LMFDB - Embedded newform 117.2.l.b.88.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(4,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.8
Character	$\chi$	$=$	117.88
Dual form			117.2.l.b.4.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.05773i q^{2} +(1.56468 - 0.742818i) q^{3} +0.881215 q^{4} +(-2.71101 + 1.56520i) q^{5} +(0.785698 + 1.65500i) q^{6} +(0.784891 - 0.453157i) q^{7} +3.04754i q^{8} +(1.89644 - 2.32454i) q^{9} +(-1.65555 - 2.86750i) q^{10} -5.46416i q^{11} +(1.37882 - 0.654582i) q^{12} +(-1.56951 + 3.24602i) q^{13} +(0.479316 + 0.830200i) q^{14} +(-3.07920 + 4.46282i) q^{15} -1.46103 q^{16} +(-1.52177 + 2.63579i) q^{17} +(2.45873 + 2.00592i) q^{18} +(-5.69894 - 3.29028i) q^{19} +(-2.38898 + 1.37928i) q^{20} +(0.891490 - 1.29208i) q^{21} +5.77958 q^{22} +(2.18436 - 3.78342i) q^{23} +(2.26376 + 4.76842i) q^{24} +(2.39971 - 4.15642i) q^{25} +(-3.43340 - 1.66011i) q^{26} +(1.24061 - 5.04588i) q^{27} +(0.691657 - 0.399329i) q^{28} -2.67011 q^{29} +(-4.72045 - 3.25695i) q^{30} +(-1.19056 + 0.687369i) q^{31} +4.54970i q^{32} +(-4.05887 - 8.54965i) q^{33} +(-2.78794 - 1.60962i) q^{34} +(-1.41856 + 2.45702i) q^{35} +(1.67117 - 2.04842i) q^{36} +(1.84362 - 1.06441i) q^{37} +(3.48022 - 6.02792i) q^{38} +(-0.0445843 + 6.24484i) q^{39} +(-4.77001 - 8.26190i) q^{40} +(7.42578 + 4.28727i) q^{41} +(1.36666 + 0.942952i) q^{42} +(-1.83832 - 3.18406i) q^{43} -4.81509i q^{44} +(-1.50290 + 9.27017i) q^{45} +(4.00182 + 2.31045i) q^{46} +(5.01412 + 2.89490i) q^{47} +(-2.28605 + 1.08528i) q^{48} +(-3.08930 + 5.35082i) q^{49} +(4.39635 + 2.53823i) q^{50} +(-0.423177 + 5.25456i) q^{51} +(-1.38308 + 2.86044i) q^{52} -3.37524 q^{53} +(5.33716 + 1.31223i) q^{54} +(8.55250 + 14.8134i) q^{55} +(1.38101 + 2.39198i) q^{56} +(-11.3611 - 0.914967i) q^{57} -2.82425i q^{58} -3.14669i q^{59} +(-2.71343 + 3.93270i) q^{60} +(4.09223 + 7.08794i) q^{61} +(-0.727048 - 1.25928i) q^{62} +(0.435118 - 2.68390i) q^{63} -7.73440 q^{64} +(-0.825710 - 11.2566i) q^{65} +(9.04319 - 4.29318i) q^{66} +(11.7394 + 6.77772i) q^{67} +(-1.34101 + 2.32269i) q^{68} +(0.607429 - 7.54242i) q^{69} +(-2.59886 - 1.50045i) q^{70} +(3.07782 + 1.77698i) q^{71} +(7.08413 + 5.77948i) q^{72} -1.25464i q^{73} +(1.12586 + 1.95004i) q^{74} +(0.667314 - 8.28600i) q^{75} +(-5.02199 - 2.89945i) q^{76} +(-2.47612 - 4.28877i) q^{77} +(-6.60533 - 0.0471580i) q^{78} +(-5.59586 + 9.69232i) q^{79} +(3.96087 - 2.28681i) q^{80} +(-1.80700 - 8.81673i) q^{81} +(-4.53476 + 7.85444i) q^{82} +(-0.899143 - 0.519121i) q^{83} +(0.785594 - 1.13860i) q^{84} -9.52751i q^{85} +(3.36786 - 1.94444i) q^{86} +(-4.17787 + 1.98341i) q^{87} +16.6522 q^{88} +(-4.76108 + 2.74881i) q^{89} +(-9.80530 - 1.58965i) q^{90} +(0.239060 + 3.25901i) q^{91} +(1.92489 - 3.33400i) q^{92} +(-1.35225 + 1.95988i) q^{93} +(-3.06201 + 5.30356i) q^{94} +20.5998 q^{95} +(3.37960 + 7.11883i) q^{96} +(7.06649 - 4.07984i) q^{97} +(-5.65970 - 3.26763i) q^{98} +(-12.7017 - 10.3625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.05773i			0.747926i	0.927444	+	0.373963i	$0.122001\pi$
$2$			1.05773i			0.747926i	−0.927444	+	0.373963i	$0.877999\pi$
$3$	1.56468	−	0.742818i	0.903368	−	0.428866i
$3$	1.56468	−	0.742818i	0.903368	−	0.428866i
$4$	0.881215			0.440607
$5$	−2.71101	+	1.56520i	−1.21240	+	0.699979i	−0.963281	−	0.268494i	$-0.913474\pi$
$5$	−2.71101	+	1.56520i	−1.21240	+	0.699979i	−0.249118	+	0.968473i	$0.580141\pi$
$6$	0.785698	+	1.65500i	0.320760	+	0.675652i
$7$	0.784891	−	0.453157i	0.296661	−	0.171277i	−0.344281	−	0.938867i	$-0.611877\pi$
$7$	0.784891	−	0.453157i	0.296661	−	0.171277i	0.640942	+	0.767589i	$0.278544\pi$
$8$			3.04754i			1.07747i
$9$	1.89644	−	2.32454i	0.632148	−	0.774848i
$10$	−1.65555	−	2.86750i	−0.523532	−	0.906785i
$11$		−	5.46416i		−	1.64751i	−0.566950	−	0.823753i	$-0.691877\pi$
$11$		−	5.46416i		−	1.64751i	0.566950	−	0.823753i	$-0.308123\pi$
$12$	1.37882	−	0.654582i	0.398031	−	0.188961i
$13$	−1.56951	+	3.24602i	−0.435304	+	0.900283i
$13$	−1.56951	+	3.24602i	−0.435304	+	0.900283i
$14$	0.479316	+	0.830200i	0.128103	+	0.221880i
$15$	−3.07920	+	4.46282i	−0.795046	+	1.15230i
$16$	−1.46103			−0.365258
$17$	−1.52177	+	2.63579i	−0.369084	+	0.639272i	−0.989423	−	0.145062i	$-0.953662\pi$
$17$	−1.52177	+	2.63579i	−0.369084	+	0.639272i	0.620339	+	0.784334i	$0.286995\pi$
$18$	2.45873	+	2.00592i	0.579528	+	0.472800i
$19$	−5.69894	−	3.29028i	−1.30743	−	0.754843i	−0.325760	−	0.945453i	$-0.605620\pi$
$19$	−5.69894	−	3.29028i	−1.30743	−	0.754843i	−0.981666	+	0.190610i	$0.938953\pi$
$20$	−2.38898	+	1.37928i	−0.534192	+	0.308416i
$21$	0.891490	−	1.29208i	0.194539	−	0.281954i
$22$	5.77958			1.23221
$23$	2.18436	−	3.78342i	0.455470	−	0.788897i	−0.543245	−	0.839574i	$-0.682805\pi$
$23$	2.18436	−	3.78342i	0.455470	−	0.788897i	0.998715	+	0.0506768i	$0.0161378\pi$
$24$	2.26376	+	4.76842i	0.462089	+	0.973349i
$25$	2.39971	−	4.15642i	0.479942	−	0.831283i
$26$	−3.43340	−	1.66011i	−0.673345	−	0.325575i
$27$	1.24061	−	5.04588i	0.238756	−	0.971079i
$28$	0.691657	−	0.399329i	0.130711	−	0.0754660i
$29$	−2.67011			−0.495828			−0.247914	−	0.968782i	$-0.579745\pi$
$29$	−2.67011			−0.495828			−0.247914	+	0.968782i	$0.579745\pi$
$30$	−4.72045	−	3.25695i	−0.861832	−	0.594635i
$31$	−1.19056	+	0.687369i	−0.213830	+	0.123455i	−0.603090	−	0.797673i	$-0.706064\pi$
$31$	−1.19056	+	0.687369i	−0.213830	+	0.123455i	0.389260	+	0.921128i	$0.372731\pi$
$32$			4.54970i			0.804281i
$33$	−4.05887	−	8.54965i	−0.706559	−	1.48830i
$34$	−2.78794	−	1.60962i	−0.478128	−	0.276047i
$35$	−1.41856	+	2.45702i	−0.239781	+	0.415313i
$36$	1.67117	−	2.04842i	0.278529	−	0.341404i
$37$	1.84362	−	1.06441i	0.303088	−	0.174988i	−0.340741	−	0.940157i	$-0.610678\pi$
$37$	1.84362	−	1.06441i	0.303088	−	0.174988i	0.643829	+	0.765169i	$0.277345\pi$
$38$	3.48022	−	6.02792i	0.564566	−	0.977857i
$39$	−0.0445843	+	6.24484i	−0.00713920	+	0.999975i
$40$	−4.77001	−	8.26190i	−0.754204	−	1.30632i
$41$	7.42578	+	4.28727i	1.15971	+	0.669560i	0.951235	−	0.308468i	$-0.0998162\pi$
$41$	7.42578	+	4.28727i	1.15971	+	0.669560i	0.208476	+	0.978027i	$0.433150\pi$
$42$	1.36666	+	0.942952i	0.210881	+	0.145501i
$43$	−1.83832	−	3.18406i	−0.280341	−	0.485564i	0.691128	−	0.722732i	$-0.257114\pi$
$43$	−1.83832	−	3.18406i	−0.280341	−	0.485564i	−0.971469	+	0.237168i	$0.923781\pi$
$44$		−	4.81509i		−	0.725903i
$45$	−1.50290	+	9.27017i	−0.224039	+	1.38192i
$46$	4.00182	+	2.31045i	0.590037	+	0.340658i
$47$	5.01412	+	2.89490i	0.731384	+	0.422265i	0.818928	−	0.573896i	$-0.194569\pi$
$47$	5.01412	+	2.89490i	0.731384	+	0.422265i	−0.0875442	+	0.996161i	$0.527902\pi$
$48$	−2.28605	+	1.08528i	−0.329962	+	0.156647i
$49$	−3.08930	+	5.35082i	−0.441328	+	0.764403i
$50$	4.39635	+	2.53823i	0.621738	+	0.358961i
$51$	−0.423177	+	5.25456i	−0.0592566	+	0.735785i
$52$	−1.38308	+	2.86044i	−0.191798	+	0.396671i
$53$	−3.37524			−0.463625			−0.231812	−	0.972761i	$-0.574466\pi$
$53$	−3.37524			−0.463625			−0.231812	+	0.972761i	$0.574466\pi$
$54$	5.33716	+	1.31223i	0.726295	+	0.178572i
$55$	8.55250	+	14.8134i	1.15322	+	1.99743i
$56$	1.38101	+	2.39198i	0.184546	+	0.319642i
$57$	−11.3611	−	0.914967i	−1.50481	−	0.121190i
$58$		−	2.82425i		−	0.370842i
$59$		−	3.14669i		−	0.409664i	−0.978797	−	0.204832i	$-0.934335\pi$
$59$		−	3.14669i		−	0.409664i	0.978797	−	0.204832i	$-0.0656648\pi$
$60$	−2.71343	+	3.93270i	−0.350303	+	0.507710i
$61$	4.09223	+	7.08794i	0.523956	+	0.907518i	0.999611	+	0.0278863i	$0.00887764\pi$
$61$	4.09223	+	7.08794i	0.523956	+	0.907518i	−0.475655	+	0.879632i	$0.657789\pi$
$62$	−0.727048	−	1.25928i	−0.0923352	−	0.159929i
$63$	0.435118	−	2.68390i	0.0548198	−	0.338140i
$64$	−7.73440			−0.966801
$65$	−0.825710	−	11.2566i	−0.102417	−	1.39621i
$66$	9.04319	−	4.29318i	1.11314	−	0.528453i
$67$	11.7394	+	6.77772i	1.43419	+	0.828031i	0.997437	−	0.0715499i	$-0.0227945\pi$
$67$	11.7394	+	6.77772i	1.43419	+	0.828031i	0.436755	+	0.899581i	$0.356128\pi$
$68$	−1.34101	+	2.32269i	−0.162621	+	0.281668i
$69$	0.607429	−	7.54242i	0.0731259	−	0.908000i
$70$	−2.59886	−	1.50045i	−0.310623	−	0.179338i
$71$	3.07782	+	1.77698i	0.365270	+	0.210889i	0.671390	−	0.741104i	$-0.265698\pi$
$71$	3.07782	+	1.77698i	0.365270	+	0.210889i	−0.306120	+	0.951993i	$0.599031\pi$
$72$	7.08413	+	5.77948i	0.834873	+	0.681119i
$73$		−	1.25464i		−	0.146844i	−0.997301	−	0.0734222i	$-0.976608\pi$
$73$		−	1.25464i		−	0.146844i	0.997301	−	0.0734222i	$-0.0233921\pi$
$74$	1.12586	+	1.95004i	0.130878	+	0.226688i
$75$	0.667314	−	8.28600i	0.0770548	−	0.956785i
$76$	−5.02199	−	2.89945i	−0.576061	−	0.332589i
$77$	−2.47612	−	4.28877i	−0.282180	−	0.488750i
$78$	−6.60533	−	0.0471580i	−0.747907	−	0.00533959i
$79$	−5.59586	+	9.69232i	−0.629584	+	1.09047i	0.358051	+	0.933702i	$0.383441\pi$
$79$	−5.59586	+	9.69232i	−0.629584	+	1.09047i	−0.987635	+	0.156770i	$0.949892\pi$
$80$	3.96087	−	2.28681i	0.442839	−	0.255673i
$81$	−1.80700	−	8.81673i	−0.200778	−	0.979637i
$82$	−4.53476	+	7.85444i	−0.500781	+	0.867378i
$83$	−0.899143	−	0.519121i	−0.0986938	−	0.0569809i	0.449841	−	0.893109i	$-0.351481\pi$
$83$	−0.899143	−	0.519121i	−0.0986938	−	0.0569809i	−0.548535	+	0.836128i	$0.684814\pi$
$84$	0.785594	−	1.13860i	0.0857153	−	0.124231i
$85$		−	9.52751i		−	1.03340i
$86$	3.36786	−	1.94444i	0.363166	−	0.209674i
$87$	−4.17787	+	1.98341i	−0.447915	+	0.212644i
$88$	16.6522			1.77513
$89$	−4.76108	+	2.74881i	−0.504674	+	0.291374i	−0.730642	−	0.682761i	$-0.760779\pi$
$89$	−4.76108	+	2.74881i	−0.504674	+	0.291374i	0.225968	+	0.974135i	$0.427446\pi$
$90$	−9.80530	−	1.58965i	−1.03357	−	0.167564i
$91$	0.239060	+	3.25901i	0.0250603	+	0.341637i
$92$	1.92489	−	3.33400i	0.200683	−	0.347594i
$93$	−1.35225	+	1.95988i	−0.140222	+	0.203230i
$94$	−3.06201	+	5.30356i	−0.315823	+	0.547021i
$95$	20.5998			2.11350
$96$	3.37960	+	7.11883i	0.344929	+	0.726562i
$97$	7.06649	−	4.07984i	0.717493	−	0.414245i	−0.0963363	−	0.995349i	$-0.530712\pi$
$97$	7.06649	−	4.07984i	0.717493	−	0.414245i	0.813829	+	0.581104i	$0.197379\pi$
$98$	−5.65970	−	3.26763i	−0.571717	−	0.330081i
$99$	−12.7017	−	10.3625i	−1.27657	−	1.04147i
$100$	2.11466	−	3.66269i	0.211466	−	0.366269i
$101$	4.56126			0.453862			0.226931	−	0.973911i	$-0.427131\pi$
$101$	4.56126			0.453862			0.226931	+	0.973911i	$0.427131\pi$
$102$	−5.55789	−	0.447605i	−0.550313	−	0.0443195i
$103$	3.06623	+	5.31087i	0.302125	+	0.523296i	0.976617	−	0.214986i	$-0.0689707\pi$
$103$	3.06623	+	5.31087i	0.302125	+	0.523296i	−0.674492	+	0.738282i	$0.735637\pi$
$104$	−9.89236	−	4.78315i	−0.970026	−	0.469026i
$105$	−0.394476	+	4.89819i	−0.0384969	+	0.478014i
$106$		−	3.57008i		−	0.346757i
$107$	−2.14217	−	3.71034i	−0.207091	−	0.358692i	0.743706	−	0.668507i	$-0.233066\pi$
$107$	−2.14217	−	3.71034i	−0.207091	−	0.358692i	−0.950797	+	0.309815i	$0.899733\pi$
$108$	1.09325	−	4.44650i	0.105198	−	0.427865i
$109$		−	16.3835i		−	1.56925i	−0.619969	−	0.784626i	$-0.712855\pi$
$109$		−	16.3835i		−	1.56925i	0.619969	−	0.784626i	$-0.287145\pi$
$110$	−15.6685	+	9.04621i	−1.49393	+	0.862522i
$111$	2.09400	−	3.03493i	0.198754	−	0.288063i
$112$	−1.14675	+	0.662077i	−0.108358	+	0.0625604i
$113$	−2.80827			−0.264180			−0.132090	−	0.991238i	$-0.542169\pi$
$113$	−2.80827			−0.264180			−0.132090	+	0.991238i	$0.542169\pi$
$114$	0.967785	−	12.0169i	0.0906413	−	1.12549i
$115$			13.6758i			1.27528i
$116$	−2.35294			−0.218465
$117$	4.56902	+	9.80429i	0.422406	+	0.906407i
$118$	3.32834			0.306398
$119$			2.75841i			0.252863i
$120$	−13.6006	−	9.38397i	−1.24156	−	0.856636i
$121$	−18.8570			−1.71427
$122$	−7.49711	+	4.32846i	−0.678756	+	0.391880i
$123$	14.8036	+	1.19221i	1.33480	+	0.107498i
$124$	−1.04914	+	0.605719i	−0.0942152	+	0.0543952i
$125$		−	0.627908i		−	0.0561618i
$126$	2.83883	+	0.460236i	0.252903	+	0.0410011i
$127$	1.63802	+	2.83714i	0.145351	+	0.251755i	0.929504	−	0.368812i	$-0.120236\pi$
$127$	1.63802	+	2.83714i	0.145351	+	0.251755i	−0.784153	+	0.620568i	$0.786902\pi$
$128$			0.918519i			0.0811863i
$129$	−5.24155	−	3.61650i	−0.461493	−	0.318415i
$130$	11.9064	−	0.873376i	1.04426	−	0.0766001i
$131$	−1.43797	−	2.49063i	−0.125636	−	0.217608i	0.796345	−	0.604842i	$-0.206764\pi$
$131$	−1.43797	−	2.49063i	−0.125636	−	0.217608i	−0.921981	+	0.387234i	$0.873430\pi$
$132$	−3.57674	−	7.53408i	−0.311315	−	0.655757i
$133$	−5.96406			−0.517150
$134$	−7.16898	+	12.4170i	−0.619306	+	1.07267i
$135$	4.53450	+	15.6212i	0.390267	+	1.34446i
$136$	−8.03266	−	4.63766i	−0.688795	−	0.397676i
$137$	−0.453535	+	0.261849i	−0.0387481	+	0.0223712i	−0.519249	−	0.854623i	$-0.673788\pi$
$137$	−0.453535	+	0.261849i	−0.0387481	+	0.0223712i	0.480501	+	0.876994i	$0.340455\pi$
$138$	7.97782	+	0.642494i	0.679117	+	0.0546927i
$139$	−3.81287			−0.323404			−0.161702	−	0.986840i	$-0.551698\pi$
$139$	−3.81287			−0.323404			−0.161702	+	0.986840i	$0.551698\pi$
$140$	−1.25006	+	2.16517i	−0.105649	+	0.182990i
$141$	9.99587	+	0.805019i	0.841804	+	0.0677948i
$142$	−1.87956	+	3.25549i	−0.157729	+	0.273195i
$143$	17.7367	+	8.57606i	1.48322	+	0.717166i
$144$	−2.77076	+	3.39623i	−0.230897	+	0.283019i
$145$	7.23870	−	4.17926i	0.601141	−	0.347069i
$146$	1.32707			0.109829
$147$	−0.859076	+	10.6671i	−0.0708554	+	0.879808i
$148$	1.62462	−	0.937975i	0.133543	−	0.0771011i
$149$		−	2.08034i		−	0.170428i	−0.996363	−	0.0852142i	$-0.972843\pi$
$149$		−	2.08034i		−	0.170428i	0.996363	−	0.0852142i	$-0.0271575\pi$
$150$	8.76433	+	0.705836i	0.715604	+	0.0576313i
$151$	−7.72274	−	4.45873i	−0.628468	−	0.362846i	0.151691	−	0.988428i	$-0.451528\pi$
$151$	−7.72274	−	4.45873i	−0.628468	−	0.362846i	−0.780158	+	0.625582i	$0.784862\pi$
$152$	10.0273	−	17.3677i	0.813318	−	1.40871i
$153$	3.24104	+	8.53604i	0.262023	+	0.690098i
$154$	4.53634	−	2.61906i	0.365549	−	0.211050i
$155$	2.15174	−	3.72692i	0.172832	−	0.299354i
$156$	−0.0392883	+	5.50304i	−0.00314558	+	0.440596i
$157$	−8.99174	−	15.5741i	−0.717619	−	1.24295i	−0.961941	−	0.273258i	$-0.911899\pi$
$157$	−8.99174	−	15.5741i	−0.717619	−	1.24295i	0.244322	−	0.969694i	$-0.421435\pi$
$158$	−10.2518	−	5.91890i	−0.815592	−	0.470882i
$159$	−5.28116	+	2.50719i	−0.418824	+	0.198833i
$160$	−7.12120	−	12.3343i	−0.562980	−	0.975110i
$161$		−	3.95943i		−	0.312047i
$162$	9.32569	−	1.91131i	0.732695	−	0.150167i
$163$	−3.20901	−	1.85272i	−0.251349	−	0.145116i	0.369033	−	0.929416i	$-0.379689\pi$
$163$	−3.20901	−	1.85272i	−0.251349	−	0.145116i	−0.620382	+	0.784300i	$0.713022\pi$
$164$	6.54370	+	3.77801i	0.510977	+	0.295013i
$165$	24.3856	+	16.8252i	1.89841	+	1.30984i
$166$	0.549088	−	0.951048i	0.0426175	−	0.0738156i
$167$	−6.11049	−	3.52789i	−0.472844	−	0.272996i	0.244586	−	0.969628i	$-0.421348\pi$
$167$	−6.11049	−	3.52789i	−0.472844	−	0.272996i	−0.717429	+	0.696631i	$0.754681\pi$
$168$	3.93765	+	2.71685i	0.303796	+	0.209609i
$169$	−8.07326	−	10.1893i	−0.621020	−	0.783795i
$170$	10.0775			0.772909
$171$	−18.4561	+	7.00759i	−1.41137	+	0.535884i
$172$	−1.61995	−	2.80584i	−0.123520	−	0.213943i
$173$	5.71558	+	9.89968i	0.434548	+	0.752659i	0.997259	−	0.0739950i	$-0.0235749\pi$
$173$	5.71558	+	9.89968i	0.434548	+	0.752659i	−0.562711	+	0.826654i	$0.690242\pi$
$174$	−2.09790	−	4.41905i	−0.159042	−	0.335007i
$175$		−	4.34978i		−	0.328812i
$176$			7.98331i			0.601764i
$177$	−2.33742	−	4.92356i	−0.175691	−	0.370078i
$178$	−2.90749	−	5.03593i	−0.217926	−	0.377459i
$179$	4.43441	+	7.68062i	0.331443	+	0.574076i	0.982795	−	0.184700i	$-0.0591312\pi$
$179$	4.43441	+	7.68062i	0.331443	+	0.574076i	−0.651352	+	0.758776i	$0.725798\pi$
$180$	−1.32437	+	8.16901i	−0.0987130	+	0.608882i
$181$	11.9595			0.888944			0.444472	−	0.895793i	$-0.353391\pi$
$181$	11.9595			0.888944			0.444472	+	0.895793i	$0.353391\pi$
$182$	−3.44714	+	0.252860i	−0.255519	+	0.0187432i
$183$	11.6681	+	8.05058i	0.862529	+	0.595116i
$184$	11.5301	+	6.65691i	0.850011	+	0.490754i
$185$	−3.33204	+	5.77126i	−0.244976	+	0.424311i
$186$	−2.07302	−	1.43031i	−0.152001	−	0.104876i
$187$	14.4023	+	8.31520i	1.05320	+	0.608068i
$188$	4.41851	+	2.55103i	0.322253	+	0.186053i
$189$	−1.31283	−	4.52266i	−0.0954941	−	0.328975i
$190$			21.7890i			1.58074i
$191$	−13.6748	−	23.6854i	−0.989471	−	1.71381i	−0.620079	−	0.784539i	$-0.712899\pi$
$191$	−13.6748	−	23.6854i	−0.989471	−	1.71381i	−0.369392	−	0.929274i	$-0.620434\pi$
$192$	−12.1019	+	5.74525i	−0.873377	+	0.414628i
$193$	11.3391	+	6.54666i	0.816210	+	0.471239i	0.849108	−	0.528220i	$-0.177140\pi$
$193$	11.3391	+	6.54666i	0.816210	+	0.471239i	−0.0328980	+	0.999459i	$0.510474\pi$
$194$	4.31535	+	7.47441i	0.309824	+	0.536631i
$195$	−9.65356	−	16.9996i	−0.691306	−	1.21737i
$196$	−2.72233	+	4.71522i	−0.194452	+	0.336801i
$197$	−5.79799	+	3.34747i	−0.413090	+	0.238497i	−0.692116	−	0.721786i	$-0.743322\pi$
$197$	−5.79799	+	3.34747i	−0.413090	+	0.238497i	0.279027	+	0.960283i	$0.409988\pi$
$198$	10.9607	−	13.4349i	0.778940	−	0.954776i
$199$	5.98313	−	10.3631i	0.424133	−	0.734620i	−0.572206	−	0.820110i	$-0.693912\pi$
$199$	5.98313	−	10.3631i	0.424133	−	0.734620i	0.996339	+	0.0854901i	$0.0272456\pi$
$200$	12.6668	+	7.31320i	0.895680	+	0.517121i
$201$	23.4030	+	1.88476i	1.65072	+	0.132941i
$202$			4.82457i			0.339455i
$203$	−2.09575	+	1.20998i	−0.147093	+	0.0849240i
$204$	−0.372909	+	4.63039i	−0.0261089	+	0.324192i
$205$	−26.8418			−1.87471
$206$	−5.61745	+	3.24324i	−0.391386	+	0.225967i
$207$	−4.65221	−	12.2527i	−0.323351	−	0.851620i
$208$	2.29311	−	4.74254i	0.158998	−	0.328836i
$209$	−17.9786	+	31.1399i	−1.24361	+	2.15399i
$210$	−5.18094	−	0.417248i	−0.357519	−	0.0287928i
$211$	10.2741	−	17.7952i	0.707296	−	1.22507i	−0.258560	−	0.965995i	$-0.583248\pi$
$211$	10.2741	−	17.7952i	0.707296	−	1.22507i	0.965857	−	0.259078i	$-0.0834185\pi$
$212$	−2.97431			−0.204276
$213$	6.13578	+	0.494145i	0.420416	+	0.0338583i
$214$	3.92453	−	2.26583i	0.268275	−	0.154889i
$215$	9.96738	+	5.75467i	0.679770	+	0.392465i
$216$	15.3775	+	3.78082i	1.04631	+	0.257252i
$217$	−0.622972	+	1.07902i	−0.0422901	+	0.0732486i
$218$	17.3292			1.17368
$219$	−0.931968	−	1.96311i	−0.0629766	−	0.132655i
$220$	7.53659	+	13.0538i	0.508117	+	0.880084i
$221$	−6.16737	−	9.07660i	−0.414862	−	0.610558i
$222$	3.21013	+	2.21488i	0.215450	+	0.148653i
$223$		−	9.60170i		−	0.642977i	−0.946913	−	0.321489i	$-0.895817\pi$
$223$		−	9.60170i		−	0.642977i	0.946913	−	0.321489i	$-0.104183\pi$
$224$	2.06173	+	3.57102i	0.137755	+	0.238599i
$225$	−5.11086	−	13.4606i	−0.340724	−	0.897376i
$226$		−	2.97038i		−	0.197587i
$227$	−24.6520	+	14.2329i	−1.63621	+	0.944668i	−0.654092	+	0.756415i	$0.726949\pi$
$227$	−24.6520	+	14.2329i	−1.63621	+	0.944668i	−0.982121	+	0.188252i	$0.939718\pi$
$228$	−10.0116	−	0.806282i	−0.663032	−	0.0533973i
$229$	−18.8514	+	10.8839i	−1.24574	+	0.719227i	−0.970256	−	0.242080i	$-0.922170\pi$
$229$	−18.8514	+	10.8839i	−1.24574	+	0.719227i	−0.275481	+	0.961307i	$0.588837\pi$
$230$	−14.4653			−0.953813
$231$	−7.06011	−	4.87124i	−0.464521	−	0.320504i
$232$		−	8.13727i		−	0.534238i
$233$	−11.2240			−0.735307			−0.367653	−	0.929963i	$-0.619839\pi$
$233$	−11.2240			−0.735307			−0.367653	+	0.929963i	$0.619839\pi$
$234$	−10.3703	+	4.83277i	−0.677925	+	0.315928i
$235$	−18.1244			−1.18231
$236$		−	2.77291i		−	0.180501i
$237$	−1.55611	+	19.3221i	−0.101080	+	1.25510i
$238$	−2.91764			−0.189122
$239$	−10.4481	+	6.03219i	−0.675829	+	0.390190i	−0.798282	−	0.602284i	$-0.794257\pi$
$239$	−10.4481	+	6.03219i	−0.675829	+	0.390190i	0.122453	+	0.992474i	$0.460924\pi$
$240$	4.49881	−	6.52033i	0.290397	−	0.420885i
$241$	12.5509	−	7.24627i	0.808476	−	0.466774i	−0.0379507	−	0.999280i	$-0.512083\pi$
$241$	12.5509	−	7.24627i	0.808476	−	0.466774i	0.846426	+	0.532506i	$0.178750\pi$
$242$		−	19.9456i		−	1.28215i
$243$	−9.37660	−	12.4531i	−0.601509	−	0.798866i
$244$	3.60613	+	6.24600i	0.230859	+	0.399859i
$245$		−	19.3415i		−	1.23568i
$246$	−1.26103	+	15.6582i	−0.0804006	+	0.998329i
$247$	19.6249	−	13.3347i	1.24870	−	0.848467i
$248$	−2.09478	−	3.62827i	−0.133019	−	0.230395i
$249$	−1.79248	−	0.144358i	−0.113594	−	0.00914830i
$250$	0.664155			0.0420049
$251$	7.10222	−	12.3014i	0.448288	−	0.776457i	−0.549987	−	0.835173i	$-0.685367\pi$
$251$	7.10222	−	12.3014i	0.448288	−	0.776457i	0.998275	+	0.0587159i	$0.0187006\pi$
$252$	0.383433	−	2.36509i	0.0241540	−	0.148987i
$253$	−20.6732	−	11.9357i	−1.29971	−	0.750389i
$254$	−3.00092	+	1.73258i	−0.188294	+	0.108712i
$255$	−7.07721	−	14.9075i	−0.443192	−	0.933544i
$256$	−16.4404			−1.02752
$257$	12.1179	−	20.9889i	0.755896	−	1.30925i	−0.189032	−	0.981971i	$-0.560535\pi$
$257$	12.1179	−	20.9889i	0.755896	−	1.30925i	0.944928	−	0.327279i	$-0.106132\pi$
$258$	3.82526	−	5.54413i	0.238151	−	0.345162i
$259$	0.964691	−	1.67089i	0.0599430	−	0.103824i
$260$	−0.727628	−	9.91946i	−0.0451256	−	0.615179i
$261$	−5.06372	+	6.20679i	−0.313436	+	0.384191i
$262$	2.63441	−	1.52098i	0.162754	−	0.0939663i
$263$	16.7367			1.03203			0.516014	−	0.856580i	$-0.327415\pi$
$263$	16.7367			1.03203			0.516014	+	0.856580i	$0.327415\pi$
$264$	26.0554	−	12.3696i	1.60360	−	0.761294i
$265$	9.15029	−	5.28292i	0.562098	−	0.324527i
$266$		−	6.30834i		−	0.386789i
$267$	−5.40770	+	7.83763i	−0.330946	+	0.479655i
$268$	10.3449	+	5.97263i	0.631915	+	0.364836i
$269$	−9.55494	+	16.5496i	−0.582575	+	1.00905i	0.412598	+	0.910913i	$0.364621\pi$
$269$	−9.55494	+	16.5496i	−0.582575	+	1.00905i	−0.995173	+	0.0981359i	$0.968712\pi$
$270$	−16.5230	+	4.79626i	−1.00556	+	0.291891i
$271$	−14.2160	+	8.20761i	−0.863561	+	0.498577i	−0.865203	−	0.501422i	$-0.832811\pi$
$271$	−14.2160	+	8.20761i	−0.863561	+	0.498577i	0.00164242	+	0.999999i	$0.499477\pi$
$272$	2.22336	−	3.85097i	0.134811	−	0.233499i
$273$	2.79490	+	4.92172i	0.169155	+	0.297876i
$274$	−0.276964	−	0.479716i	−0.0167320	−	0.0289807i
$275$	−22.7113	−	13.1124i	−1.36954	−	0.790706i
$276$	0.535276	−	6.64649i	0.0322198	−	0.400072i
$277$	15.8827	+	27.5097i	0.954301	+	1.65290i	0.735959	+	0.677026i	$0.236732\pi$
$277$	15.8827	+	27.5097i	0.954301	+	1.65290i	0.218343	+	0.975872i	$0.429935\pi$
$278$		−	4.03298i		−	0.241882i
$279$	−0.660007	+	4.07106i	−0.0395136	+	0.243728i
$280$	−7.48787	−	4.32313i	−0.447486	−	0.258356i
$281$	13.7907	+	7.96208i	0.822686	+	0.474978i	0.851342	−	0.524611i	$-0.175789\pi$
$281$	13.7907	+	7.96208i	0.822686	+	0.474978i	−0.0286560	+	0.999589i	$0.509123\pi$
$282$	−0.851490	+	10.5729i	−0.0507055	+	0.629607i
$283$	−7.70224	+	13.3407i	−0.457850	+	0.793020i	−0.998847	−	0.0480046i	$-0.984714\pi$
$283$	−7.70224	+	13.3407i	−0.457850	+	0.793020i	0.540997	+	0.841025i	$0.318047\pi$
$284$	2.71222	+	1.56590i	0.160941	+	0.0929191i
$285$	32.2321	−	15.3019i	1.90927	−	0.906407i
$286$	−9.07113	+	18.7606i	−0.536387	+	1.10934i
$287$	7.77123			0.458721
$288$	10.5760	+	8.62825i	0.623196	+	0.508425i
$289$	3.86842	+	6.70030i	0.227554	+	0.394135i
$290$	4.42052	+	7.65656i	0.259582	+	0.449609i
$291$	8.02621	−	11.6327i	0.470505	−	0.681924i
$292$		−	1.10561i		−	0.0647007i
$293$			21.5144i			1.25689i	0.777856	+	0.628443i	$0.216307\pi$
$293$			21.5144i			1.25689i	−0.777856	+	0.628443i	$0.783693\pi$
$294$	−11.2829	−	0.908668i	−0.658031	−	0.0529946i
$295$	4.92520	+	8.53070i	0.286756	+	0.496677i
$296$	3.24383	+	5.61849i	0.188544	+	0.326568i
$297$	−27.5715	−	6.77891i	−1.59986	−	0.393352i
$298$	2.20043			0.127468
$299$	8.85267	+	13.0286i	0.511963	+	0.753463i
$300$	0.588047	−	7.30175i	0.0339509	−	0.421567i
$301$	−2.88576	−	1.66609i	−0.166332	−	0.0960320i
$302$	4.71611	−	8.16855i	0.271382	−	0.470047i
$303$	7.13691	−	3.38818i	0.410005	−	0.194646i
$304$	8.32633	+	4.80721i	0.477548	+	0.275712i
$305$	−22.1881	−	12.8103i	−1.27049	−	0.733516i
$306$	−9.02880	+	3.42814i	−0.516142	+	0.195974i
$307$		−	13.4448i		−	0.767336i	−0.923471	−	0.383668i	$-0.874661\pi$
$307$		−	13.4448i		−	0.767336i	0.923471	−	0.383668i	$-0.125339\pi$
$308$	−2.18199	−	3.77932i	−0.124331	−	0.215347i
$309$	8.74268	+	6.03216i	0.497354	+	0.343158i
$310$	3.94207	+	2.27595i	0.223894	+	0.129265i
$311$	5.08321	+	8.80438i	0.288242	+	0.499251i	0.973390	−	0.229153i	$-0.0735958\pi$
$311$	5.08321	+	8.80438i	0.288242	+	0.499251i	−0.685148	+	0.728404i	$0.740262\pi$
$312$	−19.0314	−	0.135872i	−1.07744	−	0.00769225i
$313$	11.9631	−	20.7207i	0.676193	−	1.17120i	−0.299926	−	0.953963i	$-0.596962\pi$
$313$	11.9631	−	20.7207i	0.676193	−	1.17120i	0.976119	−	0.217238i	$-0.0697047\pi$
$314$	16.4732	−	9.51080i	0.929636	−	0.536725i
$315$	3.02123	+	7.95712i	0.170227	+	0.448333i
$316$	−4.93116	+	8.54102i	−0.277399	+	0.480470i
$317$	−3.01218	−	1.73908i	−0.169181	−	0.0976766i	0.413019	−	0.910723i	$-0.364474\pi$
$317$	−3.01218	−	1.73908i	−0.169181	−	0.0976766i	−0.582200	+	0.813046i	$0.697808\pi$
$318$	−2.65192	−	5.58603i	−0.148712	−	0.313249i
$319$			14.5899i			0.816878i
$320$	20.9680	−	12.1059i	1.17215	−	0.676740i
$321$	−6.10792	−	4.21426i	−0.340911	−	0.235217i
$322$	4.18799			0.233388
$323$	17.3450	−	10.0141i	0.965100	−	0.557201i
$324$	−1.59236	−	7.76943i	−0.0884643	−	0.431635i
$325$	9.72543	+	14.3130i	0.539470	+	0.793945i
$326$	1.95967	−	3.39426i	0.108536	−	0.187990i
$327$	−12.1699	−	25.6349i	−0.672999	−	1.41761i
$328$	−13.0656	+	22.6303i	−0.721428	+	1.24955i
$329$	5.24738			0.289297
$330$	−17.7965	+	25.7933i	−0.979664	+	1.41987i
$331$	16.5596	−	9.56069i	0.910198	−	0.525503i	0.0297028	−	0.999559i	$-0.490544\pi$
$331$	16.5596	−	9.56069i	0.910198	−	0.525503i	0.880495	+	0.474056i	$0.157211\pi$
$332$	−0.792338	−	0.457457i	−0.0434852	−	0.0251062i
$333$	1.02204	−	6.30416i	0.0560075	−	0.345466i
$334$	3.73155	−	6.46323i	0.204181	−	0.353652i
$335$	−42.4340			−2.31842
$336$	−1.30249	+	1.88776i	−0.0710569	+	0.102986i
$337$	0.667895	+	1.15683i	0.0363825	+	0.0630164i	0.883643	−	0.468161i	$-0.155083\pi$
$337$	0.667895	+	1.15683i	0.0363825	+	0.0630164i	−0.847261	+	0.531177i	$0.821750\pi$
$338$	10.7775	−	8.53930i	0.586220	−	0.464477i
$339$	−4.39405	+	2.08603i	−0.238652	+	0.113298i
$340$		−	8.39578i		−	0.455325i
$341$	3.75589	+	6.50539i	0.203393	+	0.352287i
$342$	−7.41211	−	19.5215i	−0.400801	−	1.05560i
$343$			11.9439i			0.644912i
$344$	9.70354	−	5.60234i	0.523180	−	0.302058i
$345$	10.1587	+	21.3983i	0.546924	+	1.15205i
$346$	−10.4712	+	6.04552i	−0.562933	+	0.325009i
$347$	26.7765			1.43744			0.718719	−	0.695301i	$-0.244729\pi$
$347$	26.7765			1.43744			0.718719	+	0.695301i	$0.244729\pi$
$348$	−3.68160	+	1.74781i	−0.197355	+	0.0936923i
$349$		−	25.6939i		−	1.37536i	−0.726013	−	0.687681i	$-0.758629\pi$
$349$		−	25.6939i		−	1.37536i	0.726013	−	0.687681i	$-0.241371\pi$
$350$	4.60088			0.245927
$351$	14.4318	+	11.9466i	0.770315	+	0.637664i
$352$	24.8603			1.32506
$353$		−	1.09910i		−	0.0584992i	−0.999572	−	0.0292496i	$-0.990688\pi$
$353$		−	1.09910i		−	0.0584992i	0.999572	−	0.0292496i	$-0.00931176\pi$
$354$	5.20778	−	2.47235i	0.276791	−	0.131404i
$355$	−11.1253			−0.590471
$356$	−4.19554	+	2.42229i	−0.222363	+	0.128381i
$357$	2.04899	+	4.31602i	0.108444	+	0.228428i
$358$	−8.12399	+	4.69039i	−0.429366	+	0.247895i
$359$			12.6655i			0.668460i	0.942491	+	0.334230i	$0.108476\pi$
$359$			12.6655i			0.668460i	−0.942491	+	0.334230i	$0.891524\pi$
$360$	−28.2512	−	4.58013i	−1.48897	−	0.241394i
$361$	12.1519	+	21.0477i	0.639575	+	1.10778i
$362$			12.6499i			0.664864i
$363$	−29.5052	+	14.0073i	−1.54862	+	0.735193i
$364$	0.210663	+	2.87188i	0.0110417	+	0.150528i
$365$	1.96376	+	3.40134i	0.102788	+	0.178034i
$366$	−8.51531	+	12.3416i	−0.445103	+	0.645107i
$367$	−0.157466			−0.00821965			−0.00410983	−	0.999992i	$-0.501308\pi$
$367$	−0.157466			−0.00821965			−0.00410983	+	0.999992i	$0.501308\pi$
$368$	−3.19142	+	5.52770i	−0.166364	+	0.288151i
$369$	24.0485	−	9.13096i	1.25192	−	0.475339i
$370$	−6.10441	−	3.52438i	−0.317353	−	0.183224i
$371$	−2.64919	+	1.52951i	−0.137539	+	0.0794083i
$372$	−1.19162	+	1.72707i	−0.0617828	+	0.0895446i
$373$	6.74577			0.349283			0.174641	−	0.984632i	$-0.444123\pi$
$373$	6.74577			0.349283			0.174641	+	0.984632i	$0.444123\pi$
$374$	−8.79521	+	15.2337i	−0.454789	+	0.787718i
$375$	−0.466421	−	0.982475i	−0.0240859	−	0.0507348i
$376$	−8.82232	+	15.2807i	−0.454976	+	0.788042i
$377$	4.19078	−	8.66723i	0.215836	−	0.446385i
$378$	4.78373	−	1.38861i	0.246049	−	0.0714225i
$379$	−26.5106	+	15.3059i	−1.36176	+	0.786213i	−0.989858	−	0.142059i	$-0.954628\pi$
$379$	−26.5106	+	15.3059i	−1.36176	+	0.786213i	−0.371902	+	0.928272i	$0.621294\pi$
$380$	18.1529			0.931222
$381$	4.67046	+	3.22246i	0.239275	+	0.165092i
$382$	25.0526	−	14.4642i	1.28180	−	0.740050i
$383$			18.1039i			0.925068i	0.886601	+	0.462534i	$0.153060\pi$
$383$			18.1039i			0.925068i	−0.886601	+	0.462534i	$0.846940\pi$
$384$	0.682292	+	1.43719i	0.0348181	+	0.0733412i
$385$	13.4256	+	7.75125i	0.684230	+	0.395040i
$386$	−6.92457	+	11.9937i	−0.352452	+	0.610464i
$387$	−10.8877	−	1.76514i	−0.553455	−	0.0897271i
$388$	6.22709	−	3.59521i	0.316133	−	0.182519i
$389$	7.32837	−	12.6931i	0.371563	−	0.643566i	−0.618243	−	0.785987i	$-0.712155\pi$
$389$	7.32837	−	12.6931i	0.371563	−	0.643566i	0.989806	+	0.142421i	$0.0454886\pi$
$390$	17.9809	−	10.2108i	0.910499	−	0.517045i
$391$	6.64819	+	11.5150i	0.336213	+	0.582339i
$392$	−16.3068	−	9.41475i	−0.823619	−	0.475517i
$393$	−4.10005	−	2.82889i	−0.206820	−	0.142699i
$394$	−3.54071	−	6.13269i	−0.178378	−	0.308960i
$395$		−	35.0346i		−	1.76278i
$396$	−11.1929	−	9.13155i	−0.562464	−	0.458878i
$397$	−13.1303	−	7.58075i	−0.658988	−	0.380467i	0.132903	−	0.991129i	$-0.457570\pi$
$397$	−13.1303	−	7.58075i	−0.658988	−	0.380467i	−0.791891	+	0.610662i	$0.790903\pi$
$398$	10.9613	+	6.32852i	0.549441	+	0.317220i
$399$	−9.33184	+	4.43021i	−0.467176	+	0.221788i
$400$	−3.50605	+	6.07266i	−0.175303	+	0.303633i
$401$	27.0059	+	15.5919i	1.34861	+	0.778622i	0.988053	−	0.154115i	$-0.0492525\pi$
$401$	27.0059	+	15.5919i	1.34861	+	0.778622i	0.360559	+	0.932736i	$0.382586\pi$
$402$	−1.99356	+	24.7539i	−0.0994298	+	1.23461i
$403$	−0.362616	−	4.94340i	−0.0180632	−	0.246248i
$404$	4.01945			0.199975
$405$	18.6988	+	21.0739i	0.929148	+	1.04717i
$406$	−1.27983	−	2.21673i	−0.0635168	−	0.110014i
$407$	−5.81611	−	10.0738i	−0.288294	−	0.499340i
$408$	−16.0135	−	1.28965i	−0.792785	−	0.0638470i
$409$		−	23.5084i		−	1.16241i	−0.813756	−	0.581207i	$-0.802581\pi$
$409$		−	23.5084i		−	1.16241i	0.813756	−	0.581207i	$-0.197419\pi$
$410$		−	28.3913i		−	1.40214i
$411$	−0.515131	+	0.746603i	−0.0254096	+	0.0368272i
$412$	2.70201	+	4.68002i	0.133118	+	0.230568i
$413$	−1.42594	−	2.46981i	−0.0701662	−	0.121531i
$414$	12.9600	−	4.92077i	0.636948	−	0.241842i
$415$	3.25011			0.159542
$416$	−14.7684	−	7.14081i	−0.724081	−	0.350107i
$417$	−5.96593	+	2.83227i	−0.292153	+	0.138697i
$418$	−32.9375	−	19.0165i	−1.61102	−	0.930126i
$419$	16.4315	−	28.4602i	0.802732	−	1.39037i	−0.115080	−	0.993356i	$-0.536712\pi$
$419$	16.4315	−	28.4602i	0.802732	−	1.39037i	0.917812	−	0.397016i	$-0.129954\pi$
$420$	−0.347618	+	4.31636i	−0.0169620	+	0.210617i
$421$	−30.6615	−	17.7024i	−1.49435	−	0.862763i	−0.494370	−	0.869252i	$-0.664601\pi$
$421$	−30.6615	−	17.7024i	−1.49435	−	0.862763i	−0.999979	+	0.00648875i	$0.997935\pi$
$422$	18.8225	+	10.8672i	0.916263	+	0.529005i
$423$	16.2383	−	6.16551i	0.789534	−	0.299778i
$424$		−	10.2862i		−	0.499540i
$425$	7.30362	+	12.6502i	0.354277	+	0.613626i
$426$	−0.522671	+	6.48997i	−0.0253235	+	0.314440i
$427$	6.42390	+	3.70884i	0.310874	+	0.179483i
$428$	−1.88771	−	3.26961i	−0.0912459	−	0.158043i
$429$	34.1228	+	0.243615i	1.64746	+	0.0117619i
$430$	−6.08687	+	10.5428i	−0.293535	+	0.508417i
$431$	7.97114	−	4.60214i	0.383956	−	0.221677i	−0.295582	−	0.955317i	$-0.595514\pi$
$431$	7.97114	−	4.60214i	0.383956	−	0.221677i	0.679538	+	0.733640i	$0.262180\pi$
$432$	−1.81258	+	7.37219i	−0.0872077	+	0.354695i
$433$	−13.7330	+	23.7863i	−0.659967	+	1.14310i	0.320657	+	0.947195i	$0.396096\pi$
$433$	−13.7330	+	23.7863i	−0.659967	+	1.14310i	−0.980624	+	0.195900i	$0.937237\pi$
$434$	−1.14131	−	0.658934i	−0.0547845	−	0.0316298i
$435$	8.22181	−	11.9162i	0.394206	−	0.571340i
$436$		−	14.4374i		−	0.691424i
$437$	−24.8970	+	14.3743i	−1.19099	+	0.687617i
$438$	2.07643	−	0.985768i	0.0992157	−	0.0471018i
$439$	−17.0253			−0.812574			−0.406287	−	0.913745i	$-0.633177\pi$
$439$	−17.0253			−0.812574			−0.406287	+	0.913745i	$0.633177\pi$
$440$	−45.1443	+	26.0641i	−2.15217	+	1.24256i
$441$	6.57953	+	17.3287i	0.313311	+	0.825178i
$442$	9.60056	−	6.52339i	0.456652	−	0.310286i
$443$	−1.77702	+	3.07788i	−0.0844285	+	0.146235i	−0.905148	−	0.425098i	$-0.860240\pi$
$443$	−1.77702	+	3.07788i	−0.0844285	+	0.146235i	0.820719	+	0.571332i	$0.193573\pi$
$444$	1.84527	−	2.67443i	0.0875724	−	0.126923i
$445$	8.60489	−	14.9041i	0.407911	−	0.706523i
$446$	10.1560			0.480899
$447$	−1.54532	−	3.25507i	−0.0730909	−	0.153960i
$448$	−6.07066	+	3.50490i	−0.286812	+	0.165591i
$449$	0.352419	+	0.203469i	0.0166317	+	0.00960230i	0.508293	−	0.861184i	$-0.330277\pi$
$449$	0.352419	+	0.203469i	0.0166317	+	0.00960230i	−0.491661	+	0.870787i	$0.663610\pi$
$450$	14.2377	−	5.40589i	0.671170	−	0.254836i
$451$	23.4263	−	40.5756i	1.10310	−	1.91063i
$452$	−2.47469			−0.116400
$453$	−15.3956	−	1.23989i	−0.723350	−	0.0582551i
$454$	−15.0545	−	26.0751i	−0.706541	−	1.22377i
$455$	−5.74909	−	8.46101i	−0.269522	−	0.396658i
$456$	2.78840	−	34.6233i	0.130579	−	1.62139i
$457$			26.7236i			1.25008i	0.780593	+	0.625040i	$0.214917\pi$
$457$			26.7236i			1.25008i	−0.780593	+	0.625040i	$0.785083\pi$
$458$	−11.5122	−	19.9397i	−0.537928	−	0.931719i
$459$	11.4119	+	10.9487i	0.532663	+	0.511040i
$460$			12.0513i			0.561897i
$461$	4.36719	−	2.52140i	0.203401	−	0.117433i	−0.394840	−	0.918750i	$-0.629200\pi$
$461$	4.36719	−	2.52140i	0.203401	−	0.117433i	0.598241	+	0.801316i	$0.295867\pi$
$462$	5.15244	−	7.46766i	0.239713	−	0.347427i
$463$	11.3461	−	6.55069i	0.527299	−	0.304436i	−0.212617	−	0.977136i	$-0.568199\pi$
$463$	11.3461	−	6.55069i	0.527299	−	0.304436i	0.739916	+	0.672699i	$0.234865\pi$
$464$	3.90112			0.181105
$465$	0.598359	−	7.42979i	0.0277482	−	0.344548i
$466$		−	11.8719i		−	0.549955i
$467$	−22.0084			−1.01843			−0.509213	−	0.860640i	$-0.670064\pi$
$467$	−22.0084			−1.01843			−0.509213	+	0.860640i	$0.670064\pi$
$468$	4.02628	+	8.63968i	0.186115	+	0.399369i
$469$	12.2855			0.567291
$470$		−	19.1707i		−	0.884277i
$471$	−25.6379	−	17.6893i	−1.18133	−	0.815081i
$472$	9.58966			0.441400
$473$	−17.3982	+	10.0449i	−0.799970	+	0.461863i
$474$	−20.4375	−	1.64594i	−0.938725	−	0.0756003i
$475$	−27.3516	+	15.7914i	−1.25498	+	0.724561i
$476$			2.43075i			0.111413i
$477$	−6.40095	+	7.84589i	−0.293079	+	0.359238i
$478$	−6.38041	−	11.0512i	−0.291833	−	0.505470i
$479$		−	27.8329i		−	1.27172i	−0.771806	−	0.635858i	$-0.780646\pi$
$479$		−	27.8329i		−	1.27172i	0.771806	−	0.635858i	$-0.219354\pi$
$480$	−20.3045	−	14.0094i	−0.926770	−	0.639440i
$481$	0.561523	+	7.65501i	0.0256032	+	0.349039i
$482$	7.66458	+	13.2754i	0.349112	+	0.604680i
$483$	−2.94113	−	6.19524i	−0.133826	−	0.281893i
$484$	−16.6171			−0.755321
$485$	−12.7715	+	22.1209i	−0.579925	+	1.00446i
$486$	13.1720	−	9.91788i	0.597492	−	0.449884i
$487$	22.4699	+	12.9730i	1.01821	+	0.587863i	0.913585	−	0.406649i	$-0.133303\pi$
$487$	22.4699	+	12.9730i	1.01821	+	0.587863i	0.104624	+	0.994512i	$0.466636\pi$
$488$	−21.6008	+	12.4712i	−0.977821	+	0.564545i
$489$	−6.39731	−	0.515208i	−0.289296	−	0.0232985i
$490$	20.4580			0.924198
$491$	−6.26997	+	10.8599i	−0.282960	+	0.490101i	−0.972112	−	0.234516i	$-0.924650\pi$
$491$	−6.26997	+	10.8599i	−0.282960	+	0.490101i	0.689153	+	0.724616i	$0.257983\pi$
$492$	13.0452	+	1.05059i	0.588121	+	0.0473644i
$493$	4.06330	−	7.03785i	0.183002	−	0.316969i
$494$	14.1045	+	20.7577i	0.634590	+	0.933935i
$495$	50.6537	+	8.21206i	2.27671	+	0.369105i
$496$	1.73944	−	1.00427i	0.0781033	−	0.0450929i
$497$	3.22100			0.144482
$498$	0.152691	−	1.89596i	0.00684225	−	0.0849599i
$499$	−21.6338	+	12.4903i	−0.968464	+	0.559143i	−0.898768	−	0.438425i	$-0.855536\pi$
$499$	−21.6338	+	12.4903i	−0.968464	+	0.559143i	−0.0696964	+	0.997568i	$0.522203\pi$
$500$		−	0.553322i		−	0.0247453i
$501$	−12.1815	−	0.981041i	−0.544231	−	0.0438297i
$502$	13.0115	+	7.51220i	0.580732	+	0.335286i
$503$	−20.8658	+	36.1406i	−0.930358	+	1.61143i	−0.147650	+	0.989040i	$0.547171\pi$
$503$	−20.8658	+	36.1406i	−0.930358	+	1.61143i	−0.782709	+	0.622388i	$0.786162\pi$
$504$	8.17928	+	1.32604i	0.364334	+	0.0590665i
$505$	−12.3656	+	7.13929i	−0.550262	+	0.317694i
$506$	12.6247	−	21.8666i	0.561235	−	0.972088i
$507$	−20.2009	−	9.94607i	−0.897153	−	0.441721i
$508$	1.44345	+	2.50013i	0.0640427	+	0.110925i
$509$	−8.39674	−	4.84786i	−0.372179	−	0.214878i	0.302231	−	0.953235i	$-0.402269\pi$
$509$	−8.39674	−	4.84786i	−0.372179	−	0.214878i	−0.674410	+	0.738357i	$0.735602\pi$
$510$	15.7681	−	7.48575i	0.698222	−	0.331475i
$511$	−0.568549	−	0.984755i	−0.0251511	−	0.0435630i
$512$		−	15.5524i		−	0.687324i
$513$	−23.6725	+	24.6742i	−1.04517	+	1.08939i
$514$	22.2005	+	12.8175i	0.979222	+	0.565354i
$515$	−16.6252	−	9.59854i	−0.732592	−	0.422962i
$516$	−4.61893	−	3.18691i	−0.203337	−	0.140296i
$517$	15.8182	−	27.3979i	0.695683	−	1.20496i
$518$	1.76735	+	1.02038i	0.0776529	+	0.0448329i
$519$	16.2967	+	11.2442i	0.715346	+	0.493565i
$520$	34.3048	−	2.51638i	1.50437	−	0.110351i
$521$	−19.1154			−0.837463			−0.418731	−	0.908110i	$-0.637525\pi$
$521$	−19.1154			−0.837463			−0.418731	+	0.908110i	$0.637525\pi$
$522$	−6.56509	−	5.35603i	−0.287346	−	0.234427i
$523$	−19.4707	−	33.7243i	−0.851396	−	1.47466i	−0.879949	−	0.475069i	$-0.842423\pi$
$523$	−19.4707	−	33.7243i	−0.851396	−	1.47466i	0.0285525	−	0.999592i	$-0.490910\pi$
$524$	−1.26716	−	2.19478i	−0.0553561	−	0.0958795i
$525$	−3.23109	−	6.80601i	−0.141016	−	0.297039i
$526$			17.7028i			0.771881i
$527$		−	4.18407i		−	0.182261i
$528$	5.93014	+	12.4913i	0.258076	+	0.543615i
$529$	1.95716	+	3.38990i	0.0850939	+	0.147387i
$530$	5.58789	+	9.67851i	0.242722	+	0.420408i
$531$	−7.31462	−	5.96752i	−0.317427	−	0.258968i
$532$	−5.25562			−0.227860
$533$	−25.5714	+	17.3753i	−1.10762	+	0.752606i
$534$	−8.29007	−	5.71987i	−0.358746	−	0.247523i
$535$	11.6149	+	6.70585i	0.502155	+	0.289919i
$536$	−20.6554	+	35.7761i	−0.892176	+	1.54529i
$537$	12.6437	+	8.72375i	0.545617	+	0.376457i
$538$	−17.5050	−	10.1065i	−0.754694	−	0.435723i
$539$	29.2377	+	16.8804i	1.25936	+	0.727090i
$540$	3.99586	+	13.7656i	0.171955	+	0.592379i
$541$		−	21.3234i		−	0.916764i	−0.888755	−	0.458382i	$-0.848429\pi$
$541$		−	21.3234i		−	0.916764i	0.888755	−	0.458382i	$-0.151571\pi$
$542$	−8.68141	−	15.0366i	−0.372898	−	0.645879i
$543$	18.7128	−	8.88374i	0.803043	−	0.381238i
$544$	−11.9920	−	6.92361i	−0.514155	−	0.296847i
$545$	25.6434	+	44.4157i	1.09844	+	1.90256i
$546$	−5.20584	+	2.95624i	−0.222789	+	0.126515i
$547$	0.895067	−	1.55030i	0.0382703	−	0.0662861i	−0.846256	−	0.532777i	$-0.821149\pi$
$547$	0.895067	−	1.55030i	0.0382703	−	0.0662861i	0.884526	+	0.466491i	$0.154482\pi$
$548$	−0.399662	+	0.230745i	−0.0170727	+	0.00985693i
$549$	24.2369	+	3.92933i	1.03441	+	0.167700i
$550$	13.8693	−	24.0224i	0.591389	−	1.02432i
$551$	15.2168	+	8.78543i	0.648258	+	0.374272i
$552$	22.9858	+	1.85116i	0.978341	+	0.0787908i
$553$			10.1432i			0.431334i
$554$	−29.0978	+	16.7996i	−1.23625	+	0.713746i
$555$	−0.926578	+	11.5053i	−0.0393310	+	0.488371i
$556$	−3.35996			−0.142494
$557$	10.4179	−	6.01476i	0.441419	−	0.254853i	−0.262780	−	0.964856i	$-0.584639\pi$
$557$	10.4179	−	6.01476i	0.441419	−	0.254853i	0.704199	+	0.710002i	$0.251306\pi$
$558$	−4.30607	−	0.698107i	−0.182290	−	0.0295532i
$559$	13.2208	−	0.969791i	0.559179	−	0.0410178i
$560$	2.07257	−	3.58979i	0.0875819	−	0.151696i
$561$	28.7117	+	2.31230i	1.21221	+	0.0976255i
$562$	−8.42170	+	14.5868i	−0.355248	+	0.615308i
$563$	−3.70043			−0.155954			−0.0779772	−	0.996955i	$-0.524846\pi$
$563$	−3.70043			−0.155954			−0.0779772	+	0.996955i	$0.524846\pi$
$564$	8.80851	+	0.709394i	0.370905	+	0.0298709i
$565$	7.61325	−	4.39551i	0.320292	−	0.184920i
$566$	−14.1108	−	8.14686i	−0.593120	−	0.342438i
$567$	−5.41366	−	6.10132i	−0.227352	−	0.256231i
$568$	−5.41541	+	9.37977i	−0.227226	+	0.393567i
$569$	40.7830			1.70971			0.854856	−	0.518866i	$-0.173646\pi$
$569$	40.7830			1.70971			0.854856	+	0.518866i	$0.173646\pi$
$570$	16.1852	+	34.0928i	0.677925	+	1.42799i
$571$	10.9395	+	18.9478i	0.457805	+	0.792941i	0.998845	−	0.0480557i	$-0.0153025\pi$
$571$	10.9395	+	18.9478i	0.457805	+	0.792941i	−0.541040	+	0.840997i	$0.681969\pi$
$572$	15.6299	+	7.55735i	0.653518	+	0.315989i
$573$	−38.9905	−	26.9022i	−1.62885	−	1.12385i
$574$			8.21984i			0.343089i
$575$	−10.4836	−	18.1582i	−0.437198	−	0.757249i
$576$	−14.6679	+	17.9790i	−0.611161	+	0.749123i
$577$			9.29992i			0.387161i	0.981084	+	0.193580i	$0.0620100\pi$
$577$			9.29992i			0.387161i	−0.981084	+	0.193580i	$0.937990\pi$
$578$	−7.08709	+	4.09173i	−0.294784	+	0.170194i
$579$	22.6051	+	1.82050i	0.939436	+	0.0756576i
$580$	6.37884	−	3.68283i	0.264867	−	0.152921i
$581$	−0.940972			−0.0390381
$582$	12.3043	+	8.48953i	0.510028	+	0.351903i
$583$			18.4428i			0.763824i
$584$	3.82356			0.158220
$585$	−27.7323	−	19.4281i	−1.14659	−	0.803252i
$586$	−22.7564			−0.940057
$587$		−	1.85679i		−	0.0766380i	−0.999266	−	0.0383190i	$-0.987800\pi$
$587$		−	1.85679i		−	0.0766380i	0.999266	−	0.0383190i	$-0.0122003\pi$
$588$	−0.757031	+	9.40001i	−0.0312194	+	0.387650i
$589$	9.04655			0.372757
$590$	−9.02315	+	5.20952i	−0.371477	+	0.214472i
$591$	−6.58544	+	9.54457i	−0.270889	+	0.392611i
$592$	−2.69358	+	1.55514i	−0.110705	+	0.0639158i
$593$			18.1809i			0.746599i	0.927711	+	0.373299i	$0.121774\pi$
$593$			18.1809i			0.746599i	−0.927711	+	0.373299i	$0.878226\pi$
$594$	7.17024	−	29.1631i	0.294198	−	1.19658i
$595$	−4.31746	−	7.47806i	−0.176999	−	0.306571i
$596$		−	1.83323i		−	0.0750920i
$597$	1.66380	−	20.6593i	0.0680947	−	0.845528i
$598$	−13.7807	+	9.36370i	−0.563534	+	0.382910i
$599$	−9.32811	−	16.1568i	−0.381136	−	0.660148i	0.610089	−	0.792333i	$-0.291134\pi$
$599$	−9.32811	−	16.1568i	−0.381136	−	0.660148i	−0.991225	+	0.132186i	$0.957801\pi$
$600$	25.2519	+	2.03367i	1.03090	+	0.0830240i
$601$	19.9553			0.813994			0.406997	−	0.913430i	$-0.366576\pi$
$601$	19.9553			0.813994			0.406997	+	0.913430i	$0.366576\pi$
$602$	1.76227	−	3.05234i	0.0718248	−	0.124404i
$603$	38.0182	−	14.4351i	1.54822	−	0.587842i
$604$	−6.80539	−	3.92910i	−0.276907	−	0.159873i
$605$	51.1215	−	29.5150i	2.07838	−	1.19996i
$606$	3.58377	+	7.54890i	0.145581	+	0.306653i
$607$	−46.6970			−1.89537			−0.947686	−	0.319205i	$-0.896584\pi$
$607$	−46.6970			−1.89537			−0.947686	+	0.319205i	$0.896584\pi$
$608$	14.9698	−	25.9285i	0.607106	−	1.05154i
$609$	−2.38038	+	3.44999i	−0.0964578	+	0.139801i
$610$	13.5498	−	23.4690i	0.548616	−	0.950230i
$611$	−17.2666	+	11.7323i	−0.698533	+	0.474639i
$612$	2.85606	+	7.52209i	0.115449	+	0.304062i
$613$	11.5030	−	6.64124i	0.464600	−	0.268237i	−0.249376	−	0.968407i	$-0.580226\pi$
$613$	11.5030	−	6.64124i	0.464600	−	0.268237i	0.713977	+	0.700169i	$0.246892\pi$
$614$	14.2209			0.573911
$615$	−41.9988	+	19.9385i	−1.69355	+	0.804000i
$616$	13.0702	−	7.54607i	0.526612	−	0.304040i
$617$		−	31.0895i		−	1.25162i	−0.779976	−	0.625809i	$-0.784769\pi$
$617$		−	31.0895i		−	1.25162i	0.779976	−	0.625809i	$-0.215231\pi$
$618$	−6.38038	+	9.24737i	−0.256656	+	0.371984i
$619$	−10.8760	−	6.27924i	−0.437142	−	0.252384i	0.265243	−	0.964182i	$-0.414548\pi$
$619$	−10.8760	−	6.27924i	−0.437142	−	0.252384i	−0.702385	+	0.711798i	$0.747881\pi$
$620$	1.89614	−	3.28422i	0.0761510	−	0.131897i
$621$	−16.3807	−	15.7158i	−0.657336	−	0.630652i
$622$	−9.31263	+	5.37665i	−0.373402	+	0.215584i
$623$	−2.49129	+	4.31504i	−0.0998114	+	0.172878i
$624$	0.0651391	−	9.12391i	0.00260765	−	0.365249i
$625$	12.9813	+	22.4843i	0.519254	+	0.899374i
$626$	21.9168	+	12.6537i	0.875971	+	0.505742i
$627$	−4.99952	+	62.0788i	−0.199662	+	2.47919i
$628$	−7.92365	−	13.7242i	−0.316188	−	0.547654i
$629$			6.47917i			0.258341i
$630$	−8.41646	+	3.19564i	−0.335320	+	0.127317i
$631$	23.5583	+	13.6014i	0.937843	+	0.541464i	0.889283	−	0.457357i	$-0.151204\pi$
$631$	23.5583	+	13.6014i	0.937843	+	0.541464i	0.0485592	+	0.998820i	$0.484537\pi$
$632$	−29.5377	−	17.0536i	−1.17495	−	0.678356i
$633$	2.85703	−	35.4756i	0.113557	−	1.41003i
$634$	1.83947	−	3.18606i	0.0730548	−	0.126535i
$635$	−8.88138	−	5.12767i	−0.352447	−	0.203485i
$636$	−4.65384	+	2.20937i	−0.184537	+	0.0876072i
$637$	−12.5202	−	18.4261i	−0.496067	−	0.730068i
$638$	−15.4321			−0.610964
$639$	9.96758	−	3.78458i	0.394311	−	0.149716i
$640$	−1.43767	−	2.49011i	−0.0568288	−	0.0984303i
$641$	−23.7483	−	41.1333i	−0.938002	−	1.62467i	−0.769192	−	0.639018i	$-0.779341\pi$
$641$	−23.7483	−	41.1333i	−0.938002	−	1.62467i	−0.168810	−	0.985649i	$-0.553992\pi$
$642$	4.45753	−	6.46050i	0.175925	−	0.254976i
$643$		−	12.8063i		−	0.505031i	−0.967593	−	0.252516i	$-0.918742\pi$
$643$		−	12.8063i		−	0.505031i	0.967593	−	0.252516i	$-0.0812579\pi$
$644$		−	3.48911i		−	0.137490i
$645$	19.8704	+	1.60027i	0.782398	+	0.0630105i
$646$	10.5922	+	18.3462i	0.416745	+	0.721823i
$647$	1.16346	+	2.01516i	0.0457401	+	0.0792243i	0.887989	−	0.459865i	$-0.152102\pi$
$647$	1.16346	+	2.01516i	0.0457401	+	0.0792243i	−0.842249	+	0.539089i	$0.818769\pi$
$648$	26.8693	−	5.50691i	1.05553	−	0.216332i
$649$	−17.1940			−0.674924
$650$	−15.1393	+	10.2868i	−0.593812	+	0.403483i
$651$	−0.173237	+	2.15107i	−0.00678969	+	0.0843072i
$652$	−2.82783	−	1.63265i	−0.110746	−	0.0639394i
$653$	−7.98119	+	13.8238i	−0.312328	+	0.540968i	−0.978866	−	0.204503i	$-0.934442\pi$
$653$	−7.98119	+	13.8238i	−0.312328	+	0.540968i	0.666538	+	0.745471i	$0.267775\pi$
$654$	27.1147	−	12.8725i	1.06027	−	0.503353i
$655$	7.79668	+	4.50142i	0.304642	+	0.175885i
$656$	−10.8493	−	6.26384i	−0.423594	−	0.244562i
$657$	−2.91646	−	2.37935i	−0.113782	−	0.0928274i
$658$			5.55029i			0.216373i
$659$	11.4688	+	19.8645i	0.446761	+	0.773813i	0.998173	−	0.0604202i	$-0.0192441\pi$
$659$	11.4688	+	19.8645i	0.446761	+	0.773813i	−0.551412	+	0.834233i	$0.685911\pi$
$660$	21.4889	+	14.8266i	0.836455	+	0.577126i
$661$	12.5361	+	7.23773i	0.487598	+	0.281515i	0.723578	−	0.690243i	$-0.242496\pi$
$661$	12.5361	+	7.23773i	0.487598	+	0.281515i	−0.235979	+	0.971758i	$0.575830\pi$
$662$	10.1126	+	17.5155i	0.393037	+	0.680760i
$663$	−16.3922	−	9.62073i	−0.636621	−	0.373638i
$664$	1.58204	−	2.74017i	0.0613950	−	0.106339i
$665$	16.1686	−	9.33495i	0.626992	−	0.361994i
$666$	6.66808	+	1.08104i	0.258383	+	0.0418895i
$667$	−5.83248	+	10.1022i	−0.225835	+	0.391157i
$668$	−5.38465	−	3.10883i	−0.208338	−	0.120284i
$669$	−7.13231	−	15.0236i	−0.275751	−	0.580845i
$670$		−	44.8836i		−	1.73400i
$671$	38.7296	−	22.3606i	1.49514	−	0.863220i
$672$	5.87856	+	4.05601i	0.226770	+	0.156464i
$673$	−7.29796			−0.281316			−0.140658	−	0.990058i	$-0.544922\pi$
$673$	−7.29796			−0.281316			−0.140658	+	0.990058i	$0.544922\pi$
$674$	−1.22361	+	0.706450i	−0.0471316	+	0.0272114i
$675$	−17.9957	−	17.2651i	−0.692653	−	0.664536i
$676$	−7.11428	−	8.97899i	−0.273626	−	0.345346i
$677$	−4.78574	+	8.28915i	−0.183931	+	0.318578i	−0.943216	−	0.332181i	$-0.892216\pi$
$677$	−4.78574	+	8.28915i	−0.183931	+	0.318578i	0.759285	+	0.650759i	$0.225549\pi$
$678$	−2.20645	−	4.64770i	−0.0847383	−	0.178494i
$679$	3.69761	−	6.40445i	0.141901	−	0.245780i
$680$	29.0355			1.11346
$681$	−28.0001	+	40.5818i	−1.07297	+	1.55510i
$682$	−6.88092	+	3.97270i	−0.263484	+	0.152123i
$683$	18.6712	+	10.7798i	0.714432	+	0.412478i	0.812700	−	0.582682i	$-0.197997\pi$
$683$	18.6712	+	10.7798i	0.714432	+	0.412478i	−0.0982678	+	0.995160i	$0.531330\pi$
$684$	−16.2638	+	6.17519i	−0.621862	+	0.236114i
$685$	0.819692	−	1.41975i	0.0313188	−	0.0542458i
$686$	−12.6334			−0.482347
$687$	−21.4117	+	31.0329i	−0.816907	+	1.18398i
$688$	2.68584	+	4.65201i	0.102397	+	0.177356i
$689$	5.29748	−	10.9561i	0.201818	−	0.417393i
$690$	−22.6336	+	10.7451i	−0.861645	+	0.409058i
$691$			4.09130i			0.155640i	0.996967	+	0.0778202i	$0.0247960\pi$
$691$			4.09130i			0.155640i	−0.996967	+	0.0778202i	$0.975204\pi$
$692$	5.03666	+	8.72374i	0.191465	+	0.331627i
$693$	−14.6652	−	2.37756i	−0.557087	−	0.0903159i
$694$			28.3222i			1.07510i
$695$	10.3367	−	5.96791i	0.392095	−	0.226376i
$696$	−6.04451	−	12.7322i	−0.229116	−	0.482613i
$697$	−22.6007	+	13.0485i	−0.856061	+	0.494247i
$698$	27.1771			1.02867
$699$	−17.5619	+	8.33736i	−0.664252	+	0.315348i
$700$		−	3.83309i		−	0.144877i
$701$	−43.7027			−1.65063			−0.825314	−	0.564674i	$-0.809002\pi$
$701$	−43.7027			−1.65063			−0.825314	+	0.564674i	$0.809002\pi$
$702$	−12.6363	+	15.2649i	−0.476925	+	0.576138i
$703$	−14.0089			−0.528354
$704$			42.2620i			1.59281i
$705$	−28.3589	+	13.4631i	−1.06806	+	0.507051i
$706$	1.16255			0.0437530
$707$	3.58009	−	2.06697i	0.134643	−	0.0777363i
$708$	−2.05977	−	4.33871i	−0.0774108	−	0.163059i
$709$	−1.44795	+	0.835973i	−0.0543788	+	0.0313956i	−0.526943	−	0.849901i	$-0.676662\pi$
$709$	−1.44795	+	0.835973i	−0.0543788	+	0.0313956i	0.472564	+	0.881296i	$0.343329\pi$
$710$		−	11.7676i		−	0.441628i
$711$	11.9180	+	31.3888i	0.446959	+	1.17717i
$712$	−8.37711	−	14.5096i	−0.313946	−	0.543770i
$713$			6.00584i			0.224920i
$714$	−4.56517	+	2.16727i	−0.170847	+	0.0811082i
$715$	−61.5077	+	4.51181i	−2.30026	+	0.168732i
$716$	3.90766	+	6.76827i	0.146036	+	0.252942i
$717$	−11.8671	+	17.1995i	−0.443183	+	0.642325i
$718$	−13.3967			−0.499959
$719$	9.71239	−	16.8223i	0.362211	−	0.627368i	−0.626114	−	0.779732i	$-0.715355\pi$
$719$	9.71239	−	16.8223i	0.362211	−	0.627368i	0.988324	+	0.152364i	$0.0486887\pi$
$720$	2.19578	−	13.5440i	0.0818319	−	0.504756i
$721$	4.81332	+	2.77897i	0.179257	+	0.103494i
$722$	−22.2628	+	12.8534i	−0.828534	+	0.478354i
$723$	14.2555	−	20.6611i	0.530168	−	0.768396i
$724$	10.5389			0.391675
$725$	−6.40749	+	11.0981i	−0.237968	+	0.412173i
$726$	−14.8159	−	31.2084i	−0.549870	−	1.15825i
$727$	9.48379	−	16.4264i	0.351734	−	0.609222i	−0.634819	−	0.772661i	$-0.718925\pi$
$727$	9.48379	−	16.4264i	0.351734	−	0.609222i	0.986553	+	0.163439i	$0.0522587\pi$
$728$	−9.93194	+	0.728543i	−0.368102	+	0.0270016i
$729$	−23.9218	−	12.5200i	−0.885991	−	0.463703i
$730$	−3.59768	+	2.07712i	−0.133156	+	0.0768778i
$731$	11.1900			0.413877
$732$	10.2821	+	7.09429i	0.380036	+	0.262212i
$733$	0.657094	−	0.379374i	0.0242703	−	0.0140125i	−0.487816	−	0.872947i	$-0.662206\pi$
$733$	0.657094	−	0.379374i	0.0242703	−	0.0140125i	0.512086	+	0.858934i	$0.328873\pi$
$734$		−	0.166556i		−	0.00614769i
$735$	−14.3672	−	30.2632i	−0.529942	−	1.11628i
$736$	17.2134	+	9.93818i	0.634495	+	0.366326i
$737$	37.0345	−	64.1457i	1.36419	−	2.36284i
$738$	9.65806	+	25.4368i	0.355518	+	0.936340i
$739$	29.7100	−	17.1530i	1.09290	−	0.630985i	0.158552	−	0.987351i	$-0.449318\pi$
$739$	29.7100	−	17.1530i	1.09290	−	0.630985i	0.934347	+	0.356366i	$0.115984\pi$
$740$	−2.93624	+	5.08571i	−0.107938	+	0.186955i
$741$	20.8014	−	35.4422i	0.764157	−	1.30200i
$742$	−1.61781	−	2.80212i	−0.0593915	−	0.102869i
$743$	26.2261	+	15.1417i	0.962144	+	0.555494i	0.896832	−	0.442371i	$-0.145863\pi$
$743$	26.2261	+	15.1417i	0.962144	+	0.555494i	0.0653116	+	0.997865i	$0.479196\pi$
$744$	−5.97280	−	4.12104i	−0.218974	−	0.151084i
$745$	3.25616	+	5.63983i	0.119296	+	0.206627i
$746$			7.13518i			0.261237i
$747$	−2.91189	+	1.10561i	−0.106541	+	0.0404523i
$748$	12.6916	+	7.32747i	0.464049	+	0.267919i
$749$	−3.36274	−	1.94148i	−0.122872	−	0.0709400i
$750$	1.03919	−	0.493346i	0.0379459	−	0.0180145i
$751$	13.8624	−	24.0104i	0.505847	−	0.876153i	−0.494130	−	0.869388i	$-0.664513\pi$
$751$	13.8624	−	24.0104i	0.505847	−	0.876153i	0.999977	−	0.00676508i	$-0.00215341\pi$
$752$	−7.32579	−	4.22954i	−0.267144	−	0.154236i
$753$	1.97499	−	24.5234i	0.0719728	−	0.893682i
$754$	9.16756	+	4.43269i	0.333863	+	0.161429i
$755$	27.9152			1.01594
$756$	−1.15688	−	3.98543i	−0.0420754	−	0.144949i
$757$	11.2745	+	19.5281i	0.409780	+	0.709760i	0.994865	−	0.101212i	$-0.0322722\pi$
$757$	11.2745	+	19.5281i	0.409780	+	0.709760i	−0.585085	+	0.810972i	$0.698939\pi$
$758$	−16.1895	−	28.0410i	−0.588029	−	1.01850i
$759$	−41.2129	−	3.31909i	−1.49594	−	0.120475i
$760$			62.7787i			2.27722i
$761$		−	38.2438i		−	1.38634i	−0.720776	−	0.693168i	$-0.756214\pi$
$761$		−	38.2438i		−	1.38634i	0.720776	−	0.693168i	$-0.243786\pi$
$762$	−3.40848	+	4.94007i	−0.123476	+	0.178960i
$763$	−7.42429	−	12.8592i	−0.268777	−	0.465536i
$764$	−12.0504	−	20.8719i	−0.435968	−	0.755119i
$765$	−22.1471	−	18.0684i	−0.800731	−	0.653264i
$766$	−19.1490			−0.691882
$767$	10.2142	+	4.93877i	0.368814	+	0.178329i
$768$	−25.7239	+	12.2122i	−0.928231	+	0.440669i
$769$	12.3754	+	7.14495i	0.446269	+	0.257653i	0.706253	−	0.707959i	$-0.250384\pi$
$769$	12.3754	+	7.14495i	0.446269	+	0.257653i	−0.259984	+	0.965613i	$0.583717\pi$
$770$	−8.19871	+	14.2006i	−0.295461	+	0.511753i
$771$	3.36977	−	41.8423i	0.121359	−	1.50691i
$772$	9.99222	+	5.76901i	0.359628	+	0.207631i
$773$	−15.9621	−	9.21572i	−0.574117	−	0.331466i	0.184675	−	0.982800i	$-0.440877\pi$
$773$	−15.9621	−	9.21572i	−0.574117	−	0.331466i	−0.758792	+	0.651333i	$0.774210\pi$
$774$	1.86704	−	11.5163i	0.0671092	−	0.413943i
$775$			6.59794i			0.237005i
$776$	12.4335	+	21.5354i	0.446335	+	0.773075i
$777$	0.268263	−	3.33100i	0.00962387	−	0.119499i
$778$	13.4258	+	7.75142i	0.481340	+	0.277902i
$779$	−28.2127	−	48.8658i	−1.01082	−	1.75080i
$780$	−8.50686	−	14.9803i	−0.304594	−	0.536380i
$781$	9.70970	−	16.8177i	0.347440	−	0.601784i
$782$	−12.1797	+	7.03197i	−0.435546	+	0.251463i
$783$	−3.31258	+	13.4731i	−0.118382	+	0.481488i
$784$	4.51356	−	7.81772i	0.161199	−	0.279204i
$785$	48.7533	+	28.1477i	1.74008	+	1.00464i
$786$	2.99220	−	4.33673i	0.106728	−	0.154686i
$787$		−	6.93282i		−	0.247128i	−0.992337	−	0.123564i	$-0.960568\pi$
$787$		−	6.93282i		−	0.247128i	0.992337	−	0.123564i	$-0.0394325\pi$
$788$	−5.10927	+	2.94984i	−0.182010	+	0.105084i
$789$	26.1876	−	12.4323i	0.932302	−	0.442602i
$790$	37.0570			1.31843
$791$	−2.20419	+	1.27259i	−0.0783719	+	0.0452480i
$792$	31.5800	−	38.7088i	1.12215	−	1.37546i
$793$	−29.4304	+	2.15882i	−1.04510	+	0.0766621i
$794$	8.01836	−	13.8882i	0.284561	−	0.492874i
$795$	10.3930	−	15.0631i	0.368603	−	0.534233i
$796$	5.27242	−	9.13210i	0.186876	−	0.323679i
$797$	−52.6639			−1.86545			−0.932726	−	0.360586i	$-0.882577\pi$
$797$	−52.6639			−1.86545			−0.932726	+	0.360586i	$0.882577\pi$
$798$	−4.68595	−	9.87054i	−0.165881	−	0.349413i
$799$	−15.2607	+	8.81076i	−0.539884	+	0.311702i
$800$	18.9105	+	10.9180i	0.668586	+	0.386008i
$801$	−2.63939	+	16.2803i	−0.0932584	+	0.575237i
$802$	−16.4920	+	28.5649i	−0.582351	+	1.00866i
$803$	−6.85554			−0.241927
$804$	20.6230	+	1.66088i	0.727318	+	0.0585746i
$805$	6.19730	+	10.7340i	0.218426	+	0.378325i
$806$	5.22877	−	0.383549i	0.184176	−	0.0135099i
$807$	−2.65705	+	32.9924i	−0.0935326	+	1.16139i
$808$			13.9006i			0.489022i
$809$	−19.1749	−	33.2118i	−0.674152	−	1.16767i	−0.976716	−	0.214537i	$-0.931176\pi$
$809$	−19.1749	−	33.2118i	−0.674152	−	1.16767i	0.302564	−	0.953129i	$-0.402157\pi$
$810$	−22.2904	+	19.7782i	−0.783206	+	0.694934i
$811$			43.2075i			1.51722i	0.651544	+	0.758610i	$0.274121\pi$
$811$			43.2075i			1.51722i	−0.651544	+	0.758610i	$0.725879\pi$
$812$	−1.84680	+	1.06625i	−0.0648101	+	0.0374181i
$813$	−16.1467	+	23.4022i	−0.566290	+	0.820750i
$814$	10.6553	−	6.15186i	0.373469	−	0.215622i
$815$	11.5995			0.406314
$816$	0.618274	−	7.67708i	0.0216439	−	0.268752i
$817$			24.1943i			0.846453i
$818$	24.8654			0.869399
$819$	8.02906	+	5.62482i	0.280558	+	0.196547i
$820$	−23.6534			−0.826011
$821$			24.4217i			0.852322i	0.904647	+	0.426161i	$0.140134\pi$
$821$			24.4217i			0.852322i	−0.904647	+	0.426161i	$0.859866\pi$
$822$	−0.789702	−	0.544868i	−0.0275440	−	0.0190045i
$823$	45.9119			1.60039			0.800193	−	0.599742i	$-0.204730\pi$
$823$	45.9119			1.60039			0.800193	+	0.599742i	$0.204730\pi$
$824$	−16.1851	+	9.34446i	−0.563834	+	0.325530i
$825$	−45.2760	−	3.64631i	−1.57631	−	0.126948i
$826$	2.61238	−	1.50826i	0.0908964	−	0.0524791i
$827$		−	25.7255i		−	0.894562i	−0.894394	−	0.447281i	$-0.852392\pi$
$827$		−	25.7255i		−	0.894562i	0.894394	−	0.447281i	$-0.147608\pi$
$828$	−4.09959	−	10.7972i	−0.142471	−	0.375230i
$829$	9.54053	+	16.5247i	0.331356	+	0.573926i	0.982778	−	0.184790i	$-0.0591605\pi$
$829$	9.54053	+	16.5247i	0.331356	+	0.573926i	−0.651422	+	0.758716i	$0.725827\pi$
$830$			3.43773i			0.119325i
$831$	45.2861	+	31.2459i	1.57096	+	1.08391i
$832$	12.1392	−	25.1060i	0.420853	−	0.870394i
$833$	−9.40241	−	16.2855i	−0.325774	−	0.564258i
$834$	−2.99577	−	6.31032i	−0.103735	−	0.218508i
$835$	22.0874			0.764367
$836$	−15.8430	+	27.4409i	−0.547942	+	0.949064i
$837$	1.99135	+	6.86017i	0.0688313	+	0.237122i
$838$	30.1031	+	17.3800i	1.03989	+	0.600384i
$839$	−0.146881	+	0.0848018i	−0.00507090	+	0.00292768i	−0.502533	−	0.864558i	$-0.667599\pi$
$839$	−0.146881	+	0.0848018i	−0.00507090	+	0.00292768i	0.497462	+	0.867486i	$0.334265\pi$
$840$	−14.9274	−	1.20218i	−0.515045	−	0.0414792i
$841$	−21.8705			−0.754155
$842$	18.7243	−	32.4315i	0.645282	−	1.11766i
$843$	27.4924	+	2.21411i	0.946890	+	0.0762579i
$844$	9.05366	−	15.6814i	0.311640	−	0.539776i
$845$	37.8350	+	14.9871i	1.30156	+	0.515571i
$846$	6.52143	+	17.1757i	0.224211	+	0.590513i
$847$	−14.8007	+	8.54518i	−0.508558	+	0.293616i
$848$	4.93133			0.169343
$849$	−2.14185	+	26.5952i	−0.0735081	+	0.912746i
$850$	−13.3805	+	7.72523i	−0.458947	+	0.264973i
$851$		−	9.30022i		−	0.318808i
$852$	5.40693	+	0.435448i	0.185239	+	0.0149182i
$853$	−17.4904	−	10.0981i	−0.598860	−	0.345752i	0.169733	−	0.985490i	$-0.445709\pi$
$853$	−17.4904	−	10.0981i	−0.598860	−	0.345752i	−0.768593	+	0.639738i	$0.779043\pi$
$854$	−3.92294	+	6.79473i	−0.134240	+	0.232511i
$855$	39.0664	−	47.8852i	1.33604	−	1.63764i
$856$	11.3074	−	6.52834i	0.386479	−	0.223134i
$857$	10.7290	−	18.5831i	0.366494	−	0.634787i	−0.622520	−	0.782604i	$-0.713891\pi$
$857$	10.7290	−	18.5831i	0.366494	−	0.634787i	0.989015	+	0.147817i	$0.0472245\pi$
$858$	−0.257679	+	36.0926i	−0.00879700	+	1.23218i
$859$	2.57202	+	4.45488i	0.0877564	+	0.151998i	0.906562	−	0.422072i	$-0.138697\pi$
$859$	2.57202	+	4.45488i	0.0877564	+	0.151998i	−0.818806	+	0.574070i	$0.805364\pi$
$860$	8.78340	+	5.07110i	0.299512	+	0.172923i
$861$	12.1595	−	5.77261i	0.414394	−	0.196730i
$862$	4.86780	+	8.43128i	0.165798	+	0.287171i
$863$			12.6069i			0.429143i	0.976708	+	0.214572i	$0.0688355\pi$
$863$			12.6069i			0.429143i	−0.976708	+	0.214572i	$0.931164\pi$
$864$	22.9572	+	5.64443i	0.781021	+	0.192027i
$865$	−30.9900	−	17.8921i	−1.05369	−	0.608349i
$866$	−25.1594	−	14.5258i	−0.854951	−	0.493606i
$867$	11.0299	+	7.61029i	0.374596	+	0.258459i
$868$	−0.548972	+	0.950847i	−0.0186333	+	0.0322739i
$869$	52.9604	+	30.5767i	1.79656	+	1.03724i
$870$	12.6041	+	8.69643i	0.427320	+	0.294836i
$871$	−40.4257	+	27.4685i	−1.36977	+	0.930733i
$872$	49.9293			1.69082
$873$	3.91743	−	24.1635i	0.132585	−	0.817812i
$874$	−15.2041	−	26.3343i	−0.514286	−	0.890770i
$875$	−0.284541	−	0.492840i	−0.00961924	−	0.0166610i
$876$	−0.821264	−	1.72992i	−0.0277479	−	0.0584486i
$877$			47.2411i			1.59522i	0.603175	+	0.797609i	$0.293902\pi$
$877$			47.2411i			1.59522i	−0.603175	+	0.797609i	$0.706098\pi$
$878$		−	18.0081i		−	0.607745i
$879$	15.9813	+	33.6632i	0.539035	+	1.13543i
$880$	−12.4955	−	21.6428i	−0.421223	−	0.729579i
$881$	16.7272	+	28.9724i	0.563554	+	0.976105i	0.997183	+	0.0750128i	$0.0238998\pi$
$881$	16.7272	+	28.9724i	0.563554	+	0.976105i	−0.433628	+	0.901092i	$0.642767\pi$
$882$	−18.3291	+	6.95935i	−0.617172	+	0.234333i
$883$	−8.75971			−0.294788			−0.147394	−	0.989078i	$-0.547088\pi$
$883$	−8.75971			−0.294788			−0.147394	+	0.989078i	$0.547088\pi$
$884$	−5.43477	−	7.99843i	−0.182791	−	0.269016i
$885$	14.0431	+	9.68929i	0.472054	+	0.325702i
$886$	−3.25556	−	1.87960i	−0.109373	−	0.0631463i
$887$	−23.2430	+	40.2581i	−0.780424	+	1.35173i	0.151271	+	0.988492i	$0.451663\pi$
$887$	−23.2430	+	40.2581i	−0.780424	+	1.35173i	−0.931695	+	0.363242i	$0.881670\pi$
$888$	9.24907	+	6.38155i	0.310378	+	0.214151i
$889$	2.57134	+	1.48456i	0.0862399	+	0.0497906i
$890$	15.7645	+	9.10162i	0.528426	+	0.305087i
$891$	−48.1760	+	9.87374i	−1.61396	+	0.330783i
$892$		−	8.46116i		−	0.283300i
$893$	−19.0501	−	32.9957i	−0.637487	−	1.10416i
$894$	3.44298	−	1.63452i	0.115150	−	0.0546666i
$895$	−24.0434	−	13.8815i	−0.803683	−	0.464006i
$896$	0.416233	+	0.720937i	0.0139054	+	0.0240848i
$897$	23.5295	+	13.8096i	0.785626	+	0.461091i
$898$	−0.215215	+	0.372763i	−0.00718180	+	0.0124392i
$899$	3.17892	−	1.83535i	0.106023	−	0.0612124i
$900$	−4.50376	−	11.8617i	−0.150125	−	0.395390i
$901$	5.13634	−	8.89640i	0.171116	−	0.296382i
$902$	42.9179	+	24.7787i	1.42901	+	0.825039i
$903$	−5.75289	−	0.463310i	−0.191444	−	0.0154180i
$904$		−	8.55831i		−	0.284645i
$905$	−32.4223	+	18.7190i	−1.07775	+	0.622242i
$906$	1.31146	−	16.2844i	0.0435705	−	0.541012i
$907$	32.6681			1.08473			0.542363	−	0.840144i	$-0.317530\pi$
$907$	32.6681			1.08473			0.542363	+	0.840144i	$0.317530\pi$
$908$	−21.7237	+	12.5422i	−0.720927	+	0.416227i
$909$	8.65017	−	10.6028i	0.286908	−	0.351674i
$910$	8.94944	−	6.08097i	0.296671	−	0.201582i
$911$	0.978692	−	1.69514i	0.0324255	−	0.0561627i	−0.849357	−	0.527818i	$-0.823010\pi$
$911$	0.978692	−	1.69514i	0.0324255	−	0.0561627i	0.881783	+	0.471656i	$0.156343\pi$
$912$	16.5989	+	1.33680i	0.549645	+	0.0442657i
$913$	−2.83656	+	4.91306i	−0.0938763	+	0.162599i
$914$	−28.2663			−0.934967
$915$	−44.2330	−	3.56231i	−1.46230	−	0.117766i
$916$	−16.6121	+	9.59103i	−0.548881	+	0.316896i
$917$	−2.25730	−	1.30325i	−0.0745425	−	0.0430371i
$918$	−11.5807	+	12.0707i	−0.382220	+	0.398392i
$919$	−6.72231	+	11.6434i	−0.221748	+	0.384079i	−0.955339	−	0.295512i	$-0.904510\pi$
$919$	−6.72231	+	11.6434i	−0.221748	+	0.384079i	0.733591	+	0.679592i	$0.237843\pi$
$920$	−41.6776			−1.37407
$921$	−9.98705	−	21.0368i	−0.329084	−	0.693187i
$922$	2.66695	+	4.61930i	0.0878314	+	0.152128i
$923$	−10.5988	+	7.20167i	−0.348863	+	0.237046i
$924$	−6.22147	−	4.29261i	−0.204671	−	0.141216i
$925$		−	10.2171i		−	0.335936i
$926$	6.92884	+	12.0011i	0.227696	+	0.394381i
$927$	18.1603	+	2.94418i	0.596462	+	0.0966995i
$928$		−	12.1482i		−	0.398785i
$929$	−4.93887	+	2.85146i	−0.162039	+	0.0935533i	−0.578827	−	0.815451i	$-0.696489\pi$
$929$	−4.93887	+	2.85146i	−0.162039	+	0.0935533i	0.416788	+	0.909004i	$0.363156\pi$
$930$	7.85869	+	0.632900i	0.257696	+	0.0207536i
$931$	35.2114	−	20.3293i	1.15401	−	0.666267i
$932$	−9.89072			−0.323981
$933$	14.4936	+	10.0001i	0.474501	+	0.327390i
$934$		−	23.2789i		−	0.761707i
$935$	−52.0598			−1.70254
$936$	−29.8789	+	13.9242i	−0.976624	+	0.455128i
$937$	34.2859			1.12007			0.560035	−	0.828469i	$-0.310788\pi$
$937$	34.2859			1.12007			0.560035	+	0.828469i	$0.310788\pi$
$938$			12.9947i			0.424292i
$939$	3.32671	−	41.3076i	0.108563	−	1.34802i
$940$	−15.9715			−0.520933
$941$	−17.1301	+	9.89004i	−0.558424	+	0.322406i	−0.752513	−	0.658578i	$-0.771158\pi$
$941$	−17.1301	+	9.89004i	−0.558424	+	0.322406i	0.194089	+	0.980984i	$0.437825\pi$
$942$	18.7105	−	27.1179i	0.609620	−	0.883550i
$943$	32.4411	−	18.7299i	1.05643	−	0.609929i
$944$			4.59742i			0.149633i
$945$	10.6380	+	10.2061i	0.346053	+	0.332005i
$946$	−10.6247	−	18.4025i	−0.345439	−	0.598318i
$947$			43.9714i			1.42888i	0.699698	+	0.714439i	$0.253318\pi$
$947$			43.9714i			1.42888i	−0.699698	+	0.714439i	$0.746682\pi$
$948$	−1.37126	+	17.0269i	−0.0445366	+	0.553008i
$949$	4.07258	+	1.96917i	0.132202	+	0.0639220i
$950$	−16.7030	−	28.9305i	−0.541918	−	0.938629i
$951$	−6.00492	−	0.483607i	−0.194723	−	0.0156820i
$952$	−8.40635			−0.272451
$953$	22.0792	−	38.2422i	0.715214	−	1.23879i	−0.247663	−	0.968846i	$-0.579663\pi$
$953$	22.0792	−	38.2422i	0.715214	−	1.23879i	0.962877	−	0.269941i	$-0.0870041\pi$
$954$	−8.29880	−	6.77045i	−0.268684	−	0.219202i
$955$	74.1447	+	42.8075i	2.39927	+	1.38522i
$956$	−9.20698	+	5.31565i	−0.297775	+	0.171921i
$957$	10.8376	+	22.8285i	0.350331	+	0.737942i
$958$	29.4396			0.951149
$959$	−0.237317	+	0.411045i	−0.00766337	+	0.0132733i
$960$	23.8158	−	34.5173i	0.768651	−	1.11404i
$961$	−14.5550	+	25.2101i	−0.469518	+	0.813229i
$962$	−8.09691	+	0.593937i	−0.261055	+	0.0191493i
$963$	−12.6874	−	2.05690i	−0.408844	−	0.0662826i
$964$	11.0600	−	6.38552i	0.356220	−	0.205664i
$965$	−40.9873			−1.31943
$966$	6.55287	−	3.11092i	0.210835	−	0.100092i
$967$	−22.2824	+	12.8647i	−0.716553	+	0.413702i	−0.813483	−	0.581589i	$-0.802431\pi$
$967$	−22.2824	+	12.8647i	−0.716553	+	0.413702i	0.0969294	+	0.995291i	$0.469098\pi$
$968$		−	57.4674i		−	1.84707i
$969$	19.7006	−	28.5530i	0.632876	−	0.917256i
$970$	−23.3979	−	13.5088i	−0.751261	−	0.433741i
$971$	−21.9999	+	38.1050i	−0.706012	+	1.22285i	0.260313	+	0.965524i	$0.416174\pi$
$971$	−21.9999	+	38.1050i	−0.706012	+	1.22285i	−0.966325	+	0.257324i	$0.917159\pi$
$972$	−8.26280	−	10.9738i	−0.265029	−	0.351986i
$973$	−2.99269	+	1.72783i	−0.0959413	+	0.0553917i
$974$	−13.7219	+	23.7670i	−0.439678	+	0.761544i
$975$	25.8492	+	15.1711i	0.827836	+	0.485864i
$976$	−5.97887	−	10.3557i	−0.191379	−	0.331478i
$977$	−28.0805	−	16.2123i	−0.898373	−	0.518676i	−0.0217013	−	0.999764i	$-0.506908\pi$
$977$	−28.0805	−	16.2123i	−0.898373	−	0.518676i	−0.876672	+	0.481088i	$0.840242\pi$
$978$	0.544949	−	6.76660i	0.0174255	−	0.216372i
$979$	15.0199	+	26.0153i	0.480040	+	0.831453i
$980$		−	17.0440i		−	0.544451i
$981$	−38.0841	−	31.0703i	−1.21593	−	0.992000i
$982$	−11.4868	−	6.63191i	−0.366559	−	0.211633i
$983$	42.9964	+	24.8240i	1.37137	+	0.791762i	0.991101	−	0.133113i	$-0.0424972\pi$
$983$	42.9964	+	24.8240i	1.37137	+	0.791762i	0.380272	+	0.924875i	$0.375831\pi$
$984$	−3.63331	+	45.1146i	−0.115826	+	1.43820i
$985$	10.4789	−	18.1500i	0.333887	−	0.578308i
$986$	7.44412	+	4.29786i	0.237069	+	0.136872i
$987$	8.21047	−	3.89785i	0.261342	−	0.124070i
$988$	17.2937	−	11.7507i	0.550187	−	0.373841i
$989$	−16.0622			−0.510747
$990$	−8.68611	+	53.5777i	−0.276063	+	1.70281i
$991$	−3.15118	−	5.45800i	−0.100100	−	0.173379i	0.811625	−	0.584178i	$-0.198583\pi$
$991$	−3.15118	−	5.45800i	−0.100100	−	0.173379i	−0.911726	+	0.410799i	$0.865250\pi$
$992$	−3.12732	−	5.41668i	−0.0992926	−	0.171980i
$993$	18.8086	−	27.2602i	0.596873	−	0.865075i
$994$			3.40694i			0.108062i
$995$			37.4592i			1.18754i
$996$	−1.57956	−	0.127210i	−0.0500503	−	0.00403081i
$997$	−4.10656	−	7.11277i	−0.130056	−	0.225264i	0.793642	−	0.608385i	$-0.208182\pi$
$997$	−4.10656	−	7.11277i	−0.130056	−	0.225264i	−0.923698	+	0.383122i	$0.874849\pi$
$998$	−13.2113	−	22.8827i	−0.418197	−	0.724339i
$999$	−3.08367	−	10.6232i	−0.0975631	−	0.336103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.88.8	yes	22
3.2	odd	2		351.2.l.b.127.4		22
9.4	even	3		117.2.r.b.49.4	yes	22
9.5	odd	6		351.2.r.b.10.8		22
13.4	even	6		117.2.r.b.43.4	yes	22
39.17	odd	6		351.2.r.b.316.8		22
117.4	even	6	inner	117.2.l.b.4.4	✓	22
117.95	odd	6		351.2.l.b.199.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.4	✓	22	117.4	even	6	inner
117.2.l.b.88.8	yes	22	1.1	even	1	trivial
117.2.r.b.43.4	yes	22	13.4	even	6
117.2.r.b.49.4	yes	22	9.4	even	3
351.2.l.b.127.4		22	3.2	odd	2
351.2.l.b.199.8		22	117.95	odd	6
351.2.r.b.10.8		22	9.5	odd	6
351.2.r.b.316.8		22	39.17	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.05773i q^{2} +(1.56468 - 0.742818i) q^{3} +0.881215 q^{4} +(-2.71101 + 1.56520i) q^{5} +(0.785698 + 1.65500i) q^{6} +(0.784891 - 0.453157i) q^{7} +3.04754i q^{8} +(1.89644 - 2.32454i) q^{9} +(-1.65555 - 2.86750i) q^{10} -5.46416i q^{11} +(1.37882 - 0.654582i) q^{12} +(-1.56951 + 3.24602i) q^{13} +(0.479316 + 0.830200i) q^{14} +(-3.07920 + 4.46282i) q^{15} -1.46103 q^{16} +(-1.52177 + 2.63579i) q^{17} +(2.45873 + 2.00592i) q^{18} +(-5.69894 - 3.29028i) q^{19} +(-2.38898 + 1.37928i) q^{20} +(0.891490 - 1.29208i) q^{21} +5.77958 q^{22} +(2.18436 - 3.78342i) q^{23} +(2.26376 + 4.76842i) q^{24} +(2.39971 - 4.15642i) q^{25} +(-3.43340 - 1.66011i) q^{26} +(1.24061 - 5.04588i) q^{27} +(0.691657 - 0.399329i) q^{28} -2.67011 q^{29} +(-4.72045 - 3.25695i) q^{30} +(-1.19056 + 0.687369i) q^{31} +4.54970i q^{32} +(-4.05887 - 8.54965i) q^{33} +(-2.78794 - 1.60962i) q^{34} +(-1.41856 + 2.45702i) q^{35} +(1.67117 - 2.04842i) q^{36} +(1.84362 - 1.06441i) q^{37} +(3.48022 - 6.02792i) q^{38} +(-0.0445843 + 6.24484i) q^{39} +(-4.77001 - 8.26190i) q^{40} +(7.42578 + 4.28727i) q^{41} +(1.36666 + 0.942952i) q^{42} +(-1.83832 - 3.18406i) q^{43} -4.81509i q^{44} +(-1.50290 + 9.27017i) q^{45} +(4.00182 + 2.31045i) q^{46} +(5.01412 + 2.89490i) q^{47} +(-2.28605 + 1.08528i) q^{48} +(-3.08930 + 5.35082i) q^{49} +(4.39635 + 2.53823i) q^{50} +(-0.423177 + 5.25456i) q^{51} +(-1.38308 + 2.86044i) q^{52} -3.37524 q^{53} +(5.33716 + 1.31223i) q^{54} +(8.55250 + 14.8134i) q^{55} +(1.38101 + 2.39198i) q^{56} +(-11.3611 - 0.914967i) q^{57} -2.82425i q^{58} -3.14669i q^{59} +(-2.71343 + 3.93270i) q^{60} +(4.09223 + 7.08794i) q^{61} +(-0.727048 - 1.25928i) q^{62} +(0.435118 - 2.68390i) q^{63} -7.73440 q^{64} +(-0.825710 - 11.2566i) q^{65} +(9.04319 - 4.29318i) q^{66} +(11.7394 + 6.77772i) q^{67} +(-1.34101 + 2.32269i) q^{68} +(0.607429 - 7.54242i) q^{69} +(-2.59886 - 1.50045i) q^{70} +(3.07782 + 1.77698i) q^{71} +(7.08413 + 5.77948i) q^{72} -1.25464i q^{73} +(1.12586 + 1.95004i) q^{74} +(0.667314 - 8.28600i) q^{75} +(-5.02199 - 2.89945i) q^{76} +(-2.47612 - 4.28877i) q^{77} +(-6.60533 - 0.0471580i) q^{78} +(-5.59586 + 9.69232i) q^{79} +(3.96087 - 2.28681i) q^{80} +(-1.80700 - 8.81673i) q^{81} +(-4.53476 + 7.85444i) q^{82} +(-0.899143 - 0.519121i) q^{83} +(0.785594 - 1.13860i) q^{84} -9.52751i q^{85} +(3.36786 - 1.94444i) q^{86} +(-4.17787 + 1.98341i) q^{87} +16.6522 q^{88} +(-4.76108 + 2.74881i) q^{89} +(-9.80530 - 1.58965i) q^{90} +(0.239060 + 3.25901i) q^{91} +(1.92489 - 3.33400i) q^{92} +(-1.35225 + 1.95988i) q^{93} +(-3.06201 + 5.30356i) q^{94} +20.5998 q^{95} +(3.37960 + 7.11883i) q^{96} +(7.06649 - 4.07984i) q^{97} +(-5.65970 - 3.26763i) q^{98} +(-12.7017 - 10.3625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Introduction

L-functions

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