LMFDB - Embedded newform 1218.2.p.b.289.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(289,1218)] 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("1218.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] 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:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.12
Character	$\chi$	$=$	1218.289
Dual form			1218.2.p.b.1159.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.09965 + 1.90465i) q^{5} -1.00000 q^{6} +(-2.59884 - 0.496020i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.90465 + 1.09965i) q^{10} +(-4.17005 + 2.40758i) q^{11} +(-0.866025 - 0.500000i) q^{12} +0.594482 q^{13} +(-2.00265 - 1.72899i) q^{14} -2.19930i q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.33711 - 3.65873i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-5.49013 - 3.16973i) q^{19} -2.19930 q^{20} +(2.49867 - 0.869854i) q^{21} -4.81516 q^{22} +(1.91009 - 3.30837i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.0815493 + 0.141248i) q^{25} +(0.514836 + 0.297241i) q^{26} +1.00000i q^{27} +(-0.869854 - 2.49867i) q^{28} +(-2.42359 - 4.80897i) q^{29} +(1.09965 - 1.90465i) q^{30} +(-4.91922 + 2.84011i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.40758 - 4.17005i) q^{33} +7.31747 q^{34} +(3.80255 - 4.40442i) q^{35} +1.00000 q^{36} +(4.45835 + 2.57403i) q^{37} +(-3.16973 - 5.49013i) q^{38} +(-0.514836 + 0.297241i) q^{39} +(-1.90465 - 1.09965i) q^{40} -9.19954i q^{41} +(2.59884 + 0.496020i) q^{42} -0.843054i q^{43} +(-4.17005 - 2.40758i) q^{44} +(1.09965 + 1.90465i) q^{45} +(3.30837 - 1.91009i) q^{46} +(-7.67146 - 4.42912i) q^{47} -1.00000i q^{48} +(6.50793 + 2.57815i) q^{49} +0.163099i q^{50} +(-3.65873 + 6.33711i) q^{51} +(0.297241 + 0.514836i) q^{52} +(-1.10529 - 1.91441i) q^{53} +(-0.500000 + 0.866025i) q^{54} -10.5900i q^{55} +(0.496020 - 2.59884i) q^{56} +6.33946 q^{57} +(0.305592 - 5.37649i) q^{58} +(4.27285 + 7.40079i) q^{59} +(1.90465 - 1.09965i) q^{60} +(-12.8544 - 7.42151i) q^{61} -5.68023 q^{62} +(-1.72899 + 2.00265i) q^{63} -1.00000 q^{64} +(-0.653720 + 1.13228i) q^{65} +(4.17005 - 2.40758i) q^{66} +(5.60937 + 9.71571i) q^{67} +(6.33711 + 3.65873i) q^{68} +3.82018i q^{69} +(5.49532 - 1.91307i) q^{70} -5.95717 q^{71} +(0.866025 + 0.500000i) q^{72} +(-13.8612 + 8.00279i) q^{73} +(2.57403 + 4.45835i) q^{74} +(-0.141248 - 0.0815493i) q^{75} -6.33946i q^{76} +(12.0315 - 4.18848i) q^{77} -0.594482 q^{78} +(1.18751 + 0.685608i) q^{79} +(-1.09965 - 1.90465i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.59977 - 7.96703i) q^{82} -12.2828 q^{83} +(2.00265 + 1.72899i) q^{84} +16.0933i q^{85} +(0.421527 - 0.730106i) q^{86} +(4.50338 + 2.95289i) q^{87} +(-2.40758 - 4.17005i) q^{88} +(-2.58959 - 1.49510i) q^{89} +2.19930i q^{90} +(-1.54496 - 0.294875i) q^{91} +3.82018 q^{92} +(2.84011 - 4.91922i) q^{93} +(-4.42912 - 7.67146i) q^{94} +(12.0744 - 6.97117i) q^{95} +(0.500000 - 0.866025i) q^{96} -7.38538i q^{97} +(4.34696 + 5.48671i) q^{98} +4.81516i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 22 q^{4} - 44 q^{6} - 8 q^{7} + 22 q^{9} - 16 q^{13} - 22 q^{16} - 4 q^{23} - 22 q^{24} - 22 q^{25} - 4 q^{28} + 4 q^{29} - 16 q^{34} - 10 q^{35} + 44 q^{36} + 4 q^{38} + 8 q^{42} - 52 q^{49} + 8 q^{51}+ \cdots + 22 q^{96}+O(q^{100}) $ 44 * q + 22 * q^4 - 44 * q^6 - 8 * q^7 + 22 * q^9 - 16 * q^13 - 22 * q^16 - 4 * q^23 - 22 * q^24 - 22 * q^25 - 4 * q^28 + 4 * q^29 - 16 * q^34 - 10 * q^35 + 44 * q^36 + 4 * q^38 + 8 * q^42 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 6 * q^53 - 22 * q^54 - 8 * q^57 + 14 * q^58 + 24 * q^59 + 16 * q^62 - 4 * q^63 - 44 * q^64 - 24 * q^65 + 28 * q^67 - 24 * q^71 - 16 * q^74 + 16 * q^78 - 22 * q^81 - 28 * q^83 + 4 * q^86 + 14 * q^87 + 112 * q^91 - 8 * q^92 - 8 * q^93 - 36 * q^94 + 22 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.09965	+	1.90465i	−0.491777	+	0.851784i	−0.999955	−	0.00946869i	$-0.996986\pi$
$5$	−1.09965	+	1.90465i	−0.491777	+	0.851784i	0.508178	+	0.861252i	$0.330319\pi$
$6$	−1.00000			−0.408248
$7$	−2.59884	−	0.496020i	−0.982269	−	0.187478i
$7$	−2.59884	−	0.496020i	−0.982269	−	0.187478i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.90465	+	1.09965i	−0.602302	+	0.347739i
$11$	−4.17005	+	2.40758i	−1.25732	+	0.725912i	−0.972552	−	0.232685i	$-0.925249\pi$
$11$	−4.17005	+	2.40758i	−1.25732	+	0.725912i	−0.284765	+	0.958598i	$0.591915\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	0.594482			0.164880			0.0824398	−	0.996596i	$-0.473729\pi$
$13$	0.594482			0.164880			0.0824398	+	0.996596i	$0.473729\pi$
$14$	−2.00265	−	1.72899i	−0.535231	−	0.462091i
$15$		−	2.19930i		−	0.567856i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.33711	−	3.65873i	1.53698	−	0.887373i	0.537962	−	0.842969i	$-0.319195\pi$
$17$	6.33711	−	3.65873i	1.53698	−	0.887373i	0.999014	−	0.0444037i	$-0.0141388\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−5.49013	−	3.16973i	−1.25952	−	0.727186i	−0.286541	−	0.958068i	$-0.592506\pi$
$19$	−5.49013	−	3.16973i	−1.25952	−	0.727186i	−0.972982	+	0.230882i	$0.925839\pi$
$20$	−2.19930			−0.491777
$21$	2.49867	−	0.869854i	0.545255	−	0.189818i
$22$	−4.81516			−1.02659
$23$	1.91009	−	3.30837i	0.398281	−	0.689843i	−0.595233	−	0.803553i	$-0.702940\pi$
$23$	1.91009	−	3.30837i	0.398281	−	0.689843i	0.993514	+	0.113710i	$0.0362735\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.0815493	+	0.141248i	0.0163099	+	0.0282495i
$26$	0.514836	+	0.297241i	0.100968	+	0.0582937i
$27$			1.00000i			0.192450i
$28$	−0.869854	−	2.49867i	−0.164387	−	0.472204i
$29$	−2.42359	−	4.80897i	−0.450050	−	0.893003i
$29$	−2.42359	−	4.80897i	−0.450050	−	0.893003i
$30$	1.09965	−	1.90465i	0.200767	−	0.347739i
$31$	−4.91922	+	2.84011i	−0.883518	+	0.510100i	−0.871817	−	0.489832i	$-0.837058\pi$
$31$	−4.91922	+	2.84011i	−0.883518	+	0.510100i	−0.0117015	+	0.999932i	$0.503725\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.40758	−	4.17005i	0.419106	−	0.725912i
$34$	7.31747			1.25494
$35$	3.80255	−	4.40442i	0.642748	−	0.744483i
$36$	1.00000			0.166667
$37$	4.45835	+	2.57403i	0.732947	+	0.423167i	0.819499	−	0.573080i	$-0.194252\pi$
$37$	4.45835	+	2.57403i	0.732947	+	0.423167i	−0.0865520	+	0.996247i	$0.527585\pi$
$38$	−3.16973	−	5.49013i	−0.514198	−	0.890617i
$39$	−0.514836	+	0.297241i	−0.0824398	+	0.0475966i
$40$	−1.90465	−	1.09965i	−0.301151	−	0.173870i
$41$		−	9.19954i		−	1.43673i	−0.695668	−	0.718363i	$-0.744892\pi$
$41$		−	9.19954i		−	1.43673i	0.695668	−	0.718363i	$-0.255108\pi$
$42$	2.59884	+	0.496020i	0.401010	+	0.0765375i
$43$		−	0.843054i		−	0.128564i	−0.997932	−	0.0642822i	$-0.979524\pi$
$43$		−	0.843054i		−	0.128564i	0.997932	−	0.0642822i	$-0.0204758\pi$
$44$	−4.17005	−	2.40758i	−0.628658	−	0.362956i
$45$	1.09965	+	1.90465i	0.163926	+	0.283928i
$46$	3.30837	−	1.91009i	0.487793	−	0.281627i
$47$	−7.67146	−	4.42912i	−1.11900	−	0.646054i	−0.177853	−	0.984057i	$-0.556915\pi$
$47$	−7.67146	−	4.42912i	−1.11900	−	0.646054i	−0.941145	+	0.338004i	$0.890248\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.50793	+	2.57815i	0.929704	+	0.368307i
$50$			0.163099i			0.0230656i
$51$	−3.65873	+	6.33711i	−0.512325	+	0.887373i
$52$	0.297241	+	0.514836i	0.0412199	+	0.0713949i
$53$	−1.10529	−	1.91441i	−0.151823	−	0.262965i	0.780075	−	0.625686i	$-0.215181\pi$
$53$	−1.10529	−	1.91441i	−0.151823	−	0.262965i	−0.931898	+	0.362722i	$0.881848\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		−	10.5900i		−	1.42795i
$56$	0.496020	−	2.59884i	0.0662834	−	0.347284i
$57$	6.33946			0.839682
$58$	0.305592	−	5.37649i	0.0401262	−	0.705967i
$59$	4.27285	+	7.40079i	0.556277	+	0.963501i	0.997803	+	0.0662519i	$0.0211041\pi$
$59$	4.27285	+	7.40079i	0.556277	+	0.963501i	−0.441526	+	0.897249i	$0.645563\pi$
$60$	1.90465	−	1.09965i	0.245889	−	0.141964i
$61$	−12.8544	−	7.42151i	−1.64584	−	0.950227i	−0.978700	−	0.205296i	$-0.934184\pi$
$61$	−12.8544	−	7.42151i	−1.64584	−	0.950227i	−0.667141	−	0.744931i	$-0.732482\pi$
$62$	−5.68023			−0.721390
$63$	−1.72899	+	2.00265i	−0.217832	+	0.252310i
$64$	−1.00000			−0.125000
$65$	−0.653720	+	1.13228i	−0.0810840	+	0.140442i
$66$	4.17005	−	2.40758i	0.513297	−	0.296352i
$67$	5.60937	+	9.71571i	0.685293	+	1.18696i	0.973345	+	0.229348i	$0.0736593\pi$
$67$	5.60937	+	9.71571i	0.685293	+	1.18696i	−0.288051	+	0.957615i	$0.593007\pi$
$68$	6.33711	+	3.65873i	0.768488	+	0.443687i
$69$			3.82018i			0.459895i
$70$	5.49532	−	1.91307i	0.656816	−	0.228655i
$71$	−5.95717			−0.706986			−0.353493	−	0.935437i	$-0.615006\pi$
$71$	−5.95717			−0.706986			−0.353493	+	0.935437i	$0.615006\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−13.8612	+	8.00279i	−1.62234	+	0.936656i	−0.636043	+	0.771654i	$0.719430\pi$
$73$	−13.8612	+	8.00279i	−1.62234	+	0.936656i	−0.986293	+	0.165002i	$0.947237\pi$
$74$	2.57403	+	4.45835i	0.299225	+	0.518272i
$75$	−0.141248	−	0.0815493i	−0.0163099	−	0.00941651i
$76$		−	6.33946i		−	0.727186i
$77$	12.0315	−	4.18848i	1.37112	−	0.477322i
$78$	−0.594482			−0.0673118
$79$	1.18751	+	0.685608i	0.133605	+	0.0771369i	0.565313	−	0.824877i	$-0.308755\pi$
$79$	1.18751	+	0.685608i	0.133605	+	0.0771369i	−0.431708	+	0.902014i	$0.642089\pi$
$80$	−1.09965	−	1.90465i	−0.122944	−	0.212946i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.59977	−	7.96703i	0.507960	−	0.879812i
$83$	−12.2828			−1.34822			−0.674108	−	0.738632i	$-0.735472\pi$
$83$	−12.2828			−1.34822			−0.674108	+	0.738632i	$0.735472\pi$
$84$	2.00265	+	1.72899i	0.218507	+	0.188648i
$85$			16.0933i			1.74556i
$86$	0.421527	−	0.730106i	0.0454544	−	0.0787293i
$87$	4.50338	+	2.95289i	0.482813	+	0.316583i
$88$	−2.40758	−	4.17005i	−0.256649	−	0.444529i
$89$	−2.58959	−	1.49510i	−0.274496	−	0.158481i	0.356433	−	0.934321i	$-0.383993\pi$
$89$	−2.58959	−	1.49510i	−0.274496	−	0.158481i	−0.630929	+	0.775840i	$0.717326\pi$
$90$			2.19930i			0.231826i
$91$	−1.54496	−	0.294875i	−0.161956	−	0.0309113i
$92$	3.82018			0.398281
$93$	2.84011	−	4.91922i	0.294506	−	0.510100i
$94$	−4.42912	−	7.67146i	−0.456829	−	0.791251i
$95$	12.0744	−	6.97117i	1.23881	−	0.715227i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	7.38538i		−	0.749871i	−0.927051	−	0.374936i	$-0.877665\pi$
$97$		−	7.38538i		−	0.749871i	0.927051	−	0.374936i	$-0.122335\pi$
$98$	4.34696	+	5.48671i	0.439109	+	0.554241i
$99$			4.81516i			0.483941i
$100$	−0.0815493	+	0.141248i	−0.00815493	+	0.0141248i
$101$	5.47566	−	3.16138i	0.544849	−	0.314569i	−0.202193	−	0.979346i	$-0.564807\pi$
$101$	5.47566	−	3.16138i	0.544849	−	0.314569i	0.747042	+	0.664777i	$0.231473\pi$
$102$	−6.33711	+	3.65873i	−0.627468	+	0.362269i
$103$	5.69644	−	9.86652i	0.561287	−	0.972178i	−0.436098	−	0.899899i	$-0.643640\pi$
$103$	5.69644	−	9.86652i	0.561287	−	0.972178i	0.997385	−	0.0722781i	$-0.0230269\pi$
$104$			0.594482i			0.0582937i
$105$	−1.09089	+	5.71562i	−0.106460	+	0.557787i
$106$		−	2.21057i		−	0.214710i
$107$	−0.110178	+	0.190834i	−0.0106513	+	0.0184486i	−0.871302	−	0.490747i	$-0.836724\pi$
$107$	−0.110178	+	0.190834i	−0.0106513	+	0.0184486i	0.860651	+	0.509196i	$0.170057\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	1.66862	+	2.89013i	0.159825	+	0.276824i	0.934805	−	0.355161i	$-0.115574\pi$
$109$	1.66862	+	2.89013i	0.159825	+	0.276824i	−0.774981	+	0.631985i	$0.782240\pi$
$110$	5.29498	−	9.17117i	0.504856	−	0.874436i
$111$	−5.14805			−0.488632
$112$	1.72899	−	2.00265i	0.163374	−	0.189233i
$113$		−	2.35527i		−	0.221565i	−0.993845	−	0.110782i	$-0.964664\pi$
$113$		−	2.35527i		−	0.221565i	0.993845	−	0.110782i	$-0.0353357\pi$
$114$	5.49013	+	3.16973i	0.514198	+	0.296872i
$115$	4.20085	+	7.27609i	0.391731	+	0.678498i
$116$	2.95289	−	4.50338i	0.274169	−	0.418128i
$117$	0.297241	−	0.514836i	0.0274799	−	0.0475966i
$118$			8.54569i			0.786695i
$119$	−18.2839	+	6.36513i	−1.67609	+	0.583490i
$120$	2.19930			0.200767
$121$	6.09286	−	10.5531i	0.553897	−	0.959377i
$122$	−7.42151	−	12.8544i	−0.671912	−	1.16379i
$123$	4.59977	+	7.96703i	0.414747	+	0.718363i
$124$	−4.91922	−	2.84011i	−0.441759	−	0.255050i
$125$	−11.3552			−1.01564
$126$	−2.49867	+	0.869854i	−0.222599	+	0.0774927i
$127$			0.218107i			0.0193539i	0.999953	+	0.00967695i	$0.00308032\pi$
$127$			0.218107i			0.0193539i	−0.999953	+	0.00967695i	$0.996920\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	0.421527	+	0.730106i	0.0371134	+	0.0642822i
$130$	−1.13228	+	0.653720i	−0.0993073	+	0.0573351i
$131$	−3.00694	−	1.73606i	−0.262717	−	0.151680i	0.362856	−	0.931845i	$-0.381802\pi$
$131$	−3.00694	−	1.73606i	−0.262717	−	0.151680i	−0.625573	+	0.780165i	$0.715135\pi$
$132$	4.81516			0.419106
$133$	12.6957	+	10.9608i	1.10086	+	0.950425i
$134$			11.2187i			0.969151i
$135$	−1.90465	−	1.09965i	−0.163926	−	0.0946426i
$136$	3.65873	+	6.33711i	0.313734	+	0.543403i
$137$	−11.9558	+	6.90268i	−1.02145	+	0.589736i	−0.914524	−	0.404531i	$-0.867435\pi$
$137$	−11.9558	+	6.90268i	−1.02145	+	0.589736i	−0.106928	+	0.994267i	$0.534102\pi$
$138$	−1.91009	+	3.30837i	−0.162598	+	0.281627i
$139$	0.425359			0.0360785			0.0180392	−	0.999837i	$-0.494258\pi$
$139$	0.425359			0.0360785			0.0180392	+	0.999837i	$0.494258\pi$
$140$	5.71562	+	1.09089i	0.483058	+	0.0921974i
$141$	8.85824			0.745998
$142$	−5.15906	−	2.97858i	−0.432939	−	0.249957i
$143$	−2.47902	+	1.43126i	−0.207306	+	0.119688i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	11.8245	+	0.672087i	0.981970	+	0.0558138i
$146$	−16.0056			−1.32463
$147$	−6.92511	+	1.02122i	−0.571173	+	0.0842288i
$148$			5.14805i			0.423167i
$149$	−7.40768	+	12.8305i	−0.606861	+	1.05111i	0.384894	+	0.922961i	$0.374238\pi$
$149$	−7.40768	+	12.8305i	−0.606861	+	1.05111i	−0.991754	+	0.128153i	$0.959095\pi$
$150$	−0.0815493	−	0.141248i	−0.00665848	−	0.0115328i
$151$	6.28229	+	10.8813i	0.511246	+	0.885504i	0.999915	+	0.0130345i	$0.00414914\pi$
$151$	6.28229	+	10.8813i	0.511246	+	0.885504i	−0.488669	+	0.872469i	$0.662518\pi$
$152$	3.16973	−	5.49013i	0.257099	−	0.445309i
$153$		−	7.31747i		−	0.591582i
$154$	12.5138	+	2.38841i	1.00839	+	0.192464i
$155$		−	12.4925i		−	1.00342i
$156$	−0.514836	−	0.297241i	−0.0412199	−	0.0237983i
$157$	−10.9715	+	6.33439i	−0.875619	+	0.505539i	−0.869211	−	0.494440i	$-0.835373\pi$
$157$	−10.9715	+	6.33439i	−0.875619	+	0.505539i	−0.00640771	+	0.999979i	$0.502040\pi$
$158$	0.685608	+	1.18751i	0.0545440	+	0.0944730i
$159$	1.91441	+	1.10529i	0.151823	+	0.0876549i
$160$		−	2.19930i		−	0.173870i
$161$	−6.60503	+	7.65048i	−0.520549	+	0.602942i
$162$		−	1.00000i		−	0.0785674i
$163$	3.28121	+	1.89441i	0.257004	+	0.148382i	0.622967	−	0.782248i	$-0.285927\pi$
$163$	3.28121	+	1.89441i	0.257004	+	0.148382i	−0.365963	+	0.930629i	$0.619260\pi$
$164$	7.96703	−	4.59977i	0.622121	−	0.359182i
$165$	5.29498	+	9.17117i	0.412213	+	0.713974i
$166$	−10.6373	−	6.14142i	−0.825611	−	0.476667i
$167$	6.26854			0.485074			0.242537	−	0.970142i	$-0.422020\pi$
$167$	6.26854			0.485074			0.242537	+	0.970142i	$0.422020\pi$
$168$	0.869854	+	2.49867i	0.0671107	+	0.192777i
$169$	−12.6466			−0.972815
$170$	−8.04664	+	13.9372i	−0.617149	+	1.06893i
$171$	−5.49013	+	3.16973i	−0.419841	+	0.242395i
$172$	0.730106	−	0.421527i	0.0556700	−	0.0321411i
$173$	7.73083	−	13.3902i	0.587764	−	1.01804i	−0.406761	−	0.913535i	$-0.633342\pi$
$173$	7.73083	−	13.3902i	0.587764	−	1.01804i	0.994525	−	0.104502i	$-0.0333249\pi$
$174$	2.42359	+	4.80897i	0.183732	+	0.364567i
$175$	−0.141872	−	0.407530i	−0.0107245	−	0.0308064i
$176$		−	4.81516i		−	0.362956i
$177$	−7.40079	−	4.27285i	−0.556277	−	0.321167i
$178$	−1.49510	−	2.58959i	−0.112063	−	0.194098i
$179$	1.12603	+	1.95034i	0.0841636	+	0.145776i	0.905034	−	0.425338i	$-0.139845\pi$
$179$	1.12603	+	1.95034i	0.0841636	+	0.145776i	−0.820871	+	0.571114i	$0.806512\pi$
$180$	−1.09965	+	1.90465i	−0.0819629	+	0.141964i
$181$	−7.53342			−0.559955			−0.279977	−	0.960007i	$-0.590327\pi$
$181$	−7.53342			−0.559955			−0.279977	+	0.960007i	$0.590327\pi$
$182$	−1.19054	−	1.02785i	−0.0882486	−	0.0761893i
$183$	14.8430			1.09723
$184$	3.30837	+	1.91009i	0.243896	+	0.140814i
$185$	−9.80522	+	5.66105i	−0.720894	+	0.416208i
$186$	4.91922	−	2.84011i	0.360695	−	0.208247i
$187$	−17.6174	+	30.5142i	−1.28831	+	2.23142i
$188$		−	8.85824i		−	0.646054i
$189$	0.496020	−	2.59884i	0.0360801	−	0.189038i
$190$	13.9423			1.01148
$191$	3.63023	+	2.09591i	0.262674	+	0.151655i	0.625554	−	0.780181i	$-0.284873\pi$
$191$	3.63023	+	2.09591i	0.262674	+	0.151655i	−0.362880	+	0.931836i	$0.618206\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−13.8057	+	7.97072i	−0.993755	+	0.573745i	−0.906395	−	0.422432i	$-0.861176\pi$
$193$	−13.8057	+	7.97072i	−0.993755	+	0.573745i	−0.0873604	+	0.996177i	$0.527843\pi$
$194$	3.69269	−	6.39592i	0.265120	−	0.459201i
$195$		−	1.30744i		−	0.0936278i
$196$	1.02122	+	6.92511i	0.0729443	+	0.494651i
$197$	−17.2700			−1.23044			−0.615219	−	0.788356i	$-0.710932\pi$
$197$	−17.2700			−1.23044			−0.615219	+	0.788356i	$0.710932\pi$
$198$	−2.40758	+	4.17005i	−0.171099	+	0.296352i
$199$	−7.21660	−	12.4995i	−0.511571	−	0.886067i	−0.999910	−	0.0134129i	$-0.995730\pi$
$199$	−7.21660	−	12.4995i	−0.511571	−	0.886067i	0.488339	−	0.872654i	$-0.337603\pi$
$200$	−0.141248	+	0.0815493i	−0.00998771	+	0.00576641i
$201$	−9.71571	−	5.60937i	−0.685293	−	0.395654i
$202$	6.32275			0.444867
$203$	3.91318	+	13.6999i	0.274652	+	0.961544i
$204$	−7.31747			−0.512325
$205$	17.5219	+	10.1163i	1.22378	+	0.706550i
$206$	9.86652	−	5.69644i	0.687433	−	0.396890i
$207$	−1.91009	−	3.30837i	−0.132760	−	0.229948i
$208$	−0.297241	+	0.514836i	−0.0206099	+	0.0356975i
$209$	30.5255			2.11149
$210$	−3.80255	+	4.40442i	−0.262401	+	0.303934i
$211$			18.9257i			1.30290i	0.758693	+	0.651449i	$0.225838\pi$
$211$			18.9257i			1.30290i	−0.758693	+	0.651449i	$0.774162\pi$
$212$	1.10529	−	1.91441i	0.0759113	−	0.131482i
$213$	5.15906	−	2.97858i	0.353493	−	0.204089i
$214$	−0.190834	+	0.110178i	−0.0130451	+	0.00753161i
$215$	1.60572	+	0.927062i	0.109509	+	0.0632251i
$216$	−1.00000			−0.0680414
$217$	14.1930	−	4.94097i	0.963485	−	0.335415i
$218$			3.33723i			0.226026i
$219$	8.00279	−	13.8612i	0.540779	−	0.936656i
$220$	9.17117	−	5.29498i	0.618320	−	0.356987i
$221$	3.76730	−	2.17505i	0.253416	−	0.146310i
$222$	−4.45835	−	2.57403i	−0.299225	−	0.172757i
$223$	−7.55452			−0.505888			−0.252944	−	0.967481i	$-0.581399\pi$
$223$	−7.55452			−0.505888			−0.252944	+	0.967481i	$0.581399\pi$
$224$	2.49867	−	0.869854i	0.166949	−	0.0581196i
$225$	0.163099			0.0108732
$226$	1.17763	−	2.03972i	0.0783351	−	0.135680i
$227$	−9.64323	−	16.7026i	−0.640044	−	1.10859i	−0.985423	−	0.170125i	$-0.945583\pi$
$227$	−9.64323	−	16.7026i	−0.640044	−	1.10859i	0.345379	−	0.938463i	$-0.387750\pi$
$228$	3.16973	+	5.49013i	0.209920	+	0.363593i
$229$	16.1917	+	9.34830i	1.06998	+	0.617753i	0.928176	−	0.372142i	$-0.121377\pi$
$229$	16.1917	+	9.34830i	1.06998	+	0.617753i	0.141803	+	0.989895i	$0.454710\pi$
$230$			8.40170i			0.553992i
$231$	−8.32533	+	9.64308i	−0.547767	+	0.634468i
$232$	4.80897	−	2.42359i	0.315724	−	0.159117i
$233$	7.57598	−	13.1220i	0.496319	−	0.859649i	−0.503672	−	0.863895i	$-0.668018\pi$
$233$	7.57598	−	13.1220i	0.496319	−	0.859649i	0.999991	+	0.00424549i	$0.00135138\pi$
$234$	0.514836	−	0.297241i	0.0336559	−	0.0194312i
$235$	16.8718	−	9.74094i	1.10060	−	0.635429i
$236$	−4.27285	+	7.40079i	−0.278139	+	0.481750i
$237$	−1.37122			−0.0890700
$238$	−19.0169	−	3.62961i	−1.23268	−	0.235272i
$239$	−13.2370			−0.856233			−0.428117	−	0.903723i	$-0.640823\pi$
$239$	−13.2370			−0.856233			−0.428117	+	0.903723i	$0.640823\pi$
$240$	1.90465	+	1.09965i	0.122944	+	0.0709820i
$241$	−2.46882	−	4.27613i	−0.159031	−	0.275450i	0.775489	−	0.631362i	$-0.217504\pi$
$241$	−2.46882	−	4.27613i	−0.159031	−	0.275450i	−0.934519	+	0.355912i	$0.884170\pi$
$242$	10.5531	−	6.09286i	0.678382	−	0.391664i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		−	14.8430i		−	0.950227i
$245$	−12.0669	+	9.56024i	−0.770926	+	0.610781i
$246$			9.19954i			0.586541i
$247$	−3.26378	−	1.88435i	−0.207670	−	0.119898i
$248$	−2.84011	−	4.91922i	−0.180347	−	0.312371i
$249$	10.6373	−	6.14142i	0.674108	−	0.389197i
$250$	−9.83387	−	5.67759i	−0.621949	−	0.359082i
$251$			7.59532i			0.479412i	0.970846	+	0.239706i	$0.0770511\pi$
$251$			7.59532i			0.479412i	−0.970846	+	0.239706i	$0.922949\pi$
$252$	−2.59884	−	0.496020i	−0.163711	−	0.0312463i
$253$			18.3948i			1.15647i
$254$	−0.109054	+	0.188886i	−0.00684264	+	0.0118518i
$255$	−8.04664	−	13.9372i	−0.503900	−	0.872780i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.6870	+	20.2424i	−0.729012	+	1.26269i	0.228289	+	0.973593i	$0.426687\pi$
$257$	−11.6870	+	20.2424i	−0.729012	+	1.26269i	−0.957301	+	0.289093i	$0.906646\pi$
$258$			0.843054i			0.0524862i
$259$	−10.3098	−	8.90091i	−0.640617	−	0.553076i
$260$	−1.30744			−0.0810840
$261$	−5.37649	−	0.305592i	−0.332796	−	0.0189157i
$262$	−1.73606	−	3.00694i	−0.107254	−	0.185769i
$263$	25.8393	−	14.9183i	1.59332	−	0.919903i	0.600587	−	0.799560i	$-0.294934\pi$
$263$	25.8393	−	14.9183i	1.59332	−	0.919903i	0.992732	−	0.120343i	$-0.0383996\pi$
$264$	4.17005	+	2.40758i	0.256649	+	0.148176i
$265$	4.86170			0.298652
$266$	5.51440	+	15.8402i	0.338110	+	0.971226i
$267$	2.99020			0.182998
$268$	−5.60937	+	9.71571i	−0.342647	+	0.593481i
$269$	−0.465468	+	0.268738i	−0.0283801	+	0.0163853i	−0.514123	−	0.857717i	$-0.671882\pi$
$269$	−0.465468	+	0.268738i	−0.0283801	+	0.0163853i	0.485743	+	0.874102i	$0.338549\pi$
$270$	−1.09965	−	1.90465i	−0.0669224	−	0.115913i
$271$	17.6764	+	10.2055i	1.07377	+	0.619939i	0.929208	−	0.369557i	$-0.120491\pi$
$271$	17.6764	+	10.2055i	1.07377	+	0.619939i	0.144558	+	0.989496i	$0.453824\pi$
$272$			7.31747i			0.443687i
$273$	1.48541	−	0.517112i	0.0899013	−	0.0312971i
$274$	−13.8054			−0.834013
$275$	−0.680129	−	0.392673i	−0.0410133	−	0.0236791i
$276$	−3.30837	+	1.91009i	−0.199141	+	0.114974i
$277$	−0.659387	−	1.14209i	−0.0396187	−	0.0686216i	0.845536	−	0.533918i	$-0.179281\pi$
$277$	−0.659387	−	1.14209i	−0.0396187	−	0.0686216i	−0.885155	+	0.465297i	$0.845948\pi$
$278$	0.368372	+	0.212679i	0.0220935	+	0.0127557i
$279$			5.68023i			0.340066i
$280$	4.40442	+	3.80255i	0.263215	+	0.227246i
$281$	31.0763			1.85386			0.926929	−	0.375236i	$-0.122438\pi$
$281$	31.0763			1.85386			0.926929	+	0.375236i	$0.122438\pi$
$282$	7.67146	+	4.42912i	0.456829	+	0.263750i
$283$	16.4363	+	28.4685i	0.977035	+	1.69227i	0.673050	+	0.739597i	$0.264984\pi$
$283$	16.4363	+	28.4685i	0.977035	+	1.69227i	0.303985	+	0.952677i	$0.401683\pi$
$284$	−2.97858	−	5.15906i	−0.176746	−	0.306134i
$285$	−6.97117	+	12.0744i	−0.412937	+	0.715227i
$286$	−2.86252			−0.169264
$287$	−4.56315	+	23.9081i	−0.269354	+	1.41125i
$288$			1.00000i			0.0589256i
$289$	18.2727	−	31.6492i	1.07486	−	1.86172i
$290$	9.90426	+	6.49429i	0.581598	+	0.381358i
$291$	3.69269	+	6.39592i	0.216469	+	0.374936i
$292$	−13.8612	−	8.00279i	−0.811168	−	0.468328i
$293$		−	0.0962519i		−	0.00562310i	−0.999996	−	0.00281155i	$-0.999105\pi$
$293$		−	0.0962519i		−	0.00562310i	0.999996	−	0.00281155i	$-0.000894945\pi$
$294$	−6.50793	−	2.57815i	−0.379550	−	0.150361i
$295$	−18.7945			−1.09426
$296$	−2.57403	+	4.45835i	−0.149612	+	0.259136i
$297$	−2.40758	−	4.17005i	−0.139702	−	0.241971i
$298$	−12.8305	+	7.40768i	−0.743250	+	0.429115i
$299$	1.13551	−	1.96677i	0.0656684	−	0.113741i
$300$		−	0.163099i		−	0.00941651i
$301$	−0.418171	+	2.19096i	−0.0241030	+	0.126285i
$302$			12.5646i			0.723011i
$303$	−3.16138	+	5.47566i	−0.181616	+	0.314569i
$304$	5.49013	−	3.16973i	0.314881	−	0.181796i
$305$	28.2707	−	16.3221i	1.61878	−	0.934600i
$306$	3.65873	−	6.33711i	0.209156	−	0.362269i
$307$			11.5432i			0.658802i	0.944190	+	0.329401i	$0.106847\pi$
$307$			11.5432i			0.658802i	−0.944190	+	0.329401i	$0.893153\pi$
$308$	9.64308	+	8.32533i	0.549465	+	0.474380i
$309$			11.3929i			0.648118i
$310$	6.24625	−	10.8188i	0.354763	−	0.614468i
$311$	−21.3002	+	12.2977i	−1.20782	+	0.697338i	−0.962283	−	0.272049i	$-0.912299\pi$
$311$	−21.3002	+	12.2977i	−1.20782	+	0.697338i	−0.245541	+	0.969386i	$0.578965\pi$
$312$	−0.297241	−	0.514836i	−0.0168279	−	0.0291469i
$313$	−15.5072	+	26.8593i	−0.876519	+	1.51818i	−0.0213837	+	0.999771i	$0.506807\pi$
$313$	−15.5072	+	26.8593i	−0.876519	+	1.51818i	−0.855136	+	0.518404i	$0.826526\pi$
$314$	−12.6688			−0.714940
$315$	−1.91307	−	5.49532i	−0.107789	−	0.309626i
$316$			1.37122i			0.0771369i
$317$	13.8606	+	8.00240i	0.778487	+	0.449459i	0.835894	−	0.548891i	$-0.184950\pi$
$317$	13.8606	+	8.00240i	0.778487	+	0.449459i	−0.0574070	+	0.998351i	$0.518283\pi$
$318$	1.10529	+	1.91441i	0.0619813	+	0.107355i
$319$	21.6845	+	14.2186i	1.21410	+	0.796091i
$320$	1.09965	−	1.90465i	0.0614722	−	0.106473i
$321$		−	0.220356i		−	0.0122991i
$322$	−9.54537	+	3.32300i	−0.531942	+	0.185183i
$323$	−46.3888			−2.58114
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	0.0484796	+	0.0839691i	0.00268916	+	0.00465777i
$326$	1.89441	+	3.28121i	0.104922	+	0.181729i
$327$	−2.89013	−	1.66862i	−0.159825	−	0.0922747i
$328$	9.19954			0.507960
$329$	17.7400	+	15.3158i	0.978036	+	0.844386i
$330$			10.5900i			0.582958i
$331$	−2.37104	−	1.36892i	−0.130324	−	0.0752426i	0.433421	−	0.901192i	$-0.357306\pi$
$331$	−2.37104	−	1.36892i	−0.130324	−	0.0752426i	−0.563745	+	0.825949i	$0.690640\pi$
$332$	−6.14142	−	10.6373i	−0.337054	−	0.583795i
$333$	4.45835	−	2.57403i	0.244316	−	0.141056i
$334$	5.42872	+	3.13427i	0.297046	+	0.171500i
$335$	−24.6733			−1.34805
$336$	−0.496020	+	2.59884i	−0.0270601	+	0.141778i
$337$		−	17.2240i		−	0.938251i	−0.883131	−	0.469126i	$-0.844569\pi$
$337$		−	17.2240i		−	0.938251i	0.883131	−	0.469126i	$-0.155431\pi$
$338$	−10.9523	−	6.32330i	−0.595725	−	0.343942i
$339$	1.17763	+	2.03972i	0.0639603	+	0.110782i
$340$	−13.9372	+	8.04664i	−0.755850	+	0.436390i
$341$	13.6756	−	23.6868i	0.740575	−	1.28271i
$342$	−6.33946			−0.342799
$343$	−15.6342	−	9.92826i	−0.844170	−	0.536076i
$344$	0.843054			0.0454544
$345$	−7.27609	−	4.20085i	−0.391731	−	0.226166i
$346$	13.3902	−	7.73083i	0.719861	−	0.415612i
$347$	−1.38423	−	2.39755i	−0.0743092	−	0.128707i	0.826476	−	0.562971i	$-0.190342\pi$
$347$	−1.38423	−	2.39755i	−0.0743092	−	0.128707i	−0.900786	+	0.434264i	$0.857009\pi$
$348$	−0.305592	+	5.37649i	−0.0163814	+	0.288210i
$349$	0.676478			0.0362110			0.0181055	−	0.999836i	$-0.494237\pi$
$349$	0.676478			0.0362110			0.0181055	+	0.999836i	$0.494237\pi$
$350$	0.0809002	−	0.423867i	0.00432430	−	0.0226567i
$351$			0.594482i			0.0317311i
$352$	2.40758	−	4.17005i	0.128324	−	0.222264i
$353$	−3.36614	−	5.83033i	−0.179162	−	0.310317i	0.762432	−	0.647068i	$-0.224005\pi$
$353$	−3.36614	−	5.83033i	−0.179162	−	0.310317i	−0.941594	+	0.336751i	$0.890672\pi$
$354$	−4.27285	−	7.40079i	−0.227099	−	0.393347i
$355$	6.55079	−	11.3463i	0.347680	−	0.602199i
$356$		−	2.99020i		−	0.158481i
$357$	12.6518	−	14.6543i	0.669604	−	0.775589i
$358$			2.25206i			0.119025i
$359$	−21.1481	−	12.2099i	−1.11615	−	0.644412i	−0.175738	−	0.984437i	$-0.556231\pi$
$359$	−21.1481	−	12.2099i	−1.11615	−	0.644412i	−0.940416	+	0.340025i	$0.889565\pi$
$360$	−1.90465	+	1.09965i	−0.100384	+	0.0579565i
$361$	10.5944	+	18.3500i	0.557599	+	0.965789i
$362$	−6.52413	−	3.76671i	−0.342901	−	0.197974i
$363$			12.1857i			0.639585i
$364$	−0.517112	−	1.48541i	−0.0271040	−	0.0778568i
$365$		−	35.2010i		−	1.84251i
$366$	12.8544	+	7.42151i	0.671912	+	0.387929i
$367$	1.99693	−	1.15293i	0.104239	−	0.0601822i	−0.446974	−	0.894547i	$-0.647498\pi$
$367$	1.99693	−	1.15293i	0.104239	−	0.0601822i	0.551213	+	0.834365i	$0.314165\pi$
$368$	1.91009	+	3.30837i	0.0995703	+	0.172461i
$369$	−7.96703	−	4.59977i	−0.414747	−	0.239454i
$370$	−11.3221			−0.588608
$371$	1.92287	+	5.52349i	0.0998306	+	0.286765i
$372$	5.68023			0.294506
$373$	−4.71187	+	8.16120i	−0.243971	+	0.422571i	−0.961842	−	0.273606i	$-0.911784\pi$
$373$	−4.71187	+	8.16120i	−0.243971	+	0.422571i	0.717871	+	0.696177i	$0.245117\pi$
$374$	−30.5142	+	17.6174i	−1.57785	+	0.910972i
$375$	9.83387	−	5.67759i	0.507819	−	0.293189i
$376$	4.42912	−	7.67146i	0.228414	−	0.395625i
$377$	−1.44078	−	2.85884i	−0.0742040	−	0.147238i
$378$	1.72899	−	2.00265i	0.0889294	−	0.103005i
$379$		−	31.2425i		−	1.60482i	−0.596772	−	0.802411i	$-0.703551\pi$
$379$		−	31.2425i		−	1.60482i	0.596772	−	0.802411i	$-0.296449\pi$
$380$	12.0744	+	6.97117i	0.619405	+	0.357614i
$381$	−0.109054	−	0.188886i	−0.00558699	−	0.00967695i
$382$	2.09591	+	3.63023i	0.107236	+	0.185739i
$383$	15.2148	−	26.3529i	0.777442	−	1.34657i	−0.155970	−	0.987762i	$-0.549850\pi$
$383$	15.2148	−	26.3529i	0.777442	−	1.34657i	0.933412	−	0.358807i	$-0.116816\pi$
$384$	1.00000			0.0510310
$385$	−5.25282	+	27.5216i	−0.267709	+	1.40263i
$386$	−15.9414			−0.811398
$387$	−0.730106	−	0.421527i	−0.0371134	−	0.0214274i
$388$	6.39592	−	3.69269i	0.324704	−	0.187468i
$389$	−9.19895	+	5.31102i	−0.466405	+	0.269279i	−0.714734	−	0.699397i	$-0.753452\pi$
$389$	−9.19895	+	5.31102i	−0.466405	+	0.269279i	0.248328	+	0.968676i	$0.420119\pi$
$390$	0.653720	−	1.13228i	0.0331024	−	0.0573351i
$391$		−	27.9540i		−	1.41370i
$392$	−2.57815	+	6.50793i	−0.130216	+	0.328700i
$393$	3.47211			0.175145
$394$	−14.9563	−	8.63501i	−0.753486	−	0.435026i
$395$	−2.61168	+	1.50785i	−0.131408	+	0.0758684i
$396$	−4.17005	+	2.40758i	−0.209553	+	0.120985i
$397$	−13.5822	+	23.5250i	−0.681669	+	1.18069i	0.292802	+	0.956173i	$0.405412\pi$
$397$	−13.5822	+	23.5250i	−0.681669	+	1.18069i	−0.974471	+	0.224513i	$0.927921\pi$
$398$		−	14.4332i		−	0.723471i
$399$	−16.4752	−	3.14450i	−0.824793	−	0.157422i
$400$	−0.163099			−0.00815493
$401$	18.3307	−	31.7496i	0.915389	−	1.58550i	0.109059	−	0.994035i	$-0.465216\pi$
$401$	18.3307	−	31.7496i	0.915389	−	1.58550i	0.806330	−	0.591466i	$-0.201450\pi$
$402$	−5.60937	−	9.71571i	−0.279770	−	0.484576i
$403$	−2.92439	+	1.68840i	−0.145674	+	0.0841050i
$404$	5.47566	+	3.16138i	0.272424	+	0.157284i
$405$	2.19930			0.109284
$406$	−3.46103	+	13.8210i	−0.171768	+	0.685927i
$407$	−24.7887			−1.22873
$408$	−6.33711	−	3.65873i	−0.313734	−	0.181134i
$409$	18.8936	−	10.9082i	0.934230	−	0.539378i	0.0460828	−	0.998938i	$-0.485326\pi$
$409$	18.8936	−	10.9082i	0.934230	−	0.539378i	0.888147	+	0.459560i	$0.151993\pi$
$410$	10.1163	+	17.5219i	0.499606	+	0.865343i
$411$	6.90268	−	11.9558i	0.340484	−	0.589736i
$412$	11.3929			0.561287
$413$	−7.43351	−	21.3529i	−0.365779	−	1.05071i
$414$		−	3.82018i		−	0.187751i
$415$	13.5068	−	23.3945i	0.663023	−	1.14839i
$416$	−0.514836	+	0.297241i	−0.0252419	+	0.0145734i
$417$	−0.368372	+	0.212679i	−0.0180392	+	0.0104150i
$418$	26.4358	+	15.2627i	1.29302	+	0.746525i
$419$	−0.0979001			−0.00478273			−0.00239137	−	0.999997i	$-0.500761\pi$
$419$	−0.0979001			−0.00478273			−0.00239137	+	0.999997i	$0.500761\pi$
$420$	−5.49532	+	1.91307i	−0.268144	+	0.0933481i
$421$			7.35008i			0.358221i	0.983829	+	0.179110i	$0.0573219\pi$
$421$			7.35008i			0.358221i	−0.983829	+	0.179110i	$0.942678\pi$
$422$	−9.46284	+	16.3901i	−0.460644	+	0.797859i
$423$	−7.67146	+	4.42912i	−0.372999	+	0.215351i
$424$	1.91441	−	1.10529i	0.0929720	−	0.0536774i
$425$	1.03357	+	0.596734i	0.0501357	+	0.0289459i
$426$	5.95717			0.288626
$427$	29.7254	+	25.6634i	1.43851	+	1.24194i
$428$	−0.220356			−0.0106513
$429$	1.43126	−	2.47902i	0.0691019	−	0.119688i
$430$	0.927062	+	1.60572i	0.0447069	+	0.0774346i
$431$	−10.3116	−	17.8602i	−0.496691	−	0.860294i	0.503302	−	0.864111i	$-0.332118\pi$
$431$	−10.3116	−	17.8602i	−0.496691	−	0.860294i	−0.999993	+	0.00381655i	$0.998785\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			24.1177i			1.15902i	0.814964	+	0.579512i	$0.196757\pi$
$433$			24.1177i			1.15902i	−0.814964	+	0.579512i	$0.803243\pi$
$434$	14.7620	+	2.81751i	0.708599	+	0.135245i
$435$	−10.5763	+	5.33020i	−0.507097	+	0.255563i
$436$	−1.66862	+	2.89013i	−0.0799123	+	0.138412i
$437$	−20.9733	+	12.1089i	−1.00329	+	0.579249i
$438$	13.8612	−	8.00279i	0.662316	−	0.382388i
$439$	7.01332	−	12.1474i	0.334727	−	0.579765i	−0.648705	−	0.761040i	$-0.724689\pi$
$439$	7.01332	−	12.1474i	0.334727	−	0.579765i	0.983432	+	0.181275i	$0.0580224\pi$
$440$	10.5900			0.504856
$441$	5.48671	−	4.34696i	0.261272	−	0.206998i
$442$	4.35010			0.206913
$443$	−27.3057	−	15.7650i	−1.29733	−	0.749016i	−0.317392	−	0.948295i	$-0.602807\pi$
$443$	−27.3057	−	15.7650i	−1.29733	−	0.749016i	−0.979943	+	0.199278i	$0.936140\pi$
$444$	−2.57403	−	4.45835i	−0.122158	−	0.211584i
$445$	5.69528	−	3.28817i	0.269982	−	0.155874i
$446$	−6.54240	−	3.77726i	−0.309792	−	0.178858i
$447$		−	14.8154i		−	0.700743i
$448$	2.59884	+	0.496020i	0.122784	+	0.0234347i
$449$			30.8736i			1.45702i	0.685038	+	0.728508i	$0.259786\pi$
$449$			30.8736i			1.45702i	−0.685038	+	0.728508i	$0.740214\pi$
$450$	0.141248	+	0.0815493i	0.00665848	+	0.00384427i
$451$	22.1486	+	38.3625i	1.04294	+	1.80642i
$452$	2.03972	−	1.17763i	0.0959405	−	0.0553912i
$453$	−10.8813	−	6.28229i	−0.511246	−	0.295168i
$454$		−	19.2865i		−	0.905158i
$455$	2.26055	−	2.61835i	0.105976	−	0.122750i
$456$			6.33946i			0.296872i
$457$	−10.3166	+	17.8689i	−0.482591	+	0.835873i	−0.999800	−	0.0199865i	$-0.993638\pi$
$457$	−10.3166	+	17.8689i	−0.482591	+	0.835873i	0.517209	+	0.855859i	$0.326971\pi$
$458$	9.34830	+	16.1917i	0.436817	+	0.756590i
$459$	3.65873	+	6.33711i	0.170775	+	0.295791i
$460$	−4.20085	+	7.27609i	−0.195866	+	0.339249i
$461$		−	14.0889i		−	0.656187i	−0.944645	−	0.328094i	$-0.893594\pi$
$461$		−	14.0889i		−	0.656187i	0.944645	−	0.328094i	$-0.106406\pi$
$462$	−12.0315	+	4.18848i	−0.559755	+	0.194866i
$463$	−18.6875			−0.868481			−0.434240	−	0.900797i	$-0.642983\pi$
$463$	−18.6875			−0.868481			−0.434240	+	0.900797i	$0.642983\pi$
$464$	5.37649	+	0.305592i	0.249597	+	0.0141868i
$465$	6.24625	+	10.8188i	0.289663	+	0.501711i
$466$	13.1220	−	7.57598i	0.607864	−	0.350950i
$467$	−28.4612	−	16.4321i	−1.31703	−	0.760385i	−0.333776	−	0.942652i	$-0.608323\pi$
$467$	−28.4612	−	16.4321i	−1.31703	−	0.760385i	−0.983249	+	0.182268i	$0.941656\pi$
$468$	0.594482			0.0274799
$469$	−9.75866	−	28.0319i	−0.450613	−	1.29439i
$470$	19.4819			0.898633
$471$	6.33439	−	10.9715i	0.291873	−	0.505539i
$472$	−7.40079	+	4.27285i	−0.340649	+	0.196674i
$473$	2.02972	+	3.51557i	0.0933265	+	0.161646i
$474$	−1.18751	−	0.685608i	−0.0545440	−	0.0314910i
$475$		−	1.03396i		−	0.0474412i
$476$	−14.6543	−	12.6518i	−0.671680	−	0.579894i
$477$	−2.21057			−0.101215
$478$	−11.4636	−	6.61852i	−0.524334	−	0.302724i
$479$	34.1441	−	19.7131i	1.56008	−	0.900715i	0.562836	−	0.826569i	$-0.309710\pi$
$479$	34.1441	−	19.7131i	1.56008	−	0.900715i	0.997247	−	0.0741458i	$-0.0236230\pi$
$480$	1.09965	+	1.90465i	0.0501918	+	0.0869348i
$481$	2.65040	+	1.53021i	0.120848	+	0.0697717i
$482$		−	4.93765i		−	0.224904i
$483$	1.89488	−	9.92803i	0.0862202	−	0.451741i
$484$	12.1857			0.553897
$485$	14.0665	+	8.12131i	0.638728	+	0.368770i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−10.8732	−	18.8330i	−0.492714	−	0.853406i	0.507251	−	0.861798i	$-0.330662\pi$
$487$	−10.8732	−	18.8330i	−0.492714	−	0.853406i	−0.999965	+	0.00839286i	$0.997328\pi$
$488$	7.42151	−	12.8544i	0.335956	−	0.581893i
$489$	−3.78882			−0.171336
$490$	−15.2304	+	2.24597i	−0.688037	+	0.101462i
$491$			1.51305i			0.0682831i	0.999417	+	0.0341415i	$0.0108697\pi$
$491$			1.51305i			0.0682831i	−0.999417	+	0.0341415i	$0.989130\pi$
$492$	−4.59977	+	7.96703i	−0.207374	+	0.359182i
$493$	−32.9533	−	21.6077i	−1.48414	−	0.973162i
$494$	−1.88435	−	3.26378i	−0.0847807	−	0.146845i
$495$	−9.17117	−	5.29498i	−0.412213	−	0.237991i
$496$		−	5.68023i		−	0.255050i
$497$	15.4817	+	2.95487i	0.694450	+	0.132544i
$498$	12.2828			0.550407
$499$	3.46991	−	6.01005i	0.155334	−	0.269047i	−0.777846	−	0.628454i	$-0.783688\pi$
$499$	3.46991	−	6.01005i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$500$	−5.67759	−	9.83387i	−0.253910	−	0.439784i
$501$	−5.42872	+	3.13427i	−0.242537	+	0.140029i
$502$	−3.79766	+	6.57774i	−0.169498	+	0.293579i
$503$		−	28.4017i		−	1.26637i	−0.774002	−	0.633184i	$-0.781748\pi$
$503$		−	28.4017i		−	1.26637i	0.774002	−	0.633184i	$-0.218252\pi$
$504$	−2.00265	−	1.72899i	−0.0892052	−	0.0770151i
$505$			13.9056i			0.618791i
$506$	−9.19738	+	15.9303i	−0.408873	+	0.708189i
$507$	10.9523	−	6.32330i	0.486407	−	0.280827i
$508$	−0.188886	+	0.109054i	−0.00838048	+	0.00483847i
$509$	9.94763	−	17.2298i	0.440921	−	0.763697i	−0.556837	−	0.830622i	$-0.687985\pi$
$509$	9.94763	−	17.2298i	0.440921	−	0.763697i	0.997758	+	0.0669244i	$0.0213186\pi$
$510$		−	16.0933i		−	0.712622i
$511$	39.9927	−	13.9225i	1.76917	−	0.615896i
$512$		−	1.00000i		−	0.0441942i
$513$	3.16973	−	5.49013i	0.139947	−	0.242395i
$514$	−20.2424	+	11.6870i	−0.892854	+	0.515489i
$515$	12.5282	+	21.6994i	0.552057	+	0.956190i
$516$	−0.421527	+	0.730106i	−0.0185567	+	0.0321411i
$517$	42.6538			1.87591
$518$	−4.47805	−	12.8633i	−0.196754	−	0.565181i
$519$			15.4617i			0.678691i
$520$	−1.13228	−	0.653720i	−0.0496536	−	0.0286675i
$521$	8.50149	+	14.7250i	0.372457	+	0.645115i	0.989943	−	0.141467i	$-0.0451820\pi$
$521$	8.50149	+	14.7250i	0.372457	+	0.645115i	−0.617486	+	0.786582i	$0.711849\pi$
$522$	−4.50338	−	2.95289i	−0.197108	−	0.129245i
$523$	−3.92688	+	6.80155i	−0.171710	+	0.297411i	−0.939018	−	0.343868i	$-0.888263\pi$
$523$	−3.92688	+	6.80155i	−0.171710	+	0.297411i	0.767308	+	0.641279i	$0.221596\pi$
$524$		−	3.47211i		−	0.151680i
$525$	0.326630	+	0.281995i	0.0142553	+	0.0123073i
$526$	29.8366			1.30094
$527$	−20.7824	+	35.9962i	−0.905297	+	1.56802i
$528$	2.40758	+	4.17005i	0.104776	+	0.181478i
$529$	4.20312	+	7.28002i	0.182744	+	0.316523i
$530$	4.21036	+	2.43085i	0.182886	+	0.105589i
$531$	8.54569			0.370852
$532$	−3.14450	+	16.4752i	−0.136331	+	0.714292i
$533$		−	5.46896i		−	0.236887i
$534$	2.58959	+	1.49510i	0.112063	+	0.0646994i
$535$	−0.242314	−	0.419700i	−0.0104761	−	0.0181452i
$536$	−9.71571	+	5.60937i	−0.419655	+	0.242288i
$537$	−1.95034	−	1.12603i	−0.0841636	−	0.0485919i
$538$	−0.537477			−0.0231723
$539$	−33.3455	+	4.91734i	−1.43629	+	0.211805i
$540$		−	2.19930i		−	0.0946426i
$541$	−27.7397	−	16.0156i	−1.19262	−	0.688562i	−0.233724	−	0.972303i	$-0.575091\pi$
$541$	−27.7397	−	16.0156i	−1.19262	−	0.688562i	−0.958901	+	0.283741i	$0.908425\pi$
$542$	10.2055	+	17.6764i	0.438363	+	0.759267i
$543$	6.52413	−	3.76671i	0.279977	−	0.161645i
$544$	−3.65873	+	6.33711i	−0.156867	+	0.271701i
$545$	−7.33957			−0.314392
$546$	1.54496	+	0.294875i	0.0661183	+	0.0126195i
$547$	−26.3098			−1.12492			−0.562462	−	0.826823i	$-0.690146\pi$
$547$	−26.3098			−1.12492			−0.562462	+	0.826823i	$0.690146\pi$
$548$	−11.9558	−	6.90268i	−0.510726	−	0.294868i
$549$	−12.8544	+	7.42151i	−0.548614	+	0.316742i
$550$	−0.392673	−	0.680129i	−0.0167436	−	0.0290008i
$551$	−1.93729	+	34.0840i	−0.0825312	+	1.45203i
$552$	−3.82018			−0.162598
$553$	−2.74607	−	2.37081i	−0.116775	−	0.100817i
$554$		−	1.31877i		−	0.0560293i
$555$	5.66105	−	9.80522i	0.240298	−	0.416208i
$556$	0.212679	+	0.368372i	0.00901962	+	0.0156224i
$557$	−1.32808	−	2.30031i	−0.0562727	−	0.0974672i	0.836517	−	0.547941i	$-0.184588\pi$
$557$	−1.32808	−	2.30031i	−0.0562727	−	0.0974672i	−0.892789	+	0.450474i	$0.851255\pi$
$558$	−2.84011	+	4.91922i	−0.120232	+	0.208247i
$559$		−	0.501180i		−	0.0211976i
$560$	1.91307	+	5.49532i	0.0808418	+	0.232219i
$561$		−	35.2347i		−	1.48761i
$562$	26.9129	+	15.5382i	1.13525	+	0.655438i
$563$	6.94323	−	4.00868i	0.292622	−	0.168946i	−0.346502	−	0.938049i	$-0.612630\pi$
$563$	6.94323	−	4.00868i	0.292622	−	0.168946i	0.639124	+	0.769104i	$0.279297\pi$
$564$	4.42912	+	7.67146i	0.186500	+	0.323027i
$565$	4.48595	+	2.58997i	0.188725	+	0.108961i
$566$			32.8725i			1.38174i
$567$	0.869854	+	2.49867i	0.0365304	+	0.104934i
$568$		−	5.95717i		−	0.249957i
$569$	15.7831	+	9.11237i	0.661661	+	0.382010i	0.792910	−	0.609339i	$-0.208565\pi$
$569$	15.7831	+	9.11237i	0.661661	+	0.382010i	−0.131248	+	0.991350i	$0.541899\pi$
$570$	−12.0744	+	6.97117i	−0.505742	+	0.291990i
$571$	−5.13597	−	8.89576i	−0.214934	−	0.372276i	0.738318	−	0.674452i	$-0.235620\pi$
$571$	−5.13597	−	8.89576i	−0.214934	−	0.372276i	−0.953252	+	0.302176i	$0.902287\pi$
$572$	−2.47902	−	1.43126i	−0.103653	−	0.0598440i
$573$	−4.19182			−0.175116
$574$	−15.9059	+	18.4235i	−0.663898	+	0.768981i
$575$	0.623066			0.0259836
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.72202	−	1.57156i	0.113319	−	0.0654249i	−0.442269	−	0.896882i	$-0.645826\pi$
$577$	2.72202	−	1.57156i	0.113319	−	0.0654249i	0.555588	+	0.831457i	$0.312493\pi$
$578$	31.6492	−	18.2727i	1.31643	−	0.760042i
$579$	7.97072	−	13.8057i	0.331252	−	0.573745i
$580$	5.33020	+	10.5763i	0.221324	+	0.439159i
$581$	31.9211	+	6.09253i	1.32431	+	0.252761i
$582$			7.38538i			0.306134i
$583$	9.21819	+	5.32212i	0.381778	+	0.220420i
$584$	−8.00279	−	13.8612i	−0.331158	−	0.573582i
$585$	0.653720	+	1.13228i	0.0270280	+	0.0468139i
$586$	0.0481260	−	0.0833566i	0.00198807	−	0.00344343i
$587$	10.4362			0.430746			0.215373	−	0.976532i	$-0.430903\pi$
$587$	10.4362			0.430746			0.215373	+	0.976532i	$0.430903\pi$
$588$	−4.34696	−	5.48671i	−0.179265	−	0.226268i
$589$	36.0096			1.48375
$590$	−16.2765	−	9.39725i	−0.670094	−	0.386879i
$591$	14.9563	−	8.63501i	0.615219	−	0.355197i
$592$	−4.45835	+	2.57403i	−0.183237	+	0.105792i
$593$	7.91664	−	13.7120i	0.325098	−	0.563085i	−0.656435	−	0.754383i	$-0.727936\pi$
$593$	7.91664	−	13.7120i	0.325098	−	0.563085i	0.981532	+	0.191298i	$0.0612695\pi$
$594$		−	4.81516i		−	0.197568i
$595$	7.98258	−	41.8238i	0.327254	−	1.71461i
$596$	−14.8154			−0.606861
$597$	12.4995	+	7.21660i	0.511571	+	0.295356i
$598$	1.96677	−	1.13551i	0.0804270	−	0.0464346i
$599$	−9.06748	+	5.23511i	−0.370487	+	0.213901i	−0.673671	−	0.739031i	$-0.735284\pi$
$599$	−9.06748	+	5.23511i	−0.370487	+	0.213901i	0.303184	+	0.952932i	$0.401950\pi$
$600$	0.0815493	−	0.141248i	0.00332924	−	0.00576641i
$601$		−	13.3306i		−	0.543766i	−0.962330	−	0.271883i	$-0.912354\pi$
$601$		−	13.3306i		−	0.543766i	0.962330	−	0.271883i	$-0.0876464\pi$
$602$	−1.45763	+	1.68834i	−0.0594084	+	0.0688117i
$603$	11.2187			0.456862
$604$	−6.28229	+	10.8813i	−0.255623	+	0.442752i
$605$	13.4000	+	23.2095i	0.544788	+	0.943600i
$606$	−5.47566	+	3.16138i	−0.222434	+	0.128422i
$607$	−31.6093	−	18.2496i	−1.28298	−	0.740730i	−0.305589	−	0.952163i	$-0.598853\pi$
$607$	−31.6093	−	18.2496i	−1.28298	−	0.740730i	−0.977392	+	0.211433i	$0.932187\pi$
$608$	6.33946			0.257099
$609$	−10.2389	−	9.90786i	−0.414900	−	0.401487i
$610$	32.6442			1.32172
$611$	−4.56054	−	2.63303i	−0.184500	−	0.106521i
$612$	6.33711	−	3.65873i	0.256163	−	0.147896i
$613$	−13.5539	−	23.4760i	−0.547436	−	0.948187i	−0.998449	−	0.0556695i	$-0.982271\pi$
$613$	−13.5539	−	23.4760i	−0.547436	−	0.948187i	0.451013	−	0.892517i	$-0.351063\pi$
$614$	−5.77158	+	9.99666i	−0.232922	+	0.403432i
$615$	−20.2325			−0.815853
$616$	4.18848	+	12.0315i	0.168759	+	0.484762i
$617$			22.4580i			0.904124i	0.891987	+	0.452062i	$0.149311\pi$
$617$			22.4580i			0.904124i	−0.891987	+	0.452062i	$0.850689\pi$
$618$	−5.69644	+	9.86652i	−0.229144	+	0.396890i
$619$	−19.2527	+	11.1155i	−0.773831	+	0.446772i	−0.834240	−	0.551402i	$-0.814093\pi$
$619$	−19.2527	+	11.1155i	−0.773831	+	0.446772i	0.0604084	+	0.998174i	$0.480760\pi$
$620$	10.8188	−	6.24625i	0.434494	−	0.250855i
$621$	3.30837	+	1.91009i	0.132760	+	0.0766492i
$622$	−24.5954			−0.986184
$623$	5.98834	+	5.17002i	0.239918	+	0.207132i
$624$		−	0.594482i		−	0.0237983i
$625$	12.0790	−	20.9214i	0.483158	−	0.836854i
$626$	−26.8593	+	15.5072i	−1.07351	+	0.619793i
$627$	−26.4358	+	15.2627i	−1.05575	+	0.609535i
$628$	−10.9715	−	6.33439i	−0.437810	−	0.252769i
$629$	37.6707			1.50203
$630$	1.09089	−	5.71562i	0.0434623	−	0.227716i
$631$	−9.95203			−0.396184			−0.198092	−	0.980183i	$-0.563474\pi$
$631$	−9.95203			−0.396184			−0.198092	+	0.980183i	$0.563474\pi$
$632$	−0.685608	+	1.18751i	−0.0272720	+	0.0472365i
$633$	−9.46284	−	16.3901i	−0.376114	−	0.651449i
$634$	8.00240	+	13.8606i	0.317816	+	0.550473i
$635$	−0.415417	−	0.239841i	−0.0164853	−	0.00951781i
$636$			2.21057i			0.0876549i
$637$	3.86884	+	1.53266i	0.153289	+	0.0607263i
$638$	11.6700	+	23.1559i	0.462019	+	0.916753i
$639$	−2.97858	+	5.15906i	−0.117831	+	0.204089i
$640$	1.90465	−	1.09965i	0.0752877	−	0.0434674i
$641$	37.3377	−	21.5569i	1.47475	−	0.851448i	0.475156	−	0.879902i	$-0.342392\pi$
$641$	37.3377	−	21.5569i	1.47475	−	0.851448i	0.999595	+	0.0284535i	$0.00905824\pi$
$642$	0.110178	−	0.190834i	0.00434837	−	0.00753161i
$643$	40.8857			1.61237			0.806187	−	0.591661i	$-0.201527\pi$
$643$	40.8857			1.61237			0.806187	+	0.591661i	$0.201527\pi$
$644$	−9.92803	−	1.89488i	−0.391219	−	0.0746689i
$645$	−1.85412			−0.0730061
$646$	−40.1739	−	23.1944i	−1.58062	−	0.912571i
$647$	13.6476	+	23.6383i	0.536541	+	0.929316i	0.999087	+	0.0427211i	$0.0136027\pi$
$647$	13.6476	+	23.6383i	0.536541	+	0.929316i	−0.462546	+	0.886595i	$0.653064\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−35.6359	−	20.5744i	−1.39883	−	0.807617i
$650$			0.0969592i			0.00380305i
$651$	−9.82103	+	11.3755i	−0.384917	+	0.445842i
$652$			3.78882i			0.148382i
$653$	29.7105	+	17.1533i	1.16266	+	0.671262i	0.951940	−	0.306284i	$-0.0990857\pi$
$653$	29.7105	+	17.1533i	1.16266	+	0.671262i	0.210720	+	0.977546i	$0.432419\pi$
$654$	−1.66862	−	2.89013i	−0.0652481	−	0.113013i
$655$	6.61314	−	3.81810i	0.258397	−	0.149185i
$656$	7.96703	+	4.59977i	0.311060	+	0.179591i
$657$			16.0056i			0.624437i
$658$	7.70537	+	22.1338i	0.300387	+	0.862866i
$659$		−	0.359595i		−	0.0140078i	−0.999975	−	0.00700392i	$-0.997771\pi$
$659$		−	0.359595i		−	0.0140078i	0.999975	−	0.00700392i	$-0.00222944\pi$
$660$	−5.29498	+	9.17117i	−0.206107	+	0.356987i
$661$	−12.8208	−	22.2064i	−0.498673	−	0.863727i	0.501326	−	0.865259i	$-0.332846\pi$
$661$	−12.8208	−	22.2064i	−0.498673	−	0.863727i	−0.999999	+	0.00153143i	$0.999513\pi$
$662$	−1.36892	−	2.37104i	−0.0532045	−	0.0921529i
$663$	−2.17505	+	3.76730i	−0.0844719	+	0.146310i
$664$		−	12.2828i		−	0.476667i
$665$	−34.8373	+	12.1278i	−1.35093	+	0.470296i
$666$	5.14805			0.199483
$667$	−20.5391	−	1.16742i	−0.795279	−	0.0452025i
$668$	3.13427	+	5.42872i	0.121269	+	0.210043i
$669$	6.54240	−	3.77726i	0.252944	−	0.146037i
$670$	−21.3677	−	12.3367i	−0.825507	−	0.476607i
$671$	71.4715			2.75912
$672$	−1.72899	+	2.00265i	−0.0666971	+	0.0772539i
$673$	24.5495			0.946312			0.473156	−	0.880979i	$-0.343115\pi$
$673$	24.5495			0.946312			0.473156	+	0.880979i	$0.343115\pi$
$674$	8.61200	−	14.9164i	0.331722	−	0.574559i
$675$	−0.141248	+	0.0815493i	−0.00543662	+	0.00313884i
$676$	−6.32330	−	10.9523i	−0.243204	−	0.421241i
$677$	−41.9508	−	24.2203i	−1.61230	−	0.930861i	−0.988836	−	0.149008i	$-0.952392\pi$
$677$	−41.9508	−	24.2203i	−1.61230	−	0.930861i	−0.623463	−	0.781853i	$-0.714275\pi$
$678$			2.35527i			0.0904535i
$679$	−3.66329	+	19.1934i	−0.140584	+	0.736575i
$680$	−16.0933			−0.617149
$681$	16.7026	+	9.64323i	0.640044	+	0.369529i
$682$	23.6868	−	13.6756i	0.907015	−	0.523666i
$683$	6.86776	+	11.8953i	0.262788	+	0.455162i	0.966982	−	0.254846i	$-0.0820248\pi$
$683$	6.86776	+	11.8953i	0.262788	+	0.455162i	−0.704194	+	0.710008i	$0.748691\pi$
$684$	−5.49013	−	3.16973i	−0.209920	−	0.121198i
$685$		−	30.3621i		−	1.16008i
$686$	−8.57552	−	16.4152i	−0.327415	−	0.626737i
$687$	−18.6966			−0.713320
$688$	0.730106	+	0.421527i	0.0278350	+	0.0160706i
$689$	−0.657072	−	1.13808i	−0.0250325	−	0.0433575i
$690$	−4.20085	−	7.27609i	−0.159924	−	0.276996i
$691$	0.0388295	−	0.0672547i	0.00147714	−	0.00255849i	−0.865286	−	0.501279i	$-0.832863\pi$
$691$	0.0388295	−	0.0672547i	0.00147714	−	0.00255849i	0.866763	+	0.498720i	$0.166196\pi$
$692$	15.4617			0.587764
$693$	2.38841	−	12.5138i	0.0907283	−	0.475361i
$694$		−	2.76845i		−	0.105089i
$695$	−0.467745	+	0.810158i	−0.0177426	+	0.0307310i
$696$	−2.95289	+	4.50338i	−0.111929	+	0.170700i
$697$	−33.6587	−	58.2985i	−1.27491	−	2.20821i
$698$	0.585847	+	0.338239i	0.0221746	+	0.0128025i
$699$			15.1520i			0.573100i
$700$	0.281995	−	0.326630i	0.0106584	−	0.0123454i
$701$	27.7163			1.04683			0.523416	−	0.852077i	$-0.324658\pi$
$701$	27.7163			1.04683			0.523416	+	0.852077i	$0.324658\pi$
$702$	−0.297241	+	0.514836i	−0.0112186	+	0.0194312i
$703$	−16.3179	−	28.2635i	−0.615443	−	1.06598i
$704$	4.17005	−	2.40758i	0.157165	−	0.0907390i
$705$	−9.74094	+	16.8718i	−0.366865	+	0.635429i
$706$		−	6.73229i		−	0.253373i
$707$	−15.7985	+	5.49987i	−0.594163	+	0.206844i
$708$		−	8.54569i		−	0.321167i
$709$	5.17825	−	8.96899i	0.194473	−	0.336837i	−0.752255	−	0.658873i	$-0.771034\pi$
$709$	5.17825	−	8.96899i	0.194473	−	0.336837i	0.946728	+	0.322035i	$0.104367\pi$
$710$	11.3463	−	6.55079i	0.425819	−	0.245847i
$711$	1.18751	−	0.685608i	0.0445350	−	0.0257123i
$712$	1.49510	−	2.58959i	0.0560313	−	0.0970491i
$713$			21.6995i			0.812652i
$714$	18.2839	−	6.36513i	0.684259	−	0.238209i
$715$		−	6.29553i		−	0.235440i
$716$	−1.12603	+	1.95034i	−0.0420818	+	0.0728878i
$717$	11.4636	−	6.61852i	0.428117	−	0.247173i
$718$	−12.2099	−	21.1481i	−0.455668	−	0.789240i
$719$	5.10322	−	8.83904i	0.190318	−	0.329641i	−0.755038	−	0.655682i	$-0.772381\pi$
$719$	5.10322	−	8.83904i	0.190318	−	0.329641i	0.945356	+	0.326041i	$0.105715\pi$
$720$	−2.19930			−0.0819629
$721$	−19.6981	+	22.8160i	−0.733596	+	0.849711i
$722$			21.1887i			0.788564i
$723$	4.27613	+	2.46882i	0.159031	+	0.0918166i
$724$	−3.76671	−	6.52413i	−0.139989	−	0.242467i
$725$	0.481613	−	0.734495i	0.0178867	−	0.0272785i
$726$	−6.09286	+	10.5531i	−0.226127	+	0.391664i
$727$		−	5.51741i		−	0.204629i	−0.994752	−	0.102315i	$-0.967375\pi$
$727$		−	5.51741i		−	0.204629i	0.994752	−	0.102315i	$-0.0326249\pi$
$728$	0.294875	−	1.54496i	0.0109288	−	0.0572601i
$729$	−1.00000			−0.0370370
$730$	17.6005	−	30.4850i	0.651424	−	1.12830i
$731$	−3.08451	−	5.34252i	−0.114085	−	0.197600i
$732$	7.42151	+	12.8544i	0.274307	+	0.475113i
$733$	18.4472	+	10.6505i	0.681365	+	0.393386i	0.800369	−	0.599508i	$-0.204637\pi$
$733$	18.4472	+	10.6505i	0.681365	+	0.393386i	−0.119004	+	0.992894i	$0.537970\pi$
$734$	2.30585			0.0851105
$735$	5.67012	−	14.3129i	0.209145	−	0.527938i
$736$			3.82018i			0.140814i
$737$	−46.7827	−	27.0100i	−1.72326	−	0.994925i
$738$	−4.59977	−	7.96703i	−0.169320	−	0.293271i
$739$	34.0872	−	19.6802i	1.25392	−	0.723949i	0.282031	−	0.959405i	$-0.408992\pi$
$739$	34.0872	−	19.6802i	1.25392	−	0.723949i	0.971885	+	0.235456i	$0.0756585\pi$
$740$	−9.80522	−	5.66105i	−0.360447	−	0.208104i
$741$	3.76869			0.138446
$742$	−1.09649	+	5.74492i	−0.0402533	+	0.210903i
$743$			13.6231i			0.499781i	0.968274	+	0.249891i	$0.0803947\pi$
$743$			13.6231i			0.499781i	−0.968274	+	0.249891i	$0.919605\pi$
$744$	4.91922	+	2.84011i	0.180347	+	0.104124i
$745$	−16.2917	−	28.2180i	−0.596881	−	1.03383i
$746$	−8.16120	+	4.71187i	−0.298803	+	0.172514i
$747$	−6.14142	+	10.6373i	−0.224703	+	0.389197i
$748$	−35.2347			−1.28831
$749$	0.380992	−	0.441296i	0.0139211	−	0.0161246i
$750$	11.3552			0.414633
$751$	12.0272	+	6.94389i	0.438878	+	0.253386i	0.703121	−	0.711070i	$-0.251789\pi$
$751$	12.0272	+	6.94389i	0.438878	+	0.253386i	−0.264244	+	0.964456i	$0.585122\pi$
$752$	7.67146	−	4.42912i	0.279749	−	0.161513i
$753$	−3.79766	−	6.57774i	−0.138394	−	0.239706i
$754$	0.181669	−	3.19622i	0.00661599	−	0.116400i
$755$	−27.6332			−1.00568
$756$	2.49867	−	0.869854i	0.0908758	−	0.0316363i
$757$			41.6790i			1.51485i	0.652922	+	0.757425i	$0.273543\pi$
$757$			41.6790i			1.51485i	−0.652922	+	0.757425i	$0.726457\pi$
$758$	15.6213	−	27.0568i	0.567390	−	0.982748i
$759$	−9.19738	−	15.9303i	−0.333844	−	0.578234i
$760$	6.97117	+	12.0744i	0.252871	+	0.437985i
$761$	−9.59660	+	16.6218i	−0.347876	+	0.602540i	−0.985872	−	0.167500i	$-0.946430\pi$
$761$	−9.59660	+	16.6218i	−0.347876	+	0.602540i	0.637996	+	0.770040i	$0.279764\pi$
$762$		−	0.218107i		−	0.00790120i
$763$	−2.90291	−	8.33865i	−0.105092	−	0.301879i
$764$			4.19182i			0.151655i
$765$	13.9372	+	8.04664i	0.503900	+	0.290927i
$766$	26.3529	−	15.2148i	0.952168	−	0.549734i
$767$	2.54013	+	4.39963i	0.0917188	+	0.158862i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$			35.9710i			1.29715i	0.761152	+	0.648574i	$0.224634\pi$
$769$			35.9710i			1.29715i	−0.761152	+	0.648574i	$0.775366\pi$
$770$	−18.3099	+	21.2080i	−0.659842	+	0.764282i
$771$		−	23.3739i		−	0.841791i
$772$	−13.8057	−	7.97072i	−0.496877	−	0.286872i
$773$	−17.0590	+	9.84902i	−0.613570	+	0.354245i	−0.774361	−	0.632744i	$-0.781929\pi$
$773$	−17.0590	+	9.84902i	−0.613570	+	0.354245i	0.160792	+	0.986988i	$0.448595\pi$
$774$	−0.421527	−	0.730106i	−0.0151515	−	0.0262431i
$775$	−0.802319	−	0.463219i	−0.0288201	−	0.0166393i
$776$	7.38538			0.265120
$777$	13.3790	+	2.55354i	0.479968	+	0.0916076i
$778$	−10.6220			−0.380818
$779$	−29.1601	+	50.5067i	−1.04477	+	1.80959i
$780$	1.13228	−	0.653720i	0.0405420	−	0.0234069i
$781$	24.8417	−	14.3423i	0.888905	−	0.513209i
$782$	13.9770	−	24.2089i	0.499817	−	0.865708i
$783$	4.80897	−	2.42359i	0.171859	−	0.0866122i
$784$	−5.48671	+	4.34696i	−0.195954	+	0.155248i
$785$		−	27.8624i		−	0.994451i
$786$	3.00694	+	1.73606i	0.107254	+	0.0619231i
$787$	−4.41594	−	7.64863i	−0.157411	−	0.272644i	0.776523	−	0.630089i	$-0.216981\pi$
$787$	−4.41594	−	7.64863i	−0.157411	−	0.272644i	−0.933934	+	0.357445i	$0.883648\pi$
$788$	−8.63501	−	14.9563i	−0.307610	−	0.532795i
$789$	−14.9183	+	25.8393i	−0.531106	+	0.919903i
$790$	−3.01571			−0.107294
$791$	−1.16826	+	6.12096i	−0.0415385	+	0.217636i
$792$	−4.81516			−0.171099
$793$	−7.64172	−	4.41195i	−0.271366	−	0.156673i
$794$	−23.5250	+	13.5822i	−0.834871	+	0.482013i
$795$	−4.21036	+	2.43085i	−0.149326	+	0.0862134i
$796$	7.21660	−	12.4995i	0.255785	−	0.443033i
$797$		−	41.7705i		−	1.47959i	−0.672834	−	0.739794i	$-0.734923\pi$
$797$		−	41.7705i		−	1.47959i	0.672834	−	0.739794i	$-0.265077\pi$
$798$	−12.6957	−	10.9608i	−0.449424	−	0.388009i
$799$	−64.8199			−2.29316
$800$	−0.141248	−	0.0815493i	−0.00499386	−	0.00288320i
$801$	−2.58959	+	1.49510i	−0.0914988	+	0.0528268i
$802$	31.7496	−	18.3307i	1.12112	−	0.647278i
$803$	38.5347	−	66.7440i	1.35986	−	2.35535i
$804$		−	11.2187i		−	0.395654i
$805$	−7.30825	−	20.9931i	−0.257582	−	0.739909i
$806$	−3.37679			−0.118942
$807$	0.268738	−	0.465468i	0.00946004	−	0.0163853i
$808$	3.16138	+	5.47566i	0.111217	+	0.192633i
$809$	−32.5186	+	18.7746i	−1.14329	+	0.660081i	−0.947244	−	0.320513i	$-0.896145\pi$
$809$	−32.5186	+	18.7746i	−1.14329	+	0.660081i	−0.196050	+	0.980594i	$0.562811\pi$
$810$	1.90465	+	1.09965i	0.0669224	+	0.0386377i
$811$	39.0441			1.37102			0.685512	−	0.728062i	$-0.259579\pi$
$811$	39.0441			1.37102			0.685512	+	0.728062i	$0.259579\pi$
$812$	−9.90786	+	10.2389i	−0.347698	+	0.359314i
$813$	−20.4110			−0.715844
$814$	−21.4676	−	12.3943i	−0.752440	−	0.434421i
$815$	−7.21635	+	4.16636i	−0.252778	+	0.145941i
$816$	−3.65873	−	6.33711i	−0.128081	−	0.221843i
$817$	−2.67225	+	4.62848i	−0.0934903	+	0.161930i
$818$	21.8165			0.762795
$819$	−1.02785	+	1.19054i	−0.0359160	+	0.0416008i
$820$			20.2325i			0.706550i
$821$	20.5571	−	35.6060i	0.717448	−	1.24266i	−0.244560	−	0.969634i	$-0.578643\pi$
$821$	20.5571	−	35.6060i	0.717448	−	1.24266i	0.962008	−	0.273022i	$-0.0880233\pi$
$822$	11.9558	−	6.90268i	0.417006	−	0.240759i
$823$	−39.2672	+	22.6710i	−1.36877	+	0.790260i	−0.990771	−	0.135546i	$-0.956721\pi$
$823$	−39.2672	+	22.6710i	−1.36877	+	0.790260i	−0.377999	+	0.925806i	$0.623388\pi$
$824$	9.86652	+	5.69644i	0.343717	+	0.198445i
$825$	0.785346			0.0273422
$826$	4.23883	−	22.2089i	0.147488	−	0.772746i
$827$			4.37760i			0.152224i	0.997099	+	0.0761120i	$0.0242506\pi$
$827$			4.37760i			0.152224i	−0.997099	+	0.0761120i	$0.975749\pi$
$828$	1.91009	−	3.30837i	0.0663802	−	0.114974i
$829$	−32.2022	+	18.5919i	−1.11843	+	0.645725i	−0.940999	−	0.338409i	$-0.890111\pi$
$829$	−32.2022	+	18.5919i	−1.11843	+	0.645725i	−0.177429	+	0.984134i	$0.556778\pi$
$830$	23.3945	−	13.5068i	0.812034	−	0.468828i
$831$	1.14209	+	0.659387i	0.0396187	+	0.0228739i
$832$	−0.594482			−0.0206099
$833$	50.6742	−	7.47275i	1.75576	−	0.258915i
$834$	−0.425359			−0.0147290
$835$	−6.89319	+	11.9394i	−0.238549	+	0.413178i
$836$	15.2627	+	26.4358i	0.527873	+	0.914303i
$837$	−2.84011	−	4.91922i	−0.0981687	−	0.170033i
$838$	−0.0847839	−	0.0489500i	−0.00292881	−	0.00169095i
$839$			37.3737i			1.29028i	0.764063	+	0.645142i	$0.223202\pi$
$839$			37.3737i			1.29028i	−0.764063	+	0.645142i	$0.776798\pi$
$840$	−5.71562	−	1.09089i	−0.197207	−	0.0376394i
$841$	−17.2524	+	23.3100i	−0.594910	+	0.803792i
$842$	−3.67504	+	6.36535i	−0.126650	+	0.219365i
$843$	−26.9129	+	15.5382i	−0.926929	+	0.535163i
$844$	−16.3901	+	9.46284i	−0.564171	+	0.325724i
$845$	13.9068	−	24.0873i	0.478408	−	0.828628i
$846$	−8.85824			−0.304553
$847$	−21.0689	+	24.4038i	−0.723937	+	0.838523i
$848$	2.21057			0.0759113
$849$	−28.4685	−	16.4363i	−0.977035	−	0.564091i
$850$	0.596734	+	1.03357i	0.0204678	+	0.0354513i
$851$	17.0317	−	9.83324i	0.583838	−	0.337079i
$852$	5.15906	+	2.97858i	0.176746	+	0.102045i
$853$		−	20.8969i		−	0.715495i	−0.933818	−	0.357748i	$-0.883545\pi$
$853$		−	20.8969i		−	0.715495i	0.933818	−	0.357748i	$-0.116455\pi$
$854$	12.9113	+	37.0878i	0.441814	+	1.26912i
$855$		−	13.9423i		−	0.476818i
$856$	−0.190834	−	0.110178i	−0.00652256	−	0.00376580i
$857$	9.60532	+	16.6369i	0.328112	+	0.568306i	0.982137	−	0.188166i	$-0.0602545\pi$
$857$	9.60532	+	16.6369i	0.328112	+	0.568306i	−0.654026	+	0.756472i	$0.726921\pi$
$858$	2.47902	−	1.43126i	0.0846322	−	0.0488624i
$859$	19.1511	+	11.0569i	0.653428	+	0.377257i	0.789769	−	0.613405i	$-0.210201\pi$
$859$	19.1511	+	11.0569i	0.653428	+	0.377257i	−0.136340	+	0.990662i	$0.543534\pi$
$860$			1.85412i			0.0632251i
$861$	−8.00225	−	22.9866i	−0.272716	−	0.783382i
$862$		−	20.6232i		−	0.702427i
$863$	−13.0635	+	22.6266i	−0.444686	+	0.770218i	−0.998030	−	0.0627342i	$-0.980018\pi$
$863$	−13.0635	+	22.6266i	−0.444686	+	0.770218i	0.553345	+	0.832952i	$0.313351\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	17.0024	+	29.4490i	0.578098	+	1.00130i
$866$	−12.0589	+	20.8866i	−0.409777	+	0.709754i
$867$			36.5453i			1.24114i
$868$	11.3755	+	9.82103i	0.386110	+	0.333348i
$869$	−6.60262			−0.223978
$870$	−11.8245	−	0.672087i	−0.400888	−	0.0227859i
$871$	3.33467	+	5.77581i	0.112991	+	0.195706i
$872$	−2.89013	+	1.66862i	−0.0978721	+	0.0565065i
$873$	−6.39592	−	3.69269i	−0.216469	−	0.124979i
$874$	−24.2179			−0.819181
$875$	29.5103	+	5.63239i	0.997630	+	0.190410i
$876$	16.0056			0.540779
$877$	−25.4202	+	44.0290i	−0.858378	+	1.48675i	0.0150975	+	0.999886i	$0.495194\pi$
$877$	−25.4202	+	44.0290i	−0.858378	+	1.48675i	−0.873475	+	0.486868i	$0.838139\pi$
$878$	12.1474	−	7.01332i	0.409956	−	0.236688i
$879$	0.0481260	+	0.0833566i	0.00162325	+	0.00281155i
$880$	9.17117	+	5.29498i	0.309160	+	0.178494i
$881$			44.8685i			1.51166i	0.654770	+	0.755829i	$0.272766\pi$
$881$			44.8685i			1.51166i	−0.654770	+	0.755829i	$0.727234\pi$
$882$	6.92511	−	1.02122i	0.233180	−	0.0343863i
$883$	5.97292			0.201005			0.100502	−	0.994937i	$-0.467955\pi$
$883$	5.97292			0.201005			0.100502	+	0.994937i	$0.467955\pi$
$884$	3.76730	+	2.17505i	0.126708	+	0.0731548i
$885$	16.2765	−	9.39725i	0.547129	−	0.315885i
$886$	−15.7650	−	27.3057i	−0.529635	−	0.917354i
$887$	25.3985	+	14.6638i	0.852798	+	0.492363i	0.861594	−	0.507598i	$-0.169466\pi$
$887$	25.3985	+	14.6638i	0.852798	+	0.492363i	−0.00879574	+	0.999961i	$0.502800\pi$
$888$		−	5.14805i		−	0.172757i
$889$	0.108186	−	0.566826i	0.00362843	−	0.0190107i
$890$	6.57634			0.220440
$891$	4.17005	+	2.40758i	0.139702	+	0.0806569i
$892$	−3.77726	−	6.54240i	−0.126472	−	0.219056i
$893$	28.0782	+	48.6329i	0.939602	+	1.62744i
$894$	7.40768	−	12.8305i	0.247750	−	0.429115i
$895$	−4.95295			−0.165559
$896$	2.00265	+	1.72899i	0.0669039	+	0.0577613i
$897$			2.27103i			0.0758273i
$898$	−15.4368	+	26.7373i	−0.515133	+	0.892236i
$899$	25.5802	+	16.7731i	0.853148	+	0.559415i
$900$	0.0815493	+	0.141248i	0.00271831	+	0.00470825i
$901$	−14.0086	−	8.08789i	−0.466695	−	0.269447i
$902$			44.2972i			1.47494i
$903$	−0.733333	−	2.10651i	−0.0244038	−	0.0701004i
$904$	2.35527			0.0783351
$905$	8.28411	−	14.3485i	0.275373	−	0.476960i
$906$	−6.28229	−	10.8813i	−0.208715	−	0.361505i
$907$	−13.9247	+	8.03940i	−0.462361	+	0.266944i	−0.713036	−	0.701127i	$-0.752681\pi$
$907$	−13.9247	+	8.03940i	−0.462361	+	0.266944i	0.250676	+	0.968071i	$0.419347\pi$
$908$	9.64323	−	16.7026i	0.320022	−	0.554294i
$909$		−	6.32275i		−	0.209712i
$910$	3.26686	−	1.13728i	0.108295	−	0.0377006i
$911$		−	32.7926i		−	1.08647i	−0.839581	−	0.543234i	$-0.817200\pi$
$911$		−	32.7926i		−	1.08647i	0.839581	−	0.543234i	$-0.182800\pi$
$912$	−3.16973	+	5.49013i	−0.104960	+	0.181796i
$913$	51.2200	−	29.5719i	1.69514	−	0.978687i
$914$	−17.8689	+	10.3166i	−0.591051	+	0.341244i
$915$	−16.3221	+	28.2707i	−0.539592	+	0.934600i
$916$			18.6966i			0.617753i
$917$	6.95343	+	6.00323i	0.229622	+	0.198244i
$918$			7.31747i			0.241512i
$919$	−0.631039	+	1.09299i	−0.0208161	+	0.0360545i	−0.876246	−	0.481864i	$-0.839960\pi$
$919$	−0.631039	+	1.09299i	−0.0208161	+	0.0360545i	0.855430	+	0.517919i	$0.173293\pi$
$920$	−7.27609	+	4.20085i	−0.239885	+	0.138498i
$921$	−5.77158	−	9.99666i	−0.190180	−	0.329401i
$922$	7.04447	−	12.2014i	0.231997	−	0.401831i
$923$	−3.54143			−0.116567
$924$	−12.5138	−	2.38841i	−0.411674	−	0.0785730i
$925$			0.839641i			0.0276072i
$926$	−16.1838	−	9.34374i	−0.531834	−	0.307054i
$927$	−5.69644	−	9.86652i	−0.187096	−	0.324059i
$928$	4.50338	+	2.95289i	0.147831	+	0.0969335i
$929$	18.9876	−	32.8875i	0.622963	−	1.07900i	−0.365968	−	0.930628i	$-0.619262\pi$
$929$	18.9876	−	32.8875i	0.622963	−	1.07900i	0.988931	−	0.148377i	$-0.0474048\pi$
$930$			12.4925i			0.409645i
$931$	−27.5574	−	34.7828i	−0.903156	−	1.13996i
$932$	15.1520			0.496319
$933$	12.2977	−	21.3002i	0.402608	−	0.697338i
$934$	−16.4321	−	28.4612i	−0.537673	−	0.931277i
$935$	−38.7458	−	67.1097i	−1.26712	−	2.19472i
$936$	0.514836	+	0.297241i	0.0168279	+	0.00971562i
$937$	31.7681			1.03782			0.518909	−	0.854829i	$-0.326338\pi$
$937$	31.7681			1.03782			0.518909	+	0.854829i	$0.326338\pi$
$938$	5.56471	−	29.1557i	0.181694	−	0.951967i
$939$		−	31.0144i		−	1.01212i
$940$	16.8718	+	9.74094i	0.550298	+	0.317715i
$941$	1.35369	+	2.34466i	0.0441290	+	0.0764336i	0.887246	−	0.461296i	$-0.152615\pi$
$941$	1.35369	+	2.34466i	0.0441290	+	0.0764336i	−0.843117	+	0.537730i	$0.819282\pi$
$942$	10.9715	−	6.33439i	0.357470	−	0.206385i
$943$	−30.4355	−	17.5719i	−0.991116	−	0.572221i
$944$	−8.54569			−0.278139
$945$	4.40442	+	3.80255i	0.143276	+	0.123697i
$946$			4.05943i			0.131984i
$947$	44.2413	+	25.5427i	1.43765	+	0.830027i	0.997686	−	0.0679897i	$-0.0216585\pi$
$947$	44.2413	+	25.5427i	1.43765	+	0.830027i	0.439962	+	0.898016i	$0.354992\pi$
$948$	−0.685608	−	1.18751i	−0.0222675	−	0.0385684i
$949$	−8.24025	+	4.75751i	−0.267490	+	0.154435i
$950$	0.516979	−	0.895433i	0.0167730	−	0.0290517i
$951$	−16.0048			−0.518991
$952$	−6.36513	−	18.2839i	−0.206295	−	0.592586i
$953$	−30.5273			−0.988878			−0.494439	−	0.869212i	$-0.664626\pi$
$953$	−30.5273			−0.988878			−0.494439	+	0.869212i	$0.664626\pi$
$954$	−1.91441	−	1.10529i	−0.0619813	−	0.0357849i
$955$	−7.98394	+	4.60953i	−0.258354	+	0.149161i
$956$	−6.61852	−	11.4636i	−0.214058	−	0.370760i
$957$	−25.8886	−	1.47147i	−0.836860	−	0.0475660i
$958$	39.4262			1.27380
$959$	34.4951	−	12.0087i	1.11390	−	0.387780i
$960$			2.19930i			0.0709820i
$961$	0.632500	−	1.09552i	0.0204032	−	0.0353394i
$962$	1.53021	+	2.65040i	0.0493360	+	0.0854525i
$963$	0.110178	+	0.190834i	0.00355043	+	0.00614953i
$964$	2.46882	−	4.27613i	0.0795155	−	0.137725i
$965$		−	35.0599i		−	1.12862i
$966$	6.60503	−	7.65048i	0.212513	−	0.246150i
$967$			11.2033i			0.360274i	0.983642	+	0.180137i	$0.0576541\pi$
$967$			11.2033i			0.360274i	−0.983642	+	0.180137i	$0.942346\pi$
$968$	10.5531	+	6.09286i	0.339191	+	0.195832i
$969$	40.1739	−	23.1944i	1.29057	−	0.745111i
$970$	8.12131	+	14.0665i	0.260760	+	0.451649i
$971$	14.8620	+	8.58056i	0.476943	+	0.275363i	0.719142	−	0.694863i	$-0.244535\pi$
$971$	14.8620	+	8.58056i	0.476943	+	0.275363i	−0.242199	+	0.970227i	$0.577869\pi$
$972$			1.00000i			0.0320750i
$973$	−1.10544	−	0.210986i	−0.0354388	−	0.00676391i
$974$		−	21.7465i		−	0.696803i
$975$	−0.0839691	−	0.0484796i	−0.00268916	−	0.00155259i
$976$	12.8544	−	7.42151i	0.411460	−	0.237557i
$977$	−28.1935	−	48.8325i	−0.901989	−	1.56229i	−0.824909	−	0.565266i	$-0.808773\pi$
$977$	−28.1935	−	48.8325i	−0.901989	−	1.56229i	−0.0770805	−	0.997025i	$-0.524560\pi$
$978$	−3.28121	−	1.89441i	−0.104922	−	0.0605765i
$979$	14.3983			0.460172
$980$	−14.3129	−	5.67012i	−0.457208	−	0.181125i
$981$	3.33723			0.106550
$982$	−0.756526	+	1.31034i	−0.0241417	+	0.0418147i
$983$	−1.92723	+	1.11269i	−0.0614691	+	0.0354892i	−0.530420	−	0.847735i	$-0.677966\pi$
$983$	−1.92723	+	1.11269i	−0.0614691	+	0.0354892i	0.468950	+	0.883224i	$0.344632\pi$
$984$	−7.96703	+	4.59977i	−0.253980	+	0.146635i
$985$	18.9909	−	32.8933i	0.605102	−	1.04807i
$986$	−17.7346	−	35.1895i	−0.564783	−	1.12066i
$987$	−23.0211	−	4.39386i	−0.732771	−	0.139858i
$988$		−	3.76869i		−	0.119898i
$989$	−2.78913	−	1.61031i	−0.0886893	−	0.0512048i
$990$	−5.29498	−	9.17117i	−0.168285	−	0.291479i
$991$	5.43610	+	9.41560i	0.172683	+	0.299096i	0.939357	−	0.342940i	$-0.111423\pi$
$991$	5.43610	+	9.41560i	0.172683	+	0.299096i	−0.766674	+	0.642037i	$0.778090\pi$
$992$	2.84011	−	4.91922i	0.0901737	−	0.156185i
$993$	2.73784			0.0868826
$994$	11.9301	+	10.2999i	0.378401	+	0.326691i
$995$	31.7429			1.00632
$996$	10.6373	+	6.14142i	0.337054	+	0.194598i
$997$	−48.1281	+	27.7867i	−1.52423	+	0.880015i	−0.524643	+	0.851323i	$0.675801\pi$
$997$	−48.1281	+	27.7867i	−1.52423	+	0.880015i	−0.999588	+	0.0286926i	$0.990866\pi$
$998$	6.01005	−	3.46991i	0.190245	−	0.109838i
$999$	−2.57403	+	4.45835i	−0.0814386	+	0.141056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.p.b.289.12	yes	44
7.4	even	3	inner	1218.2.p.b.1159.4	yes	44
29.28	even	2	inner	1218.2.p.b.289.4	✓	44
203.144	even	6	inner	1218.2.p.b.1159.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.p.b.289.4	✓	44	29.28	even	2	inner
1218.2.p.b.289.12	yes	44	1.1	even	1	trivial
1218.2.p.b.1159.4	yes	44	7.4	even	3	inner
1218.2.p.b.1159.12	yes	44	203.144	even	6	inner

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:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.09965 + 1.90465i) q^{5} -1.00000 q^{6} +(-2.59884 - 0.496020i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.90465 + 1.09965i) q^{10} +(-4.17005 + 2.40758i) q^{11} +(-0.866025 - 0.500000i) q^{12} +0.594482 q^{13} +(-2.00265 - 1.72899i) q^{14} -2.19930i q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.33711 - 3.65873i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-5.49013 - 3.16973i) q^{19} -2.19930 q^{20} +(2.49867 - 0.869854i) q^{21} -4.81516 q^{22} +(1.91009 - 3.30837i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.0815493 + 0.141248i) q^{25} +(0.514836 + 0.297241i) q^{26} +1.00000i q^{27} +(-0.869854 - 2.49867i) q^{28} +(-2.42359 - 4.80897i) q^{29} +(1.09965 - 1.90465i) q^{30} +(-4.91922 + 2.84011i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.40758 - 4.17005i) q^{33} +7.31747 q^{34} +(3.80255 - 4.40442i) q^{35} +1.00000 q^{36} +(4.45835 + 2.57403i) q^{37} +(-3.16973 - 5.49013i) q^{38} +(-0.514836 + 0.297241i) q^{39} +(-1.90465 - 1.09965i) q^{40} -9.19954i q^{41} +(2.59884 + 0.496020i) q^{42} -0.843054i q^{43} +(-4.17005 - 2.40758i) q^{44} +(1.09965 + 1.90465i) q^{45} +(3.30837 - 1.91009i) q^{46} +(-7.67146 - 4.42912i) q^{47} -1.00000i q^{48} +(6.50793 + 2.57815i) q^{49} +0.163099i q^{50} +(-3.65873 + 6.33711i) q^{51} +(0.297241 + 0.514836i) q^{52} +(-1.10529 - 1.91441i) q^{53} +(-0.500000 + 0.866025i) q^{54} -10.5900i q^{55} +(0.496020 - 2.59884i) q^{56} +6.33946 q^{57} +(0.305592 - 5.37649i) q^{58} +(4.27285 + 7.40079i) q^{59} +(1.90465 - 1.09965i) q^{60} +(-12.8544 - 7.42151i) q^{61} -5.68023 q^{62} +(-1.72899 + 2.00265i) q^{63} -1.00000 q^{64} +(-0.653720 + 1.13228i) q^{65} +(4.17005 - 2.40758i) q^{66} +(5.60937 + 9.71571i) q^{67} +(6.33711 + 3.65873i) q^{68} +3.82018i q^{69} +(5.49532 - 1.91307i) q^{70} -5.95717 q^{71} +(0.866025 + 0.500000i) q^{72} +(-13.8612 + 8.00279i) q^{73} +(2.57403 + 4.45835i) q^{74} +(-0.141248 - 0.0815493i) q^{75} -6.33946i q^{76} +(12.0315 - 4.18848i) q^{77} -0.594482 q^{78} +(1.18751 + 0.685608i) q^{79} +(-1.09965 - 1.90465i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.59977 - 7.96703i) q^{82} -12.2828 q^{83} +(2.00265 + 1.72899i) q^{84} +16.0933i q^{85} +(0.421527 - 0.730106i) q^{86} +(4.50338 + 2.95289i) q^{87} +(-2.40758 - 4.17005i) q^{88} +(-2.58959 - 1.49510i) q^{89} +2.19930i q^{90} +(-1.54496 - 0.294875i) q^{91} +3.82018 q^{92} +(2.84011 - 4.91922i) q^{93} +(-4.42912 - 7.67146i) q^{94} +(12.0744 - 6.97117i) q^{95} +(0.500000 - 0.866025i) q^{96} -7.38538i q^{97} +(4.34696 + 5.48671i) q^{98} +4.81516i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 22 q^{4} - 44 q^{6} - 8 q^{7} + 22 q^{9} - 16 q^{13} - 22 q^{16} - 4 q^{23} - 22 q^{24} - 22 q^{25} - 4 q^{28} + 4 q^{29} - 16 q^{34} - 10 q^{35} + 44 q^{36} + 4 q^{38} + 8 q^{42} - 52 q^{49} + 8 q^{51}+ \cdots + 22 q^{96}+O(q^{100}) \) 44 * q + 22 * q^4 - 44 * q^6 - 8 * q^7 + 22 * q^9 - 16 * q^13 - 22 * q^16 - 4 * q^23 - 22 * q^24 - 22 * q^25 - 4 * q^28 + 4 * q^29 - 16 * q^34 - 10 * q^35 + 44 * q^36 + 4 * q^38 + 8 * q^42 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 6 * q^53 - 22 * q^54 - 8 * q^57 + 14 * q^58 + 24 * q^59 + 16 * q^62 - 4 * q^63 - 44 * q^64 - 24 * q^65 + 28 * q^67 - 24 * q^71 - 16 * q^74 + 16 * q^78 - 22 * q^81 - 28 * q^83 + 4 * q^86 + 14 * q^87 + 112 * q^91 - 8 * q^92 - 8 * q^93 - 36 * q^94 + 22 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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