LMFDB - Embedded newform 99.2.m.b.58.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(4,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("99.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			58.4
Character	$\chi$	$=$	99.58
Dual form			99.2.m.b.70.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.606887 - 0.270203i) q^{2} +(1.10264 + 1.33574i) q^{3} +(-1.04296 - 1.15832i) q^{4} +(1.02009 - 0.454172i) q^{5} +(-0.308255 - 1.10858i) q^{6} +(3.81922 - 0.811800i) q^{7} +(0.730548 + 2.24840i) q^{8} +(-0.568386 + 2.94566i) q^{9} -0.741796 q^{10} +(-2.09587 + 2.57048i) q^{11} +(0.397211 - 2.67033i) q^{12} +(-0.279928 - 2.66333i) q^{13} +(-2.53719 - 0.539295i) q^{14} +(1.73144 + 0.861780i) q^{15} +(-0.161688 + 1.53836i) q^{16} +(-4.48727 - 3.26019i) q^{17} +(1.14087 - 1.63411i) q^{18} +(-1.58598 - 4.88115i) q^{19} +(-1.58999 - 0.707907i) q^{20} +(5.29556 + 4.20635i) q^{21} +(1.96651 - 0.993678i) q^{22} +(-1.05719 + 1.83110i) q^{23} +(-2.19774 + 3.45498i) q^{24} +(-2.51135 + 2.78914i) q^{25} +(-0.549758 + 1.69198i) q^{26} +(-4.56135 + 2.48878i) q^{27} +(-4.92362 - 3.57722i) q^{28} +(-1.05937 + 0.225177i) q^{29} +(-0.817931 - 0.990844i) q^{30} +(0.0449642 + 0.427806i) q^{31} +(2.87790 - 4.98467i) q^{32} +(-5.74446 + 0.0347740i) q^{33} +(1.84235 + 3.19104i) q^{34} +(3.52724 - 2.56269i) q^{35} +(4.00484 - 2.41383i) q^{36} +(-2.69024 + 8.27970i) q^{37} +(-0.356392 + 3.39084i) q^{38} +(3.24885 - 3.31060i) q^{39} +(1.76638 + 1.96176i) q^{40} +(2.85529 + 0.606910i) q^{41} +(-2.07724 - 3.98366i) q^{42} +(1.11628 + 1.93346i) q^{43} +(5.16335 - 0.253209i) q^{44} +(0.758035 + 3.26298i) q^{45} +(1.13637 - 0.825618i) q^{46} +(8.58861 - 9.53861i) q^{47} +(-2.23313 + 1.48028i) q^{48} +(7.53259 - 3.35373i) q^{49} +(2.27774 - 1.01411i) q^{50} +(-0.593068 - 9.58862i) q^{51} +(-2.79305 + 3.10200i) q^{52} +(-4.56381 + 3.31581i) q^{53} +(3.44070 - 0.277916i) q^{54} +(-0.970527 + 3.57399i) q^{55} +(4.61537 + 7.99405i) q^{56} +(4.77117 - 7.50058i) q^{57} +(0.703764 + 0.149590i) q^{58} +(-1.58943 - 1.76524i) q^{59} +(-0.807599 - 2.90437i) q^{60} +(0.426942 - 4.06208i) q^{61} +(0.0883065 - 0.271779i) q^{62} +(0.220502 + 11.7116i) q^{63} +(-0.590604 + 0.429099i) q^{64} +(-1.49516 - 2.58969i) q^{65} +(3.49563 + 1.53107i) q^{66} +(4.87584 - 8.44521i) q^{67} +(0.903682 + 8.59796i) q^{68} +(-3.61157 + 0.606917i) q^{69} +(-2.83308 + 0.602190i) q^{70} +(-5.11062 - 3.71308i) q^{71} +(-7.03825 + 0.873994i) q^{72} +(-3.60705 + 11.1014i) q^{73} +(3.86988 - 4.29793i) q^{74} +(-6.49466 - 0.279099i) q^{75} +(-3.99983 + 6.92792i) q^{76} +(-5.91786 + 11.5186i) q^{77} +(-2.86622 + 1.13131i) q^{78} +(4.12439 + 1.83630i) q^{79} +(0.533744 + 1.64269i) q^{80} +(-8.35388 - 3.34855i) q^{81} +(-1.56885 - 1.13983i) q^{82} +(-0.0503831 + 0.479363i) q^{83} +(-0.650739 - 10.5210i) q^{84} +(-6.05809 - 1.28769i) q^{85} +(-0.155030 - 1.47502i) q^{86} +(-1.46888 - 1.16676i) q^{87} +(-7.31058 - 2.83448i) q^{88} +16.0830 q^{89} +(0.421626 - 2.18508i) q^{90} +(-3.23120 - 9.94461i) q^{91} +(3.22362 - 0.685201i) q^{92} +(-0.521857 + 0.531775i) q^{93} +(-7.78968 + 3.46819i) q^{94} +(-3.83471 - 4.25888i) q^{95} +(9.83148 - 1.65216i) q^{96} +(7.32266 + 3.26026i) q^{97} -5.47762 q^{98} +(-6.38050 - 7.63474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) $ 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.606887	−	0.270203i	−0.429134	−	0.191063i	0.180792	−	0.983521i	$-0.442134\pi$
$2$	−0.606887	−	0.270203i	−0.429134	−	0.191063i	−0.609926	+	0.792459i	$0.708801\pi$
$3$	1.10264	+	1.33574i	0.636607	+	0.771188i
$3$	1.10264	+	1.33574i	0.636607	+	0.771188i
$4$	−1.04296	−	1.15832i	−0.521480	−	0.579162i
$5$	1.02009	−	0.454172i	0.456196	−	0.203112i	−0.165756	−	0.986167i	$-0.553006\pi$
$5$	1.02009	−	0.454172i	0.456196	−	0.203112i	0.621952	+	0.783055i	$0.286340\pi$
$6$	−0.308255	−	1.10858i	−0.125845	−	0.452575i
$7$	3.81922	−	0.811800i	1.44353	−	0.306832i	0.581440	−	0.813589i	$-0.302489\pi$
$7$	3.81922	−	0.811800i	1.44353	−	0.306832i	0.862089	+	0.506758i	$0.169156\pi$
$8$	0.730548	+	2.24840i	0.258288	+	0.794928i
$9$	−0.568386	+	2.94566i	−0.189462	+	0.981888i
$10$	−0.741796			−0.234576
$11$	−2.09587	+	2.57048i	−0.631928	+	0.775027i
$11$	−2.09587	+	2.57048i	−0.631928	+	0.775027i
$12$	0.397211	−	2.67033i	0.114665	−	0.770858i
$13$	−0.279928	−	2.66333i	−0.0776380	−	0.738676i	−0.962217	−	0.272285i	$-0.912221\pi$
$13$	−0.279928	−	2.66333i	−0.0776380	−	0.738676i	0.884579	−	0.466391i	$-0.154446\pi$
$14$	−2.53719	−	0.539295i	−0.678091	−	0.144133i
$15$	1.73144	+	0.861780i	0.447055	+	0.222511i
$16$	−0.161688	+	1.53836i	−0.0404221	+	0.384590i
$17$	−4.48727	−	3.26019i	−1.08832	−	0.790713i	−0.109207	−	0.994019i	$-0.534831\pi$
$17$	−4.48727	−	3.26019i	−1.08832	−	0.790713i	−0.979115	+	0.203306i	$0.934831\pi$
$18$	1.14087	−	1.63411i	0.268907	−	0.385162i
$19$	−1.58598	−	4.88115i	−0.363849	−	1.11981i	−0.950699	−	0.310116i	$-0.899632\pi$
$19$	−1.58598	−	4.88115i	−0.363849	−	1.11981i	0.586850	−	0.809696i	$-0.300368\pi$
$20$	−1.58999	−	0.707907i	−0.355532	−	0.158293i
$21$	5.29556	+	4.20635i	1.15559	+	0.917901i
$22$	1.96651	−	0.993678i	0.419260	−	0.211853i
$23$	−1.05719	+	1.83110i	−0.220439	+	0.381812i	−0.954941	−	0.296795i	$-0.904082\pi$
$23$	−1.05719	+	1.83110i	−0.220439	+	0.381812i	0.734502	+	0.678606i	$0.237416\pi$
$24$	−2.19774	+	3.45498i	−0.448611	+	0.705245i
$25$	−2.51135	+	2.78914i	−0.502270	+	0.557827i
$26$	−0.549758	+	1.69198i	−0.107816	+	0.331825i
$27$	−4.56135	+	2.48878i	−0.877833	+	0.478967i
$28$	−4.92362	−	3.57722i	−0.930476	−	0.676030i
$29$	−1.05937	+	0.225177i	−0.196721	+	0.0418143i	−0.305218	−	0.952282i	$-0.598729\pi$
$29$	−1.05937	+	0.225177i	−0.196721	+	0.0418143i	0.108497	+	0.994097i	$0.465396\pi$
$30$	−0.817931	−	0.990844i	−0.149333	−	0.180903i
$31$	0.0449642	+	0.427806i	0.00807581	+	0.0768362i	0.997817	−	0.0660323i	$-0.0210340\pi$
$31$	0.0449642	+	0.427806i	0.00807581	+	0.0768362i	−0.989742	+	0.142869i	$0.954367\pi$
$32$	2.87790	−	4.98467i	0.508746	−	0.881173i
$33$	−5.74446	+	0.0347740i	−0.999982	+	0.00605338i
$34$	1.84235	+	3.19104i	0.315960	+	0.547259i
$35$	3.52724	−	2.56269i	0.596212	−	0.433173i
$36$	4.00484	−	2.41383i	0.667473	−	0.402306i
$37$	−2.69024	+	8.27970i	−0.442273	+	1.36118i	0.443175	+	0.896435i	$0.353852\pi$
$37$	−2.69024	+	8.27970i	−0.442273	+	1.36118i	−0.885447	+	0.464740i	$0.846148\pi$
$38$	−0.356392	+	3.39084i	−0.0578144	+	0.550067i
$39$	3.24885	−	3.31060i	0.520233	−	0.530120i
$40$	1.76638	+	1.96176i	0.279289	+	0.310182i
$41$	2.85529	+	0.606910i	0.445921	+	0.0947834i	0.425399	−	0.905006i	$-0.360134\pi$
$41$	2.85529	+	0.606910i	0.445921	+	0.0947834i	0.0205221	+	0.999789i	$0.493467\pi$
$42$	−2.07724	−	3.98366i	−0.320525	−	0.614692i
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	0.938501	−	0.345277i	$-0.112215\pi$
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	−0.768269	+	0.640127i	$0.778882\pi$
$44$	5.16335	−	0.253209i	0.778404	−	0.0381728i
$45$	0.758035	+	3.26298i	0.113001	+	0.486416i
$46$	1.13637	−	0.825618i	0.167548	−	0.121731i
$47$	8.58861	−	9.53861i	1.25278	−	1.39135i	0.365044	−	0.930990i	$-0.381054\pi$
$47$	8.58861	−	9.53861i	1.25278	−	1.39135i	0.887733	−	0.460359i	$-0.152279\pi$
$48$	−2.23313	+	1.48028i	−0.322324	+	0.213660i
$49$	7.53259	−	3.35373i	1.07608	−	0.479104i
$50$	2.27774	−	1.01411i	0.322121	−	0.143418i
$51$	−0.593068	−	9.58862i	−0.0830462	−	1.34267i
$52$	−2.79305	+	3.10200i	−0.387326	+	0.430169i
$53$	−4.56381	+	3.31581i	−0.626888	+	0.455461i	−0.855321	−	0.518099i	$-0.826640\pi$
$53$	−4.56381	+	3.31581i	−0.626888	+	0.455461i	0.228433	+	0.973560i	$0.426640\pi$
$54$	3.44070	−	0.277916i	0.468221	−	0.0378196i
$55$	−0.970527	+	3.57399i	−0.130866	+	0.481917i
$56$	4.61537	+	7.99405i	0.616755	+	1.06825i
$57$	4.77117	−	7.50058i	0.631956	−	0.993476i
$58$	0.703764	+	0.149590i	0.0924087	+	0.0196421i
$59$	−1.58943	−	1.76524i	−0.206927	−	0.229815i	0.630744	−	0.775991i	$-0.282750\pi$
$59$	−1.58943	−	1.76524i	−0.206927	−	0.229815i	−0.837671	+	0.546176i	$0.816083\pi$
$60$	−0.807599	−	2.90437i	−0.104261	−	0.374952i
$61$	0.426942	−	4.06208i	0.0546643	−	0.520096i	−0.932589	−	0.360940i	$-0.882456\pi$
$61$	0.426942	−	4.06208i	0.0546643	−	0.520096i	0.987253	−	0.159156i	$-0.0508773\pi$
$62$	0.0883065	−	0.271779i	0.0112149	−	0.0345160i
$63$	0.220502	+	11.7116i	0.0277806	+	1.47552i
$64$	−0.590604	+	0.429099i	−0.0738255	+	0.0536374i
$65$	−1.49516	−	2.58969i	−0.185452	−	0.321212i
$66$	3.49563	+	1.53107i	0.430283	+	0.188462i
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	−0.397772	−	0.917484i	$-0.630216\pi$
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	0.993451	−	0.114262i	$-0.0364503\pi$
$68$	0.903682	+	8.59796i	0.109587	+	1.04266i
$69$	−3.61157	+	0.606917i	−0.434782	+	0.0730642i
$70$	−2.83308	+	0.602190i	−0.338618	+	0.0719754i
$71$	−5.11062	−	3.71308i	−0.606519	−	0.440662i	0.241668	−	0.970359i	$-0.422306\pi$
$71$	−5.11062	−	3.71308i	−0.606519	−	0.440662i	−0.848187	+	0.529697i	$0.822306\pi$
$72$	−7.03825	+	0.873994i	−0.829466	+	0.103001i
$73$	−3.60705	+	11.1014i	−0.422174	+	1.29932i	0.483501	+	0.875344i	$0.339365\pi$
$73$	−3.60705	+	11.1014i	−0.422174	+	1.29932i	−0.905675	+	0.423973i	$0.860635\pi$
$74$	3.86988	−	4.29793i	0.449864	−	0.499625i
$75$	−6.49466	−	0.279099i	−0.749938	−	0.0322275i
$76$	−3.99983	+	6.92792i	−0.458812	+	0.794686i
$77$	−5.91786	+	11.5186i	−0.674403	+	1.31267i
$78$	−2.86622	+	1.13131i	−0.324536	+	0.128095i
$79$	4.12439	+	1.83630i	0.464030	+	0.206600i	0.625416	−	0.780292i	$-0.284929\pi$
$79$	4.12439	+	1.83630i	0.464030	+	0.206600i	−0.161385	+	0.986891i	$0.551596\pi$
$80$	0.533744	+	1.64269i	0.0596744	+	0.183659i
$81$	−8.35388	−	3.34855i	−0.928208	−	0.372061i
$82$	−1.56885	−	1.13983i	−0.173250	−	0.125874i
$83$	−0.0503831	+	0.479363i	−0.00553026	+	0.0526169i	−0.996939	−	0.0781834i	$-0.975088\pi$
$83$	−0.0503831	+	0.479363i	−0.00553026	+	0.0526169i	0.991409	+	0.130800i	$0.0417547\pi$
$84$	−0.650739	−	10.5210i	−0.0710015	−	1.14794i
$85$	−6.05809	−	1.28769i	−0.657092	−	0.139669i
$86$	−0.155030	−	1.47502i	−0.0167174	−	0.159055i
$87$	−1.46888	−	1.16676i	−0.157481	−	0.125089i
$88$	−7.31058	−	2.83448i	−0.779310	−	0.302157i
$89$	16.0830			1.70480			0.852399	−	0.522891i	$-0.175147\pi$
$89$	16.0830			1.70480			0.852399	+	0.522891i	$0.175147\pi$
$90$	0.421626	−	2.18508i	0.0444433	−	0.230328i
$91$	−3.23120	−	9.94461i	−0.338722	−	1.04248i
$92$	3.22362	−	0.685201i	0.336085	−	0.0714371i
$93$	−0.521857	+	0.531775i	−0.0541141	+	0.0551425i
$94$	−7.78968	+	3.46819i	−0.803444	+	0.357716i
$95$	−3.83471	−	4.25888i	−0.393433	−	0.436952i
$96$	9.83148	−	1.65216i	1.00342	−	0.168623i
$97$	7.32266	+	3.26026i	0.743504	+	0.331029i	0.743289	−	0.668971i	$-0.233265\pi$
$97$	7.32266	+	3.26026i	0.743504	+	0.331029i	0.000215058		1.00000i	$0.499932\pi$
$98$	−5.47762			−0.553323
$99$	−6.38050	−	7.63474i	−0.641264	−	0.767320i
$100$	5.84996			0.584996
$101$	1.60904	+	0.716391i	0.160106	+	0.0712836i	0.485225	−	0.874389i	$-0.338738\pi$
$101$	1.60904	+	0.716391i	0.160106	+	0.0712836i	−0.325119	+	0.945673i	$0.605404\pi$
$102$	−2.23095	+	5.97945i	−0.220897	+	0.592054i
$103$	1.79840	+	1.99732i	0.177202	+	0.196802i	0.825202	−	0.564838i	$-0.191061\pi$
$103$	1.79840	+	1.99732i	0.177202	+	0.196802i	−0.648001	+	0.761640i	$0.724395\pi$
$104$	5.78373	−	2.57508i	0.567141	−	0.252507i
$105$	7.31233	+	1.88575i	0.713611	+	0.184030i
$106$	3.66566	−	0.779160i	0.356041	−	0.0756787i
$107$	−3.17558	−	9.77342i	−0.306995	−	0.944833i	−0.978925	−	0.204219i	$-0.934535\pi$
$107$	−3.17558	−	9.77342i	−0.306995	−	0.944833i	0.671931	−	0.740614i	$-0.265465\pi$
$108$	7.64012	+	2.68783i	0.735171	+	0.258636i
$109$	2.36284			0.226319			0.113160	−	0.993577i	$-0.463903\pi$
$109$	2.36284			0.226319			0.113160	+	0.993577i	$0.463903\pi$
$110$	1.55470	−	1.90677i	0.148235	−	0.181803i
$111$	−14.0259	+	5.53605i	−1.33128	+	0.525459i
$112$	0.631319	+	6.00659i	0.0596540	+	0.567570i
$113$	−1.49895	−	0.318611i	−0.141009	−	0.0299724i	0.136866	−	0.990590i	$-0.456297\pi$
$113$	−1.49895	−	0.318611i	−0.141009	−	0.0299724i	−0.277875	+	0.960617i	$0.589630\pi$
$114$	−4.92224	+	3.26282i	−0.461010	+	0.305591i
$115$	−0.246788	+	2.34803i	−0.0230131	+	0.218955i
$116$	1.36571	+	0.992247i	0.126803	+	0.0921279i
$117$	8.00439	+	0.689227i	0.740006	+	0.0637191i
$118$	0.487631	+	1.50077i	0.0448901	+	0.138157i
$119$	−19.7845	−	8.80862i	−1.81364	−	0.807485i
$120$	−0.672725	+	4.52253i	−0.0614111	+	0.412849i
$121$	−2.21469	−	10.7747i	−0.201335	−	0.979522i
$122$	−1.35669	+	2.34986i	−0.122829	+	0.212746i
$123$	2.33767	+	4.48311i	0.210781	+	0.404229i
$124$	0.448642	−	0.498267i	0.0402892	−	0.0447457i
$125$	−3.02032	+	9.29560i	−0.270146	+	0.831424i
$126$	3.03068	−	7.16717i	0.269995	−	0.638502i
$127$	6.19006	+	4.49734i	0.549279	+	0.399074i	0.827519	−	0.561437i	$-0.189751\pi$
$127$	6.19006	+	4.49734i	0.549279	+	0.399074i	−0.278241	+	0.960511i	$0.589751\pi$
$128$	−10.7857	+	2.29256i	−0.953328	+	0.202636i
$129$	−1.35174	+	3.62297i	−0.119014	+	0.318984i
$130$	0.207649	+	1.97565i	0.0182120	+	0.173276i
$131$	2.67956	−	4.64113i	0.234114	−	0.405498i	−0.724901	−	0.688853i	$-0.758114\pi$
$131$	2.67956	−	4.64113i	0.234114	−	0.405498i	0.959015	+	0.283356i	$0.0914477\pi$
$132$	6.03152	+	6.61767i	0.524976	+	0.575995i
$133$	−10.0197	−	17.3547i	−0.868820	−	1.50484i
$134$	−5.24101	+	3.80782i	−0.452754	+	0.328945i
$135$	−3.52264	+	4.61041i	−0.303181	+	0.396801i
$136$	4.05203	−	12.4709i	0.347459	−	1.06937i
$137$	−1.74889	+	16.6395i	−0.149417	+	1.42161i	0.620869	+	0.783914i	$0.286780\pi$
$137$	−1.74889	+	16.6395i	−0.149417	+	1.42161i	−0.770287	+	0.637698i	$0.779887\pi$
$138$	2.35581	+	0.607529i	0.200539	+	0.0517163i
$139$	9.19393	+	10.2109i	0.779819	+	0.866077i	0.993848	−	0.110751i	$-0.0353255\pi$
$139$	9.19393	+	10.2109i	0.779819	+	0.866077i	−0.214029	+	0.976827i	$0.568659\pi$
$140$	−6.64718	−	1.41290i	−0.561790	−	0.119412i
$141$	22.2112	+	0.954494i	1.87052	+	0.0803829i
$142$	2.09828	+	3.63433i	0.176084	+	0.304986i
$143$	7.43273	+	4.86244i	0.621556	+	0.406618i
$144$	−4.43959	−	1.35066i	−0.369966	−	0.112555i
$145$	−0.978384	+	0.710837i	−0.0812503	+	0.0590318i
$146$	5.18870	−	5.76264i	0.429420	−	0.476919i
$147$	12.7854	+	6.36362i	1.05452	+	0.524863i
$148$	12.3964	−	5.51923i	1.01898	−	0.453678i
$149$	5.07900	−	2.26132i	0.416088	−	0.185254i	−0.188005	−	0.982168i	$-0.560202\pi$
$149$	5.07900	−	2.26132i	0.416088	−	0.185254i	0.604093	+	0.796914i	$0.293536\pi$
$150$	3.86611	+	1.92426i	0.315666	+	0.157115i
$151$	−0.109676	+	0.121807i	−0.00892527	+	0.00991252i	−0.747591	−	0.664159i	$-0.768790\pi$
$151$	−0.109676	+	0.121807i	−0.00892527	+	0.00991252i	0.738666	+	0.674072i	$0.235456\pi$
$152$	9.81611	−	7.13182i	0.796192	−	0.578467i
$153$	12.1539	−	11.3649i	0.982587	−	0.918801i
$154$	6.70385	−	5.39148i	0.540211	−	0.434458i
$155$	0.240165	+	0.415978i	0.0192905	+	0.0334121i
$156$	−7.22317	−	0.310405i	−0.578316	−	0.0248523i
$157$	−23.3318	−	4.95932i	−1.86208	−	0.395797i	−0.867294	−	0.497797i	$-0.834142\pi$
$157$	−23.3318	−	4.95932i	−1.86208	−	0.395797i	−0.994784	+	0.102000i	$0.967476\pi$
$158$	−2.00687	−	2.22885i	−0.159658	−	0.177318i
$159$	−9.46127	−	2.43993i	−0.750328	−	0.193499i
$160$	0.671811	−	6.39185i	0.0531113	−	0.505320i
$161$	−2.55114	+	7.85161i	−0.201058	+	0.618794i
$162$	4.16507	+	4.28944i	0.327239	+	0.337010i
$163$	3.39466	−	2.46636i	0.265890	−	0.193180i	−0.446850	−	0.894609i	$-0.647454\pi$
$163$	3.39466	−	2.46636i	0.265890	−	0.193180i	0.712740	+	0.701429i	$0.247454\pi$
$164$	−2.27495	−	3.94033i	−0.177644	−	0.307688i
$165$	−5.84405	+	2.64444i	−0.454959	+	0.205870i
$166$	0.160102	−	0.277306i	0.0124264	−	0.0215231i
$167$	−1.65577	−	15.7536i	−0.128128	−	1.21905i	−0.849909	−	0.526930i	$-0.823343\pi$
$167$	−1.65577	−	15.7536i	−0.128128	−	1.21905i	0.721781	−	0.692121i	$-0.243324\pi$
$168$	−5.58888	+	14.9795i	−0.431191	+	1.15569i
$169$	5.70093	−	1.21177i	0.438533	−	0.0932131i
$170$	3.32864	+	2.41840i	0.255295	+	0.185482i
$171$	15.2797	−	1.89739i	1.16847	−	0.145097i
$172$	1.07533	−	3.30954i	0.0819935	−	0.252350i
$173$	−1.74167	+	1.93432i	−0.132417	+	0.147064i	−0.805706	−	0.592315i	$-0.798214\pi$
$173$	−1.74167	+	1.93432i	−0.132417	+	0.147064i	0.673290	+	0.739379i	$0.264881\pi$
$174$	0.576183	+	1.10499i	0.0436803	+	0.0837688i
$175$	−7.32717	+	12.6910i	−0.553882	+	0.959352i
$176$	−3.61544	−	3.63981i	−0.272524	−	0.274361i
$177$	0.605335	−	4.06949i	0.0454997	−	0.305881i
$178$	−9.76059	−	4.34569i	−0.731587	−	0.325724i
$179$	2.34483	+	7.21663i	0.175261	+	0.539396i	0.999645	−	0.0266334i	$-0.00847867\pi$
$179$	2.34483	+	7.21663i	0.175261	+	0.539396i	−0.824385	+	0.566030i	$0.808479\pi$
$180$	2.98898	−	4.28120i	0.222786	−	0.319102i
$181$	1.94179	+	1.41080i	0.144332	+	0.104864i	0.657608	−	0.753360i	$-0.271568\pi$
$181$	1.94179	+	1.41080i	0.144332	+	0.104864i	−0.513276	+	0.858224i	$0.671568\pi$
$182$	−0.726095	+	6.90833i	−0.0538218	+	0.512080i
$183$	5.89663	−	3.90871i	0.435891	−	0.288940i
$184$	−4.88937	−	1.03927i	−0.360449	−	0.0766159i
$185$	1.01613	+	9.66784i	0.0747074	+	0.710794i
$186$	0.460396	−	0.181720i	0.0337579	−	0.0133243i
$187$	17.7850	−	4.70149i	1.30056	−	0.343807i
$188$	−20.0064			−1.45911
$189$	−15.4004	+	13.2081i	−1.12022	+	0.960749i
$190$	1.17647	+	3.62081i	0.0853504	+	0.262681i
$191$	16.1573	−	3.43433i	1.16910	−	0.248500i	0.417849	−	0.908517i	$-0.362784\pi$
$191$	16.1573	−	3.43433i	1.16910	−	0.248500i	0.751251	+	0.660017i	$0.229451\pi$
$192$	−1.22438	−	0.315751i	−0.0883623	−	0.0227874i
$193$	−7.43166	+	3.30879i	−0.534942	+	0.238172i	−0.656384	−	0.754427i	$-0.727915\pi$
$193$	−7.43166	+	3.30879i	−0.534942	+	0.238172i	0.121442	+	0.992599i	$0.461248\pi$
$194$	−3.56310	−	3.95722i	−0.255815	−	0.284112i
$195$	1.81053	−	4.85263i	0.129655	−	0.347504i
$196$	−11.7409	−	5.22738i	−0.838635	−	0.373384i
$197$	−22.9072			−1.63207			−0.816035	−	0.578003i	$-0.803832\pi$
$197$	−22.9072			−1.63207			−0.816035	+	0.578003i	$0.803832\pi$
$198$	1.80931	+	6.35746i	0.128582	+	0.451805i
$199$	9.27177			0.657259			0.328629	−	0.944459i	$-0.393413\pi$
$199$	9.27177			0.657259			0.328629	+	0.944459i	$0.393413\pi$
$200$	−8.10574	−	3.60891i	−0.573162	−	0.255188i
$201$	16.6569	−	2.79915i	1.17488	−	0.197437i
$202$	−0.782935	−	0.869537i	−0.0550871	−	0.0611804i
$203$	−3.86318	+	1.72000i	−0.271142	+	0.120720i
$204$	−10.4882	+	10.6875i	−0.734319	+	0.748275i
$205$	3.18828	−	0.677690i	0.222679	−	0.0473319i
$206$	−0.551741	−	1.69808i	−0.0384416	−	0.118311i
$207$	−4.79293	−	4.15490i	−0.333132	−	0.288785i
$208$	4.14243			0.287226
$209$	15.8709	+	6.15351i	1.09781	+	0.425647i
$210$	−3.92822	−	3.12025i	−0.271073	−	0.215318i
$211$	−0.440125	−	4.18751i	−0.0302995	−	0.288280i	−0.999171	−	0.0407153i	$-0.987036\pi$
$211$	−0.440125	−	4.18751i	−0.0302995	−	0.288280i	0.968871	−	0.247565i	$-0.0796303\pi$
$212$	8.60065	+	1.82812i	0.590695	+	0.125556i
$213$	−0.675455	−	10.9206i	−0.0462814	−	0.748269i
$214$	−0.713596	+	6.78942i	−0.0487804	+	0.464115i
$215$	2.01683	+	1.46531i	0.137547	+	0.0999334i
$216$	−8.92806	−	8.43755i	−0.607477	−	0.574103i
$217$	0.519021	+	1.59738i	0.0352335	+	0.108437i
$218$	−1.43398	−	0.638448i	−0.0971212	−	0.0432412i
$219$	−18.8058	+	7.42270i	−1.27078	+	0.501580i
$220$	5.15206	−	2.60334i	0.347352	−	0.175517i
$221$	−7.42687	+	12.8637i	−0.499585	+	0.865307i
$222$	10.0080	+	0.430078i	0.671691	+	0.0288650i
$223$	−4.58961	+	5.09728i	−0.307343	+	0.341339i	−0.876953	−	0.480576i	$-0.840428\pi$
$223$	−4.58961	+	5.09728i	−0.307343	+	0.341339i	0.569610	+	0.821915i	$0.307094\pi$
$224$	6.94477	−	21.3738i	0.464017	−	1.42810i
$225$	−6.78844	−	8.98290i	−0.452563	−	0.598860i
$226$	0.823601	+	0.598381i	0.0547851	+	0.0398037i
$227$	−27.5152	+	5.84854i	−1.82625	+	0.388181i	−0.987664	−	0.156590i	$-0.949950\pi$
$227$	−27.5152	+	5.84854i	−1.82625	+	0.388181i	−0.838585	+	0.544771i	$0.816617\pi$
$228$	−13.6642	+	2.29625i	−0.904936	+	0.152073i
$229$	1.46703	+	13.9578i	0.0969438	+	0.922358i	0.929600	+	0.368569i	$0.120152\pi$
$229$	1.46703	+	13.9578i	0.0969438	+	0.922358i	−0.832657	+	0.553789i	$0.813181\pi$
$230$	0.784218	−	1.35831i	0.0517098	−	0.0895640i
$231$	−21.9111	+	4.79616i	−1.44165	+	0.315564i
$232$	−1.28021	−	2.21739i	−0.0840499	−	0.145579i
$233$	11.7385	−	8.52854i	0.769017	−	0.558723i	−0.132646	−	0.991163i	$-0.542347\pi$
$233$	11.7385	−	8.52854i	0.769017	−	0.558723i	0.901663	+	0.432440i	$0.142347\pi$
$234$	−4.67153	−	2.58110i	−0.305388	−	0.168732i
$235$	4.42895	−	13.6309i	0.288913	−	0.889182i
$236$	−0.387010	+	3.68216i	−0.0251922	+	0.239688i
$237$	2.09489	+	7.53387i	0.136078	+	0.489377i
$238$	9.62682	+	10.6917i	0.624014	+	0.693038i
$239$	24.5986	+	5.22859i	1.59115	+	0.338209i	0.916533	−	0.399959i	$-0.130976\pi$
$239$	24.5986	+	5.22859i	1.59115	+	0.338209i	0.674617	+	0.738168i	$0.264309\pi$
$240$	−1.60568	+	2.52424i	−0.103646	+	0.162939i
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	−0.996419	−	0.0845570i	$-0.973053\pi$
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	0.424981	−	0.905202i	$-0.360281\pi$
$242$	−1.56731	+	7.13747i	−0.100750	+	0.458814i
$243$	−4.73851	−	14.8508i	−0.303976	−	0.952680i
$244$	−5.15048	+	3.74205i	−0.329726	+	0.239560i
$245$	6.16073	−	6.84218i	0.393594	−	0.437131i
$246$	−0.207350	−	3.35239i	−0.0132201	−	0.213741i
$247$	−12.5562	+	5.59036i	−0.798929	+	0.355706i
$248$	−0.929029	+	0.413630i	−0.0589934	+	0.0262655i
$249$	−0.695857	+	0.461265i	−0.0440982	+	0.0292315i
$250$	4.34470	−	4.82528i	0.274783	−	0.305177i
$251$	17.6993	−	12.8593i	1.11717	−	0.811670i	0.133390	−	0.991064i	$-0.457414\pi$
$251$	17.6993	−	12.8593i	1.11717	−	0.811670i	0.983777	+	0.179394i	$0.0574136\pi$
$252$	13.3358	−	12.4701i	0.840076	−	0.785541i
$253$	−2.49108	−	6.55523i	−0.156613	−	0.412124i
$254$	−2.54147	−	4.40195i	−0.159466	−	0.276203i
$255$	−4.95986	−	9.51186i	−0.310598	−	0.595656i
$256$	8.59329	+	1.82656i	0.537081	+	0.114160i
$257$	3.45520	+	3.83739i	0.215530	+	0.239370i	0.841209	−	0.540711i	$-0.181845\pi$
$257$	3.45520	+	3.83739i	0.215530	+	0.239370i	−0.625679	+	0.780081i	$0.715178\pi$
$258$	1.79929	−	1.83349i	0.112019	−	0.114148i
$259$	−3.55315	+	33.8059i	−0.220782	+	2.10060i
$260$	−1.44031	+	4.43283i	−0.0893244	+	0.274912i
$261$	−0.0611627	−	3.24855i	−0.00378587	−	0.201080i
$262$	−2.88024	+	2.09262i	−0.177942	+	0.129282i
$263$	13.9491	+	24.1605i	0.860135	+	1.48980i	0.871798	+	0.489866i	$0.162954\pi$
$263$	13.9491	+	24.1605i	0.860135	+	1.48980i	−0.0116625	+	0.999932i	$0.503712\pi$
$264$	−4.27479	−	12.8904i	−0.263095	−	0.793350i
$265$	−3.14954	+	5.45516i	−0.193475	+	0.335108i
$266$	1.39155	+	13.2397i	0.0853212	+	0.811777i
$267$	17.7337	+	21.4827i	1.08529	+	1.31472i
$268$	−14.8676	+	3.16020i	−0.908183	+	0.193040i
$269$	−2.44290	−	1.77487i	−0.148946	−	0.108216i	0.510816	−	0.859690i	$-0.329343\pi$
$269$	−2.44290	−	1.77487i	−0.148946	−	0.108216i	−0.659763	+	0.751474i	$0.729343\pi$
$270$	3.38359	−	1.84617i	0.205919	−	0.112354i
$271$	−7.84125	+	24.1329i	−0.476322	+	1.46597i	0.367845	+	0.929887i	$0.380096\pi$
$271$	−7.84125	+	24.1329i	−0.476322	+	1.46597i	−0.844167	+	0.536081i	$0.819904\pi$
$272$	5.74089	−	6.37590i	0.348093	−	0.386596i
$273$	9.72054	−	15.2813i	0.588314	−	0.924868i
$274$	5.55744	−	9.62577i	0.335737	−	0.581514i
$275$	−1.90595	−	12.3010i	−0.114933	−	0.741779i
$276$	4.46973	+	3.55038i	0.269046	+	0.213708i
$277$	−9.65105	−	4.29692i	−0.579875	−	0.258177i	0.0957707	−	0.995403i	$-0.469468\pi$
$277$	−9.65105	−	4.29692i	−0.579875	−	0.258177i	−0.675646	+	0.737226i	$0.736135\pi$
$278$	−2.82066	−	8.68109i	−0.169172	−	0.520657i
$279$	−1.28573	−	0.110709i	−0.0769746	−	0.00662799i
$280$	8.33875	+	6.05845i	0.498335	+	0.362062i
$281$	2.35926	−	22.4469i	0.140742	−	1.33907i	−0.665019	−	0.746827i	$-0.731576\pi$
$281$	2.35926	−	22.4469i	0.140742	−	1.33907i	0.805761	−	0.592241i	$-0.201757\pi$
$282$	−13.2218	−	6.58081i	−0.787345	−	0.391882i
$283$	5.74880	+	1.22195i	0.341731	+	0.0726371i	0.375580	−	0.926790i	$-0.377443\pi$
$283$	5.74880	+	1.22195i	0.341731	+	0.0726371i	−0.0338497	+	0.999427i	$0.510777\pi$
$284$	1.02922	+	9.79234i	0.0610728	+	0.581069i
$285$	1.46045	−	9.81817i	0.0865095	−	0.581578i
$286$	−3.19697	−	4.95930i	−0.189041	−	0.293250i
$287$	11.3977			0.672782
$288$	13.0474	+	11.3105i	0.768826	+	0.666480i
$289$	4.25344	+	13.0907i	0.250202	+	0.770044i
$290$	0.785839	−	0.167035i	0.0461461	−	0.00980865i
$291$	3.71939	+	13.3760i	0.218034	+	0.784117i
$292$	16.6210	−	7.40014i	0.972670	−	0.433061i
$293$	4.74689	+	5.27195i	0.277316	+	0.307991i	0.865672	−	0.500611i	$-0.166891\pi$
$293$	4.74689	+	5.27195i	0.277316	+	0.307991i	−0.588356	+	0.808602i	$0.700225\pi$
$294$	−6.03982	−	7.31666i	−0.352250	−	0.426716i
$295$	−2.42308	−	1.07883i	−0.141077	−	0.0628117i
$296$	−20.5814			−1.19627
$297$	3.16263	−	16.9410i	0.183515	−	0.983017i
$298$	−3.69339			−0.213953
$299$	5.17278	+	2.30307i	0.299150	+	0.133190i
$300$	6.45038	+	7.81400i	0.372413	+	0.451142i
$301$	5.83291	+	6.47811i	0.336204	+	0.373392i
$302$	0.0994733	−	0.0442884i	0.00572405	−	0.00254851i
$303$	0.817277	+	2.93917i	0.0469514	+	0.168851i
$304$	7.76540	−	1.65059i	0.445376	−	0.0946676i
$305$	−1.40936	−	4.33757i	−0.0806999	−	0.248369i
$306$	−10.4469	+	3.61320i	−0.597210	+	0.206553i
$307$	−18.5370			−1.05796			−0.528981	−	0.848633i	$-0.677426\pi$
$307$	−18.5370			−1.05796			−0.528981	+	0.848633i	$0.677426\pi$
$308$	19.5144	−	5.15867i	1.11194	−	0.293942i
$309$	−0.684919	+	4.60451i	−0.0389637	+	0.261941i
$310$	−0.0333543	−	0.317345i	−0.00189440	−	0.0180240i
$311$	−6.72598	−	1.42965i	−0.381395	−	0.0810680i	0.0132247	−	0.999913i	$-0.495790\pi$
$311$	−6.72598	−	1.42965i	−0.381395	−	0.0810680i	−0.394620	+	0.918845i	$0.629124\pi$
$312$	9.81698	+	4.88616i	0.555777	+	0.276624i
$313$	2.64727	−	25.1871i	0.149632	−	1.42366i	−0.619715	−	0.784827i	$-0.712752\pi$
$313$	2.64727	−	25.1871i	0.149632	−	1.42366i	0.769348	−	0.638830i	$-0.220581\pi$
$314$	12.8197	+	9.31407i	0.723459	+	0.525624i
$315$	5.54398	+	11.8466i	0.312368	+	0.667483i
$316$	−2.17455	−	6.69256i	−0.122328	−	0.376486i
$317$	10.0301	+	4.46567i	0.563344	+	0.250817i	0.668593	−	0.743629i	$-0.266897\pi$
$317$	10.0301	+	4.46567i	0.563344	+	0.250817i	−0.105248	+	0.994446i	$0.533564\pi$
$318$	5.08265	+	4.03723i	0.285021	+	0.226397i
$319$	1.64149	−	3.19503i	0.0919060	−	0.178888i
$320$	−0.407582	+	0.705953i	−0.0227845	+	0.0394640i
$321$	9.55321	−	15.0183i	0.533208	−	0.838238i
$322$	3.66979	−	4.07571i	0.204509	−	0.227131i
$323$	−8.79675	+	27.0736i	−0.489464	+	1.50642i
$324$	4.83405	+	13.1689i	0.268558	+	0.731605i
$325$	8.13140	+	5.90780i	0.451049	+	0.327706i
$326$	−2.72659	+	0.579555i	−0.151012	+	0.0320986i
$327$	2.60536	+	3.15613i	0.144076	+	0.174535i
$328$	0.721351	+	6.86319i	0.0398299	+	0.378956i
$329$	25.0583	−	43.4023i	1.38151	−	2.39284i
$330$	4.26121	−	0.0257952i	0.234572	−	0.00141998i
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	0.912495	−	0.409088i	$-0.134153\pi$
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	−0.810528	+	0.585700i	$0.800820\pi$
$332$	0.607805	−	0.441596i	0.0333576	−	0.0242357i
$333$	−22.8601	−	12.6306i	−1.25273	−	0.692153i
$334$	−3.25182	+	10.0081i	−0.177931	+	0.547617i
$335$	1.13821	−	10.8293i	0.0621869	−	0.591668i
$336$	−7.32711	+	7.46637i	−0.399727	+	0.407324i
$337$	−21.5428	−	23.9257i	−1.17351	−	1.30331i	−0.943976	−	0.330013i	$-0.892947\pi$
$337$	−21.5428	−	23.9257i	−1.17351	−	1.30331i	−0.229533	−	0.973301i	$-0.573720\pi$
$338$	−3.78725	−	0.805004i	−0.205999	−	0.0437864i
$339$	−1.22721	−	2.35351i	−0.0666530	−	0.127825i
$340$	4.82678	+	8.36023i	0.261769	+	0.453397i
$341$	−1.19390	−	0.781045i	−0.0646535	−	0.0422960i
$342$	−9.78571	−	2.97712i	−0.529151	−	0.160984i
$343$	3.93417	−	2.85834i	0.212425	−	0.154336i
$344$	−3.53168	+	3.92233i	−0.190416	+	0.211478i
$345$	−3.40847	+	2.25938i	−0.183506	+	0.121641i
$346$	1.57966	−	0.703310i	0.0849230	−	0.0378102i
$347$	−19.6618	+	8.75398i	−1.05550	+	0.469939i	−0.859750	−	0.510715i	$-0.829381\pi$
$347$	−19.6618	+	8.75398i	−1.05550	+	0.469939i	−0.195749	+	0.980654i	$0.562714\pi$
$348$	0.180502	+	2.91832i	0.00967592	+	0.156438i
$349$	−11.2547	+	12.4997i	−0.602453	+	0.669092i	−0.964810	−	0.262948i	$-0.915305\pi$
$349$	−11.2547	+	12.4997i	−0.602453	+	0.669092i	0.362357	+	0.932039i	$0.381972\pi$
$350$	7.87593	−	5.72219i	0.420986	−	0.305864i
$351$	7.90531	+	11.4517i	0.421954	+	0.611248i
$352$	6.78127	+	17.8448i	0.361443	+	0.951129i
$353$	−1.56543	−	2.71140i	−0.0833193	−	0.144313i	0.821355	−	0.570418i	$-0.193219\pi$
$353$	−1.56543	−	2.71140i	−0.0833193	−	0.144313i	−0.904674	+	0.426105i	$0.859885\pi$
$354$	−1.46696	+	2.30615i	−0.0779680	+	0.122571i
$355$	−6.89965	−	1.46657i	−0.366195	−	0.0778372i
$356$	−16.7740	−	18.6294i	−0.889018	−	0.987355i
$357$	−10.0491	−	36.1396i	−0.531855	−	1.91271i
$358$	0.526915	−	5.01326i	0.0278483	−	0.264959i
$359$	2.62315	−	8.07323i	0.138445	−	0.426089i	−0.857665	−	0.514208i	$-0.828086\pi$
$359$	2.62315	−	8.07323i	0.138445	−	0.426089i	0.996110	+	0.0881197i	$0.0280858\pi$
$360$	−6.78268	+	4.08812i	−0.357479	+	0.215463i
$361$	−5.93893	+	4.31489i	−0.312575	+	0.227099i
$362$	−0.797247	−	1.38087i	−0.0419024	−	0.0725770i
$363$	11.9502	−	14.8389i	0.627224	−	0.778839i
$364$	−8.14907	+	14.1146i	−0.427127	+	0.739806i
$365$	1.36242	+	12.9626i	0.0713124	+	0.678492i
$366$	−4.63474	+	0.778858i	−0.242262	+	0.0407116i
$367$	10.7703	−	2.28931i	0.562208	−	0.119501i	0.0819628	−	0.996635i	$-0.473881\pi$
$367$	10.7703	−	2.28931i	0.562208	−	0.119501i	0.480245	+	0.877134i	$0.340548\pi$
$368$	−2.64596	−	1.92241i	−0.137930	−	0.100212i
$369$	−3.41066	+	8.06576i	−0.177552	+	0.419887i
$370$	1.99561	−	6.14185i	0.103747	−	0.319300i
$371$	−14.7384	+	16.3687i	−0.765181	+	0.849820i
$372$	1.16024	+	0.0498598i	0.0601558	+	0.00258511i
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	−0.972599	−	0.232491i	$-0.925312\pi$
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	0.687642	+	0.726050i	$0.258646\pi$
$374$	−12.0638	−	1.95229i	−0.623805	−	0.100950i
$375$	−15.7468	+	6.21531i	−0.813161	+	0.320957i
$376$	27.7210	+	12.3422i	1.42960	+	0.636499i
$377$	0.896269	+	2.75843i	0.0461602	+	0.142067i
$378$	12.9152	−	3.85459i	0.664286	−	0.198259i
$379$	−20.5384	−	14.9220i	−1.05499	−	0.766492i	−0.0818315	−	0.996646i	$-0.526077\pi$
$379$	−20.5384	−	14.9220i	−1.05499	−	0.766492i	−0.973154	+	0.230154i	$0.926077\pi$
$380$	−0.933713	+	8.88368i	−0.0478984	+	0.455723i
$381$	0.818121	+	13.2272i	0.0419136	+	0.677651i
$382$	−10.7336	−	2.28150i	−0.549179	−	0.116732i
$383$	1.26633	+	12.0484i	0.0647067	+	0.615643i	0.978038	+	0.208426i	$0.0668340\pi$
$383$	1.26633	+	12.0484i	0.0647067	+	0.615643i	−0.913331	+	0.407217i	$0.866499\pi$
$384$	−14.9549	−	11.8789i	−0.763166	−	0.606195i
$385$	−0.805292	+	14.4377i	−0.0410415	+	0.735814i
$386$	5.40422			0.275068
$387$	−6.32980	+	2.18925i	−0.321762	+	0.111286i
$388$	−3.86080	−	11.8823i	−0.196003	−	0.603234i
$389$	−14.0375	+	2.98376i	−0.711728	+	0.151283i	−0.549528	−	0.835475i	$-0.685192\pi$
$389$	−14.0375	+	2.98376i	−0.711728	+	0.151283i	−0.162200	+	0.986758i	$0.551859\pi$
$390$	−2.40999	+	2.45579i	−0.122034	+	0.124354i
$391$	10.7136	−	4.77002i	0.541812	−	0.241230i
$392$	13.0434	+	14.4862i	0.658792	+	0.731663i
$393$	9.15391	−	1.53830i	0.461754	−	0.0775968i
$394$	13.9021	+	6.18960i	0.700376	+	0.311828i
$395$	5.04123			0.253652
$396$	−2.18890	+	15.3534i	−0.109996	+	0.771538i
$397$	−5.03882			−0.252891			−0.126446	−	0.991974i	$-0.540357\pi$
$397$	−5.03882			−0.252891			−0.126446	+	0.991974i	$0.540357\pi$
$398$	−5.62692	−	2.50527i	−0.282052	−	0.125578i
$399$	12.1332	−	32.5196i	0.607417	−	1.62802i
$400$	−3.88464	−	4.31433i	−0.194232	−	0.215717i
$401$	−16.6267	+	7.40268i	−0.830297	+	0.369672i	−0.777461	−	0.628931i	$-0.783493\pi$
$401$	−16.6267	+	7.40268i	−0.830297	+	0.369672i	−0.0528362	+	0.998603i	$0.516826\pi$
$402$	−10.8652	−	2.80197i	−0.541906	−	0.139750i
$403$	1.12680	−	0.239509i	0.0561301	−	0.0119308i
$404$	−0.848352	−	2.61096i	−0.0422071	−	0.129900i
$405$	−10.0425	+	0.378288i	−0.499015	+	0.0187973i
$406$	2.80926			0.139421
$407$	−15.6444	−	24.2683i	−0.775464	−	1.20294i
$408$	21.1257	−	8.33840i	1.04588	−	0.412812i
$409$	−1.71745	−	16.3404i	−0.0849224	−	0.807983i	−0.951232	−	0.308476i	$-0.900181\pi$
$409$	−1.71745	−	16.3404i	−0.0849224	−	0.807983i	0.866310	−	0.499507i	$-0.166486\pi$
$410$	−2.11804	−	0.450203i	−0.104603	−	0.0222340i
$411$	−24.1544	+	16.0113i	−1.19145	+	0.789780i
$412$	0.437891	−	4.16626i	0.0215733	−	0.205257i
$413$	−7.50342	−	5.45155i	−0.369219	−	0.268253i
$414$	1.78610	+	3.81662i	0.0877820	+	0.187577i
$415$	0.166318	+	0.511874i	0.00816423	+	0.0251269i
$416$	−14.0814	−	6.26946i	−0.690399	−	0.307386i
$417$	−3.50150	+	23.5396i	−0.171469	+	1.15274i
$418$	−7.96912	−	8.02285i	−0.389783	−	0.392410i
$419$	8.70324	−	15.0745i	0.425181	−	0.736435i	−0.571256	−	0.820772i	$-0.693544\pi$
$419$	8.70324	−	15.0745i	0.425181	−	0.736435i	0.996437	+	0.0843365i	$0.0268771\pi$
$420$	−5.44216	−	10.4368i	−0.265550	−	0.509264i
$421$	3.04364	−	3.38030i	0.148338	−	0.164746i	−0.664397	−	0.747380i	$-0.731311\pi$
$421$	3.04364	−	3.38030i	0.148338	−	0.164746i	0.812734	+	0.582634i	$0.197978\pi$
$422$	−0.864374	+	2.66027i	−0.0420771	+	0.129500i
$423$	23.2159	+	30.7208i	1.12880	+	1.49369i
$424$	−10.7893	−	7.83890i	−0.523976	−	0.380691i
$425$	20.3622	−	4.32812i	0.987712	−	0.209945i
$426$	−2.54087	+	6.81009i	−0.123105	+	0.329950i
$427$	−1.66701	−	15.8606i	−0.0806723	−	0.767546i
$428$	−8.00879	+	13.8716i	−0.387120	+	0.670511i
$429$	1.70065	+	15.2897i	0.0821080	+	0.738192i
$430$	−0.828055	−	1.43423i	−0.0399323	−	0.0691648i
$431$	−10.1004	+	7.33838i	−0.486520	+	0.353477i	−0.803844	−	0.594840i	$-0.797216\pi$
$431$	−10.1004	+	7.33838i	−0.486520	+	0.353477i	0.317325	+	0.948317i	$0.397216\pi$
$432$	−3.09113	−	7.41942i	−0.148722	−	0.356967i
$433$	8.86451	−	27.2822i	0.426001	−	1.31110i	−0.476031	−	0.879428i	$-0.657925\pi$
$433$	8.86451	−	27.2822i	0.426001	−	1.31110i	0.902032	−	0.431668i	$-0.142075\pi$
$434$	0.116631	−	1.10967i	0.00559848	−	0.0532660i
$435$	−2.02829	−	0.523068i	−0.0972492	−	0.0250792i
$436$	−2.46435	−	2.73694i	−0.118021	−	0.131075i
$437$	10.6146	+	2.25620i	0.507764	+	0.107929i
$438$	13.4186	+	0.576646i	0.641167	+	0.0275532i
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	0.910871	−	0.412692i	$-0.135411\pi$
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	−0.812837	+	0.582491i	$0.802078\pi$
$440$	−8.74476	+	0.428841i	−0.416890	+	0.0204442i
$441$	5.59753	+	24.0947i	0.266549	+	1.14737i
$442$	7.98309	−	5.80005i	0.379717	−	0.275880i
$443$	−14.2054	+	15.7767i	−0.674921	+	0.749576i	−0.979176	−	0.203015i	$-0.934926\pi$
$443$	−14.2054	+	15.7767i	−0.674921	+	0.749576i	0.304255	+	0.952591i	$0.401593\pi$
$444$	21.0409	+	10.4726i	0.998559	+	0.497008i
$445$	16.4061	−	7.30446i	0.777723	−	0.346265i
$446$	4.16267	−	1.85334i	0.197108	−	0.0877583i
$447$	8.62081	+	4.29080i	0.407751	+	0.202948i
$448$	−1.90730	+	2.11827i	−0.0901116	+	0.100079i
$449$	−20.9494	+	15.2206i	−0.988663	+	0.718306i	−0.959628	−	0.281273i	$-0.909243\pi$
$449$	−20.9494	+	15.2206i	−0.988663	+	0.718306i	−0.0290350	+	0.999578i	$0.509243\pi$
$450$	1.69261	+	7.28586i	0.0797903	+	0.343459i
$451$	−7.54435	+	6.06744i	−0.355249	+	0.285705i
$452$	1.19428	+	2.06856i	0.0561744	+	0.0972970i
$453$	−0.283634	−	0.0121888i	−0.0133263	−	0.000572679i
$454$	18.2789	+	3.88530i	0.857872	+	0.182346i
$455$	−7.81266	−	8.67684i	−0.366263	−	0.406776i
$456$	20.3498	+	5.24793i	0.952969	+	0.245757i
$457$	1.07705	−	10.2474i	0.0503821	−	0.479354i	−0.940018	−	0.341124i	$-0.889192\pi$
$457$	1.07705	−	10.2474i	0.0503821	−	0.479354i	0.990400	−	0.138229i	$-0.0441411\pi$
$458$	2.88113	−	8.86721i	0.134626	−	0.414338i
$459$	28.5819	+	3.70305i	1.33409	+	0.172844i
$460$	2.97717	−	2.16304i	0.138811	−	0.100852i
$461$	12.7266	+	22.0432i	0.592738	+	1.02665i	0.993862	+	0.110628i	$0.0352863\pi$
$461$	12.7266	+	22.0432i	0.592738	+	1.02665i	−0.401124	+	0.916024i	$0.631380\pi$
$462$	14.5935	+	3.00973i	0.678951	+	0.140025i
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.136368	−	0.990658i	$-0.456457\pi$
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.789751	−	0.613427i	$-0.210210\pi$
$464$	−0.175115	−	1.66611i	−0.00812951	−	0.0773471i
$465$	−0.290822	+	0.779469i	−0.0134866	+	0.0361470i
$466$	−9.42840	+	2.00407i	−0.436762	+	0.0928367i
$467$	14.0582	+	10.2139i	0.650537	+	0.472643i	0.863454	−	0.504427i	$-0.168296\pi$
$467$	14.0582	+	10.2139i	0.650537	+	0.472643i	−0.212917	+	0.977070i	$0.568296\pi$
$468$	−7.54991	−	9.99052i	−0.348995	−	0.461812i
$469$	11.7661	−	36.2123i	0.543308	−	1.67213i
$470$	−6.37099	+	7.07570i	−0.293872	+	0.326378i
$471$	−19.1021	−	36.6334i	−0.880179	−	1.68798i
$472$	2.80781	−	4.86327i	0.129240	−	0.223850i
$473$	−7.30949	−	1.18289i	−0.336091	−	0.0543896i
$474$	0.764314	−	5.13826i	0.0351061	−	0.236008i
$475$	17.5971	+	7.83475i	0.807412	+	0.359483i
$476$	10.4312	+	32.1039i	0.478112	+	1.47148i
$477$	−7.17324	−	15.3281i	−0.328440	−	0.701826i
$478$	−13.5158	−	9.81979i	−0.618197	−	0.449147i
$479$	2.28875	−	21.7760i	0.104576	−	0.994972i	−0.808863	−	0.587997i	$-0.799917\pi$
$479$	2.28875	−	21.7760i	0.104576	−	0.994972i	0.913439	−	0.406975i	$-0.133416\pi$
$480$	9.27859	−	6.15053i	0.423508	−	0.280732i
$481$	22.8047	+	4.84729i	1.03980	+	0.221017i
$482$	1.23203	+	11.7219i	0.0561172	+	0.533920i
$483$	−13.3007	+	5.24982i	−0.605202	+	0.238875i
$484$	−10.1708	+	13.8029i	−0.462310	+	0.627407i
$485$	8.95046			0.406420
$486$	−1.13700	+	10.2931i	−0.0515753	+	0.466906i
$487$	1.01084	+	3.11106i	0.0458057	+	0.140975i	0.971344	−	0.237679i	$-0.0763867\pi$
$487$	1.01084	+	3.11106i	0.0458057	+	0.140975i	−0.925538	+	0.378655i	$0.876387\pi$
$488$	9.44506	−	2.00761i	0.427558	−	0.0908802i
$489$	7.03748	+	1.81487i	0.318246	+	0.0820711i
$490$	−5.58764	+	2.48778i	−0.252424	+	0.112386i
$491$	−4.83373	−	5.36841i	−0.218143	−	0.242273i	0.624134	−	0.781318i	$-0.285452\pi$
$491$	−4.83373	−	5.36841i	−0.218143	−	0.242273i	−0.842277	+	0.539045i	$0.818785\pi$
$492$	2.75480	−	7.38349i	0.124196	−	0.332873i
$493$	5.48781	+	2.44333i	0.247159	+	0.110042i
$494$	9.13071			0.410810
$495$	−9.97614	−	4.89025i	−0.448394	−	0.219800i
$496$	−0.665390			−0.0298769
$497$	−22.5328	−	10.0323i	−1.01074	−	0.450009i
$498$	0.546942	−	0.0919125i	0.0245091	−	0.00411870i
$499$	9.92622	+	11.0242i	0.444359	+	0.493511i	0.923162	−	0.384412i	$-0.125596\pi$
$499$	9.92622	+	11.0242i	0.444359	+	0.493511i	−0.478803	+	0.877922i	$0.658929\pi$
$500$	13.9174	−	6.19642i	0.622405	−	0.277112i
$501$	19.2170	−	19.5822i	0.858551	−	0.874868i
$502$	−14.2161	+	3.02172i	−0.634494	+	0.134866i
$503$	−10.1918	−	31.3671i	−0.454430	−	1.39859i	−0.871803	−	0.489856i	$-0.837049\pi$
$503$	−10.1918	−	31.3671i	−0.454430	−	1.39859i	0.417374	−	0.908735i	$-0.362951\pi$
$504$	−26.1711	+	9.05162i	−1.16575	+	0.403191i
$505$	1.96673			0.0875181
$506$	−0.259440	+	4.65138i	−0.0115335	+	0.206779i
$507$	7.90466	+	6.27880i	0.351058	+	0.278851i
$508$	−1.24660	−	11.8606i	−0.0553090	−	0.526230i
$509$	−37.8244	−	8.03982i	−1.67654	−	0.356359i	−0.731126	−	0.682243i	$-0.761005\pi$
$509$	−37.8244	−	8.03982i	−1.67654	−	0.356359i	−0.945410	+	0.325884i	$0.894338\pi$
$510$	0.439936	+	7.11279i	0.0194807	+	0.314960i
$511$	−4.76404	+	45.3268i	−0.210749	+	2.00514i
$512$	13.1198	+	9.53213i	0.579821	+	0.421264i
$513$	19.3823	+	18.3175i	0.855751	+	0.808736i
$514$	−1.06004	−	3.26247i	−0.0467564	−	0.143901i
$515$	2.74165	+	1.22066i	0.120812	+	0.0537888i
$516$	5.60638	−	2.21285i	0.246807	−	0.0974155i
$517$	6.51820	+	42.0685i	0.286670	+	1.85017i
$518$	11.2908	−	19.5563i	0.496091	−	0.859255i
$519$	−4.50418	−	0.193561i	−0.197711	−	0.00849637i
$520$	4.73037	−	5.25361i	0.207440	−	0.230386i
$521$	−5.40297	+	16.6286i	−0.236708	+	0.728514i	0.760182	+	0.649710i	$0.225110\pi$
$521$	−5.40297	+	16.6286i	−0.236708	+	0.728514i	−0.996890	+	0.0788032i	$0.974890\pi$
$522$	−0.840650	+	1.98803i	−0.0367942	+	0.0870136i
$523$	−11.7211	−	8.51591i	−0.512530	−	0.372375i	0.301253	−	0.953544i	$-0.402595\pi$
$523$	−11.7211	−	8.51591i	−0.512530	−	0.372375i	−0.813782	+	0.581170i	$0.802595\pi$
$524$	−8.17061	+	1.73672i	−0.356935	+	0.0758688i
$525$	−25.0311	+	4.20642i	−1.09245	+	0.183583i
$526$	−1.93726	−	18.4318i	−0.0844683	−	0.803663i
$527$	1.19296	−	2.06627i	0.0519663	−	0.0900082i
$528$	0.875316	−	8.84267i	0.0380933	−	0.384828i
$529$	9.26470	+	16.0469i	0.402813	+	0.697693i
$530$	3.38542	−	2.45965i	0.147053	−	0.106840i
$531$	6.10323	−	3.67860i	0.264857	−	0.159637i
$532$	−9.65216	+	29.7063i	−0.418474	+	1.28793i
$533$	0.817130	−	7.77447i	0.0353938	−	0.336750i
$534$	−4.95768	−	17.8293i	−0.214540	−	0.771549i
$535$	−7.67818	−	8.52748i	−0.331956	−	0.368675i
$536$	22.5502	+	4.79319i	0.974021	+	0.207034i
$537$	−7.05403	+	11.0894i	−0.304404	+	0.478543i
$538$	1.00299	+	1.73722i	0.0432418	+	0.0748971i
$539$	−7.16664	+	26.3913i	−0.308689	+	1.13675i
$540$	9.01432	−	0.728114i	0.387915	−	0.0313330i
$541$	−26.7771	+	19.4547i	−1.15124	+	0.836422i	−0.988645	−	0.150272i	$-0.951985\pi$
$541$	−26.7771	+	19.4547i	−1.15124	+	0.836422i	−0.162591	+	0.986694i	$0.551985\pi$
$542$	11.2795	−	12.5272i	0.484498	−	0.538089i
$543$	0.256641	+	4.14932i	0.0110135	+	0.178064i
$544$	−29.1649	+	12.9850i	−1.25043	+	0.556729i
$545$	2.41030	−	1.07314i	0.103246	−	0.0459681i
$546$	−10.0283	+	6.64751i	−0.429173	+	0.284487i
$547$	6.16546	−	6.84744i	0.263616	−	0.292775i	−0.596776	−	0.802408i	$-0.703552\pi$
$547$	6.16546	−	6.84744i	0.263616	−	0.292775i	0.860392	+	0.509633i	$0.170219\pi$
$548$	21.0980	−	15.3286i	0.901262	−	0.654805i
$549$	11.7229	+	3.56645i	0.500319	+	0.152213i
$550$	−2.16708	+	7.98032i	−0.0924046	+	0.340282i
$551$	2.77927	+	4.81383i	0.118401	+	0.205076i
$552$	−4.00301	−	7.67685i	−0.170380	−	0.326749i
$553$	17.2427	+	3.66504i	0.733232	+	0.155853i
$554$	4.69605	+	5.21549i	0.199516	+	0.221585i
$555$	−11.7933	+	12.0174i	−0.500596	+	0.510110i
$556$	2.23863	−	21.2991i	0.0949388	−	0.903283i
$557$	11.4496	−	35.2384i	0.485137	−	1.49310i	−0.346645	−	0.937996i	$-0.612679\pi$
$557$	11.4496	−	35.2384i	0.485137	−	1.49310i	0.831782	−	0.555102i	$-0.187321\pi$
$558$	0.750379	+	0.414597i	0.0317661	+	0.0175513i
$559$	4.83697	−	3.51427i	0.204582	−	0.148638i
$560$	3.37202	+	5.84052i	0.142494	+	0.246807i
$561$	25.8903	+	18.5720i	1.09309	+	0.784110i
$562$	−7.49703	+	12.9852i	−0.316243	+	0.547749i
$563$	2.82165	+	26.8462i	0.118918	+	1.13143i	0.877407	+	0.479746i	$0.159271\pi$
$563$	2.82165	+	26.8462i	0.118918	+	1.13143i	−0.758489	+	0.651686i	$0.774062\pi$
$564$	−22.0598	−	26.7232i	−0.928883	−	1.12525i
$565$	−1.67376	+	0.355768i	−0.0704155	+	0.0149673i
$566$	−3.15870	−	2.29493i	−0.132770	−	0.0964630i
$567$	−34.6236	−	6.00715i	−1.45406	−	0.252277i
$568$	4.61492	−	14.2033i	0.193638	−	0.595956i
$569$	−18.3848	+	20.4184i	−0.770733	+	0.855985i	−0.992891	−	0.119025i	$-0.962023\pi$
$569$	−18.3848	+	20.4184i	−0.770733	+	0.855985i	0.222159	+	0.975011i	$0.428690\pi$
$570$	−3.53923	+	5.56390i	−0.148242	+	0.233046i
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	−0.0921492	−	0.995745i	$-0.529374\pi$
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	0.908415	−	0.418069i	$-0.137293\pi$
$572$	−2.11974	−	13.6808i	−0.0886310	−	0.572024i
$573$	22.4030	+	17.7950i	0.935897	+	0.743398i
$574$	−6.91709	−	3.07969i	−0.288714	−	0.128544i
$575$	−2.45223	−	7.54719i	−0.102265	−	0.314739i
$576$	−0.928290	−	1.98361i	−0.0386788	−	0.0826506i
$577$	23.5957	+	17.1433i	0.982302	+	0.713684i	0.958222	−	0.286026i	$-0.0923344\pi$
$577$	23.5957	+	17.1433i	0.982302	+	0.713684i	0.0240800	+	0.999710i	$0.492334\pi$
$578$	0.955807	−	9.09390i	0.0397563	−	0.378256i
$579$	−12.6141	−	6.27835i	−0.524223	−	0.260919i
$580$	1.84379	+	0.391910i	0.0765594	+	0.0162732i
$581$	0.196723	+	1.87169i	0.00816144	+	0.0776509i
$582$	1.35700	−	9.12273i	0.0562496	−	0.378149i
$583$	1.04195	−	18.6807i	0.0431532	−	0.773674i
$584$	−27.5954			−1.14191
$585$	8.47820	−	2.93230i	0.350530	−	0.121236i
$586$	−1.45632	−	4.48210i	−0.0601602	−	0.185154i
$587$	4.97675	−	1.05784i	0.205412	−	0.0436618i	−0.104056	−	0.994571i	$-0.533182\pi$
$587$	4.97675	−	1.05784i	0.205412	−	0.0436618i	0.309469	+	0.950910i	$0.399849\pi$
$588$	−5.96353	−	21.4466i	−0.245932	−	0.884444i
$589$	2.01687	−	0.897969i	0.0831037	−	0.0370002i
$590$	1.17903	+	1.30945i	0.0485401	+	0.0539092i
$591$	−25.2583	−	30.5980i	−1.03899	−	1.25863i
$592$	−12.3022	−	5.47729i	−0.505617	−	0.225115i
$593$	3.46422			0.142258			0.0711292	−	0.997467i	$-0.477340\pi$
$593$	3.46422			0.142258			0.0711292	+	0.997467i	$0.477340\pi$
$594$	−6.49688	+	9.42672i	−0.266570	+	0.386783i
$595$	−24.1825			−0.991386
$596$	−7.91653	−	3.52466i	−0.324274	−	0.144376i
$597$	10.2234	+	12.3846i	0.418416	+	0.506870i
$598$	−2.51700	−	2.79541i	−0.102928	−	0.114313i
$599$	22.7243	−	10.1175i	0.928489	−	0.413390i	0.113942	−	0.993487i	$-0.463652\pi$
$599$	22.7243	−	10.1175i	0.928489	−	0.413390i	0.814547	+	0.580097i	$0.196985\pi$
$600$	−4.11713	−	14.8065i	−0.168081	−	0.604471i
$601$	−10.8263	+	2.30119i	−0.441612	+	0.0938676i	−0.423351	−	0.905966i	$-0.639146\pi$
$601$	−10.8263	+	2.30119i	−0.441612	+	0.0938676i	−0.0182611	+	0.999833i	$0.505813\pi$
$602$	−1.78951	−	5.50755i	−0.0729351	−	0.224471i
$603$	22.1054	+	19.1627i	0.900201	+	0.780367i
$604$	0.255479			0.0103953
$605$	−7.15276	−	9.98532i	−0.290801	−	0.405961i
$606$	0.298180	−	2.00458i	0.0121127	−	0.0814304i
$607$	2.92272	+	27.8078i	0.118630	+	1.12869i	0.878211	+	0.478273i	$0.158737\pi$
$607$	2.92272	+	27.8078i	0.118630	+	1.12869i	−0.759582	+	0.650412i	$0.774596\pi$
$608$	−28.8952	−	6.14186i	−1.17185	−	0.249085i
$609$	−6.55715	−	3.26366i	−0.265709	−	0.132250i
$610$	−0.316703	+	3.01323i	−0.0128229	+	0.122002i
$611$	−27.8087	−	20.2042i	−1.12502	−	0.817375i
$612$	−25.8403	−	2.22501i	−1.04453	−	0.0899407i
$613$	3.39680	+	10.4543i	0.137196	+	0.422245i	0.995925	−	0.0901845i	$-0.0287457\pi$
$613$	3.39680	+	10.4543i	0.137196	+	0.422245i	−0.858729	+	0.512429i	$0.828746\pi$
$614$	11.2499	+	5.00876i	0.454008	+	0.202137i
$615$	4.42073	+	3.51146i	0.178261	+	0.141596i
$616$	−30.2217	−	4.89078i	−1.21767	−	0.197055i
$617$	−9.31311	+	16.1308i	−0.374932	+	0.649401i	−0.990317	−	0.138826i	$-0.955667\pi$
$617$	−9.31311	+	16.1308i	−0.374932	+	0.649401i	0.615385	+	0.788227i	$0.289001\pi$
$618$	1.65982	−	2.60935i	0.0667679	−	0.104963i
$619$	1.79895	−	1.99793i	0.0723057	−	0.0803036i	−0.705906	−	0.708305i	$-0.749460\pi$
$619$	1.79895	−	1.99793i	0.0723057	−	0.0803036i	0.778212	+	0.628001i	$0.216127\pi$
$620$	0.231355	−	0.712036i	0.00929142	−	0.0285961i
$621$	0.264990	−	10.9834i	0.0106337	−	0.440750i
$622$	3.69561	+	2.68502i	0.148180	+	0.107659i
$623$	61.4246	−	13.0562i	2.46093	−	0.523086i
$624$	4.56759	+	5.53320i	0.182850	+	0.221505i
$625$	−0.820749	−	7.80890i	−0.0328299	−	0.312356i
$626$	−8.41222	+	14.5704i	−0.336220	+	0.582350i
$627$	9.28033	+	27.9844i	0.370621	+	1.11759i
$628$	18.5896	+	32.1981i	0.741805	+	1.28484i
$629$	39.0652	−	28.3826i	1.55763	−	1.13169i
$630$	−0.163567	−	8.68758i	−0.00651667	−	0.346121i
$631$	−12.1224	+	37.3089i	−0.482585	+	1.48524i	0.352863	+	0.935675i	$0.385208\pi$
$631$	−12.1224	+	37.3089i	−0.482585	+	1.48524i	−0.835448	+	0.549569i	$0.814792\pi$
$632$	−1.11566	+	10.6148i	−0.0443784	+	0.422233i
$633$	5.10811	−	5.20519i	0.203029	−	0.206888i
$634$	−4.88047	−	5.42031i	−0.193828	−	0.215268i
$635$	8.35695	+	1.77633i	0.331636	+	0.0704913i
$636$	7.04150	+	13.5040i	0.279213	+	0.535467i
$637$	−11.0407	−	19.1230i	−0.437447	−	0.757681i
$638$	−1.85951	+	1.49549i	−0.0736187	+	0.0592069i
$639$	13.8423	−	12.9437i	0.547593	−	0.512045i
$640$	−9.96109	+	7.23716i	−0.393747	+	0.286074i
$641$	17.2294	−	19.1352i	0.680521	−	0.755795i	−0.299628	−	0.954056i	$-0.596863\pi$
$641$	17.2294	−	19.1352i	0.680521	−	0.755795i	0.980149	+	0.198261i	$0.0635293\pi$
$642$	−9.85571	+	6.53308i	−0.388974	+	0.257840i
$643$	−12.1794	+	5.42264i	−0.480310	+	0.213848i	−0.632586	−	0.774490i	$-0.718007\pi$
$643$	−12.1794	+	5.42264i	−0.480310	+	0.213848i	0.152276	+	0.988338i	$0.451340\pi$
$644$	11.7555	−	5.23386i	0.463230	−	0.206243i
$645$	0.266558	+	4.30966i	0.0104957	+	0.169693i
$646$	12.6540	−	14.0537i	0.497866	−	0.552936i
$647$	−19.2955	+	14.0190i	−0.758585	+	0.551145i	−0.898476	−	0.439022i	$-0.855325\pi$
$647$	−19.2955	+	14.0190i	−0.758585	+	0.551145i	0.139891	+	0.990167i	$0.455325\pi$
$648$	1.42595	−	21.2291i	0.0560165	−	0.833957i
$649$	7.86876	−	0.385882i	0.308876	−	0.0151472i
$650$	−3.33853	−	5.78250i	−0.130948	−	0.226808i
$651$	−1.56139	+	2.45461i	−0.0611958	+	0.0962037i
$652$	−6.39733	−	1.35979i	−0.250539	−	0.0532537i
$653$	8.51464	+	9.45647i	0.333204	+	0.370060i	0.886344	−	0.463028i	$-0.153237\pi$
$653$	8.51464	+	9.45647i	0.333204	+	0.370060i	−0.553140	+	0.833088i	$0.686570\pi$
$654$	−0.728358	−	2.61939i	−0.0284810	−	0.102426i
$655$	0.625511	−	5.95134i	0.0244407	−	0.232538i
$656$	−1.39531	+	4.29433i	−0.0544778	+	0.167666i
$657$	−30.6507	−	16.9350i	−1.19580	−	0.660698i
$658$	−26.9350	+	19.5694i	−1.05004	+	0.762896i
$659$	13.6263	+	23.6015i	0.530806	+	0.919383i	0.999354	+	0.0359452i	$0.0114442\pi$
$659$	13.6263	+	23.6015i	0.530806	+	0.919383i	−0.468547	+	0.883438i	$0.655223\pi$
$660$	9.15822	+	4.01125i	0.356483	+	0.156138i
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	0.0335234	+	0.999438i	$0.489327\pi$
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	−0.882300	+	0.470687i	$0.844006\pi$
$662$	−0.257641	−	2.45129i	−0.0100135	−	0.0952723i
$663$	−25.3717	+	4.26366i	−0.985354	+	0.165587i
$664$	−1.11461	+	0.236917i	−0.0432551	+	0.00919415i
$665$	−18.1030	−	13.1526i	−0.702003	−	0.510035i
$666$	10.4607	+	13.8422i	0.405343	+	0.536376i
$667$	0.707636	−	2.17788i	0.0273998	−	0.0843278i
$668$	−16.5209	+	18.3483i	−0.639212	+	0.709917i
$669$	−11.8693	−	0.510066i	−0.458893	−	0.0197203i
$670$	−3.61688	+	6.26462i	−0.139732	+	0.242023i
$671$	9.54666	+	9.61102i	0.368545	+	0.371029i
$672$	36.2074	−	14.2912i	1.39673	−	0.551294i
$673$	−24.3795	−	10.8545i	−0.939761	−	0.418408i	−0.121070	−	0.992644i	$-0.538633\pi$
$673$	−24.3795	−	10.8545i	−0.939761	−	0.418408i	−0.818690	+	0.574236i	$0.805299\pi$
$674$	6.60922	+	20.3411i	0.254578	+	0.783510i
$675$	4.51360	−	18.9724i	0.173729	−	0.730250i
$676$	−7.34946	−	5.33970i	−0.282672	−	0.205373i
$677$	−2.83095	+	26.9347i	−0.108802	+	1.03518i	0.794817	+	0.606849i	$0.207567\pi$
$677$	−2.83095	+	26.9347i	−0.108802	+	1.03518i	−0.903620	+	0.428336i	$0.859100\pi$
$678$	0.108853	+	1.75991i	0.00418046	+	0.0675889i
$679$	30.6135	+	6.50711i	1.17484	+	0.249720i
$680$	−1.53050	−	14.5617i	−0.0586918	−	0.558415i
$681$	−38.1514	−	30.3043i	−1.46196	−	1.16126i
$682$	0.513524	+	0.796603i	0.0196638	+	0.0305035i
$683$	−16.7343			−0.640322			−0.320161	−	0.947363i	$-0.603737\pi$
$683$	−16.7343			−0.640322			−0.320161	+	0.947363i	$0.603737\pi$
$684$	−18.1339	−	15.7199i	−0.693366	−	0.601065i
$685$	5.77319	+	17.7681i	0.220582	+	0.678883i
$686$	−3.15993	+	0.671665i	−0.120647	+	0.0256443i
$687$	−17.0264	+	17.3500i	−0.649596	+	0.661942i
$688$	−3.15485	+	1.40463i	−0.120278	+	0.0535510i
$689$	10.1086	+	11.2268i	0.385108	+	0.427706i
$690$	2.67905	−	0.450208i	0.101990	−	0.0171391i
$691$	−34.2758	−	15.2606i	−1.30391	−	0.580540i	−0.367039	−	0.930205i	$-0.619629\pi$
$691$	−34.2758	−	15.2606i	−1.30391	−	0.580540i	−0.936875	+	0.349665i	$0.886295\pi$
$692$	4.05707			0.154226
$693$	−30.5664	−	23.9791i	−1.16112	−	0.910889i
$694$	14.2978			0.542738
$695$	14.0161	+	6.24037i	0.531661	+	0.236711i
$696$	1.55024	−	4.15500i	0.0587617	−	0.157495i
$697$	−10.8338	−	12.0322i	−0.410359	−	0.455750i
$698$	10.2078	−	4.54481i	0.386371	−	0.172024i
$699$	24.3352	+	6.27570i	0.920442	+	0.237369i
$700$	22.3423	−	4.74899i	0.844458	−	0.179495i
$701$	3.15219	+	9.70143i	0.119056	+	0.366418i	0.992771	−	0.120020i	$-0.0382959\pi$
$701$	3.15219	+	9.70143i	0.119056	+	0.366418i	−0.873715	+	0.486438i	$0.838296\pi$
$702$	−1.70333	−	9.08595i	−0.0642881	−	0.342927i
$703$	44.6811			1.68518
$704$	0.134839	−	2.41747i	0.00508193	−	0.0911117i
$705$	23.0908	−	9.11402i	0.869651	−	0.343254i
$706$	0.217408	+	2.06850i	0.00818225	+	0.0778489i
$707$	6.72685	+	1.42984i	0.252989	+	0.0537745i
$708$	−5.34512	+	3.54314i	−0.200882	+	0.133159i
$709$	1.51542	−	14.4183i	0.0569128	−	0.541489i	−0.928503	−	0.371325i	$-0.878904\pi$
$709$	1.51542	−	14.4183i	0.0569128	−	0.541489i	0.985416	−	0.170164i	$-0.0544297\pi$
$710$	3.79104	+	2.75435i	0.142275	+	0.103369i
$711$	−7.75336	+	11.1053i	−0.290774	+	0.416483i
$712$	11.7494	+	36.1610i	0.440329	+	1.35519i
$713$	−0.830893	−	0.369938i	−0.0311172	−	0.0138543i
$714$	−3.66637	+	24.6479i	−0.137210	+	0.922426i
$715$	9.79040	+	1.58438i	0.366140	+	0.0592525i
$716$	5.91364	−	10.2427i	0.221003	−	0.382789i
$717$	20.1393	+	38.6225i	0.752115	+	1.44238i
$718$	−3.77337	+	4.19075i	−0.140821	+	0.156397i
$719$	5.94135	−	18.2856i	0.221575	−	0.681938i	−0.777046	−	0.629444i	$-0.783283\pi$
$719$	5.94135	−	18.2856i	0.221575	−	0.681938i	0.998621	−	0.0524943i	$-0.0167171\pi$
$720$	−5.14220	+	0.638546i	−0.191638	+	0.0237972i
$721$	8.48991	+	6.16828i	0.316181	+	0.229719i
$722$	4.77016	−	1.01393i	0.177527	−	0.0377345i
$723$	10.7423	−	28.7917i	0.399509	−	1.07077i
$724$	−0.391054	−	3.72063i	−0.0145334	−	0.138276i
$725$	2.03241	−	3.52023i	0.0754818	−	0.130738i
$726$	−11.2620	+	5.77652i	−0.417970	+	0.214387i
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	0.859208	−	0.511627i	$-0.170957\pi$
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	−0.872686	+	0.488282i	$0.837624\pi$
$728$	19.9989	−	14.5300i	0.741207	−	0.538519i
$729$	14.6119	−	22.7044i	0.541182	−	0.840905i
$730$	2.67570	−	8.23495i	0.0990320	−	0.304789i
$731$	1.29439	−	12.3153i	0.0478746	−	0.455496i
$732$	−10.6775	−	2.75358i	−0.394652	−	0.101775i
$733$	−1.25521	−	1.39406i	−0.0463624	−	0.0514907i	0.719518	−	0.694474i	$-0.244363\pi$
$733$	−1.25521	−	1.39406i	−0.0463624	−	0.0514907i	−0.765880	+	0.642984i	$0.777696\pi$
$734$	−7.15496	−	1.52083i	−0.264095	−	0.0561350i
$735$	15.9324	+	0.684672i	0.587675	+	0.0252545i
$736$	6.08497	+	10.5395i	0.224295	+	0.388490i
$737$	11.4891	+	30.2333i	0.423206	+	1.11366i
$738$	4.24928	−	3.97343i	0.156418	−	0.146264i
$739$	42.5402	−	30.9073i	1.56487	−	1.13694i	0.632993	−	0.774157i	$-0.281826\pi$
$739$	42.5402	−	30.9073i	1.56487	−	1.13694i	0.931873	−	0.362784i	$-0.118174\pi$
$740$	10.1387	−	11.2602i	0.372706	−	0.413932i
$741$	−21.3121	−	10.6076i	−0.782921	−	0.389679i
$742$	13.3674	−	5.95157i	0.490734	−	0.218489i
$743$	−30.4510	+	13.5577i	−1.11714	+	0.497383i	−0.880420	−	0.474195i	$-0.842739\pi$
$743$	−30.4510	+	13.5577i	−1.11714	+	0.497383i	−0.236720	+	0.971578i	$0.576072\pi$
$744$	−1.57688	−	0.784854i	−0.0578113	−	0.0287741i
$745$	4.15399	−	4.61348i	0.152190	−	0.169025i
$746$	5.91558	−	4.29792i	0.216585	−	0.157358i
$747$	−1.38341	−	0.420875i	−0.0506162	−	0.0153990i
$748$	−23.9948	−	15.6973i	−0.877338	−	0.573949i
$749$	−20.0623	−	34.7489i	−0.733060	−	1.26970i
$750$	11.2359	+	0.482848i	0.410278	+	0.0176311i
$751$	22.8535	+	4.85766i	0.833937	+	0.177259i	0.605043	−	0.796193i	$-0.293156\pi$
$751$	22.8535	+	4.85766i	0.833937	+	0.177259i	0.228894	+	0.973451i	$0.426489\pi$
$752$	13.2852	+	14.7547i	0.484460	+	0.538047i
$753$	36.6924	+	9.46246i	1.33715	+	0.344831i
$754$	0.201404	−	1.91623i	0.00733470	−	0.0697851i
$755$	−0.0565572	+	0.174065i	−0.00205833	+	0.00633488i
$756$	31.3613	+	4.06314i	1.14060	+	0.147775i
$757$	27.3472	−	19.8689i	0.993952	−	0.722148i	0.0331687	−	0.999450i	$-0.489440\pi$
$757$	27.3472	−	19.8689i	0.993952	−	0.722148i	0.960783	+	0.277302i	$0.0894401\pi$
$758$	8.43250	+	14.6055i	0.306282	+	0.530496i
$759$	6.00930	−	10.5555i	0.218124	−	0.383139i
$760$	6.77421	−	11.7333i	0.245726	−	0.425611i
$761$	−2.10227	−	20.0017i	−0.0762071	−	0.725062i	−0.964195	−	0.265195i	$-0.914564\pi$
$761$	−2.10227	−	20.0017i	−0.0762071	−	0.725062i	0.887988	−	0.459867i	$-0.152103\pi$
$762$	3.07753	−	8.24848i	0.111487	−	0.298811i
$763$	9.02421	−	1.91815i	0.326698	−	0.0694419i
$764$	−20.8294	−	15.1335i	−0.753583	−	0.547510i
$765$	7.23642	−	17.1132i	0.261633	−	0.618729i
$766$	2.48699	−	7.65417i	0.0898586	−	0.276556i
$767$	−4.25651	+	4.72733i	−0.153694	+	0.170694i
$768$	7.03547	+	13.4924i	0.253871	+	0.486865i
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	−0.871623	−	0.490178i	$-0.836932\pi$
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	0.860318	+	0.509759i	$0.170265\pi$
$770$	4.38984	−	8.54447i	0.158199	−	0.307921i
$771$	−1.31591	+	8.84649i	−0.0473914	+	0.318598i
$772$	11.5836	+	5.15733i	0.416902	+	0.185617i
$773$	8.88046	+	27.3313i	0.319408	+	0.983037i	0.973902	+	0.226970i	$0.0728818\pi$
$773$	8.88046	+	27.3313i	0.319408	+	0.983037i	−0.654494	+	0.756067i	$0.727118\pi$
$774$	4.43302	+	0.381710i	0.159342	+	0.0137203i
$775$	−1.30613	−	0.948959i	−0.0469176	−	0.0340876i
$776$	−1.98080	+	18.8460i	−0.0711064	+	0.676533i
$777$	−49.0737	+	32.5296i	−1.76051	+	1.16699i
$778$	9.32539	+	1.98217i	0.334331	+	0.0710643i
$779$	−1.56601	−	14.8996i	−0.0561083	−	0.533834i
$780$	−7.50923	+	2.96392i	−0.268874	+	0.106125i
$781$	20.2556	−	5.35460i	0.724801	−	0.191603i
$782$	−7.79085			−0.278600
$783$	4.27176	−	3.66366i	0.152660	−	0.130929i
$784$	3.94131	+	12.1301i	0.140761	+	0.433218i
$785$	−26.0528	+	5.53769i	−0.929864	+	0.197649i
$786$	−5.97104	−	1.53985i	−0.212980	−	0.0549245i
$787$	−12.8837	+	5.73618i	−0.459254	+	0.204473i	−0.623305	−	0.781979i	$-0.714210\pi$
$787$	−12.8837	+	5.73618i	−0.459254	+	0.204473i	0.164051	+	0.986452i	$0.447544\pi$
$788$	23.8913	+	26.5339i	0.851091	+	0.945233i
$789$	−16.8913	+	45.2725i	−0.601346	+	1.61174i
$790$	−3.05946	−	1.36216i	−0.108851	−	0.0484634i
$791$	−5.98345			−0.212747
$792$	12.5047	−	19.9234i	0.444334	−	0.707948i
$793$	−10.9382			−0.388426
$794$	3.05800	+	1.36151i	0.108524	+	0.0483181i
$795$	−10.7595	+	1.80811i	−0.381599	+	0.0641269i
$796$	−9.67008	−	10.7397i	−0.342747	−	0.380659i
$797$	23.8935	−	10.6381i	0.846351	−	0.376820i	0.0627086	−	0.998032i	$-0.480026\pi$
$797$	23.8935	−	10.6381i	0.846351	−	0.376820i	0.783642	+	0.621212i	$0.213359\pi$
$798$	−16.1504	+	16.4573i	−0.571717	+	0.582582i
$799$	−69.6371	+	14.8018i	−2.46358	+	0.523651i
$800$	6.67551	+	20.5451i	0.236015	+	0.726379i
$801$	−9.14137	+	47.3752i	−0.322994	+	1.67392i
$802$	12.0908			0.426939
$803$	−20.9759	−	32.5388i	−0.740223	−	1.14827i
$804$	−20.6148	−	16.3746i	−0.727026	−	0.577489i
$805$	0.963594	+	9.16798i	0.0339622	+	0.323129i
$806$	−0.748559	−	0.159111i	−0.0263669	−	0.00560445i
$807$	−0.322870	−	5.22010i	−0.0113656	−	0.183756i
$808$	−0.435249	+	4.14112i	−0.0153120	+	0.145684i
$809$	−12.8256	−	9.31836i	−0.450925	−	0.327616i	0.339036	−	0.940773i	$-0.389899\pi$
$809$	−12.8256	−	9.31836i	−0.450925	−	0.327616i	−0.789961	+	0.613157i	$0.789899\pi$
$810$	6.19687	+	2.48394i	0.217736	+	0.0872766i
$811$	−11.2255	−	34.5484i	−0.394179	−	1.21316i	−0.929599	−	0.368573i	$-0.879846\pi$
$811$	−11.2255	−	34.5484i	−0.394179	−	1.21316i	0.535420	−	0.844586i	$-0.320154\pi$
$812$	6.02146	+	2.68093i	0.211312	+	0.0940820i
$813$	−40.8812	+	16.1360i	−1.43377	+	0.565913i
$814$	2.93699	+	18.9553i	0.102941	+	0.664383i
$815$	2.34269	−	4.05766i	0.0820608	−	0.142134i
$816$	14.8466	+	0.638013i	0.519736	+	0.0223349i
$817$	7.66710	−	8.51517i	0.268238	−	0.297908i
$818$	−3.37295	+	10.3809i	−0.117932	+	0.362958i
$819$	31.1300	−	3.86566i	1.08777	−	0.135077i
$820$	−4.11023	−	2.98626i	−0.143535	−	0.104285i
$821$	15.9993	−	3.40076i	0.558379	−	0.118687i	0.0799271	−	0.996801i	$-0.474531\pi$
$821$	15.9993	−	3.40076i	0.558379	−	0.118687i	0.478452	+	0.878113i	$0.341198\pi$
$822$	18.9853	−	3.19045i	0.662189	−	0.111280i
$823$	2.73598	+	26.0311i	0.0953703	+	0.907388i	0.932691	+	0.360676i	$0.117454\pi$
$823$	2.73598	+	26.0311i	0.0953703	+	0.907388i	−0.837321	+	0.546712i	$0.815879\pi$
$824$	−3.17696	+	5.50265i	−0.110675	+	0.191694i
$825$	14.3293	−	16.1094i	0.498884	−	0.560857i
$826$	3.08070	+	5.33592i	0.107191	+	0.185661i
$827$	−4.48139	+	3.25592i	−0.155833	+	0.113219i	−0.662969	−	0.748647i	$-0.730704\pi$
$827$	−4.48139	+	3.25592i	−0.155833	+	0.113219i	0.507136	+	0.861866i	$0.330704\pi$
$828$	0.186115	+	9.88515i	0.00646793	+	0.343533i
$829$	5.71784	−	17.5977i	0.198589	−	0.611194i	−0.801327	−	0.598227i	$-0.795872\pi$
$829$	5.71784	−	17.5977i	0.198589	−	0.611194i	0.999916	−	0.0129672i	$-0.00412771\pi$
$830$	0.0373740	−	0.355590i	0.00129727	−	0.0123427i
$831$	−4.90204	−	17.6292i	−0.170050	−	0.611550i
$832$	1.30816	+	1.45286i	0.0453523	+	0.0503688i
$833$	−44.7346	−	9.50862i	−1.54996	−	0.329454i
$834$	8.48549	−	13.3397i	0.293829	−	0.461918i
$835$	−8.84388	−	15.3180i	−0.306055	−	0.530103i
$836$	−9.42492	−	24.8015i	−0.325968	−	0.857776i
$837$	−1.26981	−	1.83947i	−0.0438912	−	0.0635813i
$838$	−9.35505	+	6.79684i	−0.323165	+	0.234793i
$839$	−12.0211	+	13.3508i	−0.415015	+	0.460921i	−0.914015	−	0.405681i	$-0.867034\pi$
$839$	−12.0211	+	13.3508i	−0.415015	+	0.460921i	0.498999	+	0.866602i	$0.333701\pi$
$840$	1.10211	+	17.8186i	0.0380263	+	0.614802i
$841$	−25.4213	+	11.3183i	−0.876595	+	0.390285i
$842$	−2.76051	+	1.22906i	−0.0951336	+	0.0423562i
$843$	32.5845	−	21.5994i	1.12227	−	0.743922i
$844$	−4.39146	+	4.87721i	−0.151160	+	0.167881i
$845$	5.26509	−	3.82531i	0.181125	−	0.131595i
$846$	−5.78858	−	24.9170i	−0.199015	−	0.856666i
$847$	−17.2053	−	39.3532i	−0.591182	−	1.35219i
$848$	−4.36299	−	7.55692i	−0.149826	−	0.259506i
$849$	4.70664	+	9.02624i	0.161531	+	0.309780i
$850$	−13.5270	−	2.87526i	−0.463973	−	0.0986206i
$851$	−12.3169	−	13.6793i	−0.422218	−	0.468921i
$852$	−11.9451	+	12.1722i	−0.409234	+	0.417011i
$853$	−2.91771	+	27.7602i	−0.0999006	+	0.950490i	0.823672	+	0.567067i	$0.191922\pi$
$853$	−2.91771	+	27.7602i	−0.0999006	+	0.950490i	−0.923573	+	0.383424i	$0.874745\pi$
$854$	−3.27389	+	10.0760i	−0.112030	+	0.344794i
$855$	14.7248	−	8.87510i	0.503579	−	0.303522i
$856$	19.6546	−	14.2799i	0.671781	−	0.488077i
$857$	4.24983	+	7.36093i	0.145172	+	0.251445i	0.929437	−	0.368981i	$-0.120293\pi$
$857$	4.24983	+	7.36093i	0.145172	+	0.251445i	−0.784265	+	0.620426i	$0.786960\pi$
$858$	3.09922	−	9.73862i	0.105806	−	0.332471i
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	−0.999595	−	0.0284667i	$-0.990938\pi$
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	0.524450	+	0.851441i	$0.324271\pi$
$860$	−0.406165	−	3.86440i	−0.0138501	−	0.131775i
$861$	12.5675	+	15.2243i	0.428298	+	0.518842i
$862$	8.11267	−	1.72440i	0.276318	−	0.0587333i
$863$	−10.9978	−	7.99035i	−0.374368	−	0.271995i	0.384652	−	0.923062i	$-0.374322\pi$
$863$	−10.9978	−	7.99035i	−0.374368	−	0.271995i	−0.759020	+	0.651067i	$0.774322\pi$
$864$	−0.721361	+	29.8993i	−0.0245412	+	1.01720i
$865$	−0.898141	+	2.76419i	−0.0305377	+	0.0939854i
$866$	−12.7515	+	14.1620i	−0.433313	+	0.481243i
$867$	−12.7958	+	20.1158i	−0.434568	+	0.683169i
$868$	1.30897	−	2.26720i	0.0444293	−	0.0769538i
$869$	−13.3643	+	6.75301i	−0.453354	+	0.229080i
$870$	1.08961	+	0.865495i	0.0369412	+	0.0293430i
$871$	−23.8573	−	10.6220i	−0.808374	−	0.359911i
$872$	1.72617	+	5.31260i	0.0584555	+	0.179907i
$873$	−13.7657	+	19.7170i	−0.465899	+	0.667320i
$874$	−5.83221	−	4.23735i	−0.197278	−	0.143331i
$875$	−3.98911	+	37.9538i	−0.134856	+	1.28307i
$876$	28.2116	+	14.0416i	0.953180	+	0.474422i
$877$	−35.3874	−	7.52182i	−1.19495	−	0.253994i	−0.432856	−	0.901463i	$-0.642494\pi$
$877$	−35.3874	−	7.52182i	−1.19495	−	0.253994i	−0.762092	+	0.647469i	$0.775827\pi$
$878$	−0.285266	−	2.71413i	−0.00962727	−	0.0915973i
$879$	−1.80785	+	12.1536i	−0.0609772	+	0.409932i
$880$	−5.34116	−	2.07089i	−0.180051	−	0.0698098i
$881$	26.6423			0.897601			0.448800	−	0.893632i	$-0.351851\pi$
$881$	26.6423			0.897601			0.448800	+	0.893632i	$0.351851\pi$
$882$	3.11340	−	16.1352i	0.104834	−	0.543301i
$883$	−6.32757	−	19.4743i	−0.212940	−	0.655361i	−0.999293	−	0.0375844i	$-0.988034\pi$
$883$	−6.32757	−	19.4743i	−0.212940	−	0.655361i	0.786354	−	0.617776i	$-0.211966\pi$
$884$	22.6463	−	4.81361i	0.761676	−	0.161899i
$885$	−1.23075	−	4.42615i	−0.0413713	−	0.148783i
$886$	12.8840	−	5.73634i	0.432847	−	0.192716i
$887$	−21.4130	−	23.7815i	−0.718977	−	0.798505i	0.267299	−	0.963614i	$-0.413869\pi$
$887$	−21.4130	−	23.7815i	−0.718977	−	0.798505i	−0.986275	+	0.165109i	$0.947202\pi$
$888$	−22.6938	−	27.4913i	−0.761554	−	0.922549i
$889$	27.2921	+	12.1512i	0.915348	+	0.407539i
$890$	−11.9303			−0.399906
$891$	26.1160	−	14.4553i	0.874918	−	0.484272i
$892$	10.6911			0.357963
$893$	−60.1807	−	26.7942i	−2.01387	−	0.896633i
$894$	−4.07247	−	4.93340i	−0.136204	−	0.164998i
$895$	5.66951	+	6.29663i	0.189511	+	0.210473i
$896$	−39.3317	+	17.5116i	−1.31398	+	0.585022i
$897$	2.62740	+	9.44892i	0.0877263	+	0.315490i
$898$	16.8266	−	3.57660i	0.561510	−	0.119353i
$899$	−0.143966	−	0.443082i	−0.00480153	−	0.0147776i
$900$	−3.32503	+	17.2320i	−0.110834	+	0.574400i
$901$	31.2892			1.04239
$902$	6.21801	−	1.64374i	0.207037	−	0.0547307i
$903$	−2.22146	+	14.9342i	−0.0739256	+	0.496980i
$904$	−0.378689	−	3.60298i	−0.0125950	−	0.119833i
$905$	2.62154	+	0.557225i	0.0871429	+	0.0185228i
$906$	0.168841	+	0.0840362i	0.00560935	+	0.00279192i
$907$	5.12715	−	48.7816i	0.170244	−	1.61977i	−0.492082	−	0.870549i	$-0.663764\pi$
$907$	5.12715	−	48.7816i	0.170244	−	1.61977i	0.662326	−	0.749216i	$-0.269569\pi$
$908$	35.4717	+	25.7717i	1.17717	+	0.855265i
$909$	−3.02480	+	4.33251i	−0.100326	+	0.143700i
$910$	2.39689	+	7.37687i	0.0794561	+	0.244541i
$911$	−21.3599	−	9.51002i	−0.707684	−	0.315081i	0.0211457	−	0.999776i	$-0.493269\pi$
$911$	−21.3599	−	9.51002i	−0.707684	−	0.315081i	−0.728829	+	0.684695i	$0.759935\pi$
$912$	10.7672	+	8.55253i	0.356536	+	0.283203i
$913$	−1.12659	−	1.13419i	−0.0372849	−	0.0375362i
$914$	−3.42253	+	5.92800i	−0.113207	+	0.196081i
$915$	4.23984	−	6.66531i	0.140165	−	0.220348i
$916$	14.6376	−	16.2567i	0.483641	−	0.537137i
$917$	6.46615	−	19.9008i	0.213531	−	0.657181i
$918$	−16.3454	−	9.97027i	−0.539479	−	0.329068i
$919$	6.14797	+	4.46676i	0.202803	+	0.147345i	0.684551	−	0.728965i	$-0.259998\pi$
$919$	6.14797	+	4.46676i	0.202803	+	0.147345i	−0.481749	+	0.876309i	$0.659998\pi$
$920$	−5.45959	+	1.16047i	−0.179997	+	0.0382596i
$921$	−20.4396	−	24.7606i	−0.673507	−	0.815888i
$922$	−1.76748	−	16.8165i	−0.0582090	−	0.553821i
$923$	−8.45857	+	14.6507i	−0.278417	+	0.482233i
$924$	28.4079	+	20.3780i	0.934551	+	0.670386i
$925$	−16.3371	−	28.2967i	−0.537160	−	0.930389i
$926$	−21.4202	+	15.5627i	−0.703910	+	0.511421i
$927$	−6.90563	+	4.16223i	−0.226811	+	0.136706i
$928$	−1.92634	+	5.92866i	−0.0632352	+	0.194618i
$929$	1.55504	−	14.7953i	0.0510193	−	0.485417i	−0.938942	−	0.344076i	$-0.888192\pi$
$929$	1.55504	−	14.7953i	0.0510193	−	0.485417i	0.989961	−	0.141340i	$-0.0451412\pi$
$930$	0.387111	−	0.394468i	0.0126939	−	0.0129351i
$931$	−28.3166	−	31.4487i	−0.928038	−	1.03069i
$932$	−22.1216	−	4.70209i	−0.724618	−	0.154022i
$933$	−5.50667	−	10.5605i	−0.180280	−	0.345736i
$934$	−5.77192	−	9.99727i	−0.188863	−	0.327121i
$935$	16.0069	−	12.8733i	0.523482	−	0.421003i
$936$	4.29794	+	18.5006i	0.140482	+	0.604710i
$937$	−14.4192	+	10.4762i	−0.471056	+	0.342242i	−0.797853	−	0.602853i	$-0.794031\pi$
$937$	−14.4192	+	10.4762i	−0.471056	+	0.342242i	0.326797	+	0.945095i	$0.394031\pi$
$938$	−16.9254	+	18.7975i	−0.552633	+	0.613761i
$939$	36.5623	−	24.2361i	1.19316	−	0.790916i
$940$	−20.4082	+	9.08632i	−0.665643	+	0.296363i
$941$	38.9710	−	17.3510i	1.27042	−	0.565627i	0.342890	−	0.939376i	$-0.388594\pi$
$941$	38.9710	−	17.3510i	1.27042	−	0.565627i	0.927530	+	0.373748i	$0.121928\pi$
$942$	1.69434	+	27.3938i	0.0552047	+	0.892539i
$943$	−4.12989	+	4.58671i	−0.134488	+	0.149364i
$944$	2.97257	−	2.15970i	0.0967491	−	0.0702923i
$945$	−9.71100	+	20.4678i	−0.315899	+	0.665819i
$946$	4.11641	+	2.69293i	0.133836	+	0.0875548i
$947$	−3.44670	−	5.96986i	−0.112003	−	0.193994i	0.804575	−	0.593851i	$-0.202393\pi$
$947$	−3.44670	−	5.96986i	−0.112003	−	0.193994i	−0.916578	+	0.399857i	$0.869060\pi$
$948$	6.54177	−	10.2841i	0.212467	−	0.334012i
$949$	30.5764	+	6.49921i	0.992551	+	0.210973i
$950$	−8.56249	−	9.50961i	−0.277804	−	0.308533i
$951$	5.09455	+	18.3215i	0.165202	+	0.594116i
$952$	5.35175	−	50.9185i	0.173451	−	1.65028i
$953$	−7.31766	+	22.5214i	−0.237042	+	0.729541i	0.759802	+	0.650155i	$0.225296\pi$
$953$	−7.31766	+	22.5214i	−0.237042	+	0.729541i	−0.996844	+	0.0793863i	$0.974704\pi$
$954$	0.211636	+	11.2407i	0.00685197	+	0.363930i
$955$	14.9220	−	10.8415i	0.482866	−	0.350822i
$956$	−19.5989	−	33.9463i	−0.633874	−	1.09790i
$957$	6.07770	−	1.33036i	0.196464	−	0.0430043i
$958$	−7.27297	+	12.5972i	−0.234979	+	0.406996i
$959$	6.82860	+	64.9698i	0.220507	+	2.09798i
$960$	−1.39238	+	0.233987i	−0.0449390	+	0.00755190i
$961$	30.1416	−	6.40679i	0.972309	−	0.206671i
$962$	−12.5301	−	9.10366i	−0.403987	−	0.293514i
$963$	30.5942	−	3.79911i	0.985884	−	0.122425i
$964$	−8.54567	+	26.3009i	−0.275238	+	0.847094i
$965$	−6.07817	+	6.75050i	−0.195663	+	0.217306i
$966$	9.49053	+	0.407842i	0.305353	+	0.0131221i
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	−0.499303	−	0.866427i	$-0.666411\pi$
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	1.00000		0.000804082i	$-0.000255947\pi$
$968$	22.6080	−	12.8510i	0.726647	−	0.413046i
$969$	−45.8628	+	18.1022i	−1.47333	+	0.581527i
$970$	−5.43192	−	2.41845i	−0.174408	−	0.0776516i
$971$	4.12687	+	12.7012i	0.132438	+	0.407601i	0.995183	−	0.0980383i	$-0.0312568\pi$
$971$	4.12687	+	12.7012i	0.132438	+	0.407601i	−0.862745	+	0.505639i	$0.831257\pi$
$972$	−12.2600	+	20.9775i	−0.393239	+	0.672854i
$973$	43.4028	+	31.5340i	1.39143	+	1.01093i
$974$	0.227151	−	2.16119i	0.00727838	−	0.0692491i
$975$	1.07470	+	17.3756i	0.0344180	+	0.556463i
$976$	6.17991	+	1.31358i	0.197814	+	0.0420467i
$977$	0.931968	+	8.86709i	0.0298163	+	0.283683i	0.999263	+	0.0383817i	$0.0122203\pi$
$977$	0.931968	+	8.86709i	0.0298163	+	0.283683i	−0.969447	+	0.245302i	$0.921113\pi$
$978$	−3.78057	−	3.00297i	−0.120889	−	0.0960244i
$979$	−33.7079	+	41.3411i	−1.07731	+	1.32127i
$980$	−14.3508			−0.458421
$981$	−1.34301	+	6.96014i	−0.0428789	+	0.222220i
$982$	1.48297	+	4.56411i	0.0473234	+	0.145647i
$983$	16.4901	−	3.50509i	0.525954	−	0.111795i	0.0627203	−	0.998031i	$-0.480022\pi$
$983$	16.4901	−	3.50509i	0.525954	−	0.111795i	0.463234	+	0.886236i	$0.346689\pi$
$984$	−8.37203	+	8.53114i	−0.266891	+	0.271963i
$985$	−23.3673	+	10.4038i	−0.744544	+	0.331492i
$986$	−2.67029	−	2.96565i	−0.0850392	−	0.0944456i
$987$	85.6042	−	14.3856i	2.72481	−	0.457899i
$988$	19.5710	+	8.71358i	0.622637	+	0.277216i
$989$	−4.72049			−0.150103
$990$	4.73303	+	5.66342i	0.150425	+	0.179995i
$991$	−33.5356			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$991$	−33.5356			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$992$	2.26187	+	1.00705i	0.0718146	+	0.0319739i
$993$	−2.24642	+	6.02092i	−0.0712881	+	0.191068i
$994$	10.9641	+	12.1769i	0.347761	+	0.386228i
$995$	9.45801	−	4.21098i	0.299839	−	0.133497i
$996$	1.26004	+	0.324948i	0.0399260	+	0.0102964i
$997$	3.17279	−	0.674397i	0.100483	−	0.0213584i	−0.157396	−	0.987536i	$-0.550310\pi$
$997$	3.17279	−	0.674397i	0.100483	−	0.0213584i	0.257879	+	0.966177i	$0.416976\pi$
$998$	−3.04532	−	9.37254i	−0.0963980	−	0.296682i
$999$	−8.33526	−	44.4621i	−0.263716	−	1.40672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.b.58.4	yes	72
3.2	odd	2		297.2.n.b.91.6		72
9.2	odd	6		297.2.n.b.289.4		72
9.4	even	3		891.2.f.f.487.6		36
9.5	odd	6		891.2.f.e.487.4		36
9.7	even	3	inner	99.2.m.b.25.6	yes	72
11.2	odd	10		1089.2.e.o.364.8		36
11.4	even	5	inner	99.2.m.b.4.6	✓	72
11.9	even	5		1089.2.e.p.364.11		36
33.26	odd	10		297.2.n.b.37.4		72
99.4	even	15		891.2.f.f.730.6		36
99.13	odd	30		9801.2.a.co.1.11		18
99.31	even	15		9801.2.a.cm.1.8		18
99.59	odd	30		891.2.f.e.730.4		36
99.68	even	30		9801.2.a.cn.1.8		18
99.70	even	15	inner	99.2.m.b.70.4	yes	72
99.79	odd	30		1089.2.e.o.727.8		36
99.86	odd	30		9801.2.a.cp.1.11		18
99.92	odd	30		297.2.n.b.235.6		72
99.97	even	15		1089.2.e.p.727.11		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.6	✓	72	11.4	even	5	inner
99.2.m.b.25.6	yes	72	9.7	even	3	inner
99.2.m.b.58.4	yes	72	1.1	even	1	trivial
99.2.m.b.70.4	yes	72	99.70	even	15	inner
297.2.n.b.37.4		72	33.26	odd	10
297.2.n.b.91.6		72	3.2	odd	2
297.2.n.b.235.6		72	99.92	odd	30
297.2.n.b.289.4		72	9.2	odd	6
891.2.f.e.487.4		36	9.5	odd	6
891.2.f.e.730.4		36	99.59	odd	30
891.2.f.f.487.6		36	9.4	even	3
891.2.f.f.730.6		36	99.4	even	15
1089.2.e.o.364.8		36	11.2	odd	10
1089.2.e.o.727.8		36	99.79	odd	30
1089.2.e.p.364.11		36	11.9	even	5
1089.2.e.p.727.11		36	99.97	even	15
9801.2.a.cm.1.8		18	99.31	even	15
9801.2.a.cn.1.8		18	99.68	even	30
9801.2.a.co.1.11		18	99.13	odd	30
9801.2.a.cp.1.11		18	99.86	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.606887 - 0.270203i) q^{2} +(1.10264 + 1.33574i) q^{3} +(-1.04296 - 1.15832i) q^{4} +(1.02009 - 0.454172i) q^{5} +(-0.308255 - 1.10858i) q^{6} +(3.81922 - 0.811800i) q^{7} +(0.730548 + 2.24840i) q^{8} +(-0.568386 + 2.94566i) q^{9} -0.741796 q^{10} +(-2.09587 + 2.57048i) q^{11} +(0.397211 - 2.67033i) q^{12} +(-0.279928 - 2.66333i) q^{13} +(-2.53719 - 0.539295i) q^{14} +(1.73144 + 0.861780i) q^{15} +(-0.161688 + 1.53836i) q^{16} +(-4.48727 - 3.26019i) q^{17} +(1.14087 - 1.63411i) q^{18} +(-1.58598 - 4.88115i) q^{19} +(-1.58999 - 0.707907i) q^{20} +(5.29556 + 4.20635i) q^{21} +(1.96651 - 0.993678i) q^{22} +(-1.05719 + 1.83110i) q^{23} +(-2.19774 + 3.45498i) q^{24} +(-2.51135 + 2.78914i) q^{25} +(-0.549758 + 1.69198i) q^{26} +(-4.56135 + 2.48878i) q^{27} +(-4.92362 - 3.57722i) q^{28} +(-1.05937 + 0.225177i) q^{29} +(-0.817931 - 0.990844i) q^{30} +(0.0449642 + 0.427806i) q^{31} +(2.87790 - 4.98467i) q^{32} +(-5.74446 + 0.0347740i) q^{33} +(1.84235 + 3.19104i) q^{34} +(3.52724 - 2.56269i) q^{35} +(4.00484 - 2.41383i) q^{36} +(-2.69024 + 8.27970i) q^{37} +(-0.356392 + 3.39084i) q^{38} +(3.24885 - 3.31060i) q^{39} +(1.76638 + 1.96176i) q^{40} +(2.85529 + 0.606910i) q^{41} +(-2.07724 - 3.98366i) q^{42} +(1.11628 + 1.93346i) q^{43} +(5.16335 - 0.253209i) q^{44} +(0.758035 + 3.26298i) q^{45} +(1.13637 - 0.825618i) q^{46} +(8.58861 - 9.53861i) q^{47} +(-2.23313 + 1.48028i) q^{48} +(7.53259 - 3.35373i) q^{49} +(2.27774 - 1.01411i) q^{50} +(-0.593068 - 9.58862i) q^{51} +(-2.79305 + 3.10200i) q^{52} +(-4.56381 + 3.31581i) q^{53} +(3.44070 - 0.277916i) q^{54} +(-0.970527 + 3.57399i) q^{55} +(4.61537 + 7.99405i) q^{56} +(4.77117 - 7.50058i) q^{57} +(0.703764 + 0.149590i) q^{58} +(-1.58943 - 1.76524i) q^{59} +(-0.807599 - 2.90437i) q^{60} +(0.426942 - 4.06208i) q^{61} +(0.0883065 - 0.271779i) q^{62} +(0.220502 + 11.7116i) q^{63} +(-0.590604 + 0.429099i) q^{64} +(-1.49516 - 2.58969i) q^{65} +(3.49563 + 1.53107i) q^{66} +(4.87584 - 8.44521i) q^{67} +(0.903682 + 8.59796i) q^{68} +(-3.61157 + 0.606917i) q^{69} +(-2.83308 + 0.602190i) q^{70} +(-5.11062 - 3.71308i) q^{71} +(-7.03825 + 0.873994i) q^{72} +(-3.60705 + 11.1014i) q^{73} +(3.86988 - 4.29793i) q^{74} +(-6.49466 - 0.279099i) q^{75} +(-3.99983 + 6.92792i) q^{76} +(-5.91786 + 11.5186i) q^{77} +(-2.86622 + 1.13131i) q^{78} +(4.12439 + 1.83630i) q^{79} +(0.533744 + 1.64269i) q^{80} +(-8.35388 - 3.34855i) q^{81} +(-1.56885 - 1.13983i) q^{82} +(-0.0503831 + 0.479363i) q^{83} +(-0.650739 - 10.5210i) q^{84} +(-6.05809 - 1.28769i) q^{85} +(-0.155030 - 1.47502i) q^{86} +(-1.46888 - 1.16676i) q^{87} +(-7.31058 - 2.83448i) q^{88} +16.0830 q^{89} +(0.421626 - 2.18508i) q^{90} +(-3.23120 - 9.94461i) q^{91} +(3.22362 - 0.685201i) q^{92} +(-0.521857 + 0.531775i) q^{93} +(-7.78968 + 3.46819i) q^{94} +(-3.83471 - 4.25888i) q^{95} +(9.83148 - 1.65216i) q^{96} +(7.32266 + 3.26026i) q^{97} -5.47762 q^{98} +(-6.38050 - 7.63474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more