.648684i	−0.653686	+	0.756766i	$0.726778\pi$
$114$	−15.8342	−	2.33432i	−1.48301	−	0.218629i
$115$	8.84259	+	0.534878i	0.824575	+	0.0498776i
$116$	0.713829	−	0.175943i	0.0662773	−	0.0163359i
$117$	7.21082	−	8.06251i	0.666641	−	0.745379i
$118$	1.16086	+	0.286125i	0.106865	+	0.0263400i
$119$	−20.3675	−	6.34677i	−1.86709	−	0.581808i
$120$	1.01382	+	4.61768i	0.0925489	+	0.421535i
$121$	9.29974	−	3.52693i	0.845431	−	0.320630i
$122$	7.82697	−	17.3908i	0.708621	−	1.57449i
$123$	8.95282	+	4.30754i	0.807248	+	0.388398i
$124$	1.85221	+	3.06393i	0.166334	+	0.275149i
$125$	10.0692	+	1.84526i	0.900620	+	0.165045i
$126$	−16.6877	−	12.8243i	−1.48666	−	1.14248i
$127$	1.97686	−	0.749724i	0.175418	−	0.0665273i	−0.265332	−	0.964157i	$-0.585482\pi$
$127$	1.97686	−	0.749724i	0.175418	−	0.0665273i	0.440750	+	0.897630i	$0.354712\pi$
$128$	13.0318	−	4.06088i	1.15186	−	0.358934i
$129$	−11.8659	+	9.98329i	−1.04474	+	0.878979i
$130$	5.96112	−	3.49021i	0.522824	−	0.306112i
$131$	4.12587	−	2.84788i	0.360479	−	0.248821i	−0.374034	−	0.927415i	$-0.622026\pi$
$131$	4.12587	−	2.84788i	0.360479	−	0.248821i	0.734513	+	0.678594i	$0.237410\pi$
$132$	−0.610112	−	0.821106i	−0.0531035	−	0.0714681i
$133$	−24.4412	+	6.02422i	−2.11932	+	0.522366i
$134$	1.66215	−	2.40804i	0.143588	−	0.208023i
$135$	−4.57608	−	4.18829i	−0.393846	−	0.360471i
$136$	−3.31934	+	10.6521i	−0.284631	+	0.913412i
$137$	−9.37033	−	11.9603i	−0.800562	−	1.02184i	−0.999128	−	0.0417539i	$-0.986705\pi$
$137$	−9.37033	−	11.9603i	−0.800562	−	1.02184i	0.198566	−	0.980087i	$-0.436371\pi$
$138$	12.3012	+	16.5553i	1.04715	+	1.40928i
$139$	−12.2968	−	10.8940i	−1.04300	−	0.924021i	−0.0458149	−	0.998950i	$-0.514588\pi$
$139$	−12.2968	−	10.8940i	−1.04300	−	0.924021i	−0.997189	+	0.0749293i	$0.976127\pi$
$140$	−1.70561	−	2.47100i	−0.144150	−	0.208838i
$141$	14.9749	−	6.28490i	1.26111	−	0.529284i
$142$	14.5725	−	1.76942i	1.22290	−	0.148487i
$143$	2.14528	−	3.01642i	0.179397	−	0.252246i
$144$	−8.81038	+	11.4646i	−0.734198	+	0.955382i
$145$	1.30562	−	0.789277i	0.108426	−	0.0655459i
$146$			15.9363i			1.31890i
$147$	−20.2321	−	5.53843i	−1.66872	−	0.456802i
$148$	−1.86228	+	1.12579i	−0.153078	+	0.0925392i
$149$	4.20968	−	9.35353i	0.344871	−	0.766271i	−0.655072	−	0.755566i	$-0.727362\pi$
$149$	4.20968	−	9.35353i	0.344871	−	0.766271i	0.999943	−	0.0107047i	$-0.00340748\pi$
$150$	4.92154	+	8.63165i	0.401842	+	0.704771i
$151$	15.7808	−	7.10235i	1.28422	−	0.577981i	0.350695	−	0.936490i	$-0.385945\pi$
$151$	15.7808	−	7.10235i	1.28422	−	0.577981i	0.933526	+	0.358509i	$0.116715\pi$
$152$	3.15064	+	12.7827i	0.255551	+	1.03681i
$153$	−4.48582	−	13.9359i	−0.362657	−	1.12665i
$154$	−6.16340	−	3.72591i	−0.496661	−	0.300242i
$155$	5.56120	+	4.92680i	0.446687	+	0.395730i
$156$	3.38508	+	1.20377i	0.271023	+	0.0963787i
$157$	−14.6479	+	12.9769i	−1.16903	+	1.03567i	−0.170290	+	0.985394i	$0.554471\pi$
$157$	−14.6479	+	12.9769i	−1.16903	+	1.03567i	−0.998736	+	0.0502725i	$0.983991\pi$
$158$	1.69409	−	0.310453i	0.134775	−	0.0246983i
$159$	−2.11435	−	1.17952i	−0.167679	−	0.0935418i
$160$	−3.10650	+	2.14426i	−0.245590	+	0.169519i
$161$	27.7604	+	16.7817i	2.18783	+	1.32259i
$162$	0.602613	−	14.4304i	0.0473458	−	1.13376i
$163$	−10.3760	+	13.2440i	−0.812711	+	1.03735i	0.185788	+	0.982590i	$0.440516\pi$
$163$	−10.3760	+	13.2440i	−0.812711	+	1.03735i	−0.998500	+	0.0547596i	$0.982561\pi$
$164$	−0.199247	+	3.29395i	−0.0155586	+	0.257214i
$165$	−1.71569	−	1.25012i	−0.133566	−	0.0973217i
$166$	9.36173	−	17.8373i	0.726612	−	1.38444i
$167$	−6.64423	−	1.21760i	−0.514146	−	0.0942208i	−0.0830831	−	0.996543i	$-0.526477\pi$
$167$	−6.64423	−	1.21760i	−0.514146	−	0.0942208i	−0.431063	+	0.902322i	$0.641861\pi$
$168$	−4.57079	+	16.6973i	−0.352644	+	1.28822i
$169$	−0.365252	+	12.9949i	−0.0280963	+	0.999605i
$170$		−	9.34943i		−	0.717068i
$171$	−13.0368	−	11.3340i	−0.996946	−	0.866734i
$172$	−4.56066	−	2.39362i	−0.347747	−	0.182512i
$173$	2.77616	−	7.32013i	0.211067	−	0.556539i	−0.787115	−	0.616806i	$-0.788426\pi$
$173$	2.77616	−	7.32013i	0.211067	−	0.556539i	0.998182	+	0.0602675i	$0.0191954\pi$
$174$	3.36314	+	1.14300i	0.254959	+	0.0866507i
$175$	12.3015	+	9.63761i	0.929906	+	0.728535i
$176$	−2.55972	+	4.23430i	−0.192946	+	0.319172i
$177$	0.888868	+	0.935468i	0.0668114	+	0.0703141i
$178$	−13.0804	−	18.9503i	−0.980421	−	1.42038i
$179$	0.681271	+	0.167918i	0.0509206	+	0.0125508i	0.264694	−	0.964333i	$-0.414729\pi$
$179$	0.681271	+	0.167918i	0.0509206	+	0.0125508i	−0.213773	+	0.976883i	$0.568575\pi$
$180$	0.712624	−	1.93330i	0.0531159	−	0.144100i
$181$	15.0848	+	17.0272i	1.12124	+	1.26562i	0.960395	+	0.278642i	$0.0898844\pi$
$181$	15.0848	+	17.0272i	1.12124	+	1.26562i	0.160848	+	0.986979i	$0.448577\pi$
$182$	25.2672	−	1.17236i	1.87293	−	0.0869012i
$183$	17.2330	−	11.2564i	1.27390	−	0.832097i
$184$	8.77678	−	14.5186i	0.647033	−	1.07032i
$185$	−2.99454	+	3.38014i	−0.220163	+	0.248513i
$186$	−0.441705	+	17.2924i	−0.0323874	+	1.26794i
$187$	−2.05612	−	4.56851i	−0.150358	−	0.334082i
$188$	3.81428	+	3.81428i	0.278185	+	0.278185i
$189$	−7.70993	−	21.3670i	−0.560815	−	1.55422i
$190$	−5.70725	−	9.44095i	−0.414048	−	0.684919i
$191$		−	11.6963i		−	0.846315i	−0.906056	−	0.423158i	$-0.860922\pi$
$191$		−	11.6963i		−	0.846315i	0.906056	−	0.423158i	$-0.139078\pi$
$192$	7.62678	+	2.08779i	0.550415	+	0.150673i
$193$	1.69566	+	2.80496i	0.122056	+	0.201906i	0.910834	−	0.412773i	$-0.135440\pi$
$193$	1.69566	+	2.80496i	0.122056	+	0.201906i	−0.788778	+	0.614678i	$0.789286\pi$
$194$	1.43278	−	11.8000i	0.102867	−	0.847189i
$195$	7.44973	+	0.295072i	0.533486	+	0.0211306i
$196$	−0.839818	−	6.91653i	−0.0599870	−	0.494038i
$197$	−5.91987	+	4.63792i	−0.421773	+	0.330438i	−0.805062	−	0.593190i	$-0.797868\pi$
$197$	−5.91987	+	4.63792i	−0.421773	+	0.330438i	0.383289	+	0.923628i	$0.374791\pi$
$198$	−0.344479	−	4.93040i	−0.0244811	−	0.350389i
$199$	−11.6082	+	13.1029i	−0.822881	+	0.928841i	−0.998452	−	0.0556261i	$-0.982285\pi$
$199$	−11.6082	+	13.1029i	−0.822881	+	0.928841i	0.175571	+	0.984467i	$0.443823\pi$
$200$	5.04043	−	6.43364i	0.356412	−	0.454927i
$201$	2.91199	−	1.22215i	0.205396	−	0.0862036i
$202$	−9.26859	−	2.88821i	−0.652136	−	0.203214i
$203$	5.57638	−	0.337309i	0.391385	−	0.0236745i
$204$	3.72094	−	3.13057i	0.260518	−	0.219184i
$205$	1.63883	+	6.64901i	0.114461	+	0.464387i
$206$	−1.07353	−	0.841057i	−0.0747964	−	0.0585992i
$207$	1.55156	+	22.2069i	0.107841	+	1.54348i
$208$	−0.805420	−	17.3587i	−0.0558458	−	1.20361i
$209$	−4.86504	−	3.35810i	−0.336522	−	0.232284i
$210$	−0.505847	−	14.4977i	−0.0349068	−	1.00043i
$211$	−5.21301	−	13.7456i	−0.358878	−	0.946285i	−0.985908	−	0.167289i	$-0.946499\pi$
$211$	−5.21301	−	13.7456i	−0.358878	−	0.946285i	0.627029	−	0.778996i	$-0.284271\pi$
$212$	0.0969318	−	0.798305i	0.00665730	−	0.0548278i
$213$	14.2772	+	6.86931i	0.978258	+	0.470677i
$214$	−0.121427	+	0.0734054i	−0.00830061	+	0.00501789i
$215$	−10.5134	−	1.92665i	−0.717007	−	0.131396i
$216$	−11.1748	+	4.03226i	−0.760352	+	0.274361i
$217$	9.64730	+	25.4379i	0.654902	+	1.72683i
$218$	11.5652	−	6.06988i	0.783294	−	0.411104i
$219$	−9.27129	+	14.4876i	−0.626496	+	0.978982i
$220$	0.168740	−	0.684607i	0.0113765	−	0.0461562i
$221$	14.9283	+	9.31332i	1.00418	+	0.626481i
$222$	−10.5104	−	0.268471i	−0.705414	−	0.0180186i
$223$	−0.715912	+	11.8354i	−0.0479410	+	0.792559i	0.892172	+	0.451696i	$0.149181\pi$
$223$	−0.715912	+	11.8354i	−0.0479410	+	0.792559i	−0.940113	+	0.340863i	$0.889281\pi$
$224$	−13.7212	+	1.66605i	−0.916786	+	0.111318i
$225$	−0.547505	+	10.7102i	−0.0365003	+	0.714014i
$226$	−11.9315	+	3.71801i	−0.793673	+	0.247319i
$227$	−18.5904	+	8.36688i	−1.23389	+	0.555329i	−0.919172	−	0.393856i	$-0.871141\pi$
$227$	−18.5904	+	8.36688i	−1.23389	+	0.555329i	−0.314719	+	0.949185i	$0.601910\pi$
$228$	1.84634	−	5.43262i	0.122277	−	0.359784i
$229$	2.10255	−	1.64724i	0.138940	−	0.108853i	−0.544842	−	0.838538i	$-0.683411\pi$
$229$	2.10255	−	1.64724i	0.138940	−	0.108853i	0.683783	+	0.729686i	$0.260334\pi$
$230$	−3.40218	+	13.8032i	−0.224333	+	0.910155i
$231$	−3.43549	−	6.97290i	−0.226039	−	0.458783i
$232$	−0.176411	−	2.91642i	−0.0115820	−	0.191473i
$233$	−1.68590	+	0.884827i	−0.110447	+	0.0579669i	−0.519042	−	0.854749i	$-0.673711\pi$
$233$	−1.68590	+	0.884827i	−0.110447	+	0.0579669i	0.408595	+	0.912716i	$0.366019\pi$
$234$	10.6407	+	13.7144i	0.695604	+	0.896540i
$235$	9.91173	+	5.20208i	0.646570	+	0.339346i
$236$	−0.175908	+	0.390852i	−0.0114507	+	0.0254423i
$237$	1.72070	+	0.703342i	0.111772	+	0.0456870i
$238$	15.9100	−	30.3139i	1.03129	−	1.96496i
$239$	18.2781	+	18.2781i	1.18231	+	1.18231i	0.979144	+	0.203169i	$0.0651242\pi$
$239$	18.2781	+	18.2781i	1.18231	+	1.18231i	0.203169	+	0.979144i	$0.434876\pi$
$240$	−9.95999	+	0.347520i	−0.642914	+	0.0224323i
$241$	0.791433	+	13.0839i	0.0509807	+	0.842811i	0.930350	+	0.366672i	$0.119503\pi$
$241$	0.791433	+	13.0839i	0.0509807	+	0.842811i	−0.879370	+	0.476140i	$0.842036\pi$
$242$	2.87709	+	15.6998i	0.184946	+	1.00922i
$243$	8.94303	−	12.7680i	0.573696	−	0.819069i
$244$	5.62658	+	3.88375i	0.360205	+	0.248632i
$245$	−5.93392	−	13.1846i	−0.379104	−	0.842335i
$246$	−9.38917	+	12.8859i	−0.598632	+	0.821573i
$247$	20.7596	+	0.291692i	1.32090	+	0.0185599i
$248$	13.3039	−	5.04550i	0.844798	−	0.320390i
$249$	18.8879	−	10.7694i	1.19698	−	0.682483i
$250$	−5.82543	+	15.3604i	−0.368432	+	0.971476i
$251$	2.60191	+	21.4286i	0.164231	+	1.35256i	0.808830	+	0.588042i	$0.200101\pi$
$251$	2.60191	+	21.4286i	0.164231	+	1.35256i	−0.644600	+	0.764520i	$0.722976\pi$
$252$	5.60048	−	5.05574i	0.352797	−	0.318481i
$253$	1.37314	+	7.49300i	0.0863288	+	0.471081i
$254$	0.611587	+	3.33732i	0.0383744	+	0.209402i
$255$	5.43924	−	8.49952i	0.340618	−	0.532261i
$256$	1.53977	+	12.6812i	0.0962357	+	0.792572i
$257$	10.2223	−	26.9539i	0.637648	−	1.68134i	−0.0904787	−	0.995898i	$-0.528840\pi$
$257$	10.2223	−	26.9539i	0.637648	−	1.68134i	0.728127	−	0.685442i	$-0.240391\pi$
$258$	−12.3261	−	21.6181i	−0.767387	−	1.34588i
$259$	−15.4613	+	5.86370i	−0.960719	+	0.364353i
$260$	0.845514	+	2.32755i	0.0524365	+	0.144349i
$261$	2.39245	+	2.99568i	0.148089	+	0.185428i
$262$	3.30186	+	7.33644i	0.203990	+	0.453247i
$263$	6.10527	+	4.21417i	0.376467	+	0.259857i	0.741240	−	0.671240i	$-0.234238\pi$
$263$	6.10527	+	4.21417i	0.376467	+	0.259857i	−0.364773	+	0.931097i	$0.618853\pi$
$264$	−3.64680	+	1.79675i	−0.224445	+	0.110582i
$265$	−0.300808	−	1.64145i	−0.0184785	−	0.100834i
$266$	−2.43908	−	40.3228i	−0.149549	−	2.47235i
$267$	−0.866620	−	24.8375i	−0.0530363	−	1.52003i
$268$	0.741718	+	0.741718i	0.0453076	+	0.0453076i
$269$	7.61326	−	14.5059i	0.464189	−	0.884437i	−0.535027	−	0.844835i	$-0.679699\pi$
$269$	7.61326	−	14.5059i	0.464189	−	0.884437i	0.999216	−	0.0396024i	$-0.0126091\pi$
$270$	7.93488	−	6.01175i	0.482902	−	0.365863i
$271$	−1.97461	+	4.38739i	−0.119949	+	0.266515i	−0.962085	−	0.272749i	$-0.912067\pi$
$271$	−1.97461	+	4.38739i	−0.119949	+	0.266515i	0.842136	+	0.539265i	$0.181298\pi$
$272$	−20.8259	−	10.9303i	−1.26275	−	0.662744i
$273$	23.6524	+	13.6340i	1.43151	+	0.825166i
$274$	21.5898	−	11.3312i	1.30429	−	0.684543i
$275$	0.221580	+	3.66315i	0.0133618	+	0.220896i
$276$	−6.63266	+	3.26786i	−0.399239	+	0.196702i
$277$	−4.63662	+	18.8115i	−0.278588	+	1.13027i	0.650230	+	0.759737i	$0.274673\pi$
$277$	−4.63662	+	18.8115i	−0.278588	+	1.13027i	−0.928818	+	0.370537i	$0.879174\pi$
$278$	20.7532	−	16.2591i	1.24469	−	0.975156i
$279$	−10.4618	+	15.4635i	−0.626330	+	0.925773i
$280$	−10.8811	+	4.89718i	−0.650269	+	0.292662i
$281$	22.1148	−	6.89124i	1.31926	−	0.411097i	0.444551	−	0.895753i	$-0.353363\pi$
$281$	22.1148	−	6.89124i	1.31926	−	0.411097i	0.874705	+	0.484657i	$0.161055\pi$
$282$	5.58886	+	25.4557i	0.332812	+	1.51587i
$283$	4.43288	−	0.538249i	0.263507	−	0.0319956i	0.0122834	−	0.999925i	$-0.496090\pi$
$283$	4.43288	−	0.538249i	0.263507	−	0.0319956i	0.251224	+	0.967929i	$0.419167\pi$
$284$	−0.317743	+	5.25291i	−0.0188546	+	0.311703i
$285$	0.304043	−	11.9030i	0.0180100	−	0.705076i
$286$	4.14083	+	4.25885i	0.244852	+	0.251831i
$287$	−6.00103	+	24.3471i	−0.354229	+	1.43716i
$288$	−6.35597	−	7.04081i	−0.374529	−	0.414884i
$289$	6.03411	−	3.16694i	0.354948	−	0.186291i
$290$	0.868188	+	2.28922i	0.0509818	+	0.134428i
$291$	8.16743	−	9.89376i	0.478783	−	0.579982i
$292$	−5.61947	−	1.02981i	−0.328854	−	0.0602648i
$293$	−12.7350	+	7.69858i	−0.743987	+	0.449756i	−0.837900	−	0.545825i	$-0.816217\pi$
$293$	−12.7350	+	7.69858i	−0.743987	+	0.449756i	0.0939123	+	0.995580i	$0.470063\pi$
$294$	14.5949	−	30.3340i	0.851189	−	1.76912i
$295$	−0.107211	+	0.882961i	−0.00624206	+	0.0514080i
$296$	3.06669	+	8.08620i	0.178248	+	0.470001i
$297$	2.55521	−	4.68262i	0.148268	−	0.271713i
$298$	13.5467	+	9.35062i	0.784740	+	0.541667i
$299$	−18.6506	−	19.1821i	−1.07859	−	1.10933i
$300$	−3.36173	+	1.17766i	−0.194089	+	0.0679921i
$301$	−30.8093	−	24.1375i	−1.77582	−	1.39126i
$302$	6.64609	+	26.9642i	0.382439	+	1.55162i
$303$	−6.74575	−	8.01786i	−0.387533	−	0.460614i
$304$	−27.7020	+	1.67566i	−1.58882	+	0.0961058i
$305$	13.5452	+	4.22084i	0.775594	+	0.241685i
$306$	23.2953	−	3.04959i	1.33170	−	0.174334i
$307$	−10.4520	+	13.3409i	−0.596525	+	0.761408i	−0.987263	−	0.159094i	$-0.949143\pi$
$307$	−10.4520	+	13.3409i	−0.596525	+	0.761408i	0.390739	+	0.920502i	$0.372220\pi$
$308$	1.71211	−	1.93257i	0.0975566	−	0.110119i
$309$	−0.486638	−	1.38915i	−0.0276839	−	0.0790260i
$310$	−9.38557	+	7.35313i	−0.533065	+	0.417629i
$311$	−1.63000	−	13.4243i	−0.0924291	−	0.761222i	−0.963060	−	0.269286i	$-0.913212\pi$
$311$	−1.63000	−	13.4243i	−0.0924291	−	0.761222i	0.870631	−	0.491936i	$-0.163711\pi$
$312$	7.13052	−	12.3701i	0.403686	−	0.700319i
$313$	1.72812	−	14.2324i	0.0976792	−	0.804461i	−0.858730	−	0.512429i	$-0.828746\pi$
$313$	1.72812	−	14.2324i	0.0976792	−	0.804461i	0.956409	−	0.292031i	$-0.0943312\pi$
$314$	−16.2467	−	26.8753i	−0.916852	−	1.51666i
$315$	7.97447	−	13.4740i	0.449311	−	0.759177i
$316$			0.617432i			0.0347333i
$317$	−12.0805	−	19.9836i	−0.678510	−	1.12239i	−0.985336	−	0.170627i	$-0.945421\pi$
$317$	−12.0805	−	19.9836i	−0.678510	−	1.12239i	0.306825	−	0.951766i	$-0.400733\pi$
$318$	2.47347	−	2.99628i	0.138705	−	0.168023i
$319$	0.927676	+	0.927676i	0.0519399	+	0.0519399i
$320$	2.23687	+	4.97013i	0.125045	+	0.277839i
$321$	−0.153094	−	0.00391054i	−0.00854489	−	0.000218265i
$322$	−34.5200	+	38.9650i	−1.92372	+	2.17143i
$323$	14.5374	−	24.0478i	0.808883	−	1.33806i
$324$	5.04951	+	1.14499i	0.280528	+	0.0636104i
$325$	−7.80548	−	10.2566i	−0.432970	−	0.568933i
$326$	−17.9040	−	20.2095i	−0.991612	−	1.11930i
$327$	14.0452	+	1.21020i	0.776699	+	0.0669245i
$328$	12.7334	+	3.13851i	0.703087	+	0.173295i
$329$	23.2847	+	33.7337i	1.28373	+	1.85980i
$330$	2.46959	−	2.34657i	0.135947	−	0.129175i
$331$	4.75021	−	7.85781i	0.261095	−	0.431905i	−0.697538	−	0.716548i	$-0.745721\pi$
$331$	4.75021	−	7.85781i	0.261095	−	0.431905i	0.958634	+	0.284643i	$0.0918751\pi$
$332$	5.68484	+	4.45379i	0.311996	+	0.244433i
$333$	−9.39880	−	6.35874i	−0.515051	−	0.348457i
$334$	3.84394	−	10.1356i	0.210331	−	0.554597i
$335$	1.92741	+	1.01158i	0.105306	+	0.0552688i
$336$	−32.8850	−	15.8222i	−1.79402	−	0.863172i
$337$			9.12563i			0.497105i	0.968618	+	0.248552i	$0.0799548\pi$
$337$			9.12563i			0.497105i	−0.968618	+	0.248552i	$0.920045\pi$
$338$	−20.4066	−	4.33555i	−1.10997	−	0.235823i
$339$	−13.0099	−	3.56140i	−0.706602	−	0.193429i
$340$	3.29680	+	0.604161i	0.178794	+	0.0327652i
$341$	−2.96908	+	5.65710i	−0.160784	+	0.306349i
$342$	21.6617	−	17.2998i	1.17133	−	0.935465i
$343$	1.34899	−	22.3014i	0.0728385	−	1.20416i
$344$	−12.6238	+	16.1131i	−0.680631	+	0.868762i
$345$	−11.1232	+	10.5691i	−0.598854	+	0.569022i
$346$	10.7517	+	6.49961i	0.578014	+	0.349421i
$347$	20.3366	−	14.0373i	1.09173	−	0.753564i	0.120736	−	0.992685i	$-0.461475\pi$
$347$	20.3366	−	14.0373i	1.09173	−	0.753564i	0.970990	+	0.239121i	$0.0768592\pi$
$348$	−0.620372	+	1.11205i	−0.0332555	+	0.0596123i
$349$	−9.55510	+	1.75104i	−0.511473	+	0.0937308i	−0.429792	−	0.902928i	$-0.641413\pi$
$349$	−9.55510	+	1.75104i	−0.511473	+	0.0937308i	−0.0816802	+	0.996659i	$0.526029\pi$
$350$	−18.7713	+	16.6299i	−1.00337	+	0.888906i
$351$	1.69474	+	18.6582i	0.0904587	+	0.995900i
$352$	−2.42959	−	2.15243i	−0.129498	−	0.114725i
$353$	23.9022	+	14.4494i	1.27218	+	0.769062i	0.982176	−	0.187962i	$-0.0601883\pi$
$353$	23.9022	+	14.4494i	1.27218	+	0.769062i	0.290008	+	0.957024i	$0.406342\pi$
$354$	−1.73375	+	1.13247i	−0.0921476	+	0.0601899i
$355$	2.61348	+	10.6033i	0.138709	+	0.562764i
$356$	7.52753	−	3.38786i	0.398958	−	0.179556i
$357$	32.0995	−	18.3023i	1.69889	−	0.968659i
$358$	−0.462127	+	1.02680i	−0.0244242	+	0.0542683i
$359$	−21.2670	+	12.8563i	−1.12243	+	0.678532i	−0.951774	−	0.306799i	$-0.900742\pi$
$359$	−21.2670	+	12.8563i	−1.12243	+	0.678532i	−0.170654	+	0.985331i	$0.554588\pi$
$360$	−7.04687	−	4.17062i	−0.371403	−	0.219811i
$361$		−	14.1574i		−	0.745128i
$362$	−31.2408	+	18.8857i	−1.64198	+	0.992611i
$363$	−6.51813	+	15.9464i	−0.342113	+	0.836968i
$364$	−1.21937	+	8.98551i	−0.0639125	+	0.470969i
$365$	−11.7691	+	1.42903i	−0.616024	+	0.0747989i
$366$	12.7831	+	30.4581i	0.668185	+	1.59207i
$367$	10.9297	+	15.8344i	0.570526	+	0.826549i	0.996956	−	0.0779715i	$-0.0248443\pi$
$367$	10.9297	+	15.8344i	0.570526	+	0.826549i	−0.426430	+	0.904521i	$0.640229\pi$
$368$	26.7692	+	23.7154i	1.39544	+	1.23625i
$369$	−16.0323	+	6.25213i	−0.834608	+	0.325473i
$370$	−4.46928	−	5.70462i	−0.232347	−	0.296569i
$371$	1.81796	−	5.83402i	0.0943835	−	0.302887i
$372$	−6.06911	−	1.27319i	−0.314669	−	0.0660119i
$373$	−3.90765	+	5.66121i	−0.202331	+	0.293126i	−0.910993	−	0.412421i	$-0.864683\pi$
$373$	−3.90765	+	5.66121i	−0.202331	+	0.293126i	0.708663	+	0.705547i	$0.249299\pi$
$374$	7.80611	−	1.92403i	0.403644	−	0.0994893i
$375$	−14.2321	+	10.5750i	−0.734943	+	0.546090i
$376$	17.6426	−	12.1778i	0.909847	−	0.628022i
$377$	−4.52005	−	0.894142i	−0.232794	−	0.0460507i
$378$	35.9578	−	5.98923i	1.84947	−	0.308053i
$379$	21.6062	−	6.73276i	1.10984	−	0.345839i	0.312829	−	0.949810i	$-0.398723\pi$
$379$	21.6062	−	6.73276i	1.10984	−	0.345839i	0.797006	+	0.603971i	$0.206416\pi$
$380$	3.69788	−	1.40242i	0.189697	−	0.0719426i
$381$	−1.38557	+	3.38975i	−0.0709849	+	0.173662i
$382$	18.4625	+	3.38338i	0.944623	+	0.173109i
$383$	−18.1385	−	30.0048i	−0.926836	−	1.53317i	−0.843821	−	0.536625i	$-0.819699\pi$
$383$	−18.1385	−	30.0048i	−0.926836	−	1.53317i	−0.0830147	−	0.996548i	$-0.526455\pi$
$384$	−10.2504	+	21.3046i	−0.523091	+	1.08719i
$385$	2.19894	−	4.88585i	0.112068	−	0.249006i
$386$	−4.91810	+	1.86519i	−0.250325	+	0.0949357i
$387$	1.37123	−	26.8238i	0.0697037	−	1.36353i
$388$	4.06833	+	1.26774i	0.206538	+	0.0643599i
$389$	5.67571	+	1.39894i	0.287770	+	0.0709289i	0.380558	−	0.924757i	$-0.375732\pi$
$389$	5.67571	+	1.39894i	0.287770	+	0.0709289i	−0.0927884	+	0.995686i	$0.529578\pi$
$390$	−2.62074	+	11.6740i	−0.132706	+	0.591134i
$391$	−35.1592	+	8.66597i	−1.77808	+	0.438257i
$392$	−27.6386	−	1.67183i	−1.39596	−	0.0844400i
$393$	−1.26643	+	8.59045i	−0.0638828	+	0.433331i
$394$	−5.60847	−	10.6861i	−0.282551	−	0.538355i
$395$	0.381185	+	1.22326i	0.0191795	+	0.0615491i
$396$	1.76082	+	0.197133i	0.0884847	+	0.00990630i
$397$	17.4113	+	1.05319i	0.873849	+	0.0528581i	0.491211	−	0.871040i	$-0.336554\pi$
$397$	17.4113	+	1.05319i	0.873849	+	0.0528581i	0.382638	+	0.923899i	$0.375016\pi$
$398$	−17.3249	−	22.1136i	−0.868419	−	1.10846i
$399$	21.2413	−	38.0762i	1.06340	−	1.90620i
$400$	11.4249	+	12.8960i	0.571243	+	0.644800i
$401$	18.1482	−	1.09777i	0.906279	−	0.0548198i	0.399341	−	0.916802i	$-0.369239\pi$
$401$	18.1482	−	1.09777i	0.906279	−	0.0548198i	0.506938	+	0.861983i	$0.330777\pi$
$402$	1.08680	+	4.95007i	0.0542046	+	0.246887i
$403$	−2.39144	−	22.3107i	−0.119126	−	1.11138i
$404$	1.61738	−	3.08166i	0.0804677	−	0.153318i
$405$	10.7110	−	0.848957i	0.532235	−	0.0421850i
$406$	−1.08063	+	8.89982i	−0.0536310	+	0.441691i
$407$	−3.43843	−	1.80463i	−0.170436	−	0.0894520i
$408$	−9.57202	−	16.7879i	−0.473885	−	0.831125i
$409$	−21.2613	+	6.62528i	−1.05130	+	0.327599i	−0.774002	−	0.633184i	$-0.781748\pi$
$409$	−21.2613	+	6.62528i	−1.05130	+	0.327599i	−0.277301	+	0.960783i	$0.589440\pi$
$410$	−10.9694	+	0.663529i	−0.541742	+	0.0327694i
$411$	26.2194	+	2.25920i	1.29331	+	0.111438i
$412$	0.365946	−	0.324200i	0.0180289	−	0.0159722i
$413$	−1.85015	+	2.68041i	−0.0910401	+	0.131894i
$414$	−35.5021	−	3.97464i	−1.74483	−	0.195343i
$415$	14.0125	+	5.31424i	0.687847	+	0.260866i
$416$	11.2964	+	1.53297i	0.553851	+	0.0751601i
$417$	28.3257	−	2.70744i	1.38712	−	0.132584i
$418$	6.70802	−	6.70802i	0.328100	−	0.328100i
$419$	−15.4341	−	5.85338i	−0.754005	−	0.285956i	−0.0525001	−	0.998621i	$-0.516719\pi$
$419$	−15.4341	−	5.85338i	−0.754005	−	0.285956i	−0.701505	+	0.712664i	$0.747488\pi$
$420$	5.14486	+	0.758469i	0.251044	+	0.0370095i
$421$	2.15690	−	6.92174i	0.105121	−	0.337345i	−0.887142	−	0.461496i	$-0.847313\pi$
$421$	2.15690	−	6.92174i	0.105121	−	0.337345i	0.992263	+	0.124151i	$0.0396206\pi$
$422$	23.2052	−	4.25251i	1.12961	−	0.207009i
$423$	−9.72862	+	26.3931i	−0.473022	+	1.28328i
$424$	−3.05117	−	0.950783i	−0.148178	−	0.0461741i
$425$	−17.3176	+	2.10274i	−0.840027	+	0.101998i
$426$	−14.9731	+	20.5493i	−0.725448	+	0.995618i
$427$	36.7353	+	36.7353i	1.77774	+	1.77774i
$428$	−0.0180376	−	0.0475613i	−0.000871881	−	0.00229896i
$429$	1.28673	+	6.28072i	0.0621237	+	0.303236i
$430$	6.08238	−	16.0379i	0.293319	−	0.773418i
$431$	−21.5175	+	9.68425i	−1.03646	+	0.466474i	−0.855928	−	0.517095i	$-0.827013\pi$
$431$	−21.5175	+	9.68425i	−1.03646	+	0.466474i	−0.180534	+	0.983569i	$0.557783\pi$
$432$	−4.11464	−	24.7032i	−0.197966	−	1.18853i
$433$	−25.0387	−	28.2628i	−1.20328	−	1.35822i	−0.916403	−	0.400256i	$-0.868921\pi$
$433$	−25.0387	−	28.2628i	−1.20328	−	1.35822i	−0.286878	−	0.957967i	$-0.592617\pi$
$434$	−42.9440	+	7.86978i	−2.06138	+	0.377762i
$435$	−0.542541	+	2.58621i	−0.0260128	+	0.123999i
$436$	1.39302	+	4.47036i	0.0667136	+	0.214092i
$437$	−30.2134	+	30.2134i	−1.44530	+	1.44530i
$438$	−20.1866	−	18.8254i	−0.964554	−	0.899514i
$439$	−9.99440	−	1.21354i	−0.477007	−	0.0579191i	−0.121497	−	0.992592i	$-0.538770\pi$
$439$	−9.99440	−	1.21354i	−0.477007	−	0.0579191i	−0.355510	+	0.934673i	$0.615693\pi$
$440$	−2.55528	−	1.15004i	−0.121818	−	0.0548259i
$441$	30.9156	−	19.0857i	1.47217	−	0.908841i
$442$	−19.0192	+	20.8700i	−0.904653	+	0.992686i
$443$	10.0265	+	19.1038i	0.476371	+	0.907649i	0.998498	+	0.0547818i	$0.0174463\pi$
$443$	10.0265	+	19.1038i	0.476371	+	0.907649i	−0.522127	+	0.852868i	$0.674861\pi$
$444$	0.773854	−	3.68885i	0.0367255	−	0.175065i
$445$	12.8221	−	11.3593i	0.607823	−	0.538485i
$446$	−18.4750	−	4.55368i	−0.874816	−	0.215623i
$447$	6.87532	+	16.3817i	0.325191	+	0.774828i
$448$	−1.20502	+	19.9213i	−0.0569317	+	0.941194i
$449$	1.18046	+	2.62287i	0.0557094	+	0.123781i	0.937652	−	0.347576i	$-0.112995\pi$
$449$	1.18046	+	2.62287i	0.0557094	+	0.123781i	−0.881942	+	0.471357i	$0.843764\pi$
$450$	−16.7475	−	3.96236i	−0.789487	−	0.186787i
$451$	−5.21419	+	2.73662i	−0.245527	+	0.128862i
$452$	−0.540032	−	4.44756i	−0.0254010	−	0.209196i
$453$	−9.64511	+	28.3796i	−0.453167	+	1.33339i
$454$	−7.82938	−	31.7651i	−0.367451	−	1.49081i
$455$	3.13155	+	18.5550i	0.146809	+	0.869871i
$456$	−19.9137	−	11.1091i	−0.932545	−	0.520232i
$457$	4.72659	−	15.1682i	0.221100	−	0.709536i	−0.775808	−	0.630969i	$-0.782658\pi$
$457$	4.72659	−	15.1682i	0.221100	−	0.709536i	0.996909	−	0.0785676i	$-0.0250346\pi$
$458$	1.99195	+	3.79534i	0.0930776	+	0.177345i
$459$	22.9518	+	10.7802i	1.07130	+	0.503175i
$460$	−4.64744	−	2.09164i	−0.216688	−	0.0975234i
$461$	5.95706	−	32.5066i	0.277448	−	1.51398i	−0.489346	−	0.872090i	$-0.662764\pi$
$461$	5.95706	−	32.5066i	0.277448	−	1.51398i	0.766794	−	0.641894i	$-0.221851\pi$
$462$	12.0004	−	3.40584i	0.558310	−	0.158454i
$463$	−1.57628	+	8.60148i	−0.0732559	+	0.399745i	0.926471	+	0.376367i	$0.122827\pi$
$463$	−1.57628	+	8.60148i	−0.0732559	+	0.399745i	−0.999727	+	0.0233779i	$0.992558\pi$
$464$	6.11423	+	0.742403i	0.283846	+	0.0344652i
$465$	−12.8102	+	1.22443i	−0.594060	+	0.0567816i
$466$	−0.909011	−	2.91712i	−0.0421091	−	0.135133i
$467$	11.9390	−	17.2966i	0.552470	−	0.800390i	−0.442894	−	0.896574i	$-0.646048\pi$
$467$	11.9390	−	17.2966i	0.552470	−	0.800390i	0.995364	+	0.0961836i	$0.0306636\pi$
$468$	−5.52359	+	2.86590i	−0.255328	+	0.132476i
$469$	4.52789	+	6.55979i	0.209079	+	0.302903i
$470$	−11.0786	+	14.1407i	−0.511016	+	0.652264i
$471$	0.865510	−	33.8840i	0.0398806	−	1.56129i
$472$	1.40184	+	0.967623i	0.0645251	+	0.0445385i
$473$	−0.554950	−	9.17441i	−0.0255166	−	0.421840i
$474$	−1.60796	+	2.51265i	−0.0738561	+	0.115410i
$475$	−16.2035	+	12.6947i	−0.743469	+	0.582471i
$476$	9.66122	+	7.56908i	0.442821	+	0.346928i
$477$	3.99177	−	1.28491i	0.182771	−	0.0588319i
$478$	−34.1391	+	23.5645i	−1.56148	+	1.07781i
$479$	0.130241	+	0.166240i	0.00595086	+	0.00759572i	0.790150	−	0.612914i	$-0.210003\pi$
$479$	0.130241	+	0.166240i	0.00595086	+	0.00759572i	−0.784199	+	0.620510i	$0.786926\pi$
$480$	0.953532	−	6.46802i	0.0435226	−	0.295223i
$481$	13.5606	−	1.45354i	0.618310	−	0.0662755i
$482$	−20.8818	−	2.53551i	−0.951139	−	0.115489i
$483$	−54.0507	+	15.3401i	−2.45939	+	0.698001i
$484$	−5.72198			−0.260090
$485$	8.84289			0.401535
$486$	17.5672	+	17.8098i	0.796865	+	0.807871i
$487$	−22.7024	−	10.2175i	−1.02874	−	0.463000i	−0.175482	−	0.984483i	$-0.556149\pi$
$487$	−22.7024	−	10.2175i	−1.02874	−	0.463000i	−0.853262	+	0.521482i	$0.825379\pi$
$488$	19.2124	−	19.2124i	0.869704	−	0.869704i
$489$	−4.51916	−	28.7884i	−0.204364	−	1.30186i
$490$	22.5283	−	5.55272i	1.01772	−	0.250846i
$491$	8.42354	+	7.46260i	0.380149	+	0.336782i	0.831460	−	0.555584i	$-0.187505\pi$
$491$	8.42354	+	7.46260i	0.380149	+	0.336782i	−0.451312	+	0.892366i	$0.649044\pi$
$492$	−3.93710	−	4.14350i	−0.177498	−	0.186804i
$493$	−4.13545	+	4.66796i	−0.186251	+	0.210234i
$494$	−6.46554	+	32.6844i	−0.290898	+	1.47054i
$495$	3.61027	−	0.696518i	0.162269	−	0.0313061i
$496$	5.40659	+	29.5028i	0.242763	+	1.32471i
$497$	−9.56994	+	38.8268i	−0.429270	+	1.74162i
$498$	11.5357	+	32.9296i	0.516926	+	1.47561i
$499$	8.88132	−	14.6915i	0.397582	−	0.657682i	−0.591288	−	0.806460i	$-0.701380\pi$
$499$	8.88132	−	14.6915i	0.397582	−	0.657682i	0.988871	+	0.148779i	$0.0475342\pi$
$500$	−5.03995	−	3.04676i	−0.225393	−	0.136255i
$501$	9.39113	−	6.97795i	0.419565	−	0.311752i
$502$	−34.5775	−	2.09155i	−1.54327	−	0.0933505i
$503$	18.3240	+	6.94939i	0.817029	+	0.309858i	0.727484	−	0.686125i	$-0.240690\pi$
$503$	18.3240	+	6.94939i	0.817029	+	0.309858i	0.0895447	+	0.995983i	$0.471459\pi$
$504$	−15.7511	−	25.5142i	−0.701611	−	1.13649i
$505$	1.30185	−	7.10394i	0.0579314	−	0.316121i
$506$	−12.2248			−0.543459
$507$	−16.0292	−	15.8134i	−0.711883	−	0.702298i
$508$	−1.21633			−0.0539659
$509$	2.50934	−	13.6930i	0.111224	−	0.606932i	−0.880025	−	0.474928i	$-0.842474\pi$
$509$	2.50934	−	13.6930i	0.111224	−	0.606932i	0.991249	−	0.132004i	$-0.0421413\pi$
$510$	11.8430	+	11.0444i	0.524416	+	0.489055i
$511$	−40.5912	−	15.3942i	−1.79565	−	0.681000i
$512$	6.78746	+	0.410566i	0.299966	+	0.0181446i
$513$	29.7571	−	3.12497i	1.31381	−	0.137971i
$514$	39.5895	+	23.9327i	1.74622	+	1.05563i
$515$	0.524865	−	0.868232i	0.0231283	−	0.0382589i
$516$	8.41949	−	2.94946i	0.370647	−	0.129843i
$517$	−2.30361	+	9.34613i	−0.101313	+	0.411042i
$518$	−4.78331	−	26.1017i	−0.210166	−	1.14684i
$519$	5.99300	+	12.1638i	0.263064	+	0.533931i
$520$	9.70418	−	1.63779i	0.425557	−	0.0718217i
$521$	8.05113	−	9.08785i	0.352726	−	0.398146i	−0.545190	−	0.838313i	$-0.683542\pi$
$521$	8.05113	−	9.08785i	0.352726	−	0.398146i	0.897916	+	0.440167i	$0.145081\pi$
$522$	−5.42070	+	2.90990i	−0.237258	+	0.127363i
$523$	−14.5247	−	12.8678i	−0.635122	−	0.562669i	0.282924	−	0.959142i	$-0.408695\pi$
$523$	−14.5247	−	12.8678i	−0.635122	−	0.562669i	−0.918046	+	0.396473i	$0.870234\pi$
$524$	−2.80035	+	0.690224i	−0.122334	+	0.0301526i
$525$	−26.7397	+	4.19757i	−1.16702	+	0.183197i
$526$	−8.41807	+	8.41807i	−0.367045	+	0.367045i
$527$	−27.6944	−	12.4642i	−1.20639	−	0.542950i
$528$	−2.33983	−	8.24436i	−0.101828	−	0.358790i
$529$	32.0614			1.39397
$530$	2.67803			0.116326
$531$	−2.23498	+	0.0208747i	−0.0969898	+	0.000905886i
$532$	14.3763	+	1.74559i	0.623290	+	0.0756811i
$533$	9.86762	−	18.1759i	0.427414	−	0.787287i
$534$	39.4563	+	5.81675i	1.70744	+	0.251715i
$535$	−0.0650993	−	0.0830931i	−0.00281449	−	0.00359243i
$536$	3.43074	−	2.36807i	0.148185	−	0.102285i
$537$	−1.01748	+	0.664610i	−0.0439077	+	0.0286801i
$538$	20.6950	+	16.2135i	0.892226	+	0.699015i
$539$	9.78707	−	7.66768i	0.421559	−	0.330270i
$540$	1.60711	+	3.18648i	0.0691591	+	0.137124i
$541$	−1.66474	−	27.5215i	−0.0715729	−	1.18324i	−0.839739	−	0.542990i	$-0.817292\pi$
$541$	−1.66474	−	27.5215i	−0.0715729	−	1.18324i	0.768166	−	0.640251i	$-0.221170\pi$
$542$	−6.35426	−	4.38603i	−0.272939	−	0.188396i
$543$	−39.3880	−	1.00610i	−1.69030	−	0.0431759i
$544$	9.51569	−	12.1459i	0.407982	−	0.520751i
$545$	5.51974	+	7.99672i	0.236440	+	0.342542i
$546$	−28.3630	+	33.3911i	−1.21382	+	1.42901i
$547$	5.79661	−	8.39784i	0.247845	−	0.359066i	−0.679240	−	0.733916i	$-0.737691\pi$
$547$	5.79661	−	8.39784i	0.247845	−	0.359066i	0.927085	+	0.374850i	$0.122306\pi$
$548$	2.60048	+	8.34523i	0.111087	+	0.356491i
$549$	−6.09860	+	35.1262i	−0.260282	+	1.49915i
$550$	−5.84634	−	0.709874i	−0.249289	−	0.0302691i
$551$	−1.32643	+	7.23809i	−0.0565078	+	0.308353i
$552$	8.02283	+	28.2683i	0.341474	+	1.20318i
$553$	−0.845710	+	4.61489i	−0.0359633	+	0.196245i
$554$	−28.3525	−	12.7604i	−1.20458	−	0.542139i
$555$	−0.744217	−	7.78614i	−0.0315902	−	0.330503i
$556$	4.39222	+	8.36867i	0.186272	+	0.354911i
$557$	−2.20469	+	7.07510i	−0.0934157	+	0.299782i	−0.989589	−	0.143923i	$-0.954028\pi$
$557$	−2.20469	+	7.07510i	−0.0934157	+	0.299782i	0.896173	+	0.443704i	$0.146336\pi$
$558$	−21.3826	−	20.9869i	−0.905198	−	0.888446i
$559$	19.5489	+	25.6877i	0.826831	+	1.08648i
$560$	−6.01967	−	24.4228i	−0.254377	−	1.03205i
$561$	8.21584	+	2.79224i	0.346873	+	0.117889i
$562$	4.48063	+	36.9013i	0.189004	+	1.55659i
$563$	−38.3652	+	20.1356i	−1.61690	+	0.848615i	−0.618897	+	0.785472i	$0.712420\pi$
$563$	−38.3652	+	20.1356i	−1.61690	+	0.848615i	−0.998004	+	0.0631433i	$0.979887\pi$
$564$	−9.33737	+	0.325796i	−0.393174	+	0.0137185i
$565$	−3.81571	−	8.47816i	−0.160528	−	0.356679i
$566$	−0.432674	+	7.15295i	−0.0181866	+	0.300661i
$567$	36.1734	+	15.4744i	1.51914	+	0.649865i
$568$	20.3062	+	5.00504i	0.852031	+	0.210007i
$569$	−20.5957	+	18.2462i	−0.863416	+	0.764920i	−0.973424	−	0.229011i	$-0.926451\pi$
$569$	−20.5957	+	18.2462i	−0.863416	+	0.764920i	0.110008	+	0.993931i	$0.464913\pi$
$570$	18.7009	+	3.92311i	0.783293	+	0.164321i
$571$	−8.48680	−	16.1703i	−0.355162	−	0.676704i	0.640680	−	0.767808i	$-0.278653\pi$
$571$	−8.48680	−	16.1703i	−0.355162	−	0.676704i	−0.995841	+	0.0911043i	$0.970960\pi$
$572$	−1.76934	+	1.18493i	−0.0739798	+	0.0495446i
$573$	14.8158	+	13.8168i	0.618939	+	0.577204i
$574$	−36.6957	−	16.5154i	−1.53165	−	0.689340i
$575$	26.3323	+	3.19732i	1.09813	+	0.133337i
$576$	−11.6541	+	7.19461i	−0.485587	+	0.299775i
$577$	−6.65824	+	6.65824i	−0.277186	+	0.277186i	−0.831985	−	0.554799i	$-0.812795\pi$
$577$	−6.65824	+	6.65824i	−0.277186	+	0.277186i	0.554799	+	0.831985i	$0.312795\pi$
$578$	3.25350	+	10.4409i	0.135328	+	0.434283i
$579$	−5.55614	−	1.16558i	−0.230905	−	0.0484398i
$580$	−0.863330	+	0.158211i	−0.0358478	+	0.00656936i
$581$	36.3899	+	41.0757i	1.50971	+	1.70411i
$582$	13.2546	+	15.7541i	0.549421	+	0.653030i
$583$	1.30859	−	0.588950i	0.0541964	−	0.0243918i
$584$	−8.05111	+	21.2290i	−0.333157	+	0.878463i
$585$	−9.17408	+	9.08806i	−0.379302	+	0.375745i
$586$	−8.46828	−	22.3290i	−0.349821	−	0.922403i
$587$	−3.15530	−	3.15530i	−0.130233	−	0.130233i	0.638985	−	0.769219i	$-0.279354\pi$
$587$	−3.15530	−	3.15530i	−0.130233	−	0.130233i	−0.769219	+	0.638985i	$0.779354\pi$
$588$	9.75329	+	7.10664i	0.402219	+	0.293073i
$589$	−35.5741	+	4.31948i	−1.46581	+	0.177981i
$590$	−1.36273	−	0.424644i	−0.0561027	−	0.0174823i
$591$	1.11821	−	12.9775i	0.0459970	−	0.533823i
$592$	−17.9320	+	3.28616i	−0.737001	+	0.135060i
$593$	−10.2702	+	32.9582i	−0.421747	+	1.35343i	0.462586	+	0.886575i	$0.346922\pi$
$593$	−10.2702	+	32.9582i	−0.421747	+	1.35343i	−0.884332	+	0.466858i	$0.845386\pi$
$594$	6.65231	+	5.38790i	0.272948	+	0.221068i
$595$	23.8138	+	9.03140i	0.976272	+	0.370251i
$596$	−4.17261	+	4.17261i	−0.170917	+	0.170917i
$597$	−2.88491	−	30.1825i	−0.118072	−	1.23529i
$598$	35.6738	−	23.8909i	1.45881	−	0.976971i
$599$	7.41159	+	2.81085i	0.302829	+	0.114848i	0.501339	−	0.865251i	$-0.332841\pi$
$599$	7.41159	+	2.81085i	0.302829	+	0.114848i	−0.198510	+	0.980099i	$0.563610\pi$
$600$	2.19531	+	13.9848i	0.0896231	+	0.570925i
$601$	6.96038	−	10.0839i	0.283920	−	0.411329i	−0.654912	−	0.755705i	$-0.727294\pi$
$601$	6.96038	−	10.0839i	0.283920	−	0.411329i	0.938832	+	0.344376i	$0.111910\pi$
$602$	47.0130	−	41.6498i	1.91610	−	1.69752i
$603$	−1.89181	+	5.13235i	−0.0770403	+	0.209005i
$604$	−9.93762	+	0.601115i	−0.404356	+	0.0244590i
$605$	−11.3364	+	3.53258i	−0.460892	+	0.143620i
$606$	14.6074	−	8.32877i	0.593387	−	0.338333i
$607$	−4.91448	−	2.57932i	−0.199473	−	0.104691i	0.362029	−	0.932167i	$-0.382084\pi$
$607$	−4.91448	−	2.57932i	−0.199473	−	0.104691i	−0.561502	+	0.827475i	$0.689776\pi$
$608$	2.19452	−	18.0735i	0.0889997	−	0.732979i
$609$	−6.16007	+	7.46211i	−0.249619	+	0.302380i
$610$	−10.5807	+	20.1599i	−0.428402	+	0.816251i
$611$	−11.5428	−	31.7753i	−0.466972	−	1.28549i
$612$	−0.429993	+	8.41146i	−0.0173815	+	0.340013i
$613$	38.2409	−	2.31315i	1.54453	−	0.0934271i	0.734012	−	0.679136i	$-0.237645\pi$
$613$	38.2409	−	2.31315i	1.54453	−	0.0934271i	0.810521	+	0.585709i	$0.199184\pi$
$614$	−18.0351	−	20.3574i	−0.727837	−	0.821558i
$615$	−10.3583	−	5.77851i	−0.417687	−	0.233012i
$616$	−6.32803	−	8.07713i	−0.254964	−	0.325437i
$617$	−16.0597	−	0.971433i	−0.646539	−	0.0391084i	−0.266145	−	0.963933i	$-0.585750\pi$
$617$	−16.0597	−	0.971433i	−0.646539	−	0.0391084i	−0.380394	+	0.924825i	$0.624212\pi$
$618$	2.33353	−	0.366314i	0.0938682	−	0.0147353i
$619$	5.51646	+	17.7029i	0.221725	+	0.711541i	0.996819	+	0.0796953i	$0.0253947\pi$
$619$	5.51646	+	17.7029i	0.221725	+	0.711541i	−0.775094	+	0.631846i	$0.782298\pi$
$620$	−1.98637	−	3.78471i	−0.0797744	−	0.151997i
$621$	−29.9625	−	24.2674i	−1.20235	−	0.973819i
$622$	21.6616	+	1.31029i	0.868551	+	0.0525376i
$623$	60.9036	−	15.0114i	2.44005	−	0.601419i
$624$	22.9399	+	19.4855i	0.918331	+	0.780045i
$625$	5.48809	+	1.35269i	0.219524	+	0.0541077i
$626$	21.9657	+	6.84479i	0.877927	+	0.273573i
$627$	10.0008	−	2.19569i	0.399392	−	0.0876874i
$628$	10.5266	−	3.99222i	0.420058	−	0.159307i
$629$	7.57585	−	16.8328i	0.302069	−	0.671169i
$630$	18.9619	+	16.4852i	0.755458	+	0.656787i
$631$	−2.23769	−	3.70159i	−0.0890811	−	0.147358i	0.808063	−	0.589096i	$-0.200516\pi$
$631$	−2.23769	−	3.70159i	−0.0890811	−	0.147358i	−0.897144	+	0.441738i	$0.854362\pi$
$632$	2.41357	+	0.442303i	0.0960066	+	0.0175939i
$633$	23.5697	+	9.63419i	0.936812	+	0.382925i
$634$	35.0385	−	13.2883i	1.39155	−	0.527747i
$635$	−2.40980	+	0.750926i	−0.0956302	+	0.0297996i
$636$	0.896714	+	1.06582i	0.0355570	+	0.0422624i
$637$	−13.5752	+	41.5022i	−0.537869	+	1.64438i
$638$	−1.73267	+	1.19598i	−0.0685972	+	0.0473492i
$639$	−25.5670	+	9.97039i	−1.01141	+	0.394422i
$640$	−15.8223	+	3.89985i	−0.625432	+	0.154155i
$641$	14.3028	−	20.7212i	0.564928	−	0.818439i	−0.431568	−	0.902080i	$-0.642040\pi$
$641$	14.3028	−	20.7212i	0.564928	−	0.818439i	0.996496	+	0.0836411i	$0.0266549\pi$
$642$	0.0504581	−	0.240526i	0.00199142	−	0.00949282i
$643$	2.38235	−	7.64522i	0.0939506	−	0.301498i	−0.895769	−	0.444520i	$-0.853374\pi$
$643$	2.38235	−	7.64522i	0.0939506	−	0.301498i	0.989720	+	0.143022i	$0.0456820\pi$
$644$	−11.5092	−	14.6904i	−0.453525	−	0.578882i
$645$	14.8599	−	11.0414i	0.585107	−	0.434756i
$646$	33.7540	+	29.9034i	1.32803	+	1.17653i
$647$	−1.49279	−	2.16268i	−0.0586877	−	0.0850238i	0.792541	−	0.609818i	$-0.208758\pi$
$647$	−1.49279	−	2.16268i	−0.0586877	−	0.0850238i	−0.851229	+	0.524794i	$0.824142\pi$
$648$	8.09307	−	18.9185i	0.317926	−	0.743190i
$649$	−0.759273	+	0.0921924i	−0.0298041	+	0.00361887i
$650$	18.4478	−	9.35395i	0.723581	−	0.366892i
$651$	−43.6186	−	17.8292i	−1.70955	−	0.698783i
$652$	8.28324	−	5.00739i	0.324397	−	0.196105i
$653$		−	14.7552i		−	0.577417i	−0.957417	−	0.288708i	$-0.906774\pi$
$653$		−	14.7552i		−	0.577417i	0.957417	−	0.288708i	$-0.0932258\pi$
$654$	−5.97312	+	21.8200i	−0.233567	+	0.853231i
$655$	−5.12195	+	3.09633i	−0.200131	+	0.120984i
$656$	−11.3462	+	25.2102i	−0.442994	+	0.984292i
$657$	−7.39946	−	28.8581i	−0.288680	−	1.12586i
$658$	−59.9838	+	26.9965i	−2.33841	+	1.05243i
$659$	4.37204	+	17.7381i	0.170311	+	0.690977i	0.992550	+	0.121836i	$0.0388781\pi$
$659$	4.37204	+	17.7381i	0.170311	+	0.690977i	−0.822240	+	0.569141i	$0.807276\pi$
$660$	0.667864	+	1.02247i	0.0259966	+	0.0397994i
$661$	8.45661	+	5.11220i	0.328924	+	0.198841i	0.672157	−	0.740409i	$-0.265368\pi$
$661$	8.45661	+	5.11220i	0.328924	+	0.198841i	−0.343233	+	0.939250i	$0.611522\pi$
$662$	11.0294	+	9.77117i	0.428669	+	0.379767i
$663$	−29.4319	+	7.90799i	−1.14304	+	0.307121i
$664$	21.4824	−	19.0318i	0.833680	−	0.738576i
$665$	29.5601	−	5.41708i	1.14629	−	0.210066i
$666$	12.7560	−	12.9965i	0.494284	−	0.503604i
$667$	7.80408	−	5.38676i	0.302175	−	0.208576i
$668$	3.32563	+	2.01042i	0.128673	+	0.0777853i
$669$	−14.1463	−	14.8880i	−0.546929	−	0.575602i
$670$	−2.15431	+	2.74978i	−0.0832284	+	0.106233i
$671$	−0.736624	+	12.1779i	−0.0284371	+	0.470121i
$672$	14.0983	−	19.3488i	0.543855	−	0.746397i
$673$	18.2418	−	34.7568i	0.703169	−	1.33978i	−0.227451	−	0.973789i	$-0.573039\pi$
$673$	18.2418	−	34.7568i	0.703169	−	1.33978i	0.930620	−	0.365987i	$-0.119268\pi$
$674$	−14.4047	−	2.63976i	−0.554848	−	0.101680i
$675$	−12.9199	−	13.3454i	−0.497288	−	0.513665i
$676$	2.84748	−	6.91562i	0.109519	−	0.265985i
$677$		−	33.1467i		−	1.27393i	−0.770893	−	0.636965i	$-0.780190\pi$
$677$		−	33.1467i		−	1.27393i	0.770893	−	0.636965i	$-0.219810\pi$
$678$	9.38499	−	19.5058i	0.360428	−	0.749116i
$679$	28.6716	+	15.0480i	1.10031	+	0.577489i
$680$	4.72338	−	12.4545i	0.181133	−	0.477610i
$681$	11.3624	−	33.4324i	0.435407	−	1.28113i
$682$	−8.07080	−	6.32307i	−0.309047	−	0.242123i
$683$	−1.68370	+	2.78517i	−0.0644248	+	0.106572i	−0.886333	−	0.463048i	$-0.846756\pi$
$683$	−1.68370	+	2.78517i	−0.0644248	+	0.106572i	0.821908	+	0.569620i	$0.192910\pi$
$684$	4.70048	+	8.75629i	0.179727	+	0.334805i
$685$	10.3042	+	14.9282i	0.393703	+	0.570378i
$686$	34.8123	+	8.58046i	1.32914	+	0.327604i
$687$	−0.397152	+	4.60919i	−0.0151523	+	0.175851i
$688$	−28.6137	−	32.2982i	−1.09089	−	1.23136i
$689$	−2.66768	+	4.27602i	−0.101631	+	0.162903i
$690$	−13.4656	−	20.6152i	−0.512628	−	0.784806i
$691$	−5.72534	+	9.47087i	−0.217802	+	0.360289i	−0.945507	−	0.325601i	$-0.894433\pi$
$691$	−5.72534	+	9.47087i	−0.217802	+	0.360289i	0.727705	+	0.685890i	$0.240587\pi$
$692$	−2.98667	+	3.37126i	−0.113536	+	0.128156i
$693$	12.8909	+	3.88527i	0.489687	+	0.147589i
$694$	16.2750	+	36.1616i	0.617792	+	1.37268i
$695$	13.8685	+	13.8685i	0.526061	+	0.526061i
$696$	3.90265	+	3.22169i	0.147930	+	0.122118i
$697$	−14.4814	−	23.9552i	−0.548524	−	0.907369i
$698$		−	15.5891i		−	0.590057i
$699$	0.870721	−	3.18078i	0.0329337	−	0.120308i
$700$	−4.65105	−	7.69377i	−0.175793	−	0.290797i
$701$	−0.784074	+	6.45743i	−0.0296141	+	0.243894i	0.970383	+	0.241571i	$0.0776625\pi$
$701$	−0.784074	+	6.45743i	−0.0296141	+	0.243894i	−0.999997	+	0.00232307i	$0.999261\pi$
$702$	−29.9420	−	2.72210i	−1.13009	−	0.102739i
$703$	−2.62541	−	21.6222i	−0.0990193	−	0.815497i
$704$	−3.68937	+	2.89044i	−0.139049	+	0.108938i
$705$	−18.2982	+	6.41008i	−0.689148	+	0.241418i
$706$	−29.7223	+	33.5495i	−1.11861	+	1.26265i
$707$	16.3098	−	20.8180i	0.613395	−	0.782941i
$708$	−0.287296	−	0.684535i	−0.0107972	−	0.0257264i
$709$	−23.5683	−	7.34417i	−0.885124	−	0.275816i	−0.178954	−	0.983857i	$-0.557271\pi$
$709$	−23.5683	−	7.34417i	−0.885124	−	0.275816i	−0.706171	+	0.708042i	$0.749579\pi$
$710$	−17.4932	+	1.05814i	−0.656507	+	0.0397113i
$711$	−2.92358	+	1.34877i	−0.109643	+	0.0505829i
$712$	−7.85090	−	31.8523i	−0.294225	−	1.19372i
$713$	36.3515	+	28.4795i	1.36137	+	1.06657i
$714$	19.6046	+	55.9629i	0.733682	+	2.09436i
$715$	−2.77389	+	3.43994i	−0.103738	+	0.128646i
$716$	−0.332210	−	0.229308i	−0.0124153	−	0.00856964i
$717$	−44.7448	+	1.56122i	−1.67103	+	0.0583048i
$718$	−14.1417	−	37.2886i	−0.527764	−	1.39160i
$719$	2.64462	−	21.7804i	0.0986278	−	0.812273i	−0.856514	−	0.516124i	$-0.827374\pi$
$719$	2.64462	−	21.7804i	0.0986278	−	0.812273i	0.955142	−	0.296149i	$-0.0957026\pi$
$720$	11.3255	−	13.0269i	0.422075	−	0.485484i
$721$	3.17926	−	1.92193i	0.118402	−	0.0715765i
$722$	22.3473	+	4.09530i	0.831681	+	0.152411i
$723$	−17.5084	−	14.4535i	−0.651146	−	0.537530i
$724$	−4.64071	−	12.2365i	−0.172471	−	0.454767i
$725$	4.04498	−	2.12297i	0.150227	−	0.0788452i
$726$	−23.2857	−	14.9016i	−0.864213	−	0.553050i
$727$	−2.75777	+	11.1887i	−0.102280	+	0.414966i	−0.999654	−	0.0263045i	$-0.991626\pi$
$727$	−2.75777	+	11.1887i	−0.102280	+	0.414966i	0.897374	+	0.441271i	$0.145472\pi$
$728$	34.2512	+	11.2034i	1.26943	+	0.415227i
$729$	5.60901	+	26.4110i	0.207741	+	0.978184i
$730$	1.14873	−	18.9908i	0.0425164	−	0.702881i
$731$	43.3721	−	5.26633i	1.60418	−	0.194782i
$732$	−11.5662	+	2.53939i	−0.427500	+	0.0938585i
$733$	18.7341	−	5.83778i	0.691960	−	0.215623i	0.0686991	−	0.997637i	$-0.478115\pi$
$733$	18.7341	−	5.83778i	0.691960	−	0.215623i	0.623261	+	0.782014i	$0.285807\pi$
$734$	−28.1560	+	12.6720i	−1.03926	+	0.467732i
$735$	23.7107	+	8.05836i	0.874584	+	0.297237i
$736$	−18.4684	+	14.4691i	−0.680756	+	0.533338i
$737$	−0.447956	+	1.81743i	−0.0165007	+	0.0669458i
$738$	−5.23128	−	27.1153i	−0.192566	−	0.998129i
$739$	−1.38997	−	22.9789i	−0.0511309	−	0.845294i	−0.929846	−	0.367948i	$-0.880060\pi$
$739$	−1.38997	−	22.9789i	−0.0511309	−	0.845294i	0.878715	−	0.477346i	$-0.158401\pi$
$740$	2.30037	−	1.20733i	0.0845633	−	0.0443823i
$741$	−24.8927	+	25.9518i	−0.914455	+	0.953362i
$742$	8.68306	+	4.55722i	0.318765	+	0.167301i
$743$	−0.893457	+	1.98518i	−0.0327778	+	0.0728292i	−0.927561	−	0.373671i	$-0.878099\pi$
$743$	−0.893457	+	1.98518i	−0.0327778	+	0.0728292i	0.894784	+	0.446500i	$0.147330\pi$
$744$	−9.32462	+	22.8123i	−0.341857	+	0.836341i
$745$	−5.69078	+	10.8429i	−0.208494	+	0.397252i
$746$	−7.80579	−	7.80579i	−0.285790	−	0.285790i
$747$	−8.67051	+	36.6473i	−0.317237	+	1.34086i
$748$	0.174022	+	2.87693i	0.00636287	+	0.105191i
$749$	−0.0696733	−	0.380195i	−0.00254581	−	0.0138920i
$750$	−12.5756	−	25.5242i	−0.459195	−	0.932013i
$751$	−11.1542	−	7.69922i	−0.407024	−	0.280948i	0.346910	−	0.937898i	$-0.387231\pi$
$751$	−11.1542	−	7.69922i	−0.407024	−	0.280948i	−0.753934	+	0.656950i	$0.771846\pi$
$752$	18.5468	+	41.2092i	0.676331	+	1.50275i
$753$	−30.2174	−	22.0176i	−1.10118	−	0.802366i
$754$	2.71890	−	6.87619i	0.0990165	−	0.250416i
$755$	−19.3174	+	7.32613i	−0.703033	+	0.266625i
$756$	−0.211669	+	13.0665i	−0.00769834	+	0.475223i
$757$	15.5222	−	40.9286i	0.564163	−	1.48758i	−0.284518	−	0.958671i	$-0.591833\pi$
$757$	15.5222	−	40.9286i	0.564163	−	1.48758i	0.848681	−	0.528905i	$-0.177397\pi$
$758$	4.37759	+	36.0527i	0.159001	+	1.30949i
$759$	−11.1135	−	7.11206i	−0.403395	−	0.258151i
$760$	−2.83311	−	15.4598i	−0.102768	−	0.560786i
$761$	0.606022	+	3.30696i	0.0219683	+	0.119877i	0.992776	−	0.119982i	$-0.0382835\pi$
$761$	0.606022	+	3.30696i	0.0219683	+	0.119877i	−0.970808	+	0.239859i	$0.922899\pi$
$762$	−4.94987	−	3.16765i	−0.179315	−	0.114752i
$763$	4.28875	+	35.3210i	0.155263	+	1.27871i
$764$	−2.38610	+	6.29162i	−0.0863259	+	0.227623i
$765$	4.34108	+	16.9303i	0.156952	+	0.612118i
$766$	52.6091	−	19.9520i	1.90084	−	0.720895i
$767$	2.03550	−	1.75287i	0.0734976	−	0.0632926i
$768$	−17.8822	−	13.0297i	−0.645270	−	0.470170i
$769$	−17.4366	−	38.7426i	−0.628781	−	1.39709i	−0.900559	−	0.434734i

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+(-0.289269 + 1.57849i) q^{2} +(-1.18129 + 1.26671i) q^{3} +(-0.537915 - 0.204004i) q^{4} +(-1.19167 - 0.0720827i) q^{5} +(-1.65777 - 2.23107i) q^{6} +(-3.74112 - 2.26159i) q^{7} +(-1.18280 + 1.95659i) q^{8} +(-0.209095 - 2.99270i) q^{9} +(0.458494 - 1.86018i) q^{10} +(-0.185051 - 1.00979i) q^{11} +(0.893848 - 0.440392i) q^{12} +(2.51344 + 2.58508i) q^{13} +(4.65208 - 5.25111i) q^{14} +(1.49902 - 1.42435i) q^{15} +(-3.60754 - 3.19601i) q^{16} +(4.73822 - 1.16787i) q^{17} +(4.78443 + 0.535641i) q^{18} +(4.07170 - 4.07170i) q^{19} +(0.626311 + 0.281880i) q^{20} +(7.28413 - 2.06731i) q^{21} +1.64747 q^{22} -7.42034 q^{23} +(-1.08119 - 3.80957i) q^{24} +(-3.54867 - 0.430886i) q^{25} +(-4.80757 + 3.21965i) q^{26} +(4.03788 + 3.27040i) q^{27} +(1.55103 + 1.97975i) q^{28} +(-1.05171 + 0.725946i) q^{29} +(1.81469 + 2.77820i) q^{30} +(-4.89889 - 3.83804i) q^{31} +(2.48890 - 1.94993i) q^{32} +(1.49771 + 0.958455i) q^{33} +(0.472845 + 7.81706i) q^{34} +(4.29516 + 2.96473i) q^{35} +(-0.498049 + 1.65248i) q^{36} +(2.33279 - 2.97758i) q^{37} +(5.24931 + 7.60494i) q^{38} +(-6.24364 + 0.130058i) q^{39} +(1.55054 - 2.24635i) q^{40} +(-1.70650 - 5.47636i) q^{41} +(1.15615 + 12.0959i) q^{42} +(8.88768 + 1.07916i) q^{43} +(-0.106460 + 0.580934i) q^{44} +(0.0334502 + 3.58138i) q^{45} +(2.14647 - 11.7129i) q^{46} +(-8.55029 - 3.84817i) q^{47} +(8.30997 - 0.794285i) q^{48} +(5.62816 + 10.7236i) q^{49} +(1.70667 - 5.47688i) q^{50} +(-4.11788 + 7.38154i) q^{51} +(-0.824649 - 1.90330i) q^{52} +(0.334521 + 1.35721i) q^{53} +(-6.33031 + 5.42773i) q^{54} +(0.147731 + 1.21668i) q^{55} +(8.85000 - 4.64484i) q^{56} +(0.347783 + 9.96751i) q^{57} +(-0.841669 - 1.87011i) q^{58} +(0.0449835 - 0.743666i) q^{59} +(-1.09692 + 0.460370i) q^{60} +(-11.5386 - 2.84400i) q^{61} +(7.47539 - 6.62262i) q^{62} +(-5.98601 + 11.6690i) q^{63} +(-2.12161 - 4.04240i) q^{64} +(-2.80885 - 3.26173i) q^{65} +(-1.94615 + 2.08687i) q^{66} +(-1.66267 - 0.748308i) q^{67} +(-2.78701 - 0.338404i) q^{68} +(8.76559 - 9.39940i) q^{69} +(-5.92225 + 5.92225i) q^{70} +(-2.72139 - 8.73324i) q^{71} +(6.10282 + 3.13066i) q^{72} +(9.76789 - 1.79003i) q^{73} +(4.02528 + 4.54360i) q^{74} +(4.73782 - 3.98612i) q^{75} +(-3.02087 + 1.35958i) q^{76} +(-1.59143 + 4.19627i) q^{77} +(1.60079 - 9.89314i) q^{78} +(-0.380575 - 1.00349i) q^{79} +(4.06862 + 4.06862i) q^{80} +(-8.91256 + 1.25152i) q^{81} +(9.13800 - 1.10955i) q^{82} +(-11.9846 - 3.73456i) q^{83} +(-4.33998 - 0.373956i) q^{84} +(-5.73058 + 1.05017i) q^{85} +(-4.27437 + 13.7169i) q^{86} +(0.322821 - 2.18977i) q^{87} +(2.19463 + 0.832313i) q^{88} +(-10.1460 + 10.1460i) q^{89} +(-5.66285 - 0.983182i) q^{90} +(-3.55670 - 15.3555i) q^{91} +(3.99151 + 1.51378i) q^{92} +(10.6487 - 1.67162i) q^{93} +(8.54762 - 12.3834i) q^{94} +(-5.14561 + 4.55862i) q^{95} +(-0.470130 + 5.45614i) q^{96} +(-7.39354 + 0.447227i) q^{97} +(-18.5551 + 5.78199i) q^{98} +(-2.98332 + 0.764947i) 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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