LMFDB - Embedded newform 288.2.bc.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	288.13
Dual form			288.2.bc.a.133.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39065 + 0.257088i) q^{2} +(1.59735 - 0.669693i) q^{3} +(1.86781 - 0.715038i) q^{4} +(-0.422585 + 3.20986i) q^{5} +(-2.04918 + 1.34197i) q^{6} +(3.16032 + 0.846806i) q^{7} +(-2.41364 + 1.47456i) q^{8} +(2.10302 - 2.13946i) q^{9} +O(q^{10})$	\(q+(-1.39065 + 0.257088i) q^{2} +(1.59735 - 0.669693i) q^{3} +(1.86781 - 0.715038i) q^{4} +(-0.422585 + 3.20986i) q^{5} +(-2.04918 + 1.34197i) q^{6} +(3.16032 + 0.846806i) q^{7} +(-2.41364 + 1.47456i) q^{8} +(2.10302 - 2.13946i) q^{9} +(-0.237547 - 4.57243i) q^{10} +(-1.95472 + 2.54745i) q^{11} +(2.50468 - 2.39302i) q^{12} +(-4.65422 + 3.57131i) q^{13} +(-4.61261 - 0.365129i) q^{14} +(1.47460 + 5.41025i) q^{15} +(2.97744 - 2.67111i) q^{16} -3.19756i q^{17} +(-2.37454 + 3.51590i) q^{18} +(-0.917962 - 0.380232i) q^{19} +(1.50586 + 6.29757i) q^{20} +(5.61523 - 0.763804i) q^{21} +(2.06342 - 4.04514i) q^{22} +(7.31806 - 1.96087i) q^{23} +(-2.86792 + 3.97178i) q^{24} +(-5.29496 - 1.41878i) q^{25} +(5.55425 - 6.16298i) q^{26} +(1.92647 - 4.82584i) q^{27} +(6.50839 - 0.678079i) q^{28} +(-1.03162 + 0.135816i) q^{29} +(-3.44156 - 7.14466i) q^{30} +(-1.14946 + 1.99093i) q^{31} +(-3.45386 + 4.48005i) q^{32} +(-1.41636 + 5.37822i) q^{33} +(0.822055 + 4.44669i) q^{34} +(-4.05363 + 9.78633i) q^{35} +(2.39825 - 5.49985i) q^{36} +(10.0952 - 4.18156i) q^{37} +(1.37432 + 0.292773i) q^{38} +(-5.04271 + 8.82151i) q^{39} +(-3.71315 - 8.37057i) q^{40} +(6.82422 - 1.82855i) q^{41} +(-7.61245 + 2.50579i) q^{42} +(-0.639878 + 0.833905i) q^{43} +(-1.82953 + 6.15585i) q^{44} +(5.97865 + 7.65451i) q^{45} +(-9.67274 + 4.60827i) q^{46} +(-5.34450 + 3.08565i) q^{47} +(2.96717 - 6.26066i) q^{48} +(3.20839 + 1.85236i) q^{49} +(7.72819 + 0.611756i) q^{50} +(-2.14138 - 5.10761i) q^{51} +(-6.13958 + 9.99847i) q^{52} +(-5.16512 - 12.4697i) q^{53} +(-1.43838 + 7.20632i) q^{54} +(-7.35090 - 7.35090i) q^{55} +(-8.87656 + 2.61620i) q^{56} +(-1.72094 + 0.00739026i) q^{57} +(1.39971 - 0.454091i) q^{58} +(0.111828 - 0.849416i) q^{59} +(6.62282 + 9.05093i) q^{60} +(5.72711 - 0.753989i) q^{61} +(1.08666 - 3.06419i) q^{62} +(8.45794 - 4.98054i) q^{63} +(3.65135 - 7.11812i) q^{64} +(-9.49657 - 16.4485i) q^{65} +(0.586990 - 7.84334i) q^{66} +(-4.18147 - 5.44940i) q^{67} +(-2.28638 - 5.97244i) q^{68} +(10.3763 - 8.03303i) q^{69} +(3.12123 - 14.6515i) q^{70} +(2.92094 - 2.92094i) q^{71} +(-1.92118 + 8.26493i) q^{72} +(-4.48292 - 4.48292i) q^{73} +(-12.9638 + 8.41043i) q^{74} +(-9.40803 + 1.27972i) q^{75} +(-1.98646 - 0.0538242i) q^{76} +(-8.33475 + 6.39548i) q^{77} +(4.74474 - 13.5640i) q^{78} +(-7.00349 + 4.04346i) q^{79} +(7.31567 + 10.6859i) q^{80} +(-0.154587 - 8.99867i) q^{81} +(-9.02000 + 4.29729i) q^{82} +(-0.210565 - 1.59940i) q^{83} +(9.94204 - 5.44175i) q^{84} +(10.2637 + 1.35124i) q^{85} +(0.675458 - 1.32417i) q^{86} +(-1.55691 + 0.907817i) q^{87} +(0.961646 - 9.03098i) q^{88} +(1.97258 - 1.97258i) q^{89} +(-10.2821 - 9.10769i) q^{90} +(-17.7330 + 7.34527i) q^{91} +(12.2667 - 8.89523i) q^{92} +(-0.502779 + 3.94998i) q^{93} +(6.63905 - 5.66507i) q^{94} +(1.60841 - 2.78584i) q^{95} +(-2.51676 + 9.46921i) q^{96} +(-0.192235 - 0.332960i) q^{97} +(-4.93796 - 1.75115i) q^{98} +(1.33933 + 9.53939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.39065	+	0.257088i	−0.983338	+	0.181789i
$2$	−1.39065	+	0.257088i	−0.983338	+	0.181789i
$3$	1.59735	−	0.669693i	0.922228	−	0.386647i
$3$	1.59735	−	0.669693i	0.922228	−	0.386647i
$4$	1.86781	−	0.715038i	0.933906	−	0.357519i
$5$	−0.422585	+	3.20986i	−0.188986	+	1.43549i	0.589469	+	0.807791i	$0.299337\pi$
$5$	−0.422585	+	3.20986i	−0.188986	+	1.43549i	−0.778455	+	0.627700i	$0.783996\pi$
$6$	−2.04918	+	1.34197i	−0.836573	+	0.547855i
$7$	3.16032	+	0.846806i	1.19449	+	0.320063i	0.800659	−	0.599120i	$-0.204483\pi$
$7$	3.16032	+	0.846806i	1.19449	+	0.320063i	0.393831	+	0.919183i	$0.371150\pi$
$8$	−2.41364	+	1.47456i	−0.853352	+	0.521336i
$9$	2.10302	−	2.13946i	0.701008	−	0.713154i
$10$	−0.237547	−	4.57243i	−0.0751189	−	1.44593i
$11$	−1.95472	+	2.54745i	−0.589372	+	0.768084i	−0.988891	−	0.148641i	$-0.952510\pi$
$11$	−1.95472	+	2.54745i	−0.589372	+	0.768084i	0.399520	+	0.916725i	$0.369177\pi$
$12$	2.50468	−	2.39302i	0.723040	−	0.690806i
$13$	−4.65422	+	3.57131i	−1.29085	+	0.990502i	−0.291423	+	0.956594i	$0.594129\pi$
$13$	−4.65422	+	3.57131i	−1.29085	+	0.990502i	−0.999425	+	0.0339081i	$0.989205\pi$
$14$	−4.61261	−	0.365129i	−1.23277	−	0.0975849i
$15$	1.47460	+	5.41025i	0.380741	+	1.39692i
$16$	2.97744	−	2.67111i	0.744360	−	0.667779i
$17$		−	3.19756i		−	0.775523i	−0.921760	−	0.387761i	$-0.873248\pi$
$17$		−	3.19756i		−	0.775523i	0.921760	−	0.387761i	$-0.126752\pi$
$18$	−2.37454	+	3.51590i	−0.559684	+	0.828706i
$19$	−0.917962	−	0.380232i	−0.210595	−	0.0872312i	0.274892	−	0.961475i	$-0.411358\pi$
$19$	−0.917962	−	0.380232i	−0.210595	−	0.0872312i	−0.485487	+	0.874244i	$0.661358\pi$
$20$	1.50586	+	6.29757i	0.336721	+	1.40818i
$21$	5.61523	−	0.763804i	1.22534	−	0.166676i
$22$	2.06342	−	4.04514i	0.439922	−	0.862427i
$23$	7.31806	−	1.96087i	1.52592	−	0.408869i	0.604235	−	0.796806i	$-0.293479\pi$
$23$	7.31806	−	1.96087i	1.52592	−	0.408869i	0.921686	+	0.387937i	$0.126812\pi$
$24$	−2.86792	+	3.97178i	−0.585412	+	0.810736i
$25$	−5.29496	−	1.41878i	−1.05899	−	0.283756i
$26$	5.55425	−	6.16298i	1.08928	−	1.20866i
$27$	1.92647	−	4.82584i	0.370750	−	0.928733i
$28$	6.50839	−	0.678079i	1.22997	−	0.128145i
$29$	−1.03162	+	0.135816i	−0.191568	+	0.0252204i	−0.225700	−	0.974197i	$-0.572467\pi$
$29$	−1.03162	+	0.135816i	−0.191568	+	0.0252204i	0.0341317	+	0.999417i	$0.489133\pi$
$30$	−3.44156	−	7.14466i	−0.628341	−	1.30443i
$31$	−1.14946	+	1.99093i	−0.206450	+	0.357581i	−0.950594	−	0.310438i	$-0.899524\pi$
$31$	−1.14946	+	1.99093i	−0.206450	+	0.357581i	0.744144	+	0.668019i	$0.232858\pi$
$32$	−3.45386	+	4.48005i	−0.610563	+	0.791968i
$33$	−1.41636	+	5.37822i	−0.246557	+	0.936227i
$34$	0.822055	+	4.44669i	0.140981	+	0.762601i
$35$	−4.05363	+	9.78633i	−0.685189	+	1.65419i
$36$	2.39825	−	5.49985i	0.399709	−	0.916642i
$37$	10.0952	−	4.18156i	1.65964	−	0.687444i	0.661587	−	0.749869i	$-0.269883\pi$
$37$	10.0952	−	4.18156i	1.65964	−	0.687444i	0.998050	+	0.0624246i	$0.0198833\pi$
$38$	1.37432	+	0.292773i	0.222943	+	0.0474940i
$39$	−5.04271	+	8.82151i	−0.807481	+	1.41257i
$40$	−3.71315	−	8.37057i	−0.587101	−	1.32350i
$41$	6.82422	−	1.82855i	1.06576	−	0.285571i	0.317013	−	0.948421i	$-0.397320\pi$
$41$	6.82422	−	1.82855i	1.06576	−	0.285571i	0.748752	+	0.662851i	$0.230654\pi$
$42$	−7.61245	+	2.50579i	−1.17463	+	0.386652i
$43$	−0.639878	+	0.833905i	−0.0975804	+	0.127169i	−0.839591	−	0.543218i	$-0.817206\pi$
$43$	−0.639878	+	0.833905i	−0.0975804	+	0.127169i	0.742011	+	0.670388i	$0.233872\pi$
$44$	−1.82953	+	6.15585i	−0.275813	+	0.928030i
$45$	5.97865	+	7.65451i	0.891245	+	1.14107i
$46$	−9.67274	+	4.60827i	−1.42617	+	0.679452i
$47$	−5.34450	+	3.08565i	−0.779576	+	0.450088i	−0.836280	−	0.548303i	$-0.815274\pi$
$47$	−5.34450	+	3.08565i	−0.779576	+	0.450088i	0.0567040	+	0.998391i	$0.481941\pi$
$48$	2.96717	−	6.26066i	0.428275	−	0.903649i
$49$	3.20839	+	1.85236i	0.458341	+	0.264623i
$50$	7.72819	+	0.611756i	1.09293	+	0.0865154i
$51$	−2.14138	−	5.10761i	−0.299854	−	0.715208i
$52$	−6.13958	+	9.99847i	−0.851407	+	1.38654i
$53$	−5.16512	−	12.4697i	−0.709484	−	1.71285i	−0.701285	−	0.712881i	$-0.747390\pi$
$53$	−5.16512	−	12.4697i	−0.709484	−	1.71285i	−0.00819895	−	0.999966i	$-0.502610\pi$
$54$	−1.43838	+	7.20632i	−0.195739	+	0.980656i
$55$	−7.35090	−	7.35090i	−0.991195	−	0.991195i
$56$	−8.87656	+	2.61620i	−1.18618	+	0.349604i
$57$	−1.72094	+	0.00739026i	−0.227944	+	0.000978864i
$58$	1.39971	−	0.454091i	0.183791	−	0.0596250i
$59$	0.111828	−	0.849416i	0.0145587	−	0.110585i	−0.982622	−	0.185615i	$-0.940572\pi$
$59$	0.111828	−	0.849416i	0.0145587	−	0.110585i	0.997181	+	0.0750308i	$0.0239055\pi$
$60$	6.62282	+	9.05093i	0.855002	+	1.16847i
$61$	5.72711	−	0.753989i	0.733282	−	0.0965384i	0.245368	−	0.969430i	$-0.421091\pi$
$61$	5.72711	−	0.753989i	0.733282	−	0.0965384i	0.487914	+	0.872892i	$0.337758\pi$
$62$	1.08666	−	3.06419i	0.138005	−	0.389153i
$63$	8.45794	−	4.98054i	1.06560	−	0.627489i
$64$	3.65135	−	7.11812i	0.456418	−	0.889765i
$65$	−9.49657	−	16.4485i	−1.17791	−	2.04019i
$66$	0.586990	−	7.84334i	0.0722535	−	0.965449i
$67$	−4.18147	−	5.44940i	−0.510848	−	0.665750i	0.464717	−	0.885459i	$-0.346156\pi$
$67$	−4.18147	−	5.44940i	−0.510848	−	0.665750i	−0.975566	+	0.219709i	$0.929489\pi$
$68$	−2.28638	−	5.97244i	−0.277264	−	0.724265i
$69$	10.3763	−	8.03303i	1.24916	−	0.967064i
$70$	3.12123	−	14.6515i	0.373059	−	1.75119i
$71$	2.92094	−	2.92094i	0.346652	−	0.346652i	−0.512209	−	0.858861i	$-0.671173\pi$
$71$	2.92094	−	2.92094i	0.346652	−	0.346652i	0.858861	+	0.512209i	$0.171173\pi$
$72$	−1.92118	+	8.26493i	−0.226414	+	0.974031i
$73$	−4.48292	−	4.48292i	−0.524687	−	0.524687i	0.394297	−	0.918983i	$-0.370988\pi$
$73$	−4.48292	−	4.48292i	−0.524687	−	0.524687i	−0.918983	+	0.394297i	$0.870988\pi$
$74$	−12.9638	+	8.41043i	−1.50701	+	0.977693i
$75$	−9.40803	+	1.27972i	−1.08635	+	0.147769i
$76$	−1.98646	−	0.0538242i	−0.227863	−	0.00617405i
$77$	−8.33475	+	6.39548i	−0.949833	+	0.728833i
$78$	4.74474	−	13.5640i	0.537237	−	1.53583i
$79$	−7.00349	+	4.04346i	−0.787954	+	0.454925i	−0.839242	−	0.543759i	$-0.817001\pi$
$79$	−7.00349	+	4.04346i	−0.787954	+	0.454925i	0.0512879	+	0.998684i	$0.483667\pi$
$80$	7.31567	+	10.6859i	0.817916	+	1.19472i
$81$	−0.154587	−	8.99867i	−0.0171763	−	0.999852i
$82$	−9.02000	+	4.29729i	−0.996093	+	0.474556i
$83$	−0.210565	−	1.59940i	−0.0231125	−	0.175557i	0.975995	−	0.217792i	$-0.0698854\pi$
$83$	−0.210565	−	1.59940i	−0.0231125	−	0.175557i	−0.999108	+	0.0422352i	$0.986552\pi$
$84$	9.94204	−	5.44175i	1.08477	−	0.593743i
$85$	10.2637	+	1.35124i	1.11326	+	0.146563i
$86$	0.675458	−	1.32417i	0.0728366	−	0.142789i
$87$	−1.55691	+	0.907817i	−0.166918	+	0.0973282i
$88$	0.961646	−	9.03098i	0.102512	−	0.962706i
$89$	1.97258	−	1.97258i	0.209093	−	0.209093i	−0.594789	−	0.803882i	$-0.702764\pi$
$89$	1.97258	−	1.97258i	0.209093	−	0.209093i	0.803882	+	0.594789i	$0.202764\pi$
$90$	−10.2821	−	9.10769i	−1.08383	−	0.960035i
$91$	−17.7330	+	7.34527i	−1.85893	+	0.769993i
$92$	12.2667	−	8.89523i	1.27889	−	0.927391i
$93$	−0.502779	+	3.94998i	−0.0521357	+	0.409594i
$94$	6.63905	−	5.66507i	0.684765	−	0.584307i
$95$	1.60841	−	2.78584i	0.165019	−	0.285822i
$96$	−2.51676	+	9.46921i	−0.256866	+	0.966447i
$97$	−0.192235	−	0.332960i	−0.0195185	−	0.0338070i	0.856101	−	0.516808i	$-0.172880\pi$
$97$	−0.192235	−	0.332960i	−0.0195185	−	0.0338070i	−0.875620	+	0.483001i	$0.839547\pi$
$98$	−4.93796	−	1.75115i	−0.498810	−	0.176893i
$99$	1.33933	+	9.53939i	0.134608	+	0.958745i
$100$	−10.9045	+	1.13609i	−1.09045	+	0.113609i
$101$	0.570950	+	0.438106i	0.0568117	+	0.0435931i	0.636777	−	0.771048i	$-0.280267\pi$
$101$	0.570950	+	0.438106i	0.0568117	+	0.0435931i	−0.579965	+	0.814641i	$0.696934\pi$
$102$	4.29102	+	6.55237i	0.424874	+	0.648781i
$103$	2.35717	+	8.79709i	0.232259	+	0.866803i	0.979365	+	0.202098i	$0.0647760\pi$
$103$	2.35717	+	8.79709i	0.232259	+	0.866803i	−0.747106	+	0.664705i	$0.768557\pi$
$104$	5.96752	−	15.4828i	0.585163	−	1.51821i
$105$	0.0787872	+	18.3468i	0.00768884	+	1.79047i
$106$	10.3887	+	16.0131i	1.00904	+	1.55533i
$107$	−0.118579	−	0.286276i	−0.0114635	−	0.0276753i	0.918044	−	0.396478i	$-0.129768\pi$
$107$	−0.118579	−	0.286276i	−0.0114635	−	0.0276753i	−0.929508	+	0.368803i	$0.879768\pi$
$108$	0.147628	−	10.3913i	0.0142055	−	0.999899i
$109$	−6.88950	−	2.85373i	−0.659895	−	0.273337i	0.0274995	−	0.999622i	$-0.491246\pi$
$109$	−6.88950	−	2.85373i	−0.659895	−	0.273337i	−0.687394	+	0.726284i	$0.741246\pi$
$110$	12.1123	+	8.33269i	1.15487	+	0.794491i
$111$	13.3251	−	13.4401i	1.26476	−	1.27567i
$112$	11.6716	−	5.92027i	1.10286	−	0.559413i
$113$	−13.3738	−	7.72138i	−1.25810	−	0.726367i	−0.285398	−	0.958409i	$-0.592126\pi$
$113$	−13.3738	−	7.72138i	−1.25810	−	0.726367i	−0.972706	+	0.232043i	$0.925459\pi$
$114$	2.39132	−	0.452710i	0.223968	−	0.0424002i
$115$	3.20160	+	24.3185i	0.298551	+	2.26772i
$116$	−1.82977	+	0.991330i	−0.169890	+	0.0920427i
$117$	−2.14726	+	17.4681i	−0.198514	+	1.61492i
$118$	0.0628614	+	1.20999i	0.00578686	+	0.111389i
$119$	2.70771	−	10.1053i	0.248216	−	0.926354i
$120$	−11.5369	−	10.8840i	−1.05317	−	0.993571i
$121$	0.178474	+	0.666075i	0.0162249	+	0.0605523i
$122$	−7.77056	+	2.52091i	−0.703514	+	0.228232i
$123$	9.67608	−	7.49095i	0.872462	−	0.675436i
$124$	−0.723390	+	4.54059i	−0.0649623	+	0.407757i
$125$	0.596868	−	1.44097i	0.0533855	−	0.128884i
$126$	−10.4816	+	9.10062i	−0.933775	+	0.810747i
$127$	5.50843			0.488794			0.244397	−	0.969675i	$-0.421410\pi$
$127$	5.50843			0.488794			0.244397	+	0.969675i	$0.421410\pi$
$128$	−3.24776	+	10.8375i	−0.287064	+	0.957911i
$129$	−0.463645	+	1.76055i	−0.0408217	+	0.155008i
$130$	17.4351	+	20.4327i	1.52916	+	1.79207i
$131$	6.95825	+	9.06817i	0.607945	+	0.792290i	0.991344	−	0.131293i	$-0.0419130\pi$
$131$	6.95825	+	9.06817i	0.607945	+	0.792290i	−0.383398	+	0.923583i	$0.625246\pi$
$132$	1.20013	+	11.0582i	0.104458	+	0.962497i
$133$	−2.57907	−	1.97899i	−0.223634	−	0.171600i
$134$	7.21594	+	6.50320i	0.623362	+	0.561791i
$135$	14.6761	+	8.22303i	1.26312	+	0.707725i
$136$	4.71500	+	7.71777i	0.404308	+	0.661794i
$137$	−0.131459	+	0.490612i	−0.0112313	+	0.0419158i	−0.971314	−	0.237800i	$-0.923574\pi$
$137$	−0.131459	+	0.490612i	−0.0112313	+	0.0419158i	0.960083	+	0.279716i	$0.0902403\pi$
$138$	−12.3646	+	13.8388i	−1.05254	+	1.17803i
$139$	−12.1362	−	1.59776i	−1.02938	−	0.135521i	−0.403131	−	0.915142i	$-0.632078\pi$
$139$	−12.1362	−	1.59776i	−1.02938	−	0.135521i	−0.626251	+	0.779622i	$0.715411\pi$
$140$	−0.573816	+	21.1775i	−0.0484963	+	1.78983i
$141$	−6.47058	+	8.50802i	−0.544921	+	0.716505i
$142$	−3.31107	+	4.81295i	−0.277859	+	0.403894i
$143$		−	18.8373i		−	1.57525i
$144$	0.546881	−	11.9875i	0.0455734	−	0.998961i
$145$		−	3.36876i		−	0.279760i
$146$	7.38668	+	5.08167i	0.611326	+	0.420562i
$147$	6.36542	+	0.810230i	0.525011	+	0.0668266i
$148$	15.8659	−	15.0288i	1.30417	−	1.23536i
$149$	−3.77663	−	0.497203i	−0.309394	−	0.0407325i	−0.0257693	−	0.999668i	$-0.508204\pi$
$149$	−3.77663	−	0.497203i	−0.309394	−	0.0407325i	−0.283624	+	0.958935i	$0.591537\pi$
$150$	12.7543	−	4.19833i	1.04138	−	0.342792i
$151$	−4.15404	+	15.5031i	−0.338051	+	1.26162i	0.562472	+	0.826816i	$0.309850\pi$
$151$	−4.15404	+	15.5031i	−0.338051	+	1.26162i	−0.900523	+	0.434808i	$0.856816\pi$
$152$	2.77631	−	0.435844i	0.225188	−	0.0353516i
$153$	−6.84106	−	6.72455i	−0.553067	−	0.543647i
$154$	9.94652	−	11.0366i	0.801513	−	0.889358i
$155$	−5.90484	−	4.53094i	−0.474288	−	0.363934i
$156$	−3.11112	+	20.0826i	−0.249089	+	1.60790i
$157$	−4.64757	−	6.05683i	−0.370917	−	0.483388i	0.570183	−	0.821518i	$-0.306872\pi$
$157$	−4.64757	−	6.05683i	−0.370917	−	0.483388i	−0.941099	+	0.338130i	$0.890206\pi$
$158$	8.69987	−	7.42355i	0.692124	−	0.590586i
$159$	−16.6014	−	16.4594i	−1.31657	−	1.30531i
$160$	−12.9208	−	12.9796i	−1.02148	−	1.02613i
$161$	24.7879			1.95356
$162$	2.52843	+	12.4743i	0.198652	+	0.980070i
$163$	1.18238	−	2.85452i	0.0926111	−	0.223583i	−0.870786	−	0.491663i	$-0.836389\pi$
$163$	1.18238	−	2.85452i	0.0926111	−	0.223583i	0.963397	+	0.268080i	$0.0863892\pi$
$164$	11.4389	−	8.29496i	0.893227	−	0.647727i
$165$	−16.6648	−	6.81908i	−1.29735	−	0.530864i
$166$	0.704008	+	2.17007i	0.0546416	+	0.168430i
$167$	−0.446610	−	1.66677i	−0.0345597	−	0.128979i	0.946491	−	0.322731i	$-0.104601\pi$
$167$	−0.446610	−	1.66677i	−0.0345597	−	0.128979i	−0.981050	+	0.193752i	$0.937934\pi$
$168$	−12.4269	+	10.1235i	−0.958755	+	0.781048i
$169$	5.54286	−	20.6862i	0.426374	−	1.59125i
$170$	−14.6206	+	0.759571i	−1.12135	+	0.0582564i
$171$	−2.74399	+	1.16431i	−0.209838	+	0.0890367i
$172$	−0.598897	+	2.01511i	−0.0456655	+	0.153651i
$173$	−1.83970	−	13.9739i	−0.139870	−	1.06242i	−0.907061	−	0.420999i	$-0.861679\pi$
$173$	−1.83970	−	13.9739i	−0.139870	−	1.06242i	0.767191	−	0.641419i	$-0.221654\pi$
$174$	1.93172	−	1.66272i	0.146443	−	0.126050i
$175$	−15.5324	−	8.96762i	−1.17414	−	0.677888i
$176$	0.984445	+	12.8062i	0.0742054	+	0.965301i
$177$	−0.390220	−	1.43170i	−0.0293307	−	0.107613i
$178$	−2.23604	+	3.25029i	−0.167598	+	0.243619i
$179$	20.8995	+	8.65686i	1.56210	+	0.647044i	0.985453	−	0.169947i	$-0.0543597\pi$
$179$	20.8995	+	8.65686i	1.56210	+	0.647044i	0.576650	+	0.816991i	$0.304360\pi$
$180$	16.6403	+	10.0222i	1.24029	+	0.747011i
$181$	6.90156	+	16.6618i	0.512989	+	1.23846i	0.942136	+	0.335230i	$0.108814\pi$
$181$	6.90156	+	16.6618i	0.512989	+	1.23846i	−0.429147	+	0.903234i	$0.641186\pi$
$182$	22.7721	−	14.7736i	1.68798	−	1.09510i
$183$	8.64323	−	5.03979i	0.638926	−	0.372552i
$184$	−14.7718	+	15.5238i	−1.08899	+	1.14443i
$185$	9.15612	+	34.1711i	0.673172	+	2.51231i
$186$	−0.316305	−	5.62230i	−0.0231926	−	0.412247i
$187$	8.14562	+	6.25035i	0.595666	+	0.457071i
$188$	−7.77617	+	9.58494i	−0.567135	+	0.699054i
$189$	10.1748	−	13.6199i	0.740110	−	0.990699i
$190$	−1.52052	+	4.28763i	−0.110310	+	0.311058i
$191$	5.92947	+	10.2701i	0.429041	+	0.743121i	0.996788	−	0.0800819i	$-0.0255182\pi$
$191$	5.92947	+	10.2701i	0.429041	+	0.743121i	−0.567747	+	0.823203i	$0.692185\pi$
$192$	1.06551	−	13.8154i	0.0768964	−	0.997039i
$193$	6.24993	−	10.8252i	0.449880	−	0.779215i	−0.548498	−	0.836152i	$-0.684800\pi$
$193$	6.24993	−	10.8252i	0.449880	−	0.779215i	0.998378	+	0.0569372i	$0.0181335\pi$
$194$	0.352931	+	0.413610i	0.0253390	+	0.0296954i
$195$	−26.1848	−	19.9142i	−1.87513	−	1.42609i
$196$	7.31717	+	1.16575i	0.522655	+	0.0832675i
$197$	−14.0411	+	5.81603i	−1.00039	+	0.414375i	−0.821940	−	0.569574i	$-0.807108\pi$
$197$	−14.0411	+	5.81603i	−1.00039	+	0.414375i	−0.178450	+	0.983949i	$0.557108\pi$
$198$	−4.31500	−	12.9216i	−0.306654	−	0.918300i
$199$	−1.49055	+	1.49055i	−0.105662	+	0.105662i	−0.757961	−	0.652299i	$-0.773805\pi$
$199$	−1.49055	+	1.49055i	−0.105662	+	0.105662i	0.652299	+	0.757961i	$0.273805\pi$
$200$	14.8722	−	4.38331i	1.05163	−	0.309947i
$201$	−10.3287	−	5.90427i	−0.728529	−	0.416455i
$202$	−0.906623	−	0.462467i	−0.0637898	−	0.0325390i
$203$	−3.37528	−	0.444364i	−0.236898	−	0.0311882i
$204$	−7.65184	−	8.00888i	−0.535736	−	0.560734i
$205$	2.98555	+	22.6775i	0.208520	+	1.58386i
$206$	−5.53963	−	11.6277i	−0.385964	−	0.810138i
$207$	11.1948	−	19.7805i	0.778096	−	1.37484i
$208$	−4.31829	+	23.0653i	−0.299419	+	1.59929i
$209$	2.76298	−	1.59521i	0.191120	−	0.110343i
$210$	−4.82632	−	25.4938i	−0.333048	−	1.75924i
$211$	14.3747	−	11.0301i	0.989597	−	0.759345i	0.0189422	−	0.999821i	$-0.493970\pi$
$211$	14.3747	−	11.0301i	0.989597	−	0.759345i	0.970655	+	0.240476i	$0.0773035\pi$
$212$	−18.5638	−	19.5978i	−1.27497	−	1.34598i
$213$	2.70962	−	6.62189i	0.185660	−	0.453725i
$214$	0.238500	+	0.367624i	0.0163036	+	0.0251303i
$215$	−2.40631	−	2.40631i	−0.164109	−	0.164109i
$216$	2.46617	+	14.4885i	0.167801	+	0.985821i
$217$	−5.31860	+	5.31860i	−0.361050	+	0.361050i
$218$	10.3145	+	2.19732i	0.698589	+	0.148822i
$219$	−10.1630	−	4.15860i	−0.686749	−	0.281012i
$220$	−18.9863	−	8.47391i	−1.28005	−	0.571311i
$221$	11.4195	+	14.8821i	0.768157	+	1.00108i
$222$	−15.0753	+	22.1161i	−1.01179	+	1.48434i
$223$	−11.6777	−	20.2264i	−0.781997	−	1.35446i	−0.930776	−	0.365589i	$-0.880868\pi$
$223$	−11.6777	−	20.2264i	−0.781997	−	1.35446i	0.148779	−	0.988870i	$-0.452466\pi$
$224$	−14.7091	+	11.2336i	−0.982790	+	0.750580i
$225$	−14.1709	+	8.34464i	−0.944724	+	0.556309i
$226$	20.5834	+	7.29949i	1.36919	+	0.485555i
$227$	−1.72166	+	0.226661i	−0.114271	+	0.0150440i	−0.187445	−	0.982275i	$-0.560021\pi$
$227$	−1.72166	+	0.226661i	−0.114271	+	0.0150440i	0.0731739	+	0.997319i	$0.476687\pi$
$228$	−3.20911	+	1.24434i	−0.212528	+	0.0824086i
$229$	−2.44295	+	18.5560i	−0.161434	+	1.22622i	0.698424	+	0.715684i	$0.253885\pi$
$229$	−2.44295	+	18.5560i	−0.161434	+	1.22622i	−0.859859	+	0.510532i	$0.829448\pi$
$230$	−10.7043	−	32.9955i	−0.705821	−	2.17566i
$231$	−9.03047	+	15.7975i	−0.594161	+	1.03940i
$232$	2.28971	−	1.84900i	0.150327	−	0.121393i
$233$	−2.43002	−	2.43002i	−0.159196	−	0.159196i	0.623014	−	0.782210i	$-0.285908\pi$
$233$	−2.43002	−	2.43002i	−0.159196	−	0.159196i	−0.782210	+	0.623014i	$0.785908\pi$
$234$	−1.50475	−	24.8440i	−0.0983684	−	1.62410i
$235$	−7.64598	−	18.4590i	−0.498769	−	1.20413i
$236$	−0.398492	−	1.66651i	−0.0259396	−	0.108481i
$237$	−8.47911	+	11.1490i	−0.550777	+	0.724205i
$238$	−1.16752	+	14.7491i	−0.0756793	+	0.956042i
$239$	6.39630	+	3.69291i	0.413742	+	0.238874i	0.692396	−	0.721517i	$-0.256555\pi$
$239$	6.39630	+	3.69291i	0.413742	+	0.238874i	−0.278654	+	0.960392i	$0.589888\pi$
$240$	18.8419	+	12.1699i	1.21624	+	0.785561i
$241$	−11.9933	+	6.92431i	−0.772554	+	0.446034i	−0.833785	−	0.552089i	$-0.813831\pi$
$241$	−11.9933	+	6.92431i	−0.772554	+	0.446034i	0.0612310	+	0.998124i	$0.480497\pi$
$242$	−0.419435	−	0.880393i	−0.0269623	−	0.0565938i
$243$	−6.27327	−	14.2705i	−0.402431	−	0.915450i
$244$	10.1580	−	5.50341i	0.650302	−	0.352320i
$245$	−7.30164	+	9.51568i	−0.466484	+	0.607934i
$246$	−11.5302	+	12.9049i	−0.735138	+	0.822786i
$247$	5.63032	−	1.50864i	0.358249	−	0.0959924i
$248$	−0.161349	−	6.50034i	−0.0102457	−	0.412772i
$249$	−1.40745	−	2.41378i	−0.0891935	−	0.152967i
$250$	−0.459579	+	2.15733i	−0.0290663	+	0.136441i
$251$	1.73159	−	0.717250i	0.109297	−	0.0452724i	−0.327365	−	0.944898i	$-0.606161\pi$
$251$	1.73159	−	0.717250i	0.109297	−	0.0452724i	0.436662	+	0.899626i	$0.356161\pi$
$252$	12.2366	−	15.3505i	0.770831	−	0.966988i
$253$	−9.30958	+	22.4753i	−0.585288	+	1.41301i
$254$	−7.66030	+	1.41615i	−0.480650	+	0.0888573i
$255$	17.2996	−	4.71513i	1.08334	−	0.295273i
$256$	1.73030	−	15.9062i	0.108144	−	0.994135i
$257$	2.38358	−	4.12849i	0.148684	−	0.257528i	−0.782057	−	0.623206i	$-0.785830\pi$
$257$	2.38358	−	4.12849i	0.148684	−	0.257528i	0.930741	+	0.365678i	$0.119163\pi$
$258$	0.192151	−	2.56751i	0.0119628	−	0.159846i
$259$	35.4450	−	4.66642i	2.20244	−	0.289957i
$260$	−29.4992	−	23.9324i	−1.82946	−	1.48422i
$261$	−1.87896	+	2.49275i	−0.116305	+	0.154297i
$262$	−12.0078	−	10.8218i	−0.741845	−	0.668571i
$263$	12.2339	+	3.27806i	0.754373	+	0.202134i	0.615457	−	0.788171i	$-0.288972\pi$
$263$	12.2339	+	3.27806i	0.754373	+	0.202134i	0.138916	+	0.990304i	$0.455638\pi$
$264$	−4.51190	−	15.0696i	−0.277689	−	0.927470i
$265$	42.2087	−	11.3098i	2.59286	−	0.694754i
$266$	4.09536	+	2.08904i	0.251103	+	0.128087i
$267$	1.82986	−	4.47190i	0.111986	−	0.273676i
$268$	−11.7067	−	7.18854i	−0.715103	−	0.439110i
$269$	−21.8241	−	9.03984i	−1.33064	−	0.551169i	−0.399801	−	0.916602i	$-0.630921\pi$
$269$	−21.8241	−	9.03984i	−1.33064	−	0.551169i	−0.930838	+	0.365433i	$0.880921\pi$
$270$	−22.5234	−	7.66229i	−1.37073	−	0.466312i
$271$			29.6716i			1.80242i	0.433383	+	0.901210i	$0.357320\pi$
$271$			29.6716i			1.80242i	−0.433383	+	0.901210i	$0.642680\pi$
$272$	−8.54105	−	9.52055i	−0.517877	−	0.577268i
$273$	−23.4067	+	23.6086i	−1.41664	+	1.42886i
$274$	0.0566831	−	0.716066i	0.00342435	−	0.0432591i
$275$	13.9645	−	10.7153i	0.842089	−	0.646157i
$276$	13.6370	−	22.4236i	0.820852	−	1.34974i
$277$	8.95689	−	11.6728i	0.538167	−	0.701354i	−0.442559	−	0.896739i	$-0.645929\pi$
$277$	8.95689	−	11.6728i	0.538167	−	0.701354i	0.980726	+	0.195386i	$0.0625959\pi$
$278$	17.2880	−	0.898148i	1.03687	−	0.0538673i
$279$	1.84217	+	6.64620i	0.110288	+	0.397897i
$280$	−4.64651	−	29.5980i	−0.277682	−	1.76882i
$281$	−1.36751	−	0.366424i	−0.0815791	−	0.0218591i	0.217799	−	0.975994i	$-0.430112\pi$
$281$	−1.36751	−	0.366424i	−0.0815791	−	0.0218591i	−0.299378	+	0.954135i	$0.596779\pi$
$282$	6.81100	−	13.4952i	0.405589	−	0.803627i
$283$	0.475060	−	3.60844i	0.0282394	−	0.214499i	−0.971507	−	0.237010i	$-0.923833\pi$
$283$	0.475060	−	3.60844i	0.0282394	−	0.214499i	0.999747	+	0.0225105i	$0.00716592\pi$
$284$	3.36719	−	7.54436i	0.199806	−	0.447675i
$285$	0.703523	−	5.52709i	0.0416731	−	0.327397i
$286$	4.84284	+	26.1961i	0.286363	+	1.54901i
$287$	23.1152			1.36445
$288$	2.32133	+	16.8111i	0.136786	+	0.990601i
$289$	6.77560			0.398565
$290$	0.866068	+	4.68477i	0.0508573	+	0.275099i
$291$	−0.530046	−	0.403114i	−0.0310719	−	0.0236310i
$292$	−11.5787	−	5.16779i	−0.677593	−	0.302422i
$293$	2.88518	−	21.9151i	0.168554	−	1.28030i	−0.672805	−	0.739820i	$-0.734911\pi$
$293$	2.88518	−	21.9151i	0.168554	−	1.28030i	0.841359	−	0.540476i	$-0.181756\pi$
$294$	−9.06036	+	0.509726i	−0.528411	+	0.0297278i
$295$	2.67925	+	0.717902i	0.155992	+	0.0417979i
$296$	−18.2002	+	24.9787i	−1.05786	+	1.45186i
$297$	8.52784	+	14.3408i	0.494835	+	0.832136i
$298$	5.37980	−	0.279491i	0.311643	−	0.0161905i
$299$	−27.0570	+	35.2613i	−1.56475	+	2.03922i
$300$	−16.6574	+	9.11737i	−0.961715	+	0.526392i
$301$	−2.72838	+	2.09356i	−0.157261	+	0.120671i
$302$	1.79116	−	22.6273i	0.103070	−	1.30206i
$303$	1.20540	+	0.317445i	0.0692485	+	0.0182367i
$304$	−3.74882	+	1.31986i	−0.215010	+	0.0756993i
$305$			18.7018i			1.07086i
$306$	11.2423	+	7.59273i	0.642680	+	0.434048i
$307$	−3.09982	−	1.28399i	−0.176916	−	0.0732812i	0.292467	−	0.956276i	$-0.405524\pi$
$307$	−3.09982	−	1.28399i	−0.176916	−	0.0732812i	−0.469383	+	0.882994i	$0.655524\pi$
$308$	−10.9947	+	17.9052i	−0.626483	+	1.02024i
$309$	9.65657	+	12.4734i	0.549343	+	0.709587i
$310$	9.37642	+	4.78289i	0.532545	+	0.271650i
$311$	−21.5190	+	5.76600i	−1.22023	+	0.326960i	−0.810769	−	0.585367i	$-0.800951\pi$
$311$	−21.5190	+	5.76600i	−1.22023	+	0.326960i	−0.409463	+	0.912327i	$0.634284\pi$
$312$	−0.836524	−	28.7278i	−0.0473589	−	1.62639i
$313$	−10.9146	−	2.92455i	−0.616928	−	0.165305i	−0.0631970	−	0.998001i	$-0.520130\pi$
$313$	−10.9146	−	2.92455i	−0.616928	−	0.165305i	−0.553731	+	0.832696i	$0.686796\pi$
$314$	8.02028	+	7.22810i	0.452611	+	0.407905i
$315$	12.4126	+	29.2535i	0.699371	+	1.64825i
$316$	−10.1900	+	12.5602i	−0.573230	+	0.706566i
$317$	2.66607	−	0.350994i	0.149741	−	0.0197138i	−0.0552829	−	0.998471i	$-0.517606\pi$
$317$	2.66607	−	0.350994i	0.149741	−	0.0197138i	0.205024	+	0.978757i	$0.434273\pi$
$318$	27.3182	+	18.6212i	1.53193	+	1.04423i
$319$	1.67056	−	2.89349i	0.0935333	−	0.162004i
$320$	21.3051	+	14.7283i	1.19099	+	0.823338i
$321$	−0.381129	−	0.377870i	−0.0212726	−	0.0210906i
$322$	−34.4713	+	6.37267i	−1.92101	+	0.355135i
$323$	−1.21582	+	2.93524i	−0.0676498	+	0.163321i
$324$	−6.72314	−	16.6973i	−0.373508	−	0.927627i
$325$	29.7108	−	12.3066i	1.64806	−	0.682649i
$326$	−0.910413	+	4.27361i	−0.0504231	+	0.236693i
$327$	−12.9160	+	0.0554656i	−0.714258	+	0.00306725i
$328$	−13.7749	+	14.4762i	−0.760594	+	0.799313i
$329$	−19.5033	+	5.22590i	−1.07525	+	0.288113i
$330$	24.9279	+	5.19864i	1.37224	+	0.286175i
$331$	20.3459	−	26.5153i	1.11831	−	1.45741i	0.245473	−	0.969403i	$-0.421057\pi$
$331$	20.3459	−	26.5153i	1.11831	−	1.45741i	0.872839	−	0.488009i	$-0.162277\pi$
$332$	−1.53693	−	2.83681i	−0.0843498	−	0.155690i
$333$	12.2841	−	30.3921i	0.673165	−	1.66548i
$334$	1.04958	+	2.20308i	0.0574307	+	0.120547i
$335$	19.2588	−	11.1191i	1.05222	−	0.607501i
$336$	14.6788	−	17.2731i	0.800794	−	0.942325i
$337$	6.19798	+	3.57841i	0.337626	+	0.194928i	0.659222	−	0.751949i	$-0.270886\pi$
$337$	6.19798	+	3.57841i	0.337626	+	0.194928i	−0.321596	+	0.946877i	$0.604219\pi$
$338$	−2.38999	+	30.1923i	−0.129999	+	1.64225i
$339$	−26.5336	−	3.37736i	−1.44111	−	0.183433i
$340$	20.1369	−	4.81508i	1.09207	−	0.261134i
$341$	−2.82490	−	6.81991i	−0.152977	−	0.369319i
$342$	3.51659	−	2.32459i	0.190156	−	0.125699i
$343$	−7.62367	−	7.62367i	−0.411640	−	0.411640i
$344$	0.314794	−	2.95629i	0.0169726	−	0.159392i
$345$	21.4000	+	36.7010i	1.15214	+	1.97592i
$346$	6.15091	+	18.9599i	0.330675	+	1.01929i
$347$	−3.83083	+	29.0980i	−0.205649	+	1.56206i	0.507874	+	0.861431i	$0.330432\pi$
$347$	−3.83083	+	29.0980i	−0.205649	+	1.56206i	−0.713523	+	0.700631i	$0.752902\pi$
$348$	−2.25888	+	2.80888i	−0.121089	+	0.150572i
$349$	−29.5141	+	3.88561i	−1.57986	+	0.207992i	−0.868807	−	0.495151i	$-0.835113\pi$
$349$	−29.5141	+	3.88561i	−1.57986	+	0.207992i	−0.711049	+	0.703143i	$0.751780\pi$
$350$	23.9055	+	8.47763i	1.27781	+	0.453148i
$351$	8.26832	+	29.3405i	0.441330	+	1.56608i
$352$	−4.66133	−	17.5558i	−0.248450	−	0.935727i
$353$	7.49907	+	12.9888i	0.399135	+	0.691322i	0.993619	−	0.112785i	$-0.0359771\pi$
$353$	7.49907	+	12.9888i	0.399135	+	0.691322i	−0.594484	+	0.804107i	$0.702644\pi$
$354$	0.910732	+	1.89067i	0.0484049	+	0.100488i
$355$	8.14146	+	10.6102i	0.432104	+	0.563129i
$356$	2.27393	−	5.09487i	0.120518	−	0.270027i
$357$	−2.44231	−	17.9550i	−0.129261	−	0.950281i
$358$	−31.2895	−	6.66565i	−1.65370	−	0.352290i
$359$	−6.56704	+	6.56704i	−0.346595	+	0.346595i	−0.858840	−	0.512245i	$-0.828814\pi$
$359$	−6.56704	+	6.56704i	−0.346595	+	0.346595i	0.512245	+	0.858840i	$0.328814\pi$
$360$	−25.7174	−	9.65936i	−1.35542	−	0.509093i
$361$	−12.7370	−	12.7370i	−0.670366	−	0.670366i
$362$	−13.8812	−	21.3965i	−0.729580	−	1.12457i
$363$	0.731151	+	0.944429i	0.0383755	+	0.0495697i
$364$	−27.8698	+	26.3994i	−1.46078	+	1.38370i
$365$	16.2840	−	12.4951i	0.852341	−	0.654024i
$366$	−10.7240	+	9.23065i	−0.560555	+	0.482494i
$367$	−11.4275	+	6.59770i	−0.596513	+	0.344397i	−0.767669	−	0.640847i	$-0.778583\pi$
$367$	−11.4275	+	6.59770i	−0.596513	+	0.344397i	0.171156	+	0.985244i	$0.445250\pi$
$368$	16.5514	−	25.3857i	0.862800	−	1.32332i
$369$	10.4394	−	18.4456i	0.543453	−	0.960241i
$370$	−21.5179	−	45.1661i	−1.11866	−	2.34807i
$371$	−5.76404	−	43.7822i	−0.299254	−	2.27306i
$372$	1.88530	+	7.73733i	0.0977480	+	0.401162i
$373$	−15.2210	−	2.00389i	−0.788116	−	0.103757i	−0.274284	−	0.961649i	$-0.588441\pi$
$373$	−15.2210	−	2.00389i	−0.788116	−	0.103757i	−0.513831	+	0.857891i	$0.671774\pi$
$374$	−12.9346	−	6.59791i	−0.668832	−	0.341170i
$375$	−0.0116008	−	2.70144i	−0.000599065	−	0.139502i
$376$	8.34975	−	15.3284i	0.430605	−	0.790504i
$377$	4.31637	−	4.31637i	0.222304	−	0.222304i
$378$	−10.6481	+	21.5563i	−0.547680	+	1.10874i
$379$	27.7834	−	11.5083i	1.42714	−	0.591140i	0.470495	−	0.882403i	$-0.344075\pi$
$379$	27.7834	−	11.5083i	1.42714	−	0.591140i	0.956643	+	0.291263i	$0.0940754\pi$
$380$	1.01222	−	6.35350i	0.0519256	−	0.325928i
$381$	8.79887	−	3.68896i	0.450780	−	0.188991i
$382$	−10.8861	−	12.7578i	−0.556983	−	0.652744i
$383$	−4.98005	+	8.62570i	−0.254469	+	0.440752i	−0.964751	−	0.263164i	$-0.915234\pi$
$383$	−4.98005	+	8.62570i	−0.254469	+	0.440752i	0.710282	+	0.703917i	$0.248567\pi$
$384$	2.07002	+	19.4863i	0.105635	+	0.994405i
$385$	−17.0064	−	29.4560i	−0.866728	−	1.50122i
$386$	−5.90843	+	16.6608i	−0.300731	+	0.848014i
$387$	0.438429	+	3.12271i	0.0222866	+	0.158736i
$388$	−0.597138	−	0.484452i	−0.0303151	−	0.0245943i
$389$	6.46549	+	4.96114i	0.327813	+	0.251540i	0.759534	−	0.650467i	$-0.225427\pi$
$389$	6.46549	+	4.96114i	0.327813	+	0.251540i	−0.431721	+	0.902007i	$0.642094\pi$
$390$	41.5336	+	20.9619i	2.10313	+	1.06145i
$391$	−6.27000	−	23.3999i	−0.317087	−	1.18339i
$392$	−10.4753	+	0.260014i	−0.529084	+	0.0131327i
$393$	17.1876	+	9.82511i	0.867001	+	0.495611i
$394$	18.0311	−	11.6979i	0.908392	−	0.589330i
$395$	−10.0194	−	24.1889i	−0.504129	−	1.21707i
$396$	9.32265	+	16.8601i	0.468481	+	0.847253i
$397$	31.6589	+	13.1136i	1.58892	+	0.658150i	0.989794	−	0.142507i	$-0.0455164\pi$
$397$	31.6589	+	13.1136i	1.58892	+	0.658150i	0.599122	+	0.800658i	$0.295516\pi$
$398$	1.68963	−	2.45603i	0.0846933	−	0.123110i
$399$	−5.44499	−	1.43395i	−0.272590	−	0.0717872i
$400$	−19.5552	+	9.91912i	−0.977758	+	0.495956i
$401$	−30.2179	−	17.4463i	−1.50901	−	0.871227i	−0.999945	−	0.0104983i	$-0.996658\pi$
$401$	−30.2179	−	17.4463i	−1.50901	−	0.871227i	−0.509064	−	0.860729i	$-0.670008\pi$
$402$	15.8815	+	5.55539i	0.792097	+	0.277078i
$403$	−1.76036	−	13.3713i	−0.0876900	−	0.666072i
$404$	1.37969	+	0.410047i	0.0686421	+	0.0204006i
$405$	28.9498	+	3.30651i	1.43853	+	0.164302i
$406$	4.80807	−	0.249789i	0.238621	−	0.0123968i
$407$	−9.08099	+	33.8907i	−0.450128	+	1.67990i
$408$	12.7000	+	9.17035i	0.628744	+	0.454000i
$409$	1.52810	+	5.70295i	0.0755597	+	0.281993i	0.993360	−	0.115051i	$-0.0367030\pi$
$409$	1.52810	+	5.70295i	0.0755597	+	0.281993i	−0.917800	+	0.397043i	$0.870036\pi$
$410$	−9.98196	−	30.7689i	−0.492974	−	1.51957i
$411$	0.118574	+	0.871714i	0.00584881	+	0.0429985i
$412$	10.6930	+	14.7458i	0.526807	+	0.726475i
$413$	1.07270	−	2.58973i	0.0527842	−	0.127432i
$414$	−10.4828	+	30.3857i	−0.515201	+	1.49338i
$415$	5.22282			0.256378
$416$	0.0754111	−	33.1859i	0.00369733	−	1.62707i
$417$	−20.4558	+	5.57536i	−1.00172	+	0.273027i
$418$	−3.43223	+	2.92871i	−0.167876	+	0.143248i
$419$	16.5020	+	21.5058i	0.806175	+	1.05063i	0.997608	+	0.0691222i	$0.0220198\pi$
$419$	16.5020	+	21.5058i	0.806175	+	1.05063i	−0.191433	+	0.981506i	$0.561313\pi$
$420$	13.2659	+	34.2121i	0.647308	+	1.66938i
$421$	0.603364	+	0.462978i	0.0294062	+	0.0225642i	0.623360	−	0.781935i	$-0.285767\pi$
$421$	0.603364	+	0.462978i	0.0294062	+	0.0225642i	−0.593954	+	0.804499i	$0.702434\pi$
$422$	−17.1545	+	19.0346i	−0.835068	+	0.926590i
$423$	−4.63799	+	17.9236i	−0.225507	+	0.871473i
$424$	30.8541	+	22.4812i	1.49841	+	1.09178i
$425$	−4.53664	+	16.9310i	−0.220059	+	0.821273i
$426$	−2.06572	+	9.90534i	−0.100085	+	0.479915i
$427$	18.7380	+	2.46691i	0.906796	+	0.119382i
$428$	−0.426182	−	0.449921i	−0.0206003	−	0.0217477i
$429$	−12.6152	−	30.0897i	−0.609067	−	1.45274i
$430$	3.96497	+	2.72770i	0.191208	+	0.131541i
$431$			28.0930i			1.35319i	0.736355	+	0.676596i	$0.236546\pi$
$431$			28.0930i			1.35319i	−0.736355	+	0.676596i	$0.763454\pi$
$432$	−7.15441	−	19.5145i	−0.344217	−	0.938890i
$433$		−	28.2028i		−	1.35534i	−0.735367	−	0.677669i	$-0.762990\pi$
$433$		−	28.2028i		−	1.35534i	0.735367	−	0.677669i	$-0.237010\pi$
$434$	6.02896	−	8.76366i	0.289399	−	0.420669i
$435$	−2.25603	−	5.38107i	−0.108169	−	0.258003i
$436$	−14.9088	−	0.403962i	−0.714003	−	0.0193463i
$437$	−7.46328	−	0.982560i	−0.357017	−	0.0470022i
$438$	15.2022	+	3.17037i	0.726391	+	0.151486i
$439$	−2.79407	+	10.4276i	−0.133354	+	0.497682i	−0.999999	−	0.00124189i	$-0.999605\pi$
$439$	−2.79407	+	10.4276i	−0.133354	+	0.497682i	0.866646	+	0.498924i	$0.166271\pi$
$440$	28.5818	+	6.90311i	1.36258	+	0.329093i
$441$	10.7104	−	2.96866i	0.510018	−	0.141365i
$442$	−19.7065	−	17.7600i	−0.937343	−	0.844759i
$443$	5.71962	+	4.38882i	0.271747	+	0.208519i	0.735641	−	0.677372i	$-0.236881\pi$
$443$	5.71962	+	4.38882i	0.271747	+	0.208519i	−0.463893	+	0.885891i	$0.653548\pi$
$444$	15.2787	−	34.6315i	0.725093	−	1.64354i
$445$	5.49810	+	7.16526i	0.260635	+	0.339666i
$446$	21.4396	+	25.1256i	1.01519	+	1.18973i
$447$	−6.36556	+	1.73498i	−0.301081	+	0.0820616i
$448$	17.5671	−	19.4036i	0.829968	−	0.916733i
$449$	12.9753			0.612344			0.306172	−	0.951976i	$-0.400952\pi$
$449$	12.9753			0.612344			0.306172	+	0.951976i	$0.400952\pi$
$450$	17.5614	−	15.2476i	0.827852	−	0.718780i
$451$	−8.68135	+	20.9586i	−0.408789	+	0.986904i
$452$	−30.5009	−	4.85929i	−1.43464	−	0.228562i
$453$	3.74687	+	27.5457i	0.176043	+	1.29421i
$454$	2.33596	−	0.757825i	0.109632	−	0.0355665i
$455$	−16.0835	−	60.0245i	−0.754007	−	2.81399i
$456$	4.14284	−	2.55547i	0.194006	−	0.119671i
$457$	−4.64656	+	17.3412i	−0.217357	+	0.811187i	0.767967	+	0.640490i	$0.221269\pi$
$457$	−4.64656	+	17.3412i	−0.217357	+	0.811187i	−0.985324	+	0.170697i	$0.945398\pi$
$458$	−1.37325	−	26.4330i	−0.0641676	−	1.23513i
$459$	−15.4309	−	6.16001i	−0.720253	−	0.287525i
$460$	23.3687	+	43.1332i	1.08957	+	2.01110i
$461$	1.43653	+	10.9115i	0.0669059	+	0.508201i	0.991783	+	0.127934i	$0.0408345\pi$
$461$	1.43653	+	10.9115i	0.0669059	+	0.508201i	−0.924877	+	0.380267i	$0.875832\pi$
$462$	8.49687	−	24.2904i	0.395310	−	1.13009i
$463$	−16.6538	−	9.61509i	−0.773969	−	0.446851i	0.0603199	−	0.998179i	$-0.480788\pi$
$463$	−16.6538	−	9.61509i	−0.773969	−	0.446851i	−0.834288	+	0.551328i	$0.814121\pi$
$464$	−2.70882	+	3.15997i	−0.125754	+	0.146698i
$465$	−12.4664	−	3.28305i	−0.578116	−	0.152248i
$466$	4.00404	+	2.75458i	0.185484	+	0.127604i
$467$	36.6428	+	15.1780i	1.69563	+	0.702352i	0.999873	−	0.0159280i	$-0.00507026\pi$
$467$	36.6428	+	15.1780i	1.69563	+	0.702352i	0.695754	+	0.718280i	$0.255070\pi$
$468$	8.47966	+	34.1624i	0.391973	+	1.57916i
$469$	−8.60022	−	20.7628i	−0.397121	−	0.958736i
$470$	15.3785	+	23.7044i	0.709356	+	1.09340i
$471$	−11.4800	−	6.56241i	−0.528970	−	0.302380i
$472$	0.982602	+	2.21508i	0.0452279	+	0.101957i
$473$	−0.873543	−	3.26011i	−0.0401656	−	0.149900i
$474$	8.92519	−	17.6842i	0.409948	−	0.812263i
$475$	4.32111	+	3.31570i	0.198266	+	0.152135i
$476$	−2.16820	−	20.8110i	−0.0993792	−	0.953869i
$477$	−37.5408	−	15.1735i	−1.71888	−	0.694748i
$478$	−9.84442	−	3.49113i	−0.450273	−	0.159680i
$479$	−10.4848	−	18.1603i	−0.479065	−	0.829764i	0.520647	−	0.853772i	$-0.325691\pi$
$479$	−10.4848	−	18.1603i	−0.479065	−	0.829764i	−0.999712	+	0.0240077i	$0.992357\pi$
$480$	−29.3312	−	12.0800i	−1.33878	−	0.551373i
$481$	−32.0515	+	55.5149i	−1.46142	+	2.53126i
$482$	14.8983	−	12.7126i	0.678597	−	0.579044i
$483$	39.5949	−	16.6003i	1.80163	−	0.755339i
$484$	0.809626	+	1.11649i	0.0368012	+	0.0507494i
$485$	1.14999	−	0.476341i	0.0522183	−	0.0216295i
$486$	12.3927	+	18.2324i	0.562144	+	0.827040i
$487$	−21.4292	+	21.4292i	−0.971049	+	0.971049i	−0.999593	−	0.0285433i	$-0.990913\pi$
$487$	−21.4292	+	21.4292i	−0.971049	+	0.971049i	0.0285433	+	0.999593i	$0.490913\pi$
$488$	−12.7114	+	10.2648i	−0.575418	+	0.464667i
$489$	−0.0229809	−	5.35148i	−0.00103923	−	0.242002i
$490$	7.70765	−	15.1101i	0.348196	−	0.682606i
$491$	13.1758	+	1.73463i	0.594617	+	0.0782828i	0.421828	−	0.906676i	$-0.361389\pi$
$491$	13.1758	+	1.73463i	0.594617	+	0.0782828i	0.172789	+	0.984959i	$0.444722\pi$
$492$	12.7168	−	20.9105i	0.573316	−	0.942716i
$493$	0.434280	+	3.29868i	0.0195590	+	0.148565i
$494$	−7.44195	+	3.54548i	−0.334829	+	0.159519i
$495$	−31.1861	+	0.267851i	−1.40171	+	0.0120390i
$496$	1.89554	+	8.99821i	0.0851122	+	0.404032i
$497$	11.7046	−	6.75766i	0.525023	−	0.303122i
$498$	2.57782	+	2.99488i	0.115515	+	0.134204i
$499$	−18.9077	+	14.5084i	−0.846427	+	0.649486i	−0.938123	−	0.346301i	$-0.887438\pi$
$499$	−18.9077	+	14.5084i	−0.846427	+	0.649486i	0.0916968	+	0.995787i	$0.470771\pi$
$500$	0.0844903	−	3.11824i	0.00377852	−	0.139452i
$501$	−1.82962	−	2.36332i	−0.0817412	−	0.105585i
$502$	−2.22364	+	1.44262i	−0.0992461	+	0.0643871i
$503$	13.9955	+	13.9955i	0.624028	+	0.624028i	0.946559	−	0.322531i	$-0.104534\pi$
$503$	13.9955	+	13.9955i	0.624028	+	0.624028i	−0.322531	+	0.946559i	$0.604534\pi$
$504$	−13.0704	+	24.4930i	−0.582200	+	1.09100i
$505$	−1.64753	+	1.64753i	−0.0733142	+	0.0733142i
$506$	7.16823	−	33.6487i	0.318667	−	1.49587i
$507$	−4.99956	−	36.7551i	−0.222038	−	1.63235i
$508$	10.2887	−	3.93874i	0.456488	−	0.174753i
$509$	17.9211	+	23.3552i	0.794338	+	1.03520i	0.998417	+	0.0562475i	$0.0179136\pi$
$509$	17.9211	+	23.3552i	0.794338	+	1.03520i	−0.204078	+	0.978955i	$0.565420\pi$
$510$	−22.8455	+	11.0046i	−1.01161	+	0.487293i
$511$	−10.3713	−	17.9637i	−0.458800	−	0.794665i
$512$	1.68304	+	22.5647i	0.0743808	+	0.997230i
$513$	−3.60337	+	3.69743i	−0.159092	+	0.163245i
$514$	−2.25334	+	6.35407i	−0.0993908	+	0.280266i
$515$	−29.2335	+	3.84866i	−1.28818	+	0.169592i
$516$	0.392862	+	3.61991i	0.0172948	+	0.159358i
$517$	2.58650	−	19.6464i	0.113754	−	0.864049i
$518$	−48.0919	+	15.6018i	−2.11304	+	0.685505i
$519$	−12.2969	−	21.0892i	−0.539773	−	0.925711i
$520$	47.1757	+	25.6977i	2.06879	+	1.12692i
$521$	24.3784	+	24.3784i	1.06804	+	1.06804i	0.997510	+	0.0705269i	$0.0224681\pi$
$521$	24.3784	+	24.3784i	1.06804	+	1.06804i	0.0705269	+	0.997510i	$0.477532\pi$
$522$	1.97212	−	3.94959i	0.0863172	−	0.172869i
$523$	−3.69577	−	8.92238i	−0.161605	−	0.390148i	0.822248	−	0.569130i	$-0.192720\pi$
$523$	−3.69577	−	8.92238i	−0.161605	−	0.390148i	−0.983852	+	0.178981i	$0.942720\pi$
$524$	19.4808	+	11.9622i	0.851022	+	0.522572i
$525$	−30.8161	−	3.92246i	−1.34492	−	0.171190i
$526$	−17.8558	−	1.41345i	−0.778549	−	0.0616292i
$527$	6.36611	+	3.67548i	0.277312	+	0.160106i
$528$	10.1487	+	19.7966i	0.441665	+	0.861536i
$529$	29.7904	−	17.1995i	1.29524	−	0.747804i
$530$	−55.7899	+	26.5793i	−2.42336	+	1.15453i
$531$	−1.58212	−	2.02559i	−0.0686580	−	0.0879032i
$532$	−6.23228	−	1.85225i	−0.270204	−	0.0803051i
$533$	−25.2311	+	32.8818i	−1.09288	+	1.42427i
$534$	−1.39503	+	6.68929i	−0.0603687	+	0.289474i
$535$	0.969014	−	0.259647i	0.0418941	−	0.0112255i
$536$	18.1281	+	6.98708i	0.783013	+	0.301796i
$537$	39.1812	−	0.168256i	1.69079	−	0.00726080i
$538$	32.6737	+	6.96053i	1.40866	+	0.300090i
$539$	−10.9903	+	4.55234i	−0.473386	+	0.196083i
$540$	33.2920	+	4.86506i	1.43266	+	0.209359i
$541$	14.1287	−	34.1097i	0.607440	−	1.46649i	−0.258334	−	0.966056i	$-0.583174\pi$
$541$	14.1287	−	34.1097i	0.607440	−	1.46649i	0.865774	−	0.500434i	$-0.166826\pi$
$542$	−7.62820	−	41.2628i	−0.327659	−	1.77239i
$543$	22.1825	+	21.9928i	0.951941	+	0.943801i
$544$	14.3252	+	11.0439i	0.614189	+	0.473505i
$545$	12.0715	−	20.9084i	0.517084	−	0.895616i
$546$	26.4810	−	38.8489i	1.13328	−	1.66258i
$547$	−29.2110	+	3.84570i	−1.24897	+	0.164430i	−0.725865	−	0.687837i	$-0.758560\pi$
$547$	−29.2110	+	3.84570i	−1.24897	+	0.164430i	−0.523107	+	0.852267i	$0.675227\pi$
$548$	0.105266	+	1.01037i	0.00449673	+	0.0431608i
$549$	10.4311	−	13.8386i	0.445189	−	0.590617i
$550$	−16.6649	+	18.4913i	−0.710594	+	0.788473i
$551$	0.998634	+	0.267583i	0.0425432	+	0.0113994i
$552$	−13.1995	+	34.6893i	−0.561807	+	1.47648i
$553$	−25.5573	+	6.84806i	−1.08681	+	0.291209i
$554$	−9.45495	+	18.5355i	−0.401702	+	0.787500i
$555$	37.5096	+	48.4513i	1.59220	+	2.05664i
$556$	−23.8107	+	5.69355i	−1.00980	+	0.241460i
$557$	−5.54466	−	2.29667i	−0.234935	−	0.0973132i	0.262110	−	0.965038i	$-0.415582\pi$
$557$	−5.54466	−	2.29667i	−0.234935	−	0.0973132i	−0.497045	+	0.867725i	$0.665582\pi$
$558$	−4.27046	−	8.76893i	−0.180783	−	0.371218i
$559$		−	6.16637i		−	0.260810i
$560$	14.0710	+	39.9659i	0.594607	+	1.68887i
$561$	17.1972	+	4.52891i	0.726065	+	0.191211i
$562$	1.99594	+	0.157996i	0.0841935	+	0.00666468i
$563$	−32.0609	+	24.6012i	−1.35120	+	1.03682i	−0.356472	+	0.934306i	$0.616021\pi$
$563$	−32.0609	+	24.6012i	−1.35120	+	1.03682i	−0.994732	+	0.102510i	$0.967313\pi$
$564$	−6.00226	+	20.5181i	−0.252741	+	0.863968i
$565$	30.4361	−	39.6651i	1.28046	−	1.66872i
$566$	0.267044	+	5.14021i	0.0112247	+	0.216059i
$567$	7.13159	−	28.5696i	0.299498	−	1.19981i
$568$	−2.74301	+	11.3572i	−0.115094	+	0.476539i
$569$	0.913900	+	0.244879i	0.0383127	+	0.0102659i	0.277924	−	0.960603i	$-0.410353\pi$
$569$	0.913900	+	0.244879i	0.0383127	+	0.0102659i	−0.239612	+	0.970869i	$0.577020\pi$
$570$	0.442596	+	7.86711i	0.0185383	+	0.329517i
$571$	1.85721	−	14.1069i	0.0777216	−	0.590354i	−0.907624	−	0.419784i	$-0.862106\pi$
$571$	1.85721	−	14.1069i	0.0777216	−	0.590354i	0.985346	−	0.170570i	$-0.0545609\pi$
$572$	−13.4694	−	35.1845i	−0.563183	−	1.47114i
$573$	16.3492	+	12.4340i	0.682999	+	0.519439i
$574$	−32.1451	+	5.94263i	−1.34171	+	0.248041i
$575$	−41.5309			−1.73196
$576$	−7.55008	−	22.7815i	−0.314586	−	0.949229i
$577$	42.7863			1.78122			0.890608	−	0.454771i	$-0.150279\pi$
$577$	42.7863			1.78122			0.890608	+	0.454771i	$0.150279\pi$
$578$	−9.42248	+	1.74193i	−0.391924	+	0.0724545i
$579$	2.73374	−	21.4771i	0.113610	−	0.892558i
$580$	−2.40879	−	6.29221i	−0.100020	−	0.261270i
$581$	0.688928	−	5.23293i	0.0285815	−	0.217098i
$582$	0.840744	+	0.424322i	0.0348500	+	0.0175887i
$583$	41.8623	+	11.2170i	1.73376	+	0.464560i
$584$	17.4305	+	4.20984i	0.721280	+	0.174204i
$585$	−55.1625	−	14.2741i	−2.28069	−	0.590163i
$586$	1.62184	+	31.2180i	0.0669976	+	1.28960i
$587$	3.17863	−	4.14248i	0.131196	−	0.170978i	−0.723136	−	0.690706i	$-0.757300\pi$
$587$	3.17863	−	4.14248i	0.131196	−	0.170978i	0.854332	+	0.519728i	$0.173967\pi$
$588$	12.4687	−	3.03816i	0.514202	−	0.125292i
$589$	1.81218	−	1.39053i	0.0746694	−	0.0572959i
$590$	−3.91045	−	0.309548i	−0.160991	−	0.0127439i
$591$	−18.5336	+	18.6935i	−0.762370	+	0.768946i
$592$	18.8884	−	39.4157i	0.776307	−	1.61998i
$593$			3.77979i			0.155217i	0.996984	+	0.0776086i	$0.0247285\pi$
$593$			3.77979i			0.155217i	−0.996984	+	0.0776086i	$0.975272\pi$
$594$	−15.5461	−	17.7506i	−0.637863	−	0.728315i
$595$	31.2924	+	12.9617i	1.28286	+	0.531379i
$596$	−7.40956	+	1.77176i	−0.303507	+	0.0725739i
$597$	−1.38271	+	3.37913i	−0.0565905	+	0.138298i
$598$	28.5615	−	55.9922i	1.16797	−	2.28969i
$599$	−31.7717	+	8.51319i	−1.29815	+	0.347839i	−0.840752	−	0.541420i	$-0.817887\pi$
$599$	−31.7717	+	8.51319i	−1.29815	+	0.347839i	−0.457402	+	0.889260i	$0.651220\pi$
$600$	20.8206	−	16.9615i	0.849998	−	0.692450i
$601$	−24.7383	−	6.62862i	−1.00910	−	0.270387i	−0.283846	−	0.958870i	$-0.591610\pi$
$601$	−24.7383	−	6.62862i	−1.00910	−	0.270387i	−0.725252	+	0.688483i	$0.758277\pi$
$602$	3.25599	−	3.61284i	0.132704	−	0.147248i
$603$	−20.4525	−	2.51412i	−0.832891	−	0.102383i
$604$	3.32634	+	31.9272i	0.135347	+	1.29910i
$605$	−2.21343	+	0.291403i	−0.0899885	+	0.0118472i
$606$	−1.75790	−	0.131560i	−0.0714098	−	0.00534426i
$607$	12.5507	−	21.7385i	0.509419	−	0.882339i	−0.490522	−	0.871429i	$-0.663194\pi$
$607$	12.5507	−	21.7385i	0.509419	−	0.882339i	0.999940	−	0.0109103i	$-0.00347291\pi$
$608$	4.87397	−	2.79924i	0.197666	−	0.113524i
$609$	−5.68907	+	1.55060i	−0.230533	+	0.0628334i
$610$	−4.80801	−	26.0077i	−0.194671	−	1.05302i
$611$	13.8547	−	33.4482i	0.560500	−	1.35317i
$612$	−17.5861	−	7.66857i	−0.710877	−	0.309983i
$613$	−15.0232	+	6.22283i	−0.606783	+	0.251338i	−0.664852	−	0.746975i	$-0.731505\pi$
$613$	−15.0232	+	6.22283i	−0.606783	+	0.251338i	0.0580695	+	0.998313i	$0.481505\pi$
$614$	4.64087	+	0.988652i	0.187290	+	0.0398987i
$615$	19.9559	+	34.2244i	0.804699	+	1.38006i
$616$	10.6866	−	27.7265i	0.430576	−	1.11713i
$617$	15.4595	−	4.14237i	0.622377	−	0.166765i	0.0661689	−	0.997808i	$-0.478922\pi$
$617$	15.4595	−	4.14237i	0.622377	−	0.166765i	0.556208	+	0.831043i	$0.312256\pi$
$618$	−16.6357	−	14.8635i	−0.669184	−	0.597900i
$619$	13.1526	−	17.1408i	0.528646	−	0.688945i	−0.450343	−	0.892856i	$-0.648698\pi$
$619$	13.1526	−	17.1408i	0.528646	−	0.688945i	0.978990	+	0.203910i	$0.0653650\pi$
$620$	−14.2689	−	4.24076i	−0.573054	−	0.170313i
$621$	4.63521	−	39.0933i	0.186005	−	1.56876i
$622$	28.4430	−	13.5508i	1.14046	−	0.543336i
$623$	7.90437	−	4.56359i	0.316682	−	0.182836i
$624$	8.54887	+	39.7352i	0.342229	+	1.59068i
$625$	−19.3636	−	11.1796i	−0.774544	−	0.447183i
$626$	15.9302	+	1.26102i	0.636699	+	0.0504005i
$627$	3.34514	−	4.39845i	0.133592	−	0.175657i
$628$	−13.0117	−	7.98983i	−0.519222	−	0.318829i
$629$	−13.3708	−	32.2799i	−0.533128	−	1.28709i
$630$	−24.7823	−	37.4902i	−0.987350	−	1.49365i
$631$	8.06758	+	8.06758i	0.321165	+	0.321165i	0.849214	−	0.528049i	$-0.177076\pi$
$631$	8.06758	+	8.06758i	0.321165	+	0.321165i	−0.528049	+	0.849214i	$0.677076\pi$
$632$	10.9416	−	20.0865i	0.435233	−	0.799000i
$633$	15.5746	−	27.2456i	0.619035	−	1.08291i
$634$	−3.61733	+	1.17352i	−0.143662	+	0.0466066i
$635$	−2.32778	+	17.6813i	−0.0923753	+	0.701660i
$636$	−42.7773	−	18.8724i	−1.69623	−	0.748340i
$637$	−21.5479	+	2.83683i	−0.853759	+	0.112399i
$638$	−1.57928	+	4.45331i	−0.0625243	+	0.176308i
$639$	−0.106433	−	12.3921i	−0.00421042	−	0.490222i
$640$	−33.4144	−	15.0046i	−1.32082	−	0.593110i
$641$	−2.19241	−	3.79736i	−0.0865949	−	0.149987i	0.819475	−	0.573115i	$-0.194265\pi$
$641$	−2.19241	−	3.79736i	−0.0865949	−	0.149987i	−0.906070	+	0.423128i	$0.860932\pi$
$642$	0.627163	+	0.427501i	0.0247521	+	0.0168721i
$643$	−10.1958	−	13.2874i	−0.402083	−	0.524005i	0.547800	−	0.836609i	$-0.315465\pi$
$643$	−10.1958	−	13.2874i	−0.402083	−	0.524005i	−0.949884	+	0.312604i	$0.898799\pi$
$644$	46.2992	−	17.7243i	1.82444	−	0.698436i
$645$	−5.45520	−	2.23222i	−0.214798	−	0.0878936i
$646$	0.936159	−	4.39446i	0.0368327	−	0.172898i
$647$	9.86054	−	9.86054i	0.387658	−	0.387658i	−0.486193	−	0.873851i	$-0.661615\pi$
$647$	9.86054	−	9.86054i	0.387658	−	0.387658i	0.873851	+	0.486193i	$0.161615\pi$
$648$	13.6422	+	21.4916i	0.535916	+	0.844271i
$649$	1.94525	+	1.94525i	0.0763577	+	0.0763577i
$650$	−38.1535	+	24.7525i	−1.49650	+	0.970873i
$651$	−4.93381	+	12.0575i	−0.193371	+	0.472570i
$652$	0.167373	−	6.17714i	0.00655483	−	0.241916i
$653$	−15.9077	+	12.2064i	−0.622516	+	0.477673i	−0.871211	−	0.490908i	$-0.836665\pi$
$653$	−15.9077	+	12.2064i	−0.622516	+	0.477673i	0.248695	+	0.968582i	$0.419998\pi$
$654$	17.9474	−	3.39769i	0.701800	−	0.132860i
$655$	−32.0480	+	18.5029i	−1.25222	+	0.722968i
$656$	15.4345	−	23.6727i	0.602615	−	0.924262i
$657$	−19.0187	+	0.163348i	−0.741991	+	0.00637281i
$658$	25.7788	−	12.2815i	1.00496	−	0.478781i
$659$	−1.12518	−	8.54661i	−0.0438309	−	0.332929i	−0.999286	−	0.0377912i	$-0.987968\pi$
$659$	−1.12518	−	8.54661i	−0.0438309	−	0.332929i	0.955455	−	0.295138i	$-0.0953655\pi$
$660$	−36.0025	−	0.820805i	−1.40140	−	0.0319498i
$661$	−33.5892	−	4.42211i	−1.30647	−	0.172000i	−0.555046	−	0.831820i	$-0.687299\pi$
$661$	−33.5892	−	4.42211i	−1.30647	−	0.172000i	−0.751424	+	0.659820i	$0.770633\pi$
$662$	−21.4772	+	42.1042i	−0.834737	+	1.63642i
$663$	28.2073	+	16.1244i	1.09548	+	0.626219i
$664$	2.86664	+	3.54989i	0.111247	+	0.137762i
$665$	7.44216	−	7.44216i	0.288594	−	0.288594i
$666$	−9.26943	+	45.4229i	−0.359183	+	1.76010i
$667$	−7.28318	+	3.01679i	−0.282006	+	0.116811i
$668$	−2.02599	−	2.79387i	−0.0783879	−	0.108098i
$669$	−32.1988	−	24.4880i	−1.24488	−	0.946763i
$670$	−23.9237	+	20.4140i	−0.924253	+	0.788660i
$671$	−9.27418	+	16.0634i	−0.358026	+	0.620119i
$672$	−15.9724	+	27.7946i	−0.616147	+	1.07220i
$673$	18.8856	+	32.7108i	0.727987	+	1.26091i	0.957733	+	0.287660i	$0.0928772\pi$
$673$	18.8856	+	32.7108i	0.727987	+	1.26091i	−0.229746	+	0.973251i	$0.573790\pi$
$674$	−9.53919	−	3.38288i	−0.367436	−	0.130304i
$675$	−17.0474	+	22.8194i	−0.656155	+	0.878319i
$676$	−4.43844	−	42.6014i	−0.170709	−	1.63851i
$677$	−23.9374	−	18.3678i	−0.919988	−	0.705931i	0.0359958	−	0.999352i	$-0.488540\pi$
$677$	−23.9374	−	18.3678i	−0.919988	−	0.705931i	−0.955983	+	0.293421i	$0.905206\pi$
$678$	37.7672	−	2.12474i	1.45044	−	0.0816002i
$679$	−0.325571	−	1.21505i	−0.0124943	−	0.0466292i
$680$	−26.7654	+	11.8730i	−1.02641	+	0.455310i
$681$	−2.59829	+	1.51504i	−0.0995669	+	0.0580565i
$682$	5.68176	+	8.75785i	0.217566	+	0.335355i
$683$	−7.16855	−	17.3064i	−0.274297	−	0.662211i	0.725361	−	0.688369i	$-0.241673\pi$
$683$	−7.16855	−	17.3064i	−0.274297	−	0.662211i	−0.999658	+	0.0261574i	$0.991673\pi$
$684$	−4.29273	+	4.13676i	−0.164136	+	0.158173i
$685$	−1.51924	−	0.629290i	−0.0580472	−	0.0240439i
$686$	12.5618	+	8.64190i	0.479612	+	0.329949i
$687$	8.52461	+	31.2764i	0.325234	+	1.19327i
$688$	0.322257	+	4.19209i	0.0122860	+	0.159822i
$689$	68.5728	+	39.5905i	2.61242	+	1.50828i
$690$	−39.1953	−	45.5366i	−1.49214	−	1.73355i
$691$	1.65542	+	12.5742i	0.0629753	+	0.478345i	0.993652	+	0.112501i	$0.0358862\pi$
$691$	1.65542	+	12.5742i	0.0629753	+	0.478345i	−0.930676	+	0.365844i	$0.880780\pi$
$692$	−13.4281	−	24.7852i	−0.510460	−	0.942192i
$693$	−3.84530	+	31.2817i	−0.146071	+	1.18829i
$694$	−2.15341	−	41.4500i	−0.0817424	−	1.57342i
$695$	10.2572	−	38.2803i	0.389077	−	1.45206i
$696$	2.41919	−	4.48690i	0.0916990	−	0.170075i
$697$	−5.84689	−	21.8209i	−0.221467	−	0.826524i
$698$	40.0449	−	12.9913i	1.51572	−	0.491726i
$699$	−5.50896	−	2.25422i	−0.208368	−	0.0852623i
$700$	−35.4237	−	5.64358i	−1.33889	−	0.213307i
$701$	−0.135361	+	0.326791i	−0.00511253	+	0.0123427i	−0.926415	−	0.376504i	$-0.877126\pi$
$701$	−0.135361	+	0.326791i	−0.00511253	+	0.0123427i	0.921303	+	0.388846i	$0.127126\pi$
$702$	−19.0414	−	38.6767i	−0.718673	−	1.45976i
$703$	−10.8569			−0.409477
$704$	10.9957	+	23.2156i	0.414414	+	0.874970i
$705$	−24.5752	−	24.3650i	−0.925554	−	0.917639i
$706$	−13.7678	−	16.1349i	−0.518159	−	0.607245i
$707$	1.43340	+	1.86804i	0.0539084	+	0.0702549i
$708$	−1.75258	−	2.39512i	−0.0658659	−	0.0900143i
$709$	−20.9866	−	16.1036i	−0.788169	−	0.604783i	0.134262	−	0.990946i	$-0.457134\pi$
$709$	−20.9866	−	16.1036i	−0.788169	−	0.604783i	−0.922431	+	0.386163i	$0.873800\pi$
$710$	−14.0497	−	12.6619i	−0.527274	−	0.475194i
$711$	−6.07766	+	23.4872i	−0.227930	+	0.880838i
$712$	−1.85241	+	7.66977i	−0.0694221	+	0.287437i
$713$	−4.50789	+	16.8237i	−0.168822	+	0.630051i
$714$	8.01242	+	24.3413i	0.299857	+	0.910949i
$715$	60.4650	+	7.96037i	2.26126	+	0.297701i
$716$	45.2263	+	1.22543i	1.69019	+	0.0457965i
$717$	12.6902	+	1.61529i	0.473925	+	0.0603241i
$718$	7.44414	−	10.8208i	0.277813	−	0.403827i
$719$		−	18.7851i		−	0.700565i	−0.936644	−	0.350282i	$-0.886086\pi$
$719$		−	18.7851i		−	0.700565i	0.936644	−	0.350282i	$-0.113914\pi$
$720$	38.2471	+	6.82117i	1.42539	+	0.254210i
$721$			29.7977i			1.10973i
$722$	20.9872	+	14.4381i	0.781061	+	0.537331i
$723$	−14.5202	+	19.0923i	−0.540013	+	0.710051i
$724$	24.8047	+	26.1863i	0.921858	+	0.973206i
$725$	5.65511	+	0.744509i	0.210026	+	0.0276504i
$726$	−1.25958	−	1.12540i	−0.0467472	−	0.0417675i
$727$	1.69012	−	6.30762i	0.0626831	−	0.233937i	−0.927476	−	0.373883i	$-0.878026\pi$
$727$	1.69012	−	6.30762i	0.0626831	−	0.233937i	0.990159	+	0.139946i	$0.0446929\pi$
$728$	31.9702	−	43.8773i	1.18489	−	1.62620i
$729$	−19.5774	−	18.5937i	−0.725089	−	0.688655i
$730$	−19.4329	+	21.5627i	−0.719245	+	0.798073i
$731$	2.66646	+	2.04605i	0.0986226	+	0.0756758i
$732$	12.5403	−	15.5936i	0.463503	−	0.576357i
$733$	15.7391	+	20.5116i	0.581337	+	0.757613i	0.987745	−	0.156079i	$-0.0498853\pi$
$733$	15.7391	+	20.5116i	0.581337	+	0.757613i	−0.406407	+	0.913692i	$0.633219\pi$
$734$	14.1955	−	12.1130i	0.523966	−	0.447098i
$735$	−5.29065	+	20.0897i	−0.195149	+	0.741019i
$736$	−16.4908	+	39.5578i	−0.607859	+	1.45812i
$737$	22.0557			0.812432
$738$	−9.77539	+	28.3353i	−0.359837	+	1.04303i
$739$	−12.9826	+	31.3427i	−0.477572	+	1.15296i	0.483172	+	0.875525i	$0.339485\pi$
$739$	−12.9826	+	31.3427i	−0.477572	+	1.15296i	−0.960744	+	0.277436i	$0.910515\pi$
$740$	41.5356	+	57.2782i	1.52688	+	2.10559i
$741$	7.98324	−	6.18040i	0.293272	−	0.227043i
$742$	19.2716	+	59.4038i	0.707484	+	2.18078i
$743$	−7.62720	−	28.4651i	−0.279815	−	1.04428i	−0.952546	−	0.304395i	$-0.901546\pi$
$743$	−7.62720	−	28.4651i	−0.279815	−	1.04428i	0.672731	−	0.739887i	$-0.265121\pi$
$744$	−4.61096	−	10.2752i	−0.169046	−	0.376708i
$745$	3.19190	−	11.9123i	0.116942	−	0.436434i
$746$	21.6823	−	1.12644i	0.793846	−	0.0412419i
$747$	−3.86467	−	2.91308i	−0.141401	−	0.106584i
$748$	19.6837	+	5.85005i	0.719708	+	0.213899i
$749$	−0.132329	−	1.00514i	−0.00483520	−	0.0367270i
$750$	0.710640	+	3.75377i	0.0259489	+	0.137068i
$751$	21.6131	+	12.4783i	0.788672	+	0.455340i	0.839495	−	0.543368i	$-0.182851\pi$
$751$	21.6131	+	12.4783i	0.788672	+	0.455340i	−0.0508231	+	0.998708i	$0.516184\pi$
$752$	−7.67081	+	23.4631i	−0.279726	+	0.855612i
$753$	2.28562	−	2.30533i	0.0832925	−	0.0840110i
$754$	−4.89287	+	7.11224i	−0.178188	+	0.259012i
$755$	−48.0073	−	19.8853i	−1.74716	−	0.723699i
$756$	9.26593	−	32.7147i	0.336999	−	1.18982i
$757$	−3.98806	−	9.62802i	−0.144948	−	0.349936i	0.834686	−	0.550726i	$-0.185649\pi$
$757$	−3.98806	−	9.62802i	−0.144948	−	0.349936i	−0.979634	+	0.200790i	$0.935649\pi$
$758$	−35.6783	+	23.1467i	−1.29590	+	0.840728i
$759$	0.180943	+	42.1354i	0.00656781	+	1.52942i
$760$	0.225771	+	9.09572i	0.00818956	+	0.329937i
$761$	−8.63913	−	32.2417i	−0.313168	−	1.16876i	−0.925683	−	0.378301i	$-0.876508\pi$
$761$	−8.63913	−	32.2417i	−0.313168	−	1.16876i	0.612514	−	0.790459i	$-0.290158\pi$
$762$	−11.2878	+	7.39213i	−0.408912	+	0.267789i
$763$	−19.3565	−	14.8528i	−0.700753	−	0.537707i
$764$	18.4187	+	14.9429i	0.666364	+	0.540615i
$765$	24.4758	−	19.1171i	0.884923	−	0.691181i
$766$	4.70794	−	13.2756i	0.170105	−	0.479668i
$767$	2.51305	+	4.35274i	0.0907411	+	0.157168i
$768$	−7.88836	−	26.5664i	−0.284647	−	0.958633i
$769$	−8.08638	+	14.0060i	−0.291602	+	0.505070i	−0.974189	−	0.225735i	$-0.927522\pi$
$769$	−8.08638	+	14.0060i	−0.291602	+	0.505070i	0.682587	+	0.730805i	$0.260855\pi$
$770$	31.2228	+	36.5908i	1.12519	+	1.31864i
$771$	1.04259	−	8.19089i	0.0375479	−	0.294988i
$772$	3.93326	−	24.6884i	0.141561	−	0.888554i
$773$	−25.4216	+	10.5300i	−0.914351	+	0.378737i	−0.789721	−	0.613467i	$-0.789774\pi$
$773$	−25.4216	+	10.5300i	−0.914351	+	0.378737i	−0.124630	+	0.992203i	$0.539774\pi$
$774$	−1.41251	−	4.22989i	−0.0507717	−	0.152040i
$775$	8.91105	−	8.91105i	0.320094	−	0.320094i
$776$	0.954956	+	0.520186i	0.0342809	+	0.0186736i
$777$	53.4928	−	31.1911i	1.91904	−	1.11898i
$778$	−10.2667	−	5.23701i	−0.368078	−	0.187756i
$779$	−6.95965	−	0.916255i	−0.249355	−	0.0328282i
$780$	−63.1477	−	18.4729i	−2.26105	−	0.661436i
$781$	1.73131	+	13.1506i	0.0619511	+	0.470565i
$782$	14.7352	+	30.9292i	0.526930	+	1.10603i
$783$	−1.33197	+	5.24010i	−0.0476008	+	0.187266i
$784$	14.5007	−	3.05467i	0.517881	−	0.109095i
$785$	21.4056	−	12.3585i	0.763997	−	0.441094i
$786$	−26.4279	−	9.24455i	−0.942651	−	0.329742i
$787$	−24.8260	+	19.0496i	−0.884950	+	0.679046i	−0.947762	−	0.318979i	$-0.896660\pi$
$787$	−24.8260	+	19.0496i	−0.884950	+	0.679046i	0.0628116	+	0.998025i	$0.479993\pi$
$788$	−22.0675	+	20.9032i	−0.786123	+	0.744646i
$789$	21.7370	−	2.95675i	0.773858	−	0.105263i
$790$	20.1521	+	31.0624i	0.716979	+	1.10515i
$791$	−35.7271	−	35.7271i	−1.27031	−	1.27031i
$792$	−17.2991	−	21.0498i	−0.614696	−	0.747971i
$793$	−23.9625	+	23.9625i	−0.850934	+	0.850934i
$794$	−47.3978	−	10.0972i	−1.68209	−	0.358337i
$795$	59.8478	−	46.3325i	2.12258	−	1.64324i
$796$	−1.71826	+	3.84986i	−0.0609022	+	0.136455i
$797$	7.80924	+	10.1772i	0.276618	+	0.360495i	0.910915	−	0.412594i	$-0.135377\pi$
$797$	7.80924	+	10.1772i	0.276618	+	0.360495i	−0.634297	+	0.773089i	$0.718711\pi$
$798$	7.94072	+	0.594277i	0.281098	+	0.0210372i
$799$	9.86656	+	17.0894i	0.349054	+	0.604579i
$800$	24.6443	−	18.8214i	0.871307	−	0.665437i
$801$	−0.0718764	−	8.36862i	−0.00253963	−	0.295691i
$802$	46.5077	+	16.4930i	1.64224	+	0.582389i
$803$	20.1829	−	2.65713i	0.712239	−	0.0937680i
$804$	−23.5138	−	3.64267i	−0.829268	−	0.128467i
$805$	−10.4750	+	79.5656i	−0.369196	+	2.80432i
$806$	5.88565	+	18.1422i	0.207313	+	0.639032i
$807$	−40.9145	+	0.175700i	−1.44026	+	0.00618493i
$808$	−2.02408	−	0.215530i	−0.0712070	−	0.00758233i
$809$	−16.2429	−	16.2429i	−0.571069	−	0.571069i	0.361358	−	0.932427i	$-0.382313\pi$
$809$	−16.2429	−	16.2429i	−0.571069	−	0.571069i	−0.932427	+	0.361358i	$0.882313\pi$
$810$	−41.1090	+	2.84444i	−1.44442	+	0.0999436i
$811$	−1.39355	−	3.36433i	−0.0489342	−	0.118138i	0.897522	−	0.440969i	$-0.145365\pi$
$811$	−1.39355	−	3.36433i	−0.0489342	−	0.118138i	−0.946456	+	0.322832i	$0.895365\pi$
$812$	−6.62212	+	1.58347i	−0.232391	+	0.0555688i
$813$	19.8708	+	47.3957i	0.696901	+	1.66224i
$814$	3.91558	−	49.4647i	0.137241	−	1.73374i
$815$	8.66293	+	5.00154i	0.303449	+	0.175196i
$816$	−20.0188	−	9.48772i	−0.700800	−	0.332137i
$817$	0.904460	−	0.522190i	0.0316431	−	0.0182691i
$818$	−3.59121	−	7.53794i	−0.125564	−	0.263558i
$819$	−21.5781	+	53.3864i	−0.753999	+	1.86547i
$820$	21.7917	+	40.2225i	0.761000	+	1.40463i
$821$	26.8081	−	34.9369i	0.935608	−	1.21931i	−0.0398692	−	0.999205i	$-0.512694\pi$
$821$	26.8081	−	34.9369i	0.935608	−	1.21931i	0.975477	−	0.220103i	$-0.0706392\pi$
$822$	−0.389002	−	1.18176i	−0.0135680	−	0.0412188i
$823$	52.6145	−	14.0980i	1.83403	−	0.491426i	0.835697	−	0.549190i	$-0.185064\pi$
$823$	52.6145	−	14.0980i	1.83403	−	0.491426i	0.998330	+	0.0577638i	$0.0183970\pi$
$824$	−18.6612	−	17.7572i	−0.650094	−	0.618603i
$825$	15.1301	−	26.4679i	0.526763	−	0.921496i
$826$	−0.825964	+	3.87719i	−0.0287390	+	0.134905i
$827$	−33.5301	+	13.8886i	−1.16596	+	0.482955i	−0.879854	−	0.475244i	$-0.842360\pi$
$827$	−33.5301	+	13.8886i	−1.16596	+	0.482955i	−0.286102	+	0.958199i	$0.592360\pi$
$828$	6.76608	−	44.9509i	0.235138	−	1.56215i
$829$	2.85146	−	6.88403i	0.0990352	−	0.239092i	−0.866595	−	0.499012i	$-0.833696\pi$
$829$	2.85146	−	6.88403i	0.0990352	−	0.239092i	0.965630	+	0.259920i	$0.0836962\pi$
$830$	−7.26311	+	1.34272i	−0.252106	+	0.0466066i
$831$	6.49003	−	24.6439i	0.225136	−	0.854889i
$832$	8.42683	+	46.1694i	0.292148	+	1.60064i
$833$	5.92305	−	10.2590i	0.205221	−	0.355454i
$834$	27.0134	−	13.0123i	0.935399	−	0.450579i
$835$	5.53883	−	0.729200i	0.191679	−	0.0252350i
$836$	4.02010	−	4.95519i	0.139038	−	0.171379i
$837$	7.39348	+	9.38258i	0.255556	+	0.324310i
$838$	−28.4774	−	25.6646i	−0.983735	−	0.886568i
$839$	−2.03799	−	0.546077i	−0.0703591	−	0.0188527i	0.223468	−	0.974711i	$-0.428262\pi$
$839$	−2.03799	−	0.546077i	−0.0703591	−	0.0188527i	−0.293827	+	0.955859i	$0.594929\pi$
$840$	−27.2437	−	44.1666i	−0.939996	−	1.52389i
$841$	−26.9660	+	7.22553i	−0.929864	+	0.249156i
$842$	−0.958094	−	0.488722i	−0.0330181	−	0.0168425i
$843$	−2.42978	+	0.330508i	−0.0836862	+	0.0113833i
$844$	18.9623	−	30.8807i	0.652710	−	1.06296i
$845$	64.0575	+	26.5335i	2.20365	+	0.912780i
$846$	1.84188	−	26.1177i	0.0633252	−	0.897947i
$847$			2.25615i			0.0775221i
$848$	−48.6869	−	23.3312i	−1.67191	−	0.801196i
$849$	−1.65771	−	6.08207i	−0.0568925	−	0.208736i
$850$	1.95613	−	24.7114i	0.0670946	−	0.847593i
$851$	65.6776	−	50.3962i	2.25140	−	1.72756i
$852$	0.326154	−	14.3059i	0.0111739	−	0.490113i
$853$	−12.8319	+	16.7228i	−0.439354	+	0.572578i	−0.959575	−	0.281454i	$-0.909183\pi$
$853$	−12.8319	+	16.7228i	−0.439354	+	0.572578i	0.520220	+	0.854032i	$0.325850\pi$
$854$	−26.6922	+	1.38672i	−0.913389	+	0.0474524i
$855$	−2.57769	−	9.29982i	−0.0881550	−	0.318047i
$856$	0.708339	+	0.516116i	0.0242105	+	0.0176405i
$857$	40.2904	+	10.7958i	1.37630	+	0.368777i	0.869774	−	0.493450i	$-0.164264\pi$
$857$	40.2904	+	10.7958i	1.37630	+	0.368777i	0.506521	+	0.862227i	$0.330931\pi$
$858$	25.2790	+	38.6009i	0.863011	+	1.31781i
$859$	2.16949	−	16.4789i	0.0740219	−	0.562252i	−0.913742	−	0.406295i	$-0.866820\pi$
$859$	2.16949	−	16.4789i	0.0740219	−	0.562252i	0.987764	−	0.155957i	$-0.0498462\pi$
$860$	−6.21514	−	2.77393i	−0.211934	−	0.0945902i
$861$	36.9229	−	15.4801i	1.25833	−	0.527559i
$862$	−7.22237	−	39.0675i	−0.245995	−	1.33064i
$863$	0.332738			0.0113265			0.00566326	−	0.999984i	$-0.498197\pi$
$863$	0.332738			0.0113265			0.00566326	+	0.999984i	$0.498197\pi$
$864$	14.9662	+	25.2985i	0.509161	+	0.860672i
$865$	45.6317			1.55153
$866$	7.25059	+	39.2201i	0.246385	+	1.33275i
$867$	10.8230	−	4.53757i	0.367567	−	0.154104i
$868$	−6.13114	+	13.7372i	−0.208105	+	0.466269i
$869$	3.38938	−	25.7449i	0.114977	−	0.873335i
$870$	4.52076	+	6.90319i	0.153268	+	0.234040i
$871$	38.9230	+	10.4294i	1.31885	+	0.353386i
$872$	20.8368	−	3.27111i	0.705623	−	0.110774i
$873$	−1.11663	−	0.288944i	−0.0377922	−	0.00977929i
$874$	10.6314	−	0.552324i	0.359613	−	0.0186826i
$875$	3.10652	−	4.04849i	0.105019	−	0.136864i
$876$	−21.9560	−	0.500566i	−0.741826	−	0.0169126i
$877$	4.39861	−	3.37517i	0.148531	−	0.113971i	−0.531823	−	0.846855i	$-0.678493\pi$
$877$	4.39861	−	3.37517i	0.148531	−	0.113971i	0.680354	+	0.732884i	$0.261826\pi$
$878$	1.20476	−	15.2195i	0.0406586	−	0.513632i
$879$	−10.0678	−	36.9382i	−0.339578	−	1.24589i
$880$	−41.5219	−	2.25177i	−1.39970	−	0.0759071i
$881$			40.7751i			1.37375i	0.726777	+	0.686874i	$0.241017\pi$
$881$			40.7751i			1.37375i	−0.726777	+	0.686874i	$0.758983\pi$
$882$	−14.1312	+	6.88187i	−0.475821	+	0.231725i
$883$	−8.08271	−	3.34797i	−0.272005	−	0.112668i	0.242512	−	0.970148i	$-0.422029\pi$
$883$	−8.08271	−	3.34797i	−0.272005	−	0.112668i	−0.514517	+	0.857480i	$0.672029\pi$
$884$	31.9707	+	19.6317i	1.07529	+	0.660285i
$885$	4.76045	−	0.647535i	0.160021	−	0.0217666i
$886$	−9.08229	−	4.63286i	−0.305126	−	0.155644i
$887$	29.3455	−	7.86310i	0.985325	−	0.264017i	0.270039	−	0.962849i	$-0.412963\pi$
$887$	29.3455	−	7.86310i	0.985325	−	0.264017i	0.715285	+	0.698832i	$0.246297\pi$
$888$	−12.3439	+	52.0882i	−0.414235	+	1.74797i
$889$	17.4084	+	4.66458i	0.583860	+	0.156445i
$890$	−9.48803	−	8.55088i	−0.318040	−	0.286626i
$891$	23.2258	+	17.1961i	0.778094	+	0.576092i
$892$	−36.2744	−	29.4291i	−1.21456	−	0.985358i
$893$	6.07931	−	0.800357i	0.203436	−	0.0267829i
$894$	8.40622	−	4.04925i	0.281146	−	0.135427i
$895$	−36.6191	+	63.4262i	−1.22404	+	2.12010i
$896$	−19.4413	+	31.4999i	−0.649487	+	1.05234i
$897$	−19.6051	+	74.4444i	−0.654594	+	2.48563i
$898$	−18.0441	+	3.33580i	−0.602141	+	0.111317i
$899$	0.915414	−	2.21001i	0.0305308	−	0.0737078i
$900$	−20.5018	+	25.7189i	−0.683392	+	0.857297i
$901$	−39.8727	+	16.5158i	−1.32835	+	0.550221i
$902$	6.68450	−	31.3780i	0.222570	−	1.04477i
$903$	−2.95612	+	5.17131i	−0.0983735	+	0.172090i
$904$	43.6653	−	1.08384i	1.45229	−	0.0360481i
$905$	−56.3986	+	15.1120i	−1.87475	+	0.502338i
$906$	−12.2923	−	37.3432i	−0.408383	−	1.24064i
$907$	−24.5965	+	32.0548i	−0.816714	+	1.06436i	0.180024	+	0.983662i	$0.442382\pi$
$907$	−24.5965	+	32.0548i	−0.816714	+	1.06436i	−0.996738	+	0.0807005i	$0.974284\pi$
$908$	−3.05367	+	1.65441i	−0.101340	+	0.0549037i
$909$	2.13803	−	0.300180i	0.0709140	−	0.00995633i
$910$	37.7981	+	79.3382i	1.25300	+	2.63003i
$911$	7.74287	−	4.47035i	0.256533	−	0.148109i	−0.366219	−	0.930529i	$-0.619348\pi$
$911$	7.74287	−	4.47035i	0.256533	−	0.148109i	0.622752	+	0.782419i	$0.286015\pi$
$912$	−5.10426	+	4.61883i	−0.169019	+	0.152945i
$913$	4.48598	+	2.58998i	0.148464	+	0.0857159i
$914$	2.00352	−	25.3101i	0.0662706	−	0.837184i
$915$	12.5245	+	29.8733i	0.414046	+	0.987580i
$916$	8.70531	+	36.4060i	0.287631	+	1.20289i
$917$	14.3113	+	34.5506i	0.472602	+	1.14096i
$918$	23.0427	+	4.59932i	0.760521	+	0.151800i
$919$	14.7125	+	14.7125i	0.485319	+	0.485319i	0.906825	−	0.421506i	$-0.138498\pi$
$919$	14.7125	+	14.7125i	0.485319	+	0.485319i	−0.421506	+	0.906825i	$0.638498\pi$
$920$	−43.5867	−	53.9754i	−1.43701	−	1.77951i
$921$	−5.81137	+	0.0249559i	−0.191491	+	0.000822324i
$922$	−4.80293	−	14.8048i	−0.158176	−	0.487570i
$923$	−3.16312	+	24.0263i	−0.104115	+	0.790835i
$924$	−5.57139	+	35.9639i	−0.183285	+	1.18313i
$925$	−59.3863	+	7.81836i	−1.95261	+	0.257066i
$926$	25.6315	+	9.08972i	0.842305	+	0.298707i
$927$	23.7782	+	13.4574i	0.780979	+	0.441999i
$928$	2.95463	−	5.09082i	0.0969905	−	0.167114i
$929$	−13.7882	−	23.8819i	−0.452376	−	0.783539i	0.546157	−	0.837683i	$-0.316090\pi$
$929$	−13.7882	−	23.8819i	−0.452376	−	0.783539i	−0.998533	+	0.0541440i	$0.982757\pi$
$930$	18.1804	+	1.36061i	0.596160	+	0.0446162i
$931$	−2.24085	−	2.92033i	−0.0734408	−	0.0957100i
$932$	−6.27639	−	2.80127i	−0.205590	−	0.0917585i
$933$	−30.5118	+	23.6214i	−0.998913	+	0.773331i
$934$	−54.8594	−	11.6868i	−1.79505	−	0.382403i
$935$	−23.5049	+	23.5049i	−0.768694	+	0.768694i
$936$	−20.5750	−	45.3279i	−0.672514	−	1.48159i
$937$	13.3238	+	13.3238i	0.435269	+	0.435269i	0.890416	−	0.455147i	$-0.150413\pi$
$937$	13.3238	+	13.3238i	0.435269	+	0.435269i	−0.455147	+	0.890416i	$0.650413\pi$
$938$	17.2978	+	26.6627i	0.564792	+	0.870569i
$939$	−19.3929	+	2.63789i	−0.632863	+	0.0860843i
$940$	−27.4802	−	29.0108i	−0.896305	−	0.946229i
$941$	35.7137	−	27.4041i	1.16423	−	0.893347i	0.168506	−	0.985701i	$-0.446106\pi$
$941$	35.7137	−	27.4041i	1.16423	−	0.893347i	0.995726	+	0.0923534i	$0.0294390\pi$
$942$	17.6518	+	6.17464i	0.575125	+	0.201181i
$943$	46.3545	−	26.7628i	1.50951	−	0.871517i
$944$	−1.93593	−	2.82779i	−0.0630090	−	0.0920367i
$945$	39.4180	+	38.4153i	1.28227	+	1.24965i
$946$	2.05293	+	4.30909i	0.0667464	+	0.140101i
$947$	3.00061	+	22.7919i	0.0975066	+	0.740636i	0.968442	+	0.249239i	$0.0801804\pi$
$947$	3.00061	+	22.7919i	0.0975066	+	0.740636i	−0.870936	+	0.491397i	$0.836486\pi$
$948$	−7.86541	+	26.8871i	−0.255457	+	0.873253i
$949$	36.8744	+	4.85461i	1.19699	+	0.157587i
$950$	−6.86157	−	3.50007i	−0.222619	−	0.113557i
$951$	4.02357	−	2.34610i	0.130473	−	0.0760776i
$952$	8.36545	+	28.3833i	0.271126	+	0.919910i
$953$	−24.0511	+	24.0511i	−0.779093	+	0.779093i	−0.979677	−	0.200584i	$-0.935716\pi$
$953$	−24.0511	+	24.0511i	−0.779093	+	0.779093i	0.200584	+	0.979677i	$0.435716\pi$
$954$	56.1071	+	11.4497i	1.81653	+	0.370699i
$955$	−35.4714	+	14.6927i	−1.14783	+	0.475445i
$956$	14.5877	+	2.32405i	0.471799	+	0.0751652i
$957$	0.730708	−	5.74067i	0.0236204	−	0.185569i
$958$	19.2495	+	22.5591i	0.621924	+	0.728850i
$959$	−0.830907	+	1.43917i	−0.0268314	+	0.0464733i
$960$	43.8951	+	9.25830i	1.41671	+	0.298810i
$961$	12.8575	+	22.2698i	0.414757	+	0.718381i
$962$	30.3002	−	85.4418i	0.976918	−	2.75475i
$963$	−0.861851	−	0.348349i	−0.0277728	−	0.0112254i
$964$	−17.4500	+	21.5090i	−0.562027	+	0.692757i
$965$	32.1062	+	24.6359i	1.03353	+	0.793059i
$966$	−50.7948	+	33.2645i	−1.63430	+	1.07027i
$967$	−6.59045	−	24.5959i	−0.211934	−	0.790950i	−0.987223	−	0.159343i	$-0.949062\pi$
$967$	−6.59045	−	24.5959i	−0.211934	−	0.790950i	0.775289	−	0.631607i	$-0.217604\pi$
$968$	−1.41294	−	1.34450i	−0.0454136	−	0.0432138i
$969$	0.0236308	+	5.50281i	0.000759131	+	0.176776i
$970$	−1.47677	+	0.958072i	−0.0474163	+	0.0307618i
$971$	13.5920	+	32.8139i	0.436187	+	1.05305i	0.977255	+	0.212070i	$0.0680204\pi$
$971$	13.5920	+	32.8139i	0.436187	+	1.05305i	−0.541067	+	0.840979i	$0.681980\pi$
$972$	−21.9212	−	22.1689i	−0.703124	−	0.711068i
$973$	−37.0014	−	15.3265i	−1.18621	−	0.491345i
$974$	24.2913	−	35.3097i	0.778344	−	1.13140i
$975$	39.2168	−	39.5551i	1.25594	−	1.26678i
$976$	15.0381	−	17.5427i	0.481359	−	0.561529i
$977$	−14.9389	−	8.62499i	−0.477938	−	0.275938i	0.241619	−	0.970371i	$-0.422322\pi$
$977$	−14.9389	−	8.62499i	−0.477938	−	0.275938i	−0.719557	+	0.694433i	$0.755655\pi$
$978$	1.40776	+	7.43612i	0.0450152	+	0.237781i
$979$	1.16919	+	8.88087i	0.0373674	+	0.283834i
$980$	−6.83401	+	22.9944i	−0.218304	+	0.734531i
$981$	−20.5942	+	8.73837i	−0.657523	+	0.278995i
$982$	−18.7689	+	0.975084i	−0.598940	+	0.0311162i
$983$	2.21670	−	8.27282i	0.0707016	−	0.263862i	−0.921523	−	0.388324i	$-0.873054\pi$
$983$	2.21670	−	8.27282i	0.0707016	−	0.263862i	0.992224	+	0.124462i	$0.0397206\pi$
$984$	−12.3087	+	32.3484i	−0.392388	+	1.03123i
$985$	−12.7350	−	47.5278i	−0.405772	−	1.51436i
$986$	−1.45198	−	4.47567i	−0.0462406	−	0.142534i
$987$	−27.6538	+	21.4088i	−0.880229	+	0.681449i
$988$	9.43764	−	6.84375i	0.300251	−	0.217729i
$989$	−3.04748	+	7.35728i	−0.0969044	+	0.233948i
$990$	43.3000	−	8.39005i	1.37616	−	0.266653i
$991$	−61.2959			−1.94713			−0.973564	−	0.228414i	$-0.926646\pi$
$991$	−61.2959			−1.94713			−0.973564	+	0.228414i	$0.926646\pi$
$992$	−4.94936	−	12.0260i	−0.157142	−	0.381827i
$993$	14.7423	−	55.9796i	0.467834	−	1.77646i
$994$	−14.5397	+	12.4066i	−0.461171	+	0.393515i
$995$	−4.15456	−	5.41432i	−0.131708	−	0.171646i
$996$	−4.35480	−	3.50210i	−0.137987	−	0.110968i
$997$	41.5150	+	31.8556i	1.31479	+	1.00888i	0.998179	+	0.0603228i	$0.0192130\pi$
$997$	41.5150	+	31.8556i	1.31479	+	1.00888i	0.316615	+	0.948554i	$0.397454\pi$
$998$	22.5641	−	25.0371i	0.714254	−	0.792535i
$999$	−0.731444	−	56.7733i	−0.0231419	−	1.79623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.13.3	✓	368
3.2	odd	2		864.2.bk.a.685.44		368
9.2	odd	6		864.2.bk.a.397.13		368
9.7	even	3	inner	288.2.bc.a.205.34	yes	368
32.5	even	8	inner	288.2.bc.a.229.34	yes	368
96.5	odd	8		864.2.bk.a.37.13		368
288.101	odd	24		864.2.bk.a.613.44		368
288.133	even	24	inner	288.2.bc.a.133.3	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.3	✓	368	1.1	even	1	trivial
288.2.bc.a.133.3	yes	368	288.133	even	24	inner
288.2.bc.a.205.34	yes	368	9.7	even	3	inner
288.2.bc.a.229.34	yes	368	32.5	even	8	inner
864.2.bk.a.37.13		368	96.5	odd	8
864.2.bk.a.397.13		368	9.2	odd	6
864.2.bk.a.613.44		368	288.101	odd	24
864.2.bk.a.685.44		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39065 + 0.257088i) q^{2} +(1.59735 - 0.669693i) q^{3} +(1.86781 - 0.715038i) q^{4} +(-0.422585 + 3.20986i) q^{5} +(-2.04918 + 1.34197i) q^{6} +(3.16032 + 0.846806i) q^{7} +(-2.41364 + 1.47456i) q^{8} +(2.10302 - 2.13946i) q^{9} +O(q^{10})\)	\(q+(-1.39065 + 0.257088i) q^{2} +(1.59735 - 0.669693i) q^{3} +(1.86781 - 0.715038i) q^{4} +(-0.422585 + 3.20986i) q^{5} +(-2.04918 + 1.34197i) q^{6} +(3.16032 + 0.846806i) q^{7} +(-2.41364 + 1.47456i) q^{8} +(2.10302 - 2.13946i) q^{9} +(-0.237547 - 4.57243i) q^{10} +(-1.95472 + 2.54745i) q^{11} +(2.50468 - 2.39302i) q^{12} +(-4.65422 + 3.57131i) q^{13} +(-4.61261 - 0.365129i) q^{14} +(1.47460 + 5.41025i) q^{15} +(2.97744 - 2.67111i) q^{16} -3.19756i q^{17} +(-2.37454 + 3.51590i) q^{18} +(-0.917962 - 0.380232i) q^{19} +(1.50586 + 6.29757i) q^{20} +(5.61523 - 0.763804i) q^{21} +(2.06342 - 4.04514i) q^{22} +(7.31806 - 1.96087i) q^{23} +(-2.86792 + 3.97178i) q^{24} +(-5.29496 - 1.41878i) q^{25} +(5.55425 - 6.16298i) q^{26} +(1.92647 - 4.82584i) q^{27} +(6.50839 - 0.678079i) q^{28} +(-1.03162 + 0.135816i) q^{29} +(-3.44156 - 7.14466i) q^{30} +(-1.14946 + 1.99093i) q^{31} +(-3.45386 + 4.48005i) q^{32} +(-1.41636 + 5.37822i) q^{33} +(0.822055 + 4.44669i) q^{34} +(-4.05363 + 9.78633i) q^{35} +(2.39825 - 5.49985i) q^{36} +(10.0952 - 4.18156i) q^{37} +(1.37432 + 0.292773i) q^{38} +(-5.04271 + 8.82151i) q^{39} +(-3.71315 - 8.37057i) q^{40} +(6.82422 - 1.82855i) q^{41} +(-7.61245 + 2.50579i) q^{42} +(-0.639878 + 0.833905i) q^{43} +(-1.82953 + 6.15585i) q^{44} +(5.97865 + 7.65451i) q^{45} +(-9.67274 + 4.60827i) q^{46} +(-5.34450 + 3.08565i) q^{47} +(2.96717 - 6.26066i) q^{48} +(3.20839 + 1.85236i) q^{49} +(7.72819 + 0.611756i) q^{50} +(-2.14138 - 5.10761i) q^{51} +(-6.13958 + 9.99847i) q^{52} +(-5.16512 - 12.4697i) q^{53} +(-1.43838 + 7.20632i) q^{54} +(-7.35090 - 7.35090i) q^{55} +(-8.87656 + 2.61620i) q^{56} +(-1.72094 + 0.00739026i) q^{57} +(1.39971 - 0.454091i) q^{58} +(0.111828 - 0.849416i) q^{59} +(6.62282 + 9.05093i) q^{60} +(5.72711 - 0.753989i) q^{61} +(1.08666 - 3.06419i) q^{62} +(8.45794 - 4.98054i) q^{63} +(3.65135 - 7.11812i) q^{64} +(-9.49657 - 16.4485i) q^{65} +(0.586990 - 7.84334i) q^{66} +(-4.18147 - 5.44940i) q^{67} +(-2.28638 - 5.97244i) q^{68} +(10.3763 - 8.03303i) q^{69} +(3.12123 - 14.6515i) q^{70} +(2.92094 - 2.92094i) q^{71} +(-1.92118 + 8.26493i) q^{72} +(-4.48292 - 4.48292i) q^{73} +(-12.9638 + 8.41043i) q^{74} +(-9.40803 + 1.27972i) q^{75} +(-1.98646 - 0.0538242i) q^{76} +(-8.33475 + 6.39548i) q^{77} +(4.74474 - 13.5640i) q^{78} +(-7.00349 + 4.04346i) q^{79} +(7.31567 + 10.6859i) q^{80} +(-0.154587 - 8.99867i) q^{81} +(-9.02000 + 4.29729i) q^{82} +(-0.210565 - 1.59940i) q^{83} +(9.94204 - 5.44175i) q^{84} +(10.2637 + 1.35124i) q^{85} +(0.675458 - 1.32417i) q^{86} +(-1.55691 + 0.907817i) q^{87} +(0.961646 - 9.03098i) q^{88} +(1.97258 - 1.97258i) q^{89} +(-10.2821 - 9.10769i) q^{90} +(-17.7330 + 7.34527i) q^{91} +(12.2667 - 8.89523i) q^{92} +(-0.502779 + 3.94998i) q^{93} +(6.63905 - 5.66507i) q^{94} +(1.60841 - 2.78584i) q^{95} +(-2.51676 + 9.46921i) q^{96} +(-0.192235 - 0.332960i) q^{97} +(-4.93796 - 1.75115i) q^{98} +(1.33933 + 9.53939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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